zhpmv(3)

NAME

ZHPMV - perform the matrix-vector operation y := al

pha*A*x + beta*y,

SYNOPSIS

SUBROUTINE  ZHPMV  ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y,
INCY )
    COMPLEX*16   ALPHA, BETA
    INTEGER      INCX, INCY, N
    CHARACTER*1  UPLO
    COMPLEX*16   AP( * ), X( * ), Y( * )

PURPOSE

ZHPMV performs the matrix-vector operation

where alpha and beta are scalars, 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 low

er triangular
part of the matrix A is supplied in the packed ar

ray 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. Un

changed 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. Before entry with

UPLO = 'L' or
'l', the array AP must contain the lower triangu

lar 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. Note that

the imaginary parts of the diagonal elements need not

be set and are
assumed to be zero. 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. Un

changed on exit.

INCX - INTEGER.

On entry, INCX specifies the increment for the el

ements of X.
INCX must not be zero. Unchanged on exit.

BETA - COMPLEX*16 .

On entry, BETA specifies the scalar beta. When BE

TA is supplied
as zero then Y need not be set on input. 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. On ex

it, Y is overwritten by the updated vector y.

INCY - INTEGER.

On entry, INCY specifies the increment for the el

ements of Y.
INCY must not be zero. Unchanged on exit.

Level 2 Blas routine.

-- Written on 22-October-1986. Jack Dongarra, Ar

gonne National
Lab. Jeremy Du Croz, Nag Central Office. Sven

Hammarling, Nag
Central Office. Richard Hanson, Sandia National

Labs.

BLAS routine 16 October 1992

ZHPMV(3)