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.