MLinalg

MLinalg is an educational project designed for learning and practicing numerical linear algebra using modern C++. This project is ideal for any one who wishes to gain hands-on experience with numerical methods and modern C++ techniques.

Overview

MLinalg serves as both a learning tool and a proof-of-concept for building numerical linear algebra libraries. It demonstrates:

• Self-Initiative & Learning: A project built from scratch to understand and implement core linear algebra concepts.
• Technical Breadth: Implementation of matrices and vectors (both static and dynamic), along with standard operations such as addition, subtraction, multiplication, transposition, and determinant calculation.
• Advanced Algorithms: Includes efficient methods like Strassen's algorithm for matrix multiplication.
• Modern C++ Practices: Uses C++23 features, templates, concepts, and compile-time optimizations to ensure type safety and performance.
• Robustness: Incorporates fuzzy comparisons for floating point arithmetic to handle numerical precision issues, with extensive unit tests (using Catch2) to verify correctness.

Features

• Data Structures:

  • Matrix and vector classes with support for both static and dynamic sizing.
  • 2D and 3D vector implementations.

• Basic Operations:

  • Addition, subtraction, scalar multiplication, and division.
  • Matrix multiplication (both matrix–matrix and matrix–vector).
  • Transposition of matrices and vectors.

• Advanced Operations:

  • Determinant calculation.
  • Matrix augmentation with other matrices or vectors.
  • Efficient multiplication via Strassen's algorithm.

• Numerical Robustness:

  • Fuzzy comparisons for floating point operations to mitigate precision issues.
  • Comprehensive test suite to ensure stability and correctness.

Project Structure

• CMakeLists.txt
  CMake build configuration file.

• src/
  Source code directory:

  • pub/structures/:
    • Matrix.hpp: Implementation of the Matrix class and related functions.
    • Vector.hpp: Implementation of the Vector class and related functions.
  • pub/Numeric.hpp:
    Defines fuzzy comparisons and numerical constants.
  • Concepts.hpp:
    Contains C++ concept definitions used in the project.
  • Helpers.hpp:
    Contains utility functions to support the core implementations.

• test/
  Unit tests (using Catch2) to verify the correctness of all implemented functions.

  • examples.cpp: Contains examples of using the library.

Requirements

• CMake: Version 3.20 or later.
• C++ Compiler: A compiler that supports C++23 (e.g., GCC 11+, Clang 12+, or the latest MSVC).

Building the Project

To build the project, follow these steps:

1. Clone the repository:

git clone https://github.com/madstone0-0/MLinalg.git
cd MLinalg

2. Run build.sh

Debug build

./build.sh

Release build

./build.sh release

Usage

Once the project is built, you can install an link the library to your project using the following commands:

Install

Requirements

• Ninja / Make

ninja -C ./build-release install

Linking

The library can be linked using CMake's find_package command. Add the following lines to your CMakeLists.txt file:

find_package(mlinalg REQUIRED)

add_executable(exe exe.cpp)

target_link_libraries(exe PRIVATE mlinalg::mlinalg)

The project includes test cases using Catch2 to verify the correctness of the implemented functions.