idft

[lanougue]

Hi,
I became quite a fan of this xrft library but I am missing the "idft" function. Is it possible to implement it ?
Ideally, it would transform back a 'freq_x' coordinate back to 'x' coordinate and wrap the ifft function.
Thanks

[rabernat]

Hi @lanougue - thanks for you comments! xrft is simple, but we find it very useful for our needs.

We would love to have the inverse functions implemented. Is this something you'd like to take on yourself? A pull request would be most welcome.

[lanougue]

I can try but I'm not used to play with Github (newbie)...

[lanougue]

Hi @rabernat ,
I extended the dft code for the following points:

1. forward (df) and backward (idft) fft (sharing the same main code)
2. Take coordinates lag into account to ensure a=idft(dft(a)) (see comment below)
3. Allow other prefix than 'freq_'
4. Change back 'freq_x' into 'x' instead of 'freq_freq_x' (same for 'spacing')
5. idft is working wether or not frequency coordinate of input is fftshifted (shift= False/True).

Important point:
idft (as well as dft) returns centered coordinates (fftfreq style).If coordinates of input A is of fftfreq style, coordinates of idft(dft(A)) are the same as A (in other words: idft(dft(A)) = A for both amplitude and coordinates). If coordinates of A are not of fftfreqstyle (probably the most common case), A and idft(dft(A)) are the same on common coordinates only (expected behaviour from my point of view).

Consequences:
If theses changes are accepted, this point leads to a different dft output than previous version. However, this will only change the phase of the output, all spectra output will be preserved.

Can you help me for my first pull-request ? Correct me:

1. Clone dft repository
2. Create a new branch with my modifications
3. Pull request or ask for merging ?
   Thanks

[roxyboy]

Thank you for working on this @lanougue ! But, it's kind of hard to exactly understand what you have implemented without actually seeing the code. I personally do not think changing the conventions of dft is a good idea... If you could submit your changes as a PR, we could discuss more details about the changes you've made :) To submit a PR, you would first need to:

1. Fork the xgcm/xrft repository.
2. Clone your fork.
3. Create a new branch in your forked repository and make the edits there.
4. git push your branch to origin.
5. Submit a PR from your forked repository on Github.

[lanougue]

Thanks @roxyboy. I will try the PR procedure.

I agree with you on the fact that changing dft convention is generally not a good idea. However, it seems to be a necessity as soon as coordinates start entering into account.
From my point of view, absolute phase of dft is pointless if no coordinates are taken into account. Only difference of phase between two dft may matter (only if coordinates are the same for both input and, in that case, my modifications are transparent).
Moreover, people usually use abs(dft(A))**2 for spectrum computation or dft(A)*conj(dft(B)) for cross-spectrum. In all these cases, the proposed modifications should not change the results.

The proposed modifications purpose only serves for consistency for forth and back transforms when absolute phase matters.

I hope it will be more clear when the code will be shared. Working on it ...

[lanougue]

I tried the PR.
Here is a short example to exemplify my point with uncentered coordinates:

import xarray as xr
import numpy as np
import xrft
a = xr.DataArray(np.random.rand(10),dims=('x',), coords={'x':np.arange(-7,3)})
ta = xrft.dft(a, dim=('x',), shift=False)
tta = xrft.idft(ta, dim=('freq_x',))
a.plot()
np.real(tta).plot(linestyle='--')

[navidcy]

hey @lanougue, xrft.idft would be great. It's something I want to use as well...
did you end up submitting a PR?

@roxyboy, from what I see this was never implemented, no?

[lanougue]

Hi @navidcy,
The PR was submitted but did not pass the tests because of profound modification of what the result should be. Look @ #81 discussion.
I was away from this for some time. I will try to get back in soon!

[lanougue]

resolved in #129

[roxyboy]

Resolved by PR #129