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cstein

 NAME
      CSTEIN - compute the eigenvectors of a real symmetric tridi-
      agonal matrix T corresponding to specified eigenvalues,
      using inverse iteration

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

          INTEGER        INFO, LDZ, M, N

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

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

          COMPLEX        Z( LDZ, * )

 PURPOSE
      CSTEIN computes the eigenvectors of a real symmetric tridi-
      agonal matrix T corresponding to specified eigenvalues,
      using inverse iteration.

      The maximum number of iterations allowed for each eigenvec-
      tor 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 CUNMTR or CUPMTR 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) 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, 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) 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 sub-
              matrices.  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. )

      Z       (output) COMPLEX array, dimension (LDZ, M)
              The computed eigenvectors.  The eigenvector associ-
              ated 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) 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 MAX-
              ITS 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 con-
              verge 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.