% Illustrating Jacobi's Method
% Based on code from Kyle Mandli

clear all;
close all;

% Settings
TOLERANCE = 10^(-7);
max_iterations = 1000;

% Initial guess
x(1)=1;
y(1)=2;
z(1)=2;

for i=1:max_iterations-1
    % Convergent iteration scheme
    x(i+1) = -1*(15 - y(i) -5*z(i))/2;
    y(i+1) = -1*(-21 - 4*x(i) - z(i))/8;
    z(i+1) = 7 -  4*x(i) + y(i);
    
    % Check to see if we have converged yet.  Here, norm checks for
    % Euclidean distance between solution on subsequent iterations -- type  
    % help norm!
    if ( norm([x(i+1) y(i+1) z(i+1)]-[x(i) y(i) z(i)],2) < TOLERANCE )
        break;
    end
end

figure
% Plot convergence
set(gca,'FontSize',16)
plot(x,'o-')
hold on
plot(y,'ro-')
plot(z,'ko-')
legend('x','y','z')
title('Convergence of Jacobi Method')
xlabel('Iteration');
ylabel('Value of (x y z)');
axis([1 15 -10^6 10^6])  %set axis limits; use help to see more on this