# 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 beartype.typing as tp
import jax.numpy as jnp
from jaxtyping import Float
from paramax import AbstractUnwrappable
from gpjax.kernels.base import AbstractKernel, _val
from gpjax.kernels.computations import (
AbstractKernelComputation,
DenseKernelComputation,
)
from gpjax.parameters import NonNegativeReal
from gpjax.typing import (
Array,
ScalarFloat,
)
[docs]
class Linear(AbstractKernel):
r"""The linear kernel.
Computes the covariance for pairs of inputs $(x, y)$ with variance $\sigma^2$:
$$
k(x, y) = \sigma^2 x^{\top}y
$$
"""
name: str = "Linear"
variance: tp.Any
def __init__(
self,
active_dims: tp.Union[list[int], slice, None] = None,
variance: tp.Union[ScalarFloat, AbstractUnwrappable] = 1.0,
n_dims: tp.Union[int, None] = None,
compute_engine: AbstractKernelComputation = DenseKernelComputation(),
):
"""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.
"""
if isinstance(variance, AbstractUnwrappable):
self.variance = variance
else:
self.variance = NonNegativeReal(variance)
super().__init__(active_dims, n_dims, compute_engine)
def __call__(
self,
x: Float[Array, " D"],
y: Float[Array, " D"],
) -> ScalarFloat:
x = self.slice_input(x)
y = self.slice_input(y)
K = _val(self.variance) * jnp.matmul(x.T, y)
return K.squeeze()