SG++
Interaction-Term aware sparse grids.

This example shows how grids with more interaction terms differ from simpler grids.

#include <cstdlib>
#include <tuple>
#include <unordered_set>
#include <vector>

decodeCoords

Parameters
coordsare the coordinates of a grid point
resultis the boolean version of the vector, each entry is true if the corresponding dimension is used, i.e. not equal to 0.5
void decodeCoords(sgpp::base::DataVector& coords, std::vector<bool>& result) {
for (size_t i = 0; i < coords.getSize(); ++i) {
result[i] = coords[i] != 0.5;
}

main creates a grid with dimension three and level five and adds more and more interaction points.

This is done by using interaction-term aware sparse grids. First, we create a grid with interaction terms, that model only one feature, then we add the pairwise interactions and finally all interactions. The differences between the grids are printed.

int main(int argc, char** argv) {

Create our first grid.

auto& storage = grid->getStorage();
auto generator = sgpp::base::HashGenerator();
generator.regular_inter(storage, level, terms);
std::cout << "Grid size with one level terms is " << grid->getSize() << std::endl;
for (size_t i = 0; i < grid->getSize(); ++i) {
sgpp::base::HashGridPoint gridIndex = storage.getPoint(i);
gridIndex.getStandardCoordinates(coords);
decodeCoords(coords, boolCoords);
std::tie(std::ignore, isInserted) = realCoords.insert(boolCoords);
if (isInserted) {
std::cout << "New point" << coords.toString() << std::endl;
}

Add all two-level-interactions

for (auto i = 0; i < dimensions; ++i) {
for (auto j = 0; j < dimensions; ++j) {
auto vec = std::vector<bool>(dimensions, false);
vec[i] = true;
vec[j] = true;
terms.insert(vec);
}

Add all three-level-interactions

auto vec = std::vector<bool>(dimensions, true);
terms.insert(vec);
{
auto& storage = grid->getStorage();
auto generator = sgpp::base::HashGenerator();
generator.regular_inter(storage, level, terms);
std::cout << "Grid size with three level terms is " << grid->getSize() << std::endl;
for (size_t i = 0; i < grid->getSize(); ++i) {
sgpp::base::HashGridPoint gridIndex = storage.getPoint(i);
gridIndex.getStandardCoordinates(coords);
decodeCoords(coords, boolCoords);
std::tie(std::ignore, isInserted) = realCoords.insert(boolCoords);
if (isInserted) {
std::cout << "New point" << coords.toString() << std::endl;
}