target = desired output vector
point = training point matrix

procedure takeStep(i1,i2)
   if(i1==i2) return 0
   alph1 = Lagrange multiplier for i1
   y1 = target[i1]
   E1 = SVM output on point[i1] - y1(check in error cache)
   s=y1*y2
   Compute L ,H
   if(L==H)
       return 0
   k11 = kernel(point[i1],point[i1])
   k12 = kernel(point[i1],point[i2])
   k22 = kernel(point[i2],point[i2])
   eta = 2*k12-k11-k22
   if(eta<0)
     { a2=alph2 - y2*(E1-E2)/eta
        if(a2<L) a2=L
        else if(a2>H) a2=H
      }
            else
       {Lobj=objective function at a2=L
        Hobj=objective function at a2=H
        if(Lobj>Hobj+eps)
            a2=L
        else if(Lobj<Hobj-eps)
             a2=H
            else
               a2=alph2
        }
        if(|a2-alpha2|<eps*(a2+alpha2+eps))
            return 0
          a1=alpha1+s*(alpha2-a2)
       Update threshold to reflect change in Lagrange multipliers
       Update weight vector to reflect change in a1&a2,if linear SVM
       Update error cache using new Lagrange multipliers
       Store a1 in the alpha array 
       Store a2 in the alpha array
       return 1
       endprocedure
       
       procedure examineExample(i2)
         y2=target[i2]
         alpha2=Lagrange multiplier for i2
         E2=SVM output on point[i2]-y2(check in error cache)
         r2=E2*y2
         if((r2<-tol&&alph2<C)||(r2>tol&&alph2>0))
          {if(number of non-zero&non-C alpha>1)
              {i1=result of second choice heuristic
                 if takeStep(i1,i2)
                   return 1
              }
            loop over all possible i1,starting at random point
            {i1=identity of current alpha
             if takeStep(i1,i2)
              return 1
             }
            }
            return 0
            endprocedure
            
            main routine:
               initialize alpha array to all zero
               initialize threshold to zero
               numChange=0
               examineAll=1
               while(numChange>0|examineAll)
                   {numChanged =0
                     if(examineAll)
                       loop I over all training examples
                         numChanged+=examineExample(I)
                      if(examineAll==1)
                          examineAll=0
                      else if(numChanged==0)
                         examineAll=1
                      }