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freealg is a Python package that employs free probability to evaluate the spectral densities of large matrix forms. The fundamental algorithm employed by freealg is free decompression, which extrapolates from the empirical spectral densities of small submatrices to infer the eigenspectrum of extremely large matrices.
Install with pip:
pip install freealg
Alternatively, clone the source code and install with
cd source_dir pip install .
Documentation is available at ameli.github.io/freealg.
The following code estimates the eigenvalues of a very large Wishart matrix using a much smaller Wishart matrix.
>>> import freealg as fa
>>> mp = fa.distributions.MarchenkoPastur(1/50) # Wishart matrices with aspect ratio 1/50
>>> A = mp.matrix(1000) # Sample a 1000 x 1000 Wishart matrix
>>> eigs = fa.eigvalsh(A, 100_000) # Estimate the eigenvalues of 100000 x 100000For more details on how to interface with freealg check out the Live Demo.
You may test the package with tox:
cd source_dir tox
Alternatively, test with pytest:
cd source_dir pytest
We welcome contributions via GitHub's pull request. Developers should review our Contributing Guidelines before submitting their code. If you do not feel comfortable modifying the code, we also welcome feature requests and bug reports.
If you use this work, please cite our arXiv paper.
@article{spectral2025,
title={Spectral Estimation with Free Decompression},
author={Siavash Ameli and Chris van der Heide and Liam Hodgkinson and Michael W. Mahoney},
year={2025},
eprint={2506.11994},
archivePrefix={arXiv},
primaryClass={stat.ML},
url={https://arxiv.org/abs/2506.11994},
journal={arXiv preprint arXiv:2506.11994},
}
