jax.numpy.fft.irfft2

jax.numpy.fft.irfft2(a, s=None, axes=(-2, -1), norm=None)

Compute a real-valued two-dimensional inverse discrete Fourier transform.

JAX implementation of numpy.fft.irfft2().

Parameters:

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

• s (Shape | None | None) – optional length-2 sequence of integers. Specifies the size of the output in each specified axis. If not specified, the dimension of output along axis axes[1] is 2*(m-1), m is the size of input along axis axes[1] and the dimension along other axes will be the same as that of input.

• 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:

A real-valued array containing the two-dimensional inverse discrete Fourier transform of a.

Return type:

Array

See also

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

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

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

Examples

jnp.fft.irfft2 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]]])
>>> jnp.fft.irfft2(x)
Array([[[ 3.5, -1. ,  0. , -1. ],
        [-0.5,  0. ,  0. ,  0. ]],

       [[ 9.5, -1. ,  0. , -1. ],
        [-0.5,  0. ,  0. ,  0. ]]], dtype=float32)

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

>>> with jnp.printoptions(precision=2, suppress=True):
...   jnp.fft.irfft2(x, s=[3, 3])
Array([[[ 1.89, -0.44, -0.44],
        [ 0.22, -0.78,  0.56],
        [ 0.22,  0.56, -0.78]],

       [[ 5.89, -0.44, -0.44],
        [ 1.22, -1.78,  1.56],
        [ 1.22,  1.56, -1.78]]], dtype=float32)

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

>>> with jnp.printoptions(precision=2, suppress=True):
...   jnp.fft.irfft2(x, s=[2, 3], axes=(0, 1))
Array([[[ 4.67,  6.67,  8.67],
        [-0.33, -0.33, -0.33],
        [-0.33, -0.33, -0.33]],

       [[-3.  , -3.  , -3.  ],
        [ 0.  ,  0.  ,  0.  ],
        [ 0.  ,  0.  ,  0.  ]]], dtype=float32)