Incomplete LU factorization with dual-threshold strategy. More...

#include <IncompleteLUT.h>

Inheritance diagram for Eigen::IncompleteLUT< _Scalar, _StorageIndex >:

Classes
struct	keep_diag

Public Types
enum	{ ColsAtCompileTime = Dynamic, MaxColsAtCompileTime = Dynamic }

typedef SparseMatrix< Scalar, RowMajor, StorageIndex >	FactorType

typedef NumTraits< Scalar >::Real	RealScalar

typedef _Scalar	Scalar

typedef _StorageIndex	StorageIndex

typedef Matrix< Scalar, Dynamic, 1 >	Vector

typedef Matrix< StorageIndex, Dynamic, 1 >	VectorI

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

template<typename _MatrixType >
void	analyzePattern (const _MatrixType &amat)

template<typename MatrixType >
void	analyzePattern (const MatrixType &amat)

EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

template<typename MatrixType >
IncompleteLUT &	compute (const MatrixType &amat)

template<typename _MatrixType >
void	factorize (const _MatrixType &amat)

template<typename MatrixType >
void	factorize (const MatrixType &amat)

	IncompleteLUT ()

template<typename MatrixType >
	IncompleteLUT (const MatrixType &mat, const RealScalar &droptol=NumTraits< Scalar >::dummy_precision(), int fillfactor=10)

ComputationInfo	info () const
	Reports whether previous computation was successful. More...

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

void	setDroptol (const RealScalar &droptol)

void	setFillfactor (int fillfactor)

Public Member Functions inherited from Eigen::SparseSolverBase< IncompleteLUT< _Scalar, int > >
void	_solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const

IncompleteLUT< _Scalar, int > &	derived ()

const IncompleteLUT< _Scalar, int > &	derived () const

const Solve< IncompleteLUT< _Scalar, int >, Rhs >	solve (const MatrixBase< Rhs > &b) const

const Solve< IncompleteLUT< _Scalar, int >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const

	SparseSolverBase ()

	~SparseSolverBase ()

Protected Types
typedef SparseSolverBase< IncompleteLUT >	Base

Protected Attributes
bool	m_analysisIsOk

RealScalar	m_droptol

bool	m_factorizationIsOk

int	m_fillfactor

ComputationInfo	m_info

bool	m_isInitialized

FactorType	m_lu

PermutationMatrix< Dynamic, Dynamic, StorageIndex >	m_P

PermutationMatrix< Dynamic, Dynamic, StorageIndex >	m_Pinv

Protected Attributes inherited from Eigen::SparseSolverBase< IncompleteLUT< _Scalar, int > >
bool	m_isInitialized

Detailed Description

template<typename _Scalar, typename _StorageIndex = int>
class Eigen::IncompleteLUT< _Scalar, _StorageIndex >

Incomplete LU factorization with dual-threshold strategy.

\implsparsesolverconcept

During the numerical factorization, two dropping rules are used : 1) any element whose magnitude is less than some tolerance is dropped. This tolerance is obtained by multiplying the input tolerance droptol by the average magnitude of all the original elements in the current row. 2) After the elimination of the row, only the fill largest elements in the L part and the fill largest elements in the U part are kept (in addition to the diagonal element ). Note that fill is computed from the input parameter fillfactor which is used the ratio to control the fill_in relatively to the initial number of nonzero elements.

The two extreme cases are when droptol=0 (to keep all the fill*2 largest elements) and when fill=n/2 with droptol being different to zero.

References : Yousef Saad, ILUT: A dual threshold incomplete LU factorization, Numerical Linear Algebra with Applications, 1(4), pp 387-402, 1994.

NOTE : The following implementation is derived from the ILUT implementation in the SPARSKIT package, Copyright (C) 2005, the Regents of the University of Minnesota released under the terms of the GNU LGPL: http://www-users.cs.umn.edu/~saad/software/SPARSKIT/README However, Yousef Saad gave us permission to relicense his ILUT code to MPL2. See the Eigen mailing list archive, thread: ILUT, date: July 8, 2012: http://listengine.tuxfamily.org/lists.tuxfamily.org/eigen/2012/07/msg00064.html alternatively, on GMANE: http://comments.gmane.org/gmane.comp.lib.eigen/3302

Definition at line 99 of file IncompleteLUT.h.

Member Typedef Documentation

◆ Base

template<typename _Scalar , typename _StorageIndex = int>

typedef SparseSolverBase<IncompleteLUT> Eigen::IncompleteLUT< _Scalar, _StorageIndex >::Base

protected

Definition at line 102 of file IncompleteLUT.h.

