Struct DualNumber 

pub struct DualNumber<T>
where
    T: Float,
{
    pub real: T,
    pub dual: T,
}

A dual number: a + bε where ε² = 0

The real part stores the function value, the dual part stores the derivative.

Fields

real: T

Real part (function value)

dual: T

Dual part (derivative with respect to input variable)

Implementations

impl<T> DualNumber<T>

where T: Float,

pub fn new(real: T, dual: T) -> DualNumber<T>

Create a new dual number

pub fn variable(value: T) -> DualNumber<T>

Create a variable (derivative = 1)

pub fn new_variable(value: T) -> DualNumber<T>

Create a variable (derivative = 1) - alias for consistency

pub fn constant(value: T) -> DualNumber<T>

Create a constant (derivative = 0)

pub fn value(&self) -> T

Get the value (real part)

pub fn derivative(&self) -> T

Get the derivative (dual part)

pub fn apply_with_derivative<F, G>(&self, f: F, df: G) -> DualNumber<T>

where F: Fn(T) -> T, G: Fn(T) -> T,

Apply a function with known derivative

pub fn sin(self) -> DualNumber<T>

Sine function

pub fn cos(self) -> DualNumber<T>

Cosine function

pub fn exp(self) -> DualNumber<T>

Exponential function

pub fn ln(self) -> DualNumber<T>

Natural logarithm

pub fn powf(self, n: T) -> DualNumber<T>

Power function

pub fn sqrt(self) -> DualNumber<T>

Square root

pub fn tanh(self) -> DualNumber<T>

Hyperbolic tangent

pub fn relu(self) -> DualNumber<T>

ReLU activation function

pub fn sigmoid(self) -> DualNumber<T>

Sigmoid activation function

pub fn softplus(self) -> DualNumber<T>

Softplus activation function

pub fn max(self, other: DualNumber<T>) -> DualNumber<T>

Maximum of two dual numbers

pub fn min(self, other: DualNumber<T>) -> DualNumber<T>

Minimum of two dual numbers

pub fn tan(self) -> DualNumber<T>

Tangent function

pub fn sinh(self) -> DualNumber<T>

Hyperbolic sine

pub fn cosh(self) -> DualNumber<T>

Hyperbolic cosine

pub fn powi(self, n: i32) -> DualNumber<T>

Integer power

impl DualNumber<f32>

pub const ZERO: DualNumber<f32>

Zero dual number (0 + 0ε)

pub const ONE: DualNumber<f32>

One dual number (1 + 0ε)

pub const fn new_variable_const(value: f32) -> DualNumber<f32>

Variable dual number (value + 1ε) - useful for GPU operations

pub const fn new_constant_const(value: f32) -> DualNumber<f32>

Constant dual number (value + 0ε) - useful for GPU operations

Trait Implementations

impl<T> Add<T> for DualNumber<T>

where T: Float,

type Output = DualNumber<T>

The resulting type after applying the + operator.

fn add(self, scalar: T) -> DualNumber<T>

Performs the + operation.

impl<T> Add for DualNumber<T>

where T: Float,

type Output = DualNumber<T>

The resulting type after applying the + operator.

fn add(self, other: DualNumber<T>) -> DualNumber<T>

Performs the + operation.

impl<T> Clone for DualNumber<T>

where T: Clone + Float,

fn clone(&self) -> DualNumber<T>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T> Debug for DualNumber<T>

where T: Debug + Float,

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

Formats the value using the given formatter.

impl<T> Div<T> for DualNumber<T>

where T: Float,

type Output = DualNumber<T>

The resulting type after applying the / operator.

fn div(self, scalar: T) -> DualNumber<T>

Performs the / operation.

impl<T> Div for DualNumber<T>

where T: Float,

type Output = DualNumber<T>

The resulting type after applying the / operator.

fn div(self, other: DualNumber<T>) -> DualNumber<T>

Performs the / operation.

impl<T, const P: usize, const Q: usize, const R: usize> Mul<DualNumber<T>> for DualMultivector<T, P, Q, R>

where T: Float,

type Output = DualMultivector<T, P, Q, R>

The resulting type after applying the * operator.

fn mul(self, scalar: DualNumber<T>) -> DualMultivector<T, P, Q, R>

Performs the * operation.

impl<T> Mul<T> for DualNumber<T>

where T: Float,

type Output = DualNumber<T>

The resulting type after applying the * operator.

fn mul(self, scalar: T) -> DualNumber<T>

Performs the * operation.

impl<T> Mul for DualNumber<T>

where T: Float,

type Output = DualNumber<T>

The resulting type after applying the * operator.

fn mul(self, other: DualNumber<T>) -> DualNumber<T>

Performs the * operation.

impl<T> Neg for DualNumber<T>

where T: Float,

type Output = DualNumber<T>

The resulting type after applying the - operator.

fn neg(self) -> DualNumber<T>

Performs the unary - operation.

impl<T> One for DualNumber<T>

where T: Float,

fn one() -> DualNumber<T>

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl<T> PartialEq for DualNumber<T>

where T: PartialEq + Float,

fn eq(&self, other: &DualNumber<T>) -> 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<T> Sub<T> for DualNumber<T>

where T: Float,

type Output = DualNumber<T>

The resulting type after applying the - operator.

fn sub(self, scalar: T) -> DualNumber<T>

Performs the - operation.

impl<T> Sub for DualNumber<T>

where T: Float,

type Output = DualNumber<T>

The resulting type after applying the - operator.

fn sub(self, other: DualNumber<T>) -> DualNumber<T>

Performs the - operation.

impl<T> Zero for DualNumber<T>

where T: Float,

fn zero() -> DualNumber<T>

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl<T> Copy for DualNumber<T>

where T: Copy + Float,

impl<T> StructuralPartialEq for DualNumber<T>

where T: Float,