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.
xixj(mat,mat.new=NULL,a=NULL)Input data, could be a matrix or a vector.
Second input data, could be a vector or a matrix. Default to be NULL. If NULL, mat.new=mat.
Weight to be add on each column of the matrix.
A symmetric matrix used to build the linear kernel or similar
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').
Shi, J Q., and Choi, T. (2011), Gaussian Process Regression Analysis for Functional Data, Springer, New York.