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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
  1. 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.