CODEWITHSUNDEEP
rvectorization
JWallmark
JWallmark

Reputation: 31

Vectorization of nested for loop

I have the following function:

g.Bn = function(n) {
  Bn = 0
  for(k in 0:n) {
    res.of.loop = 0
    for(j in 0:k) {
      res.of.loop = res.of.loop + (-1)^j * (j + 1)^n * choose(k, j)
    }
    Bn = res.of.loop * 1/(k+1) + Bn
  }
  return(Bn)
}

Is here a way to vectorize it instead of using for loops?

Upvotes: 3

Views: 656

Answers (2)

waferthin
waferthin

Reputation: 1602

You could vectorise the inner loop (as per @DaveT), and use sapply:

g.Bn2 = function(n) {
  sum(sapply(0:n, function(k) {
    sum((-1)^(0:k) * (0:k + 1)^n * choose(k, 0:k)) * 1/(k+1)
  }))
}

Or another possibility to vectorise the outer loop:

g.Bn3 = function(n) {
  f <- function(k, n) sum((-1)^(0:k) * (0:k + 1)^n * choose(k, 0:k)) * 1/(k+1)
  sum(Vectorize(f, vectorize.args = "k")(0:n, n))
}

> microbenchmark(g.Bn(100), g.Bn2(100), g.Bn3(100))
       expr      min        lq      mean   median        uq      max neval
  g.Bn(100) 1493.086 1533.9280 1841.3455 1585.354 1675.3575 9023.316   100
 g.Bn2(100)  617.063  650.7850  905.6899  738.230  788.7305 9224.460   100
 g.Bn3(100)  685.094  772.3785 1015.9182  816.945  860.1775 8213.777   100

Upvotes: 4

Yifu Yan
Yifu Yan

Reputation: 6116

You can convert for-loop to map and reduce instead.

In the example below purrr::map iterate all data, and sum reduces a numeric vector into a scaler(a numeric vector with length of one).

g.Bn = function(n) {
    sum(
        purrr::map_dbl(0:n,function(k){
            sum(
                purrr::map_dbl(0:k,function(j){
                    (-1)^j * (j + 1)^n * choose(k, j)
                })
            ) * 1/(k+1)

        })
    )
}

And it seems like all js in inner loop can be replaced with 0:k

g.Bn = function(n) {
    sum(
        purrr::map_dbl(0:n,function(k){
            sum((-1)^(0:k) * (0:k + 1)^n * choose(k, 0:k)) * 1/(k+1)
        })
    )
}

Upvotes: 0

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