Module operator 

Linear operators on function spaces.

This module provides traits and types for linear operators between Hilbert spaces, including bounded operators, compact operators, and self-adjoint operators.

Operator Hierarchy

LinearOperator
    ↓
BoundedOperator (adds ||T|| < ∞)
    ↓
CompactOperator (maps bounded sets to precompact sets)
    ↓
FiniteRankOperator (finite-dimensional range)

Example

use amari_functional::operator::{LinearOperator, IdentityOperator};
use amari_functional::space::MultivectorHilbertSpace;

let space: MultivectorHilbertSpace<2, 0, 0> = MultivectorHilbertSpace::new();
let identity = IdentityOperator::new();

let x = space.from_coefficients(&[1.0, 2.0, 0.0, 0.0]).unwrap();
let y = identity.apply(&x)?;
assert_eq!(x, y);

Structs

CompactMatrixOperator

Wrapper to mark a matrix operator as compact.

CompositeOperator

Composition of two operators: (S ∘ T)(x) = S(T(x)).

FiniteRankOperator

A finite-rank operator represented as a sum of rank-1 operators.

FredholmMatrixOperator

Wrapper to mark a matrix operator as Fredholm.

IdentityOperator

The identity operator I: x ↦ x.

MatrixOperator

A linear operator represented as a matrix.

ProjectionOperator

Orthogonal projection operator onto a subspace.

ScalingOperator

Scaling operator αI: x ↦ αx.

ZeroOperator

The zero operator 0: x ↦ 0.

Traits

AdjointableOperator

An operator that has an adjoint.

BoundedOperator

A bounded linear operator.

CompactOperator

Trait for compact operators.

FredholmOperator

Trait for Fredholm operators.

LinearOperator

A linear operator between vector spaces.

OperatorNorm

Trait for computing operator norms.

SelfAdjointOperator

A self-adjoint operator (T = T*).