Issue 195 code optimization

[rccreswell]

My current ideas for cutting cpu and memory usage, in the hope of getting it to run with 1000 serial interval samples on heroku.

• [X] Write a new gamma distribution class which is smaller than scipy
• [X] Write a fast gamma pdf for arrays
• [X] Change the inference sliding window to reuse infectives_in_tau when possible

closes #195

[codecov[bot]]

Codecov Report

Merging #196 (553ef23) into main (afba556) will not change coverage. The diff coverage is 100.00%.

@@            Coverage Diff            @@
##              main      #196   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files           11        11           
  Lines          659       697   +38     
=========================================
+ Hits           659       697   +38     

Impacted Files	Coverage Δ
branchpro/__init__.py	100.00% <100.00%> (ø)
branchpro/posterior.py	100.00% <100.00%> (ø)

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[rccreswell]

Looks good to me, thanks @rcw5890 ! My initial thought was that we potentially could have vectorised this using numpy to avoid the dependence on numexp, but I think this is all fine.

Thanks @DavAug . I had the same thought and did that first, but for arrays of our size numexpr manages to be about 4x faster than numpy. I don't think it's difficult to install and it can be made an optional dependency if anyone has trouble with it.

By the way, I just realized that my original gamma pdf fails in the special case of shape=1, x=0. I just added a potential fix.