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 MatrixType::Scalar	Scalar

typedef MatrixType::RealScalar	RealScalar

typedef _Preconditioner	Preconditioner

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::Scalar	Scalar

typedef MatrixType::StorageIndex	StorageIndex

typedef MatrixType::RealScalar	RealScalar

Public Member Functions
	ConjugateGradient ()

template<typename MatrixDerived >
	ConjugateGradient (const EigenBase< MatrixDerived > &A)

	~ConjugateGradient ()

template<typename Rhs , typename Dest >
void	_solve_vector_with_guess_impl (const Rhs &b, Dest &x) const

Public Member Functions inherited from Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
	IterativeSolverBase ()

	IterativeSolverBase (const EigenBase< MatrixDerived > &A)

	~IterativeSolverBase ()

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

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

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

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

RealScalar	tolerance () const

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	setTolerance (const RealScalar &tolerance)

Preconditioner &	preconditioner ()

const Preconditioner &	preconditioner () const

Index	maxIterations () const

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	setMaxIterations (Index maxIters)

Index	iterations () const

RealScalar	error () const

const SolveWithGuess< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >, Rhs, Guess >	solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const

ComputationInfo	info () const

void	_solve_with_guess_impl (const Rhs &b, SparseMatrixBase< DestDerived > &aDest) const

internal::enable_if< Rhs::ColsAtCompileTime!=1 &&DestDerived::ColsAtCompileTime!=1 >::type	_solve_with_guess_impl (const Rhs &b, MatrixBase< DestDerived > &aDest) const

internal::enable_if< Rhs::ColsAtCompileTime==1\|\|DestDerived::ColsAtCompileTime==1 >::type	_solve_with_guess_impl (const Rhs &b, MatrixBase< DestDerived > &dest) const

void	_solve_impl (const Rhs &b, Dest &x) const

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	derived ()

const ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	derived () const

Public Member Functions inherited from Eigen::SparseSolverBase< Derived >
	SparseSolverBase ()

	~SparseSolverBase ()

Derived &	derived ()

const Derived &	derived () const

template<typename Rhs >
const Solve< Derived, Rhs >	solve (const MatrixBase< Rhs > &b) const

template<typename Rhs >
const Solve< Derived, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const

template<typename Rhs , typename Dest >
void	_solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const

Additional Inherited Members
Protected Types inherited from Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
typedef SparseSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >	Base

typedef internal::generic_matrix_wrapper< MatrixType >	MatrixWrapper

typedef MatrixWrapper::ActualMatrixType	ActualMatrixType

Protected Member Functions inherited from Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
void	init ()

const ActualMatrixType &	matrix () const

void	grab (const InputType &A)

Protected Attributes inherited from Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
MatrixWrapper	m_matrixWrapper

Preconditioner	m_preconditioner

Index	m_maxIterations

RealScalar	m_tolerance

RealScalar	m_error

Index	m_iterations

ComputationInfo	m_info

bool	m_analysisIsOk

bool	m_factorizationIsOk

bool	m_isInitialized

Protected Attributes inherited from Eigen::SparseSolverBase< Derived >
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

\implsparsesolverconcept

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 Eigen and multi-threading 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

Member Typedef Documentation

◆ MatrixType

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

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

◆ Preconditioner

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

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

◆ RealScalar

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

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

◆ Scalar

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

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

Member Enumeration Documentation

◆ anonymous enum

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

anonymous enum

Enumerator
UpLo

Constructor & Destructor Documentation

◆ ConjugateGradient() [1/2]

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

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

inline

Default constructor.

◆ ConjugateGradient() [2/2]

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.

◆ ~ConjugateGradient()

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

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

inline

Member Function Documentation

◆ _solve_vector_with_guess_impl()

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

template<typename Rhs , typename Dest >

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

inline

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

core/util/algorithms/eigen-3.4.0/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ MatrixType

◆ Preconditioner

◆ RealScalar

◆ Scalar

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ ConjugateGradient() [1/2]

◆ ConjugateGradient() [2/2]

◆ ~ConjugateGradient()

Member Function Documentation

◆ _solve_vector_with_guess_impl()