Eigen  3.3.4
Eigen::IncompleteLUT< _Scalar, _StorageIndex > Class Template Reference

Detailed Description

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

Incomplete LU factorization with dual-threshold strategy.

This class follows the sparse solver concept .

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

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


struct  keep_diag

Public Member Functions

template<typename MatrixType >
IncompleteLUTcompute (const MatrixType &amat)
ComputationInfo info () const
 Reports whether previous computation was successful. More...
void setDroptol (const RealScalar &droptol)
void setFillfactor (int fillfactor)
- Public Member Functions inherited from Eigen::SparseSolverBase< IncompleteLUT< _Scalar, _StorageIndex > >
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 ()

Member Function Documentation

◆ compute()

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

Compute an incomplete LU factorization with dual threshold on the matrix mat No pivoting is done in this version

◆ info()

template<typename _Scalar , typename _StorageIndex = int>
ComputationInfo Eigen::IncompleteLUT< _Scalar, _StorageIndex >::info ( ) const

Reports whether previous computation was successful.

Success if computation was succesful, NumericalIssue if the matrix.appears to be negative.

◆ setDroptol()

template<typename Scalar , typename StorageIndex >
void Eigen::IncompleteLUT< Scalar, StorageIndex >::setDroptol ( const RealScalar &  droptol)

Set control parameter droptol

droptolDrop any element whose magnitude is less than this tolerance

◆ setFillfactor()

template<typename Scalar , typename StorageIndex >
void Eigen::IncompleteLUT< Scalar, StorageIndex >::setFillfactor ( int  fillfactor)

Set control parameter fillfactor

fillfactorThis is used to compute the number fill_in of largest elements to keep on each row.

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