pyriemann.geometry.geodesic.geodesic_riemann¶

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

Affine-invariant Riemannian geodesic between SPD/HPD matrices.

The matrix at position \(\alpha\) on the affine-invariant Riemannian geodesic between two SPD/HPD matrices \(\mathbf{A}\) and \(\mathbf{B}\) is:

\[\mathbf{C} = \mathbf{A}^{1/2} \left( \mathbf{A}^{-1/2} \mathbf{B} \mathbf{A}^{-1/2} \right)^\alpha \mathbf{A}^{1/2}\]

\(\mathbf{C}\) 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:

Cndarray, shape (…, n, n): SPD/HPD matrices on the affine-invariant Riemannian geodesic.