Slicing and merging of CartesianIndices

General Usage
1

Hello,

Let’s assume I have a two-dimensional array and the list of Cartesian indices which allow me to extract some subset of the array elements:

A = zeros((6, 9))

ci = CartesianIndices((2:2:6, 3:3:9))

A[ci]

Now, having ci, how I can extract the Cartesian indices which correspond separately to the first and second dimensions of the array? If I will define them manually, they will be

ci1 = CartesianIndices((2:2:6,))
ci2 = CartesianIndices((3:3:9,))

A[ci1, :]
A[:, ci2]

And the other way around, having ci1 and ci2, how I can merge them into the original ci?
The last question is related to my earlier post https://discourse.julialang.org/t/combine-cartesianindices-for-effective-cuda-kernels/

Thank you.

2

You can do use ci.indices though I think that’s an undocumented internal:

ci1 = CartesianIndices(ci.indices[1])
ci2 = CartesianIndices(ci.indices[2])

You can get the same information with first(ci), step(ci), last(ci) but that’s less convenient.

To recover the full list:

CartesianIndices((ci1.indices[1], ci2.indices[1]))

Another idea using arrays of CartesianIndex rather than CartesianIndices:

julia> i1 = getindex.(ci[:, 1], 1)
3-element Vector{Int64}:
 2
 4
 6

julia> i2 = getindex.(ci[1, :], 2)
3-element Vector{Int64}:
 3
 6
 9

julia> CartesianIndex.(i1, i2')
3×3 Matrix{CartesianIndex{2}}:
 CartesianIndex(2, 3)  CartesianIndex(2, 6)  CartesianIndex(2, 9)
 CartesianIndex(4, 3)  CartesianIndex(4, 6)  CartesianIndex(4, 9)
 CartesianIndex(6, 3)  CartesianIndex(6, 6)  CartesianIndex(6, 9)
1 Like
3

Thank you.
indices is exactly what I need.