NAME
ZHPR2 - perform the hermitian rank 2 operation A := alpha*x*conjg( y’
) + conjg( alpha )*y*conjg( x’ ) + A,
SYNOPSIS
SUBROUTINE ZHPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP )
COMPLEX*16 ALPHA
INTEGER INCX, INCY, N
CHARACTER*1 UPLO
COMPLEX*16 AP( * ), X( * ), Y( * )
PURPOSE
ZHPR2 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.
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 - COMPLEX*16 .
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.
Y - COMPLEX*16 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*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.