"""
=============================================
Density Estimation for a mixture of Gaussians
=============================================

Plot the density estimation of a mixture of two gaussians. Data is
generated from two gaussians with different centers and covariance
matrices.
"""

import itertools
import numpy as np
import pylab as pl
from scikits.learn import gmm

n, m = 300, 2

# generate random sample, two components
np.random.seed(0)
C = np.array([[0., -0.7], [3.5, .7]])
X_train = np.r_[np.dot(np.random.randn(n, 2), C),
          np.random.randn(n, 2) + np.array([20, 20])]

clf = gmm.GMM(n_states=2, n_dim=2, cvtype='full')
clf.fit(X_train)

x = np.linspace(-20.0, 30.0) 
y = np.linspace(-20.0, 40.0) 
X, Y = np.meshgrid(x, y)
XX = np.c_[X.ravel(), Y.ravel()]
Z =  np.log(-clf.eval(XX)[0])
Z = Z.reshape(X.shape)

CS = pl.contour(X, Y, Z)
CB = pl.colorbar(CS, shrink=0.8, extend='both')
pl.scatter(X_train[:, 0], X_train[:, 1], .8)

pl.axis('tight')
pl.show()