Incomplete LU factorization with dual-threshold strategy. More...
#include <IncompleteLUT.h>
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
typedef SparseMatrix<Scalar,RowMajor> Eigen::IncompleteLUT< _Scalar >::FactorType [private] |
Definition at line 101 of file IncompleteLUT.h.
typedef FactorType::Index Eigen::IncompleteLUT< _Scalar >::Index [private] |
Definition at line 103 of file IncompleteLUT.h.
| typedef Matrix<Scalar,Dynamic,Dynamic> Eigen::IncompleteLUT< _Scalar >::MatrixType |
Definition at line 106 of file IncompleteLUT.h.
typedef SparseMatrix<Scalar,ColMajor> Eigen::IncompleteLUT< _Scalar >::PermutType [private] |
Definition at line 102 of file IncompleteLUT.h.
typedef NumTraits<Scalar>::Real Eigen::IncompleteLUT< _Scalar >::RealScalar [private] |
Definition at line 99 of file IncompleteLUT.h.
typedef _Scalar Eigen::IncompleteLUT< _Scalar >::Scalar [private] |
Definition at line 98 of file IncompleteLUT.h.
typedef Matrix<Scalar,Dynamic,1> Eigen::IncompleteLUT< _Scalar >::Vector [private] |
Definition at line 100 of file IncompleteLUT.h.
Constructor & Destructor Documentation
| Eigen::IncompleteLUT< _Scalar >::IncompleteLUT | ( | ) | [inline] |
Definition at line 108 of file IncompleteLUT.h.
| 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
| void Eigen::IncompleteLUT< _Scalar >::_solve | ( | const Rhs & | b, |
| Dest & | x | ||
| ) | const [inline] |
Definition at line 161 of file IncompleteLUT.h.
| void Eigen::IncompleteLUT< _Scalar >::analyzePattern | ( | const MatrixType & | amat | ) |
| void Eigen::IncompleteLUT< _Scalar >::analyzePattern | ( | const _MatrixType & | amat | ) |
Definition at line 223 of file IncompleteLUT.h.
| Index Eigen::IncompleteLUT< _Scalar >::cols | ( | void | ) | const [inline] |
Definition at line 124 of file IncompleteLUT.h.
| 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.
| void Eigen::IncompleteLUT< _Scalar >::factorize | ( | const MatrixType & | amat | ) |
| void Eigen::IncompleteLUT< _Scalar >::factorize | ( | const _MatrixType & | amat | ) |
Definition at line 242 of file IncompleteLUT.h.
| ComputationInfo Eigen::IncompleteLUT< _Scalar >::info | ( | ) | const [inline] |
Reports whether previous computation was successful.
- Returns:
Successif computation was succesful,NumericalIssueif the matrix.appears to be negative.
Definition at line 131 of file IncompleteLUT.h.
| Index Eigen::IncompleteLUT< _Scalar >::rows | ( | void | ) | const [inline] |
Definition at line 122 of file IncompleteLUT.h.
| 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.
| void Eigen::IncompleteLUT< Scalar >::setFillfactor | ( | int | fillfactor | ) |
Set control parameter fillfactor
- Parameters:
-
fillfactor This is used to compute the number fill_inof largest elements to keep on each row.
Definition at line 216 of file IncompleteLUT.h.
| 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
bool Eigen::IncompleteLUT< _Scalar >::m_analysisIsOk [protected] |
Definition at line 193 of file IncompleteLUT.h.
RealScalar Eigen::IncompleteLUT< _Scalar >::m_droptol [protected] |
Definition at line 191 of file IncompleteLUT.h.
bool Eigen::IncompleteLUT< _Scalar >::m_factorizationIsOk [protected] |
Definition at line 194 of file IncompleteLUT.h.
int Eigen::IncompleteLUT< _Scalar >::m_fillfactor [protected] |
Definition at line 192 of file IncompleteLUT.h.
ComputationInfo Eigen::IncompleteLUT< _Scalar >::m_info [protected] |
Definition at line 196 of file IncompleteLUT.h.
bool Eigen::IncompleteLUT< _Scalar >::m_isInitialized [protected] |
Definition at line 195 of file IncompleteLUT.h.
FactorType Eigen::IncompleteLUT< _Scalar >::m_lu [protected] |
Definition at line 190 of file IncompleteLUT.h.
PermutationMatrix<Dynamic,Dynamic,Index> Eigen::IncompleteLUT< _Scalar >::m_P [protected] |
Definition at line 197 of file IncompleteLUT.h.
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: