NAME

       ilut - incomplete LU factorization preconditionner (rheolef-7.1)

SYNOPSIS

           solver pa = ilut(a);

DESCRIPTION

       ilut is a function that returns the dual threshold incomplete LU factorization preconditionner of its
       argument as a solver(4). The method is described in

           Yousef Saad,
           ILUT: a dual threshold incomplete LU factorization,
           Numer. Lin. Algebra Appl., 1(4), pp 387-402, 1994.

OPTIONS

       During the factorization, two dropping rules are used and ilut supports two options:

       drop_tol (float)

           Any element whose magnitude is less than some tolerance is dropped. This tolerance is obtained by
           multiplying the option tolerance drop_tol by the average magnitude of all the original elements in
           the current row. By default, drop_tol is 1000*epsilon where epsilon is the machine precision
           associated to the Float_2 type.

       fill_factor (integer)

           On each row, after elimination, only the n_fillin 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 fill_factor is used
           to compute n_fillin: n_fillin = (nnz*fill_factor)/n + 1 where n is the matrix size and nnz is its
           total number of non-zero entires. With fill_factor=1, the incomplete factorization as about the same
           non-zero entries as the initial matrix. With fill_factor=n, the factorization is complete, up to the
           dropped elements. By default fill_factor=10.

EXAMPLE

       int fill_factor = 10; double drop_tol = 1e-12; solver pa = ilut (a, fill_factor, drop_tol);

IMPLEMENTATION

       This documentation has been generated from file linalg/lib/ilut.h

AUTHOR

       Pierre  Saramito  <Pierre.Saramito@imag.fr>

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.