Intrepid
test_20.cpp
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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
59using namespace Intrepid;
60
61template<class Scalar>
62class StdVector {
63private:
64 Teuchos::RefCountPtr<std::vector<Scalar> > std_vec_;
65
66public:
67
68 StdVector( const Teuchos::RefCountPtr<std::vector<Scalar> > & std_vec )
69 : std_vec_(std_vec) {}
70
71 Teuchos::RefCountPtr<StdVector<Scalar> > Create() const {
72 return Teuchos::rcp( new StdVector<Scalar>(
73 Teuchos::rcp(new std::vector<Scalar>(std_vec_->size(),0))));
74 }
75
76 void Update( StdVector<Scalar> & s ) {
77 int dimension = (int)(std_vec_->size());
78 for (int i=0; i<dimension; i++)
79 (*std_vec_)[i] += s[i];
80 }
81
82 void Update( Scalar alpha, StdVector<Scalar> & s ) {
83 int dimension = (int)(std_vec_->size());
84 for (int i=0; i<dimension; i++)
85 (*std_vec_)[i] += alpha*s[i];
86 }
87
88 Scalar operator[](int i) {
89 return (*std_vec_)[i];
90 }
91
92 void clear() {
93 std_vec_->clear();
94 }
95
96 void resize(int n, Scalar p) {
97 std_vec_->resize(n,p);
98 }
99
100 int size() {
101 return (int)std_vec_->size();
102 }
103
104 void Set( Scalar alpha ) {
105 int dimension = (int)(std_vec_->size());
106 for (int i=0; i<dimension; i++)
107 (*std_vec_)[i] = alpha;
108 }
109};
110
111template<class Scalar, class UserVector>
112class ASGdata :
113 public Intrepid::AdaptiveSparseGridInterface<Scalar,UserVector> {
114public:
115 ~ASGdata() {}
116
117 ASGdata(int dimension,std::vector<EIntrepidBurkardt> rule1D,
118 std::vector<EIntrepidGrowth> growth1D, int maxLevel,
119 bool isNormalized) : AdaptiveSparseGridInterface<Scalar,UserVector>(
120 dimension,rule1D,growth1D,maxLevel,isNormalized) {}
121
122 void eval_integrand(UserVector & output, std::vector<Scalar> & input) {
123 output.clear(); output.resize(1,std::exp(-input[0]*input[0])
124 +10.0*std::exp(-input[1]*input[1]));
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
139long double adaptSG(StdVector<long double> & iv,
141 problem_data,long double TOL) {
142
143 // Construct a Container for the adapted rule
144 int dimension = problem_data.getDimension();
145 std::vector<int> index(dimension,1);
146
147 // Initialize global error indicator
148 long double eta = 1.0;
149
150 // Initialize the Active index set
151 std::multimap<long double,std::vector<int> > activeIndex;
152 activeIndex.insert(std::pair<long double,std::vector<int> >(eta,index));
153
154 // Initialize the old index set
155 std::set<std::vector<int> > oldIndex;
156
157 // Perform Adaptation
158 while (eta > TOL) {
160 activeIndex,oldIndex,iv,eta,problem_data);
161 }
162 return eta;
163}
164
165int main(int argc, char *argv[]) {
166
167 Teuchos::GlobalMPISession mpiSession(&argc, &argv);
168
169 // This little trick lets us print to std::cout only if
170 // a (dummy) command-line argument is provided.
171 int iprint = argc - 1;
172 Teuchos::RCP<std::ostream> outStream;
173 Teuchos::oblackholestream bhs; // outputs nothing
174 if (iprint > 0)
175 outStream = Teuchos::rcp(&std::cout, false);
176 else
177 outStream = Teuchos::rcp(&bhs, false);
178
179 // Save the format state of the original std::cout.
180 Teuchos::oblackholestream oldFormatState;
181 oldFormatState.copyfmt(std::cout);
182
183 *outStream \
184 << "===============================================================================\n" \
185 << "| |\n" \
186 << "| Unit Test (AdaptiveSparseGrid) |\n" \
187 << "| |\n" \
188 << "| 1) Integrate a sum of Gaussians in 2D (Gerstner and Griebel). |\n" \
189 << "| |\n" \
190 << "| Questions? Contact Drew Kouri (dpkouri@sandia.gov) or |\n" \
191 << "| Denis Ridzal (dridzal@sandia.gov). |\n" \
192 << "| |\n" \
193 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
194 << "| Trilinos website: http://trilinos.sandia.gov |\n" \
195 << "| |\n" \
196 << "===============================================================================\n"\
197 << "| TEST 20: Integrate an anisotropic sum of Gaussians in 2D |\n"\
198 << "===============================================================================\n";
199
200
201 // internal variables:
202 int errorFlag = 0;
203 long double TOL = INTREPID_TOL;
204 int dimension = 2;
205 int maxLevel = 25;
206 bool isNormalized = true;
207
208 std::vector<EIntrepidBurkardt> rule1D(dimension,BURK_CLENSHAWCURTIS);
209 std::vector<EIntrepidGrowth> growth1D(dimension,GROWTH_FULLEXP);
210
212 dimension,rule1D,growth1D,maxLevel,isNormalized);
213 Teuchos::RCP<std::vector<long double> > integralValue =
214 Teuchos::rcp(new std::vector<long double>(1,0.0));
215 StdVector<long double> sol(integralValue); sol.Set(0.0);
216 problem_data.init(sol);
217
218 long double eta = adaptSG(sol,problem_data,TOL);
219
220 long double analyticInt = (1.0+10.0)*std::sqrt(M_PI)/2.0*erff(1.0);
221 long double abstol = 1.0e1*std::sqrt(INTREPID_TOL);
222 long double absdiff = std::abs(analyticInt-sol[0]);
223 try {
224 *outStream << "Adaptive Sparse Grid exited with global error "
225 << std::scientific << std::setprecision(16) << eta << "\n"
226 << "Approx = " << std::scientific << std::setprecision(16) << sol[0]
227 << ", Exact = " << std::scientific << std::setprecision(16) << analyticInt << "\n"
228 << "Error = " << std::scientific << std::setprecision(16) << absdiff << " "
229 << "<?" << " " << abstol << "\n";
230 if (absdiff > abstol) {
231 errorFlag++;
232 *outStream << std::right << std::setw(104) << "^^^^---FAILURE!\n";
233 }
234 }
235 catch (const std::logic_error & err) {
236 *outStream << err.what() << "\n";
237 errorFlag = -1;
238 };
239
240 if (errorFlag != 0)
241 std::cout << "End Result: TEST FAILED\n";
242 else
243 std::cout << "End Result: TEST PASSED\n";
244
245 // reset format state of std::cout
246 std::cout.copyfmt(oldFormatState);
247
248 return errorFlag;
249}
Header file for the Intrepid::AdaptiveSparseGrid class.
Intrepid utilities.
void eval_integrand(UserVector &output, std::vector< Scalar > &input)
Evaluate the integrand function.
Definition: test_20.cpp:122
Scalar error_indicator(UserVector &input)
User defined error indicator function.
Definition: test_20.cpp:126
bool isNormalized()
Return whether or not cubature weights are normalized.
Builds general adaptive sparse grid rules (Gerstner and Griebel) using the 1D cubature rules in the I...