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CHPR(1)				 BLAS routine			       CHPR(1)

NAME
       CHPR - performs the hermitian rank 1 operation	A := alpha*x*conjg( x'
       ) + A,

SYNOPSIS
       SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP)

	   REAL				       ALPHA

	   INTEGER			       INCX,N

	   CHARACTER			       UPLO

	   COMPLEX			       AP(*),X(*)

PURPOSE
       CHPR    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.

ARGUMENTS
       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  - REAL		.
	      On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       X      - COMPLEX		 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		 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 sequen‐
	      tially, 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.

FURTHER DETAILS
       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			 November 2008			       CHPR(1)
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