.TH "ilut" 5rheolef "Sat Mar 13 2021" "Version 7.1" "rheolef" \" -*- nroff -*-
.ad l
.nh
.SH NAME
ilut \- incomplete LU factorization preconditionner (rheolef-7\&.1)
.SH "SYNOPSIS"
.PP
.PP
.nf
    solver pa = ilut(a);
.fi
.PP
 
.SH "DESCRIPTION"
.PP
\fCilut\fP is a function that returns the dual threshold incomplete LU factorization preconditionner of its argument as a \fBsolver(4)\fP\&. The method is described in 
.PP
.nf
    Yousef Saad,
    ILUT: a dual threshold incomplete LU factorization,
    Numer. Lin. Algebra Appl., 1(4), pp 387-402, 1994.

.fi
.PP
 
.SH "OPTIONS"
.PP
During the factorization, two dropping rules are used and \fCilut\fP supports two options:
.PP
\fCdrop_tol\fP (float) 
.PP
.RS 4
Any element whose magnitude is less than some tolerance is dropped\&. This tolerance is obtained by multiplying the option tolerance \fCdrop_tol\fP by the average magnitude of all the original elements in the current row\&. By default, \fCdrop_tol\fP is \fC1000*epsilon\fP where \fCepsilon\fP is the machine precision associated to the \fBFloat_2\fP type\&. 
.RE
.PP
\fCfill_factor\fP (integer) 
.PP
.RS 4
On each row, after elimination, only the \fCn_fillin\fP largest elements in the L part and the fill largest elements in the U part are kept, in addition to the diagonal elements\&. The option \fCfill_factor\fP is used to compute \fCn_fillin\fP: \fCn_fillin = (nnz*fill_factor)/n + 1\fP where \fCn\fP is the matrix size and \fCnnz\fP is its total number of non-zero entires\&. With \fCfill_factor=1\fP, the incomplete factorization as about the same non-zero entries as the initial matrix\&. With \fCfill_factor=n\fP, the factorization is complete, up to the dropped elements\&. By default \fCfill_factor=10\fP\&. 
.RE
.PP
.SH "EXAMPLE"
.PP
int fill_factor = 10; double drop_tol = 1e-12; solver pa = ilut (a, fill_factor, drop_tol);
.SH "IMPLEMENTATION"
.PP
This documentation has been generated from file linalg/lib/ilut\&.h 
.SH AUTHOR
Pierre  Saramito  <Pierre.Saramito@imag.fr>
.SH COPYRIGHT
Copyright   (C)  2000-2018  Pierre  Saramito  <Pierre.Saramito@imag.fr>
GPLv3+: GNU GPL version 3 or later  <http://gnu.org/licenses/gpl.html>.
This  is  free  software:  you  are free to change and redistribute it.
There is NO WARRANTY, to the extent permitted by law.