CHPR2(1)

NAME
LAPACK-3 - performs the hermitian rank 2 operation A := alpha*x*y**H + conjg( alpha )*y*x**H + A,

SYNOPSIS

SUBROUTINE CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)

COMPLEX
    ALPHA

INTEGER
    INCX,INCY,N

CHARACTER
    UPLO

COMPLEX
    AP(*),X(*),Y(*)

PURPOSE
CHPR2 performs the hermitian rank 2 operation
 where alpha is a scalar, x and y are n element vectors 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 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  - COMPLEX         .
     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.

Y      - COMPLEX          array of dimension at least
     ( 1 + ( n - 1 )*abs( INCY ) ).
     Before entry, the incremented array Y must contain the n
     element vector y.
     Unchanged on exit.

INCY   - INTEGER.
     On entry, INCY specifies the increment for the elements of
     Y. INCY 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 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.

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.