Add benchmark suite

[lkdvos]

This sets up a benchmark/benchmarks.jl script to have a dedicated SUITE to run our benchmarks, similar to BaseBenchmarks.jl.

The goal is to start adding more coverage so we can better assess the actual performance improvements and/or regressions between versions.

(This is not meant as being illustrative for the performance of this package, for which I am creating separate scripts to generate proper figures etc)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 82.65%. Comparing base (8e3af86) to head (32f5128).
Report is 7 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #233      +/-   ##
==========================================
+ Coverage   82.64%   82.65%   +0.01%     
==========================================
  Files          43       43              
  Lines        5559     5593      +34     
==========================================
+ Hits         4594     4623      +29     
- Misses        965      970       +5     

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[Jutho]

Strictly speaking, this is not correctly normalised. If we assume that SU2Irrep(j) is indeed generated with dimension poisson_pdf(2*j) = D * exp(-sigma) * sigma^(2j) / factorial(2j), then the total dimension is, with n=2j

$$\sum_{n=0}^{+\infty} D * (n+1) * exp(-\sigma) * \sigma^n / n! \neq D$$

due to the extra factor $$n+1=2j+1$$, which comes from the dimension of the irrep.

Maybe poisson_pdf(x) = ceil(Int, D * exp(-sigma) * sigma^x / factorial(x) / (x+1))

which happens to be

Maybe poisson_pdf(x) = ceil(Int, D * exp(-sigma) * sigma^x / factorial(x+1))

as alternative

[Jutho]

Also, for large sigma, the poisson distribution is peaked away from zero, so I do not know if that is really the distribution we want, versus just a half gaussian, but I guess those details don't really matter (but we probably do not want to change them afterwards).

[lkdvos]

I'm definitely happy to switch that, although I think the peak is reasonable too: I like poisson for SU(2) since in the Heisenberg virtual spaces often there are more values of spin 1 than spin 0.

Probably it doesn't matter too much for the actual representativeness of the benchmarks though