Onesided 2D rfft - discards "half" of the signal only for the last dimension

vision
1

Why does the onesided option work only for the last dimension, but not for the last but one in case of the 2D rfft:

z = np.array([[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]])
np.fft.fft2(z)
Out[31]: 
array([[136. +0.j,  -8. +8.j,  -8. +0.j,  -8. -8.j],
       [-32.+32.j,   0. +0.j,   0. +0.j,   0. +0.j],
       [-32. +0.j,   0. +0.j,   0. +0.j,   0. +0.j],
       [-32.-32.j,   0. +0.j,   0. +0.j,   0. +0.j]])
ztorch = torch.tensor(z, dtype=torch.float)
torch.rfft(ztorch, 2)
Out[35]: 
tensor([[[136.,   0.], [ -8.,   8.], [ -8.,   0.]],
        [[-32.,  32.], [  0.,   0.], [  0.,   0.]],
        [[-32.,   0.], [  0.,   0.], [  0.,   0.]],
        [[-32., -32.], [  0.,   0.], [  0.,   0.]]])

Shouldn’t the last line [[-32., -32.], [ 0., 0.], [ 0., 0.]] be discarded as well for the onesided 2D rfft?

2

Yes you can indeed infer using the 2nd row. but onesided never says that it gives you the minimum set of values that has no redundant information. It just discards ~half on the last dimension, which is also the convention many fft libraries use: e.g., mklfft, fftw, cufft.