Section: BLAS routine (3)Updated: 16 October 1992Local indexUp

NAME

ZHPR - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A,

SYNOPSIS

SUBROUTINE ZHPR

( UPLO, N, ALPHA, X, INCX, AP )

DOUBLE
PRECISION ALPHA

INTEGER
INCX, N

CHARACTER*1
UPLO

COMPLEX*16
AP( * ), X( * )

PURPOSE

ZHPR 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 - DOUBLE PRECISION.

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.

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.