NAME

       ZHPR - perform the hermitian rank 1 operation   A := alpha*x*conjg( x' ) + A,

SYNOPSIS

       SUBROUTINE ZHPR ( UPLO, N, ALPHA, X, INCX, AP )

           DOUBLE      PRECISION ALPHA

           INTEGER     INCX, N

           CHARACTER*1 UPLO

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

PURPOSE

       ZHPR    performs the hermitian rank 1 operation

       where  alpha  is  a  real  scalar,  x  is an n element vector 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  - DOUBLE PRECISION.
              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.

       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.