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 gwz@163.shufe.edu.cn 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.