Core types

The abstract interfaces every Ginkgo class lives behind. LinOp is the linear-operator interface — matrices, solvers, preconditioners, and any composed operator inherits from it. LinOpFactory is the matching factory interface that generates a LinOp from a system matrix. The remaining types in this section are mixins and trait classes that concrete operators implement.

The operator interface

• LinOp — abstract base for every linear operator in Ginkgo. Defines apply, copy/clone, size, executor, and the logging hooks that flow through every operation.

• LinOpFactory — abstract base for factories that produce a LinOp (typically a solver or preconditioner) when given a system matrix.

Operator algebra

• Combination — a linear combination of LinOps, \(c_1\, A_1 + c_2\, A_2 + \cdots + c_k\, A_k\), as a single LinOp.

• Composition — function composition of LinOps, \(A_1 \cdot A_2 \cdot \ldots \cdot A_n\), evaluated right-to-left.

Memory containers

• array — owning, executor-aware contiguous buffer; the storage unit that backs every Ginkgo data structure.

• matrix_data — host-side (row, col, value) triple-list used as the executor-independent assembly format for every sparse matrix type.

Mixins and traits

• EnableLinOp — CRTP mixin that supplies the boilerplate LinOp overrides — apply_impl dispatch, default copy/clone, polymorphic-object plumbing — so concrete operators only need to implement the algorithm.

• Transposable — trait interface for operators that can produce their transpose and conjugate transpose.