Base class for linear iterative solvers. More...

#include <src/eigen/Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h>

Inheritance diagram for Eigen::IterativeSolverBase< Derived >:

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Public Types
enum	{ ColsAtCompileTime = MatrixType::ColsAtCompileTime , MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }

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

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

typedef MatrixType::Scalar	Scalar

typedef MatrixType::StorageIndex	StorageIndex

typedef MatrixType::RealScalar	RealScalar

Public Member Functions
	IterativeSolverBase ()

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

	~IterativeSolverBase ()

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

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

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

Index	rows () const

Index	cols () const

RealScalar	tolerance () const

Derived &	setTolerance (const RealScalar &tolerance)

Preconditioner &	preconditioner ()

const Preconditioner &	preconditioner () const

Index	maxIterations () const

Derived &	setMaxIterations (Index maxIters)

Index	iterations () const

RealScalar	error () const

template<typename Rhs , typename Guess >
const SolveWithGuess< Derived, Rhs, Guess >	solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const

ComputationInfo	info () const

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

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

template<typename Rhs , typename Dest >
void	_solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const

Protected Types
typedef SparseSolverBase< Derived >	Base

typedef internal::generic_matrix_wrapper< MatrixType >	MatrixWrapper

typedef MatrixWrapper::ActualMatrixType	ActualMatrixType

Protected Member Functions
void	init ()

const ActualMatrixType &	matrix () const

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

Protected Attributes
MatrixWrapper	m_matrixWrapper

Preconditioner	m_preconditioner

Index	m_maxIterations

RealScalar	m_tolerance

RealScalar	m_error

Index	m_iterations

ComputationInfo	m_info

bool	m_analysisIsOk

bool	m_factorizationIsOk

bool	m_isInitialized

Detailed Description

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

Base class for linear iterative solvers.

See also: class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Member Typedef Documentation

◆ ActualMatrixType

template<typename Derived >

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

protected

◆ Base

template<typename Derived >

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

protected

◆ MatrixType

template<typename Derived >

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

◆ MatrixWrapper

template<typename Derived >

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

protected

◆ Preconditioner

template<typename Derived >

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

◆ RealScalar

template<typename Derived >

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

◆ Scalar

template<typename Derived >

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

◆ StorageIndex

template<typename Derived >

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

Member Enumeration Documentation

◆ anonymous enum

template<typename Derived >

anonymous enum

Enumerator
ColsAtCompileTime
MaxColsAtCompileTime

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

Constructor & Destructor Documentation

◆ IterativeSolverBase() [1/2]

template<typename Derived >

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

inline

Default constructor.

  {
    init();
  }

References Eigen::IterativeSolverBase< Derived >::init().

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◆ IterativeSolverBase() [2/2]

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.

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

References Eigen::IterativeSolverBase< Derived >::compute(), Eigen::IterativeSolverBase< Derived >::init(), and Eigen::IterativeSolverBase< Derived >::matrix().

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◆ ~IterativeSolverBase()

template<typename Derived >

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

inline

189{}

Member Function Documentation

◆ _solve_impl() [1/2]

template<typename Derived >

template<typename Rhs , typename DestDerived >

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

inline

  {
    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);
    for(Index k=0; k<rhsCols; ++k)
    {
      tb = b.col(k);
      tx = derived().solve(tb);
      tmp.col(k) = tx.sparseView(0);
    }
    dest.swap(tmp);
  }

References Eigen::IterativeSolverBase< Derived >::cols(), Eigen::IterativeSolverBase< Derived >::derived(), Eigen::SparseMatrixBase< Derived >::derived(), eigen_assert, Eigen::IterativeSolverBase< Derived >::rows(), and Eigen::PlainObjectBase< Derived >::swap().

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◆ _solve_impl() [2/2]

template<typename Derived >

template<typename Rhs , typename Dest >

void Eigen::SparseSolverBase< Derived >::_solve_impl	(	const SparseMatrixBase< Rhs > &	b,
		SparseMatrixBase< Dest > &	dest
	)		const

inlineinherited

    {
      internal::solve_sparse_through_dense_panels(derived(), b.derived(), dest.derived());
    }

References Eigen::SparseSolverBase< Derived >::derived(), Eigen::SparseMatrixBase< Derived >::derived(), and Eigen::internal::solve_sparse_through_dense_panels().

