function TCM_fourier_series

% TCM_FOURIER_SERIES Illustration of the approximation by a trigonometric polynom.
%
%   TCM_FOURIER_SERIES illustrates the approximation of a T-periodic function  
%   y = f(x) by a trigonometric polynom. 
%
%   EXAMPLES
%
%   Basic example: The powers of the sine and cosine function can be 
%   represented exactly; only a finite number of Fourier coefficients are 
%   nonzero.
%
%   Periodic exponential function: The fast convergence for a smooth
%   function with rapid decay of the Fourier coefficients is illustrated.
%
%   Gibb's phenomenom: For a function with discontinuities, the convergence 
%   is very slow, caused by oscillations near the jumps. 
%
%   To investigate other cases, insert a function and its period T in the 
%   corresponding fields.
%
%   TCM_FOURIER_SERIES is part of the <a href="http://www2.imng.uni-stuttgart.de/LstNumGeoMod/TCM/">TCM</a> project.
%   Related course materials can be found at <a href="http://www.mathematics-online.org/inhalt/aussage/aussage805/">Mathematics Online</a>.

% Authors: Florian Martin, Lars von Wolff
% Last updated: 01.04.2017

% Initialize data
TCM_Data.fun = @(x) cos(x).^2+sin(x).^3;
TCM_Data.funstring = '@(x) cos(x).^2+sin(x).^3';
TCM_Data.T = 6.283185307179586; 
TCM_Data.n = -1;
TCM_Data.C = [];
TCM_Data.npts = 0;

% Do not delete these Variables
TCM_Data.plot_window = [0 2*pi 0 3];
TCM_Data.LmbMenuString = '';
TCM_Data.examples = {'Basic example','Periodic exponential function','Gibb''s phenomenon'};

% Layout:
% ---------------------------------------
% |               Title                 |
% | ------------ --------- ------------ |
% | | Settings | |Buttons| | Feedback | |
% | ------------ --------- ------------ |
% | ----------------------------------- |
% | |           Axis (Plot)           | |
% | ----------------------------------- |
% | Info-Button         Hint            |
% ---------------------------------------
% Initialize Layout:
TCM_UI.TitleHeightMin = 10;        % minimal height of the title
TCM_UI.TitleHeightMax = 32;        % maximal height of the title
TCM_UI.HintHeightMin = 8;          % minimal height of the hint
TCM_UI.HintHeightMax = 15;         % maximal height of the hint
TCM_UI.SettingsHeightMin = 40;     % minimal height of the feedback, buttons and 
                                   % setting panel
TCM_UI.SettingsHeightMax = 70;     % maximal height of the feedback, buttons and 
                                   % setting panel
TCM_UI.SettingsRatio = 4.5;          % aspect ratio of the settings  
                                   % (increase if more settings needed)
TCM_UI.ButtonsRatio = 1.4;         % aspect ratio of the Buttons panel
TCM_UI.FeedbackRatio = 3.4;        % aspect ratio of the feedback
TCM_UI.AxisHeightTarget = 0.73;    % desired fraction of figure 
                                   % used for the plot
TCM_UI.InfoPortion = 1/8;          % Portion of the Info Button in the last  
                                   % line 
TCM_UI.Title = 'Real Fourier Series';
TCM_UI.mono = get(0,'FixedWidthFontName');
% Strings for generating the information window
TCM_UI.Author = 'F. Martin and L. von Wolff';
TCM_UI.Date = '01.04.2017';
TCM_UI.Web = 'http://www.mathematics-online.org/inhalt/aussage/aussage805/';
      
CreateUI();

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% UI-Elements in Settings %%%%%%%%%%%%%%%%%%%%
% Text for Function
TCM_UI.funtext = uicontrol('Units','normalized','Parent',TCM_UI.settingspanel, ...
        'BackgroundColor',get(gcf,'Color'), ...
        'FontUnits','normalized','FontSize',0.67,...
        'HorizontalAlignment','left', ...
	'Position',[.01,.70,.29,.30],...
	'String','Function:',...
	'Style','text');

% Input for Function
TCM_UI.funinput=uicontrol('Units','normalized', 'Parent',TCM_UI.settingspanel, ...
        'BackgroundColor',get(gcf,'Color'), ...
        'FontWeight','bold',...
        'FontUnits','normalized','FontSize',0.65,'FontName',TCM_UI.mono,...
        'HorizontalAlignment','left', ...
	'Position',[.30,.70,.69,.30],...
	'String','',...
	'Style','edit',...
	'Callback',@function_update);

