Intrepid
test_17.cpp
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43 
44 
52 //#include "Intrepid_CubatureLineSorted.hpp"
53 #include "Intrepid_Utils.hpp"
54 #include "Teuchos_oblackholestream.hpp"
55 #include "Teuchos_RCP.hpp"
56 #include "Teuchos_RefCountPtr.hpp"
57 #include "Teuchos_GlobalMPISession.hpp"
58 
59 using namespace Intrepid;
60 
61 
62 template<class Scalar>
63 class StdVector {
64 private:
65  Teuchos::RefCountPtr<std::vector<Scalar> > std_vec_;
66 
67 public:
68 
69  StdVector( const Teuchos::RefCountPtr<std::vector<Scalar> > & std_vec )
70  : std_vec_(std_vec) {}
71 
72  Teuchos::RefCountPtr<StdVector<Scalar> > Create() const {
73  return Teuchos::rcp( new StdVector<Scalar>(
74  Teuchos::rcp(new std::vector<Scalar>(std_vec_->size(),0))));
75  }
76 
77  void Update( StdVector<Scalar> & s ) {
78  int dimension = (int)(std_vec_->size());
79  for (int i=0; i<dimension; i++)
80  (*std_vec_)[i] += s[i];
81  }
82 
83  void Update( Scalar alpha, StdVector<Scalar> & s ) {
84  int dimension = (int)(std_vec_->size());
85  for (int i=0; i<dimension; i++)
86  (*std_vec_)[i] += alpha*s[i];
87  }
88 
89  Scalar operator[](int i) {
90  return (*std_vec_)[i];
91  }
92 
93  void clear() {
94  std_vec_->clear();
95  }
96 
97  void resize(int n, Scalar p) {
98  std_vec_->resize(n,p);
99  }
100 
101  int size() {
102  return (int)std_vec_->size();
103  }
104 
105  void Set( Scalar alpha ) {
106  int dimension = (int)(std_vec_->size());
107  for (int i=0; i<dimension; i++)
108  (*std_vec_)[i] = alpha;
109  }
110 };
111 
112 template<class Scalar, class UserVector>
113 class ASGdata : public Intrepid::AdaptiveSparseGridInterface<Scalar,UserVector>
114 {
115 public:
116  ~ASGdata() {}
117 
118  ASGdata(int dimension,std::vector<EIntrepidBurkardt> rule1D,
119  std::vector<EIntrepidGrowth> growth1D, int maxLevel,
121  dimension,rule1D,growth1D,maxLevel,isNormalized) {}
122 
124  UserVector & output,
125  std::vector<Scalar> & input) {
126 
127  output.clear(); output.resize(1,0.0);
128  int dimension = (int)input.size();
129  std::vector<Scalar> point = input;
130  for (int i=0; i<dimension; i++) {
131  point[i] = 0.5*point[i]+0.5;
132  }
133  Teuchos::RCP<std::vector<long double> > etmp =
134  Teuchos::rcp(new std::vector<long double>(1,0.0));
135  StdVector<long double> tmp(etmp);
136  Scalar gamma = 0.5;
137  Scalar x = 0.0;
138 
139  Scalar prod1 = gamma*(1.0-x);
140  Scalar prod2 = (1.0-x)*point[0];
141 
142  for (int i=1; i<dimension; i++) {
143  prod1 = powl(gamma*(1.0-x),(long double)i); prod2 = 1.0-x;
144  for (int j=0; j<i; j++) {
145  prod2 *= point[j];
146  if (j<i-1) {
147  prod1 *= powl(point[j],(long double)(i-(j+1)));
148  }
149  }
150  (*etmp)[0] = prod1*(1.0-prod2);
151  //output[0] += prod1*(1.0-prod2);
152  output.Update(tmp); tmp.Set(0.0);
153  }
154  }
155  Scalar error_indicator(UserVector & input) {
156  int dimension = (int)input.size();
157  Scalar norm2 = 0.0;
158  for (int i=0; i<dimension; i++)
159  norm2 += input[i]*input[i];
160 
163  norm2 = std::sqrt(norm2)/ID;
164  return norm2;
165  }
166 };
167 
168 long double adaptSG(StdVector<long double> & iv,
170  problem_data, long double TOL) {
171 
172  // Construct a Container for the adapted rule
173  int dimension = problem_data.getDimension();
174  std::vector<int> index(dimension,1);
175 
176  // Initialize global error indicator
177  long double eta = 1.0;
178 
179  // Initialize the Active index set
180  std::multimap<long double,std::vector<int> > activeIndex;
181  activeIndex.insert(std::pair<long double,std::vector<int> >(eta,index));
182 
183  // Initialize the old index set
184  std::set<std::vector<int> > oldIndex;
185  // Perform Adaptation
186  while (eta > TOL) {
188  activeIndex,oldIndex,iv,eta,problem_data);
189  }
190  return eta;
191 }
192 
193 int main(int argc, char *argv[]) {
194 
195  Teuchos::GlobalMPISession mpiSession(&argc, &argv);
196 
197  // This little trick lets us print to std::cout only if
198  // a (dummy) command-line argument is provided.
