ZHEEV (3lapack)

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

SYNOPSIS

  SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO )

      CHARACTER     JOBZ, UPLO

      INTEGER       INFO, LDA, LWORK, N

      DOUBLE        PRECISION RWORK( * ), W( * )

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

PURPOSE

  ZHEEV computes all eigenvalues and, optionally, eigenvectors of a complex
  Hermitian matrix A.

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 INFO = 0, WORK(1) returns the optimal LWORK.

  LWORK   (input) INTEGER
          The length of the array WORK.  LWORK >= max(1,2*N-1).  For optimal
          efficiency, LWORK >= (NB+1)*N, where NB is the blocksize for ZHETRD
          returned by ILAENV.

  RWORK   (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))

  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.