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#! /usr/bin/env python
import openturns as ot
from openturns.usecases import ishigami_function
ot.TESTPREAMBLE()
# Problem parameters
im = ishigami_function.IshigamiModel()
distribution = im.inputDistribution
model = im.model
dimension = im.inputDistribution.getDimension()
sobolFirstOrderReference = [im.S1, im.S2, im.S3]
sobolSecondOrderReference = [im.S12, im.S13, im.S23]
sobolTotalReference = [im.ST1, im.ST2, im.ST3]
sobolInteractionTotalReference2 = [im.S12 + im.S123, im.S13 + im.S123, im.S23 + im.S123]
sobolInteractionTotalReference3 = [im.S123]
sobolGroupedIndex2 = [
im.S1 + im.S2 + im.S12,
im.S1 + im.S3 + im.S13,
im.S2 + im.S3 + im.S23,
]
sobolGroupedIndex3 = [im.S1 + im.S2 + im.S3 + im.S12 + im.S13 + im.S23 + im.S123]
# Create the orthogonal basis
enumerateFunction = ot.LinearEnumerateFunction(dimension)
productBasis = ot.OrthogonalProductPolynomialFactory(
[ot.LegendreFactory()] * dimension, enumerateFunction
)
# Create the adaptive strategy
# We can choose amongst several strategies
# First, the most efficient (but more complex!) strategy
listAdaptiveStrategy = list()
degree = 6
indexMax = enumerateFunction.getBasisSizeFromTotalDegree(degree)
basisDimension = enumerateFunction.getBasisSizeFromTotalDegree(degree // 2)
threshold = 1.0e-6
listAdaptiveStrategy.append(
ot.CleaningStrategy(productBasis, indexMax, basisDimension, threshold)
)
# Second, the most used (and most basic!) strategy
listAdaptiveStrategy.append(
ot.FixedStrategy(
productBasis, enumerateFunction.getBasisSizeFromTotalDegree(degree)
)
)
for adaptiveStrategyIndex in range(len(listAdaptiveStrategy)):
adaptiveStrategy = listAdaptiveStrategy[adaptiveStrategyIndex]
# Create the projection strategy
samplingSize = 250
listExperiment = list()
# We have only the LeastSquaresStrategy up to now (0.13.0) but we can choose several sampling schemes
# Monte Carlo sampling
listExperiment.append(ot.MonteCarloExperiment(distribution, samplingSize))
# LHS sampling
listExperiment.append(ot.LHSExperiment(distribution, samplingSize))
# Low Discrepancy sequence
listExperiment.append(
ot.LowDiscrepancyExperiment(ot.SobolSequence(), distribution, samplingSize)
)
for experiment in listExperiment:
# Create the polynomial chaos algorithm
maximumResidual = 1.0e-10
ot.RandomGenerator.SetSeed(0)
X = experiment.generate()
Y = model(X)
algo = ot.FunctionalChaosAlgorithm(X, Y, distribution, adaptiveStrategy)
algo.setMaximumResidual(maximumResidual)
algo.run()
# Examine the results
result = algo.getResult()
pGrad = result.getMetaModel().parameterGradient(distribution.getMean())
print("###################################")
print(algo.getAdaptiveStrategy())
print(algo.getProjectionStrategy())
# print "coefficients=", result.getCoefficients()
residuals = result.getResiduals()
print("residuals=", residuals)
relativeErrors = result.getRelativeErrors()
print("relativeErrors=", relativeErrors)
isLeastSquaresPCE = result.isLeastSquares()
assert isLeastSquaresPCE
involvesModelSelectionPCE = result.involvesModelSelection()
involvesModelSelection = adaptiveStrategy.involvesModelSelection()
assert involvesModelSelection == involvesModelSelectionPCE
# Post-process the results
vector = ot.FunctionalChaosRandomVector(result)
mean = vector.getMean()[0]
print("mean=%.8f" % mean, "absolute error=%.10f" % abs(mean - im.expectation))
variance = vector.getCovariance()[0, 0]
print(
"variance=%.8f" % variance,
"absolute error=%.10f" % abs(variance - im.variance),
)
sensitivity = ot.FunctionalChaosSobolIndices(result)
for i in range(dimension):
value = sensitivity.getSobolIndex(i)
print(
"Sobol index",
i,
"= %.8f" % value,
"absolute error=%.10f" % abs(value - sobolFirstOrderReference[i]),
)
indices = ot.Indices(2)
k = 0
for i in range(dimension):
indices[0] = i
for j in range(i + 1, dimension):
indices[1] = j
value = sensitivity.getSobolIndex(indices)
print(
"Sobol index",
indices,
"=%.8f" % value,
"absolute error=%.10f" % abs(value - sobolSecondOrderReference[k]),
)
k = k + 1
indices = ot.Indices([0, 1, 2])
value = sensitivity.getSobolIndex(indices)
print(
"Sobol index",
indices,
"=%.8f" % value,
"absolute error=%.10f" % abs(value - im.S123),
)
for i in range(dimension):
value = sensitivity.getSobolTotalIndex(i)
print(
"Sobol total index",
i,
"=%.8f" % value,
"absolute error=%.10f" % abs(value - sobolTotalReference[i]),
)
indices = ot.Indices(2)
k = 0
for i in range(dimension):
indices[0] = i
for j in range(i + 1, dimension):
indices[1] = j
value = sensitivity.getSobolTotalIndex(indices)
print(
"Sobol total index",
indices,
"=%.8f" % value,
"absolute error=%.10f"
% abs(value - sobolInteractionTotalReference2[k]),
)
k = k + 1
indices = ot.Indices([0, 1, 2])
value = sensitivity.getSobolTotalIndex(indices)
print(
"Sobol total index ",
indices,
"=%.8f" % value,
"absolute error=%.10f" % abs(value - sobolInteractionTotalReference3[0]),
)
indices = ot.Indices(2)
k = 0
for i in range(dimension):
indices[0] = i
for j in range(i + 1, dimension):
indices[1] = j
value = sensitivity.getSobolGroupedIndex(indices)
print(
"Sobol grouped index",
indices,
"=%.8f" % value,
"absolute error=%.10f" % abs(value - sobolGroupedIndex2[k]),
)
k = k + 1
indices = ot.Indices([0, 1, 2])
value = sensitivity.getSobolGroupedIndex(indices)
print(
"Sobol grouped index ",
indices,
"=%.8f" % value,
"absolute error=%.10f" % abs(value - sobolGroupedIndex3[0]),
)
indices = ot.Indices([0, 1, 2])
value = sensitivity.getSobolGroupedTotalIndex(indices)
print(
"Sobol grouped total index ",
indices,
"=%.8f" % value,
"absolute error=%.10f" % abs(value - 1.0),
)
# Get part of variance indices
print("Part of variance")
partOfVariance = sensitivity.getPartOfVariance()
result = sensitivity.getFunctionalChaosResult()
orthogonalBasis = result.getOrthogonalBasis()
enumerateFunction = orthogonalBasis.getEnumerateFunction()
indices = result.getIndices()
basisSize = indices.getSize()
for i in range(basisSize):
globalIndex = indices[i]
multiIndex = enumerateFunction(globalIndex)
if partOfVariance[i] > 1.0e-3:
print(
"%d, %d, %s, %.4f" % (i, globalIndex, multiIndex, partOfVariance[i])
)
# Print summary
print(sensitivity)
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