dn.poly: Mutli-dimensional Chebychev approximation

In squipbar/cheby: Computes Chebychev approximations to 1- and 2-dimensional functions

Description

Standard Chebychev approximation of an arbitrary function. **Currently only works for two-dimensional approximation**

Usage

dn.poly(fn, range, iOrder, iPts, fn.opts = NULL, fn.vals = NULL,
  grid = NULL, details = FALSE)

Arguments

fn	a function f(x_1,..., x_n) or f(x_1, ..., x_n,β) for β a list of function parameters. If the latter, must be coded with second argument a list names opts, i.e. fn <- function( x, opts )
range	the range of the approximation, given as a list of vectors. Eg for a 3-dimensional function approximated over [1,2] * [-1,2] * [0,4], would be range = list( c(1,2), c(-1,2), c(0,4) )
iOrder	the vector of orders of the polynomial approximation. Eg. to approximate using polynomials of order 3 and 5 in the 1st and 2nd dimensions respectively, would be iOrder=c(5,6)
iPts	the vector of number of points at which the approximation is computed. Must be at least as large as iOrder (element-by-element).
fn.opts	(optional) options passed to fn [NOT YET FUNCTIONAL]
fn.vals	the values of fn on grid. Useful if fn is very slow to evaluate.
grid	(optional) the grid on which the function is to be approximated. Should be submitted as a list of vectors for the grids in each dimension.
details	If TRUE, returns extra details about the approximation.

Value

A function which approximates the input fn over the box defined by range. If details=TRUE, also includes the polynomial desciption over [-1,1], as well as the approximation errors

See Also

d1.poly

Examples

test.fn <- function( x,y ) x^2*y^.5
ff <- dn.poly( test.fn, list( c(0,4), c(0,4) ), c( 6, 6), c(12,12) )
XX <- seq(0,4,.05)
plot( XX, mapply( test.fn, XX, 1 ), type='l' )
lines( XX, mapply( ff, XX, 1 ), col=2 )
plot( XX, mapply( test.fn, 1, XX ), type='l' )
lines( XX, mapply( ff, 1, XX ), col=2 )

squipbar/cheby documentation built on May 30, 2019, 8 a.m.