.. versionadded:: 1.5.0 Returns ------- out : ndarray The truncated or zero-padded input, transformed along the axes indicated by `axes`, or by a combination of `s` or `x`, as explained in the parameters section above. The length of each transformed axis is as given by the corresponding element of `s`, or the length of the input in every axis except for the last one if `s` is not given. In the final transformed axis the length of the output when `s` is not given is ``2*(m-1)``, where ``m`` is the length of the final transformed axis of the input. To get an odd number of output points in the final axis, `s` must be specified. Raises ------ ValueError If `s` and `axes` have different length. IndexError If an element of `axes` is larger than the number of axes of `x`. See Also -------- rfftn : The forward N-D FFT of real input, of which `ifftn` is the inverse. fft : The 1-D FFT, with definitions and conventions used. irfft : The inverse of the 1-D FFT of real input. irfft2 : The inverse of the 2-D FFT of real input. Notes ----- See `fft` for definitions and conventions used. See `rfft` for definitions and conventions used for real input. The default value of `s` assumes an even output length in the final transformation axis. When performing the final complex to real transformation, the Hermitian symmetry requires that the last imaginary component along that axis must be 0 and so it is ignored. To avoid losing information, the correct length of the real input *must* be given. Examples -------- >>> import scipy.fft >>> import numpy as np >>> x = np.zeros((3, 2, 2)) >>> x[0, 0, 0] = 3 * 2 * 2 >>> scipy.fft.irfftn(x) array([[[1., 1.], [1., 1.]], [[1., 1.], [1., 1.]], [[1., 1.], [1., 1.]]]) r