def test_sdtw(self):
X, Y = _make_time_series(size_X=3, size_Y=4, num_dim=2)
C = squared_euclidean_cost(X, Y)
assert_almost_equal(sdtw_C(C), _sdtw_brute_force(C))
assert_almost_equal(sdtw_C(C), sdtw_value_and_grad_C(C)[0])
assert_almost_equal(sdtw_C(C), sdtw(X, Y))
assert_almost_equal(sdtw_C(C, gamma=0.1),
_sdtw_brute_force(C, gamma=0.1))
assert_almost_equal(sdtw_C(C, gamma=0.1),
sdtw_value_and_grad_C(C, gamma=0.1)[0])
def test_sdtw_entropy(self):
X, Y = _make_time_series(size_X=3, size_Y=4, num_dim=2)
C = squared_euclidean_cost(X, Y)
gamma = 1.0
eps = 1e-6
p = _probas(C, gamma=gamma)
H1 = -np.dot(p, np.log(p))
H2 = sdtw_entropy_C(C, gamma=gamma)
H3 = -(sdtw_C(C, gamma + eps) - sdtw_C(C, gamma - eps)) / (2 * eps)
H4 = sdtw_entropy(X, Y, gamma=gamma)
assert_almost_equal(H1, H2)
assert_almost_equal(H1, H3)
assert_almost_equal(H1, H4)
def test_sdtw_grad_C(self):
X, Y = _make_time_series(size_X=3, size_Y=4, num_dim=2)
C = squared_euclidean_cost(X, Y)
V, P = sdtw_C(C, return_all=True)
G = sdtw_grad_C(P)
G_num = _num_gradient(sdtw_C, C)
G_bf = _expectation_brute_force(C)
assert_array_almost_equal(G, G_num)
assert_array_almost_equal(G, G_bf)
# Check value_and_grad.
for gamma in (0.1, 1.0):
G = sdtw_value_and_grad_C(C, gamma=gamma)[1]
G_bf = _expectation_brute_force(C, gamma=gamma)
assert_array_almost_equal(G, G_bf)
def test_sdtw_hessian_product(self):
def f(C, M):
V, P = sdtw_C(C, return_all=True)
return sdtw_directional_derivative_C(P, M)
X, Y = _make_time_series(size_X=3, size_Y=4, num_dim=2)
C = squared_euclidean_cost(X, Y)
V, P = sdtw_C(C, return_all=True)
E = sdtw_grad_C(P, return_all=True)
V_dot = sdtw_directional_derivative_C(P, C, return_all=True)
hvp = sdtw_hessian_product_C(P, E, V_dot)
hvp_num = _num_gradient(functools.partial(f, M=C), C)
# The Hessian product is equal to the gradient of the directional derivative.
assert_array_almost_equal(hvp, hvp_num)
# Check that wrong inputs raise an exception.
assert_raises(ValueError, sdtw_hessian_product_C, P, E, X)
assert_raises(ValueError, sdtw_hessian_product_C, P, X, V_dot)
def f(X, Y):
C = squared_euclidean_cost(X, Y, log=True)
return sdtw_C(C)
def f(C, M):
V, P = sdtw_C(C, return_all=True)
return sdtw_directional_derivative_C(P, M)