Module phi 

Barrett & Seth 2011 geometric Phi under Gaussian assumption. Phi* = MI(past; future) - max_partition sum MI(past_k; future_k)

Functions

covariance_matrix 🔒

Compute covariance matrix with regularization.

determinant 🔒

Determinant via LU decomposition (in-place, partial pivoting).

gaussian_mi 🔒

Gaussian mutual information: MI(X;Y) = 0.5 * ln(det(Cov_X) * det(Cov_Y) / det(Cov_XY))

phi_star

Compute Phi* for a multi-channel time series. data: [n_channels][n_timesteps], row-major.