Chordal Matrix Package—a library for chordal matrix computations¶
Chompack is a library for chordal matrix computations. It includes routines for:
- symbolic factorization
- numeric Cholesky factorization
- forward and back substitution
- maximum determinant positive definite completion
- minimum rank completion
- Euclidean distance matrix completion
- computations with logarithmic barriers for sparse matrix cones
- chordal conversion
- computing a maximal chordal subgraph
The implementation is based on the supernodal-multifrontal algorithms described in these papers:
See also
L. Vandenberghe and M. S. Andersen, Chordal Graphs and Semidefinite Optimization, Foundations and Trends in Optimization, 2015. [doi | bib ]
M. S. Andersen, J. Dahl, and L. Vandenberghe, Logarithmic barriers for sparse matrix cones, Optimization Methods and Software, 2013. [doi | bib ]
Applications of these algorithms in optimization include sparse matrix cone programs, covariance selection, graphical models, and decomposition and relaxation methods.