Plan for runtime kernel fitting

[DiamonDinoia]

Hi all,

I spent some time planning and thinking what is the best route to implement this in FINUFFT. The fastest route I could come up with is:

• Implement polynomial fitting using polyfit: get rid of precomputed coefficients tables but no tweaks to kernel and kernel parameters. Polyfit and & runtime coefficients fitting #748
• change scalar horner eval to use the runtime fitted coeffs, and purge the precomputed. Use the scalar horner for the deconvolve step (onedim_*fseries) .. This is in branch corehorner but I'm stuck making it a PR!
• (optional) use DUCC kernel and parameters as a baseline? @mreineck do you think we can just copy your tables directly?
• use a different cost model and density to optimize performance
• Improve upon kernel and kernel parameter selection using a different approach.

Feel free to edit/comment!

[mreineck]

(optional) use DUCC kernel and parameters as a baseline? @mreineck do you think we can just copy your tables directly?

You can certainly do that, but that forces you to adopt a lot of things at the same time (generalized ES formula and the full ducc error model). This is of course totally fine, but in case you want to do that in steps, I also have a script that computes the coefficient tables and can be adjusted for any kernel function (ducc0/python/demos/kernel_helper.py).

[DiamonDinoia]

I would say, let me integrate the runtime polynomial fitting then we choose the best route. I am okay with using the generalized ES kernel but ultimately @ahbarnett is expert here :)

EDIT: Yes, using the generalized ES kernel is a good idea. I might need some help to integrate it though. Do you think is complicated?

[ahbarnett]

https://doi.org/10.1051/0004-6361/202039723
has Martin's kernel params and explanation.