lyap_exp_of_discrete_map.m

主成分分析和偏最小二乘SquaresPrincipal成分分析（ PCA ）和偏最小二乘（ PLS ）

function varargout = lyap_exp_of_discrete_map(varargin)
% LYAP_EXP_OF_DISCRETE_MAP computes Lyapunov exponents of discrete map
% gui-mode using:
% LyapExps=lyap_exp_of_discrete_map;
% batch-mode using:
% LyapExps=lyap_exp_of_discrete_map(Fx,init,len,trans)
% Parameters:
% Fx - cell array of right-side map equations
% init - cell array of initial conditions
% len - number of iterations
% trans - number of transient iterations
%
% LyapExps - Lyapunov exponents
%
% Example:
% LyapExps=lyap_exp_of_discrete_map({'3.42*x1*(1-x1-x2)' '3.42*x1*x2'},{'0.1' '0.1'},'5000','100')

% Last Modified by GUIDE v2.5 26-Oct-2004 10:52:04
% last modified 8.12.05

% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...
                   'gui_Singleton',  gui_Singleton, ...
                   'gui_OpeningFcn', @lyap_exp_of_discrete_map_OpeningFcn, ...
                   'gui_OutputFcn',  @lyap_exp_of_discrete_map_OutputFcn, ...
                   'gui_LayoutFcn',  [] , ...
                   'gui_Callback',   []);
if nargin && ischar(varargin{1})
    gui_State.gui_Callback = str2func(varargin{1});
end

if nargout
    [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
    gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT


% --- Executes just before lyap_exp_of_discrete_map is made visible.
function lyap_exp_of_discrete_map_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject    handle to figure
% handles    structure with handles and user data (see GUIDATA)
% varargin   command line arguments to lyap_exp_of_discrete_map (see VARARGIN)

% Choose default command line output for lyap_exp_of_discrete_map
handles.output = hObject;

% Update handles structure
guidata(hObject, handles);
handles.auto=0;
try
	N=length(varargin{1});
	x={};
	for i=1:N
        x{i}=['x' num2str(i)];
	end
	set(handles.x,'string',x);
    set(handles.f,'string',varargin{1});
    set(handles.init,'string',varargin{2});
	set(handles.edit_length,'string',varargin{3});
	set(handles.e_tr_steps,'string',varargin{4});
catch
end

if length(varargin)==4    % batch mode OK 
    handles.auto=1;
end
guidata(hObject, handles);

% --- Outputs from this function are returned to the command line.
function varargout = lyap_exp_of_discrete_map_OutputFcn(hObject, eventdata, handles)
% varargout  cell array for returning output args (see VARARGOUT);
% hObject    handle to figure
% handles    structure with handles and user data (see GUIDATA)

% Get default command line output from handles structure
global ledm

if handles.auto
    ok_Callback(handles.ok, [], handles);
    if nargout
        varargout{1} =ledm;
    end
    close(handles.figure);
else
    if nargout
        uiwait;
        if nargout
            varargout{1} =ledm;
        end
    end
end


% --- Executes on button press in ok.
function ok_Callback(hObject, eventdata, handles)
% hObject    handle to ok (see GCBO)
% handles    structure with handles and user data (see GUIDATA)
global ledm
ledm=[];

try 
    syms asddaewrrjfsd;
catch
    warndlg('Symbolic toolbox not installed. Computation aborted.','Symbolic toolbox needed');
    return
end
clear tmp_map

x=get(handles.x,'string');
L=str2num(get(handles.edit_length,'string'));
init=get(handles.init,'string');
f=get(handles.f,'string');
Dim=length(f);

if isempty(x)
    msgbox('No data for map');
    return
end
s = which('lyap_exp_of_discrete_map');
[pathstr,name,ext,versn] = fileparts(s);

fid = fopen([pathstr '/tmp_map.m'],'w');
fprintf(fid,'function Y=tmp_map(X); \n');
fprintf(fid,'Y=zeros(1,%s); \n',num2str(length(x)));
for i=1:Dim
	fprintf(fid,'%s=X(%i); \n',x{i},i);
end
for i=1:Dim
	fprintf(fid,'Y(%s)=%s; \n',num2str(i),f{i});
end
fclose(fid);
clear fid
for i=1:Dim
    Init(i)=str2double(init{i});
end
for i=1:str2num(get(handles.e_tr_steps,'string'))
    Init=tmp_map(Init);
end

F=[]; X=[];
for i=1:Dim
    F=[F; sym(f{i})];
    X=[X sym(['x' num2str(i)])];
end
J=jacobian(F,X);

