[ot-users] Orthogonal basis of a polynomial chaos

BAUDIN Michael michael.baudin at edf.fr
Wed Apr 19 13:20:06 CEST 2017


Hi again,
Here is a script in attachment to experiment with the objects.
Regards,
Michaël

De : BAUDIN Michael
Envoyé : mercredi 19 avril 2017 11:50
À : 'users at openturns.org'
Objet : Orthogonal basis of a polynomial chaos

Hi,

After a (functionnal) polynomial chaos has been run, I am searching a way to explore what basis was used. For example, if a Uniform distribution was used, I would like to confirm that a Hermite polynomial was used. Of course, this cannot always been done, especially if one of the input distributions was « non-standard ».

However, even in the classical case, I was not able to find out what method of the polynomialChaosAlgorithm could be used to retrieve the information. For example :

[...]
# Create Polynomial Chaos
polynomialChaosAlgorithm = FunctionalChaosAlgorithm(myFunction, \
    inputDistribution, fixedStrategy, evalStrategy)
# Compute expansion coefficients
polynomialChaosAlgorithm.run()

# Explore the result
myAdapStrat = polynomialChaosAlgorithm.getAdaptiveStrategy() # a AdaptiveStrategy
mybasis = myAdapStrat.getBasis() # a OrthogonalBasis
# and after ... ?

Afterwhile, I thought that this was not possible, because the basis was an hidden internal object. This is why I tried a second solution : directly explore the polynomial collection used to create the collection of univariate polynomials :

# Create a coolection of standard univariate polynomials
polyColl = PolynomialFamilyCollection(dim)
for i in range(dim):
    marginali=inputDistribution.getMarginal(i)
    polyColl[i] = StandardDistributionPolynomialFactory(marginali)

# Explore the first polynomial
poly0 = polyColl[0]
# and after ... ?

But I was not able to find a way to the Hermite polynomial neither.

Has anyone an idea ?

Regards,

Michaël



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