Intrepid
test_10.cpp
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4// Intrepid Package
5// Copyright (2007) Sandia Corporation
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7// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
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37// Questions? Contact Pavel Bochev (pbboche@sandia.gov)
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
57#define INTREPID_CUBATURE_LINE_MAX 61
58
59using namespace Intrepid;
60
61
62/*
63 Monomial evaluation.
64 in 1D, for point p(x) : x^xDeg
65 in 2D, for point p(x,y) : x^xDeg * y^yDeg
66 in 3D, for point p(x,y,z): x^xDeg * y^yDeg * z^zDeg
67*/
68double computeMonomial(FieldContainer<double> & p, int xDeg, int yDeg=0, int zDeg=0) {
69 double val = 1.0;
70 int polydeg[3];
71 polydeg[0] = xDeg; polydeg[1] = yDeg; polydeg[2] = zDeg;
72 for (int i=0; i<p.dimension(0); i++) {
73 val *= std::pow(p(i),polydeg[i]);
74 }
75 return val;
76}
77
78
79/*
80 Computes integrals of monomials over a given reference cell.
81*/
82double computeIntegral(int cubDegree, int polyDegree, EIntrepidPLPoly poly_type) {
83
84 CubaturePolylib<double> lineCub(cubDegree, poly_type);
85 double val = 0.0;
86
87 int cubDim = lineCub.getDimension();
88
89 int numCubPoints = lineCub.getNumPoints();
90
91 FieldContainer<double> point(cubDim);
92 FieldContainer<double> cubPoints(numCubPoints, cubDim);
93 FieldContainer<double> cubWeights(numCubPoints);
94
95 lineCub.getCubature(cubPoints, cubWeights);
96
97 for (int i=0; i<numCubPoints; i++) {
98 for (int j=0; j<cubDim; j++) {
99 point(j) = cubPoints(i,j);
100 }
101 val += computeMonomial(point, polyDegree)*cubWeights(i);
102 }
103
104 return val;
105}
106
107
108int main(int argc, char *argv[]) {
109
110 Teuchos::GlobalMPISession mpiSession(&argc, &argv);
111
112 // This little trick lets us print to std::cout only if
113 // a (dummy) command-line argument is provided.
114 int iprint = argc - 1;
115 Teuchos::RCP<std::ostream> outStream;
116 Teuchos::oblackholestream bhs; // outputs nothing
117 if (iprint > 0)
118 outStream = Teuchos::rcp(&std::cout, false);
119 else
120 outStream = Teuchos::rcp(&bhs, false);
121
122 // Save the format state of the original std::cout.
123 Teuchos::oblackholestream oldFormatState;
124 oldFormatState.copyfmt(std::cout);
125
126 *outStream \
127 << "===============================================================================\n" \
128 << "| |\n" \
129 << "| Unit Test (CubaturePolylib) |\n" \
130 << "| |\n" \
131 << "| 1) Computing integrals of monomials on reference cells in 1D |\n" \
132 << "| |\n" \
133 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov) or |\n" \
134 << "| Denis Ridzal (dridzal@sandia.gov). |\n" \
135 << "| |\n" \
136 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
137 << "| Trilinos website: http://trilinos.sandia.gov |\n" \
138 << "| |\n" \
139 << "===============================================================================\n"\
140 << "| TEST 1: integrals of monomials in 1D |\n"\
141 << "===============================================================================\n";
142
143 // internal variables:
144 int errorFlag = 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 testInt.assign(INTREPID_CUBATURE_LINE_MAX+1, tmparray);
150 analyticInt.assign(INTREPID_CUBATURE_LINE_MAX+1, tmparray);
151
152 // open file with analytic values
153 std::string basedir = "./data";
154 std::stringstream namestream;
155 std::string filename;
156 namestream << basedir << "/EDGE_integrals" << ".dat";
157 namestream >> filename;
158 std::ifstream filecompare(&filename[0]);
159
160 *outStream << "\nIntegrals of monomials on a reference line (edge):\n";
161
162 // compute and compare integrals
163 try {
164 for (EIntrepidPLPoly poly_type=PL_GAUSS; poly_type <= PL_GAUSS_LOBATTO; poly_type++) {
165 // compute integrals
166 for (int cubDeg=0; cubDeg <= INTREPID_CUBATURE_LINE_MAX; cubDeg++) {
167 testInt[cubDeg].resize(cubDeg+1);
168 for (int polyDeg=0; polyDeg <= cubDeg; polyDeg++) {
169 testInt[cubDeg][polyDeg] = computeIntegral(cubDeg, polyDeg, poly_type);
170 }
171 }
172 // get analytic values
173 if (filecompare.is_open()) {
174 getAnalytic(analyticInt, filecompare);
175 // close file
176 filecompare.close();
177 }
178 // perform comparison
179 for (int cubDeg=0; cubDeg <= INTREPID_CUBATURE_LINE_MAX; cubDeg++) {
180 for (int polyDeg=0; polyDeg <= cubDeg; polyDeg++) {
181 double abstol = ( analyticInt[polyDeg][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyDeg][0]) );
182 double absdiff = std::fabs(analyticInt[polyDeg][0] - testInt[cubDeg][polyDeg]);
183 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
184 << "x^" << std::setw(2) << std::left << polyDeg << ":" << " "
185 << std::scientific << std::setprecision(16) << testInt[cubDeg][polyDeg] << " " << analyticInt[polyDeg][0] << " "
186 << std::setprecision(4) << absdiff << " " << "<?" << " " << abstol << "\n";
187 if (absdiff > abstol) {
188 errorFlag++;
189 *outStream << std::right << std::setw(104) << "^^^^---FAILURE!\n";
190 }
191 }
192 *outStream << "\n";
193 } // end for cubDeg
194 } // end for poly_type
195 }
196 catch (const std::logic_error & err) {
197 *outStream << err.what() << "\n";
198 errorFlag = -1;
199 };
200
201
202 if (errorFlag != 0)
203 std::cout << "End Result: TEST FAILED\n";
204 else
205 std::cout << "End Result: TEST PASSED\n";
206
207 // reset format state of std::cout
208 std::cout.copyfmt(oldFormatState);
209
210 return errorFlag;
211}
Header file for the Intrepid::CubaturePolylib 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...
Utilizes cubature (integration) rules contained in the library Polylib (Spencer Sherwin,...
Implementation of a templated lexicographical container for a multi-indexed scalar quantity....
int dimension(const int whichDim) const
Returns the specified dimension.