Euclidean on Cartesian indices

[Dale-Black]

Is there a way to compute the euclidean distance between arrays that are of the type CartesianIndex?

[dkarrasch]

Do you mean something like this?

julia> A = reshape(collect(1:9), 3, 3)
3×3 Array{Int64,2}:
 1  4  7
 2  5  8
 3  6  9

julia> inds1 = findall(iseven, A)
4-element Array{CartesianIndex{2},1}:
 CartesianIndex(2, 1)
 CartesianIndex(1, 2)
 CartesianIndex(3, 2)
 CartesianIndex(2, 3)

julia> inds2 = findall(isodd, A)
5-element Array{CartesianIndex{2},1}:
 CartesianIndex(1, 1)
 CartesianIndex(3, 1)
 CartesianIndex(2, 2)
 CartesianIndex(1, 3)
 CartesianIndex(3, 3)

julia> pairwise(SqEuclidean(), inds1, inds2)
4×5 Array{Int64,2}:
 1  1  1  5  5
 1  5  1  1  5
 5  1  1  5  1
 5  5  1  1  1

julia> euclidean(inds1[1], inds1[1]) === 0.0
true

I have added support for this special, noniterable type in #194.

[nalimilan]

Could you explain why this would be useful? Since CartesianIndex isn't iterable (on purpose), this would require specific support in Distances.

[Dale-Black]

I think what @dkarrasch implemented is what I wanted. I would have to go back to this specific project to find out for sure but from what I can tell that solves my use case

[nalimilan]

Yes but we decided to revert that change until we have a clearer view of why this would be needed.

[dkarrasch]

@nalimilan convinced me that supporting CartesianIndexes directly (at least in the context of #194) is awkward, because it targets iterable objects, and CartesianIndexes are intentionally non-iterable. I believe the correct way of handling it is to pass the responsibility to the callee, asking her/him to pass iterable objects to Distances.jl. In the context here, this would mean to convert CartesianIndexes to tuples via Tuple(cartind), as suggested by the error message. Once you have that, the new iterator-based implementation will work just fast and fine.