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

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#ifndef _NUMERICS4CPP_INTEGRATION_ADAPTIVE_H_
#define _NUMERICS4CPP_INTEGRATION_ADAPTIVE_H_

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

NUM_NAMESPACE_BEGIN

template<class Function>
class adaptive_integrator : public iterative_method {

public:
    adaptive_integrator(Function& f, unsigned int iterations = 100,
        double relative_error = 1.0e-15)
        : iterative_method(iterations, relative_error), _function(f)
    {
    }
    
    ~adaptive_integrator() {
    }

    double integrate(double a, double b) {
        double ret;
        
        if (is_nan(a) || is_nan(b)) {
            ret = std::numeric_limits<double>::quiet_NaN();
        } else {
            unsigned int level = 1;
            double tolerance = 10.0 * maximum_relative_error();
            double h = (b - a) / 2.0;
            double fa = _function(a);
            double fc = _function(a + h);
            double fb = _function(b);
            double s = h * (fa + 4.0 * fc + fb) / 3.0;
            ret = integrate(a, b, fa, fb, fc, h, tolerance, s, level);
        }
        
        return ret;
    }
    
private:
    double integrate(double a, double b, double fa, double fb, double fc,
        double h, double tolerance, double s, unsigned int level)
    {
        double ret = s;
        
        if (level < maximum_iterations()) {
            double fd = _function(a + h / 2.0);
            double fe = _function(a + 3.0 * h / 2.0);
            double s1 = h * (fa + (4.0 * fd) + fc) / 6.0;
            double s2 = h * (fc + (4.0 * fe) + fb) / 6.0;
            double sn = s1 + s2;
            if (std::fabs(sn - s) <= tolerance) {
                ret = sn;
            } else {
                double pivot = a + h;
                h /= 2.0;
                tolerance /= 2;
                ++level;
                ret = integrate(a, pivot, fa, fc, fd, h, tolerance, s1, level) +
                    integrate(pivot, b, fc, fb, fe, h, tolerance, s2, level);
            }
        } else {
            throw convergence_exception(
                "Adaptive quadrature failed to converge.");
        }
        
        return ret;
    }

    Function& _function;
};

NUM_NAMESPACE_END

#endif

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