Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > Class Template Reference

A conjugate gradient solver for sparse (or dense) self-adjoint problems. More...

#include <ConjugateGradient.h>

Inheritance diagram for Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >:

Public Types
enum	{ UpLo = _UpLo }
typedef _MatrixType	MatrixType
typedef _Preconditioner	Preconditioner
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::Scalar	Scalar
Public Types inherited from Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
enum
typedef internal::traits< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::MatrixType	MatrixType
typedef internal::traits< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::Preconditioner	Preconditioner
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::Scalar	Scalar
typedef MatrixType::StorageIndex	StorageIndex

Public Member Functions
template<typename Rhs , typename Dest >
void	_solve_impl (const MatrixBase< Rhs > &b, Dest &x) const
template<typename Rhs , typename Dest >
void	_solve_with_guess_impl (const Rhs &b, Dest &x) const
	ConjugateGradient ()
template<typename MatrixDerived >
	ConjugateGradient (const EigenBase< MatrixDerived > &A)
	~ConjugateGradient ()
Public Member Functions inherited from Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
void	_solve_impl (const Rhs &b, SparseMatrixBase< DestDerived > &aDest) const
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	analyzePattern (const EigenBase< MatrixDerived > &A)
Index	cols () const
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	compute (const EigenBase< MatrixDerived > &A)
RealScalar	error () const
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	factorize (const EigenBase< MatrixDerived > &A)
ComputationInfo	info () const
Index	iterations () const
	IterativeSolverBase ()
	IterativeSolverBase (const EigenBase< MatrixDerived > &A)
Index	maxIterations () const
Preconditioner &	preconditioner ()
const Preconditioner &	preconditioner () const
Index	rows () const
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	setMaxIterations (Index maxIters)
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	setTolerance (const RealScalar &tolerance)
const SolveWithGuess< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >, Rhs, Guess >	solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const
RealScalar	tolerance () const
	~IterativeSolverBase ()
Public Member Functions inherited from Eigen::SparseSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
void	_solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	derived ()
const ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	derived () const
const Solve< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >, Rhs >	solve (const MatrixBase< Rhs > &b) const
const Solve< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const
	SparseSolverBase ()
	~SparseSolverBase ()

Private Types
typedef IterativeSolverBase< ConjugateGradient >	Base

Additional Inherited Members
Protected Types inherited from Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
typedef MatrixWrapper::ActualMatrixType	ActualMatrixType
typedef SparseSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >	Base
typedef internal::generic_matrix_wrapper< MatrixType >	MatrixWrapper
Protected Member Functions inherited from Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
void	grab (const InputType &A)
void	init ()
const ActualMatrixType &	matrix () const
Protected Attributes inherited from Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
bool	m_analysisIsOk
RealScalar	m_error
bool	m_factorizationIsOk
ComputationInfo	m_info
Index	m_iterations
MatrixWrapper	m_matrixWrapper
Index	m_maxIterations
Preconditioner	m_preconditioner
RealScalar	m_tolerance
Protected Attributes inherited from Eigen::SparseSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
bool	m_isInitialized

Detailed Description

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
class Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >

A conjugate gradient solver for sparse (or dense) self-adjoint problems.

This class allows to solve for A.x = b linear problems using an iterative conjugate gradient algorithm. The matrix A must be selfadjoint. The matrix A and the vectors x and b can be either dense or sparse.

Template Parameters

_MatrixType	the type of the matrix A, can be a dense or a sparse matrix.
_UpLo	the triangular part that will be used for the computations. It can be Lower, Upper, or Lower|Upper in which the full matrix entries will be considered. Default is Lower, best performance is Lower|Upper.
_Preconditioner	the type of the preconditioner. Default is DiagonalPreconditioner

The maximal number of iterations and tolerance value can be controlled via the setMaxIterations() and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations and NumTraits<Scalar>::epsilon() for the tolerance.

The tolerance corresponds to the relative residual error: |Ax-b|/|b|

Performance: Even though the default value of _UpLo is Lower, significantly higher performance is achieved when using a complete matrix and Lower|Upper as the _UpLo template parameter. Moreover, in this case multi-threading can be exploited if the user code is compiled with OpenMP enabled. See TopicMultiThreading for details.

This class can be used as the direct solver classes. Here is a typical usage example:

int n = 10000;
VectorXd x(n), b(n);
SparseMatrix<double> A(n,n);
// fill A and b
ConjugateGradient<SparseMatrix<double>, Lower|Upper> cg;
cg.compute(A);
x = cg.solve(b);
std::cout << "#iterations:     " << cg.iterations() << std::endl;
std::cout << "estimated error: " << cg.error()      << std::endl;
// update b, and solve again
x = cg.solve(b);

By default the iterations start with x=0 as an initial guess of the solution. One can control the start using the solveWithGuess() method.

ConjugateGradient can also be used in a matrix-free context, see the following example .

See also

class LeastSquaresConjugateGradient, class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Definition at line 96 of file ConjugateGradient.h.

Member Typedef Documentation

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

typedef IterativeSolverBase<ConjugateGradient> Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >::Base

private

Definition at line 159 of file ConjugateGradient.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

typedef _MatrixType Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >::MatrixType

Definition at line 166 of file ConjugateGradient.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

typedef _Preconditioner Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >::Preconditioner

Definition at line 169 of file ConjugateGradient.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

typedef MatrixType::RealScalar Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >::RealScalar

Definition at line 168 of file ConjugateGradient.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

typedef MatrixType::Scalar Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >::Scalar

Definition at line 167 of file ConjugateGradient.h.

Member Enumeration Documentation

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

anonymous enum

Enumerator
UpLo

Definition at line 171 of file ConjugateGradient.h.

Constructor & Destructor Documentation

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >::ConjugateGradient ( )

inline

Default constructor.

Definition at line 178 of file ConjugateGradient.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

template<typename MatrixDerived >

Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >::ConjugateGradient ( const EigenBase< MatrixDerived > &  A )

inlineexplicit

Initialize the solver with matrix A for further Ax=b solving.

This constructor is a shortcut for the default constructor followed by a call to compute().

Warning

this class stores a reference to the matrix A as well as some precomputed values that depend on it. Therefore, if A is changed this class becomes invalid. Call compute() to update it with the new matrix A, or modify a copy of A.

Definition at line 191 of file ConjugateGradient.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >::~ConjugateGradient ( )

inline

Definition at line 193 of file ConjugateGradient.h.

Member Function Documentation

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

template<typename Rhs , typename Dest >

void Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >::_solve_impl ( const MatrixBase< Rhs > &  b, Dest &  x  ) const

inline

Definition at line 233 of file ConjugateGradient.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

template<typename Rhs , typename Dest >

void Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >::_solve_with_guess_impl ( const Rhs &  b, Dest &  x  ) const

inline

Definition at line 197 of file ConjugateGradient.h.

---

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

• ConjugateGradient.h