ps5.py

import numpy as np
import scipy as sc
import networkx as nx
from matplotlib.colors import LogNorm
from pylab import *


def sample(n):
    m = sc.misc.comb(n, 2)
    r_vals = np.random.random(m)
    w_vals = [-log(1-r) for r in r_vals]
    return w_vals


def calc_s(n, t):
    a = np.zeros((n,n))
    il = np.tril_indices(n, -1)
    a[il] = [1 if w>=t else 0 for w in sample(n)]
    g = nx.from_numpy_matrix(a)
    s = len(nx.connected_components(g).next())
    return s


n = 500
t_min = 0
t_max = 13
n_slices = 50
n_iter = 30
x = []
y = []
for t in np.linspace(t_min, t_max, n_slices):
    print "thresholder:", t
    for i in range(n_iter):
        s = calc_s(n, t)
        y.append(float(s)/float(n))
        x.append(t)

hist2d(x, y, bins=40, norm=LogNorm())
colorbar()
xlabel('Threshold')
ylabel('s/n')
savefig('ps5-1b.png')