# ANN: InplaceRealFFT.jl : inplace real-to-complex and complex-to-real FFT

**URL:** <https://discourse.julialang.org/t/ann-inplacerealfft-jl-inplace-real-to-complex-and-complex-to-real-fft/8116>\
**Category:** Numerics\
**Tags:** fftw\
**Created:** [January 2, 2018, 9:30pm UTC](https://discourse.julialang.org/t/ann-inplacerealfft-jl-inplace-real-to-complex-and-complex-to-real-fft/8116 "2018-01-02T21:30:43Z")\
**Posts on this page:** 6\
**Page:** 2

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**Author:** ![favba](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/favba/32/2735_2.png) [@favba](https://discourse.julialang.org/u/favba)\
**Post date:** [January 4, 2018, 4:51am UTC](https://discourse.julialang.org/t/ann-inplacerealfft-jl-inplace-real-to-complex-and-complex-to-real-fft/8116/21 "2018-01-04T04:51:29Z")

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Aliasing arrays with `Complex{Float64}` and `Float64` is exactly what `rfft!` and `irfft!` are about 😞.

I was mainly using it for pseudo-spectral [fluid flow simulation code](https://github.com/favba/FluidFlowSimulation.jl), where part of the PDE is calculated in real space and part in Fourier space. Then I believe using lazy-reinterpretation would be a deal breaker 😧.

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**Author:** ![antoine-levitt](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/antoine-levitt/32/4008_2.png) [@antoine-levitt](https://discourse.julialang.org/u/antoine-levitt)\
**Post date:** [January 4, 2018, 8:36am UTC](https://discourse.julialang.org/t/ann-inplacerealfft-jl-inplace-real-to-complex-and-complex-to-real-fft/8116/22 "2018-01-04T08:36:06Z")

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Optim.jl also will be hit by this.

@Keno stated on [Sign in to GitHub · GitHub](https://github.com/JuliaImages/ImageCore.jl/pull/52:)

> I intend to have the performance fixed by the time 0.7 is released. The  
> performance was optimal at some point on my branch, but something clearly  
> regressed. Just busy with semantic changes at the moment.

so hopefully this will go away soon and those tricks will be unnecessary.

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**Author:** ![ssfrr](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ssfrr/32/3736_2.png) [@ssfrr](https://discourse.julialang.org/u/ssfrr)\
**Post date:** [January 4, 2018, 4:30pm UTC](https://discourse.julialang.org/t/ann-inplacerealfft-jl-inplace-real-to-complex-and-complex-to-real-fft/8116/23 "2018-01-04T16:30:30Z")

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I haven’t looked at this implementation yet, but FWIW I’ve often wanted  
an rfft! function that took a pre-allocated Complex array to put the  
result in, not necessarily re-using the input array. Would that work for  
your usecase or does it really need to be the same array with in-place  
operation?

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<div class="post-metadata">

**Author:** ![favba](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/favba/32/2735_2.png) [@favba](https://discourse.julialang.org/u/favba)\
**Post date:** [January 4, 2018, 4:41pm UTC](https://discourse.julialang.org/t/ann-inplacerealfft-jl-inplace-real-to-complex-and-complex-to-real-fft/8116/24 "2018-01-04T16:41:08Z")

