pyriemann.utils.distance.distance_logchol¶

pyriemann.utils.distance.distance_logchol(A, B, squared=False)¶

Log-Cholesky distance between SPD/HPD matrices.

The log-Cholesky distance between two SPD/HPD matrices \(\mathbf{A}\) and \(\mathbf{B}\) is [1]:

\[d(\mathbf{A},\mathbf{B}) = \left( \Vert \text{lower}(\text{chol}(\mathbf{A})) - \text{lower}(\text{chol}(\mathbf{B})) \Vert_F^2 + \Vert \log(\text{diag}(\text{chol}(\mathbf{A}))) - \log(\text{diag}(\text{chol}(\mathbf{B}))) \Vert_F^2 \right)^\frac{1}{2}\]

Parameters:

Andarray, shape (…, n, n): First SPD/HPD matrices, at least 2D ndarray.
Bndarray, shape (…, n, n): Second SPD/HPD matrices, same dimensions as A.
squaredbool, default=False: Return squared distance.

Returns:

dfloat or ndarray, shape (…,): Log-Cholesky distance between A and B.