How to iterate over whole array when I need i, j, k?

Question

Given A is a multi-dimensional array, can I collapse iteration through every element into one for statement if I need i,j,k,etc.? In other words, I am looking for a more compact version of the following:

for k in 1:size(A,3)
  for j in 1:size(A,2)
    for i in 1:size(A,1)
      # Do something with A[i+1,j,k], A[i,j+1,k], A[i,j,k+1], etc.
    end
  end
end

I think the solution is with axes or CartesianIndices, but I can't get the syntax right. Failed attempts:

julia> for (i,j,k) in axes(A)
         println(i)
       end
1
1
1

julia> for (i,j,k) in CartesianIndices(A)
           println(i)
       end
ERROR: iteration is deliberately unsupported for CartesianIndex. Use `I` rather than `I...`, or use `Tuple(I)...`

It would be great if in addition to a solution which defines i,j,k, you could also provide a solution that works regardless of the number of dimensions in A.

Answer 1

You are almost there. Read the message carefully:

ERROR: iteration is deliberately unsupported for CartesianIndex.

It is the "pattern matching" in (i,j,k) in CartesianIndices(...) that fails, not the approach in general (I made the same mistake when reproducing the problem!). You have to convert the individual CartesianIndexes to tuples first:

julia> for ix in CartesianIndices(A)
           println(Tuple(ix))
       end
(1, 1, 1)
(2, 1, 1)
(3, 1, 1)
(1, 2, 1)
(2, 2, 1)
(3, 2, 1)
...