Struct RPlusAlgebra 

pub struct RPlusAlgebra(/* private fields */);

Lie algebra of ℝ⁺, isomorphic to (ℝ, +)

Elements represent infinitesimal scaling factors. The exponential map converts these to finite scalings: exp(x) = eˣ.

Examples

use lie_groups::rplus::RPlusAlgebra;
use lie_groups::traits::LieAlgebra;

let v = RPlusAlgebra::from_components(&[0.5]);
let w = v.scale(2.0);
assert!((w.value() - 1.0).abs() < 1e-10);

Implementations

impl RPlusAlgebra

pub fn new(value: f64) -> Self

Create a new ℝ⁺ algebra element.

The value represents an infinitesimal scaling factor.

pub fn value(&self) -> f64

Get the real value

Trait Implementations

impl AbsDiffEq for RPlusAlgebra

type Epsilon = f64

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together.

fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

impl Add<&RPlusAlgebra> for &RPlusAlgebra

type Output = RPlusAlgebra

The resulting type after applying the + operator.

fn add(self, rhs: &RPlusAlgebra) -> RPlusAlgebra

Performs the + operation.

impl Add<&RPlusAlgebra> for RPlusAlgebra

type Output = RPlusAlgebra

The resulting type after applying the + operator.

fn add(self, rhs: &RPlusAlgebra) -> RPlusAlgebra

Performs the + operation.

impl Add<RPlusAlgebra> for &RPlusAlgebra

type Output = RPlusAlgebra

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add for RPlusAlgebra

type Output = RPlusAlgebra

The resulting type after applying the + operator.

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

Performs the + operation.

impl Clone for RPlusAlgebra

fn clone(&self) -> RPlusAlgebra

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for RPlusAlgebra

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

Formats the value using the given formatter.

impl Display for RPlusAlgebra

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

Formats the value using the given formatter.

impl LieAlgebra for RPlusAlgebra

const DIM: usize = 1

Dimension of the Lie algebra as a compile-time constant.

fn zero() -> Self

Zero element (additive identity) 0 ∈ 𝔤.

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

Add two algebra elements: v + w

fn scale(&self, scalar: f64) -> Self

Scalar multiplication: α · v

fn norm(&self) -> f64

Euclidean norm of the coefficient vector: ||v|| = √(Σᵢ vᵢ²)

fn basis_element(i: usize) -> Self

Get the i-th basis element of the Lie algebra.

fn from_components(components: &[f64]) -> Self

Construct algebra element from basis coordinates.

fn to_components(&self) -> Vec<f64>

Extract basis coordinates from algebra element.

fn bracket(&self, _other: &Self) -> Self

Lie bracket operation: [X, Y] ∈ 𝔤

fn inner(&self, other: &Self) -> f64

Inner product on coefficient space: ⟨v, w⟩ = Σᵢ vᵢ wᵢ

impl Mul<RPlusAlgebra> for f64

type Output = RPlusAlgebra

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<f64> for RPlusAlgebra

type Output = RPlusAlgebra

The resulting type after applying the * operator.

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

Performs the * operation.

impl Neg for RPlusAlgebra

type Output = RPlusAlgebra

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl PartialEq for RPlusAlgebra

fn eq(&self, other: &RPlusAlgebra) -> 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 RelativeEq for RPlusAlgebra

fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart.

fn relative_eq( &self, other: &Self, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

A test for equality that uses a relative comparison if the values are far apart.

fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

The inverse of RelativeEq::relative_eq.

impl Sub for RPlusAlgebra

type Output = RPlusAlgebra

The resulting type after applying the - operator.

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

Performs the - operation.

impl Copy for RPlusAlgebra

impl StructuralPartialEq for RPlusAlgebra