ott.geometry.costs.Bures.covariance_fixpoint_iter

Bures.covariance_fixpoint_iter(covs, weights, tolerance=0.0001, sqrtm_kw=None, **kwargs)

Iterate fix-point updates to compute barycenter of Gaussians.

Parameters:

• covs (Array) – [batch, d^2] covariance matrices

• weights (Array) – simplicial weights (non-negative, sum to 1)

• tolerance (float) – tolerance of the fixed-point procedure. That tolerance is applied to the Frobenius norm (normalized by total size) of two successive iterations of the algorithm

• sqrtm_kw (Optional[Dict[str, Any]]) – keyword arguments for sqrtm()

• kwargs (Any) – keyword arguments for the outer fixed-point iteration

Return type:

Array

Returns:

List containing Weighted Bures average of the covariance matrices, and vector of (normalized) 2-norms of successive differences between iterates, to monitor convergence.