# Gaussian processes¶

This module provides a collection of tools that are useful when performing Gaussian process regression.

## Numpy¶

 abs_diff(x, xp) Gets matrix of differences between $$D$$-dimensional vectors x and xp i.e. exponential_squared(x, xp, sigmaf, l[, pspec]) Create exponential squared covariance function between $$D$$ dimensional vectors $$x$$ and $$x_p$$ i.e.
africanus.gps.abs_diff(x, xp)[source]

Gets matrix of differences between $$D$$-dimensional vectors x and xp i.e.

$X_{ij} = |x_i - x_j|$
Parameters
xnumpy.ndarray

Array of inputs of shape (N, D).

xpnumpy.ndarray

Array of inputs of shape (Np, D).

Returns
XXnumpy.ndarray

Array of differences of shape (N, Np).

africanus.gps.exponential_squared(x, xp, sigmaf, l, pspec=False)[source]

Create exponential squared covariance function between $$D$$ dimensional vectors $$x$$ and $$x_p$$ i.e.

$k(x, x_p) = \sigma_f^2 \exp\left(-\frac{(x-x_p)^2}{2l^2}\right)$
Parameters
xnumpy.ndarray

Array of shape (N, D).

xpnumpy.ndarray

Array of shape (Np, D).

sigmaffloat

The signal variance hyper-parameter

lfloat

The length scale hyper-parameter

Returns
Knumpy.ndarray

Array of shape (N, Np)