zspmv(3)

NAME

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

pha*A*x + beta*y,

SYNOPSIS

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

PURPOSE

ZSPMV performs the matrix-vector operation y := alpha*A*x

+ beta*y, where alpha and beta are scalars, x and y are n element

vectors and A is an n by n symmetric matrix, supplied in packed

form.

ARGUMENTS

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. Un

changed on exit.

AP - COMPLEX*16 array, 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 symmetric 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 triangular

part of the symmetric matrix packed sequentially, column by col

umn, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) con

tain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. Unchanged

on exit.

X - COMPLEX*16 array, 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 ele

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

BETA - COMPLEX*16

On entry, BETA specifies the scalar beta. When BETA

is supplied as zero then Y need not be set on input. Unchanged

on exit.

Y - COMPLEX*16 array, dimension at least

( 1 + ( N - 1 )*abs( INCY ) ). Before entry, the

incremented array Y must contain the n element vector y. On exit,

Y is overwritten by the updated vector y.

INCY - INTEGER

On entry, INCY specifies the increment for the ele

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

LAPACK version 3.0 15 June 2000

ZSPMV(3)