A package for Polynomial Chaos basis rotation
The package chaos_basispy defines the chaos_basispy module which attempts to collect the recently developed Basis Adaptation (BA) techniques that have been developed particularly for Polynomial Chaos expansions (PCE).The core idea behind Basis Adaptation is to apply a transformation on the input variables in a way such that the Quantity of Interest (QoI) which we are approximating via a PCE can be expressed with respect to a reduced basis. Provided that the input variables are Gaussian and the transformation is through an isometry (unitary matrix), the new variables preserve “Gaussianity” and a new PCE can be constructed with respect to them. This makes the BA framework particularly attractive on Hermite PCEs and in fact inapplicable (yet) to generalized PCEs. An expeption is when the new variables is 1-dimensional which can be mapped to a uniform r.v. through its own cdf and therefore the Legendre adapted PCE can be constructed. Due to the above, this module considers only Hermite and Legendre Chaos expansions.
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