pyriemann.utils.geodesic.geodesic_riemann¶
- pyriemann.utils.geodesic.geodesic_riemann(A, B, alpha=0.5)¶
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, default=0.5
The position on the geodesic.
- Returns:
- Cndarray, shape (…, n, n)
SPD/HPD matrices on the affine-invariant Riemannian geodesic.