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tools/math_tools.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 Provides mathematical tools needed for the Gaussian process toolbox.
18 */
19
20#ifndef GP_MATH_TOOLS_H
21#define GP_MATH_TOOLS_H
22
23#define MINIMAL_THETA 1e-7
24
25#include <Eigen/Dense>
26#include <unsupported/Eigen/FFT>
27#include <limits>
28#include <vector>
29#include <stdexcept>
30#include <cstdint>
31#include <cmath>
32
33// M_PI not part of the standard
34#ifndef M_PI
35#define M_PI 3.14159265358979323846
36#endif
37
38namespace math_tools
39{
40 /*!
41 * The squareDistance is the pairwise distance between all points of the passed
42 * vectors. I.e. it generates a symmetric matrix when two vectors are passed.
43 *
44 * The first dimension (rows) is the dimensionality of the input space, the
45 * second dimension (columns) is the number of datapoints. The number of
46 * rows must be identical.
47
48 @param a
49 a Matrix of size Dxn
50
51 @param b
52 a Matrix of size Dxm
53
54 @result
55 a Matrix of size nxm containing all pairwise squared distances
56 */
57 Eigen::MatrixXd squareDistance(
58 const Eigen::MatrixXd& a,
59 const Eigen::MatrixXd& b);
60
61 /*!
62 * Single-input version of squaredDistance. For single inputs, it is assumed
63 * that the pairwise distance matrix should be computed between the passed
64 * vector itself.
65 */
66 Eigen::MatrixXd squareDistance(const Eigen::MatrixXd& a);
67
68 /*!
69 * Generates a uniformly distributed random matrix of values between 0 and 1.
70 */
71 Eigen::MatrixXd generate_uniform_random_matrix_0_1(const size_t n, const size_t m);
72
73 /*!
74 * Apply the Box-Muller transform, which transforms uniform random samples
75 * to Gaussian distributed random samples.
76 */
77 Eigen::MatrixXd box_muller(const Eigen::VectorXd& vRand);
78
79 /*!
80 * Generates normal random samples. First it gets some uniform random samples
81 * and then uses the Box-Muller transform to get normal samples out of it
82 */
83 Eigen::MatrixXd generate_normal_random_matrix(const size_t n, const size_t m);
84
85 /*!
86 * Checks if a value is NaN by comparing it with itself.
87 *
88 * The rationale is that NaN is the only value that does not evaluate to true
89 * when comparing it with itself.
90 * Taken from:
91 * http://stackoverflow.com/questions/3437085/check-nan-number
92 * http://stackoverflow.com/questions/570669/checking-if-a-double-or-float-is-nan-in-c
93 */
94 inline bool isNaN(double x)
95 {
96 return x != x;
97 }
98
99 static const double NaN = std::numeric_limits<double>::quiet_NaN();
100
101 /*!
102 * Checks if a double is infinite via std::numeric_limits<double> functions.
103 *
104 * Taken from:
105 * http://bytes.com/topic/c/answers/588254-how-check-double-inf-nan#post2309761
106 */
107 inline bool isInf(double x)
108 {
109 return x == std::numeric_limits<double>::infinity() ||
110 x == -std::numeric_limits<double>::infinity();
111 }
112
113 /*!
114 * Calculates the spectrum of a data vector.
115 *
116 * Does pre-and postprocessing:
117 * - The data is zero-padded until the desired resolution is reached.
118 * - ditfft2 is called to compute the FFT.
119 * - The frequencies from the padding are removed.
120 * - The constant coefficient is removed.
121 * - A list of frequencies is generated.
122 */
123 std::pair< Eigen::VectorXd, Eigen::VectorXd > compute_spectrum(Eigen::VectorXd& data, int N = 0);
124
125 /*!
126 * Computes a Hamming window (used to reduce spectral leakage of subsequent DFT).
127 */
128 Eigen::VectorXd hamming_window(int N);
129
130 /*!
131 * Computes the standard deviation of a vector... which is not part of Eigen.
132 */
133 double stdandard_deviation(Eigen::VectorXd& input);
134
135} // namespace math_tools
136
137#endif // define GP_MATH_TOOLS_H
Eigen::VectorXd hamming_window(int N)
Eigen::MatrixXd squareDistance(const Eigen::MatrixXd &a, const Eigen::MatrixXd &b)
Eigen::MatrixXd generate_normal_random_matrix(const size_t n, const size_t m)
Eigen::MatrixXd box_muller(const Eigen::VectorXd &vRand)
Eigen::MatrixXd generate_uniform_random_matrix_0_1(const size_t n, const size_t m)
std::pair< Eigen::VectorXd, Eigen::VectorXd > compute_spectrum(Eigen::VectorXd &data, int N)
double stdandard_deviation(Eigen::VectorXd &input)
bool isInf(double x)
bool isNaN(double x)
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