Base class for linear iterative solvers. More...

Inheritance diagram for Eigen::IterativeSolverBase< Derived >:

Public Types
enum	{ ColsAtCompileTime , MaxColsAtCompileTime }

typedef internal::traits< Derived >::MatrixType	MatrixType

typedef internal::traits< Derived >::Preconditioner	Preconditioner

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Scalar	Scalar

typedef MatrixType::StorageIndex	StorageIndex

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

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

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

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

template<typename MatrixDerived >
Derived &	analyzePattern (const EigenBase< MatrixDerived > &A)

EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

template<typename MatrixDerived >
Derived &	compute (const EigenBase< MatrixDerived > &A)

Derived &	derived ()

const Derived &	derived () const

RealScalar	error () const

template<typename MatrixDerived >
Derived &	factorize (const EigenBase< MatrixDerived > &A)

ComputationInfo	info () const

Index	iterations () const

	IterativeSolverBase ()

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

	IterativeSolverBase (IterativeSolverBase &&)=default

Index	maxIterations () const

Preconditioner &	preconditioner ()

const Preconditioner &	preconditioner () const

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

Derived &	setMaxIterations (Index maxIters)

Derived &	setTolerance (const RealScalar &tolerance)

template<typename Rhs , typename Guess >
const SolveWithGuess< Derived, 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 ()

Protected Types
typedef MatrixWrapper::ActualMatrixType	ActualMatrixType

typedef SparseSolverBase< Derived >	Base

typedef internal::generic_matrix_wrapper< MatrixType >	MatrixWrapper

Protected Member Functions
template<typename InputType >
void	grab (const InputType &A)

void	init ()

const ActualMatrixType &	matrix () const

Protected Attributes
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 Derived>
class Eigen::IterativeSolverBase< Derived >

Base class for linear iterative solvers.

See also: class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Definition at line 145 of file IterativeSolverBase.h.

Member Typedef Documentation

◆ ActualMatrixType

template<typename Derived >

typedef MatrixWrapper::ActualMatrixType Eigen::IterativeSolverBase< Derived >::ActualMatrixType

protected

Definition at line 422 of file IterativeSolverBase.h.

◆ Base

template<typename Derived >

typedef SparseSolverBase<Derived> Eigen::IterativeSolverBase< Derived >::Base

protected

Definition at line 148 of file IterativeSolverBase.h.

◆ MatrixType

template<typename Derived >

typedef internal::traits<Derived>::MatrixType Eigen::IterativeSolverBase< Derived >::MatrixType

Definition at line 152 of file IterativeSolverBase.h.

◆ MatrixWrapper

template<typename Derived >

typedef internal::generic_matrix_wrapper<MatrixType> Eigen::IterativeSolverBase< Derived >::MatrixWrapper

protected

Definition at line 421 of file IterativeSolverBase.h.

◆ Preconditioner

template<typename Derived >

typedef internal::traits<Derived>::Preconditioner Eigen::IterativeSolverBase< Derived >::Preconditioner

Definition at line 153 of file IterativeSolverBase.h.

◆ RealScalar

template<typename Derived >

typedef MatrixType::RealScalar Eigen::IterativeSolverBase< Derived >::RealScalar

Definition at line 156 of file IterativeSolverBase.h.

◆ Scalar

template<typename Derived >

typedef MatrixType::Scalar Eigen::IterativeSolverBase< Derived >::Scalar

Definition at line 154 of file IterativeSolverBase.h.

◆ StorageIndex

template<typename Derived >

typedef MatrixType::StorageIndex Eigen::IterativeSolverBase< Derived >::StorageIndex

Definition at line 155 of file IterativeSolverBase.h.

Member Enumeration Documentation

◆ anonymous enum

template<typename Derived >

anonymous enum

Enumerator
ColsAtCompileTime
MaxColsAtCompileTime

Definition at line 158 of file IterativeSolverBase.h.

        {
     ColsAtCompileTime = MatrixType::ColsAtCompileTime,
     MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
   };

Constructor & Destructor Documentation

◆ IterativeSolverBase() [1/3]

template<typename Derived >

Eigen::IterativeSolverBase< Derived >::IterativeSolverBase ( )

inline

Default constructor.

Definition at line 168 of file IterativeSolverBase.h.

   {
     init();
   }

◆ IterativeSolverBase() [2/3]

template<typename Derived >

template<typename MatrixDerived >

Eigen::IterativeSolverBase< Derived >::IterativeSolverBase ( 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 184 of file IterativeSolverBase.h.

     : m_matrixWrapper(A.derived())
   {
     init();
     compute(matrix());
   }

◆ IterativeSolverBase() [3/3]

template<typename Derived >

Eigen::IterativeSolverBase< Derived >::IterativeSolverBase ( IterativeSolverBase< Derived > && )

default

◆ ~IterativeSolverBase()

template<typename Derived >

Eigen::IterativeSolverBase< Derived >::~IterativeSolverBase ( )

inline

Definition at line 194 of file IterativeSolverBase.h.

