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Eigen::IncompleteLUT< _Scalar, _StorageIndex > Class Template Reference

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

#include <IncompleteLUT.h>

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

struct  keep_diag
 

Public Types

enum  { ColsAtCompileTime = Dynamic, MaxColsAtCompileTime = Dynamic }
 
typedef SparseMatrix< Scalar, RowMajor, StorageIndexFactorType
 
typedef NumTraits< Scalar >::Real RealScalar
 
typedef _Scalar Scalar
 
typedef _StorageIndex StorageIndex
 
typedef Matrix< Scalar, Dynamic, 1 > Vector
 
typedef Matrix< StorageIndex, Dynamic, 1 > VectorI
 

Public Member Functions

template<typename Rhs , typename Dest >
void _solve_impl (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 >
IncompleteLUTcompute (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)
 
- Public Member Functions inherited from Eigen::SparseSolverBase< IncompleteLUT< _Scalar, _StorageIndex > >
void _solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const
 
IncompleteLUT< _Scalar, _StorageIndex > & derived ()
 
const IncompleteLUT< _Scalar, _StorageIndex > & derived () const
 
const Solve< IncompleteLUT< _Scalar, _StorageIndex >, Rhs > solve (const MatrixBase< Rhs > &b) const
 
const Solve< IncompleteLUT< _Scalar, _StorageIndex >, Rhs > solve (const SparseMatrixBase< Rhs > &b) const
 
 SparseSolverBase ()
 
 ~SparseSolverBase ()
 

Protected Types

typedef SparseSolverBase< IncompleteLUTBase
 

Protected Attributes

bool m_analysisIsOk
 
RealScalar m_droptol
 
bool m_factorizationIsOk
 
int m_fillfactor
 
ComputationInfo m_info
 
FactorType m_lu
 
PermutationMatrix< Dynamic, Dynamic, StorageIndexm_P
 
PermutationMatrix< Dynamic, Dynamic, StorageIndexm_Pinv
 
- Protected Attributes inherited from Eigen::SparseSolverBase< IncompleteLUT< _Scalar, _StorageIndex > >
bool m_isInitialized
 

Detailed Description

template<typename _Scalar, typename _StorageIndex = int>
class Eigen::IncompleteLUT< _Scalar, _StorageIndex >

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 99 of file IncompleteLUT.h.

Member Typedef Documentation

template<typename _Scalar , typename _StorageIndex = int>
typedef SparseSolverBase<IncompleteLUT> Eigen::IncompleteLUT< _Scalar, _StorageIndex >::Base
protected

Definition at line 102 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
typedef SparseMatrix<Scalar,RowMajor,StorageIndex> Eigen::IncompleteLUT< _Scalar, _StorageIndex >::FactorType

Definition at line 110 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
typedef NumTraits<Scalar>::Real Eigen::IncompleteLUT< _Scalar, _StorageIndex >::RealScalar

Definition at line 107 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
typedef _Scalar Eigen::IncompleteLUT< _Scalar, _StorageIndex >::Scalar

Definition at line 105 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
typedef _StorageIndex Eigen::IncompleteLUT< _Scalar, _StorageIndex >::StorageIndex

Definition at line 106 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
typedef Matrix<Scalar,Dynamic,1> Eigen::IncompleteLUT< _Scalar, _StorageIndex >::Vector

Definition at line 108 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
typedef Matrix<StorageIndex,Dynamic,1> Eigen::IncompleteLUT< _Scalar, _StorageIndex >::VectorI

Definition at line 109 of file IncompleteLUT.h.

Member Enumeration Documentation

template<typename _Scalar , typename _StorageIndex = int>
anonymous enum
Enumerator
ColsAtCompileTime 
MaxColsAtCompileTime 

Definition at line 112 of file IncompleteLUT.h.

Constructor & Destructor Documentation

template<typename _Scalar , typename _StorageIndex = int>
Eigen::IncompleteLUT< _Scalar, _StorageIndex >::IncompleteLUT ( )
inline

Definition at line 119 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
template<typename MatrixType >
Eigen::IncompleteLUT< _Scalar, _StorageIndex >::IncompleteLUT ( const MatrixType mat,
const RealScalar droptol = NumTraits<Scalar>::dummy_precision(),
int  fillfactor = 10 
)
inlineexplicit

Definition at line 125 of file IncompleteLUT.h.

Member Function Documentation

template<typename _Scalar , typename _StorageIndex = int>
template<typename Rhs , typename Dest >
void Eigen::IncompleteLUT< _Scalar, _StorageIndex >::_solve_impl ( const Rhs &  b,
Dest &  x 
) const
inline

Definition at line 171 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
template<typename MatrixType >
void Eigen::IncompleteLUT< _Scalar, _StorageIndex >::analyzePattern ( const MatrixType amat)
template<typename _Scalar , typename _StorageIndex = int>
template<typename _MatrixType >
void Eigen::IncompleteLUT< _Scalar, _StorageIndex >::analyzePattern ( const _MatrixType &  amat)

Definition at line 223 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
Index Eigen::IncompleteLUT< _Scalar, _StorageIndex >::cols ( void  ) const
inline

Definition at line 135 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
template<typename MatrixType >
IncompleteLUT& Eigen::IncompleteLUT< _Scalar, _StorageIndex >::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 160 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
template<typename MatrixType >
void Eigen::IncompleteLUT< _Scalar, _StorageIndex >::factorize ( const MatrixType amat)
template<typename _Scalar , typename _StorageIndex = int>
template<typename _MatrixType >
void Eigen::IncompleteLUT< _Scalar, _StorageIndex >::factorize ( const _MatrixType &  amat)

Definition at line 253 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
ComputationInfo Eigen::IncompleteLUT< _Scalar, _StorageIndex >::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 142 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
Index Eigen::IncompleteLUT< _Scalar, _StorageIndex >::rows ( void  ) const
inline

Definition at line 133 of file IncompleteLUT.h.

template<typename Scalar , typename StorageIndex >
void Eigen::IncompleteLUT< Scalar, StorageIndex >::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 , typename StorageIndex >
void Eigen::IncompleteLUT< Scalar, StorageIndex >::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.

Member Data Documentation

template<typename _Scalar , typename _StorageIndex = int>
bool Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_analysisIsOk
protected

Definition at line 194 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
RealScalar Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_droptol
protected

Definition at line 192 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
bool Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_factorizationIsOk
protected

Definition at line 195 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
int Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_fillfactor
protected

Definition at line 193 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
ComputationInfo Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_info
protected

Definition at line 196 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
FactorType Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_lu
protected

Definition at line 191 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
PermutationMatrix<Dynamic,Dynamic,StorageIndex> Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_P
protected

Definition at line 197 of file IncompleteLUT.h.

template<typename _Scalar , typename _StorageIndex = int>
PermutationMatrix<Dynamic,Dynamic,StorageIndex> Eigen::IncompleteLUT< _Scalar, _StorageIndex >::m_Pinv
protected

Definition at line 198 of file IncompleteLUT.h.


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


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autogenerated on Sat May 8 2021 02:52:45