ZHPR2(3) BLAS routine ZHPR2(3)
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 ele-
ments 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 Cen-
tral Office. Richard Hanson, Sandia National Labs.
BLAS routine 16 October 1992 ZHPR2(3)