Numerical experiments for the papers BayesCG As An Uncertainty Aware Version of CG and Statistical Properties of the Probabilistic Numeric Linear Solver BayesCG by Tim W. Reid, Ilse C. F. Ipsen, Jon Cockayne, and Chris J. Oates.
Both papers share implementations of some algorithms, but each paper has their own Jupyter notebook containing the Python commands that run the numerical experiments and generate the plots.
ArXiv link: https://arxiv.org/abs/2008.03225
Jupyter notebook: BayesCG-as-Uncertainty-Aware-CG.ipynb
ArXiv link: https://arxiv.org/abs/2208.03885
Jupyter notebook: Statistical-Properties-BayesCG.ipynb
- a_lanczos.py
- Implementation of a modified Lanczos method
- bayescg.py
- Implementation of the Bayesian Conjugate Gradient Method
- bayescg_k.py
- Implementation of BayesCG under the Krylov Prior
- cgqs.py
- Implementation of CG with Gauss-Radau and S Statistic error estimates
- kn_plots.py
- Creates plots that are in the paper BayesCG As An Uncertainty Aware Version of CG
- matrix2tabular.py
- Converts numpy arrays into LaTeX tabular format
- test_statistics_plots.py
- Implements the Z and S test statistics and creates the plots that are in the paper Statistical Properties of the Probabilistic Numeric Linear Solver BayesCG
- utilities.py
- Generates random matrices and samples multivariate Gaussian distributions
- bcsstk14.mtx
- Sparse matrix used in the paper Statistical Properties of the Probabilistic Numeric Linear Solver BayesCG
- Originally from the Matrix Market
- bcsstk18.mtx
- Sparse matrix used in the paper BayesCG As An Uncertainty Aware Version of CG
- Originally from the Matrix Market
- bcsstk18_ichol.mtx
- Incomplete Cholesky factor of bcsstk18.mtx
- bcsstk18_prec.mtx
- bcsstk18.mtx preconditioned with the incomplete Cholesky factor