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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 // Redistribution and use in source and binary forms, with or without 00011 // modification, are permitted provided that the following conditions are 00012 // met: 00013 // 00014 // 1. Redistributions of source code must retain the above copyright 00015 // notice, this list of conditions and the following disclaimer. 00016 // 00017 // 2. Redistributions in binary form must reproduce the above copyright 00018 // notice, this list of conditions and the following disclaimer in the 00019 // documentation and/or other materials provided with the distribution. 00020 // 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. 00024 // 00025 // THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY 00026 // EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 00027 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 00028 // PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE 00029 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 00030 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 00031 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 00032 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF 00033 // LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING 00034 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 00035 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 00036 // 00037 // Questions? Contact Pavel Bochev (pbboche@sandia.gov) 00038 // Denis Ridzal (dridzal@sandia.gov), or 00039 // Kara Peterson (kjpeter@sandia.gov) 00040 // 00041 // ************************************************************************ 00042 // @HEADER 00043 00044 00051 #include "Intrepid_DefaultCubatureFactory.hpp" 00052 #include "Intrepid_Utils.hpp" 00053 #include "Teuchos_oblackholestream.hpp" 00054 #include "Teuchos_RCP.hpp" 00055 #include "Teuchos_BLAS.hpp" 00056 #include "Teuchos_GlobalMPISession.hpp" 00057 00058 using namespace Intrepid; 00059 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 void computeIntegral(Teuchos::Array<double>& testIntFixDeg, shards::CellTopology & cellTopology, int cubDegree) { 00082 00083 DefaultCubatureFactory<double> cubFactory; // create factory 00084 Teuchos::RCP<Cubature<double> > myCub = cubFactory.create(cellTopology, cubDegree); // create default cubature 00085 00086 int cubDim = myCub->getDimension(); 00087 int numCubPoints = myCub->getNumPoints(); 00088 int numPolys = (cubDegree+1)*(cubDegree+2)*(cubDegree+3)/6; 00089 00090 FieldContainer<double> point(cubDim); 00091 FieldContainer<double> cubPoints(numCubPoints, cubDim); 00092 FieldContainer<double> cubWeights(numCubPoints); 00093 FieldContainer<double> functValues(numCubPoints, numPolys); 00094 00095 myCub->getCubature(cubPoints, cubWeights); 00096 00097 int polyCt = 0; 00098 for (int xDeg=0; xDeg <= cubDegree; xDeg++) { 00099 for (int yDeg=0; yDeg <= cubDegree-xDeg; yDeg++) { 00100 for (int zDeg=0; zDeg <= cubDegree-xDeg-yDeg; zDeg++) { 00101 for (int i=0; i<numCubPoints; i++) { 00102 for (int j=0; j<cubDim; j++) { 00103 point(j) = cubPoints(i,j); 00104 } 00105 functValues(i,polyCt) = computeMonomial(point, xDeg, yDeg, zDeg); 00106 } 00107 polyCt++; 00108 } 00109 } 00110 } 00111 00112 Teuchos::BLAS<int, double> myblas; 00113 int inc = 1; 00114 double alpha = 1.0; 00115 double beta = 0.0; 00116 myblas.GEMV(Teuchos::NO_TRANS, numPolys, numCubPoints, alpha, &functValues[0], numPolys, 00117 &cubWeights[0], inc, beta, &testIntFixDeg[0], inc); 00118 } 00119 00120 00121 int main(int argc, char *argv[]) { 00122 00123 Teuchos::GlobalMPISession mpiSession(&argc, &argv); 00124 00125 // This little trick lets us print to std::cout only if 00126 // a (dummy) command-line argument is provided. 