local_basis function

Construct a set of local basis functions

Construct a set of local basis functions based on pre-specified location and scale parameters.

local_basis(
  manifold = sphere(),
  loc = matrix(c(1, 0), nrow = 1),
  scale = 1,
  type = c("bisquare", "Gaussian", "exp", "Matern32"),
  res = 1,
  regular = FALSE
)

radial_basis(
  manifold = sphere(),
  loc = matrix(c(1, 0), nrow = 1),
  scale = 1,
  type = c("bisquare", "Gaussian", "exp", "Matern32")
)

Arguments

• manifold: object of class manifold, for example, sphere
• loc: a matrix of size n by dimensions(manifold) indicating centres of basis functions
• scale: vector of length n containing the scale parameters of the basis functions; see details
• type: either "bisquare", "Gaussian", "exp", or "Matern32"
• res: vector of length n containing the resolutions of the basis functions
• regular: logical indicating if the basis functions (of each resolution) are in a regular grid

Details

This functions lays out local basis functions in a domain of interest based on pre-specified location and scale parameters. If type is ``bisquare'', then

and scale is given by $R$, the range of support of the bisquare function. If type is ``Gaussian'', then

and scale is given by $\sigma$, the standard deviation. If type is ``exp'', then

and scale is given by $\tau$, the e-folding length. If type is ``Matern32'', then

and scale is given by $\kappa$, the function's scale.

Examples

library(ggplot2)
G <-  local_basis(manifold = real_line(),
                   loc=matrix(1:10,10,1),
                   scale=rep(2,10),
                   type="bisquare")
## Not run: show_basis(G)

See Also

auto_basis for constructing basis functions automatically, and show_basis for visualising basis functions.