quadpy, orthopy

[nschloe]

I see that chaospy does many things around quadrature and orthogonal polynomials. Perhaps you can use what's been implemented in https://github.com/nschloe/quadpy and https://github.com/nschloe/orthopy (two projects of mine). I'm currently updating the documentation, let me know if there's anything I can help you with.

[jonathf]

Interesting couple of projects you have there. Thank you for the offer. I'll take a closer look over the summer. I imagine there are some functionality that make sense to port.

Also feel free to take anything you find of interest.

[jonathf]

You have a few extra quadrature rules I'd love to add to the fold. Namely Kronrod, Lobatto and Newton-Cotes. You even have a few I haven't heard about before like Radau and Tanh-Sinh. I'll tag you to review some of the PRs. If you have the time, I would appreciate your input.

[nschloe]

Radau and Tanh-Sinh

Gauss-Radau is series of quadrature schemes that simply includes the left endpoint of the integration domain. It's classical.

tanh-sinh is a different beast. It's pretty new (1970s or so) and integrates almost no function exactly, not even constant functions or polynomials of low degree for that matter. The upside is that it can integrate many functions with stunning precision (error below machine precision), even if there are (integrable) singularities at the endpoints of the integration domain.

[jonathf]

Thanks. Radau is straiht forward it seems. Tanh-sinh seems to be a bit work to adapt. I'll see if I can get my head around it.

I am currently working on porting the modified-Chebyshev algorithm. I see that it done in two levels where the outer function takes moments only, and the inner function takes an additional a and b. However, a and b is always set to be the zero-vector, and if I insert any non-zero values into the vector, I get a different answer.

Do the a and the b serve any interpretable purpose? If so, would a user be interested in modifying them?