Intrepid
test_06.cpp
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52#include "Intrepid_Utils.hpp"
53#include "Teuchos_oblackholestream.hpp"
54#include "Teuchos_RCP.hpp"
55#include "Teuchos_BLAS.hpp"
56#include "Teuchos_GlobalMPISession.hpp"
57
58using namespace Intrepid;
59
60
61/*
62 Monomial evaluation.
63 in 1D, for point p(x) : x^xDeg
64 in 2D, for point p(x,y) : x^xDeg * y^yDeg
65 in 3D, for point p(x,y,z): x^xDeg * y^yDeg * z^zDeg
66*/
67double computeMonomial(FieldContainer<double> & p, int xDeg, int yDeg=0, int zDeg=0) {
68 double val = 1.0;
69 int polydeg[3];
70 polydeg[0] = xDeg; polydeg[1] = yDeg; polydeg[2] = zDeg;
71 for (int i=0; i<p.dimension(0); i++) {
72 val *= std::pow(p(i),polydeg[i]);
73 }
74 return val;
75}
76
77
78/*
79 Computes integrals of monomials over a given reference cell.
80*/
81void computeIntegral(Teuchos::Array<double>& testIntFixDeg, shards::CellTopology & cellTopology, int cubDegree) {
82
83 DefaultCubatureFactory<double> cubFactory; // create factory
84 Teuchos::RCP<Cubature<double> > myCub = cubFactory.create(cellTopology, cubDegree); // create default cubature
85
86 int cubDim = myCub->getDimension();
87 int numCubPoints = myCub->getNumPoints();
88 int numPolys = (cubDegree+1)*(cubDegree+2)*(cubDegree+3)/6;
89
90 FieldContainer<double> point(cubDim);
91 FieldContainer<double> cubPoints(numCubPoints, cubDim);
92 FieldContainer<double> cubWeights(numCubPoints);
93 FieldContainer<double> functValues(numCubPoints, numPolys);
94
95 myCub->getCubature(cubPoints, cubWeights);
96
97 int polyCt = 0;
98 for (int xDeg=0; xDeg <= cubDegree; xDeg++) {
99 for (int yDeg=0; yDeg <= cubDegree-xDeg; yDeg++) {
100 for (int zDeg=0; zDeg <= cubDegree-xDeg-yDeg; zDeg++) {
101 for (int i=0; i<numCubPoints; i++) {
102 for (int j=0; j<cubDim; j++) {
103 point(j) = cubPoints(i,j);
104 }
105 functValues(i,polyCt) = computeMonomial(point, xDeg, yDeg, zDeg);
106 }
107 polyCt++;
108 }
109 }
110 }
111
112 Teuchos::BLAS<int, double> myblas;
113 int inc = 1;
114 double alpha = 1.0;
115 double beta = 0.0;
116 myblas.GEMV(Teuchos::NO_TRANS, numPolys, numCubPoints, alpha, &functValues[0], numPolys,
117 &cubWeights[0], inc, beta, &testIntFixDeg[0], inc);
118}
119
120
121int main(int argc, char *argv[]) {
122
123 Teuchos::GlobalMPISession mpiSession(&argc, &argv);
124
125 // This little trick lets us print to std::cout only if
126 // a (dummy) command-line argument is provided.
127 int iprint = argc - 1;
128 Teuchos::RCP<std::ostream> outStream;
129 Teuchos::oblackholestream bhs; // outputs nothing
130 if (iprint > 0)
131 outStream = Teuchos::rcp(&std::cout, false);
132 else
133 outStream = Teuchos::rcp(&bhs, false);
134
135 // Save the format state of the original std::cout.
136 Teuchos::oblackholestream oldFormatState;
137 oldFormatState.copyfmt(std::cout);
138
139 *outStream \
140 << "===============================================================================\n" \
141 << "| |\n" \
142 << "| Unit Test (CubatureDirect,CubatureTensor,DefaultCubatureFactory) |\n" \
143 << "| |\n" \
144 << "| 1) Computing integrals of monomials on reference cells in 3D |\n" \
145 << "| - using Level 2 BLAS - |\n" \
146 << "| |\n" \
147 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov) or |\n" \
148 << "| Denis Ridzal (dridzal@sandia.gov). |\n" \
149 << "| |\n" \
150 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
151 << "| Trilinos website: http://trilinos.sandia.gov |\n" \
152 << "| |\n" \
153 << "===============================================================================\n"\
154 << "| TEST 1: integrals of monomials in 3D (Level 2 BLAS version) |\n"\
155 << "===============================================================================\n";
156
157 // internal variables:
158 int errorFlag = 0;
159 int polyCt = 0;
160 int offset = 0;
161 Teuchos::Array< Teuchos::Array<double> > testInt;
162 Teuchos::Array< Teuchos::Array<double> > analyticInt;
163 Teuchos::Array<double> tmparray(1);
164 double reltol = 1.0e+04 * INTREPID_TOL;
165 int maxDeg[4];
166 int maxOffset[4];
167 int numPoly[4];
168 int numAnalytic[4];
169 // max polynomial degree tested, per cell type:
171 maxDeg[1] = 20; // can be as large as INTREPID_CUBATURE_LINE_GAUSS_MAX, but runtime is excessive
174 // max polynomial degree recorded in analytic comparison files, per cell type:
179 for (int i=0; i<4; i++) {
180 numPoly[i] = (maxDeg[i]+1)*(maxDeg[i]+2)*(maxDeg[i]+3)/6;
181 }
182 for (int i=0; i<4; i++) {
183 numAnalytic[i] = (maxOffset[i]+1)*(maxOffset[i]+2)*(maxOffset[i]+3)/6;
