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Commit b9b11430 authored by Guilherme Tegoni Goedert's avatar Guilherme Tegoni Goedert
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added some code from the 2016 course

parent 5df0b18f
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Programas_2016/Aula_Lorenz/Lorenz.m 0 → 100644
View file @ b9b11430
function dw = Lorentz(t,w,sigma,rho,beta)
dw(1) = sigma*(w(2) - w(1));
dw(2) = w(1)*(rho - w(3)) - w(2);
dw(3) = w(1)*w(2) - beta*w(3);
end
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Programas_2016/Aula_Lorenz/Main.m 0 → 100644
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% main
% Initial conditions
t0 = 0;
w0 = [1,1,1];
% Maximum time of integration
T = 100;
% Step definitions
h0 = 0.01; % initial step size
h = h0; % used step size
hmin = (1e-5)*h0; % minimum step size allowed
% Model parameters and definitions
sigma = 10;
rho = 28;
beta = 8/3;
F = @(s,w) Lorenz(s,w,sigma,rho,beta);
% Poincare Section definition
Section = @ (w) w(3) - 15;
tsec = [];
wsec = [];
% Result allocation
t = zeros(100000,1);
w = zeros(100000,max(size(w0)));
t(1) = t0;
w(1,:) = w0;
counter = 2;
% Initiate figure object
figure;
az = 0; el = 0; % viewpoint definition
%%%%%% ITERATE
while t(counter) <= T
% iterate a step
[t(counter), w(counter,:)] = RK4(t(counter-1),w(counter-1,:),h,F);
% evaluete if solutuion passes through the poincare section
if or(sign(Section(w(counter,:))) > sign(Section(w(counter-1,:))), sign(Section(w(counter,:))) < sign(Section(w(counter-1,:))))
h = h/2;
if h <= hmin
h = h0;
tsec = [tsec;t(counter)];
wsec = [wsec;w(counter,:)];
counter = counter + 1;
end
else
% plot result
plot3(w(1:counter,1),w(1:counter,2),w(1:counter,3))
xlabel('x'); ylabel('y'); zlabel('z')
hold on;
% plot points that pass through Poincare section
if max(size(wsec))>0
plot3(wsec(:,1),wsec(:,2),wsec(:,3),'o');
end
% plot current point in trajectory
plot3(w(counter,1),w(counter,2),w(counter,3),'*')
hold off
% rotate and view solution
az = mod(az + 0.5,360);
view(az,el)
pause(0.005);
%iterate
counter = counter + 1;
end
end
% eliminate unused entries in solution vector
t(counter+1:end) = [];
w(counter+1,:) = [];
Programas_2016/Aula_Lorenz/PoincareSection.m 0 → 100644
View file @ b9b11430
% main
t0 = 0;
w0 = [1,1,1];
T = 100;
h = 0.01;
sigma = 10;
rho = 28;
beta = 8/3;
F = @(s,w) Lorentz(s,w,sigma,rho,beta);
t = zeros(2000,1);
w = zeros(2000,max(size(w0)));
t(1) = t0;
w(1,:) = w0;
counter = 1;
figure;
az = 0; el = 45;
while t <= T
counter = counter + 1;
[t(counter), w(counter,:)] = RK4(t(counter-1),w(counter-1,:),h,F);
plot3(w(1:counter,1),w(1:counter,2),w(1:counter,3))
hold on;
plot3(w(counter,1),w(counter,2),w(counter,3),'*')
hold off
az = az + 0.5;
view(az,el)
pause(0.01);
end
t(counter+1:end) = [];
w(counter+1,:) = [];
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Programas_2016/Aula_Lorenz/RK4.m 0 → 100644
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function [t,x] = RK4(t0,x0,h,F)
t = t0 + h;
k1 = F(t0,x0);
k2 = F(t0 + h/2, x0 + h.*k1./2);
k3 = F(t0 + h/2, x0 + h.*k2./2);
k4 = F(t0 + h, x0 + h.*k3);
x = x0 + (h/6).*(k1 + 2.*k2 + 2.*k3 + k4);
end
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Programas_2016/Aula_Lorenz/Rotate.m 0 → 100644
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function varargout = Rotate(varargin)
% ROTATE MATLAB code for Rotate.fig
% ROTATE, by itself, creates a new ROTATE or raises the existing
% singleton*.
%
% H = ROTATE returns the handle to a new ROTATE or the handle to
% the existing singleton*.
%
% ROTATE('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in ROTATE.M with the given input arguments.
%
% ROTATE('Property','Value',...) creates a new ROTATE or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before Rotate_OpeningFcn gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to Rotate_OpeningFcn via varargin.
%
% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one
% instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help Rotate
% Last Modified by GUIDE v2.5 11-May-2016 14:43:26
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @Rotate_OpeningFcn, ...
