function holo(action,input)

if nargin == 0
	action = 'initialize';
end


if strcmp(action,'initialize')

	defval = 1;
	deffcn = ' exp(z)';

	ss = get(0,'screensize');
	ww = ss(3); ht = ss(4);
	
	left = 80;
	right = 30;

	fw = min(ww - left,840);
	aw = (fw-2*left-right)/2;
	ah = aw;
	top = 0;
	bott = 40;
	texth = 20;
	separation = texth + 7;

	wequals = 40;
	equatw = aw -wequals;

	fleft = ww - fw - left;
	fht = ah + top + bott + 4*separation;
	fbot = ht - fht - 50;
	abot = bott + 2*separation;

	ud.fig = figure('pos',[fleft,fbot,fw,fht],'name','Holomorphic Map',...
		'numb','off','paperorient','landscape',...
		'paperposition',[.25,2,10,5.5]);

	aleft = left/fw; awidth=aw/fw;
	abott = abot/fht; aheight = ah/fht;

	ud.zaxes = axes('pos',[aleft,abott,awidth,aheight],'next','add',...
		'box','on','xgrid','on','ygrid','on',...
		'xlim',[-4,4],'ylim',[-4,4]);
	xlabel('z - plane');

	ud.zh = plot(1000,1000,'o','erase','xor','color','r');
	ud.waxes = axes('pos',[2*aleft+awidth,abott,awidth,aheight],...
		'next','add','box','on',...
		'xgrid','on','ygrid','on','xlim',[-10,10],'ylim',[-10,10]);
	xlabel('w - plane');
	title(['w = ',deffcn]);
	ud.wh = plot(1000,1000,'+','erase','xor','markersize',12,'linewidth',2.5,'color','r');
	boxl = 50;

	tbott = separation; 


	qleft = (fw - right-60);
	qbott = fht -25;
	clbutt = uicontrol('pos',[qleft,tbott,60,texth],...
		'string','Clear','call','holo(''clear'')');
	ud.qbutt = uicontrol('pos',[qleft,qbott,60,texth],...
		'string','Quit','call','close');
	weq = uicontrol('pos',[left,tbott,wequals,texth],...
		'style','text','horiz','right','string','w = ');
	ud.fcns = uicontrol('pos',[left+wequals,tbott,equatw,texth],...
		'style','edit','horiz','left','call','holo(''eqcall'')',...
      'string',deffcn);
   ud.fcn = deffcn;
	set(ud.fcns,'user',deffcn);
	
	modew = 140;
   ud.modes = uicontrol('pos',[2*left+aw,tbott,modew,texth],...
      'style','popup',...
      'string','Points|Lines|Circles|Rectangular grid|Polar grid',...
      'call','holo(''modecall'')','value',defval);
   ud.actbot = tbott + texth + 10;
   ud.acttop = abot + ah + 50;
   ud.colorder = get(0,'defaultaxescolororder');
   ud.ptno = 0;
   ud.lineno = 0;
   ud.circno = 0;
   options = uimenu(ud.fig,'label','Opt&ions');
   rect = uimenu(options,'label','Map a rectangular grid ...',...
      'call','holo(''rectmap'')');
   polar = uimenu(options,'label','Map a polar grid ...',...
      'call','holo(''polarmap'')');
   zchange = uimenu(options,'label','Change the z limits ...',...
      'call','holo(''zchange'')');
   wchange = uimenu(options,'label','Change the w limits ...',...
      'call','holo(''wchange'')');
   set(ud.fig,'user',ud);
	axes(ud.zaxes);
	set(ud.zaxes,'buttondownfcn','holo(''points'')');
	set(ud.fig,'pointer','crosshair');
	set(ud.fig,'windowbuttonmotionfcn','holo(''pointm'')');
	

elseif strcmp(action,'clear')

   ud = get(gcf,'user');
   delete(findobj([ud.zaxes,ud.waxes],'tag','holoplot'));

