Add CartesianIndices and LinearIndices

Needed in particular to get linear indices once find() returns cartesian indices.

README.md

@@ -222,6 +222,10 @@ Currently, the `@compat` macro supports the following syntaxes:
 * `replace` accepts a pair of pattern and replacement, with the number of replacements as
   a keyword argument ([#25165]).
 
+* `CartesianIndices` and `LinearIndices` types represent cartesian and linear indices of
+  an array (respectively), and indexing such objects allows translating from one kind of index
+  to the other ([#25113]).
+
 ## Renaming
 
 
@@ -431,3 +435,4 @@ includes this fix. Find the minimum version from there.
 [#25162]: https://github.com/JuliaLang/julia/issues/25162
 [#25165]: https://github.com/JuliaLang/julia/issues/25165
 [#25168]: https://github.com/JuliaLang/julia/issues/25168
+[#25113]: https://github.com/JuliaLang/julia/issues/25113

src/Compat.jl

@@ -1070,6 +1070,85 @@ end
         replace(s, first(pat_rep), last(pat_rep), count)
 end
 
+@static if VERSION < v"0.7.0-DEV.3025"
+    import Base: convert, ndims, getindex
+    export CartesianIndices, LinearIndices
+
+    struct CartesianIndices{N,R<:NTuple{N,AbstractUnitRange{Int}}} <: AbstractArray{CartesianIndex{N},N}
+        indices::R
+    end
+
+    CartesianIndices(::Tuple{}) = CartesianIndices{0,typeof(())}(())
+    CartesianIndices(inds::NTuple{N,AbstractUnitRange{Int}}) where {N} =
+        CartesianIndices{N,typeof(inds)}(inds)
+    CartesianIndices(inds::Vararg{AbstractUnitRange{Int},N}) where {N} =
+        CartesianIndices(inds)
+    CartesianIndices(inds::NTuple{N,AbstractUnitRange{<:Integer}}) where {N} =
+        CartesianIndices(map(r->convert(AbstractUnitRange{Int}, r), inds))
+    CartesianIndices(inds::Vararg{AbstractUnitRange{<:Integer},N}) where {N} =
+        CartesianIndices(inds)
+
+    CartesianIndices(index::CartesianIndex) = CartesianIndices(index.I)
+    CartesianIndices(sz::NTuple{N,<:Integer}) where {N} = CartesianIndices(map(Base.OneTo, sz))
+    CartesianIndices(inds::NTuple{N,Union{<:Integer,AbstractUnitRange{<:Integer}}}) where {N} =
+        CartesianIndices(map(i->first(i):last(i), inds))
+
+    CartesianIndices(A::AbstractArray) = CartesianIndices(axes(A))
+
+    convert(::Type{Tuple{}}, R::CartesianIndices{0}) = ()
+    convert(::Type{NTuple{N,AbstractUnitRange{Int}}}, R::CartesianIndices{N}) where {N} =
+        R.indices
+
+    convert(::Type{NTuple{N,AbstractUnitRange}}, R::CartesianIndices{N}) where {N} =
+        convert(NTuple{N,AbstractUnitRange{Int}}, R)
+    convert(::Type{NTuple{N,UnitRange{Int}}}, R::CartesianIndices{N}) where {N} =
+        UnitRange{Int}.(convert(NTuple{N,AbstractUnitRange}, R))
+    convert(::Type{NTuple{N,UnitRange}}, R::CartesianIndices{N}) where {N} =
+        UnitRange.(convert(NTuple{N,AbstractUnitRange}, R))
+    convert(::Type{Tuple{Vararg{AbstractUnitRange{Int}}}}, R::CartesianIndices{N}) where {N} =
+        convert(NTuple{N,AbstractUnitRange{Int}}, R)
+    convert(::Type{Tuple{Vararg{AbstractUnitRange}}}, R::CartesianIndices) =
+        convert(Tuple{Vararg{AbstractUnitRange{Int}}}, R)
