1 //                                               -*- C++ -*-
2 /**
3  *  @brief The test file of class RandomMixture for standard methods
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   setRandomGenerator();
32 
33   ResourceMap::SetAsUnsignedInteger("RandomMixture-DefaultMaxSize", 4000000);
34 
35   try
36   {
37     // Create a collection of test-cases and the associated references
38     UnsignedInteger numberOfTests = 3;
39     Collection< Collection< Distribution > > testCases(numberOfTests);
40     Collection< Distribution > references(numberOfTests);
41     testCases[0] = Collection<Distribution>(2);
42     testCases[0][0] = Uniform(-1.0, 3.0);
43     testCases[0][1] = Uniform(-1.0, 3.0);
44     references[0] = Triangular(-2.0, 2.0, 6.0);
45     testCases[1] = Collection<Distribution>(3);
46     testCases[1][0] = Normal();
47     testCases[1][1] = Normal(1.0, 2.0);
48     testCases[1][2] = Normal(-2.0, 2.0);
49     references[1] = Normal(-1.0, 3.0);
50     testCases[2] = Collection<Distribution>(3);
51     testCases[2][0] = Exponential();
52     testCases[2][1] = Exponential();
53     testCases[2][2] = Exponential();
54     references[2] = Gamma(3.0, 1.0, 0.0);
55     fullprint << "testCases=" << testCases << std::endl;
56     fullprint << "references=" << references << std::endl;
57     for (UnsignedInteger testIndex = 0; testIndex < testCases.getSize(); ++testIndex)
58     {
59       // Instanciate one distribution object
60       RandomMixture distribution(testCases[testIndex]);
61       distribution.setBlockMin(5);
62       distribution.setBlockMax(20);
63       Distribution distributionReference(references[testIndex]);
64       fullprint << "Distribution " << distribution << std::endl;
65       std::cout << "Distribution " << distribution << std::endl;
66 
67       // Is this distribution elliptical ?
68       fullprint << "Elliptical = " << (distribution.isElliptical() ? "true" : "false") << std::endl;
69 
70       // Is this distribution continuous ?
71       fullprint << "Continuous = " << (distribution.isContinuous() ? "true" : "false") << std::endl;
72 
73       // Test for realization of distribution
74       Point oneRealization = distribution.getRealization();
75       fullprint << "oneRealization=" << oneRealization << std::endl;
76 
77       // Test for sampling
78       UnsignedInteger size = 10000;
79       Sample oneSample = distribution.getSample( size );
80       fullprint << "oneSample first=" << oneSample[0] << " last=" << oneSample[size - 1] << std::endl;
81       fullprint << "mean=" << oneSample.computeMean() << std::endl;
82       fullprint << "covariance=" << oneSample.computeCovariance() << std::endl;
83 
84       size = 100;
85       for (UnsignedInteger i = 0; i < 2; ++i)
86       {
87         fullprint << "Kolmogorov test for the generator, sample size=" << size << " is " << (FittingTest::Kolmogorov(distribution.getSample(size), distribution).getBinaryQualityMeasure() ? "accepted" : "rejected") << std::endl;
88         size *= 10;
89       }
90 
91       // Define a point
92       Point point(distribution.getDimension(), 0.5);
93       fullprint << "Point= " << point << std::endl;
94 
95       // Show PDF and CDF of point
96       Scalar eps = 1e-5;
97       UnsignedInteger oldPrecision = PlatformInfo::GetNumericalPrecision();
98       PlatformInfo::SetNumericalPrecision(5);
99       Point DDF = distribution.computeDDF(point);
100       fullprint << "ddf      =" << DDF << std::endl;
101       fullprint << "ddf (ref)=" << distributionReference.computeDDF(point) << std::endl;
102       PlatformInfo::SetNumericalPrecision(oldPrecision);
