# 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 typing as tp
from jax import vmap
import jax.numpy as jnp
from jaxtyping import Float
import lineax as lx
import gpjax
from gpjax.kernels.computations import AbstractKernelComputation
from gpjax.typing import Array
K = tp.TypeVar("K", bound="gpjax.kernels.base.AbstractKernel")
[docs]
class ConstantDiagonalKernelComputation(AbstractKernelComputation):
r"""Computation engine for constant diagonal kernels."""
[docs]
def gram(self, kernel: K, x: Float[Array, "N D"]) -> lx.AbstractLinearOperator:
value = kernel(x[0], x[0])
diag = jnp.full(x.shape[0], value)
return lx.TaggedLinearOperator(
lx.DiagonalLinearOperator(diag), lx.positive_semidefinite_tag
)
def _diagonal(
self, kernel: K, inputs: Float[Array, "N D"]
) -> lx.AbstractLinearOperator:
diag = vmap(lambda x: kernel(x, x))(inputs)
return lx.TaggedLinearOperator(
lx.DiagonalLinearOperator(diag), lx.positive_semidefinite_tag
)
def _cross_covariance(
self, kernel: K, x: Float[Array, "N D"], y: Float[Array, "M D"]
) -> Float[Array, "N M"]:
# TODO: This is currently a dense implementation. We should implement
# a sparse LinearOperator for non-square cross-covariance matrices.
cross_cov = vmap(lambda x: vmap(lambda y: kernel(x, y))(y))(x)
return cross_cov