pint.models.noise_model.periodic_kernel
- pint.models.noise_model.periodic_kernel(nodes: ndarray, log10_sigma: float = -7, log10_ell: float = 2, log10_gam_p: float = 0, log10_p: float = 0) ndarray[source]
Quasi-periodic (SE × periodic) covariance matrix.
Matches the
periodic_kernelconvention in enterprise_extensions.- Parameters:
nodes (np.ndarray) – 1-D array of evaluation points in seconds (e.g. average TOA at each epoch).
log10_sigma (float) – Log10 of the amplitude, in the units of the Gaussian process coefficients (\(\mathrm{cm}^{-3}\) as used by
TimeDomainSWNoise).log10_ell (float) – Log10 of the squared-exponential length scale in days.
log10_gam_p (float) – Log10 of the periodic damping amplitude (larger -> stronger periodic decay).
log10_p (float) – Log10 of the periodicity in years.
- Returns:
Covariance matrix of shape
(len(nodes), len(nodes)).- Return type:
np.ndarray
Notes
The kernel is
\[K(\tau) = \sigma^2 \exp\!\left( -\frac{\tau^2}{2\ell^2} - \gamma_p \sin^2\!\left(\frac{\pi\tau}{p}\right) \right) + d\,\delta_{ij}\]where \(d = (\sigma / 50000)^2\) is a small diagonal regulariser.