88 lines
3.1 KiB
Matlab
88 lines
3.1 KiB
Matlab
%%
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% Parameters
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alpha = 0.5; % Example value for alpha
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N = linspace(1e4, 1e6, 100); % Atom number range
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OD = linspace(0, 3, 100); % Optical depth range
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N1 = 100; % Example parameter for N1 controlling transition steepness
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% Smoothed Heaviside function as given in the appendix
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SmoothedHeaviside = @(N) (N > 0) .* (2 ./ (1 + exp(N1 ./ N)));
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% Initialize the cost function
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CostFunction = zeros(length(N), length(OD));
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% Calculate the cost function for each N and OD
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for i = 1:length(N)
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for j = 1:length(OD)
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% Smoothed Heaviside step function
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H_N = SmoothedHeaviside(N(i));
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% Cost function: OD^3 * N^(alpha - 9/5) multiplied by smoothed Heaviside
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CostFunction(i, j) = H_N * OD(j)^3 * N(i)^(alpha - 9/5);
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end
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end
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% Create a meshgrid for plotting
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[OD_grid, N_grid] = meshgrid(OD, N);
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% Plot the cost function as a surface plot
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figure(1);
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clf
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set(gcf,'Position',[50 50 950 750])
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set(gca,'FontSize',16,'Box','On','Linewidth',2);
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surf(OD_grid, N_grid, CostFunction);
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xlabel('Optical Depth (OD)','FontSize',16);
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ylabel('Number of Atoms (N)','FontSize',16);
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zlabel('Cost Function','FontSize',16);
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title(['|C(X)| = OD^3 * N^{\alpha - 9/5} * Smoothed Heaviside Function with Alpha = ', num2str(alpha)],'Interpreter', 'tex','FontSize',16);
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% title('Cost Function: OD^3 * N^{\alpha - 9/5} with Smoothed Heaviside Function');
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%%
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% Parameters
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N = linspace(1e3, 1e6, 100); % Atom number range
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OD = linspace(0, 3, 100); % Optical depth range
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N1 = 1e5; % Example parameter for N1 controlling transition steepness
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% Smoothed Heaviside function as given in the appendix
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% Create figure and initial plot
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fig = figure(2);
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clf
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set(gcf,'Position',[50 50 950 750])
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set(gca,'FontSize',16,'Box','On','Linewidth',2);
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alpha = 0.5; % Initial value for alpha
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% Nested function to calculate and update the cost function plot
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function update_plot(alpha_value, N, N1, OD)
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SmoothedHeaviside = @(x) (x > 0) .* (2 ./ (1 + exp(N1 ./ x)));
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% Calculate the cost function for the given alpha
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CostFunction = zeros(length(N), length(OD));
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for i = 1:length(N)
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for j = 1:length(OD)
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H_N = SmoothedHeaviside(N(i)); % Smoothed Heaviside function
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CostFunction(i, j) = H_N * OD(j)^3 * N(i)^(alpha_value - 9/5);
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end
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end
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% Create a meshgrid for plotting
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[OD_grid, N_grid] = meshgrid(OD, N);
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% Plot the cost function as a surface plot
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surf(OD_grid, N_grid, CostFunction);
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xlabel('Optical Depth (OD)','FontSize',16);
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ylabel('Number of Atoms (N)','FontSize',16);
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zlabel('Cost Function','FontSize',16);
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title(['|C(X)| = OD^3 * N^{\alpha - 9/5} * Smoothed Heaviside Function with Alpha = ', num2str(alpha_value)],'Interpreter', 'tex','FontSize',16);
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end
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% Initial plot
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update_plot(alpha, N, N1, OD);
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% Add a slider to control alpha
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uicontrol('Style', 'slider', ...
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'Min', 0.1, 'Max', 2, 'Value', alpha, ... % Set the range for alpha
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'Position', [100 20 200 20], ...
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'Callback', @(src, event) update_plot(src.Value, N, N1, OD));
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% Add a label for the slider
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uicontrol('Style', 'text', ...
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'Position', [150 45 120 20], ...
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'String', 'Adjust Alpha');
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