def test_kernel_rbf_complex_proper(self) -> None: # pylint: disable=missing-function-docstring
m, d = self.m, self.d
X1 = np.random.randn(m, d) + 1j * np.random.randn(m, d)
X2 = np.random.randn(m, d) + 1j * np.random.randn(m, d)
# Hyper parameters
l = 2.3
sigma_f = 1.5
cov = kernel_rbf_complex_proper(X1, X2, l=l, sigma_f=sigma_f)
self.assertEqual(cov.shape, (m, m))
expected_cov = np.empty(shape=(m, m), dtype=float)
for i, j in product(range(m), range(m)):
krr = kernel_rbf(X1.real[i:i + 1],
X2.real[j:j + 1],
l=l,
sigma_f=sigma_f)
kii = kernel_rbf(X1.imag[i:i + 1],
X2.imag[j:j + 1],
l=l,
sigma_f=sigma_f)
# sqrdist = np.linalg.norm(d)**2
expected_cov[i, j] = krr + kii
np.testing.assert_array_almost_equal(cov, expected_cov)
def test_kernel_rbf(self) -> None: # pylint: disable=missing-function-docstring
m, X1, X2 = self.m, self.X1, self.X2
# Hyper parameters
l = 2.3
sigma_f = 1.5
cov = kernel_rbf(X1, X2, l=l, sigma_f=sigma_f)
self.assertEqual(cov.shape, (m, m))
expected_cov = np.empty(shape=(m, m))
for i, j in product(range(m), range(m)):
sqrdist = np.sum((X1[i] - X2[j])**2)
expected_cov[i, j] = sigma_f**2 * math.exp(-0.5 * sqrdist / l**2)
np.testing.assert_array_almost_equal(cov, expected_cov)
def test_compute_loglikelihood(self) -> None: # pylint: disable=missing-function-docstring
m = self.m
X1 = self.X1
y1 = X1 @ [1, -2]
noise_power = 0.0
l = 1.0
sigma_f = 1.0
nll = -compute_loglikelihood(
X1, y1, noise_power, kernel=kernel_rbf, theta=[l, sigma_f])
# Compute the expected likelihood
K = kernel_rbf(X1, X1, l=l, sigma_f=sigma_f)
expected_nll = 0.5 * np.log(np.linalg.det(K)) + \
+0.5 * y1.T @ np.linalg.inv(K).dot(y1) + \
+0.5 * m * math.log(2*np.pi)
self.assertAlmostEqual(nll, expected_nll)