dpnp.fft.irfftn

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

Computes the inverse of dpnp.fft.rfftn.

This function computes the inverse of the N-dimensional discrete Fourier Transform for real input over any number of axes in an M-dimensional array by means of the Fast Fourier Transform (FFT). In other words, irfftn(rfftn(a), a.shape) == a to within numerical accuracy. (The a.shape is necessary like len(a) is for dpnp.fft.irfft, and for the same reason.)

The input should be ordered in the same way as is returned by dpnp.fft.rfftn, i.e. as for dpnp.fft.irfft for the final transformation axis, and as for dpnp.fft.irfftn along all the other axes.

For full documentation refer to numpy.fft.irfftn.

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.). s is also the number of input points used along this axis, except for the last axis, where s[-1]//2+1 points of the input are used. 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. Except for the last axis which is taken to be 2*(m-1) where m is the length of the input along that axis. If s is not None, axes must not be None 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}, 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 each transformed axis is as given by the corresponding element of s, or the length of the input in every axis except for the last one if s is not given. In the final transformed axis the length of the output when s is not given is 2*(m-1) where m is the length of the final transformed axis of the input. To get an odd number of output points in the final axis, s must be specified.

Return type:

dpnp.ndarray

See also

dpnp.fft

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

dpnp.fft.rfftn

The n-dimensional FFT of real input.

dpnp.fft.fft

The one-dimensional FFT, with definitions and conventions used.

dpnp.fft.irfft

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

dpnp.fft.irfft2

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

Notes

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

See dpnp.fft.rfft for definitions and conventions used for real input.

The correct interpretation of the Hermitian input depends on the shape of the original data, as given by s. This is because each input shape could correspond to either an odd or even length signal. By default, dpnp.fft.irfftn assumes an even output length which puts the last entry at the Nyquist frequency; aliasing with its symmetric counterpart. When performing the final complex to real transform, the last value is thus treated as purely real. To avoid losing information, the correct shape of the real input must be given.

Examples

>>> import dpnp as np
>>> a = np.zeros((3, 2, 2))
>>> a[0, 0, 0] = 3 * 2 * 2
>>> np.fft.irfftn(a)
array([[[1.,  1.],
        [1.,  1.]],
       [[1.,  1.],
        [1.,  1.]],
       [[1.,  1.],
        [1.,  1.]]])