Illustration of the different standard random distributions and different random number generators

"""
Illustration of the different standard random distributions and different random number generators

"""

import numpy
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
import scipy.stats
import pyNN.random as random

try:
    from neuron import h
except ImportError:
    have_nrn = False
else:
    have_nrn = True
    from pyNN.neuron.random import NativeRNG

n = 100000
nbins = 100

rnglist = [random.NumpyRNG(seed=984527)]
if random.have_gsl:
    rnglist.append(random.GSLRNG(seed=668454))
if have_nrn:
    rnglist.append(NativeRNG(seed=321245))


cases = (
    ("uniform", {"low": -65, "high": -55}, (-65, -55), scipy.stats.uniform(loc=-65, scale=10)),
    ("gamma", {"k": 2.0, "theta": 0.5}, (0, 5), scipy.stats.gamma(2.0, loc=0.0, scale=0.5)),
    ("normal", {"mu": -1.0, "sigma": 0.5}, (-3, 1), scipy.stats.norm(loc=-1, scale=0.5)),
    ("exponential", {'beta': 10.0}, (0, 50), scipy.stats.expon(loc=0, scale=10)),
    ("normal_clipped", {"mu": 0.5, "sigma": 0.5, "low": 0, "high": 10}, (-0.5, 3.0), None),
)

fig = plt.figure(1)
rows = len(cases)
cols = len(rnglist)

settings = {
    'lines.linewidth': 0.5,
    'axes.linewidth': 0.5,
    'axes.labelsize': 'small',
    'axes.titlesize': 'small',
    'legend.fontsize': 'small',
    'font.size': 8,
    'savefig.dpi': 150,
}
plt.rcParams.update(settings)
width, height = (2 * cols, 2 * rows)
fig = plt.figure(1, figsize=(width, height))
gs = gridspec.GridSpec(rows, cols)
gs.update(hspace=0.4)


for i, case in enumerate(cases):
    distribution, parameters, xlim, rv = case
    bins = numpy.linspace(*xlim, num=nbins)
    for j, rng in enumerate(rnglist):
        rd = random.RandomDistribution(distribution, rng=rng, **parameters)
        values = rd.next(n)
        assert values.size == n
        plt.subplot(gs[i, j])
        counts, bins, _ = plt.hist(values, bins, range=xlim)
        plt.title("%s.%s%s" % (rng, distribution, parameters.values()))
        if rv is not None:
            pdf = rv.pdf(bins)
            scaled_pdf = n * pdf / pdf.sum()
            plt.plot(bins, scaled_pdf, 'r-')
            plt.ylim(0, 1.2 * scaled_pdf.max())
        plt.xlim(xlim)

plt.savefig("Results/random_distributions.png")