def test_fit_returns_min_1d_grid(): N = 100 D = 3 m = 1 omega = np.random.randn(D, m) u = np.random.uniform(0, 2 * np.pi, m) X = np.random.randn(N, D) C = compute_C_memory(X, omega, u) b = compute_b_memory(X, omega, u) theta = fit(X, omega, u) J = objective(X, theta, omega, u, b, C) thetas_test = np.linspace(theta - 3, theta + 3) Js = np.zeros(len(thetas_test)) for i, theta_test in enumerate(thetas_test): Js[i] = objective(X, np.array([theta_test]), omega, u, b, C) # plt.plot(thetas_test, Js) # plt.plot([theta, theta], [Js.min(), Js.max()]) # plt.title(str(theta)) # plt.show() assert_almost_equal(Js.min(), J, delta=thetas_test[1] - thetas_test[0]) assert_almost_equal(thetas_test[Js.argmin()], theta[0], delta=thetas_test[1] - thetas_test[0])
def test_compute_b_storage_1d2n(): X = np.array([[1.], [2.]]) u = np.array([2.]) omega = np.array([[2.]]) d = 0 b_manual = -np.mean(rff_feature_map_grad2_d(X, omega, u, d)) b = compute_b_memory(X, omega, u) assert_allclose(b_manual, b)
def test_compute_b_equals_compute_b_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) b = compute_b(X, omega, u) b_storage = compute_b_memory(X, omega, u) assert_allclose(b, b_storage)
def test_fit(): 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_memory(X, omega, u) b = compute_b_memory(X, omega, u) theta = fit(X, omega, u) theta_manual = np.linalg.solve(C, b) assert_allclose(theta, theta_manual)
def test_objective_sym_equals_completely_manual_manually(): N = 100 D = 3 m = 3 omega = np.random.randn(D, m) u = np.random.uniform(0, 2 * np.pi, m) X = np.random.randn(N, D) theta = np.random.randn(m) J_manual = 0. for n in range(N): b_manual = np.zeros(m) C_manual = np.zeros((m, m)) J_n_manual = 0. for d in range(D): b_term_manual = -np.sqrt(2. / m) * np.cos(np.dot(X[n], omega) + u) * (omega[d, :]**2) b_term = rff_feature_map_grad2_d(X[n], omega, u, d) assert_allclose(b_term_manual, b_term) b_manual -= b_term_manual J_manual += np.dot(b_term_manual, theta) J_n_manual += np.dot(b_term_manual, theta) c_vec_manual = -np.sqrt(2. / m) * np.sin(np.dot(X[n], omega) + u) * omega[d, :] c_vec = rff_feature_map_grad_d(X[n], omega, u, d) assert_allclose(c_vec_manual, c_vec) C_term = np.outer(c_vec_manual, c_vec_manual) C_manual += C_term # not regularised here, done afterwards J_manual += 0.5 * np.dot(theta, np.dot(C_term, theta)) J_n_manual += 0.5 * np.dot(theta, np.dot(C_term, theta)) b = compute_b_memory(X[n].reshape(1, m), omega, u) C = compute_C_memory(X[n].reshape(1, m), omega, u) assert_allclose(b_manual, b) assert_allclose(C_manual, C) # discard regularisation for these internal checks J_n = objective(X[n].reshape(1, m), theta, omega, u) J_n_2 = 0.5 * np.dot(theta, np.dot(C, theta)) - np.dot(theta, b) assert_allclose(J_n_2, J_n, rtol=1e-4) assert_allclose(J_n_manual, J_n, rtol=1e-4) J_manual /= N J = objective(X, theta, omega, u) assert_close(J, J_manual, decimal=5)
def test_objective_sym_given_b_C_equals_given_nothing(): 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_memory(X, omega, u) b = compute_b_memory(X, omega, u) theta = np.random.randn(m) J = objective(X, theta, omega, u, b, C) J2 = objective(X, theta, omega, u) assert_close(J, J2)
def test_objective_sym_given_b_C(): 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_memory(X, omega, u) b = compute_b_memory(X, omega, u) theta = np.random.randn(m) J = objective(X, theta, omega, u, b, C) J_manual = 0.5 * np.dot(theta.T, np.dot(C, theta)) - np.dot(theta, b) assert_close(J, J_manual)
def test_fit_returns_min_random_search(): 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_memory(X, omega, u) b = compute_b_memory(X, omega, u) theta = fit(X, omega, u) J = objective(X, theta, omega, u, b, C) for noise in [0.0001, 0.001, 0.1, 1, 10, 100]: for _ in range(10): theta_test = np.random.randn(m) * noise + theta J_test = objective(X, theta_test, omega, u, b, C) assert_less_equal(J, J_test)