GP.eigen.value {BayesGPfit} | R Documentation |
Compute eigen values for the standard modified exponential squared correlation kernel.
Description
Compute eigen values for the standard modified exponential squared correlation kernel.
Usage
GP.eigen.value(poly_degree = 10, a = 1, b = 1, d = 2)
Arguments
poly_degree |
A positive integer number specifies the highest degree of Hermite polynomials. The default value is 10L. |
a |
A positive real number specifying the concentration parameter in the modified exponetial squared kernel. The larger value the more the GP concentrates around the center. The default value is 0.01. |
b |
A positive real number specifying the smoothness parameter in the modeified exponetial squared kernel. The smaller value the smoother the GP is. The default value is 1.0. |
d |
A positive integer number specifying the dimension of grid points. |
Details
Compute eigen values of the standard modified exponential squared kernel on d-dimensional grids
cor(X(s_1),X(s_2)) = \exp{-a*(s_1^2+*s_2^2)-b*(s_1-s_2)^2}
where a
is the concentration parameter and b
is the smoothness parameter. The expected ranges of each coordinate is from -6 to 6.
Value
A matrix represents a set of eigen functions evaluated at grid points. The number of rows is equal to the number of grid points. The number of columns is choose(poly_degree+d,d), where d is the dimnension of the grid points.
Author(s)
Jian Kang <jiankang@umich.edu>
Examples
library(BayesGPfit)
Lambda = GP.eigen.value(poly_degree=10L,a=0.01,b=0.5,d=2)
plot(Lambda)