function [tree,p]=PNF_createRoot()
  tree.T=[0];
  tree.D(1).isLeaf=1;
  p=1;
  S=load('training.mat'); 
  tree.D(1).remaining_samples=1:size(S.X,1);
end
  
function [tree,p1,p2]=add2nodes(tree,p)
  tree.T=[tree.T p p];
  p1=length(tree.T)-1; 
  p2=length(tree.T);
  tree.D(p).isLeaf=0;
  tree.D(p1).isLeaf=1;
  tree.D(p2).isLeaf=1;
  tree.D(p1).remaining_samples=[];
  tree.D(p2).remaining_samples=[];
  for n=tree.D(p).remaining_samples
    s=tree.D(p).sign;
    l=tree.D(p).lambda;
    test=(x(tree.D(p).feature)*s<=l*s);
    if test 
      tree.D(p1).remaining_samples=[tree.D(p1).remaining_samples n];
    else 
      tree.D(p2).remaining_samples=[tree.D(p1).remaining_samples n];
    end
  end
  tree.D(p1).remaining_samples
end

function  tree=PNF_fillNode(tree,p,feature,lambda,s)
  tree.D(p).isLeaf=0;
  tree.D(p).feature=feature;
  tree.D(p).sign=s;
  tree.D(p).lambda=lambda;
end

function tree=PNF_fillLeaf(tree,p,class)
  tree.D(p).class=class;
  tree.D(p).isLeaf=1;
end


function p=PNF_findRoot(tree)
  p=find(tree.T==0);
end

function [test,c]=PNF_isLeaf(tree,p)
  if tree.D(p).isLeaf 
    test=1; 
    c=tree.D(p).class;
  else
    test=0; 
    c=NaN; 
  end
end

function p_new=PNF_child_of(tree,p,x)
  s=tree.D(p).sign;
  l=tree.D(p).lambda;
  test=(x(tree.D(p).feature)*s<=l*s);
  p_l=find(tree.T==p);
  if test 
    p_new=min(p_l);
  else 
    p_new=max(p_l);
  end
end




function info=PNF_train1()
  [tree,p]=PNF_createRoot();
  S=load('training.mat');
  counter=0; 
  while(1)
    counter=counter+1; 
    if counter>50 break; end
    p=ceil(rand(1)*length(tree.T));
    if ~PNF_isLeaf(tree,p) continue, end
    if length(tree.T(p).remaining_samples)<=3 continue, end
    lambda_min=min(S.X(tree.T(p).remaining_samples));
    lambda_max=max(S.X(tree.T(p).remaining_samples));
    lambda=lambda_min+rand(1)*(lambda_max-lambda_min);
    tree=PNF_fillNode(tree,p,ceil(rand(1)*S.metadata.F),lambda,ceil(rand(1)>0.5));
  end
  for p=1:length(tree.T)
    if PNF_isLeaf(tree,p)
      Y=S.Y(tree.T(p).remaining_samples);
      labels=unique(Y);
      count=zeros(1,length(labels));
      for l=1:length(labels)
        count(l)=sum(Y==labels(l));
      end
      [val,c_]=max(count);
      tree.D(p).class=labels(c_);
    end
  end
  info.tree=tree;
end


function y_hat=PNF_predict1(info,x)
  p=PNF_find_root(info.tree);
  while (1)
    [test,c]=PNF_isLeaf(tree,p);
    if test 
      y_hat=c; break;
    end
    p=PNF_child_of(tree,p,x);
  end
end

function score=PNF_score1(info,name_of_file,predict_function)
  S=load([name_of_file,'.mat']); 
  Y_hat=zeros(size(S.X,1),1);
  Y=S.Y;
  for n=1:size(S.X,1)
    Y_hat(n)=PNF_predict1(info,x);
  end
  ....
end


function info=PNF_train2()
  score_OA_max=-Inf;
  info_best=[];
  exp_n=500;
  for exp=1:exp_n
    info=PNF_train1();
    score=PNF_score1(info,'training',@PNF_predict1)
    if score.overall_accuracy>score_OA_max
      score_OA_max=score.overall_accuracy;
      info_best=info;
    end
  end
  info=info_best;
end