+    convert(::Type{Tuple{Vararg{UnitRange{Int}}}}, R::CartesianIndices{N}) where {N} =
+        convert(NTuple{N,UnitRange{Int}}, R)
+    convert(::Type{Tuple{Vararg{UnitRange}}}, R::CartesianIndices) =
+        convert(Tuple{Vararg{UnitRange{Int}}}, R)
+
+    # AbstractArray implementation
+    Base.IndexStyle(::Type{CartesianIndices{N,R}}) where {N,R} = IndexCartesian()
+    @inline Base.getindex(iter::CartesianIndices{N,R}, I::Vararg{Int, N}) where {N,R} = CartesianIndex(first.(iter.indices) .- 1 .+ I)
+
+    ndims(R::CartesianIndices) = ndims(typeof(R))
+    ndims(::Type{CartesianIndices{N}}) where {N} = N
+    ndims(::Type{CartesianIndices{N,TT}}) where {N,TT} = N
+
+    struct LinearIndices{N,R<:NTuple{N,AbstractUnitRange{Int}}} <: AbstractArray{Int,N}
+        indices::R
+    end
+
+    LinearIndices(inds::CartesianIndices{N,R}) where {N,R} = LinearIndices{N,R}(inds.indices)
+    LinearIndices(::Tuple{}) = LinearIndices(CartesianIndices(()))
+    LinearIndices(inds::NTuple{N,AbstractUnitRange{Int}}) where {N} = LinearIndices(CartesianIndices(inds))
+    LinearIndices(inds::Vararg{AbstractUnitRange{Int},N}) where {N} = LinearIndices(CartesianIndices(inds))
+    LinearIndices(inds::NTuple{N,AbstractUnitRange{<:Integer}}) where {N} = LinearIndices(CartesianIndices(inds))
+    LinearIndices(inds::Vararg{AbstractUnitRange{<:Integer},N}) where {N} = LinearIndices(CartesianIndices(inds))
+    LinearIndices(index::CartesianIndex) = LinearIndices(CartesianIndices(index))
+    LinearIndices(sz::NTuple{N,<:Integer}) where {N} = LinearIndices(CartesianIndices(sz))
+    LinearIndices(inds::NTuple{N,Union{<:Integer,AbstractUnitRange{<:Integer}}}) where {N} = LinearIndices(CartesianIndices(inds))
+    LinearIndices(A::AbstractArray) = LinearIndices(CartesianIndices(A))
+
+    # AbstractArray implementation
+    Base.IndexStyle(::Type{LinearIndices{N,R}}) where {N,R} = IndexCartesian()
+    Compat.axes(iter::LinearIndices{N,R}) where {N,R} = iter.indices
+    @inline function Base.getindex(iter::LinearIndices{N,R}, I::Vararg{Int, N}) where {N,R}
+        dims = length.(iter.indices)
+        #without the inbounds, this is slower than Base._sub2ind(iter.indices, I...)
+        @inbounds result = reshape(1:prod(dims), dims)[(I .- first.(iter.indices) .+ 1)...]
+        return result
+    end
+end
+
+
 include("deprecated.jl")
 
 end # module Compat

test/runtests.jl

@@ -1076,6 +1076,20 @@ end
 @test replace("abcb", "b"=>"c") == "accc"
 @test replace("abcb", "b"=>"c", count=1) == "accb"
 
+# 0.7.0-DEV.3025
+let c = CartesianIndices(1:3, 1:2), l = LinearIndices(1:3, 1:2)
+    @test LinearIndices(c) == collect(l)
+    @test CartesianIndices(l) == collect(c)
+    @test size(c) == (3, 2)
+    @test c == collect(c) == [CartesianIndex(1, 1) CartesianIndex(1, 2)
+                              CartesianIndex(2, 1) CartesianIndex(2, 2)
+                              CartesianIndex(3, 1) CartesianIndex(3, 2)]
+    @test l == collect(l) == reshape(1:6, 3, 2)
+    @test c[1:6] == vec(c)
+    @test l == l[c] == map(i -> l[i], c)
+    @test l[vec(c)] == collect(1:6)
+end
+
 if VERSION < v"0.6.0"
     include("deprecated.jl")
 end