184 }
185
186
187 // get names of files with analytic values
188 std::string basedir = "./data";
189 std::stringstream namestream[4];
190 std::string filename[4];
191 namestream[0] << basedir << "/TET_integrals" << ".dat";
192 namestream[0] >> filename[0];
193 namestream[1] << basedir << "/HEX_integrals" << ".dat";
194 namestream[1] >> filename[1];
195 namestream[2] << basedir << "/TRIPRISM_integrals" << ".dat";
196 namestream[2] >> filename[2];
197 namestream[3] << basedir << "/PYR_integrals" << ".dat";
198 namestream[3] >> filename[3];
199
200 // reference cells tested
201 shards::CellTopology cellType[] = {shards::getCellTopologyData< shards::Tetrahedron<> >(),
202 shards::getCellTopologyData< shards::Hexahedron<> >(),
203 shards::getCellTopologyData< shards::Wedge<> >(),
204 shards::getCellTopologyData< shards::Pyramid<> >() };
205 // format of data files with analytic values
206 TypeOfExactData dataFormat[] = {INTREPID_UTILS_SCALAR, INTREPID_UTILS_FRACTION, INTREPID_UTILS_FRACTION, INTREPID_UTILS_FRACTION};
207
208 // compute and compare integrals
209 try {
210 for (int cellCt=0; cellCt < 4; cellCt++) {
211 testInt.assign(numPoly[cellCt], tmparray);
212 analyticInt.assign(numAnalytic[cellCt], tmparray);
213
214 *outStream << "\nIntegrals of monomials on a reference " << cellType[cellCt].getBaseCellTopologyData()->name << ":\n";
215 std::ifstream filecompare(&filename[cellCt][0]);
216 // compute integrals
217 for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) {
218 int numMonomials = (cubDeg+1)*(cubDeg+2)*(cubDeg+3)/6;
219 testInt[cubDeg].resize(numMonomials);
220 computeIntegral(testInt[cubDeg], cellType[cellCt], cubDeg);
221 }
222 // get analytic values
223 if (filecompare.is_open()) {
224 getAnalytic(analyticInt, filecompare, dataFormat[cellCt]);
225 // close file
226 filecompare.close();
227 }
228 // perform comparison
229 for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) {
230 polyCt = 0;
231 offset = 0;
232 int oldErrorFlag = errorFlag;
233 for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
234 for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
235 for (int zDeg=0; zDeg <= cubDeg-xDeg-yDeg; zDeg++) {
236 double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) );
237 double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]);
238 if (absdiff > abstol) {
239 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
240 << "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg
241 << " * z^" << std::setw(2) << zDeg << ":" << " "
242 << std::scientific << std::setprecision(16)
243 << testInt[cubDeg][polyCt] << " " << analyticInt[polyCt+offset][0] << " "
244 << std::setprecision(4) << absdiff << " " << "<?" << " " << abstol << "\n";
245 errorFlag++;
246 *outStream << std::right << std::setw(118) << "^^^^---FAILURE!\n";
247 }
248 polyCt++;
249 }
250 offset = offset + maxOffset[cellCt] - cubDeg;
251 }
252 offset = offset + (maxOffset[cellCt] - cubDeg)*(maxOffset[cellCt] - cubDeg + 1)/2;
253 }
254 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg;
255 if (errorFlag == oldErrorFlag)
256 *outStream << " passed.\n";
257 else
258 *outStream << " failed.\n";
259 }
260 *outStream << "\n";
261 } // end for cellCt
262 }
263 catch (const std::logic_error & err) {
264 *outStream << err.what() << "\n";
265 errorFlag = -1;
266 };
267
268
269 if (errorFlag != 0)
270 std::cout << "End Result: TEST FAILED\n";
271 else
272 std::cout << "End Result: TEST PASSED\n";
273
274 // reset format state of std::cout
275 std::cout.copyfmt(oldFormatState);
276
277 return errorFlag;
278}
#define INTREPID_CUBATURE_LINE_GAUSSJACOBI20_MAX
The maximum degree of the polynomial that can be integrated exactly by a direct line rule of the Gaus...
#define INTREPID_CUBATURE_LINE_GAUSS_MAX
The maximum degree of the polynomial that can be integrated exactly by a direct line rule of the Gaus...
#define INTREPID_CUBATURE_TET_DEFAULT_MAX
The maximum degree of the polynomial that can be integrated exactly by a direct tetrahedron rule of t...
#define INTREPID_CUBATURE_TRI_DEFAULT_MAX
The maximum degree of the polynomial that can be integrated exactly by a direct triangle rule of the ...
Header file for the abstract base class Intrepid::DefaultCubatureFactory.
Intrepid utilities.
void getAnalytic(Teuchos::Array< Teuchos::Array< Scalar > > &testMat, std::ifstream &inputFile, TypeOfExactData analyticDataType=INTREPID_UTILS_FRACTION)
Loads analytic values stored in a file into the matrix testMat, where the output matrix is an array o...