Preconditioned Low-Rank Riemannian Optimization for Symmetric Positive Definite Linear Matrix Equations

Code accompanying the paper "Preconditioned Low-Rank Riemannian Optimization for Symmetric Positive Definite Linear Matrix Equations".

Reproducing Experiments

Prerequisites

The code is written in MATLAB, R2024a. Ensure you have the appropriate MATLAB version installed.

Installation

Clone the repository, including the Manopt submodule, using the following commands:

git clone https://github.com/IvanBioli/riemannian-spdmatrixeq.git
cd riemannian-spdmatrixeq
git submodule update --init 

Running Experiments

To replicate all experiments detailed in the Paper, follow these steps:

1. Run the MATLAB script src\PAPER_run_experiments.m.

2. Allow the script to execute fully. Ignore temporary plots generated and deleted during execution; relevant plots will be generated at the end. Results are saved in .mat files in the folder src\results. All plots are saved in the folder report\figures and can be produced after one complete execution by running the last section of src\PAPER_run_experiments.m.

Repository description

A detailed documentation can be found in each file. The repository is structured as follows.

• report
  • configs
  • figures: figure folder
• src: code folder
  • PAPER_run_experiments.m: main script reproducing experiments and figures in the paper
  • baseline_solvers: non-Riemannian solvers for SPD linear matrix equations
  • examples: code and data for the numerical tests in the paper
    • pdes_FD: finite difference discretization of 2D PDEs on square domain
    • rail_problem: modified Bilinear Rail problem
    • stoch_diff: stochastic Galerkin matrix equations
  • init.m: adds necessary folders to MATLAB's path
  • manifold_optimization: code for Riemannian solvers (including manifolds and preconditioners)
  • manopt: fork of Manopt's repository
  • paper_experiments: code for setting up the numerical experimens in the paper
  • results: folder where results are saved in .mat format
  • utils: code utilities

Authors

• Ivan Bioli (Università di Pavia)
• Daniel Kressner (EPFL)
• Leonardo Robol (Università di Pisa)