elseif strcmp(action,'eqcall')
   
   fig = gcf;
	ud = get(fig,'user');
   fcnstr = get(gcbo,'string');
   zax = ud.zaxes;
   wax = ud.waxes;
	wlabel = ['w = ',fcnstr];
	l = length(fcnstr);
	for (k=fliplr(find((fcnstr == '^')|(fcnstr == '*')|(fcnstr == '/'))))
		fcnstr = [fcnstr(1:k-1) '.' fcnstr(k:l)];
		l  = l+1;
   end
   ud.fcn = fcnstr;
   set(fig,'user',ud);
   set(gcbo,'user',fcnstr);
   set(get(wax,'title'),'string',wlabel);
   delete(findobj([zax,wax],'tag','holoplot'));
   
elseif strcmp(action,'modecall')
   
   fig = gcf;
   ud = get(fig,'user');
   set(fig,'windowbuttonmotionfcn','');
	mode = get(ud.modes,'value');
	hh = ud.zaxes;
   if mode == 1  
		set(findobj(hh),'buttondownfcn','holo(''points'')');
		set(gcf,'windowbuttonupfcn',' ');
	elseif mode == 2
		set(findobj(hh),'buttondownfcn','holo(''lines'')');
	elseif mode == 3
		set(findobj(hh),'buttondownfcn','holo(''circles'')');
	elseif mode == 4
		set(findobj(hh),'buttondownfcn','holo(''rect'')');
	elseif mode == 5
		set(findobj(hh),'buttondownfcn','holo(''polar'')');
	end
   set(fig,'windowbuttonmotionfcn','holo(''pointm'')');

elseif strcmp(action,'pointm')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(fig,'user');
   pt = get(fig,'currentpoint');
   ht = pt(2);
   if ht > ud.actbot & ht < ud.acttop
      set(fig,'pointer','crosshair');
      point = get(ud.zaxes,'currentpoint');
      point = point(1,[1,2]);
      z = point(1)+i*point(2);
      FFF = get(ud.fcns,'user');
      w = eval(FFF);
      set(ud.wh,'xdata',real(w),'ydata',imag(w));
   else
      set(fig,'pointer','arrow')
   end
   
		
elseif strcmp(action,'points')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(fig,'user');
   col = ud.colorder(ud.ptno+1,:);
   ud.ptno = rem(ud.ptno+1,size(ud.colorder,1));
	point = get(ud.zaxes,'currentpoint');
	point = point(1,[1,2]);
	z = point(1)+i*point(2);
   plot(real(z),imag(z),'color',col,...
      'parent',ud.zaxes,'tag','holoplot',...
      'marker','.','markersize',12);
	w = eval(ud.fcn);
   plot(real(w),imag(w),'parent',ud.waxes,...
      'color',col,'tag','holoplot',...
      'marker','.','markersize',12);
   set(ud.zaxes,'buttondownfcn','holo(''points'')');
   set(fig,'user',ud);

elseif strcmp(action,'lines')
   
   %  Line buttondownfcn
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(fig,'user');
   col = ud.colorder(ud.lineno+1,:);
   ud.lineno = rem(ud.lineno+1,size(ud.colorder,1));
   zax = ud.zaxes;
   wax = ud.waxes;
	point = get(zax,'currentpoint');
	point = point(1,[1,2]);
	z = point(1)+i*point(2);
   plot(real(z),imag(z),'.',...
      'markersize',12,'color',col,...
      'tag','holoplot','parent',zax);
   zlineh = plot(real([z,z]),imag([z,z]),'erase','xor',...
      'parent',zax,'color',col,...
      'tag','holoplot');
   w = eval(ud.fcn);
   wlineh = plot(real([w,w]),imag([w,w]),'erase','xor',...
      'parent',wax,'color',col,...
      'tag','holoplot');
   plot(real(w),imag(w),'.',...
      'markersize',12,'color',col,...
      'tag','holoplot','parent',wax);
	set(zax,'user',[z,zlineh,wlineh])
   set(fig,'user',ud,...
      'windowbuttonmotionfcn','holo(''linem'')',...
      'windowbuttonupfcn','holo(''lineu'')');

