original_docstring: 
      Compute the 2-dimensional inverse discrete Fourier Transform.
  
      This function computes the inverse of the 2-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, ``ifft2(fft2(a)) == a``
      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
      ----------
      a : 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.  A repeated index in `axes` means the transform over
          that axis is performed multiple times.  A one-element sequence means
          that a one-dimensional FFT is performed.
      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 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 than the number of axes of `a`.
  
      See Also
      --------
      numpy.fft : Overall view of discrete Fourier transforms, with definitions
           and conventions used.
      fft2 : The forward 2-dimensional FFT, of which `ifft2` is the inverse.
      ifftn : The inverse of the *n*-dimensional FFT.
      fft : The one-dimensional FFT.
      ifft : The one-dimensional inverse FFT.
  
      Notes
      -----
      `ifft2` is just `ifftn` with a different default for `axes`.
  
      See `ifftn` for details and a plotting example, and `numpy.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.
  
      Examples
      --------
      >>> a = 4 * np.eye(4)
      >>> np.fft.ifft2(a)
      array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],
             [ 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]])
  
      
docstring: Compute the 2-dimensional inverse discrete Fourier Transform.
  This function computes the inverse of the 2-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, ``ifft2(fft2(a)) == a``
  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
  
  a : array_like
  Input array, can be complex.
  
  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
  
  
  
  See Also
  
  numpy.fft : Overall view of discrete Fourier transforms, with definitions
  and conventions used.
  fft2 : The forward 2-dimensional FFT, of which `ifft2` is the inverse.
  ifftn : The inverse of the *n*-dimensional FFT.
  fft : The one-dimensional FFT.
  ifft : The one-dimensional inverse FFT.
  
  Notes
  
  
  
  See `ifftn` for details and a plotting example, and `numpy.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.
  
  Examples
  
  
docstring_tokens: Compute the 2 - dimensional inverse discrete Fourier Transform . This function computes the inverse of the 2 - 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 ` ` ifft2 ( fft2 ( a )) == a ` ` 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 a : array_like Input array can be complex . 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 See Also numpy . fft : Overall view of discrete Fourier transforms with definitions and conventions used . fft2 : The forward 2 - dimensional FFT of which ` ifft2 ` is the inverse . ifftn : The inverse of the * n * - dimensional FFT . fft : The one - dimensional FFT . ifft : The one - dimensional inverse FFT . Notes See ` ifftn ` for details and a plotting example and ` numpy . 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 . Examples
code: def ifft2(a, s=None, axes=(-2, -1), norm=None):
      """
      Compute the 2-dimensional inverse discrete Fourier Transform.
  
      This function computes the inverse of the 2-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, ``ifft2(fft2(a)) == a``
      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
      ----------
      a : 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.  A repeated index in `axes` means the transform over
          that axis is performed multiple times.  A one-element sequence means
          that a one-dimensional FFT is performed.
      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 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 than the number of axes of `a`.
  
      See Also
      --------
      numpy.fft : Overall view of discrete Fourier transforms, with definitions
           and conventions used.
      fft2 : The forward 2-dimensional FFT, of which `ifft2` is the inverse.
      ifftn : The inverse of the *n*-dimensional FFT.
      fft : The one-dimensional FFT.
      ifft : The one-dimensional inverse FFT.
  
      Notes
      -----
      `ifft2` is just `ifftn` with a different default for `axes`.
  
      See `ifftn` for details and a plotting example, and `numpy.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.
  
      Examples
      --------
      >>> a = 4 * np.eye(4)
      >>> np.fft.ifft2(a)
      array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],
             [ 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]])
  
      """
  
      return _raw_fftnd(a, s, axes, ifft, norm)
code_tokens: def ifft2 ( a , s = None , axes = ( - 2 , - 1 ) , norm = None ) : return _raw_fftnd ( a , s , axes , ifft , norm )
short_docstring: Compute the 2-dimensional inverse discrete Fourier Transform.
short_docstring_tokens: Compute the 2 - dimensional inverse discrete Fourier Transform .
comment: """
      Compute the 2-dimensional inverse discrete Fourier Transform.
  
      This function computes the inverse of the 2-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, ``ifft2(fft2(a)) == a``
      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
      ----------
      a : 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.  A repeated index in `axes` means the transform over
          that axis is performed multiple times.  A one-element sequence means
          that a one-dimensional FFT is performed.
      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 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 than the number of axes of `a`.
  
      See Also
      --------
      numpy.fft : Overall view of discrete Fourier transforms, with definitions
           and conventions used.
      fft2 : The forward 2-dimensional FFT, of which `ifft2` is the inverse.
      ifftn : The inverse of the *n*-dimensional FFT.
      fft : The one-dimensional FFT.
      ifft : The one-dimensional inverse FFT.
  
      Notes
      -----
      `ifft2` is just `ifftn` with a different default for `axes`.
  
      See `ifftn` for details and a plotting example, and `numpy.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.
  
      Examples
      --------
      >>> a = 4 * np.eye(4)
      >>> np.fft.ifft2(a)
      array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],
             [ 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]])
  
      """