Bachelor theses
Task-based implementation of Cholesky decomposition
Author
Vít Břichňáč
Year
2023
Type
Bachelor thesis
Supervisor
Ing. Jakub Šístek, Ph.D.
Reviewers
Ing. Karel Klouda, Ph.D.
Department
Summary
The aim of this thesis is to present the blocked algorithm for finding a Cholesky decomposition of a symmetric positive definite matrix and to provide an implementation of the algorithm using the StarPU and OpenMP task-based runtime systems. The implementation is tested using test routines from the LAPACK library and its performance is compared to several available libraries for numerical linear algebra on three different compute nodes. On all three of them, the implementation delivers a competitive performance, especially for larger matrices. In the theoretical part of the thesis, custom proofs of correctness are formulated for both the blocked and the unblocked algorithms for Cholesky decomposition. The rest of the thesis explores matrix storage schemes, the BLAS interface and basic concepts of task-based programming.