def gmm(X,C,eps):
import numpy as np
from norm_density import norm_density
from copy import deepcopy
# Initialisations
counter = 0;
mu_est = 2*np.mean(X) * np.sort(np.random.uniform(0,1,C));
sigma_est = np.ones(C)*np.std(X);
p_est = np.ones(C)/C;
difference = eps;
dens = np.tile(np.zeros(len(X)),(C,1))
# Perform EM algorithm to find means and sigmas
while (difference >= eps) & (counter < 25000):
# E step: soft densification of the X into one of the mixtures
for j in range(0,C):
dens[j] = p_est[j] * norm_density(X, mu_est[j], sigma_est[j]);
#normalize
dens = dens / np.tile(sum(dens), (C, 1));
#M step: ML estimate the parameters of each dens (i.e., p, mu, sigma)
mu_est_old = deepcopy(mu_est);
sigma_est_old = deepcopy(sigma_est);
p_est_old = deepcopy(p_est);
# Get next values for all means, sigmas and pis
for j in range(0,C):
mu_est[j] = sum( dens[j,:]*X ) / sum(dens[j,:]);
sigma_est[j] = np.sqrt( sum(dens[j,:]*(X - mu_est[j])**2) / sum(dens[j,:]) );
p_est[j] = np.mean(dens[j,:]);
# Compute Mean square errors of all estimates
difference = sum(abs(np.array(mu_est_old)-np.array(mu_est))) + sum(abs(np.array(sigma_est_old)-np.array(sigma_est))) + sum(abs(np.array(p_est_old)-np.array(p_est)))
counter = counter + 1;
return mu_est, sigma_est, p_est, counter, difference
print('------Means--------')
print('mu_1=%1.4f'%mu_est[0])
print('mu_2=%1.4f'%mu_est[1])
print('mu_3=%1.4f'%mu_est[2])
print('------Variance--------')
print('sigma_1=%1.4f'%sigma_est[0])
print('sigma_2=%1.4f'%sigma_est[1])
print('sigma_3=%1.4f'%sigma_est[2])
print('------Weights-------')
print('W_1=%1.4f'%p_est[0])
print('W_2=%1.4f'%p_est[1])
print('W_3=%1.4f'%p_est[2])
x = np.linspace(min(mu_est)-4*max(sigma_est),max(mu_est)+4*max(sigma_est),1000);
pdf = np.tile(np.zeros(1000),(C,1))
for i in range(0,C):
pdf[i] = p_est[i]*norm_density(x,mu_est[i],sigma_est[i])
# plt.plot(x,pdf[i])
plt.hist(ib, bins=60, normed=True,histtype='step', color='grey',label='2014 Data')
plt.plot(x, sum(pdf), lw=1.5, color='black',label='fit');
plt.xlabel('$I_{base}$')
plt.ylim((0.0,0.17))
plt.xlim((-2,35))
plt.ylabel('fraction')
plt.legend()
plt.title('Prior distribution of baseline magnification')
plt.show()