pyriemann.utils.geodesic.geodesic_chol

pyriemann.utils.geodesic.geodesic_chol(A, B, alpha=0.5)

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, default=0.5

Position on the geodesic.

Returns:

Cndarray, shape (…, n, n)

SPD/HPD matrices on the Cholesky geodesic.

See also

geodesic

Notes

..versionadded:: 0.10

References

[1]

Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging I.L. Dryden, A. Koloydenko, D. Zhou. Ann Appl Stat, 2009, 3(3), pp. 1102-1123.