dpnp.fft.ifftn

dpnp.fft.ifftn(a, s=None, axes=None, norm=None, out=None)[source]

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 dpnp.fft.

The input, analogously to dpnp.fft.ifft, should be ordered in the same way as is returned by dpnp.fft.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.

For full documentation refer to numpy.fft.ifftn.

Parameters:

  • a ({dpnp.ndarray, usm_ndarray}) -- Input array, can be complex.

  • s ({None, 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 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 it is -1, the whole input is used (no padding/trimming). if s is not given, the shape of the input along the axes specified by axes is used. If s is not None, axes must not be None either. Default: None.

  • axes ({None, sequence of ints}, optional) -- Axes over which to compute the inverse FFT. 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 transform over that axis is performed multiple times. If s is specified, the corresponding axes to be transformed must be explicitly specified too. A one-element sequence means that a one-dimensional FFT is performed. An empty sequence means that no FFT is performed. Default: None.

  • norm ({None, "backward", "ortho", "forward"}, optional) -- Normalization mode (see dpnp.fft). Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor. None is an alias of the default option "backward". Default: "backward".

  • out ({None, dpnp.ndarray or usm_ndarray of complex dtype}, optional) -- If provided, the result will be placed in this array. It should be of the appropriate shape (consistent with the choice of s) and dtype. Default: None.

Returns:

out -- The truncated or zero-padded input, transformed along the axes indicated by axes, or by a combination of s and a, as explained in the parameters section above.

Return type:

dpnp.ndarray of complex dtype

See also

dpnp.fft

Overall view of discrete Fourier transforms, with definitions and conventions used.

dpnp.fft.fftn

The N-dimensional FFT.

dpnp.fft.ifft

The one-dimensional inverse FFT.

dpnp.fft.ifft2

The two-dimensional inverse FFT.

dpnp.fft.ifftshift

Undoes dpnp.fft.fftshift, shifts zero-frequency terms to the center of the array.

Notes

See dpnp.fft for details, definitions and conventions used.

Zero-padding, analogously with dpnp.fft.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 dpnp.fft.ifftn is called.

Examples

>>> import dpnp as np
>>> 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], # may vary
       [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]])