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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_BLAS.hpp" 00042 #include "Teuchos_GlobalMPISession.hpp" 00043 00044 using namespace Intrepid; 00045 00046 00047 /* 00048 Monomial evaluation. 00049 in 1D, for point p(x) : x^xDeg 00050 in 2D, for point p(x,y) : x^xDeg * y^yDeg 00051 in 3D, for point p(x,y,z): x^xDeg * y^yDeg * z^zDeg 00052 */ 00053 double computeMonomial(FieldContainer<double> & p, int xDeg, int yDeg=0, int zDeg=0) { 00054 double val = 1.0; 00055 int polydeg[3]; 00056 polydeg[0] = xDeg; polydeg[1] = yDeg; polydeg[2] = zDeg; 00057 for (int i=0; i<p.dimension(0); i++) { 00058 val *= std::pow(p(i),polydeg[i]); 00059 } 00060 return val; 00061 } 00062 00063 00064 /* 00065 Computes integrals of monomials over a given reference cell. 00066 */ 00067 void computeIntegral(Teuchos::Array<double>& testIntFixDeg, shards::CellTopology & cellTopology, int cubDegree) { 00068 00069 DefaultCubatureFactory<double> cubFactory; // create factory 00070 Teuchos::RCP<Cubature<double> > myCub = cubFactory.create(cellTopology, cubDegree); // create default cubature 00071 00072 int cubDim = myCub->getDimension(); 00073 int numCubPoints = myCub->getNumPoints(); 00074 int numPolys = (cubDegree+1)*(cubDegree+2)*(cubDegree+3)/6; 00075 00076 FieldContainer<double> point(cubDim); 00077 FieldContainer<double> cubPoints(numCubPoints, cubDim); 00078 FieldContainer<double> cubWeights(numCubPoints); 00079 FieldContainer<double> functValues(numCubPoints, numPolys); 00080 00081 myCub->getCubature(cubPoints, cubWeights); 00082 00083 int polyCt = 0; 00084 for (int xDeg=0; xDeg <= cubDegree; xDeg++) { 00085 for (int yDeg=0; yDeg <= cubDegree-xDeg; yDeg++) { 00086 for (int zDeg=0; zDeg <= cubDegree-xDeg-yDeg; zDeg++) { 00087 for (int i=0; i<numCubPoints; i++) { 00088 for (int j=0; j<cubDim; j++) { 00089 point(j) = cubPoints(i,j); 00090 } 00091 functValues(i,polyCt) = computeMonomial(point, xDeg, yDeg, zDeg); 00092 } 00093 polyCt++; 00094 } 00095 } 00096 } 00097 00098 Teuchos::BLAS<int, double> myblas; 00099 int inc = 1; 00100 double alpha = 1.0; 00101 double beta = 0.0; 00102 myblas.GEMV(Teuchos::NO_TRANS, numPolys, numCubPoints, alpha, &functValues[0], numPolys, 00103 &cubWeights[0], inc, beta, &testIntFixDeg[0], inc); 00104 } 00105 00106 00107 int main(int argc, char *argv[]) { 00108 00109 Teuchos::GlobalMPISession mpiSession(&argc, &argv); 00110 00111 // This little trick lets us print to std::cout only if 00112 // a (dummy) command-line argument is provided. 00113 int iprint = argc - 1; 00114 Teuchos::RCP<std::ostream> outStream; 00115 Teuchos::oblackholestream bhs; // outputs nothing 00116 if (iprint > 0) 00117 outStream = Teuchos::rcp(&std::cout, false); 00118 else 00119 outStream = Teuchos::rcp(&bhs, false); 00120 00121 // Save the format state of the original std::cout. 00122 Teuchos::oblackholestream oldFormatState; 00123 oldFormatState.copyfmt(std::cout); 00124 00125 *outStream \ 00126 << "===============================================================================\n" \ 00127 << "| |\n" \ 00128 << "| Unit Test (CubatureDirect,CubatureTensor,DefaultCubatureFactory) |\n" \ 00129 << "| |\n" \ 00130 << "| 1) Computing integrals of monomials on reference cells in 3D |\n" \ 00131 << "| - using Level 2 BLAS - |\n" \ 00132 << "| |\n" \ 00133 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov) or |\n" \ 00134 << "| Denis Ridzal (dridzal@sandia.gov). |\n" \ 00135 << "| |\n" \ 00136 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \ 00137 << "| Trilinos website: http://trilinos.sandia.gov |\n" \ 00138 << "| |\n" \ 00139 << "===============================================================================\n"\ 00140 << "| TEST 1: integrals of monomials in 3D (Level 2 BLAS version) |\n"\ 00141 << "===============================================================================\n"; 00142 00143 // internal variables: 00144 int errorFlag = 0; 00145 int polyCt = 0; 00146 int offset = 0; 00147 Teuchos::Array< Teuchos::Array<double> > testInt; 00148 Teuchos::Array< Teuchos::Array<double> > analyticInt; 00149 Teuchos::Array<double> tmparray(1); 00150 double reltol = 1.0e+04 * INTREPID_TOL; 00151 int maxDeg[3]; 00152 int maxOffset[3]; 00153 int numPoly[3]; 00154 int numAnalytic[3]; 