hmer (version 1.6.2)

gamma_exp: Gamma-exponential correlation function

Description

For points x, xp, and a pair of hyperparameters gamma and theta, gives the gamma-exponential correlation between the two points.

Usage

gamma_exp(x, xp, hp)

Value

The gamma-exponential correlation between x and xp.

Arguments

x

A data.frame of rows corresponding to position vectors

xp

A data.frame of rows corresponding to position vectors

hp

The hyperparameters theta (correlation length) and gamma (exponent), as a named list

Details

The gamma-exponential correlation function, for d = |x-x'|, is given by \(\exp(-(d/\theta)^\gamma)\). Gamma must be between 0 (exclusive) and 2 (inclusive).

References

Rasmussen & Williams (2005) <ISBN: 9780262182539>

Examples

gamma_exp(data.frame(a=1), data.frame(a=2), list(gamma = 1.5, theta = 0.1))
#> 1.846727e-14
gamma_exp(data.frame(a=1,b=2,c=-1),data.frame(a=1.5,b=2.9,c=-0.7), list(gamma = 1.3, theta = 0.2))
#> 0.0001399953