Struct MinPlus 

#[repr(transparent)]
pub struct MinPlus<T>(pub T);

Min-plus tropical scalar: ⊕ = min, ⊗ = +.

Used for shortest-path problems (Dijkstra, Bellman–Ford).

Examples

use tenferro_ext_tropical::MinPlus;

let a = MinPlus(3.0_f64);
let b = MinPlus(5.0_f64);

// Tropical addition = min
let c = a + b;
assert_eq!(c, MinPlus(3.0));

// Tropical multiplication = ordinary addition
let d = a * b;
assert_eq!(d, MinPlus(8.0));

Tuple Fields

0: T

Trait Implementations

impl<T: Copy + PartialOrd> Add for MinPlus<T>

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

Tropical addition: min(a, b).

type Output = MinPlus<T>

The resulting type after applying the + operator.

impl<T: Clone> Clone for MinPlus<T>

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: Copy> Conjugate for MinPlus<T>

fn conj(self) -> Self

Return the complex conjugate of this value.

impl<T: Debug> Debug for MinPlus<T>

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

Formats the value using the given formatter.

impl<T: Display> Display for MinPlus<T>

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

Formats the value using the given formatter.

impl HasAlgebra for MinPlus<f32>

type Algebra = MinPlusAlgebra<f32>

The algebra associated with this scalar type.

impl HasAlgebra for MinPlus<f64>

type Algebra = MinPlusAlgebra<f64>

The algebra associated with this scalar type.

impl<T: Copy + Add<Output = T>> Mul for MinPlus<T>

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

Tropical multiplication: a + b (ordinary addition).

type Output = MinPlus<T>

The resulting type after applying the * operator.

impl<T: Float> One for MinPlus<T>

fn one() -> Self

Multiplicative identity: 0.

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> PartialEq for MinPlus<T>

fn eq(&self, other: &MinPlus<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: PartialOrd> PartialOrd for MinPlus<T>

fn partial_cmp(&self, other: &MinPlus<T>) -> 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 TropicalScalar for MinPlus<f32>

type Inner = f32

The inner floating-point type.

fn inner(&self) -> f32

Extract the inner value.

fn from_inner(v: f32) -> Self

Wrap an inner value into the tropical type.

fn mul_backward_a(_a: f32, _b: f32, dout: f32) -> f32

Backward contribution for tropical multiplication w.r.t. the first operand.

fn mul_backward_b(_a: f32, _b: f32, dout: f32) -> f32

Backward contribution for tropical multiplication w.r.t. the second operand.

impl TropicalScalar for MinPlus<f64>

type Inner = f64

The inner floating-point type.

fn inner(&self) -> f64

Extract the inner value.

fn from_inner(v: f64) -> Self

Wrap an inner value into the tropical type.

fn mul_backward_a(_a: f64, _b: f64, dout: f64) -> f64

Backward contribution for tropical multiplication w.r.t. the first operand.

fn mul_backward_b(_a: f64, _b: f64, dout: f64) -> f64

Backward contribution for tropical multiplication w.r.t. the second operand.

impl<T: Float> Zero for MinPlus<T>

fn zero() -> Self

Additive identity: +∞ (positive infinity).

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> Copy for MinPlus<T>

impl<T> StructuralPartialEq for MinPlus<T>