Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner > Class Template Reference

A conjugate gradient solver for sparse self-adjoint problems with additional constraints. More...

#include <ConstrainedConjugateGradient.h>

Inherits IterativeSolverBase< ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner > >.

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

Public Member Functions
	ConstrainedConjugateGradient ()
	ConstrainedConjugateGradient (const MatrixType &A)
	~ConstrainedConjugateGradient ()
FilterMatrixType &	filter ()
const FilterMatrixType &	filter () const
template<typename Rhs , typename Guess >
const internal::solve_retval_with_guess< ConstrainedConjugateGradient, Rhs, Guess >	solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const
template<typename Rhs , typename Dest >
void	_solveWithGuess (const Rhs &b, Dest &x) const
template<typename Rhs , typename Dest >
void	_solve (const Rhs &b, Dest &x) const

Protected Attributes
FilterMatrixType	m_filter

Detailed Description

template<typename _MatrixType, int _UpLo, typename _FilterMatrixType, typename _Preconditioner>
class Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >

A conjugate gradient solver for sparse self-adjoint problems with additional constraints.

This class allows to solve for A.x = b sparse linear problems using a conjugate gradient algorithm. The sparse matrix A must be selfadjoint. The vectors x and b can be either dense or sparse.

Template Parameters

_MatrixType	the type of the sparse 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 or Upper. Default is Lower.
_Preconditioner	the type of the preconditioner. Default is DiagonalPreconditioner

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 n = 10000;
VectorXd x(n), b(n);
SparseMatrix<double> A(n,n);
// fill A and b
ConjugateGradient<SparseMatrix<double> > 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. Here is a step by step execution example starting with a random guess and printing the evolution of the estimated error:

• x = VectorXd::Random(n);
  cg.setMaxIterations(1);
  int i = 0;
  do {
    x = cg.solveWithGuess(b,x);
    std::cout << i << " : " << cg.error() << std::endl;
    ++i;
  } while (cg.info()!=Success && i<100);

  Note that such a step by step execution is slightly slower.

See also

class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Definition at line 213 of file ConstrainedConjugateGradient.h.

Member Typedef Documentation

FilterMatrixType

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

typedef _FilterMatrixType Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::FilterMatrixType

Definition at line 228 of file ConstrainedConjugateGradient.h.

Index

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

typedef MatrixType::Index Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::Index

Definition at line 226 of file ConstrainedConjugateGradient.h.

MatrixType

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

typedef _MatrixType Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::MatrixType

Definition at line 224 of file ConstrainedConjugateGradient.h.

Preconditioner

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

typedef _Preconditioner Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::Preconditioner

Definition at line 229 of file ConstrainedConjugateGradient.h.

RealScalar

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

typedef MatrixType::RealScalar Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::RealScalar

Definition at line 227 of file ConstrainedConjugateGradient.h.

Scalar

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

typedef MatrixType::Scalar Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::Scalar

Definition at line 225 of file ConstrainedConjugateGradient.h.

Member Enumeration Documentation

anonymous enum

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

anonymous enum

Enumerator
UpLo

Definition at line 231 of file ConstrainedConjugateGradient.h.

Constructor & Destructor Documentation

ConstrainedConjugateGradient() [1/2]

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

Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::ConstrainedConjugateGradient ( )

inline

Default constructor.

Definition at line 235 of file ConstrainedConjugateGradient.h.

ConstrainedConjugateGradient() [2/2]

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

Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::ConstrainedConjugateGradient ( const MatrixType &  A )

inline

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 249 of file ConstrainedConjugateGradient.h.

References A.

~ConstrainedConjugateGradient()

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

Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::~ConstrainedConjugateGradient ( )

inline

Definition at line 253 of file ConstrainedConjugateGradient.h.

Member Function Documentation

_solve()

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

template<typename Rhs , typename Dest >

void Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::_solve ( const Rhs &  b, Dest &  x  ) const

inline

Definition at line 308 of file ConstrainedConjugateGradient.h.

References Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::_solveWithGuess(), and x.

_solveWithGuess()

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

template<typename Rhs , typename Dest >

void Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::_solveWithGuess ( const Rhs &  b, Dest &  x  ) const

inline

Definition at line 284 of file ConstrainedConjugateGradient.h.

References Eigen::internal::constrained_conjugate_gradient(), Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::m_filter, and x.

Referenced by Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::_solve().

filter() [1/2]

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

FilterMatrixType& Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::filter ( )

inline

Definition at line 257 of file ConstrainedConjugateGradient.h.

References Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::m_filter.

filter() [2/2]

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

const FilterMatrixType& Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::filter ( ) const

inline

Definition at line 261 of file ConstrainedConjugateGradient.h.

References Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::m_filter.

solveWithGuess()

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

template<typename Rhs , typename Guess >

const internal::solve_retval_with_guess<ConstrainedConjugateGradient, Rhs, Guess> Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::solveWithGuess ( const MatrixBase< Rhs > &  b, const Guess &  x0  ) const

inline

Returns

the solution x of using the current decomposition of A x0 as an initial solution.

See also

compute()

Definition at line 273 of file ConstrainedConjugateGradient.h.

Member Data Documentation

m_filter

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

FilterMatrixType Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::m_filter

protected

Definition at line 315 of file ConstrainedConjugateGradient.h.

Referenced by Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::_solveWithGuess(), and Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::filter().

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

• ConstrainedConjugateGradient.h