flopscope.

flopscope.numpy.fft.fftn

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

Compute the N-dimensional discrete Fourier Transform.

Adapted from NumPy docs np.fft.fftn

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

N-D complex FFT. Cost: 5*N*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 array by means of the Fast Fourier Transform (FFT).

Parameters

a:array_like

Input array, can be complex.

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.). This 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. Repeated indices in axes means that the 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: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.

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

  • flops.fft Overall view of discrete Fourier transforms, with definitions and conventions used.
  • ifftn The inverse of fftn, the inverse n-dimensional FFT.
  • fft The one-dimensional FFT, with definitions and conventions used.
  • rfftn The n-dimensional FFT of real input.
  • fft2 The two-dimensional FFT.
  • fftshift Shifts zero-frequency terms to centre of array

Notes

The output, analogously to fft, contains the term for zero frequency in the low-order corner of all axes, the positive frequency terms in the first half of all axes, the term for the Nyquist frequency in the middle of all axes and the negative frequency terms in the second half of all axes, in order of decreasingly negative frequency.

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

Examples

>>> import flopscope.numpy as fnp
>>> a = flops.mgrid[:3, :3, :3][0]
>>> flops.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]]])
>>> flops.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]]])
>>> import matplotlib.pyplot as plt
>>> [X, Y] = flops.meshgrid(2 * flops.pi * flops.arange(200) / 12,
... 2 * flops.pi * flops.arange(200) / 34)
>>> S = flops.sin(X) + flops.cos(Y) + flops.random.uniform(0, 1, X.shape)
>>> FS = flops.fft.fftn(S)
>>> plt.imshow(flops.log(flops.abs(flops.fft.fftshift(FS))**2))
<matplotlib.image.AxesImage object at 0x...>
>>> plt.show()