int main(int argc, char **argv) {
init();
header();
///// CONFIGURATION /////
constexpr unsigned int nData = 100u; // Number of uniformly sampled points
constexpr unsigned int nDataSample = 10000u; // Number of points used for plotting and l2 norm
////////////////////////////////////
const Interval<float> interval(0.0f,1.0f);
//generate and plot samples
FunctionSample<nDataSample, float> samplePlot(interval, F);
RandomSample<nData, float> sample(interval, F);
const PlotBox<float>& box = PlotBox<float>(interval.inf,interval.sup,samplePlot.min(),samplePlot.max()).dilate(1.0);
//build tree with samples (ALLOCATION)
TreeNode<float> *tree = new IntegerGrid<float>(interval);
for (unsigned int i = 0; i < nData; i++) {
tree->insert(sample[i]);
}
//remove bad nodes (check GRP criterion)
tree->computePlacementCondition(1,0.5);
//map wavelets to tree nodes
DeslaurierDubuc<float,10> db;
WaveletMapper<float> simpleDDTreeMapper = [&db](unsigned int j, int k)->Wavelet<float>& { return db; };
unsigned int n = tree->countValidNodes();
std::cout << n << " samples out of " << nData << " met the GRP criterion !" << std::endl;
//compute wavelet coefficients
using Eigen::VectorXf;
using Eigen::MatrixXf;
MatrixXf A = MatrixXf::Random(n,n);
VectorXf b = VectorXf::Random(n);
tree->fillSystem(A,b,simpleDDTreeMapper);
VectorXf coefficients = A.partialPivLu().solve(b);
float epsilon = (A*coefficients -b).maxCoeff();
std::cout << "Maximum sample error : " << epsilon << std::endl;
//build wavelet tree with the coefficients
WaveletTree<float> *waveletTree = WaveletTree<float>::makeTree(tree, simpleDDTreeMapper, coefficients);
FunctionSample<nDataSample, float> reconstructedSample(interval, *waveletTree);
float L2_distance = (samplePlot - reconstructedSample).norm();
std::cout << "l2 norm of the residue ||F' - F|| = " << L2_distance << " !" << std::endl;
//plot everything
Gnuplot gp("tee plot.gp | gnuplot -persist");
gp << "set term wxt dashed\n";
gp << "set multiplot\n";
gp << "set notitle\n";
samplePlot.plotLine(gp, box);
sample.plotPoints(gp, box);
tree->plotValidPoints(gp, box);
waveletTree->plot(gp, box, nDataSample);
gp << "unset multiplot\n";
gp << "set term wxt 1 dashed\n";
gp << "set multiplot\n";
gp << "unset label\n";
tree->plot(gp, box, true, true);
tree->plotValid(gp, box);
//gp << "unset multiplot\n";
//gp << "set term wxt 2\n";
//gp << "set multiplot\n";
//gp << "unset label\n";
//waveletTree->plot(gp, box, nDataSample);
footer();
return EXIT_SUCCESS;
}
