integration.hpp

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#pragma once

#include "math.hpp"

namespace matrix {

template<typename Type, size_t M, size_t N>
int integrate_rk4(
    Vector<Type, M> (*f)(Type, const Matrix<Type, M, 1> &x, const Matrix<Type, N, 1> & u),
    const Matrix<Type, M, 1> & y0,
    const Matrix<Type, N, 1> & u,
    Type t0,
    Type tf,
    Type h0,
    Matrix<Type, M, 1> & y1
)
{
    // https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
    Type t1 = t0;
    y1 = y0;
    Type h = h0;
    Vector<Type, M> k1, k2, k3, k4;
    if (tf < t0) return -1; // make sure t1 > t0
    while (t1 < tf) {
        if (t1 + h0 < tf) {
            h = h0;
        } else {
            h = tf - t1;
        }
        k1 = f(t1, y1, u);
        k2 = f(t1 + h/2, y1 + k1*h/2, u);
        k3 = f(t1 + h/2, y1 + k2*h/2, u);
        k4 = f(t1 + h, y1 + k3*h, u);
        y1 += (k1 + k2*2 + k3*2 + k4)*(h/6);
        t1 += h;
    }
    return 0;
}

} // namespace matrix

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