# Copyright 2022 The thomaspinder Contributors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
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# See the License for the specific language governing permissions and
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# ==============================================================================
import jax.numpy as jnp
from jaxtyping import Float
import numpyro.distributions as npd
from gpjax.kernels.base import _val
from gpjax.kernels.stationary.base import StationaryKernel
from gpjax.kernels.stationary.utils import (
build_student_t_distribution,
euclidean_distance,
)
from gpjax.typing import (
Array,
ScalarFloat,
)
[docs]
class Matern12(StationaryKernel):
r"""The Matérn kernel with smoothness parameter fixed at 0.5.
Computes the covariance on a pair of inputs $(x, y)$ with
lengthscale parameter $\ell$ and variance $\sigma^2$.
$$
k(x, y) = \sigma^2\exp\Bigg(-\frac{\lvert x-y \rvert}{\ell}\Bigg)
$$
"""
name: str = "Matérn12"
def __call__(self, x: Float[Array, " D"], y: Float[Array, " D"]) -> ScalarFloat:
x = self.slice_input(x) / _val(self.lengthscale)
y = self.slice_input(y) / _val(self.lengthscale)
K = _val(self.variance) * jnp.exp(-euclidean_distance(x, y))
return K.squeeze()
@property
def spectral_density(self) -> npd.MultivariateStudentT:
r"""The spectral measure of the Matérn-1/2 kernel: a multivariate
Student's t with 1 degree of freedom and scale $\mathrm{diag}(\ell)^{-1}$."""
return build_student_t_distribution(
nu=1, scale_tril=self._spectral_scale_tril()
)