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covariance_functions.h
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1/*
2 SPDX-FileCopyrightText: 2014-2017 Max Planck Society.
3 All rights reserved.
4
5 SPDX-License-Identifier: BSD-3-Clause
6*/
7
8/**
9 * @file
10 * @date 2014-2017
11 * @copyright Max Planck Society
12 *
13 * @author Edgar D. Klenske <edgar.klenske@tuebingen.mpg.de>
14 * @author Stephan Wenninger <stephan.wenninger@tuebingen.mpg.de>
15 * @author Raffi Enficiaud <raffi.enficiaud@tuebingen.mpg.de>
16 *
17 * @brief The file holds the covariance functions that can be used with the GP class.
18 */
19
20#ifndef COVARIANCE_FUNCTIONS_H
21#define COVARIANCE_FUNCTIONS_H
22
23#include <Eigen/Dense>
24#include <vector>
25#include <list>
26#include <utility>
27#include <cstdint>
28
29// HY: Added all the "override" qualifiers below to silence the compiler.
30
31namespace covariance_functions
32{
33 /*!@brief Base class definition for covariance functions
34 */
35 class CovFunc
36 {
37 public:
38 CovFunc() {}
39 virtual ~CovFunc() {}
40
41 /*!
42 * Evaluates the covariance function, caches the quantities that are needed
43 * to calculate gradient and Hessian.
44 */
45 virtual Eigen::MatrixXd evaluate(const Eigen::VectorXd& x1, const Eigen::VectorXd& x2) = 0;
46
47 //! Method to set the hyper-parameters.
48 virtual void setParameters(const Eigen::VectorXd& params) = 0;
49 virtual void setExtraParameters(const Eigen::VectorXd& params) = 0;
50
51 //! Returns the hyper-parameters.
52 virtual const Eigen::VectorXd& getParameters() const = 0;
53 virtual const Eigen::VectorXd& getExtraParameters() const = 0;
54
55 //! Returns the number of hyper-parameters.
56 virtual int getParameterCount() const = 0;
57 virtual int getExtraParameterCount() const = 0;
58
59 //! Produces a clone to be able to copy the object.
60 virtual CovFunc* clone() const = 0;
61 };
62
63 /*!
64 * The function computes a combined covariance function. It is a periodic
65 * covariance function with an additional square exponential. This
66 * combination makes it possible to learn a signal that consists of both
67 * periodic and aperiodic parts.
68 *
69 * Square Exponential Component:
70 * @f[
71 * k _{\textsc{se}}(t,t';\theta_\textsc{se},\ell_\textsc{se}) =
72 * \theta_\textsc{se} \cdot
73 * \exp\left(-\frac{(t-t')^2}{2\ell_\textsc{se}^{2}}\right)
74 * @f]
75 *
76 * Periodic Component:
77 * @f[
78 * k_\textsc{p}(t,t';\theta_\textsc{p},\ell_\textsc{p},\lambda) =
79 * \theta_\textsc{p} \cdot
80 * \exp\left(-\frac{2\sin^2\left(\frac{\pi}{\lambda}
81 * (t-t')\right)}{\ell_\textsc{p}^2}\right)
82 * @f]
83 *
84 * Kernel Combination:
85 * @f[
86 * k _\textsc{c}(t,t';\theta_\textsc{se},\ell_\textsc{se},\theta_\textsc{p},
87 * \ell_\textsc{p},\lambda) =
88 * k_{\textsc{se}}(t,t';\theta_\textsc{se},\ell_\textsc{se})
89 * +
90 * k_\textsc{p}(t,t';\theta_\textsc{p},\ell_\textsc{p},\lambda)
91 * @f]
92 */
94 {
95 private:
96 Eigen::VectorXd hyperParameters;
97 Eigen::VectorXd extraParameters;
98
99 public:
101 explicit PeriodicSquareExponential(const Eigen::VectorXd& hyperParameters);
102
103 /*!
104 * Evaluates the covariance function, caches the quantities that are needed
105 * to calculate gradient and Hessian.
106 */
107 Eigen::MatrixXd evaluate(const Eigen::VectorXd& x1, const Eigen::VectorXd& x2) override;
108
109 //! Method to set the hyper-parameters.
110 void setParameters(const Eigen::VectorXd& params) override;
111 void setExtraParameters(const Eigen::VectorXd& params) override;
112
113 //! Returns the hyper-parameters.
114 const Eigen::VectorXd& getParameters() const override;
115 const Eigen::VectorXd& getExtraParameters() const override;
116
117 //! Returns the number of hyper-parameters.
