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 (input) 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 (input) INTEGER

On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.

ALPHA (input) COMPLEX*16

On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

AP (input) 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 (input) 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 (input) INTEGER

On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.

BETA (input) 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 (input/output) 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 (input) INTEGER

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