Struct FunctionAlgebraElement 

pub struct FunctionAlgebraElement {
    pub values: Vec<f64>,
}

Represents a function in a function algebra, stored as a lookup table.

This models C(K) – the algebra of continuous functions on a compact set K, approximated by sampling at discrete points.

Fields

values: Vec<f64>

Sampled function values at equally-spaced points in [0, 1].

Implementations

impl FunctionAlgebraElement

pub fn from_fn<F: Fn(f64) -> f64>(f: F, n: usize) -> Self

Create from a Rust closure, sampling at n equally-spaced points in [0,1].

pub fn add(&self, other: &FunctionAlgebraElement) -> FunctionAlgebraElement

Pointwise addition: (f + g)(x) = f(x) + g(x).

pub fn multiply(&self, other: &FunctionAlgebraElement) -> FunctionAlgebraElement

Pointwise multiplication: (f * g)(x) = f(x) * g(x).

pub fn scale(&self, c: f64) -> FunctionAlgebraElement

Scalar multiplication: (c * f)(x) = c * f(x).

pub fn sup_norm(&self) -> f64

The supremum norm: ||f||_inf = max |f(x)|.

pub fn l2_norm(&self) -> f64

The L2 norm (approximated by the trapezoidal rule on the samples).

pub fn compose(&self, g: &FunctionAlgebraElement) -> FunctionAlgebraElement

Composition: (f o g)(x) = f(g(x)).

Since we store sampled values, we interpolate g’s output to find f’s value. Clamps g’s output to [0, 1] for lookups.

pub fn one(n: usize) -> Self

The multiplicative identity in C(K): the constant function 1.

pub fn zero_fn(n: usize) -> Self

The zero element in C(K): the constant function 0.

Trait Implementations

impl Clone for FunctionAlgebraElement

fn clone(&self) -> FunctionAlgebraElement

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for FunctionAlgebraElement

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

Formats the value using the given formatter.