slaed0(3S)

NAME
     SLAED0 - compute all eigenvalues and corresponding eigenvectors of a
     symmetric tridiagonal matrix using the divide and conquer method

SYNOPSIS
     SUBROUTINE SLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK,
                        IWORK, INFO )

         INTEGER        ICOMPQ, INFO, LDQ, LDQS, N, QSIZ

         INTEGER        IWORK( * )

         REAL           D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), WORK(
                        * )

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
     SLAED0 computes all eigenvalues and corresponding eigenvectors of a
     symmetric tridiagonal matrix using the divide and conquer method.

ARGUMENTS
     ICOMPQ  (input) INTEGER
             = 0:  Compute eigenvalues only.
             = 1:  Compute eigenvectors of original dense symmetric matrix
             also.  On entry, Q contains the orthogonal matrix used to reduce
             the original matrix to tridiagonal form.  = 2:  Compute
             eigenvalues and eigenvectors of tridiagonal matrix.

     QSIZ   (input) INTEGER
            The dimension of the orthogonal matrix used to reduce the full
            matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.

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

     D      (input/output) REAL array, dimension (N)
            On entry, the main diagonal of the tridiagonal matrix.  On exit,
            its eigenvalues.
     E      (input) REAL array, dimension (N-1)
            The off-diagonal elements of the tridiagonal matrix.  On exit, E
            has been destroyed.

     Q      (input/output) REAL array, dimension (LDQ, N)
            On entry, Q must contain an N-by-N orthogonal matrix.  If ICOMPQ =
            0    Q is not referenced.  If ICOMPQ = 1    On entry, Q is a
            subset of the columns of the orthogonal matrix used to reduce the
            full matrix to tridiagonal form corresponding to the subset of the
            full matrix which is being decomposed at this time.  If ICOMPQ = 2
            On entry, Q will be the identity matrix.  On exit, Q contains the
            eigenvectors of the tridiagonal matrix.

     LDQ    (input) INTEGER
            The leading dimension of the array Q.  If eigenvectors are
            desired, then  LDQ >= max(1,N).  In any case,  LDQ >= 1.

            QSTORE (workspace) REAL array, dimension (LDQS, N) Referenced only
            when ICOMPQ = 1.  Used to store parts of the eigenvector matrix
            when the updating matrix multiplies take place.

     LDQS   (input) INTEGER
            The leading dimension of the array QSTORE.  If ICOMPQ = 1, then
            LDQS >= max(1,N).  In any case,  LDQS >= 1.

     WORK   (workspace) REAL array,
            If ICOMPQ = 0 or 1, the dimension of WORK must be at least 1 + 3*N
            + 2*N*lg N + 2*N**2 ( lg( N ) = smallest integer k such that 2^k
            >= N ) If ICOMPQ = 2, the dimension of WORK must be at least 4*N +
            N**2.

     IWORK  (workspace) INTEGER array,
            If ICOMPQ = 0 or 1, the dimension of IWORK must be at least 6 +
            6*N + 5*N*lg N.  ( lg( N ) = smallest integer k such that 2^k >= N
            ) If ICOMPQ = 2, the dimension of IWORK must be at least 3 + 5*N.

     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.