与列表或向量输出等效的“外部”

Question

With map you can apply a function to each pair of arguments :

> mapply(rep, 1:4, 4:1)
[[1]]
[1] 1 1 1 1

[[2]]
[1] 2 2 2

[[3]]
[1] 3 3

[[4]]
[1] 4

I expected to do something similar but for each combination of arguments with outer but it does not work because the output of outer should be a 4x4 array in this example :

> outer(1:4, 4:1, rep)
Error in dim(robj) <- c(dX, dY) : 
  dims [produit 16] ne correspond pas à la longueur de l'objet [40]

Is there some R function (base R ideally) to do this as easily as mapply or outer ?

The expected output in this minimal example should look like this :

> c(mapply(rep, 1:4, 4), mapply(rep, 1:4, 3), mapply(rep, 1:4, 2), mapply(rep, 1:4, 1))
 [1] 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 1 1 1 2 2 2 3 3 3 4 4 4 1 1 2 2 3 3 4 4 1 2 3 4
# Or
> c(rep(1:4, each = 4), rep(1:4, each = 3), rep(1:4, each = 2), rep(1:4, each = 1))
 [1] 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 1 1 1 2 2 2 3 3 3 4 4 4 1 1 2 2 3 3 4 4 1 2 3 4

I could use a combination of expand.grid and apply but I expect that there is some easier solution :

> unlist(apply(expand.grid(1:4, 4:1), 1, function(x) rep(x[1], x[2])))
Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 
   1    1    1    1    2    2    2    2    3    3    3    3    4    4    4    4    1    1 
Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 Var1 
   1    2    2    2    3    3    3    4    4    4    1    1    2    2    3    3    4    4 
Var1 Var1 Var1 Var1 
   1    2    3    4 

---

Based on 李哲源 Zheyuan Li' reply (for the record) : with outer and Vectorize you obtain a unusual object : a matrix with each element being a list :

> res <- outer(1:4, 4:1, Vectorize(rep.int))
> class(res)
[1] "matrix"
> typeof(res)
[1] "list"
> res
     [,1]      [,2]      [,3]      [,4]
[1,] Integer,4 Integer,3 Integer,2 1   
[2,] Integer,4 Integer,3 Integer,2 2   
[3,] Integer,4 Integer,3 Integer,2 3   
[4,] Integer,4 Integer,3 Integer,2 4   

You can unlist it to obtain a vector or remove the dimension attribute to obtain a regular list :

> unlist(res)
 [1] 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 1 1 1 2 2 2 3 3 3 4 4 4 1 1 2 2 3 3 4 4 1 2 3 4
> 
> dim(res) <- NULL
> # res <- c(res)  # equivalent
> res[1:5] # show the first 5 elements of the list
[[1]]
[1] 1 1 1 1

[[2]]
[1] 2 2 2 2

[[3]]
[1] 3 3 3 3

[[4]]
[1] 4 4 4 4

[[5]]
[1] 1 1 1

In this case outer(1:4, 4:1, Vectorize(rep.int)) works but in many situations you will need outer(1:4, 4:1, Vectorize(rep.int, SIMPLIFY = TRUE)) . See 李哲源 Zheyuan Li answer for more explanations

Here, the output of myfun is a length 2 vector --> works only with SIMPLIFY = FALSE because you need that the result of each run of myfun is a length 1 list

> myfun <- function(x, y) c(sum(x,y), mean(x,y))
> myfun(1,4)
[1] 5 1
> res <- outer(1:4, 4:1, Vectorize(myfun, SIMPLIFY = TRUE))
Error in dim(robj) <- c(dX, dY) : 
  dims [produit 16] ne correspond pas à la longueur de l'objet [32]
> res <- outer(1:4, 4:1, Vectorize(myfun, SIMPLIFY = FALSE))
> 

Here the output of myfun is a length 2 list --> works only with SIMPLIFY = FALSE

> myfun <- function(x, y) list(sum(x,y), mean(x,y))
> myfun(1,4)
[[1]]
[1] 5

[[2]]
[1] 1

> res <- outer(1:4, 4:1, Vectorize(myfun, SIMPLIFY = TRUE))
Error in dim(robj) <- c(dX, dY) : 
  dims [produit 16] ne correspond pas à la longueur de l'objet [32]
> res <- outer(1:4, 4:1, Vectorize(myfun, SIMPLIFY = FALSE))
> 

Here the output of myfun is a length 1 list containing a length 2 vector --> works with both SIMPLIFY = FALSE and SIMPLIFY = TRUE

> myfun <- function(x, y) return(list(c(sum(x,y),mean(x,y))))
> myfun(1,4)
[[1]]
[1] 5 1

> res <- outer(1:4, 4:1, Vectorize(myfun, SIMPLIFY = TRUE))
> res <- outer(1:4, 4:1, Vectorize(myfun, SIMPLIFY = FALSE))

Answer 1

Just use FUN = Vectorize(rep.int, SIMPLIFY = FALSE) inside outer , to get a matrix list.

Related: How to perform pairwise operation like `%in%` and set operations for a list of vectors

Answer 2

If we need an option with Map

unlist(do.call(Map, c(f= rep, unname(expand.grid(1:4, 4:1)))))
#[1] 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 1 1 1 2 2 2 3 3 3 4 4 4 1 1 2 2 3 3 4 4 1 2 3 4