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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.