clear all

load fisheriris
NumObs = size(meas,1);
NameObs = strcat({'Obs'},num2str((1:NumObs)','%-d'));
iris = dataset({nominal(species),'species'},...
               {meas,'SL','SW','PL','PW'},...
               'ObsNames',NameObs);
x=iris.SL;
y=iris.PL;
[x Ind]=sortrows(x);
y=y(Ind);

m=length(x);
subplot(3,1,1)
plot(x,y,'.')
hold on
grid on

epochMax=1000;
alpha=0.05;
iterCount=0;

% Parameters:
theta0(1)=rand;
theta1(1)=rand;

% Hypothesis:
h=theta0(1)+theta1(1).*x;

plot(x,h,'r')


for thetaX=0:100
for thetaY=0:100
hContour=((thetaX-50)./50)+((thetaY-50)./50).*x;
JContour(thetaX+1,thetaY+1)=(1/m).*sum((hContour-y).^2);
end
end

subplot(3,1,3)
contour([-1:0.02:1],[-1:0.02:1],JContour)
hold on
axis([-1 1 -1 1])

% Cost Function:
J(1)=(1/(2*m))*sum((h-y).^2);

% Minimize Cost Function (Gradient Descent):
for iterCount=1:epochMax
theta0(iterCount+1)=theta0(iterCount)-alpha*(1/m)*sum(h-y);
theta1(iterCount+1)=theta1(iterCount)-alpha*(1/m)*sum((h-y).*x);
h=theta0(iterCount+1)+theta1(iterCount+1).*x;
J(iterCount+1)=(1/(2*m))*sum((h-y).^2);

subplot(3,1,1)
plot(x,y,'.')
hold on
grid on
plot(sort(x),h,'r')
hold off

subplot(3,1,2)
plot(0:iterCount,J)
axis([0 iterCount+1 0.5*mean(J) J(1)+0.2])
hold on
grid on

subplot(3,1,3)
plot(theta0,theta1)
hold on

pause(0.1)

end