Array range complement - arrays

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
julia> a[-1] == a[2:8]
julia> a[-(1:3)] == a[4:8]
julia> a[-end] == a[1:7]

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

Answer 2

Directly overwriting [](i.e. getindex) is prone to break many indexing-related things in Base, but we can write an array wrapper to work around it. We only need to define the following three methods to get your specific test cases passed:
immutable ComplementVector{T} <: AbstractArray{T,1}
data::Vector{T}
end
Base.size(A:: ComplementVector) = size(A.data)
Base.getindex(A:: ComplementVector, i::Integer) = i > 0 ? A.data[i] : A.data[setdiff(1:end, (-i))]
Base.getindex(A:: ComplementVector, I::StepRange) = all(x->x>0, I) ? A.data[I] : A.data[setdiff(1:end, -I)]
julia> a = ComplementVector([1:8...])
julia> a[-1] == a[2:8]
true
julia> a[-(1:3)] == a[4:8]
true
julia> a[-end] == a[1:7]
true
If you would like to extend ComplementVector further more, please read the doc about Interfaces.
Update:
For safety sake, we'd better not extend AbstractArray as #Fengyang Wang suggested in the comment blow:
immutable ComplementVector{T}
data::Vector{T}
end
Base.endof(A::ComplementVector) = length(A.data)
Base.getindex(A::ComplementVector, i::Integer) = i > 0 ? A.data[i] : A.data[setdiff(1:end, (-i))]
Base.getindex(A::ComplementVector, I::OrdinalRange) = all(x->x>0, I) ? A.data[I] : A.data[setdiff(1:end, -I)]