local_basis: Construct a set of local basis functions

Description Usage Arguments Details See Also Examples

View source: R/basisfns.R

Description

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

Usage

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

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”

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

φ(u) = ≤ft(1- ≤ft(\frac{\| u \|}{R}\right)^2\right)^2 I(\|u\| < R),

and scale is given by R, the range of support of the bisquare function. If type is “Gaussian”, then

φ(u) = \exp≤ft(-\frac{\|u \|^2}{2σ^2}\right),

and scale is given by σ, the standard deviation. If type is “exp”, then

φ(u) = \exp≤ft(-\frac{\|u\|}{ τ}\right),

and scale is given by τ, the e-folding length. If type is “Matern32”, then

φ(u) = ≤ft(1 + \frac{√{3}\|u\|}{κ}\right)\exp≤ft(-\frac{√{3}\| u \|}{κ}\right),

and scale is given by κ, the function's scale.

See Also

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

Examples

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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)

Example output



FRK documentation built on May 2, 2019, 8:11 a.m.