conjugateFunction.m

%% Illustration of a conjugate function
%
%%

% This file is from pmtk3.googlecode.com

function conjugateFunction

f = @(x) -log(5*x) - 5;
domain = 0.01:0.01:5;
offset = 0.04;
t = @(x) -(1/3)*x + f(3)+1-offset;
figureA;
printPmtkFigure('conjugateFunctionA');
figureB;
printPmtkFigure('conjugateFunctionB');

    function figureA
        setup;
        t1 = @(x) t(x) - 0.5;
        plot([1,1],[t1(1),f(1)],'--g',...
            [2,2],[t1(2),f(2)],'--g',...
            [3,3],[t1(3),f(3)],'--g',...
            [4,4],[t1(4),f(4)],'--g','LineWidth',3);
        plot(domain,t1(domain),'-b','LineWidth',3);
        plot(domain,f(domain),'-r','LineWidth',5);
        
        annotation(gcf,'textbox',[0.3392 0.3309 0.05723 0.09903],...
            'String',{'\lambdax'},...
            'FontSize',18,...
            'FitBoxToText','off',...
            'LineStyle','none');
        
        
    end

    function figureB
        setup;
        plot(domain,t(domain),'-b','LineWidth',3);
        plot(domain,f(domain),'-r','LineWidth',5);
        annotation(gcf,'textbox',[0 0.68 0.06955 0.07246],...
            'String',{'-f^*(\lambda)'},...
            'FontSize',18,...
            'FitBoxToText','off',...
            'LineStyle','none');
        
        annotation(gcf,'textbox',[0.63 0.23 0.2 0.1014],...
            'String',{'\lambdax - f^*(\lambda)'},...
            'FontSize',18,...
            'FitBoxToText','off',...
            'LineStyle','none');
    end


    function setup
        figure; hold on;
        set(gca,'XTick',[],'YTick',[],'box','on','LineWidth',2);
        axis([0.2,5,-9,-6])
        xlabel('x','FontSize',20); ylabel('y','FontSize',20);
        pdfcrop;
        
        annotation(gcf,'textbox',[0.238 0.7681 0.05723 0.09662],...
            'String',{'f(x)'},...
            'FontSize',18,...
            'FitBoxToText','off',...
            'LineStyle','none');
        
    end


end