Struct Dual 

pub struct Dual<const N: usize> {
    pub v: f64,
    pub d: [f64; N],
}

A forward-mode dual number: a primal value paired with an N-slot gradient.

Each arithmetic and elementary operation propagates the derivative slots alongside the value, so evaluating an expression on Dual<N> computes both the result and its partial derivatives with respect to N seeded directions in a single pass. N is the number of independent directions (inputs) tracked; Dual<0> carries no gradient and reduces to plain f64 arithmetic on the value.

Examples

Differentiate f(x) = x * x + 3 * x at x = 2, where f'(x) = 2x + 3 = 7:

use sim_lib_numbers_ad::Dual;

let x = Dual::<1>::var(2.0, 0);
let y = x * x + Dual::<1>::cst(3.0) * x;
assert_eq!(y.v, 10.0);
assert_eq!(y.d, [7.0]);

Fields

v: f64

The primal value of the number.

d: [f64; N]

The gradient: one partial derivative per tracked direction.

Implementations

impl<const N: usize> Dual<N>

pub fn cst(v: f64) -> Self

Builds a constant: the given value with a zero gradient.

pub fn var(v: f64, slot: usize) -> Self

Builds an independent variable: the given value seeded with derivative 1.0 in gradient slot slot (and zero elsewhere).

A slot outside 0..N seeds no direction, yielding a constant.

Trait Implementations

impl<const N: usize> Add for Dual<N>

type Output = Dual<N>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<const N: usize> Clone for Dual<N>

fn clone(&self) -> Dual<N>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const N: usize> Copy for Dual<N>

impl<const N: usize> Debug for Dual<N>

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

Formats the value using the given formatter.

impl<const N: usize> Div for Dual<N>

type Output = Dual<N>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<const N: usize> Mul for Dual<N>

type Output = Dual<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<const N: usize> Neg for Dual<N>

type Output = Dual<N>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<const N: usize> PartialEq for Dual<N>

fn eq(&self, other: &Dual<N>) -> 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<const N: usize> Scalarish for Dual<N>

fn from_f64(x: f64) -> Self

Lifts a plain f64 into this scalar type (as a constant with zero derivative, for the differentiable types).

fn sin(self) -> Self

Returns the sine of self.

fn cos(self) -> Self

Returns the cosine of self.

fn exp(self) -> Self

Returns e raised to the power of self.

fn ln(self) -> Self

Returns the natural logarithm of self.

fn sqrt(self) -> Self

Returns the square root of self.

fn recip(self) -> Self

Returns the reciprocal 1 / self.

impl<const N: usize> StructuralPartialEq for Dual<N>

impl<const N: usize> Sub for Dual<N>

type Output = Dual<N>

The resulting type after applying the - operator.

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

Performs the - operation.