103       Scalar PDF = distribution.computePDF(point);
104       fullprint << "pdf      =" << PDF << std::endl;
105       fullprint << "pdf  (FD)=" << (distribution.computeCDF( point + Point(1, eps) ) - distribution.computeCDF( point  + Point(1, -eps) )) / (2.0 * eps) << std::endl;
106       fullprint << "pdf (ref)=" << distributionReference.computePDF(point) << std::endl;
107       Scalar CDF = distribution.computeCDF( point );
108       fullprint << "cdf      =" << CDF << std::endl;
109       fullprint << "cdf (ref)=" << distributionReference.computeCDF(point) << std::endl;
110       Complex CF = distribution.computeCharacteristicFunction( point[0] );
111       fullprint << "characteristic function=" << CF << std::endl;
112       Complex LCF = distribution.computeLogCharacteristicFunction( point[0] );
113       fullprint << "log characteristic function=" << LCF << std::endl;
114       Point quantile = distribution.computeQuantile( 0.95 );
115       fullprint << "quantile      =" << quantile << std::endl;
116       fullprint << "quantile (ref)=" << distributionReference.computeQuantile(0.95) << std::endl;
117       fullprint << "cdf(quantile)=" << distribution.computeCDF(quantile) << std::endl;
118       Point quantileComp = distribution.computeQuantile( 0.95, true );
119       fullprint << "quantile comp.=" << quantileComp << std::endl;
120       fullprint << "cdfComp(quantileComp)=" << distribution.computeComplementaryCDF(quantileComp) << std::endl;
121       fullprint << "entropy      =" << distribution.computeEntropy() << std::endl;
122       fullprint << "entropy (ref)=" << distributionReference.computeEntropy() << std::endl;
123       fullprint << "entropy (MC)=" << -distribution.computeLogPDF(distribution.getSample(1000000)).computeMean()[0] << std::endl;
124       Point mean = distribution.getMean();
125       fullprint << "mean      =" << mean << std::endl;
126       fullprint << "mean (ref)=" << distributionReference.getMean() << std::endl;
127       Point standardDeviation = distribution.getStandardDeviation();
128       fullprint << "standard deviation      =" << standardDeviation << std::endl;
129       fullprint << "standard deviation (ref)=" << distributionReference.getStandardDeviation() << std::endl;
130       Point skewness = distribution.getSkewness();
131       fullprint << "skewness      =" << skewness << std::endl;
132       fullprint << "skewness (ref)=" << distributionReference.getSkewness() << std::endl;
133       Point kurtosis = distribution.getKurtosis();
134       fullprint << "kurtosis      =" << kurtosis << std::endl;
135       fullprint << "kurtosis (ref)=" << distributionReference.getKurtosis() << std::endl;
136       CovarianceMatrix covariance = distribution.getCovariance();
137       fullprint << "covariance      =" << covariance << std::endl;
138       fullprint << "covariance (ref)=" << distributionReference.getCovariance() << std::endl;
139       RandomMixture::PointWithDescriptionCollection parameters = distribution.getParametersCollection();
140       fullprint << "parameters=" << parameters << std::endl;
141       /*    distribution.setIntegrationNodesNumber(6);
142             for (UnsignedInteger i = 0; i < 6; ++i) fullprint << "standard moment n=" << i << ", value=" << distribution.getStandardMoment(i) << std::endl;*/
143       fullprint << "Standard representative=" << distribution.getStandardRepresentative().__str__() << std::endl;
144       fullprint << "blockMin=" << distribution.getBlockMin() << std::endl;
145       fullprint << "blockMax=" << distribution.getBlockMax() << std::endl;
146       fullprint << "maxSize=" << distribution.getMaxSize() << std::endl;
