Intrepid
test_18.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;
60std::vector<long double> alpha(1,0);
61std::vector<long double> beta(1,0);
62
63template<class Scalar>
64class StdVector {
65private:
66 Teuchos::RefCountPtr<std::vector<Scalar> > std_vec_;
67
68public:
69
70 StdVector( const Teuchos::RefCountPtr<std::vector<Scalar> > & std_vec )
71 : std_vec_(std_vec) {}
72
73 Teuchos::RefCountPtr<StdVector<Scalar> > Create() const {
74 return Teuchos::rcp( new StdVector<Scalar>(
75 Teuchos::rcp(new std::vector<Scalar>(std_vec_->size(),0))));
76 }
77
78 void Update( StdVector<Scalar> & s ) {
79 int dimension = (int)(std_vec_->size());
80 for (int i=0; i<dimension; i++)
81 (*std_vec_)[i] += s[i];
82 }
83
84 void Update( Scalar alpha, StdVector<Scalar> & s ) {
85 int dimension = (int)(std_vec_->size());
86 for (int i=0; i<dimension; i++)
87 (*std_vec_)[i] += alpha*s[i];
88 }
89
90 Scalar operator[](int i) {
91 return (*std_vec_)[i];
92 }
93
94 void clear() {
95 std_vec_->clear();
96 }
97
98 void resize(int n, Scalar p) {
99 std_vec_->resize(n,p);
100 }
101
102 int size() {
103 return (int)std_vec_->size();
104 }
105
106 void Set( Scalar alpha ) {
107 int dimension = (int)(std_vec_->size());
108 for (int i=0; i<dimension; i++)
109 (*std_vec_)[i] = alpha;
110 }
111};
112
113template<class Scalar,class UserVector>
114class ASGdata :
115 public Intrepid::AdaptiveSparseGridInterface<Scalar,UserVector> {
116public:
117 ~ASGdata() {}
118
119 ASGdata(int dimension,std::vector<EIntrepidBurkardt> rule1D,
120 std::vector<EIntrepidGrowth> growth1D, int maxLevel,
121 bool isNormalized) : AdaptiveSparseGridInterface<Scalar,UserVector>(
122 dimension,rule1D,growth1D,maxLevel,isNormalized) {}
123
124 void eval_integrand(UserVector & output, std::vector<Scalar> & input) {
125 int dimension = (int)alpha.size();
126 Scalar total = 1.0;
127 Scalar point = 0;
128 for (int i=0; i<dimension; i++) {
129 point = 0.5*input[i]+0.5;
130 total *= ( 1.0/powl(alpha[i],(long double)2.0)
131 + powl(point-beta[i],(long double)2.0) );
132 }
133 output.clear(); output.resize(1,1.0/total);
134 }
135
136 Scalar error_indicator(UserVector & input) {
137 int dimension = (int)input.size();
138 Scalar norm2 = 0.0;
139 for (int i=0; i<dimension; i++)
140 norm2 += input[i]*input[i];
141
144 norm2 = std::sqrt(norm2)/ID;
145 return norm2;
146 }
147};
148
149long double compExactInt(void) {
150 double val = 1.0;
151 int dimension = alpha.size();
152 for (int i=0; i<dimension; i++) {
153 val *= alpha[i]*( std::atan((1.0-beta[i])*alpha[i])
154 +std::atan(beta[i]*alpha[i]) );
155 }
156 return val;
157}
158
159long double adaptSG(StdVector<long double> & iv,
160 AdaptiveSparseGridInterface<long double,StdVector<long double> > &
161 problem_data,long double TOL) {
162
163 // Construct a Container for the adapted rule
164 int dimension = problem_data.getDimension();
165 std::vector<int> index(dimension,1);
166
167 // Initialize global error indicator
168 long double eta = 1.0;
169
170 // Initialize the Active index set
171 std::multimap<long double,std::vector<int> > activeIndex;
172 activeIndex.insert(std::pair<long double,std::vector<int> >(eta,index));
173
174 // Initialize the old index set
175 std::set<std::vector<int> > oldIndex;
176 /*
177 std::vector<long double> output(1,0);
178 std::vector<long double> input(dimension,0.5);
179 problem_data.eval_integrand(output,input);
180 */
181 // Perform Adaptation
182 while (eta > TOL) {
183 eta = AdaptiveSparseGrid<long double,StdVector<long double> >::refine_grid(
184 activeIndex,oldIndex,
185 iv,eta,
186 problem_data);
187 }
188 return eta;
189}
190
191int main(int argc, char *argv[]) {
192
193 Teuchos::GlobalMPISession mpiSession(&argc, &argv);
194
195 // This little trick lets us print to std::cout only if
196 // a (dummy) command-line argument is provided.
