Template Numerical Library version\ main:6a1fe78
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Public Types | Public Member Functions | Static Public Member Functions | List of all members
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 >:
Inheritance graph
[legend]

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 auxiliary 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 ()=default
 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
Matrixis type of matrix describing the linear system.

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

1#include <iostream>
2#include <memory>
3#include <TNL/Matrices/SparseMatrix.h>
4#include <TNL/Devices/Host.h>
5#include <TNL/Devices/Cuda.h>
6#include <TNL/Solvers/Linear/TFQMR.h>
7#include <TNL/Solvers/Linear/Preconditioners/Diagonal.h>
8
9template< typename Device >
10void
11iterativeLinearSolverExample()
12{
13 /***
14 * Set the following matrix (dots represent zero matrix elements):
15 *
16 * / 2.5 -1 . . . \
17 * | -1 2.5 -1 . . |
18 * | . -1 2.5 -1. . |
19 * | . . -1 2.5 -1 |
20 * \ . . . -1 2.5 /
21 */
22 using MatrixType = TNL::Matrices::SparseMatrix< double, Device >;
23 using Vector = TNL::Containers::Vector< double, Device >;
24 const int size( 5 );
25 auto matrix_ptr = std::make_shared< MatrixType >();
26 matrix_ptr->setDimensions( size, size );
27 matrix_ptr->setRowCapacities( Vector( { 2, 3, 3, 3, 2 } ) );
28
29 auto f = [ = ] __cuda_callable__( typename MatrixType::RowView & row ) mutable
30 {
31 const int rowIdx = row.getRowIndex();
32 if( rowIdx == 0 ) {
33 row.setElement( 0, rowIdx, 2.5 ); // diagonal element
34 row.setElement( 1, rowIdx + 1, -1 ); // element above the diagonal
35 }
36 else if( rowIdx == size - 1 ) {
37 row.setElement( 0, rowIdx - 1, -1.0 ); // element below the diagonal
38 row.setElement( 1, rowIdx, 2.5 ); // diagonal element
39 }
40 else {
41 row.setElement( 0, rowIdx - 1, -1.0 ); // element below the diagonal
42 row.setElement( 1, rowIdx, 2.5 ); // diagonal element
43 row.setElement( 2, rowIdx + 1, -1.0 ); // element above the diagonal
44 }
45 };
46
47 /***
48 * Set the matrix elements.
49 */
50 matrix_ptr->forAllRows( f );
51 std::cout << *matrix_ptr << std::endl;
52
53 /***
54 * Set the right-hand side vector.
55 */
56 Vector x( size, 1.0 );
57 Vector b( size );
58 matrix_ptr->vectorProduct( x, b );
59 x = 0.0;
60 std::cout << "Vector b = " << b << std::endl;
61
62 /***
63 * Solve the linear system using diagonal (Jacobi) preconditioner.
64 */
65 using LinearSolver = TNL::Solvers::Linear::TFQMR< MatrixType >;
66 using Preconditioner = TNL::Solvers::Linear::Preconditioners::Diagonal< MatrixType >;
67 auto preconditioner_ptr = std::make_shared< Preconditioner >();
68 preconditioner_ptr->update( matrix_ptr );
69 LinearSolver solver;
70 solver.setMatrix( matrix_ptr );
71 solver.setPreconditioner( preconditioner_ptr );
72 solver.setConvergenceResidue( 1.0e-6 );
73 solver.solve( b, x );
74 std::cout << "Vector x = " << x << std::endl;
75}
76
77int
78main( int argc, char* argv[] )
79{
80 std::cout << "Solving linear system on host: " << std::endl;
81 iterativeLinearSolverExample< TNL::Devices::Sequential >();
82
83#ifdef __CUDACC__
84 std::cout << "Solving linear system on CUDA device: " << std::endl;
85 iterativeLinearSolverExample< TNL::Devices::Cuda >();
86#endif
87}
__cuda_callable__
#define __cuda_callable__
Definition Macros.h:49
TNL::Containers::Vector
Vector extends Array with algebraic operations.
Definition Vector.h:36
TNL::Matrices::SparseMatrix
Implementation of sparse matrix, i.e. matrix storing only non-zero elements.
Definition SparseMatrix.h:55
TNL::Solvers::Linear::Preconditioners::Diagonal
Diagonal (Jacobi) preconditioner for iterative solvers of linear systems.
Definition Diagonal.h:21
TNL::Solvers::Linear::Preconditioners::Preconditioner::MatrixType
Matrix MatrixType
Type of the matrix representing the linear system.
Definition Preconditioner.h:62
TNL::Solvers::Linear::TFQMR
Iterative solver of linear systems based on the Transpose-free quasi-minimal residual (TFQMR) method.
Definition TFQMR.h:21
std::endl
T endl(T... args)
std::make_shared
T make_shared(T... args)

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 auxiliary data will alloacted on.

See Devices::Host or Devices::Cuda.

Member Function Documentation

◆ configSetup()

template<typename Matrix>
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
configcontains description of configuration parameters.
prefixis 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
parameterscontains values of the define configuration entries.
prefixis 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
bis the input vector the preconditioner is applied on.
xis the result of the preconditioning.

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 >.

◆ 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
matrixPointersmart 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 >.

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