Helper Functions#

Configuration Functions#
Function Name	Description
`run_config()`	Generates and caches all precomputed arrays.

Statistics Functions#
Function Name	Description
`compute_mean_variance()`	Computes the mean and variance of spherical harmonic coefficients \(f_{\ell m}\).
`normalize_map()`	Normalises a spherical map to zero mean and unit variance.
`compute_C01_and_C11()`	Stand alone function to compute the fourth and sixth order covariance statistics.
`add_to_S1()`	Computes and appends the mean field statistic \(\text{S1}_j = \langle \|\Psi^\lambda f\| \rangle\) at scale \(j\).
`add_to_P00()`	Computes and appends the second order power statistic \(\text{P00}_j = \langle \|\Psi^\lambda f\|^2 \rangle\) at scale \(j\).
`add_to_C01()`	Computes and appends the fourth order covariance statistic \(\text{C01}_j = \text{Cov}\big [ \Psi^{\lambda_1} f, \Psi^{\lambda_1} \| \Psi^{\lambda_2} f \| \big ]\) at scale \(j\).
`add_to_C11()`	Computes and appends the sixth order covariance statistic \(\text{C11}_j = \text{Cov}\big [ \Psi^{\lambda_1} \| \Psi^{\lambda_3} f \|, \Psi^{\lambda_1} \| \Psi^{\lambda_2} f \| \big ]\) at scale \(j\).

Statistical Normalisation Functions#
Function Name	Description
`compute_norm()`	Computes normalisation for the scattering covariance statistics.
`apply_norm()`	Applies normalisation to a complete list of covariance statistics.

Reindexing Functions#
Function Name	Description
`nested_list_to_list_of_arrays()`	Specific reindexing function which switches covariance wavelet scale list ordering.
`list_to_array()`	Converts list of covariance statistics to array of statistics for e.g. Loss functions.