Utility functions for constructing tensor product smooths

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)

Arguments

X

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

Value

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

References

Wood, S.N. (2006) “Low Rank Scale Invariant Tensor Product Smooths for Generalized Additive Mixed Models”. Biometrics 62(4):1025-1036

Author

Simon N. Wood simon.wood@r-project.org

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)
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    5    7    9   15   21   27
#> [2,]   12   16   20   24   32   40