elseif strcmp(action,'linem')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(fig,'user');
   pt = get(fig,'currentpoint');
   if pt(2)>ud.actbot
      zax = ud.zaxes;
      set(fig,'pointer','custom',...
         'pointershapecdata',NaN*ones(16));
      set(ud.wh,'marker','none');
      u = get(zax,'user');
      z=u(1);
      zlineh = u(2);
      wlineh = u(3);
      wh = ud.wh;
      point = get(zax,'currentpoint');
      point = point(1,[1,2]);
      z1 = point(1)+i*point(2);
      arrow = [-1+0.5i 0 -1-0.5i];
      xlim = get(zax,'xlim');
      ll = xlim(2) - xlim(1);
      zarr = z1 + ll*sign(z1-z)*arrow/30;
      zp = [z z1 zarr];
      set(zlineh,'xdata',real(zp),'ydata',imag(zp),'linestyle','--');
      z = z + (z1 - z)*linspace(0,1);
      FFF = ud.fcn;
      w = eval(FFF);
      xlim = get(ud.waxes,'xlim');
      ll = xlim(2) - xlim(1);
      warr = w(100) + ll*sign(w(100) - w(99))*arrow/30;
      w = [w(:);warr(:)];
      set(wlineh,'xdata',real(w),'ydata',imag(w),'linestyle','--');
      z=z1;w=eval(FFF);
      set(wh,'xdata',real(w),'ydata',imag(w));
   else
      set(fig,'pointer','arrow')
   end

      
elseif strcmp(action,'lineu')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
	ud = get(fig,'user');
	u = get(ud.zaxes,'user');
	z=u(1);
	zlineh = u(2);
   wlineh = u(3);
   zax = ud.zaxes;
   wax = ud.waxes;
   set(zlineh,'linestyle','-','erase','none','tag','holoplot');
   set(wlineh,'linestyle','-','erase','none');
   set(ud.wh,'marker','+');
   set(fig,'windowbuttonmotionfcn','holo(''pointm'')',...
      'windowbuttonupfcn','',...
      'user',ud);
	set(findobj(zax),'buttondownfcn','holo(''lines'')');
	
elseif strcmp(action,'circles')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(fig,'user');
   col = ud.colorder(ud.circno+1,:);
   ud.circno = rem(ud.circno+1,size(ud.colorder,1));
   zax = ud.zaxes;
   wax = ud.waxes;
	point = get(zax,'currentpoint');
	point = point(1,[1,2]);
	z = point(1)+i*point(2);
   plot(real(z),imag(z),'tag','holoplot',...
      'marker','.','markersize',12,...
      'parent',zax,'color',col);
   circh = plot(real(z),imag(z),'erase','xor',...
      'tag','holoplot','parent',zax,...
      'color',col,'linestyle','--');
   w = eval(ud.fcn);
   plot(real(w),imag(w),'tag','holoplot',...
      'marker','.','markersize',12,...
      'parent',wax,'color',col);
   wlineh = plot(real(w),imag(w),'erase','xor',...
      'tag','holoplot','parent',wax,...
      'color',col,'linestyle','--');
	set(zax,'user',[z,circh,wlineh]);
   set(fig,'windowbuttonmotionfcn','holo(''circlem'')',...
      'windowbuttonupfcn','holo(''circleu'')',...
      'user',ud);

elseif strcmp(action,'circlem')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(fig,'user');
   pt = get(fig,'currentpoint');
   if pt(2)>ud.actbot
      set(fig,'pointer','crosshair');
      zax = ud.zaxes;
      wax = ud.waxes;

