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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 Hermi-
     tian  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, * )



     #include <sunperf.h>

     void zlaed0(int qsiz, int n, double  *d,  double  *e,  doub-
               lecomplex  *q, int ldq, doublecomplex *qstore, int
               ldqs, int *info) ;

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 Hermi-
     tian  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  tridi-
               agonal 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  Hermi-
               tian 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 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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