Tasmanian Sparse Grids module, example 11

Functions
void	sparse_grids_example_11 ()
	Sparse Grids Example 11: Unstructured data.

Detailed Description

Example 11

Constructing a grid from unstructured data.

Function Documentation

sparse_grids_example_11()

void sparse_grids_example_11

(

)

Sparse Grids Example 11: Unstructured data.

Sparse grid approximation (or surrogates) can be constructed from a set of points not necessarily aligned to the points on the grid, using a least-squares fit.

• the fit will not interpolate the data, i.e., there will be a difference between the surrogate and the data at each point
• the overall accuracy will be lower and more points are needed to reach the same accuracy as in the structured case, the fit should be used when the model cannot be sampled exactly at the sparse grid points
• solving the fit requires the solution to a system of linear equations and uses significant amount of flops and memory, at the minimum BLAS must be enabled but GPU acceleration is preferable with the MAGMA library which provides advanced out-of-core methods

#endif
 
    cout << "\n---------------------------------------------------------------------------------------------------\n";
    cout << std::scientific; cout.precision(4);
    cout << "Example 11: construction using unstructured data\n\n";
 
    int const num_inputs = 2;
 
    // using random points to test the error
    int const num_test_points = 1000;
    std::vector<double> test_points(num_test_points * num_inputs);
    std::minstd_rand park_miller(42);
    std::uniform_real_distribution<double> domain(-1.0, 1.0);
    for(auto &t : test_points) t = domain(park_miller);
 
    // computes the error between the gird surrogate model and the actual model
    // using the test points, finds the largest absolute error
    auto get_error = [&](TasGrid::TasmanianSparseGrid const &grid,
                         std::function<void(double const x[], double y[], size_t)> model)->
        double{
            std::vector<double> grid_result;
            grid.evaluateBatch(test_points, grid_result);
            double err = 0.0;
            for(int i=0; i<num_test_points; i++){
                double model_result; // using only one output
                model(&test_points[i*num_inputs], &model_result, 0);
                err = std::max(err, std::abs(grid_result[i] - model_result));
            }
            return err;
        };
 
    // using a simple model
    auto model = [](double const x[], double y[], size_t)->
        void{ y[0] = std::exp(-x[0]*x[0] -x[1]-x[1]); };
 
    auto grid = TasGrid::makeGlobalGrid(num_inputs, 1, 4, TasGrid::type_level, TasGrid::rule_clenshawcurtis);
 
    // generate random data for the inputs, and compute the corresponding outputs
    int const num_data_points = 2000;
    std::vector<double> data_input(num_inputs * num_data_points);
    std::vector<double> data_output(num_data_points);
 
    for(auto &d : data_input) d = domain(park_miller);
    for(int i=0; i<num_data_points; i++) model(&data_input[i * num_inputs], &data_output[i], 0);
 
    // check if capability is available
    if (not grid.isAccelerationAvailable(TasGrid::accel_cpu_blas) and
        not grid.isAccelerationAvailable(TasGrid::accel_gpu_cuda) and
        not grid.isAccelerationAvailable(TasGrid::accel_gpu_magma)){
        cout << "Skipping example 11, BLAS, CUDA, or MAGMA acceleration required.\n";
        return;
    }
 
    // accel_cpu_blas: works on the CPU and can utilize all available RAM
    // accel_gpu_cuda: works on the GPU but it is restricted to the case
    //                 where the data can fit in GPU memory
    // accel_gpu_magma: works out-of-core, the data is stored in CPU RAM
    //                  while computations are still done on the GPU
    grid.enableAcceleration(TasGrid::accel_gpu_magma);
 
    // constructs the grid, depending on the amount of data data,
    // the side of the grid and the enabled acceleration
    // this can take significant amount of time
    TasGrid::loadUnstructuredDataL2(data_input, data_output, 1.E-4, grid);
 
    cout << "Using construction from unstructured (random) data\n";
    cout << "   approximatino error = " << get_error(grid, model) << "\n\n";
 
#ifndef __TASMANIAN_DOXYGEN_SKIP