% Text for period
TCM_UI.periodtext = uicontrol('Units','normalized', 'Parent',TCM_UI.settingspanel, ...
        'BackgroundColor',get(gcf,'Color'), ...
        'FontUnits','normalized','FontSize',0.67,...
        'HorizontalAlignment','left', ...
	'Position',[.01,.35,.29,.30],...
	'String','Period T:',...
	'Style','text');

% Input the period
TCM_UI.periodinput=uicontrol('Units','normalized', 'Parent',TCM_UI.settingspanel, ...
        'BackgroundColor',get(gcf,'Color'), ...
        'FontWeight','bold',...
        'FontUnits','normalized','FontSize',0.65,'FontName',TCM_UI.mono,...
        'HorizontalAlignment','left', ...
	'Position',[.30,.35,.3,.30],...
	'String','6.283185307179586',...
	'Style','edit','Callback',@period_update);

% Text for degree 
TCM_UI.degreetext = uicontrol('Units','normalized', 'Parent',TCM_UI.settingspanel, ...
        'BackgroundColor',get(gcf,'Color'), ...
        'FontUnits','normalized','FontSize',0.67,...
        'HorizontalAlignment','left', ...
	'Position',[.01,.00,.3,.30],...
	'String','Degree:',...
	'Style','text');

% Input degree
TCM_UI.degreeinput=uicontrol('Units','normalized', 'Parent',TCM_UI.settingspanel, ...
        'BackgroundColor',get(gcf,'Color'), ...
        'FontWeight','bold',...
        'FontUnits','normalized','FontSize',0.65,'FontName',TCM_UI.mono,...
        'HorizontalAlignment','left', ...
	'Position',[.30,.00,.3,.30],...
	'String','NaN',...
	'Style','edit','Callback',@degree_update);

%%%%%%%%%%%%%%%%%%%%%%%%% UI-Elements in Buttons Panel %%%%%%%%%%%%%%%%%%%%
% Reset-Button
TCM_UI.reset=uicontrol('Units','normalized','Parent',TCM_UI.buttonspanel, ...
	'BackgroundColor',get(gcf,'Color'), ...
	'String','Reset', ...
    'FontUnits','normalized','FontSize',0.7,...
	'Position',[.01,.70,.98,.30], ...
	'Callback',@reset,...
	'Style','pushbutton');

% Example button
TCM_UI.examples=uicontrol('Units','normalized','Parent',TCM_UI.buttonspanel, ...
	'BackgroundColor',get(gcf,'Color'), ...
	'String','Examples', ...
    'FontUnits','normalized','FontSize',0.7,...
	'Position',[.01,.35,.98,.30], 'Callback',@OpenExampleMenu,...
	'Style','pushbutton');

% Next-Button
TCM_UI.next=uicontrol('Units','normalized','Parent',TCM_UI.buttonspanel, ...
	'BackgroundColor',get(gcf,'Color'), ...
	'String','Next', ...
    'FontUnits','normalized','FontSize',0.7,...
	'Position',[.01,.0,.98,.30], ...
	'Callback',@next,...
	'Style','pushbutton');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% UI-Elements in Feedback %%%%%%%%%%%%%%%%%%%%

% Text for max error
TCM_UI.maxerrortext=uicontrol('Units','normalized','Parent',TCM_UI.feedbackpanel,...
        'BackgroundColor',get(gcf,'Color'), ...
        'HorizontalAlignment','left', ...
        'FontUnits','normalized','FontSize',0.7,...
	'Position',[.01,.7,.9,.3],...
	'String','Max error: NaN',...
	'Style','text');

