tools/math_tools.h

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/*
    SPDX-FileCopyrightText: 2014-2017 Max Planck Society.
    All rights reserved.
 
    SPDX-License-Identifier: BSD-3-Clause
*/
 
/**
 * @file
 * @date      2014-2017
 * @copyright Max Planck Society
 *
 * @author    Edgar D. Klenske <[email protected]>
 * @author    Stephan Wenninger <[email protected]>
 * @author    Raffi Enficiaud <[email protected]>
 *
 * @brief     Provides mathematical tools needed for the Gaussian process toolbox.
 */
 
#ifndef GP_MATH_TOOLS_H
#define GP_MATH_TOOLS_H
 
#define MINIMAL_THETA 1e-7
 
#include <Eigen/Dense>
#include <unsupported/Eigen/FFT>
#include <limits>
#include <vector>
#include <stdexcept>
#include <cstdint>
#include <cmath>
 
// M_PI not part of the standard
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif 
 
namespace math_tools
{
    /*!
     * The squareDistance is the pairwise distance between all points of the passed
     * vectors. I.e. it generates a symmetric matrix when two vectors are passed.
     *
     * The first dimension (rows) is the dimensionality of the input space, the
     * second dimension (columns) is the number of datapoints. The number of
     * rows must be identical.
 
      @param a
      a Matrix of size Dxn
 
      @param b
      a Matrix of size Dxm
 
      @result
      a Matrix of size nxm containing all pairwise squared distances
    */
    Eigen::MatrixXd squareDistance(
        const Eigen::MatrixXd& a,
        const Eigen::MatrixXd& b);
 
    /*!
     * Single-input version of squaredDistance. For single inputs, it is assumed
     * that the pairwise distance matrix should be computed between the passed
     * vector itself.
     */
    Eigen::MatrixXd squareDistance(const Eigen::MatrixXd& a);
 
    /*!
     * Generates a uniformly distributed random matrix of values between 0 and 1.
     */
    Eigen::MatrixXd generate_uniform_random_matrix_0_1(const size_t n, const size_t m);
 
    /*!
     * Apply the Box-Muller transform, which transforms uniform random samples
     * to Gaussian distributed random samples.
     */
    Eigen::MatrixXd box_muller(const Eigen::VectorXd& vRand);
 
    /*!
     * Generates normal random samples. First it gets some uniform random samples
     * and then uses the Box-Muller transform to get normal samples out of it
     */
    Eigen::MatrixXd generate_normal_random_matrix(const size_t n, const size_t m);
 
    /*!
     * Checks if a value is NaN by comparing it with itself.
     *
     * The rationale is that NaN is the only value that does not evaluate to true
     * when comparing it with itself.
     * Taken from:
     * http://stackoverflow.com/questions/3437085/check-nan-number
     * http://stackoverflow.com/questions/570669/checking-if-a-double-or-float-is-nan-in-c
     */
    inline bool isNaN(double x)
    {
        return x != x;
    }
 
    static const double NaN = std::numeric_limits<double>::quiet_NaN();
 
    /*!
     * Checks if a double is infinite via std::numeric_limits<double> functions.
     *
     * Taken from:
     * http://bytes.com/topic/c/answers/588254-how-check-double-inf-nan#post2309761
     */
    inline bool isInf(double x)
    {
        return x == std::numeric_limits<double>::infinity() ||
               x == -std::numeric_limits<double>::infinity();
    }
 
    /*!
     * Calculates the spectrum of a data vector.
     *
     * Does pre-and postprocessing:
     * - The data is zero-padded until the desired resolution is reached.
     * - ditfft2 is called to compute the FFT.
     * - The frequencies from the padding are removed.
     * - The constant coefficient is removed.
     * - A list of frequencies is generated.
     */
    std::pair< Eigen::VectorXd, Eigen::VectorXd > compute_spectrum(Eigen::VectorXd& data, int N = 0);
 
    /*!
     * Computes a Hamming window (used to reduce spectral leakage of subsequent DFT).
     */
    Eigen::VectorXd hamming_window(int N);
 
    /*!
     * Computes the standard deviation of a vector... which is not part of Eigen.
     */
    double stdandard_deviation(Eigen::VectorXd& input);
 
}  // namespace math_tools
 
#endif  // define GP_MATH_TOOLS_H