simpson.hpp

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#pragma once
 
#include <functional>
 
#include "NumCpp/Core/Types.hpp"
 
namespace nc::integrate
{
    //============================================================================
    // Method Description:
    inline double
        simpson(const double low, const double high, const uint32 n, const std::function<double(double)>& f) noexcept
    {
        const double width = (high - low) / static_cast<double>(n);
 
        double simpson_integral = 0.;
        for (uint32 step = 0; step < n; ++step)
        {
            const double x1 = low + static_cast<double>(step) * width;
            const double x2 = low + static_cast<double>(step + 1) * width;
 
            simpson_integral += (x2 - x1) / 6. * (f(x1) + 4. * f(0.5 * (x1 + x2)) + f(x2));
        }
 
        return simpson_integral;
    }
} // namespace nc::integrate