def test_neg_log_mvnormal():
mu = np.arange(10)
cov = 0.8 * np.ones((10, 10)) + 0.2 * np.eye(10)
neg_log_p = neg_log_mvnormal(mu, cov)
true_rv = st.multivariate_normal(mu, cov)
for x in np.random.randn(10, mu.shape[0]):
assert_almost_equal(neg_log_p(x), -true_rv.logpdf(x))
def test_hamiltonian_monte_carlo_mv():
np.random.seed(1)
mu = np.arange(2)
cov = 0.8 * np.ones((2, 2)) + 0.2 * np.eye(2)
neg_log_p = AutogradPotential(neg_log_mvnormal(mu, cov))
samples, *_ = hamiltonian_monte_carlo(100,
neg_log_p,
np.zeros(mu.shape),
path_len=2.0)
assert_allclose(mu, np.mean(samples, axis=0), atol=0.21)
assert_allclose(cov, np.cov(samples.T), atol=0.31)
def test_leapfrog_mv():
mu = np.arange(10)
cov = 0.8 * np.ones((10, 10)) + 0.2 * np.eye(10)
neg_log_p = neg_log_mvnormal(mu, cov)
dlogp = grad(neg_log_p)
q, p = np.zeros(mu.shape), np.ones(mu.shape)
path_len, step_size = 1, 0.1
# Should be reversible
q_new, p_new, *_ = leapfrog(q, p, dlogp, path_len, step_size)
q_new, p_new, *_ = leapfrog(q_new, p_new, dlogp, path_len, step_size)
assert_almost_equal(q_new, q)
assert_almost_equal(p_new, p)
def test_leapfrog_mv():
mu = np.arange(10)
cov = 0.8 * np.ones((10, 10)) + 0.2 * np.eye(10)
neg_log_p = AutogradPotential(neg_log_mvnormal(mu, cov))
q, p = np.zeros(mu.shape), np.ones(mu.shape)
path_len, step_size = 1, 0.1
V, dVdq = neg_log_p(q)
# Should be reversible
q_new, p_new, _, dVdq = leapfrog(q, p, dVdq, neg_log_p, path_len,
step_size)
q_new, p_new, _, _ = leapfrog(q_new, p_new, dVdq, neg_log_p, path_len,
step_size)
assert_almost_equal(q_new, q)
assert_almost_equal(p_new, p)
fig, ax = plt.subplots(figsize=FIGSIZE)
for q, p in zip(positions, momentums):
ax.plot(q, p)
y_min, _ = ax.get_ylim()
ax.plot(samples, y_min + np.zeros_like(samples), "ko")
ax.set_xlabel("Position")
ax.set_ylabel("Momentum")
ax.set_title("1D Gaussian trajectories in phase space!")
plt.savefig(os.path.join(HERE, "plot2.png"))
### Example 3 ###
mu = np.zeros(2)
cov = np.array([[1.0, 0.8], [0.8, 1.0]])
neg_log_p = AutogradPotential(neg_log_mvnormal(mu, cov))
samples = hamiltonian_monte_carlo(1000, neg_log_p, np.zeros(2))
### Plot 3 ###
fig, ax = plt.subplots(figsize=FIGSIZE)
ax.plot(samples[:, 0], samples[:, 1], "o")
ax.plot(mu[0], mu[1], "o", color="w", ms=20, mfc="C1")
ax.set_title("Multivariate Gaussians!")
plt.savefig(os.path.join(HERE, "plot3.png"))
### Example 4 ###
np.random.seed(19)
samples, positions, momentums, accepted, p_accepts = hmc_slow(
10, neg_log_p, np.random.randn(2), path_len=4, step_size=0.01,
fig, ax = plt.subplots(figsize=FIGSIZE)
for q, p in zip(positions, momentums):
ax.plot(q, p)
y_min, _ = ax.get_ylim()
ax.plot(samples, y_min + np.zeros_like(samples), "ko")
ax.set_xlabel("Position")
ax.set_ylabel("Momentum")
ax.set_title("1D Gaussian trajectories in phase space!")
plt.savefig(os.path.join(HERE, "plot2.png"))
### Example 3 ###
mu = np.zeros(2)
cov = np.array([[1.0, 0.8], [0.8, 1.0]])
neg_log_p = neg_log_mvnormal(mu, cov)
samples = hamiltonian_monte_carlo(1000, neg_log_p, np.zeros(2))
### Plot 3 ###
fig, ax = plt.subplots(figsize=FIGSIZE)
ax.plot(samples[:, 0], samples[:, 1], "o")
ax.plot(mu[0], mu[1], "o", color="w", ms=20, mfc="C1")
ax.set_title("Multivariate Gaussians!")
plt.savefig(os.path.join(HERE, "plot3.png"))
### Example 4 ###
np.random.seed(19)
samples, positions, momentums, accepted = hmc_slow(10,
neg_log_p,