Matern12.Kernel {rkriging} | R Documentation |
Matern(1/2) Kernel
Description
This function specifies the Matern kernel with smoothness parameter \nu
=1/2.
It is also known as the Exponential kernel.
Usage
Matern12.Kernel(lengthscale)
Arguments
lengthscale |
a vector for the positive length scale parameters |
Details
The Matern(1/2) kernel is given by
k(r)=\exp(-r),
where
r(x,x^{\prime})=\sqrt{\sum_{i=1}^{p}\left(\frac{x_{i}-x_{i}^{\prime}}{l_{i}}\right)^2}
is the euclidean distance between x
and x^{\prime}
weighted by
the length scale parameters l_{i}
's.
Value
A Matern(1/2) Kernel Class Object.
Author(s)
Chaofan Huang and V. Roshan Joseph
References
Duvenaud, D. (2014). The kernel cookbook: Advice on covariance functions.
Rasmussen, C. E. & Williams, C. K. (2006). Gaussian Processes for Machine Learning. The MIT Press.
See Also
Matern.Kernel, Get.Kernel, Evaluate.Kernel.
Examples
n <- 5
p <- 3
X <- matrix(rnorm(n*p), ncol=p)
lengthscale <- c(1:p)
# approach 1
kernel <- Matern12.Kernel(lengthscale)
Evaluate.Kernel(kernel, X)
# approach 2
kernel <- Get.Kernel(lengthscale, type="Matern12")
Evaluate.Kernel(kernel, X)
[Package rkriging version 1.0.1 Index]