How to access numerical basis constructed with Stieltjes procedure - UqpyLab


I am currently using UqpyLab to construct numerical bases corresponding to arbitrary input distributions approximated with kernel smoothing. I am employing LAR (Least Angle Regression) to compute the coefficients. Once the Polynomial Chaos Expansion (PCE) model is trained, I can access the indices of the numerical basis and the coefficients computed with LAR.

However, I am unsure how to access the alpha_n​ and beta_n​ coefficients (following the notation in the UqpyLab user manual) of the Christoffel-Darboux formulae computed using the Stieltjes procedure.

My objective is to utilize the constructed PCE model in an external code, and I believe I need this information along with the indices and coefficients obtained via LAR.

I would greatly appreciate any guidance on how to retrieve these​ coefficients.

Thank you!

Hi @mridula

The information you are looking for can be found under YourModel.PCE.Basis. More specificially, you can find the recurrence coefficients in the field PolyTypesAB. The code for their computation is located in the file uq_arbitrary_ml_integrator.m. For how to use them during the PCE evaluation you can have a look at the file uq_eval_univ_basis.m.

This should give you everything you need. However, it may still require some effort to delve into the code. UQLab has to handle many (edge) cases and sometimes performs optimizations that complicate the code and may result in the code not exactly reflecting the equations you find in the manuals.

Best regards

Thank you very much for the response!