gko::factorization

Matrix factorisations used to build preconditioners and direct solvers. Each factorisation is a LinOpFactory that consumes a system matrix and produces its factors in CSR format. The exact factorisations Cholesky and Lu return a Factorization object; the incomplete factorisations return a Composition of the factor matrices.

Exact factorisations (experimental)

• experimental::Cholesky: sparse Cholesky for symmetric positive-definite systems.

• experimental::Lu: sparse LU for general systems.

Incomplete factorisations (exact IC(0) and ILU(0))

• Ic: IC(0), incomplete Cholesky with the same sparsity pattern as the input matrix; the algorithm parameter selects the sparselib or syncfree implementation.

• Ilu: ILU(0), incomplete LU with the same sparsity pattern as the input matrix; the algorithm parameter selects the sparselib or syncfree implementation.

Incomplete factorisations (fine-grained parallel)

• ParIc: ParIC, asynchronous fixed-point iteration for IC(0) (Chow & Patel).

• ParIlu: ParILU, asynchronous fixed-point iteration for ILU(0) (Chow & Patel).

• ParIct: ParICT, threshold-based incomplete Cholesky with sparsity-pattern refinement (Anzt et al.).

• ParIlut: ParILUT, threshold-based incomplete LU with sparsity-pattern refinement (Anzt et al.).

The factor container

• experimental::Factorization: the LinOp that Cholesky and Lu return; it owns the factors, which gko::experimental::solver::Direct uses for its triangular solves; apply multiplies by the factors when they are kept as a composition.