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#! /usr/bin/env python
from __future__ import print_function
from openturns import *
from math import *
TESTPREAMBLE()
try:
#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
model = NumericalMathFunction(['xi1', 'xi2', 'xi3'], ['y'], [
"sin(xi1) + (" + str(a) + ") * (sin(xi2)) ^ 2 + (" + str(b) + ") * xi3^4 * sin(xi1)"])
# Create the input distribution
marginalX = DistributionCollection(dimension)
for i in range(dimension):
marginalX[i] = Uniform(-pi, pi)
distribution = Distribution(ComposedDistribution(marginalX))
# Create the orthogonal basis
polynomialCollection = PolynomialFamilyCollection(dimension)
for i in range(dimension):
polynomialCollection[
i] = OrthogonalUniVariatePolynomialFamily(LegendreFactory())
enumerateFunction = LinearEnumerateFunction(dimension)
productBasis = OrthogonalBasis(
OrthogonalProductPolynomialFactory(polynomialCollection, enumerateFunction))
# design experiment
samplingSize = 75
experiment = Experiment(LowDiscrepancyExperiment(
SobolSequence(dimension), distribution, samplingSize))
# iso transfo
algo = FunctionalChaosAlgorithm(model, distribution, AdaptiveStrategy(
FixedStrategy(productBasis, enumerateFunction.getStrataCumulatedCardinal(1))))
algo.run()
result = algo.getResult()
xToU = result.getTransformation()
# generate samples
x = experiment.generate()
u = xToU(x)
y = model(x)
# build basis
degree = 10
basisSize = enumerateFunction.getStrataCumulatedCardinal(degree)
basis = Basis()
for i in range(basisSize):
basis.add(productBasis.build(i))
# run algorithm
factory = BasisSequenceFactory(LAR())
factory.setVerbose(True)
print("factory = ", factory)
seq = factory.build(u, y, basis, list(range(basisSize)))
first = 20
if (seq.getSize() >= first):
print("first ", first, " indices = ", seq.getIndices(first - 1))
except:
import sys
print("t_LAR.py", sys.exc_info()[0], sys.exc_info()[1])
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