Array range complement

Question

Is there a way to overwrite [] to have complement of range in array?

julia> a=[1:8...]
8-element Array{Int64,1}:
 1
 2
 3
 4
 5
 6
 7
 8

jul         


        

Answer 1

I haven't looked into the internals of indexing before, but at a first glance, the following might work without breaking too much:

immutable Not{T}
    idx::T
end    

if :to_indices in names(Base)
    # 0.6
    import Base: to_indices, uncolon, tail, _maybetail

    @inline to_indices(A, inds, I::Tuple{Not, Vararg{Any}}) =
       (setdiff(uncolon(inds, (:, tail(I)...)), I[1].idx), to_indices(A, _maybetail(inds), tail(I))...)       
else
    # 0.5
    import Base: getindex, _getindex

    not_index(a::AbstractArray, I, i::Int) = I
    not_index(a::AbstractArray, I::Not, i::Int) = setdiff(indices(a, i), I.idx)

    getindex(a::AbstractArray, I::Not) = getindex(a, setdiff(linearindices(a), I.idx))
    _getindex(::Base.LinearIndexing, a::AbstractArray, I::Vararg{Union{Real, AbstractArray, Colon, Not}}) = 
        Base._getindex(Base.linearindexing(a), a, (not_index(a, idx, i) for (i,idx) in enumerate(I))...)
end

For example:

julia> a = reshape(1:9, (3, 3))
3×3 Base.ReshapedArray{Int64,2,UnitRange{Int64},Tuple{}}:
1  4  7
2  5  8
3  6  9

julia> a[Not(2:8)]
2-element Array{Int64,1}:
1
9

julia> a[Not(1:2), :]
1×3 Array{Int64,2}:
3  6  9


julia> a[Not(end), end]
2-element Array{Int64,1}:
7
8

I didn't care for performance and also did no extensive testing, so things can certainly be improved.

Edit:

I replaced the code for 0.6 with Matt B. version from his github comment linked in the comments.

Thanks to his great design of the array indexing implementation for 0.6, only a single function needs to be extended to get complement indexing for getindex, setindex and view, e.g.,

julia> view(a, Not(2:8))
2-element SubArray{Int64,1,UnitRange{Int64},Tuple{Array{Int64,1}},false}:
1
9

# collect because ranges are immutable
julia> b = collect(a); b[Not(2), Not(2)] = 10; b
3×3 Array{Int64,2}:
10  4  10
 2  5   8
10  6  10