| | DEFUN_DLD (luinc, args, nargout,"-*- texinfo -*-\n\
@deftypefn {Loadable Function} {[@var{l}, @var{u}, @var{p}, @var{q}] =} luinc (@var{a}, '0')\n\
@deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{p}, @var{q}] =} luinc (@var{a}, @var{droptol})\n\
@deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{p}, @var{q}] =} luinc (@var{a}, @var{opts})\n\
@cindex LU decomposition\n\
Produce the incomplete LU factorization of the sparse matrix @var{a}.\n\
Two types of incomplete factorization are possible, and the type\n\
is determined by the second argument to @dfn{luinc}.\n\
\n\
Called with a second argument of '0', the zero-level incomplete\n\
LU factorization is produced. This creates a factorization of @var{a}\n\
where the position of the non-zero arguments correspond to the same\n\
positions as in the matrix @var{a}.\n\
\n\
Alternatively, the fill-in of the incomplete LU factorization can\n\
be controlled through the variable @var{droptol} or the structure\n\
@var{opts}. The UMFPACK multifrontal factorization code by Tim A.\n\
Davis is used for the incomplete LU factorization, (availability\n\
@url{http://www.cise.ufl.edu/research/sparse/umfpack/})\n\
\n\
@var{droptol} determines the values below which the values in the LU\n\
factorization are dropped and replaced by zero. It must be a positive\n\
scalar, and any values in the factorization whose absolute value are\n\
less than this value are dropped, expect if leaving them increase the\n\
sparsity of the matrix. Setting @var{droptol} to zero results in a\n\
complete LU factorization which is the default.\n\
\n\
@var{opts} is a structure containing one or more of the fields\n\
\n\
@table @code\n\
@item droptol\n\
The drop tolerance as above. If @var{opts} only contains @code{droptol}\n\
then this is equivalent to using the variable @var{droptol}.\n\
\n\
@item milu\n\
A logical variable flagging whether to use the modified incomplete LU\n\
factorization. In the case that @code{milu} is true, the dropped values\n\
are subtracted from the diagonal of the matrix U of the factorization.\n\
The default is @code{false}.\n\
\n\
@item udiag\n\
A logical variable that flags whether zero elements on the diagonal of U\n\
should be replaced with @var{droptol} to attempt to avoid singular\n\
factors. The default is @code{false}.\n\
\n\
@item thresh\n\
Defines the pivot threshold in the interval [0,1]. Values outside that\n\
range are ignored.\n\
@end table\n\
\n\
All other fields in @var{opts} are ignored. The outputs from @dfn{luinc}\n\
are the same as for @dfn{lu}.\n\
\n\
Given the string argument 'vector', @dfn{luinc} returns the values of @var{p}\n\
@var{q} as vector values.\n\
@seealso{sparse, lu}\n\
@end deftypefn") |
