jax.numpy.fft.irfftn

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

Compute a real-valued multidimensional inverse discrete Fourier transform.

JAX implementation of numpy.fft.irfftn().

Parameters:

• a (ArrayLike) – input array.

• s (Shape | None) – optional 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] | 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) – string, default=”backward”. The normalization mode. “backward”, “ortho” and “forward” are supported.

Returns:

A real-valued array containing the multidimensional inverse discrete Fourier transform of a with size s along specified axes, and the same as the input along other axes.

Return type:

Array

See also

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

Examples

jnp.fft.irfftn computes the transform along all the axes by default.

>>> x = jnp.array([[[1, 3, 5],
...                 [2, 4, 6]],
...                [[7, 9, 11],
...                 [8, 10, 12]]])
>>> jnp.fft.irfftn(x)
Array([[[ 6.5, -1. ,  0. , -1. ],
        [-0.5,  0. ,  0. ,  0. ]],

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

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

>>> with jnp.printoptions(precision=2, suppress=True):
...   jnp.fft.irfftn(x, s=[3, 4])
Array([[[ 2.33, -0.67,  0.  , -0.67],
        [ 0.33, -0.74,  0.  ,  0.41],
        [ 0.33,  0.41,  0.  , -0.74]],

       [[ 6.33, -0.67,  0.  , -0.67],
        [ 1.33, -1.61,  0.  ,  1.28],
        [ 1.33,  1.28,  0.  , -1.61]]], dtype=float32)

When s=[3] and axes=[0], size of the transform along axes 0 will be 3 and dimension along other axes will be same as that of input.

>>> with jnp.printoptions(precision=2, suppress=True):
...   jnp.fft.irfftn(x, s=[3], axes=[0])
Array([[[ 5.,  7.,  9.],
        [ 6.,  8., 10.]],

       [[-2., -2., -2.],
        [-2., -2., -2.]],

       [[-2., -2., -2.],
        [-2., -2., -2.]]], dtype=float32)