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NAME

       ZHPR2  -  perform the hermitian rank 2 operation   A := alpha*x*conjg( y' ) + conjg( alpha
       )*y*conjg( x' ) + A,

SYNOPSIS

       SUBROUTINE ZHPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP )

           COMPLEX*16   ALPHA

           INTEGER      INCX, INCY, N

           CHARACTER*1  UPLO

           COMPLEX*16   AP( * ), X( * ), Y( * )

PURPOSE

       ZHPR2  performs the hermitian rank 2 operation

       where alpha is a scalar, x and y are n element vectors and  A  is  an  n  by  n  hermitian
       matrix, supplied in packed form.

PARAMETERS

       UPLO   - CHARACTER*1.
              On entry, UPLO specifies whether the upper or lower triangular part of the matrix A
              is supplied in the packed array AP as follows:

              UPLO = 'U' or 'u'   The upper triangular part of A is supplied in AP.

              UPLO = 'L' or 'l'   The lower triangular part of A is supplied in AP.

              Unchanged on exit.

       N      - INTEGER.
              On entry, N specifies the order of  the  matrix  A.   N  must  be  at  least  zero.
              Unchanged on exit.

       ALPHA  - COMPLEX*16      .
              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       X      - COMPLEX*16       array of dimension at least
              (  1 + ( n - 1 )*abs( INCX ) ).  Before entry, the incremented array X must contain
              the n element vector x.  Unchanged on exit.

       INCX   - INTEGER.
              On entry, INCX specifies the increment for the elements of  X.  INCX  must  not  be
              zero.  Unchanged on exit.

       Y      - COMPLEX*16       array of dimension at least
              (  1 + ( n - 1 )*abs( INCY ) ).  Before entry, the incremented array Y must contain
              the n element vector y.  Unchanged on exit.

       INCY   - INTEGER.
              On entry, INCY specifies the increment for the elements of  Y.  INCY  must  not  be
              zero.  Unchanged on exit.

       AP     - COMPLEX*16       array of DIMENSION at least
              (  (  n*(  n  + 1 ) )/2 ).  Before entry with  UPLO = 'U' or 'u', the array AP must
              contain the upper triangular part of  the  hermitian  matrix  packed  sequentially,
              column  by  column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain
              a( 1, 2 ) and a( 2, 2 )  respectively,  and  so  on.  On  exit,  the  array  AP  is
              overwritten  by the upper triangular part of the updated matrix.  Before entry with
              UPLO = 'L' or 'l', the array AP must contain  the  lower  triangular  part  of  the
              hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a(
              1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )  respectively,  and  so
              on.  On  exit,  the  array  AP  is  overwritten by the lower triangular part of the
              updated matrix.  Note that the imaginary parts of the diagonal elements need not be
              set, they are assumed to be zero, and on exit they are set to zero.

              Level 2 Blas routine.

              --  Written  on  22-October-1986.   Jack Dongarra, Argonne National Lab.  Jeremy Du
              Croz, Nag Central Office.  Sven Hammarling, Nag Central  Office.   Richard  Hanson,
              Sandia National Labs.