1 // -*- C++ -*-
2 /**
3 * @brief The test file of class SobolIndicesAlgorithm
4 *
5 * Copyright 2005-2021 Airbus-EDF-IMACS-ONERA-Phimeca
6 *
7 * This library is free software: you can redistribute it and/or modify
8 * it under the terms of the GNU Lesser General Public License as published by
9 * the Free Software Foundation, either version 3 of the License, or
10 * (at your option) any later version.
11 *
12 * This library is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU Lesser General Public License for more details.
16 *
17 * You should have received a copy of the GNU Lesser General Public License
18 * along with this library. If not, see <http://www.gnu.org/licenses/>.
19 *
20 */
21 #include "openturns/OT.hxx"
22 #include "openturns/OTtestcode.hxx"
23
24 using namespace OT;
25 using namespace OT::Test;
26
main(int,char * [])27 int main(int, char *[])
28 {
29 TESTPREAMBLE;
30 OStream fullprint(std::cout);
31 try
32 {
33
34 RandomGenerator::SetSeed(0);
35
36 UnsignedInteger inputDimension = 3;
37 //UnsignedInteger outputDimension = 1;
38
39 Description inputName(inputDimension);
40 inputName[0] = "X1";
41 inputName[1] = "X2";
42 inputName[2] = "X3";
43 Description formula(1);
44 formula[0] = "sin(pi_*X1)+7*sin(pi_*X2)*sin(pi_*X2)+0.1*((pi_*X3)*(pi_*X3)*(pi_*X3)*(pi_*X3))*sin(pi_*X1)";
45
46 SymbolicFunction model(inputName, formula);
47
48 ComposedDistribution::DistributionCollection marginals(inputDimension);
49 marginals[0] = Uniform(-1.0, 1.0);
50 // marginals[0].setDescription("Marginal 1");
51 marginals[1] = Uniform(-1.0, 1.0);
52 // marginals[1].setDescription("Marginal 2");
53 marginals[2] = Uniform(-1.0, 1.0);
54 // marginals[2].setDescription("Marginal 3");
55 ComposedDistribution maDistribution(ComposedDistribution(marginals, IndependentCopula(inputDimension)));
56
57
58 const UnsignedInteger size = 10000;
59 const UnsignedInteger nr_bootstrap = 100;
60 const Scalar confidence_level = 0.95;
61
62 Description methods;
63 methods.add("MonteCarlo");
64 methods.add("LHS");
65 methods.add("QMC");
66 for (UnsignedInteger i = 0; i < methods.getSize(); ++i)
67 {
68 ResourceMap::SetAsString("SobolIndicesExperiment-SamplingMethod", methods[i]);
69 fullprint << "Sampling method=" << methods[i] << std::endl;
70 const SobolIndicesExperiment sobolExperiment(maDistribution, size, true);
71 const Sample inputDesign(sobolExperiment.generate());
72 const Sample outputDesign(model(inputDesign));
73
74 {
75 SaltelliSensitivityAlgorithm sensitivitySobol(inputDesign, outputDesign, size);
76
77 const SymmetricMatrix secondOrderIndices( sensitivitySobol.getSecondOrderIndices() );
78 const Point firstOrderIndices(sensitivitySobol.getFirstOrderIndices());
79 const Point totalOrderIndices(sensitivitySobol.getTotalOrderIndices());
80
81 fullprint << "Method = " << sensitivitySobol.getClassName() << std::endl;
82 fullprint << "First order Sobol indice of Y|X1 = " << firstOrderIndices[0] << std::endl;
83 fullprint << "Total order Sobol indice of Y|X3 = " << totalOrderIndices[2] << std::endl;
84 fullprint << "Second order Sobol indice of Y|X1,X3 = " << secondOrderIndices(0, 2) << std::endl;
85 // Confidence interval
86 sensitivitySobol.setBootstrapSize(nr_bootstrap);
87 sensitivitySobol.setConfidenceLevel(confidence_level);
88
89 const Interval confidenceIntervalFirstOrder(sensitivitySobol.getFirstOrderIndicesInterval());
90 const Interval confidenceIntervalTotalOrder(sensitivitySobol.getTotalOrderIndicesInterval());
91 fullprint << "Confidence interval of first order Y|X1 = [" << confidenceIntervalFirstOrder.getLowerBound()[0]
92 << ", " << confidenceIntervalFirstOrder.getUpperBound()[0] << "]" << std::endl;
93 fullprint << "Confidence interval of total order Y|X3 = [" << confidenceIntervalTotalOrder.getLowerBound()[2]
94 << ", " << confidenceIntervalTotalOrder.getUpperBound()[2] << "]" << std::endl;
95 }
96
97 {
98 JansenSensitivityAlgorithm sensitivitySobol(inputDesign, outputDesign, size);
99
100 const SymmetricMatrix secondOrderIndices( sensitivitySobol.getSecondOrderIndices() );
101 const Point firstOrderIndices(sensitivitySobol.getFirstOrderIndices());
102 const Point totalOrderIndices(sensitivitySobol.getTotalOrderIndices());
103
104 fullprint << "Method = " << sensitivitySobol.getClassName() << std::endl;
105 fullprint << "First order Sobol indice of Y|X1 = " << firstOrderIndices[0] << std::endl;
106 fullprint << "Total order Sobol indice of Y|X3 = " << totalOrderIndices[2] << std::endl;
107 fullprint << "Second order Sobol indice of Y|X1,X3 = " << secondOrderIndices(0, 2) << std::endl;
108 // Confidence interval
109 sensitivitySobol.setBootstrapSize(nr_bootstrap);
110 sensitivitySobol.setConfidenceLevel(confidence_level);
