gwzwpxz / opt_dpcond Goto Github PK

This repository contains implementations and detailed experiment results for the paper Optimal Diagonal Preconditioning.

Prerequisites

The toolbox relies on solving semidefinite programs and needs to invoke optimization solvers through CVX. Users have to install

• CVX MATLAB toolbox at http://cvxr.com/cvx/

For testing purposes users need to install

• HDSDP at https://github.com/COPT-Public/HDSDP
• LIBSVM datasets at https://www.csie.ntu.edu.tw/~cjlin/libsvm/
• SuiteSparse matlab interface at https://sparse.tamu.edu/interfaces
• Intel MKL at https://www.intel.com/content/www/us/en/developer/tools/oneapi/onemkl-download.html

and ensure that they are added to MATLAB search path.

Install

To install the package, simple clone the repo with

git clone https://github.com/Gwzwpxz/opt_dpcond.git

and run

optpcd_setup

in MATLAB. Upon installation, a toy example will be solved to test the installation.

Setting up the optimal diagonal preconditioning repo 
The repo depends on:  

1. CVX   matlab toolbox    at http://cvxr.com/cvx/
2. HDSDP binary (optional) at https://github.com/COPT-Public/HDSDP 

To reproduce the experiments, execute 

    git checkout opt-precond 

and ensure that the following data repos are installed 

3. LIBSVM datasets              at https://www.csie.ntu.edu.tw/~cjlin/libsvm/
4. SuiteSparse matlab interface at https://sparse.tamu.edu/interfaces

Running a toy example.

Solving a two-sided preconditioning problem using bisection 
     kappa    ub - lb 
 5.000e+05  1.000e+06 
 7.500e+05  5.000e+05 
 6.250e+05  2.500e+05 
 5.625e+05  1.250e+05 
 5.313e+05  6.250e+04 
 5.156e+05  3.125e+04 
 5.234e+05  1.562e+04 
Condition number of X  : 2.06e+03 
Condition number of XE : 1.62e+03 
Condition number of DX : 1.28e+03 
Condition number of DXE: 7.23e+02 
Exporting SDP to ./Eprob-R.dat-s 

Installation completes. Check README.md for usage details. 

Usage

The optimal preconditioning toolbox provides several utilities that allow users to

• Compute the optimal Left/Right/Two-sided preconditioner
• Export the Left/Right preconditioning SDP to standard SDPA format

The basic usage can be demonstrated by the following lines of code

% Choose preconditioning type
param.ptype = 'R'; 
% Generate preconditioning problem. X is the user data
prob = getoptprob(X, param); 
% Solve the preconditioning problem
sol = optprecond(prob); 
% Get preconditioned matrix
pX = sol.pX;
% Get diagonal preconditioner
E = sol.E; 
% Export problem to SDPA
path = fullfile('.');
pname = 'Eprob';
exportoptprob(prob, path, pname);

Testing

The experiments from paper Optimal Diagonal Preconditioning: Theory and Practice are available at the testing branch, which can be accessed through

git checkout opt-precond 

in the command line. The tests can be done by modifying and running the testing scripts from test directory

• test_precond_libsvm (LIBSVM)
• test_precond_suitesparse (SuiteSparse)
• test_precond_random (Random)

To test preconditioned CG, the users need to install CG from Intel RCI interface using Cmake build system from utils/rci

mkdir build
cd build
cmake ..
make

and obtain the mexfile for CG implementation of multiple RHSs.

Contact

Please contact [email protected] for questions on the toolbox.

Cite as

Qu, Z., Gao, W., Hinder, O., Ye, Y., & Zhou, Z. (2022). Optimal Diagonal Preconditioning. arXiv preprint arXiv:2209.00809.