spd_learn.functional.exp_map_lsm

spd_learn.functional.exp_map_lsm(X: Tensor) → Tensor

Log-Scaled Metric (LSM) exponential map [Hu et al., 2025].

Maps a hollow symmetric matrix \(X \in \text{Hol}(\mathcal{S}^n)\) to the correlation manifold \(\mathcal{C}_{++}^n\):

\[\Phi_{\text{LSM}}^{-1}(X) = \text{cov\_to\_corr}(\exp(\text{off\_diag}(X)))\]

Parameters:

X (torch.Tensor) – Hollow symmetric tangent matrix of shape (…, n, n).

Returns:

Correlation matrix with unit diagonal, shape (…, n, n).

Return type:

torch.Tensor