GP.eigen.value: Compute eigen values for the standard modified exponential...

In BayesGPfit: Fast Bayesian Gaussian Process Regression Fitting

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 <[e-mail]>

Examples

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

BayesGPfit documentation built on Aug. 6, 2022, 5:06 p.m.