dlaed0(3F)

NAME
     DLAED0 - compute all eigenvalues and corresponding eigenvectors of a
     symmetric tridiagonal matrix using the divide and conquer method

SYNOPSIS
     SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK,
                        IWORK, INFO )

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

         INTEGER        IWORK( * )

         DOUBLE         PRECISION D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, *
                        ), WORK( * )

PURPOSE
     DLAED0 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) DOUBLE PRECISION array, dimension (N)
            On entry, the main diagonal of the tridiagonal matrix.  On exit,
            its eigenvalues.

     E      (input) DOUBLE PRECISION array, dimension (N-1)
            The off-diagonal elements of the tridiagonal matrix.  On exit, E
            has been destroyed.

     Q      (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array,
            dimension (1 + 3*N + 2*N*lg N + 2*N**2) ( lg( N ) = smallest
            integer k such that 2^k >= N )

     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 2 + 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).