rcage (version 1.2)

wendland: Wendland Basis Functions

Description

Provides an implementation of the Wendland basis functions defined as $$ \Psi_{j}(s) = \{ 1 - d_{j}(s)\}^6 \{35 d_{j}(s)^2 + 18 d_j(s) + 3\}/3 \mathrm{I}( 0 \leq d_{j} \leq 1 ),$$ 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.

Value

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

Details

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

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

# NOT RUN {
  data(countyExample)

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

# }