# scipy.fft.rfftn

scipy.fft.rfftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *, plan=None)

  Compute the N-D discrete Fourier Transform for real input.

  This function computes the N-D discrete Fourier Transform over any number of axes in an M-D real array by means of the Fast Fourier Transform (FFT). By default, all axes are transformed, with the real transform performed over the last axis, while the remaining transforms are complex.

  Parameters:
    x array_like

      Input array, taken to be real.

    s sequence of ints, optional

      Shape (length along each transformed axis) to use from the input. (`s[0]` refers to axis 0, `s[1]` to axis 1, etc.). The final element of s corresponds to n for `rfft(x, n)`, while for the remaining axes, it corresponds to n for `fft(x, n)`. Along any axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. if s is not given, the shape of the input along the axes specified by axes is used.

    axes sequence of ints, optional

      Axes over which to compute the FFT. If not given, the last `len(s)` axes are used, or all axes if s is also not specified.

    norm{“backward”, “ortho”, “forward”}, optional

      Normalization mode (see `fft`). Default is “backward”.

    overwrite_x bool, optional

      If True, the contents of x can be destroyed; the default is False. See `fft` for more details.

    workers int, optional

      Maximum number of workers to use for parallel computation. If negative, the value wraps around from `os.cpu_count()`. See `fft` for more details.

    plan object, optional

      This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.

      New in version 1.5.0.

  Returns:
    out complex ndarray

      The truncated or zero-padded input, transformed along the axes indicated by axes, or by a combination of s and x, 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 the number of axes of x.

  See also

  `irfftn`

    The inverse of `rfftn`, i.e., the inverse of the N-D FFT of real input.

  `fft`

    The 1-D FFT, with definitions and conventions used.

  `rfft`

    The 1-D FFT of real input.

  `fftn`

    The N-D FFT.

  `rfft2`

    The 2-D 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

      >>> import scipy.fft
      >>> import numpy as np
      >>> x = np.ones((2, 2, 2))
      >>> scipy.fft.rfftn(x)
      array([[[8.+0.j,  0.+0.j], # may vary
              [0.+0.j,  0.+0.j]],
             [[0.+0.j,  0.+0.j],
              [0.+0.j,  0.+0.j]]])

      >>> scipy.fft.rfftn(x, axes=(2, 0))
      array([[[4.+0.j,  0.+0.j], # may vary
              [4.+0.j,  0.+0.j]],
             [[0.+0.j,  0.+0.j],
              [0.+0.j,  0.+0.j]]])