147       fullprint << "alpha=" << distribution.getAlpha() << std::endl;
148       fullprint << "beta=" << distribution.getBeta() << std::endl;
149     }
150     // Tests of the simplification mechanism
151     Point weights(0);
152     Collection< Distribution > coll(0);
153     //      coll.add(Dirac(0.5));
154     //      weights.add(1.0);
155     coll.add(Normal(1.0, 2.0));
156     weights.add(1.0);
157     coll.add(Normal(2.0, 1.0));
158     weights.add(1.0);
159     coll.add(Uniform(-2.0, 2.0));
160     weights.add(1.0);
161     coll.add(Exponential(2.0, 0.0));
162     weights.add(1.0);
163     //      RandomMixture rm(coll, weights);
164     //      coll.add(rm);
165     //      weights.add(-2.5);
166     coll.add(Gamma(3.0, 4.0, 0.0));
167     weights.add(1.0);
168     RandomMixture distribution(coll, weights);
169     fullprint << "distribution=" << distribution << std::endl;
170     fullprint << "distribution=" << distribution.__str__() << std::endl;
171     for (UnsignedInteger i = 0; i < 30; ++i)
172     {
173       Scalar x = -12.0 + i;
174       fullprint << "pdf(" << x << ")=" << distribution.computePDF(x) << std::endl;
175     }
176     Graph graph(distribution.drawPDF());
177     Distribution ks(KernelSmoothing().build(distribution.getSample(1000000)));
178     graph.add(ks.drawPDF());
179     Description colors(2);
180     colors[0] = "red";
181     colors[1] = "green";
182     graph.setColors(colors);
183     //     graph.draw("validation");
184     // Test for the projection
185     Collection<DistributionFactory> collFactories(0);
186     collFactories.add(UniformFactory());
187     collFactories.add(NormalFactory());
188     collFactories.add(TriangularFactory());
189     collFactories.add(ExponentialFactory());
190     collFactories.add(GammaFactory());
191 //     collFactories.add(TrapezoidalFactory());
192     Point norms;
193     Collection< Distribution > result(distribution.project(collFactories, norms));
194     fullprint << "projections=" << result << std::endl;
195     fullprint << "norms=" << norms << std::endl;
196     //------------------------------ Multivariate tests ------------------------------//
197     // 2D RandomMixture
198     Collection< Distribution > collection(0);
199     collection.add(Normal(0.0, 1.0));
200     collection.add(Normal(0.0, 1.0));
201     collection.add(Normal(0.0, 1.0));
202 
203     Matrix weightMatrix(2, 3);
204     weightMatrix(0, 0) = 1.0;
205     weightMatrix(0, 1) = -2.0;
206     weightMatrix(0, 2) = 1.0;
207     weightMatrix(1, 0) = 1.0;
208     weightMatrix(1, 1) = 1.0;
209     weightMatrix(1, 2) = -3.0;
210 
211     // Build the RandomMixture
212     RandomMixture distribution2D(collection, weightMatrix);
213     fullprint << "distribution = " << distribution2D << std::endl;
214     fullprint << "range = " << distribution2D.getRange() << std::endl;
215     fullprint << "mean = " <<  distribution2D.getMean() << std::endl;
216     fullprint << "cov = " << distribution2D.getCovariance() << std::endl;
217     fullprint << "sigma = " << distribution2D.getStandardDeviation() << std::endl;
218     fullprint << "entropy      =" << distribution.computeEntropy() << std::endl;
219     distribution2D.setBlockMin(3);
220     distribution2D.setBlockMax(10);
221 
222     // Build a grid for validation
223     const Scalar xMin = distribution2D.getRange().getLowerBound()[0];
224     const Scalar xMax = distribution2D.getRange().getUpperBound()[0];
225     const Scalar yMin = distribution2D.getRange().getLowerBound()[1];
226     const Scalar yMax = distribution2D.getRange().getUpperBound()[1];
