[R] Functional programming?

[Duncan Murdoch]

On 02/03/2016 11:47 AM, Roger Koenker wrote:
> I have a (remarkably ugly!!) code snippet  (below) that, given
> two simple functions, f and g,  generates
> a list of new functions h_{k+1} =  h_k * g, k= 1, …, K.  Surely, there are vastly
> better ways to do this.  I don’t particularly care about the returned list,
> I’d be happy to have the final  h_K version of the function,
> but I keep losing my way and running into the dreaded:
>
> Error in h[[1]] : object of type 'closure' is not subsettable
> or
> Error: evaluation nested too deeply: infinite recursion / options(expressions=)?
>
> Mainly I’d like to get rid of the horrible, horrible paste/parse/eval evils.  Admittedly
> the f,g look a bit strange, so you may have to suspend disbelief to imagine that there is
> something more sensible lurking beneath this minimal (toy)  example.
>
>      f <- function(u) function(x) u * x^2
>      g <- function(u) function(x) u * log(x)
>      set.seed(3)
>      a <- runif(5)
>      h <- list()
>      hit <- list()
>      h[[1]] <- f(a[1])
>      hit[[1]] <- f(a[1])
>      for(i in 2:5){
> 	ht <- paste("function(x) h[[", i-1, "]](x) * g(", a[i], ")(x)")
> 	h[[i]] <- eval(parse(text = ht))
> 	hit[[i]] <- function(x) {force(i); return(h[[i]] (x))}
> 	}
>      x <- 1:99/10
>      plot(x, h[[1]](x), type = "l")
>      for(i in 2:5)
> 	lines(x, h[[i]](x), col = i)

I don't understand what "hit" is for, but something like this should do it:


hlist <- function(maxk, f,g,a) {
   h <- list()
   h[[1]] <- f(a[1])
   for (j in 2:maxk) {
     h[[j]] <- local({
       k <- j
       function(x) {
         result <- h[[1]](x)
         for (i in 2:k) {
           result <- result*g(a[i])(x)
         }
         result
       }
     })
   }
   h
}

f <- function(u) function(x) u * x^2
g <- function(u) function(x) u * log(x)
set.seed(3)
a <- runif(5)
h <- hlist(5, f, g, a)