Feature/412 add faer rs backend

[geo-ant]

Fixes: #412 add faer as math backend

This PR adds faer support to argmin-math. faer is a fast and rapidly evolving matrix backend that is gaining popularity in the numeric Rust ecosystem. I'm not associated with the project.

I've closely followed the logic of the nalgebra implementation and even manually copied and translated the tests, so that the behavior of the nalgebra implementation is kept with the faer implementation. The one exception I made is that an eye_like identity matrix can also be requested for non-square matrices without panicking. Otherwise I've kept the original behavior.

All implementations are available on the owned Mat<T> type and many (but not all) are available on the non-owning reference-type MatRef<T>.

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 92.11%. Comparing base (40a25e6) to head (146db74).

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #549   +/-   ##
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  Coverage   92.11%   92.11%           
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  Files         177      177           
  Lines       23672    23672           
=======================================
  Hits        21806    21806           
  Misses       1866     1866           

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[stefan-k]

This is excellent, thank you! Rebasing on the current main should fix the failing CI. Could you add running the faer tests to the CI (section tests-argmin-math in .github/workflows/ci.yml), please?

[geo-ant]

done and done, fingers crossed this works now :)

[geo-ant]

Hi, not meaning to rush you, just checking in to see whether there's something else I can do.

[humphreylee]

@geo-ant - really great work here - THANKS! If I may ask, can you make an example, say from this lbfgs example? Thanks in advance.

[geo-ant]

Hey @humphreylee, I'm definitely open to that but I'll wait until the maintainers get back to me with requests for changes so I can do it in one go. Right now I don't know what the status of this is.

[stefan-k]

Hi @geo-ant , I'm very sorry for the long wait, I have difficulty finding the time nowadays. In general this looks pretty good to me, I just need to find some time to review this with the amount of attention that this PR deserves. I can't promise it, but I will try to do this this weekend.
Thanks again, this is a really amazing addition to argmin! :)

[geo-ant]

Hey @stefan-k, no need to apologise, none of us are getting paid for this. If you want, ping me and I can also hop on a call and take 20 min to guide you through the PR. The thing is pretty big but very formulaic and not nearly as complex as it might seem from the number of lines of code. Again, don't worry about being fast. I'll be happy to see this merged eventually, but life comes before open source :)