194 {}

Member Function Documentation

◆ _solve_impl()

template<typename Derived >

template<typename Rhs , typename Dest >

void Eigen::IterativeSolverBase< Derived >::_solve_impl	(	const Rhs &	b,
		Dest &	x
	)		const

inline

Definition at line 405 of file IterativeSolverBase.h.

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

◆ _solve_with_guess_impl() [1/3]

template<typename Derived >

template<typename Rhs , typename DestDerived >

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

inline

Definition at line 373 of file IterativeSolverBase.h.

   {
     eigen_assert(rows()==b.rows());
  
     Index rhsCols = b.cols();
     DestDerived& dest(aDest.derived());
     ComputationInfo global_info = Success;
     for(Index k=0; k<rhsCols; ++k)
     {
       typename DestDerived::ColXpr xk(dest,k);
       typename Rhs::ConstColXpr bk(b,k);
       derived()._solve_vector_with_guess_impl(bk,xk);
  
       // The call to _solve_vector_with_guess updates m_info, so if it failed for a previous column
       // we need to restore it to the worst value.
       if(m_info==NumericalIssue)
         global_info = NumericalIssue;
       else if(m_info==NoConvergence)
         global_info = NoConvergence;
     }
     m_info = global_info;
   }

◆ _solve_with_guess_impl() [2/3]

template<typename Derived >

template<typename Rhs , typename DestDerived >

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

inline

Definition at line 398 of file IterativeSolverBase.h.

   {
     derived()._solve_vector_with_guess_impl(b,dest.derived());
   }

◆ _solve_with_guess_impl() [3/3]

template<typename Derived >

template<typename Rhs , typename DestDerived >

void Eigen::IterativeSolverBase< Derived >::_solve_with_guess_impl	(	const Rhs &	b,
		SparseMatrixBase< DestDerived > &	aDest
	)		const

inline

Definition at line 339 of file IterativeSolverBase.h.

   {
     eigen_assert(rows()==b.rows());
  
     Index rhsCols = b.cols();
     Index size = b.rows();
     DestDerived& dest(aDest.derived());
     typedef typename DestDerived::Scalar DestScalar;
     Eigen::Matrix<DestScalar,Dynamic,1> tb(size);
     Eigen::Matrix<DestScalar,Dynamic,1> tx(cols());
     // We do not directly fill dest because sparse expressions have to be free of aliasing issue.
     // For non square least-square problems, b and dest might not have the same size whereas they might alias each-other.
     typename DestDerived::PlainObject tmp(cols(),rhsCols);
     ComputationInfo global_info = Success;
     for(Index k=0; k<rhsCols; ++k)
     {
       tb = b.col(k);
       tx = dest.col(k);
       derived()._solve_vector_with_guess_impl(tb,tx);
       tmp.col(k) = tx.sparseView(0);
  
       // The call to _solve_vector_with_guess_impl updates m_info, so if it failed for a previous column
       // we need to restore it to the worst value.
       if(m_info==NumericalIssue)
         global_info = NumericalIssue;
       else if(m_info==NoConvergence)
         global_info = NoConvergence;
     }
     m_info = global_info;
     dest.swap(tmp);
   }

◆ analyzePattern()

template<typename Derived >

template<typename MatrixDerived >

Derived& Eigen::IterativeSolverBase< Derived >::analyzePattern ( const EigenBase< MatrixDerived > & A )

inline

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

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

Definition at line 202 of file IterativeSolverBase.h.

   {
     grab(A.derived());
     m_preconditioner.analyzePattern(matrix());
     m_isInitialized = true;
     m_analysisIsOk = true;
     m_info = m_preconditioner.info();
     return derived();
   }

◆ cols()

template<typename Derived >

EIGEN_CONSTEXPR Index Eigen::IterativeSolverBase< Derived >::cols ( void ) const

inline

Definition at line 258 of file IterativeSolverBase.h.

258 { return matrix().cols(); }

◆ compute()

template<typename Derived >

template<typename MatrixDerived >

Derived& Eigen::IterativeSolverBase< Derived >::compute ( const EigenBase< MatrixDerived > & A )

inline

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

Currently, this function mostly initializes/computes the preconditioner. In the future we might, for instance, implement column reordering 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.

Definition at line 243 of file IterativeSolverBase.h.

   {
     grab(A.derived());
     m_preconditioner.compute(matrix());
     m_isInitialized = true;
     m_analysisIsOk = true;
     m_factorizationIsOk = true;
     m_info = m_preconditioner.info();
     return derived();
   }

◆ derived() [1/2]

template<typename Derived >

Derived& Eigen::SparseSolverBase< Derived >::derived

inline

Definition at line 83 of file SparseSolverBase.h.

