`ProjectTo(::AbstractArray)` does not infer

[mzgubic]

e.g. see

julia> @inferred ProjectTo(rand(3, 3))(Diagonal(rand(3)))
ERROR: return type Diagonal{Float64, Vector{Float64}} does not match inferred return type Union{Base.ReshapedArray{Float64, 2, Diagonal{Float64, Vector{Float64}}, Tuple{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64}}}, Diagonal{Float64, Vector{Float64}}}

the reason for the failure is https://github.com/JuliaDiff/ChainRulesCore.jl/blob/6efb2d258dc225a50d961fb17fa5ba88d7296ce7/src/projection.jl#L174-L183 which decides whether to dy is dx or a reshape(dx, ...) based on the values of the axes.

We could instead do

    dy = if length(axes(dx)) == length(project.axes)
        axes(dx) == project.axes || throw(_projection_mismatch(project.axes, size(dx)))
        dx
    else
        for d in 1:max(M, length(project.axes))
            if size(dx, d) != length(get(project.axes, d, 1))
                throw(_projection_mismatch(project.axes, size(dx)))
            end
        end
        reshape(dx, project.axes)
    end

which does infer, but throws an error for the arrays that need to be reshaped. In practice, this only means that only

        poffv = ProjectTo(OffsetArray(rand(3), 0:2))
        @test axes(poffv([1, 2, 3])) == (0:2,)

test fails in ChainRulesCore and all the rrule inference tests (but not the one where inplaceablethunk inference fails) in https://github.com/JuliaDiff/ChainRules.jl/pull/459#issuecomment-884757000 are fixed.

do we want this tradeoff or not?

[mzgubic]

Lyndon says "It is a union of <=4 elements. It is fine."

My reply: I found a “solution” with a small tradeoff.

It is a union of <=4 elements. It is fine.

I’ve heard small unions are fine, but never understood this really. Does this mean that a thing happens (JIT?) for each of the elements, and not all possible elements? My concern (that may be unjustified) is that having a few of these small unions through the program means that the inferred union snowballs when functions are called

i.e. something like

julia> inner(x) = x > 0 ? 3.0 : 3
inner (generic function with 1 method)

julia> wrapper(x::Int) = x > 0 ? rand(2, 3) : Diagonal(rand(2))
wrapper (generic function with 1 method)

julia> wrapper(x::Float64) = x > 0 ? "hello" : :world
wrapper (generic function with 2 methods)

julia> together(x) = wrapper(inner(x))
together (generic function with 1 method)

julia> @code_warntype together(2.0)
Variables
  #self#::Core.Const(together)
  x::Float64
Body::Any
1 ─ %1 = Main.inner(x)::Union{Float64, Int64}
│   %2 = Main.wrapper(%1)::Any
└──      return %2

where the result is actually Any rather than a Union of four types

[oxinabox]

I wonder if we actually only want the reshape for if the dx is a Array. That is the case that we know we will never get ReshapedArray out, but will just get another Array that reference the same memory. The ReshapedArray is probably not a friend, it is still a view but idk how consistently it is used and how nice it plays with BLAS etc. Maybe not having the reshape always work though would defeat utility of the feature

[mcabbott]

Surely this can be made to infer.

The trick if length(axes(dx)) == length(project.axes) is clever, but what I think it will miss is that the reshape at present restores OffsetArrays, which tend to go missing e.g. hcat(OffsetArray(rand(3), 0:2)) isa Matrix.