pyriemann.utils.tangentspace.log_map_riemann¶
- pyriemann.utils.tangentspace.log_map_riemann(X, Cref, C12=False)¶
Project matrices in tangent space by Riemannian logarithmic map.
The projection of a matrix \(\mathbf{X}\) from SPD/HPD manifold to tangent space by Riemannian logarithmic map according to a SPD/HPD reference matrix \(\mathbf{C}_\text{ref}\) is:
\[\mathbf{X}_\text{new} = \log ( \mathbf{C}_\text{ref}^{-1/2} \mathbf{X} \mathbf{C}_\text{ref}^{-1/2})\]When C12=True, it returns the full Riemannian logarithmic map:
\[\mathbf{X}_\text{new} = \mathbf{C}_\text{ref}^{1/2} \log( \mathbf{C}_\text{ref}^{-1/2} \mathbf{X} \mathbf{C}_\text{ref}^{-1/2}) \mathbf{C}_\text{ref}^{1/2}\]- Parameters:
- Xndarray, shape (…, n, n)
Matrices in SPD/HPD manidold.
- Crefndarray, shape (n, n)
The reference SPD/HPD matrix.
- C12bool, default=False
If True, it returns the full Riemannian logarithmic map.
- Returns:
- X_newndarray, shape (…, n, n)
Matrices projected in tangent space.
Notes
New in version 0.4.