root/applications/robust/robustlib.h @ 1214

/*!
  \file
  \brief Robust Bayesian auto-regression model
  \author Jan Sindelar.
*/

#ifndef ROBUST_H
#define ROBUST_H

#include <stat/exp_family.h>
#include <limits>
#include <vector>
#include <list>
#include <algorithm>
        
using namespace bdm;
using namespace std;
using namespace itpp;

const double max_range = numeric_limits<double>::max()/10e-5;

enum actions {MERGE, SPLIT};

class polyhedron;
class vertex;

/// A class describing a single polyhedron of the split complex. From a collection of such classes a Hasse diagram
/// of the structure in the exponent of a Laplace-Inverse-Gamma density will be created.
class polyhedron
{
        /// A property having a value of 1 usually, with higher value only if the polyhedron arises as a coincidence of
        /// more than just the necessary number of conditions. For example if a newly created line passes through an already
        /// existing point, the points multiplicity will rise by 1.
        int multiplicity;       

        int split_state;

        int merge_state;

        

public:
        /// A list of polyhedrons parents within the Hasse diagram.
        list<polyhedron*> parents;

        /// A list of polyhedrons children withing the Hasse diagram.
        list<polyhedron*> children;

        /// All the vertices of the given polyhedron
        list<vertex*> vertices;

        /// A list used for storing children that lie in the positive region related to a certain condition
        list<polyhedron*> positivechildren;

        /// A list used for storing children that lie in the negative region related to a certain condition
        list<polyhedron*> negativechildren;

        /// Children intersecting the condition
        list<polyhedron*> neutralchildren;

        list<polyhedron*> totallyneutralgrandchildren;

        list<polyhedron*> totallyneutralchildren;

        bool totally_neutral;

        list<polyhedron*> mergechildren;

        polyhedron* positiveparent;

        polyhedron* negativeparent;

        polyhedron* next_poly;

        polyhedron* prev_poly;

        int message_counter;

        /// List of triangulation polyhedrons of the polyhedron given by their relative vertices. 
        list<list<vertex*>> triangulations;

        /// A list of relative addresses serving for Hasse diagram construction.
        list<int> kids_rel_addresses;

        /// Default constructor
        polyhedron()
        {
                multiplicity = 1;

                message_counter = 0;

                totally_neutral = NULL;
        }
        
        /// Setter for raising multiplicity
        void raise_multiplicity()
        {
                multiplicity++;
        }

        /// Setter for lowering multiplicity
        void lower_multiplicity()
        {
                multiplicity--;
        }
        
        /// An obligatory operator, when the class is used within a C++ STL structure like a vector
        int operator==(polyhedron polyhedron2)
        {
                return true;
        }

        /// An obligatory operator, when the class is used within a C++ STL structure like a vector
        int operator<(polyhedron polyhedron2)
        {
                return false;
        }

        

        void set_state(double state_indicator, actions action)
        {
                switch(action)
                {
                        case MERGE:
                                merge_state = (int)sign(state_indicator);                       
                        break;
                        case SPLIT:
                                split_state = (int)sign(state_indicator);
                        break;
                }
        }

        int get_state(actions action)
        {
                switch(action)
                {
                        case MERGE:
                                return merge_state;                     
                        break;
                        case SPLIT:
                                return split_state;
                        break;
                }
        }

        int number_of_children()
        {
                return children.size();
        }

        
};

/// A class for representing 0-dimensional polyhedron - a vertex. It will be located in the bottom row of the Hasse
/// diagram representing a complex of polyhedrons. It has its coordinates in the parameter space.
class vertex : public polyhedron
{
        /// A dynamic array representing coordinates of the vertex
        vec coordinates;        

        

public:



        /// Default constructor
        vertex();

        /// Constructor of a vertex from a set of coordinates
        vertex(vec coordinates)
        {
                this->coordinates = coordinates;
        }

        /// A method that widens the set of coordinates of given vertex. It is used when a complex in a parameter
        /// space of certain dimension is established, but the dimension is not known when the vertex is created.
        void push_coordinate(double coordinate)
        {
                coordinates = concat(coordinates,coordinate);
        }

        /// A method obtaining the set of coordinates of a vertex. These coordinates are not obtained as a pointer 
        /// (not given by reference), but a new copy is created (they are given by value).
        vec get_coordinates()
        {               
                return coordinates;
        }

                
};

/// A class representing a polyhedron in a top row of the complex. Such polyhedron has a condition that differitiates
/// it from polyhedrons in other rows. 
class toprow : public polyhedron
{
        
public:
        /// A condition used for determining the function of a Laplace-Inverse-Gamma density resulting from Bayesian estimation
        vec condition;