83 { return *static_cast<Derived*>(this); }

◆ derived() [2/2]

template<typename Derived >

const Derived& Eigen::SparseSolverBase< Derived >::derived

inline

Definition at line 84 of file SparseSolverBase.h.

84 { return *static_cast<const Derived*>(this); }

◆ error()

template<typename Derived >

RealScalar Eigen::IterativeSolverBase< Derived >::error ( ) const

inline

Returns: the tolerance error reached during the last solve. It is a close approximation of the true relative residual error |Ax-b|/|b|.

Definition at line 310 of file IterativeSolverBase.h.

   {
     eigen_assert(m_isInitialized && "IterativeSolverBase is not initialized.");
     return m_error;
   }

◆ factorize()

template<typename Derived >

template<typename MatrixDerived >

Derived& Eigen::IterativeSolverBase< Derived >::factorize ( const EigenBase< MatrixDerived > & A )

inline

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

Currently, this function mostly calls 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.

Definition at line 222 of file IterativeSolverBase.h.

   {
     eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
     grab(A.derived());
     m_preconditioner.factorize(matrix());
     m_factorizationIsOk = true;
     m_info = m_preconditioner.info();
     return derived();
   }

◆ grab()

template<typename Derived >

template<typename InputType >

void Eigen::IterativeSolverBase< Derived >::grab ( const InputType & A )

inlineprotected

Definition at line 430 of file IterativeSolverBase.h.

   {
     m_matrixWrapper.grab(A);
   }

◆ info()

template<typename Derived >

ComputationInfo Eigen::IterativeSolverBase< Derived >::info ( ) const

inline

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

Definition at line 331 of file IterativeSolverBase.h.

   {
     eigen_assert(m_isInitialized && "IterativeSolverBase is not initialized.");
     return m_info;
   }

◆ init()

template<typename Derived >

void Eigen::IterativeSolverBase< Derived >::init ( )

inlineprotected

Definition at line 412 of file IterativeSolverBase.h.

   {
     m_isInitialized = false;
     m_analysisIsOk = false;
     m_factorizationIsOk = false;
     m_maxIterations = -1;
     m_tolerance = NumTraits<Scalar>::epsilon();
   }

◆ iterations()

template<typename Derived >

Index Eigen::IterativeSolverBase< Derived >::iterations ( ) const

inline

Returns: the number of iterations performed during the last solve

Definition at line 301 of file IterativeSolverBase.h.

   {
     eigen_assert(m_isInitialized && "IterativeSolverBase is not initialized.");
     return m_iterations;
   }

◆ matrix()

template<typename Derived >

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

inlineprotected

Definition at line 424 of file IterativeSolverBase.h.

   {
     return m_matrixWrapper.matrix();
   }

◆ maxIterations()

template<typename Derived >

Index Eigen::IterativeSolverBase< Derived >::maxIterations ( ) const

inline

Returns: the max number of iterations. It is either the value set by setMaxIterations or, by default, twice the number of columns of the matrix.

Definition at line 286 of file IterativeSolverBase.h.

   {
     return (m_maxIterations<0) ? 2*matrix().cols() : m_maxIterations;
   }

◆ preconditioner() [1/2]

template<typename Derived >

Preconditioner& Eigen::IterativeSolverBase< Derived >::preconditioner ( )

inline

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

Definition at line 277 of file IterativeSolverBase.h.

277 { return m_preconditioner; }

◆ preconditioner() [2/2]

template<typename Derived >

const Preconditioner& Eigen::IterativeSolverBase< Derived >::preconditioner ( ) const

inline

Returns: a read-only reference to the preconditioner.

Definition at line 280 of file IterativeSolverBase.h.

280 { return m_preconditioner; }

◆ rows()

template<typename Derived >

EIGEN_CONSTEXPR Index Eigen::IterativeSolverBase< Derived >::rows ( void ) const

inline

Definition at line 255 of file IterativeSolverBase.h.

255 { return matrix().rows(); }

◆ setMaxIterations()

template<typename Derived >

Derived& Eigen::IterativeSolverBase< Derived >::setMaxIterations ( Index maxIters )

inline

Sets the max number of iterations. Default is twice the number of columns of the matrix.

Definition at line 294 of file IterativeSolverBase.h.

   {
     m_maxIterations = maxIters;
     return derived();
   }

◆ setTolerance()

template<typename Derived >

Derived& Eigen::IterativeSolverBase< Derived >::setTolerance ( const RealScalar & tolerance )

inline

Sets the tolerance threshold used by the stopping criteria.

This value is used as an upper bound to the relative residual error: |Ax-b|/|b|. The default value is the machine precision given by NumTraits<Scalar>::epsilon()

Definition at line 270 of file IterativeSolverBase.h.

