pint.models.noise_model.matern_kernel

pint.models.noise_model.matern_kernel(nodes: ndarray, log10_sigma: float = -7, log10_ell: float = 2, nu: float = 1.5) → ndarray[source]

Matérn covariance matrix.

Parameters:

nodes (np.ndarray) – 1-D array of evaluation points in seconds.
log10_sigma (float) – Log10 of the amplitude.
log10_ell (float) – Log10 of the length scale in days.
nu (float) – Smoothness parameter; must be one of {0.5, 1.5, 2.5}.

Returns:

Covariance matrix of shape (len(nodes), len(nodes)).

Return type:

np.ndarray

Raises:

ValueError – If nu is not in {0.5, 1.5, 2.5}.

Notes

The Matérn-1/2 (nu=0.5), Matérn-3/2 (nu=1.5), and Matérn-5/2 (nu=2.5) closed-form kernels are supported. A small diagonal regulariser \(d = (\sigma / 50000)^2\) is added for numerical stability.