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Intrepid
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00001 // @HEADER 00002 // ************************************************************************ 00003 // 00004 // Intrepid Package 00005 // Copyright (2007) Sandia Corporation 00006 // 00007 // Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive 00008 // license for use of this work by or on behalf of the U.S. Government. 00009 // 00010 // This library is free software; you can redistribute it and/or modify 00011 // it under the terms of the GNU Lesser General Public License as 00012 // published by the Free Software Foundation; either version 2.1 of the 00013 // License, or (at your option) any later version. 00014 // 00015 // This library is distributed in the hope that it will be useful, but 00016 // WITHOUT ANY WARRANTY; without even the implied warranty of 00017 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 00018 // Lesser General Public License for more details. 00019 // 00020 // You should have received a copy of the GNU Lesser General Public 00021 // License along with this library; if not, write to the Free Software 00022 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 00023 // USA 00024 // Questions? Contact Pavel Bochev (pbboche@sandia.gov) or 00025 // Denis Ridzal (dridzal@sandia.gov). 00026 // 00027 // ************************************************************************ 00028 // @HEADER 00029 00030 00037 #include "Intrepid_DefaultCubatureFactory.hpp" 00038 #include "Intrepid_Utils.hpp" 00039 #include "Teuchos_oblackholestream.hpp" 00040 #include "Teuchos_RCP.hpp" 00041 #include "Teuchos_GlobalMPISession.hpp" 00042 00043 using namespace Intrepid; 00044 00045 /* 00046 Monomial evaluation. 00047 in 1D, for point p(x) : x^xDeg 00048 in 2D, for point p(x,y) : x^xDeg * y^yDeg 00049 in 3D, for point p(x,y,z): x^xDeg * y^yDeg * z^zDeg 00050 */ 00051 double computeMonomial(FieldContainer<double> & p, int xDeg, int yDeg=0, int zDeg=0) { 00052 double val = 1.0; 00053 int polydeg[3]; 00054 polydeg[0] = xDeg; polydeg[1] = yDeg; polydeg[2] = zDeg; 00055 for (int i=0; i<p.dimension(0); i++) { 00056 val *= std::pow(p(i),polydeg[i]); 00057 } 00058 return val; 00059 } 00060 00061 00062 /* 00063 Computes integrals of monomials over a given reference cell. 00064 */ 00065 double computeIntegral(shards::CellTopology & cellTopology, int cubDegree, int xDeg, int yDeg, int zDeg) { 00066 00067 DefaultCubatureFactory<double> cubFactory; // create factory 00068 Teuchos::RCP<Cubature<double> > myCub = cubFactory.create(cellTopology, cubDegree); // create default cubature 00069 00070 double val = 0.0; 00071 int cubDim = myCub->getDimension(); 00072 int numCubPoints = myCub->getNumPoints(); 00073 00074 FieldContainer<double> point(cubDim); 00075 FieldContainer<double> cubPoints(numCubPoints, cubDim); 00076 FieldContainer<double> cubWeights(numCubPoints); 00077 00078 myCub->getCubature(cubPoints, cubWeights); 00079 00080 for (int i=0; i<numCubPoints; i++) { 00081 for (int j=0; j<cubDim; j++) { 00082 point(j) = cubPoints(i,j); 00083 } 00084 val += computeMonomial(point, xDeg, yDeg, zDeg)*cubWeights(i); 00085 } 00086 00087 return val; 00088 } 00089 00090 00091 int main(int argc, char *argv[]) { 00092 00093 Teuchos::GlobalMPISession mpiSession(&argc, &argv); 00094 00095 // This little trick lets us print to std::cout only if 00096 // a (dummy) command-line argument is provided. 00097 int iprint = argc - 1; 00098 Teuchos::RCP<std::ostream> outStream; 00099 Teuchos::oblackholestream bhs; // outputs nothing 00100 if (iprint > 0) 00101 outStream = Teuchos::rcp(&std::cout, false); 00102 else 00103 outStream = Teuchos::rcp(&bhs, false); 00104 00105 // Save the format state of the original std::cout. 00106 Teuchos::oblackholestream oldFormatState; 00107 oldFormatState.copyfmt(std::cout); 00108 00109 *outStream \ 00110 << "===============================================================================\n" \ 00111 << "| |\n" \ 00112 << "| Unit Test (CubatureDirect,CubatureTensor,DefaultCubatureFactory) |\n" \ 00113 << "| |\n" \ 00114 << "| 1) Computing integrals of monomials on reference cells in 3D |\n" \ 00115 << "| - no BLAS, i.e. standard addition loops - |\n" \ 00116 << "| |\n" \ 00117 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov) or |\n" \ 00118 << "| Denis Ridzal (dridzal@sandia.gov). |\n" \ 00119 << "| |\n" \ 00120 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \ 00121 << "| Trilinos website: http://trilinos.sandia.gov |\n" \ 00122 << "| |\n" \ 00123 << "===============================================================================\n"\ 00124 << "| TEST 1: integrals of monomials in 3D (non-BLAS version) |\n"\ 00125 << "===============================================================================\n"; 00126 00127 // internal variables: 