GP.eigen.funcs.fast {BayesGPfit}R Documentation

Compute eigen functions

Description

Compute eigen functions for the standard modified exponential squared correlation kernel.

Usage

GP.eigen.funcs.fast(grids, poly_degree = 10L, a = 0.01, b = 1)

Arguments

grids

A matrix where rows represent points and columns are coordinates.

poly_degree

A integer number specifies the highest degree of Hermite polynomials. The default value is 10L.

a

A positive real number specifies 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 specifies the smoothness parameter in the modeified exponetial squared kernel. The smaller value the smoother the GP is. The default value is 1.0.

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(lattice)
grids = GP.generate.grids(d=2L)
Psi_mat = GP.eigen.funcs.fast(grids)
fig = list()
for(i in 1:4){
   fig[[i]] = levelplot(Psi_mat[,i]~grids[,1]+grids[,2])
}
plot(fig[[1]],split=c(1,1,2,2),more=TRUE)
plot(fig[[2]],split=c(1,2,2,2),more=TRUE)
plot(fig[[3]],split=c(2,1,2,2),more=TRUE)
plot(fig[[4]],split=c(2,2,2,2))

[Package BayesGPfit version 0.1.0 Index]