pyriemann.geometry.geodesic.geodesic_logchol

pyriemann.geometry.geodesic.geodesic_logchol(A, B, alpha=0.5)

Log-Cholesky geodesic between SPD/HPD matrices.

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

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 log-Cholesky geodesic.

See also

geodesic

Notes

Added in version 0.7.

Changed in version 0.12: Add support for NumPy and PyTorch. Add support for array-valued alpha.

References

[1]

Riemannian geometry of symmetric positive definite matrices via Cholesky decomposition Z. Lin. SIAM J Matrix Anal Appl, 2019, 40(4), pp. 1353-1370.