Intrepid
test_07.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 //Teuchos::RCP<std::ostream> outStream;
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 */
67 double 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 */
81 double computeIntegral(int cubDegree, int xDeg, int yDeg) {
82 
83  CubatureSparse<double,2> myCub(cubDegree);
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 
106 int 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 (CubatureSparse) |\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), |\n" \
132  << "| Denis Ridzal (dridzal@sandia.gov) or |\n" \
133  << "| Matthew Keegan (mskeega@sandia.gov) |\n" \
134  << "| |\n" \
135  << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
136  << "| Trilinos website: http://trilinos.sandia.gov |\n" \
137  << "| |\n" \
138  << "===============================================================================\n"\
139  << "| TEST 1: integrals of monomials in 2D for Sparse Grid Construction |\n"\
140  << "===============================================================================\n";
141 
142  // internal variables:
143  int errorFlag = 0;
144  int polyCt = 0;
145  int offset = 0;
146  Teuchos::Array< Teuchos::Array<double> > testInt;
147  Teuchos::Array< Teuchos::Array<double> > analyticInt;
148  Teuchos::Array<double> tmparray(1);
149  double reltol = 1.0e+03 * INTREPID_TOL;
150  int maxDeg = 30; // can be as large as INTREPID_CUBATURE_SPARSE2D_GAUSS_MAX, but runtime is excessive
151  int maxOffset = INTREPID_CUBATURE_LINE_GAUSS_MAX;
152  int numPoly = (maxDeg+1)*(maxDeg+2)/2;
153  int numAnalytic = (maxOffset+1)*(maxOffset+2)/2;
154  testInt.assign(numPoly, tmparray);
155  analyticInt.assign(numAnalytic, tmparray);
156 
157  // get names of files with analytic values
158  std::string basedir = "./data";
159  std::stringstream namestream;
160  std::string filename;
161  namestream << basedir << "/QUAD_integrals" << ".dat";
162  namestream >> filename;
163 
164  // compute and compare integrals
165  try {
166  *outStream << "\nIntegrals of monomials:\n";
167 
168  std::ifstream filecompare(&filename[0]);
169  // compute integrals
170  for (int cubDeg=0; cubDeg <= maxDeg; cubDeg++) {
171  polyCt = 0;
172  testInt[cubDeg].resize((cubDeg+1)*(cubDeg+2)/2);
173  for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
174  for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
175  testInt[cubDeg][polyCt] = computeIntegral(cubDeg, xDeg, yDeg);
176  polyCt++;
177  }
178  }
179  }
180 
181  // get analytic values
182  if (filecompare.is_open()) {
183  getAnalytic(analyticInt, filecompare);
184  // close file
185  filecompare.close();
186  }
187  // perform comparison
188  for (int cubDeg=0; cubDeg <= maxDeg; cubDeg++) {
189  polyCt = 0;
190  offset = 0;
191  for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
192  for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
193  double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) );
194  double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]);
195  *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
196  << "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg << ":" << " "
197  << std::scientific << std::setprecision(16) << testInt[cubDeg][polyCt] << " " << analyticInt[polyCt+offset][0] << " "
198  << std::setprecision(4) << absdiff << " " << "<?" << " " << abstol << "\n";
199  if (absdiff > abstol) {
200  errorFlag++;
201  *outStream << std::right << std::setw(111) << "^^^^---FAILURE!\n";
202  }
203  polyCt++;
204  }
205  offset = offset + maxOffset - cubDeg;
206  }
207  *outStream << "\n";
208  }
209  *outStream << "\n";
210  }
211  catch (std::logic_error err) {
212  *outStream << err.what() << "\n";
213  errorFlag = -1;
214  };
215 
216 
217  if (errorFlag != 0)
218  std::cout << "End Result: TEST FAILED\n";
219  else
220  std::cout << "End Result: TEST PASSED\n";
221 
222  // reset format state of std::cout
223  std::cout.copyfmt(oldFormatState);
224 
225  return errorFlag;
226 }
Header file for the Intrepid::CubatureSparse class.
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.