        /// Default constructor
        toprow(){};

        /// Constructor creating a toprow from the condition
        toprow(vec condition)
        {
                this->condition = condition;
        }

};

class condition
{       
public:
        vec value;      

        int multiplicity;

        condition(vec value)
        {
                this->value = value;
                multiplicity = 1;
        }
};

class c_statistic
{
        polyhedron* end_poly;
        polyhedron* start_poly;

public:
        vector<polyhedron*> rows;

        vector<polyhedron*> row_ends;

        c_statistic()
        {
                end_poly   = new polyhedron();
                start_poly = new polyhedron();
        };

        void append_polyhedron(int row, polyhedron* appended_start, polyhedron* appended_end)
        {
                if(row>((int)rows.size())-1)
                {
                        if(row>rows.size())
                        {
                                throw new exception("You are trying to append a polyhedron whose children are not in the statistic yet!");
                                return;
                        }

                        rows.push_back(end_poly);
                        row_ends.push_back(end_poly);
                }

                // POSSIBLE FAILURE: the function is not checking if start and end are connected

                if(rows[row] != end_poly)
                {
                        appended_start->prev_poly = row_ends[row];
                        row_ends[row]->next_poly = appended_start;                      
                                                
                }
                else if((row>0 && rows[row-1]!=end_poly)||row==0)
                {
                        appended_start->prev_poly = start_poly;
                        rows[row]= appended_start;                      
                }
                else
                {
                        throw new exception("Wrong polyhedron insertion into statistic: missing intermediary polyhedron!");
                }

                appended_end->next_poly = end_poly;
                row_ends[row] = appended_end;
        }

        void append_polyhedron(int row, polyhedron* appended_poly)
        {
                append_polyhedron(row,appended_poly,appended_poly);
        }

        void insert_polyhedron(int row, polyhedron* inserted_poly, polyhedron* following_poly)
        {               
                if(following_poly != end_poly)
                {
                        inserted_poly->next_poly = following_poly;
                        inserted_poly->prev_poly = following_poly->prev_poly;

                        if(following_poly->prev_poly == start_poly)
                        {
                                rows[row] = inserted_poly;
                        }
                        else
                        {                               
                                inserted_poly->prev_poly->next_poly = inserted_poly;                                                            
                        }

                        following_poly->prev_poly = inserted_poly;
                }
                else
                {
                        this->append_polyhedron(row, inserted_poly);
                }               
        
        }


        

        void delete_polyhedron(int row, polyhedron* deleted_poly)
        {
                if(deleted_poly->prev_poly != start_poly)
                {
                        deleted_poly->prev_poly->next_poly = deleted_poly->next_poly;
                }
                else
                {
                        rows[row] = deleted_poly->next_poly;
                }

                if(deleted_poly->next_poly!=end_poly)
                {
                        deleted_poly->next_poly->prev_poly = deleted_poly->prev_poly;
                }
                else
                {
                        row_ends[row] = deleted_poly->prev_poly;
                }

                

                deleted_poly->next_poly = NULL;
                deleted_poly->prev_poly = NULL;                                 
        }

        int size()
        {
                return rows.size();
        }

        polyhedron* get_end()
        {
                return end_poly;
        }

        polyhedron* get_start()
        {
                return start_poly;
        }

        int row_size(int row)
        {
                if(this->size()>row && row>=0)
                {
                        int row_size = 0;
                        
                        for(polyhedron* row_poly = rows[row]; row_poly!=end_poly; row_poly=row_poly->next_poly)
                        {
                                row_size++;
                        }

                        return row_size;
                }
                else
                {
                        throw new exception("There is no row to obtain size from!");
                }
        }
};


//! Conditional(e) Multicriteria-Laplace-Inverse-Gamma distribution density
class emlig // : eEF
{

        /// A statistic in a form of a Hasse diagram representing a complex of convex polyhedrons obtained as a result
        /// of data update from Bayesian estimation or set by the user if this emlig is a prior density
        c_statistic statistic;

        vector<list<polyhedron*>> for_splitting;
                
        vector<list<polyhedron*>> for_merging;

        list<condition*> conditions;

        double normalization_factor;

        void alter_toprow_conditions(vec condition, bool should_be_added)
        {
                for(polyhedron* horiz_ref = statistic.rows[statistic.size()-1];horiz_ref!=statistic.get_end();horiz_ref=horiz_ref->next_poly)
                {
                        double product = 0;

