Struct CountingTropical 

#[repr(C)]
pub struct CountingTropical<T: TropicalScalar, C: TropicalScalar = T> {
    pub value: T,
    pub count: C,
}

CountingTropical semiring: tracks both the tropical value and the count of optimal paths.

For TropicalMaxPlus semantics:

• Multiplication: (n₁, c₁) ⊗ (n₂, c₂) = (n₁ + n₂, c₁ × c₂)
• Addition: (n₁, c₁) ⊕ (n₂, c₂) =
  • if n₁ > n₂: (n₁, c₁)
  • if n₁ < n₂: (n₂, c₂)
  • if n₁ = n₂: (n₁, c₁ + c₂)

This is used for:

• Counting optimal paths in dynamic programming
• Computing partition functions
• Gradient computations in certain neural network architectures

Fields

value: T

The tropical value (using MaxPlus semantics).

count: C

The count of paths achieving this value.

Implementations

impl<T: TropicalScalar, C: TropicalScalar> CountingTropical<T, C>

pub fn new(value: T, count: C) -> Self

Create a new CountingTropical value.

pub fn from_value(value: T) -> Self

Create a CountingTropical from a single value with count 1.

Trait Implementations

impl<T: TropicalScalar, C: TropicalScalar> Add for CountingTropical<T, C>

type Output = CountingTropical<T, C>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T: Clone + TropicalScalar, C: Clone + TropicalScalar> Clone for CountingTropical<T, C>

fn clone(&self) -> CountingTropical<T, C>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: TropicalScalar, C: TropicalScalar> Debug for CountingTropical<T, C>

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

Formats the value using the given formatter.

impl<T: TropicalScalar, C: TropicalScalar> Default for CountingTropical<T, C>

fn default() -> Self

Returns the “default value” for a type.

impl<T: TropicalScalar, C: TropicalScalar> Display for CountingTropical<T, C>

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

Formats the value using the given formatter.

impl<T: TropicalScalar, C: TropicalScalar> From<T> for CountingTropical<T, C>

fn from(value: T) -> Self

Converts to this type from the input type.

impl<T: TropicalScalar, C: TropicalScalar> Mul for CountingTropical<T, C>

type Output = CountingTropical<T, C>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: PartialEq + TropicalScalar, C: PartialEq + TropicalScalar> PartialEq for CountingTropical<T, C>

fn eq(&self, other: &CountingTropical<T, C>) -> 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: TropicalScalar, C: TropicalScalar> SimdTropical for CountingTropical<T, C>

const SIMD_AVAILABLE: bool = true

Whether SIMD operations are available for this type.

const SIMD_WIDTH: usize = 8

The SIMD width in elements.

impl<T: TropicalScalar, C: TropicalScalar> TropicalSemiring for CountingTropical<T, C>

type Scalar = T

The underlying scalar type.

fn tropical_zero() -> Self

Returns the additive identity (zero element for ⊕).

fn tropical_one() -> Self

Returns the multiplicative identity (one element for ⊗).

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

Tropical addition (⊕).

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

Tropical multiplication (⊗).

fn value(&self) -> T

Get the underlying scalar value.

fn from_scalar(s: T) -> Self

Create from a scalar value.

impl<T: TropicalScalar, C: TropicalScalar> TropicalWithArgmax for CountingTropical<T, C>

type Index = u32

The index type used for argmax tracking.

fn tropical_add_argmax( self, self_idx: u32, rhs: Self, rhs_idx: u32, ) -> (Self, u32)

Tropical addition with argmax tracking.

impl<T: Copy + TropicalScalar, C: Copy + TropicalScalar> Copy for CountingTropical<T, C>

impl<T: TropicalScalar, C: TropicalScalar> StructuralPartialEq for CountingTropical<T, C>