feat: implement inverse fast fourier transform (irfftn) function for paddle frontend

[xingshuodong]

PR Description

feat: implement inverse fast Fourier transform (irfftn) function for paddle frontend

Add paddle.fft Fast Fourier Transform Functions to Paddle Frontend #15047
This pull request is related to resolves [irfftn #22913].

• irfftn #22913
  Close irfftn #22913

Checklist

• Did you add a function?
• Did you add the tests?
• Did you follow the steps we provided?

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ins: xingshuodong

[github-actions]

PR Compliance Checks Passed!

[xingshuodong]

@tomatillos please reply me at this PR, i think the old PR is going to be closed.
As far as the irfftn is working for n-dim case, please let me know if I need to do some improvement.

[tomatillos]

Also fix the lint and PR compliance checks please.

[mobley-trent]

@xingshuodong this is a great PR ⚡
Just resolve the minor issues and this should be good to merge.
Is there a valid reason why you've set s to None in the tests ? There might be a bug in your code you aren't aware about

[mobley-trent]

As well as axes

[xingshuodong]

Also fix the lint and PR compliance checks please.

@tomatillos Hi Tom, i cant pass the lint check becasue the file itself can't pass the lint check specific to rfftfreq,
should i modify it?

[xingshuodong]

@xingshuodong this is a great PR ⚡ Just resolve the minor issues and this should be good to merge. Is there a valid reason why you've set s to None in the tests ? There might be a bug in your code you aren't aware about

@mobley-trent Hi Eddy, during learning of development, as there is a general rule for manuplate the shape of x tensor, none is a better choice

The valid reason that here should set to be none, is the setup method for frontend test is only supporting the axis but not axes, the frontend is expecting the single axis as test input rather than the axes, this is out scope with the specific use of s.
so the functionality of irfftn will support range of axes as input (it works in loop), it will always work for s=None, the extra step can be add the 0 pad as following describtion

Take example of input a tensor x which is 3 dim with 2 dim size, (2, 2, 2)
Same as Input: If you want the output to be of the same shape as the input, you could specify s=(2, 2, 2).

irfftn(my_tensor, s=(2, 2, 2), axes=(0, 1, 2))
Different Size: If you want to zero-pad or truncate along specific dimensions, you can specify different sizes.

irfftn(my_tensor, s=(3, 3, 3), axes=(0, 1, 2))
This will zero-pad the frequency-domain data before transforming, giving you a (3, 3, 3) output tensor.

Specific Axes: If you want to transform along specific axes but not others, specify the axes and shape accordingly.

irfftn(my_tensor, s=(3, 3), axes=(0, 1))
This will perform the inverse FFT along the first two axes and zero-pad to (3, 3) along those axes, leaving the third axis unchanged.

[xingshuodong]

@mobley-trent Hi Eddy I have carefully review the irfftn explnation, and rewrite the function.

1. for nomral axes, irfftn use ifftn
2. for last axis, irfftn use the developed calculation represents irfft

Now this is a true irfftn function for any dims any size, it enable:

1. input axes like [0, 2, 3, 4] or [int] or None
2. input shape as None, or a customerized shape, the ifftn function used in irfftn is supporting this function

[xingshuodong]

In Tensorflow, in some cases the assert_all_close function is resulting issue of result doesn't match, this is an backend issue, but may occur during irfftn. ifftn in jax only support 3 D

[mobley-trent]

Hey @xingshuodong your function should at least pass for the minimal example I provided earlier from the paddle docs

[xingshuodong]

Hey @xingshuodong your function should at least pass for the minimal example I provided earlier from the paddle docs

it does pass, you can check the picture, what i mean is the test method fixed doesn't mean it works in limited case, it depends on how the backend developed in other backend, just like in tensorflow there is no nature irfftn function, so it is better to have irfftn special for tensorflow itself, or just rasie the error.

Please check this picture, it works for most cases, not only limit one. @mobley-trent , this function is work well for numpy and paddle, for those who dont have ifftn support N-D, it will only work for 3-D.

[xingshuodong]

Please pay attention to check, it is tested. @tomatillos， it should meet the irfftn performance for paddle, becasue it can work in paddle.

[mobley-trent]

Only the paddle backend seems to be running in this case. We can just merge for now
Thanks again for your PR @xingshuodong 🚀

[xingshuodong]

The case here is this irfftn is working correctly in numpy backend and paddle backend.
Jax and tensorflow backend with over 3 - D dims, need some specific consideration.