ZHPEVD (3lapack)

compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage

SYNOPSIS

  SUBROUTINE ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
                     LRWORK, IWORK, LIWORK, INFO )

      CHARACTER      JOBZ, UPLO

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

      INTEGER        IWORK( * )

      DOUBLE         PRECISION RWORK( * ), W( * )

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

PURPOSE

  ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of a
  complex Hermitian matrix A in packed storage.  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.

  AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
          On entry, the upper or lower triangle of the Hermitian matrix A,
          packed columnwise in a linear array.  The j-th column of A is
          stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2)
          = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) =
          A(i,j) for j<=i<=n.

          On exit, AP is overwritten by values generated during the reduction
          to tridiagonal form.  If UPLO = 'U', the diagonal and first
          superdiagonal of the tridiagonal matrix T overwrite the
          corresponding elements of A, and if UPLO = 'L', the diagonal and
          first subdiagonal of T overwrite the corresponding elements of A.

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

  Z       (output) COMPLEX*16 array, dimension (LDZ, N)
          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
          eigenvectors of the matrix A, with the i-th column of Z holding the
          eigenvector associated with W(i).  If JOBZ = 'N', then Z is not
          referenced.

  LDZ     (input) INTEGER
          The leading dimension of the array Z.  LDZ >= 1, and if JOBZ = 'V',
          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 array WORK.  If N <= 1,               LWORK must
          be at least 1.  If JOBZ = 'N' and N > 1, LWORK must be at least N.
          If JOBZ = 'V' and N > 1, LWORK must be at least 2*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 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 array IWORK.  If JOBZ  = 'N' or 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.