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 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 ()
	Default constructor. More...
template<typename MatrixDerived >
	ConjugateGradient (const EigenBase< MatrixDerived > &A)
	Initialize the solver with matrix A for further Ax=b solving. More...
template<typename Rhs , typename Dest >
void	_solve_with_guess_impl (const Rhs &b, Dest &x) const
template<typename Rhs , typename Dest >
void	_solve_impl (const MatrixBase< Rhs > &b, Dest &x) const
Public Member Functions inherited from Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
	IterativeSolverBase ()
	Default constructor. More...
	IterativeSolverBase (const EigenBase< MatrixDerived > &A)
	Initialize the solver with matrix A for further Ax=b solving. More...
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	analyzePattern (const EigenBase< MatrixDerived > &A)
	Initializes the iterative solver for the sparsity pattern of the matrix A for further solving Ax=b problems. More...
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	factorize (const EigenBase< MatrixDerived > &A)
	Initializes the iterative solver with the numerical values of the matrix A for further solving Ax=b problems. More...
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	compute (const EigenBase< MatrixDerived > &A)
	Initializes the iterative solver with the matrix A for further solving Ax=b problems. More...
Index	rows () const
Index	cols () const
RealScalar	tolerance () const
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	setTolerance (const RealScalar &tolerance)
	Sets the tolerance threshold used by the stopping criteria. More...
Preconditioner &	preconditioner ()
const Preconditioner &	preconditioner () const
Index	maxIterations () const
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	setMaxIterations (Index maxIters)
	Sets the max number of iterations. More...
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_impl (const Rhs &b, SparseMatrixBase< DestDerived > &aDest) const
Public Member Functions inherited from Eigen::SparseSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
	SparseSolverBase ()
	Default constructor.
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
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
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 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

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.

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

• third-party-libs/eigen3/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h