Eigen::IncompleteLUT< _Scalar > Class Template Reference

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

#include <IncompleteLUT.h>

Inheritance diagram for Eigen::IncompleteLUT< _Scalar >:

Collaboration diagram for Eigen::IncompleteLUT< _Scalar >:

Classes
struct	keep_diag

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

Public Member Functions
template<typename MatrixType >
	IncompleteLUT (const MatrixType &mat, const RealScalar &droptol=NumTraits< Scalar >::dummy_precision(), int fillfactor=10)
Index	rows () const
Index	cols () const
ComputationInfo	info () const
	Reports whether previous computation was successful. More...
template<typename MatrixType >
void	analyzePattern (const MatrixType &amat)
template<typename MatrixType >
void	factorize (const MatrixType &amat)
template<typename MatrixType >
IncompleteLUT< Scalar > &	compute (const MatrixType &amat)
void	setDroptol (const RealScalar &droptol)
void	setFillfactor (int fillfactor)
template<typename Rhs , typename Dest >
void	_solve (const Rhs &b, Dest &x) const
template<typename Rhs >
const internal::solve_retval< IncompleteLUT, Rhs >	solve (const MatrixBase< Rhs > &b) const
template<typename _MatrixType >
void	analyzePattern (const _MatrixType &amat)
template<typename _MatrixType >
void	factorize (const _MatrixType &amat)

Protected Attributes
FactorType	m_lu
RealScalar	m_droptol
int	m_fillfactor
bool	m_analysisIsOk
bool	m_factorizationIsOk
bool	m_isInitialized
ComputationInfo	m_info
PermutationMatrix< Dynamic, Dynamic, Index >	m_P
PermutationMatrix< Dynamic, Dynamic, Index >	m_Pinv

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 Function Documentation

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.

    {
      analyzePattern(amat); 
      factorize(amat);
      m_isInitialized = m_factorizationIsOk;
      return *this;
    }

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.

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

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.

{
  this->m_droptol = droptol;   
}

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.

{
  this->m_fillfactor = fillfactor;   
}

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

• C:/Users/Brig/Documents/ShapeWorksStudio/src/Surfworks/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h