mgcv (version 1.3-22)

tensor.prod.model.matrix: Utility functions for constructing tensor product smooths

Description

Produce model matrices or penalty matrices for a tensor product smooth from the model matrices or penalty matrices for the marginal bases of the smooth.

Usage

tensor.prod.model.matrix(X)
tensor.prod.penalties(S)

Arguments

X

a list of model matrices for the marginal bases of a smooth

S

a list of penalties for the marginal bases of a smooth.

Value

• Either a single model matrix for a tensor product smooth, or a list of penalty terms for a tensor product smooth.

Details

If X[[1]], X[[2]] ... X[[m]] are the model matrices of the marginal bases of a tensor product smooth then the ith row of the model matrix for the whole tensor product smooth is given by X[[1]][i,]%x%X[[2]][i,]%x% ... X[[m]][i,], where %x% is the Kronecker product. Of course the routine operates column-wise, not row-wise!

If S[[1]], S[[2]] ... S[[m]] are the penalty matrices for the marginal bases, and I[[1]], I[[2]] ... I[[m]] are corresponding identity matrices, each of the same dimension as its corresponding penalty, then the tensor product smooth has m associate penalties of the form:

S[[1]]%x%I[[2]]%x% ... I[[m]],

I[[1]]%x%S[[2]]%x% ... I[[m]]

...

I[[1]]%x%I[[2]]%x% ... S[[m]].

Of course it's important that the model matrices and penalty matrices are presented in the same order when constructing tensor product smooths.

References

http://www.maths.bath.ac.uk/~sw283/

See Also

te, smooth.construct.tensor.smooth.spec

Examples

X <- list(matrix(1:4,2,2),matrix(5:10,2,3))
tensor.prod.model.matrix(X)

S<-list(matrix(c(2,1,1,2),2,2),matrix(c(2,1,0,1,2,1,0,1,2),3,3))
tensor.prod.penalties(S)