function phasespace(varargin)
% PHASESPACE Embedding of time series in a phase space
% PHASESPACE(X) shows the 3D phase space trajectory of
% the system which is presented by the observation X.
% The phase vectors are a reconstruction by using the
% time delay method (Takens, 1981). A GUI provides to
% change the embedding dimension to 2D.
%
% PHASESPACE(X,Y) uses the two one-column vectors
% X and Y as components of the phase space trajectory.
% The representation is 2D only and cannot be switched
% to 3D.
%
% PHASESPACE(X,Y,Z) uses the three one-column vectors
% X, Y and Z as components of the phase space trajectory.
% The representation is 3D only and cannot be switched
% to 2D.
%
% PHASESPACE without any arguments calls a demo (the
% same as the example below).
%
% Example: phasespace(cos(0:.1:32).*[321:-1:1])
%
% See also FNN, PSS.
%
% References:
% Takens, F.:
% Detecting Strange Attractors in Turbulence,
% Lecture Notes in Mathematics, 898, Springer, Berlin, 1981
% Copyright (c) 2008-2009
% Norbert Marwan, Potsdam Institute for Climate Impact Research, Germany
% http://www.pik-potsdam.de
%
% Copyright (c) 2002-2008
% Norbert Marwan, Potsdam University, Germany
% http://www.agnld.uni-potsdam.de
%
% $Date$
% $Revision$
%
% $Log$
% Revision 2.4 2007/12/20 16:26:06 marwan
% changed gpl splash behaviour
%
% Revision 2.3 2006/03/29 13:07:55 marwan
% problems regarding OPRPs and embedding resolved
%
% Revision 2.2 2006/02/14 11:46:15 marwan
% *** empty log message ***
%
% Revision 2.1 2004/11/10 07:07:56 marwan
% initial import
%
%
% This program is part of the new generation XXII series.
%
% This program is free software; you can redistribute it and/or
% modify it under the terms of the GNU General Public License
% as published by the Free Software Foundation; either version 2
% of the License, or any later version.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% programme properties
global props
init_properties
try
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% check and read the input
slidebar_off=0;
error(nargchk(0,3,nargin));
x=[]; lag=50;
if isempty(varargin)
varargin{1}='init';
end
if ischar(varargin{1})
action=varargin{1};
else
if nargin==3
dim=3;
x(:,3)=varargin{3}(:,1);
x(:,2)=varargin{2}(:,1);
x(:,1)=varargin{1}(:,1);
elseif nargin==2
dim=2;
x(:,2)=varargin{2}(:,1);
x(:,1)=varargin{1}(:,1);
elseif nargin==1
dim=3;
x=varargin{1};
if size(x,1)==1, x=x(1,:)'; else, x=x(:,1); end
end
m=size(x,2);
if m>3
h=errordlg('Only the first three columns of the vector will be used.','Vector size');
waitfor(h);
m=3; x(:,4:end)=[];
end
action='init';
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% splash the GPL
splash_gpl('crp');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% switch routines
switch(action)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% initialization
case 'init'
if isempty(x), x(:,1)=(cos(0:.1:62).*[621:-1:1])'; m=1; dim=3; lag=53; end
h=figure(props.window,... % Plot Figure
'Tag','phasespace_fig',...
'MenuBar','Figure',...
'Position',[69.5000 39.6429 120.0000 30.0714],...
'Name','Phase Space Reconstruction',...
'DeleteFcn','phasespace close',...
'WindowButtonMotionFcn','phasespace motion',...
'PaperPosition',[0.25 0.25 7.7677 11.193],...
'PaperType','a4',...
'PaperOrientation','portrait',...
'UserData',x);
ha=guihandles(h);
ha_fn=fieldnames(ha);
for i=1:length(ha);
try
set(eval(['ha.',ha_fn{i}]),props.menubar)
end
end
set(0,'showhidden','on')
h=findobj('Label','&Help','Type','uimenu');
if isempty(h)
h=uimenu('Label','&Help');
h2=uimenu('Parent',h(1),'Label','&Help Phasespace','Callback','helpwin phasespace');
else
h1=flipud(get(h(1),'Children'));
set(h1(1),'Separator','on')
h2=uimenu('Parent',h(1),'Label','&Help Phasespace','Callback','helpwin phasespace');
copyobj(h1,h(1))
delete(h1)
end
set(0,'showhidden','off')
h=axes(props.axes,...
