def test_cardinality(self):
def delannoy(m, n):
s = 0
for k in range(min(m, n) + 1):
s += binom(m, k) * binom(n, k) * 2**k
return s
for size_X in (1, 2, 3):
for size_Y in (1, 2, 3, 4):
card = cardinality(size_X, size_Y)
card2 = len(list(alignment_matrices(size_X, size_Y)))
assert_equal(card, card2)
assert_equal(card, delannoy(size_X - 1, size_Y - 1))
def test_mean_cost_grad(self):
X, Y = _make_time_series(size_X=3, size_Y=4, num_dim=2)
C = squared_euclidean_cost(X, Y)
A_sum = np.zeros_like(C)
n = 0
for A in alignment_matrices(*C.shape):
A_sum += A
n += 1
A_mean1 = A_sum / n
A_mean2 = mean_cost_value_and_grad_C(C)[1]
assert_array_almost_equal(A_mean1, A_mean2)
G = _num_gradient(mean_cost_C, A_sum) # Any matrix can be used.
assert_array_almost_equal(A_mean1, G)
def test_mean_cost(self):
X, Y = _make_time_series(size_X=3, size_Y=4, num_dim=2)
C = squared_euclidean_cost(X, Y)
scores = []
for A in alignment_matrices(*C.shape):
scores.append(np.vdot(A, C))
val1 = np.mean(scores)
val2 = mean_cost_C(C)
val3 = mean_cost_value_and_grad_C(C)[0]
val4 = mean_cost(X, Y)
val5 = mean_cost_value_and_grad(X, Y)[0]
assert_almost_equal(val1, val2)
assert_almost_equal(val1, val3)
assert_almost_equal(val1, val4)
assert_almost_equal(val1, val5)
def _expectation_brute_force(C, gamma=1.0):
p = _probas(C, gamma=gamma)
E = np.zeros_like(C)
for i, A in enumerate(alignment_matrices(*C.shape)):
E += p[i] * A
return E
def _probas(C, gamma=1.0):
scores = []
for A in alignment_matrices(*C.shape):
scores.append(np.vdot(A, C))
scores = np.array(scores)
return softmax(-scores / gamma)
def _sdtw_brute_force(C, gamma=1.0):
scores = []
for A in alignment_matrices(*C.shape):
scores.append(np.vdot(A, C))
scores = np.array(scores)
return -gamma * logsumexp(-scores / gamma)