Characteristic roots

Root equations and numerical solution of the characteristic spectrum.

Characteristic roots for the analytical unsaturated solution.

characteristic_equation

characteristic_equation(root: float, alpha_depth: float) -> float

Evaluate the pole-free rewrite of Baum et al. (2010), Eq. (6): sin(alpha_depthr) + 2rcos(alpha_depthr), where alpha_depth = a*z_w0.

compute_roots(transformed_alpha: float, depth: float, n_roots: int, *, eps: float = 1e-10) -> np.ndarray

Compute characteristic roots for the analytical series.