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◆ 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.

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

References Eigen::EigenBase< Derived >::derived(), Eigen::IterativeSolverBase< Derived >::derived(), Eigen::IterativeSolverBase< Derived >::grab(), Eigen::IterativeSolverBase< Derived >::m_analysisIsOk, Eigen::IterativeSolverBase< Derived >::m_info, Eigen::IterativeSolverBase< Derived >::m_isInitialized, Eigen::IterativeSolverBase< Derived >::m_preconditioner, and Eigen::IterativeSolverBase< Derived >::matrix().

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◆ cols()

template<typename Derived >

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

inline

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

References Eigen::IterativeSolverBase< Derived >::matrix().

Referenced by Eigen::IterativeSolverBase< Derived >::_solve_impl().

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◆ 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.

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

References Eigen::EigenBase< Derived >::derived(), Eigen::IterativeSolverBase< Derived >::derived(), Eigen::IterativeSolverBase< Derived >::grab(), Eigen::IterativeSolverBase< Derived >::m_analysisIsOk, Eigen::IterativeSolverBase< Derived >::m_factorizationIsOk, Eigen::IterativeSolverBase< Derived >::m_info, Eigen::IterativeSolverBase< Derived >::m_isInitialized, Eigen::IterativeSolverBase< Derived >::m_preconditioner, and Eigen::IterativeSolverBase< Derived >::matrix().

Referenced by Eigen::IterativeSolverBase< Derived >::IterativeSolverBase().

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◆ derived() [1/2]

template<typename Derived >

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

inline

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

Referenced by Eigen::IterativeSolverBase< Derived >::_solve_impl(), Eigen::IterativeSolverBase< Derived >::analyzePattern(), Eigen::IterativeSolverBase< Derived >::compute(), Eigen::IterativeSolverBase< Derived >::factorize(), Eigen::IterativeSolverBase< Derived >::setMaxIterations(), Eigen::IterativeSolverBase< Derived >::setTolerance(), and Eigen::IterativeSolverBase< Derived >::solveWithGuess().

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◆ derived() [2/2]

template<typename Derived >

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

inline

80{ 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|.

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

References eigen_assert, Eigen::IterativeSolverBase< Derived >::m_error, and Eigen::IterativeSolverBase< Derived >::m_isInitialized.

◆ 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.

  {
    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();
  }

References Eigen::EigenBase< Derived >::derived(), Eigen::IterativeSolverBase< Derived >::derived(), eigen_assert, Eigen::IterativeSolverBase< Derived >::grab(), Eigen::IterativeSolverBase< Derived >::m_analysisIsOk, Eigen::IterativeSolverBase< Derived >::m_factorizationIsOk, Eigen::IterativeSolverBase< Derived >::m_info, Eigen::IterativeSolverBase< Derived >::m_preconditioner, and Eigen::IterativeSolverBase< Derived >::matrix().

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◆ grab()

template<typename Derived >

template<typename InputType >

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

inlineprotected

  {
    m_matrixWrapper.grab(A);
  }

References Eigen::IterativeSolverBase< Derived >::m_matrixWrapper.

Referenced by Eigen::IterativeSolverBase< Derived >::analyzePattern(), Eigen::IterativeSolverBase< Derived >::compute(), and Eigen::IterativeSolverBase< Derived >::factorize().

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◆ info()

template<typename Derived >

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

inline

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

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

References eigen_assert, Eigen::IterativeSolverBase< Derived >::m_info, and Eigen::IterativeSolverBase< Derived >::m_isInitialized.

◆ init()

template<typename Derived >

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

inlineprotected

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

References Eigen::IterativeSolverBase< Derived >::m_analysisIsOk, Eigen::IterativeSolverBase< Derived >::m_factorizationIsOk, Eigen::IterativeSolverBase< Derived >::m_isInitialized, Eigen::IterativeSolverBase< Derived >::m_maxIterations, and Eigen::IterativeSolverBase< Derived >::m_tolerance.

