Bisection.hpp

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#pragma once
 
#include <cmath>
#include <functional>
#include <utility>
 
#include "NumCpp/Core/Types.hpp"
#include "NumCpp/Roots/Iteration.hpp"
 
namespace nc::roots
{
    //================================================================================
    // Class Description:
    class Bisection : public Iteration
    {
    public:
        //============================================================================
        // Method Description:
        Bisection(const double epsilon, std::function<double(double)> f) noexcept :
            Iteration(epsilon),
            f_(std::move(f))
        {
        }
 
        //============================================================================
        // Method Description:
        Bisection(const double epsilon, const uint32 maxNumIterations, std::function<double(double)> f) noexcept :
            Iteration(epsilon, maxNumIterations),
            f_(std::move(f))
        {
        }
 
        //============================================================================
        // Method Description:
        ~Bisection() override = default;
 
        //============================================================================
        // Method Description:
        double solve(double a, double b)
        {
            resetNumberOfIterations();
            checkAndFixAlgorithmCriteria(a, b);
 
            double x  = 0.5 * (a + b);
            double fx = f_(x);
 
            while (std::fabs(fx) >= epsilon_)
            {
                x  = calculateX(x, a, b, fx);
                fx = f_(x);
 
                incrementNumberOfIterations();
            }
 
            return x;
        }
 
    private:
        //============================================================================
        const std::function<double(double)> f_;
 
        //============================================================================
        // Method Description:
        void checkAndFixAlgorithmCriteria(double &a, double &b) const noexcept
        {
            // Algorithm works in range [a,b] if criteria f(a)*f(b) < 0 and f(a) > f(b) is fulfilled
            if (f_(a) < f_(b))
            {
                std::swap(a, b);
            }
        }
 
        //============================================================================
        // Method Description:
        static double calculateX(double x, double &a, double &b, double fx) noexcept
        {
            if (fx < 0)
            {
                b = x;
            }
            else
            {
                a = x;
            }
 
            return 0.5 * (a + b);
        }
    };
} // namespace nc::roots