   {
     m_tolerance = tolerance;
     return derived();
   }

◆ solveWithGuess()

template<typename Derived >

template<typename Rhs , typename Guess >

const SolveWithGuess<Derived, Rhs, Guess> Eigen::IterativeSolverBase< Derived >::solveWithGuess	(	const MatrixBase< Rhs > &	b,
		const Guess &	x0
	)		const

inline

Returns: the solution x of \( A x = b \) using the current decomposition of A and x0 as an initial solution.

See also: solve(), compute()

Definition at line 323 of file IterativeSolverBase.h.

   {
     eigen_assert(m_isInitialized && "Solver is not initialized.");
     eigen_assert(derived().rows()==b.rows() && "solve(): invalid number of rows of the right hand side matrix b");
     return SolveWithGuess<Derived, Rhs, Guess>(derived(), b.derived(), x0);
   }

◆ tolerance()

template<typename Derived >

RealScalar Eigen::IterativeSolverBase< Derived >::tolerance ( ) const

inline

Returns: the tolerance threshold used by the stopping criteria.

See also: setTolerance()

Definition at line 263 of file IterativeSolverBase.h.

263 { return m_tolerance; }

Member Data Documentation

◆ m_analysisIsOk

template<typename Derived >

bool Eigen::IterativeSolverBase< Derived >::m_analysisIsOk

mutableprotected

Definition at line 444 of file IterativeSolverBase.h.

◆ m_error

template<typename Derived >

RealScalar Eigen::IterativeSolverBase< Derived >::m_error

mutableprotected

Definition at line 441 of file IterativeSolverBase.h.

◆ m_factorizationIsOk

template<typename Derived >

bool Eigen::IterativeSolverBase< Derived >::m_factorizationIsOk

protected

Definition at line 444 of file IterativeSolverBase.h.

◆ m_info

template<typename Derived >

ComputationInfo Eigen::IterativeSolverBase< Derived >::m_info

mutableprotected

Definition at line 443 of file IterativeSolverBase.h.

◆ m_isInitialized

template<typename Derived >

bool Eigen::SparseSolverBase< Derived >::m_isInitialized

mutableprotected

Definition at line 123 of file SparseSolverBase.h.

◆ m_iterations

template<typename Derived >

Index Eigen::IterativeSolverBase< Derived >::m_iterations

mutableprotected

Definition at line 442 of file IterativeSolverBase.h.

◆ m_matrixWrapper

template<typename Derived >

MatrixWrapper Eigen::IterativeSolverBase< Derived >::m_matrixWrapper

protected

Definition at line 435 of file IterativeSolverBase.h.

◆ m_maxIterations

template<typename Derived >

Index Eigen::IterativeSolverBase< Derived >::m_maxIterations

protected

Definition at line 438 of file IterativeSolverBase.h.

◆ m_preconditioner

template<typename Derived >

Preconditioner Eigen::IterativeSolverBase< Derived >::m_preconditioner

protected

Definition at line 436 of file IterativeSolverBase.h.

◆ m_tolerance

template<typename Derived >

RealScalar Eigen::IterativeSolverBase< Derived >::m_tolerance

protected

Definition at line 439 of file IterativeSolverBase.h.

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

IterativeSolverBase.h

Public Types

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Detailed Description

template<typename Derived> class Eigen::IterativeSolverBase< Derived >

Member Typedef Documentation

◆ ActualMatrixType

◆ Base

◆ MatrixType

◆ MatrixWrapper

◆ Preconditioner

◆ RealScalar

◆ Scalar

◆ StorageIndex

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ IterativeSolverBase() [1/3]

◆ IterativeSolverBase() [2/3]

◆ IterativeSolverBase() [3/3]

◆ ~IterativeSolverBase()

Member Function Documentation

◆ _solve_impl()

◆ _solve_with_guess_impl() [1/3]

◆ _solve_with_guess_impl() [2/3]

◆ _solve_with_guess_impl() [3/3]

◆ analyzePattern()

◆ cols()

◆ compute()

◆ derived() [1/2]

◆ derived() [2/2]

◆ error()

◆ factorize()

◆ grab()

◆ info()

◆ init()

◆ iterations()

◆ matrix()

◆ maxIterations()

◆ preconditioner() [1/2]

◆ preconditioner() [2/2]

◆ rows()

◆ setMaxIterations()

◆ setTolerance()

◆ solveWithGuess()

◆ tolerance()

Member Data Documentation

◆ m_analysisIsOk

◆ m_error

◆ m_factorizationIsOk

◆ m_info

◆ m_isInitialized

◆ m_iterations

◆ m_matrixWrapper

◆ m_maxIterations

◆ m_preconditioner

◆ m_tolerance

template<typename Derived>
class Eigen::IterativeSolverBase< Derived >