ZHPEVD  -  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  assump­
       tions  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 with­
       out 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 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',


               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  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/output) COMPLEX*16 array, dimension
               (LWORK)
               On exit, if INFO = 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.

               If LWORK = -1, then a workspace query is  assumed;
               the  routine  only  calculates the optimal size of
               the WORK array, returns this value  as  the  first
               entry  of  the  WORK  array,  and no error message
               related to LWORK is issued by XERBLA.

       RWORK   (workspace/output) DOUBLE PRECISION array,
               dimension (LRWORK) On exit, if INFO = 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 + 5*N + 2*N**2.

               If LRWORK = -1, then a workspace query is assumed;
               the  routine  only  calculates the optimal size of
               the RWORK array, returns this value as  the  first

               related to LRWORK is issued by XERBLA.

       IWORK   (workspace/output) INTEGER array, dimension
               (LIWORK)
               On exit, if INFO = 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 3 + 5*N.

               If LIWORK = -1, then a workspace query is assumed;
               the  routine  only  calculates the optimal size of
               the IWORK array, returns this value as  the  first
               entry  of  the  IWORK  array, and no error message
               related to LIWORK is issued by XERBLA.

       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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