Celerite

class tinygp.kernels.quasisep.Celerite(a: tinygp.helpers.JAXArray, b: tinygp.helpers.JAXArray, c: tinygp.helpers.JAXArray, d: tinygp.helpers.JAXArray)

Bases: Quasisep

The baseline kernel from the celerite package

This form of the kernel was introduced by Foreman-Mackey et al. (2017), and implemented in the celerite package. It shouldn’t generally be used on its own, and other kernels described in this subpackage should generally be preferred.

This kernel takes the form:

\[k(\tau)=\exp(-c\,\tau)\,\left[a\,\cos(d\,\tau)+b\,\sin(d\,\tau)\right]\]

for \(\tau = |x_i - x_j|\).

In order to be positive definite, the parameters of this kernel must satisfy \(a\,c - b\,d > 0\), and you will see NaNs if you use parameters that don’t satisfy this relationship.

coord_to_sortable(X: tinygp.helpers.JAXArray) → tinygp.helpers.JAXArray

A helper function used to convert coordinates to sortable 1-D values

By default, this is the identity, but in cases where X is structured (e.g. multivariate inputs), this can be used to appropriately unwrap that structure.

design_matrix() → tinygp.helpers.JAXArray

The design matrix for the process

evaluate(X1: tinygp.helpers.JAXArray, X2: tinygp.helpers.JAXArray) → tinygp.helpers.JAXArray

The kernel evaluated via the quasiseparable representation

evaluate_diag(X: tinygp.helpers.JAXArray) → tinygp.helpers.JAXArray

For quasiseparable kernels, the variance is simple to compute

observation_model(X: tinygp.helpers.JAXArray) → tinygp.helpers.JAXArray

The observation model for the process

stationary_covariance() → tinygp.helpers.JAXArray

The stationary covariance of the process

to_general_qsm(X1: tinygp.helpers.JAXArray, X2: tinygp.helpers.JAXArray) → GeneralQSM

The generalized quasiseparable representation of this kernel

to_symm_qsm(X: tinygp.helpers.JAXArray) → SymmQSM

The symmetric quasiseparable representation of this kernel

transition_matrix(X1: tinygp.helpers.JAXArray, X2: tinygp.helpers.JAXArray) → tinygp.helpers.JAXArray

The transition matrix between two coordinates