original_docstring: 
      Compute the N-dimensional inverse discrete Fourier Transform.
  
      This function computes the inverse of the N-dimensional discrete
      Fourier Transform over any number of axes in an M-dimensional array by
      means of the Fast Fourier Transform (FFT).  In other words,
      ``ifftn(fftn(a)) == a`` to within numerical accuracy.
      For a description of the definitions and conventions used, see `numpy.fft`.
  
      The input, analogously to `ifft`, should be ordered in the same way as is
      returned by `fftn`, i.e. it should have the term for zero frequency
      in all axes in the low-order corner, the positive frequency terms in the
      first half of all axes, the term for the Nyquist frequency in the middle
      of all axes and the negative frequency terms in the second half of all
      axes, in order of decreasingly negative frequency.
  
      Parameters
      ----------
      a : array_like
          Input array, can be complex.
      s : sequence of ints, optional
          Shape (length of each transformed 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 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.  See notes for issue on `ifft` zero padding.
      axes : sequence of ints, optional
          Axes over which to compute the IFFT.  If not given, the last ``len(s)``
          axes are used, or all axes if `s` is also not specified.
          Repeated indices in `axes` means that the inverse transform over that
          axis is performed multiple times.
      norm : {None, "ortho"}, optional
          .. versionadded:: 1.10.0
          Normalization mode (see `numpy.fft`). Default is None.
  
      Returns
      -------
      out : complex ndarray
          The truncated or zero-padded input, transformed along the axes
          indicated by `axes`, or by a combination of `s` or `a`,
          as explained in the parameters section above.
  
      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
      --------
      numpy.fft : Overall view of discrete Fourier transforms, with definitions
           and conventions used.
      fftn : The forward *n*-dimensional FFT, of which `ifftn` is the inverse.
      ifft : The one-dimensional inverse FFT.
      ifft2 : The two-dimensional inverse FFT.
      ifftshift : Undoes `fftshift`, shifts zero-frequency terms to beginning
          of array.
  
      Notes
      -----
      See `numpy.fft` for definitions 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 `ifftn` is called.
  
      Examples
      --------
      >>> a = np.eye(4)
      >>> np.fft.ifftn(np.fft.fftn(a, axes=(0,)), axes=(1,))
      array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],
             [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],
             [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],
             [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j]])
  
  
      Create and plot an image with band-limited frequency content:
  
      >>> import matplotlib.pyplot as plt
      >>> n = np.zeros((200,200), dtype=complex)
      >>> n[60:80, 20:40] = np.exp(1j*np.random.uniform(0, 2*np.pi, (20, 20)))
      >>> im = np.fft.ifftn(n).real
      >>> plt.imshow(im)
      <matplotlib.image.AxesImage object at 0x...>
      >>> plt.show()
  
      
docstring: Compute the N-dimensional inverse discrete Fourier Transform.
  This function computes the inverse of the N-dimensional discrete
  Fourier Transform over any number of axes in an M-dimensional array by
  means of the Fast Fourier Transform (FFT).  In other words,
  ``ifftn(fftn(a)) == a`` to within numerical accuracy.
  For a description of the definitions and conventions used, see `numpy.fft`.
  
  The input, analogously to `ifft`, should be ordered in the same way as is
  returned by `fftn`, i.e. it should have the term for zero frequency
  in all axes in the low-order corner, the positive frequency terms in the
  first half of all axes, the term for the Nyquist frequency in the middle
  of all axes and the negative frequency terms in the second half of all
  axes, in order of decreasingly negative frequency.
  
  Parameters
  
  a : array_like
  Input array, can be complex.
  
  Returns
  
  
  
  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
  
  numpy.fft : Overall view of discrete Fourier transforms, with definitions
  and conventions used.
  fftn : The forward *n*-dimensional FFT, of which `ifftn` is the inverse.
  ifft : The one-dimensional inverse FFT.
  ifft2 : The two-dimensional inverse FFT.
  ifftshift : Undoes `fftshift`, shifts zero-frequency terms to beginning
  of array.
  
  Notes
  
  See `numpy.fft` for definitions 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 `ifftn` is called.
  
  Examples
  
  
  
  Create and plot an image with band-limited frequency content.
  
  
docstring_tokens: Compute the N - dimensional inverse discrete Fourier Transform . This function computes the inverse of the N - dimensional discrete Fourier Transform over any number of axes in an M - dimensional array by means of the Fast Fourier Transform ( FFT ) . In other words ` ` ifftn ( fftn ( a )) == a ` ` to within numerical accuracy . For a description of the definitions and conventions used see ` numpy . fft ` . The input analogously to ` ifft ` should be ordered in the same way as is returned by ` fftn ` i . e . it should have the term for zero frequency in all axes in the low - order corner the positive frequency terms in the first half of all axes the term for the Nyquist frequency in the middle of all axes and the negative frequency terms in the second half of all axes in order of decreasingly negative frequency . Parameters a : array_like Input array can be complex . Returns 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 numpy . fft : Overall view of discrete Fourier transforms with definitions and conventions used . fftn : The forward * n * - dimensional FFT of which ` ifftn ` is the inverse . ifft : The one - dimensional inverse FFT . ifft2 : The two - dimensional inverse FFT . ifftshift : Undoes ` fftshift ` shifts zero - frequency terms to beginning of array . Notes See ` numpy . fft ` for definitions 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 ` ifftn ` is called . Examples Create and plot an image with band - limited frequency content .
code: def ifftn(a, s=None, axes=None, norm=None):
      """
      Compute the N-dimensional inverse discrete Fourier Transform.
  
