Intrepid
test_04.cpp
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4// Intrepid Package
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38// Denis Ridzal (dridzal@sandia.gov), or
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44
52#include "Intrepid_Utils.hpp"
53#include "Teuchos_oblackholestream.hpp"
54#include "Teuchos_RCP.hpp"
55#include "Teuchos_GlobalMPISession.hpp"
56
57using namespace Intrepid;
58
59/*
60 Monomial evaluation.
61 in 1D, for point p(x) : x^xDeg
62 in 2D, for point p(x,y) : x^xDeg * y^yDeg
63 in 3D, for point p(x,y,z): x^xDeg * y^yDeg * z^zDeg
64*/
65double computeMonomial(FieldContainer<double> & p, int xDeg, int yDeg=0, int zDeg=0) {
66 double val = 1.0;
67 int polydeg[3];
68 polydeg[0] = xDeg; polydeg[1] = yDeg; polydeg[2] = zDeg;
69 for (int i=0; i<p.dimension(0); i++) {
70 val *= std::pow(p(i),polydeg[i]);
71 }
72 return val;
73}
74
75
76/*
77 Computes integrals of monomials over a given reference cell.
78*/
79double computeIntegral(shards::CellTopology & cellTopology, int cubDegree, int xDeg, int yDeg, int zDeg) {
80
81 DefaultCubatureFactory<double> cubFactory; // create factory
82 Teuchos::RCP<Cubature<double> > myCub = cubFactory.create(cellTopology, cubDegree); // create default cubature
83
84 double val = 0.0;
85 int cubDim = myCub->getDimension();
86 int numCubPoints = myCub->getNumPoints();
87
88 FieldContainer<double> point(cubDim);
89 FieldContainer<double> cubPoints(numCubPoints, cubDim);
90 FieldContainer<double> cubWeights(numCubPoints);
91
92 myCub->getCubature(cubPoints, cubWeights);
93
94 for (int i=0; i<numCubPoints; i++) {
95 for (int j=0; j<cubDim; j++) {
96 point(j) = cubPoints(i,j);
97 }
98 val += computeMonomial(point, xDeg, yDeg, zDeg)*cubWeights(i);
99 }
100
101 return val;
102}
103
104
105int main(int argc, char *argv[]) {
106
107 Teuchos::GlobalMPISession mpiSession(&argc, &argv);
108
109 // This little trick lets us print to std::cout only if
110 // a (dummy) command-line argument is provided.
111 int iprint = argc - 1;
112 Teuchos::RCP<std::ostream> outStream;
113 Teuchos::oblackholestream bhs; // outputs nothing
114 if (iprint > 0)
115 outStream = Teuchos::rcp(&std::cout, false);
116 else
117 outStream = Teuchos::rcp(&bhs, false);
118
119 // Save the format state of the original std::cout.
120 Teuchos::oblackholestream oldFormatState;
121 oldFormatState.copyfmt(std::cout);
122
123 *outStream \
124 << "===============================================================================\n" \
125 << "| |\n" \
126 << "| Unit Test (CubatureDirect,CubatureTensor,DefaultCubatureFactory) |\n" \
127 << "| |\n" \
128 << "| 1) Computing integrals of monomials on reference cells in 3D |\n" \
129 << "| - no BLAS, i.e. standard addition loops - |\n" \
130 << "| |\n" \
131 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov) or |\n" \
132 << "| Denis Ridzal (dridzal@sandia.gov). |\n" \
133 << "| |\n" \
134 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
135 << "| Trilinos website: http://trilinos.sandia.gov |\n" \
136 << "| |\n" \
137 << "===============================================================================\n"\
138 << "| TEST 1: integrals of monomials in 3D (non-BLAS version) |\n"\
139 << "===============================================================================\n";
140
141 // internal variables:
142 int errorFlag = 0;
143 int polyCt = 0;
144 int offset = 0;
145 Teuchos::Array< Teuchos::Array<double> > testInt;
146 Teuchos::Array< Teuchos::Array<double> > analyticInt;
147 Teuchos::Array<double> tmparray(1);
148 double reltol = 1.0e+04 * INTREPID_TOL;
149 int maxDeg[4];
150 int maxOffset[4];
151 int numPoly[4];
152 int numAnalytic[4];
153 // max polynomial degree tested, per cell type:
155 maxDeg[1] = 20; // can be as large as INTREPID_CUBATURE_LINE_GAUSS_MAX, but runtime is excessive
158 // max polynomial degree recorded in analytic comparison files, per cell type:
163 for (int i=0; i<4; i++) {
164 numPoly[i] = (maxDeg[i]+1)*(maxDeg[i]+2)*(maxDeg[i]+3)/6;
165 }
166 for (int i=0; i<4; i++) {
167 numAnalytic[i] = (maxOffset[i]+1)*(maxOffset[i]+2)*(maxOffset[i]+3)/6;
168 }
169
170 // get names of files with analytic values
