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