src/main/cpp/numerics4cpp/root/newton.h

/*
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#ifndef _NUMERICS4CPP_ROOT_NEWTON_H_
#define _NUMERICS4CPP_ROOT_NEWTON_H_

#include <cmath>
#include <limits>
#include "../iterativemethod.h"
#include "../math.h"

NUM_NAMESPACE_BEGIN

template<class Function>
class newton_root_finder : public iterative_method {

public:
        newton_root_finder(Function& f, Function& d, unsigned int iterations = 100,
        double relative_error = 1.0e-15)
        : iterative_method(iterations, relative_error), _function(f),
          _derivative(d)
    {
        }
        
        double find_root(double x0) {
        double ret;
        
        if (is_nan(x0)) {
            ret = std::numeric_limits<double>::quiet_NaN();
        } else {
            unsigned int n = 0;
            double x = x0;
            double error;
            double delta;
            double fx;
            double dx;
            do {
                ++n;
                fx = _function(x);
                dx = _derivative(x);
                delta = fx / dx;
                
                error = std::max(std::fabs(fx), std::fabs(delta / x));
                x = x - delta;
            } while (n < maximum_iterations() &&
                error > maximum_relative_error());
                
            if (n >= maximum_iterations()) {
                throw convergence_exception(
                    "Newton's method failed to converge.");
            }
            
            ret = x;
        }
        
        return ret;
        }
                        
private:
    Function& _function;

    Function& _derivative;
};

NUM_NAMESPACE_END

#endif

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