171 std::string basedir = "./data";
172 std::stringstream namestream[4];
173 std::string filename[4];
174 namestream[0] << basedir << "/TET_integrals" << ".dat";
175 namestream[0] >> filename[0];
176 namestream[1] << basedir << "/HEX_integrals" << ".dat";
177 namestream[1] >> filename[1];
178 namestream[2] << basedir << "/TRIPRISM_integrals" << ".dat";
179 namestream[2] >> filename[2];
180 namestream[3] << basedir << "/PYR_integrals" << ".dat";
181 namestream[3] >> filename[3];
182
183 // reference cells tested
184 shards::CellTopology cellType[] = {shards::getCellTopologyData< shards::Tetrahedron<> >(),
185 shards::getCellTopologyData< shards::Hexahedron<> >(),
186 shards::getCellTopologyData< shards::Wedge<> >(),
187 shards::getCellTopologyData< shards::Pyramid<> >() };
188 // format of data files with analytic values
189 TypeOfExactData dataFormat[] = {INTREPID_UTILS_SCALAR, INTREPID_UTILS_FRACTION, INTREPID_UTILS_FRACTION, INTREPID_UTILS_FRACTION};
190
191 // compute and compare integrals
192 try {
193 for (int cellCt=0; cellCt < 4; cellCt++) {
194 testInt.assign(numPoly[cellCt], tmparray);
195 analyticInt.assign(numAnalytic[cellCt], tmparray);
196 *outStream << "\nIntegrals of monomials on a reference " << cellType[cellCt].getBaseCellTopologyData()->name << ":\n";
197 std::ifstream filecompare(&filename[cellCt][0]);
198 // compute integrals
199 for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) {
200 polyCt = 0;
201 testInt[cubDeg].resize((cubDeg+1)*(cubDeg+2)*(cubDeg+3)/6);
202 for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
203 for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
204 for (int zDeg=0; zDeg <= cubDeg-xDeg-yDeg; zDeg++) {
205 testInt[cubDeg][polyCt] = computeIntegral(cellType[cellCt], cubDeg, xDeg, yDeg, zDeg);
206 polyCt++;
207 }
208 }
209 }
210 }
211 // get analytic values
212 if (filecompare.is_open()) {
213 getAnalytic(analyticInt, filecompare, dataFormat[cellCt]);
214 // close file
215 filecompare.close();
216 }
217 // perform comparison
218 for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) {
219 polyCt = 0;
220 offset = 0;
221 int oldErrorFlag = errorFlag;
222 for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
223 for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
224 for (int zDeg=0; zDeg <= cubDeg-xDeg-yDeg; zDeg++) {
225 double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) );
226 double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]);
227 if (absdiff > abstol) {
228 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
229 << "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg
230 << " * z^" << std::setw(2) << zDeg << ":" << " "
231 << std::scientific << std::setprecision(16)
232 << testInt[cubDeg][polyCt] << " " << analyticInt[polyCt+offset][0] << " "
233 << std::setprecision(4) << absdiff << " " << "<?" << " " << abstol << "\n";
234 errorFlag++;
235 *outStream << std::right << std::setw(118) << "^^^^---FAILURE!\n";
236 }
237 polyCt++;
238 }
239 offset = offset + maxOffset[cellCt] - cubDeg;
240 }
241 offset = offset + (maxOffset[cellCt] - cubDeg)*(maxOffset[cellCt] - cubDeg + 1)/2;
242 }
243 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg;
244 if (errorFlag == oldErrorFlag)
245 *outStream << " passed.\n";
246 else
247 *outStream << " failed.\n";
248 }
249 *outStream << "\n";
250 } // end for cellCt
251 }
252 catch (const std::logic_error & err) {
253 *outStream << err.what() << "\n";
254 errorFlag = -1;
255 };
256
257
258 if (errorFlag != 0)
259 std::cout << "End Result: TEST FAILED\n";
260 else
261 std::cout << "End Result: TEST PASSED\n";
262
263 // reset format state of std::cout
264 std::cout.copyfmt(oldFormatState);
265
266 return errorFlag;
267}
#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...
A factory class that generates specific instances of cubatures.
Teuchos::RCP< Cubature< Scalar, ArrayPoint, ArrayWeight > > create(const shards::CellTopology &cellTopology, const std::vector< int > &degree)
Factory method.
Implementation of a templated lexicographical container for a multi-indexed scalar quantity....
int dimension(const int whichDim) const
Returns the specified dimension.