spd_learn.functional.geodesic_logchol#

spd_learn.functional.geodesic_logchol(A, B, alpha=0.5)[source]#

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:

  • A (ndarray, shape (..., n, n)) – First SPD/HPD matrices.

  • B (ndarray, shape (..., n, n)) – Second SPD/HPD matrices.

  • alpha (float | ndarray, shape (...,), default=0.5) –

    Position on the geodesic. If ndarray, one value per matrix pair.

    Changed in version 0.12.

Returns:

C – SPD/HPD matrices on the log-Cholesky geodesic.

Return type:

ndarray, shape (…, n, n)

Notes

Added in version 0.7.

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

See also

geodesic

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.