Struct LameFunctionExt 

pub struct LameFunctionExt {
    pub h2: f64,
    pub k2: f64,
    pub degree: usize,
    pub species: usize,
    pub config: LameConfig,
    /* private fields */
}

Lamé function struct for computing ellipsoidal harmonics E_n^m(s).

Encapsulates the configuration and ellipsoid parameters for repeated evaluations.

Fields

h2: f64

Ellipsoid parameter h² = a² - b²

k2: f64

Ellipsoid parameter k² = a² - c²

degree: usize

Degree n

species: usize

Species index m (1-indexed: 1 to 2n+1)

config: LameConfig

Configuration

Implementations

impl LameFunction

pub fn new( h2: f64, k2: f64, degree: usize, species: usize, config: LameConfig, ) -> Result<LameFunction, SpecialError>

Create a new LameFunction for degree n and species m.

Arguments

• h2 - Parameter h² = a² - b² (must be non-negative)
• k2 - Parameter k² = a² - c² (must be >= h²)
• degree - Degree n (0 to 8)
• species - Species index m (1 to 2n+1)
• config - Configuration

Returns

A new LameFunction or an error if parameters are invalid.

pub fn compute_eigenvalue(&mut self) -> Result<f64, SpecialError>

Compute the eigenvalue h (separation parameter) for this Lamé function.

Uses continued fraction / bisection for the eigenvalue of Bôcher’s equation.

pub fn evaluate(&mut self, s: f64) -> Result<LameResult, SpecialError>

Evaluate E_n^m(s) at the given coordinate s.

For Bôcher’s equation, s is related to the ellipsoidal coordinate via s = a² - rho² (or similarly for mu, nu coordinates).

Arguments

• s - The ellipsoidal coordinate value

Returns

The value of E_n^m(s) and associated metadata.

Trait Implementations

impl Clone for LameFunction

fn clone(&self) -> LameFunction

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for LameFunction

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.