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
|
#! /usr/bin/env python
import openturns as ot
ot.TESTPREAMBLE()
# Big test case for correlated components
# Instantiate one distribution object
dim = 4
meanPoint = ot.Point(dim, 1.0)
sigma = ot.Point(dim, 1.0)
R = ot.CorrelationMatrix(dim)
for i in range(1, dim):
R[i, i - 1] = 0.5
distribution = ot.Normal(meanPoint, sigma, R)
# Test for sampling
size = 1000
oneSample = distribution.getSample(size)
print(
"sample of size ",
size,
" first=",
repr(oneSample[0]),
" last=",
repr(oneSample[oneSample.getSize() - 1]),
)
mean = oneSample.computeMean()
print("mean error=%.6f" % ((mean - meanPoint).norm() / meanPoint.norm()))
covariance = oneSample.computeCovariance()
errorCovariance = 0.0
for i in range(dim):
for j in range(dim):
errorCovariance += abs(covariance[i, j] - sigma[i] * sigma[j] * R[i, j])
print("covariance error=%.6f" % (errorCovariance / (dim * dim)))
# Define a point
zero = ot.Point(dim, 0.0)
# Show PDF and CDF of zero point
zeroPDF = distribution.computePDF(zero)
zeroCDF = distribution.computeCDF(zero)
print(
"Zero point = ",
repr(zero),
" pdf=%.6f" % zeroPDF,
repr(zero),
" cdf=%.6f" % zeroCDF,
" density generator=%.6f" % distribution.computeDensityGenerator(0.0),
)
# Extract the marginals
for i in range(dim):
margin = distribution.getMarginal(i)
print("margin=", repr(margin))
print("margin PDF=%.6f" % margin.computePDF(ot.Point(1)))
print("margin CDF=%.6f" % margin.computeCDF(ot.Point(1)))
print("margin quantile=", repr(margin.computeQuantile(0.5)))
print("margin realization=", repr(margin.getRealization()))
# Extract a 2-D marginal
indices = [1, 0]
print("indices=", repr(indices))
margins = distribution.getMarginal(indices)
print("margins=", repr(margins))
print("margins PDF=%.6f" % margins.computePDF(ot.Point(2)))
print("margins CDF=%.6f" % margins.computeCDF(ot.Point(2)))
quantile = ot.Point(margins.computeQuantile(0.5))
print("margins quantile=", repr(quantile))
print("margins CDF(qantile)=%.6f" % margins.computeCDF(quantile))
print("margins realization=", repr(margins.getRealization()))
# Very big test case for independent components
dim = 200
meanPoint = ot.Point(dim, 0.1)
sigma = ot.Point(dim, 1.0)
distribution = ot.Normal(meanPoint, sigma, ot.IdentityMatrix(dim))
print("Has independent copula? ", distribution.hasIndependentCopula())
# Test for sampling
oneSample = distribution.getSample(size // 10)
print(
"sample of size ",
size,
" first=",
repr(oneSample[0]),
" last=",
repr(oneSample[oneSample.getSize() - 1]),
)
mean = oneSample.computeMean()
print("mean error=%.6f" % ((mean - meanPoint).norm() / meanPoint.norm()))
covariance = oneSample.computeCovariance()
errorCovariance = 0.0
for i in range(dim):
for j in range(dim):
if i == j:
temp = sigma[i] * sigma[j]
else:
temp = 0.0
errorCovariance += abs(covariance[i, j] - temp)
print("covariance error=%.6f" % (errorCovariance / (dim * dim)))
# Define a point
zero = ot.Point(dim, 0.0)
# Show PDF and CDF of zero point
zeroPDF = distribution.computePDF(zero)
zeroCDF = distribution.computeCDF(zero)
print(
"Zero point= ",
repr(zero),
" pdf=%.6f" % zeroPDF,
" cdf=%.6f" % zeroCDF,
" density generator=%.6f" % distribution.computeDensityGenerator(0.0),
)
|
