CHPR2 - perform the hermitian rank 2 operation A :=
alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
SYNOPSIS
SUBROUTINE CHPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP )
COMPLEX ALPHA
INTEGER INCX, INCY, N
CHARACTER*1 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.
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 .
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 vec
tor x. Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the ele
ments of X. INCX must not be zero. Unchanged on
exit.
( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the
incremented array Y must contain the n element vec
tor y. Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the ele
ments 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 tri
angular 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 tri
angular 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.
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