Cholmod

Cholmod is a lightweight C library for solving sparse symmetric positive definite systems using Cholesky factorization. It is part of SuiteSparse, a collection of high‑performance sparse matrix algorithms developed by Timothy A. Davis. The library implements the multifrontal method, building a tree of smaller dense frontal matrices that are factorized recursively. Cholmod is designed to be memory‑efficient by factoring only nonzero elements and using compressed storage formats such as compressed column storage.

The primary interface of Cholmod consists of functions that create and destroy dense and sparse matrices, compute symbolic factorizations, perform numerical factorization, and solve linear systems using the resulting L and L transposed factors. It also provides routines to evaluate the factorization's sparsity pattern, enable or disable level‑of‑sparsity reduction, and estimate fill‑in. Users may select between sequential and multithreaded modes, allowing the library to exploit multi‑core CPUs.

Cholmod is licensed under a permissive MIT license, making it suitable for both academic research and commercial software. It is written in ANSI C and depends only on the standard C library, which facilitates integration into a wide range of programming environments. Bindings to other languages such as MATLAB, Python, and Julia are available through third‑party modules, allowing developers to harness Cholmod’s performance from higher‑level code. The library has been adopted in numerous scientific computing applications, including finite element analysis, machine learning, and large‑scale optimization, where robust and efficient sparse linear solvers are essential.