Struct Dual 

pub struct Dual { /* private fields */ }

Dual number for forward-mode automatic differentiation

A dual number is of the form a + b*ε where ε² = 0. This allows us to compute both function values and derivatives simultaneously.

Implementations

impl Dual

pub fn new(value: f64, derivative: f64) -> Self

Create a new dual number

pub fn constant(value: f64) -> Self

Create a dual number representing a constant (derivative = 0)

pub fn variable(value: f64) -> Self

Create a dual number representing a variable (derivative = 1)

pub fn value(self) -> f64

Get the real part (function value)

pub fn derivative(self) -> f64

Get the dual part (derivative)

pub fn sin(self) -> Self

Compute sine of dual number

pub fn cos(self) -> Self

Compute cosine of dual number

pub fn tan(self) -> Self

Compute tangent of dual number

pub fn exp(self) -> Self

Compute exponential of dual number

pub fn ln(self) -> Self

Compute natural logarithm of dual number

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

Compute power of dual number (self^n)

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

Compute power of dual number (self^p) where p is real

pub fn sqrt(self) -> Self

Compute square root of dual number

pub fn abs(self) -> Self

Compute absolute value of dual number

pub fn max(self, other: Self) -> Self

Compute maximum of two dual numbers

pub fn min(self, other: Self) -> Self

Compute minimum of two dual numbers

Trait Implementations

impl Add<Dual> for f64

type Output = Dual

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<f64> for Dual

type Output = Dual

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add for Dual

type Output = Dual

The resulting type after applying the + operator.

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

Performs the + operation.

impl<F> AutoDiffFunction<Dual> for FunctionWrapper<F>

where F: Fn(&ArrayView1<'_, f64>) -> f64 + Clone,

fn eval(&self, x: &[Dual]) -> Dual

Evaluate the function with AD variables

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<Dual> for f64

type Output = Dual

The resulting type after applying the / operator.

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

Performs the / operation.

impl Div<f64> for Dual

type Output = Dual

The resulting type after applying the / operator.

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

Performs the / operation.

impl Div for Dual

type Output = Dual

The resulting type after applying the / operator.

fn div(self, other: Self) -> Self

Performs the / operation.

impl DualNumber for Dual

fn value(self) -> f64

Get the value part

fn derivative(self) -> f64

Get the derivative part

fn new(value: f64, derivative: f64) -> Self

Create from value and derivative

fn constant(value: f64) -> Self

Create constant (derivative = 0)

fn variable(value: f64) -> Self

Create variable (derivative = 1)

impl From<Dual> for f64

fn from(dual: Dual) -> Self

Converts to this type from the input type.

impl From<f64> for Dual

fn from(value: f64) -> Self

Converts to this type from the input type.

impl Mul<Dual> for f64

type Output = Dual

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<f64> for Dual

type Output = Dual

The resulting type after applying the * operator.

fn mul(self, scalar: f64) -> Self

Performs the * operation.

impl Mul for Dual

type Output = Dual

The resulting type after applying the * operator.

fn mul(self, other: 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: &Self) -> 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 PartialOrd for Dual

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl Sub<Dual> for f64

type Output = Dual

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<f64> for Dual

type Output = Dual

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub for Dual

type Output = Dual

The resulting type after applying the - operator.

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

Performs the - operation.

impl Copy for Dual