rmalization mode (see `numpy.fft`). Default is "backward". Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor. .. versionadded:: 1.20.0 The "backward", "forward" values were added. Returns ------- out : complex ndarray The truncated or zero-padded input, transformed along the axes indicated by `axes`, or by a combination of `s` and `a`, as explained in the parameters section above. The length of the last axis transformed will be ``s[-1]//2+1``, while the remaining transformed axes will have lengths according to `s`, or unchanged from the input. Raises ------ ValueError If `s` and `axes` have different length. IndexError If an element of `axes` is larger than than the number of axes of `a`. See Also -------- irfftn : The inverse of `rfftn`, i.e. the inverse of the n-dimensional FFT of real input. fft : The one-dimensional FFT, with definitions and conventions used. rfft : The one-dimensional FFT of real input. fftn : The n-dimensional FFT. rfft2 : The two-dimensional FFT of real input. Notes ----- The transform for real input is performed over the last transformation axis, as by `rfft`, then the transform over the remaining axes is performed as by `fftn`. The order of the output is as for `rfft` for the final transformation axis, and as for `fftn` for the remaining transformation axes. See `fft` for details, definitions and conventions used. Examples -------- >>> a = np.ones((2, 2, 2)) >>> np.fft.rfftn(a) array([[[ 8.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j]], [[ 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j]]]) >>> np.fft.rfftn(a, axes=(2, 0)) array([[[ 4.+0.j, 0.+0.j], [ 4.+0.j, 0.+0.j]], [[ 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j]]]) r@