test_23.cpp

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#include "Intrepid_AdaptiveSparseGrid.hpp"
//#include "Intrepid_CubatureLineSorted.hpp"
#include "Intrepid_Utils.hpp"
#include "Teuchos_oblackholestream.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_RefCountPtr.hpp"
#include "Teuchos_GlobalMPISession.hpp"

using namespace Intrepid;


template<class Scalar>
class StdVector {
private:
  Teuchos::RefCountPtr<std::vector<Scalar> >  std_vec_;

public:

  StdVector( const Teuchos::RefCountPtr<std::vector<Scalar> > & std_vec ) 
  : std_vec_(std_vec) {}

  Teuchos::RefCountPtr<StdVector<Scalar> > Create() const {
    return Teuchos::rcp( new StdVector<Scalar>(
           Teuchos::rcp(new std::vector<Scalar>(std_vec_->size(),0))));
  }

  void Update( StdVector<Scalar> & s ) {
    int dimension  = (int)(std_vec_->size());
    for (int i=0; i<dimension; i++)
      (*std_vec_)[i] += s[i]; 
  }

  void Update( Scalar alpha, StdVector<Scalar> & s )  {
    int dimension  = (int)(std_vec_->size());
    for (int i=0; i<dimension; i++)
      (*std_vec_)[i] += alpha*s[i];
  }

  Scalar operator[](int i) {
    return (*std_vec_)[i];
  }

  void clear() {
    std_vec_->clear();
  }

  void resize(int n, Scalar p) {
    std_vec_->resize(n,p);
  }

  int size() {
    return (int)std_vec_->size();
  }

  void Set( Scalar alpha )  {
    int dimension  = (int)(std_vec_->size());
    for (int i=0; i<dimension; i++)
      (*std_vec_)[i] = alpha;
  }
};

template<class Scalar, class UserVector>
class ASGdata : 
  public Intrepid::AdaptiveSparseGridInterface<Scalar,UserVector> {  
public:  
  ~ASGdata() {}

  ASGdata(int dimension,std::vector<EIntrepidBurkardt> rule1D,
          std::vector<EIntrepidGrowth> growth1D, int maxLevel,
          bool isNormalized) : AdaptiveSparseGridInterface<Scalar,UserVector>(
          dimension,rule1D,growth1D,maxLevel,isNormalized) {}

  void eval_integrand(UserVector & output, std::vector<Scalar> & input) {
    output.clear(); output.resize(1,powl(input[0]+input[1],(long double)6.0));
  }  
  Scalar error_indicator(UserVector & input) {
    int dimension = (int)input.size();
    Scalar norm2  = 0.0;
    for (int i=0; i<dimension; i++)
      norm2 += input[i]*input[i];
    
    Scalar ID = AdaptiveSparseGridInterface<Scalar,UserVector>::
      getInitialDiff();
    norm2 = std::sqrt(norm2)/ID;
    return norm2;
  }
};

long double adaptSG(StdVector<long double> & iv,
                    std::multimap<long double,std::vector<int> > & activeIndex,
                    std::set<std::vector<int> > & oldIndex,
                    AdaptiveSparseGridInterface<long double,StdVector<long double> > & problem_data,
                    CubatureTensorSorted<long double> & cubRule,
                    long double TOL) {

  // Construct a Container for the adapted rule
  int dimension = problem_data.getDimension();
  std::vector<int> index(dimension,1);
  
  // Initialize global error indicator
  long double eta = 1.0;
  
  // Initialize the Active index set
  activeIndex.insert(std::pair<long double,std::vector<int> >(eta,index));

  // Perform Adaptation
  while (eta > TOL) {
    eta = AdaptiveSparseGrid<long double,StdVector<long double> >::refine_grid(
                                                       activeIndex,oldIndex,
                                                       iv,cubRule,
                                                       eta,problem_data);
  }
  cubRule.normalize();
  return eta;
}

long double evalQuad(CubatureTensorSorted<long double> & lineCub) {

  int size = lineCub.getNumPoints();
  int dimension = lineCub.getDimension();
  FieldContainer<long double> cubPoints(size,dimension);
  FieldContainer<long double> cubWeights(size);
  lineCub.getCubature(cubPoints,cubWeights);
  
  long double Q = 0.0;
  for (int k=0; k<size; k++) 
    Q += cubWeights(k)*powl(cubPoints(k,0)+cubPoints(k,1),(long double)6.0);

  return Q;
}

int main(int argc, char *argv[]) {
  
  Teuchos::GlobalMPISession mpiSession(&argc, &argv);

  // This little trick lets us print to std::cout only if
  // a (dummy) command-line argument is provided.
  int iprint     = argc - 1;
  Teuchos::RCP<std::ostream> outStream;
  Teuchos::oblackholestream bhs; // outputs nothing
  if (iprint > 0)
    outStream = Teuchos::rcp(&std::cout, false);
  else
    outStream = Teuchos::rcp(&bhs, false);

  // Save the format state of the original std::cout.
  Teuchos::oblackholestream oldFormatState;
  oldFormatState.copyfmt(std::cout);
 
