%%
% Parameters
alpha = 8;         % Example value for alpha
N = linspace(1e4, 1e6, 100); % Atom number range
OD = linspace(0, 3, 100);   % Optical depth range
N1 = 100;            % Example parameter for N1 controlling transition steepness

% Smoothed Heaviside function as given in the appendix
SmoothedHeaviside = @(N) (N > 0) .* (2 ./ (1 + exp(N1 ./ N)));

% Initialize the cost function
CostFunction = zeros(length(N), length(OD));

% Calculate the cost function for each N and OD
for i = 1:length(N)
    for j = 1:length(OD)
        % Smoothed Heaviside step function
        H_N = SmoothedHeaviside(N(i));
        % Cost function: OD^3 * N^(alpha - 9/5) multiplied by smoothed Heaviside
        CostFunction(i, j) = H_N * OD(j)^3 * N(i)^(alpha - 9/5);
    end
end

% Create a meshgrid for plotting
[OD_grid, N_grid] = meshgrid(OD, N);

% Plot the cost function as a surface plot
figure(1);
clf
set(gcf,'Position',[50 50 950 750])
set(gca,'FontSize',16,'Box','On','Linewidth',2);
surf(OD_grid, N_grid, CostFunction);
xlabel('Optical Depth (OD)','FontSize',16);
ylabel('Number of Atoms (N)','FontSize',16);
zlabel('Cost Function','FontSize',16);
title(['|C(X)| = OD^3 * N^{\alpha - 9/5} * Smoothed Heaviside Function with Alpha = ', num2str(alpha)],'Interpreter', 'tex','FontSize',16);
% title('Cost Function: OD^3 * N^{\alpha - 9/5} with Smoothed Heaviside Function');
%%
% Parameters
N  = linspace(1e3, 1e6, 100); % Atom number range
OD = linspace(0, 3, 100);     % Optical depth range
N1 = 1e5;                     % Example parameter for N1 controlling transition steepness

% Create figure and initial plot
fig = figure(2);
clf
set(gcf,'Position',[50 50 950 750])
set(gca,'FontSize',16,'Box','On','Linewidth',2);
alpha = 0.5;  % Initial value for alpha

function cf = getSmoothedHeaviside(x, N1)
    if x > 0
        cf = (2 ./ (1 + exp(N1 ./ x)));
    else
        cf = 0;
    end
end

% Nested function to calculate and update the cost function plot
function update_plot(alpha_value, N, N1, OD)
    
    % Calculate the cost function for the given alpha
    CostFunction = zeros(length(N), length(OD));
    for i = 1:length(N)
        for j = 1:length(OD)
            H_N = getSmoothedHeaviside(N(i), N1);  % Smoothed Heaviside function
            CostFunction(i, j) = H_N * OD(j)^3 * N(i)^(alpha_value - 9/5);
        end
    end

    % Create a meshgrid for plotting
    [OD_grid, N_grid] = meshgrid(OD, N);
    % Plot the cost function as a surface plot
    surf(OD_grid, N_grid, CostFunction);
    xlabel('Optical Depth (OD)','FontSize',16);
    ylabel('Number of Atoms (N)','FontSize',16);
    zlabel('Cost Function','FontSize',16);
    title(['|C(X)| = OD^3 * N^{\alpha - 9/5} * Smoothed Heaviside Function with Alpha = ', num2str(alpha_value)],'Interpreter', 'tex','FontSize',16);
end

% Initial plot
update_plot(alpha, N, N1, OD);

% Add a slider to control alpha
uicontrol('Style', 'slider', ...
    'Min', 0.1, 'Max', 2, 'Value', alpha, ...  % Set the range for alpha
    'Position', [100 20 200 20], ...
    'Callback', @(src, event) update_plot(src.Value, N, N1, OD));

% Add a label for the slider
uicontrol('Style', 'text', ...
    'Position', [150 45 120 20], ...
    'String', 'Adjust Alpha');