rat_quad {hmer}

Rational Quadratic correlation function

Description

For points x, xp, and a pair of hyperparameters alpha and theta, gives the rational quadratic correlation between the two points.

Usage

rat_quad(x, xp, hp)

Arguments

x

A data.frame of rows corresponding to position vectors

xp

A data.frame of rows corresponding to position vectors

hp

The hyperparameters alpha (exponent and scale) and theta (correlation length)

Details

This correlation function, for d = |x-x'|, has the form (1+d^2/(2\alpha\theta^2))^{-\alpha}, and can be seen as a superposition of exponential-squared correlation functions.

Value

The rational quadratic correlation between x and xp.

References

Rasmussen & Williams (2005) <ISBN: 9780262182539>

Examples

rat_quad(data.frame(a=1), data.frame(a=2), list(alpha = 1.5, theta = 0.1))
#> 0.004970797
rat_quad(data.frame(a=1,b=2,c=-1),data.frame(a=1.5,b=2.9,c=-0.7), list(alpha = 1.5, theta = 0.2))
#> 0.02904466