118 int getParameterCount() const override;
119 int getExtraParameterCount() const override;
120
121 /**
122 * Produces a clone to be able to copy the object.
123 */
124 virtual CovFunc* clone() const override
125 {
126 return new PeriodicSquareExponential(*this);
127 }
128 };
129
130
131 /*!
132 * The function computes a combined covariance function. It is a periodic
133 * covariance function with two additional square exponential components.
134 * This combination makes it possible to learn a signal that consists of
135 * periodic parts, long-range aperiodic parts and small-range deformations.
136 *
137 * Square Exponential Component:
138 * @f[
139 * k _{\textsc{se}}(t,t';\theta_\textsc{se},\ell_\textsc{se}) =
140 * \theta_\textsc{se} \cdot
141 * \exp\left(-\frac{(t-t')^2}{2\ell_\textsc{se}^{2}}\right)
142 * @f]
143 *
144 * Periodic Component:
145 * @f[
146 * k_\textsc{p}(t,t';\theta_\textsc{p},\ell_\textsc{p},\lambda) =
147 * \theta_\textsc{p} \cdot
148 * \exp\left(-\frac{2\sin^2\left(\frac{\pi}{\lambda}
149 * (t-t')\right)}{\ell_\textsc{p}^2}\right)
150 * @f]
151 *
152 * Kernel Combination:
153 * @f[
154 * k _\textsc{c}(t,t';\theta_\textsc{se},\ell_\textsc{se},\theta_\textsc{p},
155 * \ell_\textsc{p},\lambda) =
156 * k_{\textsc{se},1}(t,t';\theta_{\textsc{se},1},\ell_{\textsc{se},1})
157 * +
158 * k_\textsc{p}(t,t';\theta_\textsc{p},\ell_\textsc{p},\lambda)
159 * +
160 * k_{\textsc{se},2}(t,t';\theta_{\textsc{se},2},\ell_{\textsc{se},2})
161 * @f]
162 */
164 {
165 private:
166 Eigen::VectorXd hyperParameters;
167 Eigen::VectorXd extraParameters;
168
169 public:
171 explicit PeriodicSquareExponential2(const Eigen::VectorXd& hyperParameters);
172
173 Eigen::MatrixXd evaluate(const Eigen::VectorXd& x1, const Eigen::VectorXd& x2) override;
174
175 //! Method to set the hyper-parameters.
176 void setParameters(const Eigen::VectorXd& params) override;
177 void setExtraParameters(const Eigen::VectorXd& params) override;
178
179 //! Returns the hyper-parameters.
180 const Eigen::VectorXd& getParameters() const override;
181 const Eigen::VectorXd& getExtraParameters() const override;
182
183 //! Returns the number of hyper-parameters.
184 int getParameterCount() const override;
185 int getExtraParameterCount() const override;
186
187 /**
188 * Produces a clone to be able to copy the object.
189 */
190 virtual CovFunc* clone() const override
191 {
192 return new PeriodicSquareExponential2(*this);
193 }
194 };
195} // namespace covariance_functions
196#endif // ifndef COVARIANCE_FUNCTIONS_H
Base class definition for covariance functions.
virtual Eigen::MatrixXd evaluate(const Eigen::VectorXd &x1, const Eigen::VectorXd &x2)=0
virtual void setParameters(const Eigen::VectorXd &params)=0
Method to set the hyper-parameters.
virtual int getParameterCount() const =0
Returns the number of hyper-parameters.
virtual const Eigen::VectorXd & getParameters() const =0
Returns the hyper-parameters.
virtual CovFunc * clone() const =0
Produces a clone to be able to copy the object.
Eigen::MatrixXd evaluate(const Eigen::VectorXd &x1, const Eigen::VectorXd &x2) override
const Eigen::VectorXd & getParameters() const override
Returns the hyper-parameters.
void setParameters(const Eigen::VectorXd &params) override
Method to set the hyper-parameters.
virtual CovFunc * clone() const override
Produces a clone to be able to copy the object.
int getParameterCount() const override
Returns the number of hyper-parameters.
virtual CovFunc * clone() const override
Produces a clone to be able to copy the object.
int getParameterCount() const override
Returns the number of hyper-parameters.
void setParameters(const Eigen::VectorXd &params) override
Method to set the hyper-parameters.
const Eigen::VectorXd & getParameters() const override
Returns the hyper-parameters.
Eigen::MatrixXd evaluate(const Eigen::VectorXd &x1, const Eigen::VectorXd &x2) override
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