pyriemann.utils.tangentspace.exp_map_riemann¶
- pyriemann.utils.tangentspace.exp_map_riemann(X, Cref, Cm12=False)¶
Project matrices back to manifold by Riemannian exponential map.
The projection of a matrix \(\mathbf{X}\) from tangent space to SPD/HPD manifold with Riemannian exponential map according to a reference SPD/HPD matrix \(\mathbf{C}_\text{ref}\) is:
\[\mathbf{X}_\text{original} = \mathbf{C}_\text{ref}^{1/2} \exp(\mathbf{X}) \mathbf{C}_\text{ref}^{1/2}\]When Cm12=True, it returns the full Riemannian exponential map:
\[\mathbf{X}_\text{original} = \mathbf{C}_\text{ref}^{1/2} \exp( \mathbf{C}_\text{ref}^{-1/2} \mathbf{X} \mathbf{C}_\text{ref}^{-1/2}) \mathbf{C}_\text{ref}^{1/2}\]- Parameters:
- Xndarray, shape (…, n, n)
Matrices in tangent space.
- Crefndarray, shape (n, n)
The reference SPD/HPD matrix.
- Cm12bool, default=False
If True, it returns the full Riemannian exponential map.
- Returns:
- X_originalndarray, shape (…, n, n)
Matrices in SPD/HPD manifold.
Notes
New in version 0.4.