Rename ProjectionStyle -> AdjointStyle, _mul -> AdjointMul, and improve docs

docs/src/api.md

@@ -21,6 +21,10 @@ AbstractFFTs.plan_brfft
 AbstractFFTs.plan_irfft
 AbstractFFTs.fftdims
 Base.adjoint
+AbstractFFTs.FFTAdjointStyle
+AbstractFFTs.RFFTAdjointStyle
+AbstractFFTs.IRFFTAdjointStyle
+AbstractFFTs.UnitaryAdjointStyle
 AbstractFFTs.fftshift
 AbstractFFTs.fftshift!
 AbstractFFTs.ifftshift

docs/src/implementations.md

@@ -32,10 +32,11 @@ To define a new FFT implementation in your own module, you should
 
 * You can also define similar methods of `plan_rfft` and `plan_brfft` for real-input FFTs.
 
-* To enable automatic computation of adjoint plans via [`Base.adjoint`](@ref) (used in rules for reverse-mode differentiation), define the trait `AbstractFFTs.ProjectionStyle(::MyPlan)`, which can return:
-    * `AbstractFFTs.NoProjectionStyle()`,
-    * `AbstractFFTs.RealProjectionStyle()`, for plans that halve one of the output's dimensions analogously to [`rfft`](@ref),
-    * `AbstractFFTs.RealInverseProjectionStyle(d::Int)`, for plans that expect an input with a halved dimension analogously to [`irfft`](@ref), where `d` is the original length of the dimension.
+* We offer an experimental `AdjointStyle` trait to enable automatic computation of adjoint plans via [`Base.adjoint`](@ref). 
+  To support adjoints in a new plan, define the trait `AbstractFFTs.AdjointStyle(::MyPlan)`. This should return a subtype of `AS <: AbstractFFTs.AdjointStyle` supporting `AbstractFFTs.adjoint_mul(::Plan, ::AbstractArray, ::AS)` and 
+  `AbstractFFTs._output_size(::Plan, ::AS)`. 
+
+  `AbstractFFTs` pre-implements the following adjoint styles: [`AbstractFFTs.FFTAdjointStyle`](@ref), [`AbstractFFTs.RFFTAdjointStyle`](@ref), [`AbstractFFTs.IRFFTAdjointStyle`](@ref), and [`AbstractFFTs.UnitaryAdjointStyle`](@ref).
 
 The normalization convention for your FFT should be that it computes ``y_k = \sum_j x_j \exp(-2\pi i j k/n)`` for a transform of
 length ``n``, and the "backwards" (unnormalized inverse) transform computes the same thing but with ``\exp(+2\pi i jk/n)``.

src/definitions.jl

@@ -583,17 +583,58 @@ plan_brfft
 
 ##############################################################################
 
-struct NoProjectionStyle end
-struct RealProjectionStyle end 
-struct RealInverseProjectionStyle 
+abstract type AdjointStyle end
+
+"""
+    FFTAdjointStyle()
+
+Projection style for complex to complex discrete Fourier transforms that normalize 
+the output analogously to [`fft`](@ref).
+
+Since the Fourier transform is unitary up to a scaling, the adjoint simply applies 
+the transform's inverse with an appropriate scaling.
+"""
+struct FFTAdjointStyle <: AdjointStyle end
+
+"""
+    RFFTAdjointStyle()
+
+Projection style for real to complex discrete Fourier transforms that halve
+one of the output's dimensions and normalize the output analogously to [`rfft`](@ref).
+
+Since the Fourier transform is unitary up to a scaling, the adjoint applies the transform's 
+inverse, but with additional logic to handle the fact that the output is projected 
+to exploit its conjugate symmetry (see [`rfft`](@ref)). 
+"""
+struct RFFTAdjointStyle <: AdjointStyle end 
+
+"""
+    IRFFTAdjointStyle(d::Dim)
+
+Projection style for complex to real discrete Fourier transforms that expect
+an input with a halved dimension and normalize the output analogously to [`irfft`](@ref), 
+where `d` is the original length of the dimension.
+
+Since the Fourier transform is unitary up to a scaling, the adjoint applies the transform's 
+inverse, but with additional logic to handle the fact that the input is projected 
+to exploit its conjugate symmetry (see [`irfft`](@ref)). 
+"""
+struct IRFFTAdjointStyle <: AdjointStyle
     dim::Int
 end
-const ProjectionStyle = Union{NoProjectionStyle, RealProjectionStyle, RealInverseProjectionStyle}
 
-output_size(p::Plan) = _output_size(p, ProjectionStyle(p))
-_output_size(p::Plan, ::NoProjectionStyle) = size(p)
-_output_size(p::Plan, ::RealProjectionStyle) = rfft_output_size(size(p), fftdims(p))
-_output_size(p::Plan, s::RealInverseProjectionStyle) = brfft_output_size(size(p), s.dim, fftdims(p))
+"""
+    UnitaryAdjointStyle()
+
+Projection style for unitary transforms, whose adjoint equals their inverse.
+"""
+struct UnitaryAdjointStyle <: AdjointStyle end
+
+output_size(p::Plan) = _output_size(p, AdjointStyle(p))
+_output_size(p::Plan, ::FFTAdjointStyle) = size(p)
+_output_size(p::Plan, ::RFFTAdjointStyle) = rfft_output_size(size(p), fftdims(p))
+_output_size(p::Plan, s::IRFFTAdjointStyle) = brfft_output_size(size(p), s.dim, fftdims(p))
+_output_size(p::Plan, ::UnitaryAdjointStyle) = size(p)
 
 struct AdjointPlan{T,P<:Plan} <: Plan{T}
     p::P
@@ -620,40 +661,42 @@ Base.adjoint(p::ScaledPlan) = ScaledPlan(p.p', p.scale)
 size(p::AdjointPlan) = output_size(p.p)
 output_size(p::AdjointPlan) = size(p.p)
 
