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 }
using	MatrixType = _MatrixType
using	Scalar = typename MatrixType::Scalar
using	Index = typename MatrixType::Index
using	RealScalar = typename MatrixType::RealScalar
using	FilterMatrixType = _FilterMatrixType
using	Preconditioner = _Preconditioner

Public Member Functions
	ConstrainedConjugateGradient ()
	ConstrainedConjugateGradient (const MatrixType &A)
	~ConstrainedConjugateGradient ()=default
FilterMatrixType &	filter ()
const FilterMatrixType &	filter () const
template<typename Rhs, typename Guess>
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 self-adjoint. 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 pre-conditioner. 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);

uiBlockAlertLevel::Success
@ Success
Definition interface_intern.hh:586

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

See also: class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Definition at line 198 of file ConstrainedConjugateGradient.h.

Member Typedef Documentation

◆ FilterMatrixType

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

using Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::FilterMatrixType = _FilterMatrixType

Definition at line 213 of file ConstrainedConjugateGradient.h.

◆ Index

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

using Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::Index = typename MatrixType::Index

Definition at line 211 of file ConstrainedConjugateGradient.h.

◆ MatrixType

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

using Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::MatrixType = _MatrixType

Definition at line 209 of file ConstrainedConjugateGradient.h.

◆ Preconditioner

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

using Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::Preconditioner = _Preconditioner

Definition at line 214 of file ConstrainedConjugateGradient.h.

◆ RealScalar

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

using Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::RealScalar = typename MatrixType::RealScalar

Definition at line 212 of file ConstrainedConjugateGradient.h.

◆ Scalar

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

using Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _FilterMatrixType, _Preconditioner >::Scalar = typename MatrixType::Scalar

Definition at line 210 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 216 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 219 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 232 of file ConstrainedConjugateGradient.h.

◆ ~ConstrainedConjugateGradient()

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

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

default

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 288 of file ConstrainedConjugateGradient.h.

◆ _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 264 of file ConstrainedConjugateGradient.h.

Referenced by Eigen::ConstrainedConjugateGradient< _MatrixType, _UpLo, _Filter, _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 236 of file ConstrainedConjugateGradient.h.

◆ 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 240 of file ConstrainedConjugateGradient.h.

◆ solveWithGuess()

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

template<typename Rhs, typename Guess>

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 252 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 295 of file ConstrainedConjugateGradient.h.

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

ConstrainedConjugateGradient.h

Public Types

Public Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ FilterMatrixType

◆ Index

◆ MatrixType

◆ Preconditioner

◆ RealScalar

◆ Scalar

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ ConstrainedConjugateGradient() [1/2]

◆ ConstrainedConjugateGradient() [2/2]

◆ ~ConstrainedConjugateGradient()

Member Function Documentation

◆ _solve()

◆ _solveWithGuess()

◆ filter() [1/2]

◆ filter() [2/2]

◆ solveWithGuess()

Member Data Documentation

◆ m_filter