Intrepid
test_02.cpp
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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 using 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 */
66 double 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 */
80 double computeIntegral(int cubDegree, int polyDegree) {
81 
82  DefaultCubatureFactory<double> cubFactory; // create factory
83  shards::CellTopology line(shards::getCellTopologyData< shards::Line<> >()); // create cell topology
84  Teuchos::RCP<Cubature<double> > lineCub = cubFactory.create(line, cubDegree); // create default cubature
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 
108 int 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 (CubatureDirectLineGauss) |\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+01 * INTREPID_TOL;
149  testInt.assign(INTREPID_CUBATURE_LINE_GAUSS_MAX+1, tmparray);
150  analyticInt.assign(INTREPID_CUBATURE_LINE_GAUSS_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  // compute integrals
165  for (int cubDeg=0; cubDeg <= INTREPID_CUBATURE_LINE_GAUSS_MAX; cubDeg++) {
166  testInt[cubDeg].resize(cubDeg+1);
167  for (int polyDeg=0; polyDeg <= cubDeg; polyDeg++) {
168  testInt[cubDeg][polyDeg] = computeIntegral(cubDeg, polyDeg);
169  }
170  }
171  // get analytic values
172  if (filecompare.is_open()) {
173  getAnalytic(analyticInt, filecompare);
174  // close file
175  filecompare.close();
176  }
177  // perform comparison
178  for (int cubDeg=0; cubDeg <= INTREPID_CUBATURE_LINE_GAUSS_MAX; cubDeg++) {
179  for (int polyDeg=0; polyDeg <= cubDeg; polyDeg++) {
180  double abstol = ( analyticInt[polyDeg][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyDeg][0]) );
181  double absdiff = std::fabs(analyticInt[polyDeg][0] - testInt[cubDeg][polyDeg]);
182  *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
183  << "x^" << std::setw(2) << std::left << polyDeg << ":" << " "
184  << std::scientific << std::setprecision(16) << testInt[cubDeg][polyDeg] << " " << analyticInt[polyDeg][0] << " "
185  << std::setprecision(4) << absdiff << " " << "<?" << " " << abstol << "\n";
186  if (absdiff > abstol) {
187  errorFlag++;
188  *outStream << std::right << std::setw(104) << "^^^^---FAILURE!\n";
189  }
190  }
191  *outStream << "\n";
192  } // end for cubDeg
193  }
194  catch (const std::logic_error & err) {
195  *outStream << err.what() << "\n";
196  errorFlag = -1;
197  };
198 
199 
200  if (errorFlag != 0)
201  std::cout << "End Result: TEST FAILED\n";
202  else
203  std::cout << "End Result: TEST PASSED\n";
204 
205  // reset format state of std::cout
206  std::cout.copyfmt(oldFormatState);
207 
208  return errorFlag;
209 }
int dimension(const int whichDim) const
Returns the specified dimension.
#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...
Intrepid utilities.
Header file for the abstract base class Intrepid::DefaultCubatureFactory.
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.