% Text for mean error
TCM_UI.meanerrortext=uicontrol('Units','normalized','Parent',TCM_UI.feedbackpanel,...
        'BackgroundColor',get(gcf,'Color'), ...
        'HorizontalAlignment','left', ...
        'FontUnits','normalized','FontSize',0.7,...
	'Position',[.01,.35,.9,.3],...
	'String','Mean error: NaN',...
	'Style','text');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% UI-Elements in Axis %%%%%%%%%%%%%%%%%%%%%%%%
%TCM_UI.ax=axes('Position',[.05,.1,.9,.85],'Parent',TCM_UI.axispanel);
TCM_UI.ax=axes('Position',[.05,.4,.9,.55],'Parent',TCM_UI.axispanel);
axis(TCM_UI.ax,'equal');
TCM_UI.modification = uicontextmenu('Callback',@reset_zoom_limits); 
TCM_UI.mpan = uimenu('Parent',TCM_UI.modification,'Label','Enable pan',...
        'Callback',@axis_context);
TCM_UI.mzoomi = uimenu('Parent',TCM_UI.modification,'Label','Enable zoom in',...
    'Callback',@axis_context); 
TCM_UI.mzoomo = uimenu('Parent',TCM_UI.modification,'Label','Enable zoom out',...
        'Callback',@axis_context); 
TCM_UI.ax.UIContextMenu = TCM_UI.modification;

% functions for smoothless zooming and panning
panfun = pan(TCM_UI.fig);
panfun.UIContextMenu = TCM_UI.modification;
set(panfun,'ActionPostCallback',@pan_modify);
zoomfun = zoom(TCM_UI.fig);
zoomfun.UIContextMenu = TCM_UI.modification; 
set(zoomfun,'ActionPostCallback',@zoom_modify);
set(zoomfun,'ButtonDownFilter',@set_zoom_limits);
set(zoomfun,'RightClickAction','PostContextMenu');
set(findall(TCM_UI.fig,'tag','Exploration.Pan'),'enable','off');
set(findall(TCM_UI.fig,'tag','Exploration.ZoomOut'),'enable','off');
set(findall(TCM_UI.fig,'tag','Exploration.ZoomIn'),'enable','off');

TCM_UI.ax2=axes('Position',[.05,.1,.9,.2],'Parent',TCM_UI.axispanel);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Start the program %%%%%%%%%%%%%%%%%%%%%%%%%%
changeexample(1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% Callback functions %%%%%%%%%%%%%%%%%%%%%%%%%%%

% new function input
function function_update(varargin)
TCM_Data.funstring = get(TCM_UI.funinput,'String');
var = TCM_Data.funstring(find(TCM_Data.funstring=='(',1)+1:...
    find(TCM_Data.funstring==')',1)-1);
TCM_Data.fun = eval([TCM_Data.funstring '+0*' var]);
TCM_Data.C = [];
compute_window
reset;
end

function period_update(varargin)
Tstr = get(TCM_UI.periodinput,'String');
ind = find(Tstr == '.');
if length(Tstr(ind+1:end)) > 4
    Tstr = Tstr(1:ind+4);
    set(TCM_UI.periodinput,'String',Tstr);
end
T = str2double(Tstr);
if T > 0
    TCM_Data.T = T;
    TCM_Data.plot_window(1:2) = [0 T];
    compute_window;
    reset;
end
end

% calculate y-range depending von the size of the function
function compute_window
x = linspace(TCM_Data.plot_window(1),TCM_Data.plot_window(2),1000);
fmin = min(TCM_Data.fun(x));
fmax = max(TCM_Data.fun(x));
dy = fmax-fmin;   
if abs(dy) < 10^-8
    TCM_Data.plot_window(3) = min(fmin-1,-1);
    TCM_Data.plot_window(4) = max(fmax+1,1);
else
    TCM_Data.plot_window(3:4) = [min(-dy/4,fmin-dy/4), max(dy/4,fmax+dy/4)];
end
end

% degree input
function degree_update(varargin)
n = str2double(get(TCM_UI.degreeinput,'String'));
if n > 20
    n = 20;
    set(TCM_UI.degreeinput,'String','20');
end
if n>TCM_Data.n 
   for i=TCM_Data.n+1:n
       TCM_Data.C(:,i+1) = midpoint(i,10+2*i);
       if i==0
           TCM_Data.C(1,i+1) = TCM_Data.C(1,i+1)/2;
       end
   end
end
if isnan(n)
    TCM_Data.n = -1;
else
    TCM_Data.n = n;
end
myplot;
end

% refresh all data from UI
function reset(varargin)
set(TCM_UI.maxerrortext,'String','Max error: NaN');
set(TCM_UI.meanerrortext,'String','Mean error: NaN');
TCM_Data.n = -1;
TCM_Data.npts = 0;
set(TCM_UI.degreeinput,'String','');
window_disable.Label = 'Disable pan';
axis_context(window_disable);
myplot;
end