  *outStream \
  << "===============================================================================\n" \
  << "|                                                                             |\n" \
  << "|                         Unit Test (AdaptiveSparseGrid)                      |\n" \
  << "|                                                                             |\n" \
  << "|     1) Integrate a sum of Gaussians in 2D and compare index sets.           |\n" \
  << "|                                                                             |\n" \
  << "|  Questions? Contact  Drew Kouri (dpkouri@sandia.gov) or                     |\n" \
  << "|                      Denis Ridzal (dridzal@sandia.gov).                     |\n" \
  << "|                                                                             |\n" \
  << "|  Intrepid's website: http://trilinos.sandia.gov/packages/intrepid           |\n" \
  << "|  Trilinos website:   http://trilinos.sandia.gov                             |\n" \
  << "|                                                                             |\n" \
  << "===============================================================================\n"\
  << "| TEST 23: Compare index sets for different instances of refine grid          |\n"\
  << "===============================================================================\n";


  // internal variables:
  int         errorFlag    = 0;
  long double TOL          = INTREPID_TOL;
  int         dimension    = 2;
  int         maxLevel     = 4;
  bool        isNormalized = false;                  

  std::vector<EIntrepidBurkardt> rule1D(dimension,BURK_CLENSHAWCURTIS);
  std::vector<EIntrepidGrowth>   growth1D(dimension,GROWTH_FULLEXP);

  ASGdata<long double,StdVector<long double> > problem_data(dimension,rule1D,
                                                            growth1D,maxLevel,
                                                            isNormalized);  
  Teuchos::RCP<std::vector<long double> > integralValue = 
    Teuchos::rcp(new std::vector<long double>(1,0.0));
  StdVector<long double> sol(integralValue); sol.Set(0.0);
  problem_data.init(sol);

  try { 
    
    // Initialize the index sets
    std::multimap<long double,std::vector<int> > activeIndex1;
    std::set<std::vector<int> > oldIndex1;  
    std::vector<int> index(dimension,1);
    CubatureTensorSorted<long double> adaptedRule(dimension,index,rule1D,
                                                  growth1D,isNormalized);
    adaptSG(sol,activeIndex1,oldIndex1,problem_data,adaptedRule,TOL);
    long double Q1  = sol[0];
    
    CubatureTensorSorted<long double> fullRule(0,dimension);
    AdaptiveSparseGrid<long double,StdVector<long double> >::buildSparseGrid(
                                                     fullRule,dimension,
                                                     maxLevel,rule1D,
                                                     growth1D,isNormalized);
    long double Q2 = evalQuad(fullRule);
    fullRule.normalize();
    
    long double diff = std::abs(Q1-Q2);

    *outStream << "Q1 = " << Q1 << "   Q2 = " << Q2 
               << "   |Q1-Q2| = " << diff << "\n";

    int size1 = adaptedRule.getNumPoints(); 
    FieldContainer<long double> aPoints(size1,dimension);
    FieldContainer<long double> aWeights(size1);
    adaptedRule.getCubature(aPoints,aWeights);

    *outStream << "\n\nAdapted Rule Nodes and Weights\n";
    for (int i=0; i<size1; i++) 
      *outStream << aPoints(i,0) << "\t" << aPoints(i,1) 
                 << "\t" << aWeights(i) << "\n";

    int size2 = fullRule.getNumPoints();
    FieldContainer<long double> fPoints(size2,dimension);
    FieldContainer<long double> fWeights(size2);
    fullRule.getCubature(fPoints,fWeights);

    *outStream << "\n\nFull Rule Nodes and Weights\n";
    for (int i=0; i<size2; i++) 
      *outStream << fPoints(i,0) << "\t" << fPoints(i,1) 
                 << "\t" << fWeights(i) << "\n";  

    *outStream << "\n\nSize of adapted rule = " << size1 
               << "    Size of full rule = " << size2 << "\n";
    if (diff > TOL*std::abs(Q2)||size1!=size2) {
      errorFlag++;
      *outStream << std::right << std::setw(104) << "^^^^---FAILURE!\n";
    }
    else {
      long double sum1 = 0.0, sum2 = 0.0;
      for (int i=0; i<size1; i++) {
        //diff = std::abs(fWeights(i)-aWeights(i));
        sum1 += fWeights(i);
        sum2 += aWeights(i);
      }
      *outStream << "Check if weights are normalized:" 
                 << "  Adapted Rule Sum = " << sum2
                 << "  Full Rule Sum = " << sum1 << "\n";
      if (std::abs(sum1-1.0) > TOL || std::abs(sum2-1.0) > TOL) {
        errorFlag++;
        *outStream << std::right << std::setw(104) << "^^^^---FAILURE!\n";
      }
    }
  }
  catch (const std::logic_error & err) {    
    *outStream << err.what() << "\n";
    errorFlag = -1;
  };  

  if (errorFlag != 0)
    std::cout << "End Result: TEST FAILED\n";
  else
    std::cout << "End Result: TEST PASSED\n";

  // reset format state of std::cout
  std::cout.copyfmt(oldFormatState);

  return errorFlag;
}