def test_ellipse_plotter():
f = plt.figure(figsize=(7, 7))
for i, Sig in enumerate([np.array([[1.0, 0.0], [0.0, 0.25]]),
np.array([[0.25, 0.0], [0.0, 1.0]]),
np.array([[1.0, 0.8], [0.8, 1.0]]),
np.array([[1.0, -0.8], [-0.8, 1.0]])]):
ax = f.add_subplot(2, 2, i+1)
ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)
plot_ellipse([0., 0.], Sig)
ax.set_title("$\Sigma$={}".format(Sig))
f.tight_layout()
f.savefig("plots/ellipse.png")
def test_NormInvWish():
mu_0 = np.r_[0.3, -0.2]
d = len(mu_0)
Lam_0 = np.linalg.inv(np.array([[2, 1.1], [1.1, 1.2]]))
kappa_0 = 2.1
nu_0 = 8
model = dpmm.NormInvWish(mu_0, kappa_0, Lam_0, nu_0)
# First check some numerics
Nsample = 5000
samples = model.sample(size=Nsample)
mu_samples = [s[0] for s in samples]
cov_samples = [s[1] for s in samples]
mean = np.mean(mu_samples, axis=0)
std = np.std(mu_samples, axis=0)/np.sqrt(Nsample)
print "NormInvWish mu_0 = {}".format(mu_0)
print "NormInvWish E(mu) = {} +/- {}".format(mean, std)
mean_cov = np.mean(cov_samples, axis=0)
std_cov = np.std(cov_samples, axis=0)/np.sqrt(Nsample)
print "NormInvWish (Lam_0)^(-1)/(nu_0-d-1) = \n{}".format(np.linalg.inv(Lam_0)/(nu_0-d-1))
print "NormInvWish E(Sig) = \n{}\n +/-\n{}".format(mean_cov, std_cov)
# Now try some plots with different values of kappa_0 and nu_0
f = plt.figure(figsize=(7, 7))
for i, (kappa_0, nu_0) in enumerate(zip([0.4, 0.4, 6.5, 6.5],
[10, 4, 10, 4])):
model = dpmm.NormInvWish(mu_0, kappa_0, Lam_0, nu_0)
samples = model.sample(size=25)
ax = f.add_subplot(2, 2, i+1)
for sample in samples:
mu, Sig = sample
plot_ellipse(mu, Sig, ax=ax, facecolor='none', edgecolor='k', alpha=0.2)
plot_ellipse(mu_0, np.linalg.inv(Lam_0)/(nu_0-d-1), ax=ax, facecolor='none', edgecolor='r')
ax.set_xlim(-3, 3)
ax.set_ylim(-3, 3)
ax.axvline(mu_0[0], c='r', alpha=0.1)
ax.axhline(mu_0[1], c='r', alpha=0.1)
ax.set_title(r"$\kappa_0$={}, $\nu_0$={}".format(kappa_0, nu_0))
print np.mean([s[1] for s in samples], axis=0)
f.savefig("plots/NormInvWish_samples.png")