coeffs: Calculate coefficients of a function's series expansion
In USP: U-Statistic Permutation Tests of Independence for all Data Types

Description Usage Arguments Value References Examples

View source: R/coeffs.R

This function is used in InfKern to produce the kernel matrix from functional data defined on the interval [0,1]. For further details see Section 7.4 of \insertCiteBKS2020USP.

1	coeffs(X, Ntrunc)

`X`	The discretised functions whose coefficients are required. This should be a matrix with one row per function, and with Ndisc columns, where Ndisc is the grid size of the discretisation.
`Ntrunc`	The number of coefficients that are required. The function returns coefficients 1,...,Ntrunc.

The coefficients of X in its expansion in terms of sine functions. See \insertCiteBKS2020USP for more detail.

\insertRef

BKS2020USP

t=seq(from=0,to=1,length.out=1000); X=t^2
U=coeffs(X,100)[1,]; L=5
plot(t,X,type="l")
approx=rep(0,1000)
for(l in 1:L){
approx=approx+qnorm(U[l])*sqrt(2)*sin((l-1/2)*pi*t)/((l-1/2)*pi)
lines(t,approx,col=l+1)
}