Add nengo.dists.ScatteredSimplex

[carlosgmartin]

Is your feature request related to a problem? Please describe.

I'd like to use a quasirandom distribution over the standard simplex.

Describe the solution you'd like

Add a class nengo.dists.ScatteredSimplex analogous to nengo.dists.ScatteredHypersphere.

Describe alternatives you've considered

Example:

import numpy as np
from matplotlib import pyplot as plt
import mpltern

from nengo.dists import Distribution, QuasirandomSequence


class ScatteredSimplex(Distribution):

    def __init__(
        self,
        base=QuasirandomSequence()
    ):
        self.base = base

    def sample(self, n, d=1, rng=np.random):
        # uniform distribution
        u = self.base.sample(n, d, rng)
        # exponential distribution
        e = -np.log(u)
        # uniform simplex distribution
        x = e / e.sum(-1, keepdims=True)
        return x


def main():
    x = ScatteredSimplex().sample(10**5, 3)
    fig, ax = plt.subplots(subplot_kw={'projection': 'ternary'})
    ax.scatter(*x.T, lw=0, s=.5)
    plt.show()


if __name__ == '__main__':
    main()

Result: