Computes a periodic kernel for a distance vector or matrix:
$$k(d) = \exp\left(-\frac{2\sin^2(\pi d / p)}{\alpha^2}\right).$$
Usage
periodic_kernel(x, alpha, period)
Arguments
- x
A numeric vector or matrix of distances.
- alpha
A positive numeric scalar controlling how sharply correlation
falls within each cycle: smaller values allow sharp seasonal peaks;
larger values give a gentler, smoother cycle.
- period
A positive numeric scalar giving the period \(p\).
Value
A numeric vector or matrix of periodic kernel values.