function_SVM_SMO.m

%{
SVM implemented by SMO(sequential minization optimization?
%}
function [w,b] = function_SVM_SMO(x1,x2,C,mini)
    x = [x1,x2];
    n = size(x,2);
    y = zeros(1,n);
    y(1,1:size(x1,2)) = 1;
    y(1,size(x1,2)+1:n) = -1;
    alp = zeros(1,n);
    
    % yi * yj * xi' * xj
    x_y = zeros(n,n);
    for i = 1 : n
       for j = 1 : n
           x_y(i,j) = y(1,i) * y(1,j) * x(:,i)' * x(:,j);
       end
    end
    
    %init w,b
    w = function_SVM_w(alpha, x, y);
    b = function_SVM_b(alpha, y, x, C, x_y);
    
    %the distance from satisfied kkt
    delta = zeros(1,n);
    % satisfied kkt
    while 1 = 1
       k = 0;
       type = 0;% type 1: 0<alp<C,type 2: 0=alp,type 3: alp=C,
        %0<alp<C       
        for i = 1 : n
           sum = y(1,i) * (w' * x(:,i) + b);
           if 0 < alp(1,i) && alp(1,i) < C
              if abs(sum - 1) >= min
                  type = 1;
                  k = i;
                  break;
              end
           end
        end
        % alpha = 0
        if type == 0
             for i = 1 : n
               sum = y(1,i) * (w' * x(:,i) + b);
               if alp(1,i) == 0
                  if sum < 1
                      type = 2;
                      k = i;
                      break;
                  end
               end
            end 
        end
        % alpha = C
        if type == 0
             for i = 1 : n
               sum = y(1,i) * (w' * x(:,i) + b);
               if abs(alp(1,i) - C) < mini
                  if sum >= 1
                      type = 3;
                      k = i;
                      break;
                  end
               end
            end 
        end
        
        % all satisfied kkt
        if type == 0
            break;
        end
        
        % chose k,k+1
        k_1 = mod(k,n) + 1;
        
        if type == 1
           alpha(1,k) 
        end
    end
end