def test_RBF_times_ConstantKernel(self):
n = 3
m = 4
n_dim = 12
X = np.random.randn(n, n_dim)
Y = np.random.randn(m, n_dim)
factor = 10.0
prod_kernel = Product(RBFKernel(), ConstantKernel(constant=factor))
ref_kernel = RBFKernel()
K_prod, dK_prod = prod_kernel(
X, Y, dx=True, dy=True, eval_gradient=True)
K_ref, dK_ref1 = ref_kernel(X, Y, dx=True, dy=True, eval_gradient=True)
# Derivative with respect to the second hyperparameter:
dK_ref2 = np.zeros((n*(1+n_dim), m*(1+n_dim), 1))
dK_ref2[:, :, 0] = K_ref
K_ref *= factor
dK_ref1 *= factor
np.testing.assert_allclose(K_prod, K_ref)
np.testing.assert_allclose(dK_prod[:, :, :-1], dK_ref1)
np.testing.assert_allclose(dK_prod[:, :, -1:], dK_ref2)
def test_comparison2product(self):
X = np.random.randn(3, 4)
Y = np.random.randn(3, 4)
kernel1 = Exponentiation(RBFKernel(length_scale=1.23), exponent=2)
kernel2 = Product(RBFKernel(length_scale=1.23),
RBFKernel(length_scale=1.23))
K1 = kernel1(X, Y, dx=True, dy=True)
K2 = kernel2(X, Y, dx=True, dy=True)
np.testing.assert_allclose(K1, K2)
def test_versus_anisotropic_rbf(self):
X = np.random.randn(8, 2)
Y = np.random.randn(8, 2)
kernel = Product(Masking(RBFKernel(length_scale=1.5), slice(0, 1)),
Masking(RBFKernel(length_scale=0.5), slice(1, 2)))
ref_kernel = RBFKernel(length_scale=np.array([1.5, 0.5]))
K, dK = kernel(X, Y, dx=True, dy=True, eval_gradient=True)
K_ref, dK_ref = ref_kernel(X, Y, dx=True, dy=True, eval_gradient=True)
np.testing.assert_allclose(K, K_ref)
np.testing.assert_allclose(dK, dK_ref)
def test_2times2is4(self):
n = 3
m = 4
n_dim = 12
X = np.random.randn(n, n_dim)
Y = np.random.randn(m, n_dim)
kernel1 = Product(DotProductKernel(), DotProductKernel())
kernel2 = DotProductKernel(exponent=4)
K1 = kernel1(X, Y, dx=True, dy=True)
K2 = kernel2(X, Y, dx=True, dy=True)
np.testing.assert_allclose(K1, K2)
def test_comparison2product(self):
n = 3
m = 4
n_dim = 12
X = np.random.randn(n, n_dim)
Y = np.random.randn(m, n_dim)
factor = 10.0
kernel1 = Rescaling(RBFKernel(), factor)
kernel2 = Product(ConstantKernel(constant=factor), RBFKernel())
K1, dK1 = kernel1(X, Y, dx=True, dy=True, eval_gradient=True)
K2, dK2 = kernel2(X, Y, dx=True, dy=True, eval_gradient=True)
np.testing.assert_allclose(K1, K2)
np.testing.assert_allclose(dK1, dK2)
class DottimeDotTest(KernelTest.KernelTest):
kernel = Product(DotProductKernel(exponent=1, sigma0=0.1),
DotProductKernel(sigma0=0.1))
def test_2times2is4(self):
n = 3
m = 4
n_dim = 12
X = np.random.randn(n, n_dim)
Y = np.random.randn(m, n_dim)
kernel1 = Product(DotProductKernel(), DotProductKernel())
kernel2 = DotProductKernel(exponent=4)
K1 = kernel1(X, Y, dx=True, dy=True)
K2 = kernel2(X, Y, dx=True, dy=True)
np.testing.assert_allclose(K1, K2)
class DottimesConstantTest(KernelTest.KernelTest):
kernel = Product(DotProductKernel(exponent=2),
ConstantKernel(constant=10.0))
class RBFtimesRBFTest(KernelTest.KernelTest):
kernel = Product(RBFKernel(length_scale=0.8),
RBFKernel(length_scale=1.2))