% button next pressed
function next(varargin)
set(TCM_UI.degreeinput,'String',num2str(TCM_Data.n+1));
degree_update;
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% kernel functions %%%%%%%%%%%%%%%%%%%%%%%%%%%
function f = period_f(x)
f = 0*x;
n1 = floor(x(1)/TCM_Data.T);
n2 = x(end)/TCM_Data.T;
for i=n1:n2-1
   ind = x>=i*TCM_Data.T & x<(i+1)*TCM_Data.T; 
   f(ind) = TCM_Data.fun(x(ind)-i*TCM_Data.T);
end
end

function [s,npts] = midpoint(l,H)
% integration of periodic functions 

T = TCM_Data.T;
STEPS = 15; TOL = 1.0e-6;
oldH = H;
x = T*[1/2:H]'/H;
f = {@(x) 2*TCM_Data.fun(x).*cos(2*pi*l*x/T)/T, ...
    @(x) 2*TCM_Data.fun(x).*sin(2*pi*l*x/T)/T};
s_old = [sum(T*f{1}(x)/H); sum(T*f{2}(x)/H)];
for i=1:2
    H = oldH;
    x = T*[1/2:H]'/H;
    for k=1:STEPS
       H = 2*H;
       x = T*[1/2:H]'/H;
       npts = length(x);
       s(i) = sum(T*f{i}(x)/H);
       if abs(s(i)-s_old(i))<TOL
          break
       elseif k == STEPS
           display('no convergence of numerical integration')
       end
       s_old(i) = s(i);
    end
    TCM_Data.npts = max(TCM_Data.npts,npts);
end
end


% plot function
function myplot
subplot(TCM_UI.ax)
cla reset; hold on

h = TCM_Data.T;
x = linspace(TCM_Data.plot_window(1)-h,TCM_Data.plot_window(2)+h,1000);
fx = period_f(x);
plot(x,fx,'b','LineWidth',2);
plot([x(1) x(end)],[0 0],'k');

% plot the Taylor polynomials
x2 = h*[1/2:TCM_Data.npts]/TCM_Data.npts;
f2 = TCM_Data.fun(x2);
if TCM_Data.n >=0
    px1 = 0;
    px2 = 0;
    for n=0:TCM_Data.n
        px1 = px1 + TCM_Data.C(1,n+1)*cos(2*pi*x*n/TCM_Data.T) + ...
            TCM_Data.C(2,n+1)*sin(2*pi*x*n/TCM_Data.T);
        px2 = px2 + TCM_Data.C(1,n+1)*cos(2*pi*x2*n/TCM_Data.T) + ...
            TCM_Data.C(2,n+1)*sin(2*pi*x2*n/TCM_Data.T);
    end
   
    % plot highest order
    plot(x,px1,'Color',[0 0.5 0],'LineWidth',2);
end

xlim([TCM_Data.plot_window(1) TCM_Data.plot_window(2)]);
ylim([TCM_Data.plot_window(3) TCM_Data.plot_window(4)]);

cla(TCM_UI.ax2,'reset');
if TCM_Data.n > -1
    errmax = norm(f2-px2,inf);
    errmean = sqrt(sum((f2-px2).^2 * TCM_Data.T / TCM_Data.npts));
    colormap jet
    if n > 0        
        bar(TCM_UI.ax2,[0:TCM_Data.n]',TCM_Data.C(:,1:TCM_Data.n+1)')
    else
        bar(TCM_UI.ax2,0,TCM_Data.C(1,1))
        ax = axis(TCM_UI.ax2);
        xlim(TCM_UI.ax2,[ax(1) 1]);        
    end
else
    errmax = NaN; errmean = errmax;
    xlim(TCM_UI.ax2,[0 1]);
    ylim(TCM_UI.ax2,[0 1]);
    TCM_UI.ax2.XTick = [0 1];
    TCM_UI.ax2.YTick = [0 1];
end
xlabel = get(TCM_UI.ax2,'XTickLabel');
xlabel{1} = 'a_0';
for i=2:numel(xlabel)
    num = str2double(xlabel{i});
    xlabel{i} = sprintf('a_{%d},b_{%d}',num,num);
end
set(TCM_UI.ax2,'XTickLabel',xlabel);

set(TCM_UI.maxerrortext,'String',sprintf('Max error: %5.3e',errmax));
set(TCM_UI.meanerrortext,'String',sprintf('Mean error: %5.3e',errmean));

