A conjugate gradient solver for sparse (or dense) self-adjoint problems. More...

Inheritance diagram for Eigen::ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >:

Public Types
enum	{ UpLo }

typedef MatrixType_	MatrixType

typedef Preconditioner_	Preconditioner

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Scalar	Scalar

Public Types inherited from Eigen::IterativeSolverBase< ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > >
enum

typedef internal::traits< ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > >::MatrixType	MatrixType

typedef internal::traits< ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > >::Preconditioner	Preconditioner

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Scalar	Scalar

typedef MatrixType::StorageIndex	StorageIndex

Public Member Functions
template<typename Rhs , typename Dest >
void	_solve_vector_with_guess_impl (const Rhs &b, Dest &x) const

	ConjugateGradient ()

template<typename MatrixDerived >
	ConjugateGradient (const EigenBase< MatrixDerived > &A)

	~ConjugateGradient ()

Public Member Functions inherited from Eigen::IterativeSolverBase< ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > >
void	_solve_impl (const Rhs &b, Dest &x) const

std::enable_if_t< Rhs::ColsAtCompileTime!=1 &&DestDerived::ColsAtCompileTime!=1 >	_solve_with_guess_impl (const Rhs &b, MatrixBase< DestDerived > &aDest) const

std::enable_if_t< Rhs::ColsAtCompileTime==1\|\|DestDerived::ColsAtCompileTime==1 >	_solve_with_guess_impl (const Rhs &b, MatrixBase< DestDerived > &dest) const

void	_solve_with_guess_impl (const Rhs &b, SparseMatrixBase< DestDerived > &aDest) const

ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > &	analyzePattern (const EigenBase< MatrixDerived > &A)

EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > &	compute (const EigenBase< MatrixDerived > &A)

ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > &	derived ()

const ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > &	derived () const

RealScalar	error () const

ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > &	factorize (const EigenBase< MatrixDerived > &A)

ComputationInfo	info () const

Index	iterations () const

	IterativeSolverBase ()

	IterativeSolverBase (const EigenBase< MatrixDerived > &A)

	IterativeSolverBase (IterativeSolverBase &&)=default

Index	maxIterations () const

Preconditioner &	preconditioner ()

const Preconditioner &	preconditioner () const

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > &	setMaxIterations (Index maxIters)

ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > &	setTolerance (const RealScalar &tolerance)

const SolveWithGuess< ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >, Rhs, Guess >	solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const

RealScalar	tolerance () const

	~IterativeSolverBase ()

Public Member Functions inherited from Eigen::SparseSolverBase< Derived >
Derived &	derived ()

const Derived &	derived () const

template<typename Rhs >
const Solve< Derived, Rhs >	solve (const MatrixBase< Rhs > &b) const

template<typename Rhs >
const Solve< Derived, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const

	SparseSolverBase ()

	SparseSolverBase (SparseSolverBase &&other)

	~SparseSolverBase ()

Private Types
typedef IterativeSolverBase< ConjugateGradient >	Base

Private Member Functions
const ActualMatrixType &	matrix () const

Private Attributes
RealScalar	m_error

ComputationInfo	m_info

Index	m_iterations

Additional Inherited Members
Protected Types inherited from Eigen::IterativeSolverBase< ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > >
typedef MatrixWrapper::ActualMatrixType	ActualMatrixType

typedef SparseSolverBase< ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > >	Base

typedef internal::generic_matrix_wrapper< MatrixType >	MatrixWrapper

Protected Member Functions inherited from Eigen::IterativeSolverBase< ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > >
void	grab (const InputType &A)

void	init ()

const ActualMatrixType &	matrix () const

Protected Attributes inherited from Eigen::IterativeSolverBase< ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ > >
bool	m_analysisIsOk

RealScalar	m_error

bool	m_factorizationIsOk

ComputationInfo	m_info

bool	m_isInitialized

Index	m_iterations

MatrixWrapper	m_matrixWrapper

Index	m_maxIterations

Preconditioner	m_preconditioner

RealScalar	m_tolerance

Protected Attributes inherited from Eigen::SparseSolverBase< Derived >
bool	m_isInitialized

Detailed Description

template<typename MatrixType_, int UpLo_, typename Preconditioner_>
class Eigen::ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >

A conjugate gradient solver for sparse (or dense) self-adjoint problems.

This class allows to solve for A.x = b linear problems using an iterative conjugate gradient algorithm. The matrix A must be selfadjoint. 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.
UpLo_	the triangular part that will be used for the computations. It can be Lower, `Upper`, or `Lower\|Upper` in which the full matrix entries will be considered. Default is `Lower`, best performance is `Lower\|Upper`.
Preconditioner_	the type of the preconditioner. Default is DiagonalPreconditioner

This class follows the sparse solver concept .

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.

The tolerance corresponds to the relative residual error: |Ax-b|/|b|

Performance: Even though the default value of UpLo_ is Lower, significantly higher performance is achieved when using a complete matrix and Lower|Upper as the UpLo_ template parameter. Moreover, in this case multi-threading can be exploited if the user code is compiled with OpenMP enabled. See Eigen and multi-threading for details.

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>, Lower|Upper> 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);

Code

By default the iterations start with x=0 as an initial guess of the solution. One can control the start using the solveWithGuess() method.

ConjugateGradient can also be used in a matrix-free context, see the following example .

See also: class LeastSquaresConjugateGradient, class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Definition at line 158 of file ConjugateGradient.h.

Member Typedef Documentation

◆ Base

template<typename MatrixType_ , int UpLo_, typename Preconditioner_ >

typedef IterativeSolverBase<ConjugateGradient> Eigen::ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >::Base

private

Definition at line 160 of file ConjugateGradient.h.