                        list<vertex*>::iterator vertex_ref = horiz_ref->vertices.begin();

                        do
                        {
                                product = (*vertex_ref)->get_coordinates()*condition;
                        }
                        while(product == 0);

                        if((product>0 && should_be_added)||(product<0 && !should_be_added))
                        {
                                ((toprow*) horiz_ref)->condition += condition;
                        }
                        else
                        {
                                ((toprow*) horiz_ref)->condition -= condition;
                        }                               
                }
        }


        void send_state_message(polyhedron* sender, vec toadd, vec toremove, int level)
        {                       

                bool shouldmerge = (toremove.size() != 0);
                bool shouldsplit    = (toadd.size() != 0);
                
                if(shouldsplit||shouldmerge)
                {
                        for(list<polyhedron*>::iterator parent_iterator = sender->parents.begin();parent_iterator!=sender->parents.end();parent_iterator++)
                        {
                                polyhedron* current_parent = *parent_iterator;

                                current_parent->message_counter++;

                                bool is_last = (current_parent->message_counter == current_parent->number_of_children());

                                if(shouldmerge)
                                {
                                        int child_state  = sender->get_state(MERGE);
                                        int parent_state = current_parent->get_state(MERGE);

                                        if(parent_state == 0)
                                        {
                                                current_parent->set_state(child_state, MERGE);

                                                if(child_state == 0)
                                                {
                                                        current_parent->mergechildren.push_back(sender);
                                                }
                                        }
                                        else
                                        {
                                                if(child_state == 0)
                                                {
                                                        if(parent_state > 0)
                                                        {
                                                                sender->positiveparent = current_parent;
                                                        }
                                                        else
                                                        {
                                                                sender->negativeparent = current_parent;
                                                        }
                                                }
                                        }

                                        if(is_last)
                                        {
                                                if(parent_state > 0)
                                                {
                                                        for(list<polyhedron*>::iterator merge_child = current_parent->mergechildren.begin(); merge_child != current_parent->mergechildren.end();merge_child++)
                                                        {
                                                                (*merge_child)->positiveparent = current_parent;
                                                        }
                                                }

                                                if(parent_state < 0)
                                                {
                                                        for(list<polyhedron*>::iterator merge_child = current_parent->mergechildren.begin(); merge_child != current_parent->mergechildren.end();merge_child++)
                                                        {
                                                                (*merge_child)->negativeparent = current_parent;
                                                        }
                                                }

                                                if(parent_state == 0)
                                                {
                                                        for_merging[level+1].push_back(current_parent);
                                                }

                                                current_parent->mergechildren.clear();
                                        }

                                        
                                }

                                if(shouldsplit)
                                        {
                                                current_parent->totallyneutralgrandchildren.insert(current_parent->totallyneutralgrandchildren.end(),sender->totallyneutralchildren.begin(),sender->totallyneutralchildren.end());

                                                switch(sender->get_state(SPLIT))
                                                {
                                                case 1:
                                                        current_parent->positivechildren.push_back(sender);     
                                                break;
                                                case 0:
                                                        current_parent->neutralchildren.push_back(sender);

                                                        if(current_parent->totally_neutral == NULL)
                                                        {
                                                                current_parent->totally_neutral = sender->totally_neutral;
                                                        }
                                                        else
                                                        {
                                                                current_parent->totally_neutral = current_parent->totally_neutral && sender->totally_neutral;
                                                        }

                                                        if(sender->totally_neutral)
                                                        {
                                                                current_parent->totallyneutralchildren.push_back(sender);
                                                        }
                                                        
                                                break;
                                                case -1:
                                                        current_parent->negativechildren.push_back(sender);
                                                break;
                                                }

                                                if(is_last)
                                                {
                                                        unique(current_parent->totallyneutralgrandchildren.begin(),current_parent->totallyneutralgrandchildren.end());

                                                        if((current_parent->negativechildren.size()>0&&current_parent->positivechildren.size()>0)||
                                                                                                                (current_parent->neutralchildren.size()>0&&current_parent->totally_neutral==false))
                                                        {                                                               
                                                                
                                                                        for_splitting[level+1].push_back(current_parent);
                                                                
                                                                        current_parent->set_state(0, SPLIT);
                                                        }
                                                        else
                                                        {
                                                                if(current_parent->negativechildren.size()>0)
                                                                {
                                                                        current_parent->set_state(-1, SPLIT);

