Module direct_factorization 

Sparse direct solvers: supernodal Cholesky and multifrontal LU.

Provides direct factorization methods for sparse linear systems, complementing the iterative solvers (CG, GMRES, etc.) with exact methods for when iterative convergence is slow or reliability is paramount.

• SupernodalCholeskySolver — supernodal Cholesky for symmetric positive definite systems
• MultifrontalLUSolver — multifrontal LU with partial pivoting for general sparse systems

(C) 2026 COOLJAPAN OU (Team KitaSan)

Structs

EliminationTree

Elimination tree of a sparse matrix.

MultifrontalLUSolver

Multifrontal LU solver for general (non-symmetric) sparse systems.

SupernodalCholeskySolver

Supernodal Cholesky solver for symmetric positive definite sparse systems.

SupernodalStructure

Supernodal partition of the matrix.

Supernode

A supernode: a contiguous set of columns with identical sparsity below the diagonal.

SymbolicFactorization

Reusable symbolic factorization for repeated numeric factorizations with the same sparsity pattern.

Functions

column_counts

Compute the number of non-zeros in each column of L.

sparse_cholesky_solve

Solve a symmetric positive definite sparse system A * x = b via supernodal Cholesky.

sparse_lu_solve

Solve a general sparse system A * x = b via multifrontal LU.