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

Inheritance diagram for ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >:

Public Types
enum	{ UpLo }
typedef MatrixType::Index	Index
typedef _MatrixType	MatrixType
typedef _Preconditioner	Preconditioner
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::Scalar	Scalar
Public Member Functions
template<typename Rhs , typename Dest >
void	_solve (const Rhs &b, Dest &x) const
void	_solve_sparse (const Rhs &b, SparseMatrix< DestScalar, DestOptions, DestIndex > &dest) const
template<typename Rhs , typename Dest >
void	_solveWithGuess (const Rhs &b, Dest &x) const
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	analyzePattern (const MatrixType &A)
Index	cols () const
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	compute (const MatrixType &A)
	ConjugateGradient ()
	ConjugateGradient (const MatrixType &A)
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	derived ()
const ConjugateGradient < _MatrixType, _UpLo, _Preconditioner > &	derived () const
RealScalar	error () const
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	factorize (const MatrixType &A)
ComputationInfo	info () const
int	iterations () const
int	maxIterations () const
Preconditioner &	preconditioner ()
const Preconditioner &	preconditioner () const
Index	rows () const
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	setMaxIterations (int maxIters)
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > &	setTolerance (RealScalar tolerance)
const internal::solve_retval < ConjugateGradient < _MatrixType, _UpLo, _Preconditioner >, Rhs >	solve (const MatrixBase< Rhs > &b) const
const internal::sparse_solve_retval < IterativeSolverBase, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const
template<typename Rhs , typename Guess >
const internal::solve_retval_with_guess < ConjugateGradient, Rhs, Guess >	solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const
RealScalar	tolerance () const
	~ConjugateGradient ()
Protected Member Functions
void	init ()
Protected Attributes
bool	m_analysisIsOk
RealScalar	m_error
bool	m_factorizationIsOk
ComputationInfo	m_info
bool	m_isInitialized
int	m_iterations
int	m_maxIterations
Preconditioner	m_preconditioner
RealScalar	m_tolerance
const MatrixType *	mp_matrix

Detailed Description

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

A conjugate gradient solver for sparse self-adjoint problems.

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 excution is slightly slower.

See also:: class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Member Typedef Documentation

typedef MatrixType::Index Index

Reimplemented from IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >.

typedef _MatrixType MatrixType

Reimplemented from IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >.

typedef _Preconditioner Preconditioner

Reimplemented from IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >.

typedef MatrixType::RealScalar RealScalar

Reimplemented from IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >.

typedef MatrixType::Scalar Scalar

Reimplemented from IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >.

Member Enumeration Documentation

anonymous enum

Enumerator:

UpLo

Constructor & Destructor Documentation

ConjugateGradient ( ) [inline]

Default constructor.

ConjugateGradient ( 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.

~ConjugateGradient ( ) [inline]

Member Function Documentation

void _solve	(	const Rhs &	b,
		Dest &	x
	)		const `[inline]`

void _solve_sparse	(	const Rhs &	b,
		SparseMatrix< DestScalar, DestOptions, DestIndex > &	dest
	)		const `[inline, inherited]`

void _solveWithGuess	(	const Rhs &	b,
		Dest &	x
	)		const `[inline]`

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & analyzePattern ( const MatrixType & A ) [inline, inherited]

Initializes the iterative solver for the sparcity pattern of the matrix A for further solving Ax=b problems.

Currently, this function mostly call analyzePattern on the preconditioner. In the future we might, for instance, implement column reodering for faster matrix vector products.

Index cols ( void ) const [inline, inherited]

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & compute ( const MatrixType & A ) [inline, inherited]

Initializes the iterative solver with the matrix A for further solving Ax=b problems.

Currently, this function mostly initialized/compute the preconditioner. In the future we might, for instance, implement column reodering for faster matrix vector products.

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.

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & derived ( ) [inline, inherited]

const ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & derived ( ) const [inline, inherited]

RealScalar error ( ) const [inline, inherited]

Returns:: the tolerance error reached during the last solve

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & factorize ( const MatrixType & A ) [inline, inherited]

Initializes the iterative solver with the numerical values of the matrix A for further solving Ax=b problems.

Currently, this function mostly call factorize on the preconditioner.

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.

ComputationInfo info ( ) const [inline, inherited]

Returns:: Success if the iterations converged, and NoConvergence otherwise.

void init ( ) [inline, protected, inherited]

int iterations ( ) const [inline, inherited]

Returns:: the number of iterations performed during the last solve

int maxIterations ( ) const [inline, inherited]

Returns:: the max number of iterations

Preconditioner& preconditioner ( ) [inline, inherited]

Returns:: a read-write reference to the preconditioner for custom configuration.

const Preconditioner& preconditioner ( ) const [inline, inherited]

Returns:: a read-only reference to the preconditioner.

Index rows ( void ) const [inline, inherited]

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & setMaxIterations ( int maxIters ) [inline, inherited]

Sets the max number of iterations

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & setTolerance ( RealScalar tolerance ) [inline, inherited]

Sets the tolerance threshold used by the stopping criteria

const internal::solve_retval<ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > , Rhs> solve ( const MatrixBase< Rhs > & b ) const [inline, inherited]

Returns:: the solution x of using the current decomposition of A.

See also:: compute()

const internal::sparse_solve_retval<IterativeSolverBase, Rhs> solve ( const SparseMatrixBase< Rhs > & b ) const [inline, inherited]

Returns:: the solution x of using the current decomposition of A.

See also:: compute()

const internal::solve_retval_with_guess<ConjugateGradient, Rhs, Guess> 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()

RealScalar tolerance ( ) const [inline, inherited]

Returns:: the tolerance threshold used by the stopping criteria

Member Data Documentation

bool m_analysisIsOk [mutable, protected, inherited]

RealScalar m_error [mutable, protected, inherited]

bool m_factorizationIsOk [mutable, protected, inherited]

ComputationInfo m_info [mutable, protected, inherited]

bool m_isInitialized [mutable, protected, inherited]

int m_iterations [mutable, protected, inherited]

int m_maxIterations [protected, inherited]

Preconditioner m_preconditioner [protected, inherited]

RealScalar m_tolerance [protected, inherited]

const MatrixType* mp_matrix [protected, inherited]

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

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

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

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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