Intrepid
http://trilinos.sandia.gov/packages/docs/r10.10/packages/intrepid/test/Discretization/Integration/test_07.cpp
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00004 //                           Intrepid Package
00005 //                 Copyright (2007) Sandia Corporation
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00017 // 2. Redistributions in binary form must reproduce the above copyright
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00021 // 3. Neither the name of the Corporation nor the names of the
00022 // contributors may be used to endorse or promote products derived from
00023 // this software without specific prior written permission.
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00025 // THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
00026 // EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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00036 //
00037 // Questions? Contact Pavel Bochev  (pbboche@sandia.gov)
00038 //                    Denis Ridzal  (dridzal@sandia.gov), or
00039 //                    Kara Peterson (kjpeter@sandia.gov)
00040 //
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00043 
00044 
00051 #include "Intrepid_CubatureSparse.hpp"
00052 #include "Intrepid_Utils.hpp"
00053 #include "Teuchos_oblackholestream.hpp"
00054 #include "Teuchos_RCP.hpp"
00055 #include "Teuchos_GlobalMPISession.hpp"
00056 
00057 using namespace Intrepid;
00058 
00059 //Teuchos::RCP<std::ostream> outStream;
00060 
00061 /*
00062   Monomial evaluation.
00063     in 1D, for point p(x)    : x^xDeg
00064     in 2D, for point p(x,y)  : x^xDeg * y^yDeg
00065     in 3D, for point p(x,y,z): x^xDeg * y^yDeg * z^zDeg
00066 */
00067 double computeMonomial(FieldContainer<double> & p, int xDeg, int yDeg=0, int zDeg=0) {
00068   double val = 1.0;
00069   int polydeg[3];
00070   polydeg[0] = xDeg; polydeg[1] = yDeg; polydeg[2] = zDeg;
00071   for (int i=0; i<p.dimension(0); i++) {
00072     val *= std::pow(p(i),polydeg[i]);
00073   }
00074   return val;
00075 }
00076 
00077 
00078 /*
00079   Computes integrals of monomials over a given reference cell.
00080 */
00081 double computeIntegral(int cubDegree, int xDeg, int yDeg) {
00082 
00083   CubatureSparse<double,2> myCub(cubDegree);
00084 
00085   double val       = 0.0;
00086   int cubDim       = myCub.getDimension();
00087   int numCubPoints = myCub.getNumPoints();
00088 
00089   FieldContainer<double> point(cubDim);
00090   FieldContainer<double> cubPoints(numCubPoints, cubDim);
00091   FieldContainer<double> cubWeights(numCubPoints);
00092 
00093   myCub.getCubature(cubPoints, cubWeights);
00094 
00095   for (int i=0; i<numCubPoints; i++) {
00096     for (int j=0; j<cubDim; j++) {
00097       point(j) = cubPoints(i,j);
00098     }
00099     val += computeMonomial(point, xDeg, yDeg)*cubWeights(i);
00100   }
00101 
00102   return val;
00103 }
00104 
00105 
00106 int main(int argc, char *argv[]) {
00107 
00108   Teuchos::GlobalMPISession mpiSession(&argc, &argv);
00109 
00110   // This little trick lets us print to std::cout only if
00111   // a (dummy) command-line argument is provided.
00112   int iprint     = argc - 1;
00113   Teuchos::RCP<std::ostream> outStream;
00114   Teuchos::oblackholestream bhs; // outputs nothing
00115   if (iprint > 0)
00116     outStream = Teuchos::rcp(&std::cout, false);
00117   else
00118     outStream = Teuchos::rcp(&bhs, false);
00119 
00120   // Save the format state of the original std::cout.
