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
|
#! /usr/bin/env python
import openturns as ot
ot.TESTPREAMBLE()
# Log.Show( Log.Flags() | Log.INFO )
# Problem parameters
dimension = 8
# Create the GSobol' function
# Reference analytical values
meanTh = 1.0
covTh = 1.0
a = ot.Point(dimension)
a[0] = 1.0
a[1] = 2.0
a[2] = 5.0
a[3] = 10.0
a[4] = 20.0
a[5] = 50.0
a[6] = 100.0
a[7] = 500.0
inputVariables = ot.Description(dimension)
formula = ot.Description(1)
formula[0] = "1.0"
for i in range(dimension):
covTh = covTh * (1.0 + 1.0 / (3.0 * (1.0 + a[i]) ** 2))
inputVariables[i] = "xi" + str(i)
formula[0] = (
formula[0]
+ " * ((abs(4.0 * xi"
+ str(i)
+ " - 2.0) + "
+ str(a[i])
+ ") / (1.0 + "
+ str(a[i])
+ "))"
)
covTh = covTh - 1.0
model = ot.SymbolicFunction(inputVariables, formula)
# Create the input distribution
distribution = ot.JointDistribution([ot.Uniform(0.0, 1.0)] * dimension)
# Create the orthogonal basis
q = 0.4
enumerateFunction = ot.HyperbolicAnisotropicEnumerateFunction(dimension, q)
productBasis = ot.OrthogonalProductPolynomialFactory(
[ot.LegendreFactory()] * dimension, enumerateFunction
)
# design experiment
samplingSize = 75
# build basis
basisSize = enumerateFunction.getStrataCumulatedCardinal(30)
listFittingAlgorithm = list()
listFittingAlgorithm.append(ot.KFold())
listFittingAlgorithm.append(ot.CorrectedLeaveOneOut())
for fittingAlgorithmIndex in range(len(listFittingAlgorithm)):
fittingAlgorithm = listFittingAlgorithm[fittingAlgorithmIndex]
adaptiveStrategy = ot.FixedStrategy(productBasis, basisSize)
lsSelectionFactory = ot.LeastSquaresMetaModelSelectionFactory(
ot.LARS(), fittingAlgorithm
)
projectionStrategy = ot.LeastSquaresStrategy(lsSelectionFactory)
experiment = ot.LowDiscrepancyExperiment(
ot.SobolSequence(), distribution, samplingSize
)
ot.RandomGenerator.SetSeed(0)
X = experiment.generate()
Y = model(X)
algo = ot.FunctionalChaosAlgorithm(
X, Y, distribution, adaptiveStrategy, projectionStrategy
)
algo.run()
result = algo.getResult()
print("coeffs = ", result.getCoefficients())
print("residuals = ", result.getResiduals())
print("relative errors = ", result.getRelativeErrors())
isLeastSquaresPCE = result.isLeastSquares()
assert isLeastSquaresPCE
involvesModelSelectionPCE = result.involvesModelSelection()
involvesModelSelection = (
adaptiveStrategy.involvesModelSelection()
or projectionStrategy.involvesModelSelection()
)
assert involvesModelSelection == involvesModelSelectionPCE
|
