Trigivs

A Rust library for solving tridiagonal systems of linear equations using Givens rotations. This library is designed to work in both std and no_std environments, with optional heap allocation.

Features

The library supports three modes of operation, controlled by Cargo features:

Usage

Add trigivs to your Cargo.toml:

[dependencies]

trigivs = "0.1"

To use the library in no_std mode (no heap allocation):

[dependencies]

trigivs = { version = "0.1", default-features = false }

To use the library with heap allocation but without std:

[dependencies]

trigivs = { version = "0.1", default-features = false, features = ["alloc"] }

Examples

Compute the Determinant

use trigivs::prelude::compute_tridiag_determinant;

fn main() {
    let sup = [-4.0];
    let diag = [3.0, 2.0];
    let sub = [5.0];
    let determinant = compute_tridiag_determinant(&sup, &diag, &sub);
    println!("Determinant: {}", determinant);
}

Solve a Tridiagonal System

use trigivs::prelude::solve_givens;

fn main() {
    let sup = [-4.0];
    let diag = [3.0, 2.0];
    let sub = [5.0];
    let rhs = [-3.0, 21.0];
    let x = solve_givens(&sup, &diag, &sub, &rhs).unwrap();
    println!("Solution: {:?}", x);
}

Precompute a System for Multiple Right-Hand Sides

use trigivs::prelude::{precompute_givens, TridiagonalSystemPrecomputed};

fn main() {
    let sup = [-4.0];
    let diag = [3.0, 2.0];
    let sub = [5.0];
    let precomputed = precompute_givens(&sup, &diag, &sub).unwrap();

    let rhs1 = [-3.0, 21.0];
    let rhs2 = [-23.0, 5.0];

    let x1 = precomputed.solve_givens_rhs(&rhs1).unwrap();
    let x2 = precomputed.solve_givens_rhs(&rhs2).unwrap();

    println!("Solution 1: {:?}", x1);
    println!("Solution 2: {:?}", x2);
}

Error Handling

SolverErrors:

• InvalidDiagonals - The superdiagonal and subdiagonal must be equal in length and exactly one element shorter than the main diagonal.
• InvalidRhsSizing - The right-hand side (RHS) must match the length of the main diagonal.
• DivisionByZero - Division by zero was attempted during computation.

License

This project is licensed under the MIT License.