R ranges: 1:0 - illogical behavior - r

Question

I have an array X of length N, and I'd like to compute sum(X[(i+1):N]) - sum(X[1:(i-1)]. This works fine if my index, i, is within 2..(N-1). If it's equal to 1, the second term will return the first element of the array rather than exclude it. If it's equal to N, the first term will return the last element of the array rather than exclude it. seq_len is the only function I'm aware of that does the job, but only for the 2nd term (it indexes 1:n). What I need is a range function that will return NULL (rather than throw an exception like seq) when its 2nd argument is below its first. The sum function will do the rest. Is anyone aware of one, or do I have to write one myself?

Answer 1

I suggest an alternate path for generating indexing sequences: seq_len, which reacts intuitively in the extremes.
Bottom Line Up Front: use sum(X[-seq_len(i)]) - sum(X[seq_len(i-1)]) instead.
First, some sample data:
X <- 1:10
N <- length(X)
Your approach, at the two extremes:
i <- 1
X[(i+1):N]
# [1] 2 3 4 5 6 7 8 9 10
X[1:(i-1)] # oops
# [1] 1
That should return "nothing", I believe. (More the point, sum(...) should return 0. For the record, sum(integer(0)) is 0.)
i <- 10
X[(i+1):N] # oops
# [1] NA 10
X[1:(i-1)]
# [1] 1 2 3 4 5 6 7 8 9
There's your other error, where you'd expect "nothing" in the first subset.
Instead, I suggest you use seq_len:
i <- 1
X[-seq_len(i)]
# [1] 2 3 4 5 6 7 8 9 10
X[seq_len(i-1)]
# integer(0)
i <- 10
X[-seq_len(i)]
# integer(0)
X[seq_len(i-1)]
# [1] 1 2 3 4 5 6 7 8 9
Both seem fine, and something in the middle makes sense.
i <- 5
X[-seq_len(i)]
# [1] 6 7 8 9 10
X[seq_len(i-1)]
# [1] 1 2 3 4
In this contrived example, what we're looking for at any value of i:
1: sum(2:10) - 0 = 54 - 0 = 54
2: sum(3:10) - sum(1:1) = 52 - 1 = 51
3: sum(4:10) - sum(1:2) = 49 - 3 = 46
...
10: 0 - sum(1:9) = 0 - 45 = -45
And we now get that:
func <- function(i, x) sum(x[-seq_len(i)]) - sum(x[seq_len(i-1)])
sapply(c(1,2,3,10), func, X)
# [1] 54 51 46 -45
Edit:
李哲源's answer got me to thinking that you don't need to re-sum the numbers before and after all the time. Just do it once and re-use it. This method could be easily a bit faster if your vector is large.
Xb <- c(0, cumsum(X)[-N])
Xb
# [1] 0 1 3 6 10 15 21 28 36 45
Xa <- c(rev(cumsum(rev(X)))[-1], 0)
Xa
# [1] 54 52 49 45 40 34 27 19 10 0
sapply(c(1,2,3,10), function(i) Xa[i] - Xb[i])
# [1] 54 51 46 -45
So this suggests that your summed value at any value of i is
Xs <- Xa - Xb
Xs
# [1] 54 51 46 39 30 19 6 -9 -26 -45
where you can find the specific value with Xs[i]. No repeated summing required.