Generic basis-function constructor

This function is meant to be used for manual construction of arbitrary basis functions. For `local' basis functions, please use the function local_basis instead.

Usage

Basis(manifold, n, fn, pars, df, regular = FALSE)

Arguments

manifold

object of class manifold, for example, sphere

n

number of basis functions (should be an integer)

fn

a list of functions, one for each basis function. Each function should be encapsulated within an environment in which the manifold and any other parameters required to evaluate the function are defined. The function itself takes a single input s which can be of class numeric, matrix, or Matrix, and returns a vector which contains the basis function evaluations at s.

pars

A list containing a list of parameters for each function. For local basis functions these would correspond to location and scale parameters.

df

A data frame containing one row per basis function, typically for providing informative summaries.

regular

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

Details

This constructor checks that all parameters are valid before constructing the basis functions. The requirement that every function is encapsulated is tedious, but necessary for FRK to work with a large range of basis functions in the future. Please see the example below which exemplifies the process of constructing linear basis functions from scratch using this function.

See also

auto_basis for constructing basis functions automatically, local_basis for constructing `local' basis functions, and show_basis for visualising basis functions.

Examples

## Construct two linear basis functions on [0, 1]
manifold <- real_line()
n <- 2
lin_basis_fn <- function(manifold, grad, intercept) {
   function(s) grad*s + intercept
}
pars <- list(list(grad = 1, intercept = 0),
             list(grad = -1, intercept = 1))
fn <- list(lin_basis_fn(manifold, 1, 0),
           lin_basis_fn(manifold, -1, 1))
df <- data.frame(n = 1:2, grad = c(1, -1), m = c(1, -1))
G <- Basis(manifold = manifold, n = n, fn = fn, pars = pars, df = df)
if (FALSE) { # \dontrun{
eval_basis(G, s = matrix(seq(0,1, by = 0.1), 11, 1))} # }