def apply_C_matches_sym():
sigma = 1.
N_X = 100
X = np.random.randn(N_X, 2)
kernel = lambda X, Y: gaussian_kernel(X, Y, sigma=sigma)
temp = incomplete_cholesky(X, kernel, eta=0.1)
I, R, nu = (temp["I"], temp["R"], temp["nu"])
R_test = incomplete_cholesky_new_points(X, X, kernel, I, R, nu)
v = np.random.randn(N_X.shape[0])
lmbda = 1.
x = gaussian_low_rank.apply_left_C(v, X, X, R.T, R_test.T, lmbda)
y = develop_gaussian_low_rank.apply_left_C_sym(v, X, R.T, lmbda)
assert_allclose(x, y)
def apply_C_matches_sym():
sigma = 1.
N_X = 100
X = np.random.randn(N_X, 2)
kernel = lambda X, Y: gaussian_kernel(X, Y, sigma=sigma)
temp = incomplete_cholesky(X, kernel, eta=0.1)
I, R, nu = (temp["I"], temp["R"], temp["nu"])
R_test = incomplete_cholesky_new_points(X, X, kernel, I, R, nu)
v = np.random.randn(N_X.shape[0])
lmbda = 1.
x = gaussian_low_rank.apply_left_C(v, X, X, R.T, R_test.T, lmbda)
y = develop_gaussian_low_rank.apply_left_C_sym(v, X, R.T, lmbda)
assert_allclose(x, y)
def test_apply_C_left_matches_full():
sigma = 1.
N = 100
X = np.random.randn(N, 2)
Y = np.random.randn(20, 2)
low_rank_dim = int(len(X) * .9)
kernel = lambda X, Y = None: gaussian_kernel(X, Y, sigma=sigma)
K_XY = kernel(X, Y)
K = kernel(X)
temp = incomplete_cholesky(X, kernel, eta=low_rank_dim)
I, R, nu = (temp["I"], temp["R"], temp["nu"])
R_test = incomplete_cholesky_new_points(X, Y, kernel, I, R, nu)
v = np.random.randn(X.shape[0])
lmbda = 1.
x = (gaussian.compute_C(X, Y, K_XY, sigma) + (K + np.eye(len(X))) * lmbda).dot(v)
y = gaussian_low_rank.apply_left_C(v, X, Y, R.T, R_test.T, lmbda)
assert_allclose(x, y, atol=1e-1)
def test_apply_C_left_matches_full():
sigma = 1.
N = 100
X = np.random.randn(N, 2)
Y = np.random.randn(20, 2)
low_rank_dim = int(len(X) * .9)
kernel = lambda X, Y=None: gaussian_kernel(X, Y, sigma=sigma)
K_XY = kernel(X, Y)
K = kernel(X)
temp = incomplete_cholesky(X, kernel, eta=low_rank_dim)
I, R, nu = (temp["I"], temp["R"], temp["nu"])
R_test = incomplete_cholesky_new_points(X, Y, kernel, I, R, nu)
v = np.random.randn(X.shape[0])
lmbda = 1.
x = (gaussian.compute_C(X, Y, K_XY, sigma) +
(K + np.eye(len(X))) * lmbda).dot(v)
y = gaussian_low_rank.apply_left_C(v, X, Y, R.T, R_test.T, lmbda)
assert_allclose(x, y, atol=1e-1)
