test_12.cpp

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//#include "Intrepid_CubatureTensorSorted.hpp"
#include "Intrepid_CubatureTensorSorted.hpp"
//#include "Intrepid_CubatureLineSorted.hpp"
#include "Intrepid_Utils.hpp"
#include "Teuchos_oblackholestream.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_GlobalMPISession.hpp"

using namespace Intrepid;

/*
  Computes integrals of monomials over a given reference cell.
*/
long double evalQuad(std::vector<int> power, 
                     int dimension, std::vector<int> order, 
                     std::vector<EIntrepidBurkardt> rule) {
 
  CubatureTensorSorted<long double> lineCub(dimension,order,rule,false);  
  int size = lineCub.getNumPoints();
  FieldContainer<long double> cubPoints(size,dimension);
  FieldContainer<long double> cubWeights(size);
  lineCub.getCubature(cubPoints,cubWeights);

  int mid  = size/2;
  long double Q = 0.0;
  if (size%2) {
    Q  = cubWeights(mid);
    for (int i=0; i<dimension; i++) {
      Q *= powl(cubPoints(mid,i),power[i]);
    }
  }

  for (int i=0; i<mid; i++) {
    long double value1 = cubWeights(i);
    long double value2 = cubWeights(size-i-1);
    for (int j=0; j<dimension; j++) {
      value1 *= powl(cubPoints(i,j),power[j]);
      value2 *= powl(cubPoints(size-i-1,j),power[j]);
    }
    Q += value1+value2;
  }
  return Q;
}

long double evalInt(int dimension, std::vector<int> power, 
                    std::vector<EIntrepidBurkardt> rule) {
  long double I = 1.0;

  for (int i=0; i<dimension; i++) {
    if (rule[i]==BURK_CLENSHAWCURTIS||rule[i]==BURK_FEJER2||
        rule[i]==BURK_LEGENDRE||rule[i]==BURK_PATTERSON || 
        rule[i]==BURK_TRAPEZOIDAL) {
      if (power[i]%2)
        I *= 0.0;
      else 
        I *= 2.0/((long double)power[i]+1.0);
    }
    else if (rule[i]==BURK_LAGUERRE) {
      I *= tgammal((long double)(power[i]+1));
    }
    else if (rule[i]==BURK_CHEBYSHEV1) {
      long double bot, top;
      if (!(power[i]%2)) {
        top = 1; bot = 1;
        for (int j=2;j<=power[i];j+=2) {
          top *= (long double)(j-1);
          bot *= (long double)j;
        }
        I *= M_PI*top/bot;
      }
      else {
        I *= 0.0;
      }
    }
    else if (rule[i]==BURK_CHEBYSHEV2) {
      long double bot, top;
      if (!(power[i]%2)) {
      top = 1; bot = 1;
      for (int j=2;j<=power[i];j+=2) {
        top *= (long double)(j-1);
        bot *= (long double)j;
      }
      bot *= (long double)(power[i]+2);
      I   *= M_PI*top/bot;
      }
      else {
        I *= 0.0;
      }
    }
    else if (rule[i]==BURK_HERMITE||rule[i]==BURK_GENZKEISTER) {
      if (power[i]%2) {
        I *= 0.0;
      }
      else {  
        long double value = 1.0;
        if ((power[i]-1)>=1) {
          int n_copy = power[i]-1;
          while (1<n_copy) {
            value  *= (long double)n_copy;
            n_copy -= 2;
          }
        }
        I *= value*sqrt(M_PI)/powl(2.0,(long double)power[i]/2.0);
      }
    }
  }
  return I;
}

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 (CubatureTensorSorted)                    |\n" \
  << "|                                                                             |\n" \
  << "|     1) Computing integrals of monomials in 2D                               |\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 12: integrals of monomials in 2D - Anisotropic but no growth rules     |\n"\
  << "===============================================================================\n";


  // internal variables:
  int dimension = 2;
  int         errorFlag   = 0;
  long double reltol      = 1.0e+05*INTREPID_TOL;
  int         maxDeg      = 0;    
  long double analyticInt = 0;
  long double testInt     = 0;
  int         maxOrder    = 14;
  std::vector<int> power(2,0);
  std::vector<EIntrepidBurkardt> rule1(2,BURK_CLENSHAWCURTIS);
  std::vector<int> order(2,0);

