NAME
DSPMV - perform the matrix-vector operation y := alpha*A*x + beta*y,
SYNOPSIS
SUBROUTINE DSPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
DOUBLE PRECISION ALPHA, BETA
INTEGER INCX, INCY, N
CHARACTER*1 UPLO
DOUBLE PRECISION AP( * ), X( * ), Y( * )
PURPOSE
DSPMV 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.
PARAMETERS
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 - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
AP - DOUBLE PRECISION 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 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 - DOUBLE PRECISION array of 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 - DOUBLE PRECISION.
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 - DOUBLE PRECISION array of 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.
Level 2 Blas routine.
-- Written on 22-October-1986. Jack Dongarra, Argonne National
Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag
Central Office. Richard Hanson, Sandia National Labs.