197 int iprint = argc - 1;
198 Teuchos::RCP<std::ostream> outStream;
199 Teuchos::oblackholestream bhs; // outputs nothing
200 if (iprint > 0)
201 outStream = Teuchos::rcp(&std::cout, false);
202 else
203 outStream = Teuchos::rcp(&bhs, false);
204
205 // Save the format state of the original std::cout.
206 Teuchos::oblackholestream oldFormatState;
207 oldFormatState.copyfmt(std::cout);
208
209 *outStream \
210 << "===============================================================================\n" \
211 << "| |\n" \
212 << "| Unit Test (AdaptiveSparseGrid) |\n" \
213 << "| |\n" \
214 << "| 1) Integrate product peaks in 5 dimensions (Genz integration test). |\n" \
215 << "| |\n" \
216 << "| Questions? Contact Drew Kouri (dpkouri@sandia.gov) or |\n" \
217 << "| Denis Ridzal (dridzal@sandia.gov). |\n" \
218 << "| |\n" \
219 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
220 << "| Trilinos website: http://trilinos.sandia.gov |\n" \
221 << "| |\n" \
222 << "===============================================================================\n"\
223 << "| TEST 18: Integrate a product of peaks functions in 5D |\n"\
224 << "===============================================================================\n";
225
226
227 // internal variables:
228 int errorFlag = 0;
229 long double TOL = INTREPID_TOL;
230 int dimension = 5;
231 int maxLevel = 7;
232 bool isNormalized = true;
233
234 std::vector<EIntrepidBurkardt> rule1D(dimension,BURK_PATTERSON);
235 std::vector<EIntrepidGrowth> growth1D(dimension,GROWTH_FULLEXP);
236
237 alpha.resize(dimension,0); beta.resize(dimension,0);
238 for (int i=0; i<dimension; i++) {
239 alpha[i] = (long double)std::rand()/(long double)RAND_MAX;
240 beta[i] = (long double)std::rand()/(long double)RAND_MAX;
241 }
242
243 ASGdata<long double,StdVector<long double> > problem_data(
244 dimension,rule1D,growth1D,
245 maxLevel,isNormalized);
246 Teuchos::RCP<std::vector<long double> > integralValue =
247 Teuchos::rcp(new std::vector<long double>(1,0.0));
248 StdVector<long double> sol(integralValue); sol.Set(0.0);
249 problem_data.init(sol);
250
251 long double eta = adaptSG(sol,problem_data,TOL);
252
253 long double analyticInt = compExactInt();
254 long double abstol = std::sqrt(INTREPID_TOL);
255 long double absdiff = std::abs(analyticInt-(*integralValue)[0]);
256 try {
257 *outStream << "Adaptive Sparse Grid exited with global error "
258 << std::scientific << std::setprecision(16) << eta << "\n"
259 << "Approx = " << std::scientific
260 << std::setprecision(16) << (*integralValue)[0]
261 << ", Exact = " << std::scientific
262 << std::setprecision(16) << analyticInt << "\n"
263 << "Error = " << std::scientific << std::setprecision(16)
264 << absdiff << " "
265 << "<?" << " " << abstol << "\n";
266 if (absdiff > abstol) {
267 errorFlag++;
268 *outStream << std::right << std::setw(104) << "^^^^---FAILURE!\n";
269 }
270 }
271 catch (const std::logic_error & err) {
272 *outStream << err.what() << "\n";
273 errorFlag = -1;
274 };
275
276 if (errorFlag != 0)
277 std::cout << "End Result: TEST FAILED\n";
278 else
279 std::cout << "End Result: TEST PASSED\n";
280
281 // reset format state of std::cout
282 std::cout.copyfmt(oldFormatState);
283
284 return errorFlag;
285}
Header file for the Intrepid::AdaptiveSparseGrid class.
Intrepid utilities.
void eval_integrand(UserVector &output, std::vector< Scalar > &input)
Evaluate the integrand function.
Definition test_18.cpp:124
Scalar error_indicator(UserVector &input)
User defined error indicator function.
Definition test_18.cpp:136
bool isNormalized()
Return whether or not cubature weights are normalized.