Intrepid
test_08.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, int cubDegree) {
82
83 CubatureSparse<double,3> myCub(cubDegree);
84
85 int cubDim = myCub.getDimension();
86 int numCubPoints = myCub.getNumPoints();
87 int numPolys = (cubDegree+1)*(cubDegree+2)*(cubDegree+3)/6;
88
89 FieldContainer<double> point(cubDim);
90 FieldContainer<double> cubPoints(numCubPoints, cubDim);
91 FieldContainer<double> cubWeights(numCubPoints);
92 FieldContainer<double> functValues(numCubPoints, numPolys);
93
94 myCub.getCubature(cubPoints, cubWeights);
95
96 int polyCt = 0;
97 for (int xDeg=0; xDeg <= cubDegree; xDeg++) {
98 for (int yDeg=0; yDeg <= cubDegree-xDeg; yDeg++) {
99 for (int zDeg=0; zDeg <= cubDegree-xDeg-yDeg; zDeg++) {
100 for (int i=0; i<numCubPoints; i++) {
101 for (int j=0; j<cubDim; j++) {
102 point(j) = cubPoints(i,j);
103 }
104 functValues(i,polyCt) = computeMonomial(point, xDeg, yDeg, zDeg);
105 }
106 polyCt++;
107 }
108 }
109 }
110
111 Teuchos::BLAS<int, double> myblas;
112 int inc = 1;
113 double alpha = 1.0;
114 double beta = 0.0;
115 myblas.GEMV(Teuchos::NO_TRANS, numPolys, numCubPoints, alpha, &functValues[0], numPolys,
116 &cubWeights[0], inc, beta, &testIntFixDeg[0], inc);
117}
118
119
120int main(int argc, char *argv[]) {
121
122 Teuchos::GlobalMPISession mpiSession(&argc, &argv);
123
124 // This little trick lets us print to std::cout only if
125 // a (dummy) command-line argument is provided.
126 int iprint = argc - 1;
127 Teuchos::RCP<std::ostream> outStream;
128 Teuchos::oblackholestream bhs; // outputs nothing
129 if (iprint > 0)
130 outStream = Teuchos::rcp(&std::cout, false);
131 else
132 outStream = Teuchos::rcp(&bhs, false);
133
134 // Save the format state of the original std::cout.
135 Teuchos::oblackholestream oldFormatState;
136 oldFormatState.copyfmt(std::cout);
137
138 *outStream \
139 << "===============================================================================\n" \
140 << "| |\n" \
141 << "| Unit Test (CubatureSparse) |\n" \
142 << "| |\n" \
143 << "| 1) Computing integrals of monomials on reference cells in 3D |\n" \
144 << "| - using Level 2 BLAS - |\n" \
145 << "| |\n" \
146 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov), |\n" \
147 << "| Denis Ridzal (dridzal@sandia.gov) or |\n" \
148 << "| Matthew Keegan (mskeega@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) using Sparse |\n"\
155 << "| Grid Construction |\n"\
156 << "===============================================================================\n";
157
158 // internal variables:
159 int errorFlag = 0;
160 int polyCt = 0;
161 int offset = 0;
162 Teuchos::Array< Teuchos::Array<double> > testInt;
163 Teuchos::Array< Teuchos::Array<double> > analyticInt;
164 Teuchos::Array<double> tmparray(1);
165 double reltol = 1.0e+04 * INTREPID_TOL;
166 int maxDeg = 20; // can be as large as INTREPID_CUBATURE_SPARSE3D_GAUSS_MAX, but runtime is excessive
167 int maxOffset = INTREPID_CUBATURE_LINE_GAUSS_MAX;
168 int numPoly = (maxDeg+1)*(maxDeg+2)*(maxDeg+3)/6;
169 int numAnalytic = (maxOffset+1)*(maxOffset+2)*(maxOffset+3)/6;
170 testInt.assign(numPoly, tmparray);
171 analyticInt.assign(numAnalytic, tmparray);
172
173 // get names of files with analytic values
174 std::string basedir = "./data";
175 std::stringstream namestream;
176 std::string filename;
177 namestream << basedir << "/HEX_integrals" << ".dat";
178 namestream >> filename;
179
180 // format of data files with analytic values
181 TypeOfExactData dataFormat = INTREPID_UTILS_FRACTION;
182
183 // compute and compare integrals
184 try {
185 *outStream << "\nIntegrals of monomials:\n";
186 std::ifstream filecompare(&filename[0]);
187 // compute integrals
188 for (int cubDeg=0; cubDeg <= maxDeg; cubDeg++) {
189 int numMonomials = (cubDeg+1)*(cubDeg+2)*(cubDeg+3)/6;
190 testInt[cubDeg].resize(numMonomials);
191 computeIntegral(testInt[cubDeg], cubDeg);
192 }
193 // get analytic values
194 if (filecompare.is_open()) {
195 getAnalytic(analyticInt, filecompare, dataFormat);
196 // close file
197 filecompare.close();
198 }
199 // perform comparison
200 for (int cubDeg=0; cubDeg <= maxDeg; cubDeg++) {
201 polyCt = 0;
202 offset = 0;
203 int oldErrorFlag = errorFlag;
204 for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
205 for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
206 for (int zDeg=0; zDeg <= cubDeg-xDeg-yDeg; zDeg++) {
207 double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) );
208 double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]);
209 if (absdiff > abstol) {
210 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
211 << "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg
212 << " * z^" << std::setw(2) << zDeg << ":" << " "
213 << std::scientific << std::setprecision(16)
214 << testInt[cubDeg][polyCt] << " " << analyticInt[polyCt+offset][0] << " "
215 << std::setprecision(4) << absdiff << " " << "<?" << " " << abstol << "\n";
216 errorFlag++;
217 *outStream << std::right << std::setw(118) << "^^^^---FAILURE!\n";
218 }
219 polyCt++;
220 }
221 offset = offset + maxOffset - cubDeg;
222 }
223 offset = offset + (maxOffset - cubDeg)*(maxOffset - cubDeg + 1)/2;
224 }
225 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg;
226 if (errorFlag == oldErrorFlag)
227 *outStream << " passed.\n";
228 else
229 *outStream << " failed.\n";
230 }
231 *outStream << "\n";
232 }
233 catch (const std::logic_error & err) {
234 *outStream << err.what() << "\n";
235 errorFlag = -1;
236 };
237
238
239 if (errorFlag != 0)
240 std::cout << "End Result: TEST FAILED\n";
241 else
242 std::cout << "End Result: TEST PASSED\n";
243
244 // reset format state of std::cout
245 std::cout.copyfmt(oldFormatState);
246 return errorFlag;
247}
#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...
Header file for the Intrepid::CubatureSparse class.
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...
Implementation of a templated lexicographical container for a multi-indexed scalar quantity....
int dimension(const int whichDim) const
Returns the specified dimension.