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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.