src/main/cpp/numerics4cpp/integration/trapezoid.h

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#ifndef _NUMERICS4CPP_INTEGRATION_TRAPEZOID_H_
#define _NUMERICS4CPP_INTEGRATION_TRAPEZOID_H_

#include <limits>
#include "../iterativemethod.h"
#include "../exception/exception.h"

NUM_NAMESPACE_BEGIN

template<class Function>
class trapezoidal_integrator_state {
public:
    trapezoidal_integrator_state(Function &f, double a, double b) :
        _function(f), _a(a), _b(b), _n(0), _k(2)
    {
        double fa = f(a);
        double fb = f(b);
        _s = (b - a) * (fa / 2.0 + fb / 2.0);
    }

    unsigned int iterations() const {
        return _n;
    }
        
    void iterate() {
        ++_n;
        
        // compute function at next set of points
        double sn = 0.0;
        double h = (_b - _a) / _k;
        for (int i = _k - 1; i >= 1; i -= 2) {
            double x = _a + (i * h);
            sn += _function(x);
        }
        sn = (0.5 * _s) + (h * sn);

        _k *= 2;
        _s = sn;
    }

    double result() const {
        return _s;
    }

private:
    Function& _function;
    
    double _a;
    
    double _b;
    
    unsigned int _n;
    
    double _s;
    
    unsigned int _k;
};


template<class Function>
class trapezoidal_integrator : public iterative_method {

public:
    trapezoidal_integrator(Function& f, unsigned int iterations = 100,
        double relative_error = 1.0e-13)
        : iterative_method(iterations, relative_error), _function(f)
    {
    }
    
    ~trapezoidal_integrator() {
    }

    double integrate(double a, double b) {
        trapezoidal_integrator_state<Function> state(_function, a, b);

        double s = state.result();
        double sn = s;
        double error = std::numeric_limits<double>::max();
        do {
            state.iterate();
            sn = state.result();
            error = std::fabs(sn / s - 1.0);
            s = sn;
        } while (state.iterations() < maximum_iterations() &&
            error > maximum_relative_error());
        
        if (state.iterations() >= maximum_iterations()) {
            throw convergence_exception("Trapezoidal integration failed to converge.");
        }
        
        return s;
    }
    
private:
    Function& _function;
};

NUM_NAMESPACE_END

#endif

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