111
112 const Interval confidenceIntervalFirstOrder(sensitivitySobol.getFirstOrderIndicesInterval());
113 const Interval confidenceIntervalTotalOrder(sensitivitySobol.getTotalOrderIndicesInterval());
114 fullprint << "Confidence interval of first order Y|X1 = [" << confidenceIntervalFirstOrder.getLowerBound()[0]
115 << ", " << confidenceIntervalFirstOrder.getUpperBound()[0] << "]" << std::endl;
116 fullprint << "Confidence interval of total order Y|X3 = [" << confidenceIntervalTotalOrder.getLowerBound()[2]
117 << ", " << confidenceIntervalTotalOrder.getUpperBound()[2] << "]" << std::endl;
118 }
119 {
120 MauntzKucherenkoSensitivityAlgorithm sensitivitySobol(inputDesign, outputDesign, size);
121
122 const SymmetricMatrix secondOrderIndices( sensitivitySobol.getSecondOrderIndices() );
123 const Point firstOrderIndices(sensitivitySobol.getFirstOrderIndices());
124 const Point totalOrderIndices(sensitivitySobol.getTotalOrderIndices());
125
126 fullprint << "Method = " << sensitivitySobol.getClassName() << std::endl;
127 fullprint << "First order Sobol indice of Y|X1 = " << firstOrderIndices[0] << std::endl;
128 fullprint << "Total order Sobol indice of Y|X3 = " << totalOrderIndices[2] << std::endl;
129 fullprint << "Second order Sobol indice of Y|X1,X3 = " << secondOrderIndices(0, 2) << std::endl;
130 // Confidence interval
131 sensitivitySobol.setBootstrapSize(nr_bootstrap);
132 sensitivitySobol.setConfidenceLevel(confidence_level);
133
134 const Interval confidenceIntervalFirstOrder(sensitivitySobol.getFirstOrderIndicesInterval());
135 const Interval confidenceIntervalTotalOrder(sensitivitySobol.getTotalOrderIndicesInterval());
136 fullprint << "Confidence interval of first order Y|X1 = [" << confidenceIntervalFirstOrder.getLowerBound()[0]
137 << ", " << confidenceIntervalFirstOrder.getUpperBound()[0] << "]" << std::endl;
138 fullprint << "Confidence interval of total order Y|X3 = [" << confidenceIntervalTotalOrder.getLowerBound()[2]
139 << ", " << confidenceIntervalTotalOrder.getUpperBound()[2] << "]" << std::endl;
140 }
141 {
142 MartinezSensitivityAlgorithm sensitivitySobol(inputDesign, outputDesign, size);
143 const SymmetricMatrix secondOrderIndices( sensitivitySobol.getSecondOrderIndices() );
144 const Point firstOrderIndices(sensitivitySobol.getFirstOrderIndices());
145 const Point totalOrderIndices(sensitivitySobol.getTotalOrderIndices());
146
147 fullprint << "Method = " << sensitivitySobol.getClassName() << std::endl;
148 fullprint << "First order Sobol indice of Y|X1 = " << firstOrderIndices[0] << std::endl;
149 fullprint << "Total order Sobol indice of Y|X3 = " << totalOrderIndices[2] << std::endl;
150 fullprint << "Second order Sobol indice of Y|X1,X3 = " << secondOrderIndices(0, 2) << std::endl;
151 // Confidence interval
152 sensitivitySobol.setBootstrapSize(nr_bootstrap);
153 sensitivitySobol.setConfidenceLevel(confidence_level);
154
155 const Interval confidenceIntervalFirstOrder(sensitivitySobol.getFirstOrderIndicesInterval());
156 const Interval confidenceIntervalTotalOrder(sensitivitySobol.getTotalOrderIndicesInterval());
157 fullprint << "Confidence interval of first order Y|X1 = [" << confidenceIntervalFirstOrder.getLowerBound()[0]
158 << ", " << confidenceIntervalFirstOrder.getUpperBound()[0] << "]" << std::endl;
159 fullprint << "Confidence interval of total order Y|X3 = [" << confidenceIntervalTotalOrder.getLowerBound()[2]
160 << ", " << confidenceIntervalTotalOrder.getUpperBound()[2] << "]" << std::endl;
161
162
163 fullprint << "Asymptotic estimate" << std::endl;
164 sensitivitySobol.setUseAsymptoticDistribution(true);
165 const Interval asymptoticConfidenceIntervalFirstOrder(sensitivitySobol.getFirstOrderIndicesInterval());
166 const Interval asymptoticConfidenceIntervalTotalOrder(sensitivitySobol.getTotalOrderIndicesInterval());
167 fullprint << "Confidence interval of first order Y|X1 = [" << asymptoticConfidenceIntervalFirstOrder.getLowerBound()[0]
168 << ", " << asymptoticConfidenceIntervalFirstOrder.getUpperBound()[0] << "]" << std::endl;
169 fullprint << "Confidence interval of total order Y|X3 = [" << asymptoticConfidenceIntervalTotalOrder.getLowerBound()[2]
170 << ", " << asymptoticConfidenceIntervalTotalOrder.getUpperBound()[2] << "]" << std::endl;
171 fullprint << "First order indices distribution = " << sensitivitySobol.getFirstOrderIndicesDistribution() << std::endl;
172 fullprint << "Total order indices distribution = " << sensitivitySobol.getTotalOrderIndicesDistribution() << std::endl;
173 }
174 } // Sampling method
175 }
176 catch (TestFailed & ex)
177 {
178 std::cerr << ex << std::endl;
179 return ExitCode::Error;
180 }
181
182 return ExitCode::Success;
183 }
184