Tasmanian Sparse Grids module, example 1

Collaboration diagram for Tasmanian Sparse Grids module, example 1:

Functions
void	sparse_grids_example_01 ()
	Sparse Grids Example 1: integrate a simple function over a canonical domain. More...

Detailed Description

Example 1

Compute using a sparse grid with Clenshaw-Curtis nodes and weights.

Function Documentation

sparse_grids_example_01()

void sparse_grids_example_01

(

)

Sparse Grids Example 1: integrate a simple function over a canonical domain.

#endif
 
    cout << "\n---------------------------------------------------------------------------------------------------\n";
    cout << std::scientific; cout.precision(17);
    cout << "Example 1:  integrate f(x,y) = exp(-x^2) * cos(y),\n"
         << "            using clenshaw-curtis nodes and grid of type level\n";
 
    int dimension = 2;
    int level = 6;
 
    TasGrid::TasmanianSparseGrid grid;
    grid.makeGlobalGrid(dimension, 0, level, TasGrid::type_level, TasGrid::rule_clenshawcurtis);
    std::vector<double> points  = grid.getPoints();
    std::vector<double> weights = grid.getQuadratureWeights();
    int num_points = grid.getNumPoints(); // also equal to weights.size()
 
    double I = 0.0;
    for(int i=0; i<num_points; i++){
        double x = points[i*dimension];
        double y = points[i*dimension+1];
        I += weights[i] * std::exp(-x*x) * std::cos(y);
    }
 
    double exact = 2.513723354063905e+00;
    double E = std::abs(exact - I);
    cout <<   "      at level: " << level
         << "\n      the grid has: " << num_points
         << "\n      integral: " << I
         << "\n         error: " << E << "\n\n";
 
    level = 7;
 
    grid.makeGlobalGrid(dimension, 0, level, TasGrid::type_level, TasGrid::rule_clenshawcurtis);
    points = grid.getPoints();
    weights = grid.getQuadratureWeights();
    num_points = grid.getNumPoints();
 
    I = 0.0;
    for(int i=0; i<num_points; i++){
        double x = points[i*dimension];
        double y = points[i*dimension+1];
        I += weights[i] * std::exp(-x*x) * std::cos(y);
    }
 
    E = std::abs(exact - I);
    cout <<   "      at level: " << level
         << "\n      the grid has: " << num_points
         << "\n      integral: " << I
         << "\n         error: " << E << endl;
 
#ifndef __TASMANIAN_DOXYGEN_SKIP