ZHPEV  -  compute  all  the  eigenvalues  and, optionally,
       eigenvectors of a complex Hermitian matrix in packed stor­
       age


SYNOPSIS

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

           CHARACTER     JOBZ, UPLO

           INTEGER       INFO, LDZ, N

           DOUBLE        PRECISION RWORK( * ), W( * )

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


PURPOSE

       ZHPEV 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*16 array, dimension
               (N*(N+1)/2)
               On entry, the upper or lower triangle of the  Her­
               mitian  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.

               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 associ­
               ated with W(i).  If JOBZ = 'N', then Z is not ref­
               erenced.

       LDZ     (input) INTEGER
               The  leading  dimension of the array Z.  LDZ >= 1,
               and if JOBZ = 'V', LDZ >= max(1,N).

       WORK    (workspace) COMPLEX*16 array, dimension (max(1,
               2*N-1))

       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 ille­
               gal value.
               > 0:  if INFO = i, the algorithm  failed  to  con­
               verge;  i off-diagonal elements of an intermediate
               tridiagonal form did not converge to zero.


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