Signal on the Sphere

e3nn_jax.s2_irreps(lmax: int, p_val: int = 1, p_arg: int = -1) → Irreps

The Irreps of coefficients of a spherical harmonics expansion.

\[f(\vec x) = \sum_{l=0}^{L} \sum_{m=-l}^{l} c_l^m Y_{l,m}(\vec x)\]

When the inversion operator is applied to the signal, the new function \(I f\) is given by

\[[I f](\vec x) = p_{\text{val}} f(p_{\text{arg}} \vec x)\]

Parameters:

• lmax (int) – maximum degree of the expansion

• p_val (int) – parity of the value of the signal on the sphere (1 or -1)

• p_arg (int) – parity of the argument of the signal on the sphere (1 or -1)

e3nn_jax.s2_dirac(position: Array | IrrepsArray, lmax: int, *, p_val: int = 1, p_arg: int = -1) → IrrepsArray

Spherical harmonics expansion of a Dirac delta on the sphere.

The integral of the Dirac delta is 1.

Parameters:

• position (jax.Array or IrrepsArray) – position of the delta, shape (3,). It will be normalized to have a norm of 1.

• lmax (int) – maximum degree of the spherical harmonics expansion

• p_val (int) – parity of the value of the signal on the sphere (1 or -1)

• p_arg (int) – parity of the argument of the signal on the sphere (1 or -1)

Returns:

Spherical harmonics coefficients

Return type:

IrrepsArray

Examples:

position = jnp.array([0.0, 0.0, 1.0])

coeffs_3 = e3nn.s2_dirac(position, 3, p_val=1, p_arg=-1)
coeffs_6 = e3nn.s2_dirac(position, 6, p_val=1, p_arg=-1)
coeffs_9 = e3nn.s2_dirac(position, 9, p_val=1, p_arg=-1)