Speed up core.prior classes

Extended from #411 (closed)

1. • Profile all of the priors which use scipy: LogNormal, Exponential, StudentT, Logistic, Cauchy, Gamma.
2. • See if we can make them run faster by using analytical solutions in the rescale, prob, logprob, cdf methods.
     • Uniform: merged and dealt with in #411 (closed). O(1)-O(2) faster.
     • LogNormal: 8x to 20x faster.
     • Exponential: 5x to 50x faster.
     • StudentT: 3x to 40x faster.
     • Logistic: 5x to 60x faster.
     • Cauchy: 2x to 500x faster.
     • Gamma: 2x to 600x faster.
     • Beta: 2x to 300x faster.
3. • Add unit tests to ensure that calculations are correct.

(Biggest speed-up is when inputting (float, int), smaller speed-up is inputting np.ndarray)

added Efficiency Good First Issue Priors + 1 deleted label

marked the checklist item Profile all of the priors which use scipy: LogNormal, Exponential, StudentT, Logistic, Cauchy, Gamma. as completed

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marked the checklist item Logistic: as completed

marked the checklist item Exponential: scipy is faster, as np.log() and np.exp() are too costly. as completed

marked the checklist item Logistic: as incomplete

marked the checklist item Cauchy: as completed

Nice work @liting.xiao. Something else which could be added is a regression tests of the accuracy. Essentially add something to this script: https://git.ligo.org/lscsoft/bilby/blob/master/test/prior_test.py which creates a uniform prior object, then calculates say the pdf, log_pdf, and rescales a number from the unit cobe and compares the output to the equivalent scipy version.

The benefits of this would be two-fold. 1) We'd be certain the implications as they stand are correct (I trust everyone, it is just paranoia!) and 2) we'd know if at some point in the future someone accidentally changes something which means this isn't the case.

You can run the test locally by doing

$ python test/prior_test.py

Yes I will put that in. I did a separate test of the exact same nature before committing these function changes. Should be easy to add in.

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marked the checklist item LogNormal: 8x to 20x faster. as incomplete

marked the checklist item StudentT: 3x to 40x faster. as incomplete

marked the checklist item Logistic: 5x to 60x faster. as incomplete

marked the checklist item Gamma: 2x to 600x faster. as incomplete

marked the checklist item StudentT: 3x to 40x faster. as completed

marked the checklist item Gamma: 2x to 600x faster. as completed

marked the checklist item LogNormal: 8x to 20x faster. as completed

marked the checklist item Logistic: 5x to 60x faster. as completed

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mentioned in merge request !627 (merged)

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Closing after !627 (merged).

closed

unassigned @liting.xiao