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
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
|
#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# Instantiate one distribution object
dimension = 3
meanPoint = ot.Point(dimension, 1.0)
meanPoint[0] = 0.5
meanPoint[1] = -0.5
sigma = ot.Point(dimension, 1.0)
sigma[0] = 2.0
sigma[1] = 3.0
R = ot.CorrelationMatrix(dimension)
for i in range(1, dimension):
R[i, i - 1] = 0.5
# Create a collection of distribution
aCollection = ot.DistributionCollection()
aCollection.add(ot.Normal(meanPoint, sigma, R))
meanPoint += ot.Point(meanPoint.getDimension(), 1.0)
aCollection.add(ot.Normal(meanPoint, sigma, R))
meanPoint += ot.Point(meanPoint.getDimension(), 1.0)
aCollection.add(ot.Normal(meanPoint, sigma, R))
# Instantiate one distribution object
distribution = ot.Mixture(aCollection, ot.Point(aCollection.getSize(), 2.0))
print("Distribution ", repr(distribution))
print("Weights = ", repr(distribution.getWeights()))
weights = distribution.getWeights()
weights[0] = 2.0 * weights[0]
distribution.setWeights(weights)
print("After update, new weights = ", repr(distribution.getWeights()))
distribution = ot.Mixture(aCollection)
print("Distribution ", repr(distribution))
# Is this distribution elliptical ?
print("Elliptical = ", distribution.isElliptical())
# Is this distribution continuous ?
print("Continuous = ", distribution.isContinuous())
# Test for realization of distribution
oneRealization = distribution.getRealization()
print("oneRealization=", repr(oneRealization))
# Test for sampling
size = 1000
oneSample = distribution.getSample(size)
print("oneSample first=", repr(oneSample[0]), " last=", repr(oneSample[size - 1]))
print("mean=", repr(oneSample.computeMean()))
print("covariance=", repr(oneSample.computeCovariance()))
# Define a point
point = ot.Point(distribution.getDimension(), 1.0)
print("Point= ", repr(point))
# derivative of PDF with regards its arguments
DDF = distribution.computeDDF(point)
print("ddf =", repr(DDF))
# PDF value
LPDF = distribution.computeLogPDF(point)
print("log pdf=%.6f" % LPDF)
PDF = distribution.computePDF(point)
print("pdf =%.6f" % PDF)
x = 0.6
y = [0.2] * (dimension - 1)
print("conditional PDF%.6f" % distribution.computeConditionalPDF(x, y))
print("conditional CDF%.6f" % distribution.computeConditionalCDF(x, y))
print("conditional quantile%.6f" % distribution.computeConditionalQuantile(x, y))
pt = ot.Point([i + 1.5 for i in range(dimension)])
print(
"sequential conditional PDF=", distribution.computeSequentialConditionalPDF(point)
)
resCDF = distribution.computeSequentialConditionalCDF(pt)
print("sequential conditional CDF(", pt, ")=", resCDF)
print(
"sequential conditional quantile(",
resCDF,
")=",
distribution.computeSequentialConditionalQuantile(resCDF),
)
# derivative of the PDF with regards the parameters of the distribution
CDF = distribution.computeCDF(point)
print("cdf=%.6f" % CDF)
CCDF = distribution.computeComplementaryCDF(point)
print("ccdf=%.6f" % CCDF)
PDFgr = distribution.computePDFGradient(point)
assert distribution.computePDFGradient([point]).getDimension() == len(PDFgr)
print("pdf gradient=", PDFgr)
# derivative of the PDF with regards the parameters of the distribution
CDFgr = distribution.computeCDFGradient(point)
print("cdf gradient=", CDFgr)
# quantile
quantile = distribution.computeQuantile(0.95)
print("quantile=", repr(quantile))
print("cdf(quantile)=%.6f" % distribution.computeCDF(quantile))
# Get 95% survival function
inverseSurvival = ot.Point(distribution.computeInverseSurvivalFunction(0.95))
print("InverseSurvival=", repr(inverseSurvival))
print(
"Survival(inverseSurvival)=%.6f"
% distribution.computeSurvivalFunction(inverseSurvival)
)
# Confidence regions
if distribution.getDimension() <= 2:
(
interval,
threshold,
) = distribution.computeMinimumVolumeIntervalWithMarginalProbability(0.95)
print("Minimum volume interval=", interval)
print("threshold=", ot.Point(1, threshold))
levelSet, beta = distribution.computeMinimumVolumeLevelSetWithThreshold(0.95)
print("Minimum volume level set=", levelSet)
print("beta=", ot.Point(1, beta))
(
interval,
beta,
) = distribution.computeBilateralConfidenceIntervalWithMarginalProbability(0.95)
print("Bilateral confidence interval=", interval)
print("beta=", ot.Point(1, beta))
(
interval,
beta,
) = distribution.computeUnilateralConfidenceIntervalWithMarginalProbability(
0.95, False
)
print("Unilateral confidence interval (lower tail)=", interval)
print("beta=", ot.Point(1, beta))
(
interval,
beta,
) = distribution.computeUnilateralConfidenceIntervalWithMarginalProbability(
0.95, True
)
print("Unilateral confidence interval (upper tail)=", interval)
print("beta=", ot.Point(1, beta))
mean = distribution.getMean()
print("mean=", repr(mean))
covariance = distribution.getCovariance()
print("covariance=", repr(covariance))
parameters = distribution.getParametersCollection()
print("parameters=", repr(parameters))
parameter = distribution.getParameter()
print("parameter=", parameter)
parameterDescription = distribution.getParameterDescription()
print("parameter description=", parameterDescription)
distribution.setParameter(parameter)
print("Standard representative=", distribution.getStandardRepresentative())
# Constructor with separate weights. Also check small weights removal
weights = [1.0e-20, 2.5, 32.0]
atoms = ot.DistributionCollection(
[ot.Normal(1.0, 1.0), ot.Normal(2.0, 2.0), ot.Normal(3.0, 3.0)]
)
newMixture = ot.Mixture(atoms, weights)
print("newMixture pdf= %.12g" % newMixture.computePDF(2.5))
print("atoms kept in mixture=", newMixture.getDistributionCollection())
print("newMixture=", newMixture)
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(distribution)
validation.skipMoments() # slow
validation.skipCorrelation() # slow
validation.run()
# check for non stricly increasing CDF: must return the inf of [1, 2]
distribution = ot.Mixture([ot.Uniform(0.0, 1.0), ot.Uniform(2.0, 3.0)])
q = distribution.computeQuantile(0.5)[0]
print(f"q={q:.6f}")
|