      u = get(zax,'user');
      cent = u(1);
      circh = u(2);
      wlineh = u(3);
      wh = ud.wh;
      point = get(zax,'currentpoint');
      point = point(1,[1,2]);
      z1 = point(1)+i*point(2);
      radius = abs(cent - z1);
      ang = exp(i*pi*(-1:(2/100):1));
      z = cent+radius*ang;
      set(circh,'xdata',real(z),'ydata',imag(z));
      FFF = ud.fcn;
      w = eval(FFF);
      set(wlineh,'xdata',real(w),'ydata',imag(w));
      z=z1;w=eval(FFF);
      set(wh,'xdata',real(w),'ydata',imag(w),'marker','none');
   else
      set(fig,'pointer','arrow')
   end
   
elseif strcmp(action,'circleu')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(fig,'user');
   zax = ud.zaxes;
	u = get(zax,'user');
	cent = u(1);
	circh = u(2);
   wlineh = u(3);
   col = get(circh,'color');
	point = get(gca,'currentpoint');
	point = point(1,[1,2]);
	z = point(1)+i*point(2);
   plot(real(z),imag(z),'.',...
      'parent',zax,'markersize',12,...
      'color',col,'tag','holoplot');
   set(circh,'linestyle','-','erase','none');
	w = eval(ud.fcn);
   plot(real(w),imag(w),'parent',ud.waxes,...
      'marker','.','markersize',12,...
      'color',col,'tag','holoplot');
   set(wlineh,'linestyle','-','erase','none');
   set(ud.wh,'marker','+');
   set(fig,'windowbuttonmotionfcn','holo(''pointm'')',...
      'windowbuttonupfcn','',...
      'user',ud);
	set(findobj(zax),'buttondownfcn','holo(''circles'')');

elseif strcmp(action,'rect')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(gcf,'user');
   zax = ud.zaxes;
   wax = ud.waxes;
   point = get(zax,'currentpoint');
   point = point(1,[1,2]);
   z = point(1)+i*point(2);
   w = ud.fcn;
   % plot(real(z),imag(z),'parent',zax);
   zboxh = plot(real(z),imag(z),...
      'parent',zax,'erasemode','xor',...
      'tag','holoplot','linestyle','--');
   wboxh = plot(real(w),imag(w),...
      'parent',wax,'erase','xor',...
      'tag','holoplot','linestyle','--');
   set(zax,'user',[z,zboxh,wboxh]);
   set(fig,'windowbuttonmotionfcn','holo(''rectm'')');
   set(fig,'windowbuttonupfcn','holo(''rectu'')');
   
elseif strcmp(action,'rectm')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(fig,'user');
   pt = get(fig,'currentpoint');
   if pt(2)>ud.actbot
      set(fig,'pointer','crosshair');
      zax = ud.zaxes;
      u = get(zax,'user');
      z1 = u(1);
      zboxh = u(2);
      wboxh = u(3);
      wh = ud.wh;
      point = get(zax,'currentpoint');
      point = point(1,[1,2]);
      z2 = point(1)+i*point(2);
      x = real([z1,z1,z2,z2,z1]);
      y = imag([z1,z2,z2,z1,z1]);
      set(zboxh,'xdata',x,'ydata',y);
      
      zz = z1 + (z2 - z1)*linspace(0,1);      
      x1 = real(zz); 
      x = [real(z1)*ones(1,100),x1,real(z2)*ones(1,100),fliplr(x1)];
      y1 = imag(zz);  
      y = [y1,imag(z2)*ones(1,100),fliplr(y1),imag(z1)*ones(1,100)];
      z = x+i*y;
      FFF = ud.fcn;
      w = eval(FFF);
      set(wboxh,'xdata',real(w),'ydata',imag(w));
      z=z2;w=eval(FFF);
      set(wh,'xdata',real(w),'ydata',imag(w));
   else
      set(fig,'pointer','arrow')
   end
   