Xer=[];
for i=1:Dim^2
    Xer=[Xer; sym(['x' num2str(i) 'er'])];
end

system=[];
for i=1:Dim
    system=[system; J*Xer(1+(i-1)*Dim:i*Dim)];
end

fid = fopen([pathstr '/tmp_map.m'],'a');
for i=1:length(Xer)
    fprintf(fid,'%s=X(%i); \n',char(Xer(i)),Dim+i);
end
fprintf(fid,'Y=[Y zeros(1,%s)]; \n',num2str(length(system)));
for i=1:length(system)
    fprintf(fid,'Y(%s)=%s; \n',num2str(Dim+i),char(system(i)));
end

fclose(fid);
clear fid
clear tmp_map

Vect=eye(Dim);
S=zeros(Dim,1);
Y=Init';
Y=[Y; Vect(1:end)'];
M=str2num(get(handles.edit_length,'string'));
for i=1:M
    Y=tmp_map(Y);
    vectors=Y(end-Dim^2+1:end);
    for t=1:Dim
        Vect(:,t)=vectors(1+(t-1)*Dim:t*Dim)';
    end
    S(1)=S(1)+log(sum(Vect(:,1).^2)^.5);
    Vect(:,1)=Vect(:,1)./sum(Vect(:,1).^2)^.5;
    for j=2:Dim
        tmp_v=zeros(Dim,1);
        for k=1:j-1
            tmp_v=tmp_v+sum(Vect(:,j).*Vect(:,k)).*Vect(:,k);
        end
        Vect(:,j)=Vect(:,j)-tmp_v;
        S(j)=S(j)+log(sum(Vect(:,j).^2)^.5);
        Vect(:,j)=Vect(:,j)./sum(Vect(:,j).^2)^.5;
    end
    
    Y=[Y(1:Dim) Vect(1:end)]';
end
fprintf('\nLyapunov exponents:\n ');
Le=S./M;
for i=1:Dim
    fprintf('       %f\n',Le(i));
end
ledm=Le;


% --- Executes on button press in cancel.
function cancel_Callback(hObject, eventdata, handles)
% hObject    handle to cancel (see GCBO)
% handles    structure with handles and user data (see GUIDATA)
close(handles.figure);


% --- Executes during object creation, after setting all properties.
function edit_length_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit_length (see GCBO)
% handles    empty - handles not created until after all CreateFcns called

if ispc
    set(hObject,'BackgroundColor','white');
else
    set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));
end



function edit_length_Callback(hObject, eventdata, handles)
% hObject    handle to edit_length (see GCBO)
% handles    structure with handles and user data (see GUIDATA)


% --- Executes on button press in load.
function load_Callback(hObject, eventdata, handles)
% hObject    handle to load (see GCBO)
% handles    structure with handles and user data (see GUIDATA)
[file,path] = uigetfile2('*.mat','Load Map');
if file~=0
    try
        S=load([path file]);
        set([handles.x handles.f handles.init],'value',1); 
        set(handles.x,'string',S.map.x);
        set(handles.f,'string',S.map.f);
        set(handles.init,'string',S.map.init);
        set(handles.edit_info,'string',S.map.info);
        set(handles.e_tr_steps,'string',S.map.tr_steps);
        set(handles.edit_length,'string',S.map.length);
    catch
        errordlg('Wrong file format','File error');
    end
end


% --- Executes on button press in save.
function save_Callback(hObject, eventdata, handles)
% hObject    handle to save (see GCBO)
% handles    structure with handles and user data (see GUIDATA)
[file,path] = uiputfile('*.mat','Save Map As');
if file~=0
	map.x=get(handles.x,'string');
	map.f=get(handles.f,'string');
    tmp=map.x;
    for i=1:length(tmp)
        tmp{i}='0';
    end
	map.ignv=tmp;
	map.innv=tmp; 
	map.agnv=tmp; 
	map.annv=tmp; 
	map.init=get(handles.init,'string');
    map.info=get(handles.edit_info,'string');
    map.tr_steps=get(handles.tr_steps,'string');
    map.length=get(handles.edit_length,'string');
    save([path file],'map');
end
    


% --- Executes during object creation, after setting all properties.
function edit_info_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit_info (see GCBO)
% handles    empty - handles not created until after all CreateFcns called

if ispc
    set(hObject,'BackgroundColor','white');
else
    set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));
end



function edit_info_Callback(hObject, eventdata, handles)
% hObject    handle to edit_info (see GCBO)
% handles    structure with handles and user data (see GUIDATA)


