test_11.cpp

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//#include "Intrepid_CubatureLineSorted.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(int order, int power, EIntrepidBurkardt rule) {
 
  CubatureLineSorted<long double> lineCub(rule,order,false);  
  int size = lineCub.getNumPoints();
  FieldContainer<long double> cubPoints(size);
  FieldContainer<long double> cubWeights(size);
  lineCub.getCubature(cubPoints,cubWeights);

  int mid  = size/2;
  long double Q = 0.0;
  if (size%2) 
    Q = cubWeights(mid)*powl(cubPoints(mid),power);

  for (int i=0; i<mid; i++) {
    Q += cubWeights(i)*powl(cubPoints(i),power)+
      cubWeights(size-i-1)*powl(cubPoints(size-i-1),power);
  }
  return Q;
}

long double evalInt(int power, EIntrepidBurkardt rule) {
  double I = 0;

  if (rule==BURK_CLENSHAWCURTIS||rule==BURK_FEJER2||
      rule==BURK_LEGENDRE||rule==BURK_PATTERSON || 
      rule==BURK_TRAPEZOIDAL) {
    if (power%2)
      I = 0.0;
    else 
      I = 2.0/((long double)power+1.0);
  }
  else if (rule==BURK_LAGUERRE) {
    I = tgammal((long double)(power+1));
  }
  else if (rule==BURK_CHEBYSHEV1) {
    long double bot, top;
    if (!(power%2)) {
      top = 1; bot = 1;
      for (int i=2;i<=power;i+=2) {
        top *= (long double)(i-1);
        bot *= (long double)i;
      }
      I = M_PI*top/bot;
    }
    else {
      I = 0.0;
    }
  }
  else if (rule==BURK_CHEBYSHEV2) {
    long double bot, top;
    if (!(power%2)) {
      top = 1; bot = 1;
      for (int i=2;i<=power;i+=2) {
        top *= (long double)(i-1);
        bot *= (long double)i;
      }
      bot *= (long double)(power+2);
      I    = M_PI*top/bot;
    }
    else {
      I = 0.0;
    }
  }
  else if (rule==BURK_HERMITE||rule==BURK_GENZKEISTER) {
    if (power%2) {
      I = 0.0;
    }
    else {  
      long double value = 1.0;
      if ((power-1)>=1) {
        int n_copy = power-1;
        while (1<n_copy) {
          value  *= (long double)n_copy;
          n_copy -= 2;
        }
      }
      I = value*sqrt(M_PI)/powl(2.0,(long double)power/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 (CubatureLineSorted)                      |\n" \
  << "|                                                                             |\n" \
  << "|     1) Computing integrals of monomials in 1D                               |\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 11: integrals of monomials in 1D                                       |\n"\
  << "===============================================================================\n";

  // internal variables:
  int         errorFlag   = 0;
  long double reltol      = 1.0e+05*INTREPID_TOL;
  int         maxDeg      = 0;    
  long double analyticInt = 0;
  long double testInt     = 0;
  int         maxOrder    = 30;

  *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 = 10;
      else if (rule==BURK_TRAPEZOIDAL) 
        maxOrder = 2;
      else 
        maxOrder = 30;

      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;
          
          for (int j=0; j <= maxDeg; j++) {
            analyticInt = evalInt(j,rule);
            testInt     = evalQuad(i,j,rule);
            
            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 <<  ":" 
                       << "   "
                       << 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 j
          *outStream << "\n";
        } // end for i
      }
      else if (rule==BURK_PATTERSON) {
        for (int i=0; i < 8; 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);
          for (int j=0; j <= maxDeg; j++) {
            analyticInt = evalInt(j,rule);
            testInt     = evalQuad(l,j,rule);
            
            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 <<  ":" 
                       << "   "
                       << 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 j
          *outStream << "\n";
        } // end for i
      }
      else if (rule==BURK_GENZKEISTER) {
        reltol *= 1.0e+02;
        int o_ghk[4] = {1,3, 9,19};
        int p_ghk[4] = {1,5,15,29};
        for (int i=0; i < 4; i++) {
          int l  = o_ghk[i];
          maxDeg = p_ghk[i];
          for (int j=0; j <= maxDeg; j++) {
            analyticInt = evalInt(j,rule);
            testInt     = evalQuad(l,j,rule);
            
            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 <<  ":" 
                       << "   "
                       << 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 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;
}