function output = pplane6(action,input1,input2,input3)

% PPLANE6  is an interactive tool for studying planar autonomous systems of
%       differential equations.  When PPLANE6 is executed, a PPLANE6 Setup
%       window is opened.  The user may enter the differential
%       equation and specify a display window using the interactive
%       controls in the Setup window.  Up to 4 parameters may also be 
%       specified.  In addition the user is give a choice of the type of 
%       field displayed and the number of field points.
%
%       When the Proceed button is pressed on the Setup window, the PPLANE6
%       Display window is opened, and a field of the type requested is 
%       displayed for the system.  When the mouse button is depressed in 
%       the PPLANE6 Display window, the solution to the system with that
%       initial condition is calculated and plotted.
%
%       Other options are available in the menus.  These are
%       fairly self explanatory.  
%
%       This is version 6.0, and will only run on version 6 of MATLAB.

%  Copywright (c)  1995, 1997, 1998, 1999, 2000
%                  John C. Polking, Rice University
%                  Last Modified: January 21, 2000

startstr = 'pplane6';
if nargin < 1
  action ='initialize';
end

if get(0,'screendepth') == 1
   style = 'bw';
end

if strcmp(action,'initialize')
   
   % First we make sure that there is no other copy of PPLANE6
   % running, since this causes problems.       
   pph = findobj('tag','PPLANE6');
   if ~isempty(pph);
      qstring = {'There are some PPLANE6 figures open although they may be invisible.  ';...
            'What do you want to do?'};
      tstring = 'Only one copy of PPLANE6 can be open at one time.';
      b1str = 'Restart PPLANE6.';
      b2str = 'Just close those figures.';
      b3str = 'Do nothing.';
      answer = questdlg(qstring,tstring,b1str,b2str,b3str,b1str);
      if strcmp(answer,b1str)
         delete(pph);
         %pplane6;return
         eval(startstr);return
      elseif strcmp(answer,b2str)
         delete(pph);return
      else
         return
      end 
   end  % if ~isempty(pph);
   
   % Make sure tempdir is on the MATLABPATH.  We want to be sure that we
   % return the path to its current position when we exit.
   
   p = path;
   tmpdir = tempdir;
   ll = length(tmpdir);
   tmpdir = tmpdir(1:ll-1);
   ud.remtd = 0;
   if isempty(findstr(tmpdir,p))
     ud.remtd = 1;
     addpath(tempdir)
   end
   
   % Next we look for old files created by PPLANE6.
   % First in the current directory.
   
   oldfiles = dir('pptp*.m');
   ofiles = cell(0,1);
   kk = zeros(0,1);
   for k = 1:length(oldfiles)
      fn = oldfiles(k).name;
      fid = fopen(fn,'r');
      ll = fgetl(fid);
      ll = fgetl(fid);
      ll = fgetl(fid);
      fclose(fid);
      if strcmp(ll,'%% Created by PPLANE6')
         delete(fn)
      else
        l= length(ofiles);
        ofiles{l+1} = fn;
      end
   end
   
   %Then in the temp directory.
   
   oldfiles = dir([tempdir,'pptp*.m']);
   for k = 1:length(oldfiles)
      fn = [tempdir,oldfiles(k).name];
      fid = fopen(fn,'r');
      ll = fgetl(fid);
      ll = fgetl(fid);
      ll = fgetl(fid);
      fclose(fid);
      if strcmp(ll,'%% Created by PPLANE6')
         delete(fn)
      else
        l= length(ofiles);
        ofiles{l+1} = fn;
      end
   end
   lll = length(ofiles);
   if lll >0
     if lll == 1
       astr = 'The file';
       bstr = 'If so it can be safely deleted.';
     else
       astr = 'The files';
       bstr = 'If so they can be safely deleted.';
     end
     fprintf([astr,'\n']);
     for j = 1:lll
       fn = ofiles{j};
       disp(['     ',fn]);
     end
     fprintf('may have been created by an older version of PPLANE.\n');
     fprintf(bstr,'\n\n');
   end
   
   style = 'white';
   ppdir = pwd;
   ssize = get(0,'defaultaxesfontsize');
   npts = 20;
   solver = 'Dormand Prince';
   tol = 1e-4;
   stepsize = 0.1;
   if exist('ppstart','file')
     H = ppstart;
     if ~isempty(H)
       if isfield(H,'style')
         style = H.style;
       end
       if isfield(H,'size')
         ssize = H.size;
       end
       if isfield(H,'npts')
         npts = H.npts;
       end
      if isfield(H,'solver')
        solver = H.solver;  
      end
      if isfield(H,'ppdir')
        ppdir = H.ppdir;  
      end
      if isfield(H,'stepsize')
        stepsize = H.stepsize;  
      end
      if isfield(H,'tolerance')
        tol = H.tolerance;  
      end
    end
  end
  if get(0,'screendepth') == 1
    style = 'bw';
  end
  
  ud.ssize = ssize;
  ud.ppdir = ppdir;
  comp = computer;
  if strcmp(comp,'PCWIN')
    ud.fontsize = 0.8*ud.ssize;
  else
    ud.fontsize = ud.ssize;
  end
   
  % Set up for the menu of systems.
  
  system.name = 'default system';
  system.xvar = 'x';
  system.yvar = 'y';
  system.xder = ' 2*x - y + 3*(x^2-y^2) + 2*x*y';
  system.yder = ' x - 3*y - 3*(x^2-y^2) + 3*x*y';
  system.pname1 = '';
  system.pname2 = '';
  system.pname3 = '';
  system.pname4 = '';
  system.pval1 = '';
  system.pval2 = '';
  system.pval3 = '';
  system.pval4 = '';
  system.fieldtype = 'arrows';
   system.npts = npts;
   system.wind = [-2 4 -4 2];
   
   system(2).name = 'linear system';
   system(2).xvar = 'x';
   system(2).yvar = 'y';
   system(2).xder = ' A*x + B*y';
   system(2).yder = ' C*x + D*y';
   system(2).pname1 = 'A';
   system(2).pname2 = 'B';
   system(2).pname3 = 'C';
   system(2).pname4 = 'D';
   system(2).pval1 = '2';
   system(2).pval2 = '2';
   system(2).pval3 = '-2';
   system(2).pval4 = '-3';
   system(2).fieldtype = 'arrows';
   system(2).npts = npts;
   system(2).wind = [-5 5 -5 5];
   
   system(3).name = 'vibrating spring';
   system(3).xvar = 'x';
   system(3).yvar = 'v';
   system(3).xder = ' v';
   system(3).yder = ' -(k*x + d*v)/m';
   system(3).pname1 = 'k';
   system(3).pname2 = 'm';
   system(3).pname3 = 'd';
   system(3).pname4 = '';
   system(3).pval1 = '3';
   system(3).pval2 = '1';
   system(3).pval3 = '0';
   system(3).pval4 = '';
   system(3).fieldtype = 'arrows';
   system(3).npts = npts;
   system(3).wind = [-5 5 -5 5];
   
   system(4).name = 'pendulum';
   system(4).xvar = '\theta';
   system(4).yvar = '\omega';
   system(4).xder = ' \omega';
   system(4).yder = ' -sin(\theta) - D*\omega';
   system(4).pname1 = 'D';
   system(4).pname2 = '';
   system(4).pname3 = '';
   system(4).pname4 = '';
   system(4).pval1 = '0';
   system(4).pval2 = '';
   system(4).pval3 = '';
   system(4).pval4 = '';
   system(4).fieldtype = 'arrows';
   system(4).npts = npts;
   system(4).wind = [-10 10 -4 4];
   
   system(5).name = 'predator prey';
   system(5).xvar = 'prey';
   system(5).yvar = 'predator';
   system(5).xder = ' (A - B*predator)*prey';
   system(5).yder = ' (D*prey - C)*predator';
   system(5).pname1 = 'A';
   system(5).pname2 = 'B';
   system(5).pname3 = 'C';
   system(5).pname4 = 'D';
   system(5).pval1 = '0.4';
   system(5).pval2 = '0.01';
   system(5).pval3 = '0.3';
   system(5).pval4 = '0.005';
   system(5).fieldtype = 'arrows';
   system(5).npts = npts;
   system(5).wind = [0 120 0 80];
   
   system(6).name = 'competing species';
   system(6).xvar = 'x';
   system(6).yvar = 'y';
   system(6).xder = ' r*(1 - x - A*y)*x';
   system(6).yder = ' s*(1 - y - B*x)*y';
   system(6).pname1 = 'r';
   system(6).pname2 = 's';
   system(6).pname3 = 'A';
   system(6).pname4 = 'B';
   system(6).pval1 = '0.4';
   system(6).pval2 = '0.6';
   system(6).pval3 = '5';
   system(6).pval4 = '4';
   system(6).fieldtype = 'nullclines';
   system(6).npts = npts;
   system(6).wind = [0 1 0 1];
   
   system(7).name = 'cooperative species';
   system(7).xvar = 'x';
   system(7).yvar = 'y';
   system(7).xder = ' r*(1 - x + A*y)*x';
   system(7).yder = ' s*(1 - y + B*x)*y';
   system(7).pname1 = 'r';
   system(7).pname2 = 's';
   system(7).pname3 = 'A';
   system(7).pname4 = 'B';
   system(7).pval1 = '0.4';
   system(7).pval2 = '0.6';
   system(7).pval3 = '2';
   system(7).pval4 = '0.3';
   system(7).fieldtype = 'nullclines';
   system(7).npts = npts;
   system(7).wind = [0 9 0 5];
   
   system(8).name = 'van der Pol''s equation';
   system(8).xvar = 'x';
   system(8).yvar = 'y';
   system(8).xder = ' M*x - y - x^3';
   system(8).yder = ' x';
   system(8).pname1 = 'M';
   system(8).pname2 = '';
   system(8).pname3 = '';
   system(8).pname4 = '';
   system(8).pval1 = '2';
   system(8).pval2 = '';
   system(8).pval3 = '';
   system(8).pval4 = '';
   system(8).fieldtype = 'arrows';
   system(8).npts = npts;
   system(8).wind = [-5 5 -5 5];
   
   system(9).name = 'Duffing''s equation';
   system(9).xvar = 'x';
   system(9).yvar = 'y';
   system(9).xder = ' y';
   system(9).yder = ' -(k*x + c*y + l*x^3)/m';
   system(9).pname1 = 'k';
   system(9).pname2 = 'c';
   system(9).pname3 = 'm';
   system(9).pname4 = 'l';
   system(9).pval1 = '-1';
   system(9).pval2 = '0';
   system(9).pval3 = '1';
   system(9).pval4 = '1';
   system(9).fieldtype = 'arrows';
   system(9).npts = npts;
   system(9).wind = [-3 3 -3 3];
   
   ud.c = system(1);    % Changed values.
   ud.o = system(1);    % Original values.
   ud.h = system(1);    % This will be the handles in the
   % setup window.
   
   ud.style = style;
   ud.npts = npts;  
   ud.settings.magn = 1.25;
   ud.settings.refine = 8;
   ud.settings.tol = tol;
   ud.settings.solver = solver;
   ud.settings.stepsize = stepsize;
   ud.system = system;
   
   switch style
   case 'black'
      color.temp = [1 0 0]; % red for temporary orbits
      color.orb = [1 1 0];  % yellow for orbits
      color.eqpt = [1 0 0];  % red for eq. pts.
      %    color.arrows = [0 1 1]; % cyan for arrows
      % color.arrows = [.5 .5 .9];  % purple for arrows
      color.arrows = .5*[1 1 1];  % gray for arrows
      color.narrows = .7*[1 1 1];  % gray for nullcline arrows
      color.tx = [1 1 0]; % yellow for xt plots & 3D plots
      color.ty = [1 0 0]; % red for yt plots
      color.ta = [1 0 0]; % red for axis plots
      color.sep = [.2,1,0]; % green for separatrices
      color.xcline = [1 1 1]; % white for xclines
      color.ycline = [1 0 1]; % magenta for yclines
      color.level = [1,.5,.5];
      
   case 'white'
      color.temp = [1 0 0]; % red for temporary orbits
      color.orb = [0 0 1];  % blue for orbits
      color.eqpt = [1 0 0];  % red for eq. pts.
      color.arrows = 0.7*[1 1 1]; % gray for arrows
      color.narrows = .4*[1 1 1];  % gray for nullcline arrows
      color.tx = [0 0 1]; % blue for xt plots & 3D plots
      color.ty = [1 0 0]; % red for yt plots
      color.ta = [1 0 0]; % red for axis plots
      color.sep = [0,1,0];% green for separatrices
      color.xcline = [1 0 .75]; % magenta for xclines
      color.ycline = [1 .5 0]; %  orange for yclines
      color.level = 0.8*[.9,.5,.8];
      
    case 'test'
      color.temp = [1 0 0]; % red for temporary orbits
      color.orb = [0 0 1];  % blue for orbits
      color.arrows = .7*[1 1 1]; % gray for arrows
      color.eqpt = [1 0 0];  % red for eq. pts.
      color.narrows = .4*[1 1 1];  % gray for nullcline arrows
      color.tx = [0 0 1]; % blue for xt plots & 3D plots
      color.ty = [1 0 0]; % red for yt plots
      color.ta = [1 0 0]; % red for axis plots
      color.sep = [0,1,0];% green for separatrices
      color.xcline = [1 0 .75]; % magenta for xclines
      color.ycline = [1 .5 0]; %  orange for yclines
      color.level = [1,.5,.5];

    case 'display'
      color.temp = [1 0 0]; % red for temporary orbits
      color.orb = [0 0 1];  % blue for orbits
      color.arrows = .4*[1 1 1]; % gray for arrows
      color.eqpt = [1 0 0];  % red for eq. pts.
      color.narrows = .4*[1 1 1];  % gray for nullcline arrows
      color.tx = [0 0 1]; % blue for xt plots & 3D plots
      color.ty = [1 0 0]; % red for yt plots
      color.ta = [1 0 0]; % red for axis plots
      color.sep = [0,1,0];% green for separatrices
      color.xcline = [1 0 .75]; % magenta for xclines
      color.ycline = [1 .5 0]; %  orange for yclines
      color.level = 0.8*[.9,.5,.8];
      
   case 'bw'
      color.temp = [1 1 1]; % white for everything
      color.orb = [1 1 1];  
      color.eqpt = [1 1 1]; 
      color.arrows = [1 1 1];
      color.narrows = [1 1 1];  
      color.tx = [1 1 1]; 
      color.ty = [1 1 1]; 
      color.ta = [1 1 1]; 
      color.sep = [1 1 1];
      color.xcline = [1 1 1];
      color.ycline = [1 1 1];
      color.level = [1,1,1];
   end
   ud.color = color;
   ud.level = ' ';
   ppset = figure('name','PPLANE6 Setup','numb','off',...
      'tag','PPLANE6','visible','off',...
      'user',ud);
   
   pplane6('figdefault',ppset);
   frame(1) = uicontrol('style','frame','visible','off');
   eq(1)=uicontrol('style','text',...
      'horizon','center',...
      'string','The differential equations.','visible','off');
   ext = get(eq(1),'extent');
   rr=ext(4)/10;
   
   texth =ext(4)+4;    % 19;            % Height of text boxes.
   varw = 40*rr;                % Length of variable boxes.
   equalw =13*rr;               % Length of equals.(30)
   eqlength = 230*rr;           % Length of right hand sides of equations.
   winstrlen = 120*rr;  % Length of string boxes in display frame.
   left = 0;            % Left margin of the frames.
   frsep = 0;    %3;            % Separation between frames.
   separation = texth;  % Separation between boxes.
   
   dfigwidth =2*left + varw+equalw+eqlength+10; % Width of the figure.
   dfigurebot = 30;     % Bottom of the figure.
   buttw = dfigwidth/3;
   qwind = [0,frsep,buttw,separation];  % Quit button
   rwind = [buttw,frsep,buttw,separation];      % Revert "
   pwind = [2*buttw,frsep,buttw,separation];    % Proceed "
   
   disfrbot = 2*frsep + separation;     % Display frame.
   disfrw = winstrlen + varw +10;
   disfrht = 5*separation + 10;
   disfrwind = [left, disfrbot, disfrw, disfrht];
   
   pfrbot = disfrbot + disfrht +frsep;  % Parameter frame.
   pfrw = dfigwidth -2*left;
   pfrht = 2*separation + 10;
   pfrwind = [left, pfrbot, pfrw, pfrht];
   
   defrbot = pfrbot + pfrht + frsep;    % Equation frame.
   defrw = pfrw;
   defrht = 3*separation + 10;
   defrwind = [left, defrbot, defrw, defrht];
   
   ffrbot = disfrbot;                   % Field frame.
   ffrleft = left + disfrw + frsep;
   ffrw = dfigwidth -left - ffrleft;
   ffrht = disfrht; 
   ffrwind = [ffrleft, ffrbot, ffrw, ffrht];
   
   dfigureheight = defrbot + defrht +frsep;     % Height of the figure.
   
   set(ppset,'pos',[30 dfigurebot dfigwidth dfigureheight]);
   
   set(frame(1),'pos',defrwind);
   
   
   xname=[
      'ud = get(gcf,''user'');'...
         'Xname=get(ud.h.xvar,''string'');'...
         'set(ud.h.twind(1),''string'',[''The minimum value of '',Xname,'' = '']);'...
         'set(ud.h.twind(2),''string'',[''The maximum value of '',Xname,'' = '']);'...
         'ud.c.xvar = Xname;'...
         'ud.flag = 0;'...
         'ud.c.name = '''';',...
         'set(gcf,''user'',ud);'];
   
   yname=[
      'ud = get(gcf,''user'');'...
         'Yname=get(ud.h.yvar,''string'');'...
         'set(ud.h.twind(3),''string'',[''The minimum value of '',Yname,'' = '']);'...
         'set(ud.h.twind(4),''string'',[''The maximum value of '',Yname,'' = '']);'...
         'ud.c.yvar = Yname;'...
         'ud.flag = 0;'...
         'ud.c.name = '''';',...
         'set(gcf,''user'',ud);'];
   
   xder =[
      'ud = get(gcf,''user'');'...
         'ud.c.xder = get(ud.h.xder,''string'');'...
         'ud.flag = 0;'...
         'ud.c.name = '''';',...
         'set(gcf,''user'',ud);'];
   
   yder =[
      'ud = get(gcf,''user'');'...
         'ud.c.yder = get(ud.h.yder,''string'');'...
         'ud.flag = 0;'...
         'ud.c.name = '''';',...
         'set(gcf,''user'',ud);'];
   
   equationbot = defrbot + 5;
   eqlabelbot = equationbot + 2*separation;
   xbot = equationbot + separation;             % Bottom of x equation.
   ybot = equationbot;                          % Bottom of y equation.
   
   lablen =200*rr;
   
   eqlableft = (dfigwidth-lablen)/2;
   eqleft = left + 5;
   
   set(eq(1),'pos',[eqlableft eqlabelbot lablen texth]);
   
   ud.h.xvar=uicontrol('pos',[eqleft, xbot, varw, texth],...
      'style','edit',...
      'horizon','right',...
      'string',ud.o.xvar,...
      'call',xname,...
      'visible','off');
   
   eq(2) = uicontrol('style','text',...
      'pos',[eqleft+varw xbot equalw texth],...
      'horizon','center',...
      'string',''' = ',...
      'visible','off');
   
   ud.h.xder=uicontrol('pos',[eqleft+varw+equalw xbot eqlength texth],...
      'string',ud.o.xder,...
      'horizon','left','style','edit',...
      'call',xder,'visible','off');
   
   ud.h.yvar=uicontrol('pos',[eqleft ybot varw texth],...
      'style','edit',...
      'horizon','right',...
      'string',ud.o.yvar,...
      'call',yname,'visible','off');
   
   eq(3) = uicontrol('style','text',...
      'pos',[eqleft+varw ybot equalw texth],...
      'horizon','center','string',''' = ','visible','off');
   
   ud.h.yder=uicontrol('pos',[eqleft+varw + equalw ybot eqlength texth],...
      'string',ud.o.yder,...
      'horizon','left','style','edit',...
      'call',yder,'visible','off');
   
   
   frame(2) = uicontrol('style','frame','pos',disfrwind,'visible','off');
   
   w1 = [
      'ud = get(gcf,''user'');'...
         'nnn =         str2num(get(ud.h.wind(1),''string''));'...
         'if isempty(nnn),',...
         '  set(ud.h.wind(1),''string'',''?'');',...
         '  nnn = NaN;',...
         'end,',...
         'ud.c.wind(1) = nnn;',...          
         'ud.c.name = '''';',...
         'set(gcf,''user'',ud);'];      
   
   w2 = [
      'ud = get(gcf,''user'');'...
         'nnn =         str2num(get(ud.h.wind(2),''string''));'...
         'if isempty(nnn),',...
         '  set(ud.h.wind(2),''string'',''?'');',...
         '  nnn = NaN;',...
         'end,',...
         'ud.c.wind(2) = nnn;',...          
         'ud.c.name = '''';',...
         'set(gcf,''user'',ud);'];      
   
   w3 = [
      'ud = get(gcf,''user'');'...
         'nnn =         str2num(get(ud.h.wind(3),''string''));'...
         'if isempty(nnn),',...
         '  set(ud.h.wind(3),''string'',''?'');',...
         '  nnn = NaN;',...
         'end,',...
         'ud.c.wind(3) = nnn;',...          
         'ud.c.name = '''';',...
         'set(gcf,''user'',ud);'];      
   
   w4 = [
      'ud = get(gcf,''user'');'...
         'nnn =         str2num(get(ud.h.wind(4),''string''));'...
         'if isempty(nnn),',...
         '  set(ud.h.wind(4),''string'',''?'');',...
         '  nnn = NaN;',...
         'end,',...
         'ud.c.wind(4) = nnn;',...          
         'ud.c.name = '''';',...
         'set(gcf,''user'',ud);'];      
   
   
   winbot1 = disfrbot + disfrht - 5 - separation;
   winbot2 = winbot1 - separation;
   winbot3 = winbot2 - separation;
   winbot4 = winbot3 - separation;
   winbot5 = winbot4 - separation;
   
   dwind = uicontrol('style','text',...
      'pos',[eqleft winbot1 disfrw-10 texth],...
      'horizon','center',...
      'string','The display window.','visible','off');
   
   % ud.h.twind contains the handles to the text windows, and ud.h.wind
   % contains the handles to the edit windows.
   
   ud.h.twind(1) = uicontrol('style','text',...
      'pos',[eqleft winbot2 winstrlen texth],...
      'horizon','right',...
      'string',['The minimum value of ',ud.o.xvar,' = '],'visible','off');
   
   ud.h.wind(1) = uicontrol('style','edit',...
      'pos',[eqleft+winstrlen winbot2 40*rr texth],...
      'string',num2str(ud.o.wind(1)),...
      'call',w1,'visible','off');
   
   ud.h.twind(2) = uicontrol('style','text',...
      'pos',[eqleft winbot3 winstrlen texth],...
      'horizon','right',...
      'string',['The maximum value of ',ud.o.xvar,' = '],'visible','off');
   
   ud.h.wind(2) = uicontrol('style','edit',...
      'pos',[eqleft+winstrlen winbot3 40*rr texth],...
      'string',num2str(ud.o.wind(2)),...
      'call',w2,'visible','off');
   
   ud.h.twind(3)= uicontrol('style','text',...
      'pos',[eqleft winbot4 winstrlen texth],...
      'horizon','right',...
      'string',['The minimum value of ',ud.o.yvar,' = '],'visible','off');
   
   ud.h.wind(3) = uicontrol('style','edit',...
      'pos',[eqleft+winstrlen winbot4 40*rr texth],...
      'string',num2str(ud.o.wind(3)),...
      'call',w3,'visible','off');
   
   ud.h.twind(4) = uicontrol('style','text',...
      'pos',[eqleft winbot5 winstrlen texth],...
      'horizon','right',...
      'string',['The maximum value of ',ud.o.yvar,' = '],'visible','off');
   
   ud.h.wind(4) = uicontrol('style','edit',...
      'pos',[eqleft+winstrlen winbot5 40*rr texth],...
      'string',num2str(ud.o.wind(4)),...
      'call',w4,'visible','off');
   
   
   frame(3)=uicontrol('style','frame','pos',pfrwind,'visible','off');
   
   p1 = [
      'ud = get(gcf,''user'');'...
         'ud.c.pname1=get(ud.h.pname1,''string'');'...
         'ud.c.pval1=get(ud.h.pval1,''string'');'...
         'ud.flag = 0;'...
         'ud.c.name = '''';',...
         'set(gcf,''user'',ud);'];
   
   p2 = [
      'ud = get(gcf,''user'');'...
         'ud.c.pname2=get(ud.h.pname2,''string'');'...
         'ud.c.pval2=get(ud.h.pval2,''string'');'...
         'ud.flag = 0;'...
         'ud.c.name = '''';',...
         'set(gcf,''user'',ud);'];
   
   p3 = [
      'ud = get(gcf,''user'');'...
         'ud.c.pname3=get(ud.h.pname3,''string'');'...
         'ud.c.pval3=get(ud.h.pval3,''string'');'...
         'ud.flag = 0;'...
         'ud.c.name = '''';',...
         'set(gcf,''user'',ud);'];
   
   p4 = [
      'ud = get(gcf,''user'');'...
         'ud.c.pname4=get(ud.h.pname4,''string'');'...
         'ud.c.pval4=get(ud.h.pval4,''string'');'...
         'ud.flag = 0;'...
         'ud.c.name = '''';',...
         'set(gcf,''user'',ud);'];
   
   
   pnamew = 40*rr;
   pvalw = 50*rr;
   peqw = 10*rr;
   pbot2 = pfrbot + 5;
   pbot1 = pbot2 + separation;
   pleft1 = eqleft + 50*rr + 5;
   peqleft1 = pleft1 + pnamew;
   pvleft1 = peqleft1 + peqw;
   pleft2 = dfigwidth - 10 - pnamew - pvalw - peqw;
   peqleft2 = pleft2 + pnamew;
   pvleft2 = peqleft2 + peqw;   
   
   paratit=uicontrol('style','text',...
      'pos',[eqleft pfrbot+2 50*rr 2.1*texth],...
      'horizon','center',...
      'string',{'Parameters';'or';'expressions'},'visible','off');
   
   ud.h.pname1 = uicontrol('style','edit',...
      'pos',[pleft1 pbot1 pnamew texth],...
      'horizon','right','string',ud.o.pname1,...
      'call',p1,'visible','off');
   
   equal(1) = uicontrol('style','text',...
      'pos',[peqleft1 pbot1 peqw texth],...
      'horizon','center','string','=','visible','off');
   
   ud.h.pval1 = uicontrol('style','edit',...
      'pos',[pvleft1 pbot1 pvalw texth],...
      'string',ud.o.pval1,'call',p1,'visible','off');
   
   ud.h.pname2 = uicontrol('style','edit',...
      'pos',[pleft2 pbot1 pnamew texth],...
      'horizon','right','string',ud.o.pname2,...
      'call',p2,'visible','off');
   
   equal(2) = uicontrol('style','text',...
      'pos',[peqleft2 pbot1 peqw texth],...
      'horizon','center','string','=','visible','off');
   
   ud.h.pval2 = uicontrol('style','edit',...
      'pos',[pvleft2 pbot1 pvalw texth],...
      'string',ud.o.pval2,'call',p2,'visible','off');
   
   ud.h.pname3 = uicontrol('style','edit',...
      'pos',[pleft1 pbot2 pnamew texth],...
      'horizon','right','string',ud.o.pname3,...
      'call',p3,'visible','off');
   
   equal(3) = uicontrol('style','text',...
      'pos',[peqleft1 pbot2 peqw texth],...
      'horizon','center','string','=','visible','off');
   
   ud.h.pval3 = uicontrol('style','edit',...
      'pos',[pvleft1 pbot2 pvalw texth],...
      'string',ud.o.pval3,...
      'call',p3,'visible','off');
   
   
   ud.h.pname4 = uicontrol('style','edit',...
      'pos',[pleft2 pbot2 pnamew texth],...
      'horizon','right','string',ud.o.pname4,...
      'call',p4,'visible','off');
   
   equal(4) = uicontrol('style','text',...
      'pos',[peqleft2 pbot2 peqw texth],...
      'horizon','center','string','=','visible','off');
   
   ud.h.pval4 = uicontrol('style','edit',...
      'pos',[pvleft2 pbot2 pvalw texth],...
      'string',ud.o.pval4,'call',p4,'visible','off');
   
   butt(1) = uicontrol('style','push',...
      'pos',qwind,...
      'string','Quit','call','pplane6(''quit'')','visible','off');
   
   butt(2) = uicontrol('style','push',...
      'pos',rwind,...
      'string','Revert','call','pplane6(''revert'')','visible','off');
   
   butt(3) = uicontrol('style','push',...
      'pos',pwind,...
      'string','Proceed','call','pplane6(''proceed'')','visible','off');
   
   fframe = uicontrol('style','frame','pos',ffrwind,'visible','off');
   
