Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner > Class Template Reference

A conjugate gradient solver for sparse (or dense) least-square problems. More...

#include <LeastSquareConjugateGradient.h>

Public Types
typedef _MatrixType	MatrixType
typedef _Preconditioner	Preconditioner
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::Scalar	Scalar

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

Private Types
typedef IterativeSolverBase< LeastSquaresConjugateGradient >	Base

Private Member Functions
const ActualMatrixType &	matrix () const

Private Attributes
RealScalar	m_error
ComputationInfo	m_info
bool	m_isInitialized
Index	m_iterations

Detailed Description

template<typename _MatrixType, typename _Preconditioner>
class Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >

A conjugate gradient solver for sparse (or dense) least-square problems.

This class allows to solve for A x = b linear problems using an iterative conjugate gradient algorithm. The matrix A can be non symmetric and rectangular, but the matrix A' A should be positive-definite to guaranty stability. Otherwise, the SparseLU or SparseQR classes might be preferable. 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.
_Preconditioner	the type of the preconditioner. Default is LeastSquareDiagonalPreconditioner

\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.

This class can be used as the direct solver classes. Here is a typical usage example:

int m=1000000, n = 10000;
VectorXd x(n), b(m);
SparseMatrix<double> A(m,n);
// fill A and b
LeastSquaresConjugateGradient<SparseMatrix<double> > lscg;
lscg.compute(A);
x = lscg.solve(b);
std::cout << "#iterations:     " << lscg.iterations() << std::endl;
std::cout << "estimated error: " << lscg.error()      << std::endl;
// update b, and solve again
x = lscg.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.

See also

class ConjugateGradient, SparseLU, SparseQR

Definition at line 98 of file LeastSquareConjugateGradient.h.

Member Typedef Documentation

Base

template<typename _MatrixType , typename _Preconditioner >

typedef IterativeSolverBase<LeastSquaresConjugateGradient> Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >::Base

private

Definition at line 151 of file LeastSquareConjugateGradient.h.

MatrixType

template<typename _MatrixType , typename _Preconditioner >

typedef _MatrixType Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >::MatrixType

Definition at line 158 of file LeastSquareConjugateGradient.h.

Preconditioner

template<typename _MatrixType , typename _Preconditioner >

typedef _Preconditioner Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >::Preconditioner

Definition at line 161 of file LeastSquareConjugateGradient.h.

RealScalar

template<typename _MatrixType , typename _Preconditioner >

typedef MatrixType::RealScalar Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >::RealScalar

Definition at line 160 of file LeastSquareConjugateGradient.h.

Scalar

template<typename _MatrixType , typename _Preconditioner >

typedef MatrixType::Scalar Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >::Scalar

Definition at line 159 of file LeastSquareConjugateGradient.h.

Constructor & Destructor Documentation

LeastSquaresConjugateGradient() [1/2]

template<typename _MatrixType , typename _Preconditioner >

Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >::LeastSquaresConjugateGradient ( )

inline

Default constructor.

Definition at line 166 of file LeastSquareConjugateGradient.h.

LeastSquaresConjugateGradient() [2/2]

template<typename _MatrixType , typename _Preconditioner >

template<typename MatrixDerived >

Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >::LeastSquaresConjugateGradient ( 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.

Definition at line 179 of file LeastSquareConjugateGradient.h.

~LeastSquaresConjugateGradient()

template<typename _MatrixType , typename _Preconditioner >

Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >::~LeastSquaresConjugateGradient ( )

inline

Definition at line 181 of file LeastSquareConjugateGradient.h.

Member Function Documentation

_solve_vector_with_guess_impl()

template<typename _MatrixType , typename _Preconditioner >

template<typename Rhs , typename Dest >

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

inline

Definition at line 185 of file LeastSquareConjugateGradient.h.

matrix()

template<typename _MatrixType , typename _Preconditioner >

const ActualMatrixType& Eigen::IterativeSolverBase< Derived >::matrix

inlineprivate

Definition at line 419 of file IterativeSolverBase.h.

Member Data Documentation

m_error

template<typename _MatrixType , typename _Preconditioner >

RealScalar Eigen::IterativeSolverBase< Derived >::m_error

mutableprivate

Definition at line 436 of file IterativeSolverBase.h.

m_info

template<typename _MatrixType , typename _Preconditioner >

ComputationInfo Eigen::IterativeSolverBase< Derived >::m_info

mutableprivate

Definition at line 438 of file IterativeSolverBase.h.

m_isInitialized

template<typename _MatrixType , typename _Preconditioner >

bool Eigen::SparseSolverBase< Derived >::m_isInitialized

mutableprivate

Definition at line 119 of file SparseSolverBase.h.

m_iterations

template<typename _MatrixType , typename _Preconditioner >

Index Eigen::IterativeSolverBase< Derived >::m_iterations

mutableprivate

Definition at line 437 of file IterativeSolverBase.h.

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

• LeastSquareConjugateGradient.h