Ginkgo Generated from branch based on main. Ginkgo version 1.11.0
A numerical linear algebra library targeting many-core architectures
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gko::LinOpFactory Class Reference
Linear Operators

A LinOpFactory represents a higher order mapping which transforms one linear operator into another. More...

#include <ginkgo/core/base/lin_op.hpp>

Inheritance diagram for gko::LinOpFactory:
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Collaboration diagram for gko::LinOpFactory:
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Public Member Functions

std::unique_ptr< LinOp > generate (std::shared_ptr< const LinOp > input) const

Detailed Description

A LinOpFactory represents a higher order mapping which transforms one linear operator into another.

In Ginkgo, every linear solver is viewed as a mapping. For example, given an s.p.d linear system $Ax = b$, the solution $x = A^{-1}b$ can be computed using the CG method. This algorithm can be represented in terms of linear operators and mappings between them as follows:

  • A Cg::Factory is a higher order mapping which, given an input operator $A$, returns a new linear operator $A^{-1}$ stored in "CG format"
  • Storing the operator $A^{-1}$ in "CG format" means that the data structure used to store the operator is just a simple pointer to the original matrix $A$. The application $x = A^{-1}b$ of such an operator can then be implemented by solving the linear system $Ax = b$ using the CG method. This is achieved in code by having a special class for each of those "formats" (e.g. the "Cg" class defines such a format for the CG solver).

Another example of a LinOpFactory is a preconditioner. A preconditioner for a linear operator $A$ is a linear operator $M^{-1}$, which approximates $A^{-1}$. In addition, it is stored in a way such that both the data of $M^{-1}$ is cheap to compute from $A$, and the operation $x = M^{-1}b$ can be computed quickly. These operators are useful to accelerate the convergence of Krylov solvers. Thus, a preconditioner also fits into the LinOpFactory framework:

  • The factory maps a linear operator $A$ into a preconditioner $M^{-1}$ which is stored in suitable format (e.g. as a product of two factors in case of ILU preconditioners).
  • The resulting linear operator implements the application operation $x = M^{-1}b$ depending on the format the preconditioner is stored in (e.g. as two triangular solves in case of ILU)

Example: using CG in Ginkgo

// Suppose A is a matrix, b a rhs vector, and x an initial guess
// Create a CG which runs for at most 1000 iterations, and stops after
// reducing the residual norm by 6 orders of magnitude
auto cg_factory = solver::Cg<>::build()
.with_max_iters(1000)
.with_rel_residual_goal(1e-6)
.on(cuda);
// create a linear operator which represents the solver
auto cg = cg_factory->generate(A);
// solve the system
cg->apply(b, x);
The documentation for this class was generated from the following file: