# 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
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# ==============================================================================
import beartype.typing as tp
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,
DenseKernelComputation,
)
from gpjax.kernels.stationary.base import StationaryKernel
from gpjax.parameters import PositiveReal
from gpjax.typing import (
Array,
ScalarArray,
ScalarFloat,
)
Lengthscale = tp.Union[Float[Array, "D"], ScalarArray]
LengthscaleCompatible = tp.Union[ScalarFloat, list[float], Lengthscale]
[docs]
class Periodic(StationaryKernel):
r"""The periodic kernel.
Computes the covariance for pairs of inputs $(x, y)$ with length-scale
parameter $\ell$, variance $\sigma^2$ and period $p$.
$$
k(x, y) = \sigma^2 \exp \left( -\frac{1}{2} \sum_{i=1}^{D} \left(\frac{\sin (\pi (x_i - y_i)/p)}{\ell}\right)^2 \right)
$$
Key reference is MacKay 1998 - "Introduction to Gaussian processes".
"""
name: str = "Periodic"
period: tp.Any
def __init__(
self,
active_dims: tp.Union[list[int], slice, None] = None,
lengthscale: tp.Union[LengthscaleCompatible, AbstractUnwrappable] = 1.0,
variance: tp.Union[ScalarFloat, AbstractUnwrappable] = 1.0,
period: 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.
lengthscale: the lengthscale(s) of the kernel ℓ. If a scalar or an array of
length 1, the kernel is isotropic, meaning that the same lengthscale is
used for all input dimensions. If an array with length > 1, the kernel is
anisotropic, meaning that a different lengthscale is used for each input.
variance: the variance of the kernel σ.
period: the period of the kernel p.
n_dims: the number of input dimensions. If `lengthscale` is an array, this
argument is ignored.
compute_engine: the computation engine that the kernel uses to compute the
covariance matrix.
"""
if isinstance(period, AbstractUnwrappable):
self.period = period
else:
self.period = PositiveReal(period)
super().__init__(active_dims, lengthscale, variance, n_dims, compute_engine)
def __call__(
self, x: Float[Array, " D"], y: Float[Array, " D"]
) -> Float[Array, ""]:
x = self.slice_input(x)
y = self.slice_input(y)
period_val = _val(self.period)
sine_squared = (
jnp.sin(jnp.pi * (x - y) / period_val) / _val(self.lengthscale)
) ** 2
K = _val(self.variance) * jnp.exp(-0.5 * jnp.sum(sine_squared, axis=0))
return K.squeeze()