Compute a multidimensional discrete Fourier transform of a real-valued array.
JAX implementation of numpy.fft.rfftn().
a (ArrayLike) – real-valued input array.
s (Shape | None | None) – optional sequence of integers. Controls the effective size of the input along each specified axis. If not specified, it will default to the dimension of input along axes.
axes (Sequence[int] | None | None) – optional sequence of integers, default=None. Specifies the axes along which the transform is computed. If not specified, the transform is computed along the last len(s) axes. If neither axes nor s is specified, the transform is computed along all the axes.
norm (str | None | None) – string, default=”backward”. The normalization mode. “backward”, “ortho” and “forward” are supported.
An array containing the multidimensional discrete Fourier transform of a having size specified in s along the axes axes except along the axis axes[-1]. The size of the output along the axis axes[-1] is s[-1]//2+1.
Examples
>>> x = jnp.array([[[1, 3, 5],
... [2, 4, 6]],
... [[7, 9, 11],
... [8, 10, 12]]])
>>> with jnp.printoptions(precision=2, suppress=True):
... jnp.fft.rfftn(x)
Array([[[ 78.+0.j , -12.+6.93j],
[ -6.+0.j , 0.+0.j ]],
[[-36.+0.j , 0.+0.j ],
[ 0.+0.j , 0.+0.j ]]], dtype=complex64)
When s=[3, 3, 4], size of the transform along axes (-3, -2) will be (3, 3), and along axis -1 will be 4//2+1 = 3 and size along other axes will be the same as that of input.
>>> with jnp.printoptions(precision=2, suppress=True):
... jnp.fft.rfftn(x, s=[3, 3, 4])
Array([[[ 78. +0.j , -16. -26.j , 26. +0.j ],
[ 15. -36.37j, -16.12 +1.93j, 5. -12.12j],
[ 15. +36.37j, 8.12-11.93j, 5. +12.12j]],
[[ -7.5 -49.36j, -20.45 +9.43j, -2.5 -16.45j],
[-25.5 -7.79j, -0.6 +11.96j, -8.5 -2.6j ],
[ 19.5 -12.99j, -8.33 -6.5j , 6.5 -4.33j]],
[[ -7.5 +49.36j, 12.45 -4.43j, -2.5 +16.45j],
[ 19.5 +12.99j, 0.33 -6.5j , 6.5 +4.33j],
[-25.5 +7.79j, 4.6 +5.04j, -8.5 +2.6j ]]], dtype=complex64)
When s=[3, 5] and axes=(0, 1), size of the transform along axis 0 will be 3, along axis 1 will be 5//2+1 = 3 and dimension along other axes will be same as that of input.
>>> with jnp.printoptions(precision=2, suppress=True):
... jnp.fft.rfftn(x, s=[3, 5], axes=[0, 1])
Array([[[ 18. +0.j , 26. +0.j , 34. +0.j ],
[ 11.09 -9.51j, 16.33-13.31j, 21.56-17.12j],
[ -0.09 -5.88j, 0.67 -8.23j, 1.44-10.58j]],
[[ -4.5 -12.99j, -2.5 -16.45j, -0.5 -19.92j],
[ -9.71 -6.3j , -10.05 -9.52j, -10.38-12.74j],
[ -4.95 +0.72j, -5.78 -0.2j , -6.61 -1.12j]],
[[ -4.5 +12.99j, -2.5 +16.45j, -0.5 +19.92j],
[ 3.47+10.11j, 6.43+11.42j, 9.38+12.74j],
[ 3.19 +1.63j, 4.4 +1.38j, 5.61 +1.12j]]], dtype=complex64)
For 1-D input:
>>> x1 = jnp.array([1, 2, 3, 4]) >>> jnp.fft.rfftn(x1) Array([10.+0.j, -2.+2.j, -2.+0.j], dtype=complex64)
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