Assembling an array without looping in R

Question

Suppose there are two matrices A and B :

(A <- mdat <- matrix(c(1,2,3,4,5,6,7,8,9,10,11,12), nrow = 4, ncol = 3))
     [,1] [,2] [,3]
[1,]    1    5    9
[2,]    2    6   10
[3,]    3    7   11
[4,]    4    8   12

(B <- mdat <- matrix(rev(c(1,2,3,4,5,6,7,8,9,10,11,12)), nrow = 4, ncol = 3))
     [,1] [,2] [,3]
[1,]   12    8    4
[2,]   11    7    3
[3,]   10    6    2
[4,]    9    5    1

I want to create array C defined as below:

C <- array(0, dim=c(4,3,3))
for(i in 1:ncol(A))
for(j in 1:ncol(B))
   C[, i, j] = A[,i] + B[,j]

How can this be done nicely without looping?

Answer 1

Repeat each matrix's columns, then add and reset the dimensions:

out <- A[,rep(1:ncol(A),3)] + B[,rep(1:ncol(B),each=3)]
dim(out) <- c(4,3,3)

identical(out,C)
#[1] TRUE

Answer 2

You can construct array with the desired dimension attribute with apply method (from your comment but switch the positions of A and B):

array(apply(B, 2, "+", A), c(4,3,3))

, , 1

     [,1] [,2] [,3]
[1,]   13   17   21
[2,]   13   17   21
[3,]   13   17   21
[4,]   13   17   21

, , 2

     [,1] [,2] [,3]
[1,]    9   13   17
[2,]    9   13   17
[3,]    9   13   17
[4,]    9   13   17

, , 3

     [,1] [,2] [,3]
[1,]    5    9   13
[2,]    5    9   13
[3,]    5    9   13
[4,]    5    9   13

Answer 3

Would that work ?

i_vec <- rep(1:ncol(A),each  = ncol(B))
j_vec <- rep(1:ncol(B),ncol(A))
C <- array(0, dim=c(4,3,3))
Map(function(i,j){C[,i,j] <<- A[,i] + B[,j]},i_vec,j_vec)

# > C
# , , 1
# 
# [,1] [,2] [,3]
# [1,]   13   17   21
# [2,]   13   17   21
# [3,]   13   17   21
# [4,]   13   17   21
# 
# , , 2
# 
# [,1] [,2] [,3]
# [1,]    9   13   17
# [2,]    9   13   17
# [3,]    9   13   17
# [4,]    9   13   17
# 
# , , 3
# 
# [,1] [,2] [,3]
# [1,]    5    9   13
# [2,]    5    9   13
# [3,]    5    9   13
# [4,]    5    9   13