1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
|
// -*- C++ -*-
/**
* @brief The test file of class Chi for standard methods
*
* Copyright 2005-2025 Airbus-EDF-IMACS-ONERA-Phimeca
*
* This library is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this library. If not, see <http://www.gnu.org/licenses/>.
*
*/
#include "openturns/OT.hxx"
#include "openturns/OTtestcode.hxx"
using namespace OT;
using namespace OT::Test;
class TestObject : public Chi
{
public:
TestObject() : Chi(1.5) {}
virtual ~TestObject() {}
};
int main(int, char *[])
{
TESTPREAMBLE;
OStream fullprint(std::cout);
try
{
// Test basic functionnalities
checkClassWithClassName<TestObject>();
// Instantiate one distribution object
Chi distribution(1.5);
fullprint << "Distribution " << distribution << std::endl;
std::cout << "Distribution " << distribution << std::endl;
// Is this distribution elliptical ?
fullprint << "Elliptical = " << (distribution.isElliptical() ? "true" : "false") << std::endl;
// Is this distribution continuous ?
fullprint << "Continuous = " << (distribution.isContinuous() ? "true" : "false") << std::endl;
// Test for realization of distribution
Point oneRealization = distribution.getRealization();
fullprint << "oneRealization=" << oneRealization << std::endl;
// Test for sampling
UnsignedInteger size = 10000;
Sample oneSample = distribution.getSample( size );
fullprint << "oneSample first=" << oneSample[0] << " last=" << oneSample[size - 1] << std::endl;
fullprint << "mean=" << oneSample.computeMean() << std::endl;
fullprint << "covariance=" << oneSample.computeCovariance() << std::endl;
size = 100;
for (UnsignedInteger i = 0; i < 2; ++i)
{
fullprint << "Kolmogorov test for the generator, sample size=" << size << " is " << (FittingTest::Kolmogorov(distribution.getSample(size), distribution).getBinaryQualityMeasure() ? "accepted" : "rejected") << std::endl;
size *= 10;
}
// Define a point
Point point( distribution.getDimension(), 1.0 );
fullprint << "Point= " << point << std::endl;
// Show PDF and CDF of point
Scalar eps = 1e-5;
Point DDF = distribution.computeDDF( point );
fullprint << "ddf =" << DDF << std::endl;
Scalar LPDF = distribution.computeLogPDF( point );
fullprint << "log pdf=" << LPDF << std::endl;
Scalar PDF = distribution.computePDF( point );
fullprint << "pdf =" << PDF << std::endl;
fullprint << "pdf (FD)=" << (distribution.computeCDF( point + Point(1, eps) ) - distribution.computeCDF( point + Point(1, -eps) )) / (2.0 * eps) << std::endl;
Scalar CDF = distribution.computeCDF( point );
fullprint << "cdf=" << CDF << std::endl;
Scalar CCDF = distribution.computeComplementaryCDF( point );
fullprint << "ccdf=" << CCDF << std::endl;
Scalar Survival = distribution.computeSurvivalFunction( point );
fullprint << "survival=" << Survival << std::endl;
Point InverseSurvival = distribution.computeInverseSurvivalFunction(0.95);
fullprint << "Inverse survival=" << InverseSurvival << std::endl;
fullprint << "Survival(inverse survival)=" << distribution.computeSurvivalFunction(InverseSurvival) << std::endl;
Complex CF = distribution.computeCharacteristicFunction( point[0] );
fullprint << "characteristic function=" << CF << std::endl;
Complex LCF = distribution.computeLogCharacteristicFunction( point[0] );
fullprint << "log characteristic function=" << LCF << std::endl;
Point PDFgr = distribution.computePDFGradient( point );
fullprint << "pdf gradient =" << PDFgr << std::endl;
Point PDFgrFD(1);
PDFgrFD[0] = (Chi(distribution.getNu() + eps).computePDF(point) -
Chi(distribution.getNu() - eps).computePDF(point)) / (2.0 * eps);
fullprint << "pdf gradient (FD)=" << PDFgrFD << std::endl;
Point CDFgr = distribution.computeCDFGradient( point );
fullprint << "cdf gradient =" << CDFgr << std::endl;
Point CDFgrFD(1);
CDFgrFD[0] = (Chi(distribution.getNu() + eps).computeCDF(point) -
Chi(distribution.getNu() - eps).computeCDF(point)) / (2.0 * eps);
fullprint << "cdf gradient (FD)=" << CDFgrFD << std::endl;
Point quantile = distribution.computeQuantile( 0.95 );
fullprint << "quantile=" << quantile << std::endl;
fullprint << "cdf(quantile)=" << distribution.computeCDF(quantile) << std::endl;
// Confidence regions
Scalar threshold;
fullprint << "Minimum volume interval=" << distribution.computeMinimumVolumeIntervalWithMarginalProbability(0.95, threshold) << std::endl;
fullprint << "threshold=" << threshold << std::endl;
Scalar beta;
LevelSet levelSet(distribution.computeMinimumVolumeLevelSetWithThreshold(0.95, beta));
fullprint << "Minimum volume level set=" << levelSet << std::endl;
fullprint << "beta=" << beta << std::endl;
fullprint << "Bilateral confidence interval=" << distribution.computeBilateralConfidenceIntervalWithMarginalProbability(0.95, beta) << std::endl;
fullprint << "beta=" << beta << std::endl;
fullprint << "Unilateral confidence interval (lower tail)=" << distribution.computeUnilateralConfidenceIntervalWithMarginalProbability(0.95, false, beta) << std::endl;
fullprint << "beta=" << beta << std::endl;
fullprint << "Unilateral confidence interval (upper tail)=" << distribution.computeUnilateralConfidenceIntervalWithMarginalProbability(0.95, true, beta) << std::endl;
fullprint << "beta=" << beta << std::endl;
fullprint << "entropy=" << distribution.computeEntropy() << std::endl;
fullprint << "entropy (MC)=" << -distribution.computeLogPDF(distribution.getSample(1000000)).computeMean()[0] << std::endl;
Point mean = distribution.getMean();
fullprint << "mean=" << mean << std::endl;
CovarianceMatrix covariance = distribution.getCovariance();
fullprint << "covariance=" << covariance << std::endl;
CovarianceMatrix correlation = distribution.getCorrelation();
fullprint << "correlation=" << correlation << std::endl;
CovarianceMatrix spearman = distribution.getSpearmanCorrelation();
fullprint << "spearman=" << spearman << std::endl;
CovarianceMatrix kendall = distribution.getKendallTau();
fullprint << "kendall=" << kendall << std::endl;
Chi::PointWithDescriptionCollection parameters = distribution.getParametersCollection();
fullprint << "parameters=" << parameters << std::endl;
fullprint << "Standard representative=" << distribution.getStandardRepresentative().__str__() << std::endl;
// Specific to this distribution
Scalar nu = distribution.getNu();
fullprint << "nu=" << nu << std::endl;
Point standardDeviation = distribution.getStandardDeviation();
fullprint << "standard deviation=" << standardDeviation << std::endl;
Point skewness = distribution.getSkewness();
fullprint << "skewness=" << skewness << std::endl;
Point kurtosis = distribution.getKurtosis();
fullprint << "kurtosis=" << kurtosis << std::endl;
}
catch (TestFailed & ex)
{
std::cerr << ex << std::endl;
return ExitCode::Error;
}
return ExitCode::Success;
}
|
