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. More...

#include <IncompleteLUT.h>

Inheritance diagram for Eigen::IncompleteLUT< _Scalar >:

[legend]

List of all members.

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, RealScalar droptol=NumTraits< Scalar >::dummy_precision(), int fillfactor=10)
ComputationInfo	info () const
	Reports whether previous computation was successful.
Index	rows () const
void	setDroptol (RealScalar droptol)
void	setFillfactor (int fillfactor)
template<typename Rhs >
const internal::solve_retval < IncompleteLUT, Rhs >	solve (const MatrixBase< Rhs > &b) const
Protected Member Functions
template<typename VectorV , typename VectorI >
int	QuickSplit (VectorV &row, VectorI &ind, int ncut)
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

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 44 of file IncompleteLUT.h.

Member Typedef Documentation

template<typename _Scalar >

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

Definition at line 49 of file IncompleteLUT.h.

template<typename _Scalar >

typedef FactorType::Index Eigen::IncompleteLUT< _Scalar >::Index [private]

Definition at line 51 of file IncompleteLUT.h.

template<typename _Scalar >

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

Definition at line 54 of file IncompleteLUT.h.

template<typename _Scalar >

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

Definition at line 50 of file IncompleteLUT.h.

template<typename _Scalar >

typedef NumTraits<Scalar>::Real Eigen::IncompleteLUT< _Scalar >::RealScalar [private]

Definition at line 47 of file IncompleteLUT.h.

template<typename _Scalar >

typedef _Scalar Eigen::IncompleteLUT< _Scalar >::Scalar [private]

Definition at line 46 of file IncompleteLUT.h.

template<typename _Scalar >

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

Definition at line 48 of file IncompleteLUT.h.

Constructor & Destructor Documentation

template<typename _Scalar >

Eigen::IncompleteLUT< _Scalar >::IncompleteLUT ( ) [inline]

Definition at line 56 of file IncompleteLUT.h.

template<typename _Scalar >

template<typename MatrixType >

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

Definition at line 62 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 110 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 221 of file IncompleteLUT.h.

template<typename _Scalar >

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

Definition at line 72 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 97 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 240 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 79 of file IncompleteLUT.h.

template<typename Scalar >

template<typename VectorV , typename VectorI >

int Eigen::IncompleteLUT< Scalar >::QuickSplit	(	VectorV &	row,
		VectorI &	ind,
		int	ncut
	)		`[protected]`

Compute a quick-sort split of a vector On output, the vector row is permuted such that its elements satisfy abs(row(i)) >= abs(row(ncut)) if i<ncut abs(row(i)) <= abs(row(ncut)) if i>ncut

Parameters: