Intrepid
test_23.cpp
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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 :
114  public Intrepid::AdaptiveSparseGridInterface<Scalar,UserVector> {
115 public:
116  ~ASGdata() {}
117 
118  ASGdata(int dimension,std::vector<EIntrepidBurkardt> rule1D,
119  std::vector<EIntrepidGrowth> growth1D, int maxLevel,
120  bool isNormalized) : AdaptiveSparseGridInterface<Scalar,UserVector>(
121  dimension,rule1D,growth1D,maxLevel,isNormalized) {}
122 
123  void eval_integrand(UserVector & output, std::vector<Scalar> & input) {
124  output.clear(); output.resize(1,powl(input[0]+input[1],(long double)6.0));
125  }
126  Scalar error_indicator(UserVector & input) {
127  int dimension = (int)input.size();
128  Scalar norm2 = 0.0;
129  for (int i=0; i<dimension; i++)
130  norm2 += input[i]*input[i];
131 
134  norm2 = std::sqrt(norm2)/ID;
135  return norm2;
136  }
137 };
138 
139 long double adaptSG(StdVector<long double> & iv,
140  std::multimap<long double,std::vector<int> > & activeIndex,
141  std::set<std::vector<int> > & oldIndex,
142  AdaptiveSparseGridInterface<long double,StdVector<long double> > & problem_data,
144  long double TOL) {
145 
146  // Construct a Container for the adapted rule
147  int dimension = problem_data.getDimension();
148  std::vector<int> index(dimension,1);
149 
150  // Initialize global error indicator
151  long double eta = 1.0;
152 
153  // Initialize the Active index set
154  activeIndex.insert(std::pair<long double,std::vector<int> >(eta,index));
155 
156  // Perform Adaptation
157  while (eta > TOL) {
159  activeIndex,oldIndex,
160  iv,cubRule,
161  eta,problem_data);
162  }
163  cubRule.normalize();
164  return eta;
165 }
166 
167 long double evalQuad(CubatureTensorSorted<long double> & lineCub) {
168 
169  int size = lineCub.getNumPoints();
170  int dimension = lineCub.getDimension();
171  FieldContainer<long double> cubPoints(size,dimension);
172  FieldContainer<long double> cubWeights(size);
173  lineCub.getCubature(cubPoints,cubWeights);
174 
175  long double Q = 0.0;
176  for (int k=0; k<size; k++)
177  Q += cubWeights(k)*powl(cubPoints(k,0)+cubPoints(k,1),(long double)6.0);
178 
179  return Q;
180 }
181 
182 int main(int argc, char *argv[]) {
183 
184  Teuchos::GlobalMPISession mpiSession(&argc, &argv);
185 
186  // This little trick lets us print to std::cout only if
187  // a (dummy) command-line argument is provided.
188  int iprint = argc - 1;
189  Teuchos::RCP<std::ostream> outStream;
190  Teuchos::oblackholestream bhs; // outputs nothing
191  if (iprint > 0)
192  outStream = Teuchos::rcp(&std::cout, false);
193  else
194  outStream = Teuchos::rcp(&bhs, false);
195 
196  // Save the format state of the original std::cout.
197  Teuchos::oblackholestream oldFormatState;
198  oldFormatState.copyfmt(std::cout);
199 
200  *outStream \
201  << "===============================================================================\n" \
202  << "| |\n" \
203  << "| Unit Test (AdaptiveSparseGrid) |\n" \
204  << "| |\n" \
205  << "| 1) Integrate a sum of Gaussians in 2D and compare index sets. |\n" \
206  << "| |\n" \
207  << "| Questions? Contact Drew Kouri (dpkouri@sandia.gov) or |\n" \
208  << "| Denis Ridzal (dridzal@sandia.gov). |\n" \
209  << "| |\n" \
210  << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
211  << "| Trilinos website: http://trilinos.sandia.gov |\n" \
212  << "| |\n" \
213  << "===============================================================================\n"\
214  << "| TEST 23: Compare index sets for different instances of refine grid |\n"\
215  << "===============================================================================\n";
216 
217 
218  // internal variables:
219  int errorFlag = 0;
220  long double TOL = INTREPID_TOL;
221  int dimension = 2;
222  int maxLevel = 4;
223  bool isNormalized = false;
224 
225  std::vector<EIntrepidBurkardt> rule1D(dimension,BURK_CLENSHAWCURTIS);
