Tasmanian Sparse Grids module, example 2

Collaboration diagram for Tasmanian Sparse Grids module, example 2:

Functions
void	sparse_grids_example_02 ()
	Sparse Grids Example 2: integrate a simple function over a canonical domain. More...

Detailed Description

Example 2

Compute using a sparse grid with Gauss-Patterson nodes and weights. The grid is constructed over a non-canononical domain and the points are selected based on a total degree polynomial space.

Function Documentation

sparse_grids_example_02()

void sparse_grids_example_02

(

)

Sparse Grids Example 2: integrate a simple function over a canonical domain.

#endif
 
    cout << "\n---------------------------------------------------------------------------------------------------\n";
    cout << std::scientific; cout.precision(17);
    cout << "Example 2: integrate f(x,y) = exp(-x^2) * cos(y) over [-5,5] x [-2,3]\n"
         << "           using  Gauss-Patterson nodes and total degree polynomial space\n";
 
    int dimension = 2;
    int exactness = 20;
 
    // the type_qptotal will guarantee exact integral for all polynomials with degree 20 or less
    auto grid = TasGrid::makeGlobalGrid(dimension, 0, exactness,
                                        TasGrid::type_qptotal, TasGrid::rule_gausspatterson);
    grid.setDomainTransform({-5.0, -2.0}, {5.0, 3.0}); // set the non-canonical domain
    auto points  = grid.getPoints();
    auto weights = grid.getQuadratureWeights();
 
    double I = 0.0;
    for(int i=0; i<grid.getNumPoints(); i++){
        double x = points[i*dimension];
        double y = points[i*dimension+1];
        I += weights[i] * std::exp(-x*x) * std::cos(y);
    }
 
    double exact = 1.861816427518323e+00;
    double E = std::abs(exact - I);
    cout <<   "      at polynomial exactness: " << exactness
         << "\n      the grid has: " << weights.size()
         << "\n      integral: " << I
         << "\n         error: " << E << "\n\n";
 
 
    exactness = 40;
 
    grid = TasGrid::makeGlobalGrid(dimension, 0, exactness,
                                   TasGrid::type_qptotal, TasGrid::rule_gausspatterson);
    grid.setDomainTransform({-5.0, -2.0}, {5.0, 3.0}); // set the non-canonical domain
    points  = grid.getPoints();
    weights = grid.getQuadratureWeights();
 
    I = 0.0;
    for(int i=0; i<grid.getNumPoints(); 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 polynomial exactness: " << exactness
         << "\n      the grid has: " << weights.size()
         << "\n      integral: " << I
         << "\n         error: " << E << endl;
 
#ifndef __TASMANIAN_DOXYGEN_SKIP