%%%%%%%% JACOBI CALCULATOR %%%%%%%%%%%

% Define the matrix A and vector b
A = [2 -1 0; -1 3 -1; 0 -1 2];
b = [1; 8; -5];

% Initial guess
x0 = [0; 0; 0];

% Maximum allowed component-wise error percentage
max_error_percentage = 10;

% Initialize variables
x = x0;
n = length(b);
D = diag(diag(A));
R = A - D;
tolerance = max_error_percentage / 100;

% Display the header for the iteration table
fprintf('Iteration\t x1\t\t x2\t\t x3\t\t Max Error (%%)\n');
fprintf('-----------------------------------------------------------------------\n');

% Iteration counter
k = 1;

while true
    % Calculate the new approximation
    x_new = D \ (b - R * x);
    
    % Calculate the component-wise error
    error = abs((x_new - x) ./ x_new);
    max_error = max(error) * 100;  % Convert to percentage
    
    % Print the current iteration, the values of x, and the max error percentage
    fprintf('%d\t\t %.6f\t %.6f\t %.6f\t %.2f%%\n', k, x_new(1), x_new(2), x_new(3), max_error);
    
    % Check if the maximum component-wise error is below the tolerance
    if max_error < max_error_percentage
        break;
    end
    
    % Update the current approximation
    x = x_new;
    k = k + 1;
end

% Summary table
fprintf('\nSummary Table:\n');
fprintf('Iteration\t x1\t\t x2\t\t x3\t\t Max Error (%%)\n');
fprintf('-----------------------------------------------------------------------\n');
fprintf('%d\t\t %.6f\t %.6f\t %.6f\t %.2f%%\n', k, x_new(1), x_new(2), x_new(3), max_error);