forward_difference() [1/2]

template<size_t N, typename T >

T MayaFlux::Kinesis::forward_difference ( const Memory::HistoryBuffer< T > &  history, double  dt  )

inlinenoexcept

N-th order forward finite difference, expressed on a HistoryBuffer.

Template Parameters

N	Difference order
T	Sample type

Parameters

history	Buffer with capacity >= N + 1
dt	Elapsed time between consecutive samples

Returns

Forward-difference formula evaluated with the newest sample treated as the base point and older samples as the forward taps

Mathematically the forward and backward difference formulas are the same stencil read in opposite temporal direction. Since a HistoryBuffer only ever exposes past samples relative to [0], this computes the forward-difference coefficients but applied to the same available data as backward_difference. The two differ only for even N in sign convention on alternating terms; provided for callers whose downstream math was derived against forward-difference tables.

Definition at line 82 of file Differential.hpp.

{
    static_assert(N >= 1, "forward_difference<N> requires N >= 1");
 
    using S = scalar_t<T>;
 
    T acc = T {};
    double binomial = 1.0;
 
    for (size_t k = 0; k <= N; ++k) {
        if (k > 0)
            binomial = binomial * static_cast<double>(N - k + 1) / static_cast<double>(k);
        const double sign = ((N - k) % 2 == 0) ? 1.0 : -1.0;
        acc = acc + static_cast<S>(sign * binomial) * history[k];
    }
 
    double denom = 1.0;
    for (size_t i = 0; i < N; ++i)
        denom *= dt;
 
    return acc / static_cast<S>(denom);
}

References k, and N.