Polynomial

class tinygp.kernels.Polynomial(order: tinygp.helpers.JAXArray, scale: tinygp.helpers.JAXArray = <factory>, sigma: tinygp.helpers.JAXArray = <factory>)

Bases: Kernel

A polynomial kernel

\[k(\mathbf{x}_i,\,\mathbf{x}_j) = [(\mathbf{x}_i / \ell) \cdot (\mathbf{x}_j / \ell) + \sigma^2]^P\]

Parameters:

• order – The power \(P\).

• scale – The parameter \(\ell\).

• sigma – The parameter \(\sigma\).

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

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.