◆ FactorType

template<typename _Scalar , typename _StorageIndex = int>

typedef SparseMatrix<Scalar,RowMajor,StorageIndex> Eigen::IncompleteLUT< _Scalar, _StorageIndex >::FactorType

Definition at line 110 of file IncompleteLUT.h.

◆ RealScalar

template<typename _Scalar , typename _StorageIndex = int>

typedef NumTraits<Scalar>::Real Eigen::IncompleteLUT< _Scalar, _StorageIndex >::RealScalar

Definition at line 107 of file IncompleteLUT.h.

◆ Scalar

template<typename _Scalar , typename _StorageIndex = int>

typedef _Scalar Eigen::IncompleteLUT< _Scalar, _StorageIndex >::Scalar

Definition at line 105 of file IncompleteLUT.h.

◆ StorageIndex

template<typename _Scalar , typename _StorageIndex = int>

typedef _StorageIndex Eigen::IncompleteLUT< _Scalar, _StorageIndex >::StorageIndex

Definition at line 106 of file IncompleteLUT.h.

◆ Vector

template<typename _Scalar , typename _StorageIndex = int>

typedef Matrix<Scalar,Dynamic,1> Eigen::IncompleteLUT< _Scalar, _StorageIndex >::Vector

Definition at line 108 of file IncompleteLUT.h.

◆ VectorI

template<typename _Scalar , typename _StorageIndex = int>

typedef Matrix<StorageIndex,Dynamic,1> Eigen::IncompleteLUT< _Scalar, _StorageIndex >::VectorI

Definition at line 109 of file IncompleteLUT.h.

Member Enumeration Documentation

◆ anonymous enum

template<typename _Scalar , typename _StorageIndex = int>

anonymous enum

Enumerator
ColsAtCompileTime
MaxColsAtCompileTime

Definition at line 112 of file IncompleteLUT.h.

Constructor & Destructor Documentation

◆ IncompleteLUT() [1/2]

template<typename _Scalar , typename _StorageIndex = int>

Eigen::IncompleteLUT< _Scalar, _StorageIndex >::IncompleteLUT ( )

inline

Definition at line 119 of file IncompleteLUT.h.

◆ IncompleteLUT() [2/2]

template<typename _Scalar , typename _StorageIndex = int>

template<typename MatrixType >

Eigen::IncompleteLUT< _Scalar, _StorageIndex >::IncompleteLUT	(	const MatrixType &	mat,
		const RealScalar &	droptol = `NumTraits<Scalar>::dummy_precision()`,
		int	fillfactor = `10`
	)

inlineexplicit

Definition at line 125 of file IncompleteLUT.h.

Member Function Documentation

◆ _solve_impl()

template<typename _Scalar , typename _StorageIndex = int>

template<typename Rhs , typename Dest >

void Eigen::IncompleteLUT< _Scalar, _StorageIndex >::_solve_impl	(	const Rhs &	b,
		Dest &	x
	)		const

inline

Definition at line 171 of file IncompleteLUT.h.

◆ analyzePattern() [1/2]

template<typename _Scalar , typename _StorageIndex = int>

template<typename _MatrixType >

void Eigen::IncompleteLUT< _Scalar, _StorageIndex >::analyzePattern ( const _MatrixType & amat )

Definition at line 223 of file IncompleteLUT.h.

◆ analyzePattern() [2/2]

template<typename _Scalar , typename _StorageIndex = int>

template<typename MatrixType >

void Eigen::IncompleteLUT< _Scalar, _StorageIndex >::analyzePattern ( const MatrixType & amat )

◆ cols()

template<typename _Scalar , typename _StorageIndex = int>

EIGEN_CONSTEXPR Index Eigen::IncompleteLUT< _Scalar, _StorageIndex >::cols ( ) const

inline

Definition at line 135 of file IncompleteLUT.h.

◆ compute()

template<typename _Scalar , typename _StorageIndex = int>

template<typename MatrixType >

IncompleteLUT& Eigen::IncompleteLUT< _Scalar, _StorageIndex >::compute ( const MatrixType & amat )

inline

Compute an incomplete LU factorization with dual threshold on the matrix mat No pivoting is done in this version

Definition at line 160 of file IncompleteLUT.h.

◆ factorize() [1/2]

template<typename _Scalar , typename _StorageIndex = int>

template<typename _MatrixType >

void Eigen::IncompleteLUT< _Scalar, _StorageIndex >::factorize ( const _MatrixType & amat )

Definition at line 244 of file IncompleteLUT.h.

