---
name: "ilut"
section: "5rheolef"
platform: "linux"
package: "librheolef-dev"
version: "7.2-4"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/ilut"
---

# ilut(5rheolef)

incomplete LU factorization preconditionner (rheolef-7.2)

## NAME

ilut - incomplete LU factorization preconditionner (rheolef-7.2)

## 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.