adjoint of a Composite

[mzgubic]

julia> c = Composite{Adjoint{Float64,Array{Float64,2}}}(parent = [-1.8280580596976814 0.2779228276891495; 1.0080661406609885 -1.7102674963647622],)

julia> c'
ERROR: MethodError: no method matching adjoint(::Composite{Adjoint{Float64,Array{Float64,2}},NamedTuple{(:parent,),Tuple{Array{Float64,2}}}})
Closest candidates are:
  adjoint(::Missing) at missing.jl:100
  adjoint(::Number) at number.jl:169
  adjoint(::Adjoint{var"#s173",var"#s172"} where var"#s172"<:Union{StaticArrays.StaticArray{Tuple{N},T,1} where T where N, StaticArrays.StaticArray{Tuple{N,M},T,2} where T where M where N} where var"#s173") at /Users/mzgubic/.julia/packages/StaticArrays/NTbHj/src/linalg.jl:73
  ...
Stacktrace:
 [1] top-level scope at REPL[51]:1

Since adjoint is a linear operator there is no reason not to define adjoint on Composites, right?

[oxinabox]

I am not sure it is well defined on a structural differential type.
How would you define it?
Applying it recursively would need natural, though I am not sure it is well motivated. Maybe it is.

But what if you had a Composite{Complex}(1.0, 2.0). Applying it recursively gives you Composite{Complex}(1.0, 2.0), but the correct answer is Composite{Complex}(1.0, -2.0)

[willtebbutt]

What's the use-case @mzgubic ?

[mzgubic]

What's the use-case @mzgubic ?

In the SVD PR I've naively done:

        elseif x === :V
             C(Vt=Ȳ',)

where Ȳ is a Composite.

How would you define it?

Yeah agreed, it's hard to come up with a fallback method. We could just define more specific methods?

I.e. write something like:

function Base.adjoint(comp::Composite{<:Adjoint{P, Array{P, D}}, T}) where {P, D, T}
    return Composite{Array{P, D}}(adjoint(comp.parent))
end

And then similar one for Complex if we ever need it? Otherwise, I can just put this in the SVD but I thought it would make sense.

[mzgubic]

@oxinabox said in the PR

I am very unsure about this.
Both in what it does, (why does the primal type change?)
and where it should go (here or ChainRules.jl ?)

and

Its also kind of surprising to see a Composite{<:LinearAlgebra.Adjoint{P, Array{P, D}}, T} in the first place.
since LinearAlgebra.Adjoint{P, Array{P, D}} is a valid differential type on it's own.
It is a natural differential type, it doesn't need to have a structural differential type (Composite) used for it.

The second point in particular convinces me that we don't need this