define subtypes of ProjectionStyle

Author: vpuri3

src/dct.jl

@@ -172,4 +172,4 @@ end
 
 *(p::DCTPlan{T,K,true}, x::StridedArray{T}) where {T,K} = mul!(x, p, x)
 
-AbstractFFTs.ProjectionStyle(::DCTPlan) = AbstractFFTs.NoProjectionStyle()
+AbstractFFTs.ProjectionStyle(::DCTPlan) = AbstractFFTs.UnitaryProjectionStyle()

src/fft.jl

@@ -1050,7 +1050,47 @@ function *(p::r2rFFTWPlan{T,K,true}, x::StridedArray{T}) where {T,K}
     return x
 end
 
+#######################################################################
+
+"""
+    UnitaryProjectionStyle()
+
+Projection style for transforms that are unitary
+"""
+struct UnitaryProjectionStyle <: AbstractFFTs.ProjectionStyle end
+
+"""
+    R2RProjectionStyle(kinds)
+
+Projection style for real to real transforms
+"""
+struct R2RProjectionStyle{K} <: AbstractFFTs.ProjectionStyle
+    kinds::K
+end
+
 AbstractFFTs.ProjectionStyle(::cFFTWPlan) = AbstractFFTs.NoProjectionStyle()
 AbstractFFTs.ProjectionStyle(::rFFTWPlan{T, FORWARD}) where {T} = AbstractFFTs.RealProjectionStyle()
-AbstractFFTs.ProjectionStyle(p::rFFTWPlan{T, BACKWARD}) where {T} = AbstractFFTs.RealInverseProjectionStyle(p.osz[first(p.region)])
-AbstractFFTs.ProjectionStyle(::r2rFFTWPlan) = AbstractFFTs.NoProjectionStyle()
+AbstractFFTs.ProjectionStyle(P::rFFTWPlan{T, BACKWARD}) where {T} = AbstractFFTs.RealInverseProjectionStyle(p.osz[first(P.region)])
+AbstractFFTs.ProjectionStyle(P::r2rFFTWPlan) = AbstractFFTs.R2RProjectionStyle(P.kinds)
+
+AbstractFFTs._output_size(p::Plan, ::UnitaryProjectionStyle) = size(p)
+AbstractFFTs._output_size(p::Plan, ::R2RProjectionStyle) = size(p)
+
+function _mul(p::AdjointPlan{T}, x::AbstractArray, ::UnitaryProjectionStyle) where {T}
+    return p.p \ x
+end
+
+function _mul(p::AdjointPlan{T}, x::AbstractArray, PS::R2RProjectionStyle) where {T}
+    kinds = PS.kinds
+    dims = fftdims(p)
+
+    N = 1
+    # Normalization: P \ P * u = K * u
+    # 0, 1 , 2   : NoProjectionStyle() type: K = prod(size(N))
+    # 3, 6 : DCTs: K = 2 * (N - 1)
+    # 4, 5 : DCTs: K = 2 * N
+    # 7, 10: DSTs: K = 2 * (N + 1)
+    # 8, 9 : DSTs: K = 2 * N
+    return (p.p \ x) / N
+end
+

test/runtests.jl

@@ -556,14 +556,6 @@ end
     @test FFTW.get_num_threads() == 2 # Unchanged
 end
 
-@testset "AbstractFFTs upstream tests" begin
-    # A necessary hack since AbstractFFTsTestUtils is not its own registered package yet.
-    # See https://github.com/JuliaMath/AbstractFFTs.jl/pull/78
-    include(joinpath(pathof(AbstractFFTs), "..", "..", "test", "testbackend.jl"))
-    using .AbstractFFTsTestUtils
-    test_fft_backend()
-end
-
 @testset "type-inference in r2r plans" begin
     # Compare with definition
     function testr2r(::Type{T}) where {T}
@@ -585,3 +577,22 @@ end
         end
     end
 end
+
+@testset "adjoint" begin
+    for x in (randn(3), randn(4), randn(3, 4), randn(3, 4, 5))
+        y = randn(size(x))
+        N = ndims(x)
+        for dims in unique((1, 1:N, N))
+            for P in (plan_dct(x, dims), plan_idct(x, dims))
+                @test (P')' * x == P * x
+                @test size(P') == AbstractFFTs.output_size(P)
+                @test dot(y, P * x) ≈ dot(P' * y, x)
+                @test dot(y, P \ x) ≈ dot(P' \ y, x)
+            end # P
+        end # dims
+    end # x
+end
+
+@testset "ChainRules" begin
+
+end