cstein(3S)

NAME
     CSTEIN - 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, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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