flopscope.numpy.fft.irfftn

fnp.fft.irfftn(a, s=None, axes=None, norm=None, out=None)[flopscope source][numpy source]

Computes the inverse of `rfftn`.

Adapted from NumPy docs np.fft.irfftn

Areafft

Typecustom

Cost

5(N/2) \cdot \lceil\log_2 N\rceil

Flopscope Context

Inverse N-D real FFT. Cost: 5*(N//2)*ceil(log2(N)), N=prod(s) (Cooley-Tukey radix-2; Van Loan 1992 §1.4).

Computes the inverse of 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 irfft, and for the same reason.)

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

Parameters

a:array_like

Input array.

s: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 any axis, if the shape indicated by s is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros.

Changed in version 2.0.

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.

Deprecated since 2.0.

axes: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 inverse transform over that axis is performed multiple times.

Deprecated since 2.0.

norm:{"backward", "ortho", "forward"}, optional

Normalization mode (see flops.fft). Default is "backward". Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor.

Added in version 1.20.0.

out:ndarray, optional

If provided, the result will be placed in this array. It should be of the appropriate shape and dtype for the last transformation.

Added in version 2.0.0.

Returns

out:ndarray: The truncated or zero-padded input, transformed along the axes indicated by axes, or by a combination of s or 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.

Raises

:ValueError: If s and axes have different length.
:IndexError: If an element of axes is larger than than the number of axes of a.

Notes

See fft for definitions and conventions used.

See 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, 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 flopscope.numpy as fnp
>>> a = flops.zeros((3, 2, 2))
>>> a[0, 0, 0] = 3 * 2 * 2
>>> flops.fft.irfftn(a)
array([[[1.,  1.],
        [1.,  1.]],
       [[1.,  1.],
        [1.,  1.]],
       [[1.,  1.],
        [1.,  1.]]])