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

Question

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.

Answer 1

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

Answer 2

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.

Answer 3

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)))]