ZHPR(3)         BLAS routine of NEC Numeric Library Collection         ZHPR(3)



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

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

          A := A + alpha*x*conjg( x' )

       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  fol-
              lows:

              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 her-
              mitian 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 ) respec-
              tively, 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)