jax.numpy.fft.rfftn

jax.numpy.fft.rfftn(a, s=None, axes=None, norm=None)

Compute a multidimensional discrete Fourier transform of a real-valued array.

JAX implementation of numpy.fft.rfftn().

Parameters:

• 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.

Returns:

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.

Return type:

Array

See also

• jax.numpy.fft.rfft(): Computes a one-dimensional discrete Fourier transform of real-valued array.

• jax.numpy.fft.rfft2(): Computes a two-dimensional discrete Fourier transform of real-valued array.

• jax.numpy.fft.irfftn(): Computes a real-valued multidimensional inverse discrete Fourier transform.

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)