jax.numpy.fft.rfft2

jax.numpy.fft.rfft2(a, s=None, axes=(-2, -1), norm=None)

Compute a two-dimensional discrete Fourier transform of a real-valued array.

JAX implementation of numpy.fft.rfft2().

Parameters:

• a (ArrayLike) – real-valued input array. Must have a.ndim >= 2.

• s (Shape | None | None) – optional length-2 sequence of integers. Specifies the effective size of the output along each specified axis. If not specified, it will default to the dimension of input along axes.

• axes (Sequence[int]) – optional length-2 sequence of integers, default=(-2,-1). Specifies the axes along which the transform is computed.

• norm (str | None | None) – string, default=”backward”. The normalization mode. “backward”, “ortho” and “forward” are supported.

Returns:

An array containing the two-dimensional discrete Fourier transform of a. The size of the output along the axis axes[1] is (s[1]/2)+1, if s[1] is even and (s[1]+1)/2, if s[1] is odd. The size of the output along the axis axes[0] is s[0].

Return type:

Array

See also

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

• jax.numpy.fft.rfftn(): Computes a multidimensional discrete Fourier transform of real-valued array.

• jax.numpy.fft.irfft2(): Computes a real-valued two-dimensional inverse discrete Fourier transform.

Examples

jnp.fft.rfft2 computes the transform along the last two axes by default.

>>> x = jnp.array([[[1, 3, 5],
...                 [2, 4, 6]],
...                [[7, 9, 11],
...                 [8, 10, 12]]])
>>> with jnp.printoptions(precision=2, suppress=True):
...   jnp.fft.rfft2(x)
Array([[[21.+0.j  , -6.+3.46j],
        [-3.+0.j  ,  0.+0.j  ]],

       [[57.+0.j  , -6.+3.46j],
        [-3.+0.j  ,  0.+0.j  ]]], dtype=complex64)

When s=[2, 4], dimension of the transform along axis -2 will be 2, along axis -1 will be (4/2)+1) = 3 and dimension along other axes will be the same as that of input.

>>> with jnp.printoptions(precision=2, suppress=True):
...   jnp.fft.rfft2(x, s=[2, 4])
Array([[[21. +0.j, -8. -7.j,  7. +0.j],
        [-3. +0.j,  0. +1.j, -1. +0.j]],

       [[57. +0.j, -8.-19.j, 19. +0.j],
        [-3. +0.j,  0. +1.j, -1. +0.j]]], dtype=complex64)

When s=[3, 5] and axes=(0, 1), shape of the transform along axis 0 will be 3, along axis 1 will be (5+1)/2 = 3 and dimension along other axes will be same as that of input.

>>> with jnp.printoptions(precision=2, suppress=True):
...   jnp.fft.rfft2(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)