NAME

       SSTEIN2  -  compute  the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified
       eigenvalues, using inverse iteration

SYNOPSIS

       SUBROUTINE SSTEIN2( N, D, E, M, W, IBLOCK, ISPLIT, ORFAC, Z, LDZ, WORK, IWORK, IFAIL, INFO )

           INTEGER         INFO, LDZ, M, N

           REAL            ORFAC

           INTEGER         IBLOCK( * ), IFAIL( * ), ISPLIT( * ), IWORK( * )

           REAL            D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )

PURPOSE

       SSTEIN2 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) 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, 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  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 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. )

       ORFAC   (input) REAL
               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) REAL 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) 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.