normalisation.py

import numpy as np
import matplotlib.pyplot as plt


def normfactor(hist, edges):
    a = np.sum(hist)*(edges[1:] - edges[:-1])
    return a


def gauss(xs, loc=0.0, scale=1.0):
    norm = 1/(scale*np.sqrt(2*np.pi))
    return norm*np.exp(-np.square((xs - loc)/(np.sqrt(2)*scale)))


np.random.seed(123987)

def draw(loc, scale, color):
    range = (-0, 10e4)
    nbins = 150

    xs = np.random.normal(loc, scale, size=int(1e6))
    hist, edges = np.histogram(xs, bins=nbins, range=range)
    hist = hist.astype(edges.dtype)

    norm_factor = normfactor(hist, edges)
    hist /= norm_factor

    plt.errorbar((edges[:-1] + edges[1:])/2, hist, fmt='.',
                 color=color, alpha=0.5)

    xs = np.linspace(range[0], range[1], 2*nbins)
    ys = gauss(xs, loc, scale)
    plt.plot(xs, ys, color=color, alpha=0.5,
             label=r'$\mu = {0}$, $\sigma = {1}$'.format(loc, scale))

# draw(0, 1, 'blue')
# draw(2, 0.5, 'red')
# draw(-3, 2, 'green')
draw(1e4, 1e3, 'blue')
plt.legend(loc='best')
plt.savefig('norm.pdf')