pyriemann.geometry.geodesic.geodesic_chol¶

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

Cholesky geodesic between SPD/HPD matrices.

The matrix at position \(\alpha\) on the Cholesky geodesic between two SPD/HPD matrices \(\mathbf{A}\) and \(\mathbf{B}\) is \(\mathbf{C} = \mathbf{L} \mathbf{L}^H\), where \(\mathbf{L}\) is computed as [1]:

\[\mathbf{L} = (1-\alpha) \text{chol}(\mathbf{A}) + \alpha \text{chol}(\mathbf{B})\]

\(\mathbf{C}\) 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:

Cndarray, shape (…, n, n): SPD/HPD matrices on the Cholesky geodesic.