GPFDA (version 1.1)

xixj: Linear kernel function component.

Description

Component to build a linear kernel function or similar.

$$M=\sum a_i*x'_i*x_i^{T}$$

where $x_i$ is the $i^{th}$ column of the input matrix; $a_i$ is the i'th element of the weight vector. Note that $x$ and $x'$ might be different. It is for non-stationary kernel functions.

Usage

xixj(mat,mat.new=NULL,a=NULL)

Arguments

mat

Input data, could be a matrix or a vector.

mat.new

Second input data, could be a vector or a matrix. Default to be NULL. If NULL, mat.new=mat.

a

Weight to be add on each column of the matrix.

Value

• out
  A symmetric matrix used to build the linear kernel or similar

Details

When all 'a' are 1, this is simply mat%*%t(mat.new). If one wants to involve linear kernel components in customized covariance matrix, this function will be used in derivatives of the kernel function. See examples in demo('co2').

References

Shi, J Q., and Choi, T. (2011), Gaussian Process Regression Analysis for Functional Data, Springer, New York.

See Also

cov.linear,xixj_sta