% ***** LEAST-SQUARES 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

X=[];
Y=[];
H=[];
THETA1=[];
THETA2=[];

% Read in data points
S = readtable("simulatedDegradationData.csv", "Delimiter", ",", "ReadVariableNames", true);

for n = 1:7
    
    count = 2;
    
    x = table2array(S((((n-1)*20+1):(n*20)), 3))./max(table2array(S((((n-1)*20+1):(n*20)), 3)));
    y = table2array(S((((n-1)*20+1):(n*20)), 4))./max(table2array(S((((n-1)*20+1):(n*20)), 4)));
    
    % Initialize parameters
    theta(1) = 1.1;
    theta(2) = 1.1;
    
    % Initialize the "momentum" alpha
    alpha = [0.1 1.1];
    
    m = length(y);
    
    h = theta(1)+theta(2).*x;
    
    J(1) = (1/m).*sum(h-log(y)).^2;
    
    e=1;
    
    while (e > 0.00001)
        
        theta(1) = theta(1)-alpha(1).*(2/m).*sum((h-log(y)));
        theta(2) = theta(2)-alpha(2).*(2/m).*sum((h-log(y)).*x);
        h = theta(1)+theta(2).*x;
        J(count) = (1/m).*sum((h-log(y)).^2);
        
        e = abs(J(count)-J(count-1));
        count = count+1;
        set(gcf,'Color','white')
        
        subplot(2,1,1)
        plot(x, log(y), '.','LineWidth',2)
        hold on
        if (n > 1)
            plot(X, Y, '+','LineWidth',2)
            plot(X, H, '-','LineWidth',2)
        end
        title('Exponential Curve Fit via Linear Least Squares','fontsize',11,'fontweight','b')
        xlabel('Normalized Segment Number (Qty 20)','fontsize',10)
        ylabel('Normalized 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([-0.1 1.1 -2.1 1.1])
        hold on
        plot(x, h, 'o','LineWidth',1)
        pause(0.1)
        hold off
        
        subplot(2,1,2)
        plot(2:(count-1),J(2:(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([0 100 0 0.1])
        hold off
        
    end
    
    X = [X x];
    Y = [Y log(y)];
    H = [H h];
    THETA1 = [THETA1 theta(1)]
    THETA2 = [THETA2 theta(2)]
    
end