support multidimensional transforms

[daanhb]

We currently have:

julia> using GenericFFT

julia> x = rand(BigFloat, 16, 16);

julia> fft(x)
ERROR: MethodError: no method matching generic_fft(::Matrix{Complex{BigFloat}}, ::UnitRange{Int64})

The call fft(x,1) returns something, but fft(x,2) returns an error.

[mfherbst]

Hi @daanhb I appreciate the effort. On the DFTK side we have some hackish code to make this work at least for 3D (2D is similar). I'm lacking the time to give this a serious try at the moment, but happy for anyone to pick the code up if it helps.

[sflammia]

I also ran into this issue, and I coded up something that does fft and ifft on multidimensional arrays. It has passed some basic unit tests, so I'm passing it along for those that have the same issue and need a temporary solution. (I uploaded it with a .txt extension since Github does not support .jl file extensions.)

fft_nd.jl.txt

[dlfivefifty]

Why not make it a PR?

[sflammia]

Why not make it a PR?

It doesn't follow the whole AbstractFFTs.jl format of using a "plan". So it seemed to me more like a temporary plug rather than something that should be a PR.

[dlfivefifty]

But as a (WIP) PR it is easier for others to contribute and get it over the lne