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scipy.fft.

# ihfftn

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

  Compute the N-D inverse discrete Fourier Transform for a real spectrum.

  This function computes the N-D inverse 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.). 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.

      Added 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

  `hfftn`

    The forward N-D FFT of Hermitian input.

  `hfft`

    The 1-D FFT of Hermitian input.

  `fft`

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

  `fftn`

    The N-D FFT.

  `hfft2`

    The 2-D FFT of Hermitian input.

  Notes

  The transform for real input is performed over the last transformation axis, as by `ihfft`, then the transform over the remaining axes is performed as by `ifftn`. The order of the output is the positive part of the Hermitian output signal, in the same format as `rfft`.

  Array API Standard Support

  `ihfftn` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ✅
  JAX | ✅ | ✅
  Dask | ⚠️ computes graph | n/a

  See Support for the array API standard for more information.

  Examples

      >>> import scipy.fft
      >>> import numpy as np
      >>> x = np.ones((2, 2, 2))
      >>> scipy.fft.ihfftn(x)
      array([[[1.+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.ihfftn(x, axes=(2, 0))
      array([[[1.+0.j,  0.+0.j], # may vary
              [1.+0.j,  0.+0.j]],
             [[0.+0.j,  0.+0.j],
              [0.+0.j,  0.+0.j]]])