226  std::vector<EIntrepidGrowth> growth1D(dimension,GROWTH_FULLEXP);
227 
228  ASGdata<long double,StdVector<long double> > problem_data(dimension,rule1D,
229  growth1D,maxLevel,
230  isNormalized);
231  Teuchos::RCP<std::vector<long double> > integralValue =
232  Teuchos::rcp(new std::vector<long double>(1,0.0));
233  StdVector<long double> sol(integralValue); sol.Set(0.0);
234  problem_data.init(sol);
235 
236  try {
237 
238  // Initialize the index sets
239  std::multimap<long double,std::vector<int> > activeIndex1;
240  std::set<std::vector<int> > oldIndex1;
241  std::vector<int> index(dimension,1);
242  CubatureTensorSorted<long double> adaptedRule(dimension,index,rule1D,
243  growth1D,isNormalized);
244  adaptSG(sol,activeIndex1,oldIndex1,problem_data,adaptedRule,TOL);
245  long double Q1 = sol[0];
246 
247  CubatureTensorSorted<long double> fullRule(0,dimension);
249  fullRule,dimension,
250  maxLevel,rule1D,
251  growth1D,isNormalized);
252  long double Q2 = evalQuad(fullRule);
253  fullRule.normalize();
254 
255  long double diff = std::abs(Q1-Q2);
256 
257  *outStream << "Q1 = " << Q1 << " Q2 = " << Q2
258  << " |Q1-Q2| = " << diff << "\n";
259 
260  int size1 = adaptedRule.getNumPoints();
261  FieldContainer<long double> aPoints(size1,dimension);
262  FieldContainer<long double> aWeights(size1);
263  adaptedRule.getCubature(aPoints,aWeights);
264 
265  *outStream << "\n\nAdapted Rule Nodes and Weights\n";
266  for (int i=0; i<size1; i++)
267  *outStream << aPoints(i,0) << "\t" << aPoints(i,1)
268  << "\t" << aWeights(i) << "\n";
269 
270  int size2 = fullRule.getNumPoints();
271  FieldContainer<long double> fPoints(size2,dimension);
272  FieldContainer<long double> fWeights(size2);
273  fullRule.getCubature(fPoints,fWeights);
274 
275  *outStream << "\n\nFull Rule Nodes and Weights\n";
276  for (int i=0; i<size2; i++)
277  *outStream << fPoints(i,0) << "\t" << fPoints(i,1)
278  << "\t" << fWeights(i) << "\n";
279 
280  *outStream << "\n\nSize of adapted rule = " << size1
281  << " Size of full rule = " << size2 << "\n";
282  if (diff > TOL*std::abs(Q2)||size1!=size2) {
283  errorFlag++;
284  *outStream << std::right << std::setw(104) << "^^^^---FAILURE!\n";
285  }
286  else {
287  long double sum1 = 0.0, sum2 = 0.0;
288  for (int i=0; i<size1; i++) {
289  //diff = std::abs(fWeights(i)-aWeights(i));
290  sum1 += fWeights(i);
291  sum2 += aWeights(i);
292  }
293  *outStream << "Check if weights are normalized:"
294  << " Adapted Rule Sum = " << sum2
295  << " Full Rule Sum = " << sum1 << "\n";
296  if (std::abs(sum1-1.0) > TOL || std::abs(sum2-1.0) > TOL) {
297  errorFlag++;
298  *outStream << std::right << std::setw(104) << "^^^^---FAILURE!\n";
299  }
300  }
301  }
302  catch (std::logic_error err) {
303  *outStream << err.what() << "\n";
304  errorFlag = -1;
305  };
306 
307  if (errorFlag != 0)
308  std::cout << "End Result: TEST FAILED\n";
309  else
310  std::cout << "End Result: TEST PASSED\n";
311 
312  // reset format state of std::cout
313  std::cout.copyfmt(oldFormatState);
314 
315  return errorFlag;
316 }
void normalize()
Normalize CubatureLineSorted weights.
int getNumPoints() const
Returns the number of cubature points.
void getCubature(ArrayPoint &cubPoints, ArrayWeight &cubWeights) const
Returns cubature points and weights (return arrays must be pre-sized/pre-allocated).
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.
int getDimension() const
Returns dimension of domain of integration.
Scalar error_indicator(UserVector &input)
User defined error indicator function.
Definition: test_23.cpp:126
Implementation of a templated lexicographical container for a multi-indexed scalar quantity...
Utilizes 1D cubature (integration) rules contained in the library sandia_rules (John Burkardt...
void eval_integrand(UserVector &output, std::vector< Scalar > &input)
Evaluate the integrand function.
Definition: test_23.cpp:123