You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: fadi.m
    path of file: ./repos/chebfun/@chebop2
    
    the code of the file until where you have to start completion: function [UX, DX, VX] = fadi( A, B, M, N, p, q )
%FADI   Factored alternating direction implicit method.
% X = FADI( A, B, M, N, p, q ) solves the Sylvester equation
%
%            A*X - X*B = M*N.'
%
% using the FADI method with ADI shifts p and q. The righthand side must be
% given in low-rank form, i.e., M and N where rhs = M*N.'.

%% Reference: 

    
function [UX, DX, VX] = fadi( A, B, M, N, p, q )
%FADI   Factored alternating direction implicit method.
% X = FADI( A, B, M, N, p, q ) solves the Sylvester equation
%
%            A*X - X*B = M*N.'
%
% using the FADI method with ADI shifts p and q. The righthand side must be
% given in low-rank form, i.e., M and N where rhs = M*N.'.

%% Reference: 
%
% [1] Benner, Peter, Ren-Cang Li, and Ninoslav Truhar. 
% "On the ADI method for Sylvester equations." J. of Comp. and App. Math.
% 233.4 (2009): 1035-1045. 

[m, rho] = size( M ); 
n = size(N, 1); 
RankOfSolution = rho * numel(p);
UX = zeros(m, RankOfSolution);
VX = zeros(n, RankOfSolution);
DX = diag( kron(q-p, ones(1,rho)) );
Im = speye(m);
In = speye(n);
UX(:, 1:rho) = (A+p(1)*Im)\M;
VX(:, 1:rho) = (B+q(1)*In)\N;
for j = 1:numel(p)-1
    UX(:, j*rho+(1:rho)) = (A+q(j)*Im)*((A+p(j+1)*Im)\UX(:,(j-1)*rho+(1:rho)));
    VX(:, j*rho+(1:rho)) = (B+p(j)*In)*((B+q(j+1)*In)\VX(:,(j-1)*rho+(1:rho)));
end