Question

np.random.seed(123)

# create data set
n = 1000
_mus = np.array([[0,4], [-2,0]])
_sigmas = np.array([[[3, 0], [0, 0.5]], [[1,0],[0,2]]])
_pis = np.array([0.6, 0.4])
xs = np.concatenate([np.random.multivariate_normal(mu, sigma, int(pi*n))
                    for pi, mu, sigma in zip(_pis, _mus, _sigmas)])

# initial guesses for parameters
pis = np.random.random(2)
pis /= pis.sum()
mus = np.random.random((2,2))
sigmas = np.array([np.eye(2)] * 2)

%%time
ll1, pis1, mus1, sigmas1 = em_gmm_orig(xs, pis, mus, sigmas)

intervals = 101
ys = np.linspace(-8,8,intervals)
X, Y = np.meshgrid(ys, ys)
_ys = np.vstack([X.ravel(), Y.ravel()]).T

z = np.zeros(len(_ys))
for pi, mu, sigma in zip(pis1, mus1, sigmas1):
    z += pi*mvn(mu, sigma).pdf(_ys)
z = z.reshape((intervals, intervals))

ax = plt.subplot(111)
plt.scatter(xs[:,0], xs[:,1], alpha=0.2)
plt.contour(X, Y, z, N=10)
plt.axis([-8,6,-6,8])
ax.axes.set_aspect('equal')
plt.tight_layout()

%%time
ll2, pis2, mus2, sigmas2 = em_gmm_vect(xs, pis, mus, sigmas)

intervals = 101
ys = np.linspace(-8,8,intervals)
X, Y = np.meshgrid(ys, ys)
_ys = np.vstack([X.ravel(), Y.ravel()]).T

z = np.zeros(len(_ys))
for pi, mu, sigma in zip(pis2, mus2, sigmas2):
    z += pi*mvn(mu, sigma).pdf(_ys)
z = z.reshape((intervals, intervals))

ax = plt.subplot(111)
plt.scatter(xs[:,0], xs[:,1], alpha=0.2)
plt.contour(X, Y, z, N=10)
plt.axis([-8,6,-6,8])
ax.axes.set_aspect('equal')
plt.tight_layout()

%%time
ll3, pis3, mus3, sigmas3 = em_gmm_eins(xs, pis, mus, sigmas)

# %timeit em_gmm_orig(xs, pis, mus, sigmas)
%timeit em_gmm_vect(xs, pis, mus, sigmas)
%timeit em_gmm_eins(xs, pis, mus, sigmas)

intervals = 101
ys = np.linspace(-8,8,intervals)
X, Y = np.meshgrid(ys, ys)
_ys = np.vstack([X.ravel(), Y.ravel()]).T

z = np.zeros(len(_ys))
for pi, mu, sigma in zip(pis3, mus3, sigmas3):
    z += pi*mvn(mu, sigma).pdf(_ys)
z = z.reshape((intervals, intervals))

ax = plt.subplot(111)
plt.scatter(xs[:,0], xs[:,1], alpha=0.2)
plt.contour(X, Y, z, N=10)
plt.axis([-8,6,-6,8])
ax.axes.set_aspect('equal')
plt.tight_layout()