LU incemental.

   [a, aa, LT, UT, PT] = schur_luinc(a, b, L, U, P, A12, A21, A22, varargin)

   Performs an incremental-type LU factorization on an augmented matrix
   [A11 A12; A21 A22], where PA = LU, A11 mxm, A12 mxn, A21 nxm and A22 nxn. To 
   factorize A11 do [L, U, P] = lu(A11). The factorization of A22 is done 
   without considering the elements of A12 for pivoting. Nevertheless, A12
   is updated according to the factorization on A11.

Inputs (required)
   a   = previous solution of the problem.
   b   = rhs of the system.
   L   = lower triangular factor from LU factorization of A11.
   U   = upper triangular factor from LU factorization of A11.
   P   = permutation matrix from LU factorization of A11.
   A12 = right-upper block for augmented matrix.
   A21 = left-lower block for augmented matrix.
   A22 = right-lower block for augmented matrix.

Input (optional)
   precond = use precond or not ('no', 'ilu', 'diag').
             for 'ndiad' define: 'numbd' (number of diagonals);
             for 'ilu' define: 'milu', 'typeilu', 'droptol', 
             'thresh' and 'udiag'.

   a   = next solution of the augmented problem.
   aa  = coefficients of the error estimative.
   LT  = augmented matrix lower triangular factor.
   UT  = augmented matrix upper triangular factor.
   PT  = augmented matrix permutation matrix.

See also
  schur_luinc2, schur_nflu and schur_iter.