type

Type of factorization. Values fortypeinclude:

• 'nofill'(default)—Performs ILU factorization with0level of fill in, known as ILU(0). Withtypeset to'nofill', only themilusetup option is used; all other fields are ignored.

• 'crout'—Performs the Crout version of ILU factorization, known as ILUC. Withtypeset to'crout', only thedroptolandmilusetup options are used; all other fields are ignored.

• 'ilutp'—Performs ILU factorization with threshold and pivoting.

Iftypeis not specified, the ILU factorization with0level of fill in is performed. Pivoting is only performed withtypeset to'ilutp'.

droptol

Drop tolerance of the incomplete LU factorization.droptolis a non-negative scalar. The default value is0, which produces the complete LU factorization.

The nonzero entries ofUsatisfy

abs(U(i,j)) >= droptol*norm(A(:,j)),

with the exception of the diagonal entries, which are retained regardless of satisfying the criterion. The entries ofLare tested against the local drop tolerance before being scaled by the pivot, so for nonzeros inL

abs(L(i,j)) >= droptol*norm(A(:,j))/U(j,j).

milu

Modified incomplete LU factorization. Values formiluinclude:

• 'row'—Produces the row-sum modified incomplete LU factorization. Entries from the newly-formed column of the factors are subtracted from the diagonal of the upper triangular factor,U, preserving column sums. That is,A*e = L*U*e, whereeis the vector of ones.

• 'col'—Produces the column-sum modified incomplete LU factorization. Entries from the newly-formed column of the factors are subtracted from the diagonal of the upper triangular factor,U, preserving column sums. That is,e'*A = e'*L*U.

• 'off'(default)—No modified incomplete LU factorization is produced.

udiag

Ifudiagis1, any zeros on the diagonal of the upper triangular factor are replaced by the local drop tolerance. The default is0.

thresh

Pivot threshold between0(forces diagonal pivoting) and1, the default, which always chooses the maximum magnitude entry in the column to be the pivot.