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That is already possible using a precomputed plan:

```julia
julia> a = rand(8,8)
8×8 Array{Float64,2}:
 0.59679 0.131602 0.184409 0.558209 0.289836 0.268683 0.580835 0.289121
 0.31875 0.416771 0.409353 0.0981198 0.451174 0.260841 0.202204 0.917322
 0.124103 0.191237 0.620929 0.798103 0.589914 0.772676 0.838405 0.2102
 0.812172 0.686616 0.929844 0.341353 0.247563 0.698019 0.254909 0.687846
 0.0254606 0.385726 0.409981 0.097717 0.985738 0.29928 0.565726 0.716829
 0.40668 0.598828 0.184622 0.00956236 0.359331 0.418159 0.70267 0.66258
 0.335555 0.33336 0.244317 0.546701 0.138519 0.498856 0.971377 0.493033
 0.146153 0.832016 0.288027 0.866792 0.742087 0.545129 0.452103 0.774817

julia> b = zeros(Complex128,(5,8));

julia> p = plan_rfft(a)
FFTW real-to-complex plan for 8×8 array of Float64
(rdft2-rank>=2/1
  (rdft2-r2hc-direct-8-x8 "r2cf_8")
  (dft-direct-8-x5 "n1fv_8_avx"))

julia> A_mul_B!(b,p,a)
5×8 Array{Complex{Float64},2}:
   29.8156+0.0im -0.154824+2.44274im … -1.26989-0.730506im -0.154824-2.44274im
 -0.784323-0.402335im -1.70144+0.0786512im 0.595502-1.23948im 0.769457+0.922158im
  -1.32134+2.88848im 2.44856-1.03407im 1.55985-0.338671im -0.830614-0.666949im
 -0.389619+0.765363im 1.37924-2.20592im -0.512497+0.595245im 1.47723-2.13217im
  -1.62918+0.0im -3.22961+1.2663im -1.39024-0.926478im -3.22961-1.2663im

```

This package is to provide “truly” inplace transform. The main advantage is memory saving. I believe it is also faster because of memory locality, but that is just a guess.

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<div class="post-metadata">

**Author:** ![favba](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/favba/32/2735_2.png) [@favba](https://discourse.julialang.org/u/favba)\
**Post date:** [January 4, 2018, 5:31pm UTC](https://discourse.julialang.org/t/ann-inplacerealfft-jl-inplace-real-to-complex-and-complex-to-real-fft/8116/25 "2018-01-04T17:31:10Z")

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Here is a small benchmark:

```julia
julia> using InplaceRealFFT, BenchmarkTools

julia> a = zeros(256,256,256);

julia> op = plan_rfft(a,flags=FFTW.MEASURE);

julia> b = zeros(Complex128,(129,256,256));

julia> pa = PaddedArray(size(a));

julia> ip = plan_rfft!(pa,flags=FFTW.MEASURE);

julia> a .= rand(256,256,256);

julia> pa.r .= a;

julia> @benchmark A_mul_B!($b,$op,$a)
BenchmarkTools.Trial:
  memory estimate: 0 bytes
  allocs estimate: 0
  --------------
  minimum time: 155.066 ms (0.00% GC)
  median time: 159.190 ms (0.00% GC)
  mean time: 159.736 ms (0.00% GC)
  maximum time: 171.139 ms (0.00% GC)
  --------------
  samples: 32
  evals/sample: 1

julia> @benchmark *($ip,$pa)
BenchmarkTools.Trial:
  memory estimate: 0 bytes
  allocs estimate: 0
  --------------
  minimum time: 152.768 ms (0.00% GC)
  median time: 156.669 ms (0.00% GC)
  mean time: 156.766 ms (0.00% GC)
  maximum time: 162.761 ms (0.00% GC)
  --------------
  samples: 32
  evals/sample: 1

```

I do get consistently smaller times for `rfft!`, but it is always just a tiny bit faster…

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<div class="post-metadata">

**Author:** ![favba](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/favba/32/2735_2.png) [@favba](https://discourse.julialang.org/u/favba)\
**Post date:** [January 5, 2018, 6:32am UTC](https://discourse.julialang.org/t/ann-inplacerealfft-jl-inplace-real-to-complex-and-complex-to-real-fft/8116/26 "2018-01-05T06:32:50Z")

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A [PR](https://github.com/JuliaMath/FFTW.jl/pull/54) to FFTW.jl was made. I tried doing what at-yuyichao said was necessary but I’m not sure I did it correctly. Hopefully at-stevengj will be able to analyze it.

[Previous page](https://discourse.julialang.org/t/ann-inplacerealfft-jl-inplace-real-to-complex-and-complex-to-real-fft/8116.md?page=1)