◆ factorize() [2/2]

template<typename _Scalar , typename _StorageIndex = int>

template<typename MatrixType >

void Eigen::IncompleteLUT< _Scalar, _StorageIndex >::factorize ( const MatrixType & amat )

◆ info()

template<typename _Scalar , typename _StorageIndex = int>

ComputationInfo Eigen::IncompleteLUT< _Scalar, _StorageIndex >::info ( ) const

inline

Reports whether previous computation was successful.

Returns: Success if computation was successful, NumericalIssue if the matrix.appears to be negative.

Definition at line 142 of file IncompleteLUT.h.

◆ rows()

template<typename _Scalar , typename _StorageIndex = int>

EIGEN_CONSTEXPR Index Eigen::IncompleteLUT< _Scalar, _StorageIndex >::rows ( ) const

inline

Definition at line 133 of file IncompleteLUT.h.

◆ setDroptol()

template<typename Scalar , typename StorageIndex >

void Eigen::IncompleteLUT< Scalar, StorageIndex >::setDroptol ( const RealScalar & droptol )

Set control parameter droptol

Parameters

droptol Drop any element whose magnitude is less than this tolerance

Definition at line 206 of file IncompleteLUT.h.

◆ setFillfactor()

template<typename Scalar , typename StorageIndex >

void Eigen::IncompleteLUT< Scalar, StorageIndex >::setFillfactor ( int fillfactor )

Set control parameter fillfactor

Parameters

fillfactor This is used to compute the number fill_in of largest elements to keep on each row.

Definition at line 216 of file IncompleteLUT.h.

Member Data Documentation

◆ m_analysisIsOk

template<typename _Scalar , typename _StorageIndex = int>

bool Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_analysisIsOk

protected

Definition at line 194 of file IncompleteLUT.h.

◆ m_droptol

template<typename _Scalar , typename _StorageIndex = int>

RealScalar Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_droptol

protected

Definition at line 192 of file IncompleteLUT.h.

◆ m_factorizationIsOk

template<typename _Scalar , typename _StorageIndex = int>

bool Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_factorizationIsOk

protected

Definition at line 195 of file IncompleteLUT.h.

◆ m_fillfactor

template<typename _Scalar , typename _StorageIndex = int>

int Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_fillfactor

protected

Definition at line 193 of file IncompleteLUT.h.

◆ m_info

template<typename _Scalar , typename _StorageIndex = int>

ComputationInfo Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_info

protected

Definition at line 196 of file IncompleteLUT.h.

◆ m_isInitialized

template<typename _Scalar , typename _StorageIndex = int>

bool Eigen::SparseSolverBase< Derived >::m_isInitialized

mutableprotected

Definition at line 119 of file SparseSolverBase.h.

◆ m_lu

template<typename _Scalar , typename _StorageIndex = int>

FactorType Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_lu

protected

Definition at line 191 of file IncompleteLUT.h.

◆ m_P

template<typename _Scalar , typename _StorageIndex = int>

PermutationMatrix<Dynamic,Dynamic,StorageIndex> Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_P

protected

Definition at line 197 of file IncompleteLUT.h.

◆ m_Pinv

template<typename _Scalar , typename _StorageIndex = int>

PermutationMatrix<Dynamic,Dynamic,StorageIndex> Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_Pinv

protected

Definition at line 198 of file IncompleteLUT.h.

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

IncompleteLUT.h

Classes

Public Types

Public Member Functions

Protected Types

Protected Attributes

Detailed Description

template<typename _Scalar, typename _StorageIndex = int> class Eigen::IncompleteLUT< _Scalar, _StorageIndex >

Member Typedef Documentation

◆ Base

◆ FactorType

◆ RealScalar

◆ Scalar

◆ StorageIndex

◆ Vector

◆ VectorI

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ IncompleteLUT() [1/2]

◆ IncompleteLUT() [2/2]

Member Function Documentation

◆ _solve_impl()

◆ analyzePattern() [1/2]

◆ analyzePattern() [2/2]

◆ cols()

◆ compute()

◆ factorize() [1/2]

◆ factorize() [2/2]

◆ info()

◆ rows()

◆ setDroptol()

◆ setFillfactor()

Member Data Documentation

◆ m_analysisIsOk

◆ m_droptol

◆ m_factorizationIsOk

◆ m_fillfactor

◆ m_info

◆ m_isInitialized

◆ m_lu

◆ m_P

◆ m_Pinv

template<typename _Scalar, typename _StorageIndex = int>
class Eigen::IncompleteLUT< _Scalar, _StorageIndex >