Eigen
3.3.7

Incomplete LU factorization with dualthreshold 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 387402, 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://wwwusers.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
Classes  
struct  keep_diag 
Public Member Functions  
template<typename MatrixType >  
IncompleteLUT &  compute (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 ()  

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

inline 
Reports whether previous computation was successful.
Success
if computation was succesful, NumericalIssue
if the matrix.appears to be negative. void Eigen::IncompleteLUT< Scalar, StorageIndex >::setDroptol  (  const RealScalar &  droptol  ) 
Set control parameter droptol
droptol  Drop any element whose magnitude is less than this tolerance 
void Eigen::IncompleteLUT< Scalar, StorageIndex >::setFillfactor  (  int  fillfactor  ) 
Set control parameter fillfactor
fillfactor  This is used to compute the number fill_in of largest elements to keep on each row. 