   
   
   ffrtitle = uicontrol('style','text','pos',[ffrleft+5,winbot1,ffrw-10,texth],...
      'string','The direction field.','horizon','center','visible','off');
   
   radleft = ffrleft + 3;
   radw = 50*rr;
   
   typewindw = radw +6;
   typewind = [ffrleft, ffrbot, typewindw, ffrht-separation-3];
   textwindl = ffrleft+typewindw;
   textleft = textwindl + 3;
   textw = ffrw - typewindw;
   textwind = [textwindl, ffrbot,textw, ffrht-separation-3];
   typeframe = uicontrol('style','frame','pos',typewind,'visible','off');
   
   textframe = uicontrol('style','frame','pos',textwind,'visible','off');
   
   switch ud.o.fieldtype
   case 'nullclines'
      rval1 = 1;rval2 = 0;rval3 = 0;rval4 = 0;
   case 'lines'
      rval1 = 0;rval2 = 2;rval3 = 0;rval4 = 0;
   case 'arrows' 
      rval1 = 0;rval2 = 0;rval3 = 3;rval4 = 0;
   case 'none' 
      rval1 = 0;rval2 = 0;rval3 = 0;rval4 = 4;
   otherwise
      error(['Unknown fieldtype ',ud.o.fieldtype,'.'])
   end          
   
   ud.h.rad(1) = uicontrol('style','radio',...
      'pos',[radleft winbot4 radw texth],...
      'string','Nullclines','value',rval1,'visible','off');
   
   ud.h.rad(2) = uicontrol('style','radio',...
      'pos',[radleft winbot3 radw texth],...
      'string','Lines','value',rval2,'max',2,'visible','off');
   
   ud.h.rad(3) = uicontrol('style','radio',...
      'pos',[radleft winbot2 radw texth],...
      'string','Arrows','value',rval3,'max',3,'visible','off');
   
   ud.h.rad(4) = uicontrol('style','radio',...
      'pos',[radleft winbot5 radw texth],...
      'string','None','value',rval4,'max',4,'visible','off');
   
   for i=1:4
      set(ud.h.rad(i),'user',ud.h.rad(:,[1:(i-1),(i+1):4]));
   end
   
   callrad = [
      'me = get(gcf,''currentobject'');',...
         'kk = get(me,''max'');',...
         'set(get(me,''user''),''value'',0),',...
         'set(me,''value'',kk);',...
         'ud = get(gcf,''user'');',...
         'switch kk,',...
         '       case 1, ud.c.fieldtype = ''nullclines'';',...
         '       case 2, ud.c.fieldtype = ''lines'';',...
         '       case 3, ud.c.fieldtype = ''arrows'';',...
         '       case 4, ud.c.fieldtype = ''none'';',...
         'end,',...
         'set(gcf,''user'',ud);'];
   
   set(ud.h.rad,'call',callrad);
   
   nfptsstr = {'Number of'; 'field points per'; 'row or column.'};
   nfptstext = uicontrol('style','text',...
      'pos',[textleft winbot4 textw-5 2.5*texth],...
      'string',nfptsstr,'horizon','center','visible','off');
   
   callnfpts = [
      'ppset = findobj(''name'',''PPLANE6 Setup'');',...
         'ud = get(ppset,''user'');'...
         'me = ud.h.npts;',...
         'kk = str2num(get(me,''string''));',...
         'if isempty(kk),',...
         '  set(me,''string'',''?'');',...
         '  kk = NaN;',...
         'else,',...
         '  kk = floor(kk);',...
         '  [m,N] = computer;'...
         '  if (N <= 8192),',...
         '      N = 32;',...
         '  else,',...
         '      N = 50;',...
         '  end,'...
         '  kk = min([N,max([5,kk])]);'...
         '  set(me,''string'',num2str(kk));'...
         'end,'...
         'ud.c.npts = kk;',...
         'set(ppset,''user'',ud);'];
   
   ud.h.npts = uicontrol('style','edit',...
      'pos',[textleft+(textw -30*rr)/2,winbot5 30*rr,texth],...
      'string',ud.o.npts,'call',callnfpts,'visible','off');
   
   delgall = ['sud = get(gcf,''user'');',...
         'mh = get(sud.h.gallery,''children'');',...
         'add = findobj(sud.h.gallery,''tag'',''add system'');',...
         'mh(find(mh == add)) = [];',...
         'delete(mh);',...
         'set(sud.h.gallery,''user'',[]);',...
         'set(findobj(''tag'',''load default''),''enable'',''on'')'];
   
   
   % Menus
   
   hhsetup = get(0,'showhiddenhandles');
   set(0,'showhiddenhandles','on');
   mefile = findobj(ppset,'label','&File');
   meedit = findobj(ppset,'label','&Edit');
   delete(findobj(ppset,'label','&Tools'));
   delete(findobj(ppset,'label','&View'));
   delete(findobj(ppset,'label','&Insert'));
   
   % File menu

   meexp = findobj(mefile,'label','&Export...');
   meprev = findobj(mefile,'label','Print Pre&view...');
   mepset = findobj(mefile,'label','Pa&ge Setup...');
   set(get(mefile,'child'),'vis','off');
   meload = uimenu(mefile,'label','Load a system ...',...
                   'call','pplane6(''loadsyst'',''system'');',...
                   'pos',1);
   mesave = uimenu(mefile,'label','Save the current system ...',...
                   'call','pplane6(''savesyst'',''system'');',...
                   'pos',2);
   meloadg = uimenu(mefile,'label','Load a gallery ...',...
                    'call','pplane6(''loadsyst'',''gallery'');',...
                    'separator','on','pos',3);
   mesaveg = uimenu(mefile,'label','Save a gallery ...',...
                    'call','pplane6(''savesyst'',''gallery'');',...
                    'tag','savegal','pos',4);
   medelg = uimenu(mefile,'label','Delete the current gallery',...
                   'call',delgall,'pos',5);
   melddg = uimenu(mefile,'label','Load the default gallery',...
                   'call','pplane6(''loadsyst'',''default'');',...
                   'enable','off',...
                   'tag','load default','pos',6);
   merevert = uimenu(mefile,'label','Revert','call',...
                     'pplane6(''revert'')',...
                     'separator','on','pos',7);
   meproceed = uimenu(mefile,...
                      'label','Proceed',...
                      'call','pplane6(''proceed'')',...
                      'separator','off',...
                      'accelerator','G','pos',8);
   set(mepset,'vis','on','pos',9);
   set(meprev,'vis','on','pos',10);
   set(meexp,'vis','on','pos',11,'separator','off');
   merestart = uimenu(mefile,'label',...
                      'Restart PPLANE6',...
                      'call','pplane6(''restart'')',...
                      'separator','on','pos',12);

   mequit = uimenu(mefile,...
                   'label','Quit PPLANE6',...
                   'call','pplane6(''quit'')',...
                   'separator','off','pos',13);

   % Edit menu
   
   set(get(meedit,'child'),'vis','off');
   meclrf = uimenu(meedit,'label','Clear equations',...
      'call',['ud = get(gcf,''user'');h = ud.h;',...
         'set([h.xvar,h.xder,h.yvar,h.yder],''string'','''');'],...
      'accelerator','E');
   meclrp = uimenu(meedit,'label','Clear parameters',...
      'call',['ud = get(gcf,''user'');h = ud.h;',...
         'set([h.pname1,h.pname2,h.pname3,h.pname4,h.pval1,h.pval2,h.pval3,h.pval4],''string'','''');'],...
      'accelerator','N');
   meclrwind = uimenu(meedit,'label','Clear display window',...
      'call',['ud = get(gcf,''user'');',...
         'set(ud.h.wind,''string'','''');'],...
      'accelerator','D');
   meclrall = uimenu(meedit,'label','Clear all',...
      'call',['ud = get(gcf,''user'');h = ud.h;',...
         'set(h.wind,''string'','''');',...
         'set([h.pname1,h.pname2,h.pname3,h.pname4,h.pval1,h.pval2,h.pval3,h.pval4],''string'','''');',...
         'set([h.xvar,h.xder,h.yvar,h.yder],''string'','''');'],...
      'accelerator','A',...
      'separator','on');
   
   sysmenu = uimenu('label','Gallery','visible','off','pos',3);
   
   meadd = uimenu(sysmenu,'label','Add current system to the gallery',...
      'call','pplane6(''addgall'');','tag','add system');
   sep = 'on';
   for kk = 1:length(system)
      kkk = num2str(kk);
      if kk == 2, sep = 'off';end
      sysmen(kk) = uimenu(sysmenu,'label',system(kk).name,...
         'call',['pplane6(''system'',',kkk,')'],...
         'separator',sep,'visible','off');
   end
   set(sysmenu,'user',system);
   ud.h.gallery = sysmenu;

   ud.flag = 0;
   ud.egg = (exist('EASTEREGG') ==2);
   
   % Record the handles in the User Data of the Set Up figure.
   
   set(ppset,'user',ud);
   hhhh = findobj(ppset,'type','uicontrol');
   set(hhhh,'units','normal')
   
   set(ppset,'visible','on','resize','on');
   set(get(ppset,'children'),'visible','on');
   set(get(sysmenu,'children'),'visible','on');
 %end
  set(0,'showhiddenhandles',hhsetup);
  
elseif strcmp(action,'savesyst')
   
   ppset = findobj('name','PPLANE6 Setup');
   type = input1;
   sud = get(ppset,'user');
   
   switch type
   case 'system'  
      systems = get(sud.h.gallery,'user');
      
      newsyst = sud.c;
      fn = newsyst.name;
      if ~isempty(fn)
         fn(find(abs(fn)==32))='_';   % Replace spaces by underlines.
      end       
      comp = computer;
      switch  comp
      case 'PCWIN'
         filter = [sud.ppdir,'\*.pps'];
      case 'MAC2'
         filter = [sud.ppdir,':*.pps'];
      otherwise
         filter = [sud.ppdir,'/*.pps'];
      end
      [fname,pname] = uiputfile(filter,'Save the system as:');
      if fname == 0,return;end
      if ~strcmp(fname,fn)
         ll = length(fname);
         if (ll>4 & strcmp(fname(ll-3:ll),'.pps'))
            fn = fname(1:(ll-4));
         else
            fn =fname;
         end
         newsyst.name = fn;
         sud.c.name = fn;
         set(ppset,'user',sud);
      end
      newsysts = newsyst;
   case 'gallery'
      systems = get(sud.h.gallery,'user');
      ll = length(systems); 
      if ll == 0
         warndlg(['There are no systems to make up a gallery.'],'Warning');
         return
      end
      names = cell(ll,1);
      for j=1:ll
         names{j} = systems(j).name;
      end       
      [sel,ok] = listdlg('PromptString','Select the systems',...
         'Name','Gallery selection',...
         'ListString',names);
      if isempty(sel)
         return
      else
         newsysts = systems(sel);
      end       
      comp = computer;
      switch  comp
      case 'PCWIN'
         prompt = [sud.ppdir,'\*.ppg'];
      case 'MAC2'
         prompt = [sud.ppdir,':*.ppg'];
      otherwise
         prompt = [sud.ppdir,':/.ppg'];
      end
      [fname,pname] = uiputfile(prompt,'Save the gallery as:');
      
   end  % switch type
   
   ll = length(newsysts);
   newsystsc = cell(19*ll,1);  
   for j = 1:ll
      newsyst = newsysts(j);
      newsyst = struct2cell(newsyst);
      newsyst{15} = num2str(newsyst{15});
      wind = newsyst{16};
      for k = 1:4
         newsyst{15+k} = num2str(wind(k));
      end
      newsystc([(19*(j-1)+1):19*j]) = newsyst;
   end  
   fid = fopen([pname fname],'w');
   for kk = 1:length(newsystc)
      str = newsystc{kk};
      l = length(str);
      if l
         for (k=fliplr(find(str=='\')))
            str = [str(1:k-1) '\' str(k:l)];
            l = l+1;
         end
      end
      fprintf(fid,[str,'\n']);
   end
   fclose(fid);
   
elseif strcmp(action,'loadsyst')  % This loads either a system or a gallery.
   
   sud = get(gcf,'user');
   pos = get(gcf,'pos');
   wpos = [pos(1),pos(2)+pos(4)+20,300,20];
   waith = figure('pos',wpos,...
      'numb','off',...
      'vis','off',...
      'next','replace',...
      'menubar','none',...
      'resize','off',...
      'createfcn','');
   axes('pos',[0.01,0.01,0.98,0.98],...
      'vis','off');
   xp = [0 0 0 0];
   yp = [0 0 1 1];
   xl = [1 0 0 1 1];
   yl = [0 0 1 1 0];
   patchh = patch(xp,yp,'r','edgecolor','r','erase','none');
   lineh = line(xl,yl,'erase','none','color','k');
   type = input1;  
   set(sud.h.gallery,'enable','off');
   if strcmp(type,'default')
      set(waith,'name','Loading the default gallery.','vis','on');
      set(findobj('tag','load default'),'enable','off');
      megall = sud.h.gallery;
      mh = get(megall,'children');
      add = findobj(megall,'tag','add system');
      mh(find(mh == add)) = [];
      delete(mh);
      newsysstruct = get(megall,'user');
      system = sud.system;
      ll = length(system);
      x = 1/(ll+2);
      xp = [xp(2),x,x,xp(2)];
      set(patchh,'xdata',xp);
      set(lineh,'xdata',xl);
      drawnow;
      sep = 'on';
      for kk = 1:length(system)
         kkk = num2str(kk);
         if kk ==2, sep = 'off';end
         uimenu(megall,'label',system(kk).name,...
            'call',['pplane6(''system'',',kkk,')'],...
            'separator',sep);
      end % for
      set(megall,'user',system);
   else
      comp = computer;
      switch  comp
      case 'PCWIN'
         prompt = [sud.ppdir,'\'];
      case 'MAC2'
         prompt = [sud.ppdir,':'];
      otherwise
         prompt = [sud.ppdir,'/'];
      end
      if strcmp(type,'system')
         prompt = [prompt,'*.pps'];
         
         [fname,pname] = uigetfile(prompt,'Select a system to load.');
      elseif strcmp(type,'gallery')
         prompt = [prompt,'*.ppg'];
         
         [fname,pname] = uigetfile(prompt,'Select a gallery to load.');
      end  % if strcmp
      if fname == 0
         delete(waith);
         set(sud.h.gallery,'enable','on');
         return;
      end
      set(waith,'name',['Loading ',fname],'vis','on');
      fid = fopen([pname fname],'r');
      newsysts = {};
      kk = 0;
      while ~feof(fid)
         kk = kk + 1;
         newsysts{kk} = fgetl(fid);
      end
      fclose(fid);
      x = 19/(kk+38);
      xp = [xp(2),x,x,xp(2)];
      set(patchh,'xdata',xp);
      set(lineh,'xdata',xl);
      drawnow;
      newsysts = newsysts([1:kk]);
      if mod(kk,19)
         if strcmp(type,'system')
            warndlg(['The file ',fname, ' does not define a proper system.'],...
               'Warning');
         elseif strcmp(type,'gallery')
            warndlg(['The file ',fname, ' does not define a proper gallery.'],...
               'Warning');
         end
         set(sud.h.gallery,'enable','on');
         delete(waith);
         return
      end % if mod(kk,19)
      nnn = kk/19;
      flds = fieldnames(sud.c);flds=flds(:);
      for j = 0:(nnn-1)
         newsyst = newsysts([(j*19+1):(j+1)*19]);
         wind = newsyst(16:19);
         wind = [str2num(wind{1}),str2num(wind{2}),...
               str2num(wind{3}),str2num(wind{4})];
         newsyst{15} = str2num(newsyst{15});
         newsyst{16} = wind;
         newsyst = newsyst(1:16);
         newsyst = newsyst(:);
         newsysstruct(j+1) = cell2struct(newsyst,flds);
      end  % for j = 0:(nnn-1)    
   end  % if strcmp(type,'default') & else
   nnn = length(newsysstruct);
   ignoresyst = {};
   for j = 1:nnn
      x = (j+1)/(nnn+2);
      xp = [xp(2),x,x,xp(2)];
      set(patchh,'xdata',xp);
      set(lineh,'xdata',xl);
      drawnow;
      newsyst = newsysstruct(j);
      sname = newsyst.name;
      sname(find(abs(sname) == 95)) = ' '; % Replace underscores with spaces.
      newsyst.name = sname;
      ignore = pplane6('addgall',newsyst);
      if ignore == -1;
         ignoresyst{length(ignoresyst)+1} = sname;
      end  
   end % for j = 1:nnn
   l = length(ignoresyst);
   if l  % There was at least one system which was a dup with a
      % different name.
      if l == 1
         message = {['The system "',ignoresyst{1},'" duplicates a ',...
                  'system already in the gallery and was not added.']};
      else
         message = 'The systems ';
         for k = 1:(l-1)
            message = [message,'"',ignoresyst{k},'", ']; 
         end
         message = {[message,'and "',ignoresyst{l},'" duplicate ',...
                  'systems already in the gallery and were not added.']};
      end % if l == 1 & else
      helpdlg(message,'Ignored systems');
   end  % if l
   if strcmp(type,'system') % Added a system.
      if ignore > 0 % The system was ignored.
         kk = ignore;
      else
         systems = get(sud.h.gallery,'user');
         kk = length(systems);
      end
      pplane6('system',kk);
   end  
   if strcmp('type','default')
      pplane6('system',1);
   end  
   set(sud.h.gallery,'enable','on');
   x = 1;
   xp = [xp(2),x,x,xp(2)];
   set(patchh,'xdata',xp);
   set(lineh,'xdata',xl);
   drawnow;
   delete(waith);
   
elseif strcmp(action,'addgall')
   
   output = 0;
   ppset = findobj('name','PPLANE6 Setup');
   sud = get(ppset,'user');
   if nargin < 2    % We are adding the current system.
      
      syst = sud.c;
      sname = inputdlg('Provide a name for this system.','System name',1,{syst.name});
      if isempty(sname),return;end
      sname = sname{1};
      if ~strcmp(sname,syst.name)
         sud.c.name = sname;
         set(ppset,'user',sud);
         syst.name = sname;
      end  
   else  % We have a system coming from a file.
      syst = input1;
      sname = syst.name;
   end
   systems = get(sud.h.gallery,'user');
   ll = length(systems);
   kk = 1;
   while ((kk<=ll) & (~strcmp(sname,systems(kk).name)))
      kk = kk + 1;
   end
   nameflag = (kk<=ll);
   ssyst = rmfield(syst,'name');
   kk = 1;
   while ((kk<=ll) & (~isequal(ssyst,rmfield(systems(kk),'name'))))
      kk = kk + 1;
   end
   systflag = 2*(kk<=ll);
   flag = nameflag + systflag;
   switch flag
   case 1  % Same name but different system.
      mh = findobj(sud.h.gallery,'label',sname);
      prompt = {['The system "',sname,'", which you wish to add to the gallery has ',...
               'the same name as a different system already in the gallery.  Please ',...
               'specify the name for the newly added system.'],...
            'Specify the name for the old system.'};
      title = 'Two systems with the same name';
      lineno = 1;
      defans = {sname,sname};
      answer = inputdlg(prompt,title,lineno,defans);
      if isempty(answer),break,end
      sname = answer{1};
      systems(kk).name = answer{2};
      set(mh,'label',answer{2});
      output = kk;
   case 2  % Two names for the same system.
      oldname = systems(kk).name;
      mh = findobj(sud.h.gallery,'label',oldname);
      
      prompt = {['The system "',sname,'", which you wish to add ',...
               'to the gallery is the same as a system which is ',...
               'already in the gallery with the name "',oldname,'".  ',...
               'Please specify which name you wish to use.']};
      title = 'Two names for the same system.';
      lineno = 1;
      defans = {oldname};
      answer = inputdlg(prompt,title,lineno,defans);
      if isempty(answer),break,end
      systems(kk).name = answer{1};
      set(mh,'label',answer{1});
      output = kk;
   case 3 % Systems and names the same.
      output = -1;
   otherwise
   end  % switch
   set(sud.h.gallery,'user',systems);
   syst.name = sname;
   if flag <=1
      switch ll
      case 0
         systems = syst;
         sepstr = 'on';
      case 8
         systems(9) = syst;
         if strcmp(systems(8).name,'Duffing''s equation')
            sepstr = 'on';
         else
            sepstr = 'off';
         end
      otherwise
         systems(ll+1) = syst;
         sepstr = 'off';
      end      
      kkk = num2str(ll+1); 
      newmenu = uimenu(sud.h.gallery,'label',sname,...
         'call',['pplane6(''system'',',kkk,')'],...
         'separator',sepstr);
      set(findobj('tag','savegal'),'enable','on');
   end
   set(sud.h.gallery,'user',systems);
   
elseif strcmp(action,'system')
   
   ppset = findobj('name','PPLANE6 Setup');
   ud = get(ppset,'user');
   kk = input1;
   if isstr(kk)
      kk = str2num(input1);
   end
   system = get(ud.h.gallery,'user');
   syst = system(kk);
   ud.o = syst;
   ud.c = syst;
   xname = syst.xvar;
   yname = syst.yvar;
   set(ud.h.xvar,'string',xname);
   set(ud.h.yvar,'string',yname);
   set(ud.h.xder,'string',syst.xder);
   set(ud.h.yder,'string',syst.yder);
   set(ud.h.pname1,'string',syst.pname1);
   set(ud.h.pname2,'string',syst.pname2);
   set(ud.h.pname3,'string',syst.pname3);
   set(ud.h.pname4,'string',syst.pname4);
   set(ud.h.pval1,'string',syst.pval1);
   set(ud.h.pval2,'string',syst.pval2);
   set(ud.h.pval3,'string',syst.pval3);
   set(ud.h.pval4,'string',syst.pval4);
   set(ud.h.twind(1),'string',['The minimum value of ',xname,' = ']);
   set(ud.h.twind(2),'string',['The maximum value of ',xname,' = ']);
   set(ud.h.twind(3),'string',['The minimum value of ',yname,' = ']);
   set(ud.h.twind(4),'string',['The maximum value of ',yname,' = ']);
   set(ud.h.wind(1),'string',num2str(syst.wind(1)));
   set(ud.h.wind(2),'string',num2str(syst.wind(2)));
   set(ud.h.wind(3),'string',num2str(syst.wind(3)));
   set(ud.h.wind(4),'string',num2str(syst.wind(4)));
   set(ud.h.npts,'string',num2str(syst.npts));
   
   switch syst.fieldtype
   case 'nullclines'
      rval = [1 0 0 0];
   case 'lines'
      rval = [0 2 0 0];
   case 'arrows' 
      rval = [0 0 3 0];
   case 'none' 
      rval = [0 0 0 4];
   otherwise
      error(['Unknown fieldtype ',ud.o.fieldtype,'.'])
   end          
   
   for i=1:4
      set(ud.h.rad(i),'value',rval(i));
   end  
   ud.flag = 0;
   set(ppset,'user',ud);
   
elseif strcmp(action,'revert')
   
   ud = get(gcf,'user');
   ud.c = ud.o;
   syst = ud.o;
   xname = syst.xvar;
   yname = syst.yvar;
   set(ud.h.xvar,'string',xname);
   set(ud.h.yvar,'string',yname);
   set(ud.h.xder,'string',syst.xder);
   set(ud.h.yder,'string',syst.yder);
   set(ud.h.pname1,'string',syst.pname1);
   set(ud.h.pname2,'string',syst.pname2);
   set(ud.h.pname3,'string',syst.pname3);
   set(ud.h.pname4,'string',syst.pname4);
   set(ud.h.pval1,'string',syst.pval1);
   set(ud.h.pval2,'string',syst.pval2);
   set(ud.h.pval3,'string',syst.pval3);
   set(ud.h.pval4,'string',syst.pval4);
   set(ud.h.twind(1),'string',['The minimum value of ',xname,' = ']);
   set(ud.h.twind(2),'string',['The maximum value of ',xname,' = ']);
   set(ud.h.twind(3),'string',['The minimum value of ',yname,' = ']);
   set(ud.h.twind(4),'string',['The maximum value of ',yname,' = ']);
   set(ud.h.wind(1),'string',num2str(syst.wind(1)));
   set(ud.h.wind(2),'string',num2str(syst.wind(2)));
   set(ud.h.wind(3),'string',num2str(syst.wind(3)));
   set(ud.h.wind(4),'string',num2str(syst.wind(4)));
   set(ud.h.npts,'string',num2str(syst.npts));
   
   switch syst.fieldtype
   case 'lines'
      rval(1) = 1;
      rval(2) = 0;rval(3) = 0;
   case 'arrows' 
      rval(1) = 0;rval(2) = 2;rval(3) = 0;
   case 'none' 
      rval(1) = 0;rval(2) = 0;rval(3) = 3;
   otherwise
      error(['Unknown fieldtype ',ud.o.fieldtype,'.'])
   end          
   
   for i=1:3
      set(ud.h.rad(i),'value',rval(i));
   end  
   set(gcf,'user',ud);
   
elseif strcmp(action,'proceed')
   
   % Proceed connects Setup with the Display window.
   
   ppset = gcf;
   sud = get(ppset,'user');
   sud.o = sud.c;
   set(ppset,'user',sud);
   he = findobj('name','PPLANE6 Equilibrium point data');
   hl = findobj('name','PPLANE6 Linearization');
   close([he;hl]);
   % set([he;hl],'vis','off');
   
   % Some error checking that has to be done no matter what.
   
   WINvect = sud.c.wind;
   if any(isnan(WINvect))
      sud.flag = 0;
      set(ppset,'user',sud);
      errmsg = ['One of the entries defining the display window ',...
            'is not a number.'];
      fprintf('\a')
      errordlg(errmsg,'PPLANE error','on');
      return
   end
   xstr = sud.c.xvar;
   if isempty(xstr)
      sud.flag = 0;
      set(ppset,'user',sud);
      errmsg = 'The first dependent variable needs a name.';
      fprintf('\a')
      errordlg(errmsg,'PPLANE error','on');
      return
   end
   ystr = sud.c.yvar;
   if isempty(ystr)
      sud.flag = 0;
      set(ppset,'user',sud);
      errmsg = 'The second dependent variable needs a name.';
      fprintf('\a')
      errordlg(errmsg,'PPLANE error','on');
      return
   end
   if WINvect(2)<= WINvect(1)
      sud.flag = 0;
      set(ppset,'user',sud);
      errmsg = ['The minimum value of ', xstr,...
            ' must be smaller than the maximum value.'];
      fprintf('\a')
      errordlg(errmsg,'PPLANE error','on');
      return
   end
   if WINvect(4)<= WINvect(3)
      sud.flag = 0;
      set(ppset,'user',sud);
      errmsg = ['The minimum value of ', ystr,...
            ' must be smaller than the maximum value.'];
      fprintf('\a')
      errordlg(errmsg,'PPLANE error','on');
      return
   end
   if isnan(sud.c.npts)
      sud.flag = 0;
      set(ppset,'user',sud);
      errmsg = 'The entry for the number of field points is not a number.';
      fprintf('\a')
      errordlg(errmsg,'PPLANE error','on');
      return
   end
   
   %  sud.flag = 0 if this is the first time through for this equation, 
   %  sud.flag = 1 if only the window dimensions or the field data 
   %  have been changed.
   
