NAME¶
CHPR - perform 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*1
- 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.
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 - 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 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.