227     // Number of points of discretization
228     const UnsignedInteger nx = 4;
229     const UnsignedInteger ny = 4;
230     Point boxParameters(2);
231     boxParameters[0] = nx;
232     boxParameters[1] = ny;
233     Box boxGrid(boxParameters);
234     Sample grid(boxGrid.generate());
235     // scaling box grid
236     Point scaleFactor(2);
237     scaleFactor[0] = 0.25 * (xMax - xMin);
238     scaleFactor[1] = 0.25 * (yMax - yMin);
239     grid *= scaleFactor;
240     //translating
241     Point translateFactor(2);
242     translateFactor[0] = distribution2D.getMean()[0];
243     translateFactor[1] = distribution2D.getMean()[1];
244     grid += translateFactor;
245     // Compute PDF
246     // parameters for theoritical PDF, obtained thanks to Maple
247     const Scalar factor = sqrt(2.0) / (20 * M_PI);
248     for (UnsignedInteger index = 0; index < grid.getSize(); ++ index)
249     {
250       const Point point(grid[index]);
251       const Scalar PDF = distribution2D.computePDF(point);
252       // Very small values are not very accurate on x86, skip them
253       if (PDF < 1.e-12) continue;
254       fullprint << "pdf      =" << PDF << std::endl;
255       const Scalar y = point[1];
256       const Scalar x = point[0];
257       fullprint << "pdf (ref)=" << factor * exp(-3.0 / 50.0 * y * y - 2.0 / 25 * x * y - 11.0 / 100 * x * x) << std::endl;
258     }
259     // 2D test, but too much CPU consuming
260 
261     Collection< Distribution > collUniforme(0);
262     collUniforme.add(Uniform(0, 1));
263     collUniforme.add(Uniform(0, 1));
264     collUniforme.add(Uniform(0, 1));
265     // Build the RandomMixture
266     RandomMixture dist_2D(collUniforme, weightMatrix);
267     dist_2D.setBlockMin(3);
268     dist_2D.setBlockMax(8);
269 
270     fullprint << "new distribution = " << dist_2D << std::endl;
271     fullprint << "range = " << dist_2D.getRange() << std::endl;
272     fullprint << "mean = " <<  dist_2D.getMean() << std::endl;
273     fullprint << "cov = " << dist_2D.getCovariance() << std::endl;
274     fullprint << "sigma = " << dist_2D.getStandardDeviation() << std::endl;
275 
276     // Discretization on 2D grid [mu, mu+\sigma]
277     Sample newGrid(boxGrid.generate());
278     // scaling box grid
279     newGrid *= dist_2D.getStandardDeviation();
280     //translating
281     newGrid += dist_2D.getMean();
282     // Compute PDF
283     for (UnsignedInteger index = 0; index < newGrid.getSize(); ++ index)
284     {
285       const Point point(newGrid[index]);
286       const Scalar PDF = dist_2D.computePDF(point);
287       fullprint << "pdf      =" << PDF << std::endl;
288     }
289     // 3D test
290     ResourceMap::SetAsUnsignedInteger("RandomMixture-DefaultMaxSize", 8290688);
291     Collection<Distribution> collectionMixture(0);
292     collectionMixture.add(Normal(2.0, 1.0));
293     collectionMixture.add(Normal(-2.0, 1.0));
294     const Mixture mixture(collectionMixture);
295     Collection<Distribution> collection3D(0);
296     collection3D.add(Normal(0.0, 1.0));
297     collection3D.add(mixture);
298     collection3D.add(Uniform(0, 1));
299     collection3D.add(Uniform(0, 1));
300     // Set weights
301     weightMatrix = Matrix(3, 4);
302     weightMatrix(0, 0) = 1.0;
303     weightMatrix(0, 1) = -0.05;
304     weightMatrix(0, 2) = 1.0;
305     weightMatrix(0, 3) = -0.5;
306 
307     weightMatrix(1, 0) = 0.5;
308     weightMatrix(1, 1) = 1.0;
309     weightMatrix(1, 2) = -0.05;
310     weightMatrix(1, 3) = 0.3;
311 
312     weightMatrix(2, 0) = -0.5;
313     weightMatrix(2, 1) = -0.1;
314     weightMatrix(2, 2) = 1.2;
315     weightMatrix(2, 3) = -0.8;
