ZLAED0(3)      LAPACK routine of NEC Numeric Library Collection      ZLAED0(3)



NAME
       ZLAED0

SYNOPSIS
       SUBROUTINE ZLAED0 (QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, IWORK,
           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 Hermitian matrix and
            corresponding eigenvectors of the dense or band matrix.




ARGUMENTS
           QSIZ      (input)
                     QSIZ is INTEGER
                    The dimension of the unitary matrix used to reduce
                    the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.

           N         (input)
                     N is INTEGER
                    The dimension of the symmetric tridiagonal matrix.  N >= 0.

           D         (input/output)
                     D is DOUBLE PRECISION array, dimension (N)
                    On entry, the diagonal elements of the tridiagonal matrix.
                    On exit, the eigenvalues in ascending order.

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

           Q         (input/output)
                     Q is 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 Hermitian matrix to a
                    (reducible) symmetric tridiagonal matrix.

           LDQ       (input)
                     LDQ is INTEGER
                    The leading dimension of the array Q.  LDQ >= max(1,N).

           IWORK     (output)
                     IWORK is 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     (output)
                     RWORK is 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    (output)
                     QSTORE is COMPLEX*16 array, dimension (LDQS, N)
                    Used to store parts of
                    the eigenvector matrix when the updating matrix multiplies
                    take place.

           LDQS      (input)
                     LDQS is INTEGER
                    The leading dimension of the array QSTORE.
                    LDQS >= max(1,N).

           INFO      (output)
                     INFO is 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).



LAPACK routine                  31 October 2017                      ZLAED0(3)