   % If sud.flag == 1 we only have to update things.
   
   if (sud.flag == 1)
      Arrflag = sud.c.fieldtype;
      NumbFPts = sud.c.npts;
      ppdisp = findobj('name','PPLANE6 Display');
      dud = get(ppdisp,'user');
      aud = get(dud.axes,'user');
      wind = sud.c.wind(:);
      if (~all(wind == dud.syst.wind(:)))
         dwind = [wind(1); wind(3); -wind(2); -wind(4)];
         aud.DY = [wind(2)-wind(1); wind(4)-wind(3)];
         aud.cwind = dwind - dud.settings.magn*[aud.DY;aud.DY];
         set(dud.axes,'user',aud);
      end
      
      if ~strcmp(Arrflag,dud.syst.fieldtype)
         arr = dud.arr;
         menull = findobj('tag','null');      
         switch Arrflag
         case 'nullclines'
            set([arr.hx;arr.hy;arr.barrows],'vis','on');
            set([arr.lines;arr.arrows],'vis','off');
            set(menull,'enable','off','label','Show nullclines.');        
         case 'lines'
            set(arr.lines,'vis','on');
            set([arr.hx;arr.hy;arr.arrows;arr.barrows],'vis','off');
            set(menull,'enable','on');    
         case 'arrows'
            set(arr.arrows,'vis','on');
            set([arr.lines;arr.hx;arr.hy;arr.barrows],'vis','off');
            set(menull,'enable','on');    
         otherwise
            set([arr.hx;arr.hy;arr.lines;arr.arrows;arr.barrows],'vis','off');
            set(menull,'enable','on');    
         end
         dud.syst.fieldtype = Arrflag;
         set(ppdisp,'user',dud);
      end
      
      if ( (NumbFPts ~= dud.syst.npts) | (any(WINvect ~= dud.syst.wind) ) )
         dud.syst.wind = WINvect;                       
         dud.syst.npts = NumbFPts;
         set(ppdisp,'user',dud);
         pplane6('dirfield',ppdisp);
      end
   else
      sud.flag = 1;
      set(ppset,'user',sud);    
      
      sud = get(ppset,'user');
      %  WINvect = sud.c.wind;
      
      Xname = sud.c.xvar;
      Yname = sud.c.yvar;
      xderivstr = sud.c.xder;
      yderivstr = sud.c.yder;
      pname1 = sud.c.pname1;
      pname2 = sud.c.pname2;
      pname3 = sud.c.pname3;
      pname4 = sud.c.pname4;
      parav1 = sud.c.pval1;
      parav2 = sud.c.pval2;
      parav3 = sud.c.pval3;
      parav4 = sud.c.pval4;
      
      % Convert the parameters to their current values.
      % First remove the blanks.
      
      xderivstr(find(abs(xderivstr)==32))=[];
      yderivstr(find(abs(yderivstr)==32))=[];
      if ~isempty(parav1)
        parav1(find(abs(parav1)==32))=[];
      end
      if ~isempty(parav2)
        parav2(find(abs(parav2)==32))=[];
      end
      if ~isempty(parav3)
        parav3(find(abs(parav3)==32))=[];
      end
      if ~isempty(parav4)
        parav4(find(abs(parav4)==32))=[];
      end
      
      % Next remove the periods inserted by users attempting to make the 
      % function array smart.
      
      l=length(xderivstr);
      for ( k = fliplr(findstr('.',xderivstr)))
         if (find('*/^' == xderivstr(k+1)))
            xderivstr = [xderivstr(1:k-1), xderivstr(k+1:l)];
         end
         l=l-1;
      end
      
      l=length(yderivstr);
      for ( k = fliplr(findstr('.',yderivstr)))
         if (find('*/^' == yderivstr(k+1)))
            yderivstr = [yderivstr(1:k-1), yderivstr(k+1:l)];
         end
         l=l-1;
       end
       
       l=length(parav1);
       for ( k = fliplr(findstr('.',parav1)))
         if (find('*/^' == parav1(k+1)))
           parav1 = [parav1(1:k-1), parav1(k+1:l)];
         end
         l=l-1;
       end
    
       l=length(parav2);
       for ( k = fliplr(findstr('.',parav2)))
         if (find('*/^' == parav2(k+1)))
           parav2 = [parav2(1:k-1), parav2(k+1:l)];
         end
         l=l-1;
       end
        
       l=length(parav3);
       for ( k = fliplr(findstr('.',parav3)))
         if (find('*/^' == parav3(k+1)))
           parav3 = [parav3(1:k-1), parav3(k+1:l)];
         end
         l=l-1;
       end
       
       l=length(parav4);
       for ( k = fliplr(findstr('.',parav4)))
         if (find('*/^' == parav4(k+1)))
           parav4 = [parav4(1:k-1), parav4(k+1:l)];
         end
         l=l-1;
       end
        
       
       % Build strings for the title.
      txderstr = xderivstr;
      tyderstr = yderivstr;

      kxder = find(abs(txderstr)==42);
      txderstr(kxder)=' '*ones(size(kxder));
      txderstr = strrep(txderstr,'-',' - ');
      txderstr = strrep(txderstr,'+',' + ');
      if (abs(txderstr(1)) == 32)
        txderstr = txderstr(2:length(txderstr));
      end
       
      kxder = find(abs(tyderstr)==42);
      tyderstr(kxder)=' '*ones(size(kxder));
      tyderstr = strrep(tyderstr,'-',' - ');
      tyderstr = strrep(tyderstr,'+',' + ');
      if (abs(tyderstr(1)) == 32)
        tyderstr = tyderstr(2:length(tyderstr));
      end
      
      tstr1 = [Xname,' '' = ', txderstr];
      tstr2 = [Yname,' '' = ', tyderstr];
      tstr = str2mat(tstr1,tstr2);
      dud.tstr = tstr;
      pstr1 = {' ';' '};
      pstr2 = {' ';' '};
      
      pstring = cell(4,1);
      pstring{1} = [pname1,' = ',parav1];
      pstring{2} = [pname2,' = ',parav2];
      pstring{3} = [pname3,' = ',parav3];
      pstring{4} = [pname4,' = ',parav4];
      
    if ~isempty(parav1)
      tp1str = parav1;
      
      kxder = find(abs(tp1str)==42);  % Get rid of *s
      tp1str(kxder)=' '*ones(size(kxder));
      tp1str = strrep(tp1str,'-',' - ');  % Extra spaces
      tp1str = strrep(tp1str,'+',' + ');
      if (abs(tp1str(1)) == 32)  % Get rid of starting space
        tp1str = tp1str(2:length(tp1str));
      end
      pstring{1} = [pname1,' = ', tp1str];
    end
    
    if ~isempty(parav2)
      tp2str = parav2;
      
      kxder = find(abs(tp2str)==42);  % Get rid of *s
      tp2str(kxder)=' '*ones(size(kxder));
      tp2str = strrep(tp2str,'-',' - ');  % Extra spaces
      tp2str = strrep(tp2str,'+',' + ');
      if (abs(tp2str(1)) == 32)  % Get rid of starting space
        tp2str = tp2str(2:length(tp2str));
      end
      pstring{2} = [pname2,' = ', tp2str];
    end
    
    if ~isempty(parav3)
      tp3str = parav3;
      
      kxder = find(abs(tp3str)==42);  % Get rid of *s
      tp3str(kxder)=' '*ones(size(kxder));
      tp3str = strrep(tp3str,'-',' - ');  % Extra spaces
      tp3str = strrep(tp3str,'+',' + ');
      if (abs(tp3str(1)) == 32)  % Get rid of starting space
        tp3str = tp3str(2:length(tp3str));
      end
      pstring{3} = [pname3,' = ', tp3str];
    end
    
    if ~isempty(parav4)
      tp4str = parav4;
      
      kxder = find(abs(tp4str)==42);  % Get rid of *s
      tp4str(kxder)=' '*ones(size(kxder));
      tp4str = strrep(tp4str,'-',' - ');  % Extra spaces
      tp4str = strrep(tp4str,'+',' + ');
      if (abs(tp4str(1)) == 32)  % Get rid of starting space
        tp4str = tp4str(2:length(tp4str));
      end
      pstring{4} = [pname4,' = ', tp4str];
    end
   
    % Get ready to do some error trapping.
    
    SS = warning;
    warning off
    XxXxXx = WINvect(1) + rand*(WINvect(2)-WINvect(1));
    YyYyYy = WINvect(3) + rand*(WINvect(4)-WINvect(3));
    err = 0;

      % Now we remove the backslashes (\) used to get Greek into the
      % labels. 
      txname = Xname;
      tyname = Yname;    
      xderivstr(find(abs(xderivstr)==92))=[];
      yderivstr(find(abs(yderivstr)==92))=[];
      Xname(find(abs(Xname)==92))=[];
      Yname(find(abs(Yname)==92))=[];
      
      eval([Xname,'=XxXxXx;'],'err = 1;');
      if err
         sud.flag = 0;
         set(ppset,'user',sud);
         errmsg = ['"',xstr, '" is not a valid variable name in MATLAB.'];
         fprintf('\a')
         errordlg(errmsg,'PPLANE error','on');
         return
      end
      err = 0;
      eval([Yname,'=YyYyYy;'],'err = 1;');
      if err
         sud.flag = 0;
         set(ppset,'user',sud);
         errmsg = ['"',ystr, '" is not a valid variable name in MATLAB.'];
         fprintf('\a')
         errordlg(errmsg,'PPLANE error','on');
         return
      end
      
    
    % Replace the parameters/expressions with their values.
    pflag = zeros(1,4);
    perr = [];
    if ~isempty(pname1)
      if isempty(parav1) 
        perr = sud.h.pval1;
      else 
        if isempty(str2num(parav1)) % This is an expression.
          tparav1 = parav1;
          tparav1(find(abs(tparav1)==92))=[];
          err = 0; pval = '';
          eval(['pval = ',tparav1,';'],'err=1;');
          if (err | isempty(pval))
            errmsg = ['The expression for ',pname1,' is not valid.'];
            fprintf('\a')
            errordlg(errmsg,'PPLANE6 error','on');
            warning(SS)
            return
          end
        end
        xxderivstr = pplane6('paraeval',pname1,parav1,xderivstr);
        yyderivstr = pplane6('paraeval',pname1,parav1,yderivstr);
        if (~strcmp(xxderivstr,xderivstr) | ~strcmp(yyderivstr,yderivstr) )
          pflag(1) = 1;
          xderivstr = xxderivstr;
          yderivstr = yyderivstr;
        end
      end
    end

    if ~isempty(pname2)
      if isempty(parav2) 
        perr = sud.h.pval2;
      else 
        if isempty(str2num(parav2)) % This is an expression.
          tparav2 = parav2;
          tparav2(find(abs(tparav2)==92))=[];
          err = 0; pval = '';
          eval(['pval = ',tparav2,';'],'err=1;');
          if (err | isempty(pval))
            errmsg = ['The expression for ',pname2,' is not valid.'];
            fprintf('\a')
            errordlg(errmsg,'PPLANE6 error','on');
            warning(SS)
            return
          end
        end
        xxderivstr = pplane6('paraeval',pname2,parav2,xderivstr);
        yyderivstr = pplane6('paraeval',pname2,parav2,yderivstr);
        if (~strcmp(xxderivstr,xderivstr) | ~strcmp(yyderivstr,yderivstr) )
          pflag(2) = 1;
          xderivstr = xxderivstr;
          yderivstr = yyderivstr;
        end
      end
    end

    if ~isempty(pname3)
      if isempty(parav3) 
        perr = sud.h.pval3;
      else 
        if isempty(str2num(parav3)) % This is an expression.
          tparav3 = parav3;
          tparav3(find(abs(tparav3)==92))=[];
          err = 0; pval = '';
          eval(['pval = ',tparav3,';'],'err=1;');
          if (err | isempty(pval))
            errmsg = ['The expression for ',pname3,' is not valid.'];
            fprintf('\a')
            errordlg(errmsg,'PPLANE6 error','on');
            warning(SS)
            return
          end
        end
        xxderivstr = pplane6('paraeval',pname3,parav3,xderivstr);
        yyderivstr = pplane6('paraeval',pname3,parav3,yderivstr);
        if (~strcmp(xxderivstr,xderivstr) | ~strcmp(yyderivstr,yderivstr) )
          pflag(3) = 1;
          xderivstr = xxderivstr;
          yderivstr = yyderivstr;
        end
      end
    end

    if ~isempty(pname4)
      if isempty(parav4) 
        perr = sud.h.pval4
      else 
        if isempty(str2num(parav4)) % This is an expression.
          tparav4 = parav4;
          tparav4(find(abs(tparav4)==92))=[];
          err = 0; pval = '';
          eval(['pval = ',tparav4,';'],'err=1;');
          if (err | isempty(pval))
            errmsg = ['The expression for ',pname4,' is not valid.'];
            fprintf('\a')
            errordlg(errmsg,'PPLANE6 error','on');
            warning(SS)
            return
          end
        end
        xxderivstr = pplane6('paraeval',pname4,parav4,xderivstr);
        yyderivstr = pplane6('paraeval',pname4,parav4,yderivstr);
        if (~strcmp(xxderivstr,xderivstr) | ~strcmp(yyderivstr,yderivstr) )
          pflag(4) = 1;
          xderivstr = xxderivstr;
          yderivstr = yyderivstr;
        end
      end
    end

       
      % We have to make the derivative strings array smart.
      
      l = length(xderivstr);
      for (k=fliplr(find((xderivstr=='^')|(xderivstr=='*')|(xderivstr=='/'))))
         xderivstr = [xderivstr(1:k-1) '.' xderivstr(k:l)];
         l = l+1;
      end
      
      l = length(yderivstr);
      for (k=fliplr(find((yderivstr=='^')|(yderivstr=='*')|(yderivstr=='/'))))
         yderivstr = [yderivstr(1:k-1) '.' yderivstr(k:l)];
         l = l+1;
      end
      
      % Some more error trapping.
      
      err = 0;res = 1;
      eval(['res = ',xderivstr, ';'],'err = 1;');
      if err | isempty(res)
         if isempty(perr)
            errmsg = ['The first differential equation ',...
                  'is not entered correctly.'];
         else
            errstr1 = ['The first differential equation ',...
                  'does not evaluate correctly.'];
            errstr2 = ['At least one of the parameter values is not ',...
                  'a number.'];
            errmsg = str2mat(errstr1,errstr2);
            set(perr,'string','?');
         end
         sud.flag = 0;
         set(ppset,'user',sud);
         fprintf('\a')
         errordlg(errmsg,'PPLANE error','on');
         return;
       end

      err = 0;res = 1;
      eval(['res = ',yderivstr, ';'],'err = 1;');
      if err | isempty(res)
         if isempty(perr)
            errmsg = ['The second differential equation ',...
                  'is not entered correctly.'];
         else
            errstr1 = ['The second differential equation ',...
                  'does not evaluate correctly.'];
            errstr2 = ['At least one of the parameter values is not ',...
                  'a number.'];
            errmsg = str2mat(errstr1,errstr2);
            set(perr,'string','?');
         end
         sud.flag = 0;
         set(ppset,'user',sud);
         fprintf('\a')
         errordlg(errmsg,'PPLANE error','on');
         return;
      end
      
      % If an old function m-file exists delete it, and then build a new one.
      
      %    if (~strcmp(dfcn,'') & exist(dfcn)==2) delete([dfcn,'.m']);end
      tee = clock;
      tee = ceil(tee(6)*100);
      dfcn=['pptp',num2str(tee)];
      fcnstr = ['function YYyYypr = ',dfcn,'(t,YyYy)\n\n'];
      commstr = '%%%% Created by PPLANE6\n\n';
      varstr = [Xname,' = YyYy(1,:);', Yname,' = YyYy(2,:);\n\n'];
      lenstr = ['l = length(YyYy(1,:));\n'];
      derstr1 = ['XxXxxpr = ', xderivstr,';\n'];
      derstr2 = ['if (length(XxXxxpr) < l) XxXxxpr = XxXxxpr*ones(1,l);end\n'];
      derstr3 = ['YyYyypr = ', yderivstr,';\n'];
      derstr4 = ['if (length(YyYyypr) < l) YyYyypr = YyYyypr*ones(1,l);end\n'];
      derstr5 = 'YYyYypr = [XxXxxpr;YyYyypr];\n';
      ppf = fopen([tempdir,dfcn,'.m'],'w');
      
      fprintf(ppf,fcnstr);
      fprintf(ppf,commstr);
      fprintf(ppf,varstr);
      fprintf(ppf,lenstr);
      fprintf(ppf,derstr1);
      fprintf(ppf,derstr2);
      fprintf(ppf,derstr3);
      fprintf(ppf,derstr4);
      fprintf(ppf,derstr5);
      fclose(ppf);
      
      
      
      % Find PPLANE6 Display if it exists.      
      % If PPLANE6 Display exists, update it.  If it does not build it.
      
      ppdisp = findobj('name','PPLANE6 Display');
      if (~isempty(ppdisp))
        figure(ppdisp);
        dud = get(ppdisp,'user');
        dud.syst = sud.c;
        dud.settings = sud.settings;
        dfcnn = dud.function;
          if  exist(dfcnn)==2, delete([tempdir,dfcnn,'.m']);end
          xmstr = [txname,' vs. t'];
          ymstr = [tyname,' vs. t'];
          set(dud.menu(3),'label',xmstr);
          set(dud.menu(5),'label',ymstr);
          menull = findobj('tag','null');
          if ~isempty(menull)
            delete(get(menull,'user'));
            set(menull,'user',[]);      
          end
      else
        ppdisp = figure('name','PPLANE6 Display',...
            'numb','off',...
            'interrupt','on',...
            'visible','off',...
            'tag','PPLANE6');
        pplane6('figdefault',ppdisp);
        dud = get(ppdisp,'user');
         dud.syst = sud.c;
         switch dud.syst.name
          case 'pendulum'
           dud.level = 'omega^2 - 2*cos(theta)';
          otherwise
           dud.level = ' ';
         end
         dud.settings = sud.settings;
         dud.egg = sud.egg;      
         dud.contours = zeros(0,1);
         fs = dud.fontsize;
         ssize = dud.ssize;
         r = ssize/10;
         ppaxw = 437*1.2;       % Default axes width
         ppaxh = 315*1.2;       % Default axes height
         ppaxl = 45*1.2;        % Default axes left
         buttw = 40*1.2;     % Default button width
         titleh = 45;    % Default title height.  This is changed later.
         nframeh = 70;   % Default notice frame height
         ppaxb = 4+nframeh+35;
         bottomedge = 38;
         ppdh = bottomedge + nframeh + ppaxh + titleh;
         uni = get(0,'units');
         set(0,'units','pixels');
         ss = get(0,'screensize');
         set(0,'units',uni);
         sw = ss(3);sh = ss(4);
         bottom = 10;
         if r*ppdh > sh -bottom -35;
            r = (sh-bottom-35)/ppdh;
            fs = 10*r;
            lw = 0.5*r;
            set(gcf,'defaultaxesfontsize',fs,'defaultaxeslinewidth',lw);
            set(gcf,'defaulttextfontsize',fs);
            set(gcf,'defaultlinelinewidth',lw);
            set(gcf,'defaultuicontrolfontsize',fs*0.9);
         end
         
         % Set up the bulletin window.
         
         nframe = uicontrol('style','frame','visible','on');
         nstr = {'More';'than';'five';'lines';'of text'};
         dud.notice = uicontrol('style','text',...
            'horiz','left',...
            'string',nstr,'visible','on');
         ext = get(dud.notice,'extent');
         nframeh = ext(4)+2;
         
         
         titleh = r*titleh;
         ppaxl = r*ppaxl;
         ppaxw = r*ppaxw;
         ppaxh = r*ppaxh;
         ppaxb = nframeh+r*bottomedge;
         buttw = r*buttw;
         butth = fs+10*r;
         buttl = ppaxl + ppaxw + 5;
         buttsep = (ppaxh - butth)/2;
         
         % Set up the plot axes.
         
         dud.axes = axes('units','pix',...
            'position',[ppaxl,ppaxb,ppaxw,ppaxh],...
            'next','add',...
            'box','on',...
            'interrupt','on',...
            'xgrid','on',...
            'ygrid','on',...
            'drawmode','fast',...
            'visible','off',...
            'tag','display axes');
         
         % Set up the title.
         
         dud.title.axes = axes('box','off','xlim',[0 1],'ylim',[0 1],...
            'units','pix','vis','off','xtick',[-1],'ytick',[-1],...
            'xticklabel','','yticklabel','');
         
         dud.title.eq = text(0.01,0.5,' ','vert','middle');
         dud.title.p1 = text(0.75,0.5,' ','vert','middle');
         dud.title.p2 = text(0.65,0.5,' ','vert','middle');
         tstr = {'x_2';'y^2'};
         set(dud.title.eq,'string',tstr,'units','pix');
         ext = get(dud.title.eq ,'extent');
         titleh = ext(4)+15*r;
         set(dud.title.eq,'units','data');
         taxpos = [ppaxl,ppaxb+ppaxh,ppaxw,titleh];
         set(dud.title.axes,'pos',taxpos,'color',get(gcf,'color'));
         
         % Finish the positions.
         
         ppdw = buttl + buttw +5;
         ppdh = ppaxb+ppaxh+titleh;
         set(nframe,'pos',[10,1,ppdw-20,nframeh]);
         set(dud.notice,'pos',[15,1,ppdw-30,nframeh-2],...
            'string',{' ';' ';' ';' ';' '});
         
         ppdleft = max((sw-ppdw)/2,sw-ppdw-60);
         ppdbot = sh - ppdh - 35;
         ppdpos = [ppdleft,ppdbot,ppdw,ppdh];
         set(ppdisp,'resize','on');
         set(ppdisp,'pos',ppdpos);
         
         Arrflag = sud.c.fieldtype;
         
         % Set up the buttons
         
         stopstr = 'aud = get(gca,''user'');aud.stop = 4;set(gca,''user'',aud);';
         
         dbutt(1) = uicontrol('style','push',...
            'pos',[buttl,ppaxb+2*buttsep,buttw,butth],...
            'string','Stop','call',stopstr,'vis','off','tag','stop');
         
         dbutt(2) = uicontrol('style','push',...
            'pos',[buttl,ppaxb,buttw,butth],...
            'string','Quit',...
            'call','pplane6(''quit'')','visible','off');
         
         dbutt(3) = uicontrol('style','push',...
            'pos',[buttl,ppaxb+buttsep,buttw,butth],...
            'string','Print',...
            'call','pplane6(''print'')','visible','off');       
         
         dud.butt = dbutt;
         
         % Menus and Toolbar
         
         hhsetup = get(0,'showhiddenhandles');
         set(0,'showhiddenhandles','on');

         % Configure the Toolbar.
         
         fixtb = ['set(gcbo,''state'',''off'');'];
         
         set(ppdisp,'ToolBar','none');
         
         % Menus
         
         tmenu = findobj(ppdisp,'label','&Tools');
         delete(tmenu);
         
         
         % File menu
         
         fmenu = findobj(ppdisp,'label','&File',...
                         'pos',1);  
         delete(findobj(fmenu,'label','&New Figure'));
         delete(findobj(fmenu,'label','&Open...'));
         delete(findobj(fmenu,'label','&Close'));
         set(findobj(fmenu,'label','&Save'),...
             'pos',1,'separator','off');
         set(findobj(fmenu,'label','Save &As...'),...
             'pos',2);
         set(findobj(fmenu,'label','&Export...'),...
             'pos',3);
         delete(findobj(fmenu,'label','Pre&ferences...'));
         set(findobj(fmenu,'label','Pa&ge Setup...'),'pos',4);
         set(findobj(fmenu,'label','Print Set&up...'),'pos',5);
         set(findobj(fmenu,'label','Print Pre&view...'),'pos',6);
         set(findobj(fmenu,'label','&Print...'),'pos',7);
         mequit = uimenu(fmenu,'label','Quit PPLANE6',...
            'call','pplane6(''quit'')','separator','on');
  
         % Edit menu
         
         emenu = findobj(ppdisp,'label','&Edit',...
                         'pos',2); 
         menu(2) = uimenu(emenu,'label','Zoom in.',...
                          'call','pplane6(''zoomin'')',...
                          'pos',1);
         
         zsqmenu = uimenu(emenu,'label','Zoom in square.',...
                          'call','pplane6(''zoominsq'')',...
                          'pos',2);
         
         zbmenu = uimenu(emenu,'label','Zoom back.','call',...
                         'pplane6(''zoomback'')',...
                         'enable','off','tag','zbmenu',...
                         'pos',3);

         medallsol = uimenu(emenu,'label','Erase all solutions.',...
                            'call','pplane6(''dallsol'')',...
                            'separator','on','pos',4);
         
         medallep = uimenu(emenu,'label','Erase all equilibrium points.',...
                           'call','pplane6(''dallep'')',...
                           'separator','off',...
                           'pos',5);
         
         medalllev = uimenu(emenu,'label','Erase all level curves.',...
                            'call','pplane6(''dalllev'')',...
                            'separator','off',...
                            'pos',6);
         
         medall = uimenu(emenu,'label','Erase all graphics objects.',...
                         'call','pplane6(''dall'')',...
                         'separator','off',...
                         'pos',7);
         
         medel = uimenu(emenu,'label','Delete a graphics object.',...
                        'call','pplane6(''delete'')',...
                        'visible','on',...
                        'pos',8);
         
         menutext = uimenu(emenu,...
                           'label','Enter text on the Display Window.',...
                           'call','pplane6(''text'')',...
                           'separator','on',...
                           'pos',9);
         set(findobj(emenu,'label','&Undo'),'separator','on',...
                           'pos',10);
         set(findobj(emenu,'label','Cu&t'),'pos',11);
         set(findobj(emenu,'label','&Copy'),'pos',12);
         set(findobj(emenu,'label','&Paste'),'pos',13);
         set(findobj(emenu,'label','Clea&r'),'pos',14);
         set(findobj(emenu,'label','&Select All'),'pos',15);
         set(findobj(emenu,'label','Copy &Figure'),'pos',16);
         set(findobj(emenu,'label','Copy &Options'),'pos',17);
         set(findobj(emenu,'label','F&igure Properties'),'pos',18);
         set(findobj(emenu,'label','&Axes Properties'),'pos',19);
         set(findobj(emenu,'label','C&urrent Object Properties'),'pos',20);
         
         % Graph menu
         
         megraph  = uimenu('label','Graph','visible','off','pos',4);
         menu(3) = uimenu(megraph,'label',[txname,' vs. t'],...
            'call','pplane6(''plotxy'',1)');
         
         menu(5) = uimenu(megraph,'label',[tyname,' vs. t'],...
            'call','pplane6(''plotxy'',2)');
         
         meplot3 = uimenu(megraph,'label','Both',...
            'call','pplane6(''plotxy'',3)');
         
         meplot4 = uimenu(megraph,'label','3 D',...
            'call','pplane6(''plotxy'',4)');
         
         meplot5 = uimenu(megraph,'label','Composite',...
            'call','pplane6(''plotxy'',5)');
         
         % Solutions menu
         
         solmenu = uimenu('label','Solutions','pos',3);
         menukey = uimenu(solmenu,'label','Keyboard input.','call',...
            'pplane6(''kbd'')');
         
         mesev   = uimenu(solmenu,'label','Plot several solutions.',...
            'call','pplane6(''several'')');
         
         meeqpt  = uimenu(solmenu,'label','Find an equilibrium point.',...
            'call','pplane6(''eqpt'')','separator','on');
         
         menu(4) = uimenu(solmenu,...
            'label','List computed equilibrium points.',...
            'call','pplane6(''eqptlist'')');
         
         mestunst= uimenu(solmenu,...
                          'label','Plot stable and unstable orbits.',...
                          'call','pplane6(''stunst'')','interrupt','on');
         
         nullcall = ['me = gcbo;',...
               'dud = get(gcf,''user'');',...
               'handx = [dud.arr.hx; dud.arr.hy];',...  
               'handr = [dud.arr.hr; dud.arr.hth];',... 
               'lab = get(me,''label'');',...
               'switch lab,',...
               '  case ''Show nullclines.'',',...
               '    set(handx,''vis'',''on'');',...
               '    set(handr,''vis'',''off'');',...
               '    set(me,''label'',''Hide nullclines.'');',...
               '    set(findobj(''tag'',''rnull''),''label'',''Plot polar nullclines.'');',...
               '  case ''Hide nullclines.'','...
               '    set(handx,''vis'',''off'');',...
               '    set(me,''label'',''Show nullclines.'');',...
               'end'];
         
         rnullcall = ['me = gcbo;',...
               'dud = get(gcf,''user'');',...
               'handx = [dud.arr.hx; dud.arr.hy];',...      
               'handr = [dud.arr.hr; dud.arr.hth];',... 
               'lab = get(me,''label'');',...
               'switch lab,',...
               '  case ''Plot polar nullclines.'',',...
               '    set(handr,''vis'',''on'');',...
               '    set(handx,''vis'',''off'');',...
               '    set(me,''label'',''Delete polar nullclines.'');',...
               '    set(findobj(''tag'',''null''),''label'',''Plot nullclines.'');',...
               '  case ''Delete polar nullclines.'','...
               '    set(handr,''vis'',''off'');',...
               '    set(me,''label'',''Plot polar nullclines.'');',...
               'end'];
         
         menunull = uimenu(solmenu,'label','Show nullclines.',...
            'call',nullcall,'separator','on','tag','null');
         
         menulevel = uimenu(solmenu,'label','Plot level curves.',...
            'call','pplane6(''level'')','separator','off','tag','level');

         if dud.egg
            menurnull = uimenu(solmenu,'label','Plot polar nullclines.',...
               'call',rnullcall,'separator','off','tag','rnull');
            metest = uimenu(solmenu,'label','Test case',...
               'call','pplane6(''test case'')',...
               'separator','on','tag','testcase');
            
         end      
         
         % Options menu
         
         menu(1) = uimenu('label','Options','visible','off','pos',5);
         meset   = uimenu(menu(1),'label','Settings.',...
                          'call','pplane6(''settings'')');
         
         mesolve = uimenu(menu(1),'label','Solver.');
         
         solverstr = ['ud = get(gcf,''user'');',...
               'me = gcbo;',...
               'meud = get(me,''user'');',...
               'ud.settings.refine = meud.refine;',...
               'ud.settings.tol = meud.tol;',...
               'ud.settings.solver = meud.solver;',...
               'ud.settings.stepsize = meud.stepsize;',...
               'set(ud.solver,''checked'',''off'');',...
               'set(me,''checked'',''on'');',...
               'set(gcf,''user'',ud);',...
               'ppset = findobj(''name'',''PPLANE6 Setup'');',...
               'sud = get(ppset,''user'');',...
               'sud.settings = ud.settings;',...
               'set(ppset,''user'',sud);',...
               'pplane6(''settings'');'];
         
      solver = dud.settings.solver;
      dpset.refine = 8;
      dpset.tol = dud.settings.tol;
      dpset.solver = 'Dormand Prince';
      dpset.stepsize = dud.settings.stepsize;
      dpset.hmax = 0;
      if strcmp(solver,'Dormand Prince')
        dpch = 'on';
      else
        dpch = 'off';
      end
      rk4set.refine = 1;
      rk4set.tol = dud.settings.tol;
      rk4set.solver = 'Runge-Kutta 4';
      rk4set.stepsize = dud.settings.stepsize;
      rk4set.hmax = 0;
      if strcmp(solver,'Runge-Kutta 4')
        rk4ch = 'on';
      else
        rk4ch = 'off';
      end
      ode15sset.refine = 1;
      ode15sset.tol = dud.settings.tol;
      ode15sset.solver = 'ode15s';
      ode15sset.stepsize = dud.settings.stepsize;
      ode15sset.hmax = 0;
      if strcmp(solver,'ode15s')
        ode15sch = 'on';
      else
        ode15sch = 'off';
      end
      ode23sset.refine = 1;
      ode23sset.tol = dud.settings.tol;
      ode23sset.solver = 'ode23s';
      ode23sset.stepsize = dud.settings.stepsize;
      ode23sset.hmax = 0;
      if strcmp(solver,'ode23s')
        ode23sch = 'on';
      else
        ode23sch = 'off';
      end
      ode113set.refine = 1;
      ode113set.tol = dud.settings.tol;
      ode113set.solver = 'ode113';
      ode113set.stepsize = dud.settings.stepsize;
      ode113set.hmax = 0;
      if strcmp(solver,'ode113')
        ode113ch = 'on';
      else
        ode113ch = 'off';
      end
      ode23set.refine = 1;
      ode23set.tol = dud.settings.tol;
      ode23set.solver = 'ode23';
      ode23set.stepsize = dud.settings.stepsize;
      ode23set.hmax = 0;
      if strcmp(solver,'ode23')
        ode23ch = 'on';
      else
        ode23ch = 'off';
      end
      ode45set.refine = 8;
      ode45set.tol = dud.settings.tol;
      ode45set.solver = 'ode45';
      ode45set.stepsize = dud.settings.stepsize;
      ode45set.hmax = 0;
      if strcmp(solver,'ode45')
        ode45ch = 'on';
      else
        ode45ch = 'off';
      end
         dud.solver(1) = uimenu(mesolve,'label','Dormand Prince',...
            'checked',dpch,...
            'call',solverstr,'user',dpset);
         
         dud.solver(2) = uimenu(mesolve,'label','ode45',...
            'checked',ode45ch,...
            'call',solverstr,'user',ode45set);
         
         dud.solver(3) = uimenu(mesolve,'label','ode23',...
            'checked',ode23ch,...
            'call',solverstr,'user',ode23set);
         
         dud.solver(4) = uimenu(mesolve,'label','ode113',...
            'checked',ode113ch,...
            'call',solverstr,'user',ode113set);
         
         dud.solver(5) = uimenu(mesolve,'label','ode15s',...
            'checked',ode15sch,...
            'call',solverstr,'user',ode15sset);
         
         dud.solver(6) = uimenu(mesolve,'label','ode23s',...
            'checked',ode23sch,...
            'call',solverstr,'user',ode23sset);
         
         dud.solver(7) = uimenu(mesolve,'label','Runge-Kutta 4',...
            'checked',rk4ch,...
            'call',solverstr,'user',rk4set);
        
         if ~dud.egg
            set(dud.solver(2:5),'vis','off');
         end
         
         plotch = [
             'dud = get(gcf,''user'');',...
             'aud = get(dud.axes,''user'');',...
             'if aud.plot,',...
             '   aud.plot = 0;',...
             '   set(gcbo,''label'',''Plot while computing'');',...
             'else,',...
             '   aud.plot = 1;',...
             '   set(gcbo,''label'',''Do not plot while computing'');',...
             'end,',...
             'set(dud.axes,''user'',aud);'];
         
         medir = uimenu(menu(1),'label','Solution direction.');
         
         directionstr = ['ud = get(gcf,''user'');',...
               'me = gcbo;',...
               'ud.dir = get(me,''user'');',...
               'set(ud.direction,''checked'',''off'');',...
               'set(me,''checked'',''on'');',...
               'set(gcf,''user'',ud);'];
         
         dud.direction(1) = uimenu(medir,'label','Both',...
            'checked','on',...
            'user',0,...
            'call',directionstr);
         dud.dir = 0;
         
         dud.direction(2) = uimenu(medir,'label','Forward',...
            'user',1,...
            'call',directionstr);
         
         dud.direction(3) = uimenu(medir,'label','Back',...
            'user',-1,...
            'call',directionstr);
         
         meplot = uimenu(menu(1),'label','Do not plot while computing',...
            'call',plotch,'separator','on');
         
         menu(6) = uimenu(menu(1),'label','Make the Display Window inactive.',...
            'call','pplane6(''hotcold'')','separator','on');
         
         dud.menu = menu;