SetWindowLimits
UpdateHinttext
end

% Update the Hinttext
function UpdateHinttext
if TCM_Data.n == -1
    LmbString = 'Next = Set degree to 0. ';
else
    LmbString = 'Next = Increase degree. ';
end    
if(numel(TCM_Data.LmbMenuString) == 0)
    set(TCM_UI.hinttext,'String',[LmbString 'Right Mouse = Access window menu.']);
else
    set(TCM_UI.hinttext,'String',[TCM_Data.LmbMenuString 'Right Mouse = Access window menu.']);
end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% example functions %%%%%%%%%%%%%%%%%%%%%%%%%%%

function CreateExampleMenu
TCM_UI.UICexamples = uicontextmenu;
for i=1:numel(TCM_Data.examples)
    uimenu('Parent',TCM_UI.UICexamples,'Label',TCM_Data.examples{i},'Callback',{@changeexample,i});
end
end

function OpenExampleMenu(varargin)
TCM_UI.examples.Units = 'pixels';
TCM_UI.buttonspanel.Units = 'pixels';
TCM_UI.UICexamples.Position = TCM_UI.examples.Position(1:2) + TCM_UI.buttonspanel.Position(1:2);
TCM_UI.examples.Units = 'normalized';
TCM_UI.buttonspanel.Units = 'points';
TCM_UI.UICexamples.Visible = 'on';
end
 
              
function changeexample(varargin)  
switch varargin{numel(varargin)}
    case 1
        set(TCM_UI.funinput,'String','@(x) cos(x).^2+sin(x).^3'); 
        function_update;
        set(TCM_UI.periodinput,'String','6.283185307179586'); 
        period_update;
        TCM_Data.T = 6.283185307179586;
    case 2
        set(TCM_UI.funinput,'String','@(x) exp(sin(3*x)+cos(2*x))'); 
        function_update;
        set(TCM_UI.periodinput,'String','6.283185307179586'); 
        period_update;
        TCM_Data.T = 6.283185307179586;
    case 3
        set(TCM_UI.funinput,'String','rectangle function'); 
        TCM_Data.fun = @(x) square(x);
        TCM_Data.C = [];
        TCM_Data.T = 1;
        compute_window
        reset;
        set(TCM_UI.periodinput,'String','1'); 
        period_update;
end
end

function f = square(x)
    f = 0*x;
    ind = x>=0 & x<1/2; f(ind) = 1;
end


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% zoom functions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% function for updating the internal plot window
function zoom_modify(varargin)
if max(abs(TCM_Data.plot_window-axis(TCM_UI.ax)))< 10^-10
    ZoomOut;
end
pan_modify;
end

function pan_modify(varargin)
TCM_Data.plot_window = axis(TCM_UI.ax);
myplot;
end

% functions for proper zooming in (prevent double-click zoom out)
function [flag] = set_zoom_limits(varargin)
if(strcmp(TCM_UI.fig.SelectionType,'open'))
    flag = true;
else
    flag = false;
end
end

function reset_zoom_limits(varargin)
SetWindowLimits;
end

% handling the axis context menu
function axis_context(varargin)
zoom(TCM_UI.fig, 'off'); pan(TCM_UI.fig, 'off');
mode_strings = {'pan','zoom in','zoom out'};
status_strings = {'Enable ','Disable '};
switch varargin{1}.Label(1:7)
    case 'Enable '
        mode = strcmp(varargin{1}.Label(8:end),mode_strings);
        TCM_Data.LmbMenuString = ['Left Mouse = ' mode_strings{mode} ' the window. '];
        set(TCM_UI.mpan,'Label',horzcat(status_strings{mode(1)+1},mode_strings{1}));
        set(TCM_UI.mzoomi,'Label',horzcat(status_strings{mode(2)+1},mode_strings{2}));
        set(TCM_UI.mzoomo,'Label',horzcat(status_strings{mode(3)+1},mode_strings{3}));
        split_mode = strsplit(mode_strings{mode},' ');
        if numel(split_mode) == 1
            pan(TCM_UI.fig, 'on');
        else
            zoomh = zoom(TCM_UI.fig);
            zoomh.Enable = 'on';
            zoomh.Direction = split_mode{2};
        end
    case 'Disable'
        TCM_Data.LmbMenuString = '';
        set(TCM_UI.mpan,'Label','Enable pan');
        set(TCM_UI.mzoomi,'Label','Enable zoom in');
        set(TCM_UI.mzoomo,'Label','Enable zoom out');     
end
UpdateHinttext;
end

