Explaining a matlab code

Hello, and thank you for taking your time to read this message. I just want to understand how does this code work line by line.

R = input('Enter radii [R1, R2, R3]: ');
theta = input('Enter angles [theta1, theta2, theta3] in degrees: ');
stopping_criterion = input('Enter stopping criterion for Newton-Raphson iterations: ');
% Choose solution method
disp('Choose a solution method:');
disp('1. Gauss-Elimination with partial pivoting');
disp('2. Cramer Rule');
disp('3. Naïve Gauss-Jordan');
method = input('Enter the method number: ');
if method < 1 || method > 3
    error('Invalid method number');
end
f = @(params) [params(1)/(1 + params(2) * sind(theta(1) + params(3))) - R(1);
    params(1)/(1 + params(2) * sind(theta(2) + params(3))) - R(2);
    params(1)/(1 + params(2) * sind(theta(3) + params(3))) - R(3)];
C = 1000;  
e = 0.5;   
alpha = 30;
relative_errors_C = zeros(100, 1);
relative_errors_e = zeros(100, 1);
relative_errors_alpha = zeros(100, 1);
for iteration = 1:100
    J = numerical_jacobian(f, [C, e, alpha]);
    if det(J) == 0
        error('The Jacobian matrix is not invertible. The Newton-Raphson method cannot be used.');
    end
    switch method
        case 1
            update = gauss_elimination_pivoting(J, f([C, e, alpha]));
        case 2
            update = cramers_rule_solver(J, f([C, e, alpha]));
        case 3
            update = naive_gauss_jordan(J, f([C, e, alpha]));
    end
    % Check for convergence
    if norm(update) < stopping_criterion
        % Update constants
        C = C - update(1);
        e = e - update(2);
        alpha = alpha - update(3);
        relative_errors_C(iteration) = abs(update(1) / C);
        relative_errors_e(iteration) = abs(update(2) / e);
        relative_errors_alpha(iteration) = abs(update(3) / alpha);
        
        fprintf('Iteration %d: Relative Error in C = %f, e = %f, alpha = %f\n', iteration, relative_errors_C(iteration), relative_errors_e(iteration), relative_errors_alpha(iteration));
        break;
    end
end
figure;
subplot(3, 1, 1);
plot(1:iteration, relative_errors_C(1:iteration), 'o-');
xlabel('Iteration');
ylabel('Relative Error in C');
title('Convergence');
subplot(3, 1, 2);
plot(1:iteration, relative_errors_e(1:iteration), 'o-');
xlabel('Iteration');
ylabel('Relative Error in e');
subplot(3, 1, 3);
plot(1:iteration, relative_errors_alpha(1:iteration), 'o-');
xlabel('Iteration');
ylabel('Relative Error in alpha');
fprintf('Final values:\nC = %f\n e = %f\n alpha = %f\n', C, e, alpha);
theta_values = linspace(0, 360, 1000);
R_values = C./(1 + e * sind(theta_values + alpha));
figure;
polarplot(deg2rad(theta_values), R_values);
hold on;
polarplot(deg2rad(theta), R, 'ro');
title('Satellite Orbit');
legend('Orbit', 'Data Points');
hold off;
function J = numerical_jacobian(f, params)
n = length(params);
m = length(f(params));
J = zeros(m, n);
delta = 1e-8;
for i = 1:n
    params_plus = params;
    params_minus = params;
    params_plus(i) = params_plus(i) + delta;
    params_minus(i) = params_minus(i) - delta;
    J(:, i) = (f(params_plus) - f(params_minus)) / (2 * delta);
end
end

Answer 1

[Drew]

Using the MATLAB AI Chat Playground https://www.mathworks.com/matlabcentral/playground/new (see announcement at https://blogs.mathworks.com/community/2023/11/07/the-matlab-ai-chat-playground-has-launched/), I asked for an explanation of this code, and the AI returned: "This code solves for the orbit of a satellite given three radii and angles using the Newton-Raphson method. The user is prompted to enter the radii, angles, and stopping criterion for the iterations. The user is also prompted to choose a solution method from three options. The code then iteratively solves for the constants C, e, and alpha using the chosen method until the stopping criterion is met. The relative errors in C, e, and alpha are plotted against the iteration number. The final values of C, e, and alpha are printed. Finally, the orbit is plotted using polar coordinates."

After asking for an explanation of the full code, if you want more detailed explanation of smaller chunks of code, use follow-up questions on smaller chunks of code, as in the example below. Note that the AI also suggests other follow-up questions along with it's response.

I tried a couple of the suggested follow-up questions, and here is what the AI had to say:

Using a series of follow-up questions, you can get line-by-line or higher-level info about the code and the techniques used. Remember to validate the AI output, since the AI is sometimes incorrect, as indicated at the bottom of the MATLAB AI Chat Playground page: "Generated code and text might be inaccurate. Validate before use." While the AI is sometimes inaccurate, it can still be helpful due to the times when it is correct, or partially correct. Checkout the AI Chat Playground for yourself and see if it can help you to understand the code.

If this answer is helpful for you, please remember to accept the answer.

[John D'Errico]

Having played with the AI Chat quite a bit now, I'm both impressed with its capabilities, as in here, but also at times how clueless it seems. The trick to avoid a failure is often to know how to phrase a question, to guide it to the answer you need.

Here of course, it did well, simply by looking at the code. It managed to sort out the wheat from the chaff, so to speak. The result was a simple paragraph that gave a useful overview of the code.

As you point out, one can also ask for a deeper explanation of specific parts of the code.

Anyway, well done to the AI here.

[Torsten]

Are the answers starting with "I understand" in this forum are all given by AI ?

[Image Analyst]

@Torsten I believe that the AI answers posted here have these characteristics:

1. They all start with "I understand that you want to...."
2. They're posted by people with level 1 or level 2 (rarely) reputation.
3. They give sample code with plenty of comments (real level 1 users never give comments)
4. They finish up by giving links to where more information can be found.

They virtually all have those characteristics which makes them pretty easy to spot.

[Torsten]

They virtually all have those characteristics which makes them pretty easy to spot.

Maybe one shouldn't write this - AI is watching us and able to learn :-)

[John D'Errico]

We will just need to hope our soon to be robot overlords are benevolent.

Answer 2

[Image Analyst]

I can understand why you find it confusing. It was likely written by a novice programmer. I can tell because there are only 3 comments in there. A real programmer, a professional one, would never have just 3 comments in there. My code has about 35% of the lines of code as either totally a comment or at least with a comment on the end of a line of code. (See attached comment counter program)

What I'd recommend to you is to go through it line by line adding in the comments that the original programmer neglected to put in there. Chances are that once you do that, you will understand what it does.

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