00121   Teuchos::oblackholestream oldFormatState;
00122   oldFormatState.copyfmt(std::cout);
00123  
00124   *outStream \
00125   << "===============================================================================\n" \
00126   << "|                                                                             |\n" \
00127   << "|                         Unit Test (CubatureSparse)                          |\n" \
00128   << "|                                                                             |\n" \
00129   << "|     1) Computing integrals of monomials on reference cells in 2D            |\n" \
00130   << "|                                                                             |\n" \
00131   << "|  Questions? Contact  Pavel Bochev (pbboche@sandia.gov),                     |\n" \
00132   << "|                      Denis Ridzal (dridzal@sandia.gov) or                   |\n" \
00133   << "|                      Matthew Keegan (mskeega@sandia.gov)                    |\n" \
00134   << "|                                                                             |\n" \
00135   << "|  Intrepid's website: http://trilinos.sandia.gov/packages/intrepid           |\n" \
00136   << "|  Trilinos website:   http://trilinos.sandia.gov                             |\n" \
00137   << "|                                                                             |\n" \
00138   << "===============================================================================\n"\
00139   << "| TEST 1: integrals of monomials in 2D for Sparse Grid Construction           |\n"\
00140   << "===============================================================================\n";
00141 
00142   // internal variables:
00143   int                                      errorFlag = 0;
00144   int                                      polyCt = 0;
00145   int                                      offset = 0;
00146   Teuchos::Array< Teuchos::Array<double> > testInt;
00147   Teuchos::Array< Teuchos::Array<double> > analyticInt;
00148   Teuchos::Array<double>                   tmparray(1);
00149   double                                   reltol = 1.0e+03 * INTREPID_TOL;
00150   int maxDeg                             = 30; // can be as large as INTREPID_CUBATURE_SPARSE2D_GAUSS_MAX, but runtime is excessive
00151   int maxOffset                          = INTREPID_CUBATURE_LINE_GAUSS_MAX;
00152   int numPoly                            = (maxDeg+1)*(maxDeg+2)/2;
00153   int numAnalytic                        = (maxOffset+1)*(maxOffset+2)/2;
00154   testInt.assign(numPoly, tmparray);
00155   analyticInt.assign(numAnalytic, tmparray);
00156 
00157   // get names of files with analytic values
00158   std::string basedir = "./data";
00159   std::stringstream namestream;
00160   std::string filename;
00161   namestream << basedir << "/QUAD_integrals" << ".dat";
00162   namestream >> filename;
00163 
00164   // compute and compare integrals
00165   try {
00166       *outStream << "\nIntegrals of monomials:\n";
00167 
00168       std::ifstream filecompare(&filename[0]);
00169       // compute integrals
00170       for (int cubDeg=0; cubDeg <= maxDeg; cubDeg++) {
00171         polyCt = 0;
00172         testInt[cubDeg].resize((cubDeg+1)*(cubDeg+2)/2);
00173         for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
00174           for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
00175             testInt[cubDeg][polyCt] = computeIntegral(cubDeg, xDeg, yDeg);
00176             polyCt++; 
00177           }
00178         }
00179       }
00180 
00181       // get analytic values
00182       if (filecompare.is_open()) {
00183         getAnalytic(analyticInt, filecompare);
00184         // close file
00185         filecompare.close();
00186       }
00187       // perform comparison
00188       for (int cubDeg=0; cubDeg <= maxDeg; cubDeg++) {
00189         polyCt = 0;
00190         offset = 0;
00191         for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
00192           for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
00193             double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) );
00194             double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]);
00195             *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
00196                        << "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg << ":" << "   "
00197                        << std::scientific << std::setprecision(16) << testInt[cubDeg][polyCt] << "   " << analyticInt[polyCt+offset][0] << "   "
00198                        << std::setprecision(4) << absdiff << "   " << "<?" << "   " << abstol << "\n";
00199             if (absdiff > abstol) {
00200               errorFlag++;
00201               *outStream << std::right << std::setw(111) << "^^^^---FAILURE!\n";
00202             }
00203             polyCt++;
00204           }
00205           offset = offset + maxOffset - cubDeg;
00206         }
00207         *outStream << "\n";
00208       }
00209       *outStream << "\n";
00210   }
00211   catch (std::logic_error err) {
00212     *outStream << err.what() << "\n";
00213     errorFlag = -1;
00214   };
00215 
00216 
00217   if (errorFlag != 0)
00218     std::cout << "End Result: TEST FAILED\n";
00219   else
00220     std::cout << "End Result: TEST PASSED\n";
00221 
00222   // reset format state of std::cout
00223   std::cout.copyfmt(oldFormatState);
00224 
00225   return errorFlag;
00226 }