Struct Dual 

pub struct Dual {
    pub re: f64,
    pub eps: f64,
}

A first-order dual number re + eps·ε (ε² = 0). Evaluating f on Dual::var(x) yields f(x) in re and f'(x) in eps.

Fields

re: f64

eps: f64

Implementations

impl Dual

pub fn var(x: f64) -> Self

The active variable x (seed derivative 1).

pub fn constant(c: f64) -> Self

A constant (derivative 0).

pub fn sin(self) -> Self

Sine.

pub fn cos(self) -> Self

Cosine.

pub fn exp(self) -> Self

Exponential.

pub fn ln(self) -> Self

Natural log.

pub fn tanh(self) -> Self

Hyperbolic tangent.

pub fn powf(self, n: f64) -> Self

Real power.

Trait Implementations

impl Add for Dual

type Output = Dual

The resulting type after applying the + operator.

fn add(self, o: Dual) -> Dual

Performs the + operation.

impl Clone for Dual

fn clone(&self) -> Dual

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Dual

impl Debug for Dual

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

Formats the value using the given formatter.

impl Div for Dual

type Output = Dual

The resulting type after applying the / operator.

fn div(self, o: Dual) -> Dual

Performs the / operation.

impl Mul for Dual

type Output = Dual

The resulting type after applying the * operator.

fn mul(self, o: Dual) -> Dual

Performs the * operation.

impl Neg for Dual

type Output = Dual

The resulting type after applying the - operator.

fn neg(self) -> Dual

Performs the unary - operation.

impl Real for Dual

The bridge that makes derivatives of dynamics free: Dual satisfies the generic-scalar contract of ferromotion_core::gendyn, so seeding a dual in any state (q, q̇, q̈) or any inertial parameter (mass, COM, inertia entry) and running RNEA/forward dynamics yields the exact partial derivative in eps — no hand-derived derivative code, no finite-difference truncation error. This is the differentiation engine of gradient-based system identification and calibration.

fn from_f64(v: f64) -> Self

fn sin(self) -> Self

fn cos(self) -> Self

fn sqrt(self) -> Self

fn tanh(self) -> Self

Smooth saturation — used by smoothed Coulomb friction models in calibration.

impl Sub for Dual

type Output = Dual

The resulting type after applying the - operator.

fn sub(self, o: Dual) -> Dual

Performs the - operation.