##### 22.6.2.11 luinc

— Loadable Function: [l, u, p, q] = luinc (a, '0')
— Loadable Function: [l, u, p, q] = luinc (a, droptol)
— Loadable Function: [l, u, p, q] = luinc (a, opts)

> Produce the incomplete LU factorization of the sparse matrix a. Two types of incomplete factorization are possible, and the type is determined by the second argument to luinc.

> Called with a second argument of '0', the zero-level incomplete LU factorization is produced. This creates a factorization of a where the position of the non-zero arguments correspond to the same positions as in the matrix a.

> Alternatively, the fill-in of the incomplete LU factorization can be controlled through the variable droptol or the structure opts. The UMFPACK multifrontal factorization code by Tim A. Davis is used for the incomplete LU factorication, (availability http://www.cise.ufl.edu/research/sparse/umfpack/)

> droptol determines the values below which the values in the LU factorization are dropped and replaced by zero. It must be a positive scalar, and any values in the factorization whose absolute value are less than this value are dropped, expect if leaving them increase the sparsity of the matrix. Setting droptol to zero results in a complete LU factorization which is the default.

> opts is a structure containing one or more of the fields

> `droptol`
>   The drop tolerance as above. If opts only contains `droptol` then this is equivalent to using the variable droptol.
> `milu`
>   A logical variable flagging whether to use the modified incomplete LU factorization. In the case that `milu` is true, the dropped values are subtract from the diagonal of the matrix U of the factorization. The default is `false`.
> `udiag`
>   A logical variable that flags whether zero elements on the diagonal of U should be replaced with droptol to attempt to avoid singular factors. The default is `false`.
> `thresh`
>   Defines the pivot threshold in the interval [0,1]. Values outside that range are ignored.

> All other fields in opts are ignored. The outputs from luinc are the same as for lu.

> See also: sparse, lu, cholinc.