Struct Dual 

pub struct Dual {
    pub v: f64,
    pub dv: f64,
}

A dual number (v, dv) representing a value and its first derivative.

All arithmetic operators and elementary functions implement the standard chain-rule so that derivatives propagate automatically.

Fields

v: f64

Primal (real) value.

dv: f64

Derivative (dual) component.

Implementations

impl Dual

pub fn constant(c: f64) -> Self

Create a dual number representing the constant c (derivative = 0).

pub fn variable(x: f64) -> Self

Create a dual number representing the variable x with seed dx = 1.

pub fn sin(self) -> Self

Sine with chain rule: sin(u)' = cos(u) * u'.

pub fn cos(self) -> Self

Cosine with chain rule: cos(u)' = -sin(u) * u'.

pub fn exp(self) -> Self

Natural exponential with chain rule: exp(u)' = exp(u) * u'.

pub fn ln(self) -> Self

Natural logarithm with chain rule: ln(u)' = u'/u.

pub fn sqrt(self) -> Self

Square root with chain rule: sqrt(u)' = u' / (2 * sqrt(u)).

pub fn abs(self) -> Self

Absolute value with (sub)derivative: |u|' = sign(u) * u'.

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

Integer power with chain rule: u^n' = n * u^(n-1) * u'.

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

Floating-point power: u^p' = p * u^(p-1) * u'.

pub fn tan(self) -> Self

Tangent: tan(u)' = u' / cos²(u).

pub fn sinh(self) -> Self

Hyperbolic sine: sinh(u)' = cosh(u) * u'.

pub fn cosh(self) -> Self

Hyperbolic cosine: cosh(u)' = sinh(u) * u'.

Trait Implementations

impl Add<Dual> for f64

type Output = Dual

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<f64> for Dual

type Output = Dual

The resulting type after applying the + operator.

fn add(self, rhs: f64) -> Self

Performs the + operation.

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<f64> for Dual

type Output = Dual

The resulting type after applying the / operator.

fn div(self, rhs: f64) -> Self

Performs the / operation.

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<Dual> for f64

type Output = Dual

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<f64> for Dual

type Output = Dual

The resulting type after applying the * operator.

fn mul(self, rhs: f64) -> 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<Dual> for f64

type Output = Dual

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<f64> for Dual

type Output = Dual

The resulting type after applying the - operator.

fn sub(self, rhs: f64) -> Self

Performs the - operation.

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