TNL::Solvers::Linear::Preconditioners::Preconditioner< Matrix > Class Template Reference

Base class for preconditioners of of iterative solvers of linear systems. More...

#include <TNL/Solvers/Linear/Preconditioners/Preconditioner.h>

Inheritance diagram for TNL::Solvers::Linear::Preconditioners::Preconditioner< Matrix >:

Public Types
using	ConstVectorViewType = typename Traits< Matrix >::ConstVectorViewType
	Type for constant vector view.
using	DeviceType = typename Matrix::DeviceType
	Device where the solver will run on and auxillary data will alloacted on.
using	IndexType = typename Matrix::IndexType
	Type for indexing.
using	MatrixPointer = std::shared_ptr< std::add_const_t< MatrixType > >
	Type of shared pointer to the matrix.
using	MatrixType = Matrix
	Type of the matrix representing the linear system.
using	RealType = typename Matrix::RealType
	Floating point type used for computations.
using	VectorViewType = typename Traits< Matrix >::VectorViewType
	Type for vector view.

Public Member Functions
virtual	~Preconditioner ()
	Destructor of the preconditioner.
virtual bool	setup (const Config::ParameterContainer &parameters, const String &prefix="")
	Method for setup of the preconditioner of linear iterative solver based on configuration parameters.
virtual void	solve (ConstVectorViewType b, VectorViewType x) const
	This method applies the preconditioner.
virtual void	update (const MatrixPointer &matrixPointer)
	This method updates the preconditioner with respect to given matrix.

Static Public Member Functions
static void	configSetup (Config::ConfigDescription &config, const String &prefix="")
	This method defines configuration entries for setup of the preconditioner of linear iterative solver.

Detailed Description

template<typename Matrix>
class TNL::Solvers::Linear::Preconditioners::Preconditioner< Matrix >

Base class for preconditioners of of iterative solvers of linear systems.

Template Parameters

Matrix

is type of matrix describing the linear system.

The following example shows how to setup an iterative solver of linear systems with preconditioning:

#include <iostream>
#include <memory>
#include <TNL/Matrices/SparseMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
#include <TNL/Solvers/Linear/TFQMR.h>
#include <TNL/Solvers/Linear/Preconditioners/Diagonal.h>
 
template< typename Device >
void
iterativeLinearSolverExample()
{
   /***
    * Set the following matrix (dots represent zero matrix elements):
    *
    *   /  2.5 -1    .    .    .   \
    *   | -1    2.5 -1    .    .   |
    *   |  .   -1    2.5 -1.   .   |
    *   |  .    .   -1    2.5 -1   |
    *   \  .    .    .   -1    2.5 /
    */
   using MatrixType = TNL::Matrices::SparseMatrix< double, Device >;
   using Vector = TNL::Containers::Vector< double, Device >;
   const int size( 5 );
   auto matrix_ptr = std::make_shared< MatrixType >();
   matrix_ptr->setDimensions( size, size );
   matrix_ptr->setRowCapacities( Vector( { 2, 3, 3, 3, 2 } ) );
 
   auto f = [ = ] __cuda_callable__( typename MatrixType::RowView & row ) mutable
   {
      const int rowIdx = row.getRowIndex();
      if( rowIdx == 0 ) {
         row.setElement( 0, rowIdx, 2.5 );     // diagonal element
         row.setElement( 1, rowIdx + 1, -1 );  // element above the diagonal
      }
      else if( rowIdx == size - 1 ) {
         row.setElement( 0, rowIdx - 1, -1.0 );  // element below the diagonal
         row.setElement( 1, rowIdx, 2.5 );       // diagonal element
      }
      else {
         row.setElement( 0, rowIdx - 1, -1.0 );  // element below the diagonal
         row.setElement( 1, rowIdx, 2.5 );       // diagonal element
         row.setElement( 2, rowIdx + 1, -1.0 );  // element above the diagonal
      }
   };
 
   /***
    * Set the matrix elements.
    */
   matrix_ptr->forAllRows( f );
   std::cout << *matrix_ptr << std::endl;
 
   /***
    * Set the right-hand side vector.
    */
   Vector x( size, 1.0 );
   Vector b( size );
   matrix_ptr->vectorProduct( x, b );
   x = 0.0;
   std::cout << "Vector b = " << b << std::endl;
 
   /***
    * Solve the linear system using diagonal (Jacobi) preconditioner.
    */
   using LinearSolver = TNL::Solvers::Linear::TFQMR< MatrixType >;
   using Preconditioner = TNL::Solvers::Linear::Preconditioners::Diagonal< MatrixType >;
   auto preconditioner_ptr = std::make_shared< Preconditioner >();
   preconditioner_ptr->update( matrix_ptr );
   LinearSolver solver;
   solver.setMatrix( matrix_ptr );
   solver.setPreconditioner( preconditioner_ptr );
   solver.setConvergenceResidue( 1.0e-6 );
   solver.solve( b, x );
   std::cout << "Vector x = " << x << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Solving linear system on host: " << std::endl;
   iterativeLinearSolverExample< TNL::Devices::Sequential >();
 
