Merge pull request #4 from JuliaMath/aa/tests

Set up testing

.travis.yml

@@ -12,5 +12,5 @@ notifications:
 #  - if [[ -a .git/shallow ]]; then git fetch --unshallow; fi
 #  - julia -e 'Pkg.clone(pwd()); Pkg.build("AbstractFFTs"); Pkg.test("AbstractFFTs"; coverage=true)'
 after_success:
-#  - julia -e 'Pkg.add("Coverage"); cd(Pkg.dir("AbstractFFTs")); using Coverage; Coveralls.submit(Coveralls.process_folder())'
-#  - julia -e 'Pkg.add("Documenter"); cd(Pkg.dir("AbstractFFTs")); include(joinpath("docs", "make.jl"))'
+  - julia -e 'Pkg.add("Coverage"); cd(Pkg.dir("AbstractFFTs")); using Coverage; Coveralls.submit(Coveralls.process_folder())'
+  - julia -e 'Pkg.add("Documenter"); cd(Pkg.dir("AbstractFFTs")); include(joinpath("docs", "make.jl"))'

README.md

@@ -2,20 +2,38 @@
 
 A general framework for fast Fourier transforms (FFTs) in Julia.
 
-This package is mainly not intended to be used directly.  Instead, developers of packages that implement FFTs (such as [FFTW.jl](https://github.com/JuliaMath/FFTW.jl)) extend the types/functions defined in `AbstractFFTs`.  This multiple FFT packages to co-exist with the same underlying `fft(x)` and `plan_fft(x)` interface.
+[![Travis](https://travis-ci.org/JuliaMath/AbstractFFTs.jl.svg?branch=master)](https://travis-ci.org/JuliaMath/AbstractFFTs.jl)
+[![Coveralls](https://coveralls.io/repos/github/JuliaMath/AbstractFFTs.jl/badge.svg?branch=master)](https://coveralls.io/github/JuliaMath/AbstractFFTs.jl?branch=master)
+
+Documentation:
+[![](https://img.shields.io/badge/docs-stable-blue.svg)](https://JuliaMath.github.io/AbstractFFTs.jl/stable)
+[![](https://img.shields.io/badge/docs-latest-blue.svg)](https://JuliaMath.github.io/AbstractFFTs.jl/latest)
+
+This package is mainly not intended to be used directly.
+Instead, developers of packages that implement FFTs (such as [FFTW.jl](https://github.com/JuliaMath/FFTW.jl))
+extend the types/functions defined in `AbstractFFTs`.
+This allows multiple FFT packages to co-exist with the same underlying `fft(x)` and `plan_fft(x)` interface.
 
 ## Developer information
 
 To define a new FFT implementation in your own module, you should
 
-* Define a new subtype (e.g. `MyPlan`) of `AbstractFFTs.Plan{T}` for FFTs and related transforms on arrays of `T`.  This must have a `pinv::Plan` field, initially undefined when a `MyPlan` is created, that is used for caching the inverse plan.
+* Define a new subtype (e.g. `MyPlan`) of `AbstractFFTs.Plan{T}` for FFTs and related transforms on arrays of `T`.
+  This must have a `pinv::Plan` field, initially undefined when a `MyPlan` is created, that is used for caching the
+  inverse plan.
 
-* Define a new method `AbstractFFTs.plan_fft(x, region; kws...)` that returns a `MyPlan` for at least some types of `x` and some set of dimensions `region`. 
+* Define a new method `AbstractFFTs.plan_fft(x, region; kws...)` that returns a `MyPlan` for at least some types of
+  `x` and some set of dimensions `region`.
 
 * Define a method of `A_mul_B!(y, p::MyPlan, x)` that computes the transform `p` of `x` and stores the result in `y`.
 
-* If the inverse transform is implemented, you should also define `plan_inv(p::MyPlan)`, which should construct the inverse plan to `p`, and `plan_bfft(x, region; kws...)` for an unnormalized inverse ("backwards") transform of `x`. 
+* Define a method of `*(p::MyPlan, x)`, which can simply call your `A_mul_B!` method.
+  This is not defined generically in this package due to subtleties that arise for in-place and real-input FFTs.
+
+* If the inverse transform is implemented, you should also define `plan_inv(p::MyPlan)`, which should construct the
+  inverse plan to `p`, and `plan_bfft(x, region; kws...)` for an unnormalized inverse ("backwards") transform of `x`.
 
 * You can also define similar methods of `plan_rfft` and `plan_brfft` for real-input FFTs.
 
-The normalization convention for your FFT should be that it computes yₖ = ∑ⱼ xⱼ exp(-2πi jk/n) for a transform of length n, and the "backwards" (unnormalized inverse) transform computes the same thing but with exp(+2πi jk/n).
+The normalization convention for your FFT should be that it computes yₖ = ∑ⱼ xⱼ exp(-2πi jk/n) for a transform of
+length n, and the "backwards" (unnormalized inverse) transform computes the same thing but with exp(+2πi jk/n).

src/AbstractFFTs.jl

@@ -7,16 +7,14 @@ using Base.LinAlg: BlasReal
 import Base: show, summary, size, ndims, length, eltype,
              *, A_mul_B!, inv, \, A_ldiv_B!
 