function SetWindowLimits
ZoomOut;
xlim(TCM_UI.ax,[TCM_Data.plot_window(1) TCM_Data.plot_window(2)]);
ylim(TCM_UI.ax,[TCM_Data.plot_window(3) TCM_Data.plot_window(4)]);
end

function ZoomOut
hx = TCM_Data.plot_window(2) - TCM_Data.plot_window(1);
hy = TCM_Data.plot_window(4) - TCM_Data.plot_window(3);
xlim(TCM_UI.ax,[TCM_Data.plot_window(1)-hx/2 TCM_Data.plot_window(2)+hx/2]);
ylim(TCM_UI.ax,[TCM_Data.plot_window(3)-hy/2 TCM_Data.plot_window(4)+hy/2]);
zoom(TCM_UI.fig, 'reset');
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% layout functions %%%%%%%%%%%%%%%%%%%%%%%%%%%

% functions for creating the different UI-Parts and managing the resize of
% the window
function CreateUI
TCM_UI.fig = figure('Visible','off', 'Units','points','Toolbar','none',...
    'SizeChangedFcn',@calculate_layout,'numbertitle','off','name',TCM_UI.Title);
TCM_UI.titletext = uicontrol('Units','points','BackgroundColor',TCM_UI.fig.Color, ...
	'HorizontalAlignment','center',  'FontWeight','bold', ...
    'FontUnits','normalized',        'FontSize',0.8,...
	'String',TCM_UI.Title,        'Style','text');
TCM_UI.hinttext = uicontrol('Units','points','BackgroundColor',TCM_UI.fig.Color, ...
    'HorizontalAlignment','right',...
    'FontUnits','normalized',        'FontSize',0.63,...
	'String','','Style','text');
TCM_UI.infobutton=uicontrol('Units','points', ...
	'BackgroundColor',TCM_UI.fig.Color, ...
	'String','Info', 'HorizontalAlignment','left',...
    'FontUnits','normalized','FontSize',0.7,...
	'Callback',@information,'Style','pushbutton');
TCM_UI.feedbackpanel = uipanel('Units','points','BackgroundColor',TCM_UI.fig.Color,'BorderType','none');
TCM_UI.buttonspanel = uipanel('Units','points','BackgroundColor',TCM_UI.fig.Color,'BorderType','none');
TCM_UI.settingspanel = uipanel('Units','points','BackgroundColor',TCM_UI.fig.Color,'BorderType','none');
TCM_UI.axispanel = uipanel('Units','points','BackgroundColor',TCM_UI.fig.Color,'BorderType','none');
CreateExampleMenu
TCM_UI.fig.Visible= 'on';
end


function calculate_layout(varargin) 
figpos = TCM_UI.fig.Position;
WMax = TCM_UI.SettingsHeightMax*(TCM_UI.SettingsRatio + TCM_UI.FeedbackRatio + TCM_UI.ButtonsRatio);
WMin = TCM_UI.SettingsHeightMin*(TCM_UI.SettingsRatio + TCM_UI.FeedbackRatio + TCM_UI.ButtonsRatio);
HMax = TCM_UI.TitleHeightMax + TCM_UI.HintHeightMax;
HMin = TCM_UI.TitleHeightMin + TCM_UI.HintHeightMin;

