void AdaptiveSparseGridInterface<Scalar,UserVector>::eval_cubature( UserVector & output, CubatureTensorSorted<Scalar> & cubRule) { //int dimf = 0; // Dimension of the integrand Scalar weight = 0.0; std::vector<Scalar> point(dimension_,(Scalar)0.0); //std::vector<Scalar> f(1,0.0); Teuchos::RCP<UserVector> f = output.Create(); output.Update(-1.0,output); typename std::map<std::vector<Scalar>,int>::iterator it; for (it=cubRule.begin(); it!=cubRule.end(); it++) { // Evaluate Function point.assign((it->first).begin(),(it->first).end()); // Extract point f->Update(-1.0,*f); eval_integrand(*f,point); // Evaluate Integrand at point // Update integral weight = cubRule.getWeight(it->second); output.Update(weight,*f); } }
void AdaptiveSparseGridInterface<Scalar,UserVector>::init(UserVector & output) { std::vector<int> index(dimension_,1); CubatureTensorSorted<Scalar> cubRule( dimension_,index,rule1D_,growth1D_,isNormalized_); // Evaluate the initial contribution to the integral initialDiff_ = 1.0; output.Update(-1.0,output); eval_cubature(output,cubRule); // Compute the initial error indicator initialDiff_ = error_indicator(output); if (fabs(initialDiff_)<INTREPID_TOL) initialDiff_ = 1.0; }
Scalar AdaptiveSparseGrid<Scalar,UserVector>::refine_grid( typename std::multimap<Scalar,std::vector<int> > & activeIndex, std::set<std::vector<int> > & oldIndex, UserVector & integralValue, CubatureTensorSorted<Scalar> & cubRule, Scalar globalErrorIndicator, AdaptiveSparseGridInterface<Scalar,UserVector> & problem_data) { TEUCHOS_TEST_FOR_EXCEPTION((activeIndex.empty()),std::out_of_range, ">>> ERROR (AdaptiveSparseGrid): Active Index set is empty."); int dimension = problem_data.getDimension(); std::vector<EIntrepidBurkardt> rule1D; problem_data.getRule(rule1D); std::vector<EIntrepidGrowth> growth1D; problem_data.getGrowth(growth1D); // Initialize Flags bool maxLevelFlag = true; bool isAdmissibleFlag = true; // Initialize Cubature Rule Teuchos::RCP<UserVector> s = integralValue.Create(); // Initialize iterator at end of inOldIndex std::set<std::vector<int> >::iterator it1(oldIndex.end()); // Initialize iterator at end of inActiveIndex typename std::multimap<Scalar,std::vector<int> >::iterator it; // Obtain Global Error Indicator as sum of key values of inActiveIndex Scalar eta = globalErrorIndicator; // Select Index to refine it = activeIndex.end(); it--; // Decrement to position of final value Scalar G = it->first; // Largest Error Indicator is at End eta -= G; // Update global error indicator std::vector<int> index = it->second; // Get Corresponding index activeIndex.erase(it); // Erase Index from active index set // Insert Index into old index set oldIndex.insert(it1,index); it1 = oldIndex.end(); // Refinement process for (int k=0; k<dimension; k++) { index[k]++; // index + ek // Check Max Level maxLevelFlag = problem_data.max_level(index); if (maxLevelFlag) { // Check Admissibility isAdmissibleFlag = isAdmissible(index,k,oldIndex,problem_data); if (isAdmissibleFlag) { // If admissible // Build Differential Quarature Rule CubatureTensorSorted<Scalar> diffRule(0,dimension); build_diffRule(diffRule,index,problem_data); // Apply Rule to function problem_data.eval_cubature(*s,diffRule); // Update integral value integralValue.Update(*s); // Update local error indicator and index set G = problem_data.error_indicator(*s); if (activeIndex.end()!=activeIndex.begin()) activeIndex.insert(activeIndex.end()--, std::pair<Scalar,std::vector<int> >(G,index)); else activeIndex.insert(std::pair<Scalar,std::vector<int> >(G,index)); // Update global error indicators eta += G; // Update adapted quadrature rule nodes and weights cubRule.update(1.0,diffRule,1.0); } } else { // Max Level Exceeded //std::cout << "Maximum Level Exceeded" << std::endl; } index[k]--; } return eta; }