Source code for gpflow.kernels.periodic

# 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.
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# http://www.apache.org/licenses/LICENSE-2.0
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# Unless required by applicable law or agreed to in writing, software
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# See the License for the specific language governing permissions and
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from typing import Optional

import numpy as np
import tensorflow as tf

from ..base import Parameter, TensorType
from ..experimental.check_shapes import check_shapes, inherit_check_shapes
from ..utilities import positive
from ..utilities.ops import difference_matrix
from .base import ActiveDims, Kernel, NormalizedActiveDims
from .stationaries import IsotropicStationary


class Periodic(Kernel):
    """
    The periodic family of kernels. Can be used to wrap any Stationary kernel
    to transform it into a periodic version. The canonical form (based on the
    SquaredExponential kernel) can be found in Equation (47) of

    D.J.C.MacKay. Introduction to Gaussian processes. In C.M.Bishop, editor,
    Neural Networks and Machine Learning, pages 133--165. Springer, 1998.

    The derivation can be achieved by mapping the original inputs through the
    transformation u = (cos(x), sin(x)).

    For the SquaredExponential base kernel, the result can be expressed as:

        k(r) =  σ² exp{ -0.5 sin²(π r / γ) / ℓ²}

    where:
    r is the Euclidean distance between the input points
    ℓ is the lengthscales parameter,
    σ² is the variance parameter,
    γ is the period parameter.

    NOTE: usually we have a factor of 4 instead of 0.5 in front but this
        is absorbed into the lengthscales hyperparameter.
    NOTE: periodic kernel uses `active_dims` of a base kernel, therefore
        the constructor doesn't have it as an argument.
    """

    @check_shapes(
        "period: [broadcast n_active_dims]",
    )
    def __init__(self, base_kernel: IsotropicStationary, period: TensorType = 1.0) -> None:
        """
        :param base_kernel: the base kernel to make periodic; must inherit from Stationary
            Note that `active_dims` should be specified in the base kernel.
        :param period: the period; to induce a different period per active dimension
            this must be initialized with an array the same length as the number
            of active dimensions e.g. [1., 1., 1.]
        """
        if not isinstance(base_kernel, IsotropicStationary):
            raise TypeError("Periodic requires an IsotropicStationary kernel as the `base_kernel`")

        super().__init__()
        self.base_kernel = base_kernel
        self.period = Parameter(period, transform=positive())
        self.base_kernel._validate_ard_active_dims(self.period)

    @property
    def active_dims(self) -> NormalizedActiveDims:
        return self.base_kernel.active_dims

    @active_dims.setter
    def active_dims(self, value: ActiveDims) -> None:
        # type-ignore below is because mypy doesn't understand that getter and the setter of
        # `active_dims` have different types.
        self.base_kernel.active_dims = value  # type: ignore[assignment]

    @inherit_check_shapes
    def K_diag(self, X: TensorType) -> tf.Tensor:
        return self.base_kernel.K_diag(X)

    @inherit_check_shapes
    def K(self, X: TensorType, X2: Optional[TensorType] = None) -> tf.Tensor:
        r = np.pi * (difference_matrix(X, X2)) / self.period
        scaled_sine = tf.sin(r) / self.base_kernel.lengthscales
        if hasattr(self.base_kernel, "K_r"):
            sine_r = tf.reduce_sum(tf.abs(scaled_sine), -1)
            K = self.base_kernel.K_r(sine_r)
        else:
            sine_r2 = tf.reduce_sum(tf.square(scaled_sine), -1)
            K = self.base_kernel.K_r2(sine_r2)
        return K