# local_basis: Construct a set of local basis functions In FRK: Fixed Rank Kriging

## Description

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

## Usage

 1 2 3 4 5 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

 1 2 3 4 5 6 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.