CSTEIN (3lapack)

compute the eigenvectors of a real symmetric tridiagonal 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 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 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 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. )

  Z       (output) COMPLEX 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) 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.