% This is a sample script file showing you how to plot the contours
%   in homework problem 2.  It uses the implot.m file on our class
%   website (also available on Matlab's website).

%% Problem:  Plot several contours of the function z=sin^2(x)+(1/4)*y^2

%Window size: [xmin, xmax, ymin, ymax]
winsize=[-2 2 -2 2];

%Define the function (only the zero level curve is plotted)
%  This is the level curve at z=0.1
f=inline('sin(x).^2+0.25*y.^2-0.1','x','y');
implot(f,winsize)

hold on  %Allows you to draw over the previous plot
%  This is the level curve at z=0.5 
f=inline('sin(x).^2+0.25*y.^2-0.5','x','y');
implot(f,winsize)

%  This is the level curve at z=0.75
f=inline('sin(x).^2+0.25*y.^2-0.75','x','y');
implot(f,winsize)

%  This is the level curve at z=1.0
f=inline('sin(x).^2+0.25*y.^2-1.0','x','y');
implot(f,winsize)


%% Now we'll compute some points on the trajectory of the gradient descent

f=inline('sin(x).^2+0.25*y.^2','x','y');
df=inline('[ 2*sin(x), 0.5*y]','x','y');

x=[1.3,1.1];
alpha=0.7;

for j=1:20
    x=x-alpha*df(x(1),x(2));
    X(j,:)=x;
end

%And plot them
plot(X(1,:),X(2,:),'k-*')
hold off

%We could also plot them by iteration:
figure(2)
plot(X)