function [weight1,weight2,LF]=PNE_show_LF(feature1,feature2,class_studied,type_of_loss_function,K)
  name_of_file=PNC_BinaryDataset(class_studied);
  M=100;
  S=load('name_of_file');
  %weigth1_max=1/min(S.X(:,feature1));
  %weigth1_min=1/max(S.X(:,feature1));
  %weight1_=weight1_min+1/M*(1:M)*(weight1_max-weight1_min);
  %weigth2_max=1/min(S.X(:,feature2));
  %weigth2_min=1/max(S.X(:,feature2));
  %weight2_=weight2_min+1/M*(1:M)*(weight2_max-weight2_min);
  %%%Correction
  weigth1_max=1/min(S.X(:,feature1));
  weigth2_max=1/min(S.X(:,feature2));
  weight1_=-weight1_max+2/M*(1:M)*weight1_max;
  weight2_=-weight2_max+2/M*(1:M)*weight2_max;
  [weight1,weight2]=ndgid(weight1_,weight2_);
  info.intercept=1;
  info.weights=zeros(1,S.metadata.F);
  for ind1=1:size(weight1,1)
    for ind2=1:size(weight,2)
      LF=0;
      for n=1:size(S.X,1)
        info.weights(feature1)=weight1(ind1,ind2);
        y_hat=PND_predict1(info,S.X(n,:));
        y_hat_value=sum(info.weights.*S.X(n,:)+info.intercept);
        y=S.Y(n);
        if strcmp(type_of_loss_function,'mean_square')
          LF=LF+(y-y_hat_value)^2;
        else 
          LF=LF+(y-y_hat)^2;
        end
      end
      LF=LF/size(S.X,1);
    end
  end
end

function  info=PNE_train1()
  S=load('training.mat');
  T_max=1000;
  r=0.01;
  precision=0.1; 
  Ae=zeros(S.metadata.F+1,1)
  for t=1:T_max
    Y_hat=zeros(size(S.Y,1),1); 
    for n=1:size(S.X,1)
      x=S.X(n,:);
      info.intercept=Ae(end);
      info.weights=Ae(1:end-1).';
      Y_hat(n)=PND_predict1(info,x);
    end
    if mean(abs(Y_hat-Y)<precision
      return;
    end
    Xe=[S.X ones(size(S.X,1),1)];
    Ae=Ae-r*Xe.'*(Y_hat-Y);
  end
end

function y_hat=PNE_predict1(info,x)
  h_tilde=(x*info.weights.').'
  [val,ind]=max(h_tilde);
  y_hat=ind;
end

function info=PNE_train2()
  S='training.mat'; %multiclass context
  info.intercept=zeros(0,1);
  info.weights=zeros(0,S.metadata.F);
  for c=1:S.metadata.C
    name_of_file=PNC_BinaryDataset(c);
    copy([name_of_file,'.mat'],'training_B.mat');
    info_B=PND_train3();
    info.intercept=[info.intercept; info_B.intercept];
    info.weights=[info.weights; info_B.weights];
  end
end


function info=PNE_train3()
  S='training.mat'; %multiclass context
  info.intercept=zeros(0,1);
  info.weights=zeros(0,S.metadata.F);
  for c=1:S.metadata.C
    name_of_file=PNC_BinaryDataset(c);
    copy([name_of_file,'.mat'],'training_B.mat');
    info_B=PNE_train1();
    info.intercept=[info.intercept; info_B.intercept];
    info.weights=[info.weights; info_B.weights];
  end
end

function [im_test,im_train]=PNE_show(name_of_file,training_function,predicting_function)
  PNB_createSet(name_of_file);
  info=@training_function();
  S=load([name_of_file,'.mat']);
  N=S.size(1)*S.size(2);
  im_test=zeros(S.size);
  im_train=zeros(S.size);
  for n=1:N
    if is_it_training()
      im_test(n)=0;
      im_train(n)=@predicting_function(info,S.metadata.X_true(n,:));
    end
    if is_it_testing()
      im_train(n)=0;
      im_test(n)=@predicting_function(info,S.metadata.X_true(n,:));
    end
    if (~is_it_training())&(~is_it_testing())
      im_train(n)=0;
      im_testgin(n)=0;
    end
  end
end


%Matlab 
 h_tilde=[1,3,4,5]'

h_tilde =

     1
     3
     4
     5

>> [val,ind]=max(h_tilde)

val =

     5


ind =

     4

>> [val,ind]=min(h_tilde)

val =

     1


ind =

     1

>>