Basis functions

An object of class Basis contains the basis functions used to construct the matrix \(S\) in FRK.

Details

Basis functions are a central component of FRK, and the package is designed to work with user-defined specifications of these. For convenience, however, several functions are available to aid the user to construct a basis set for a given set of data points. Please see auto_basis for more details. The function local_basis helps the user construct a set of local basis functions (e.g., bisquare functions) from a collection of location and scale parameters.

Slots

manifold

an object of class manifold that contains information on the manifold and the distance measure used on the manifold. See manifold-class for more details

n

the number of basis functions in this set

fn

a list of length n, with each item the function of a specific basis function

pars

a list of parameters where the \(i\)-th item in the list contains the parameters of the \(i\)-th basis function, fn[[i]]

df

a data frame containing other attributes specific to each basis function (for example the geometric centre of the local basis function)

regular

logical indicating if the basis functions (of each resolution) are in a regular grid

See also

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