test_19.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;
std::vector<long double> alpha(1,0);
std::vector<long double> beta(1,0);
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) {
    int    dimension = (int)alpha.size();
    Scalar total     = 0.0;
    Scalar point     = 0.0;
    for (int i=0; i<dimension; i++) {
      point     = 0.5*input[i]+0.5;
      total    += powl(alpha[i]*(point-beta[i]),(long double)2.0);
    }
    output.clear(); output.resize(1,std::exp(-total));
  }  

  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 nCDF(long double z) {
  long double p      = 0.0, expntl = 0.0;
  long double p0     = 220.2068679123761;
  long double p1     = 221.2135961699311;
  long double p2     = 112.0792914978709;
  long double p3     = 33.91286607838300;
  long double p4     = 6.373962203531650;
  long double p5     = 0.7003830644436881;
  long double p6     = 0.03526249659989109;
  long double q0     = 440.4137358247522;
  long double q1     = 793.8265125199484;
  long double q2     = 637.3336333788311;
  long double q3     = 296.5642487796737;
  long double q4     = 86.78073220294608;
  long double q5     = 16.06417757920695;
  long double q6     = 1.755667163182642;
  long double q7     = 0.08838834764831844;
  long double rootpi = std::sqrt(M_PI);
  long double zabs   = std::abs(z);

  if (12.0 < zabs) {
    p = 0.0;
  }
  else {
    expntl = exp(-zabs*zabs/2.0);
    if (zabs < 7.0) {
      p = expntl*
        ((((((p6*zabs+p5)*zabs+p4)*zabs+p3)*zabs+p2)*zabs+p1)*zabs+p0)/ 
        (((((((q7*zabs+q6)*zabs+q5)*zabs+q4)*zabs+q3)*zabs+q2)*zabs+q1)*zabs+q0);
    }
    else {
      p = expntl/(zabs+1.0/(zabs+2.0/(zabs+3.0/(zabs+4.0/(zabs+0.65)))))/rootpi;
    }                                
  }
  if(0.0 < z){
    p = 1.0-p;
  }
  return p;
}

long double compExactInt(void) {
  long double val       = 1.0;
  int         dimension = alpha.size();    
  long double s2        = std::sqrt(2.0);
  long double sp        = std::sqrt(M_PI);
  for (int i=0; i<dimension; i++) {
    long double s2a = s2*alpha[i];
    val *= (sp/alpha[i])*(nCDF((1.0-beta[i])*s2a)-nCDF(-beta[i]*s2a));
  }
  return val;
}

long double adaptSG(StdVector<long double> & iv,
   AdaptiveSparseGridInterface<long double,StdVector<long double> > & 
   problem_data, 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
  std::multimap<long double,std::vector<int> > activeIndex;  
  activeIndex.insert(std::pair<long double,std::vector<int> >(eta,index));

  // Initialize the old index set
  std::set<std::vector<int> > oldIndex;

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

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 product Gaussians in 5 dimensions (Genz integration test). |\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 19: Integrate a product of Gaussians in 5D                             |\n"\
  << "===============================================================================\n";


  // internal variables:
  int         errorFlag    = 0;
  long double TOL          = INTREPID_TOL;
  int         dimension    = 5;
  int         maxLevel     = 7;
  bool        isNormalized = true;                  

  std::vector<EIntrepidBurkardt> rule1D(dimension,BURK_PATTERSON);
  std::vector<EIntrepidGrowth>   growth1D(dimension,GROWTH_FULLEXP);
 
  alpha.resize(dimension,0); beta.resize(dimension,0);
  for (int i=0; i<dimension; i++) {
    alpha[i] = (long double)std::rand()/(long double)RAND_MAX;
    beta[i]  = (long double)std::rand()/(long double)RAND_MAX;
  }

  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);

  long double eta = adaptSG(sol,problem_data,TOL); 

  long double analyticInt = compExactInt();
  long double abstol      = std::sqrt(INTREPID_TOL);
  long double absdiff     = std::abs(analyticInt-sol[0]);
  try { 
    *outStream << "Adaptive Sparse Grid exited with global error " 
               << std::scientific << std::setprecision(16) << eta << "\n"
               << "Approx = " << std::scientific << std::setprecision(16) << sol[0] 
               << ",  Exact = " << std::scientific << std::setprecision(16) << analyticInt << "\n"
               << "Error = " << std::scientific << std::setprecision(16) << absdiff << "   " 
               << "<?" << "   " << abstol << "\n"; 
    if (absdiff > abstol) {
      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;
}