spleaf.term.MultiFourierKernel

class spleaf.term.MultiFourierKernel(P, alpha, beta, series_index=None, vectorize=False)

Multivariate Fourier series kernel.

For \(m\) times series (\(y_1,\dots y_m\)), the covariance between two time series \(y_i, y_j\) follows:

\[k_{i,j}(\Delta t) = \sum_{k=0}^{n_\mathrm{harm}} a_{k; i,j} \cos(k \nu \Delta t) + b_{k; i,j} \sin(k \nu \Delta t),\]

where \(a_k\) and \(b_k\) are the \(m\times m\) matrices given by:

\[a_k = \alpha_k \alpha_k^\mathrm{T} + \beta_k \beta_k^\mathrm{T},\]

\[b_k = \alpha_k \beta_k^\mathrm{T} - \beta_k \alpha_k^\mathrm{T},\]

and \(\alpha_k\), \(\beta_k\) are \(m\times r\) matrices.

Parameters:

nufloat

Fundamental angular frequency.

alpha, beta: (nharm + 1, m, r) ndarrays

Fourier coefficients. beta[0] should be filled with zeros.

series_indexlist of ndarrays

Indices corresponding to each original time series in the merged time series.

vectorize

Whether alpha, beta should be directly passed as parameters or split by index.

Methods

eval(dt[, series_id])	Evaluate the kernel at lag dt.
set_conditional_coef([alpha, beta, series_id])	Set the coefficients used for the conditional computations.