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Eigen  3.3.9
Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > Class Template Reference

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
_MatrixTypethe type of the matrix A, can be a dense or a sparse matrix.
_UpLothe 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.
_Preconditionerthe type of the preconditioner. Default is DiagonalPreconditioner

This class follows the sparse solver concept .

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;
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

Public Member Functions

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

Constructor & Destructor Documentation

◆ ConjugateGradient() [1/2]

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

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)

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().

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.

The documentation for this class was generated from the following file:
@ Upper
Definition: Constants.h:206
@ Lower
Definition: Constants.h:204