Proposal to remove ShiftedArrays as far as possible

[roflmaostc]

Hi,

I'm seeing myself always writing fftshift(fft(ifftshift(x))) because CUDA compatibility.

Maybe we should do the following:

ft(x) = fftshift(fft(ifftshift(x)))


function plan_ft(x)
    buffer1 = similar(x)
    buffer2 = similar(x)
    plan = plan_fft(x)
    function p(x)
         ifftshift!(buffer, x)
         fft!(buffer)
         # or mul!(buffer, p, x)
         fftshift!(buffer2, buffer)
         return buffer2
     end
     return p

In that way, we have a naive method which works interactively and is still good in speed. Or we have an allocation free version which has also the planned FFT which is more efficient.

It would be breaking because we would need to change some code.

What do you think? For me it's just a bit sad to see that I barely use this package in differentiable, high-performance situations because it doesn't work with CUDA, AD, etc.