         % View menu
         
         set(findobj(gcf,'label','&View'),'pos',6);
         set(findobj(gcf,'label','&Figure Toolbar'),...
             'call','pplane6(''showbar'')');
         
         set(0,'showhiddenhandles',hhsetup);
         
         set(gcf,'WindowButtonDownFcn','pplane6(''down'')');
         hh1 = [dud.axes,dud.title.axes,nframe,dud.notice,dbutt([1 2 3])];
         set(hh1,'units','norm');
         hh2 = [nframe,dud.notice,dbutt(2:3),dud.axes,dud.menu(1),meplot,megraph];
         set(hh2,'visible','on');
         
         set(ppdisp,'vis','on');
         dud.printstr = 'print -noui';
      end   % if (~isempty(ppdisp))  & else
      ppdispa = dud.axes;
      axes(ppdispa);
      cla
      xlabel(txname);
      ylabel(tyname);
      % Initialize the window matrix.
      
      set(findobj('tag','zbmenu'),'enable','off');
    tstr1 = [txname,' '' = ', txderstr];
    tstr2 = [tyname,' '' = ', tyderstr];
    tstr = str2mat(tstr1,tstr2);
    dud.tstr = tstr;
      
      
      
      k = find(pflag);
      if ~isempty(k)
         lk = length(k);
         switch lk
         case 1
            pstr1 = [pstring(k);{' '}];
         case 2
            pstr1 = pstring(k);
         case 3
            pstr1 = pstring(k([2,3]));
            pstr2 = [pstring(k(1));{' '}];
         case 4
            pstr1 = pstring(k([2,4]));
            pstr2 = pstring(k([1,3]));
         end
      end
      set(dud.title.eq,'string',tstr);
      set(dud.title.p1,'string',pstr1);
      ext = get(dud.title.p1,'extent');
      pos = get(dud.title.p1,'pos');
      p1 = min(.9, .93 - ext(3));
      pos(1) = p1;
      set(dud.title.p1,'pos',pos);
      set(dud.title.p2,'string',pstr2); 
      ext = get(dud.title.p2,'extent');
      pos = get(dud.title.p2,'pos');
      pos(1) = min(.8, p1 - ext(3)-0.02);
      set(dud.title.p2,'pos',pos);
      
      % Initialize important information as user data.
      
      dud.function = dfcn;
      dud.solhand = []; % Handles to solution curves.
      dud.ephand = [];  % Handles to equilibrium points.
      dud.arr = [];     % Handles for the direction and vector fields.
      dud.eqpts = [];   % Equilibrium point data.
      dud.wmat = [];
      dud.color = sud.color;
      set(ppdisp,'user',dud);
      if strcmp(dud.syst.fieldtype,'nullclines')
         menunull = findobj('tag','null');      
         set(menunull,'enable','off');
      end      
      ud.y = zeros(2,1);
      ud.i = 0;
      ud.line = 0;
      wind = dud.syst.wind(:);
      dwind = [wind(1); wind(3); -wind(2); -wind(4)];
      ud.DY = [wind(2)-wind(1); wind(4)-wind(3)];
      ud.cwind = dwind - dud.settings.magn*[ud.DY;ud.DY];
      ud.R = zeros(2,2);
      ud.rr = zeros(2,2);
      ud.perpeps = 0;
      ud.paraeps = 0;
      ud.sinkeps = 0;
      ud.turn = zeros(2,10);
      ud.tk = 0;
      ud.stop = 0;
      ud.gstop = 1;
      ud.plot = 1;
      set(dud.axes,'user',ud);
      tc = findobj('tag','testcase');
      if ~isempty(tc)    
         if strcmp(dud.syst.name,'default system')
            set(tc,'vis','on');
         else
            set(tc,'vis','off');
         end
      end    
      ppkbd = findobj('name','PPLANE6 Keyboard input','vis','on');
      if ~isempty(ppkbd),pplane6('kbd'),end
      pplevel = findobj('name','PPLANE6 Level sets');
      if ~isempty(pplevel),delete(pplevel),end
      set(dud.title.axes,'handle','off');  
      pplane6('dirfield',ppdisp);               
   end
   
elseif strcmp(action,'linear')
   
   % Initialize linearization window.
   
   % Linear takes the information from the EQPT window and initializes
   % the Linear Display window if it already exists.  If the Linear 
   % Display window does not exist, it builds one.
   
   ppeqpt = gcf;
   
   % Get the information from PPLANE6 Equilibrium ...
   
   sud = get(ppeqpt,'user');
   WINvect = [-1 1 -1 1];
   jac = sud.jac;
   type = sud.type;
   vectors = sud.vectors;
   ppdisp = findobj('name','PPLANE6 Display');
   pdud = get(ppdisp,'user');
   settings = pdud.settings;
   system = sud.system;
   
   % Find PPLANE6 Linearization if it exists.   
   % If PPLANE6 Linearization exists, update it.  If it does not build it.
   
   pplin= findobj('name','PPLANE6 Linearization');
   if (~isempty(pplin))
      figure(pplin);
      dud = get(pplin,'user');
      dud.syst = system;
      dud.settings = settings;
      dfcn = dud.function;
   else
      pplin = figure('name','PPLANE6 Linearization',...
         'numb','off',...
         'interrupt','on',...
         'visible','off',...
         'tag','PPLANE6');
      pplane6('figdefault',pplin);
      dud = get(pplin,'user');
      dud.dir = 0;
      dud.syst = system;
      dud.settings = settings;
      dfcn = '';
      fs = dud.fontsize;
      ssize = dud.ssize;
      r = ssize/10;
      ppaxw = 300;      % Default axes width
      ppaxh = 300;      % Default axes height
      ppaxl = 45;       % Default axes left
      buttw = 40;     % Default button width
      titleh = 45;    % Default title height
      ppaxb = 35;
      ppdh = ppaxb + ppaxh + titleh;
      uni = get(0,'units');
      set(0,'units','pixels');
      ss = get(0,'screensize');
      set(0,'units',uni);
      sw = ss(3);sh = ss(4);
      if r*ppdh > sh -80;
         r = (sh-80)/ppdh;
         fs = fs*r;
         lw = 0.5*r;
         set(gcf,'defaultaxesfontsize',fs,'defaultaxeslinewidth',lw);
         set(gcf,'defaulttextfontsize',fs);
         set(gcf,'defaultlinelinewidth',lw);
         set(gcf,'defaultuicontrolfontsize',fs*0.9);
      end
      
      axpos = r*[ppaxl,ppaxb,ppaxw,ppaxh];
      
      % Set up the plot axes.
      
      dud.axes = axes('units','pix',...
         'position',axpos,...
         'next','add',...
         'box','on',...
         'interrupt','on',...
         'xgrid','on',...
         'ygrid','on',...
         'drawmode','fast',...
         'visible','off',...
         'tag','linear axes');
      
      % Set up the title.
      
      dud.title.axes = axes('box','off','xlim',[0 1],'ylim',[0 1],...
         'units','pix','vis','off','xtick',[-1],'ytick',[-1],...
         'xticklabel','','yticklabel','');
      
      dud.title.eq = text(0.07,0.5,' ','vert','middle');
      dud.title.p1 = text(0.75,0.5,' ','vert','middle');
      dud.title.p2 = text(0.65,0.5,' ','vert','middle');
      tstr = {'x_2';'y^2'};
      set(dud.title.eq,'string',tstr,'units','pix');
      ext = get(dud.title.eq ,'extent');
      titleh = ext(4)+15*r;
      set(dud.title.eq,'units','data');
      taxpos = r*[ppaxl,ppaxb+ppaxh,ppaxw,titleh];
      set(dud.title.axes,'pos',taxpos,'color',get(gcf,'color'));
      
      % Finish the positions.
      
      %                 buttw = r*buttw;
      %                 butth = fs+10*r;
      %                 buttl = ppaxl + ppaxw + 5;
      ppdw = r*(ppaxl + ppaxw + 35);
      ppdh = r*(ppaxb+ppaxh)+titleh;
      
      ppdleft = sw-ppdw-60;
      ppdbot = 60;
      ppdpos = [ppdleft,ppdbot,ppdw,ppdh];
      set(pplin,'resize','on');
      set(pplin,'pos',ppdpos);
      
      Arrflag = system.fieldtype;
      
      axpos = r*[ppaxl,ppaxb,ppaxw,ppaxh];
      
      stopstr = 'aud = get(gca,''user'');aud.stop = 4;set(gca,''user'',aud);';
      
      stoppos = [axpos(1)+axpos(3)-r*10, axpos(2)+axpos(4)+r*10, r*40,fs+10*r];    
      
      dud.butt  = uicontrol('style','push',...
         'pos',stoppos,...
         'string','Stop','call',stopstr,'vis','off','tag','stop');
      
      hhsetup = get(0,'showhiddenhandles');
      set(0,'showhiddenhandles','on');

      % Configure the Toolbar.
      
      set(pplin,'ToolBar','none');

      tmenu = findobj(gcf,'label','&Tools'); 
      delete(tmenu);
      
      % File menu
      
      fmenu = findobj(gcf,'label','&File');  
      delete(findobj(fmenu,'label','&New Figure'));
      delete(findobj(fmenu,'label','&Open...'));
      delete(findobj(fmenu,'label','Pre&ferences...'));
      set(findobj(fmenu,'label','&Close'),'pos',1);
      set(findobj(fmenu,'label','&Save'),'pos',2,...
                        'separator','off');
      set(findobj(fmenu,'label','Save &As...'),'pos',3);
      set(findobj(fmenu,'label','&Export...'),...
          'pos',4);
      delete(findobj(fmenu,'label','Pre&ferences...'));
      set(findobj(fmenu,'label','Pa&ge Setup...'),'pos',5);
      set(findobj(fmenu,'label','Print Set&up...'),'pos',6);
      set(findobj(fmenu,'label','Print Pre&view...'),'pos',7);
      set(findobj(fmenu,'label','&Print...'),'pos',8);
      
      mequit = uimenu(fmenu,'label','Quit PPLANE6',...
          'call','pplane6(''quit'')','separator','on','pos',9);
  
      % View menu
      
      set(findobj(gcf,'label','&Figure Toolbar'),...
          'call','pplane6(''showbar'')');
      
      % Solutions menu
      
      solmenu = uimenu('label','Solutions','pos',3);
      
      menukey = uimenu(solmenu,'label','Keyboard input.','call',...
         'pplane6(''kbd'')','vis','on');
      
      mesev   = uimenu(solmenu,'label','Plot several solutions.',...
         'call','pplane6(''several'')');
      
      
      fundcall = ['dud = get(gcf,''user'');',...      
                  'col = dud.color.sep;',...
                  'vect = dud.vectors;',...
                  'h = zeros(1,2);',...
                  'h(1) = plot(2*[vect(1,1),-vect(1,1)],2*[vect(2,1),-vect(2,1)]);',...
                  'h(2) = plot(2*[vect(1,2),-vect(1,2)],2*[vect(2,2),-vect(2,2)]);',...
                  'set(h,''color'',col);',...       
                  'dud.solhand = [dud.solhand;h(:)];'...
                  'set(gcf,''user'',dud);'];
      
      dud.menu = uimenu(solmenu,'call',fundcall);
      
      % Edit menu
      
      emenu = findobj(gcf,'label','&Edit');  
      
      medallsol = uimenu(emenu,'label','Erase all solutions.',...
                         'call','pplane6(''dallsol'')',...
                         'pos',1);
      
      medel = uimenu(emenu,'label','Delete a graphics object.',...
                     'call','pplane6(''delete'')',...
                     'visible','on',...
                     'pos',2);
      
      menutext = uimenu(emenu,'label','Enter text on the Display Window.',...
                        'call','pplane6(''text'')',...
                        'pos',3);
      set(findobj(emenu,'label','&Undo'),'separator','on',...
                        'pos',4);
      set(findobj(emenu,'label','Cu&t'),'pos',5);
      set(findobj(emenu,'label','&Copy'),'pos',7);
      set(findobj(emenu,'label','&Paste'),'pos',8);
      set(findobj(emenu,'label','Clea&r'),'pos',9);
      set(findobj(emenu,'label','&Select All'),'pos',10);
      set(findobj(emenu,'label','Copy &Figure'),'pos',11);
      set(findobj(emenu,'label','Copy &Options'),'pos',12);
      set(findobj(emenu,'label','F&igure Properties'),'pos',13);
      set(findobj(emenu,'label','&Axes Properties'),'pos',14);
      set(findobj(emenu,'label','C&urrent Object Properties'),'pos',15);
      
      % Options menu
      
      optmenu = uimenu('label','Options','visible','off');
      
      mehc = uimenu(optmenu,'label','Make the Display Window inactive.',...
         'call','pplane6(''hotcold'')','separator','on');

      set(0,'showhiddenhandles',hhsetup);
      
      set(pplin,'WindowButtonDownFcn',['pplane6(''down'',',num2str(pplin),')']);
      hh1 = [dud.axes,dud.title.axes];
      set(hh1,'units','norm');
      set(dud.axes,'visible','on');
      set(pplin,'vis','on');
      dud.printstr = 'print';
   end   % if (~isempty(pplin))  & else
   
   switch type
   case 1
      vstr = 'on';
      lstr = 'Plot stable and unstable orbits.';
   case {2,3}
      vstr = 'on';
      lstr = 'Plot fundamental modes.';
   otherwise
      vstr = 'off';
      lstr='';
   end
   set(dud.menu,'label',lstr,'vis',vstr);
   
   pplina = dud.axes;
   dud.vectors = sud.vectors;
   axes(pplina);
   cla
   xlabel('u');
   ylabel('v');
   
   % The title strings.
   
   tstr = {'u'' = A u + B v';'v'' = C u + D v'};
   dud.tstr = tstr;
   pstr2 = {['A = ',num2str(jac(1,1))];['C = ',num2str(jac(2,1))]};
   pstr1 = {['B = ',num2str(jac(1,2))];['D = ',num2str(jac(2,2))]};
   
   set(dud.title.eq,'string',tstr);
   set(dud.title.p1,'string',pstr1);
   ext = get(dud.title.p1,'extent');
   pos = get(dud.title.p1,'pos');
   p1 = min(.9, .93 - ext(3));
   pos(1) = p1;
   set(dud.title.p1,'pos',pos);
   set(dud.title.p2,'string',pstr2);    
   ext = get(dud.title.p2,'extent');
   pos = get(dud.title.p2,'pos');
   pos(1) = min(.8, p1 - ext(3)-0.02);
   set(dud.title.p2,'pos',pos);
   
   if (~strcmp(dfcn,'') & exist(dfcn)==2) delete([tempdir,dfcn,'.m']);end
   tee = clock;
   tee = ceil(tee(6)*100);
   dfcn=['pptp',num2str(tee)];
   fcnstr = ['function ypr = ',dfcn,'(t,y)\n\n'];
   commstr = '%%%% Created by PPLANE6\n\n';
   astr = ['A = [',num2str(jac(1,1)),',',num2str(jac(1,2)),';',...
         num2str(jac(2,1)),',',num2str(jac(2,2)),'];\n'];
   dstr = 'ypr = A * y;';
   ppf = fopen([tempdir,dfcn,'.m'],'w');
   fprintf(ppf,fcnstr);
   fprintf(ppf,commstr);
   fprintf(ppf,astr);
   fprintf(ppf,dstr);
   fclose(ppf);
   
   % Initialize important information as user data.
   
   dud.function = dfcn;
   dud.solhand = [];    % Handles to solution curves.
   dud.eqhand = [];     % Handles to equilibrium points.
   dud.arr = [];                % Handles for the direction and vector
   % fields.
   dud.eqpts = [];              % Equilibrium point data.
   dud.notice = 0;
   dud.syst.wind = [-1 1 -1 1]';
   dud.color = sud.color;
   set(pplin,'user',dud);
   
   ud.y = zeros(2,1);
   ud.i = 0;
   ud.line = 0;
   wind = [-1 1 -1 1]';
   dwind = [wind(1); wind(3); -wind(2); -wind(4)];
   ud.DY = [wind(2)-wind(1); wind(4)-wind(3)];
   ud.cwind = dwind - dud.settings.magn*[ud.DY;ud.DY];
   ud.R = zeros(2,2);
   ud.rr = zeros(2,2);
   ud.perpeps = 0;
   ud.paraeps = 0;
   ud.sinkeps = 0;
   ud.turn = zeros(2,10);
   ud.tk = 0;
   ud.stop = 0;
   ud.gstop = 1;
   ud.plot = 1;
   set(dud.axes,'user',ud);
   ppkbd = findobj('name','PPLANE6 Keyboard input','vis','on');
   if ~isempty(ppkbd),pplane6('kbd'),end
   pplane6('dirfield',pplin);           
   plot(0,0,...
        'color',dud.color.eqpt,...
        'markersize',20,...
        'marker','.');
   
elseif strcmp(action,'dirfield')
   
   % 'dirfield' computes and plots the field elements.  This is the entry
   % point both from 'display' and from later commands that require the
   % recomputation of the field elements.
   
   % Find PPLANE6 Display and get the user data.
   
   disph = input1;   % This could be ppdisp or pplin.
   
   dud = get(disph,'user');
   color = dud.color;
   
   dfcn = dud.function;
   ppdispa = dud.axes;
   WINvect = dud.syst.wind;
   settings = dud.settings;
   notice = dud.notice;
   if notice
      nstr = get(notice,'string');
      nstr(1:4)=nstr(2:5);
      nstr{5,1} = 'Computing the field elements.';
      set(notice,'string',nstr);
      
      % Augment the window matrix
      
      wmat = dud.wmat;
      wrows = size(wmat,1);
      wflag = 0;
      for k = 1:wrows
         if wmat(k,:)==WINvect
            wflag = 1;
         end
      end
      if wflag == 0
         wmat = [wmat;WINvect];
         dud.wmat = wmat;
      end
      if wrows 
        hhsetup = get(0,'showhiddenhandles');
        set(0,'showhiddenhandles','on');
        hhh = findobj('tag','zbmenu');
        set(hhh,'enable','on');
        set(0,'showhiddenhandles',hhsetup); 
      end
   end
   
   
   Xmin = WINvect(1);
   Xmax = WINvect(2);
   Ymin = WINvect(3);
   Ymax = WINvect(4);
   
   N = dud.syst.npts;
   if strcmp(get(disph,'name'),'PPLANE6 Linearization') 
      N = floor(3*N/4);
   end    
   deltax=(Xmax - Xmin)/(N-1);
   deltay=(Ymax - Ymin)/(N-1);
   
   % Set up the display window.
   
   Dxint=[Xmin-deltax,Xmax+deltax];
   Dyint=[Ymin-deltay,Ymax+deltay];
   
   % Set up the original mesh.
   
   XXXg=Xmin + deltax*[0:N-1];
   YYYg=Ymin + deltay*[0:N-1];
   
   [Xx,Yy]=meshgrid(XXXg,YYYg);
   
   % Calculate the line and vector fields.
   
   Xx=Xx(:);Yy=Yy(:);
   Ww = zeros(size(Xx));
   Ww = feval(dfcn,0,[Xx';Yy']);
   Vv = Ww(1,:) + Ww(2,:)*sqrt(-1);
   Vv = Vv.';
   Arrflag = dud.syst.fieldtype;
   
   
   mgrid = Xx+Yy.*sqrt(-1); % mgrid = mgrid(:);
   zz=Vv.';
   sc = min(deltax,deltay);
   
   arrow=[-1,1].';
   zzz=sign(zz);
   scale = sqrt((real(zzz)/deltax).^2+(imag(zzz)/deltay).^2);
   ww = (zzz == 0);
   scale = scale + ww;
   aa1 = 0.3*arrow*(zzz./scale)+ones(size(arrow))*(mgrid.');
   [r,c] = size(aa1);
   aa1=[aa1;NaN*ones(1,c)];
   aa1=aa1(:);
   
   arrow = [0,1,.7,1,.7].' + [0,0,.25,0,-.25].' * sqrt(-1);
   zz=sign(zz).*((abs(zz)).^(1/3));
   scale = 0.9*sc./max(max(abs(zz)));
   aa2 = scale*arrow*zz +ones(size(arrow))*(mgrid.');
   [r,c] = size(aa2);
   aa2=[aa2;NaN*ones(1,c)];
   aa2=aa2(:);
   axes(ppdispa);
   
   arr = dud.arr;       % Delete the old field data.
   if isstruct(arr)
      hand = [arr.hx;arr.hy;arr.lines;arr.arrows;arr.barrows];  
      delete(hand);
   end
   NN = N;
   N = 50; k = ceil(N/NN);
   deltax=(Xmax - Xmin)/(N-1);
   deltay=(Ymax - Ymin)/(N-1);
   
   % Set up the original mesh.
   
   XXXg=Xmin + deltax*[-k:N+k];
   YYYg=Ymin + deltay*[-k:N+k];
   
   [Xx,Yy]=meshgrid(XXXg,YYYg);
   
   % Calculate the line and vector fields.
   
   Xxx=Xx(:);Yyy=Yy(:);
   Ww = zeros(size(Xxx));
   Ww = feval(dfcn,0,[Xxx';Yyy']);
   DX = Ww(1,:)';
   DY = Ww(2,:)';
   minx = min(DX);
   maxx = max(DX);
   miny = min(DY);
   maxy = max(DY);
   DR = Xxx.*DX + Yyy.*DY;
   DTheta = Xxx.*DY - Yyy.*DX;
   minr = min(DR);
   maxr = max(DR);
   minth = min(DTheta);
   maxth = max(DTheta);
   DX = reshape(DX,N+2*k+1,N+2*k+1);
   DY = reshape(DY,N+2*k+1,N+2*k+1);
   DR = reshape(DR,N+2*k+1,N+2*k+1);
   DTheta = reshape(DTheta,N+2*k+1,N+2*k+1);
   if minx < 0 & 0 < maxx
      [Cx,hx] = contour(Xx,Yy,DX,[0,0],'--');
      set(hx,'visible','off','color',color.xcline,'linestyle','--');
   else
      hx = zeros(0,1);
   end
   if miny < 0 & 0 < maxy
      [Cy,hy] = contour(Xx,Yy,DY,[0,0],'--');
      set(hy,'visible','off','color',color.ycline,'linestyle','--');
   else
      hy = zeros(0,1);
   end
   if minr < 0 & 0 < maxr
      [Cr,hr] = contour(Xx,Yy,DR,[0,0],'--');
      set(hr,'visible','off','color',color.xcline,'linestyle','--');
   else
      hr = zeros(0,1);
   end
   if minth < 0 & 0 < maxth
      [Cth,hth] = contour(Xx,Yy,DTheta,[0,0],'--');
      set(hth,'visible','off','color',color.ycline,'linestyle','--');
   else
      hth = zeros(0,1);
   end
   arrh1 = plot(real(aa1),imag(aa1),'color',color.arrows,'visible','off');
   arrh2 = plot(real(aa2),imag(aa2),'color',color.arrows,'visible','off');
   
   % We plot both the line field and the vector field.  Then we
   % control which is seen by manipulating the visibility.
   Xmin = Xmin - k*deltax;
   Xmax = Xmax + k*deltax; 
   Ymin = Ymin - k*deltay;
   Ymax = Ymax + k*deltay;  
   Zz = (Xx-Xmin).*(Xmax-Xx).*(Yy-Ymin).*(Ymax-Yy).*abs(DX).*abs(DY);
   Zzc = Zz(2:N+k+2,2:N+k+2);
   Xxc = Xx(2:N+k+2,2:N+k+2);
   Yyc = Yy(2:N+k+2,2:N+k+2);
   DXc = DX(2:N+k+2,2:N+k+2);
   DYc = DY(2:N+k+2,2:N+k+2);
   Zzl = Zz(1:N+k+1,2:N+k+2);
   Zzr = Zz(3:N+k+3,2:N+k+2);
   Zzd = Zz(2:N+k+2,1:N+k+1);
   Zzu = Zz(2:N+k+2,3:N+k+3);
   Zzdl = Zz(1:N+k+1,1:N+k+1);
   Zzdr = Zz(3:N+k+3,1:N+k+1);
   Zzul = Zz(1:N+k+1,3:N+k+3);
   Zzur = Zz(3:N+k+3,3:N+k+3);
   kk = find((Zzc>Zzl)&(Zzc>Zzr)&(Zzc>Zzd)&(Zzc>Zzu)...
      &(Zzc>Zzdl)&(Zzc>Zzdr)&(Zzc>Zzul)&(Zzc>Zzur));
   Xxx = Xxc(kk);
   Yyy = Yyc(kk);
   DXx = DXc(kk);
   DYy = DYc(kk);
   ll = length(hx);
   Xxx = Xxx(:);
   Yyy = Yyy(:);
   DXx = DXx(:);
   DYy = DYy(:);
   if ~exist('both')
      Xxx = zeros(0,1);
      Yyy = zeros(0,1);
      DXx = zeros(0,1);
      DYy = zeros(0,1);
   end
   for j = 1:ll
      xd = get(hx(j),'xdata');xd = xd(:);
      yd = get(hx(j),'ydata');yd = yd(:);
      zxd = feval(dfcn,0,[xd';yd']);
      yxd = zxd(2,:);yxd = yxd(:);
      ayxd = abs(yxd).*(xd-Xmin).*(Xmax-xd).*(yd-Ymin).*(Ymax-yd);
      NNN = length(ayxd);
      ayxdc = ayxd(2:NNN-1);
      yxdc = yxd(2:NNN-1);
      ayxdl = ayxd(1:NNN-2);
      ayxdr = ayxd(3:NNN);
      lll = find((ayxdc>ayxdl)&(ayxdc>ayxdr));
      Xx = xd(lll+1);
      Yy = yd(lll+1);
      Xxx = [Xxx;Xx(:)];
      Yyy = [Yyy;Yy(:)];
      yxdcp = yxdc(lll);
      yxdcp = yxdcp(:);
      DXx = [DXx;zeros(size(yxdcp))];
      DYy = [DYy;yxdcp];
   end
   ll = length(hy);
   for j = 1:ll
      xd = get(hy(j),'xdata');xd = xd(:);
      yd = get(hy(j),'ydata');yd = yd(:);
      zxd = feval(dfcn,0,[xd';yd']);
      yxd = zxd(1,:);yxd = yxd(:);
      ayxd = abs(yxd).*(xd-Xmin).*(Xmax-xd).*(yd-Ymin).*(Ymax-yd);
      NNN = length(ayxd);
      ayxdc = ayxd(2:NNN-1);
      yxdc = yxd(2:NNN-1);
      ayxdl = ayxd(1:NNN-2);
      ayxdr = ayxd(3:NNN);
      lll = find((ayxdc>ayxdl)&(ayxdc>ayxdr));
      Xx = xd(lll+1);
      Yy = yd(lll+1);
      Xxx = [Xxx;Xx(:)];
      Yyy = [Yyy;Yy(:)];
      yxdcp = yxdc(lll);
      yxdcp = yxdcp(:);
      DXx = [DXx;yxdcp];
      DYy = [DYy;zeros(size(yxdcp))];
   end
   mgrid = Xxx(:) + Yyy(:)*sqrt(-1);
   Vv = DXx(:) + DYy(:)*sqrt(-1);
   Vv = sign(Vv);       %.*((abs(Vv)).^(1/3));
   sc = (N/20)*min(deltax,deltay);
   aa3 = sc*arrow*(Vv.') +ones(size(arrow))*(mgrid.');
   [r,c] = size(aa3);
   aa3 = [aa3;NaN*ones(1,c)];
   aa3=aa3(:);
   arrh3 = plot(real(aa3),imag(aa3),'color',color.narrows,'visible','off');
   
   switch Arrflag
   case 'nullclines'
      set([hx;hy;arrh3],'vis','on');
   case 'lines'
      set(arrh1,'visible','on');
   case 'arrows'
      set(arrh2,'visible','on');
   end
   dud.arr.lines = arrh1;          % Save the handles for later use.
   dud.arr.arrows = arrh2;         % Save the handles for later use.
   dud.arr.hx = hx;
   dud.arr.hy = hy;
   dud.arr.barrows = arrh3;
   dud.arr.hr = hr;
   dud.arr.hth = hth;
   
   menull = findobj('tag','null');
   mernull = findobj('tag','rnull');
   if strcmp(get(menull,'label'),'Delete nullclines.')
      set([hx;hy],'vis','on');
   elseif strcmp(get(mernull,'label'),'Delete polar nullclines.')
      set([hr;hth],'vis','on');
   end
   if notice
      nstr = get(notice,'string');
      nstr(1:4) = nstr(2:5);
      nstr{5,1} = 'Ready.';
      set(notice,'string',nstr);
   end
   set(disph,'user',dud);
   axis([Dxint,Dyint]);  
   
elseif strcmp(action,'hotcold')
   
