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
|
#! /usr/bin/env python
import openturns as ot
def printPoint(point, digits):
oss = "["
eps = pow(0.1, digits)
for i in range(point.getDimension()):
if i == 0:
sep = ""
else:
sep = ","
if abs(point[i]) < eps:
oss += sep + "%.6f" % abs(point[i])
else:
oss += sep + "%.6f" % point[i]
sep = ","
oss += "]"
return oss
ot.TESTPREAMBLE()
# We create a numerical math function
# Analytical construction
inputFunc = ot.Description(2)
inputFunc[0] = "x0"
inputFunc[1] = "x1"
formulas = ot.Description(1)
formulas[0] = "-(6+x0^2-x1)"
print("formulas=", formulas)
myFunction = ot.SymbolicFunction(inputFunc, formulas)
dim = myFunction.getInputDimension()
# We create a normal distribution point of dimension 1
mean = ot.Point(dim, 0.0)
# x0
mean[0] = 5.0
# x1
mean[1] = 2.1
sigma = ot.Point(dim, 0.0)
# x0
sigma[0] = 3.3
# x1
sigma[1] = 3.0
R = ot.IdentityMatrix(dim)
#
testDistributions = ot.DistributionCollection(2)
testDistributions[0] = ot.Normal(mean, sigma, R)
marginals = ot.DistributionCollection(2)
marginals[0] = testDistributions[0].getMarginal(0)
marginals[1] = testDistributions[0].getMarginal(1)
testDistributions[1] = ot.JointDistribution(marginals, ot.NormalCopula(R))
for i in range(1):
myDistribution = testDistributions[i]
# We name the components of the distribution
componentDescription = ot.Description(dim)
componentDescription[0] = "Marginal 1"
componentDescription[1] = "Marginal 2"
myDistribution.setDescription(componentDescription)
# We create a 'usual' RandomVector from the Distribution
vect = ot.RandomVector(myDistribution)
# We create a composite random vector
output = ot.CompositeRandomVector(myFunction, vect)
outputDescription = ot.Description(1)
outputDescription[0] = "Interest Variable 1"
output.setDescription(outputDescription)
# We create an Event from this RandomVector
myEvent = ot.ThresholdEvent(output, ot.Greater(), 0.0)
# We create a NearestPoint algorithm
myCobyla = ot.Cobyla()
myCobyla.setMaximumCallsNumber(200)
myCobyla.setMaximumAbsoluteError(1.0e-10)
myCobyla.setMaximumRelativeError(1.0e-10)
myCobyla.setMaximumResidualError(1.0e-10)
myCobyla.setMaximumConstraintError(1.0e-10)
print("myCobyla=", myCobyla)
# We create a FORM algorithm
# The first parameter is an OptimizationAlgorithm
# The second parameter is an event
# The third parameter is a starting point for the design point research
myAlgo = ot.FORM(myCobyla, myEvent, mean)
print("FORM=", myAlgo)
# Perform the simulation
myAlgo.run()
# Stream out the result
result = ot.FORMResult(myAlgo.getResult())
digits = 5
print("importance factors=", printPoint(result.getImportanceFactors(), digits))
print("Hasofer reliability index=%.6f" % result.getHasoferReliabilityIndex())
print("result=", result)
# Hasofer Reliability Index Sensitivity
hasoferReliabilityIndexSensitivity = result.getHasoferReliabilityIndexSensitivity()
print(
"hasoferReliabilityIndexSensitivity = ",
repr(hasoferReliabilityIndexSensitivity),
)
# Event Probability Sensitivity
eventProbabilitySensitivity = result.getEventProbabilitySensitivity()
print("eventProbabilitySensitivity = ", repr(eventProbabilitySensitivity))
|
