Classes | Public Types | Public Member Functions | Protected Attributes | Private Types
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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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, const RealScalar &droptol=NumTraits< Scalar >::dummy_precision(), int fillfactor=10)
ComputationInfo info () const
 Reports whether previous computation was successful.
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

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 Thu Aug 27 2015 12:01:56