def get_kernel(kernel_name, input_shape):
"""Return a kernel for a given name."""
if kernel_name == "white_noise":
kernel = kernels.WhiteNoise(input_shape=input_shape)
elif kernel_name == "linear":
kernel = kernels.Linear(input_shape=input_shape)
elif kernel_name == "polynomial":
kernel = kernels.Polynomial(input_shape=input_shape)
elif kernel_name == "exp_quad":
kernel = kernels.ExpQuad(input_shape=input_shape)
elif kernel_name == "rat_quad":
kernel = kernels.RatQuad(input_shape=input_shape)
elif kernel_name == "matern12":
kernel = kernels.Matern(input_shape=input_shape, nu=0.5)
elif kernel_name == "matern32":
kernel = kernels.Matern(input_shape=input_shape, nu=1.5)
elif kernel_name == "matern52":
kernel = kernels.Matern(input_shape=input_shape, nu=2.5)
elif kernel_name == "matern72":
kernel = kernels.Matern(input_shape=input_shape, nu=3.5)
else:
raise ValueError(f"Kernel name '{kernel_name}' not recognized.")
return kernel
def test_nu_large_recovers_rbf_kernel(x0: np.ndarray, x1: np.ndarray,
input_shape: ShapeType):
"""Test whether a Matern kernel with nu large is close to an RBF kernel."""
lengthscale = 1.25
rbf = kernels.ExpQuad(input_shape=input_shape, lengthscale=lengthscale)
matern = kernels.Matern(input_shape=input_shape,
lengthscale=lengthscale,
nu=15)
np.testing.assert_allclose(
rbf.matrix(x0, x1),
matern.matrix(x0, x1),
err_msg=
"RBF and Matern kernel are not sufficiently close for nu->infty.",
rtol=0.05,
atol=0.01,
)
def test_kernel_matrix(input_dim, nu):
"""Check that the product Matérn kernel matrix is an elementwise product of 1D
Matérn kernel matrices."""
lengthscale = 1.25
matern = kernels.Matern(input_shape=(1,), lengthscale=lengthscale, nu=nu)
product_matern = kernels.ProductMatern(
input_shape=(input_dim,), lengthscales=lengthscale, nus=nu
)
rng = np.random.default_rng(42)
num_xs = 15
xs = rng.random(size=(num_xs, input_dim))
kernel_matrix1 = product_matern.matrix(xs)
kernel_matrix2 = np.ones(shape=(num_xs, num_xs))
for dim in range(input_dim):
kernel_matrix2 *= matern.matrix(_utils.as_colvec(xs[:, dim]))
np.testing.assert_allclose(
kernel_matrix1,
kernel_matrix2,
)
def test_nonpositive_nu_raises_exception(nu):
"""Check whether a non-positive nu parameter raises a ValueError."""
with pytest.raises(ValueError):
kernels.Matern(input_shape=(), nu=nu)
],
name="cov",
)
def fixture_cov(request, input_dim: int) -> kernels.Kernel:
"""Covariance function."""
return request.param[0](**request.param[1], input_dim=input_dim)
@pytest.fixture(
params=[
pytest.param(randprocdef, id=randprocdef[0]) for randprocdef in [
(
"gp",
randprocs.GaussianProcess(
mean=lambda x: np.zeros(x.shape[0]),
cov=kernels.Matern(input_dim=1),
),
),
]
],
name="random_process",
)
def fixture_random_process(request) -> randprocs.RandomProcess:
"""Random process."""
return request.param[1]
@pytest.fixture(name="gaussian_process")
def fixture_gaussian_process(mean, cov) -> randprocs.GaussianProcess:
"""Gaussian process."""
return randprocs.GaussianProcess(mean=mean, cov=cov)
name="cov",
)
def fixture_cov(request, input_dim: int) -> kernels.Kernel:
"""Covariance function."""
return request.param[0](**request.param[1], input_shape=(input_dim,))
@pytest.fixture(
params=[
pytest.param(randprocdef, id=randprocdef[0])
for randprocdef in [
(
"gp",
randprocs.GaussianProcess(
mean=mean_fns.Zero(input_shape=(1,)),
cov=kernels.Matern(input_shape=(1,)),
),
),
]
],
name="random_process",
)
def fixture_random_process(request) -> randprocs.RandomProcess:
"""Random process."""
return request.param[1]
@pytest.fixture(name="gaussian_process")
def fixture_gaussian_process(mean, cov) -> randprocs.GaussianProcess:
"""Gaussian process."""
return randprocs.GaussianProcess(mean=mean, cov=cov)