function let(action,ODEfunction,DATA,AxisRange)
%LET Lyapunov Exponents Toolbox
%
% To run the program, enter LET in MATLAB command window.
% Details of the program can be obtained by pressing
% the "Information" button in the startup window. The
% program information can also be found in files README.M,
% LETHELP.M and SETHELP.M.
% by Steve Wai Kam SIU, July 5, 1998.
if nargin<1
clear; %Clear all variables initially
clc; %Clear the command window
action='Initialization';
else
%If it is a callback action, obtain the handles of the
%GUI components stored in'UserData' of the main window.
MainHandles=get(gcf,'UserData');
end
switch action
case 'Initialization'
startlet; %Show a startup window
case 'runLET'
%Default axis range
if nargin<4
AxisRange=[0,1000,-25,25];
end
%Font size of UI components
FontSize=8;
%Setup a GUI window and obtain the handles of GUI components
MainHandles=maingui(AxisRange,FontSize);
%Store the handles in "UserData" of the figure such that
%it can be accessed anywhere by using the "get" command.
set(gcf,'UserData',MainHandles);
%If no specified parameters are supplied, use default values.
if nargin<2
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Default Parameters for setting window
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
OutputFile='data.out'; %Default output file: data.out
output=0; %Don't check "Output File": 1="on", 0="off"
LEout=1; %Check "Lyapunov Exponents"
LDout=1; %Check "Lyapunov Dimension"
LEprecision=1; %Precision of output values of the
LDprecision=1; % Lyapunov exponents and dimension
% are set to 1 (4 floating points).
% 2 means %.6f, 3 means %.8f, ...
ODEfunction=''; %No default ODE function
IntMethod=2; %Integration method: 1=Discrete map, 2=ODE45, 3=ODE23
% 4=ODE113, 5=ODE23S, 6=ODE15S
InitalTime=0; %Default initial time: 0
FinalTime=1000; %Default final time: 1000
TimeStep=0.01; %Default time step: 0.01
RelTol=1e-5; %Default relative tolerance: 1E-5
AbsTol=1e-5; %Default absolute tolerance: 1E-5
IC=[]; %No default initial coniditions
LODEnum=[]; %No. of linearized equation (default: none )
%PLOTTING OPTIONS: Only one of them can be set "on" (i.e. 1)
plot1=1; %Update the plot imediately
plot2=0; %Update the plot every ... iterations
ItrNum=10; %No. of iterations for updating the plot
%Line Colors
Blue=1; Black=2; Green=3; Red=4; Yellow=5; Magenta=6; Cyan=7;
LineColor=Blue; %Default line color: Blue
Discard=100; %Default transient iterations to be discarded: 100
UpdateSteps=10; %Update the LEs every 10 time steps
%Save the default values and upload them onto the
%'UserData' of the "Setting" button
DATA=[output, LEout, LEprecision, LDout, LDprecision, ...
IntMethod, InitalTime, FinalTime, TimeStep, RelTol, ...
AbsTol, plot1, plot2, ItrNum, LineColor, ...
Discard, UpdateSteps, LODEnum, IC];
else
%No specified output file for demo
OutputFile='';
end
set(MainHandles(4),'UserData',DATA);
%Upload the output file and ODE function names
NAMES=char(OutputFile,ODEfunction);
set(MainHandles(2),'UserData',NAMES);
case 'stop'
%If "Stop" button is pressed,disable the button itself
%and enable the others.
set(MainHandles([2,4,13,15]),'Enable','On');
set(MainHandles(3),'Enable','Off');
%Set a flag to indicate "Stop" action is requested so
%that the program FINDLYAP knows during calculation
%and stops the process imediately.
set(MainHandles(3),'UserData',1);
%Note: FINDLYAP checks whether the "Stop" button is pressed
%before each iteration
case 'setting'
%Load the setting window
setting;
case {'OnPressed','OffPressed'}
%If "On" is checked, uncheck "Off" and vice versa.
%MainHandles(5) is the handle of "On" radio button
%MainHandles(6) is the handle of "Off" radio button
OnIsOn=get(MainHandles(5),'Value');
OffIsOn=get(MainHandles(6),'Value');
if ( (strcmp(action,'OnPressed') & OnIsOn)| ...
