MortSmooth_BWB: Calculates the inner product of a matrix and a sparse weight matrix

Description

This is an internal function of package MortalitySmooth which calculates the inner product of a matrix (from a Kronecker product) and a sparse weight matrix within the function Mort2Dsmooth. It construct the LHD of the IWLS algorithm following the idea proposed in the Generalized Linear Array Models (see references).

Usage

MortSmooth_BWB(RTBx, RTBy, nbx, nby, W)

Arguments

RTBx

tensors product of B-splines basis for the x-axis.

RTBy

tensors product of B-splines basis for the y-axis.

nbx

number of B-splines for the x-axis.

nby

number of B-splines for the y-axis.

matrix of weights.

Value

A matrix of inner product of a matrix and a sparse weight matrix.

Details

The function employs an arithmetic of arrays which allows to define the LHS of the Poisson system of equations as a sequence of nested matrix operations. Such way of operating with arrays leads to low storage and high speed computation when data are structure as array.

References

Eilers, P. H. C., I. D. Currie, and M. Durban (2006). Fast and compact smoothing on large multidimensional grids. Computational Statistics & Data Analysis. 50, 61-76.

Currie, I. D., M. Durban, and P. H. C. Eilers (2006). Generalized linear array models with applications to multidimentional smoothing. Journal of the Royal Statistical Society. Series B. 68, 259-280.