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]