 Eigen  3.3.7 Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > Class Template Reference

## Detailed Description

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

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

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
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 .

class LeastSquaresConjugateGradient, class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner Inheritance diagram for Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >:

## Public Member Functions

template<typename MatrixDerived >
ConjugateGradient (const EigenBase< MatrixDerived > &A) Public Member Functions inherited from Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & analyzePattern (const EigenBase< MatrixDerived > &A)

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

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

## Constructor & Destructor Documentation

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
inline

Default constructor.

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.

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