chebeval: Evaluate a Chebyshev interpolation in a point In chebpol: Multivariate Interpolation

Description

Given Chebyshev coefficients, evaluate the interpolation in a point.

Usage

 ```1 2``` ```chebeval(x, coef, intervals = NULL, threads = getOption("chebpol.threads")) ```

Arguments

 `x` The point to evaluate. `coef` The Chebyshev coefficients. Typically from a call to `chebcoef`, possibly modified. `intervals` A list of minimum and maximum values. One for each dimension of the hypercube. `threads` And integer. In case `x` is a matrix of column vectors, use this number of threads in parallel to evaluate.

Value

A numeric. The interpolated value.

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```# make a function which is known to be unsuitable for Chebyshev approximation f <- function(x) sign(x) # make a standard Chebyshev interpolation ch <- ipol(f,dims=50,method='chebyshev') # then do a truncated interpolation val <- evalongrid(f,50) coef <- chebcoef(val) # truncate the high frequencies coef[-(1:10)] <- 0 # make a truncated approximation tch <- Vectorize(function(x) chebeval(x,coef)) # make a lower degree also ch2 <- ipol(f,dims=10,method='chebyshev') # plot the functions ## Not run: s <- seq(-1,1,length.out=400) plot(s,ch(s),col='red',type='l') lines(s,tch(s),col='blue') lines(s,f(s)) lines(s,ch2(s),col='green') ## End(Not run) ```

chebpol documentation built on Dec. 9, 2019, 5:08 p.m.