   % 'hotcold' is the callback for the menu selection that makes the
   % Display Window active or inactive.
   
   ppdisp = gcf;
   dud = get(ppdisp,'user');
   nstr = get(dud.notice,'string');
   nstr(1:4) = nstr(2:5);
   mehc = dud.menu(6);
   if (findstr(get(mehc,'label'),'inactive'))
      set(ppdisp,'WindowButtonDownFcn',' ');
      set(mehc,'label','Make the Display Window active.');
      nstr{5,1} = 'The Display Window is not active.';
      set(dud.notice,'string',nstr);
   else
      set(ppdisp,'WindowButtonDownFcn','pplane6(''down'')');
      set(mehc,'label','Make the Display Window inactive.');
      nstr{5,1} = 'The Display Window is active.';
      set(dud.notice,'string',nstr);
   end
   
elseif strcmp(action,'down')
   
   % 'down' is the Window Button Down call.  It starts the computation of
   % solutions from a click of the mouse.
   
   disph = gcf;
   seltype = get(disph,'selectiontype');
   if strcmp(seltype,'alt')
      pplane6('zoom');
      return
   elseif strcmp(seltype,'extend')
      pplane6('zoomsqd');
      return
   end
   dud = get(disph,'user');
   ax = dud.axes;
   ch = findobj('type','uicontrol','enable','on');
   %  mh = findobj('type','uimenu','enable','on');
   set(ch,'enable','inactive');
   %  set(mh,'enable','off');
   wbdf = get(disph,'WindowbuttonDownFcn');
   set(disph,'WindowbuttonDownFcn','');
   axes(ax);
   initpt = get(ax,'currentpoint');
   initpt = initpt(1,[1,2]);
   pplane6('solution',initpt,disph);
   set(disph,'WindowbuttonDownFcn',wbdf);
   %  set([ch;mh],'enable','on');
   set(ch,'enable','on');
   notice = dud.notice;
   if notice
      nstr = get(notice,'string');
      nstr(1:4) = nstr(2:5);
      nstr{5,1} = 'Ready.';
      set(notice,'string',nstr)
   end
   
elseif strcmp(action,'several')
   
   % 'several' allows the user to pick several initial points at once.
   % This is not needed in X-windows, but it is on the Macintosh.
   
   disph = gcf;
   ch = findobj('type','uicontrol','enable','on');
   %  mh = findobj('type','uimenu','enable','on');
   set(ch,'enable','inactive');
   %  set(mh,'enable','off')
   wbdf = get(disph,'WindowbuttonDownFcn');
   set(disph,'WindowbuttonDownFcn','');
   dud = get(disph,'user');
   notice = dud.notice;
   if notice
      nstr = get(notice,'string');
      nstr(1:4) = nstr(2:5);
      nstr{5,1} = 'Pick initial points with the mouse. Enter "Return" when finished.';
      set(notice,'string',nstr)
   end
   [X,Y]=ginput;
   NN = length(X);
   for k = 1:NN
      initpt = [X(k),Y(k)];
      pplane6('solution',initpt,disph);
   end
   if notice
      nstr = get(notice,'string');
      nstr(1:4) = nstr(2:5);
      nstr{5,1} = 'Ready.';
      set(notice,'string',nstr);
   end
   set(ch,'enable','on');
   %  set([ch;mh],'enable','on');
   set(disph,'WindowbuttonDownFcn',wbdf);
   
elseif strcmp(action,'test case')
   
   tic  
   ppdisp = gcf;
   for k = 1:10
      initpt = k*[-.2 .2];
      pplane6('solution',initpt,ppdisp);
      initpt = k*[-.2 -.2];
      pplane6('solution',initpt,ppdisp);
   end  
   pplane6('solution',[1,-1],ppdisp);
   dud = get(gcf,'user');
   nstr = get(dud.notice,'string');
   nstr(1:4) = nstr(2:5);
   nstr{5,1} = 'Ready.';
   set(dud.notice,'string',nstr)
   toc
   
elseif strcmp(action,'solution')
   
   % 'solution' effects the computation and (erasemode == none) plotting of
   % solutions.  It also stores the data as appropriate.
   
   disph = input2;
   dud = get(disph,'user');
   tcol = dud.color.temp;
   pcol = dud.color.orb;
   notice = dud.notice;
   initpt = input1(:);
   dfcn = dud.function;
   ppdispa = dud.axes;
   settings = dud.settings;
   ptstr = [' (',num2str(initpt(1),2), ', ', num2str(initpt(2),2), ')'];
   refine = settings.refine;
   ssize = settings.stepsize;
   tol = settings.tol;
   ud = get(dud.axes,'user');
   %  rtol = tol;
   atol = tol*ud.DY*1e-4';
   
   
   if length(initpt)  == 2
      AA = -1e6;
      BB = 1e6; 
      switch dud.dir
         %      case 0
         %      intplus = [initpt(1), BB];
         %      intminus = [initpt(1), AA]; 
         %      case -1
         %      intplus = [initpt(1), initpt(1)];
         %      intminus = [initpt(1), AA]; 
         %      case 1
         %      intplus = [initpt(1), BB];
         %      intminus = [initpt(1), initpt(1)];
      case 0
         intplus = [0, BB];
         intminus = [0, AA]; 
      case -1
         intplus = [0, 0];
         intminus = [0, AA]; 
      case 1
         intplus = [0, BB];
         intminus = [0, 0];
      end
      
   else
      intplus = [initpt(3),initpt(5)];
      intminus = [initpt(3),initpt(4)];
      initpt = initpt([1:2]);
      
   end      
   stopbutt = findobj(disph,'tag','stop');
   
   set(stopbutt,'vis','on','enable','on');
   
   options = odeset('OutputFcn','ppn6out','Refine',refine,...
       'RelTol',tol,'Abstol',atol);

   cflag = 0;
   if intplus(2)>intplus(1)
      cflag = cflag + 1;
      if notice
         nstr = get(notice,'string');
         nstr(1:4) = nstr(2:5);
         nstr{5} = ['The forward orbit from',ptstr];
         set(notice,'string',nstr);
      end
      drawnow                           
      
      switch settings.solver
        case 'Dormand Prince'   
          [tp,xp] = ppdp45(dfcn,intplus,initpt,disph);
          
        case 'ode45'    
          [tp,xp] = ode45(dfcn,intplus,initpt,options);
          
        case 'ode23'    
          [tp,xp] = ode23(dfcn,intplus,initpt,options);
          
        case 'ode113'   
          [tp,xp] = ode113(dfcn,intplus,initpt,options);
          
        case 'ode15s'   
          [tp,xp] = ode15s(dfcn,intplus,initpt,options);
          
        case 'ode23s'   
          [tp,xp] = ode23s(dfcn,intplus,initpt,options);
          
        case 'Runge-Kutta 4'    
          [tp,xp] = pprk4(dfcn,intplus,initpt,disph);
          
        otherwise
          error('Undefined solver.');
      end         

      aud = get(ppdispa,'user');
      hnew1 = aud.line;
   end          
   
   if intminus(2) < intminus(1)
      cflag = cflag + 2;
      if notice 
         nstr = get(notice,'string');
         nstr(1:4) = nstr(2:5);
         nstr{5} = ['The backward orbit from',ptstr];
         set(notice,'string',nstr);
      end
      drawnow
      switch settings.solver
        case 'Dormand Prince'
          [tm,xm] = ppdp45(dfcn,intminus,initpt,disph);
          
        case 'ode45'    
          [tm,xm] = ode45(dfcn,intminus,initpt,options);
          
        case 'ode23'    
          [tm,xm] = ode23(dfcn,intminus,initpt,options);
          
        case 'ode113'   
          [tm,xm] = ode113(dfcn,intminus,initpt,options);
          
        case 'ode15s'   
          [tm,xm] = ode15s(dfcn,intminus,initpt,options);
          
        case 'ode23s'   
          [tm,xm] = ode23s(dfcn,intminus,initpt,options);
          
        case 'Runge-Kutta 4'    
          [tm,xm] = pprk4(dfcn,intminus,initpt,disph);
          
        otherwise
          error('Undefined solver.');
      end

      aud = get(ppdispa,'user');
      hnew2 = aud.line;
      
      set(stopbutt,'vis','off');
   end    % if intminus(2) < intminus(1)        
   
   
   
   % Store the trajectory.
   
   switch cflag
   case 1 % positive only
      set(hnew1,'xdata',xp(:,1),'ydata',xp(:,2),'zdata',tp,'color',pcol);
      set(hnew1,'erase','normal');
      dud.solhand = [dud.solhand;hnew1];
   case 2 % negative only
      x = flipud(xm);
      t = flipud(tm);
      set(hnew2,'xdata',x(:,1),'ydata',x(:,2),'zdata',t,'color',pcol);
      set(hnew2,'erase','normal');
      dud.solhand = [dud.solhand;hnew2];
      
   case 3 % both directions
      x = flipud(xm);
      t = flipud(tm);
      x=[x;xp];
      t=[t;tp];
      delete(hnew1);
      set(hnew2,'xdata',x(:,1),'ydata',x(:,2),'zdata',t,'color',pcol);
      set(hnew2,'erase','normal');
      dud.solhand = [dud.solhand;hnew2];
   end   % switch cflag
   set(disph,'user',dud);
   
elseif strcmp(action,'kcompute')
   
   % 'kcompute' is the call back for the Compute 
   % button on the PPLANE6 Keyboard figure.
   
   compute = 1;
   kh = get(gcf,'user');
   ppdisp = kh.fig;
   if (isempty(ppdisp))
      pplane6('confused');
   end
   dud = get(ppdisp,'user');
   ppdispa = dud.axes;
   aud = get(ppdispa,'user');
   ch = findobj('type','uicontrol','enable','on');
   %  mh = findobj('type','uimenu','enable','on');
   set(ch,'enable','inactive');
   %  set(mh,'enable','off')
   set(ppdisp,'WindowbuttonDownFcn','');
   x = str2num(get(kh.xval,'string'));
   y = str2num(get(kh.yval,'string'));
   if get(kh.spec,'value')
      tzero = str2num(get(kh.tval,'string'));
      t0 = str2num(get(kh.t0,'string'));
      tf = str2num(get(kh.tf,'string'));
      initpt = [x,y,tzero,t0,tf];
      if (length(initpt) ~= 5)
         warndlg({'Values must be entered for all of the entries.'},'Illegal input');
         compute = 0;
      elseif tf <= t0
         warndlg({'The final time of the computation interval';...
               'must be smaller than the initial time.'},'Illegal input');
         compute = 0;
      elseif (tzero < t0) | (tzero > tf)
         warndlg('The initial time must be in the computation interval.','Illegal input');
         compute = 0;
      end
      aud.gstop = 0;
      set(ppdispa,'user',aud);
   else
      initpt = [x,y];
      if (length(initpt) ~= 2)
         warndlg({'Values must be entered for all of the entries.'},'Illegal input');
         compute = 0;
      end
   end  % if get(kh.spec,'value')
   
   if compute
      pplane6('solution',initpt,ppdisp);
   end
   if dud.notice
     nstr = get(dud.notice,'string');
     nstr(1:4) = nstr(2:5);
     nstr{5} = 'Ready.';
     set(dud.notice,'string',nstr);
   end
   %  set([ch;mh],'enable','on');
   set(ch,'enable','on');
   set(ppdisp,'WindowbuttonDownFcn','pplane6(''down'')');
   aud.gstop = 1;
   set(ppdispa,'user',aud);
   
   
elseif strcmp(action,'kbd')
   
   % 'kbd' is the callback for the Keyboard Input menu selection.  It 
   % sets up the PPLANE6 Keyboard figure which allows accurate input of 
   % initial values using the keyboard.
   
   ppdisp = gcf;  % The figure to be plotted in.
   dud = get(ppdisp,'user');
   Xname = dud.syst.xvar;
   Yname = dud.syst.yvar;
   xnstr = ['The initial value of ',Xname,' = '];
   ynstr = ['The initial value of ',Yname,' = '];
   tnstr = 'The initial value of t = ';
   nudge = 3; 
   ppkbd = findobj('name','PPLANE6 Keyboard input');
   if  ~isempty(ppkbd)
     delete(ppkbd);
   end
         
   ppkbd = figure('name','PPLANE6 Keyboard input',...
                  'vis','off',...
                  'numb','off','tag','PPLANE6');
   
   pplane6('figdefault',ppkbd);
   set(ppkbd,'menubar','none');
   
   kbd.fr1 = uicontrol('style','frame');
   
   kbd.fr2 = uicontrol('style','frame');
   
   kbd.fr3 = uicontrol('style','frame');
   
   dname = get(ppdisp,'name');
   kbd.which = uicontrol('style','text','horiz','center',...
         'string',['Data for ',dname]);
   
   kbd.inst = uicontrol('style','text','horiz','left',...
         'string','Enter the initial conditions:');
      
   kbd.xname = uicontrol('style','text',...
                         'horiz','right','string',xnstr);
   
   kbd.xval = uicontrol('style','edit',...
                        'string','','call','');
   
   kbd.yname = uicontrol('style','text',...
                         'horiz','right',...
                         'string',ynstr);
   
   kbd.yval = uicontrol('style','edit',...
                        'string','');
   
   kbd.tname = uicontrol('style','text',...
                         'horiz','right',...
                         'string',tnstr);
   
   kbd.tval = uicontrol('style','edit');
   
   kbd.t0 = uicontrol('style','edit');
   
   kbd.tf = uicontrol('style','edit');
   
   kbd.t = uicontrol('style','text','string','<= t<= ');
   
   kbd.spec = uicontrol('style','check','horiz','center',...
                        'string','Specify a computation interval.');
   
   kbd.comp = uicontrol('style','push',...              
                        'string','Compute','call','pplane6(''kcompute'')');
   
   kbd.close = uicontrol('style','push',...
                         'string','Close','call','set(gcf,''vis'',''off'')');
   kbd.fig = ppdisp;
   left = 5; varl = 70; buttw = 60;
   xex = get(kbd.xname,'extent');
   ht = xex(4)+nudge;
   yex = get(kbd.yname,'extent');
   nwdth = max(xex(3),yex(3)) + nudge;
   varl = varl*ht/19;
   fr1bot = 2*left + ht;
   fr1ht = 3*nudge + 2*ht;
   fr2bot = fr1bot + fr1ht;
   frw = 2*nudge + nwdth + varl;
   intb = fr1bot + nudge;
   specb = intb + ht + nudge;
   intext = get(kbd.t,'extent');
   tw = intext(3);
   margin = (frw -tw - 2*varl)/2;
   t0l = left+margin;
   tl = t0l + varl;
   tfl = tl + tw;
   tnb = fr2bot + nudge;
   ynb = tnb + ht;
   xnb = ynb + ht;
   nl = left+nudge;
   xnwind = [nl,xnb,nwdth,ht];
   ynwind = [nl,ynb,nwdth,ht];
   tnwind = [nl,tnb,nwdth,ht];
   vl = nl + nwdth;
   xvwind = [vl,xnb,varl,ht];
   yvwind = [vl,ynb,varl,ht];
   tvwind = [vl,tnb,varl,ht];
   instb = xnb + ht + nudge;
   instw = nwdth + varl;
   instwind = [nl,instb,instw,ht];
   fr2ht = 3*nudge + 4*ht;
   fr3bot = fr2bot + fr2ht;
   fr3ht = 2*nudge + ht;
   frw = 2*nudge + nwdth + varl;
   whichbot = fr3bot + nudge;
   whichw = frw - 2*nudge;
   whichwind = [nl,whichbot,whichw,ht];
   fr3wind = [left,fr3bot,frw,fr3ht];
   fr2wind = [left,fr2bot,frw,fr2ht];
   fr1wind = [left,fr1bot,frw,fr1ht];
   specw = frw - 2*nudge;
   specwind = [nl,specb,specw,ht];
   t0wind = [t0l,intb,varl,ht];
   twind = [tl,intb,tw,ht];
   tfwind = [tfl,intb,varl,ht];
   figw = 2*left + frw;
   fight = 3*left + ht + fr1ht + fr2ht + fr3ht;
   figwind = [30,300,figw,fight];
   buttw = frw/3;
   sep = (figw - 2*buttw)/3;
   closel = sep;
   compl = 2*sep+buttw;
   clwind = [closel,left,buttw,ht];
   compwind = [compl,left,buttw,ht];
   set(ppkbd,'pos',figwind);
   set(kbd.fr1,'pos',fr1wind);
   set(kbd.fr2,'pos',fr2wind);
   set(kbd.fr3,'pos',fr3wind);
   set(kbd.which,'pos',whichwind);
   set(kbd.inst,'pos',instwind);
   set(kbd.xname,'pos',xnwind);
   set(kbd.yname,'pos',ynwind);
   set(kbd.xval,'pos',xvwind);
   set(kbd.yval,'pos',yvwind);
   set(kbd.comp,'pos',compwind);
   set(kbd.close,'pos',clwind);
   set(kbd.tname,'pos',tnwind);
   set(kbd.tval,'pos',tvwind);
   set(kbd.spec,'pos',specwind);
   set(kbd.t0,'pos',t0wind);
   set(kbd.t,'pos',twind);
   set(kbd.tf,'pos',tfwind);
   speccall = [
       'ud = get(gcf,''user'');',...
       'if get(gcbo,''value''),',...
       '  set([ud.t0,ud.t,ud.tf,ud.tname,ud.tval],''vis'',''on'');',...
       'else,',...
       '  set([ud.t0,ud.t,ud.tf,ud.tname,ud.tval],''vis'',''off'');',...
       'end'];
   
   set(kbd.spec,'call',speccall);
   set(ppkbd,'resize','on');
   set(findobj(ppkbd,'type','uicontrol'),'units','normal');
   
   set([kbd.tval,kbd.t0],'string','0');
   set(kbd.spec,'value',0);
   set(ppkbd,'user',kbd,'vis','on');
   set([kbd.t0,kbd.t,kbd.tf,kbd.tname,kbd.tval],'vis','off')
   set(findobj(ppkbd,'type','uicontrol'),'units','normal');
   figure(ppkbd)
   
elseif strcmp(action,'eqpt')
   
  % Find and classify equilibrium points.
  
  ppdisp = findobj('name','PPLANE6 Display');
  dud = get(ppdisp,'user');
  col = dud.color.eqpt;
  dfcn = dud.function;
  dbutt = dud.butt;
  menu = dud.menu;
  ppdispa =dud.axes;
  Dx = get(ppdispa,'xlim');
  Dy = get(ppdispa,'ylim');
  DY = [Dx(2)-Dx(1);Dy(2)-Dy(1)];
  
  epsilon = 1e-4;
  nstr = get(dud.notice,'string');
  nstr(1:4) = nstr(2:5);
  nstr{5} = 'Choose an approximation with the mouse.';
  set(dud.notice,'string',nstr);
  
  z0 = ginput(1);
  
  z = pplane6('newton',z0,dfcn);
  
  flag = z(:,4);
  A = z(:,2:3);
  B = real(A);
  k = find(abs(B)<1e-8);
  B(k) = zeros(size(k));
  C = imag(A);
  k = find(abs(C)<1e-8);
  C(k) = zeros(size(k));
  A = B+C*sqrt(-1);
  z = z(:,1);
  
  if (~flag | norm((z-z0')./DY) > 1/5)
    nstr(1:4) = nstr(2:5);
    nstr{5} = ['There is not an equilibrium point near (',...
               num2str(z0(1)),', ', num2str(z0(2)), ').  Ready'];
    set(dud.notice,'string',nstr);
    return
  end
  zero =find(abs(z) < epsilon);
  z(zero) = zeros(size(zero));
  D=det(A); T=trace(A);
  if (D<-epsilon)
    string1 = ['There is a saddle point at (',...
               num2str(z(1)),', ', num2str(z(2)), ').'];
    string2 = '';
    type = 1;
  elseif(D>epsilon)
    if (T*T>4*D+epsilon)
      if (T<0)
        string1 = ['There is a nodal sink at (',...
                   num2str(z(1)),', ', num2str(z(2)), ').'];
        string2 = '';
        type = 2;
      else
        string1 = ['There is a nodal source at (',...
                   num2str(z(1)),', ', num2str(z(2)), ').'];
        string2 = '';
        type = 3;
      end
    elseif(T*T<4*D-epsilon)
      if(T<-epsilon)
        string1 = ['There is a spiral sink at (',...
                   num2str(z(1)),', ', num2str(z(2)), ').'];
        string2 = '';
        type = 4;
      elseif(T>epsilon)
        string1 = ['There is a spiral source at (',...
                   num2str(z(1)),', ', num2str(z(2)), ').'];
        string2 = '';
        type = 5;
      else
        string1 = ['There is a spiral equilibrium point at (',...
                   num2str(z(1)),', ', num2str(z(2)), ').'];
        string2 = 'Its specific type has not been determined.';
        type = 6;
      end
    else
      if (T>epsilon)
        string1 = ['There is a source at (',...
                   num2str(z(1)),', ', num2str(z(2)), ').'];
        string2 = 'Its specific type has not been determined.';
        type = 7;
      elseif (T<-epsilon)
        string1 = ['There is a sink at (',...
                   num2str(z(1)),', ', num2str(z(2)), ').'];
        string2 = 'Its specific type has not been determined.';
        type = 8;
      else
        string1 = ['There is an equilibrium point at (',...
                   num2str(z(1)),', ', num2str(z(2)), ').'];
        string2 = 'Its specific type has not been determined.';
        type = 9;
      end
    end
  else
    string1 = ['There is an equilibrium point at (',...
               num2str(z(1)),', ', num2str(z(2)), ')'];
    string2 = 'Its specific type has not been determined.';
    type = 9;
  end
  
  [V,D] = eig(A);                       
  EqPtList = dud.eqpts;
  infostr{1,1} = string1;
  infostr{2,1} = string2;
  infostr{3,1} = ' ';
  infostr{4,1} = 'The Jacobian is:';
  infostr{5,1} = ['      ',num2str(A(1,1)),'   ',num2str(A(1,2))];
  infostr{6,1} = ['      ',num2str(A(2,1)),'   ',num2str(A(2,2))];
  infostr{7,1} = '';
  infostr{8,1} = 'The eigenvalues and eigenvectors are:';
  infostr{9,1} = ['     ',num2str(D(1,1)),'    (',num2str(V(1,1)),', ',num2str(V(2,1)),')'];
  infostr{10,1} = ['     ',num2str(D(2,2)),'    (',num2str(V(1,2)),', ',num2str(V(2,2)),')'];
  
  k=1; l=size(EqPtList,1);
  while ((k <= l))
    if (norm((EqPtList(k,1:2)-z')./DY') <= 1e-3)
      break;
    end
    k = k+1;
  end
  if (k > l)
    EqPtList = [EqPtList;z',type];
    dud.eqpts = EqPtList;
    newh = plot(z(1),z(2),...
                'color',col,...
                'markersize',20,...
                'marker','.','Erasemode','none');
    dud.ephand = [dud.ephand;newh];
    set(newh,'Erasemode','normal');
    drawnow
  end
  ppeqpt = findobj('name','PPLANE6 Equilibrium point data');
  
   if (isempty(ppeqpt))
     ppeqpt = figure('vis','off','resize','on',...
                    'name','PPLANE6 Equilibrium point data',...
                    'numb','off','tag','PPLANE6');
     pplane6('figdefault',ppeqpt);
     set(ppeqpt,'menubar','none');

     ud.frame = uicontrol('style','frame');
     ud.eptext = uicontrol('style','text','string',infostr,'hor','left');
     ud.goaway = uicontrol('style','push','string','Go away',...
                          'call','close');
     ud.display = uicontrol('style','push',...
                           'string','Display the linearization',...
                           'call','pplane6(''linear'')');
   else
     figure(ppeqpt);
     ud = get(ppeqpt,'user');
     set(ppeqpt,'vis','off');
     set(findobj(ppeqpt,'type','uicontrol'),'units','pixels');
     set(ud.eptext,'string',infostr);
   end
   ud.jac = A;
   ud.vectors = V;
   ud.type = type;
   ud.system = dud.syst;
   ud.settings = dud.settings;
   ud.color = dud.color;
   set(ppeqpt,'user',ud);
   left = 5; nudge = 3;
   ext = get(ud.eptext,'extent');
   n = size(infostr,1);
   ht = ext(4)/n+2*nudge;
   frbot = 3*left + 2*ht;
   txtbot = frbot + nudge;
   txtl = left + nudge;
   twind = [txtl,txtbot,ext(3)+nudge,ext(4)];
   frw = ext(3) + 3*nudge;
   frh = ext(4) + 2*nudge;
   frwind = [left,frbot,frw,frh];
   figw = frw + 2*left;
   figh = frh + 4*left + 2*ht;
   uni = get(0,'units');
   set(0,'units','pixels');
   ss = get(0,'screensize');
   set(0,'units',uni);
   sh = ss(4);
   figbot = sh - figh - 350;
   figwind = [30,figbot,figw,figh];
   buttw = frw - 4;
   buttl = left + 2;
   closewind = [buttl,left,buttw,ht];
   dispb = 2*left + ht;
   dispwind = [buttl,dispb,buttw,ht];
   set(ppeqpt,'pos',figwind);
   set(ud.frame,'pos',frwind);
   set(ud.eptext,'pos',twind);
   set(ud.goaway,'pos',closewind);
   set(ud.display,'pos',dispwind);
   set(findobj(ppeqpt,'type','uicontrol'),'units','normal');
   set(ppeqpt,'vis','on');
   set(get(ppeqpt,'child'),'vis','on');
   nstr(1:4) = nstr(2:5);
   nstr{5} = 'Ready.';
   set(dud.notice,'string',nstr);
   set(ppdisp,'user',dud);
    
elseif strcmp(action,'stunst')
   
   ppdisp = findobj('name','PPLANE6 Display');
   dud = get(ppdisp,'user');
   ecol = dud.color.eqpt;
   scol = dud.color.sep;
   ppdispa = dud.axes;
   aud = get(ppdispa,'user');
   DY = aud.DY;
   settings = dud.settings;
   dfcn = dud.function;
   EqPtList = dud.eqpts;
   Stop = norm(DY)*1e-4;
   
   %  Plot the stable and unstable orbits at a saddle point.
   
