spey.helper_functions.covariance_to_correlation

spey.helper_functions.covariance_to_correlation(covariance_matrix: ndarray) → ndarray

Convert covariance matrix into correlation matrix.

Computes \(\rho_{ij} = \Sigma_{ij} / (\sigma_i \sigma_j)\) where \(\sigma_i = \sqrt{\Sigma_{ii}}\) are the per-bin standard deviations.

Parameters:

covariance_matrix (np.ndarray) – A real NxN covariance matrix \(\Sigma\) with strictly positive diagonal entries.

Returns:

Correlation matrix \(\rho\) of shape (N, N).

Return type:

np.ndarray

Example

>>> import numpy as np
>>> from spey.helper_functions import covariance_to_correlation
>>> cov = np.array([[4.0, 2.4], [2.4, 16.0]])
>>> covariance_to_correlation(cov)
array([[1. , 0.3],
       [0.3, 1. ]])