function get_convergence_movie(f,sequence_x,sequence_fx,nframes)
% plots the real valued function f of one real variable together with 
% the sequence of points given by sequence_x and sequence_fx input 
% and produces a movie movie.avi with this plot where the points appear 
% one after another in the sequence using nframes frames. Two modes are possbile: 
% with you_can_see=1 all plots and the movie are displaied on screen;
% with you_can_see=0 no plots are displaied on screen and the movie 
% will need to be played separately from the file movie.avi, 
% using any AVI movie player.  

%Revision 1.2 by Andrew Knyazev. Oct. 21, 2002. 

you_can_see = 1;  %use 1 here is you run MATLAB in the graphics interactive mode, otherwise set 0
                  % note: 0 seems to give an error on our Linux systems  

min_x=min(sequence_x); max_x= max(sequence_x); %these are the limits for x
npoints=500; %number of point to draw the function
x = min_x:(max_x-min_x)/npoints:max_x; %function argument 
fx = feval(f,x);                       %function to draw

if nframes > size(sequence_x,1)-2 
    fprintf('the requested number of movie frames %i is too large and \n will be reduced to %i to match the data \n',nframes,size(sequence_x,1)-2);
    nframes = size(sequence_x,1)-2;
    if nframes < 1 
        warning('No frames detected, no movie generated')
        return
    end
end

% see http://www.mathworks.com/support/tech-notes/1200/1204.shtml

%These are unsuccessful attempts to reduce the color depth 
%set(0,'ScreenDepth',8) 
%map = colormap(hsv(8));

if you_can_see        %you can and want to see the figures
    
    left=0; bottom=0; width=640; height=480;
    rect = [left, bottom, width, height];
    hf=figure(1);
    set(1,'Position',rect);
    set(gca,'Xlim',[min_x max_x]); 
    axis tight
    set(gca,'nextplot','replacechildren');
    M = moviein(nframes); % for earlier versions of MATLAB (before Release 11/MATLAB 5.3) 
    for k = 1:nframes  
        plot(x,fx,'k');
        title('Convergence sequence','fontsize',16)
        ylabel('function','fontsize',16)
        xlabel('argument','fontsize',16)
        grid on
        hold on
        plot(sequence_x(1:k+1),sequence_fx(1:k+1),'bo');
        plot(sequence_x(k+2),sequence_fx(k+2),'r*');
        drawnow;
        M(k) = getframe(gcf);
        %M(k) = im2frame(gcf,map);
        hold off
    end
    
    % Play the MATLAB movie once with fps=1
    clf %to clear 
    movie(hf,M,1,1)
    
%    movie2avi(M,'movie.avi','fps',1,'compression','None','colormap',colormap(hsv(8))); %creates the AVI movie from the MATLAB movie 
     movie2avi(M,'movie.avi','fps',1,'compression','None');
     
else        %you cannot or do not want to see the figures
    aviobj=avifile('movie.avi','fps',1,'compression','None'); %creates AVI file, test.avi
    hf = figure('visible','off'); %turns visibility of figure off
    left=0; bottom=0; width=640; height=480;
    rect = [left, bottom, width, height];
    set(1,'Position',rect);
    set(gca,'Xlim',[min_x max_x]); 
    hax=axes;
    for k=1:nframes
        plot(x,fx,'k','parent',hax); %puts image in invisible axes
        grid on
        title('Convergence sequence','fontsize',16)
        ylabel('function','fontsize',16)
        xlabel('argument','fontsize',16)
        hold on
        plot(sequence_x(1:k+1),sequence_fx(1:k+1),'bo','parent',hax);
        plot(sequence_x(k+2),sequence_fx(k+2),'r*','parent',hax);
        hold off
        aviobj=addframe(aviobj,hf); %adds frames to the AVI file
    end 
    aviobj=close(aviobj); %closes the AVI file 
    close(hf); %closes the handle to invisible figure
end