pyriemann.utils.tangentspace.log_map_logchol

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

Project matrices in tangent space by log-Cholesky logarithmic map.

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

Parameters:

Xndarray, shape (…, n, n)

Matrices in SPD/HPD manifold.

Crefndarray, shape (n, n)

Reference SPD matrix.

Returns:

X_newndarray, shape (…, n, n)

Matrices projected in tangent space.

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.