Quasi Monte Carlo Rd Sampling

[arvoelke]

Resolves #152. Code is modified from http://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequences/

This is a new method for sampling points from the sphere and ball (encoders and evaluation points).
It is still possible to use the old method by passing base=Sobol() to the constructor of all of the distributions, instead of the new default of base=Rd(). The biggest benefit is the new method works for arbitrary dimension, whereas the old method regressed to Nengo's independent distribution for d > 40.

Some plots from the new method (to be in the documentation upon release):

Versus the old method (Sobol):

[codecov-io]

Codecov Report

Merging #153 into master will not change coverage.
The diff coverage is 100%.

@@          Coverage Diff          @@
##           master   #153   +/-   ##
=====================================
  Coverage     100%   100%           
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  Files          29     29           
  Lines        1374   1398   +24     
  Branches      157    162    +5     
=====================================
+ Hits         1374   1398   +24

Impacted Files	Coverage Δ
nengolib/stats/ntmdists.py	100% <100%> (ø)	⬆️

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[arvoelke]

@astoeckel Since you were using the Halton sequence, this might be of interest to you. This is a new quasi-random sequence, that's been implemented as a Nengo distribution. You can use it to generate scattered points on the cube, sphere, or ball.

Links to staging documentation (with inline code examples):

• https://arvoelke.github.io/nengolib-docs/master/nengolib.stats.Rd.html#nengolib.stats.Rd
• https://arvoelke.github.io/nengolib-docs/master/nengolib.stats.ScatteredCube.html#nengolib.stats.ScatteredCube
• https://arvoelke.github.io/nengolib-docs/master/nengolib.stats.ScatteredHypersphere.html

[carlosgmartin]

@arvoelke Could @sdementen's suggestions be incorporated? (Avoiding Python for loops, which are slow, as much as possible.)

[arvoelke]

Thanks for the feedback/request. Done in #191 which has been merged into master. It is unlikely to be released to pypi due to compatibility drift that should be sorted out. It should be possible to install/depend on master directly if this speed-up is needed.

[carlosgmartin]

@arvoelke Thanks! I see a few other places in the code could benefit from vectorization as well, if you're interested. Let me know if you'd like me to open an issue or pull request.

[arvoelke]

I'd be interested in PRs if they are motivated by things that you're running and then you found that your changes helped run them faster/etc (as opposed to just optimizing code for the sake of it).

If you are hungry for speed-ups across the board I would suggest looking into Pyston. The lite version can be installed via pip install pyston_lite_autoload and provides a boost in speed to the entire Python process. I've had good experiences with both lite and full versions.