00128 int errorFlag = 0; 00129 int polyCt = 0; 00130 int offset = 0; 00131 Teuchos::Array< Teuchos::Array<double> > testInt; 00132 Teuchos::Array< Teuchos::Array<double> > analyticInt; 00133 Teuchos::Array<double> tmparray(1); 00134 double reltol = 1.0e+04 * INTREPID_TOL; 00135 int maxDeg[3]; 00136 int maxOffset[3]; 00137 int numPoly[3]; 00138 int numAnalytic[3]; 00139 // max polynomial degree tested, per cell type: 00140 maxDeg[0] = INTREPID_CUBATURE_TET_DEFAULT_MAX; 00141 maxDeg[1] = 20; // can be as large as INTREPID_CUBATURE_LINE_GAUSS_MAX, but runtime is excessive 00142 maxDeg[2] = INTREPID_CUBATURE_TRI_DEFAULT_MAX; 00143 // max polynomial degree recorded in analytic comparison files, per cell type: 00144 maxOffset[0] = INTREPID_CUBATURE_TET_DEFAULT_MAX; 00145 maxOffset[1] = INTREPID_CUBATURE_LINE_GAUSS_MAX; 00146 maxOffset[2] = INTREPID_CUBATURE_TRI_DEFAULT_MAX; 00147 for (int i=0; i<3; i++) { 00148 numPoly[i] = (maxDeg[i]+1)*(maxDeg[i]+2)*(maxDeg[i]+3)/6; 00149 } 00150 for (int i=0; i<3; i++) { 00151 numAnalytic[i] = (maxOffset[i]+1)*(maxOffset[i]+2)*(maxOffset[i]+3)/6; 00152 } 00153 00154 // get names of files with analytic values 00155 std::string basedir = "./data"; 00156 std::stringstream namestream[3]; 00157 std::string filename[3]; 00158 namestream[0] << basedir << "/TET_integrals" << ".dat"; 00159 namestream[0] >> filename[0]; 00160 namestream[1] << basedir << "/HEX_integrals" << ".dat"; 00161 namestream[1] >> filename[1]; 00162 namestream[2] << basedir << "/TRIPRISM_integrals" << ".dat"; 00163 namestream[2] >> filename[2]; 00164 00165 // reference cells tested 00166 shards::CellTopology cellType[] = {shards::getCellTopologyData< shards::Tetrahedron<> >(), 00167 shards::getCellTopologyData< shards::Hexahedron<> >(), 00168 shards::getCellTopologyData< shards::Wedge<> >()}; 00169 // format of data files with analytic values 00170 TypeOfExactData dataFormat[] = {INTREPID_UTILS_SCALAR, INTREPID_UTILS_FRACTION, INTREPID_UTILS_FRACTION}; 00171 00172 // compute and compare integrals 00173 try { 00174 for (int cellCt=0; cellCt < 3; cellCt++) { 00175 testInt.assign(numPoly[cellCt], tmparray); 00176 analyticInt.assign(numAnalytic[cellCt], tmparray); 00177 *outStream << "\nIntegrals of monomials on a reference " << cellType[cellCt].getBaseTopology()->name << ":\n"; 00178 std::ifstream filecompare(&filename[cellCt][0]); 00179 // compute integrals 00180 for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) { 00181 polyCt = 0; 00182 testInt[cubDeg].resize((cubDeg+1)*(cubDeg+2)*(cubDeg+3)/6); 00183 for (int xDeg=0; xDeg <= cubDeg; xDeg++) { 00184 for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) { 00185 for (int zDeg=0; zDeg <= cubDeg-xDeg-yDeg; zDeg++) { 00186 testInt[cubDeg][polyCt] = computeIntegral(cellType[cellCt], cubDeg, xDeg, yDeg, zDeg); 00187 polyCt++; 00188 } 00189 } 00190 } 00191 } 00192 // get analytic values 00193 if (filecompare.is_open()) { 00194 getAnalytic(analyticInt, filecompare, dataFormat[cellCt]); 00195 // close file 00196 filecompare.close(); 00197 } 00198 // perform comparison 00199 for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) { 00200 polyCt = 0; 00201 offset = 0; 00202 int oldErrorFlag = errorFlag; 00203 for (int xDeg=0; xDeg <= cubDeg; xDeg++) { 00204 for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) { 00205 for (int zDeg=0; zDeg <= cubDeg-xDeg-yDeg; zDeg++) { 00206 double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) ); 00207 double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]); 00208 if (absdiff > abstol) { 00209 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating " 00210 << "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg 00211 << " * z^" << std::setw(2) << zDeg << ":" << " " 00212 << std::scientific << std::setprecision(16) 00213 << testInt[cubDeg][polyCt] << " " << analyticInt[polyCt+offset][0] << " " 00214 << std::setprecision(4) << absdiff << " " << "<?" << " " << abstol << "\n"; 00215 errorFlag++; 00216 *outStream << std::right << std::setw(118) << "^^^^---FAILURE!\n"; 00217 } 00218 polyCt++; 00219 } 00220 offset = offset + maxOffset[cellCt] - cubDeg; 00221 } 00222 offset = offset + (maxOffset[cellCt] - cubDeg)*(maxOffset[cellCt] - cubDeg + 1)/2; 00223 } 00224 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg; 00225 if (errorFlag == oldErrorFlag) 00226 *outStream << " passed.\n"; 00227 else 00228 *outStream << " failed.\n"; 00229 } 00230 *outStream << "\n"; 00231 } // end for cellCt 00232 } 00233 catch (std::logic_error err) { 00234 *outStream << err.what() << "\n"; 00235 errorFlag = -1; 00236 }; 00237 00238 00239 if (errorFlag != 0) 00240 std::cout << "End Result: TEST FAILED\n"; 00241 else 00242 std::cout << "End Result: TEST PASSED\n"; 00243 00244 // reset format state of std::cout 00245 std::cout.copyfmt(oldFormatState); 00246 00247 return errorFlag; 00248 }
1.7.4