gko::LinOpFactory Class Reference

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:

Collaboration diagram for gko::LinOpFactory:

Public Member Functions
std::unique_ptr< LinOp >	generate (std::shared_ptr< const LinOp > input) const
Public Member Functions inherited from gko::PolymorphicObject
virtual void	validate_data () const
	Throws gko::InvalidData exception if we found the data inside the object does not fulfill certain property up to our knowledge.
PolymorphicObject &	operator= (const PolymorphicObject &)
std::shared_ptr< const Executor >	get_executor () const noexcept
	Returns the Executor of the object. More...
Public Member Functions inherited from gko::log::EnableLogging< PolymorphicObject >
void	add_logger (std::shared_ptr< const Logger > logger) override
void	remove_logger (const Logger *logger) override
void	remove_logger (ptr_param< const Logger > logger)
const std::vector< std::shared_ptr< const Logger > > &	get_loggers () const override
void	clear_loggers () override
Public Member Functions inherited from gko::log::Loggable
void	remove_logger (ptr_param< const Logger > logger)

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

 {c++}
// 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);

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The documentation for this class was generated from the following file:

• ginkgo/core/base/lin_op.hpp