% --- Executes during object creation, after setting all properties.
function x_CreateFcn(hObject, eventdata, handles)
% hObject    handle to x (see GCBO)
% handles    empty - handles not created until after all CreateFcns called

if ispc
    set(hObject,'BackgroundColor','white');
else
    set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));
end


% --- Executes on selection change in x.
function x_Callback(hObject, eventdata, handles)
% hObject    handle to x (see GCBO)
% handles    structure with handles and user data (see GUIDATA)

set([handles.x handles.f handles.init],'value',get(hObject,'Value'));

% --- Executes during object creation, after setting all properties.
function f_CreateFcn(hObject, eventdata, handles)
% hObject    handle to f (see GCBO)
% handles    empty - handles not created until after all CreateFcns called

if ispc
    set(hObject,'BackgroundColor','white');
else
    set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));
end


% --- Executes during object creation, after setting all properties.
function init_CreateFcn(hObject, eventdata, handles)
% hObject    handle to init (see GCBO)
% handles    empty - handles not created until after all CreateFcns called

if ispc
    set(hObject,'BackgroundColor','white');
else
    set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));
end


% --- Executes on button press in add.
function add_Callback(hObject, eventdata, handles)
% hObject    handle to add (see GCBO)
% handles    structure with handles and user data (see GUIDATA)

N=length(get(handles.x,'string'));
x={};
for i=1:N
    x{i}=['x' num2str(i)];
end
set(handles.x,'string',x);
prompt = {['Enter equation x'  num2str(N+1) '(n+1)=...'],...
        'Enter initial condition:'};
dlg_title = 'Add new equation';
num_lines= 1;
def     = {'','0.5'};
answer  = inputdlg(prompt,dlg_title,num_lines,def);
if ~isempty(answer)
    x=get(handles.x,'string');
    f=get(handles.f,'string');
    init=get(handles.init,'string');
    x{N+1}=['x' num2str(N+1)];
    f{N+1}=answer{1};
    init{N+1}=answer{2};
    set([handles.x, handles.f, handles.init],'value',N+1);
    set(handles.x,'string',x);
    set(handles.f,'string',f);
    set(handles.init,'string',init);
end


% --- Executes on button press in modify.
function modify_Callback(hObject, eventdata, handles)
% hObject    handle to modify (see GCBO)
% handles    structure with handles and user data (see GUIDATA)

x=get(handles.x,'string');
f=get(handles.f,'string');
init=get(handles.init,'string');
selection=get(handles.x,'value');
if isempty(x)
    x{1}='x1'; f{1}=''; init{1}='0.7';
end

prompt = {['Enter equation '  x{selection} '(n+1)=...'],...
        'Enter initial condition:'};
dlg_title = 'Modify equation';
num_lines= 1;
def     = {f{selection},init{selection}};
answer  = inputdlg(prompt,dlg_title,num_lines,def);
if ~isempty(answer)
    f{selection}=answer{1};
    init{selection}=answer{2};
    set(handles.x,'string',x);
    set(handles.f,'string',f);
    set(handles.init,'string',init);
end



% --- Executes on button press in delete.
function delete_Callback(hObject, eventdata, handles)
% hObject    handle to delete (see GCBO)
% handles    structure with handles and user data (see GUIDATA)

x=get(handles.x,'string');
f=get(handles.f,'string');
init=get(handles.init,'string');
selection=get(handles.x,'value');
if isempty(x)
    return
end

n_f={}; n_init={}; n_x={};
k=1;
for i=1:length(x)
    if i~=selection
        n_f{k}=f{i};
        n_init{k}=init{i};
        n_x{k}=x{i};
        k=k+1;
    end
end
set([handles.x, handles.f, handles.init],'value',max([1 selection-1]));
    
set(handles.x,'string',n_x);
set(handles.f,'string',n_f);
set(handles.init,'string',n_init);


% --- Executes during object creation, after setting all properties.
function e_tr_steps_CreateFcn(hObject, eventdata, handles)
% hObject    handle to e_tr_steps (see GCBO)
% handles    empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc
    set(hObject,'BackgroundColor','white');
else
    set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));
end



function e_tr_steps_Callback(hObject, eventdata, handles)
% hObject    handle to e_tr_steps (see GCBO)
% handles    structure with handles and user data (see GUIDATA)

% Hints: get(hObject,'String') returns contents of e_tr_steps as text
%        str2double(get(hObject,'String')) returns contents of e_tr_steps as a double