'Position',[89 24.8 6.8 3.5]);
logo=load('logo');
h2=imagesc([logo.logo fliplr(logo.logo)]);
set(h2,'Tag','uniLogo')
set(h,props.logo,'Tag','axes_logo')
h=uicontrol(props.text,...
'Tag','text',...
'String','Uni Potsdam',...
'Units','Character',...
'Position',[97 24.2143 22 3.5714]);
h2=textwrap(h,{[char(169),' AGNLD'],'University of Potsdam','2002-2006'});
set(h,'String',h2)
h=axes(props.axes,...
'Tag','phasespace_axes',...
'Box','On',...
'Position',[4.8333 3.5000 76.8333 25.0714]);
h=uicontrol(props.frame,...
'Tag','frame',...
'Position',[91.5000 1.3571 23.5000 20.7857]);
h=uicontrol(props.slider,...
'Tag','slider_hori',...
'CallBack','phasespace rotate',...
'Min',-360,...
'Max',360,...
'SliderStep',[1/360 10/360],...
'Position',[4.8333 0.6429 76.8333 1.3500]);
h=uicontrol(props.slider,...
'Tag','slider_vert',...
'CallBack','phasespace rotate',...
'Min',-90,...
'Max',90,...
'SliderStep',[1/180 10/180],...
'Position',[85 3.5000 3.000 25.0714]);
h=uicontrol(props.text,...
'String','Dimension',...
'Tag','text',...
'Position',[94.8333 20.1429 16.8333 1.5000]);
if m~=1; set(h,'Enable','Off'), end
h=uicontrol(props.radio,...
'Tag','button_2d',...
'String','2D',...
'Interruptible','off',...
'CallBack','phasespace dim2',...
'Value',0,...
'Position',[94.8333 18.8857 16.8333 1.5000]);
if dim==2, set(h,'Value',1), end
if m~=1; set(h,'Enable','Off'), end
h=uicontrol(props.radio',...
'Tag','button_3d',...
'String','3D',...
'Value',0,...
'Interruptible','off',...
'CallBack','phasespace dim3',...
'Position',[94.8333 17.3857 16.8333 1.5000]);
if dim==3, set(h,'Value',1), end
if m~=1; set(h,'Enable','Off'), end
h=uicontrol(props.text,...
'Tag','text',...
'String','Lag',...
'Position',[94.8333 15.4 16.8333 1.5000]);
if m~=1; set(h,'Enable','Off'), end
if lag>(.1*length(x)), lag=ceil(.1*length(x)); end
h=uicontrol(props.edit,...
'Tag','edit_lag',...
'String',num2str(lag),...
'CallBack','phasespace update',...
'Interruptible','off',...
'Position',[94.8333 14.1214 16.8333 1.5000]);
if m~=1; set(h,'Enable','Off'), end
h=uicontrol(props.slider,...
'Tag','slider_lag',...
'Max',length(x),...
'Interruptible','off',...
'Value',lag,...
'Min',0,...
'Sliderstep',[1/length(x) 10/length(x)],...
'CallBack','phasespace lag',...
'Position',[94.8333 12.95 16.8333 1.2]);
if m~=1; set(h,'Enable','Off'), end
if slidebar_off, set(h,'Visible','off'), end
h=uicontrol(props.radio,...
'Tag','button_line',...
'Interruptible','off',...
'String','Lines',...
'CallBack','phasespace linestyle',...
'Value',1,...
'Position',[94.8333 10.7857 16.8333 1.5000]);
h=uicontrol(props.radio,...
'Tag','button_dots',...
'String','Dots',...
'CallBack','phasespace linestyle',...
'Interruptible','off',...
'Value',0,...
