analysis.hpp

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 * Copyright (C) Akiel Aries, <akiel@akiel.org>, et al.
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 * This software is licensed as described in the file LICENSE, which
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 * among other details are referenced in the official documentation
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#ifndef ANALYSIS_HPP
#define ANALYSIS_HPP
 
#include <string>
#include <vector>
 
namespace gpmp {
class NumericalAnalysis {
  public:
    /* A numerical method for derivatives is used. This may be subject
    to change, as an analytical method for calculating derivatives
    will most likely be used in the future.
    */
    double numDiff(double (*function)(double), double x);
    double numDiff_2(double (*function)(double), double x);
    double numDiff_3(double (*function)(double), double x);
 
    double constantApproximation(double (*function)(double), double c);
 
    double linearApproximation(double (*function)(double), double c, double x);
 
    double
    quadraticApproximation(double (*function)(double), double c, double x);
 
    double cubicApproximation(double (*function)(double), double c, double x);
 
    double numDiff(double (*function)(std::vector<double>),
                   std::vector<double> x,
                   int axis);
 
    double numDiff_2(double (*function)(std::vector<double>),
                     std::vector<double> x,
                     int axis1,
                     int axis2);
 
    double numDiff_3(double (*function)(std::vector<double>),
                     std::vector<double> x,
                     int axis1,
                     int axis2,
                     int axis3);
 
    double newtonRaphsonMethod(double (*function)(double),
                               double x_0,
                               double epoch_num);
 
    double
    halleyMethod(double (*function)(double), double x_0, double epoch_num);
 
    double invQuadraticInterpolation(double (*function)(double),
                                     std::vector<double> x_0,
                                     double epoch_num);
 
    double eulerianMethod(double (*derivative)(double),
                          std::vector<double> q_0,
                          double p,
                          double h); // Euler's method for solving
                                     // diffrential equations.
 
    double eulerianMethod(double (*derivative)(std::vector<double>),
                          std::vector<double> q_0,
                          double p,
                          double h); // Euler's method for solving
                                     // diffrential equations.
 
    double growthMethod(double C,
                        double k,
                        double t); // General growth-based diffrential equations
                                   // can be solved by seperation of variables.
 
    std::vector<double>
    jacobian(double (*function)(std::vector<double>),
             std::vector<double> x); // Indeed, for functions with scalar
                                     // outputs the Jacobians will be vectors.
 
    std::vector<std::vector<double>>
    hessian(double (*function)(std::vector<double>), std::vector<double> x);
 
    std::vector<std::vector<std::vector<double>>>
    thirdOrderTensor(double (*function)(std::vector<double>),
                     std::vector<double> x);
 
    double constantApproximation(double (*function)(std::vector<double>),
                                 std::vector<double> c);
 
    double linearApproximation(double (*function)(std::vector<double>),
                               std::vector<double> c,
                               std::vector<double> x);
 
    double quadraticApproximation(double (*function)(std::vector<double>),
                                  std::vector<double> c,
                                  std::vector<double> x);
 
    double cubicApproximation(double (*function)(std::vector<double>),
                              std::vector<double> c,
                              std::vector<double> x);
 
    double laplacian(double (*function)(std::vector<double>),
                     std::vector<double> x); // laplacian
 
    std::string
    secondPartialDerivativeTest(double (*function)(std::vector<double>),
                                std::vector<double> x);
};
} // namespace gpmp
 
#endif