MLib: Linear Algebra Library with Built-in Automatic Differentiation

MLib is a performant linear algebra library implemented in C with a Python interface, featuring key matrix operations and automatic differentiation capabilities. It’s designed for numerical computing and machine learning tasks, providing matrix functions optimized for speed and an intuitive Python API.

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Features

• Essential matrix operations: addition, subtraction, multiplication, division, exponentiation, logarithm, exponentials, transpose, reshape, and more.
• Optimized matrix multiplication for 2D arrays.
• Matrix inversion for square positive semi-definite matrices.
• Views and slicing with shared memory support.
• Random vector/matrix generation with flexible bounds.
• Built-in automatic differentiation (autograd) for gradient computation.
• High-performance C backend with Python bindings.

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Installation & Setup

To build the C library, use the provided Makefile:

make

Clean build artifacts with:

make clean

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Tutorial and Usage

MLib’s tutorial.ipynb notebook contains a comprehensive, step-by-step tutorial with examples on basic operations, benchmarking performance, and practical use cases like linear regression. It is highly recommended to start there for a guided introduction.

If you don’t have it installed, you may need to install matplotlib for plotting in the tutorial:

pip3 install matplotlib

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Performance

MLib significantly outperforms vanilla Python list operations in element-wise matrix computations, making it suitable for large scale numerical tasks.

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Testing

Run the unit tests to verify the installation:

python3 -m unittest discover -s tests

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Credits & Resources

The project draws from foundational and practical resources including:

• LU Decomposition - Wikipedia
• PyTorch Internals - E. Z. Yang
• Recreating PyTorch from Scratch - Towards Data Science
• DIY Autograd Engine - Medium
• Matrix differentiation notes by Randal J. Barnes, University of Minnesota
• NumPy Internals

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For an in-depth introduction, code examples, and use cases, please see the tutorial.ipynb included in this repository. It provides a clearer, interactive walkthrough of MLib’s capabilities.

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License

This project is licensed under the MIT License. See LICENSE for details.

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Thank you for exploring MLib!
Happy computing.