   nstr = get(dud.notice,'string');
   nstr(1:4) = nstr(2:5);
   nstr{5} = 'Choose a saddle point with the mouse.';
   set(dud.notice,'string',nstr);
   z0 = ginput(1);
   z = zeros(2,1);
   z = pplane6('newton',z0,dfcn);
   
   flag = z(:,4);
   A = z(:,2:3);
   k = find(abs(A)<1e-8);
   A(k) = zeros(size(k));
   z = z(:,1);
   
   if (~flag | norm((z-z0')./DY)> 1/5)
      nstr(1:4) = nstr(2:5);
      nstr{5} = ['There is not an equilibrium point near (',...
            num2str(z0(1),2),', ', num2str(z0(2),2), ').'];
      set(dud.notice,'string',nstr);
      return
   end
   zero = find(abs(z) < 1e-4);
   z(zero) = zeros(size(zero));
   D=det(A);
   if (D>=0)
      nstr(1:4) = nstr(2:5);
      nstr{5} = ['The equilibrium point at (',...
            num2str(z(1),2),', ', num2str(z(2),2),...
            ') is not a saddle point.'];
      set(dud.notice,'string',nstr);
      return
   end
   if isempty(EqPtList)
      EqPtList = [z',1];
      dud.eqpts = EqPtList;
   else
      k=1; l=size(EqPtList,1);
      while ((k <= l))
         if (norm(EqPtList(k,1:2)-z') <= Stop)
            break;
         end
         k = k+1;
      end
      if (k > l)
         EqPtList = [EqPtList;z',1];
         dud.eqpts = EqPtList;
      end
   end
   nstr(1:4) = nstr(2:5);
   nstr{5} = ['Plotting from the saddle point at (',...
         num2str(z(1),2),', ', num2str(z(2),2),').'];
   set(dud.notice,'string',nstr);
   [V,L] = eig(A);
   [L,I] = sort(diag(L));
   
   magn = settings.magn;
   refine = settings.refine;
   ssize = settings.stepsize;
   solver = settings.solver;
   tol = settings.tol;
   offset = norm(DY)/1000;      
   lm=abs(L);
   lm=lm/max(lm);
   lm = (max([lm,0.2*ones(size(lm))]'))';
   offs = offset./lm;
   ud = get(dud.axes,'user');
   atol = tol*ud.DY*1e-4';
   options = odeset('OutputFcn','ppn6out','Refine',refine,...
       'RelTol',tol,'Abstol',atol);
   stopbutt = findobj('tag','stop');
   set(stopbutt,'vis','on','enable','on');
   VV=V(:,I(1));
   newhand = zeros(4,1);
   w = z + offs(1)*VV;
   nstr = get(dud.notice,'string');
   nstr(1:4) = nstr(2:5);
   nstr{5} = 'The first stable trajectory';
   set(dud.notice,'string',nstr);
   int = [0,-1e6];

   switch settings.solver
     case 'Dormand Prince'      
       [tp,Xp] = ppdp45(dfcn,int,w,ppdisp);
       
     case 'ode45'       
       [tp,Xp] = ode45(dfcn,int,w,options);
       
     case 'ode23'       
       [tp,Xp] = ode23(dfcn,int,w,options);
       
     case 'ode113'      
       [tp,Xp] = ode113(dfcn,int,w,options);
       
     case 'ode15s'      
       [tp,Xp] = ode15s(dfcn,int,w,options);
       
     case 'ode23s'      
       [tp,Xp] = ode23s(dfcn,int,w,options);
       
     case 'Runge-Kutta 4'       
       [tp,Xp] = pprk4(dfcn,int,w,ppdisp);
       
     otherwise
       error('Undefined solver.');
   end    
%   [tp,Xp] = ppdp45(dfcn,[0,-1e6],w,ppdisp);
   set(stopbutt,'enable','off');
   aud = get(ppdispa,'user');
   newhand(1) = aud.line;
   X1=[z';Xp];
   x1 = [X1,[NaN;tp]];
   set(newhand(1),'xdata',x1(:,1),'ydata',x1(:,2),'zdata',x1(:,3));
   
   w = z - offs(1)*VV;
   nstr = get(dud.notice,'string');
   nstr(1:4) = nstr(2:5);
   nstr{5} = 'The second stable trajectory';
   set(dud.notice,'string',nstr);
   set(stopbutt,'enable','on');

   switch settings.solver
     case 'Dormand Prince'      
       [tp,Xp] = ppdp45(dfcn,int,w,ppdisp);
       
     case 'ode45'       
       [tp,Xp] = ode45(dfcn,int,w,options);
       
     case 'ode23'       
       [tp,Xp] = ode23(dfcn,int,w,options);
       
     case 'ode113'      
       [tp,Xp] = ode113(dfcn,int,w,options);
       
     case 'ode15s'      
       [tp,Xp] = ode15s(dfcn,int,w,options);
       
     case 'ode23s'      
       [tp,Xp] = ode23s(dfcn,int,w,options);
       
     case 'Runge-Kutta 4'       
       [tp,Xp] = pprk4(dfcn,int,w,ppdisp);
       
     otherwise
       error('Undefined solver.');
   end    
%   [tp,Xp] = ppdp45(dfcn,[0,-1e6],w,ppdisp);
   set(stopbutt,'enable','off');
   
   aud = get(ppdispa,'user');
   newhand(2) = aud.line;
   
   X2=[z';Xp];
   x2 = [X2,[NaN;tp]];
   set(newhand(2),'xdata',x2(:,1),'ydata',x2(:,2),'zdata',x2(:,3));
   
   VV=V(:,I(2));
   w = z + offs(2)*VV;
   nstr = get(dud.notice,'string');
   nstr(1:4) = nstr(2:5);
   nstr{5} = 'The first unstable trajectory';
   set(dud.notice,'string',nstr);
   set(stopbutt,'enable','on');
   int = [0,1e6];

   switch settings.solver
     case 'Dormand Prince'      
       [tp,Xp] = ppdp45(dfcn,int,w,ppdisp);
       
     case 'ode45'       
       [tp,Xp] = ode45(dfcn,int,w,options);
       
     case 'ode23'       
       [tp,Xp] = ode23(dfcn,int,w,options);
       
     case 'ode113'      
       [tp,Xp] = ode113(dfcn,int,w,options);
       
     case 'ode15s'      
       [tp,Xp] = ode15s(dfcn,int,w,options);
       
     case 'ode23s'      
       [tp,Xp] = ode23s(dfcn,int,w,options);
       
     case 'Runge-Kutta 4'       
       [tp,Xp] = pprk4(dfcn,int,w,ppdisp);
       
     otherwise
       error('Undefined solver.');
   end    
%   [tp,Xp] = ppdp45(dfcn,[0,1e6],w,ppdisp);
   set(stopbutt,'enable','off');
   
   aud = get(ppdispa,'user');
   newhand(3) = aud.line;
   X3=[z';Xp];
   x3 = [X3,[NaN;tp]];
   set(newhand(3),'xdata',x3(:,1),'ydata',x3(:,2),'zdata',x3(:,3));
   
   w = z - offs(2)*VV;
   nstr = get(dud.notice,'string');
   nstr(1:4) = nstr(2:5);
   nstr{5} = 'The second unstable trajectory';
   set(dud.notice,'string',nstr);
   set(stopbutt,'enable','on');
   
   switch settings.solver
     case 'Dormand Prince'      
       [tp,Xp] = ppdp45(dfcn,int,w,ppdisp);
       
     case 'ode45'       
       [tp,Xp] = ode45(dfcn,int,w,options);
       
     case 'ode23'       
       [tp,Xp] = ode23(dfcn,int,w,options);
       
     case 'ode113'      
       [tp,Xp] = ode113(dfcn,int,w,options);
       
     case 'ode15s'      
       [tp,Xp] = ode15s(dfcn,int,w,options);
       
     case 'ode23s'      
       [tp,Xp] = ode23s(dfcn,int,w,options);
       
     case 'Runge-Kutta 4'       
       [tp,Xp] = pprk4(dfcn,int,w,ppdisp);
       
     otherwise
       error('Undefined solver.');
   end    
%   [tp,Xp] = ppdp45(dfcn,[0,1e6],w,ppdisp);
   set(stopbutt,'vis','off');
   
   aud = get(ppdispa,'user');
   newhand(4) = aud.line;
   X4=[z';Xp];
   x4 = [X4,[NaN;tp]];
   set(newhand(4),'xdata',x4(:,1),'ydata',x4(:,2),'zdata',x4(:,3));
   
   eqpt = plot(z(1),z(2),...
               'color',ecol,...
               'markersize',20,...
               'marker','.','Erasemode','normal');
   dud.solhand = [dud.solhand;newhand(:)];
   dud.ephand = [dud.ephand;eqpt];
   set(newhand,'color',scol);
   set(newhand,'erase','normal');
   nstr = get(dud.notice,'string');
   nstr(1:4) = nstr(2:5);
   nstr{5} = 'Ready.';
   set(dud.notice,'string',nstr);
   set(gcf,'user',dud);
   
elseif strcmp(action,'zoomin')
   
   % 'zoomin' is the callback for the Zoomin menu item.  It allows the
   % user to pick a new display rectangle.
   
   set(gcf,'WindowButtonDownFcn','pplane6(''zoom'')',...
      'WindowButtonUpFcn','1;','inter','on');
   set(gca,'inter','on');
   dud = get(gcf,'user');
   nstr = get(dud.notice,'string');
   nstr(1:4) = nstr(2:5);
   nstr{5} = ['Pick a new display rectangle by clicking and ',...
         'dragging the mouse, or by clicking on a point.'];
   set(dud.notice,'string',nstr);
   
elseif strcmp(action,'zoom')
   
   disph = gcf;
   dud = get(disph,'user');
   axh = dud.axes;
   aud = get(axh,'user');
   DY = aud.DY;
   w = dud.syst.wind;
   q1 = get(disph,'currentpoint');
   p1 = get(axh,'currentpoint');
   p1 = p1(1,1:2);
   rbbox([q1 0 0],q1);
   p2 = get(axh,'currentpoint');
   p2 = p2(1,1:2);
   if all(abs(p1'-p2')>0.01*DY)
      a = [p1;p2];
      a = [min(a);max(a)];
      DY = (a(2,:) - a(1,:))';  
   else
      DY = DY/4;
      a(1) = max(w(1),p1(1)-DY(1));
      a(2) = min(w(2),p1(1)+DY(1));
      a(3) = max(w(3),p1(2)-DY(2));
      a(4) = min(w(4),p1(2)+DY(2));
      DY(1) = a(2) - a(1);
      DY(2) = a(4) - a(3);
   end    
   WINvect = a(:)';
   dud.syst.wind = WINvect;
   aud.DY = DY;
   dwind = [WINvect(1); WINvect(3); -WINvect(2); -WINvect(4)];
   aud.cwind = dwind - dud.settings.magn*[aud.DY;aud.DY];
   set(axh,'user',aud); 
   set(disph,'user',dud);
   set(disph,'WindowButtonDownFcn','pplane6(''down'')',...
      'WindowButtonUpFcn','');
   pplane6('dirfield',disph);
   ppset = findobj('name','PPLANE6 Setup');
   if isempty(ppset)
      pplane6('confused');
   else
      sud = get(ppset,'user');
      sud.c.wind = WINvect;
      sud.o.wind = WINvect;
      set(sud.h.wind(1),'string',num2str(WINvect(1)));
      set(sud.h.wind(2),'string',num2str(WINvect(2)));
      set(sud.h.wind(3),'string',num2str(WINvect(3)));
      set(sud.h.wind(4),'string',num2str(WINvect(4)));
      set(ppset,'user',sud);
   end
   
elseif strcmp(action,'showbar')

  sbfig = gcbf;
  domymenu('menubar','toggletoolbar',sbfig);
  hhset = get(0,'showhiddenhandles');
  set(0,'showhiddenhandles','on');
  state = get(sbfig,'toolbar');
  if strcmp(state,'figure')
    name = get(sbfig,'name');
    fixtb = ['set(gcbo,''state'',''off'');'];
    set(findobj(sbfig,'tooltipstr','Print'),...
        'clickedcallback','pplane6(''print'');');
    switch name
     case 'PPLANE6 Display'
      set(findobj(sbfig,'tooltipstr','Zoom Out'),...
          'clickedcallback',['pplane6(''zoomback'');' fixtb]);
      set(findobj(sbfig,'tooltipstr','Zoom In'),...
          'clickedcallback',['pplane6(''zoomin'');' fixtb]);
      delete(findobj(sbfig,'tooltipstr','Rotate 3D'));
      
     case 'PPLANE6 Linearization'
      delete(findobj(sbfig,'tooltipstr','Zoom Out'));
      delete(findobj(sbfig,'tooltipstr','Zoom In'));
      delete(findobj(sbfig,'tooltipstr','Rotate 3D'));
     otherwise
      delete(findobj(sbfig,'tooltipstr','Zoom Out'));
      delete(findobj(sbfig,'tooltipstr','Zoom In'));
      fud = get(sbfig,'user');
      switch fud.type
       case {4, 5}
        set(findobj(sbfig,'tooltipstr','Rotate 3D'),'vis','on');
       otherwise
        set(findobj(sbfig,'tooltipstr','Rotate 3D'),'vis','off');
      end

    end       
    sbmh = findobj(sbfig,'label','Show &Toolbar');
    set(sbmh,'label','Hide &Toolbar','checked','off');
    uni = get(0,'units');
    ss = get(0,'screensize');
    funit = get(sbfig,'units');
    set(sbfig,'units',uni);
    sw = ss(3);sh = ss(4);
    fpos = get(sbfig,'pos');
    if fpos(2)+fpos(4)>sh-40;
      fpos(2) = sh - fpos(4) -70;
      set(sbfig,'pos',fpos);
    end
    set(sbfig,'units',funit);
    
  else
    sbmh = findobj(sbfig,'label','Hide &Toolbar');
    set(sbmh,'label','Show &Toolbar','checked','off');
  end
  set(0,'showhiddenhandles',hhset)
 
elseif strcmp(action,'dall')
  
   % 'dall' is the callback for the Erase all graphics objects.  
   
   disph = gcf;
   dud = get(disph,'user');
   notice = dud.notice;
   kk = find(ishandle(dud.solhand));    
   delete(dud.solhand(kk));
   dud.solhand = [];
   kk = find(ishandle(dud.ephand));    
   delete(dud.ephand(kk));
   dud.ephand = [];
   dud.eqpts = [];
   kk = find(ishandle(dud.contours));    
   delete(dud.contours(kk));
   dud.contours = [];
   if notice
      set(dud.butt(1),'enable','off');
   end
   set(disph,'user',dud);
  
   
elseif strcmp(action,'dallsol')
   
   % 'dallsol' is the callback for the Erase all solutions option.  
   
   disph = gcf;
   dud = get(disph,'user');
   notice = dud.notice;
   kk = find(ishandle(dud.solhand));    
   delete(dud.solhand(kk));
   dud.solhand = [];
   if notice
      set(dud.butt(1),'enable','off');
   end
   set(disph,'user',dud);
   
elseif strcmp(action,'dallep')
   
   % 'dallep' is the callback for the Erase all equilibrium points option.  
   
   disph = gcf;
   dud = get(disph,'user');
   notice = dud.notice;
   kk = find(ishandle(dud.ephand));  
   delete(dud.ephand(kk));
   dud.ephand = [];
   dud.eqpts = [];
   if notice
      set(dud.butt(1),'enable','off');
   end
   set(disph,'user',dud);
   
elseif strcmp(action,'dalllev')
   
   % 'dalllev' is the callback for the Erase all level curves option.  
   
   disph = gcf;
   dud = get(disph,'user');
   notice = dud.notice;
   kk = find(ishandle(dud.contours));
   delete(dud.contours(kk));
   dud.contours = [];
   if notice
      set(dud.butt(1),'enable','off');
   end
   set(disph,'user',dud);
   
elseif strcmp(action,'newton')
   
   % Newton's method to find equilibrium points.
   
   Iterlimit = 50;
   
   Iter=0;
   
   % The increment for calculating approximate derivatives.
   
   h=.000001;   
   
   dfcn = input2;
   
   zInit = input1;
   
   zNext=zInit(:);
   functionf = zeros(2,1);      
   functionf=feval(dfcn,0,zNext);
   functionf=functionf(:);
   
   % Allow for large/small solutions.
   
   errorlim = norm(functionf,inf)*0.000001;  
   
   while ( (norm(functionf,inf) > errorlim) & (Iter < Iterlimit)        )
      Iter = Iter + 1;
      
      % Now we calculate the jacobian.  
      
      for jjw=1:2                       
         sav = zNext(jjw);
         zNext(jjw) = zNext(jjw) + h;
         functionfhj = feval(dfcn,0,zNext);     
         functionfhj = functionfhj(:);
         Jacobian(:,jjw) = (functionfhj-functionf)/h;   
         zNext(jjw) = sav;
      end
      zNext = zNext - Jacobian\(functionf);
      functionf = feval(dfcn,0,zNext);
      functionf=functionf(:);
   end
   
   if Iter > Iterlimit - 1          
      fLag=[0;0];
   else                 
      fLag=[1;1];       
      for j=1:2                 
         sav = zNext(j);
         zNext(j) = zNext(j) + h;
         functionfhj = feval(dfcn,0,zNext);     
         functionfhj = functionfhj(:);
         Jacobian(:,j) = (functionfhj-functionf)/h;     
         zNext(j) = sav;
      end
   end
   output = [zNext,Jacobian,fLag];
   
elseif strcmp(action,'paraeval')
   
   %    Replace a parameter with its value in string form.
   
   para = deblank(input1);
   value = input2;
   value = ['(',value,')'];
   str = input3;
   ll = length(str);
   lp = length(para);
   lv = length(value);
   
   if strcmp(para,str)
      str = value
   elseif (ll >= lp+1)
      k = findstr(para,str);
      
      lk = length(k);
      lopstr = '(+-*/^';
      ropstr = ')+-*/^';
      s = [];
      pos = 1;
      for jj = 1:lk
        if (((k(jj) == 1)|(find(lopstr == str(k(jj)-1))))...
            &((k(jj)+lp-1 == ll)|(find(ropstr == str(k(jj) + lp)))))
          s = [s,str(pos:(k(jj)-1)),value];
          pos = k(jj)+lp;
        end
      end
      str = [s,str(pos:ll)];
   end
   output = str;
   
   
elseif strcmp(action,'settings')
   
   % 'settings' is the call back for the Settings menu option.  It sets
   % up the PPLANE6 Settings window, which allows the user to interactively
   % change several parameters that govern the behaviour of the program.
   
   dud = get(gcf,'user');
   data.settings = dud.settings;
   solver = dud.settings.solver;
   left = 5; nudge = 3; varl = 60;
   setfig = findobj('name','PPLANE6 Settings');
   if ~isempty(setfig);
     delete(setfig);
   end
   
   setfig = figure('name','PPLANE6 Settings','numb','off',...
      'tag','PPLANE6','vis','off');
   
   pplane6('figdefault',setfig);
   set(setfig,'menubar','none');
   
   setfr = uicontrol('style','frame');  
   cwfr = uicontrol('style','frame');
   ss = uicontrol('style','text','horiz','center',...
      'string',['Settings for ',dud.settings.solver]);
   
   nstepcall =[
      'data = get(gcf,''user'');',...
         'ss = max(round(str2num(get(data.nstep,''string''))),0);',...
         'data.settings.refine = ss;',...
         'set(data.nstep,''string'',num2str(ss));',...
         'set(gcf,''user'',data);'];
   
   nstep = uicontrol('style','text','horiz','left',...
      'string','Number of plot steps per computation step:  ');
   data.nstep = uicontrol('style','edit','call',nstepcall,...
      'string',num2str(data.settings.refine));
   
   if strcmp(solver,'Runge-Kutta 4')
     rtolstr = 'Step size: ';
     rtolentry = num2str(data.settings.stepsize);
     rtolcall =['data = get(gcf,''user'');',...
           'data.settings.stepsize = str2num(get(data.rtol,''string''));',...
           'set(data.rtol,''string'',num2str(data.settings.stepsize));',...
           'set(gcf,''user'',data);'];
   else
     rtolstr = 'Relative error tolerance: ';
     rtolentry = num2str(data.settings.tol);
     rtolcall =['data = get(gcf,''user'');',...
           'data.settings.tol = str2num(get(data.rtol,''string''));',...
           'set(data.rtol,''string'',num2str(data.settings.tol));',...
           'set(gcf,''user'',data);'];
   end
   rtol = uicontrol('style','text','horiz','left',...
       'string',rtolstr); 
   data.rtol = uicontrol('style','edit','call',rtolcall,...
      'string',rtolentry);
   
   kk = 1+2*data.settings.magn;
   magcall = ['data = get(gcf,''user'');',...
         'mag =         (str2num(get(data.mag,''string''))-1)/2;',...
         'data.settings.magn = max(0,mag);',...
         'set(gcf,''user'',data);'];
   
   cw1 = uicontrol('style','text','horiz','left',...
      'string','The calculation window is');
   data.mag = uicontrol('style','edit','call',magcall,...
      'string',num2str(kk));
   cw2 = uicontrol('style','text','horiz','left',...
      'string',' times as large as the ');
   cw3 = uicontrol('style','text','horiz','left',...
      'string','display window.');
   
   gob = uicontrol('style','push','string','Go Away','call','close');
   
   chb = uicontrol('style','push',...
      'string','Change settings',...
      'call','pplane6(''setchange'')');
   
   ext = get(nstep,'extent');
   ht = ext(4)+nudge;
   stw = ext(3);                % = nstepw = rtolw
   varl = varl*ht/19;
   cwfrb = 2*left + ht;
   cwfrh = 2*nudge + 2*ht;
   setfrb = cwfrb + cwfrh;
   setfrh = 3*nudge + 3*ht;
   figh = setfrb + setfrh + left;
   bb = left;
   cw3b = cwfrb + nudge;        
   cw2b = cw3b + ht;    % = cw1b = cweb
   rtolb = setfrb + nudge;
   rtolbb = rtolb;
   if strcmp(solver,'Runge-Kutta 4')
     rtolbb = rtolbb +ht/2;
   end
   nstepb = rtolb + ht;
   ssb = nstepb + ht + nudge;
   cw1ext = get(cw1,'extent');
   cw1w = cw1ext(3);
   cw2ext = get(cw2,'extent');
   cw2w = cw2ext(3);
   cwew = 40*ht/19;
   ssw = stw + varl;
   frw = 2*nudge + ssw;
   figw = frw + 2*left;
   buttw = figw/3;
   sep = figw/9;
   sl = left + nudge;
   gobl = sep;
   chbl = 2*sep + buttw;
   
   sunit = get(0,'units');
   set(0,'units','pix');
   ssize = get(0,'screensize');
   figb = ssize(4) - figh - 50;
   
   set(setfig,'pos',[20,figb,figw,figh]);
   set(setfr,'pos',[left,setfrb,frw,setfrh]);
   set(cwfr,'pos',[left,cwfrb,frw,cwfrh]);
   set(ss,'pos',[sl,ssb,ssw,ht]);
   set(nstep,'pos',[sl,nstepb,stw,ht]);
   set(data.nstep,'pos',[sl+stw,nstepb,varl,ht]);
   set(rtol,'pos',[sl,rtolbb,stw,ht]);
   set(data.rtol,'pos',[sl+stw,rtolbb,varl,ht]);
   set(cw1,'pos',[sl,cw2b,cw1w,ht]);
   set(cw2,'pos',[sl+cw1w+cwew,cw2b,cw2w,ht]);
   set(cw3,'pos',[sl,cw3b,ssw,ht]);
   set(data.mag,'pos',[sl+cw1w,cw2b,cwew,ht]);
   set(gob,'pos',[gobl,bb,buttw,ht]);
   set(chb,'pos',[chbl,bb,buttw,ht]);
   
   
   set(setfig,'user',data);
   set(setfig,'units','normal');
   set(findobj(setfig,'type','uicontrol'),'units','normal');
   set(setfig,'vis','on','resize','on');
   ch = get(setfig,'child');
   set([nstep,data.nstep],'vis','off')
   if strcmp(solver,'Runge-Kutta 4')
     ch = setdiff(ch,[nstep,data.nstep]);
   end
   set(ch,'vis','on');
   
   
elseif strcmp(action,'setchange')
   
   % 'setchange' is the callback for the Change button 
   % on the PPLANE6 Settings window.
   
   data = get(gcf,'user');
   settings = data.settings;
   ppdisp = findobj('name','PPLANE6 Display');
   dud = get(ppdisp,'user');
   if isempty(ppdisp)
      pplane6('confused');
   else
      dud.settings = settings;
      set(ppdisp,'user',dud);
      WINvect = dud.wmat;
      dwind = [WINvect(1); WINvect(3); -WINvect(2); -WINvect(4)];
      aud = get(dud.axes,'user');  
      aud.cwind = dwind - dud.settings.magn*[aud.DY;aud.DY];
      set(dud.axes,'user',aud);
   end
   ppset = findobj('name','PPLANE6 Setup');
   if isempty(ppset)
      pplane6('confused');
   else
      sud = get(ppset,'user');
      sud.settings = settings;
      set(ppset,'user',sud);
   end  
   close
   
   
elseif strcmp(action,'delete')
   
   % 'delete' is the callback for the Delete a graphics object selection
   % on the menu.
   
   disph = gcf;
   dud = get(disph,'user');
   arr = dud.arr;
   lv = get(arr.lines,'vis');
   av = get(arr.arrows,'vis');
   if ~isempty(arr.hx)
      nv = get(arr.hx(1),'vis');
   elseif ~isempty(arr.hy)
      nv = get(arr.hx(1),'vis');
   else

      nv = zeros(1,0);
   end
   if ~isempty(arr.barrows)
      bv = get(arr.barrows,'vis');
   else
      bv = zeros(1,0);
   end
   handles = [arr.lines;arr.arrows;arr.hx;arr.hy;arr.barrows];
   set(handles,'vis','off');
   oldcall = get(disph,'WindowButtonDownFcn');
   set(disph,'WindowButtonDownFcn','');
   trjh = dud.solhand;
   notice = dud.notice;
   if notice   % Display window
      nstr = get(notice,'string');
      nstr(1:4) = nstr(2:5);
      nstr{5} = 'Select a graphics object with the mouse.';
      set(notice,'string',nstr);  
   end   
   ginput(1);
   objh = get(disph,'currentobject');
   typ = get(objh,'type');
   axh = dud.axes;
   hh = get(dud.title.axes,'children');
   hh = [hh;get(axh,'title');get(axh,'xlabel');get(axh,'ylabel')];
   if notice   % Display window
     eph = dud.ephand;
     levh = dud.contours;
     eqpt = dud.eqpts;
     nstr(1:4) = nstr(2:5);
     if strcmp(typ,'line')
       xd = get(objh,'xdata');
       if length(xd)==1;
         hh = find(eqpt(:,1) == xd);
         if length(hh) > 1
           hh = find(eqpt(hh,2) == get(objh,'ydata'));
         end
         if size(eqpt,1) == 1;
           dud.eqpts = [];
         else     
           dud.eqpts = [eqpt(1:hh-1,:);eqpt(hh+1:size(eqpt,1),:)];
         end      
       end
       dud.solhand = setdiff(dud.solhand,objh);     
       dud.ephand = setdiff(dud.ephand,objh);     
       dud.contours = setdiff(dud.contours,objh);     
       delete(objh); 
       nstr{5} = 'Ready.';
       
     elseif strcmp(typ,'text') & ~ismember(objh,hh)
       dud.contours = setdiff(dud.contours,objh)';     
       delete(objh); 
       nstr{5} = 'Ready.';
       
     else
       nstr{5} = 'The object you selected cannot be deleted.';
       
     end
     set(notice,'string',nstr);
   else     % Linearization window
     if strcmp(typ,'line')
       xd = get(objh,'xdata');  
       if length(xd)>1   % Do not delete the eq. pt. at (0,0)
         dud.solhand = setdiff(dud.solhand,objh)';    
         delete(objh); 
       end
     elseif ~ismember(objh,hh)
       delete(objh); 
     end
   end
  
   set(arr.lines,'vis',lv);
   set(arr.arrows,'vis',av);
   set([arr.hx;arr.hy],'vis',nv);
   set(arr.barrows,'vis',bv);
   set(disph,'user',dud);
   set(disph,'WindowButtonDownFcn','pplane6(''down'')');
   
elseif strcmp(action,'text')
   
   ppdisp = gcf;
   oldcall = get(ppdisp,'WindowButtonDownFcn');
   set(ppdisp,'WindowButtonDownFcn','');
   prompt = ['Enter the text here. Then choose ',...
         'the location in the Display Window.'];
   txtstr = inputdlg(prompt,'Text entry');
   if ~isempty(txtstr)
      txtstr = txtstr{1};
      figure(ppdisp);
      gtext(txtstr);
   end
   set(ppdisp,'WindowButtonDownFcn',oldcall);
   
elseif strcmp(action,'plotxy')  % Start a graph 
   
   type = input1;
   
   ppdisp =gcf;
   dud = get(ppdisp,'user');
   
   handles = dud.solhand;
   printstr = dud.printstr;
   exsol=0;
   lll = length(handles);
   
   if (lll)  % Are there any orbits?
      kk=0;
      while (kk < lll) & (exsol == 0)
         kk = kk + 1;
         xd = get(handles(kk),'xdata');
         if (length(xd) > 7)
            exsol = 1;
         end
      end
   end
   if (exsol == 0)
      nstr = get(dud.notice,'string');
      nstr(1:3) = nstr(3:5);
      nstr{4} = 'There are no solution curves.';
      nstr{5} = 'Ready.';
      set(dud.notice,'string',nstr);
      return
   end
   
   oldcall = get(ppdisp,'WindowButtonDownFcn');
   set(ppdisp,'WindowButtonDownFcn','');
   arr = dud.arr;
   lv = get(arr.lines,'vis');
   av = get(arr.arrows,'vis');
   if ~isempty(arr.hx)
      nv = get(arr.hx(1),'vis');
   elseif ~isempty(arr.hy)
      nv = get(arr.hy(1),'vis');
   else
      nv = zeros(1,0);
   end
   if ~isempty(arr.barrows)
      bv = get(arr.barrows,'vis');
   else
      bv = zeros(1,0);
   end
   handles = [arr.lines;arr.arrows;arr.hx;arr.hy;arr.barrows];
   set(handles,'vis','off');
   
   nstr = get(dud.notice,'string');
   nstr(1:4) = nstr(2:5);
   nstr{5} = 'Select a solution curve with the mouse.';
   set(dud.notice,'string',nstr);
   ginput(1);
   objh = get(ppdisp,'currentobject');
   if isempty(objh) 
      solflag = 0;
   elseif ~(strcmp(get(objh,'type'),'line'))
      solflag = 0;
   else
      t=get(objh,'zdata'); 
      if length(t)<10
         solflag = 0;
      else
         solflag = 1;
      end       
   end
   if solflag == 0
      nstr = get(dud.notice,'string');
      nstr(1:4) = nstr(2:5);
      nstr{5} = 'This object is not a solution curve.';
      set(dud.notice,'string',nstr);
      set(ppdisp,'WindowButtonDownFcn',oldcall);
      set(arr.lines,'vis',lv);
      set(arr.arrows,'vis',av);
      set([arr.hx;arr.hy],'vis',nv);
      return
   end
   set(arr.lines,'vis',lv);
   set(arr.arrows,'vis',av);
   set([arr.hx;arr.hy],'vis',nv);
   set(arr.barrows,'vis',bv);
   t=get(objh,'zdata');
   x=get(objh,'xdata');
   y=get(objh,'ydata');
   hh = pplane6('plotxyfig',type,gcf);
   set(ppdisp,'WindowButtonDownFcn',oldcall);
   aud = get(hh(2),'user');
   ud = get(hh(1),'user');
   ud.data = [t;x;y];
   set(hh(1),'user',ud);
   pplane6('plxy',aud.rad,hh(1));
   
elseif strcmp(action,'plotxyfig')  % Build the graph figure.
   
