function.hpp

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#ifndef FUNCTION_HPP
#define FUNCTION_HPP
 
#include <cmath>
#include <functional>
#include <stdexcept>
#include <vector>
 
namespace gpmp {
 
namespace optim {
 
class Func {
  public:
    std::vector<double>
    generate_random_point(const std::vector<double> &lower_bounds,
                          const std::vector<double> &upper_bounds) const;
 
    std::vector<double> generate_fibonacci_sequence(size_t length) const;
 
    std::vector<double> vector_addition(const std::vector<double> &a,
                                        const std::vector<double> &b) const;
 
    std::vector<double> vector_subtraction(const std::vector<double> &a,
                                           const std::vector<double> &b) const;
 
    std::vector<double>
    vector_scalar_multiply(double scalar, const std::vector<double> &vec) const;
 
    double calculate_midpoint(double a, double b, double fraction) const;
 
    // Golden-section search methods for univariate functions
 
    double golden_section_search(const std::function<double(double)> &func,
                                 double a,
                                 double b,
                                 double tol);
 
    // Interpolation methods for univariate functions
 
    double
    linear_interpolation(double x, double x0, double x1, double y0, double y1);
 
    double cubic_interpolation(double x,
                               double x0,
                               double x1,
                               double y0,
                               double y1,
                               double y0_prime,
                               double y1_prime);
 
    // Golden-section search methods for multivariate functions
 
    std::vector<double> golden_section_search_multivariate(
        const std::function<double(const std::vector<double> &)> &func,
        const std::vector<double> &lower_bounds,
        const std::vector<double> &upper_bounds,
        double tol);
 
    double random_search(
        const std::function<double(const std::vector<double> &)> &func,
        const std::vector<double> &lower_bounds,
        const std::vector<double> &upper_bounds,
        size_t max_iterations);
 
    std::vector<double> fit_linear(const std::vector<double> &x,
                                   const std::vector<double> &y);
 
    double fibonacci_search(
        const std::function<double(const std::vector<double> &)> &func,
        const std::vector<double> &lower_bounds,
        const std::vector<double> &upper_bounds,
        size_t max_iterations);
 
    double ternary_search(
        const std::function<double(const std::vector<double> &)> &func,
        const std::vector<double> &lower_bounds,
        const std::vector<double> &upper_bounds,
        size_t max_iterations) const;
 
    std::vector<double> bisection_method(
        const std::function<double(const std::vector<double> &)> &func,
        double lower_bound,
        double upper_bound,
        size_t max_iterations);
 
    std::vector<double> newton_method(
        const std::function<double(const std::vector<double> &)> &func,
        const std::function<double(const std::vector<double> &)> &derivative,
        double initial_guess,
        size_t max_iterations);
 
    std::vector<double>
    regula_falsi(const std::function<double(const std::vector<double> &)> &func,
                 double lower_bound,
                 double upper_bound,
                 size_t max_iterations);
 
    std::vector<double> cubic_fit(const std::vector<double> &x,
                                  const std::vector<double> &y);
 
    // Nelder–Mead method
 
    std::vector<double>
    nelder_mead(const std::function<double(const std::vector<double> &)> &func,
                std::vector<double> initial_point,
                double tolerance,
                size_t max_iterations);
 
    std::vector<double>
    calculate_centroid(const std::vector<std::vector<double>> &simplex,
                       size_t exclude_index);
 
    std::vector<double> reflect(const std::vector<double> &point,
                                const std::vector<double> &centroid,
                                double reflection_coefficient);
 
    double calculate_range(const std::vector<double> &values);
 
    bool is_valid_interval(double a, double b);
 
  private:
    // Helper methods for golden section search
 
    double
    golden_section_search_minimize(const std::function<double(double)> &func,
                                   double a,
                                   double b,
                                   double tol,
                                   double x1,
                                   double x2);
 
    // Helper methods for multivariate golden section search
 
    std::vector<double> golden_section_search_minimize_multivariate(
        const std::function<double(const std::vector<double> &)> &func,
        const std::vector<double> &lower_bounds,
        const std::vector<double> &upper_bounds,
        double tol,
        const std::vector<double> &x1,
        const std::vector<double> &x2);
};
 
} // namespace optim
 
} // namespace gpmp
 
#endif // FUNCTION_HPP