elseif strcmp(action,'rectu')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(fig,'user');
   zax = ud.zaxes;
	u = get(zax,'user');
   z1 = u(1);
   delete(u(2:3));
	point = get(zax,'currentpoint');
	point = point(1,[1,2]);
   z2 = point(1)+i*point(2);
   plotrectgrid(z1,z2,fig)
   
   set(fig,'windowbuttonmotionfcn','holo(''pointm'')',...
      'windowbuttonupfcn','');
	set(findobj(zax),'buttondownfcn','holo(''rect'')');


elseif strcmp(action,'polar')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(gcf,'user');
   zax = ud.zaxes;
   wax = ud.waxes;
	point = get(zax,'currentpoint');
	point = point(1,[1,2]);
	z = point(1)+i*point(2);
   plot(real(z),imag(z),'o',...
      'parent',zax,'tag','holoplot');
   circh = plot(real(z),imag(z),...
      'erasemode','xor','parent',zax,...
      'tag','holoplot');
   w = eval(ud.fcn);
   wlineh = plot(real(w),imag(w),...
      'erase','xor','parent',wax,...
      'tag','holoplot');
	set(zax,'user',[z,circh,wlineh]);
   set(gcf,'windowbuttonmotionfcn','holo(''circlem'')',...
      'windowbuttonupfcn','holo(''polaru'')');


elseif strcmp(action,'polarm')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(fig,'user');
   pt = get(fig,'currentpoint');
   if pt(2)>ud.actbot
      set(fig,'pointer','crosshair');
      zax = ud.zaxes;
      u = get(gca,'user');
      center = u(1);
      circh = u(2);
      wlineh = u(3);
      point = get(zax,'currentpoint');
      point = point(1,[1,2]);
      z2 = point(1)+i*point(2);
      radius = abs(center - z2);
      ang = exp(i*pi*(-1:(2/100):1));
      z = cent+radius*ang;
      set(circh,'xdata',real(z),'ydata',imag(z));
      
      % axes(ud.waxes);
      FFF = get(ud.fcns,'user');
      l = length(z);
      zz1 = z(1:l-1);zz2=z(2:l);
      N = find((real(zz1)<=0));
      y1 = (imag(zz1(N))>=0);
      y2 = (imag(zz2(N))>=0);
      M = find(y1-y2);
      z(N(M))=NaN*ones(size(M));
      
      w = eval(FFF);
      set(wlineh,'xdata',real(w),'ydata',imag(w),'linestyle','--');
      z=z1;w=eval(FFF);
      set(wh,'xdata',real(w),'ydata',imag(w));
      % axes(ud.zaxes);
   else
      set(fig,'pointer','arrow')
   end
   

elseif strcmp(action,'polaru')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(fig,'user');
   zax = ud.zaxes;
   wax = ud.waxes;
   FFF = ud.fcn;
	u = get(zax,'user');
   center = u(1);
   delete(u(2:3));
	point = get(zax,'currentpoint');
	point = point(1,[1,2]);
   z2 = point(1)+i*point(2);
   radius = abs(z2-center);
   plotradgrid(center,radius,fig)
   
   set(fig,'windowbuttonmotionfcn','holo(''pointm'')',...
      'windowbuttonupfcn','');
   set(findobj(zax),'buttondownfcn','holo(''polar'')');
   
elseif strcmp(action,'rectmap')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   prompt ={'Enter the lower left corner of the rectangle','Enter the upper right corner of the rectangle'};
   title2 = 'Input for a rectangle to be mapped.';
   answer = inputdlg(prompt,title2);
   if isempty(answer)
      return
   end
   if isempty(answer{1})
      errordlg('No lower left corner was provided.');
      return
   elseif isempty(answer{2})
      errordlg('No upper right corner was provided.');
      return
   end
   z1 = str2num(answer{1});
   z2 = str2num(answer{2});
   plotrectgrid(z1,z2,fig);

