Project R: Variable "depth" of for-loops; generalization - r

Question

Thank you for helping me out with this one. It's a problem that has been bothering me for quite a time now. I feel like I am so close to the answer, but not quite there yet.
Issue is the following:
Suppose I want to combine every possible combination of m-elements of n-vectors and store the result of, lets say, a multiplication. For the 2d-problem I need two interlaced for-loops:
dim2_Matrix <- matrix(0,nrow=2,ncol=3)
for (i in 1:2){
for (j in 1:3){
dim2_Matrix[i,j] <- i*j
}
}
The inner loop will run through all 3 items, multiplying them with the first item of the outer loop. Once that procedure is done, i will be increased and the inner loop starts from j=1 again. We have 2*3 = 6 combinations.
Now lets raise that to a 3D-Problem. We need a third loop for that:
dim3_Matrix <- array(0,dim=c(2,3,4))
for (i in 1:2){
for (j in 1:3){
for (k in 1:4){
dim3_Matrix[i,j,k] <- i*j*k
}
}
}
It runs the most inner loop 4times, increases the middle one, runs the 4 inner loops again...until we get 2*3*4 = 24 combinations in a 3D-Array.
I could continue like this with dim4, dim5 etc.
My problem now is that I want to keep the script variable. Sometimes I'll want to combine 2, sometimes 3, sometimes n-vectors. Suppose I know how many "layers" there are before the loops are run...how do I get a generalized form of this?
I am as far as this:
n_dimensions <- 3 # specify n° of dimensions
m_Elements <- c(2,3,4) # 2 elements in 1st dim, 3 in 2nd, 4 in 3rd
for (i in 1:n_dimensions){
for (j in 1:m_Elements[i]){
# ...
}
}
But this will go like:
i1 j1 --> i1 j2
i2 j1 --> i2 j2 --> i2 j3
i3 j1 --> i3 j2 --> i3 j3 --> i3 j4
so this is 2 + 3 + 4 combinations instead of 2*3*4.
Please note: multiplying is only an example. Storing the results in a matrix/tensor is not the main problem. It's how to interlace the loops and to generalize it.
Thanks for reading through, I hope you get what I mean!

Answer 1

You can try something like this.
X<-list(1:2, 1:3, 1:4) #one entry for each dimension
Z<-expand.grid(X)
Z looks like:
Var1 Var2 Var3
1 1 1 1
2 2 1 1
3 1 2 1
4 2 2 1
5 1 3 1
6 2 3 1
7 1 1 2
8 2 1 2
9 1 2 2
10 2 2 2
11 1 3 2
12 2 3 2
13 1 1 3
14 2 1 3
15 1 2 3
16 2 2 3
17 1 3 3
18 2 3 3
19 1 1 4
20 2 1 4
21 1 2 4
22 2 2 4
23 1 3 4
24 2 3 4
So now you have every combination in a data.frame and you can use apply functions or something similar to do what you need to do. Such as:
apply(Z,1,prod)
[1] 1 2 2 4 3 6 2 4 4 8 6 12 3 6 6 12 9 18 4 8 8 16 12 24

Answer 2

Your code is equivalent to:
dim2_Matrix = outer(1:2, 1:3)
dim3_Matrix = outer(dim2_Matrix, 1:4)
Which can be generalized to:
dim_n_Matrix <- function(n) {
x <- 1:2
if (n>1) {for (n in 2:n) {x <- outer(x, 1:(n+1))}} else {x <- matrix(1:2, nrow = 1)}
return(x)
}