% 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
    % Implement iteration scheme    
    x(i+1) = (7 + y(i) - z(i))/4;
    y(i+1) = (21 + 4*x(i) + z(i))/8;
    z(i+1) = (15 + 2 * x(i) - y(i)) / 5;
    
    % 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)');