orn_uhl {hmer}

Ornstein-Uhlenbeck correlation function

Description

For points x, xp, and a hyperparameter theta, gives the Ornstein-Uhlenbeck correlation between the two points.

Usage

orn_uhl(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 hyperparameter theta (correlation length) in a named list

Details

This correlation function can be seen as a specific case of the Matern correlation function when nu = 1/2.

Value

The Ornstein-Uhlenbeck correlation between x and xp.

References

Rasmussen & Williams (2005) <ISBN: 9780262182539>

Examples

orn_uhl(data.frame(a=1), data.frame(a=2), list(theta = 0.1))
#> 4.539993e-05
orn_uhl(data.frame(a=1,b=2,c=-1),data.frame(a=1.5,b=2.9,c=-0.7), list(theta = 0.2))
#> 0.00469197
orn_uhl(data.frame(a=1,b=1,c=1), data.frame(a=1.2,b=0.9,c=0.6), list(theta = 0.2)) ==
 matern(data.frame(a=1,b=1,c=1), data.frame(a=1.2,b=0.9,c=0.6), list(theta = 0.2, nu = 0.5)) #> TRUE