ZSTEDC (3lapack)

compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method

SYNOPSIS

  SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, LRWORK,
                     IWORK, LIWORK, INFO )

      CHARACTER      COMPZ

      INTEGER        INFO, LDZ, LIWORK, LRWORK, LWORK, N

      INTEGER        IWORK( * )

      DOUBLE         PRECISION D( * ), E( * ), RWORK( * )

      COMPLEX*16     WORK( * ), Z( LDZ, * )

PURPOSE

  ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a
  symmetric tridiagonal matrix using the divide and conquer method.  The
  eigenvectors of a full or band complex Hermitian matrix can also be found
  if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this matrix to
  tridiagonal form.

  This code makes very mild assumptions about floating point arithmetic. It
  will work on machines with a guard digit in add/subtract, or on those
  binary machines without guard digits which subtract like the Cray X-MP,
  Cray Y-MP, Cray C-90, or Cray-2.  It could conceivably fail on hexadecimal
  or decimal machines without guard digits, but we know of none.  See DLAED3
  for details.

ARGUMENTS

  COMPZ   (input) CHARACTER*1
          = 'N':  Compute eigenvalues only.
          = 'I':  Compute eigenvectors of tridiagonal matrix also.
          = 'V':  Compute eigenvectors of original Hermitian matrix also.  On
          entry, Z contains the unitary matrix used to reduce the original
          matrix to tridiagonal form.

  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, if INFO = 0, the eigenvalues in ascending order.

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

  Z       (input/output) COMPLEX*16 array, dimension (LDZ,N)
          On entry, if COMPZ = 'V', then Z contains the unitary matrix used
          in the reduction to tridiagonal form.  On exit, if INFO = 0, then
          if COMPZ = 'V', Z contains the orthonormal eigenvectors of the
          original Hermitian matrix, and if COMPZ = 'I', Z contains the
          orthonormal eigenvectors of the symmetric tridiagonal matrix.  If
          COMPZ = 'N', then Z is not referenced.

  LDZ     (input) INTEGER
          The leading dimension of the array Z.  LDZ >= 1.  If eigenvectors
          are desired, then LDZ >= max(1,N).

  WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)
          On exit, if LWORK > 0, WORK(1) returns the optimal LWORK.

  LWORK   (input) INTEGER
          The dimension of the array WORK.  If COMPZ = 'N' or 'I', or N <= 1,
          LWORK must be at least 1.  If COMPZ = 'V' and N > 1, LWORK must be
          at least N*N.

  RWORK   (workspace/output) DOUBLE PRECISION array,
          dimension (LRWORK) On exit, if LRWORK > 0, RWORK(1) returns the
          optimal LRWORK.

  LRWORK  (input) INTEGER
          The dimension of the array RWORK.  If COMPZ = 'N' or N <= 1, LRWORK
          must be at least 1.  If COMPZ = 'V' and N > 1, LRWORK must be at
          least 1 + 3*N + 2*N*lg N + 3*N**2 , where lg( N ) = smallest
          integer k such that 2**k >= N.  If COMPZ = 'I' and N > 1, LRWORK
          must be at least 1 + 3*N + 2*N*lg N + 3*N**2 .

  IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
          On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.

  LIWORK  (input) INTEGER
          The dimension of the array IWORK.  If COMPZ = 'N' or N <= 1, LIWORK
          must be at least 1.  If COMPZ = 'V' or N > 1,  LIWORK must be at
          least 6 + 6*N + 5*N*lg N.  If COMPZ = 'I' or N > 1,  LIWORK must be
          at least 2 + 5*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).