   type = input1;
   cfig = input2;  % This is ppdisp or a ppxy
   ppdisp = findobj('name','PPLANE6 Display');
   dud = get(ppdisp,'user');
   ppdispa = dud.axes;
   xstring = get(get(ppdispa,'XLabel'),'string');
   ystring = get(get(ppdispa,'YLabel'),'string');
   dud = get(ppdisp,'user');
   
   ppxy = figure('number','off',...
      'tag','PPLANE6','visible','off');
   name = ['PPLANE6 t-plot # ',int2str(ppxy)];
   ud.color = dud.color;
   ud.type = 0;
   set(ppxy,'name',name,'user',ud);
   pplane6('figdefault',ppxy);
         
   % Menus and Toolbar
         
   hhsetup = get(0,'showhiddenhandles');
   set(0,'showhiddenhandles','on');

   % Configure the Toolbar.
   
   set(ppxy,'ToolBar','none');
 
   % Menus

   emenu = findobj(gcf,'label','&Edit');  
   tmenu = findobj(gcf,'label','&Tools'); 
   delete(tmenu)
   
   % File menu
  
   fmenu = findobj(gcf,'label','&File');  
   delete(findobj(fmenu,'label','&New Figure'));
   delete(findobj(fmenu,'label','&Open...'));
   set(findobj(fmenu,'label','&Close'),'pos',1);
   set(findobj(fmenu,'label','&Save'),...
       'pos',2,'separator','off');
   set(findobj(fmenu,'label','Save &As...'),...
       'pos',3);
   set(findobj(fmenu,'label','&Export...'),...
       'pos',4);
   delete(findobj(fmenu,'label','Pre&ferences...'));
   set(findobj(fmenu,'label','Pa&ge Setup...'),'pos',4);
   set(findobj(fmenu,'label','Print Set&up...'),'pos',5);
   set(findobj(fmenu,'label','Print Pre&view...'),'pos',6);
   set(findobj(fmenu,'label','&Print...'),'pos',7);
   qmenu = uimenu(fmenu,'label','Quit PPLANE6',...
                  'call','pplane6(''quit'')',...
                  'separator','on');
   
   % View menu
         
   set(findobj(gcf,'label','&Figure Toolbar'),...
       'call','pplane6(''showbar'')');
   
   set(0,'showhiddenhandles',hhsetup);
   
   fs = get(ppxy,'defaultaxesfontsize');
   r = fs/10;
   axw = 437*.8;        % Default axes width
   axh = 315*.8;        % Default axes height
   axl = 45;    % Default axes left
   buttw = 40;     % Default button width
   titleh = 45;    % Default title height
   legw = 90;     % Default legend width
   axb = 35;       % Default axes bottom
   sep = 10;
   fh = axb + axh + titleh;  % Default figure height.
   fw = axl + axw + sep + legw + sep; % Default figure width.
   uni = get(0,'units');
   set(0,'units','pixels');
   ss = get(0,'screensize');
   set(0,'units',uni);
   sw = ss(3);sh = ss(4);
   if r*fh > sh -80;
      r = (sh-80)/fh;
   end
   if r*fw > sw - 50
      r = (sw - 50)/fw;
   end  
   fs = 10*r;
   lw = 0.5*r;
   set(ppxy,'defaultaxesfontsize',fs,'defaultaxeslinewidth',lw);
   set(ppxy,'defaulttextfontsize',fs);
   set(ppxy,'defaultlinelinewidth',lw);
   set(ppxy,'defaultuicontrolfontsize',fs*0.9);
   axw = r*axw;
   axh = r*axh;
   axl = r*axl;
   legw = r*legw;
   axb = r*axb;
   sep = r*sep;
   
   % The legend.
   
   
   leg = axes('units','pix','box','on','drawmode','fast','nextplot','add',...
      'xtick',[-1],'ytick',[-1],'xticklabel','','yticklabel','',...
      'xlim',[0,1],'ylim',[0,1],'clipping','on','visible','off');
   
   set(leg,'user',str2mat(xstring,ystring));
   axes(leg);
   xh = text(0,0,xstring,'units','norm','visible','off',...
      'parent',leg);
   yh = text(0,0,ystring,'units','norm','visible','off',...
      'parent',leg);
   set(xh,'units','pix')
   set(yh,'units','pix')
   xext = get(xh,'extent');
   yext = get(yh,'extent');
   set(xh,'units','norm')
   set(yh,'units','norm')
   th = max(xext(4),yext(4))+3*r;
   axhn = max(axh, 11*th + 4 + 6*r);  % Nudge the axes height if needed.
   axw = axw*axhn/axh;
   axh = axhn;
   frsep = (axh - 11*th - 4 - 6*r)/4;
   
   legh = 2*(th+3*r);
   legb = axb + axh - legh;  %frsep*4 + th*9 +4;
   legl = axl + axw + sep;
   
   
   % If the legend text is too big, make the legend and the figure larger.
   
   legpos = [legl+1, legb, legw, legh];
   set(leg,'pos',legpos);
   xext = get(xh,'extent');
   yext = get(yh,'extent');
   tw = max(xext(3),yext(3))+0.1;
   
   rrrr = 0.5;
   if (tw > rrrr)
      rrr = tw/rrrr;
      legw = legw*rrr;
      tw = rrrr;
   end
   legpos = [legl+1, legb, legw, legh];
   set(leg,'pos',legpos);
   fw = axl + axw + sep + legw + sep; % Figure width.
   
   tx = min(1-tw,2/3);
   set(xh,'pos',[tx,2/3]);
   set(yh,'pos',[tx,1/3]);
   
   line('xdata',[0.1,tx-0.1],'ydata',[2/3,2/3],'linestyle','-',...
      'color',ud.color.tx,'vis','off');
   line('xdata',[0.1,tx-0.1],'ydata',[1/3,1/3],'linestyle','--',...
      'color',ud.color.ty,'vis','off'); 
   
   % Set up the title.
   
   tax = axes('box','off','xlim',[0 1],'ylim',[0 1],...
      'units','pix','vis','off','xtick',[-1],'ytick',[-1],...
      'xticklabel','','yticklabel','');
   titb = axb + axh;
   titl = axl;
   titw = axw;
   titeq = text(0.01,0.5,dud.tstr,'vert','middle');
   set(titeq,'units','pix');
   ext = get(titeq ,'extent');
   set(titeq,'units','data');
   titleh = ext(4)+6*r;
   p1 = get(dud.title.p1,'string');
   p2 = get(dud.title.p2,'string');
   pp1 = text(0.85,0.5,p1,'vert','middle');
   ext = get(pp1,'extent');
   pp1l = 1 - ext(3);
   set(pp1,'pos',[pp1l,0.5]);
   pp2 = text(0.7,0.5,p2,'vert','middle');
   ext = get(pp2,'extent');
   pp2l = pp1l - ext(3)-0.05;
   set(pp2,'pos',[pp2l,0.5]);
   
   fh = axb + axh + titleh;  % Figure height.
   
   pos = get(cfig,'pos');
   fl = max(0,pos(1)-30);
   fb = max(20,pos(2)-30);
   fpos = [fl,fb,fw,fh];
   set(ppxy,'pos',fpos);
   
   set(tax,'pos',[titl,titb,titw,titleh]);
   
   set(tax,'color',get(ppxy,'color'));
   
   
   % The t-plot axes. 
   
   axpos = [axl,axb,axw,axh];
   
   axy = axes('units','pix','pos',axpos,'box',...
      'on','xgrid','on','ygrid','on','next','add',...
      'drawmode','fast');
   
   output = [ppxy,axy];
   
   
   
   % The position of the close button
   
   bbot = axb;
   bwid = legw;
   bleft = legl;
   bpos = [bleft,bbot,bwid,th];
   
   % The position of the print button.
   
   pbbot = bbot + th + frsep;
   pbpos = [bleft, pbbot, legw, th];
   
   % The position of the crop button.
   cbbot = pbbot + th + frsep;
   cbpos = [bleft, cbbot, legw, th];
   
   % The positions of the radio frame and its elements.
   
   frbot = cbbot + th + frsep;
   frleft = legl;
   frht = 6*th+4;
   frpos = [frleft,frbot,legw,frht];
   
   frtitleft = frleft+2;
   frtitwid = legw-4;
   frtitpos = [frtitleft, frbot+5*th, frtitwid, th];
   
   radleft = frleft + 2;
   radwid = legw - 4;
   radbot5 = frbot + 2;
   radbot4 = radbot5 + th;
   radbot3 = radbot4 + th;
   radbot2 = radbot3 + th;
   radbot1 = radbot2 + th;
   pcall = [
      'ppdisp = findobj(''name'',''PPLANE6 Display'');',...
         'dud = get(ppdisp,''user'');',...
         'eval(dud.printstr)'
   ];
   
   but = uicontrol('style','push',...
      'pos',bpos,...
      'string','Go away',...
      'call','close');
   
   pbut = uicontrol('style','push',...
      'pos',pbpos,...
      'string','Print',...
      'call',pcall);
   
   cbut = uicontrol('style','push',...
      'pos',cbpos,...
      'string','Crop',...
      'call','pplane6(''crop'')');
   
   pframe = uicontrol('style','frame','pos',frpos);
   
   pfrtitle = uicontrol('style','text','pos',frtitpos,...
      'string','Graph','horizon','center');
   
   rval1 = ~(type -1);
   rval2 = (~(type -2))*2;
   rval3 = (~(type -3))*3;
   rval4 = (~(type -4))*4;
   rval5 = (~(type -5))*5;
   
   rad(1) = uicontrol('style','radio',...
      'pos',[radleft radbot1 radwid th],...
      'string',xstring,'value',rval1);
   
   rad(2) = uicontrol('style','radio',...
      'pos',[radleft radbot2 radwid th],...
      'string',ystring,'value',rval2,'max',2);
   
   rad(3) = uicontrol('style','radio',...
      'pos',[radleft radbot3 radwid th],...
      'string','Both','value',rval3,'max',3);
   
   rad(4) = uicontrol('style','radio',...
      'pos',[radleft radbot4 radwid th],...
      'string','3 D','value',rval4,'max',4);
   
   rad(5) = uicontrol('style','radio',...
      'pos',[radleft radbot5 radwid th],...
      'string','Composite','value',rval5,'max',5);
   
   for i=1:5
      set(rad(i),'user',[rad(:,[1:(i-1),(i+1):5]),leg,axy]);
   end
   
   callrad = [
      'me = gcbo;',...
         'vv = get(me,''value'');'...
         'mm = get(me,''max'');'...
         'if vv ,'...
         '      hand = get(me,''user'');',...
         '      set(hand(1:4),''value'',0);',...
         '      pplane6(''plxy'',me,gcf);'...
         'end, '...
         'set(me,''value'',mm);'...
         'axy = gca;',...
         'aud = get(axy,''user'');',...
         'aud.rad = me;',...
         'set(axy,''user'',aud);'];
   
   
   set(rad,'call',callrad);
   
   set(findobj(ppxy,'type','axes'),'units','normal');
   set(findobj(ppxy,'type','uicontrol'),'units','normal');
   set(ppxy,'resize','on');
   
   set(ppxy,'visible','on');
   
   nstr = get(dud.notice,'string');
   nstr(1:4) = nstr(2:5);
   nstr{5} = 'Ready.';
   set(dud.notice,'string',nstr);
   aud.h = [];
   aud.int = [0 0];
   aud.crop = cbut;
   aud.rad = rad(type);
   aud.leg = leg;
   set(axy,'user',aud);
   set(cbut,'user',axy);
   
elseif strcmp(action,'plxy')
   
   radbut = input1;
   fig = input2;
   fud = get(fig,'user');
   figure(fig)
   tbh = findobj(allchild(fig),'flat','type','uitoolbar');
   r3dh = findobj(tbh,'tooltipstr','Rotate 3D');
   ud = get(radbut,'user');
   axy = ud(6);
   axis('auto');
   delete(get(axy,'children'));
   leg = ud(5);
   legch = get(leg,'children');
   type = get(radbut,'max');
   fud.type = type;
   set(fig,'user',fud);
   if type == 3
      set(leg,'visible','on');
      set(legch,'visible','on');
   else
      set(leg,'visible','off');
      set(legch,'visible','off');
   end
   
   aud = get(axy,'user');
   aud.h = [];
   set(axy,'user',aud);  
   strings = get(leg,'user');
   xstring = deblank(strings(1,:));
   ystring = deblank(strings(2,:));
   ud = get(fig,'user');
   data = ud.data;
   color = ud.color;
   
   t = data(1,:);
   x = data(2,:);
   y = data(3,:);
   tmin = min(t);
   tmax = max(t);
   xmin = min(x);
   xmax = max(x);
   ymin = min(y);
   ymax = max(y);
   et = max((tmax-tmin)/20,1e-4);
   ex = max((xmax-xmin)/20,1e-4);
   ey = max((ymax-ymin)/20,1e-4);
   tmin1 = tmin - et;
   tmax1 = tmax + et;
   xmin = xmin - ex;
   xmax = xmax + ex;
   ymin = ymin - ey;
   ymax = ymax + ey;
   
   axes(axy);
   switch type
    case 1 
      plot(t,x,'color',color.tx,'linestyle','-');
      view(2);
      axis([tmin,tmax,xmin,xmax])
      xlabel('t')
      ylabel(xstring)
      set(r3dh,'vis','off')
      set(fig,'WindowButtonDownFcn','pplane6(''plxybdf'')');
    case 2
      plot(t,y,'color',color.ty,'linestyle','-');
      view(2);
      axis([tmin,tmax,ymin,ymax])
      xlabel('t')
      ylabel(ystring)
      set(r3dh,'vis','off')
      rotate3d off
      set(fig,'WindowButtonDownFcn','pplane6(''plxybdf'')');
    case 3
      plot(t,x,'color',color.tx,'linestyle','-');
      plot(t,y,'color',color.ty,'linestyle','--');
      axis([tmin,tmax,min(xmin,ymin),max(xmax,ymax)])
      view(2);
      xlabel('t')
      ylabel([xstring,' and ',ystring])
      set(r3dh,'vis','off')
      rotate3d off
      set(fig,'WindowButtonDownFcn','pplane6(''plxybdf'')');
    case 4
      plot3(x,y,t,'color',color.tx,'linestyle','-');
      view([-30,20]);
      axis([xmin,xmax,ymin,ymax,tmin1,tmax1]);
      zlabel('t')
      xlabel(xstring);
      ylabel(ystring);
      set(r3dh,'vis','on')
      rotate3d off
      set(fig,'WindowButtonDownFcn','');
    otherwise
      ax = [xmin,xmax,ymin,ymax,tmin1,tmax1];
      view([-30,20]);
      axis(ax);
      plot3(x,y,ax(5)*ones(size(x)),'color',color.ty,'linestyle','-');
      plot3(x,ax(4)*ones(size(y)),t,'color',color.ty,'linestyle','-');
      plot3(ax(2)*ones(size(x)),y,t,'color',color.ty,'linestyle','-');
      plot3(x,y,t,'color',color.tx,'linestyle','-');
      
      zlabel('t')
      xlabel(xstring);
      ylabel(ystring);
      set(r3dh,'vis','on')
      rotate3d off
      set(fig,'WindowButtonDownFcn','');
   end
   if (type < 4)
      set(aud.crop,'vis','on','enable','off');    
   else
      set(aud.crop,'vis','off');
   end  
   if type < 4
      set(fig,'windowbuttondownfcn','pplane6(''plxybdf'')');
   elseif type == 5 
      set(fig,'windowbuttondownfcn',' ');
   end  
   
elseif strcmp(action,'crop')
   
   cb = gcbo;
   axy = get(cb,'user');
   aud = get(axy,'user');
   delete(aud.h);
   set(aud.crop,'enable','off');
   aud.h = [];
   set(axy,'user',aud);
   ppxy = gcf;
   ud = get(ppxy,'user');
   data = ud.data;
   color = ud.color;
   t = data(1,:);
   x = data(2,:);
   y = data(3,:);
   int = aud.int;
   k = find((t>=int(1)) & (t<=int(2)));
   t = t(k);
   x = x(k);
   y = y(k);
   type = get(aud.rad,'max');
   hh = pplane6('plotxyfig',type,ppxy);
   ud = get(hh(1),'user');
   ud.data = [t;x;y];
   set(hh(1),'user',ud);
   aud = get(hh(2),'user');
   pplane6('plxy',aud.rad,hh(1))  
 
elseif strcmp(action,'plxybdf')
   
   dispa = gca;
   set(gcf,'windowbuttonmotionfcn','pplane6(''plxybmf'')',...
      'windowbuttonupfcn','pplane6(''plxybuf'')',...
      'inter','on');
   aud = get(dispa,'user');
   delete(aud.h);
   aud.h = [];
   set(aud.crop,'enable','off');
   point = get(dispa,'currentpoint');
   aud.start = point(1,1);
   aud.finish = point(1,1);
   %  aud.centh = plot(point(1,1),point(1,2),'or','erase','xor');
   aud.h = plot(point(1,1),point(1,2),'--g',...
      'erase','xor','vis','off');
   set(dispa,'user',aud);
   
elseif strcmp(action,'plxybmf')
   
   dispa = gca;
   aud = get(dispa,'user');
   point = get(dispa,'currentpoint');
   finish = point(1,1);
   start = aud.start;
   xlim = get(dispa,'xlim');
   ylim = get(dispa,'ylim');
   
   if abs(finish - start)>0.05*(xlim(2)-xlim(1));
      set(aud.h,'xdata',[start,start,NaN,finish,finish],...
         'ydata',[ylim,NaN,ylim],...
         'vis','on');
   end
   aud.finish = finish;
   set(gca,'user',aud);
   
elseif strcmp(action,'plxybuf')
   
   dispa = gca;
   xlim = get(dispa,'xlim');
   ylim = get(dispa,'ylim');
   aud = get(dispa,'user');
   set(gcf,'windowbuttonmotionfcn','',...
      'windowbuttonupfcn','',...
      'inter','on');
   start = aud.start;
   finish = aud.finish;
   if abs(finish - start)>0.05*(xlim(2)-xlim(1));
      set(aud.h,'erase','normal','vis','on');
      set(aud.crop,'enable','on');
      aud.int = [min(start,finish),max(start,finish)];
   else
      set(aud.h,'vis','off');
   end
   set(gca,'user',aud);
   
   
elseif strcmp(action,'print')
   
   dud = get(gcf,'user');
   nstr = get(dud.notice,'string');
   nstr(1:4) = nstr(2:5);
   nstr{5} = 'Preparing to print the PPLANE6 Display Window.  Please be patient.';
   set(dud.notice,'string',nstr);
   
   nstr(1:4) = nstr(2:5);
   nstr{5} = 'Printing the PPLANE6 Display Window.';
   set(dud.notice,'string',nstr);
   set(gcf,'pointer','watch');
   eval(dud.printstr);
   nstr(1:4) = nstr(2:5);
   nstr{5} = 'Ready.';
   set(dud.notice,'string',nstr);
   set(gcf,'pointer','arrow');
   
elseif strcmp(action, 'eqptlist')
   
   % The labels for equilibrium points.
   
   disp(' ');
   EqPtType = ['Saddle point.            ';
      'Nodal sink.              ';
      'Nodal source.            ';
      'Spiral sink.             ';
      'Spiral source.           ';
      'Spiral equilibrium point.';
      'Source.                  ';
      'Sink.                    ';
      'Unspecified.             ';];
   dud = get(gcf,'user');
   EqPtList = dud.eqpts;
   if isempty(EqPtList)
      disp('No equilibrium points have been computed.'),disp(' ')
   else
      disp('The following equilibrium points have been calculated:')
      disp(' ')
      L = size(EqPtList,1);
      eqpttext = cell(L,1);
      for k = 1:L
         disp([sprintf('(%6.4f, %6.4f)\t',EqPtList(k,1),EqPtList(k,2)),...
               EqPtType(EqPtList(k,3),:)])
      end
      disp(' ')
   end
   
elseif strcmp (action,'zoomback')
   
   disph = gcf;
   dud = get(disph,'user');
   axh = dud.axes;
   Xname = dud.syst.xvar;
   Yname = dud.syst.yvar;
   wmat = dud.wmat;
   WINvect = dud.syst.wind;
   
   NN = size(wmat,1);
   
   wch = 0;j=0;
   while wch == 0
      j = j+1;
      if WINvect == wmat(j,:)
         wch = j;
      end
   end
   winstr = cell(1,NN);
   for j = 1:NN
      a = num2str(wmat(j,1));
      b = num2str(wmat(j,2));
      c = num2str(wmat(j,3));
      d = num2str(wmat(j,4));
      winstr{j} = [' ',a,' < ',Xname,' < ',b,'   &   ',c,' < ', Yname,' < ',d];
   end
   
   [sel,ok] = listdlg('liststring',winstr,...
      'selectionmode','single',...
      'listsize',[400,200],...
      'initialvalue',wch,...
      'name','PPLANE6 Zoomback',...
      'promptstring','Select a rectangle:',...
      'OKString','Zoom');
   
   if (~isempty(sel))
      WINvect = wmat(sel,:);
      dud.syst.wind = WINvect;
      set(gcf,'user',dud);
      ppset = findobj('name','PPLANE6 Setup');
      sud = get(ppset,'user');
      set(disph,'user',dud);
      set(sud.h.wind(1),'string',num2str(WINvect(1)));
      set(sud.h.wind(2),'string',num2str(WINvect(2)));
      set(sud.h.wind(3),'string',num2str(WINvect(3)));
      set(sud.h.wind(4),'string',num2str(WINvect(4)));
      sud.c.wind = WINvect;
      sud.o.wind = WINvect;
      set(ppset,'user',sud);
      aud = get(axh,'user');
      aud.DY = [WINvect(2) - WINvect(1);WINvect(4) - WINvect(3)];
      dwind = [WINvect(1); WINvect(3); -WINvect(2); -WINvect(4)];
      aud.cwind = dwind - dud.settings.magn*[aud.DY;aud.DY];
      set(axh,'user',aud);
      pplane6('dirfield',disph);
   end
   
elseif strcmp(action,'figdefault')
   
  fig = input1;
  set(fig,'CloseRequestFcn','pplane6(''closefcn'')');
  ppset = findobj('name','PPLANE6 Setup');
  sud = get(ppset,'user');
  ud = get(fig,'user');
  ud.ssize = sud.ssize;
  fs = sud.fontsize;
  ud.fontsize = fs;
  style = sud.style;
  set(fig,'defaulttextfontsize',fs);
  set(fig,'defaultaxesfontsize',fs);
  set(fig,'defaultuicontrolfontsize',9*fs/10)
  lw = 0.5*fs/10;
  set(fig,'defaultaxeslinewidth',lw)
  set(fig,'defaultlinelinewidth',lw)
  set(fig,'defaultaxesfontname','helvetica')
  set(fig,'defaultaxesfontweight','normal')
  
  switch style
   case 'black'
    % if isunix | isvms, gamma = 0.5; else gamma = 0.0; end
    whitebg(fig,[0,0,0])
    if isunix | isvms
      fc = [.35 .35 .35];
    else
      fc = [.2 .2 .2];
    end
    set(fig,'color',fc);    
    set(fig,'defaultaxescolor',[0 0 0])
    % whitebg(fig,brighten([.2 .2 .2],gamma))
    set(fig,'defaultaxescolor',[0 0 0])
    set(fig,'defaultaxescolororder', ...
            1-[0 0 1;0 1 0;1 0 0;0 1 1;1 0 1;1 1 0;.25 .25 .25]) % ymcrgbw
        % set(fig,'colormap',brighten(jet(64),gamma))
    set(fig,'colormap',jet(64))
    set(fig,'defaultsurfaceedgecolor',[0 0 0]);
   case 'white'
    whitebg(fig,[1 1 1])
    set(fig,'color',[.8 .8 .8])
    set(fig,'defaultaxescolor',[1 1 1])
    set(fig,'defaultaxescolororder', ...
            [0 0 1;0 .5 0;1 0 0;0 .75 .75;.75 0 .75;.75 .75 0;.25 .25 .25]) % bgrymck
    set(fig,'colormap',jet(64))
    set(fig,'defaultsurfaceedgecolor',[0 0 0])
    
   case 'display'
    whitebg(fig,[1 1 1])
    set(fig,'defaultaxescolor',[1 1 1])
    set(fig,'defaultaxescolororder', ...
            [0 0 1;0 .5 0;1 0 0;0 .75 .75;.75 0 .75;.75 .75 0;.25 .25 .25]) % bgrymck
    set(fig,'colormap',jet(64))
    set(fig,'defaultsurfaceedgecolor',[0 0 0])
    set(fig,'color',[1 1 1]*240/255);
    set(fig,'defaultuicontrolbackgroundcolor',[1 1 1]*220/255);
    set(fig,'defaultaxesfontweight','bold')
    set(fig,'defaulttextfontweight','bold')
    set(fig,'defaultaxeslinewidth',1)
    set(fig,'defaultlinelinewidth',1)
    
   case 'bw'
    whitebg(fig,[0 0 0])
    set(fig,'color',[0 0 0])
    set(fig,'defaultaxescolor',[0 0 0])
    set(fig,'defaultaxescolororder', ...
            [1 1 1])
    set(fig,'colormap',[1 1 1;0 0 0])
    set(fig,'defaultsurfaceedgecolor',[0 0 0])
    
  end 
  set(fig,'user',ud);
  
elseif strcmp(action,'zoominsq')
   
   % 'zoominsq' is the callback for the Zoom in square menu item.  
   
