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#! /usr/bin/env python
import openturns as ot
ot.ResourceMap.SetAsScalar("LinearCombinationEvaluation-SmallCoefficient", 1.0e-10)
domain = ot.Interval(-1.0, 1.0)
basis = ot.OrthogonalProductPolynomialFactory([ot.LegendreFactory()])
basisSize = 5
functions = [basis.build(i) for i in range(basisSize)]
experiment = ot.LHSExperiment(basis.getMeasure(), 100)
mustScale = False
threshold = 0.0001
model = ot.AbsoluteExponential([1.0])
algo = ot.KarhunenLoeveQuadratureAlgorithm(
domain, domain, model, experiment, functions, mustScale, threshold
)
algo.run()
result = algo.getResult()
lambd = result.getEigenvalues()
KLModes = result.getModesAsProcessSample()
print("KL modes=", KLModes)
print("KL eigenvalues=", lambd)
process = ot.GaussianProcess(model, KLModes.getMesh())
sample = process.getSample(10)
coefficients = result.project(sample)
print("KL coefficients=", coefficients)
KLFunctions = result.getModes()
print("KL functions=", KLFunctions)
print("KL lift=", result.lift(coefficients[0]))
print("KL lift as field=", result.liftAsField(coefficients[0]))
# Now using Legendre/Gauss quadrature
marginalDegree = 5
algo = ot.KarhunenLoeveQuadratureAlgorithm(
domain, domain, model, marginalDegree, threshold
)
algo.run()
result = algo.getResult()
lambd = result.getEigenvalues()
KLModes = result.getScaledModesAsProcessSample()
# Due to symmetry many results can have a sign switch depending on the CPU/compiler/BLAS used
# print("KL modes=", KLModes)
print("KL eigenvalues=", lambd)
coefficients = result.project(sample)
# print("KL coefficients=", coefficients)
KLFunctions = result.getModes()
# print("KL functions=", KLFunctions)
lifted = result.lift(coefficients[0])
# print("KL lift=", lifted)
liftedAsField = result.liftAsField(coefficients[0])
# print("KL lift as field=", liftedAsField)
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