316 
317     RandomMixture dist_3D(collection3D, weightMatrix);
318     dist_3D.setBlockMin(3);
319     dist_3D.setBlockMax(6);
320 
321     fullprint << "3D distribution = " << dist_3D << std::endl;
322     fullprint << "range = " << dist_3D.getRange() << std::endl;
323     fullprint << "mean = " <<  dist_3D.getMean() << std::endl;
324     fullprint << "cov = " << dist_3D.getCovariance() << std::endl;
325     fullprint << "sigma = " << dist_3D.getStandardDeviation() << std::endl;
326     fullprint << "entropy      =" << distribution.computeEntropy() << std::endl;
327 
328     // Total number of points (is (2+2)**3)
329     // Test is CPU consuming
330     // Number of points of discretization
331     const UnsignedInteger N = 2;
332     Point box3DParameters(3, N);
333     Box box3D(box3DParameters);
334     // Grid ==> (mu, mu+sigma)
335     Sample grid3D(box3D.generate());
336     //scaling
337     grid3D *= dist_3D.getStandardDeviation();
338     // translating
339     grid3D += dist_3D.getMean();
340     for (UnsignedInteger index = 0; index < grid3D.getSize() / 4; ++ index)
341     {
342       const Point point(grid3D[4 * index]);
343       const Scalar PDF = dist_3D.computePDF(point);
344       fullprint << "pdf      =" << PDF << std::endl;
345     }
346     // Test for ticket 882 (only one Dirac)
347     // The segfault was triggered during the construction...
348     RandomMixture mixture2(Collection<Distribution>(1, Dirac()));
349     // After what it was impossible to draw the PDF or the CDF due to a lack of support computation
350     Graph graphPDF(mixture2.drawPDF());
351     Graph graphCDF(mixture2.drawCDF());
352     // Test computeQuantile for the specific case of an analytical 1D mixture
353     RandomMixture case1(Collection<Distribution>(1, ChiSquare()), Point(1, 0.1));
354     Scalar q = case1.computeQuantile(0.95)[0];
355     fullprint << "case 1, q=" << q << std::endl;
356     q = case1.computeQuantile(0.95, true)[0];
357     fullprint << "case 1, q comp=" << q << std::endl;
358     RandomMixture case2(Collection<Distribution>(1, ChiSquare()), Point(1, -0.1));
359     q = case2.computeQuantile(0.95)[0];
360     fullprint << "case 2, q=" << q << std::endl;
361     q = case2.computeQuantile(0.95, true)[0];
362     fullprint << "case 2, q comp=" << q << std::endl;
363     // For ticket 953
364     {
365       TruncatedDistribution atom1(Uniform(0.0, 1.0), 0.0, 1.0);
366       Uniform atom2(0.0, 2.0);
367       Distribution sum(atom1 + atom2);
368       fullprint << "sum=" << sum << std::endl;
369       fullprint << "CDF=" << sum.computeCDF(2.0) << std::endl;
370       fullprint << "quantile=" << sum.computeQuantile(0.2) << std::endl;
371     }
372     {
373       Scalar minS = 0.2;
374       Scalar maxS = 10.0;
375       Scalar muS = (std::log(minS) + std::log(maxS)) / 2.0;
376       Scalar sigma = (std::log(maxS) - muS) / 3.0;
377       TruncatedDistribution atom1(LogNormal(muS, sigma), minS, maxS);
378       Uniform atom2(0.0, 2.0);
379       Distribution sum(atom1 + atom2);
380       fullprint << "sum=" << sum << std::endl;
381       fullprint << "CDF=" << sum.computeCDF(2.0) << std::endl;
382       fullprint << "quantile=" << sum.computeQuantile(0.2) << std::endl;
383     }
384     // For ticket 1129
385     {
386       distribution = RandomMixture(Collection<Distribution>(200, Uniform()));
387       fullprint << "CDF(0)=" << distribution.computeCDF(0.0) << std::endl;
388     }
389   }
390   catch (TestFailed & ex)
391   {
392     std::cerr << ex << std::endl;
393     return ExitCode::Error;
394   }
395 
396   return ExitCode::Success;
397 }
398