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
// vim: set et fenc=utf-8 ff=unix sts=0 sw=4 ts=4 :