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scipy.fft.

# ifft2

scipy.fft.ifft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *, plan=None)

  Compute the 2-D inverse discrete Fourier Transform.

  This function computes the inverse of the 2-D discrete Fourier Transform over any number of axes in an M-D array by means of the Fast Fourier Transform (FFT). In other words, `ifft2(fft2(x)) == x` to within numerical accuracy. By default, the inverse transform is computed over the last two axes of the input array.

  The input, analogously to `ifft`, should be ordered in the same way as is returned by `fft2`, i.e., it should have the term for zero frequency in the low-order corner of the two axes, the positive frequency terms in the first half of these axes, the term for the Nyquist frequency in the middle of the axes and the negative frequency terms in the second half of both axes, in order of decreasingly negative frequency.

  Parameters:
    x array_like

      Input array, can be complex.

    s sequence of ints, optional

      Shape (length of each axis) of the output (`s[0]` refers to axis 0, `s[1]` to axis 1, etc.). This corresponds to n for `ifft(x, n)`. Along each 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. See notes for issue on `ifft` zero padding.

    axes sequence of ints, optional

      Axes over which to compute the FFT. If not given, the last two axes are used.

    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 the last two axes if axes is not given.

  Raises:
    ValueError

      If s and axes have different length, or axes not given and `len(s) != 2`.

    IndexError

      If an element of axes is larger than the number of axes of x.

  See also

  `fft2`

    The forward 2-D FFT, of which `ifft2` is the inverse.

  `ifftn`

    The inverse of the N-D FFT.

  `fft`

    The 1-D FFT.

  `ifft`

    The 1-D inverse FFT.

  Notes

  `ifft2` is just `ifftn` with a different default for axes.

  See `ifftn` for details and a plotting example, and `fft` for definition and conventions used.

  Zero-padding, analogously with `ifft`, is performed by appending zeros to the input along the specified dimension. Although this is the common approach, it might lead to surprising results. If another form of zero padding is desired, it must be performed before `ifft2` is called.

  Array API Standard Support

  `ifft2` 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 = 4 * np.eye(4)
      >>> scipy.fft.ifft2(x)
      array([[1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j], # may vary
             [0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],
             [0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],
             [0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]])