Sum of subvectors of a vector in R

Question

Given a vector x of length k, I would like to obtain a k by k matrix X where X[i,j] is the sum of x[i] + ... + x[j]. The way I do it now is

set.seed(1)
x <- rnorm(10)

X <- matrix(0,10,10)
for(i in 1:10) 
  for(j in 1:10)
    X[i,j] <- sum(x[i:j])

#             [,1]       [,2]       [,3]      [,4]        [,5]       [,6]        [,7]      [,8]      [,9]      [,10]
# [1,]  -0.6264538 -0.4428105 -1.2784391 0.3168417  0.64634948 -0.1741189  0.31331014 1.0516348 1.6274162  1.3220278
# [2,]  -0.4428105  0.1836433 -0.6519853 0.9432955  1.27280329  0.4523349  0.93976395 1.6780887 2.2538700  1.9484816
# [3,]  -1.2784391 -0.6519853 -0.8356286 0.7596522  1.08915996  0.2686916  0.75612063 1.4944453 2.0702267  1.7648383
# [4,]   0.3168417  0.9432955  0.7596522 1.5952808  1.92478857  1.1043202  1.59174924 2.3300739 2.9058553  2.6004669
# [5,]   0.6463495  1.2728033  1.0891600 1.9247886  0.32950777 -0.4909606 -0.00353156 0.7347931 1.3105745  1.0051861
# [6,]  -0.1741189  0.4523349  0.2686916 1.1043202 -0.49096061 -0.8204684 -0.33303933 0.4052854 0.9810667  0.6756783
# [7,]   0.3133101  0.9397640  0.7561206 1.5917492 -0.00353156 -0.3330393  0.48742905 1.2257538 1.8015351  1.4961467
# [8,]   1.0516348  1.6780887  1.4944453 2.3300739  0.73479315  0.4052854  1.22575376 0.7383247 1.3141061  1.0087177
# [9,]   1.6274162  2.2538700  2.0702267 2.9058553  1.31057450  0.9810667  1.80153511 1.3141061 0.5757814  0.2703930
# [10,]  1.3220278  1.9484816  1.7648383 2.6004669  1.00518611  0.6756783  1.49614672 1.0087177 0.2703930 -0.3053884

but I can't help the feeling that there must be a more elegant R way (except translating this into Rcpp).

Answer 1

We can use outer():

mySum <- function(i,j) sum(x[i:j])
outer(1:10, 1:10, Vectorize(mySum))

EDIT: You could also go for a solution by foreach:

library(foreach)
mySum <- function(j) sum(x[i:j])
mySum <- Vectorize(mySum)
foreach(i = 1:10, .combine = 'rbind') %do% mySum(1:10)

and maybe run it in parallel instead.