dpnp.fft.rfftn

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

Compute the N-dimensional discrete Fourier Transform for real input.

This function computes the N-dimensional discrete Fourier Transform over any number of axes in an M-dimensional real array by means of the Fast Fourier Transform (FFT). By default, all axes are transformed, with the real transform performed over the last axis, while the remaining transforms are complex.

For full documentation refer to numpy.fft.rfftn.

Parameters:

• a ({dpnp.ndarray, usm_ndarray}) -- Input array, taken to be real.

• s ({None, sequence of ints}, optional) --

  Shape (length of each transformed axis) to use from the input. (s[0] refers to axis 0, s[1] to axis 1, etc.). The final element of s corresponds to n for rfft(x, n), while for the remaining axes, it 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 dtype and shape for the last transformation (consistent with the choice of s).

  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. The length of the last axis transformed will be s[-1]//2+1, while the remaining transformed axes will have lengths according to s, or unchanged from the input.

Return type:

dpnp.ndarray of complex dtype

See also

dpnp.fft

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

dpnp.fft.irfftn

The inverse of the N-dimensional FFT of real input.

dpnp.fft.fft

The one-dimensional FFT of general (complex) input.

dpnp.fft.rfft

The one-dimensional FFT of real input.

dpnp.fft.fftn

The N-dimensional FFT.

dpnp.fft.fftn

The two-dimensional FFT.

Notes

The transform for real input is performed over the last transformation axis, as by dpnp.fft.rfft, then the transform over the remaining axes is performed as by dpnp.fft.fftn. The order of the output is as for dpnp.fft.rfft for the final transformation axis, and as for dpnp.fft.fftn for the remaining transformation axes.

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

Examples

>>> import dpnp as np
>>> a = np.ones((2, 2, 2))
>>> np.fft.rfftn(a)
array([[[8.+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]]])

>>> np.fft.rfftn(a, axes=(2, 0))
array([[[4.+0.j,  0.+0.j], # may vary
        [4.+0.j,  0.+0.j]],
       [[0.+0.j,  0.+0.j],
        [0.+0.j,  0.+0.j]]])