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Add batched and multi-dimensional rfft/irfft support #60

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72 changes: 61 additions & 11 deletions src/fft.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -81,9 +81,9 @@ function generic_fft!(x)
end


generic_fft(x, region) = generic_fft!(copy(x), region)
generic_fft(x, region) = generic_fft!(copy(complex(x)), region)

generic_fft(x) = generic_fft!(copy(x))
generic_fft(x) = generic_fft!(copy(complex(x)))

function generic_fft(x::AbstractVector{T}) where T<:AbstractFloats
n = length(x)
Expand All @@ -105,14 +105,64 @@ generic_ifft(x::AbstractArray{T, N}, region) where {T<:AbstractFloats, N} = ldiv
generic_ifft!(x::AbstractArray{T, N}, region) where {T<:AbstractFloats, N} = ldiv!(T(_regionscale(x, region)), conj!(generic_fft!(conj!(x), region)))

generic_rfft(v::AbstractVector{T}, region) where T<:AbstractFloats = generic_fft(v, region)[1:div(length(v),2)+1]

function generic_rfft(x::AbstractArray{T, N}, region) where {T<:AbstractFloats, N}
d = first(region)
if length(region) > 1
return generic_fft(generic_rfft(x, d), region[2:end])
end

# Batched 1D RFFT along dimension d
nout = size(x, d) ÷ 2 + 1
sz = collect(size(x))
sz[d] = nout
out = similar(x, Complex{real(T)}, tuple(sz...))

Rpre = CartesianIndices(size(x)[1:d-1])
Rpost = CartesianIndices(size(x)[d+1:end])

Threads.@threads for Ipost in Rpost
for Ipre in Rpre
out[Ipre, :, Ipost] .= generic_rfft(view(x, Ipre, :, Ipost), 1)
end
end
return out
end

function generic_irfft(v::AbstractVector{T}, n::Integer, region) where T<:ComplexFloats
@assert length(v) == n>>1 + 1
r = Vector{T}(undef, n)
r[1:length(v)]=v
r[length(v)+1:n]=reverse(conj(v[2:end])[1:n-length(v)])
real(generic_ifft(r, region))
return real(generic_ifft(r, region))
end

function generic_irfft(x::AbstractArray{T, N}, n::Integer, region) where {T<:ComplexFloats, N}
d = first(region)
if length(region) > 1
return generic_irfft(generic_ifft(x, region[2:end]), n, d)
end

# Batched 1D IRFFT along dimension d
sz = collect(size(x))
sz[d] = n
out = similar(x, real(T), tuple(sz...))

Rpre = CartesianIndices(size(x)[1:d-1])
Rpost = CartesianIndices(size(x)[d+1:end])

Threads.@threads for Ipost in Rpost
for Ipre in Rpre
out[Ipre, :, Ipost] .= generic_irfft(view(x, Ipre, :, Ipost), n, 1)
end
end
return out
end

function generic_brfft(v::AbstractArray, n::Integer, region)
scale = n * _regionscale(v, region isa Integer ? () : region[2:end])
return generic_irfft(v, n, region) * scale
end
generic_brfft(v::AbstractArray, n::Integer, region) = generic_irfft(v, n, region)*n

function _conv!(u::AbstractVector{T}, v::AbstractVector{T}) where T<:AbstractFloats
nu = length(u)
Expand Down Expand Up @@ -262,7 +312,7 @@ for P in (:DummyFFTPlan, :DummyiFFTPlan, :DummybFFTPlan, :DummyDCTPlan, :DummyiD
@eval begin
mutable struct $P{T,inplace,G} <: DummyPlan{T}
region::G # region (iterable) of dims that are transformed
pinv::DummyPlan{T}
pinv::Plan
$P{T,inplace,G}(region::G) where {T<:AbstractFloats, inplace, G} = new(region)
end
end
Expand All @@ -272,7 +322,7 @@ for P in (:DummyrFFTPlan, :DummyirFFTPlan, :DummybrFFTPlan)
mutable struct $P{T,inplace,G} <: DummyPlan{T}
n::Integer
region::G # region (iterable) of dims that are transformed
pinv::DummyPlan{T}
pinv::Plan
$P{T,inplace,G}(n::Integer, region::G) where {T<:AbstractFloats, inplace, G} = new(n, region)
end
end
Expand All @@ -287,8 +337,8 @@ for (Plan,iPlan) in ((:DummyFFTPlan,:DummyiFFTPlan),
end

# Specific for rfft, irfft and brfft:
plan_inv(p::DummyirFFTPlan{T,inplace,G}) where {T,inplace,G} = DummyrFFTPlan{T,inplace,G}(p.n, p.region)
plan_inv(p::DummyrFFTPlan{T,inplace,G}) where {T,inplace,G} = DummyirFFTPlan{T,inplace,G}(p.n, p.region)
plan_inv(p::DummyirFFTPlan{T,inplace,G}) where {T,inplace,G} = DummyrFFTPlan{real(T),inplace,G}(p.n, p.region)
plan_inv(p::DummyrFFTPlan{T,inplace,G}) where {T,inplace,G} = DummyirFFTPlan{Complex{T},inplace,G}(p.n, p.region)



