pyriemann.geometry.geodesic.geodesic_wasserstein¶

pyriemann.geometry.geodesic.geodesic_wasserstein(A, B, alpha=0.5)[source]¶

Wasserstein geodesic between SPD/HPD matrices.

The matrix at position \(\alpha\) on the Wasserstein geodesic between two SPD/HPD matrices \(\mathbf{A}\) and \(\mathbf{B}\) is given in [1]:

\[\mathbf{C} = (1-\alpha)^2\mathbf{A} + \alpha^2\mathbf{B} + \alpha(1-\alpha)((\mathbf{AB})^{1/2} + (\mathbf{BA})^{1/2})\]

\(\mathbf{C}\) is equal to \(\mathbf{A}\) if \(\alpha\) = 0, and \(\mathbf{B}\) if \(\alpha\) = 1.

Parameters:

Andarray, shape (…, n, n): First SPD/HPD matrices.
Bndarray, shape (…, n, n): Second SPD/HPD matrices.
alphafloat | ndarray, shape (…,), default=0.5: Position on the geodesic. If ndarray, one value per matrix pair.

Changed in version 0.12.

Returns: