Obtain cartesian indices from dimensions only

General Usage
1

I can obtain the cartesian indices of a matrix from a linear index with:

julia> A = zeros(2,4,3);

julia> CartesianIndices(A)[5]
CartesianIndex(1, 3, 1)

I would want to obtain that without having to define A, that is, only from its dimensions. Something like:

CartesianIndices(2,4,3)[5]

Is that already explicitly implemented? Or can I define a “fake” matrix only to input it there?

2

you can always define a fake array type that has a 0 cost constructor.

struct OnlyZeros{T,N} <: AbstractArray{T,N}
    size::NTuple{N,Int}
end
OnlyZeros{T}(size::NTuple{N,Int}) where {N,T} = OnlyZeros{T,N}(size)
OnlyZeros(size::NTuple{N,Int}) where N = OnlyZeros{Int,N}(size) 
Base.size(A::OnlyZeros) = A.size
Base.getindex(A::OnlyZeros{T,N}, inds::Vararg{Int,N}) where {T,N} = zero(T)

And then you can write
CartesianIndices(OnlyZeros(2,4,3))[5]

2 Likes
3

Thank you! Indeed, I was thinking of something like that.

Yet I am thinking why that is not already defined (an EmptyArray type). Probably if nobody never needed that I might have to rethink the way I have thought my problem. :grimacing:

1 Like
4

What about:

CartesianIndices((2,4,3))[5]

?

3 Likes
5

Ah, if that works that might explain why there is no such thing as the EmptyArray type.