colsol is a column-oriented direct solver for linear systems, designed to compute an LDLᵀ factorization of a stiffness matrix or to perform reduction and back-substitution of a load vector.
This crate implements a simple direct solver for linear systems using column-oriented Gaussian elimination.
The goal of this project is not to provide a production-ready linear algebra library, but to explore how direct solvers work internally and how classical numerical algorithms can be expressed clearly and safely in Rust.
The implementation is intentionally explicit and close to the underlying mathematics, making it suitable for learning, experimentation, and reference.
This crate was written as part of a broader effort to revisit numerical methods from first principles.
Having previously worked with engineering and finite-element analysis (FEA) tools, I wanted to better understand how linear solvers are implemented internally — both to strengthen my numerical background and to support later work involving sparse systems, iterative methods, and GPU-based computation.
This project focuses on direct methods, where a linear system is solved in a finite number of algebraic steps (e.g. Gaussian elimination and matrix factorization).
In contrast, iterative methods (such as Conjugate Gradient or PCG) are explored in the companion crate:
Both approaches are widely used in numerical computing.
This crate serves as a conceptual foundation for understanding more advanced
solver techniques.
- Method: column-oriented Gaussian elimination
- Factorization: LDLᵀ
- Matrix type: symmetric, positive definite
- Focus: clarity and algorithmic structure rather than performance tuning
Note:
colsolcan be used only for symmetric and positive definite stiffness matrices.
- A — stiffness matrix stored in compact (profile/skyline) form
- NN — number of equations
- MAXA — vector containing addresses of diagonal elements of the stiffness matrix in A
- V — right-hand side (load) vector
- A — modified in place to store D and L factors of the stiffness matrix
- V — displacement (solution) vector
The solver operates on a compact storage format commonly used in structural engineering and finite-element codes.
This project is primarily intended for learning, experimentation, and as part of a broader numerical computing portfolio.
MIT (see LICENSE).