flopscope.

flopscope.numpy.fft.rfftn

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

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

Adapted from NumPy docs np.fft.rfftn

Areafft
Typecustom
NumPy Refnp.fft.rfftn
Cost
5(N/2)⋅⌈log⁡2N⌉5(N/2) \cdot \lceil\log_2 N\rceil
Flopscope Context

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

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.

Parameters

a:array_like

Input array, taken to be real.

s:sequence of ints, optional

Shape (length along 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 any 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.

Changed in version 2.0.

If s is not given, the shape of the input along the axes specified by axes is used.

Deprecated since 2.0.
Deprecated since 2.0.
axes: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.

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:complex ndarray, optional

If provided, the result will be placed in this array. It should be of the appropriate shape and dtype for all axes (and hence is incompatible with passing in all but the trivial s).

Added in version 2.0.0.

Returns

out:complex ndarray

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.

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.

See also

  • irfftn The inverse of rfftn, i.e. the inverse of the n-dimensional FFT of real input.
  • fft The one-dimensional FFT, with definitions and conventions used.
  • rfft The one-dimensional FFT of real input.
  • fftn The n-dimensional FFT.
  • rfft2 The two-dimensional FFT of real input.

Notes

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

See fft for details, definitions and conventions used.

Examples

>>> import flopscope.numpy as fnp
>>> a = flops.ones((2, 2, 2))
>>> flops.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]]])
>>> flops.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]]])