Matrix row reduction is very slow

Hi,

I’ve tried to use this library to row reduce a (quite) big matrix over a finite field. It succeeded and took quite a huge time in comparison with a naïve implementation.

As an example I copy paste the timing from the jupyter notebook.

with: https://www.nayuki.io/page/gauss-jordan-elimination-over-any-field

mat.reduced_row_echelon_form()

CPU times: user 4min 15s, sys: 18.7 ms, total: 4min 15s
Wall time: 4min 15s

with galois:

MM_reduced = MM.row_reduce()

CPU times: user 4h 21min 24s, sys: 3.06 s, total: 4h 21min 27s
Wall time: 4h 21min 28s

the matrix, for reference is sparse and defined over a 128-bit prime, the shape is: 513x1025

[mhostetter]

@ddddavidee I pushed another performance improvement to that branch. You’ll likely see another speed up.

[ddddavidee]

@nayuki, what I meant is that the same computation took a very different time (~60x times) changing from your code to the one in galois… and I was thinking that there was a problem somewhere…

@mhostetter I pulled the branch and re-tried the computation (with some other small changes, I used lru_cache from functools, and shortcut the ‘division-by-one’ case, and now the computation for the very same matrix takes less than two minutes (Wall time: 1min 43s)