Classes | Public Types | Public Member Functions | Protected Member Functions | Protected Attributes | Private Types
Eigen::IncompleteLUT< _Scalar > Class Template Reference

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. 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, RealScalar droptol=NumTraits< Scalar >::dummy_precision(), int fillfactor=10)
ComputationInfo info () const
 Reports whether previous computation was successful.
Index rows () const
void setDroptol (RealScalar droptol)
void setFillfactor (int fillfactor)
template<typename Rhs >
const internal::solve_retval
< IncompleteLUT, Rhs > 
solve (const MatrixBase< Rhs > &b) const

Protected Member Functions

template<typename VectorV , typename VectorI >
int QuickSplit (VectorV &row, VectorI &ind, int ncut)

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 44 of file IncompleteLUT.h.


Member Typedef Documentation

template<typename _Scalar >
typedef SparseMatrix<Scalar,RowMajor> Eigen::IncompleteLUT< _Scalar >::FactorType [private]

Definition at line 49 of file IncompleteLUT.h.

template<typename _Scalar >
typedef FactorType::Index Eigen::IncompleteLUT< _Scalar >::Index [private]

Definition at line 51 of file IncompleteLUT.h.

template<typename _Scalar >
typedef Matrix<Scalar,Dynamic,Dynamic> Eigen::IncompleteLUT< _Scalar >::MatrixType

Definition at line 54 of file IncompleteLUT.h.

template<typename _Scalar >
typedef SparseMatrix<Scalar,ColMajor> Eigen::IncompleteLUT< _Scalar >::PermutType [private]

Definition at line 50 of file IncompleteLUT.h.

template<typename _Scalar >
typedef NumTraits<Scalar>::Real Eigen::IncompleteLUT< _Scalar >::RealScalar [private]

Definition at line 47 of file IncompleteLUT.h.

template<typename _Scalar >
typedef _Scalar Eigen::IncompleteLUT< _Scalar >::Scalar [private]

Definition at line 46 of file IncompleteLUT.h.

template<typename _Scalar >
typedef Matrix<Scalar,Dynamic,1> Eigen::IncompleteLUT< _Scalar >::Vector [private]

Definition at line 48 of file IncompleteLUT.h.


Constructor & Destructor Documentation

template<typename _Scalar >
Eigen::IncompleteLUT< _Scalar >::IncompleteLUT ( ) [inline]

Definition at line 56 of file IncompleteLUT.h.

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

Definition at line 62 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 110 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 221 of file IncompleteLUT.h.

template<typename _Scalar >
Index Eigen::IncompleteLUT< _Scalar >::cols ( void  ) const [inline]

Definition at line 72 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 97 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 240 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 79 of file IncompleteLUT.h.

template<typename Scalar >
template<typename VectorV , typename VectorI >
int Eigen::IncompleteLUT< Scalar >::QuickSplit ( VectorV &  row,
VectorI &  ind,
int  ncut 
) [protected]

Compute a quick-sort split of a vector On output, the vector row is permuted such that its elements satisfy abs(row(i)) >= abs(row(ncut)) if i<ncut abs(row(i)) <= abs(row(ncut)) if i>ncut

Parameters:
rowThe vector of values
indThe array of index for the elements in row
ncutThe number of largest elements to keep

Definition at line 186 of file IncompleteLUT.h.

template<typename _Scalar >
Index Eigen::IncompleteLUT< _Scalar >::rows ( void  ) const [inline]

Definition at line 70 of file IncompleteLUT.h.

template<typename Scalar >
void Eigen::IncompleteLUT< Scalar >::setDroptol ( RealScalar  droptol)

Set control parameter droptol

Parameters:
droptolDrop any element whose magnitude is less than this tolerance

Definition at line 159 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 169 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 119 of file IncompleteLUT.h.


Member Data Documentation

template<typename _Scalar >
bool Eigen::IncompleteLUT< _Scalar >::m_analysisIsOk [protected]

Definition at line 146 of file IncompleteLUT.h.

template<typename _Scalar >
RealScalar Eigen::IncompleteLUT< _Scalar >::m_droptol [protected]

Definition at line 144 of file IncompleteLUT.h.

template<typename _Scalar >
bool Eigen::IncompleteLUT< _Scalar >::m_factorizationIsOk [protected]

Definition at line 147 of file IncompleteLUT.h.

template<typename _Scalar >
int Eigen::IncompleteLUT< _Scalar >::m_fillfactor [protected]

Definition at line 145 of file IncompleteLUT.h.

template<typename _Scalar >
ComputationInfo Eigen::IncompleteLUT< _Scalar >::m_info [protected]

Definition at line 149 of file IncompleteLUT.h.

template<typename _Scalar >
bool Eigen::IncompleteLUT< _Scalar >::m_isInitialized [protected]

Definition at line 148 of file IncompleteLUT.h.

template<typename _Scalar >
FactorType Eigen::IncompleteLUT< _Scalar >::m_lu [protected]

Definition at line 143 of file IncompleteLUT.h.

template<typename _Scalar >
PermutationMatrix<Dynamic,Dynamic,Index> Eigen::IncompleteLUT< _Scalar >::m_P [protected]

Definition at line 150 of file IncompleteLUT.h.

template<typename _Scalar >
PermutationMatrix<Dynamic,Dynamic,Index> Eigen::IncompleteLUT< _Scalar >::m_Pinv [protected]

Definition at line 151 of file IncompleteLUT.h.


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


win_eigen
Author(s): Daniel Stonier
autogenerated on Mon Oct 6 2014 12:27:14