Refactor integrators.py to make it more general.

[junpenglao]

Also add momentum update based on Esh dynamics

Close #587

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (16df9a6) 99.14% compared to head (8894248) 99.15%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #589      +/-   ##
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+ Coverage   99.14%   99.15%   +0.01%     
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  Files          50       50              
  Lines        2215     2252      +37     
==========================================
+ Hits         2196     2233      +37     
  Misses         19       19              

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[reubenharry]

I'm getting changed results (on a sampling run) when I substitute in the non euclidean mclachlan instead of the previous minimal_norm integrator. Have you confirmed that the two implementations yield the same results on the same inputs?

[junpenglao]

Yes the two implementation returns identical result: https://colab.research.google.com/drive/1HMnkMM8PNIaaaSAmZyKrZByCd-GKErsN

But to properly test it we still need to add some test:

• an isotropic Gaussian log_density so we could compare the analytic solution with the integrator.
• testing energy preservation (and for the Gaussian case, angular momentum preservation) as invariants under the integrator