zlaed0(3S)

NAME
     ZLAED0 - the divide and conquer method, ZLAED0 computes all eigenvalues
     of a symmetric tridiagonal matrix which is one diagonal block of those
     from reducing a dense or band Hermitian matrix and corresponding
     eigenvectors of the dense or band matrix

SYNOPSIS
     SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, IWORK,
                        INFO )

         INTEGER        INFO, LDQ, LDQS, N, QSIZ

         INTEGER        IWORK( * )

         DOUBLE         PRECISION D( * ), E( * ), RWORK( * )

         COMPLEX*16     Q( LDQ, * ), QSTORE( LDQS, * )

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
     Using the divide and conquer method, ZLAED0 computes all eigenvalues of a
     symmetric tridiagonal matrix which is one diagonal block of those from
     reducing a dense or band Hermitian matrix and corresponding eigenvectors
     of the dense or band matrix.

ARGUMENTS
     QSIZ   (input) INTEGER
            The dimension of the unitary 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) DOUBLE PRECISION array, dimension (N)
            On entry, the diagonal elements of the tridiagonal matrix.  On
            exit, the eigenvalues in ascending order.

     E      (input/output) DOUBLE PRECISION array, dimension (N-1)
            On entry, the off-diagonal elements of the tridiagonal matrix.  On
            exit, E has been destroyed.
     Q      (input/output) COMPLEX*16 array, dimension (LDQ,N)
            On entry, Q must contain an QSIZ x N matrix whose columns
            unitarily orthonormal. It is a part of the unitary matrix that
            reduces the full dense Hermitian matrix to a (reducible) symmetric
            tridiagonal matrix.

     LDQ    (input) INTEGER
            The leading dimension of the array Q.  LDQ >= max(1,N).

     IWORK  (workspace) INTEGER array,
            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 )

     RWORK  (workspace) DOUBLE PRECISION array,
            dimension (1 + 3*N + 2*N*lg N + 3*N**2) ( lg( N ) = smallest
            integer k such that 2^k >= N )

            QSTORE (workspace) COMPLEX*16 array, dimension (LDQS, N) 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.  LDQS >= max(1,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).

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

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