Eigen::IDRSTABL< MatrixType_, Preconditioner_ > Class Template Reference

The IDR(s)STAB(l) is a combination of IDR(s) and BiCGSTAB(l). It is a short-recurrences Krylov method for sparse square problems. It can outperform both IDR(s) and BiCGSTAB(l). IDR(s)STAB(l) generally closely follows the optimal GMRES convergence in terms of the number of Matrix-Vector products. However, without the increasing cost per iteration of GMRES. IDR(s)STAB(l) is suitable for both indefinite systems and systems with complex eigenvalues. More...

#include <IDRSTABL.h>

Inheritance diagram for Eigen::IDRSTABL< MatrixType_, Preconditioner_ >:

Public Types
typedef MatrixType_	MatrixType
typedef MatrixType::Scalar	Scalar
typedef MatrixType::RealScalar	RealScalar
typedef Preconditioner_	Preconditioner
Public Types inherited from Eigen::IterativeSolverBase< IDRSTABL< MatrixType_, Preconditioner_ > >
enum
typedef internal::traits< IDRSTABL< MatrixType_, Preconditioner_ > >::MatrixType	MatrixType
typedef internal::traits< IDRSTABL< MatrixType_, Preconditioner_ > >::Preconditioner	Preconditioner
typedef MatrixType::Scalar	Scalar
typedef MatrixType::StorageIndex	StorageIndex
typedef MatrixType::RealScalar	RealScalar

Public Member Functions
	IDRSTABL ()
template<typename MatrixDerived >
	IDRSTABL (const EigenBase< MatrixDerived > &A)
template<typename Rhs , typename Dest >
void	_solve_vector_with_guess_impl (const Rhs &b, Dest &x) const
void	setL (Index L)
void	setS (Index S)
Public Member Functions inherited from Eigen::IterativeSolverBase< IDRSTABL< MatrixType_, Preconditioner_ > >
	IterativeSolverBase ()
	IterativeSolverBase (const EigenBase< MatrixDerived > &A)
	IterativeSolverBase (IterativeSolverBase &&)=default
	~IterativeSolverBase ()
IDRSTABL< MatrixType_, Preconditioner_ > &	analyzePattern (const EigenBase< MatrixDerived > &A)
IDRSTABL< MatrixType_, Preconditioner_ > &	factorize (const EigenBase< MatrixDerived > &A)
IDRSTABL< MatrixType_, Preconditioner_ > &	compute (const EigenBase< MatrixDerived > &A)
EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT
EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT
RealScalar	tolerance () const
IDRSTABL< MatrixType_, Preconditioner_ > &	setTolerance (const RealScalar &tolerance)
Preconditioner &	preconditioner ()
const Preconditioner &	preconditioner () const
Index	maxIterations () const
IDRSTABL< MatrixType_, Preconditioner_ > &	setMaxIterations (Index maxIters)
Index	iterations () const
RealScalar	error () const
const SolveWithGuess< IDRSTABL< MatrixType_, Preconditioner_ >, Rhs, Guess >	solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const
ComputationInfo	info () const
void	_solve_with_guess_impl (const Rhs &b, SparseMatrixBase< DestDerived > &aDest) 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_impl (const Rhs &b, Dest &x) const
IDRSTABL< MatrixType_, Preconditioner_ > &	derived ()
const IDRSTABL< MatrixType_, Preconditioner_ > &	derived () const
Public Member Functions inherited from Eigen::SparseSolverBase< Derived >
	SparseSolverBase ()
	SparseSolverBase (SparseSolverBase &&other)
	~SparseSolverBase ()
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

Private Types
typedef IterativeSolverBase< IDRSTABL >	Base

Private Member Functions
const ActualMatrixType &	matrix () const

Private Attributes
Index	m_L
Index	m_S
RealScalar	m_error
ComputationInfo	m_info
bool	m_isInitialized
Index	m_iterations

Additional Inherited Members
Protected Types inherited from Eigen::IterativeSolverBase< IDRSTABL< MatrixType_, Preconditioner_ > >
typedef SparseSolverBase< IDRSTABL< MatrixType_, Preconditioner_ > >	Base
typedef internal::generic_matrix_wrapper< MatrixType >	MatrixWrapper
typedef MatrixWrapper::ActualMatrixType	ActualMatrixType
Protected Member Functions inherited from Eigen::IterativeSolverBase< IDRSTABL< MatrixType_, Preconditioner_ > >
void	init ()
const ActualMatrixType &	matrix () const
void	grab (const InputType &A)
Protected Attributes inherited from Eigen::IterativeSolverBase< IDRSTABL< MatrixType_, Preconditioner_ > >
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
Protected Attributes inherited from Eigen::SparseSolverBase< Derived >
bool	m_isInitialized

Detailed Description

template<typename MatrixType_, typename Preconditioner_>
class Eigen::IDRSTABL< MatrixType_, Preconditioner_ >

The IDR(s)STAB(l) is a combination of IDR(s) and BiCGSTAB(l). It is a short-recurrences Krylov method for sparse square problems. It can outperform both IDR(s) and BiCGSTAB(l). IDR(s)STAB(l) generally closely follows the optimal GMRES convergence in terms of the number of Matrix-Vector products. However, without the increasing cost per iteration of GMRES. IDR(s)STAB(l) is suitable for both indefinite systems and systems with complex eigenvalues.

