Function karcher_mean 

pub fn karcher_mean(
    data: &FdMatrix,
    argvals: &[f64],
    max_iter: usize,
    tol: f64,
    lambda: f64,
) -> KarcherMeanResult

Compute the Karcher (Frechet) mean in the elastic metric.

Iteratively aligns all curves to the current mean estimate in SRSF space, computes the pointwise mean of aligned SRSFs, and reconstructs the mean curve.

Arguments

• data — Functional data matrix (n × m)
• argvals — Evaluation points (length m)
• max_iter — Maximum number of iterations
• tol — Convergence tolerance for the SRSF mean

Returns

KarcherMeanResult with mean curve, warping functions, aligned data, and convergence info.

Examples

use fdars_core::simulation::{sim_fundata, EFunType, EValType};
use fdars_core::alignment::karcher_mean;

let t: Vec<f64> = (0..50).map(|i| i as f64 / 49.0).collect();
let data = sim_fundata(20, &t, 3, EFunType::Fourier, EValType::Exponential, Some(42));

let result = karcher_mean(&data, &t, 20, 1e-4, 0.0);
assert_eq!(result.mean.len(), 50);
assert!(result.n_iter <= 20);