pyriemann.geometry.tangentspace.transport_logeuclid¶

pyriemann.geometry.tangentspace.transport_logeuclid(X, A, B)[source]¶

Parallel transport for log-Euclidean metric.

The parallel transport of matrices \(\mathbf{X}\) in tangent space from an initial SPD/HPD matrix \(\mathbf{A}\) to a final SPD/HPD matrix \(\mathbf{B}\) for log-Euclidean metric is given in Table 4 of [1]:

\[\mathbf{X}_\text{new} = [D_{\log \mathbf{B}} \exp] \left( [D_{\mathbf{A}} \log]\left(\mathbf{X}\right) \right)\]

Warning: this function must be applied to matrices \(\mathbf{X}\) already projected in tangent space with a logarithmic map at \(\mathbf{A}\), not to SPD/HPD matrices in manifold.

Parameters:

Xndarray, shape (…, n, n): Symmetric/Hermitian matrices in tangent space at A.
Andarray, shape (n, n): Initial SPD/HPD matrix.
Bndarray, shape (n, n): Final SPD/HPD matrix.

Returns:

X_newndarray, shape (…, n, n): Matrices in tangent space transported from A to B.