00127 int iprint = argc - 1; 00128 Teuchos::RCP<std::ostream> outStream; 00129 Teuchos::oblackholestream bhs; // outputs nothing 00130 if (iprint > 0) 00131 outStream = Teuchos::rcp(&std::cout, false); 00132 else 00133 outStream = Teuchos::rcp(&bhs, false); 00134 00135 // Save the format state of the original std::cout. 00136 Teuchos::oblackholestream oldFormatState; 00137 oldFormatState.copyfmt(std::cout); 00138 00139 *outStream \ 00140 << "===============================================================================\n" \ 00141 << "| |\n" \ 00142 << "| Unit Test (CubatureDirect,CubatureTensor,DefaultCubatureFactory) |\n" \ 00143 << "| |\n" \ 00144 << "| 1) Computing integrals of monomials on reference cells in 3D |\n" \ 00145 << "| - using Level 2 BLAS - |\n" \ 00146 << "| |\n" \ 00147 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov) or |\n" \ 00148 << "| Denis Ridzal (dridzal@sandia.gov). |\n" \ 00149 << "| |\n" \ 00150 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \ 00151 << "| Trilinos website: http://trilinos.sandia.gov |\n" \ 00152 << "| |\n" \ 00153 << "===============================================================================\n"\ 00154 << "| TEST 1: integrals of monomials in 3D (Level 2 BLAS version) |\n"\ 00155 << "===============================================================================\n"; 00156 00157 // internal variables: 00158 int errorFlag = 0; 00159 int polyCt = 0; 00160 int offset = 0; 00161 Teuchos::Array< Teuchos::Array<double> > testInt; 00162 Teuchos::Array< Teuchos::Array<double> > analyticInt; 00163 Teuchos::Array<double> tmparray(1); 00164 double reltol = 1.0e+04 * INTREPID_TOL; 00165 int maxDeg[4]; 00166 int maxOffset[4]; 00167 int numPoly[4]; 00168 int numAnalytic[4]; 00169 // max polynomial degree tested, per cell type: 00170 maxDeg[0] = INTREPID_CUBATURE_TET_DEFAULT_MAX; 00171 maxDeg[1] = 20; // can be as large as INTREPID_CUBATURE_LINE_GAUSS_MAX, but runtime is excessive 00172 maxDeg[2] = std::min(INTREPID_CUBATURE_LINE_GAUSS_MAX, INTREPID_CUBATURE_TRI_DEFAULT_MAX); 00173 maxDeg[3] = std::min(INTREPID_CUBATURE_LINE_GAUSS_MAX, INTREPID_CUBATURE_LINE_GAUSSJACOBI20_MAX); 00174 // max polynomial degree recorded in analytic comparison files, per cell type: 00175 maxOffset[0] = INTREPID_CUBATURE_TET_DEFAULT_MAX; 00176 maxOffset[1] = INTREPID_CUBATURE_LINE_GAUSS_MAX; 00177 maxOffset[2] = std::min(INTREPID_CUBATURE_LINE_GAUSS_MAX, INTREPID_CUBATURE_TRI_DEFAULT_MAX); 00178 maxOffset[3] = std::min(INTREPID_CUBATURE_LINE_GAUSS_MAX, INTREPID_CUBATURE_LINE_GAUSSJACOBI20_MAX); 00179 for (int i=0; i<4; i++) { 00180 numPoly[i] = (maxDeg[i]+1)*(maxDeg[i]+2)*(maxDeg[i]+3)/6; 00181 } 00182 for (int i=0; i<4; i++) { 00183 numAnalytic[i] = (maxOffset[i]+1)*(maxOffset[i]+2)*(maxOffset[i]+3)/6; 00184 } 00185 00186 00187 // get names of files with analytic values 00188 std::string basedir = "./data"; 00189 std::stringstream namestream[4]; 00190 std::string filename[4]; 00191 namestream[0] << basedir << "/TET_integrals" << ".dat"; 00192 namestream[0] >> filename[0]; 00193 namestream[1] << basedir << "/HEX_integrals" << ".dat"; 00194 namestream[1] >> filename[1]; 00195 namestream[2] << basedir << "/TRIPRISM_integrals" << ".dat"; 00196 namestream[2] >> filename[2]; 00197 namestream[3] << basedir << "/PYR_integrals" << ".dat"; 00198 namestream[3] >> filename[3]; 00199 00200 // reference cells tested 00201 shards::CellTopology cellType[] = {shards::getCellTopologyData< shards::Tetrahedron<> >(), 00202 shards::getCellTopologyData< shards::Hexahedron<> >(), 00203 shards::getCellTopologyData< shards::Wedge<> >(), 00204 shards::getCellTopologyData< shards::Pyramid<> >() }; 00205 // format of data files with analytic values 00206 TypeOfExactData dataFormat[] = {INTREPID_UTILS_SCALAR, INTREPID_UTILS_FRACTION, INTREPID_UTILS_FRACTION, INTREPID_UTILS_FRACTION}; 00207 00208 // compute and compare integrals 00209 try { 00210 for (int cellCt=0; cellCt < 4; cellCt++) { 00211 testInt.assign(numPoly[cellCt], tmparray); 00212 analyticInt.assign(numAnalytic[cellCt], tmparray); 00213 00214 *outStream << "\nIntegrals of monomials on a reference " << cellType[cellCt].getBaseCellTopologyData()->name << ":\n"; 00215 std::ifstream filecompare(&filename[cellCt][0]); 00216 // compute integrals 00217 for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) { 00218 int numMonomials = (cubDeg+1)*(cubDeg+2)*(cubDeg+3)/6; 00219 testInt[cubDeg].resize(numMonomials); 00220 computeIntegral(testInt[cubDeg], cellType[cellCt], cubDeg); 00221 } 00222 // get analytic values 00223 if (filecompare.is_open()) { 00224 getAnalytic(analyticInt, filecompare, dataFormat[cellCt]); 00225 // close file 00226 filecompare.close(); 00227 } 00228 // perform comparison 00229 for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) { 00230 polyCt = 0; 00231 offset = 0; 00232 int oldErrorFlag = errorFlag; 00233 for (int xDeg=0; xDeg <= cubDeg; xDeg++) { 00234 for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) { 00235 for (int zDeg=0; zDeg <= cubDeg-xDeg-yDeg; zDeg++) { 00236 double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) ); 00237 double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]); 00238 if (absdiff > abstol) { 00239 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating " 00240 << "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg 00241 << " * z^" << std::setw(2) << zDeg << ":" << " " 00242 << std::scientific << std::setprecision(16) 00243 << testInt[cubDeg][polyCt] << " " << analyticInt[polyCt+offset][0] << " " 00244 << std::setprecision(4) << absdiff << " " << "<?" << " " << abstol << "\n"; 00245 errorFlag++; 00246 *outStream << std::right << std::setw(118) << "^^^^---FAILURE!\n"; 00247 } 00248 polyCt++; 00249 } 00250 offset = offset + maxOffset[cellCt] - cubDeg; 00251 } 00252 offset = offset + (maxOffset[cellCt] - cubDeg)*(maxOffset[cellCt] - cubDeg + 1)/2; 00253 } 00254 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg; 00255 if (errorFlag == oldErrorFlag) 00256 *outStream << " passed.\n"; 00257 else 00258 *outStream << " failed.\n"; 00259 } 00260 *outStream << "\n"; 00261 } // end for cellCt 00262 } 00263 catch (std::logic_error err) { 00264 *outStream << err.what() << "\n"; 00265 errorFlag = -1; 00266 }; 00267 00268 00269 if (errorFlag != 0) 00270 std::cout << "End Result: TEST FAILED\n"; 00271 else 00272 std::cout << "End Result: TEST PASSED\n"; 00273 00274 // reset format state of std::cout 00275 std::cout.copyfmt(oldFormatState); 00276 00277 return errorFlag; 00278 }
1.7.6.1