Eigen::IncompleteLUT< _Scalar > Class Template Reference

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

#include <IncompleteLUT.h>

Inheritance diagram for Eigen::IncompleteLUT< _Scalar >:

Classes
struct	keep_diag

Public Types
typedef Matrix< Scalar, Dynamic, Dynamic >	MatrixType

Public Member Functions
template<typename Rhs , typename Dest >
void	_solve (const Rhs &b, Dest &x) const
template<typename MatrixType >
void	analyzePattern (const MatrixType &amat)
template<typename _MatrixType >
void	analyzePattern (const _MatrixType &amat)
Index	cols () const
template<typename MatrixType >
IncompleteLUT< Scalar > &	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...
Index	rows () const
void	setDroptol (const RealScalar &droptol)
void	setFillfactor (int fillfactor)
template<typename Rhs >
const internal::solve_retval< IncompleteLUT, Rhs >	solve (const MatrixBase< Rhs > &b) const

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, Index >	m_P
PermutationMatrix< Dynamic, Dynamic, Index >	m_Pinv

Private Types
typedef SparseMatrix< Scalar, RowMajor >	FactorType
typedef FactorType::Index	Index
typedef SparseMatrix< Scalar, ColMajor >	PermutType
typedef NumTraits< Scalar >::Real	RealScalar
typedef _Scalar	Scalar
typedef Matrix< Scalar, Dynamic, 1 >	Vector

Additional Inherited Members
Private Member Functions inherited from Eigen::internal::noncopyable
	noncopyable ()
	~noncopyable ()

Detailed Description

template<typename _Scalar>
class Eigen::IncompleteLUT< _Scalar >

Incomplete LU factorization with dual-threshold strategy.

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 96 of file IncompleteLUT.h.

Member Typedef Documentation

template<typename _Scalar >

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

private

Definition at line 101 of file IncompleteLUT.h.

template<typename _Scalar >

typedef FactorType::Index Eigen::IncompleteLUT< _Scalar >::Index

private

Definition at line 103 of file IncompleteLUT.h.

template<typename _Scalar >

typedef Matrix<Scalar,Dynamic,Dynamic> Eigen::IncompleteLUT< _Scalar >::MatrixType

Definition at line 106 of file IncompleteLUT.h.

template<typename _Scalar >

typedef SparseMatrix<Scalar,ColMajor> Eigen::IncompleteLUT< _Scalar >::PermutType

private

Definition at line 102 of file IncompleteLUT.h.

template<typename _Scalar >

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

private

Definition at line 99 of file IncompleteLUT.h.

template<typename _Scalar >

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

private

Definition at line 98 of file IncompleteLUT.h.

template<typename _Scalar >

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

private

Definition at line 100 of file IncompleteLUT.h.

Constructor & Destructor Documentation

template<typename _Scalar >

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

inline

Definition at line 108 of file IncompleteLUT.h.

template<typename _Scalar >

template<typename MatrixType >

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

inline

Definition at line 114 of file IncompleteLUT.h.

Member Function Documentation

template<typename _Scalar >

template<typename Rhs , typename Dest >

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

inline

Definition at line 161 of file IncompleteLUT.h.

template<typename _Scalar >

template<typename MatrixType >

void Eigen::IncompleteLUT< _Scalar >::analyzePattern

(

const MatrixType &

amat

)

template<typename _Scalar >

template<typename _MatrixType >

void Eigen::IncompleteLUT< _Scalar >::analyzePattern

(

const _MatrixType &

amat

)

Definition at line 223 of file IncompleteLUT.h.

template<typename _Scalar >

Index Eigen::IncompleteLUT< _Scalar >::cols ( void  ) const

inline

Definition at line 124 of file IncompleteLUT.h.

template<typename _Scalar >

template<typename MatrixType >

IncompleteLUT<Scalar>& Eigen::IncompleteLUT< _Scalar >::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 149 of file IncompleteLUT.h.

template<typename _Scalar >

template<typename MatrixType >

void Eigen::IncompleteLUT< _Scalar >::factorize

(

const MatrixType &

amat

)

template<typename _Scalar >

template<typename _MatrixType >

void Eigen::IncompleteLUT< _Scalar >::factorize

(

const _MatrixType &

amat

)

Definition at line 242 of file IncompleteLUT.h.

template<typename _Scalar >

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

inline

Reports whether previous computation was successful.

Returns

Success if computation was succesful, NumericalIssue if the matrix.appears to be negative.

Definition at line 131 of file IncompleteLUT.h.

template<typename _Scalar >

Index Eigen::IncompleteLUT< _Scalar >::rows ( void  ) const

inline

Definition at line 122 of file IncompleteLUT.h.

template<typename Scalar >

void Eigen::IncompleteLUT< Scalar >::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.

template<typename Scalar >

void Eigen::IncompleteLUT< Scalar >::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.

template<typename _Scalar >

template<typename Rhs >

const internal::solve_retval<IncompleteLUT, Rhs> Eigen::IncompleteLUT< _Scalar >::solve ( const MatrixBase< Rhs > &  b ) const

inline

Definition at line 170 of file IncompleteLUT.h.

Member Data Documentation

template<typename _Scalar >

bool Eigen::IncompleteLUT< _Scalar >::m_analysisIsOk

protected

Definition at line 193 of file IncompleteLUT.h.

template<typename _Scalar >

RealScalar Eigen::IncompleteLUT< _Scalar >::m_droptol

protected

Definition at line 191 of file IncompleteLUT.h.

template<typename _Scalar >

bool Eigen::IncompleteLUT< _Scalar >::m_factorizationIsOk

protected

Definition at line 194 of file IncompleteLUT.h.

template<typename _Scalar >

int Eigen::IncompleteLUT< _Scalar >::m_fillfactor

protected

Definition at line 192 of file IncompleteLUT.h.

template<typename _Scalar >

ComputationInfo Eigen::IncompleteLUT< _Scalar >::m_info

protected

Definition at line 196 of file IncompleteLUT.h.

template<typename _Scalar >

bool Eigen::IncompleteLUT< _Scalar >::m_isInitialized

protected

Definition at line 195 of file IncompleteLUT.h.

template<typename _Scalar >

FactorType Eigen::IncompleteLUT< _Scalar >::m_lu

protected

Definition at line 190 of file IncompleteLUT.h.

template<typename _Scalar >

PermutationMatrix<Dynamic,Dynamic,Index> Eigen::IncompleteLUT< _Scalar >::m_P

protected

Definition at line 197 of file IncompleteLUT.h.

template<typename _Scalar >

PermutationMatrix<Dynamic,Dynamic,Index> Eigen::IncompleteLUT< _Scalar >::m_Pinv

protected

Definition at line 198 of file IncompleteLUT.h.

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

• IncompleteLUT.h