Normalisation#

s2scat.utility.normalisation.apply_norm(S1: List[float64], P00: List[float64], C01: List[float64], C11: List[float64], norm: List[Array], J_min: int, J_max: int) → Tuple[List[Array]]#

Applies multi-scale normalisation to the scattering covariances.

Parameters:

  • S1 (List[jnp.float64]) – Mean field statistic \(\langle |\Psi^\lambda f| \rangle\).

  • P00 (List[jnp.float64]) – Second order power statistic \(\langle |\Psi^\lambda f|^2 \rangle\).

  • C01 (List[jnp.float64]) – Fourth order covariance statistic \(\text{Cov}\big [ \Psi^{\lambda_1} f, \Psi^{\lambda_1} | \Psi^{\lambda_2} f | \big ]\).

  • C11 (List[jnp.float64]) – Sixth order covariance statistic \(\text{Cov}\big [ \Psi^{\lambda_1} | \Psi^{\lambda_3} f |, \Psi^{\lambda_1} | \Psi^{\lambda_2} f | \big ]\).

  • norm (List[jnp.ndarray]) – Multiscale normalisation factors for given signal.

  • J_min (int) – Minimum dyadic wavelet scale to consider.

  • J_max (int) – Maximum dyadic wavelet scale to consider.

Returns:

Tuple of normalised scattering covariance statistics.

Return type:

Tuple[List[jnp.ndarray]]

s2scat.utility.normalisation.compute_norm(flm: Array, L: int, N: int, J_min: int = 0, reality: bool = False, config: List[Array] = None, recursive: bool = True) → List[Array]#

Compute multi-scale normalisation for the scattering covariances.

Parameters:

  • flm (jnp.ndarray) – Spherical harmonic coefficients.

  • L (int) – Spherical harmonic bandlimit.

  • N (int) – Azimuthal bandlimit (directionality).

  • J_min (int, optional) – Minimum dyadic wavelet scale to consider. Defaults to 0.

  • reality (bool, optional) – Whether \(f \in \mathbb{R}\), if True exploits hermitian symmetry of harmonic coefficients. Defaults to False.

  • config (List[jnp.ndarray], optional) – All necessary precomputed arrays. Defaults to None.

  • recursive (bool, optional) – Whether to perform a memory efficient recursive transform, or a faster but less memory efficient fully precompute transform. Defaults to True.

Raises:

ValueError – If one does not pass configuration arrays.

Returns:

Normalisation for the scattering covariance statistics.

Return type:

Tuple[jnp.ndarray]