This class allows solving for A.x = b sparse linear problems. 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.
Preconditioner_	the type of the preconditioner. Default is DiagonalPreconditioner

\implsparsesolverconcept

The maximum 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 maximum number of iterations and NumTraits<Scalar>::epsilon() for the tolerance.

The tolerance is the maximum relative residual error: |Ax-b|/|b| for which the linear system is considered solved.

Performance: When using sparse matrices, best performance is achieved for a row-major sparse matrix format. 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.

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

IDR(s)STAB(l) can also be used in a matrix-free context, see the following example .

See also

class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Member Typedef Documentation

Base

template<typename MatrixType_ , typename Preconditioner_ >

typedef IterativeSolverBase<IDRSTABL> Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::Base

private

MatrixType

template<typename MatrixType_ , typename Preconditioner_ >

typedef MatrixType_ Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::MatrixType

Preconditioner

template<typename MatrixType_ , typename Preconditioner_ >

typedef Preconditioner_ Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::Preconditioner

RealScalar

template<typename MatrixType_ , typename Preconditioner_ >

typedef MatrixType::RealScalar Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::RealScalar

Scalar

template<typename MatrixType_ , typename Preconditioner_ >

typedef MatrixType::Scalar Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::Scalar

Constructor & Destructor Documentation

IDRSTABL() [1/2]

template<typename MatrixType_ , typename Preconditioner_ >

Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::IDRSTABL ( )

inline

Default constructor.

: m_L(2), m_S(4) {}

IDRSTABL() [2/2]

template<typename MatrixType_ , typename Preconditioner_ >

template<typename MatrixDerived >

Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::IDRSTABL ( 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.

: Base(A.derived()), m_L(2), m_S(4) {}

Member Function Documentation

_solve_vector_with_guess_impl()

template<typename MatrixType_ , typename Preconditioner_ >

template<typename Rhs , typename Dest >

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

inline

Loops over the number of columns of b and does the following:

1. sets the tolerance and maxIterations
2. Calls the function that has the core solver routine

                                                                  {
    m_iterations = Base::maxIterations();
    m_error = Base::m_tolerance;
    bool ret = internal::idrstabl(matrix(), b, x, Base::m_preconditioner, m_iterations, m_error, m_L, m_S);
 
    m_info = (!ret) ? NumericalIssue : m_error <= 10 * Base::m_tolerance ? Success : NoConvergence;
  }

References b, Eigen::internal::idrstabl(), Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::m_error, Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::m_info, Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::m_iterations, Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::m_L, Eigen::IterativeSolverBase< Derived >::m_preconditioner, Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::m_S, Eigen::IterativeSolverBase< Derived >::m_tolerance, Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::matrix(), Eigen::IterativeSolverBase< Derived >::maxIterations(), Eigen::NoConvergence, Eigen::NumericalIssue, ret, Eigen::Success, and plotDoE::x.

matrix()

template<typename MatrixType_ , typename Preconditioner_ >

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

inlineprivate

{ return m_matrixWrapper.matrix(); }

Referenced by Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::_solve_vector_with_guess_impl().

setL()

template<typename MatrixType_ , typename Preconditioner_ >

void Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::setL ( Index  L )

inline

Sets the parameter L, indicating the amount of minimize residual steps are used.

                     {
    eigen_assert(L >= 1 && "L needs to be positive");
    m_L = L;
  }

References eigen_assert, L, and Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::m_L.

setS()

template<typename MatrixType_ , typename Preconditioner_ >

void Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::setS ( Index  S )

inline

Sets the parameter S, indicating the dimension of the shadow residual space..

                     {
    eigen_assert(S >= 1 && "S needs to be positive");
    m_S = S;
  }

References eigen_assert, Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::m_S, and oomph::QuadTreeNames::S.

Member Data Documentation

m_error

template<typename MatrixType_ , typename Preconditioner_ >

RealScalar Eigen::IterativeSolverBase< Derived >::m_error

mutableprivate

Referenced by Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::_solve_vector_with_guess_impl().

m_info

template<typename MatrixType_ , typename Preconditioner_ >

ComputationInfo Eigen::IterativeSolverBase< Derived >::m_info

mutableprivate

Referenced by Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::_solve_vector_with_guess_impl().

m_isInitialized

template<typename MatrixType_ , typename Preconditioner_ >

bool Eigen::SparseSolverBase< Derived >::m_isInitialized

mutableprivate

m_iterations

template<typename MatrixType_ , typename Preconditioner_ >

Index Eigen::IterativeSolverBase< Derived >::m_iterations

mutableprivate

Referenced by Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::_solve_vector_with_guess_impl().

m_L

template<typename MatrixType_ , typename Preconditioner_ >

Index Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::m_L

private

Referenced by Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::_solve_vector_with_guess_impl(), and Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::setL().

m_S

template<typename MatrixType_ , typename Preconditioner_ >

Index Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::m_S

private

Referenced by Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::_solve_vector_with_guess_impl(), and Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::setS().

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

• IDRSTABL.h