wendland: Wendland Basis Functions

In rcage: Regionalization of Multiscale Spatial Processes

Wendland Basis Functions

Description

Provides an implementation of the Wendland basis functions defined as

Ψ_{j}(s) = \{ 1 - d_{j}(s)\}^6 \{35 d_{j}(s)^2 + 18 d_j(s) + 3\}/3 \mathrm{I}( 0 ≤q d_{j} ≤q 1 ),

where

d_{j}(s) = ||s - c_j||/w.

Usage

wendland(crd, knots, w = NULL, ..., longlat = TRUE)

Arguments

crd	A matrix object. The (x,y) coordinates of the reference points {nCrd x 2}.
knots	A matrix object. The (x,y) coordinates of the knots {r x 2}.
w	A numeric object. The positive scaling factor (bandwidth).
...	ignored. Included only to require naming of inputs that follow.
longlat	A logical object. If FALSE, Euclidean distance is calculated; if TRUE, Great Circle distance is calculated. See ?sp::spDists for more information.

Details

Distances between reference coordinates and knots are obtained using sp::spDists().

Value

A matrix of Wendland functions evaluated at all combinations of crd and knots { nCrd x r }.

References

Wendland, H. (1998). Error estimates for interpolation by compactly supported radial basis functions of minimal degree. Journal of Approximation Theory, 93,258-272. <doi:10.1006/jath.1997.3137>.

Examples

  data(countyExample)

  wendland(crd = sp::coordinates(county), knots = knots)

rcage documentation built on June 7, 2022, 1:07 a.m.