class tinygp.kernels.stationary.RationalQuadratic(scale: JAXArray | float = <factory>, distance: Distance = <factory>, alpha: JAXArray | float | None = None)[source]#

Bases: Stationary

The rational quadratic

\[k(\mathbf{x}_i,\,\mathbf{x}_j) = (1 + r^2 / 2\,\alpha)^{-\alpha}\]

where, by default,

\[r^2 = ||(\mathbf{x}_i - \mathbf{x}_j) / \ell||_2^2\]
  • scale – The parameter \(\ell\).

  • alpha – The parameter \(\alpha\).

evaluate(X1: tinygp.helpers.JAXArray, X2: tinygp.helpers.JAXArray) tinygp.helpers.JAXArray[source]#

Evaluate the kernel at a pair of input coordinates

This should be overridden be subclasses to return the kernel-specific value. Two things to note:

  1. Users shouldn’t generally call Kernel.evaluate(). Instead, always “call” the kernel instance directly; for example, you can evaluate the Matern-3/2 kernel using Matern32(1.5)(x1, x2), for arrays of input coordinates x1 and x2.

  2. When implementing a custom kernel, this method should treat X1 and X2 as single datapoints. In other words, these inputs will typically either be scalars of have shape n_dim, where n_dim is the number of input dimensions, rather than n_data or (n_data, n_dim), and you should let the Kernel vmap magic handle all the broadcasting for you.

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

Evaluate the kernel on its diagonal

The default implementation simply calls Kernel.evaluate() with X as both arguments, but subclasses can use this to make diagonal calcuations more efficient.