Expand Down Expand Up @@ -345,11 +395,11 @@ plan_dct!(x::StridedArray{T}, region) where {T <: AbstractFloats} = DummyDCTPlan
plan_idct(x::StridedArray{T}, region) where {T <: AbstractFloats} = DummyiDCTPlan{T,false,typeof(region)}(region)
plan_idct!(x::StridedArray{T}, region) where {T <: AbstractFloats} = DummyiDCTPlan{T,true,typeof(region)}(region)

plan_rfft(x::StridedArray{T}, region) where {T <: RealFloats} = DummyrFFTPlan{T,false,typeof(region)}(length(x), region)
plan_rfft(x::StridedArray{T}, region) where {T <: RealFloats} = DummyrFFTPlan{T,false,typeof(region)}(size(x, first(region)), region)
plan_brfft(x::StridedArray{T}, n::Integer, region) where {T <: ComplexFloats} = DummybrFFTPlan{T,false,typeof(region)}(n, region)

# A plan for irfft is created in terms of a plan for brfft.
# plan_irfft(x::StridedArray{T}, n::Integer, region) where {T <: ComplexFloats} = DummyirFFTPlan{Complex{real(T)},false,typeof(region)}(n, region)
# Explicitly define plan_irfft to ensure correct scaling
plan_irfft(x::StridedArray{T}, n::Integer, region) where {T <: ComplexFloats} = DummyirFFTPlan{T,false,typeof(region)}(n, region)

# These don't exist for now:
# plan_rfft!(x::StridedArray{T}) where {T <: RealFloats} = DummyrFFTPlan{Complex{real(T)},true}()
Expand Down
59 changes: 57 additions & 2 deletions test/fft_tests.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -44,8 +44,8 @@ function test_fft_dct(T)
@test norm(dct(idct(c))-c,Inf) < 1000eps(T)

@test_throws AssertionError irfft(c, 197)
@test norm(irfft(c, 198) - irfft(map(ComplexF64, c), 198), Inf) < 10eps(Float64)
@test norm(irfft(c, 199) - irfft(map(ComplexF64, c), 199), Inf) < 10eps(Float64)
@test norm(irfft(c, 198) - irfft(map(ComplexF64, c), 198), Inf) < 100eps(Float64)
@test norm(irfft(c, 199) - irfft(map(ComplexF64, c), 199), Inf) < 100eps(Float64)
@test_throws AssertionError irfft(c, 200)
end

Expand Down Expand Up @@ -202,3 +202,58 @@ end
@allocations generic_fft!(A2) # compile
@test N+150 > @allocations generic_fft!(A2) # a few allocations is OK
end

@testset "Batched rfft/irfft" begin
for T in (Float64, BigFloat)
X = randn(T, 10, 6)

Y1 = rfft(X, 1) # Dimension 1
@test size(Y1) == (10÷2+1, 6)
for j in 1:6
@test Y1[:, j] ≈ rfft(X[:, j])
end
@test irfft(Y1, 10, 1) ≈ X

Y2 = rfft(X, 2) # Dimension 2
@test size(Y2) == (10, 6÷2+1)
for i in 1:10
@test Y2[i, :] ≈ rfft(X[i, :])
end
@test irfft(Y2, 6, 2) ≈ X

Y12 = rfft(X, (1, 2)) # 2D RFFT
@test size(Y12) == (10÷2+1, 6)
@test Y12 ≈ fft(rfft(X, 1), 2)
@test irfft(Y12, 10, (1, 2)) ≈ X

p1 = plan_rfft(X, 1) # Plans
@test p1 * X ≈ rfft(X, 1)
@test inv(p1) * (p1 * X) ≈ X

p2 = plan_rfft(X, 2)
@test p2 * X ≈ rfft(X, 2)
@test inv(p2) * (p2 * X) ≈ X
end


for n in (7, 11) # Test a few odd lengths
X = randn(BigFloat, n, 4)
Y = rfft(X, 1)
@test size(Y) == (n÷2+1, 4)
@test irfft(Y, n, 1) ≈ X
end

data = randn(BigFloat, 10, 10)
v = view(data, 1:8, 1:6)
@test rfft(v, 1) ≈ rfft(collect(v), 1)
@test irfft(rfft(v, 1), 8, 1) ≈ v

X3 = randn(BigFloat, 4, 10, 4) # Test 3D Batched

Y3 = rfft(X3, 2) # Transform along dimension 2
@test size(Y3) == (4, 10÷2+1, 4)
for i in 1:4, k in 1:4
@test Y3[i, :, k] ≈ rfft(X3[i, :, k])
end
@test irfft(Y3, 10, 2) ≈ X3
end
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