◆ MatrixType

template<typename MatrixType_ , int UpLo_, typename Preconditioner_ >

typedef MatrixType_ Eigen::ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >::MatrixType

Definition at line 167 of file ConjugateGradient.h.

◆ Preconditioner

template<typename MatrixType_ , int UpLo_, typename Preconditioner_ >

typedef Preconditioner_ Eigen::ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >::Preconditioner

Definition at line 170 of file ConjugateGradient.h.

◆ RealScalar

template<typename MatrixType_ , int UpLo_, typename Preconditioner_ >

typedef MatrixType::RealScalar Eigen::ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >::RealScalar

Definition at line 169 of file ConjugateGradient.h.

◆ Scalar

template<typename MatrixType_ , int UpLo_, typename Preconditioner_ >

typedef MatrixType::Scalar Eigen::ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >::Scalar

Definition at line 168 of file ConjugateGradient.h.

Member Enumeration Documentation

◆ anonymous enum

template<typename MatrixType_ , int UpLo_, typename Preconditioner_ >

anonymous enum

Enumerator
UpLo

Definition at line 172 of file ConjugateGradient.h.

        {
     UpLo = UpLo_
   };

Code

Constructor & Destructor Documentation

◆ ConjugateGradient() [1/2]

template<typename MatrixType_ , int UpLo_, typename Preconditioner_ >

Eigen::ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >::ConjugateGradient ( )

inline

Default constructor.

Definition at line 179 of file ConjugateGradient.h.

179 : Base() {}

Eigen::ConjugateGradient::Base

IterativeSolverBase< ConjugateGradient > Base

Definition: ConjugateGradient.h:160

Code

◆ ConjugateGradient() [2/2]

template<typename MatrixType_ , int UpLo_, typename Preconditioner_ >

template<typename MatrixDerived >

Eigen::ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >::ConjugateGradient ( 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 192 of file ConjugateGradient.h.

192 : Base(A.derived()) {}

Code

◆ ~ConjugateGradient()

template<typename MatrixType_ , int UpLo_, typename Preconditioner_ >

Eigen::ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >::~ConjugateGradient ( )

inline

Definition at line 194 of file ConjugateGradient.h.

194 {}

Code

Member Function Documentation

◆ _solve_vector_with_guess_impl()

template<typename MatrixType_ , int UpLo_, typename Preconditioner_ >

template<typename Rhs , typename Dest >

void Eigen::ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >::_solve_vector_with_guess_impl	(	const Rhs &	b,
		Dest &	x
	)		const

inline

Definition at line 198 of file ConjugateGradient.h.

   {
     typedef typename Base::MatrixWrapper MatrixWrapper;
     typedef typename Base::ActualMatrixType ActualMatrixType;
     enum {
       TransposeInput  =   (!MatrixWrapper::MatrixFree)
                       &&  (UpLo==(Lower|Upper))
                       &&  (!MatrixType::IsRowMajor)
                       &&  (!NumTraits<Scalar>::IsComplex)
     };
     typedef std::conditional_t<TransposeInput,Transpose<const ActualMatrixType>, ActualMatrixType const&> RowMajorWrapper;
     EIGEN_STATIC_ASSERT(internal::check_implication(MatrixWrapper::MatrixFree,UpLo==(Lower|Upper)),MATRIX_FREE_CONJUGATE_GRADIENT_IS_COMPATIBLE_WITH_UPPER_UNION_LOWER_MODE_ONLY);
     typedef std::conditional_t<UpLo==(Lower|Upper),
                                     RowMajorWrapper,
                                     typename MatrixWrapper::template ConstSelfAdjointViewReturnType<UpLo>::Type
                                    > SelfAdjointWrapper;
  
     m_iterations = Base::maxIterations();
     m_error = Base::m_tolerance;
  
     RowMajorWrapper row_mat(matrix());
     internal::conjugate_gradient(SelfAdjointWrapper(row_mat), b, x, Base::m_preconditioner, m_iterations, m_error);
     m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;
   }

Code

◆ matrix()

template<typename MatrixType_ , int UpLo_, typename Preconditioner_ >

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

inlineprivate

Definition at line 424 of file IterativeSolverBase.h.

   {
     return m_matrixWrapper.matrix();
   }

Code

Member Data Documentation

◆ m_error

template<typename MatrixType_ , int UpLo_, typename Preconditioner_ >

RealScalar Eigen::IterativeSolverBase< Derived >::m_error

mutableprivate

Definition at line 441 of file IterativeSolverBase.h.

◆ m_info

template<typename MatrixType_ , int UpLo_, typename Preconditioner_ >

ComputationInfo Eigen::IterativeSolverBase< Derived >::m_info

mutableprivate

Definition at line 443 of file IterativeSolverBase.h.

◆ m_iterations

template<typename MatrixType_ , int UpLo_, typename Preconditioner_ >

Index Eigen::IterativeSolverBase< Derived >::m_iterations

mutableprivate

Definition at line 442 of file IterativeSolverBase.h.

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

ConjugateGradient.h

Public Types

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<typename MatrixType_, int UpLo_, typename Preconditioner_> class Eigen::ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >

Member Typedef Documentation

◆ Base

◆ MatrixType

◆ Preconditioner

◆ RealScalar

◆ Scalar

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ ConjugateGradient() [1/2]

◆ ConjugateGradient() [2/2]

◆ ~ConjugateGradient()

Member Function Documentation

◆ _solve_vector_with_guess_impl()

◆ matrix()

Member Data Documentation

◆ m_error

◆ m_info

◆ m_iterations

template<typename MatrixType_, int UpLo_, typename Preconditioner_>
class Eigen::ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >