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.
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    filename: tutorialFPI.m
    path of file: ./repos/mdocourse/MDA
    
    the code of the file until where you have to start completion: %% An introduction to FPI
%% Prof J. Morlier 
% 
% 
% Fixed Point Iteration is a simple iterative method for solving systems 
% of non-linear equations, such as the general two-equation non-linear system 
% illustrated below: 				
% 
% f1(x1, x2) = 0 				
% 
% f2(x1, x2) = 0 				
% 
% This can be simplified using vector notation by writing f(x) = 0. The vectors 
% in this notation could be of any size, as long as the size of the f and 0 vectors 
% are equal. If the constituent equations are independent, i.e. no equation depends 
% on the output of another equation, then the solution is trivial. In this case 
% each equation may be solved independently. The case of non-independent equations 
% (coupled) is more difficult. Consider the following example from [1]. 				
% 
% y21(y12) = 0.25*y12 ? 0.25			
% 
% y12(y21) = 2 + 2*y21 			
% 
% This is special notation commonly used in coupled system analysis. The 
% first function y21 depends on the output of the second function y12, and visa 
% versa. The subscripts indicate the information flow. For example, y21 is the 
% information generated by equation 1 that is required as input by equation 2 
% (2 ? 1). Note that although this example is linear, the method applied in this 
% section is valid for non-linear systems. The interdependence, or coupling, between 
% the two equations can be illustrated with a block diagram (Figure 1). 
% 
% 
% 
% This shows the complete information flow of the system. 			
% 
% Remember that in a general non-linear system the constituent* functions 
% may not be known explicitly, but are rather black box functions*. An intuitive 
% approach to solving this system stems from the diagram of Figure 
    
function y21 depends on the output of the second function y12, and visa 
% versa. The subscripts indicate the information flow. For example, y21 is the 
% information generated by equation 1 that is required as input by equation 2 
% (2 ? 1). Note that although this example is linear, the method applied in this 
% section is valid for non-linear systems. The interdependence, or coupling, between 
% the two equations can be illustrated with a block diagram (Figure 1). 
% 
% 
% 
% This shows the complete information flow of the system. 			
% 
% Remember that in a general non-linear system the constituent* functions 
% may not be known explicitly, but are rather black box functions*. An intuitive 
% approach to solving this system stems from the diagram of Figure 1. Make a guess 
% for one of the values, say y21, and then use that value to calculate y12, which 
% is in turn used to find an updated value of y21. This is repeated until the 
% values stop changing, and is called the Fixed Point Iteration process. Here 
% is the general algorithm:
% 
% 
% 
% In the case of this simple example the solution can be viewed graphically. 
% The functions y21 and y12 are plotted in Figure 2. The point where these functions 
% cross is the solution to the system, also called a fixed point. 
% 
% 				
% 
% Let's try to do this !!				
% 
% Implementing the Fixed Point Iteration solution in Matlab requires the 
% creation of two new functions and a script file to coordinate the functions. 

%clean up
clear all; close all;clc;		
%% 
% One possible implementation is as follows:  

% initial guess
y12_old = 10;
% stopping criteria
epsilon = 1E-3;
% initialize parameters
error = 1E3; i = 1;
figure;
while error>epsilon
    y21_new = y21(y12_old);
    y12_new = y12(y21_new);
    plot(i,y21_new,'ko')
    hold on;
    plot(i,y12_new,'k*')
    i=i+1;
    error = abs(y12_new-y12_old);
    y12_old = y12_new;
   
    legend