Writtin documentation for BICGStab(l) 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 BICGStab(l) method.

 *

 * BICGStabL implements an iterative solver for non-symmetric linear systems,

 * using the BiCGstab(l) algorithm described in [1] and [2]. It is a

 * generalization of the stabilized biconjugate-gradient (BiCGstab) algorithm

 * proposed by van der Vorst [3]. BiCGstab(1) is equivalent to BiCGstab, and

 * BiCGstab(2) is a slightly more efficient version of the BiCGstab2 algorithm

 * by Gutknecht [4], while BiCGstab(l>2) is a further generalization.

 *

 * [1] Gerard L. G. Sleijpen and Diederik R. Fokkema, "BiCGstab(l) for linear

 *     equations involving unsymmetric matrices with complex spectrum",

 *     Electronic Trans. on Numerical Analysis 1, 11-32 (1993).

 *

 * [2] Gerard L. G. Sleijpen, Henk A. van der Vorst, and Diederik R. Fokkema,

 *     "BiCGstab(l) and other Hybrid Bi-CG Methods", Numerical Algorithms 7,

 *     75-109 (1994).

 *

 * [3] Henk A. van der Vorst, "Bi-CGSTAB: A fast and smoothly converging variant

 *     of Bi-CG for the solution of nonsymmetric linear systems, SIAM Journal on

 *     scientific and Statistical Computing 13.2, 631-644 (1992).

 *

 * [4] Martin H. Gutknecht, "Variants of BiCGStab for matrices with complex

 *     spectrum", IPS Research Report No. 91-14 (1991).

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

 */

template< typename Matrix >

class BICGStabL

: 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 bicgstab-ell - number of Bi-CG iterations before the MR part starts.

       * 

       * \e bicgstab-exact-residue - says whether the BiCGstab should compute the exact residue in

       *                             each step (true) or to use a cheap approximation (false).

       *

       * \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;

      using DeviceVector = Containers::Vector< RealType, DeviceType, IndexType >;

      using HostVector = Containers::Vector< RealType, Devices::Host, IndexType >;

   } // namespace Solvers

} // namespace TNL

#include "BICGStabL.hpp"

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