Instructions

This is the code accompanying the paper "Entrywise convergence of iterative methods for eigenproblems" [1]. All code has been tested in Julia v1.1. The core utilities files, Utils.jl and IOUtils.jl, rely on the following libraries:

• Arpack
• LightGraphs
• LinearMaps
• StatsBase

The various experiments (following the naming convention test*.jl) require:

• ArgParse
• CSV
• DataFrames
• Distributions
• MatrixNetworks (only for the sweep cut experiment)

To get documentation and instructions on available parameters for each experiment, run

julia <script.jl> --help

All of the experiments set up a random seed of 999 to ensure reproducibility, and the default values for arguments are set to the ones used in the experiments reported in the manuscript, with the exception of dataset-specific parameters - please refer to the manuscript and supplementary material for these parameters.

Obtaining the datasets

All of the datasets used in our experiments are made available via the SNAP network collection. To run the experiments, you need to create a folder called "data/" in your working directory containing the following files:

• com-lj.ungraph.txt (Livejournal)
• com-dblp.ungraph.txt (Dblp)
• ca-HepPh.txt (HepPh)
• ca-AstroPh.txt (AstroPh)
• artist_edges.csv (Gemsec)

Enabling debugging output

Our subspace iteration implementation allows debugging output for inspecting its progress. To enable such output when running script.jl, use the following command:

JULIA_DEBUG=Utils julia <script.jl> ...

References

[1]: Vasileios Charisopoulos, Austin R. Benson and Anil Damle. "Entrywise convergence of iterative methods for eigenproblems". arXiv preprint abs/2002.08491.