Finding dimensional index in a multi-dimensional array in R

Question

Am looking at say 3-dimensional array M: M<-dim(3,3,3)

I want to find an efficient way to populate M with the following rule: M[i,j,k] = i/10 + j^2 + sqrt(k), ideally without having to write a loop with a for statemenet.

For clarification, there is a simple way to accomplishing this if M were 2-dimensional. If i wanted to have M[i,j] = i/10 + j^2, then i could just do M<-row(M)/10 + col(M)*col(M)

Is there something equivalent for 3-or-higher dimensional arrays?

Answer 1

@James's answer is better, but I think the narrow answer to your question (multidimensional equivalent of row()/col()) is slice.index ...

M<- array(dim=c(3,3,3))
slice.index(M,1)/10+slice.index(M,2)^2+sqrt(slice.index(M,3))

It would be a good idea if someone (I or someone else) posted a suggestion on the r-devel list to make slice.index a "See also" entry on ?row/?col ...

Alternatively (similar to @flodel's new answer):

d <- do.call(expand.grid,lapply(dim(M),seq)) ## create data.frame of indices
v <- with(d,Var1/10+Var2^2+sqrt(Var3))       ## default names Var1, ... Varn 
dim(v) <- dim(M)                             ## reshape into array

Answer 2

How about using nested outers?

outer(1:3/10,outer((1:3)^2,sqrt(1:3),"+"),"+")
, , 1

     [,1] [,2] [,3]
[1,]  2.1  5.1 10.1
[2,]  2.2  5.2 10.2
[3,]  2.3  5.3 10.3

, , 2

         [,1]     [,2]     [,3]
[1,] 2.514214 5.514214 10.51421
[2,] 2.614214 5.614214 10.61421
[3,] 2.714214 5.714214 10.71421

, , 3

         [,1]     [,2]     [,3]
[1,] 2.832051 5.832051 10.83205
[2,] 2.932051 5.932051 10.93205
[3,] 3.032051 6.032051 11.03205