-Base.:*(p::AdjointPlan, x::AbstractArray) = _mul(p, x, ProjectionStyle(p.p))
+Base.:*(p::AdjointPlan, x::AbstractArray) = adjoint_mul(p.p, x, AdjointStyle(p.p))
 
-function _mul(p::AdjointPlan{T}, x::AbstractArray, ::NoProjectionStyle) where {T}
-    dims = fftdims(p.p)
-    N = normalization(T, size(p.p), dims)
-    return (p.p \ x) / N
+function adjoint_mul(p::Plan{T}, x::AbstractArray, ::FFTAdjointStyle) where {T}
+    dims = fftdims(p)
+    N = normalization(T, size(p), dims)
+    return (p \ x) / N
 end
 
-function _mul(p::AdjointPlan{T}, x::AbstractArray, ::RealProjectionStyle) where {T<:Real}
-    dims = fftdims(p.p)
-    N = normalization(T, size(p.p), dims)
+function adjoint_mul(p::Plan{T}, x::AbstractArray, ::RFFTAdjointStyle) where {T<:Real}
+    dims = fftdims(p)
+    N = normalization(T, size(p), dims)
     halfdim = first(dims)
-    d = size(p.p, halfdim)
-    n = output_size(p.p, halfdim)
+    d = size(p, halfdim)
+    n = output_size(p, halfdim)
     scale = reshape(
         [(i == 1 || (i == n && 2 * (i - 1)) == d) ? N : 2 * N for i in 1:n],
         ntuple(i -> i == halfdim ? n : 1, Val(ndims(x)))
     )
-    return p.p \ (x ./ convert(typeof(x), scale))
+    return p \ (x ./ convert(typeof(x), scale))
 end
 
-function _mul(p::AdjointPlan{T}, x::AbstractArray, ::RealInverseProjectionStyle) where {T}
-    dims = fftdims(p.p)
-    N = normalization(real(T), output_size(p.p), dims)
+function adjoint_mul(p::Plan{T}, x::AbstractArray, ::IRFFTAdjointStyle) where {T}
+    dims = fftdims(p)
+    N = normalization(real(T), output_size(p), dims)
     halfdim = first(dims)
-    n = size(p.p, halfdim)
-    d = output_size(p.p, halfdim)
+    n = size(p, halfdim)
+    d = output_size(p, halfdim)
     scale = reshape(
         [(i == 1 || (i == n && 2 * (i - 1)) == d) ? 1 : 2 for i in 1:n],
         ntuple(i -> i == halfdim ? n : 1, Val(ndims(x)))
     )
-    return (convert(typeof(x), scale) ./ N) .* (p.p \ x)
+    return (convert(typeof(x), scale) ./ N) .* (p \ x)
 end
 
+adjoint_mul(p::Plan, x::AbstractArray, ::UnitaryAdjointStyle) = p \ x
+
 # Analogously to ScaledPlan, define both plan_inv (for no caching) and inv (caches inner plan only).
 plan_inv(p::AdjointPlan) = adjoint(plan_inv(p.p)) 
 inv(p::AdjointPlan) = adjoint(inv(p.p))

test/testplans.jl

@@ -21,8 +21,8 @@ Base.ndims(::TestPlan{T,N}) where {T,N} = N
 Base.size(p::InverseTestPlan) = p.sz
 Base.ndims(::InverseTestPlan{T,N}) where {T,N} = N
 
-AbstractFFTs.ProjectionStyle(::TestPlan) = AbstractFFTs.NoProjectionStyle()
-AbstractFFTs.ProjectionStyle(::InverseTestPlan) = AbstractFFTs.NoProjectionStyle()
+AbstractFFTs.AdjointStyle(::TestPlan) = AbstractFFTs.FFTAdjointStyle()
+AbstractFFTs.AdjointStyle(::InverseTestPlan) = AbstractFFTs.FFTAdjointStyle()
 
 function AbstractFFTs.plan_fft(x::AbstractArray{T}, region; kwargs...) where {T}
     return TestPlan{T}(region, size(x))
@@ -110,8 +110,8 @@ mutable struct InverseTestRPlan{T,N,G} <: Plan{Complex{T}}
     end
 end
 
-AbstractFFTs.ProjectionStyle(::TestRPlan) = AbstractFFTs.RealProjectionStyle()
-AbstractFFTs.ProjectionStyle(p::InverseTestRPlan) = AbstractFFTs.RealInverseProjectionStyle(p.d)
+AbstractFFTs.AdjointStyle(::TestRPlan) = AbstractFFTs.RFFTAdjointStyle()
+AbstractFFTs.AdjointStyle(p::InverseTestRPlan) = AbstractFFTs.IRFFTAdjointStyle(p.d)
 
 function AbstractFFTs.plan_rfft(x::AbstractArray{T}, region; kwargs...) where {T<:Real}
     return TestRPlan{T}(region, size(x))
@@ -241,7 +241,7 @@ end
 
 Base.size(p::InplaceTestPlan) = size(p.plan)
 Base.ndims(p::InplaceTestPlan) = ndims(p.plan)
-AbstractFFTs.ProjectionStyle(p::InplaceTestPlan) = AbstractFFTs.ProjectionStyle(p.plan)
+AbstractFFTs.AdjointStyle(p::InplaceTestPlan) = AbstractFFTs.AdjointStyle(p.plan)
 
 function AbstractFFTs.plan_fft!(x::AbstractArray, region; kwargs...)
     return InplaceTestPlan(plan_fft(x, region; kwargs...))