      This function computes the inverse of the N-dimensional discrete
      Fourier Transform over any number of axes in an M-dimensional array by
      means of the Fast Fourier Transform (FFT).  In other words,
      ``ifftn(fftn(a)) == a`` to within numerical accuracy.
      For a description of the definitions and conventions used, see `numpy.fft`.
  
      The input, analogously to `ifft`, should be ordered in the same way as is
      returned by `fftn`, i.e. it should have the term for zero frequency
      in all axes in the low-order corner, the positive frequency terms in the
      first half of all axes, the term for the Nyquist frequency in the middle
      of all axes and the negative frequency terms in the second half of all
      axes, in order of decreasingly negative frequency.
  
      Parameters
      ----------
      a : array_like
          Input array, can be complex.
      s : sequence of ints, optional
          Shape (length of each transformed 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 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.  See notes for issue on `ifft` zero padding.
      axes : sequence of ints, optional
          Axes over which to compute the IFFT.  If not given, the last ``len(s)``
          axes are used, or all axes if `s` is also not specified.
          Repeated indices in `axes` means that the inverse transform over that
          axis is performed multiple times.
      norm : {None, "ortho"}, optional
          .. versionadded:: 1.10.0
          Normalization mode (see `numpy.fft`). Default is None.
  
      Returns
      -------
      out : complex ndarray
          The truncated or zero-padded input, transformed along the axes
          indicated by `axes`, or by a combination of `s` or `a`,
          as explained in the parameters section above.
  
      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
      --------
      numpy.fft : Overall view of discrete Fourier transforms, with definitions
           and conventions used.
      fftn : The forward *n*-dimensional FFT, of which `ifftn` is the inverse.
      ifft : The one-dimensional inverse FFT.
      ifft2 : The two-dimensional inverse FFT.
      ifftshift : Undoes `fftshift`, shifts zero-frequency terms to beginning
          of array.
  
      Notes
      -----
      See `numpy.fft` for definitions 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 `ifftn` is called.
  
      Examples
      --------
      >>> a = np.eye(4)
      >>> np.fft.ifftn(np.fft.fftn(a, axes=(0,)), axes=(1,))
      array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],
             [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],
             [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],
             [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j]])
  
  
      Create and plot an image with band-limited frequency content:
  
      >>> import matplotlib.pyplot as plt
      >>> n = np.zeros((200,200), dtype=complex)
      >>> n[60:80, 20:40] = np.exp(1j*np.random.uniform(0, 2*np.pi, (20, 20)))
      >>> im = np.fft.ifftn(n).real
      >>> plt.imshow(im)
      <matplotlib.image.AxesImage object at 0x...>
      >>> plt.show()
  
      """
  
      return _raw_fftnd(a, s, axes, ifft, norm)
code_tokens: def ifftn ( a , s = None , axes = None , norm = None ) : return _raw_fftnd ( a , s , axes , ifft , norm )
short_docstring: Compute the N-dimensional inverse discrete Fourier Transform.
short_docstring_tokens: Compute the N - dimensional inverse discrete Fourier Transform .
comment: """
      Compute the N-dimensional inverse discrete Fourier Transform.
  
      This function computes the inverse of the N-dimensional discrete
      Fourier Transform over any number of axes in an M-dimensional array by
      means of the Fast Fourier Transform (FFT).  In other words,
      ``ifftn(fftn(a)) == a`` to within numerical accuracy.
      For a description of the definitions and conventions used, see `numpy.fft`.
  
      The input, analogously to `ifft`, should be ordered in the same way as is
      returned by `fftn`, i.e. it should have the term for zero frequency
      in all axes in the low-order corner, the positive frequency terms in the
      first half of all axes, the term for the Nyquist frequency in the middle
      of all axes and the negative frequency terms in the second half of all
      axes, in order of decreasingly negative frequency.
  
      Parameters
      ----------
      a : array_like
          Input array, can be complex.
      s : sequence of ints, optional
          Shape (length of each transformed 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 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.  See notes for issue on `ifft` zero padding.
      axes : sequence of ints, optional
          Axes over which to compute the IFFT.  If not given, the last ``len(s)``
          axes are used, or all axes if `s` is also not specified.
          Repeated indices in `axes` means that the inverse transform over that
          axis is performed multiple times.
      norm : {None, "ortho"}, optional
          .. versionadded:: 1.10.0
          Normalization mode (see `numpy.fft`). Default is None.
  
      Returns
      -------
      out : complex ndarray
          The truncated or zero-padded input, transformed along the axes
          indicated by `axes`, or by a combination of `s` or `a`,
          as explained in the parameters section above.
  
      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
      --------
      numpy.fft : Overall view of discrete Fourier transforms, with definitions
           and conventions used.
      fftn : The forward *n*-dimensional FFT, of which `ifftn` is the inverse.
      ifft : The one-dimensional inverse FFT.
      ifft2 : The two-dimensional inverse FFT.
      ifftshift : Undoes `fftshift`, shifts zero-frequency terms to beginning
          of array.
  
      Notes
      -----
      See `numpy.fft` for definitions 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 `ifftn` is called.
  
      Examples
      --------
      >>> a = np.eye(4)
      >>> np.fft.ifftn(np.fft.fftn(a, axes=(0,)), axes=(1,))
      array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],
             [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],
             [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],
             [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j]])
  
  
      Create and plot an image with band-limited frequency content:
  
      >>> import matplotlib.pyplot as plt
      >>> n = np.zeros((200,200), dtype=complex)
      >>> n[60:80, 20:40] = np.exp(1j*np.random.uniform(0, 2*np.pi, (20, 20)))
      >>> im = np.fft.ifftn(n).real
      >>> plt.imshow(im)
      <matplotlib.image.AxesImage object at 0x...>
      >>> plt.show()
  
      """