add tests

Author: dlfivefifty

test/TestPlans.jl

@@ -95,8 +95,8 @@ function LinearAlgebra.mul!(
     dft!(y, x, p.region, 1)
 end
 
-Base.:*(p::TestPlan, x::AbstractArray) = mul!(similar(x, complex(float(eltype(x)))), p, x)
-Base.:*(p::InverseTestPlan, x::AbstractArray) = mul!(similar(x, complex(float(eltype(x)))), p, x)
+Base.:*(p::TestPlan{T}, x::AbstractArray{T}) where T = mul!(similar(x, complex(float(eltype(x)))), p, x)
+Base.:*(p::InverseTestPlan{T}, x::AbstractArray{T}) where T = mul!(similar(x, complex(float(eltype(x)))), p, x)
 
 mutable struct TestRPlan{T,N,G} <: Plan{T}
     region::G
@@ -219,7 +219,7 @@ function LinearAlgebra.mul!(y::AbstractArray{<:Complex, N}, p::TestRPlan, x::Abs
     return y
 end
 
-function Base.:*(p::TestRPlan, x::AbstractArray)
+function Base.:*(p::TestRPlan{T}, x::AbstractArray{T}) where T
     # create output array
     firstdim = first(p.region)::Int
     d = size(x, firstdim)
@@ -241,7 +241,7 @@ function LinearAlgebra.mul!(y::AbstractArray{<:Real, N}, p::InverseTestRPlan, x:
     real_invdft!(y, x, p.region)
 end
 
-function Base.:*(p::InverseTestRPlan, x::AbstractArray)
+function Base.:*(p::InverseTestRPlan{T}, x::AbstractArray{T}) where T
     # create output array
     firstdim = first(p.region)::Int
     d = p.d

test/abstractfftsforwarddiff.jl

@@ -0,0 +1,57 @@
+using AbstractFFTs
+using ForwardDiff
+using Test
+using ForwardDiff: Dual, partials, value
+
+@testset "ForwardDiff extension tests" begin
+    x1 = Dual.(1:4.0, 2:5, 3:6)
+
+    @test AbstractFFTs.complexfloat(x1)[1] === AbstractFFTs.complexfloat(x1[1]) === Dual(1.0, 2.0, 3.0) + 0im
+    @test AbstractFFTs.realfloat(x1)[1] === AbstractFFTs.realfloat(x1[1]) === Dual(1.0, 2.0, 3.0)
+
+    @test fft(x1, 1)[1] isa Complex{<:Dual}
+
+    @testset "$f" for f in (fft, ifft, rfft, bfft)
+        @test value.(f(x1)) == f(value.(x1))
+        @test partials.(real(f(x1)), 1) + im*partials.(imag(f(x1)), 1) == f(partials.(x1, 1))
+        @test partials.(real(f(x1)), 2) + im*partials.(imag(f(x1)), 2) == f(partials.(x1, 2))
+    end
+
+    @test ifft(fft(x1)) ≈ x1
+    @test irfft(rfft(x1), length(x1)) ≈ x1
+    @test brfft(rfft(x1), length(x1)) ≈ 4x1
+
+    f = x -> real(fft([x; 0; 0])[1])
+    @test derivative(f,0.1) ≈ 1
+
+    r = x -> real(rfft([x; 0; 0])[1])
+    @test derivative(r,0.1) ≈ 1
+
+
+    n = 100
+    θ = range(0,2π; length=n+1)[1:end-1]
+    # emperical from Mathematical
+    @test derivative(ω -> fft(exp.(ω .* cos.(θ)))[1]/n, 1) ≈ 0.565159103992485
+
+    # c = x -> dct([x; 0; 0])[1]
+    # @test derivative(c,0.1) ≈ 1
+
+    @testset "matrix" begin
+        A = x1 * (1:10)'
+        @test value.(fft(A)) == fft(value.(A))
+        @test partials.(fft(A), 1) == fft(partials.(A, 1))
+        @test partials.(fft(A), 2) == fft(partials.(A, 2))
+
+        @test value.(fft(A, 1)) == fft(value.(A), 1)
+        @test partials.(fft(A, 1), 1) == fft(partials.(A, 1), 1)
+        @test partials.(fft(A, 1), 2) == fft(partials.(A, 2), 1)
+
+        @test value.(fft(A, 2)) == fft(value.(A), 2)
+        @test partials.(fft(A, 2), 1) == fft(partials.(A, 1), 2)
+        @test partials.(fft(A, 2), 2) == fft(partials.(A, 2), 2)
+    end
+
+    c1 = complex.(x1)
+    @test mul!(similar(c1), FFTW.plan_fft(x1), x1) == fft(x1)
+    @test mul!(similar(c1), FFTW.plan_fft(c1), c1) == fft(c1)
+end