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#! /usr/bin/env python
import openturns as ot
from math import pi
ot.TESTPREAMBLE()
# Log.Show( Log.Flags() | Log.INFO )
# Problem parameters
dimension = 3
a = 7.0
b = 0.1
# Reference analytical values
meanTh = a / 2
covTh = (b**2 * pi**8) / 18.0 + (b * pi**4) / 5.0 + (a**2) / 8.0 + 1.0 / 2.0
sob_1 = [
(b * pi**4 / 5.0 + b**2 * pi**8 / 50.0 + 1.0 / 2.0) / covTh,
(a**2 / 8.0) / covTh,
0.0,
]
sob_2 = [0.0, (b**2 * pi**8 / 18.0 - b**2 * pi**8 / 50.0) / covTh, 0.0]
sob_3 = [0.0]
sob_T1 = [
sob_1[0] + sob_2[0] + sob_2[1] + sob_3[0],
sob_1[1] + sob_2[0] + sob_2[2] + sob_3[0],
sob_1[2] + sob_2[1] + sob_2[2] + sob_3[0],
]
sob_T2 = [
sob_2[0] + sob_2[1] + sob_3[0],
sob_2[0] + sob_2[2] + sob_3[0],
sob_2[1] + sob_2[2] + sob_3[0],
]
sob_T3 = [sob_3[0]]
# Create the Ishigami function
inputVariables = ["xi1", "xi2", "xi3"]
formula = [
"sin(xi1) + (" + str(a) + ") * (sin(xi2)) ^ 2 + (" + str(b) + ") * xi3^4 * sin(xi1)"
]
model = ot.SymbolicFunction(inputVariables, formula)
# Create the input distribution
distribution = ot.JointDistribution([ot.Uniform(-pi, pi)] * dimension)
# Create the orthogonal basis
enumerateFunction = ot.LinearEnumerateFunction(dimension)
productBasis = ot.OrthogonalProductPolynomialFactory(
[ot.LegendreFactory()] * dimension, enumerateFunction
)
# design experiment
samplingSize = 75
# build basis
degree = 10
basisSize = enumerateFunction.getStrataCumulatedCardinal(degree)
# run algorithm
lar = ot.LARS()
listFittingAlgorithm = list()
listFittingAlgorithm.append(ot.KFold())
listFittingAlgorithm.append(ot.CorrectedLeaveOneOut())
for fittingAlgorithmIndex in range(len(listFittingAlgorithm)):
fittingAlgorithm = listFittingAlgorithm[fittingAlgorithmIndex]
adaptiveStrategy = ot.FixedStrategy(productBasis, basisSize)
projectionStrategy = ot.LeastSquaresStrategy(
ot.LeastSquaresMetaModelSelectionFactory(ot.LARS(), fittingAlgorithm)
)
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("isLeastSquares= ", result.isLeastSquares())
assert result.isLeastSquares()
print("involvesModelSelection= ", result.involvesModelSelection())
assert result.involvesModelSelection()
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