function quad_error = monomial_quadrature ( dim_num, expon, point_num, weight, x ) %*****************************************************************************80 % %% MONOMIAL_QUADRATURE applies a quadrature rule to a monomial. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 11 November 2007 % % Author: % % John Burkardt % % Parameters: % % Input, integer DIM_NUM, the spatial dimension. % % Input, integer EXPON(DIM_NUM), the exponents. % % Input, integer POINT_NUM, the number of points in the rule. % % Input, real WEIGHT(POINT_NUM), the quadrature weights. % % Input, real X(DIM_NUM,POINT_NUM), the quadrature points. % % Output, real QUAD_ERROR, the quadrature error. % % % Get the exact value of the integral of the unscaled monomial. % scale = monomial_int01 ( dim_num, expon ); % % Evaluate the monomial at the quadrature points. % value = monomial_value ( dim_num, point_num, x, expon ); % % Compute the weighted sum and divide by the exact value. % quad = ( weight * transpose ( value ) ) / scale; % % Error: % exact = 1.0; quad_error = abs ( quad - exact ); return end