User Guide for CHOLMOD: a sparse Cholesky factorization and modification package Timothy A. Davis
[email protected], http://www.suitesparse.com VERSION 3.0.14, Oct 22, 2019 Abstract CHOLMOD1 is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AAT, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level-3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. It also includes a non-supernodal LDLT factorization method that can factorize symmetric indefinite matrices if all of their leading submatrices are well-conditioned (D is diagonal). CHOLMOD is written in ANSI/ISO C, with both C and MATLAB interfaces. This code works on Microsoft Windows and many versions of Unix and Linux. CHOLMOD Copyright c 2005-2015 by Timothy A. Davis. Portions are also copyrighted by William W. Hager (the Modify Module), and the University of Florida (the Partition and Core Modules). All Rights Reserved. See CHOLMOD/Doc/License.txt for the license. CHOLMOD is also available under other licenses that permit its use in proprietary applications; contact the authors for details. See http://www.suitesparse.com for the code and all documentation, including this User Guide. 1CHOLMOD is short for CHOLesky MODification, since a key feature of the package is its ability to up- date/downdate a sparse Cholesky factorization 1 Contents 1 Overview 8 2 Primary routines and data structures 9 3 Simple example program 11 4 Installation of the C-callable library 12 5 Using CHOLMOD in MATLAB 15 5.1 analyze: order and analyze .