Writtin documentation for GMRES method.

#pragma once

#include "LinearSolver.h"

#include <TNL/Solvers/Linear/LinearSolver.h>

namespace TNL {

   namespace Solvers {

      namespace Linear {

/**

 * \brief Iterative solver of linear systems based on the Generalized minimal residual (GMRES) method.

 *

 * This method can be used for solving of non-semmetric linear systems. This implementation

 * offers various methods for the orthogonalization of vectors generated by the Arnoldi algorithm.

 * The user may choose one of the following:

 *

 * \e CGS - Classical Gramm-Schmidt,

 *

 * \e CGSR - Classical Gramm-Schmidt with reorthogonalization,

 *

 * \e MGS - Modified Gramm-Schmidt,

 *

 * \e MGSR - Modified Gramm-Schmidt with reorthogonalization (the default one),

 *

 * \e CWY - Compact WY form of the Householder reflections).

 *

 * See [Wikipedia](https://en.wikipedia.org/wiki/Generalized_minimal_residual_method) for more details.

 * 

 * \tparam Matrix is type of matrix describing the linear system.

 */

template< typename Matrix >

class GMRES

: public LinearSolver< Matrix >

   using Traits = Linear::Traits< Matrix >;

   public:

      /**

       * \brief Floating point type used for computations.

       */

      using RealType = typename Base::RealType;

      /**

       * \brief Device where the solver will run on and auxillary data will alloacted on.

       */

      using DeviceType = typename Base::DeviceType;

      /**

       * \brief Type for indexing.

       */

      using IndexType = typename Base::IndexType;

   // distributed vectors/views

      /**

       * \brief Type for vector view.

       */

      using VectorViewType = typename Base::VectorViewType;

      /**

       * \brief Type for constant vector view.

       */

      using ConstVectorViewType = typename Base::ConstVectorViewType;

   using VectorType = typename Traits::VectorType;

      /**

       * \brief This is method defines configuration entries for setup of the linear iterative solver.

       *

       * In addition to config entries defined by \ref IterativeSolver::configSetup, this method

       * defines the following:

       *

       * \e gmres-variant - Algorithm used for the orthogonalization - CGS (Classical Gramm-Schmidt),

       *     CGSR(Classical Gramm-Schmidt with reorthogonalization), MGS(Modified Gramm-Schmidt),

       *     MGSR(Modified Gramm-Schmidt with reorthogonalization), CWY(Compact WY form of the Householder reflections).

       *

       * \e gmres-restarting-min - minimal number of iterations after which the GMRES restarts.

       *

       * \e gmres-restarting-max - maximal number of iterations after which the GMRES restarts.

       *

       * \e gmres-restarting-step-min - minimal adjusting step for the adaptivity of the GMRES restarting parameter.

       *

       * \e gmres-restarting-step-max - maximal adjusting step for the adaptivity of the GMRES restarting parameter.

       *

       * \param config contains description of configuration parameters.

       * \param prefix is a prefix of particular configuration entries.

       */

      static void configSetup( Config::ConfigDescription& config,

                              const String& prefix = "" );

      /**

       * \brief Method for setup of the linear iterative solver based on configuration parameters.

       *

       * \param parameters contains values of the define configuration entries.

       * \param prefix is a prefix of particular configuration entries.

       */

      bool setup( const Config::ParameterContainer& parameters,

                  const String& prefix = "" ) override;

      /**

       * \brief Method for solving of a linear system.

       *

       * See \ref LinearSolver::solve for more details.

       *

       * \param b vector with the right-hand side of the linear system.

       * \param x vector for the solution of the linear system.

       * \return true if the solver converged.

       * \return false if the solver did not converge.

       */

      bool solve( ConstVectorViewType b, VectorViewType x ) override;

   protected:

      using VectorType = typename Traits::VectorType;

      // local vectors/views

      using ConstDeviceView = typename Traits::ConstLocalViewType;

      using DeviceView = typename Traits::LocalViewType;

   } // namespace Solvers

} // namespace TNL

#include "GMRES.hpp"

#include <TNL/Solvers/Linear/GMRES.hpp>