%% Lecture 3
%page 13
hfig = hgload('Name.fig') % load Name.fig in Folder
figure(hfig); % visualization
haxe=get(hfig,'Children') %Graphs!
% haxe contains single line–the same approach for multiple lines
ChAxes=get(haxe,'Children')% line finding!
x=get(ChAxes{2},'XData'); % X-coordinates of line
y=get(ChAxes{2},'YData'); % Y-coordinates of line
figure, plot(x,y) % check line!
title('name.fig graph reconstruction ')

%% Lecture3 p14
figure
subplot(1,2,2) 
f = @(x,n) exp(sin(n*x))*cos(x);
fplot(@(x)f(x,10),[0 2*pi],'r','linewidth',1.5)
% % Vector or element-by-element operations:
subplot(1,2,1)
f = @(x,n) exp(sin(n*x)).*cos(x).*sin(x);
fplot(@(x)f(x,10),[0 2*pi],'r','linewidth',1.5)
title('vectorized')

%% Lecture3 p 15
%% ezplot; fplot -for new versions!!!
figure
r=ezplot('x^2+(y-abs(x)^(1/2))^2=1'), hold on, grid on
set(r,'linewidth',3,'color','red' ); title(' ')
% the line of the first function with a descriptor is automatically placed in the header r title(' ')
rf=ezplot('x^2+(y-1)^2=4',[-3,3]) ; title(' ')
ra=ezplot(@(x,y) y^3+x^2-4); set(ra,'linewidth',2.5,'color','cyan' ); title(' ');
legend('x^2+(y-abs(x)^{(1/2)})^2=1',...
'x^2+(y-1)^2=4','y^3+x^2-4=0')
%% implicitplot -(New!!!)
% For function f(x,y) = 0
figure
fp = fimplicit(@(x,y) x.^2+ y.^2 -3)
fp.LineWidth =3 % Important
fp.Color=[0.7 0 0.3] % Register!
title('x^2 + y^2 -3=0','fontsize',14)
axis square % !!!!!!!!!!!!!
clear
%% Page 16 I. Extreme points are added:
x = linspace(-2,3); % 100 point -default
y = 3*x.^3-6*x.^2; % vectorized!
plot(x,y,'c-','linewidth',1.5) %the simplest way
% The inscription about the zero derivative is set by evaluating visually:
xt = [-0.2 1.5]; yt = [5 -7];str = 'dy/dx = 0';
text(xt,yt,str,'fontsize',12), hold on
% may be will add something?!
% II.TEXT. Conditions forminandmax:
% yim1<yi,yi>yip1 yim1>yi,yi<yip1% yim1~ yiminus 1
% yim1 ~y_{i-1}; yi~y_i; yip1~y_{i+1}
% reserve array for minand max finding :
yi=y(2:end-1) ; yip1=y(3:end); yim1=y(1:end-2)
% notations: yi=y_{i}; yim1= y_{i-1}; yip1=y_{i+1}
%in curly brackets indexes in notation Latex, not forMatLab!
% III.TEXT–Find and note extreme points:
trmax=and(yim1<yi,yi>yip1) %max condition
indexmax=find(trmax)
trmin=and(yim1>yi,yi<yip1) %min condition
indexmin=find(trmin) % here single min
xmin=x(indexmin+1) % min
ymin=y(indexmin+1); plot(xmin,ymin,'r*','markersize',16)
xmax=x(indexmax+1)% max
ymax=y(indexmax+1); plot(xmax,ymax, 'm*','markersize',16)
%% Try to use functions: islocalmin and islocalmax
%% Lecture 3 p 19
clear
[X,Y]=deal(-1:0.1:1);[XX,YY]=meshgrid(X,Y); % grid pointsXOY
Z=XX.^2+YY.^2-1; % vectorized surface function
[minzJ,Jmin]=min(min(Z)); % minzJ -minValue in column Jmin of Z
[minzI,Imin]=min(min(Z')); % minzI -minValue minzI in Imin row of Z
minzJJ=min(Z);[minValueJ,Jmin]=min(minzJJ);
subplot(1,2,1); rm=mesh(XX,YY,Z); title('mesh'); % see, using full size of window
hold on; Xmesh=get(rm,'xdata'); Ymesh=get(rm,'ydata');Zmesh=get(rm,'zdata');
r=plot3(XX(Imin,Jmin),YY(Imin,Jmin),minValueJ,'bO'); % minimal Value
set(r,'markersize',20,'MarkerFaceColor','red');
subplot(1,2,2), surf(Z), title('surf')