(strcmp(action,'OffPressed') & ~OffIsOn) )
check(MainHandles(5),MainHandles(6)); %Check "On" and uncheck "Off"
grid on; %Show grid lines
else
check(MainHandles(6),MainHandles(5)); %Check "Off" and uncheck "On"
grid off; %Remove grid lines
end
case 'changeAxis'
%MainHandles(7) is the handle of the "X :" edit box
%MainHandles(8) is the handle of the "Y :" edit box
%Get values input by user
xRange=str2num(get(MainHandles(7),'String'));
yRange=str2num(get(MainHandles(8),'String'));
%Check whether the input values are in correct format
if ( all(size(xRange)==[1,2]) & all(size(yRange)==[1,2]) ...
& xRange(1)<xRange(2) & yRange(1)<yRange(2) ...
& xRange(1)~=xRange(2) & yRange(1)~=yRange(2))
axis([xRange,yRange]); %Re-arrange the axis range.
%Save the data for restoring previous values if error occurs
set(MainHandles(7),'UserData',xRange);
set(MainHandles(8),'UserData',yRange);
axis('manual'); %Freeze the current axis-limits
else
%If error occurs, restore the original values
xRange=get(MainHandles(7),'UserData');
yRange=get(MainHandles(8),'UserData');
set(MainHandles(7),'String',[num2str(xRange(1)) ', ' num2str(xRange(2))]);
set(MainHandles(8),'String',[num2str(yRange(1)) ', ' num2str(yRange(2))]);
msg=['Input must be a 1 x 2 numeric matrix'...
' with format [minValue, maxValue], where'...
' minValue < maxValue.'];
errordlg(msg,'ERROR','replace');
end
case 'drawLine'
%MainHandles(9) is the handle of the "Draw line at" edit box
str=get(MainHandles(9),'String');
y=str2num(str); [ry,cy]=size(y);
LinesHandles=get(MainHandles(9),'UserData');
L=length(LinesHandles);
del=strcmp(lower(rmspace(str)),'del');
delall=strcmp(lower(rmspace(str)),'del*');
%Check whether the input values are in correct format
if (~isempty(y) & ry==1)
Y=[1;1]*y;
xRange=get(gca,'XLim');
X=xRange(:)*ones(1,length(y));
hold on; h=plot(X,Y,'k');
%Force MATLAB to draw imediately even if calculation is in progress
drawnow;
%Add the new line handle(s), store them, and
%clear the string in the edit box.
newLinesHandles=[LinesHandles,h];
set(MainHandles(9),'UserData',newLinesHandles,'String','');
elseif ( L>=1 & del)
%Delete the previous drawn line
delete(LinesHandles(L));
%Remove the line handle stored in 'UserData', and
%clear the string in the edit box.
if L>1
set(MainHandles(9),'UserData',LinesHandles(1:L-1),'String','');
else
set(MainHandles(9),'UserData',[],'String','');
end
elseif ( L>=1 & delall)
% Delete all drawn lines
delete(LinesHandles);
set(MainHandles(9),'UserData',[],'String','');
elseif ( L<1 & (del | delall) )
msg='No more line can be deleted.';
errordlg(msg,'ERROR','replace');
else
msg=['Input must be a numeric number or row vector!'...
' Use DEL to delete the previous drawn line or DEL*'...
' to delete all drawn lines.'];
errordlg(msg,'ERROR','replace');
end
case 'plot'
%Get the line handles stored in 'UserData' of the
%"New Plot" button
LineHandles=get(MainHandles(13),'UserData');
[rL,cL]=size(LineHandles);
if ~isempty(LineHandles)
%Get the current axis labels and title
xLabel=get(get(gca,'xlabel'),'String');
yLabel=get(get(gca,'ylabel'),'String');
Title=get(get(gca,'Title'),'String');
%Get the line color
DATA=get(MainHandles(4),'UserData');
Color=DATA(15);
%Construct a look-up table for the line colors
COLORS='bkgrymc';
%Map the "Line color" pop-up menu position to the look-up table
LineColor=COLORS(Color);
figure('Units','Normalized','Color',[1 1 1],'Name','Lyapunov Exponents Spectrum', ...
