Adjoint for vectors may use trailing axes of the parent (#52379)

Close #52373, or at least the part that may be addressed here. After
this, the first axis for an `Adjoint(parent::AbstractVector)` will be
the second axis of the `parent`. This will change the type of the axis
where the parent array type specializes `axes(A, d)`. In the short term,
this would improve type-stability in cases such as
```julia
julia> A = OffsetArray([1,2], 2);

julia> @code_typed axes(A')[1]
CodeInfo(
1 ─ %1 = $(Expr(:boundscheck))::Bool
│   %2 = Base.getfield(t, i, %1)::OffsetArrays.IdOffsetRange{Int64, Base.OneTo{Int64}}
└──      return %2
) => OffsetArrays.IdOffsetRange{Int64, Base.OneTo{Int64}}
```
where the result is now concretely inferred instead of being a small
`Union`.
In principle, with
JuliaArrays/StaticArrays.jl#916, this would make
the axes of the adjoint of a `StaticVector` statically sized.

Author: jishnub

stdlib/LinearAlgebra/src/adjtrans.jl

@@ -324,7 +324,7 @@ axes(A::AdjOrTrans) = reverse(axes(A.parent))
 length(A::AdjOrTrans) = length(A.parent)
 size(v::AdjOrTransAbsVec) = (1, length(v.parent))
 size(A::AdjOrTransAbsMat) = reverse(size(A.parent))
-axes(v::AdjOrTransAbsVec) = (Base.OneTo(1), axes(v.parent)...)
+axes(v::AdjOrTransAbsVec) = (axes(v.parent,2), axes(v.parent)...)
 axes(A::AdjOrTransAbsMat) = reverse(axes(A.parent))
 IndexStyle(::Type{<:AdjOrTransAbsVec}) = IndexLinear()
 IndexStyle(::Type{<:AdjOrTransAbsMat}) = IndexCartesian()

stdlib/LinearAlgebra/test/adjtrans.jl

@@ -6,6 +6,9 @@ using Test, LinearAlgebra
 
 const BASE_TEST_PATH = joinpath(Sys.BINDIR, "..", "share", "julia", "test")
 
+isdefined(Main, :OffsetArrays) || @eval Main include(joinpath($(BASE_TEST_PATH), "testhelpers", "OffsetArrays.jl"))
+using .Main.OffsetArrays
+
 @testset "Adjoint and Transpose inner constructor basics" begin
     intvec, intmat = [1, 2], [1 2; 3 4]
     # Adjoint/Transpose eltype must match the type of the Adjoint/Transpose of the input eltype
@@ -87,11 +90,15 @@ end
         @test size(Transpose(intvec)) == (1, length(intvec))
         @test size(Transpose(intmat)) == reverse(size(intmat))
     end
-    @testset "indices methods" begin
+    @testset "axes methods" begin
         @test axes(Adjoint(intvec)) == (Base.OneTo(1), Base.OneTo(length(intvec)))
         @test axes(Adjoint(intmat)) == reverse(axes(intmat))
         @test axes(Transpose(intvec)) == (Base.OneTo(1), Base.OneTo(length(intvec)))
         @test axes(Transpose(intmat)) == reverse(axes(intmat))
+
+        A = OffsetArray([1,2], 2)
+        @test (@inferred axes(A')[2]) === axes(A,1)
+        @test (@inferred axes(A')[1]) === axes(A,2)
     end
     @testset "IndexStyle methods" begin
         @test IndexStyle(Adjoint(intvec)) == IndexLinear()

test/offsetarray.jl

@@ -403,7 +403,8 @@ v2 = copy(v)
 v = OffsetArray(v0, (-3,))
 @test lastindex(v) == 1
 @test v ≈ v
-@test axes(v') === (Base.OneTo(1), OffsetArrays.IdOffsetRange(Base.OneTo(4), -3))
+@test (@inferred axes(v')[1]) === OffsetArrays.IdOffsetRange(Base.OneTo(1))
+@test (@inferred axes(v')[2]) === OffsetArrays.IdOffsetRange(Base.OneTo(4), -3)
 @test parent(v) == collect(v)
 rv = reverse(v)
 @test axes(rv) == axes(v)