elseif strcmp(action,'polarmap')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   prompt ={'Enter the center of the disk','Enter the radius of the disk'};
   title2 = 'Input for a disk to be mapped.';
   answer = inputdlg(prompt,title2);
   if isempty(answer)
      return
   end
   if isempty(answer{1})
      errordlg('No center was provided.');
      return
   elseif isempty(answer{2})
      errordlg('No radius was provided.');
      return
   end
   
   z = str2num(answer{1});
   r = str2num(answer{2});
   plotradgrid(z,r,fig);

elseif strcmp(action,'zchange')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(fig,'user');
   zax = ud.zaxes;
   prompt ={'Enter the lower left point','Enter the real increment'};
   title2 = 'Input to change the z-axes';
   answer = inputdlg(prompt,title2);
   if isempty(answer)
      return
   end
   if isempty(answer{1})
      errordlg('No lower left point was provided.');
      return
   elseif isempty(answer{2})
      errordlg('No real increment was provided.');
      return
   end
   z = str2num(answer{1});
   h = str2num(answer{2});
   x = real(z);
   y = imag(z);
   xlim = [x, x+h];
   ylim = [y, y+h];
   set(zax,'xlim',xlim,'ylim',ylim);
   
elseif strcmp(action,'wchange')
   
   fig = findobj(get(0,'children'),'flat','name','Holomorphic Map');
   ud = get(fig,'user');
   wax = ud.waxes;
   prompt ={'Enter the lower left point','Enter the real increment'};
   title2= 'Input to change the w-axes';
   answer = inputdlg(prompt,title2);
   if isempty(answer)
      return
   end
   if isempty(answer{1})
      errordlg('No lower left point was provided.');
      return
   elseif isempty(answer{2})
      errordlg('No real increment was provided.');
      return
   end
   z = str2num(answer{1});
   h = str2num(answer{2});
   x = real(z);
   y = imag(z);
   xlim = [x, x+h];
   ylim = [y, y+h];
   set(wax,'xlim',xlim,'ylim',ylim);
  
   
end

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

function plotradgrid(z1,r,fig)

ud = get(fig,'user');
zax = ud.zaxes;
wax = ud.waxes;
FFF = ud.fcn;
radius = r;
center = z1;
N=8;
M=6;

angles = exp(i*pi*((-1+2/N):(2/N):1));
ang = exp(i*pi*(-1:(2/100):1));
radi = radius*(0:(1/(M-1)):1);
rad = radius*(0:(1/100):1);

circles = center+radi'*ang;
z = circles.';
plot(real(z),imag(z),...
   'parent',zax,'tag','holoplot');
w = eval(FFF);
plot(real(w),imag(w),...
   'parent',wax,'tag','holoplot');
radii = center+angles.'*rad;
z = radii.';
plot(real(z),imag(z),...
   'parent',zax,'tag','holoplot');
w = eval(FFF);
plot(real(w),imag(w),...
   'parent',wax,'tag','holoplot');


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

function plotrectgrid(z1,z2,fig)

N = 7;
ud = get(fig,'user');
zz = z1 + (z2-z1)*linspace(0,1,N);
x = real(zz);
y = imag(zz);
x = x'*ones(1,100);
zzz = z1 + (z2 - z1)*linspace(0,1);
xxy = ones(N,1)*imag(zzz);   %linspace(imag(z1),imag(z2));
xz = x+i*xxy;
y = y'*ones(1,100);
xyy = ones(N,1)*real(zzz);   %linspace(real(z1),real(z2));

yz = xyy+i*y;
z = [xz.',yz.'];
plot(real(z),imag(z),...
   'parent',ud.zaxes,'tag','holoplot');
FFF = ud.fcn;
w = eval(FFF);
plot(real(w),imag(w),...
   'parent',ud.waxes,'tag','holoplot');

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