GL-Coarsener

A python implementation of GL-Coarsener method, as proposed in GL-Coarsener: A Graph representation learning framework to construct coarse grid hierarchy for AMG solvers, arXiv:2011.09994.

If you find our code or paper useful in your research, please consider citing:

@misc{namazi2020glcoarsener,
      title={GL-Coarsener: A Graph representation learning framework to construct coarse grid hierarchy for AMG solvers}, 
      author={Reza Namazi and Arsham Zolanvari and Mahdi Sani and Seyed Amir Ali Ghafourian Ghahramani},
      year={2020},
      eprint={2011.09994},
      archivePrefix={arXiv},
      primaryClass={math.NA}
}

Installation

pip install gl-coarsener

Usage

Import the package

from glcoarsener import Coarsener

Input

You should construct a Coarsener object with the adjacency matrix that you want to coarsen. The input must be of type scipy sparse CSR matrix.

from scipy import sparse
adjacency_matrix = sparse.random(1000, 1000, format='csr')
coarsener = Coarsener(adjacency_matrix)

Applying the method

prolongation_operator = coarsener.apply(
    dimensions=100,
    walk_length=20,
    num_walks=10,
    p=0.1,
    q=1,
    number_of_clusters=adjacency_matrix.shape[0] // 5,
    clustering_method='kmeans',
    workers=1
)

Getting the coarse (smaller) adjacency matrix

restriction_operator = prolongation_operator.transpose()
coarse_matrix = restriction_operator.dot(adjacency_matrix).dot(prolongation_operator)
print(coarse_matrix)

Contributing

Any contribution is greatly appreciated. If you think you can improve this work, please open a pull request.

1. Fork the Project
2. Create your Feature Branch (git checkout -b feature/Improvement)
3. Commit your Changes (git commit -m 'Add some Improvement')
4. Push to the Branch (git push origin feature/Improvement)
5. Open a Pull Request

Contact

If you have any questions, please do not hesitate to contact me:

• Personal Webpage: https://rezanmz.com/
• Email: rezanmz@ymail.com