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
|
#! /usr/bin/env python
from __future__ import print_function
from openturns import *
TESTPREAMBLE()
RandomGenerator.SetSeed(0)
try:
# Instanciate one distribution object
dimension = 3
meanPoint = NumericalPoint(dimension, 1.0)
meanPoint[0] = 0.5
meanPoint[1] = -0.5
sigma = NumericalPoint(dimension, 1.0)
sigma[0] = 2.0
sigma[1] = 3.0
R = CorrelationMatrix(dimension)
for i in range(1, dimension):
R[i, i - 1] = 0.5
# Create a collection of distribution
aCollection = DistributionCollection()
aCollection.add(Normal(meanPoint, sigma, R))
meanPoint += NumericalPoint(meanPoint.getDimension(), 1.0)
aCollection.add(Normal(meanPoint, sigma, R))
meanPoint += NumericalPoint(meanPoint.getDimension(), 1.0)
aCollection.add(Normal(meanPoint, sigma, R))
# Instanciate one distribution object
distribution = Mixture(
aCollection, NumericalPoint(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 = 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 = NumericalPoint(distribution.getDimension(), 1.0)
print("Point= ", repr(point))
# Show PDF and CDF of point
eps = 1e-5
# derivative of PDF with regards its arguments
DDF = distribution.computeDDF(point)
print("ddf =", repr(DDF))
# by the finite difference technique
ddfFD = NumericalPoint(dimension)
for i in range(dimension):
left = NumericalPoint(point)
left[i] += eps
right = NumericalPoint(point)
right[i] -= eps
ddfFD[i] = (distribution.computePDF(left) -
distribution.computePDF(right)) / (2.0 * eps)
print("ddf (FD)=", repr(ddfFD))
# PDF value
LPDF = distribution.computeLogPDF(point)
print("log pdf=%.6f" % LPDF)
PDF = distribution.computePDF(point)
print("pdf =%.6f" % PDF)
# by the finite difference technique from CDF
if (dimension == 1):
print("pdf (FD)=%.6f" % ((distribution.computeCDF(point + NumericalPoint(1, eps)) -
distribution.computeCDF(point + NumericalPoint(1, -eps))) / (2.0 * eps)))
# 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 )
# print "pdf gradient =" , repr(PDFgr)
# by the finite difference technique
# PDFgrFD = NumericalPoint(4)
# PDFgrFD[0] = (Mixture(distribution.getR() + eps, distribution.getT(), distribution.getA(), distribution.getB()).computePDF(point) -
# Mixture(distribution.getR() - eps, distribution.getT(), distribution.getA(), distribution.getB()).computePDF(point)) / (2.0 * eps)
# PDFgrFD[1] = (Mixture(distribution.getR(), distribution.getT() + eps, distribution.getA(), distribution.getB()).computePDF(point) -
# Mixture(distribution.getR(), distribution.getT() - eps, distribution.getA(), distribution.getB()).computePDF(point)) / (2.0 * eps)
# PDFgrFD[2] = (Mixture(distribution.getR(), distribution.getT(), distribution.getA() + eps, distribution.getB()).computePDF(point) -
# Mixture(distribution.getR(), distribution.getT(), distribution.getA() - eps, distribution.getB()).computePDF(point)) / (2.0 * eps)
# PDFgrFD[3] = (Mixture(distribution.getR(), distribution.getT(), distribution.getA(), distribution.getB() + eps).computePDF(point) -
# Mixture(distribution.getR(), distribution.getT(), distribution.getA(), distribution.getB() - eps).computePDF(point)) / (2.0 * eps)
# print "pdf gradient (FD)=" , repr(PDFgrFD)
# derivative of the PDF with regards the parameters of the distribution
# CDFgr = distribution.computeCDFGradient( point )
# print "cdf gradient =" , repr(CDFgr)
# CDFgrFD = NumericalPoint(4)
# CDFgrFD[0] = (Mixture(distribution.getR() + eps, distribution.getT(), distribution.getA(), distribution.getB()).computeCDF(point) -
# Mixture(distribution.getR() - eps, distribution.getT(), distribution.getA(), distribution.getB()).computeCDF(point)) / (2.0 * eps)
# CDFgrFD[1] = (Mixture(distribution.getR(), distribution.getT() + eps, distribution.getA(), distribution.getB()).computeCDF(point) -
# Mixture(distribution.getR(), distribution.getT() - eps, distribution.getA(), distribution.getB()).computeCDF(point)) / (2.0 * eps)
# CDFgrFD[2] = (Mixture(distribution.getR(), distribution.getT(), distribution.getA() + eps, distribution.getB()).computeCDF(point) -
# Mixture(distribution.getR(), distribution.getT(), distribution.getA() - eps, distribution.getB()).computeCDF(point)) / (2.0 * eps)
# CDFgrFD[3] = (Mixture(distribution.getR(), distribution.getT(), distribution.getA(), distribution.getB() + eps).computeCDF(point) -
# Mixture(distribution.getR(), distribution.getT(), distribution.getA(), distribution.getB() - eps).computeCDF(point)) / (2.0 * eps)
# print "cdf gradient (FD)=", repr(CDFgrFD)
# quantile
quantile = distribution.computeQuantile(0.95)
print("quantile=", repr(quantile))
print("cdf(quantile)=%.6f" % distribution.computeCDF(quantile))
mean = distribution.getMean()
print("mean=", repr(mean))
covariance = distribution.getCovariance()
print("covariance=", repr(covariance))
parameters = distribution.getParametersCollection()
print("parameters=", repr(parameters))
for i in range(6):
print("standard moment n=", i, " value=",
distribution.getStandardMoment(i))
print("Standard representative=", distribution.getStandardRepresentative())
# Constructor with separate weights. Also check small weights removal
weights = [1.0e-20, 2.5, 32.0]
atoms = DistributionCollection(
[Normal(1.0, 1.0), Normal(2.0, 2.0), Normal(3.0, 3.0)])
newMixture = Mixture(atoms, weights)
print("newMixture pdf= %.12g" % newMixture.computePDF(2.5))
print("atoms kept in mixture=", newMixture.getDistributionCollection())
print("newMixture=", newMixture)
except:
import sys
print("t_Mixture_std.py", sys.exc_info()[0], sys.exc_info()[1])
|
