# 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
# limitations under the License.
# ==============================================================================
import jax.numpy as jnp
from jaxtyping import Float
from paramax import AbstractUnwrappable
from gpjax.kernels.base import _val
from gpjax.kernels.computations import (
AbstractKernelComputation,
ConstantDiagonalKernelComputation,
)
from gpjax.kernels.stationary.base import StationaryKernel
from gpjax.typing import (
Array,
ScalarFloat,
)
[docs]
class White(StationaryKernel):
r"""The White noise kernel.
Computes the covariance for pairs of inputs $(x, y)$ with variance $\sigma^2$:
$$
k(x, y) = \sigma^2 \delta(x-y)
$$
"""
name: str = "White"
def __init__(
self,
active_dims: list[int] | slice | None = None,
variance: ScalarFloat | AbstractUnwrappable = 1.0,
n_dims: int | None = None,
compute_engine: AbstractKernelComputation = ConstantDiagonalKernelComputation(),
):
"""Initializes the kernel.
Args:
active_dims: The indices of the input dimensions that the kernel operates on.
variance: the variance of the kernel σ.
n_dims: The number of input dimensions.
compute_engine: The computation engine that the kernel uses to compute the
covariance matrix
"""
super().__init__(active_dims, 1.0, variance, n_dims, compute_engine)
def __call__(self, x: Float[Array, " D"], y: Float[Array, " D"]) -> ScalarFloat:
K = jnp.all(jnp.equal(x, y)) * _val(self.variance)
return K.squeeze()