wratio = max(0,min(1,(min(figpos(3),1.3*figpos(4))-WMin)/(WMax-WMin)));
XCoords = [1,0,0,0,0,0,0,figpos(3)];
SWidth =      wratio*TCM_UI.SettingsHeightMax*TCM_UI.SettingsRatio...
        + (1-wratio)*TCM_UI.SettingsHeightMin*TCM_UI.SettingsRatio;
BWidth =      wratio*TCM_UI.SettingsHeightMax*TCM_UI.ButtonsRatio...
        + (1-wratio)*TCM_UI.SettingsHeightMin*TCM_UI.ButtonsRatio; 
FWidth =      wratio*TCM_UI.SettingsHeightMax*TCM_UI.FeedbackRatio...
        + (1-wratio)*TCM_UI.SettingsHeightMin*TCM_UI.FeedbackRatio; 
RemWidth = figpos(3)-3-SWidth-FWidth-BWidth;
XCoords(2) = max(1,0.3*RemWidth);
XCoords(3) = XCoords(2) + 1 + SWidth;
XCoords(4) = XCoords(3) + max(0,0.2*RemWidth);
XCoords(5) = XCoords(4) + 1 + BWidth;
XCoords(6) = XCoords(5) + max(0,0.2*RemWidth);
XCoords(7) = XCoords(6) + 1 + FWidth;
SHeight = wratio*TCM_UI.SettingsHeightMax + (1-wratio)*TCM_UI.SettingsHeightMin;
if(HMin > min(figpos(4),0.9*figpos(3))*(1-TCM_UI.AxisHeightTarget)-5-SHeight)
    hratio = 0;
elseif(HMax <  min(figpos(4),0.9*figpos(3))*(1-TCM_UI.AxisHeightTarget)-5-SHeight)
    hratio = 1;
else
    hratio = (( min(figpos(4),0.9*figpos(3))*(1-TCM_UI.AxisHeightTarget)-5-SHeight)  -HMin)/(HMax-HMin);
end
YCoords = [1,0,0,0,figpos(4)-1];
YCoords(2) = YCoords(1) + 1 + hratio*TCM_UI.HintHeightMax     + (1-hratio)*TCM_UI.HintHeightMin;
YCoords(4) = YCoords(5) - 1 - hratio*TCM_UI.TitleHeightMax    - (1-hratio)*TCM_UI.TitleHeightMin;
YCoords(3) = YCoords(4) - 1 - SHeight;
TCM_UI.titletext.Position =     [XCoords(1)+1,  YCoords(4)+1,  XCoords(8)-XCoords(1)-1,  YCoords(5)-YCoords(4)-1];
TCM_UI.settingspanel.Position = [XCoords(2)+1,  YCoords(3)+1,  XCoords(3)-XCoords(2)-1,  YCoords(4)-YCoords(3)-1];
TCM_UI.buttonspanel.Position =  [XCoords(4)+1,  YCoords(3)+1,  XCoords(5)-XCoords(4)-1,  YCoords(4)-YCoords(3)-1];
TCM_UI.feedbackpanel.Position = [XCoords(6)+1,  YCoords(3)+1,  XCoords(7)-XCoords(6)-1,  YCoords(4)-YCoords(3)-1];
TCM_UI.axispanel.Position =     [XCoords(1)+1,  YCoords(2)+1,  XCoords(8)-XCoords(1)-1,  max(0,YCoords(3)-YCoords(2)-1)];
TmpXCoord = TCM_UI.InfoPortion*(XCoords(8)-XCoords(1)-1);
TCM_UI.infobutton.Position =    [XCoords(1)+1,  YCoords(1)+1,  TmpXCoord-XCoords(1)-1,   YCoords(2)-YCoords(1)-1];
TCM_UI.hinttext.Position =      [TmpXCoord+1,   YCoords(1)+1,  XCoords(8)-TmpXCoord-1,   YCoords(2)-YCoords(1)-1];
end

% function for opening the information webpage
function information(varargin)
pos = TCM_UI.fig.OuterPosition;
infodialog = dialog('Name','Information','Units','points',...
    'OuterPosition',[pos(1)+pos(3)/4 pos(2)+pos(4)/4 pos(3)/2 pos(4)/2]);
uicontrol('Units','normalized', 'Parent',infodialog, ...
        'FontUnits','normalized', 'FontSize',0.67,...
        'HorizontalAlignment','center', 'Position',[.01,.6,.98,.15],...
	'String','Mathematics Online Link', 'Style','text',...
    'ForegroundColor','blue','ButtonDownFcn',@linkfun,...
    'Enable','inactive');
uicontrol('Units','normalized', 'Parent',infodialog, ...
        'FontUnits','normalized', 'FontSize',0.4,...
        'HorizontalAlignment','center', 'Position',[.01,.4,.98,.15],...
	'String',{horzcat('Created by ',TCM_UI.Author,'.');horzcat('Version: ',TCM_UI.Date)} , 'Style','text');
end

function linkfun(varargin)
web(TCM_UI.Web)
end
end
