delta.xi: Gradient with respect to the knots locations.

In feng-li/movingknots: Efficient Bayesian multivariate surface regression

Description

Give the gradient for basis function w.r.t. the knots (subsets) locations for different types of splines.

Usage

delta.xi(x, knots, splineArgs)

Arguments

x	"matrix". The data matrix, you don't have to provide a constant column.
knots	"list". knots$thinplate.s: knots$thinplate.a:
splineArgs	NA
knotsArgs	"list". Arguments need to pass to the function, see bellow. knotsArgs$comp: "character", is the components in the design matrix; knotsArgs$thinplate.a.locate: "character", is the location for the additive spline if used, same as d.matrix() function. knotsArgs$thinplate.s.subset: "integer", is the subset label of the knots locations to be updated in the thinplate surface component; knotsArgs$thinplate.a.subset: "integer", is the subset label of the knots locations to be updated in the thinplate additive component;

Details

The function can be extended by adding new basis. This function gives the gradient for the (vecX) w.r.t. vec(xi')'. You may need the transpose of the results if you want gradient for the (vecX)' w.r.t. vec(xi'). This function is mostly used inside the function of gradient, so always consider the parameters input convenience when you update it.

Value

"list" the gradient parts for different knots components $thinplate.s: "matrix". The gradient w.r.t the input of args$thinplate.s.subset and other relevant values. Note this will only give the dense part of the full gradient matrix w.r.t. the subset. It can also give the full gradient matrix w.r.t. all knots location if args$KnotsSubset is set to same as the full set. $thinplate.a: "matrix". Same as above but for the additive spline part.

Author(s)

Feng Li, Department of Statistics, Stockholm University, Sweden.

feng-li/movingknots documentation built on March 30, 2021, 11:58 a.m.