cstedc(3S)

NAME
     CSTEDC - compute all eigenvalues and, optionally, eigenvectors of a
     symmetric tridiagonal matrix using the divide and conquer method

SYNOPSIS
     SUBROUTINE CSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, LRWORK,
                        IWORK, LIWORK, INFO )

         CHARACTER      COMPZ

         INTEGER        INFO, LDZ, LIWORK, LRWORK, LWORK, N

         INTEGER        IWORK( * )

         REAL           D( * ), E( * ), RWORK( * )

         COMPLEX        WORK( * ), 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
     CSTEDC computes all eigenvalues and, optionally, eigenvectors of a
     symmetric tridiagonal matrix using the divide and conquer method. The
     eigenvectors of a full or band complex Hermitian matrix can also be found
     if CHETRD or CHPTRD or CHBTRD has been used to reduce this matrix to
     tridiagonal form.

     This code makes very mild assumptions about floating point arithmetic. It
     will work on machines with a guard digit in add/subtract, or on those
     binary machines without guard digits which subtract like the Cray X-MP,
     Cray Y-MP, Cray C-90, or Cray-2.  It could conceivably fail on
     hexadecimal or decimal machines without guard digits, but we know of
     none.  See SLAED3 for details.


ARGUMENTS
     COMPZ   (input) CHARACTER*1
             = 'N':  Compute eigenvalues only.
             = 'I':  Compute eigenvectors of tridiagonal matrix also.
             = 'V':  Compute eigenvectors of original Hermitian matrix also.
             On entry, Z contains the unitary matrix used to reduce the
             original matrix to tridiagonal form.

     N       (input) INTEGER
             The dimension of the symmetric tridiagonal matrix.  N >= 0.

     D       (input/output) REAL array, dimension (N)
             On entry, the diagonal elements of the tridiagonal matrix.  On
             exit, if INFO = 0, the eigenvalues in ascending order.

     E       (input/output) REAL array, dimension (N-1)
             On entry, the subdiagonal elements of the tridiagonal matrix.  On
             exit, E has been destroyed.

     Z       (input/output) COMPLEX array, dimension (LDZ,N)
             On entry, if COMPZ = 'V', then Z contains the unitary matrix used
             in the reduction to tridiagonal form.  On exit, if INFO = 0, then
             if COMPZ = 'V', Z contains the orthonormal eigenvectors of the
             original Hermitian matrix, and if COMPZ = 'I', Z contains the
             orthonormal eigenvectors of the symmetric tridiagonal matrix.  If
             COMPZ = 'N', then Z is not referenced.

     LDZ     (input) INTEGER
             The leading dimension of the array Z.  LDZ >= 1.  If eigenvectors
             are desired, then LDZ >= max(1,N).

     WORK    (workspace/output) COMPLEX array, dimension (LWORK)
             On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

     LWORK   (input) INTEGER
             The dimension of the array WORK.  If COMPZ = 'N' or 'I', or N <=
             1, LWORK must be at least 1.  If COMPZ = 'V' and N > 1, LWORK
             must be at least N*N.

             If LWORK = -1, then a workspace query is assumed; the routine
             only calculates the optimal size of the WORK array, returns this
             value as the first entry of the WORK array, and no error message
             related to LWORK is issued by XERBLA.

     RWORK   (workspace/output) REAL array,
             dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the
             optimal LRWORK.

     LRWORK  (input) INTEGER
             The dimension of the array RWORK.  If COMPZ = 'N' or N <= 1,
             LRWORK must be at least 1.  If COMPZ = 'V' and N > 1, LRWORK must
             be at least 1 + 3*N + 2*N*lg N + 3*N**2 , where lg( N ) =
             smallest integer k such that 2**k >= N.  If COMPZ = 'I' and N >
             1, LRWORK must be at least 1 + 4*N + 2*N**2 .

             If LRWORK = -1, then a workspace query is assumed; the routine
             only calculates the optimal size of the RWORK array, returns this
             value as the first entry of the RWORK array, and no error message
             related to LRWORK is issued by XERBLA.

     IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
             On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

     LIWORK  (input) INTEGER
             The dimension of the array IWORK.  If COMPZ = 'N' or N <= 1,
             LIWORK must be at least 1.  If COMPZ = 'V' or N > 1,  LIWORK must
             be at least 6 + 6*N + 5*N*lg N.  If COMPZ = 'I' or N > 1,  LIWORK
             must be at least 3 + 5*N .

             If LIWORK = -1, then a workspace query is assumed; the routine
             only calculates the optimal size of the IWORK array, returns this
             value as the first entry of the IWORK array, and no error message
             related to LIWORK is issued by XERBLA.

     INFO    (output) INTEGER
             = 0:  successful exit.
             < 0:  if INFO = -i, the i-th argument had an illegal value.
             > 0:  The algorithm failed to compute an eigenvalue while working
             on the submatrix lying in rows and columns INFO/(N+1) through
             mod(INFO,N+1).

FURTHER DETAILS
     Based on contributions by
        Jeff Rutter, Computer Science Division, University of California
        at Berkeley, USA


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

     This man page is available only online.