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, * )


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 Her­
       mitian  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 tridiag­
              onal 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.

              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 eigenvalue
              while working on the submatrix lying  in  rows  and
              columns INFO/(N+1) through mod(INFO,N+1).


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