CLAED0  -  the  divide and conquer method, CLAED0 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 CLAED0( QSIZ,  N,  D,  E, Q, LDQ, QSTORE, LDQS,
                          RWORK, IWORK, INFO )

           INTEGER        INFO, LDQ, LDQS, N, QSIZ

           INTEGER        IWORK( * )

           REAL           D( * ), E( * ), RWORK( * )

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


PURPOSE

       Using the divide and conquer method, CLAED0  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) REAL array, dimension (N)
              On  entry, the diagonal elements of the tridiagonal
              matrix.  On  exit,  the  eigenvalues  in  ascending
              order.

       E      (input/output) REAL 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 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  >=


       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) REAL 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 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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