Eigen::IncompleteLUT< Scalar_, StorageIndex_ > Class Template Reference

#include <Eigen/src/IterativeLinearSolvers/IncompleteLUT.h>

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_ >:

Classes
struct	keep_diag

Public Member Functions
template<typename MatrixType>
IncompleteLUT &	compute (const MatrixType &amat)
ComputationInfo	info () const
	Reports whether previous computation was successful.
const FactorType	matrixL () const
	Extraction Method for L-Factor.
const FactorType	matrixU () const
	Extraction Method for U-Factor.
void	setDroptol (const RealScalar &droptol)
void	setFillfactor (int fillfactor)
Public Member Functions inherited from Eigen::SparseSolverBase< IncompleteLUT< Scalar_, int > >
Solve< IncompleteLUT< Scalar_, int >, Rhs >	solve (const MatrixBase< Rhs > &b) const
Solve< IncompleteLUT< Scalar_, int >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const
	SparseSolverBase ()=default

Member Function Documentation

compute()

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 partial pivoting is done in this version. A static row permutation (maximum bipartite matching) is computed in analyzePattern so that the permuted matrix has a structurally nonzero diagonal whenever one exists; without it, the lack of pivoting makes ILUT silently produce a useless preconditioner on matrices with zero diagonal entries.

info()

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 successful, NumericalIssue if a zero pivot was encountered during factorization (the resulting preconditioner is unlikely to be usable; the input matrix typically has zero diagonal entries that cannot be moved by a static row permutation, e.g. it is structurally singular).

matrixL()

template<typename Scalar, typename StorageIndex>

const IncompleteLUT< Scalar, StorageIndex >::FactorType Eigen::IncompleteLUT< Scalar, StorageIndex >::matrixL

(

)

const

Extraction Method for L-Factor.

get L-Factor

Returns

L-Factor is a matrix containing the lower triangular part of the sparse matrix. All elements of the matrix above the main diagonal are zero.

matrixU()

template<typename Scalar, typename StorageIndex>

const IncompleteLUT< Scalar, StorageIndex >::FactorType Eigen::IncompleteLUT< Scalar, StorageIndex >::matrixU

(

)

const

Extraction Method for U-Factor.

get U-Factor

Returns

U-Factor is a matrix containing the upper triangular part of the sparse matrix. All elements of the matrix below the main diagonal are zero.

setDroptol()

template<typename Scalar, typename StorageIndex>

void Eigen::IncompleteLUT< Scalar, StorageIndex >::setDroptol

(

const RealScalar &

droptol

)

Set control parameter droptol

Parameters

droptol

Drop 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

Parameters

fillfactor

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

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

• /builds/libeigen/eigen/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h