  *outStream << "\nIntegrals of monomials on a reference line (edge):\n";
  // compute and compare integrals
  try {
    for (EIntrepidBurkardt rule=BURK_CHEBYSHEV1;rule<=BURK_LAGUERRE;rule++) {   
      *outStream << "Testing " << EIntrepidBurkardtToString(rule) << "\n";
      // compute integrals
      if (rule==BURK_HERMITE)
        maxOrder = 8;
      else if (rule==BURK_TRAPEZOIDAL) 
        maxOrder = 2;
      else 
        maxOrder = 9;

      rule1[0] = rule; rule1[1] = rule;
      if (rule!=BURK_PATTERSON&&rule!=BURK_GENZKEISTER) {
        for (int i=1; i <= maxOrder; i++) {
          if ( rule==BURK_CHEBYSHEV1 ||
               rule==BURK_CHEBYSHEV2 ||
               rule==BURK_LEGENDRE   ||
               rule==BURK_LAGUERRE   ||
               rule==BURK_HERMITE      )
            maxDeg = 2*i-1;
          else if ( rule==BURK_CLENSHAWCURTIS ||
                    rule==BURK_FEJER2         ||
                    rule==BURK_TRAPEZOIDAL      ) 
            maxDeg = i-1;
          
          order[0] = i; order[1] = i;
          for (int j=0; j <= maxDeg; j++) {
            power[0] = j;
            for (int k=0; k <= maxDeg; k++) {
              power[1] = k;
              analyticInt = evalInt(dimension, power, rule1);
              testInt     = evalQuad(power,dimension,order,rule1);
              
              long double abstol  = (analyticInt == 0.0 ? reltol : std::fabs(reltol*analyticInt) );
              long double absdiff = std::fabs(analyticInt - testInt);
              *outStream << "Cubature order " << std::setw(2) 
                         << std::left << i << " integrating "
                         << "x^" << std::setw(2) << std::left << j 
                         << "y^" << std::setw(2) << std::left 
                         << k <<  ":" << "   " << std::scientific 
                         << std::setprecision(16) << testInt 
                         << "   " << analyticInt << "   " 
                         << std::setprecision(4) << absdiff << "   " 
                         << "<?" << "   " << abstol << "\n";
              if (absdiff > abstol) {
                errorFlag++;
                *outStream << std::right << std::setw(104) 
                           << "^^^^---FAILURE!\n";
              }
            } // end for k
            *outStream << "\n";
          } // end for j
          *outStream << "\n";
        } // end for i
      }
      else if (rule==BURK_PATTERSON) {
        for (int i=0; i < 3; i++) {
          int l = (int)std::pow(2.0,(double)i+1.0)-1;
          if (i==0) 
            maxDeg = 1;
          else
            maxDeg = (int)(1.5*(double)l+0.5);
          
          order[0] = l; order[1] = l;
          for (int j=0; j <= maxDeg; j++) {         
            power[0] = j;
            for (int k=0; k <= maxDeg; k++) {         
              power[1] = k;
              analyticInt = evalInt(dimension, power, rule1);
              testInt     = evalQuad(power,dimension,order,rule1);
              
              long double abstol  = (analyticInt == 0.0 ? reltol : std::fabs(reltol*analyticInt) );
              long double absdiff = std::fabs(analyticInt - testInt);
              *outStream << "Cubature order " << std::setw(2) 
                         << std::left << l << " integrating "
                         << "x^" << std::setw(2) << std::left << j 
                         << "y^" << std::setw(2) << std::left 
                         << k <<  ":" << "   " << std::scientific 
                         << std::setprecision(16) << testInt 
                         << "   " << analyticInt << "   " 
                         << std::setprecision(4) << absdiff << "   " 
                         << "<?" << "   " << abstol << "\n";
              if (absdiff > abstol) {
                errorFlag++;
                *outStream << std::right << std::setw(104) 
                           << "^^^^---FAILURE!\n";
              }
            } // end for k
            *outStream << "\n";
          } // end for j
          *outStream << "\n";
        } // end for i
      }
      else if (rule==BURK_GENZKEISTER) {
        int o_ghk[8] = {1,3,9,19,35,37,41,43};
        for (int i=0; i < 3; i++) {
          int l = o_ghk[i];
          if (i==0) 
            maxDeg = 1;
          else
            maxDeg = (int)(1.5*(double)l+0.5);

          order[0] = l; order[1] = l;
          for (int j=0; j <= maxDeg; j++) {         
            power[0] = j;           
            for (int k=0; k <= maxDeg; k++) {         
              power[1] = k;
              analyticInt = evalInt(dimension, power, rule1);
              testInt     = evalQuad(power,dimension,order,rule1);
              
              long double abstol  = (analyticInt == 0.0 ? reltol : std::fabs(reltol*analyticInt) );
              long double absdiff = std::fabs(analyticInt - testInt);
              *outStream << "Cubature order " << std::setw(2) 
                         << std::left << l << " integrating "
                         << "x^" << std::setw(2) << std::left << j 
                         << "y^" << std::setw(2) << std::left 
                         << k <<  ":" << "   " << std::scientific 
                         << std::setprecision(16) << testInt 
                         << "   " << analyticInt << "   " 
                         << std::setprecision(4) << absdiff << "   " 
                         << "<?" << "   " << abstol << "\n";
              if (absdiff > abstol) {
                errorFlag++;
                *outStream << std::right << std::setw(104) 
                           << "^^^^---FAILURE!\n";
              }
            } // end for k
            *outStream << "\n";
          } // end for j
          *outStream << "\n";
        } // end for i
        }
    } // end for rule
  }
  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;
}