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NAME
     dlaed0 - compute all eigenvalues and corresponding eigenvec-
     tors  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( * )



     #include <sunperf.h>

     void dlaed0(int icompq, int qsiz, int n, double  *d,  double
               *e,  double *q, int ldq, double *qstore, int ldqs,
               int *info) ;

PURPOSE
     DLAED0 computes all eigenvalues and corresponding  eigenvec-
     tors  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  sym-
               metric  matrix  also.   On  entry,  Q contains the
               orthogonal matrix  used  to  reduce  the  original
               matrix  to tridiagonal form.  = 2:  Compute eigen-
               values 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  eigen-
               vectors  are  desired,  then  LDQ >= max(1,N).  In
               any case,  LDQ >= 1.

               QSTORE (workspace) DOUBLE PRECISION array,  dimen-
               sion  (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 ille-
               gal value.
               > 0:  The algorithm failed to  compute  an  eigen-
               value while working on the submatrix lying in rows
               and columns INFO/(N+1) through mod(INFO,N+1).

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