Adjoint of AbstractFFTs.Plan is too general

[MikaelSlevinsky]

These two invocations of the adjoint macro seem a little too general given it's not true for the (unitary) DCT plan FFTW.DCTPlan{Float64,5,false} <: AbstractFFTs.Plan{Float64}

Zygote.jl/src/lib/array.jl

Lines 729 to 741 in 956cbcf

	@adjoint function *(P::AbstractFFTs.Plan, xs)
	return P * xs, function(Δ)
	N = prod(size(xs)[[P.region...]])
	return (nothing, N * (P \ Δ))
	end
	end
	@adjoint function \(P::AbstractFFTs.Plan, xs)
	return P \ xs, function(Δ)
	N = prod(size(Δ)[[P.region...]])
	return (nothing, (P * Δ)/N)
	end
	end

julia> using FFTW, LinearAlgebra

julia> Id = Matrix{Float64}(I, 10, 10);

julia> p = plan_dct(Id, 1)
FFTW DCT (DCT-II) plan for 10×10 array of Float64

julia> P = p*Id;

julia> N = prod(size(Id)[[p.region...]])
10

julia> P' ≈ N*inv(P)
false

It's probably false for some of the real-to-real plans as well.

[maximilian-gelbrecht]

This is also related to JuliaMath/FFTW.jl#182 as the adjoint is actually not working for ScaledPlans like some FFTs due to them having no region field.