#ifdef __CUDACC__
   std::cout << "Solving linear system on CUDA device: " << std::endl;
   iterativeLinearSolverExample< TNL::Devices::Cuda >();
#endif
}

The result looks as follows:

Solving linear system on host: 
Row: 0 ->     0:2.5     1:-1  
Row: 1 ->     0:-1      1:2.5     2:-1  
Row: 2 ->     1:-1      2:2.5     3:-1  
Row: 3 ->     2:-1      3:2.5     4:-1  
Row: 4 ->     3:-1      4:2.5 
 
Vector b = [ 1.5, 0.5, 0.5, 0.5, 1.5 ]
Vector x = [ 1, 1, 1, 1, 1 ]
Solving linear system on CUDA device: 
Row: 0 ->     0:2.5     1:-1  
Row: 1 ->     0:-1      1:2.5     2:-1  
Row: 2 ->     1:-1      2:2.5     3:-1  
Row: 3 ->     2:-1      3:2.5     4:-1  
Row: 4 ->     3:-1      4:2.5 
 
Vector b = [ 1.5, 0.5, 0.5, 0.5, 1.5 ]
Vector x = [ 1, 1, 1, 1, 1 ]

Member Typedef Documentation

DeviceType

template<typename Matrix >

using TNL::Solvers::Linear::Preconditioners::Preconditioner< Matrix >::DeviceType = typename Matrix::DeviceType

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

See Devices::Host or Devices::Cuda.

Member Function Documentation

configSetup()

template<typename Matrix >

static void TNL::Solvers::Linear::Preconditioners::Preconditioner< Matrix >::configSetup ( Config::ConfigDescription & config, const String & prefix = "" )

inlinestatic

This method defines configuration entries for setup of the preconditioner of linear iterative solver.

Parameters

config	contains description of configuration parameters.
prefix	is a prefix of particular configuration entries.

setup()

template<typename Matrix >

virtual bool TNL::Solvers::Linear::Preconditioners::Preconditioner< Matrix >::setup ( const Config::ParameterContainer & parameters, const String & prefix = "" )

inlinevirtual

Method for setup of the preconditioner of linear iterative solver based on configuration parameters.

Parameters

parameters	contains values of the define configuration entries.
prefix	is a prefix of particular configuration entries.

Reimplemented in TNL::Solvers::Linear::Preconditioners::ILUT_impl< Matrix, Real, Devices::Host, Index >.

solve()

template<typename Matrix >

virtual void TNL::Solvers::Linear::Preconditioners::Preconditioner< Matrix >::solve ( ConstVectorViewType b, VectorViewType x ) const

inlinevirtual

This method applies the preconditioner.

Parameters

b	is the input vector the preconditioner is applied on.
x	is the result of the preconditioning.

Reimplemented in TNL::Solvers::Linear::Preconditioners::Diagonal< Matrix >, TNL::Solvers::Linear::Preconditioners::ILU0_impl< Matrix, Real, Devices::Cuda, Index >, TNL::Solvers::Linear::Preconditioners::ILU0_impl< Matrix, Real, Devices::Host, Index >, TNL::Solvers::Linear::Preconditioners::ILUT_impl< Matrix, Real, Devices::Cuda, Index >, and TNL::Solvers::Linear::Preconditioners::ILUT_impl< Matrix, Real, Devices::Host, Index >.

update()

template<typename Matrix >

virtual void TNL::Solvers::Linear::Preconditioners::Preconditioner< Matrix >::update ( const MatrixPointer & matrixPointer )

inlinevirtual

This method updates the preconditioner with respect to given matrix.

Parameters

matrixPointer

smart pointer (std::shared_ptr) to matrix the preconditioner is related to.

Reimplemented in TNL::Solvers::Linear::Preconditioners::Diagonal< Matrix >, TNL::Solvers::Linear::Preconditioners::Diagonal< Matrices::DistributedMatrix< Matrix > >, TNL::Solvers::Linear::Preconditioners::ILU0_impl< Matrix, Real, Devices::Cuda, Index >, TNL::Solvers::Linear::Preconditioners::ILU0_impl< Matrix, Real, Devices::Host, Index >, TNL::Solvers::Linear::Preconditioners::ILUT_impl< Matrix, Real, Devices::Cuda, Index >, and TNL::Solvers::Linear::Preconditioners::ILUT_impl< Matrix, Real, Devices::Host, Index >.

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

• src/TNL/Solvers/Linear/Preconditioners/Preconditioner.h