Function levenberg_marquardt 

pub(crate) fn levenberg_marquardt<F>(
    start: &[f64],
    evaluate: F,
    tolerance: SolveTolerance,
    cap: usize,
) -> Result<Fitted, FitFailure>
where
    F: FnMut(&[f64]) -> (Vec<f64>, Vec<Vec<f64>>),

Levenberg-Marquardt over a parameter vector.

Converged by any of four tests: the residual norm below the tolerance, the gradient orthogonal to the residual (GRADIENT_TOLERANCE), a step below the parameters’ last digit, or an accepted step that stopped improving.

evaluate returns the residual vector and its Jacobian at one parameter point — together, because the caller obtains both from one seeded pass and splitting them would double the work. jacobian[i][j] is ∂rᵢ/∂paramⱼ.

The step solves the damped normal equations (JᵀJ + λI)δ = −Jᵀr. Damping falls when a step improves the residual norm and rises when it does not, which is what makes the method fall back toward gradient descent where Gauss-Newton would overshoot.

Errors

FitFailure::Unconverged at the cap, FitFailure::Singular when no damping makes the normal equations invertible.