How can I use a vectorised function in R in alternate sequence?

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Suppose I have a vector x with n elements. I want to use any vectorised function, say cumprod, on every alternate number of x, i.e. every 1, 3, 5 and so on and another on 2, 4, 6 and so on. I am adding a reprex and code tried. The code works, but it seems I am unnecessarily taking a long route and code can be shortened. Can it be?

x <- 5:14

cumprod((x * (seq_along(x) %% 2)) + (seq_along(x)-1) %% 2) * seq_along(x) %% 2 +
  cumprod((x * ((seq_along(x)-1) %% 2)) + seq_along(x) %% 2) * (seq_along(x)-1) %% 2
#>  [1]     5     6    35    48   315   480  3465  5760 45045 80640

Here cumprod is just an example function. I may have to use other functions in alternate sequence as well.

sequence r modulo
5 Answers

We could do this in a concise way with rowCumprods after creating a matrix (assuming the vector is of even length)

library(matrixStats)
c(rowCumprods(matrix(x, nrow = 2)))

-output

[1]     5     6    35    48   315   480  3465  5760 45045 80640

if it can be odd length, then just append an NA at the end

 c(rowCumprods(matrix(c(x,  list(NULL, NA)[[1 +
         (length(x) %%2 != 0)]]), nrow = 2)))

-output

 [1]     5     6    35    48   315   480  3465  5760 45045 80640

Or we can do this in a generalized way with ave (works both with even/odd lengths)

ave(x, seq_along(x) %% 2, FUN = cumprod)
 [1]     5     6    35    48   315   480  3465  5760 45045 80640
user_37322710

Select odd (c(TRUE, FALSE)) or even (c(FALSE, TRUE)) indices. Weave the two resulting vectors (c(rbind)

c(rbind(cumprod(x[c(TRUE, FALSE)]), cumprod(x[c(FALSE, TRUE)])))
# [1]     5     6    35    48   315   480  3465  5760 45045 80640

To handle also odd vector length, you need to truncate the result to length of the vector.

x = 1:5

c(rbind(cumprod(x[c(TRUE, FALSE)]), cumprod(x[c(FALSE, TRUE)])))[1:length(x)]
# [1]  1  2  3  8 15

There will be a warning when the shorter result vector, corresponding to the even indices (which has one element less), is recycled in the rbind step.

user_18517120

One option for both even and odd number of elements could be:

c(t(apply(matrix(x, 2, sum(seq_along(x) %% 2)), 1, cumprod)))[1:length(x)]

With x <- 1:5:

[1]  1  2  3  8 15

With x <- 1:6:

[1]  1  2  3  8 15 48

Or a less effective option, however, without any warnings:

y <- Reduce(`c`, sapply(split(setNames(x, seq_along(x)), !seq_along(x) %% 2), cumprod))
y[order(as.numeric(names(y)))]
user_59645570

Another option - take a sequence and then fill the results back in:

x <- 5:14

s <- seq(1, length(x), 2)
o <- x
o[s]  <- cumprod(x[s])
o[-s] <- cumprod(x[-s])
o 
# [1]     5     6    35    48   315   480  3465  5760 45045 80640

Or if you want to code-golf it:

s <- seq(1, length(x), 2)
replace(replace(x, s, cumprod(x[s])), -s, cumprod(x[-s]))
# [1]     5     6    35    48   315   480  3465  5760 45045 80640
user_4968030

Updated Solution

This may sound a bit verbose but it will work with odd and even number of lengths and also @Henrik's custom vector:

x <- 5:14
lapply(split(x, !(seq_len(length(x)) %% 2)), cumprod) |>
  setNames(c("a", "b")) |>
  list2env(globalenv())

c(a, b)[order(c(seq_along(a)*2 - 1, seq_along(b)*2))]

[1]     5     6    35    48   315   480  3465  5760 45045 80640

With an odd vector:

x <- 5:13
[1]     5     6    35    48   315   480  3465  5760 45045

Or with x = c(1, 0, 3, 4)

[1] 1 0 3 0

And in the end with x = c(2, 4, 2, 4):

[1]  2  4  4 16
user_143145200
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