'NumberTitle','off','Position',[0.1 0.1 0.8 0.8],'Tag','newplot');
xlabel(xLabel); ylabel(yLabel); title(Title);
for i=1:rL
for j=1:cL
xData=get(LineHandles(i,j),'xData');
yData=get(LineHandles(i,j),'yData');
plot(xData,yData,LineColor);
hold on;
end
end
hold off;
else
errordlg('No data is available!','ERROR','replace');
end
case 'help'
helpwin('lethelp','LET Help Window');
case 'start'
%When "Start" button is pressed, disable the "Start",
%"Setting", "Exit" and "New Plot" buttons, and
%enable the "Stop" button.
set(MainHandles([2,4,13,15]),'Enable','Off');
set(MainHandles(3),'Enable','On');
set(gca,'UserData',0);
%Reset the state of "Stop" button to zero (i.e. not pressed)
set(MainHandles(3),'UserData', 0);
msg='Errors in "findlyap".';
Warn=['errordlg(msg,''ERROR'',''replace'');',...
'set(MainHandles([2,4,13,15]),''Enable'',''On'');',...
'set(MainHandles(3),''Enable'',''Off'');',...
'findlyap(MainHandles)'];
%eval('findlyap(MainHandles)',Warn);
LineHandles=findlyap(MainHandles);
%Store the line handles in the 'Userdata' of the "New Plot" button.
set(MainHandles(13),'UserData',LineHandles);
otherwise
error('Incorrect input argument!');
end
%--------------------------Subroutines---------------------------
function MainHandles=maingui(AxisRange,FontSize)
%MAINGUI Function accompanied with LET
% MAINGUI creates a graphical user interface (GUI)window.
% by Steve Wai Kam SIU, Feb. 19, 1998.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Default parameters for main window
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--Grid Lines--
gOn=0; %Grid on: initial set 0 (i.e. off)
gOff=1; %Grid off: initial set 1 (i.e. on)
%--Plot Range--
%1st element is the min. value, 2nd is the max. value
xRange=AxisRange(1:2); %Plot range of X-Axis
yRange=AxisRange(3:4); %Plot range of Y-Axis
%--Draw line at--
y=[]; %No value is displayed initially
%--Current Time--
ct=0; %Current time (initial displayed value)
%--Final Time--
ft=0; %Final time (initial displayed value)
%--Time Used--
ut=0; %Time counted from starting calculation
%--Bottom text--
bttmText=''; %Nothing is displayed initially
%X-Axis Label
xLabel='Time';
%Y-Axis Label
yLabel='Lyapunov Exponents';
%Title
Title=''; %No default title
%%%%%%%%%%%%%%%%%%%%%%%%%
% GUI window setup
%%%%%%%%%%%%%%%%%%%%%%%%%
WinWidth=0.95; %Window width
WinHeight=0.78; %Window height
BtnWidth=0.12; %Button width
BtnHeight=0.05; %Button height
xPos=0.865; %X-position of buttons
%Window
a=figure('Units','Normalized','Color',[1 1 1],'BackingStore','Off',...
'Name','LET Main Program','NumberTitle','off', ...
'Position',[0.02 0.1 WinWidth WinHeight],'Visible','Off','Tag','Fig1');
%Right frame
uicontrol('Parent',a,'Units','normalized','BackgroundColor',[0.513725 0.6 0.694118], ...
'Position',[0.85 0 0.15 1],'Style','frame','Tag','Frame2');
%Bottom frame
uicontrol('Parent',a,'Units','normalized','BackgroundColor',[0.513725 0.6 0.694118], ...
'Position',[0 0 0.85 0.0676],'Style','frame','Tag','Frame1');
%Bottom text display for showing the calculated
%Lyapunov exponents at each iteration.
btmDisplay=uicontrol('Parent',a,'Units','normalized','BackgroundColor',[1 1 1], ...
'ForegroundColor',[0 0 1],'Position',[0.0057 0.01 0.835 0.045], ...
'String',bttmText,'FontSize', FontSize,'Style','text','Tag','StaticText9');
%"Start" button
startBtn=uicontrol('Parent',a,'Units','normalized','Callback','let(''start'')', ...
'FontSize', FontSize,'FontWeight','bold','Position',[xPos 0.94 BtnWidth BtnHeight], ...
'String','Start','Interruptible','on','Tag','Pushbutton1');
%"Stop" button : initial set disable
stopBtn=uicontrol('Parent',a,'Units','normalized','Callback','let(''stop'')', ...
'FontSize', FontSize,'FontWeight','bold','Position',[xPos 0.88 BtnWidth BtnHeight], ...
