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.

BLAS routine                                     16 October 1992                                         ZHPR(3)