fit parabola

function [coeffs, mean_loss] = fit_parabola(coeffs, x, y, visual)
% --------------- Do Not Edit this Part!!! ---------------
% Setup
iter = 0;
learning_rate = 1e-4;
plot_every_iters = 5;
max_iterations = 1e6;
mean_loss = 1;

if visual
    figure();
    hold on;
    plot(x, y, 'b', 'LineWidth', 2);
    title('True Parabola vs. Our Predictions');
    xlabel('X Axis [N.U.]');
    ylabel('Y Axis [N.U.]');
end

% Training loop
while(mean_loss > 1e-6)

    % --------------- Edit From Here ---------------
    predictions = coeffs(1) * x.^2 + coeffs(2) * x + coeffs(3);
    mean_loss = mean(predictions-y).^2;
    gradients = auto_diff_p2(x, y, predictions);
    coeffs = coeffs - learning_rate * gradients;

    % --------------- Do Not Edit From Here!!! ---------------
    if visual
        % Print the current mean error & plot true parabola vs. the current prediction
        disp(['The mean loss in iteration #', num2str(iter + 1), ' is: ',...
            num2str(mean_loss), '.']);

        if iter == 20
            plot_every_iters = 100;

        elseif iter == 1000
            plot_every_iters = 10000;

        end

        if mod(iter, plot_every_iters) == 0
            plot(x, predictions, 'r--')
            legend('True Parabola', 'Our Current Prediction');
            drawnow;
        end
    end

    iter = iter + 1;
end

% Plot the true parabola vs. the final prediction
if visual
    close all;
    figure();
    hold on;
    plot(x, y, 'b', 'LineWidth', 2);
    plot(x, predictions, 'r--x')
    title('True Parabola vs. Our Predictions');
    xlabel('X Axis [N.U.]');
    ylabel('Y Axis [N.U.]');
    legend('True Parabola', 'Our Final Prediction');
end

end