%%%% 2 classes non-linear-classfing


%% Produce sample set and original classfying line
% Produce samples: R0,R1
close all
clear all
M=500;                               % Maxmum allowably ierative times
N=500;                              % Nomber of total samples
alf=0.01;                           % Step length
rpr=0.0001;                          % Precision

            figure(1)
            hold on
            whitebg(1,'k')
            figure(2)
            whitebg(2,'k')

        % Produce and plot sample set R0 and R1, learning samiple set R=R0+R1
            R0=randn(N,2)+ones(N,2);
            R1=randn(N,2)-ones(N,2);         
            R=[R0;R1];
            
            figure(1)                 %在圖1畫點
            plot(R0(:,1),R0(:,2),'m*')
            plot(R1(:,1),R1(:,2),'gx')
        % Plot axies
                        Xmax=max([R0(:,1);R1(:,1)]);
                        Xmin=min([R0(:,1);R1(:,1)]);
                        Ymax=max([R0(:,2);R1(:,2)]);
                        Ymin=min([R0(:,2);R1(:,2)]);
                        Xmax=ceil(Xmax);
                        Xmin=floor(Xmin);
                        Ymax=ceil(Ymax);
                        Ymin=floor(Ymin);
            plot([Xmin,Xmax],[0,0],'b-.')  %畫坐標系
            plot([0,0],[Ymin,Ymax],'b-.')
            text(Xmin+0.3,Ymax-0.5,'R0: *'); %標注R
            text(Xmin+0.3,Ymax-0.9,'R1: x');
            
        % Produce original W and plot classfying line
        W(1)=-rand(1,1);
        W(2)=rand(1,1);
        W=W/sqrt(W(1)^2+W(2)^2);  %化為單位向量
        y0=-W(1)*Xmin/W(2);
        y1=-W(1)*Xmax/W(2);
        figure(1)
        plot([Xmin,Xmax],[y0,y1],'y-.','linewidth',3)     % Starting
        axis([Xmin,Xmax,Ymin,Ymax])
        input('Press enter key to continue--'); 
        disp(['Generation','          ','Error','          ','delta-Error','                W=   ','W(1)','            ','W(2)','               '])

      
        %% Supervised learning   
        k=1;
        dalt=1;
     while (dalt>rpr)&(k<M)     %  rpr:Relative error , M: allowable loop number   
            
         % Learning with R
            err=0;              % Estimation of square errors in current step
            grad=[0,0];         % Estimation of the grad in the step
                for n=1:2*N                 % N: Learning set size
                    X=[R(n,1),R(n,2)];      % R: N by 2 learning set
                    y=W*X';                 % y: output of current input X
                    if n<=N                 % Get designated class value of current X
                        d=1;
                    else
                        d=-1;
                    end
                    err=err+(d-y)^2;        % Get and cumulating errors by each sample for judgement the error
                    grad=grad+(y-d)*X;      % Get and cumulating grads
                end
                e(k)=err/(2*N);             %
                grad=grad/(2*N);            % Averging the summation of grads 
                W=W-alf*grad;               % to modify threshold matrix
                if k>1                      % Display algorithm track
                    dalt=abs(e(k)-e(k-1))/e(k);
                    disp([num2str(k),'                   ',num2str(e(k-1)),'            ',num2str(dalt),'                  ',num2str(W(1)),'            ',num2str(W(2)),'               '])
                end
                k=k+1;
     end
            
            
            % Plot end line
            y0=-W(1)*Xmin/W(2);
            y1=-W(1)*Xmax/W(2);
            figure(1)
            plot([Xmin,Xmax],[y0,y1],'y','linewidth',3)     % Starting
            axis([Xmin,Xmax,Ymin,Ymax])
            
         % Learning loop end   
            figure(2)   % Plot error line
            whitebg
            plot(e)
        
        % Make signs in the wrong classified samples
            figure(1)
            e1=0;
            for n=1:N
                X=[R(n,1),R(n,2)];
                y=W*X';
                if y<0
                    plot(R(n,1),R(n,2),'rs')
                    e1=e1+1;
                end
            end
            e2=0;
            for n=N+1:2*N
                X=[R(n,1),R(n,2)];
                y=W*X';
                if y>0
                    plot(R(n,1),R(n,2),'bo')
                    e2=e2+1;
                end
            end
            disp(['Weight vector W=[','  ',num2str(W),']'])
            disp(['Wrong classfied samples with R0 and R1 are ',num2str(e1),' and ',num2str(e2)])