199  int iprint = argc - 1;
200  Teuchos::RCP<std::ostream> outStream;
201  Teuchos::oblackholestream bhs; // outputs nothing
202  if (iprint > 0)
203  outStream = Teuchos::rcp(&std::cout, false);
204  else
205  outStream = Teuchos::rcp(&bhs, false);
206 
207  // Save the format state of the original std::cout.
208  Teuchos::oblackholestream oldFormatState;
209  oldFormatState.copyfmt(std::cout);
210 
211  *outStream \
212  << "===============================================================================\n" \
213  << "| |\n" \
214  << "| Unit Test (AdaptiveSparseGrid) |\n" \
215  << "| |\n" \
216  << "| 1) Particle traveling through 1D slab of length 1. |\n" \
217  << "| |\n" \
218  << "| Questions? Contact Drew Kouri (dpkouri@sandia.gov) or |\n" \
219  << "| Denis Ridzal (dridzal@sandia.gov). |\n" \
220  << "| |\n" \
221  << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
222  << "| Trilinos website: http://trilinos.sandia.gov |\n" \
223  << "| |\n" \
224  << "===============================================================================\n"\
225  << "| TEST 17: solve 1D transport problem by approximating an infinite integral |\n"\
226  << "===============================================================================\n";
227 
228 
229  // internal variables:
230  int errorFlag = 0;
231  long double TOL = INTREPID_TOL;
232  int dimension = 8;
233  std::vector<EIntrepidBurkardt> rule1D(dimension,BURK_PATTERSON);
234  std::vector<EIntrepidGrowth> growth1D(dimension,GROWTH_FULLEXP);
235  int maxLevel = 7;
236  bool isNormalized = true;
237  ASGdata<long double,StdVector<long double> > problem_data(dimension,
238  rule1D,growth1D,maxLevel,isNormalized);
239  Teuchos::RCP<std::vector<long double> > integralValue =
240  Teuchos::rcp(new std::vector<long double>(1,0.0));
241  StdVector<long double> sol(integralValue); sol.Set(0.0);
242  problem_data.init(sol);
243 
244  long double eta = adaptSG(sol,problem_data,TOL);
245  long double x = 0;
246  long double gamma = 0.5;
247  long double analyticInt = (1.0 - (1.0-gamma)*exp(gamma*(1.0-x)))/gamma;
248  long double abstol = std::sqrt(INTREPID_TOL);
249  long double absdiff = std::abs(analyticInt-(*integralValue)[0]);
250  try {
251  *outStream << "Adaptive Sparse Grid exited with global error "
252  << std::scientific << std::setprecision(16) << eta << "\n"
253  << "Approx = " << std::scientific << std::setprecision(16)
254  << (*integralValue)[0]
255  << ", Exact = " << std::scientific << std::setprecision(16)
256  << analyticInt << "\n"
257  << "Error = " << std::scientific << std::setprecision(16)
258  << absdiff << " "
259  << "<?" << " " << abstol << "\n";
260  if (absdiff > abstol) {
261  errorFlag++;
262  *outStream << std::right << std::setw(104) << "^^^^---FAILURE!\n";
263  }
264  }
265  catch (std::logic_error err) {
266  *outStream << err.what() << "\n";
267  errorFlag = -1;
268  };
269 
270  if (errorFlag != 0)
271  std::cout << "End Result: TEST FAILED\n";
272  else
273  std::cout << "End Result: TEST PASSED\n";
274 
275  // reset format state of std::cout
276  std::cout.copyfmt(oldFormatState);
277 
278  return errorFlag;
279 }
Builds general adaptive sparse grid rules (Gerstner and Griebel) using the 1D cubature rules in the I...
Scalar getInitialDiff()
Return initial error indicator.
Header file for the Intrepid::AdaptiveSparseGrid class.
Intrepid utilities.
Scalar error_indicator(UserVector &input)
User defined error indicator function.
Definition: test_17.cpp:155
void eval_integrand(UserVector &output, std::vector< Scalar > &input)
Evaluate the integrand function.
Definition: test_17.cpp:123