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

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#ifndef _NUMERICS4CPP_INTEGRATION_SIMPSONS_H_
#define _NUMERICS4CPP_INTEGRATION_SIMPSONS_H_

#include "trapezoid.h"

NUM_NAMESPACE_BEGIN

template<class Function>
class simpsons_integrator : public iterative_method {

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

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

        double sumTrapezoidal = state.result();
        double sumTrapezoidalNext = sumTrapezoidal;
        double error = std::numeric_limits<double>::max();
        double sumSimpons = sumTrapezoidal;
        do {
            state.iterate();
            sumTrapezoidalNext = state.result();
            double sumSimponsNext = (4.0 * sumTrapezoidalNext / 3.0) -
                (sumTrapezoidal / 3.0);
            error = std::fabs(sumSimponsNext / sumSimpons - 1.0);
            sumTrapezoidal = sumTrapezoidalNext;
            sumSimpons = sumSimponsNext;
        } while (state.iterations() < maximum_iterations() &&
            error > maximum_relative_error());
        
        if (state.iterations() >= maximum_iterations()) {
            throw convergence_exception(
                "Simpson's integration failed to converge.");
        }
        
        return sumSimpons;
    }
    
private:
    Function& _function;
};

NUM_NAMESPACE_END

#endif

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