pyriemann.utils.tangentspace.exp_map_logchol

pyriemann.utils.tangentspace.exp_map_logchol(X, Cref)

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:

Xndarray, shape (…, n, n)

Matrices in tangent space.

Crefndarray, shape (n, n)

Reference SPD/HPD matrix.

Returns:

X_originalndarray, shape (…, n, n)

Matrices in SPD/HPD manifold.

Notes

Added in version 0.7.

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.