dpnp.fft.fftn

dpnp.fft.fftn(a, s=None, axes=None, norm=None, out=None)

Compute the N-dimensional discrete Fourier Transform.

This function computes the N-dimensional discrete Fourier Transform over any number of axes in an M-dimensional array by means of the Fast Fourier Transform (FFT).

For full documentation refer to numpy.fft.fftn.

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 fft(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 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.ifftn

The inverse N-dimensional FFT.

dpnp.fft.fft

The one-dimensional FFT.

dpnp.fft.rfftn

The N-dimensional FFT of real input.

dpnp.fft.fft2

The two-dimensional FFT.

dpnp.fft.fftshift

Shifts zero-frequency terms to the center of the array.

Notes

The output, analogously to dpnp.fft.fft, contains the term for zero frequency in the low-order corner of the transformed 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 the axes, in order of decreasingly negative frequency.

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

Examples

>>> import dpnp as np
>>> a = np.mgrid[:3, :3, :3][0]
>>> np.fft.fftn(a, axes=(1, 2))
array([[[ 0.+0.j,   0.+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]],
       [[ 9.+0.j,   0.+0.j,   0.+0.j],
        [ 0.+0.j,   0.+0.j,   0.+0.j],
        [ 0.+0.j,   0.+0.j,   0.+0.j]],
       [[18.+0.j,   0.+0.j,   0.+0.j],
        [ 0.+0.j,   0.+0.j,   0.+0.j],
        [ 0.+0.j,   0.+0.j,   0.+0.j]]])

>>> np.fft.fftn(a, (2, 2), axes=(0, 1))
array([[[ 2.+0.j,  2.+0.j,  2.+0.j], # may vary
        [ 0.+0.j,  0.+0.j,  0.+0.j]],
       [[-2.+0.j, -2.+0.j, -2.+0.j],
        [ 0.+0.j,  0.+0.j,  0.+0.j]]])