Question

Lets assume

x = c(1, 2, 3.5, 4, 6, 7.5, 8, 9, 10, 11.5, 12) 
y = c(2.5, 6.5) 
I = split(x, findInterval(x, y))
f = function(I$'i', x) {
        d = pmax(outer(x, I$'i', "-"), 0)
        colSums(d - d^2/2)
}

I want to calculate the value of f(I$’i’, x) in each values of each interval and then find which I$’i’ actual value have the maximum value of f(I$’i’, x ) in each interval. for example if we have three intervals , my result should be three values of x which f(I$’i’, x) is maximum in each interval. how can i find these values?
In addition, it should be mentioned that in each iteration of my code the value of vector y changes.

I wrote this code but i can not find the actual values of the maximum value in each interval:

for(i in 0:length(I)-1){
    max.value = I$'i'[which.max(f(I$'i', x))]
}

and i got this error:
Error in pmax(outer(x, I, “-“), 0) :
cannot mix 0-length vectors with others

Answer 1

The problem is attempting to index the ith element of the list. Doing I$'i' is trying to get the element of the list corresponding to the string 'i', which doesn’t exist:

> i <- 1
> I$'i'
NULL

To fix this, you should index a list using the [[..]] notation (which indexes them in order, i.e. I[[1]] = I$'0'):

> i <- 1
> I[[i]]
[1] 1 2
> I$'0' # to illustrate the indexing
[1] 1 2

Assuming that f is just meant to take a vector (rather than an index into I), its definition should be something like:

f = function(vec, x) {
        d = pmax(outer(x, vec, "-"), 0)
        colSums(d - d^2/2)
}

And the loop like:

for (i in 1:length(i)) {
     max.value = I[[i]][which.max(f(I[[i]], x))]
}

Note that you can iterate directly over the elements of a list, you don’t need to index each one individually, so we could also do:

for (vec in I) {
     max.value = vec[which.max(f(vec, x))]
}

(Also, you might want something slightly different to what you have, since in each loop max.value is overwritten.)