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
|
#! /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
sample = NumericalSample(0, dimension)
# Create a collection of distribution
aCollection = DistributionCollection()
aCollection.add(Normal(meanPoint, sigma, IdentityMatrix(dimension)))
sample.add(meanPoint)
meanPoint += NumericalPoint(meanPoint.getDimension(), 1.0)
aCollection.add(Normal(meanPoint, sigma, IdentityMatrix(dimension)))
sample.add(meanPoint)
meanPoint += NumericalPoint(meanPoint.getDimension(), 1.0)
aCollection.add(Normal(meanPoint, sigma, IdentityMatrix(dimension)))
sample.add(meanPoint)
# Instanciate one distribution object
distribution = KernelMixture(Normal(), sigma, sample)
print("Distribution ", repr(distribution))
print("Distribution ", distribution)
distributionRef = Mixture(aCollection)
# 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 = 100
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))
print("ddf (ref)=", repr(distributionRef.computeDDF(point)))
# 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)
print("pdf (ref)=%.6f" % distributionRef.computePDF(point))
# 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)
print("cdf (ref)=%.6f" % distributionRef.computeCDF(point))
# quantile
quantile = distribution.computeQuantile(0.95)
print("quantile=", repr(quantile))
print("quantile (ref)=", repr(distributionRef.computeQuantile(0.95)))
print("cdf(quantile)=%.6f" % distribution.computeCDF(quantile))
mean = distribution.getMean()
print("mean=", repr(mean))
print("mean (ref)=", repr(distributionRef.getMean()))
covariance = distribution.getCovariance()
print("covariance=", repr(covariance))
print("covariance (ref)=", repr(distributionRef.getCovariance()))
#parameters = distribution.getParametersCollection()
# print "parameters=" , parameters
except:
import sys
print("t_KernelMixture_std.py", sys.exc_info()[0], sys.exc_info()[1])
|
