Add in analysis function to calculate MSDs

[hmacdope]

Fixes #2438

This is a WIP implementation for the calculation of Mean Squared Displacements

Changes made in this Pull Request:

• Add in experimental code for calculation of MSD
• both simple "windowed" calculation (N^2)
• more sophisticated FFT based calculation (Nlog(N))
• some tests

This needs a fair bit more work, including more tests and docs

PR Checklist

• Tests?
• Docs?
• CHANGELOG updated?
• Issue raised/referenced?

[codecov]

Codecov Report

Merging #2619 into develop will decrease coverage by 0.00%.
The diff coverage is 92.85%.

@@             Coverage Diff             @@
##           develop    #2619      +/-   ##
===========================================
- Coverage    91.17%   91.17%   -0.01%     
===========================================
  Files          176      177       +1     
  Lines        23798    23787      -11     
  Branches      3134     3137       +3     
===========================================
- Hits         21699    21687      -12     
- Misses        1476     1478       +2     
+ Partials       623      622       -1     

Impacted Files	Coverage Δ
package/MDAnalysis/analysis/msd.py	92.85% <92.85%> (ø)
auxiliary/base.py	90.84% <0.00%> (-0.56%)	⬇️
coordinates/base.py	94.42% <0.00%> (-0.30%)	⬇️
util.py	88.04% <0.00%> (-0.09%)	⬇️
package/MDAnalysis/lib/transformations.py	78.62% <0.00%> (+0.43%)	⬆️

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[richardjgowers]

@hmacdope this is cool, MSD is a frequent request. Have you looked at this package yet? https://github.com/pdebuyl-lab/tidynamics

Iirc the package is well implemented, so it might be a good idea to make your MSD tool just a wrapped that squeezes MDA objects into tidynamics.

[hmacdope]

Hey Richard, i'll have a look for sure!
What I have written so far covers the FCA algorithm (autocorrFFT) but they have several functions to do with cross correlations that I am missing.

I would be happy to wrap around the library, however a quick look indicates to me that it seems to deal with single particle data (2D ndarrays), ie we would need repeated calls to their MSD function for each particle, operating on some kind of slice of our 3D ndarray trajectory (time,particle,xyz). Im unsure about the overhead for this, but it can be avoided with a bit of refactoring, which is what I have tried to do.
Sorry for the long comment!
Would love to hear any thoughts

[hmacdope]

also think could benefit from some cythonization

[hmacdope]

@lilyminium is there a bilayer trajectory in the test set? This could be useful for demo purposes. I have a few lying around, but understand the desire to keep everything lightweight.

[lilyminium]

@hmacdope GRO_MEMPROT, XTC_MEMPROT. A full list of datafiles and a description of them is in testsuite/MDAnalysisTests/datafiles.py.

[hmacdope]

Thanks so much that makes my life so much easier.

[richardjgowers]

@hmacdope this is the sort of thing that might need a bigger file than we comfortably can fit in the testsuite. In which case maybe a mini regression test (ie checking you get a precalculated number again https://github.com/MDAnalysis/mdanalysis/pull/2622/files#diff-9b2087bc18e88659747785690262c888R46-R51) against the file linked above is fine. But then in addition there'll need to be some sort of larger test against g_msd or similar to check it's sane.

[hmacdope]

@richardjgowers thanks. I'll come up with some good regression tests.
Also are you happy if I add tidynamics as a dependency?
I am having some trouble with the accuracy of larger FFTs, The tidynamics implementation is efficient, and seems to dodge this problem.

[hmacdope]

Some ideas for low cost regression tests include toy problems, ie the unit step trajectory which fits y = Dx^2 exactly.

[hmacdope]

Sorry for the comment spam, it appears that FFT based algorithms (tidynamics included) are only accurate for large toy MSDs (10000+ frames) out to about the fourth dp. This was causing me some confusion. Ill keep you posted on regression tests.

[orbeckst]

@hmacdope please look at your two failures: one is messed up docs in EinsteinMSD, the other is a missing Py 2 construct: for the latter, merge develop, which removes the check for Py 2 things. (EDIT: and don’t keep Py 2 constructs in the PR... Py 2 is gone).

Once the tests pass, everything should be good to go (finally!).

[hmacdope]

I think we should be okay now? Any qualms @lilyminium, @richardjgowers?

[orbeckst]

@lilyminium @richardjgowers please make sure that you that when you're happy you squash and merge as opposed to merging these 136 commits... thanks. (Also thanks from ASV, which prefers to run on fewer commits and also likes having merge commits as opposed to rebases.)

[lilyminium]

@hmacdope are you interested in editing your commit history into a handful of commits or would you prefer this PR get squashed into 1? I did a similar thing with the hole2 module (#2523)

@orbeckst I didn't know that ASV... thanks, will consider in the future

[hmacdope]

@lilyminium difficult to collect commits that would stand on their own I think. Just squash it.

[lilyminium]

LGTM! Thank you @hmacdope!

[hmacdope]

Thanks to everyone involved, was a really fun experience. :)

[orbeckst]

Congratulations on getting this PR finally merged. 253 comments (so far) is a high number, even by our standards. Thanks for your patience and seeing it through until the end.