Joint variable expansion generation

[jwward96]

Hi! I've been working to make some parallels to this toolbox in MATLAB to aid in some work I'm doing with stochastic NMPC. I understand the implemented methods of generating the expansions for individual variables but have a question on what happens when generating a joint expansion.

I read in the code that for independent variables you can generate the expansion for each RV and use a tensor product to get the joint expansion. So for two gaussian RV's with a 3rd order expansion you get 4 terms for each RV. The tensor product would then return a 16 term expansion but with Chaospy I noticed it only returns a 10 term joint expansion.

I'm certain there is just some method of simplifying redundant terms or possibly terms that are not linearly independent. Would someone be able to explain what simplifications are made or point towards a reference for me to read more about this?

[jonathf]

https://chaospy.readthedocs.io/en/master/api/chaospy.generate_expansion.html
See cross_truncation.

Set the value to np.inf to get the full tensor product.

[jwward96]

That’s exactly what I was looking for! It seems I went too far into the code right away. Guess it pays to just read the top level function call!