%%%% 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=50;                              % 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)*4.5;
            R1=randn(N,2)-ones(N,2)*1.5;         
            R=[R0;R1];
            
            figure(1)
            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-.')
            plot([0,0],[Ymin,Ymax],'b-.')
            text(Xmin+0.3,Ymax-0.5,'R0: *');
            text(Xmin+0.3,Ymax-1.5,'R1: x');
            
        % Produce original W and plot classfying line
        W(1)=-rand(1,1);
        W(2)=rand(1,1);
        W(3)=rand(1,1)*3;
        y0=(-W(3)-W(1)*Xmin)/W(2);
        y1=(-W(3)-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)','               ','W(3)','               '])

     
       %% Supervised learning   
        k=1;
        dalt=1;
     while (dalt>rpr)&(k<M)     
            
         % Learning with R
            err=0;             % Estimation of square errors in current step
            grad=[0,0,0];      % Estimation of the grad in the step
                for n=1:2*N
                    X=[R(n,1),R(n,2),1];
                    y=W*X';
                    if n<=N
                        d=1;
                    else
                        d=-1;
                    end
                    err=err+(d-y)^2;
                    grad=grad+(y-d)*X;
                end
                e(k)=err/(2*N);
                grad=grad/(2*N);
                W=W-alf*grad;
                if k>1
                    dalt=abs(e(k)-e(k-1))/e(k);
                disp([num2str(k),'                   ',num2str(e(k-1)),'            ',num2str(dalt),'                  ',num2str(W(1)),'            ',num2str(W(2)),'               ',num2str(W(3)),'               '])
               end
                k=k+1;
            end
            
            
            % Plot end line
            y0=(-W(3)-W(1)*Xmin)/W(2);
            y1=(-W(3)-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),1];
                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),1];
                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)])