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Eigen::IncompleteLUT< _Scalar > Class Template Reference

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

#include <IncompleteLUT.h>

Inheritance diagram for Eigen::IncompleteLUT< _Scalar >:
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Classes

struct  keep_diag
 

Public Types

typedef Matrix< Scalar, Dynamic, DynamicMatrixType
 

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, Indexm_P
 
PermutationMatrix< Dynamic, Dynamic, Indexm_Pinv
 

Private Types

typedef SparseMatrix< Scalar, RowMajorFactorType
 
typedef FactorType::Index Index
 
typedef SparseMatrix< Scalar, ColMajorPermutType
 
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
droptolDrop 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
fillfactorThis 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.


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


acado
Author(s): Milan Vukov, Rien Quirynen
autogenerated on Mon Jun 10 2019 12:35:35