Referenced by Eigen::IterativeSolverBase< Derived >::IterativeSolverBase(), and Eigen::IterativeSolverBase< Derived >::IterativeSolverBase().

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◆ iterations()

template<typename Derived >

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

inline

Returns: the number of iterations performed during the last solve

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

References eigen_assert, Eigen::IterativeSolverBase< Derived >::m_isInitialized, and Eigen::IterativeSolverBase< Derived >::m_iterations.

◆ matrix()

template<typename Derived >

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

inlineprotected

  {
    return m_matrixWrapper.matrix();
  }

References Eigen::IterativeSolverBase< Derived >::m_matrixWrapper.

Referenced by Eigen::IterativeSolverBase< Derived >::IterativeSolverBase(), Eigen::IterativeSolverBase< Derived >::analyzePattern(), Eigen::IterativeSolverBase< Derived >::cols(), Eigen::IterativeSolverBase< Derived >::compute(), Eigen::IterativeSolverBase< Derived >::factorize(), Eigen::IterativeSolverBase< Derived >::maxIterations(), and Eigen::IterativeSolverBase< Derived >::rows().

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◆ maxIterations()

template<typename Derived >

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

inline

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

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

References Eigen::IterativeSolverBase< Derived >::m_maxIterations, and Eigen::IterativeSolverBase< Derived >::matrix().

Referenced by Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::_solve_with_guess_impl(), Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >::_solve_with_guess_impl(), and Eigen::LeastSquaresConjugateGradient< _MatrixType, _Preconditioner >::_solve_with_guess_impl().

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◆ preconditioner() [1/2]

template<typename Derived >

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

inline

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

272{ return m_preconditioner; }

References Eigen::IterativeSolverBase< Derived >::m_preconditioner.

◆ preconditioner() [2/2]

template<typename Derived >

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

inline

Returns: a read-only reference to the preconditioner.

275{ return m_preconditioner; }

References Eigen::IterativeSolverBase< Derived >::m_preconditioner.

◆ rows()

template<typename Derived >

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

inline

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

References Eigen::IterativeSolverBase< Derived >::matrix().

Referenced by Eigen::IterativeSolverBase< Derived >::_solve_impl(), and Eigen::IterativeSolverBase< Derived >::solveWithGuess().

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◆ 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.

  {
    m_maxIterations = maxIters;
    return derived();
  }

References Eigen::IterativeSolverBase< Derived >::derived(), and Eigen::IterativeSolverBase< Derived >::m_maxIterations.

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◆ 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()

  {
    m_tolerance = tolerance;
    return derived();
  }

References Eigen::IterativeSolverBase< Derived >::derived(), Eigen::IterativeSolverBase< Derived >::m_tolerance, and Eigen::IterativeSolverBase< Derived >::tolerance().

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◆ solve() [1/2]

template<typename Derived >

template<typename Rhs >

const Solve< Derived, Rhs > Eigen::SparseSolverBase< Derived >::solve ( const MatrixBase< Rhs > & b ) const

inlineinherited

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

See also: compute()

    {
      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 Solve<Derived, Rhs>(derived(), b.derived());
    }

References Eigen::SparseSolverBase< Derived >::derived(), eigen_assert, and Eigen::SparseSolverBase< Derived >::m_isInitialized.

Referenced by igl::embree::bone_heat(), igl::Frame_field_deformer::compute_optimal_positions(), igl::eigs(), igl::copyleft::comiso::FrameInterpolator::interpolateSymmetric(), igl::slim::solve_weighted_arap(), and igl::copyleft::comiso::NRosyField::solveNoRoundings().

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◆ solve() [2/2]

template<typename Derived >

template<typename Rhs >

const Solve< Derived, Rhs > Eigen::SparseSolverBase< Derived >::solve ( const SparseMatrixBase< Rhs > & b ) const

inlineinherited

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

See also: compute()

    {
      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 Solve<Derived, Rhs>(derived(), b.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 using the current decomposition of A and x0 as an initial solution.

See also: solve(), compute()

  {
    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);
  }