MagneticLaplacianSparsifier

Documentation

This is the code associated with the manuscript Sparsification of the regularized magnetic Laplacian thanks to multi-type spanning forests by Michaël Fanuel and Rémi Bardenet.

This code uses multiple samples of Multi-Type Spanning Forests (MTSF) to sparsify the regularized magnetic Laplacian.

Use of the code

Install Julia

If you do not have Julia installed, please visit julialang.org

Installation

MagneticLaplacianSparsifier.jl is not registered. The way to use it is to type

julia> ]add https://github.com/For-a-few-DPPs-more/MagneticLaplacianSparsifier.jl

Jupyter notebooks for reproducing the paper figures

You can execute the Jupyter notebooks to generate the paper figures.

• plotting random spanning graphs
• sparsify-and-eigensolve
• sparsify-and-precondition random graphs
• sparsify-and-precondition real graphs
• timings
• leverage score estimation
• comparisons with HKPV alg.

Usage

To use this functions of this package, simply type

julia> using MagneticLaplacianSparsifier