Intrepid
test_15.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  Computes integrals of monomials over a given reference cell.
61 */
62 long double evalQuad(int order, int power, EIntrepidBurkardt rule) {
63 
64  CubatureLineSorted<long double> lineCub(rule,order,false);
65  CubatureLineSorted<long double> lineCub2(rule,order-1,false);
66  lineCub.update(-1.0,lineCub2,1.0);
67  int size = lineCub.getNumPoints();
68  FieldContainer<long double> cubPoints(size);
69  FieldContainer<long double> cubWeights(size);
70  lineCub.getCubature(cubPoints,cubWeights);
71 
72  long double Q = 0.0;
73  for (int i=0; i<size; i++) {
74  Q += cubWeights(i)*powl(cubPoints(i),(long double)power);
75  }
76  return Q;
77 
78  /*
79  int mid = size/2;
80  long double Q = 0.0;
81  if (size%2)
82  Q = cubWeights(mid)*powl(cubPoints(mid),power);
83 
84  for (int i=0; i<mid; i++) {
85  Q += cubWeights(i)*powl(cubPoints(i),power)+
86  cubWeights(order-i-1)*powl(cubPoints(size-i-1),power);
87  }
88  return Q;
89  */
90 }
91 
92 int main(int argc, char *argv[]) {
93 
94  Teuchos::GlobalMPISession mpiSession(&argc, &argv);
95 
96  // This little trick lets us print to std::cout only if
97  // a (dummy) command-line argument is provided.
98  int iprint = argc - 1;
99  Teuchos::RCP<std::ostream> outStream;
100  Teuchos::oblackholestream bhs; // outputs nothing
101  if (iprint > 0)
102  outStream = Teuchos::rcp(&std::cout, false);
103  else
104  outStream = Teuchos::rcp(&bhs, false);
105 
106  // Save the format state of the original std::cout.
107  Teuchos::oblackholestream oldFormatState;
108  oldFormatState.copyfmt(std::cout);
109 
110  *outStream \
111  << "===============================================================================\n" \
112  << "| |\n" \
113  << "| Unit Test (CubatureLineSorted) |\n" \
114  << "| |\n" \
115  << "| 1) Computing differential integrals of monomials in 1D |\n" \
116  << "| |\n" \
117  << "| Questions? Contact Drew Kouri (dpkouri@sandia.gov) or |\n" \
118  << "| Denis Ridzal (dridzal@sandia.gov). |\n" \
119  << "| |\n" \
120  << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
121  << "| Trilinos website: http://trilinos.sandia.gov |\n" \
122  << "| |\n" \
123  << "===============================================================================\n"\
124  << "| TEST 15: differential integrals of monomials in 1D |\n"\
125  << "===============================================================================\n";
126 
127  // internal variables:
128  int errorFlag = 0;
129  long double abstol = 1.0e+05*INTREPID_TOL;
130  int maxDeg = 0;
131  long double analyticInt = 0;
132  long double testInt = 0;
133  int maxOrder = 60;
134  EIntrepidBurkardt rule = BURK_LEGENDRE;
135 
136  *outStream << "\nDifferential integrals of monomials on a reference line:\n";
137  // compute and compare integrals
138  try {
139  *outStream << "Testing " << EIntrepidBurkardtToString(rule) << "\n";
140  // compute integrals
141  for (int i=2; i <= maxOrder; i++) {
142  maxDeg = 2*(i-1)-1;
143  for (int j=0; j <= maxDeg; j++) {
144  testInt = evalQuad(i,j,rule);
145  long double absdiff = std::fabs(testInt);
146  *outStream << "Cubature order " << std::setw(2) << std::left << i
147  << " integrating "
148  << "x^" << std::setw(2) << std::left << j << ":" << " "
149  << std::scientific << std::setprecision(16) << testInt
150  << " " << analyticInt
151  << " " << std::setprecision(4) << absdiff << " "
152  << "<?" << " " << abstol
153  << "\n";
154  if (absdiff > abstol) {
155  errorFlag++;
156  *outStream << std::right << std::setw(104) << "^^^^---FAILURE!\n";
157  }
158  } // end for j
159  *outStream << "\n";
160  } // end for i
161  }
162  catch (std::logic_error err) {
163  *outStream << err.what() << "\n";
164  errorFlag = -1;
165  };
166 
167 
168  if (errorFlag != 0)
169  std::cout << "End Result: TEST FAILED\n";
170  else
171  std::cout << "End Result: TEST PASSED\n";
172 
173  // reset format state of std::cout
174  std::cout.copyfmt(oldFormatState);
175 
176  return errorFlag;
177 }
Utilizes cubature (integration) rules contained in the library sandia_rules (John Burkardt...
Header file for the Intrepid::CubatureLineSorted class.
Intrepid utilities.
Implementation of a templated lexicographical container for a multi-indexed scalar quantity...