Optimize CGC computations

[lkdvos]

This PR adds some optimizations for computing CGCs:

• Add a special case for dealing with Clebsch-Gordan coefficients when one of the sectors is trivial, i.e. $a \otimes I \rightarrow a$ or $I \otimes a \rightarrow a$. For these cases the CGCs are just the identity matrices, thus no computations are needed.
• Change the way lower_weight_CGC! works: solve equations using qr! instead of pinv, and build rhs differently.
• Purge values that are almost zero from the final result to save memory on disk and in RAM.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 96.76%. Comparing base (4107f08) to head (ad9aea9).

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #13      +/-   ##
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+ Coverage   96.30%   96.76%   +0.45%     
==========================================
  Files           7        7              
  Lines         623      649      +26     
==========================================
+ Hits          600      628      +28     
+ Misses         23       21       -2     

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[lkdvos]

I've added some benchmarks for some improved version of the CGC computations, which now use QR instead of SVD to solve the linear problems, along with some in-place optimizations etc. I'll post the results here when they are done, and then check on how to add everything.

[github-actions]

[JuliaFormatter] _{reported by reviewdog 🐶}

Suggested change

	ThreadPinning.threadinfo(;blas=true, hints=true)
	ThreadPinning.threadinfo(; blas=true, hints=true)

[github-actions]

[JuliaFormatter] _{reported by reviewdog 🐶}

Suggested change

	save("benchmark_results.png", f; px_per_unit=2)
	save("benchmark_results.png", f; px_per_unit=2)

[lkdvos]

The results are in:

https://gist.github.com/lkdvos/4030a328fc12ea3c939d0b5ccec3ad4a

Looks like a serious upgrade, so I'll clean up this PR and implement everything nicely.

[Jutho]

Looking good. I am wondering which of the changes contributes most to the nice speedup. Threading over the fusion degeneracy N123 is no longer possible with the storage recycling for building the right hand side, but I assume threading happens at the higher level anyway.

[lkdvos]

I actually think that using the threads for BLAS might actually be the best here, and even still, it would not be that hard to define the auxiliary vectors one loop lower, and re-use them only for the different m3s. In any case, the biggest speedup comes from the qr! and ldiv! from what I could find, and afterwards I changed how the arrays were built because of needing them in a dense format afterwards anyways.
I think it is probably harder to find the optimal threading strategy over a wide variety of cases/machines, so I would say that the current approach is quite nice.