This video shows the steps to run a MATLAB Live script/ function from your App designer code. In this video it creates demo live script and function. Then execute them from MATLAB command line and App Designer’s code using the file name.

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Complete source code and other details:

Initialize Array
x = 2:3:50;

Plot the Array
plot(x);

Live Function
function LiveFunctionExample(step)

y = 2:step:50;

assignin("base","y_base",y);

plot(y);

end

classdef Live_MLX_Run_Example < matlab.apps.AppBase

    % Properties that correspond to app components
    properties (Access = public)
        UIFigure            matlab.ui.Figure
        LiveFunctionButton  matlab.ui.control.Button
        LiveScriptButton    matlab.ui.control.Button
    end

    % Callbacks that handle component events
    methods (Access = private)

        % Button pushed function: LiveScriptButton
        function LiveScriptButtonPushed(app, event)
            LiveScriptExample;
        end

        % Button pushed function: LiveFunctionButton
        function LiveFunctionButtonPushed(app, event)
            LiveFunctionExample(8);
        end
    end

    % Component initialization
    methods (Access = private)

        % Create UIFigure and components
        function createComponents(app)

            % Create UIFigure and hide until all components are created
            app.UIFigure = uifigure('Visible', 'off');
            app.UIFigure.Position = [100 100 640 480];
            app.UIFigure.Name = 'MATLAB App';

            % Create LiveScriptButton
            app.LiveScriptButton = uibutton(app.UIFigure, 'push');
            app.LiveScriptButton.ButtonPushedFcn = createCallbackFcn(app, @LiveScriptButtonPushed, true);
            app.LiveScriptButton.Position = [230 398 100 22];
            app.LiveScriptButton.Text = 'Live Script';

            % Create LiveFunctionButton
            app.LiveFunctionButton = uibutton(app.UIFigure, 'push');
            app.LiveFunctionButton.ButtonPushedFcn = createCallbackFcn(app, @LiveFunctionButtonPushed, true);
            app.LiveFunctionButton.Position = [230 308 100 22];
            app.LiveFunctionButton.Text = 'Live Function';

            % Show the figure after all components are created
            app.UIFigure.Visible = 'on';
        end
    end

    % App creation and deletion
    methods (Access = public)

        % Construct app
        function app = Live_MLX_Run_Example

            % Create UIFigure and components
            createComponents(app)

            % Register the app with App Designer
            registerApp(app, app.UIFigure)

            if nargout == 0
                clear app
            end
        end

        % Code that executes before app deletion
        function delete(app)

            % Delete UIFigure when app is deleted
            delete(app.UIFigure)
        end
    end
end