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

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

#include <LeastSquareConjugateGradient.h>

Inheritance diagram for Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >:

Collaboration diagram for Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >:

List of all members.

Public Types
typedef _MatrixType	MatrixType
typedef MatrixType::Scalar	Scalar
typedef MatrixType::RealScalar	RealScalar
typedef _Preconditioner	Preconditioner
Public Member Functions
	LeastSquaresConjugateGradient ()
template<typename MatrixDerived >
	LeastSquaresConjugateGradient (const EigenBase< MatrixDerived > &A)
	~LeastSquaresConjugateGradient ()
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
Private Types
typedef IterativeSolverBase < LeastSquaresConjugateGradient >	Base

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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

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 149 of file LeastSquareConjugateGradient.h.

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Member Typedef Documentation

template<typename _MatrixType , typename _Preconditioner >

typedef IterativeSolverBase<LeastSquaresConjugateGradient> Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >::Base [private]

Reimplemented from Eigen::IterativeSolverBase< LeastSquaresConjugateGradient< _MatrixType, _Preconditioner > >.

Definition at line 151 of file LeastSquareConjugateGradient.h.

template<typename _MatrixType , typename _Preconditioner >

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

Reimplemented from Eigen::IterativeSolverBase< LeastSquaresConjugateGradient< _MatrixType, _Preconditioner > >.

Definition at line 158 of file LeastSquareConjugateGradient.h.

template<typename _MatrixType , typename _Preconditioner >

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

Reimplemented from Eigen::IterativeSolverBase< LeastSquaresConjugateGradient< _MatrixType, _Preconditioner > >.

Definition at line 161 of file LeastSquareConjugateGradient.h.

template<typename _MatrixType , typename _Preconditioner >

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

Reimplemented from Eigen::IterativeSolverBase< LeastSquaresConjugateGradient< _MatrixType, _Preconditioner > >.

Definition at line 160 of file LeastSquareConjugateGradient.h.

template<typename _MatrixType , typename _Preconditioner >

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

Reimplemented from Eigen::IterativeSolverBase< LeastSquaresConjugateGradient< _MatrixType, _Preconditioner > >.

Definition at line 159 of file LeastSquareConjugateGradient.h.

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Constructor & Destructor Documentation

template<typename _MatrixType , typename _Preconditioner >

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

(

)

[inline]

Default constructor.

Definition at line 166 of file LeastSquareConjugateGradient.h.

: Base() {}

template<typename _MatrixType , typename _Preconditioner >

template<typename MatrixDerived >

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

(

const EigenBase< MatrixDerived > &

A

)

[inline, explicit]

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.

: Base(A.derived()) {}

template<typename _MatrixType , typename _Preconditioner >

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

(

)

[inline]

Definition at line 181 of file LeastSquareConjugateGradient.h.

{}

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Member Function Documentation

template<typename _MatrixType , typename _Preconditioner >

template<typename Rhs , typename Dest >

void Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >::_solve_impl	(	const MatrixBase< Rhs > &	b,
		Dest &	x
	)		const [inline]

Definition at line 206 of file LeastSquareConjugateGradient.h.

  {
    x.setZero();
    _solve_with_guess_impl(b.derived(),x);
  }

template<typename _MatrixType , typename _Preconditioner >

template<typename Rhs , typename Dest >

void Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >::_solve_with_guess_impl	(	const Rhs &	b,
		Dest &	x
	)		const [inline]

Definition at line 185 of file LeastSquareConjugateGradient.h.

  {
    m_iterations = Base::maxIterations();
    m_error = Base::m_tolerance;

    for(Index j=0; j<b.cols(); ++j)
    {
      m_iterations = Base::maxIterations();
      m_error = Base::m_tolerance;

      typename Dest::ColXpr xj(x,j);
      internal::least_square_conjugate_gradient(matrix(), b.col(j), xj, Base::m_preconditioner, m_iterations, m_error);
    }

    m_isInitialized = true;
    m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;
  }

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

• LeastSquareConjugateGradient.h