'String','Stop','UserData',0,'Enable','off','Tag','Pushbutton2');
%"Setting" button
settingBtn=uicontrol('Parent',a,'Units','normalized','Callback','let(''setting'')', ...
'FontSize', FontSize,'FontWeight','bold','Position',[xPos 0.82 BtnWidth BtnHeight], ...
'String','Setting','Tag','Pushbutton3');
%Label: "Grid Lines"
uicontrol('Parent',a,'Units','normalized','BackgroundColor',[0.513725 0.6 0.694118], ...
'FontSize', FontSize,'FontWeight','bold','Position',[0.86 0.72 0.07 0.08], ...
'String','Grid Lines','Style','text','Tag','StaticText1');
%Grid Lines "On" radio button
gOnRadio=uicontrol('Parent',a,'Units','normalized','BackgroundColor',[0.513725 0.6 0.694118], ...
'Position',[0.925 0.765 0.07 0.043],'Callback','let(''OnPressed'')','FontSize',FontSize, ...
'String','On','Value',gOn,'Style','radiobutton','Tag','Radiobutton1');
%Grid Lines "Off" Radio Button
gOffRadio=uicontrol('Parent',a,'Units','normalized','BackgroundColor',[0.513725 0.6 0.694118], ...
'Position',[0.925 0.723 0.07 0.043],'Callback','let(''OffPressed'')','FontSize',FontSize,...
'String','Off','Style','radiobutton','Tag','Radiobutton2','Value',gOff);
%Label: "Plot Range"
uicontrol('Parent',a,'Units','normalized','BackgroundColor',[0.513725 0.6 0.694118], ...
'FontSize', FontSize,'FontWeight','bold','Position',[0.86 0.68 0.135 0.035], ...
'String','Plot Range','Style','text','Tag','StaticText10');
%Label: "X :" (X-Axis)
uicontrol('Parent',a,'Units','normalized','BackgroundColor',[0.513725 0.6 0.694118], ...
'FontSize', FontSize,'Position',[0.855 0.625 0.0365 0.037], ...
'String','X :','Style','text','Tag','StaticText11');
%Edit text box for "X :"
xRangeEdt=uicontrol('Parent',a,'Units','normalized','BackgroundColor',[1 1 1], ...
'ForegroundColor',[0 0 1],'Position',[0.89 0.62 0.1 0.045], ...
'String',[num2str(xRange(1)) ', ' num2str(xRange(2))],'FontSize', FontSize, ...
'Callback','let(''changeAxis'')','UserData', xRange,'Style','edit','Tag','EditText2');
%Label: "Y :" (Y-Axis)
uicontrol('Parent',a,'Units','normalized','BackgroundColor',[0.513725 0.6 0.694118], ...
'Position',[0.855 0.56 0.0365 0.037],'String','Y :','Style','text','Tag','StaticText12');
%Edit text box for "Y :"
yRangeEdt=uicontrol('Parent',a,'Units','normalized','BackgroundColor',[1 1 1], ...
'ForegroundColor',[0 0 1],'Position',[0.89 0.555 0.1 0.045],'FontSize', FontSize,...
'String',[num2str(yRange(1)) ', ' num2str(yRange(2))],'UserData',yRange, ...
'Callback','let(''changeAxis'')','Style','edit','Tag','EditText3');
%Label: "Draw line at"
uicontrol('Parent',a,'Units','normalized','BackgroundColor',[0.513725 0.6 0.694118], ...
'FontSize', FontSize,'Position',[0.865 0.51 0.12 0.035],'String','Draw line at', ...
'Style','text','Tag','StaticText2');
%Edit box for "Draw Line at"
drawEdt=uicontrol('Parent',a,'Units','normalized','BackgroundColor',[1 1 1], ...
'ForegroundColor',[0 0 1],'Position',[0.86 0.46 0.13 0.045],'FontSize', FontSize,...
'String',num2str(y),'Callback','let(''drawLine'')','Style','edit','Tag','EditText1');
%Label: "Current Time"
uicontrol('Parent',a,'Units','normalized','BackgroundColor',[0.513725 0.6 0.694118], ...
'FontSize', FontSize,'Position',[0.865 0.415 0.12 0.035], ...
'String','Current Time','Style','text','Tag','StaticText3');
%Display of "Current Time"
ctDisplay=uicontrol('Parent',a,'Units','normalized','BackgroundColor',[1 1 1], ...
