spd_learn.functional.exp_map_logchol#

spd_learn.functional.exp_map_logchol(X, Cref, **kwargs)[source]#

Project matrices back to manifold by log-Cholesky exponential map.

The projection of a matrix \(\mathbf{X}\) from tangent space to SPD/HPD manifold with log-Cholesky exponential map, see Table 2 of [1].

Parameters:

  • X (ndarray, shape (..., n, n)) – Matrices in tangent space.

  • Cref (ndarray, shape (n, n)) – Reference SPD/HPD matrix.

Returns:

X_original – Matrices in SPD/HPD manifold.

Return type:

ndarray, shape (…, n, n)

Notes

Added in version 0.7.

Changed in version 0.12: Add support for NumPy and PyTorch.

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.