Struct Dual 

pub struct Dual {
    pub re: Real,
    pub du: Real,
}

A dual number a + b * ε where ε² = 0.

Dual numbers support forward-mode automatic differentiation: evaluating f(a + 1*ε) gives f(a) + f'(a)*ε.

Fields

re: Real

Real part.

du: Real

Dual (infinitesimal) part.

Implementations

impl Dual

pub fn new(re: Real, du: Real) -> Self

Construct a dual number.

pub fn constant(re: Real) -> Self

Constant (derivative = 0).

pub fn variable(re: Real) -> Self

Variable (derivative = 1).

pub fn sqrt(self) -> Self

Square root: √(a + b*ε) = √a + b/(2√a) * ε.

pub fn sin(self) -> Self

Sine: sin(a + bε) = sin(a) + bcos(a)*ε.

pub fn cos(self) -> Self

Cosine: cos(a + bε) = cos(a) - bsin(a)*ε.

pub fn exp(self) -> Self

Exponential: exp(a + bε) = exp(a) + bexp(a)*ε.

pub fn ln(self) -> Self

Natural log: ln(a + b*ε) = ln(a) + b/a * ε.

pub fn powi(self, n: i32) -> Self

Raise to integer power: (a+bε)^n = a^n + nb*a^{n-1}*ε.

Trait Implementations

impl Add for Dual

type Output = Dual

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self

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 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, rhs: Self) -> Self

Performs the / operation.

impl Mul for Dual

type Output = Dual

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self

Performs the * operation.

impl Neg for Dual

type Output = Dual

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl PartialEq for Dual

fn eq(&self, other: &Dual) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Sub for Dual

type Output = Dual

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self

Performs the - operation.

impl Copy for Dual

impl StructuralPartialEq for Dual