NAME

zspmv - perform the matrix-vector operation   y := alpha∗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
 
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. Unchanged 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 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. 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. Unchanged on exit.

INCX   - INTEGER
On entry, INCX specifies the increment for the elements 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 elements of Y. INCY must not be zero. Unchanged on exit.

SunSoft, Inc.  —  Last change: 27 Jun 1995