jax.numpy.fft.rfft#

jax.numpy.fft.rfft(a,n=None,axis=-1,norm=None)[source]#

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

JAX implementation ofnumpy.fft.rfft().

Parameters:

• a (ArrayLike) – real-valued input array.

• n (int |None) – int. Specifies the effective dimension of the input alongaxis. If notspecified, it will default to the dimension of input alongaxis.

• axis (int) – int, default=-1. Specifies the axis along which the transform is computed.If not specified, the transform is computed along axis -1.

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

Returns:

An array containing the one-dimensional discrete Fourier transform ofa.The dimension of the array alongaxis is(n/2)+1, ifn is even and(n+1)/2, ifn is odd.

Return type:

Array

See also

• jax.numpy.fft.fft(): Computes a one-dimensional discrete Fouriertransform.

• jax.numpy.fft.irfft(): Computes a one-dimensional inverse discreteFourier transform for real input.

• jax.numpy.fft.rfftn(): Computes a multidimensional discrete Fouriertransform for real input.

• jax.numpy.fft.irfftn(): Computes a multidimensional inverse discreteFourier transform for real input.

Examples

jnp.fft.rfft computes the transform alongaxis-1 by default.

>>>x=jnp.array([[1,3,5],...[2,4,6]])>>>withjnp.printoptions(precision=2,suppress=True):...jnp.fft.rfft(x)Array([[ 9.+0.j  , -3.+1.73j],       [12.+0.j  , -3.+1.73j]], dtype=complex64)

Whenn=5, dimension of the transform along axis -1 will be(5+1)/2=3and dimension along other axes will be the same as that of input.

>>>withjnp.printoptions(precision=2,suppress=True):...jnp.fft.rfft(x,n=5)Array([[ 9.  +0.j  , -2.12-5.79j,  0.12+2.99j],       [12.  +0.j  , -1.62-7.33j,  0.62+3.36j]], dtype=complex64)

Whenn=4 andaxis=0, dimension of the transform alongaxis0 willbe(4/2)+1=3 and dimension along other axes will be same as that of input.

>>>withjnp.printoptions(precision=2,suppress=True):...jnp.fft.rfft(x,n=4,axis=0)Array([[ 3.+0.j,  7.+0.j, 11.+0.j],       [ 1.-2.j,  3.-4.j,  5.-6.j],       [-1.+0.j, -1.+0.j, -1.+0.j]], dtype=complex64)