'ForegroundColor',[0 0 1],'Position',[0.86 0.38 0.13 0.035],'FontSize', FontSize,...
'String',num2str(ct),'Style','text','Tag','StaticText4');
%Label: "Final Time"
uicontrol('Parent',a,'Units','normalized','BackgroundColor',[0.513725 0.6 0.694118], ...
'FontSize', FontSize,'Position',[0.865 0.33 0.12 0.035],...
'String','Final Time','Style','text','Tag','StaticText5');
%Display of "Final Time"
ftDisplay=uicontrol('Parent',a,'Units','normalized','BackgroundColor',[1 1 1], ...
'ForegroundColor',[0 0 1],'Position',[0.86 0.295 0.13 0.035], ...
'String',num2str(ft),'Style','text','FontSize', FontSize,'Tag','StaticText6');
%Label: "Time Used"
uicontrol('Parent',a,'Units','normalized','BackgroundColor',[0.513725 0.6 0.694118], ...
'FontSize', FontSize,'Position',[0.865 0.245 0.12 0.035], ...
'String','Time Used','Style','text','Tag','StaticText7');
%Display text of "Time Used"
utDisplay=uicontrol('Parent',a,'Units','normalized','BackgroundColor',[1 1 1], ...
'ForegroundColor',[0 0 1],'Position',[0.86 0.21 0.13 0.035], ...
'String',num2str(ut),'FontSize', FontSize,'Style','text','Tag','StaticText8');
%"New Plot" button
plotBtn=uicontrol('Parent',a,'Units','normalized','Callback','let(''plot'')', ...
'FontSize', FontSize,'FontWeight','bold','Position',[xPos 0.14 BtnWidth BtnHeight], ...
'String','New Plot','Enable','Off','Tag','Pushbutton4');
%"Help" button
helpBtn=uicontrol('Parent',a,'Units','normalized','Callback','let(''help'')', ...
'FontSize', FontSize,'FontWeight','bold','Position',[xPos 0.08 BtnWidth BtnHeight], ...
'String','Help','Tag','Pushbutton5');
%"Exit" button
exitBtn=uicontrol('Parent',a,'Units','normalized','Callback','close(gcf)', ...
'FontSize', FontSize,'FontWeight','bold','Position',[xPos 0.02 BtnWidth BtnHeight], ...
'String','Exit','Tag','Pushbutton6');
%Define the active region on the figure for plotting
set(gca,'Position',[0.1 0.1776 0.7024 0.7474]);
%Setup Axes using default ranges
axis(AxisRange);
%Create axis box
box;
%Add X-axis label, Y-axis label and title
xlabel(xLabel); ylabel(yLabel); title(Title);
%Freeze axes
axis('manual');
%Output the handles (or addresses) of the GUI elements
%which will be used later
MainHandles=[btmDisplay, startBtn, stopBtn, settingBtn, ...
gOnRadio, gOffRadio, xRangeEdt, yRangeEdt, ...
drawEdt, ctDisplay, ftDisplay, utDisplay, ...
plotBtn, helpBtn, exitBtn];
%Uncover the figure when setup is finished
set(a,'Visible','On');
%------------------------------------------------------------
function check(checkList,uncheckList)
%CHECK Check function for check box or radio button
%
% CHECK(CHECKLIST) checks the radio buttons or
% check boxes with handles in CHECKLIST.
%
% CHECK(CHECKLIST,UNCHECKLIST) checks the radio
% buttons or check boxes with handles in CHECKLIST
% and unchecks the ones with handles in UNCHECKLIST.
%
% CHECK([],UNCHECKLIST) unchecks the radio buttons
% or check boxes with handles in CHECKLIST.
% by Steve Wai Kam SIU, Feb. 19, 1998.
if nargin<2
uncheckList=[];
end
if ~isempty(checkList)
set(checkList,'Value',1);
end
if ~isempty(uncheckList)
set(uncheckList,'Value',0);
end
%------------------------------------------------------------------------
function outStr=rmspace(inStr)
%RMSPACE Function for removing the beginning and ending
% spaces of a string
%Remove spaces at the end of the string
outStr=strcat(inStr);
%Delete spaces at the beginning of the string
if ~isempty(outStr)
while isspace(outStr(1))
outStr=outStr(2:length(outStr));
end
end