'Position',[94.8333 9.2857 16.8333 1.5000]);
h=uicontrol(props.radio,...
'Tag','button_comet',...
'String','Comet',...
'Interruptible','off',...
'CallBack','phasespace linestyle',...
'Value',0,...
'Position',[94.8333 7.7857 16.8333 1.5000]);
h=uicontrol(props.button,...
'Tag','button_print',...
'CallBack','phasespace print',...
'String','Print',...
'Position',[94.8333 4.9286 16.8333 2.2143]);
h=uicontrol(props.button,...
'Tag','button_close',...
'CallBack','phasespace close',...
'String','Close',...
'Position',[94.8333 2.1429 16.8333 2.2143]);
tags={'phasespace_fig';'axes_logo';'text';'slider_hori';'slider_vert';'phasespace_axes';'frame';'button_2d';'button_3d';'edit_lag';'slider_lag';'button_line';'button_dots';'button_comet';'button_print';'button_close';};
h=[];
for i=1:length(tags); h=[h; findobj('Tag',tags{i})]; end
set(h,'Units','Norm');
plot_trajectory(x,dim,lag)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% dimension
case 'dim2'
h=findobj('Tag','button_2d','Style','RadioButton','Parent',gcf);
if get(h,'Value')~=1
h=findobj('Tag','button_2d','Parent',gcf);
set(h(1),'Value',1);
end
h=findobj('Tag','button_3d','Parent',gcf);
set(h(1),'Value',0);
phasespace update
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% dimension
case 'dim3'
h=findobj('Tag','button_3d','Style','RadioButton','Parent',gcf);
if get(h,'Value')~=1
h=findobj('Tag','button_3d','Parent',gcf);
set(h(1),'Value',1);
end
h=findobj('Tag','button_2d','Parent',gcf);
set(h(1),'Value',0);
phasespace update
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% lag (slider)
case 'lag'
h=findobj('Tag','slider_lag','Style','Slider','Parent',gcf);
lag=round(get(h,'Value'));
h=findobj('Tag','edit_lag','Parent',gcf);
set(h(1),'String',num2str(lag))
phasespace update
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% linestyle
case 'linestyle'
h_line=findobj('Tag','button_line','Parent',gcf); h_line=h_line(1);
h_dots=findobj('Tag','button_dots','Parent',gcf); h_dots=h_dots(1);
h_comet=findobj('Tag','button_comet','Parent',gcf); h_comet=h_comet(1);
h=findobj('Tag','phasespace_trajectory'); h=h(1);
flag=get(h_comet,'Value');
if h_line==gcbo
set(h,props.line)
set(h_line,'Value',1)
set(h_dots,'Value',0)
set(h_comet,'Value',0)
elseif h_dots==gcbo
set(h,props.marker)
set(h_line,'Value',0)
set(h_dots,'Value',1)
set(h_comet,'Value',0)
elseif h_comet==gcbo
set(h_line,'Value',0)
set(h_dots,'Value',0)
set(h_comet,'Value',1)
end
if flag
phasespace update
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% update trajectory
case 'update'
h=findobj('Tag','phasespace_fig'); h=h(1);
x=get(h,'UserData');
h=findobj('Tag','edit_lag','Parent',gcf);
lag=round(str2num(get(h,'String')));
set(h,'String',num2str(lag))
h=findobj('Tag','slider_lag','Parent',gcf);
set(h,'Value',lag)
h=findobj('Tag','button_3d','Parent',gcf);
if get(h,'Value')
dim=3;
end
h=findobj('Tag','button_2d','Parent',gcf);
if get(h,'Value')
dim=2;
end
plot_trajectory(x,dim,lag)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% rotate axes
case 'rotate'
h=findobj('Tag','slider_vert','Parent',gcf);
el=get(h,'value');
h=findobj('Tag','slider_hori','Parent',gcf);
az=get(h,'value');
view(az,el)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% print
case 'print'
h=findobj('Tag','uniLogo');
