ZLAED0 (3lapack)

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 Hermitian 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 tridiagonal 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 Hermitian 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 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).