polynomial_lags()

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

noexcept

Polynomial in several lags at once.

coefs: [L, P, C...] with L lags and highest power P, then (P + 1) numbers per lag, lag-major and power-ascending. The result is the sum over lags k and powers j of C[k][j] * window[k]^j. Power zero is a constant, so a bias is C[0][0]. In a recursive Polynomial this is any nonlinear difference equation of the last L outputs: Henon is lags 0, 1, 2 with C[0][0] = 1, C[1][2] = -a, C[2][1] = b. Lags beyond the window are skipped; an array shorter than its header gives zero.

Definition at line 268 of file Kernels.cpp.

{
    if (coefs.size() < 2)
        return 0.0;
 
    const auto lags = static_cast<size_t>(std::max(coefs[0], 0.0));
    const auto powers = static_cast<size_t>(std::max(coefs[1], 0.0)) + 1;
    if (coefs.size() < 2 + lags * powers)
        return 0.0;
 
    double sum = 0.0;
    const size_t reach = std::min(lags, window.size());
    for (size_t k = 0; k < reach; ++k) {
        const double w = window[k];
        double power = 1.0;
        for (size_t j = 0; j < powers; ++j) {
            sum += coefs[2 + k * powers + j] * power;
            power *= w;
        }
    }
    return sum;
}

References power(), sum(), and window.

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