ZHEEVD (3lapack)

compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

SYNOPSIS

  SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK,
                     IWORK, LIWORK, INFO )

      CHARACTER      JOBZ, UPLO

      INTEGER        INFO, LDA, LIWORK, LRWORK, LWORK, N

      INTEGER        IWORK( * )

      DOUBLE         PRECISION RWORK( * ), W( * )

      COMPLEX*16     A( LDA, * ), WORK( * )

PURPOSE

  ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex
  Hermitian matrix A.  If eigenvectors are desired, it uses a divide and
  conquer algorithm.

  The divide and conquer algorithm 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.

ARGUMENTS

  JOBZ    (input) CHARACTER*1
          = 'N':  Compute eigenvalues only;
          = 'V':  Compute eigenvalues and eigenvectors.

  UPLO    (input) CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

  N       (input) INTEGER
          The order of the matrix A.  N >= 0.

  A       (input/output) COMPLEX*16 array, dimension (LDA, N)
          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading N-
          by-N upper triangular part of A contains the upper triangular part
          of the matrix A.  If UPLO = 'L', the leading N-by-N lower
          triangular part of A contains the lower triangular part of the
          matrix A.  On exit, if JOBZ = 'V', then if INFO = 0, A contains the
          orthonormal eigenvectors of the matrix A.  If JOBZ = 'N', then on
          exit the lower triangle (if UPLO='L') or the upper triangle (if
          UPLO='U') of A, including the diagonal, is destroyed.

  LDA     (input) INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

  W       (output) DOUBLE PRECISION array, dimension (N)
          If INFO = 0, the eigenvalues in ascending order.

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

  LWORK   (input) INTEGER
          The length of the array WORK.  If N <= 1,                LWORK must
          be at least 1.  If JOBZ  = 'N' and N > 1, LWORK must be at least N
          + 1.  If JOBZ  = 'V' and N > 1, LWORK must be at least 2*N + N**2.

  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 N <= 1,                LRWORK
          must be at least 1.  If JOBZ  = 'N' and N > 1, LRWORK must be at
          least N.  If JOBZ  = 'V' and N > 1, LRWORK must be at least 1 + 4*N
          + 2*N*lg N + 3*N**2 , where lg( N ) = smallest integer k such that
          2**k >= N .

  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 N <= 1,                LIWORK
          must be at least 1.  If JOBZ  = 'N' and N > 1, LIWORK must be at
          least 1.  If JOBZ  = 'V' and 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:  if INFO = i, the algorithm failed to converge; i off-diagonal
          elements of an intermediate tridiagonal form did not converge to
          zero.