.TH ZSPMV 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME ZSPMV - the matrix-vector operation y := alpha*A*x + beta*y, .SH SYNOPSIS .TP 18 SUBROUTINE ZSPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY ) .TP 18 .ti +4 CHARACTER UPLO .TP 18 .ti +4 INTEGER INCX, INCY, N .TP 18 .ti +4 COMPLEX*16 ALPHA, BETA .TP 18 .ti +4 COMPLEX*16 AP( * ), X( * ), Y( * ) .SH 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. .SH ARGUMENTS .TP 9 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 = \(aqU\(aq or \(aqu\(aq The upper triangular part of A is supplied in AP. UPLO = \(aqL\(aq or \(aql\(aq The lower triangular part of A is supplied in AP. Unchanged on exit. .TP 9 N (input) INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. .TP 9 ALPHA (input) COMPLEX*16 On entry, ALPHA specifies the scalar alpha. Unchanged on exit. .TP 9 AP (input) COMPLEX*16 array, dimension at least ( ( N*( N + 1 ) )/2 ). Before entry, with UPLO = \(aqU\(aq or \(aqu\(aq, 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 = \(aqL\(aq or \(aql\(aq, 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. .TP 9 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. .TP 9 INCX (input) INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. .TP 9 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. .TP 9 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. .TP 9 INCY (input) INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.