poincare_section.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 = poincare_section(varargin)
% POINCARE_SECTION computes Poincare section for 3rd-order ODE system
% GUI-mode using:
% data=poincare_section;
% batch-mode using:
% data=poincare_section(Fx,init,time,tr_time,solver,addit_param,C,direction,pl)
% Parameters
% Fx - cell array of right-side ODE equations
% init - cell array of initial conditions
% time - a vector specifying the interval of integration.
% tr_time - a vector specifying the interval of preliminary integration
% solver - solver type:
%         1 - ode45;
%         2 - ode23;
%         3 - ode113;
%         4 - ode15s;
%         5 - ode23s;
%         6 - ode23t;
%         7 - ode23tb;
% addit_param - additional parameters of ODE solver, such as 'RelTol', 'AbsTol' and others.
% C - Poincare plane: C(1)x+C(2)y+C(3)z=C(4)
% direction - taked into account direction of crossing the plane:
%     'both' - both directions taked into account
%     '-+' - only direction from negative to positive half-spaces
%     '+-' - only direction from positive to negative half-spaces
% pl - 1 - plot projection of Poincare section on coordinate axis
%      0 - do not plot projection of Poincare section on coordinate axis
%
% data - time of crossing (first column) and coordanates of crossing (other
% columns) the plane
%
% Examples:
% data=poincare_section({'0.032*x1+0.5*x2-x3' 'x1-0.1*x2-x1^3' '0.1*x1'},{'0.01' '-0.01' '-0.02'},'[0:0.02:250]','[-10 0]',1,'',[1 1 1 0],'both',1);
% data=poincare_section({'10*(x2-x1)' '28*x1-x2-x1*x3' '-8/3*x3+x1*x2'},{'8' '5' '30'},'[0:0.005:350]','[-30 0]',1,'',[1 1 0 -20],'+-',0);
% data=poincare_section({'-x2-x3' 'x1+0.25*x2+x4' '3+x1*x3' '-0.5*x3+0.05*x4'},{'-15' '11' '0.2' '23'},'[0:0.01:1350]','[-200 0]',1,'',[0 1 0 0],'+-',1);
% data=poincare_section({'-x2-x3' 'x1+0.2*x2' '0.4+x3*(x1-8)'},{'3' '-4' '2'},'[0:0.02:1500]','[-20 0]',1,'',[-10 1 0.8 0],'-+',1);

% author: Max Logunov, [e-mail], comments welcome
% This program is a part of Lab432 software for nonlinear analysis of time
% series 

% Last Modified by GUIDE v2.5 21-Feb-2005 17:11:32
% 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', @poincare_section_OpeningFcn, ...
                   'gui_OutputFcn',  @poincare_section_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 discrete_map_generator is made visible.
function poincare_section_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 discrete_map_generator (see VARARGIN)

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

% Update handles structure
guidata(hObject, handles);
handles.auto=0;
try
	N=length(varargin{1});
	x={};
	for i=1:N
        x{i}=['dx' num2str(i) '/dt'];
	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.tr_time,'string',varargin{4});
    set(handles.solver,'value',varargin{5});
    set(handles.addit_param,'string',varargin{6});
    set(handles.e_C1,'string',num2str(varargin{7}(1)));
    set(handles.e_C2,'string',num2str(varargin{7}(2)));
    set(handles.e_C3,'string',num2str(varargin{7}(3)));
    set(handles.e_C,'string',num2str(varargin{7}(4)));
    if strcmp(varargin{8},'-+')
        set(handles.r_mp,'value',1);
        set([handles.r_pm handles.r_b],'value',0);
    end
    if strcmp(varargin{8},'+-')
        set(handles.r_pm,'value',1);
        set([handles.r_mp handles.r_b],'value',0);
    end
    set(handles.plot,'value',varargin{9});
catch
end

if length(varargin)==9 % batch mode OK
    handles.auto=1;
end
% if length(get(handles.x,'string'))~=3
%     handles.auto=0;
%     set(handles.ok,'enable','off');
% end
guidata(hObject, handles);

% --- Outputs from this function are returned to the command line.
function varargout = poincare_section_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 psDATA

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

x=get(handles.x,'string');
init=get(handles.init,'string');
f=get(handles.f,'string');
if isempty(x)
    msgbox('No data for system');
    return
end
s = which('poincare_section');
[pathstr,name,ext,versn] = fileparts(s);

init_str='';
for i=1:length(x)
    init_str=[init_str init{i} ' '];
end
init_str=['[' init_str(1:end-1) ']'];

fid = fopen([pathstr '/tmp_sys.m'],'w');
fprintf(fid,'function Y=tmp_sys(t,X); \n');
fprintf(fid,'Y=zeros(%s,1); \n',num2str(length(x)));
for i=1:length(x)
	fprintf(fid,'%s=X(%i); \n',['x' num2str(i)],i);
end
for i=1:length(x)
	fprintf(fid,'Y(%s)=%s; \n',num2str(i),f{i});
end
fclose(fid);
clear fid
 
solvers=get(handles.solver,'string');
if ~isempty(get(handles.tr_time,'string'))
	if ~isempty(get(handles.addit_param,'string'))
        [T,Y]=eval([solvers{get(handles.solver,'value')} '(@tmp_sys,' get(handles.tr_time,'string') ',' init_str ',odeset(' get(handles.addit_param,'string') '))']);
	else
        [T,Y]=eval([solvers{get(handles.solver,'value')} '(@tmp_sys,' get(handles.tr_time,'string') ',' init_str ')']); 
	end
	clear tmp_sys;
	
