Struct Dual 

pub struct Dual {
    pub value: f64,
    pub tangent: f64,
}

A forward-mode dual number: a value (primal) paired with a tangent (directional derivative).

Running a computation written against Scalar on Dual propagates the derivative through every operation via the chain rule. Seed an input’s tangent to 1.0 with Dual::seed, then extract the (value, derivative) pair.

Both PartialEq and PartialOrd compare the value (primal) field only, so equality and ordering agree on the “primal decides control flow” semantics (see the module-level docs). Two Duals with equal value but different tangents therefore compare equal and unordered-as-Equal; this keeps a == b ⟺ a.partial_cmp(&b) == Some(Equal) — the std contract that a derived (both-field) PartialEq would violate against the value-only PartialOrd.

Fields

value: f64

The primal value of the computation.

tangent: f64

The tangent (directional derivative) accumulated by the chain rule.

Implementations

impl Dual

pub fn seed(value: f64) -> Self

Seed an independent variable: value = x, tangent = 1.0.

Use this on the input you are differentiating with respect to.

pub fn constant(value: f64) -> Self

A constant: value = x, tangent = 0.0 (no gradient flows through it).

pub fn extract(self) -> (f64, f64)

Extract the (value, derivative) pair after a computation.

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 AddAssign for Dual

fn add_assign(&mut self, rhs: 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 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, 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 MulAssign for Dual

fn mul_assign(&mut self, rhs: 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

Equality operator ==.

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

Inequality operator !=.

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 Scalar for Dual

fn zero() -> Self

The additive identity (0).

fn one() -> Self

The multiplicative identity (1).

fn from_f64(v: f64) -> Self

Construct a constant from an f64 (tangent 0 for Dual).

fn infinity() -> Self

Positive infinity sentinel (used e.g. for DP recurrence initialization).

fn sqrt(self) -> Self

Square root. Requires a non-negative value; the derivative diverges at 0.

fn exp(self) -> Self

Natural exponential.

fn ln(self) -> Self

Natural logarithm. Requires a strictly positive value.

fn sin(self) -> Self

Sine.

fn cos(self) -> Self

Cosine.

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

Raise to a concrete f64 power. The tangent uses p * v^(p-1); at value == 0.0 with p < 1.0 this may be NaN/Inf.

fn abs(self) -> Self

Absolute value. The tangent uses the subdifferential convention d/dx |v| = signum(v), with the honest at-zero selection signum(0) = 0: at exactly value == 0.0 the tangent is 0.0 (the midpoint of the subdifferential [-1, 1]). The value is v.abs() (bit-for-bit f64 parity).

fn signum(self) -> Self

Sign. Piecewise-constant, so the tangent is 0.0 everywhere. The value is f64::signum(v) (+1.0 at +0.0, -1.0 at -0.0) to preserve f64 parity.

impl Sub for Dual

type Output = Dual

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign for Dual

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.