def _create_case(self, p=2, T=300):
n = 4
X = np.random.normal(size=(T, n))
X[1:] = X[:-1] + 0.5 * np.random.normal(size=(T - 1, n))
X[2:, 0] = X[:-2, -1] + 0.5 * np.random.normal(size=T - 2)
X[1:, 1] = X[:-1, 3] + 0.5 * np.random.normal(size=T - 1)
R = compute_covariance(X, p_max=p)
return R, X
def test_cost_gradient001(self):
p = 4
T = 1000
n = 2
X = np.random.normal(size=(T, n))
X[1:] = X[:-1] + 0.5 * np.random.normal(size=(T - 1, n))
R = compute_covariance(X, p_max=p)
A, _, _ = whittle_lev_durb(R)
B_hat = A_to_B(A)
g = cost_gradient(B_hat, R)
np.testing.assert_almost_equal(g, np.zeros_like(g))
return
def test_cost_function001(self):
n = 2
p = 2
T = 200
for _ in range(10):
X = np.random.normal(size=(T, n))
X[1:] = X[:-1] + 0.5 * np.random.normal(size=(T - 1, n))
R = compute_covariance(X, p_max=p)
A, _, _ = whittle_lev_durb(R)
B = A_to_B(A)
cost0 = cost_function(B, R)
cost = cost_function(B, R, lmbda=0.5)
self.assertAlmostEqual(cost, cost0 + 0.5 * np.sum(np.abs(B)))
return
def test_cost_function000(self):
n = 2
p = 2
T = 200
for _ in range(10):
X = np.random.normal(size=(T, n))
X[1:] = X[:-1] + 0.5 * np.random.normal(size=(T - 1, n))
R = compute_covariance(X, p_max=p)
A, _, _ = whittle_lev_durb(R)
B = A_to_B(A)
cost_opt = cost_function(B, R)
cost_larger = cost_function(B + 1e-3 * np.random.normal(size=B.shape), R)
self.assertGreater(cost_larger, cost_opt)
return
def _create_big_case(self, p=5, T=500):
n = 30
X = np.random.normal(size=(T, n))
X[1:] = X[:-1] + 0.5 * np.random.normal(size=(T - 1, n))
X[2:, 0] = X[:-2, -1] + 0.5 * np.random.normal(size=T - 2)
X[1:, 1] = X[:-1, 3] + 0.5 * np.random.normal(size=T - 1)
L = np.random.normal(size=(n, n))
L[2, :] = 0
L[12, :] = 0
L[9, :] = 0
X[2:] = X[:-2] @ L
R = compute_covariance(X, p_max=p)
return R, X
def _create_case(self, p=1, T=300):
n = 2
X = np.random.normal(size=(T, n))
X[1:] = X[:-1] + 0.5 * np.random.normal(size=(T - 1, n))
R = compute_covariance(X, p_max=p)
return R, X