h_axes=findobj('Tag','phasespace_axes','Parent',gcf); h_axes=h_axes(1);
h=[h; findobj('Tag','text','Parent',gcf)];
h=[h; findobj('Tag','frame','Parent',gcf)];
h=[h; findobj('Tag','slider_hori','Parent',gcf)];
h=[h; findobj('Tag','slider_vert','Parent',gcf)];
h=[h; findobj('Tag','button_2d','Parent',gcf)];
h=[h; findobj('Tag','button_3d','Parent',gcf)];
h=[h; findobj('Tag','edit_lag','Parent',gcf)];
h=[h; findobj('Tag','slider_lag','Parent',gcf)];
h=[h; findobj('Tag','button_line','Parent',gcf)];
h=[h; findobj('Tag','button_dots','Parent',gcf)];
h=[h; findobj('Tag','button_comet','Parent',gcf)];
h=[h; findobj('Tag','button_print','Parent',gcf)];
h=[h; findobj('Tag','button_close','Parent',gcf)];
set(gcf,'WindowButtonMotionFcn','')
set(h,'Visible','Off')
old_pos=get(h_axes,'Position');
set(h_axes,'Units','normalize','Position',[0.1300 0.1100 0.7750 0.8150])
h_dlg=printdlg;
waitfor(h_dlg)
set(h_axes,'Position',old_pos)
set(h,'Visible','On')
set(gcf,'WindowButtonMotionFcn','phasespace motion')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% motion
case 'motion'
h_fig=findobj('Tag','phasespace_fig'); h_fig=h_fig(1);
h=findobj('Tag','button_comet','Style','RadioButton','Parent',h_fig);
if get(h,'Value')~=1
% read data, dim and lag
h=findobj('Tag','phasespace_fig'); h=h(1);
x=get(h,'UserData');
m=size(x,2);
h=findobj('Tag','edit_lag','Style','Edit','Parent',h_fig);
lag=round(str2num(get(h,'String')));
set(h,'String',num2str(lag))
h=findobj('Tag','slider_lag');
set(h(1),'Value',lag)
h=findobj('Tag','button_3d','Style','RadioButton','Parent',h_fig);
if get(h,'Value')
dim=3;
end
h=findobj('Tag','button_2d','Style','RadioButton','Parent',h_fig);
if get(h,'Value')
dim=2;
end
h2=findobj('Tag','phasespace_trajectory','Type','Line');
if isempty(h2)
plot_trajectory(x,dim,lag);
end
% create vectors
switch(m)
case {2,3}
y=x;
if dim==2, y(:,3)=0; end
case 1
if dim==3, y=[x(1:end-2*lag),x(1+lag:end-lag),x(1+2*lag:end)];
elseif dim==2, y=[x(1:end-lag),x(1+lag:end)]; y(:,3)=0;
end
end
h_axes=findobj('Tag','phasespace_axes','Parent',h_fig); h_axes=h_axes(1);
pointer_prefs=getptr(h_fig);
pointer_prefs=cell2struct(pointer_prefs(2:2:end),pointer_prefs(1:2:end),2);
bad_pointer=setptr(props.glasspointer);
bad_pointer=cell2struct(bad_pointer(2:2:end),bad_pointer(1:2:end),2);
fnames=fieldnames(pointer_prefs);
i=find(strcmpi(fnames,'Pointer'));
if strcmpi(getfield(pointer_prefs,fnames{i}),'custom')
i=find(strcmpi(fnames,'PointerShapeCData'));
shape_pointer=getfield(pointer_prefs,fnames{i});
shape_pointer(isnan(shape_pointer))=0;
fnames_bad_pointer=fieldnames(bad_pointer);
i=find(strcmpi(fnames_bad_pointer,'PointerShapeCData'));
shape_bad_pointer=getfield(bad_pointer,fnames_bad_pointer{i});
shape_bad_pointer(isnan(shape_bad_pointer))=0;
if ~prod(prod(double(shape_pointer==shape_bad_pointer)))
set(h_axes,'UserData',pointer_prefs)
else
pointer_prefs=get(h_axes,'UserData');
end
else
set(h_axes,'UserData',pointer_prefs)
end
xlim=get(h_axes,'xlim');
ylim=get(h_axes,'ylim');
zlim=get(h_axes,'zlim');
axis_delta=[diff(xlim) diff(ylim) diff(zlim)];
% cursor hover axes?
pos=get(h_axes,'CurrentPoint');
if dim==2, pos(:,3)=0; end
if (pos(1,1)>=xlim(1) & pos(1,1)<=xlim(2) & pos(1,2)>=ylim(1) & pos(1,2)<=ylim(2) & pos(1,3)>=zlim(1) & pos(1,3)<=zlim(2)) | ...