   set(gcf,'WindowButtonDownFcn','pplane6(''zoomsqd'')',...
      'WindowButtonUpFcn','1;','inter','on');
   set(gca,'inter','on');
   dud = get(gcf,'user');
   nstr = get(dud.notice,'string');
   nstr(1:4) = nstr(2:5);
   nstr{5} = ['Pick a center and ',...
         'drag the mouse, or just click on a center.'];
   set(dud.notice,'string',nstr);
   
elseif strcmp(action,'zoomsqd')
   
   ppdispa = gca;
   aud = get(ppdispa,'user');
   point = get(ppdispa,'currentpoint');
   aud.center = point(1,[1,2]);
   aud.centh = plot(point(1,1),point(1,2),'or','erase','xor');
   aud.box = plot(point(1,1),point(1,2),'--r','erase','xor');
   set(ppdispa,'user',aud);
   set(gcf,'windowbuttonmotionfcn','pplane6(''zoomsqm'')',...
      'windowbuttonupfcn','pplane6(''zoomsqu'')');
   
   
elseif strcmp(action,'zoomsqm')
   
   ppdispa = gca;
   aud = get(ppdispa,'user');
   point = get(ppdispa,'currentpoint');
   point = point(1,[1,2])';
   un = get(ppdispa,'units');
   set(ppdispa,'units','pix');
   w = get(ppdispa,'pos'); w = w([3,4]);w = w(:);
   set(ppdispa,'units',un);
   cent = aud.center(:);
   lam = max(abs(point - cent)./w);
   v = lam*w;
   data = cent(:,[1 1 1 1 1]) + [v,[-v(1);v(2)], -v, [v(1);-v(2)],v];
   set(aud.box,'xdata',data(1,:),'ydata',data(2,:));
   
elseif strcmp(action,'zoomsqu')
   
   disph = gcf;
   dud = get(disph,'user');
   axh = dud.axes;
   aud = get(axh,'user');
   hand = [aud.centh;aud.box];
   set(hand,'erase','normal');
   delete(hand);
   DY = aud.DY(:);
   un = get(axh,'units');
   set(axh,'units','pix');
   w = dud.syst.wind;
   point = get(axh,'currentpoint');
   point = point(1,[1,2]);point = point(:);
   cent = aud.center(:);
   ww = get(axh,'pos'); ww = ww([3,4]); ww = ww(:);
   lamb = max(abs(point-cent)./ww);
   v = lamb*ww;
   if ~all(v > 0.01*DY)
      points = [w([1 1 2 2]);w([3 4 3 4])];
      for j=1:4
         lambs(j) = max(abs(points(:,j)-cent)./ww);
      end
      lamb = min(lambs);
      v = lamb*ww/4;
   end    
   p1 = cent + v; p2 = cent - v;
   a = [p2';p1'];
   a = [min(a);max(a)];
   DY = (a(2,:) - a(1,:))';    
   WINvect = a(:)';
   dud.syst.wind = WINvect;
   aud.DY = DY;
   dwind = [WINvect(1); WINvect(3); -WINvect(2); -WINvect(4)];
   aud.cwind = dwind - dud.settings.magn*[aud.DY;aud.DY];
   set(axh,'units',un,'user',aud);      
   set(disph,'user',dud);
   set(disph,'WindowButtonDownFcn','pplane6(''down'')',...
      'WindowButtonMotionFcn','',...
      'WindowButtonUpFcn','');
   pplane6('dirfield',disph);
   ppset = findobj('name','PPLANE6 Setup');
   if isempty(ppset)
      pplane6('confused');
   else
      sud = get(ppset,'user');
      sud.c.wind = WINvect;
      sud.o.wind = WINvect;
      set(sud.h.wind(1),'string',num2str(WINvect(1)));
      set(sud.h.wind(2),'string',num2str(WINvect(2)));
      set(sud.h.wind(3),'string',num2str(WINvect(3)));
      set(sud.h.wind(4),'string',num2str(WINvect(4)));
      set(ppset,'user',sud);
   end
   
elseif strcmp(action,'level')
  
  ppdisp = gcf;
  dud = get(ppdisp,'user');
  lfcn = dud.level;
  Xname = dud.syst.xvar;
  Yname = dud.syst.yvar;
  Xname(find(abs(Xname)==92))=[];  % Remove \s if any.
  Yname(find(abs(Yname)==92))=[];
  pplevel = findobj('name','PPLANE6 Level sets');
  if ~isempty(pplevel)
    delete(pplevel)
  end
  pplevel = figure('name','PPLANE6 Level sets',...
                 'vis','off',...
                 'numb','off','tag','PPLANE6');
  
  pplane6('figdefault',pplevel);
  set(pplevel,'menubar','none');
  
  lev.fr1 = uicontrol('style','frame');
  lev.fr2 = uicontrol('style','frame');
  
  inst1str = ['Enter the function in terms of the variables ',...
              Xname, ' and ', Yname,':'];

  lev.inst1 = uicontrol('style','text','horiz','left',...
                        'string',inst1str);
  
  lev.lfcn = uicontrol('style','edit','horiz','center',...
                       'string',lfcn,'call','',...
                       'background','w');
  
  lev.ch(3) = uicontrol('style','radio','horiz','center',...
                        'min',0,'max',3,...
                        'value',0,...
                        'vis','on',...
                        'string','Let PPLANE6 decide.');
  
  lev.ch(2) = uicontrol('style','radio','horiz','center',...
                        'min',0,'max',2,...
                        'value',0,...
                        'string','Select a point in the Display Window.');
      
  lev.inst2 = uicontrol('style','text','horiz','left',...
                        'string',['Choose one of the following ways to',...
                    ' choose level value(s):']);
      
  lev.ch(1)  = uicontrol('style','radio','horiz','center',...
                         'min',0,'max',1,...
                         'value',0,...
                         'string','Enter a vector of level values.');
      
  lev.rhs = uicontrol('style','edit','horiz','center',...
                      'string',' ','call','');

  lev.proc = uicontrol('style','push',...               
                          'string','Proceed',...
                          'call','pplane6(''levcomp'')');
  
  lev.close = uicontrol('style','push',...
                        'string','Close',...
                        'call','close');
      
  for i=1:3
    set(lev.ch(i),'user',lev.ch(:,[1:(i-1),(i+1):3]));
  end
  
  callrad = [
      'me = get(gcf,''currentobject'');',...
      'kk = get(me,''max'');',...
      'col = get(me,''backg'');',...
      'set(get(me,''user''),''value'',0),',...
      'set(me,''value'',kk);',...
      'ud = get(gcf,''user'');',...
      'if kk == 1,',...
      '   set(ud.rhs,''enable'',''on'',''backg'',''w'');',...
      'else,',...
      '   set(ud.rhs,''enable'',''off'',''backg'',col);',...
      'end,'];
  
  set(lev.ch,'call',callrad);
  
  left = 2; varl = 300; buttw = 60;
  nudge = 3;   
  tab = 15;
  lines1 = 5;
  lines2 = 2;
  xex = get(lev.inst1,'extent');
  ht = xex(4)+nudge;
  frw = varl + 2*tab+ 2*nudge;
  fr1bot = 2*left + ht;
  fr1ht = lines1*(nudge + ht) + nudge;
  fr2bot = fr1bot + fr1ht;
  fr2ht = lines2*(nudge + ht) + nudge;
  vbot = fr1bot + nudge;
  ch1bot = vbot + nudge + ht;
  ch2bot = ch1bot + nudge + ht;
  ch3bot = ch2bot + nudge + ht;
  inst2bot = ch3bot + nudge + ht;
  fbot =  fr2bot + nudge;
  inst1bot = fbot + nudge + ht;
  fleft = left + nudge + tab;
  instleft = left + nudge;
  chleft = instleft + tab;
  vleft = chleft + tab;
  vw = (frw - 2*vleft);
  fr1wind = [left,fr1bot,frw,fr1ht];
  fr2wind = [left,fr2bot,frw,fr2ht];
  inst1wind = [instleft,inst1bot,varl,ht];
  inst2wind = [instleft,inst2bot,varl,ht];
  fwind = [fleft,fbot,varl,ht];
  ch1wind = [chleft,ch1bot,varl,ht];
  ch2wind = [chleft,ch2bot,varl,ht];
  ch3wind = [chleft,ch3bot,varl,ht];
  vwind = [vleft,vbot,vw,ht];
  figw = 2*left + frw;
  fight = 3*left + ht + fr1ht + fr2ht;
  figwind = [40, 300, figw, fight];
  buttw = frw/2;
  sep = (figw - 2*buttw)/3;
  closel = sep;
  procl = 2*sep+buttw;
  clwind = [closel,left,buttw,ht];
  procwind = [procl,left,buttw,ht];
  set(pplevel,'pos',figwind);
  set(lev.fr1,'pos',fr1wind);
  set(lev.fr2,'pos',fr2wind);
  set(lev.inst1,'pos',inst1wind);
  set(lev.inst2,'pos',inst2wind);
  set(lev.ch(1),'pos',ch1wind);
  set(lev.ch(2),'pos',ch2wind);
  set(lev.ch(3),'pos',ch3wind);
  set(lev.rhs,'pos',vwind);
  set(lev.lfcn,'pos',fwind);
  set(lev.proc,'pos',procwind);
  set(lev.close,'pos',clwind);
  set(lev.ch(3),'value',3);
  set(lev.rhs,'enable','off');  
  
  child = get(pplevel,'children');
  set(pplevel,'vis','on','user',lev);
  set(child,'vis','on');
  
elseif strcmp(action,'levcomp')
  
  pplevel = gcf;
  ud = get(pplevel,'user');
  ppdisp = findobj('name','PPLANE6 Display');
  dud = get(ppdisp,'user');
  ch = ud.ch;
  val = zeros(1,3);
  for kk = 1:3
    val(kk) = get(ch(kk),'value');
  end
  KK = max(val);
  lfcn = get(ud.lfcn,'string');
  l=length(lfcn);
  for ( k = fliplr(findstr('.',lfcn)))
    if (find('*/^' == lfcn(k+1)))
      lfcn = [lfcn(1:k-1), lfcn(k+1:l)];
    end
    l=l-1;
  end
  l = length(lfcn);
  for (k=fliplr(find((lfcn=='^')|(lfcn=='*')|(lfcn=='/'))))
    lfcn = [lfcn(1:k-1) '.' lfcn(k:l)];
    l = l+1;
  end
  WINvect = dud.syst.wind;
  XxXxXx = WINvect(1) + rand*(WINvect(2)-WINvect(1));
  YyYyYy = WINvect(3) + rand*(WINvect(4)-WINvect(3));
  Xname = dud.syst.xvar;
  Yname = dud.syst.yvar;
  Xname(find(abs(Xname)==92))=[];  % Remove \s if any.
  Yname(find(abs(Yname)==92))=[];
  err = 0;res = 1;
  eval([Xname,'=XxXxXx;'],'err = 1;');
  eval([Yname,'=YyYyYy;'],'err = 1;');
  eval(['res = ',lfcn, ';'],'err = 1;');
  if err | isempty(res)
    errmsg = 'The function does not evaluate correctly.';
    fprintf('\a')
    errordlg(errmsg,'PPLANE error','on');
    return;
  end
  
  Xmin = WINvect(1);
  Xmax = WINvect(2);
  Ymin = WINvect(3);
  Ymax = WINvect(4);
  N = 50; k = 4;
  deltax=(Xmax - Xmin)/(N-1);
  deltay=(Ymax - Ymin)/(N-1);
  XXXg=Xmin + deltax*[-k:N+k];
  YYYg=Ymin + deltay*[-k:N+k];
  
  [Xx,Yy]=meshgrid(XXXg,YYYg);
  Xxx=Xx(:);Yyy=Yy(:);
  Ww = zeros(size(Xxx));
  eval([Xname,'=Xxx;'],'err = 1;');
  eval([Yname,'=Yyy;'],'err = 1;');
  eval(['Ww = ',lfcn, ';']);

  KKK = 3; %# of significant figures.
  
  switch KK
   case 1  % vector input
    rhs = get(ud.rhs,'string');
    rhs = str2num(rhs);
    
   case 2  % mouse input
    figure(ppdisp);
    [XX,YY] = ginput(1);
    figure(pplevel);
    eval([Xname,'=XX;'],'err = 1;');
    eval([Yname,'=YY;'],'err = 1;');
    eval(['rhs = ',lfcn, ';'],'err = 1'); 
    LL = ceil(log10(abs(rhs)));
    rhs = round(10^(KKK-LL)*rhs);
    rhs = 10^(LL-KKK)*rhs;
    
   case 3  % PPLANE6 input
    MM = max(Ww);mm = min(Ww);
    LL = ceil(log10(MM-mm));
    NN = 7;  % Number of curves
    rhs = mm+(1:NN).^2*(MM-mm)/NN^2;
    rhs = round(10^(KKK-LL)*rhs);
    rhs = 10^(LL-KKK)*rhs;
    
  end
  
  Ww = reshape(Ww,N+2*k+1,N+2*k+1);
  lrhs = length(rhs);
  if lrhs == 0
    return
  elseif lrhs == 1
    rhs = [rhs,rhs];
  end
  
  figure(ppdisp);
  [Cm,hcont] = contour(Xx,Yy,Ww,rhs,'--');
  hlabel = clabel(Cm,hcont);
%  set(hlabel,'fontsize',dud.fontsize,...
%            'color',dud.color.level,...
%            'rotation',0);
  set(hlabel,'fontsize',dud.fontsize,...
             'color',[1,0,0],...
             'rotation',0);
  set(hcont,'visible','on',...
            'color',dud.color.level,...
            'linestyle',':');
  dud.contours = [dud.contours ;hcont;hlabel];
  set(ppdisp,'user',dud);
  
elseif strcmp(action,'restart')
   
   ppset = findobj('name','PPLANE6 Setup');
   oldfiles = dir('pptp*.m');
   for k = 1:length(oldfiles)
      fn = oldfiles(k).name;
      fid = fopen(fn,'r');
      ll = fgetl(fid);
      ll = fgetl(fid);
      ll = fgetl(fid);
      fclose(fid);
      if strcmp(ll,'%% Created by PPLANE6')
         delete(fn)
      end
   end
   h = findobj('tag','PPLANE6');
   delete(setdiff(h,ppset));
   sud = get(ppset,'user');
   sud.flag = 0;
   set(ppset,'user',sud);
   figure(ppset)
   
elseif strcmp(action,'quit')
   
  ppset = findobj('name','PPLANE6 Setup');
  sud = get(ppset,'user');
  if sud.remtd 
    rmpath(tempdir);
  end
  oldfiles = dir([tempdir,'pptp*.m']);
  for k = 1:length(oldfiles)
    fn = [tempdir,oldfiles(k).name];
    fid = fopen(fn,'r');
    ll = fgetl(fid);
    ll = fgetl(fid);
    ll = fgetl(fid);
    fclose(fid);
    if strcmp(ll,'%% Created by PPLANE6')
      delete(fn)
    end
  end
  h = findobj('tag','PPLANE6');
  delete(h);
   
elseif strcmp(action,'closefcn')
   
   fig = gcf;  
   name = get(fig,'name');
   if strcmp(name,'PPLANE6 Setup') | strcmp(name,'PPLANE6 Display')
      quest = ['Closing this window will cause all PPLANE6 ',...
            'windows to close, and PPLANE6 will stop.  ',...
            'Do you want to quit PPLANE6?'];
      butt = questdlg(quest,'Quit PPLANE6?','Quit','Cancel','Quit');
      if strcmp(butt,'Quit')
         pplane6('quit');
      end
   elseif strcmp(name,'PPLANE6 Linearization')
      dud = get(fig,'user');
      fcn = dud.function;
      if (exist(fcn)==2) delete([fcn,'.m']);end    
      delete(findobj('label',name));
      delete(fig);
   else
      delete(findobj('label',name));
      delete(fig);
   end
   
elseif strcmp(action,'confused')
   
   tstring = 'PPLANE6 is totally confused';
   qstring = {['You will have to restart PPLANE6 from '...
            'the beginning in order to ',...
            'do anything new.  However, it might be possible '...
            'to save the current system ',...
            'or the gallery to make your restart easier, '...
            'or it may be possible to ',...
            'print out a figure, if the appropriate '...
            'figures are visible.  In such a case ',...
            'it would be best to do nothing now.'];
      'What do you want to do?'};
   bstr1 = 'Quit and restart PPLANE6.';
   bstr2 = 'Just quit PPLANE6.';
   bstr3 = 'Do nothing.';
   answer = questdlg(qstring,tstring,bstr1,bstr2,bstr3,bstr1);
   if strcmp(answer,bstr1)
      delete(findobj('tag','PPLANE6'));
      pplane6;return
   elseif strcmp(answer,bstr2)
      delete(findobj('tag','PPLANE6'));
      return
   else
      return
   end
   
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [tout,yout] = ppdp45(dfcn,tspan,y0,disph)

% PPDP45 is an implementation of the explicit Runge-Kutta (4,5) which
%        is described in Chapters 5 & 6 of John Dormand's book, 
%        Numerical Methods for Differential Equations.  
% 
%        This is the same algorithm used in ODE45, part of the new MATLAB 
%        ODE Suite.  Details are to be found in The MATLAB ODE Suite, 
%        L. F. Shampine and M. W. Reichelt, SIAM Journal on Scientific 
%        Computing, 18-1, 1997.


% Input the user data. 

dud = get(disph,'user');
dispha = dud.axes;
ud = get(dispha,'user');
refine = dud.settings.refine;
tol = dud.settings.tol;
gstop = ud.gstop;
plotf = ud.plot;
DY = ud.DY;
col = dud.color.temp;

% Initialize the stopping criteria.
if gstop
   
   % Initialize detection of closed orbits & limit cycles.
   % Choose a random direction & initialize the search for orbit maxima in
   % that direction.
   
   theta = rand*2*pi;
   R = [cos(theta), sin(theta); -sin(theta),cos(theta)];
   qq = R*(y0(:));
   rr = [qq,qq];
   z = DY(1) + sqrt(-1)*DY(2);
   w=exp(i*theta);
   a1 = w*z;
   a2 = w*(z');
   a=max(abs(real([a1,a2])));
   b=max(abs(imag([a1,a2])));
   perpeps = a/1000;    % We want to be real
   % close in this direction.
   paraeps = b/100;     % We do not have to be
   % so careful in this direction.
   tk = 0;
   turn = zeros(2,10);
   
   % The test for an equilibrium point.
   
   sinkeps = 0.005/refine;
   
   %  The compute window.
   
   cwind = ud.cwind;
end
% The stop button.

stop = 0;
ud.stop = 0;

% Set the the line handle.

ph = plot([y0(1),y0(1)],[y0(2),y0(2)],'color',col,...
   'erase','none',...
   'parent',dispha);
ud.line = ph;
set(dispha,'UserData',ud);

% Initialize the loop.

t0 = tspan(1);
tfinal = tspan(2);
tdir = sign(tfinal - t0);
t = t0;
y = y0(:);

% By default, hmax is 1/10 of the interval.
hmax = min(abs(0.1*(tfinal-t)),1);

rDY = DY(:,ones(1,refine));
steps = 0;
block = 120;
tout = zeros(block,1);
yout = zeros(block,2);

N = 1;
tout(N) = t;
yout(N,:) = y.';

% Initialize method parameters.
pow = 1/5;
%  C = [1/5; 3/10; 4/5; 8/9; 1; 1]; 
%  Not needed because the sytem is autonomous.
A = [
   1/5         3/40    44/45   19372/6561      9017/3168  
   0           9/40    -56/15  -25360/2187     -355/33    
   0           0       32/9    64448/6561      46732/5247      
   0           0       0       -212/729        49/176          
   0           0       0       0               -5103/18656     
   0           0       0       0               0               
   0           0       0       0               0            
];
bhat = [35/384 0 500/1113 125/192 -2187/6784 11/84 0]';
% E = bhat - b.
E = [71/57600; 0; -71/16695; 71/1920; -17253/339200; 22/525; -1/40];
if refine > 1
   sigma = (1:refine-1) / refine;
   S = cumprod(sigma(ones(4,1),:));
   bstar = [
      1       -183/64     37/12       -145/128
      0       0       0       0
      0       1500/371    -1000/159   1000/371
      0       -125/32     125/12      -375/64 
      0       9477/3392   -729/106    25515/6784
      0       -11/7       11/3        -55/28
      0       3/2     -4      5/2
   ];
   bstar = bstar*S;
   
end

f = zeros(2,7);
f0 = feval(dfcn,t,y);

mm = max(abs(f0./DY));
absh = hmax;
if mm
   absh = min(absh,1/(100*mm));
end

f(:,1) = f0;


% THE MAIN LOOP

while ~stop
   
   % hmin is a small number such that t+h is distinquishably
   % different from t if abs(h) > hmin.
   hmin = 16*eps*abs(t);
   absh = min(hmax, max(hmin, absh));    
   h = tdir * absh;
   
   % LOOP FOR ADVANCING ONE STEP.
   while stop~=5
      % hC= h * C;
      hA = h * A;
      
      f(:,2) = feval(dfcn, t, y + f*hA(:,1));
      f(:,3) = feval(dfcn, t, y + f*hA(:,2));
      f(:,4) = feval(dfcn, t, y + f*hA(:,3));
      f(:,5) = feval(dfcn, t, y + f*hA(:,4));
      f(:,6) = feval(dfcn, t, y + f*hA(:,5));
      tn = t + h;
      yn = y + f*h*bhat;
      f(:,7) = feval(dfcn, tn, yn);
      
      % Estimate the error.
      err = abs(h * f * E);
      alpha = (2*max(err./((abs(y)+abs(yn)+DY*1e-3)*tol)))^pow;
      if alpha < 1         % Step is OK
         break
      else
         if absh <= hmin        % This keeps us out of an infinite loop.
            stop = 5;
            break;
         end
         
         absh = max(hmin,0.8*absh / alpha);
         h = tdir * absh;
      end  % if alpha < 1
   end  % while stop~=5
   steps = steps + 1;
   
   
   oldN = N;
   N = N + refine;
   if N > length(tout)
      tout = [tout; zeros(block,1)];  
      yout = [yout; zeros(block,2)];
   end
   if refine > 1             % computed points, with refinement
      j = oldN+1:N-1;
      tout(j) = t + h*sigma';
      yout(j,:) = (y(:,ones(length(j),1)) + f*h*bstar).';
      tout(N) = tn;
      yout(N,:) = yn.';
   else               % computed points, no refinement
      tout(N) = tn;
      yout(N,:) = yn.';
   end
   
   
   % Update stop.   Maybe the stop button has been pressed.
   
   ud = get(dispha,'user');
   stop = max(ud.stop,stop);
   
   if gstop
      % Are we out of the compute window?
      yl = yout(N,:).';
      if any([yl;-yl] - cwind < 0);
         stop = 1;
      end  
      
      % If the step in the phase plane is small we assume there is a sink.
      if (steps > 10)
         yy = yout(oldN:N,:).';
         dyy = yy(:,1:refine) - yy(:,2:(refine+1));
         dyy = dyy./rDY;
         MMf = min(sqrt(sum(dyy.^2)));   
         if (MMf<=sinkeps*absh) 
            stop = 2; 
         end    
      end
      
      % We look for a maximum in the randomly chosen direction.  If
      % we find one, we compare it with previously found maxima.  If
      % our new one is close to an old one we stop.  If not, we
      % record the on.
      i = oldN+1:N;
      yy = yout(i,:).';
      rrr = R*yy;      
      v = [rr,rrr];
      rr = v(:,[refine+1,refine+2]);   % Use this next time. 
      [m,ii] = max(v(1,:));
      if( 1< min(ii) & max(ii)<refine+2 )  % If the max is in the middle.
         kk=0;
         while ( (kk<tk) & (~stop) )
            kk = kk+1;
            if ((abs(v(1,ii)-turn(1,kk))<perpeps) &...
                  (abs(v(2,ii)-turn(2,kk))<paraeps) )
               stop = 3;
            end  
         end
         tk = tk + 1;
         if tk > size(turn,2)
            turn = [turn,zeros(2,10)];
         end
         turn(:,tk+1) = v(:,ii);
      end
   elseif (abs(tn-tfinal) < hmin)
      stop = 6;
   end  % if gstop
   if plotf
      i = oldN:N;    
      set(ph,'Xdata',yout(i,1),'Ydata',yout(i,2));
      drawnow    
   end  % if plotf 
   
   % Compute a new step size.
   absh = max(hmin,0.8*absh / max( alpha,0.1));
   absh = min(absh,tdir*(tfinal - tn));
   h = absh*tdir;
   % Advance the integration one step.
   t = tn;
   y = yn;
   f(:,1) = f(:,7);                      % Already evaluated dfcn(tnew,ynew)
   
end  % while ~stop

tout = tout(1:N);
yout = yout(1:N,:);
if dud.notice
   nstr = get(dud.notice,'string');
   
   switch stop
   case 1
      nstr{5} = [nstr{5}, ' left the computation window.']; 
   case 2
      ystr = ['(',num2str(y(1),2), ', ', num2str(y(2),2),').'];
      nstr{5} = [nstr{5}, ' --> a possible eq. pt. near ',ystr];
   case 3
      nstr{5} = [nstr{5}, ' --> a nearly closed orbit.'];
   case 4
      nstr{5} = [nstr{5}, ' was stopped by the user.'];
   case 5 
      ystr = ['(',num2str(y(1),2), ', ', num2str(y(2),2),').'];
      nstr(1:3) = nstr(2:4);
      nstr{4} = [nstr{5},' experienced a failure at ',ystr];
      nstr{5} = 'Problem is singular or tolerances are too large.';
   end
   set(dud.notice,'string',nstr);
end
drawnow

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [tout,yout] = pprk4(dfcn,tspan,y0,disph)

% PPRK4  is an implementation of the fourth order Runge-Kutta method. 

% Input the user data. 

dud = get(disph,'user');
dispha = dud.axes;
ud = get(dispha,'user');
refine = dud.settings.refine;
tol = dud.settings.tol;
gstop = ud.gstop;
ssize = dud.settings.stepsize;
plotf = ud.plot;
DY = ud.DY;
col = dud.color.temp;

% Initialize the stopping criteria.

%  The compute window.

if gstop
   
   % Initialize detection of closed orbits & limit cycles.
   % Choose a random direction & initialize the search for orbit maxima in
   % that direction.
   
   theta = rand*2*pi;
   R = [cos(theta), sin(theta); -sin(theta),cos(theta)];
   qq = R*(y0(:));
   rr = [qq,qq];
   z = DY(1) + sqrt(-1)*DY(2);
   w=exp(i*theta);
   a1 = w*z;
   a2 = w*(z');
   a=max(abs(real([a1,a2])));
   b=max(abs(imag([a1,a2])));
   perpeps = a/1000;    % We want to be real
   % close in this direction.
   paraeps = b/100;     % We do not have to be
   % so careful in this direction.
   tk = 0;
   turn = zeros(2,10);
   
   % The test for an equilibrium point.
   
   sinkeps = 0.0001;
   
   %  The compute window.
   
   cwind = ud.cwind;
 end
 
% The stop button.

stop = 0;
ud.stop = 0;

% Set the the line handle.

ph = plot([y0(1),y0(1)],[y0(2),y0(2)],'color',col,...
   'erase','none',...
   'parent',dispha);
ud.line = ph;
set(dispha,'UserData',ud);

% Initialize the loop.

t0 = tspan(1);
tfinal = tspan(2);
tdir = sign(tfinal - t0);
t = t0;
y = y0(:);

h = ssize*tdir;

steps = 0;
block = 120;
tout = zeros(block,1);
yout = zeros(block,2);
N = 1;
tout(N) = t;
yout(N,:) = y.';

% The main loop
tic
while ~stop
  if abs(t - tfinal) < ssize 
    h = tfinal - t; 
  end

  % Compute the slope
  s1 = feval(dfcn,t,y); s1=s1(:);
  s2 = feval(dfcn, t + h/2, y + h*s1/2); s2=s2(:);
  s3 = feval(dfcn, t + h/2, y + h*s2/2); s3=s3(:);
  s4 = feval(dfcn, t + h, y + h*s3); s4=s4(:);
  
  t = t + h;
  y = y + h*(s1 + 2*s2 + 2*s3 +s4)/6;

  if N >= length(tout)
    tout = [tout;zeros(block,1)];
    yout = [yout;zeros(block,2)];
  end
  oldN = N;
  N = N + 1;  
  tout(N) = t;
  yout(N,:) = y.';
  steps = steps + 1;
  
  % Update stop.   Maybe the stop button has been pressed.

  ud = get(dispha,'user');
  stop = max(ud.stop,stop);
  
  if gstop
    % Are we out of the compute window?
    yl = yout(N,:).';
    if any([yl;-yl] - cwind < 0);
      stop = 1;
    end  
      
    % If the step in the phase plane is small we assume there is a sink.
    if (steps > 20)
      yy = yout(N-1:N,:).';
      dyy = yy(:,1) - yy(:,2);
      dyy = dyy./DY;
      MMf = sqrt(sum(dyy.^2));   
      if (MMf<=sinkeps) 
        stop = 2; 
      end       
    end
      
    % We look for a maximum in the randomly chosen direction.  If
    % we find one, we compare it with previously found maxima.  If
    % our new one is close to an old one we stop.  If not, we
    % record the on.
    i = N;
    yy = yout(i,:).';
    rrr = R*yy;      
    v = [rr,rrr];
    rr = v(:,[2,3]);   % Use this next time. 
    [m,ii] = max(v(1,:));
    if( 1< min(ii) & max(ii)<3 )  % If the max is in the middle.
      kk=0;
      while ( (kk<tk) & (~stop) )
        kk = kk+1;
        if ((abs(v(1,ii)-turn(1,kk))<perpeps) &...
              (abs(v(2,ii)-turn(2,kk))<paraeps) )
          stop = 3;
        end  
      end
      tk = tk + 1;
      if tk > size(turn,2)
        turn = [turn,zeros(2,10)];
      end
      turn(:,tk+1) = v(:,ii);
    end
  end  % if gstop
  if (abs(t-tfinal) < 0.001*ssize)
    stop = 6;
  end  

  if plotf
    i = (N-1):N;    
    set(ph,'Xdata',yout(i,1),'Ydata',yout(i,2));
    drawnow    
  end  % if plotf 
   
end  % while ~stop

tout = tout(1:N);
yout = yout(1:N,:);
if dud.notice
   nstr = get(dud.notice,'string');
   
   switch stop
   case 1
      nstr{5} = [nstr{5}, ' left the computation window.']; 
   case 2
      ystr = ['(',num2str(y(1),2), ', ', num2str(y(2),2),').'];
      nstr{5} = [nstr{5}, ' --> a possible eq. pt. near ',ystr];
   case 3
      nstr{5} = [nstr{5}, ' --> a nearly closed orbit.'];
   case 4
      nstr{5} = [nstr{5}, ' was stopped by the user.'];
   case 5 
      ystr = ['(',num2str(y(1),2), ', ', num2str(y(2),2),').'];
      nstr(1:3) = nstr(2:4);
      nstr{4} = [nstr{5},' experienced a failure at ',ystr];
      nstr{5} = 'Problem is singular or tolerances are too large.';
   end
   set(dud.notice,'string',nstr);
end
drawnow