	init_str='';
	for i=1:length(x)
        init_str=[init_str num2str(Y(end,i)) ' '];
	end
	init_str=['[' init_str(1:end-1) ']'];
end

if ~isempty(get(handles.addit_param,'string'))
    [T,Y]=eval([solvers{get(handles.solver,'value')} '(@tmp_sys,' get(handles.edit_length,'string') ',' init_str ',odeset(' get(handles.addit_param,'string') '))']);
else
    [T,Y]=eval([solvers{get(handles.solver,'value')} '(@tmp_sys,' get(handles.edit_length,'string') ',' init_str ')']); 
end
clear tmp_sys;


c1=str2num(get(handles.e_C1,'string'));
c2=str2num(get(handles.e_C2,'string'));
c3=str2num(get(handles.e_C3,'string'));
c=str2num(get(handles.e_C,'string'));

R=c1*Y(:,1)+c2*Y(:,2)+c3*Y(:,3)-c;
RES=zeros(floor(length(R)/2),4);
k=0;
if get(handles.r_b,'value')
    for i=2:length(R)-2
        if ~(sign(R(i))+sign(R(i+1)))
            t1=abs(R(i)/R(i+1))*(T(i+1)-T(i))/(1+abs(R(i)/R(i+1)));
            nT=T(i)+t1;
            nD=[spline(T(i-1:i+2),Y(i-1:i+2,1),nT),spline(T(i-1:i+2),Y(i-1:i+2,2),nT), spline(T(i-1:i+2),Y(i-1:i+2,3),nT)];
            k=k+1;
            RES(k,1)=nT; RES(k,2:end)=nD;
        end
    end
end
if get(handles.r_mp,'value')
    for i=2:length(R)-2
        if sign(R(i))<sign(R(i+1))
            t1=abs(R(i)/R(i+1))*(T(i+1)-T(i))/(1+abs(R(i)/R(i+1)));
            nT=T(i)+t1;
            nD=[spline(T(i-1:i+2),Y(i-1:i+2,1),nT),spline(T(i-1:i+2),Y(i-1:i+2,2),nT), spline(T(i-1:i+2),Y(i-1:i+2,3),nT)];
            k=k+1;
            RES(k,1)=nT; RES(k,2:end)=nD;
        end
    end
end
if get(handles.r_pm,'value')
    for i=2:length(R)-2
        if sign(R(i))>sign(R(i+1))
            t1=abs(R(i)/R(i+1))*(T(i+1)-T(i))/(1+abs(R(i)/R(i+1)));
            nT=T(i)+t1;
            nD=[spline(T(i-1:i+2),Y(i-1:i+2,1),nT),spline(T(i-1:i+2),Y(i-1:i+2,2),nT), spline(T(i-1:i+2),Y(i-1:i+2,3),nT)];
            k=k+1;
            RES(k,1)=nT; RES(k,2:end)=nD;
        end
    end
end
psDATA=RES(1:k,:);

if get(handles.plot,'value')
    figure('Name','Poincare section','numbertitle','off','color',[1 1 1]);
    subplot(221)
    plot3(Y(:,1),Y(:,2),Y(:,3)), grid on
    hold on
    plot3(psDATA(:,2),psDATA(:,3),psDATA(:,4),'r.','markersize',6);
    xlabel('x1'); ylabel('x2'); zlabel('x3');
    
    subplot(222)
    plot(psDATA(:,2),psDATA(:,3),'r.','markersize',2), grid on;
    xlabel('x1'); ylabel('x2'); 
    
    subplot(223)
    plot(psDATA(:,2),psDATA(:,4),'r.','markersize',2), grid on;
    xlabel('x1'); ylabel('x3'); 
    
    subplot(224)
    plot(psDATA(:,3),psDATA(:,4),'r.','markersize',2), grid on;
    xlabel('x2'); ylabel('x3'); 
end



% --- 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 System');
if file~=0
    try
        S=load([path file]);
        set([handles.x handles.f handles.init],'value',1);
        set(handles.x,'string',S.sys.dx);
        set(handles.f,'string',S.sys.f);
        set(handles.init,'string',S.sys.init);
        set(handles.edit_info,'string',S.sys.info);
        set(handles.tr_time,'string',S.sys.tr_time);
        set(handles.edit_length,'string',S.sys.time);
        set(handles.addit_param,'string',S.sys.addit_param);
        str=get(handles.solver,'string');
        for i=1:length(str)
            if strcmp(str{i},S.sys.solver)
                set(handles.solver,'value',i);
                break
            end
        end
    catch
        errordlg('Wrong file format','File error');
    end
end
% if length(get(handles.x,'string'))~=3
%     set(handles.ok,'enable','off');
% else
%     set(handles.ok,'enable','on');
% 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 System As');
if file~=0
	sys.dx=get(handles.x,'string');
	sys.f=get(handles.f,'string');
    tmp=sys.dx;
    for i=1:length(tmp)
        tmp{i}='0';
    end
	sys.ignv=tmp;
    sys.innv=tmp;
	sys.agnv=tmp;
	sys.annv=tmp;
	sys.init=get(handles.init,'string');
    sys.info=get(handles.edit_info,'string');
    sys.tr_time=get(handles.tr_time,'string');
    sys.time=get(handles.edit_length,'string');
        str=get(handles.solver,'string');
    sys.solver=str{get(handles.solver,'value')};
    sys.addit_param=get(handles.addit_param,'string');
    save([path file],'sys');
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