-if isdefined(Base, :DFT)
-    import Base.DFT: fft, ifft, bfft, fft!, ifft!, bfft!,
-                     plan_fft, plan_ifft, plan_bfft, plan_fft!, plan_ifft!, plan_bfft!,
-                     rfft, irfft, brfft, plan_rfft, plan_irfft, plan_brfft
-else
+if !isdefined(Base, :DFT)
     export fft, ifft, bfft, fft!, ifft!, bfft!,
            plan_fft, plan_ifft, plan_bfft, plan_fft!, plan_ifft!, plan_bfft!,
-           rfft, irfft, brfft, plan_rfft, plan_irfft, plan_brfft
+           rfft, irfft, brfft, plan_rfft, plan_irfft, plan_brfft,
+           fftshift, ifftshift
 end
 
+
 # DFT plan where the inputs are an array of eltype T
 abstract type Plan{T} end
 
@@ -358,8 +356,6 @@ plan_irfft
 
 ##############################################################################
 
-export fftshift, ifftshift
-
 fftshift(x) = circshift(x, div.([size(x)...],2))
 
 """

test/runtests.jl

@@ -1,4 +1,81 @@
+# This file contains code that was formerly part of Julia. License is MIT: https://julialang.org/license
+
 using AbstractFFTs
 using Base.Test
 
-# TODO
+import AbstractFFTs: Plan, plan_fft, plan_inv, plan_bfft
+import Base: A_mul_B!, *
+
+mutable struct TestPlan{T} <: Plan{T}
+    region
+    pinv::Plan{T}
+    TestPlan{T}(region) where {T} = new{T}(region)
+end
+
+mutable struct InverseTestPlan{T} <: Plan{T}
+    region
+    pinv::Plan{T}
+    InverseTestPlan{T}(region) where {T} = new{T}(region)
+end
+
+AbstractFFTs.plan_fft(x::Vector{T}, region; kwargs...) where {T} = TestPlan{T}(region)
+AbstractFFTs.plan_bfft(x::Vector{T}, region; kwargs...) where {T} = InverseTestPlan{T}(region)
+AbstractFFTs.plan_inv(p::TestPlan{T}) where {T} = InverseTestPlan{T}
+
+# Just a helper function since forward and backward are nearly identical
+function dft!(y::Vector, x::Vector, sign::Int)
+    n = length(x)
+    length(y) == n || throw(DimensionMismatch())
+    fill!(y, zero(complex(float(eltype(x)))))
+    c = sign * 2π / n
+    @inbounds for j = 0:n-1, k = 0:n-1
+        y[k+1] += x[j+1] * cis(c*j*k)
+    end
+    return y
+end
+
+Base.A_mul_B!(y::Vector, p::TestPlan, x::Vector) = dft!(y, x, -1)
+Base.A_mul_B!(y::Vector, p::InverseTestPlan, x::Vector) = dft!(y, x, 1)
+
+Base.:*(p::TestPlan, x::Vector) = A_mul_B!(copy(x), p, x)
+Base.:*(p::InverseTestPlan, x::Vector) = A_mul_B!(copy(x), p, x)
+
+@testset "Custom Plan" begin
+    x = AbstractFFTs.fft(collect(1:8))
+    # Result computed using FFTW
+    fftw_fft = [36.0 + 0.0im,
+                -4.0 + 9.65685424949238im,
+                -4.0 + 4.0im,
+                -4.0 + 1.6568542494923806im,
+                -4.0 + 0.0im,
+                -4.0 - 1.6568542494923806im,
+                -4.0 - 4.0im,
+                -4.0 - 9.65685424949238im]
+    @test x ≈ fftw_fft
+
+    fftw_bfft = [Complex{Float64}(8i, 0) for i in 1:8]
+    @test AbstractFFTs.bfft(x) ≈ fftw_bfft
+
+    fftw_ifft = [Complex{Float64}(i, 0) for i in 1:8]
+    @test AbstractFFTs.ifft(x) ≈ fftw_ifft
+end
+
+@testset "Shift functions" begin
+    @test AbstractFFTs.fftshift([1 2 3]) == [3 1 2]
+    @test AbstractFFTs.fftshift([1, 2, 3]) == [3, 1, 2]
+    @test AbstractFFTs.fftshift([1 2 3; 4 5 6]) == [6 4 5; 3 1 2]
+
+    @test AbstractFFTs.fftshift([1 2 3; 4 5 6], 1) == [4 5 6; 1 2 3]
+    @test AbstractFFTs.fftshift([1 2 3; 4 5 6], ()) == [1 2 3; 4 5 6]
+    @test AbstractFFTs.fftshift([1 2 3; 4 5 6], (1,2)) == [6 4 5; 3 1 2]
+    @test AbstractFFTs.fftshift([1 2 3; 4 5 6], 1:2) == [6 4 5; 3 1 2]
+
+    @test AbstractFFTs.ifftshift([1 2 3]) == [2 3 1]
+    @test AbstractFFTs.ifftshift([1, 2, 3]) == [2, 3, 1]
+    @test AbstractFFTs.ifftshift([1 2 3; 4 5 6]) == [5 6 4; 2 3 1]
+
+    @test AbstractFFTs.ifftshift([1 2 3; 4 5 6], 1) == [4 5 6; 1 2 3]
+    @test AbstractFFTs.ifftshift([1 2 3; 4 5 6], ()) == [1 2 3; 4 5 6]
+    @test AbstractFFTs.ifftshift([1 2 3; 4 5 6], (1,2)) == [5 6 4; 2 3 1]
+    @test AbstractFFTs.ifftshift([1 2 3; 4 5 6], 1:2) == [5 6 4; 2 3 1]
+end