Skip to main content

log_map

Function log_map 

Source
pub fn log_map(base: &[f64], x: &[f64], n: usize) -> Vec<f64>
Expand description

AIRM Riemannian logarithm at base point base: maps the SPD point x to the tangent vector V ∈ T_base whose geodesic reaches x:

  Log_P(X) = P^{1/2} · logm(P^{-1/2} X P^{-1/2}) · P^{1/2}

The arbitrary-base generalisation of logm (which is Log_I, the log-Euclidean tangent at the identity), and the inverse of exp_map. Its AIRM norm equals the geodesic distance, ‖Log_P(X)‖_P = δ_AIRM(P, X). base and x are row-major n×n SPD; the result is symmetric.