Intrepid
test_03.cpp
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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/*
61 Monomial evaluation.
62 in 1D, for point p(x) : x^xDeg
63 in 2D, for point p(x,y) : x^xDeg * y^yDeg
64 in 3D, for point p(x,y,z): x^xDeg * y^yDeg * z^zDeg
65*/
66double computeMonomial(FieldContainer<double> & p, int xDeg, int yDeg=0, int zDeg=0) {
67 double val = 1.0;
68 int polydeg[3];
69 polydeg[0] = xDeg; polydeg[1] = yDeg; polydeg[2] = zDeg;
70 for (int i=0; i<p.dimension(0); i++) {
71 val *= std::pow(p(i),polydeg[i]);
72 }
73 return val;
74}
75
76
77/*
78 Computes integrals of monomials over a given reference cell.
79*/
80double computeIntegral(shards::CellTopology & cellTopology, int cubDegree, int xDeg, int yDeg) {
81
82 DefaultCubatureFactory<double> cubFactory; // create factory
83 Teuchos::RCP<Cubature<double> > myCub = cubFactory.create(cellTopology, cubDegree); // create default cubature
84
85 double val = 0.0;
86 int cubDim = myCub->getDimension();
87 int numCubPoints = myCub->getNumPoints();
88
89 FieldContainer<double> point(cubDim);
90 FieldContainer<double> cubPoints(numCubPoints, cubDim);
91 FieldContainer<double> cubWeights(numCubPoints);
92
93 myCub->getCubature(cubPoints, cubWeights);
94
95 for (int i=0; i<numCubPoints; i++) {
96 for (int j=0; j<cubDim; j++) {
97 point(j) = cubPoints(i,j);
98 }
99 val += computeMonomial(point, xDeg, yDeg)*cubWeights(i);
100 }
101
102 return val;
103}
104
105
106int main(int argc, char *argv[]) {
107
108 Teuchos::GlobalMPISession mpiSession(&argc, &argv);
109
110 // This little trick lets us print to std::cout only if
111 // a (dummy) command-line argument is provided.
112 int iprint = argc - 1;
113 Teuchos::RCP<std::ostream> outStream;
114 Teuchos::oblackholestream bhs; // outputs nothing
115 if (iprint > 0)
116 outStream = Teuchos::rcp(&std::cout, false);
117 else
118 outStream = Teuchos::rcp(&bhs, false);
119
120 // Save the format state of the original std::cout.
121 Teuchos::oblackholestream oldFormatState;
122 oldFormatState.copyfmt(std::cout);
123
124 *outStream \
125 << "===============================================================================\n" \
126 << "| |\n" \
127 << "| Unit Test (CubatureDirect,CubatureTensor,DefaultCubatureFactory) |\n" \
128 << "| |\n" \
129 << "| 1) Computing integrals of monomials on reference cells in 2D |\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 2D |\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+03 * INTREPID_TOL;
149 int maxDeg[2];
150 int numPoly[2];
155
156 // get names of files with analytic values
157 std::string basedir = "./data";
158 std::stringstream namestream[2];
159 std::string filename[2];
160 namestream[0] << basedir << "/TRI_integrals" << ".dat";
161 namestream[0] >> filename[0];
162 namestream[1] << basedir << "/QUAD_integrals" << ".dat";
163 namestream[1] >> filename[1];
164
165 shards::CellTopology cellType[] = {shards::getCellTopologyData< shards::Triangle<> >(),
166 shards::getCellTopologyData< shards::Quadrilateral<> >()};
167
168 // compute and compare integrals
169 try {
170 for (int cellCt=0; cellCt < 2; cellCt++) {
171 testInt.assign(numPoly[cellCt], tmparray);
172 analyticInt.assign(numPoly[cellCt], tmparray);
173 *outStream << "\nIntegrals of monomials on a reference " << cellType[cellCt].getBaseCellTopologyData()->name << ":\n";
174 std::ifstream filecompare(&filename[cellCt][0]);
175 // compute integrals
176 for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) {
177 polyCt = 0;
178 testInt[cubDeg].resize((cubDeg+1)*(cubDeg+2)/2);
179 for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
180 for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
181 testInt[cubDeg][polyCt] = computeIntegral(cellType[cellCt], cubDeg, xDeg, yDeg);
182 polyCt++;
183 }
184 }
185 }
186 // get analytic values
187 if (filecompare.is_open()) {
188 getAnalytic(analyticInt, filecompare);
189 // close file
190 filecompare.close();
191 }
192 // perform comparison
193 for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) {
194 polyCt = 0;
195 offset = 0;
196 for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
197 for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
198 double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) );
199 double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]);
200 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
201 << "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg << ":" << " "
202 << std::scientific << std::setprecision(16) << testInt[cubDeg][polyCt] << " " << analyticInt[polyCt+offset][0] << " "
203 << std::setprecision(4) << absdiff << " " << "<?" << " " << abstol << "\n";
204 if (absdiff > abstol) {
205 errorFlag++;
206 *outStream << std::right << std::setw(111) << "^^^^---FAILURE!\n";
207 }
208 polyCt++;
209 }
210 offset = offset + maxDeg[cellCt] - cubDeg;
211 }
212 *outStream << "\n";
213 }
214 *outStream << "\n";
215 } // end for cellCt
216 }
217 catch (const std::logic_error & err) {
218 *outStream << err.what() << "\n";
219 errorFlag = -1;
220 };
221
222
223 if (errorFlag != 0)
224 std::cout << "End Result: TEST FAILED\n";
225 else
226 std::cout << "End Result: TEST PASSED\n";
227
228 // reset format state of std::cout
229 std::cout.copyfmt(oldFormatState);
230
231 return errorFlag;
232}
#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_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...