BayesGPfit (version 1.1.0)

GP.eigen.value: 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)

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.

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.

Author

Jian Kang <[e-mail]>

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.

Examples

library(BayesGPfit)
Lambda = GP.eigen.value(poly_degree=10L,a=0.01,b=0.5,d=2)
plot(Lambda)