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

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

#include <ConjugateGradient.h>

Public Types
enum	{ UpLo = _UpLo }
typedef _MatrixType	MatrixType
typedef MatrixType::Scalar	Scalar
typedef MatrixType::RealScalar	RealScalar
typedef _Preconditioner	Preconditioner

Public Member Functions
	ConjugateGradient ()
template<typename MatrixDerived >
	ConjugateGradient (const EigenBase< MatrixDerived > &A)
template<typename Rhs , typename Dest >
void	_solve_vector_with_guess_impl (const Rhs &b, Dest &x) const

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 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

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:

• ConjugateGradient.h