00155 // max polynomial degree tested, per cell type: 00156 maxDeg[0] = INTREPID_CUBATURE_TET_DEFAULT_MAX; 00157 maxDeg[1] = 20; // can be as large as INTREPID_CUBATURE_LINE_GAUSS_MAX, but runtime is excessive 00158 maxDeg[2] = INTREPID_CUBATURE_TRI_DEFAULT_MAX; 00159 // max polynomial degree recorded in analytic comparison files, per cell type: 00160 maxOffset[0] = INTREPID_CUBATURE_TET_DEFAULT_MAX; 00161 maxOffset[1] = INTREPID_CUBATURE_LINE_GAUSS_MAX; 00162 maxOffset[2] = INTREPID_CUBATURE_TRI_DEFAULT_MAX; 00163 for (int i=0; i<3; i++) { 00164 numPoly[i] = (maxDeg[i]+1)*(maxDeg[i]+2)*(maxDeg[i]+3)/6; 00165 } 00166 for (int i=0; i<3; i++) { 00167 numAnalytic[i] = (maxOffset[i]+1)*(maxOffset[i]+2)*(maxOffset[i]+3)/6; 00168 } 00169 00170 00171 // get names of files with analytic values 00172 std::string basedir = "./data"; 00173 std::stringstream namestream[3]; 00174 std::string filename[3]; 00175 namestream[0] << basedir << "/TET_integrals" << ".dat"; 00176 namestream[0] >> filename[0]; 00177 namestream[1] << basedir << "/HEX_integrals" << ".dat"; 00178 namestream[1] >> filename[1]; 00179 namestream[2] << basedir << "/TRIPRISM_integrals" << ".dat"; 00180 namestream[2] >> filename[2]; 00181 00182 // reference cells tested 00183 shards::CellTopology cellType[] = {shards::getCellTopologyData< shards::Tetrahedron<> >(), 00184 shards::getCellTopologyData< shards::Hexahedron<> >(), 00185 shards::getCellTopologyData< shards::Wedge<> >()}; 00186 // format of data files with analytic values 00187 TypeOfExactData dataFormat[] = {INTREPID_UTILS_SCALAR, INTREPID_UTILS_FRACTION, INTREPID_UTILS_FRACTION}; 00188 00189 // compute and compare integrals 00190 try { 00191 for (int cellCt=0; cellCt < 3; cellCt++) { 00192 testInt.assign(numPoly[cellCt], tmparray); 00193 analyticInt.assign(numAnalytic[cellCt], tmparray); 00194 00195 *outStream << "\nIntegrals of monomials on a reference " << cellType[cellCt].getBaseTopology()->name << ":\n"; 00196 std::ifstream filecompare(&filename[cellCt][0]); 00197 // compute integrals 00198 for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) { 00199 int numMonomials = (cubDeg+1)*(cubDeg+2)*(cubDeg+3)/6; 00200 testInt[cubDeg].resize(numMonomials); 00201 computeIntegral(testInt[cubDeg], cellType[cellCt], cubDeg); 00202 } 00203 // get analytic values 00204 if (filecompare.is_open()) { 00205 getAnalytic(analyticInt, filecompare, dataFormat[cellCt]); 00206 // close file 00207 filecompare.close(); 00208 } 00209 // perform comparison 00210 for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) { 00211 polyCt = 0; 00212 offset = 0; 00213 int oldErrorFlag = errorFlag; 00214 for (int xDeg=0; xDeg <= cubDeg; xDeg++) { 00215 for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) { 00216 for (int zDeg=0; zDeg <= cubDeg-xDeg-yDeg; zDeg++) { 00217 double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) ); 00218 double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]); 00219 if (absdiff > abstol) { 00220 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating " 00221 << "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg 00222 << " * z^" << std::setw(2) << zDeg << ":" << " " 00223 << std::scientific << std::setprecision(16) 00224 << testInt[cubDeg][polyCt] << " " << analyticInt[polyCt+offset][0] << " " 00225 << std::setprecision(4) << absdiff << " " << "<?" << " " << abstol << "\n"; 00226 errorFlag++; 00227 *outStream << std::right << std::setw(118) << "^^^^---FAILURE!\n"; 00228 } 00229 polyCt++; 00230 } 00231 offset = offset + maxOffset[cellCt] - cubDeg; 00232 } 00233 offset = offset + (maxOffset[cellCt] - cubDeg)*(maxOffset[cellCt] - cubDeg + 1)/2; 00234 } 00235 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg; 00236 if (errorFlag == oldErrorFlag) 00237 *outStream << " passed.\n"; 00238 else 00239 *outStream << " failed.\n"; 00240 } 00241 *outStream << "\n"; 00242 } // end for cellCt 00243 } 00244 catch (std::logic_error err) { 00245 *outStream << err.what() << "\n"; 00246 errorFlag = -1; 00247 }; 00248 00249 00250 if (errorFlag != 0) 00251 std::cout << "End Result: TEST FAILED\n"; 00252 else 00253 std::cout << "End Result: TEST PASSED\n"; 00254 00255 // reset format state of std::cout 00256 std::cout.copyfmt(oldFormatState); 00257 00258 return errorFlag; 00259 }
1.7.4