(pos(2,1)>=xlim(1) & pos(2,1)<=xlim(2) & pos(2,2)>=ylim(1) & pos(2,2)<=ylim(2) & pos(2,3)>=zlim(1) & pos(1,3)<=zlim(2))
% cursor hover line? (within 1% of point centers)
if dim==2, tolerance=.01; else tolerance=.05; end
is_x1=abs(y(:,1)-pos(1,1)) < tolerance*axis_delta(1);
is_x2=abs(y(:,1)-pos(2,1)) < tolerance*axis_delta(1);
is_y1=abs(y(:,2)-pos(1,2)) < tolerance*axis_delta(2);
is_y2=abs(y(:,2)-pos(2,2)) < tolerance*axis_delta(2);
% is_x1=(y(:,1)>pos(1,1) & y(:,1)<pos(2,1)) + (y(:,1)<pos(1,1) & y(:,1)>pos(2,1));
% is_y1=(y(:,2)>pos(1,2) & y(:,2)<pos(2,2)) + (y(:,2)<pos(1,2) & y(:,2)>pos(2,2));
res1=is_x1.*is_y1;
res2=is_x2.*is_y2;
% is_z1=(y(:,3)>pos(1,3) & y(:,3)<pos(2,3)) + (y(:,3)<pos(1,3) & y(:,3)>pos(2,3));
is_z1=abs(y(:,3)-pos(1,3)) < tolerance*axis_delta(3);
is_z2=abs(y(:,3)-pos(2,3)) < tolerance*axis_delta(3);
res1=res1.*is_z1;
res2=res2.*is_z2;
% show index and change cursor
index1=find(res1);index2=find(res2);
h_index_axes=findobj('Tag','index_axes','Parent',h_fig);
h=findobj('Tag','index_text','Parent',h_index_axes);
if isempty(h_index_axes)
h_index_axes=axes(props.axesindex,'Tag','index_axes');
end
if isempty(h)
h=text(props.textindex,'Units','norm','Tag','index_text','Parent',h_index_axes);
end
h=h(1); h_index_axes=h_index_axes(1);
h_point=findobj('Tag','markedPoint','Parent',h_axes);
set(h_point,'Visible','Off')
if ~isempty(index1)
setptr(h_fig,props.glasspointer)
tx_pos=[y(index1(1),1)+.04*axis_delta(1) y(index1(1),2)+.01*axis_delta(2) y(index1(1),3)+.01*axis_delta(3)];
tx=num2str(index1(1));
set(h,'String',[' ',tx],'Visible','On','Units','Pixel')
set(h_index_axes,'Visible','On')
tx_ext=get(h,'Extent');
set(h_fig,'Units','Pixel')
pos=get(h_fig,'CurrentPoint');
set(h_fig,'Units','Norm')
set(h_index_axes,'Position',[pos(1)+props.index.xoffset pos(2)+props.index.yoffset tx_ext(3) tx_ext(4)])
set(h_point,'Position',[y(index1(1),1) y(index1(1),2) y(index1(1),3)],'Visible','On')
elseif ~isempty(index2)
setptr(h_fig,props.glasspointer)
tx_pos=[y(index2(1),1)+.04*axis_delta(1) y(index2(1),2)+.01*axis_delta(2) y(index2(1),3)+.01*axis_delta(3)];
tx=num2str(index2(1));
set(h,'String',[' ',tx],'Visible','On','Units','Pixel')
set(h_index_axes,'Visible','On')
tx_ext=get(h,'Extent');
set(h_fig,'Units','Pixel')
pos=get(h_fig,'CurrentPoint');
set(h_fig,'Units','Norm')
set(h_index_axes,'Position',[pos(1)+props.index.xoffset pos(2)+props.index.yoffset tx_ext(3) tx_ext(4)])
set(h_point,'Position',[y(index2(1),1) y(index2(1),2) y(index2(1),3)],'Visible','On')
else
set(h_fig,pointer_prefs)
set(h,'Visible','Off')
set(h_index_axes,'Visible','Off')
end
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% close
case 'close'
delete(gcf)
end
try, set(0,props.root), end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% error handling
catch
%if 0
z=whos;x=lasterr;y=lastwarn;in=varargin{1};
errcode=[];
print_error('phasespace',z,x,y,in,[],action)
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% plot trajectory
function plot_trajectory(x,dim,lag)
global props
try
if (length(x)-(dim-1)*lag)<=0
h=warndlg(['No phasespace vectors available.',char(10),...
