# 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,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
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# ==============================================================================
from typing import ClassVar
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 squared_distance
from gpjax.typing import (
Array,
ScalarFloat,
)
[docs]
class RBF(StationaryKernel):
r"""The Radial Basis Function (RBF) kernel.
Computes the covariance for pair of inputs $(x, y)$ with lengthscale parameter
$\ell$ and variance $\sigma^2$:
$$
k(x,y)=\sigma^2\exp\Bigg(- \frac{\lVert x - y \rVert^2_2}{2 \ell^2} \Bigg)
$$
"""
name: ClassVar[str] = "RBF"
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(-0.5 * squared_distance(x, y))
return K.squeeze()
@property
def spectral_density(self) -> npd.MultivariateNormal:
r"""The spectral measure $\mathcal{N}(\boldsymbol{0}, \mathrm{diag}(\ell)^{-2})$."""
scale_tril = self._spectral_scale_tril()
return npd.MultivariateNormal(
jnp.zeros(scale_tril.shape[0]), scale_tril=scale_tril
)