%% Model Building with Gradient Descent

close all
clear 
clc

% Data represents housing prices.  The first column
%  is square footage, second column is price (fictional).
% We want to find a function that predicts price based
% on the square footage.

X=[1100	199000
1400	245000
1425	319000
1550	240000
1600	312000
1700	279000
1700	310000
1875	308000
2350	405000
2450	324000];

%% Step 0: Preprocess the data

plot(X(:,1),X(:,2),'k^-')

% Rescale the data
mx=mean(X,1); sx=std(X,1);  % Keep these around in case you need to rescale
Xs=(X-mx)./sx;              %   new data.

figure(1)
plot(Xs(:,1),Xs(:,2),'k^-')

% We'll break up the data for Step 2:
x=Xs(:,1);
t=Xs(:,2); %Targets

%% Step 1: Randomly initialize the training parameters and other constants
m=randn; b=randn;
MaxIters=20;
alpha = 0.1;
tol = 1e-8;
%% Main Loop:  Steps 2-4

for i=1:MaxIters

% Step 2:  Calculate the error at each point

    y=m*x+b;
    ErrVec=t-y;
    Error(i)=sum(ErrVec.*ErrVec);

% Step 3: Calculuate the gradient:
temp1=ErrVec.*(-x); temp2=ErrVec.*(-1);  %These are vectors
Em=2*sum(temp1); Eb=2*sum(temp2);        %These scalars make up gradient

% Step 3A: Adjust the step size using backtracking line search
flag=true;
while flag 
	temp=[m;b]-alpha*[Em;Eb];
        LHS=sum(temp.*temp);
        RHS=Error(i)-(alpha/2)*(Em^2+Eb^2);
        if LHS<=RHS
          flag=false;
          break
        else
          alpha=alpha/2;
        end
end  %End of while loop for step size
 
% Uncomment if you want to see the step sizes:
%fprintf('Step size is %f\n',alpha);

% Step 4: Adjust the parameters using gradient descent.
m=m-alpha*Em;
b=b-alpha*Eb;

% Stop if the gradient is very close to zero
fprintf('Gradient is %f\n',Em^2+Eb^2);
if (Em^2+Eb^2)<=tol
  fprintf('Solution found in %d steps\n',i)
  break
end


end

%% Closing:  We'll visualize our results:

figure(2)
plot(Error)

figure(1)
hold on
t=linspace(min(x),max(x));
z=m*t+b;
plot(t,z,'r-');
hold off