'Please use a smaller lag.'],'Warning');
set(h,props.msgboxwin),h2=guihandles(h);set(h2.OKButton,props.msgbox)
set(h,'Tag','helpdlgbox','HandleVisibility','On');
return
end
h_fig=findobj('Tag','phasespace_fig'); h_fig=h_fig(1);
figure(h_fig)
h_axes=findobj('Tag','phasespace_axes','Parent',h_fig); h_axes=h_axes(1);
h=findobj('Tag','button_comet','Parent',h_fig); h=h(1);
if get(h,'Value')==1
cmd='comet';
else
cmd='plot';
end
flag='';
m=size(x,2);
switch(m)
case 3
parm='x(:,1),x(:,2),x(:,3)';
flag='3';
case 2
parm='x(:,1),x(:,2)';
case 1
if dim==3
parm='x(1:end-2*lag),x(1+lag:end-lag),x(1+2*lag:end)';
flag='3';
elseif dim==2
parm='x(1:end-lag),x(1+lag:end)';
end
end
set(h_fig,'CurrentAxes',h_axes)
eval([cmd,flag,'(',parm,')']);
set(h_axes,'Tag','phasespace_axes')
h=findobj('Type','Line','Parent',gca);
h_line=findobj('Tag','button_line','Parent',h_fig); h_line=h_line(1);
h_dots=findobj('Tag','button_dots','Parent',h_fig); h_dots=h_dots(1);
if get(h_line,'Value')==1
set(h,props.line)
elseif get(h_dots,'Value')==1
set(h,props.marker)
end
set(h,'Tag','phasespace_trajectory')
if strcmp(cmd,'plot')
hold on
% marker points in trajectory
switch(m)
case 3
parm='x(i,1),x(i,2),x(i,3)';
case 2
parm='x(i,1),x(i,2)';
case 1
if dim==3, parm='x(i),x(i+lag),x(i+2*lag)';
elseif dim==2, parm='x(i),x(i+lag)';
end
end
m_size=[30, 25, 20, 15, 10];
dx=abs(round(.001*diff(get(h_axes,'xlim'))/mean(diff(x(:,1)))));
for j=1:5,
i0=round(.25*length(x-(dim-1)*lag));
i=i0+dx*j;
if i<(length(x)-(dim-1)*lag)
eval(['plot',flag,'(',parm,',''.'',''markersize'',',num2str(m_size(j)),')'])
end
i0=round(.75*length(x-(dim-1)*lag));
i=i0+dx*j;
if i<(length(x)-(dim-1)*lag)
eval(['plot',flag,'(',parm,',''.'',''markersize'',',num2str(m_size(j)),')'])
end
end
text(0,0,0,'o','Tag','markedPoint',props.glass)
hold off
axis equal
end
[az, el]=view;
h=findobj('Tag','slider_hori','Parent',gcf);
set(h,'Value',az)
h=findobj('Tag','slider_vert','Parent',gcf);
set(h,'Value',el)
if strcmp(cmd,'plot')
grid on
end
catch
end