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Fix and test the real DFT #55

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Merged
merged 1 commit into from
Mar 18, 2025
Merged

Fix and test the real DFT #55

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15 changes: 5 additions & 10 deletions src/algos.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -89,18 +89,16 @@ end

function fft_dft!(out::AbstractVector{Complex{T}}, in::AbstractVector{T}, N::Int, start_out::Int, stride_out::Int, start_in::Int, stride_in::Int, d::Direction) where {T<:Real}
halfN = N÷2
wk = wkn = w = convert(Complex{T}, cispi(direction_sign(d)*2/N))

tmpBegin = tmpHalf = in[start_in]
tmp = Complex{T}(in[start_in])
@inbounds for j in 1:N-1
tmpBegin += in[start_in + stride_in*j]
iseven(j) ? tmpHalf += in[start_in + stride_in*j] : tmpHalf -= in[start_in + stride_in*j]
tmp += in[start_in + j*stride_in]
end
out[start_out] = convert(Complex{T}, tmpBegin)
iseven(N) && (out[start_out + stride_out*halfN] = convert(Complex{T}, tmpHalf))
out[start_out] = tmp

wk = wkn = w = convert(Complex{T}, cispi(direction_sign(d)*2/N))
@inbounds for d in 1:halfN
tmp = in[start_in]
tmp = Complex{T}(in[start_in])
@inbounds for k in 1:N-1
tmp += wkn*in[start_in + k*stride_in]
wkn *= wk
Expand All @@ -109,9 +107,6 @@ function fft_dft!(out::AbstractVector{Complex{T}}, in::AbstractVector{T}, N::Int
wk *= w
wkn = wk
end
@inbounds for k in halfN+1:N-1
out[start_out + stride_out*k] = conj(out[start_out + stride_out*(N-k)])
end
end

function fft!(out::AbstractVector{T}, in::AbstractVector{U}, start_out::Int, start_in::Int, d::Direction, ::DFT, g::CallGraph{T}, idx::Int) where {T,U}
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9 changes: 8 additions & 1 deletion test/onedim/real_forward.jl
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Expand Up @@ -12,7 +12,14 @@ end

@testset verbose = true "against naive implementation. Size: $n" for n in 1:64
x = randn(n)
@test naive_1d_fourier_transform(x, FFTA.FFT_FORWARD)[1:(n ÷ 2 + 1)] ≈ rfft(x)
y = rfft(x)
@test naive_1d_fourier_transform(x, FFTA.FFT_FORWARD)[1:(n ÷ 2 + 1)] ≈ y

@testset "temporarily test real dft separately until used by rfft" begin
y_dft = similar(y)
FFTA.fft_dft!(y_dft, x, n, 1, 1, 1, 1, FFTA.FFT_FORWARD)
@test y ≈ y_dft
end
end

@testset "error messages" begin
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