Question

For a sequence of numbers x, how do I best create a function S(x, r, s) that computes sum(x[t]*x[t+r-s], where t ranges from s to length(x)-r+1 and r,s > 0.

Answer 1

You might want to enforce a relationship between the length of x, and the values of s and r as well, or you can end up with some strange results. Try 6:1 for instance.

sumfunc <- function(x, s, r) {
   s <- s[s>0]
   r <- r[r>0]
   if(!(length(r)==1 && length(s)==1)) stop("s and r should be numbers > 0")
   t <- s:(length(x)-r+1)
   return(sum(x[t]*x[t+r-s]))
}