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_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_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)
