# Copyright 2017-2020 The GPflow 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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from typing import Optional
import tensorflow as tf
from ..base import Parameter, TensorType
from ..utilities import positive
from .base import ActiveDims, Kernel
[docs]class Static(Kernel):
"""
Kernels who don't depend on the value of the inputs are 'Static'. The only
parameter is a variance, σ².
"""
def __init__(
self, variance: TensorType = 1.0, active_dims: Optional[ActiveDims] = None
) -> None:
super().__init__(active_dims)
self.variance = Parameter(variance, transform=positive())
def K_diag(self, X: TensorType) -> tf.Tensor:
return tf.fill(tf.shape(X)[:-1], tf.squeeze(self.variance))
[docs]class White(Static):
"""
The White kernel: this kernel produces 'white noise'. The kernel equation is
k(x_n, x_m) = δ(n, m) σ²
where:
δ(.,.) is the Kronecker delta,
σ² is the variance parameter.
"""
def K(self, X: TensorType, X2: Optional[TensorType] = None) -> tf.Tensor:
if X2 is None:
d = tf.fill(tf.shape(X)[:-1], tf.squeeze(self.variance))
return tf.linalg.diag(d)
else:
shape = tf.concat([tf.shape(X)[:-1], tf.shape(X2)[:-1]], axis=0)
return tf.zeros(shape, dtype=X.dtype)
[docs]class Constant(Static):
"""
The Constant (aka Bias) kernel. Functions drawn from a GP with this kernel
are constant, i.e. f(x) = c, with c ~ N(0, σ^2). The kernel equation is
k(x, y) = σ²
where:
σ² is the variance parameter.
"""
def K(self, X: TensorType, X2: Optional[TensorType] = None) -> tf.Tensor:
if X2 is None:
shape = tf.concat(
[
tf.shape(X)[:-2],
tf.reshape(tf.shape(X)[-2], [1]),
tf.reshape(tf.shape(X)[-2], [1]),
],
axis=0,
)
else:
shape = tf.concat([tf.shape(X)[:-1], tf.shape(X2)[:-1]], axis=0)
return tf.fill(shape, tf.squeeze(self.variance))