'gui_OutputFcn', @Rotate_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 Rotate is made visible.
function Rotate_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to Rotate (see VARARGIN)
% Choose default command line output for Rotate
handles.output = hObject;
handles.Az = 90;
handles.El = 0;
handles.Slider1Min = -180;
handles.Slider1Max = 180;
handles.Slider2Min = -90;
handles.Slider2Max = 90;
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes Rotate wait for user response (see UIRESUME)
% uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line.
function varargout = Rotate_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure
varargout{1} = handles.output;
% --- Executes on slider movement.
function slider1_Callback(hObject, eventdata, handles)
% hObject handle to slider1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
handles.Az = get(hObject,'Value'); %returns position of slider
get(hObject,'handles.Slider1Min');
get(hObject,'handles.Slider1Max'); %to determine range of slider
view(handles.Az,handles.El)
guidata(hObject,handles);
% --- Executes during object creation, after setting all properties.
function slider1_CreateFcn(hObject, eventdata, handles)
% hObject handle to slider1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: slider controls usually have a light gray background.
if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor',[.9 .9 .9]);
end
% --- Executes on slider movement.
function slider2_Callback(hObject, eventdata, handles)
% hObject handle to slider2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
handles.El = get(hObject,'Value'); %returns position of slider
get(hObject,'handles.Slider2Min');
get(hObject,'handles.Slider2Max'); %to determine range of slider
view(handles.Az,handles.El)
guidata(hObject,handles);
% --- Executes during object creation, after setting all properties.
function slider2_CreateFcn(hObject, eventdata, handles)
% hObject handle to slider2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: slider controls usually have a light gray background.
if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor',[.9 .9 .9]);
end
% --- Executes during object creation, after setting all properties.
function axes1_CreateFcn(hObject, eventdata, handles)
% hObject handle to axes1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: place code in OpeningFcn to populate axes1
load('Sol.mat');
handles.w = w;
% Update handles structure
guidata(hObject, handles);
plot3(w(:,1),w(:,2),w(:,guide
3));
Programas_2016/Aula_Lorenz/Rotate2.m 0 → 100644
View file @ b9b11430
function varargout = Rotate2(varargin)
% ROTATE2 MATLAB code for Rotate2.fig
% ROTATE2, by itself, creates a new ROTATE2 or raises the existing
% singleton*.
%
% H = ROTATE2 returns the handle to a new ROTATE2 or the handle to
% the existing singleton*.
%
% ROTATE2('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in ROTATE2.M with the given input arguments.
%
% ROTATE2('Property','Value',...) creates a new ROTATE2 or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before Rotate2_OpeningFcn gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to Rotate2_OpeningFcn via varargin.
%
% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one
% instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help Rotate2
% Last Modified by GUIDE v2.5 12-May-2016 13:29:44
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @Rotate2_OpeningFcn, ...
'gui_OutputFcn', @Rotate2_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 Rotate2 is made visible.
function Rotate2_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to Rotate2 (see VARARGIN)
% Choose default command line output for Rotate2
handles.output = hObject;
handles.Az = 90;
handles.El = 0;
handles.Slider1Min = -180;
handles.Slider1Max = 180;
handles.Slider2Min = -90;
handles.Slider2Max = 90;
handles.axes = [];
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes Rotate2 wait for user response (see UIRESUME)
% uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line.
function varargout = Rotate2_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure
varargout{1} = handles.output;
% --- Executes on slider movement.
function slider1_Callback(hObject, eventdata, handles)
% hObject handle to slider1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'Value') returns position of slider
% get(hObject,'Min') and get(hObject,'Max') to determine range of slider
handles.El = get(hObject,'Value');
get(hObject,'Min');
get(hObject,'Max'); %to determine range of slider
guidata(hObject, handles);
view(handles.Az,handles.El)
% --- Executes during object creation, after setting all properties.
function slider1_CreateFcn(hObject, eventdata, handles)
% hObject handle to slider1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: slider controls usually have a light gray background.
if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor',[.9 .9 .9]);
end
% --- Executes during object creation, after setting all properties.
function axes1_CreateFcn(hObject, eventdata, handles)
% hObject handle to axes1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: place code in OpeningFcn to populate axes1
load('Sol.mat');
handles.w = w;
handles.axes = gca;
% Update handles structure
guidata(hObject, handles);
plot3(handles.axes,w(:,1),w(:,2),w(:,3));
view(0,90)
% --- Executes on slider movement.
function slider2_Callback(hObject, eventdata, handles)
% hObject handle to slider2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'Value') returns position of slider
% get(hObject,'Min') and get(hObject,'Max') to determine range of slider
handles.Az = get(hObject,'Value');
get(hObject,'Min');
get(hObject,'Max'); %to determine range of slider
guidata(hObject, handles);
view(handles.Az,handles.El)
% --- Executes during object creation, after setting all properties.
function slider2_CreateFcn(hObject, eventdata, handles)
% hObject handle to slider2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: slider controls usually have a light gray background.
if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor',[.9 .9 .9]);
end
Programas_2016/CurvasFechadas/.dropbox.attr 0 → 100755
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Programas_2016/CurvasFechadas/Circle/CircleRK2C05.eps 0 → 100644
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