lorenz_attractor()

MAYAFLUX_API double MayaFlux::Kinesis::Discrete::lorenz_attractor ( std::span< const double >  window, std::span< double >  coefs  )

noexcept

Lorenz system stepped once by fourth order Runge-Kutta, returning x.

The state and parameters live in the array, so editing sigma, rho, beta or dt between calls sweeps the system through its regimes. An array shorter than seven gives zero.

Definition at line 586 of file Kernels.cpp.

{
    if (coefs.size() < 7)
        return 0.0;
 
    const double sigma = coefs[0];
    const double rho = coefs[1];
    const double beta = coefs[2];
    const double dt = coefs[3];
 
    using Vec = std::array<double, 3>;
    const auto derivative = [sigma, rho, beta](const Vec& p) -> Vec {
        return { sigma * (p[1] - p[0]), p[0] * (rho - p[2]) - p[1], p[0] * p[1] - beta * p[2] };
    };
    const auto advanced = [](const Vec& p, const Vec& d, double h) -> Vec {
        return { p[0] + h * d[0], p[1] + h * d[1], p[2] + h * d[2] };
    };
 
    const Vec start { coefs[4], coefs[5], coefs[6] };
    const Vec k1 = derivative(start);
    const Vec k2 = derivative(advanced(start, k1, 0.5 * dt));
    const Vec k3 = derivative(advanced(start, k2, 0.5 * dt));
    const Vec k4 = derivative(advanced(start, k3, dt));
 
    for (size_t i = 0; i < 3; ++i)
        coefs[4 + i] = start[i] + dt / 6.0 * (k1[i] + 2.0 * k2[i] + 2.0 * k3[i] + k4[i]);
 
    return coefs[4];
}

References h.