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)

```

[Package BayesGPfit version 0.1.0 Index]