Inverse fft in 2D backend

EDIT by EO:

• Using the appropriate normalization for the ifft (ie both backend files)
• Adding a unit test in 2d/test for testing the fft, which is not currently tested
• Normalizing the wavelet in the Fourier domain (ie the file filter_bank.py) to avoid the new code to break and satisfy the previous unit tests NOTE: this might lead to a small(not to say tiny) speed-up, because the dot-wise multiplication usually use quite some resources!

In 2D backend code, in output = torch.ifft(input, 2, normalized=False)*input.size(-2)*input.size(-3) why is the inverse fft routine multiplied by the term *input.size(-2)*input.size(-3)? I was expecting that transforming a matrix back and forth to the Fourier domain give the same result. In other words, I was expecting outputs of the following test code match.

import torch
from kymatio.scattering2d import backend as bd2

pad = bd2.Pad(2 ** 0, pre_pad=False)

# -- parameters
M = 8
N = 8
L = 8
J = 4

# -- synthesise data
y = torch.rand(1, 1, M, N)
for i in range(M):
    for j in range(N):
        y[:,:,i,j] = i+j

y_pad = pad(y)                                    # pad to add complex dimension
y_fft = bd2.fft(y_pad, 'C2C')                     # fft
y_fft_inv = bd2.fft(y_fft, 'C2C', inverse=True)   # inverse fft
y_fft_inv_un = y_fft_inv[..., 1:-1, 1:-1, 0]      # unpad

# -- print
print(y)
print(y_fft_inv_un)

[nshervt]

Hi @edouardoyallon, will do by tomorrow. My changes break test_Scattering2D in unittests, and that I had to look into.

[edouardoyallon]

Hi, This is a very good point. It’s due to a lack of testing of the FFT, however solving it is easy! I put a checklist to fix this! Would you mind doing a PR for solving this? Thanks!