def test_update_b_L_C_weighted_equals_compute_b_and_compute_L_C_constant_weights(
):
N = 2
D = 2
m = 2
omega = np.random.randn(D, m)
u = np.random.uniform(0, 2 * np.pi, m)
X1 = np.random.randn(N, D)
X2 = np.random.randn(N, D)
log_weights1 = np.log(np.ones(N))
log_weights2 = np.log(np.ones(N))
stacked = np.vstack((X1, X2))
b = compute_b(stacked, omega, u)
L_C = np.linalg.cholesky(compute_C(stacked, omega, u))
b_updated = compute_b(X1, omega, u)
L_C_updated = np.linalg.cholesky(compute_C(X1, omega, u))
log_sum_weights1 = log_sum_exp(log_weights1)
b_updated, L_C_updated = update_b_L_C_weighted(X2, b_updated, L_C_updated,
log_sum_weights1,
log_weights2, omega, u)
assert_allclose(b, b_updated)
assert_allclose(L_C, L_C_updated)
def test_update_L_C_equals_batch():
N = 100
D = 3
m = 10
omega = np.random.randn(D, m)
u = np.random.uniform(0, 2 * np.pi, m)
X = np.random.randn(N, D)
x = np.random.randn(D)
L_C = np.linalg.cholesky(compute_C(X, omega, u))
L_C = update_L_C_single(x, L_C, N, omega, u)
L_C_batch = np.linalg.cholesky(compute_C(np.vstack((X, x)), omega, u))
assert_allclose(L_C, L_C_batch)
def test_update_C_equals_batch():
N = 100
D = 3
m = 10
omega = np.random.randn(D, m)
u = np.random.uniform(0, 2 * np.pi, m)
X = np.random.randn(N, D)
x = np.random.randn(D)
C = compute_C(X, omega, u)
C = update_C(x, C, n=N, omega=omega, u=u)
C_batch = compute_C(np.vstack((X, x)), omega, u)
assert_allclose(C, C_batch)
def test_update_L_C_single_equals_compute_L_C_when_initialised_correctly():
sigma = 1.
lmbda = 2.
N = 200
D = 2
m = 10
X = np.random.randn(N, D)
# basis
omega, u = rff_sample_basis(D, m, sigma)
# initial fit and update
L_C_update = np.eye(m) * np.sqrt(lmbda)
n_update = m
for x in X:
L_C_update = update_L_C_single(x, L_C_update, n_update, omega, u)
n_update += 1
# initial fit and batch (average of "fake" b and new observations
L_C_fake = np.eye(m) * np.sqrt(lmbda)
n_fake = m
C_batch = (np.dot(L_C_fake, L_C_fake.T) * n_fake +
compute_C(X, omega, u) * N) / (n_fake + N)
L_C_batch = np.linalg.cholesky(C_batch)
assert_allclose(L_C_update, L_C_batch)
def test_compute_C_equals_compute_C_memory():
N = 100
D = 3
m = 10
omega = np.random.randn(D, m)
u = np.random.uniform(0, 2 * np.pi, m)
X = np.random.randn(N, D)
C = compute_C(X, omega, u)
C_storage = compute_C_memory(X, omega, u)
assert_allclose(C, C_storage, rtol=1e-4)
