pnkraemer / matfree Goto Github PK

Loops are very application-specific. How far can we go without doing any of them?

Make a tutorial that shows how to derive divergences and Laplacians from Jacobian-vector products by estimating traces.

Implicit differentiation should apply. I dont think it is a great idea to traditional-autodiff it.

Why? (A) convenience. (b) Because we can talk preconditioning as soon as we talk log-determinants. For general traces of matrix functions, that is a bit odd.

E.g. thick-restart Lanczos https://sdm.lbl.gov/~kewu/ps/trlan-siam.pdf

https://arxiv.org/pdf/2301.07825.pdf sounds promising

Also explains some other approaches for variance reduction.

It covers function transformations like jit, grad, etc., but also partial and other stuff that functools provide. It is also shorter.

https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance

Can we do this?

A reference implementation is, e.g., here: https://github.com/google/spectral-density/blob/master/jax/lanczos.py.

The tridiagonal() method uses no knowledge about the result being tridiagonal.

https://netlib.org/utk/people/JackDongarra/etemplates/node198.html

as an alternative to Lanczos.

• #51
• #52

Not to aim for a meaningless number, but to see which functions become unused when refactoring.

Lovely explanation here:
https://www-users.cse.umn.edu/~saad/PDF/ys-2016-04.pdf

FAST ESTIMATION OF tr(F (A)) VIA STOCHASTIC LANCZOS QUADRATURE
Ubaru, Chen, Saad.

Make a tutorial (or offer an API) for trace estimation of functions $A = J J^\top$.

It is used in almost every test.

Are there ways of estimating the variance of trace estimators? Would be great to get at least a tiny bit of UQ -- these estimators feel very noisy.

Scope of the package:
Randomised and deterministic matrix-free methods for trace estimation, matrix functions, solvers, and matrix factorisations.

Contribution guide:

• Every PR usually resolves an issue and changes ~10 lines of code (or less)
• Every PR usually contains a single commit. The commit message is usually very descriptive
• Every enhancement is usually covered by a test.

Other than that:

• Install developer dependencies as such: (...). Fork, make the change, and open a PR.

At least in text, somewhere in the readme. (I think it might be difficult to enforce, because we don't list JAX as an official dependency).

Which one? >0.4?

I have a benchmark somewhere that shows joint trace and diagonal estimation.

Put it here.

E.g. copy what https://jax.readthedocs.io/en/latest/_autosummary/jax.random.normal.html does.

Use the signature of https://jax.readthedocs.io/en/latest/_autosummary/jax.eval_shape.html to evaluate tangent shape and dtype. This is more in line with native JAX languages, and thus more familiar to a user (me; after not using this package for a couple of weeks, coming back, and being confused).

Which removes the need for a public mean_vmap, mean_map, etc.

"Flow" could be anything.

I think it is only a different Q.