def test_update_b_single_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)
b = compute_b(X, omega, u)
b = update_b_single(x, b, n=N, omega=omega, u=u)
b_batch = compute_b(np.vstack((X, x)), omega, u)
assert_allclose(b, b_batch)
def test_update_b_single_equals_compute_b_when_initialised_correctly():
sigma = 1.
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
b_update = np.zeros(m)
n_update = m
for x in X:
b_update = update_b_single(x, b_update, n_update, omega, u)
n_update += 1
# initial fit and batch (average of "fake" b and new observations
b_fake = np.zeros(m)
n_fake = m
b_batch = (b_fake * n_fake + compute_b(X, omega, u) * N) / (n_fake + N)
assert_allclose(b_update, b_batch)