Specialize indexing a CartesianIndices with a CartesianIndex StepRangeLen

[jishnub]

Since a CartesianIndices may be seen as an nD range, indexing it with a range in a specific direction would return a range. This is the nD equivalent of indexing a 1D range with another range, which returns a range as the result.
For example,

julia> C = CartesianIndices((3, 3))
CartesianIndices((3, 3))

julia> collect(C)
3×3 Matrix{CartesianIndex{2}}:
 CartesianIndex(1, 1)  CartesianIndex(1, 2)  CartesianIndex(1, 3)
 CartesianIndex(2, 1)  CartesianIndex(2, 2)  CartesianIndex(2, 3)
 CartesianIndex(3, 1)  CartesianIndex(3, 2)  CartesianIndex(3, 3)

julia> using LinearAlgebra

julia> r = diagind(C, IndexCartesian())
StepRangeLen(CartesianIndex(1, 1), CartesianIndex(1, 1), 3)

julia> C[r] # returns a materialized range
3-element Vector{CartesianIndex{2}}:
 CartesianIndex(1, 1)
 CartesianIndex(2, 2)
 CartesianIndex(3, 3)

After this PR,

julia> C[r] # returns the range without materializing it
StepRangeLen(CartesianIndex(1, 1), CartesianIndex(1, 1), 3)

julia> C[r] |> collect
3-element Vector{CartesianIndex{2}}:
 CartesianIndex(1, 1)
 CartesianIndex(2, 2)
 CartesianIndex(3, 3)

Such operations might find utility in sparse matrix constructions, when one needs a range of indices to populate. See e.g., JuliaSparse/SparseArrays.jl#600

[mbauman]

Are there any offset array packages that support an offset range of CartesianIndex? I'm not sure if we can generically support such a thing, but I think the answer should be similarly offset. The axes of the result should be the axes of the indices. For example:

julia> CartesianIndices((4,1))[CartesianIndex.(Base.IdentityUnitRange(3:4))]
2-element OffsetArray(::Vector{CartesianIndex{2}}, 3:4) with eltype CartesianIndex{2} with indices 3:4:
 CartesianIndex(3, 1)
 CartesianIndex(4, 1)

Maybe add a require_one_based_indexing here?

[jishnub]

Indeed, indexing with ranges doesn't work very well with offset indexing, as we don't use similar to construct the result. Perhaps we require something like #41284 to make this consistent. For now, disallowing offset ranges is the pragmatic approach.