rcage (version 1.2)

bisquare: Bisquare Basis Functions

Description

Provides an implementation of the bisquare basis functions defined as $$ \Psi_{j}(s) = \{ 1 - (||s - c_j||/w)^2\}^2 \mathrm{I}( ||s-c_j|| \leq w ).$$

Usage

bisquare(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 bisquare 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

Cressie, N. and Johannesson, G. (2008). Fixed rank kriging for very large spatial data sets. Journal of the Royal Statistical Society, Series B, 70, 209--226. <doi:10.1111/j.1467-9868.2007.00633.x>.

Examples

# NOT RUN {
  data(countyExample)

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

# }