riecovest.distance.frob_gevd_weighted_fullrank

riecovest.distance.frob_gevd_weighted_fullrank(A, B)

The frobenious distance between A and B, weighted by the generalized eigenvectors.

Defined by $lVert W (A - B) W^H rVert_F$, where $W$ is the matrix of eigenvectors of the generalized eigenvalue decomposition of $A$ and $B$.

Parameters:

• A (ndarray of shape (M, M)) – Positive semi-definite matrix

• B (ndarray of shape (M, M)) – Positive definite matrix

Returns:

distance – The distance between A and B in weighted Frobenius distance

Return type:

float

Notes

The defintion of the eigenvector matrix is in terms of the simultaneous diagonalization of $A$ and $B$. $A = W Sigma W^H$ $B = W W^H$