Hey everyone, I am fairly new to UQLab, but have been using Polynomial Chaos Expansions (PCEs) in my work to compare against a few other UQ/UP methods. The sparse features of UQLab are great, especially when computing models for higher and higher dimensional problems. My question is:
When implementing the ‘Quadrature’ solution technique, why is the maximum level of the quadrature equal to the degree + 1? I understand polynomial exactness in regards to Gaussian quadratures, and specifically sparse Smolyak grids, but for PCEs we are not integrating expectations of polynomials directly, we’re integrating the product of some orthogonal polynomial with the transformation, M(X).
For example, when I set the degree to 6, the maximum quadrature level that I can input without error is 7. I get the following error for level = 8:
Index in position 1 exceeds array bounds (must not exceed 7).
Error in uq_quadrature_nodes_weights_gauss (line 60)
AB = AB(1:(LEVELS(ii)),:);
My thought would be the quadrature level can/should be independent of the degree of the PCE expansion. Any help here?