function sparse_grid_composite_test04 ( dim_num, level_max ) %*****************************************************************************80 % %% SPARSE_GRID_COMPOSITE_TEST04 sums the weights and compares them to 2^DIM_NUM. % % Discussion: % % This routine gets the sparse grid indices and determines the % corresponding sparse grid abscissas. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 11 August 2009 % % Author: % % John Burkardt % % Parameters: % % Input, integer DIM_NUM, the spatial dimension. % % Input, integer LEVEL_MAX, the level. % fprintf ( 1, '\n' ); fprintf ( 1, 'SPARSE_GRID_COMPOSITE_TEST04:\n' ); fprintf ( 1, ' Compute the weights of a composite sparse grid .\n' ); fprintf ( 1, '\n' ); fprintf ( 1, ' As a simple test, sum these weights.\n' ); fprintf ( 1, ' They should sum to exactly 2^DIM_NUM.\n' ); fprintf ( 1, '\n' ); fprintf ( 1, ' LEVEL_MAX = %d\n', level_max ); fprintf ( 1, ' Spatial dimension DIM_NUM = %d\n', dim_num ); % % Determine the number of points. % point_num = sparse_grid_composite_size ( dim_num, level_max ); fprintf ( 1, '\n' ); fprintf ( 1, ' Number of unique points in the grid = %d\n', point_num ); % % Compute the weights and points. % [ grid_weight, grid_point ] = sparse_grid_composite ( dim_num, level_max, point_num ); % % Sum the weights. % weight_sum = sum ( grid_weight(1:point_num) ); weight_sum_exact = 2.0^dim_num; weight_sum_error = abs ( weight_sum - weight_sum_exact ); fprintf ( 1, '\n' ) ; fprintf ( 1, ' Weight sum Exact sum Difference\n' ); fprintf ( 1, '\n' ); fprintf ( 1, ' %12e %12e %12e\n', ... weight_sum, weight_sum_exact, weight_sum_error ); return end