% ***** GRADIENT DESCENT LINEAR REGRESSION ***** %

% m:  Number of data samples
% n:  Number of factors or dependent variables
% p:  Index value of a single sample within the set of m samples
% q:  Index value of an individual feature within the 
%     ith sample's feature (or variable) vector
% x:  Feature vector with n+1 features, i.e. x=[x0 x1 x2 x3] & x0=1
% theta:  Parameter vector with at least n+1 parameters, 
%         i.e. theta=[theta0 theta1 theta2 theta3]
% h:  "Hypothesis" or prediction model, i.e. h=theta*transpose(x)
% J:  Cost function dependent on the parameter values in vector theta 

clear all
close all

% Data Points
x=[0.1 1.2 3.0 4.6 4.9 5.7 6.2 7.0 8.4 10.1 10.3 10.9 12];
y=[1.3 4.9 3.5 3.9 5.6 4.3 6.7 4.4 7.4 7.8 9.2 11.4 10.4];

% Initialize parameters
theta(1)=2;
theta(2)=0.08;

% Initialize the "momentum" alpha
alpha=[0.1 0.001];

m=length(y);

h=theta(1)+theta(2).*x;  % "Hypothesis" model

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

e=1;

count=2;
frameCount=1;

while (e>0.01)

    theta(1)=theta(1)-alpha(1).*(2/m).*sum(h-y);
    theta(2)=theta(2)-alpha(2).*(2/m).*sum((h-y).*x);
    h=theta(1)+theta(2).*x;
    J(count)=(1/m)*sum((h-y).^2);
        
    e=abs(J(count)-J(count-1));
    count=count+1;
    set(gcf,'Color','white')
    
    subplot(2,1,1)
    plot(x,y,'bo','LineWidth',2)
    title('Data and Decision Boundary','fontsize',11,'fontweight','b')
    xlabel('Independent Variable','fontsize',10)
    ylabel('Dependent Variable','fontsize',10)
        set(gca,'XColor',[0.35,0.35,0.35])
                set(gca,'YColor',[0.35,0.35,0.35])
    grid on
    grid minor
    set(gca,'Color',[0.65,0.65,0.65])
    axis([0 12 0 12])
    hold on
    plot(x,h,'r','LineWidth',2)
    pause(0.1)
    hold off
   
        subplot(2,1,2)
        plot(1:(count-1),J(1:(count-1)),'g','LineWidth',2);
        title('Cost Function','fontsize',11,'fontweight','b')
        xlabel('Epoch Number','fontsize',10)
        ylabel('Cost Value','fontsize',10)
        grid on
        grid minor
        set(gca,'Color',[0.65,0.65,0.65])
        set(gca,'XColor',[0.35,0.35,0.35])
        set(gca,'YColor',[0.35,0.35,0.35])
        axis([0 70 0 25])
        hold off
        
        
    set(gcf,'Renderer','zbuffer')
    M(frameCount)= getframe(gcf);
    frameCount=frameCount+1;
    M(frameCount)= getframe(gcf);
    frameCount=frameCount+1;
end

movie(M)
movie2avi(M,'TrivialLinearRegressionLearner.avi')%,'compression','Cinepak')