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chpev

 NAME
      CHPEV - compute all the eigenvalues and, optionally, eigen-
      vectors of a complex Hermitian matrix in packed storage

 SYNOPSIS
      SUBROUTINE CHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
                        INFO )

          CHARACTER     JOBZ, UPLO

          INTEGER       INFO, LDZ, N

          REAL          RWORK( * ), W( * )

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

 PURPOSE
      CHPEV computes all the eigenvalues and, optionally, eigen-
      vectors of a complex Hermitian matrix in packed storage.

 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 array, dimension (N*(N+1)/2)
              On entry, the upper or lower triangle of the Hermi-
              tian 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 dur-
              ing 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) REAL array, dimension (N)
              If INFO = 0, the eigenvalues in ascending order.

      Z       (output) COMPLEX 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) COMPLEX array, dimension (max(1, 2*N-1))

      RWORK   (workspace) REAL 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 tridiago-
              nal form did not converge to zero.