                                                                        ((toprow*)current_parent)->condition-=toadd;
                                                                }
                                                                else if(current_parent->positivechildren.size()>0)
                                                                {
                                                                        current_parent->set_state(1, SPLIT);

                                                                        ((toprow*)current_parent)->condition+=toadd;
                                                                }
                                                                else
                                                                {
                                                                        current_parent->raise_multiplicity();                                                           
                                                                }

                                                                current_parent->positivechildren.clear();
                                                                current_parent->negativechildren.clear();
                                                                current_parent->neutralchildren.clear();
                                                                current_parent->totallyneutralchildren.clear();
                                                                current_parent->totallyneutralgrandchildren.clear();
                                                                current_parent->totally_neutral = NULL; 
                                                        }
                                                }
                                        }

                                        if(is_last)
                                        {
                                                send_state_message(current_parent,toadd,toremove,level+1);
                                        }
                        
                        }
                        
                }               
        }
        
public: 

        /// A default constructor creates an emlig with predefined statistic representing only the range of the given
        /// parametric space, where the number of parameters of the needed model is given as a parameter to the constructor.
        emlig(int number_of_parameters)
        {       

                create_statistic(number_of_parameters);

                for(int i = 0;i<statistic.size();i++)
                {
                        list<polyhedron*> empty_split;
                        list<polyhedron*> empty_merge;

                        for_splitting.push_back(empty_split);
                        for_merging.push_back(empty_merge);
                }
        }

        /// A constructor for creating an emlig when the user wants to create the statistic by himself. The creation of a
        /// statistic is needed outside the constructor. Used for a user defined prior distribution on the parameters.
        emlig(c_statistic statistic)
        {
                this->statistic = statistic;
        }

        void add_condition(vec toadd)
        {
                vec null_vector = "";

                add_and_remove_condition(toadd, null_vector);
        }

        void remove_condition(vec toremove)
        {
                vec null_vector = "";

                add_and_remove_condition(null_vector, toremove);
        
        }

        void add_and_remove_condition(vec toadd, vec toremove)
        {
                bool should_remove = (toremove.size() != 0);
                bool should_add    = (toadd.size() != 0);

                list<condition*>::iterator toremove_ref = conditions.end();
                bool condition_should_be_added = false;

                for(list<condition*>::iterator ref = conditions.begin();ref!=conditions.end();ref++)
                {
                        if(should_remove)
                        {
                                if((*ref)->value == toremove)
                                {
                                        if((*ref)->multiplicity>1)
                                        {
                                                (*ref)->multiplicity--;

                                                alter_toprow_conditions(toremove,false);

                                                should_remove = false;
                                        }
                                        else
                                        {
                                                toremove_ref = ref;                                                     
                                        }
                                }
                        }

                        if(should_add)
                        {
                                if((*ref)->value == toadd)
                                {
                                        (*ref)->multiplicity++;

                                        alter_toprow_conditions(toadd,true);

                                        should_add = false;
                                }
                                else
                                {
                                        condition_should_be_added = true;
                                }
                        }
                }

                if(toremove_ref!=conditions.end())
                {
                        conditions.erase(toremove_ref);
                }

                if(condition_should_be_added)
                {
                        conditions.push_back(new condition(toadd));
                }

                
                
                for(polyhedron* horizontal_position = statistic.rows[0];horizontal_position!=statistic.get_end();horizontal_position=horizontal_position->next_poly)
                {               
                        vertex* current_vertex = (vertex*)horizontal_position;
                        
                        if(should_add||should_remove)
                        {
                                vec appended_vec = current_vertex->get_coordinates();
                                appended_vec.ins(0,-1.0);

                                if(should_add)
                                {
                                        double local_condition = toadd*appended_vec;

                                        current_vertex->set_state(local_condition,SPLIT);

                                        if(local_condition == 0)
                                        {
                                                current_vertex->totally_neutral = true;

                                                current_vertex->raise_multiplicity();
                                        }                                       
                                }
                        
                                if(should_remove)
                                {
                                        double local_condition = toremove*appended_vec;

                                        current_vertex->set_state(local_condition,MERGE);

                                        if(local_condition == 0)
                                        {
                                                for_merging[0].push_back(current_vertex);
                                        }
                                }                               
                        }

                        send_state_message(current_vertex, toadd, toremove, 0);         
                        
                }

                if(should_add)
                {
                        int k = 1;

                        vector<list<polyhedron*>>::iterator beginning_ref = ++for_splitting.begin();

                        for(vector<list<polyhedron*>>::iterator vert_ref = beginning_ref;vert_ref<for_splitting.end();vert_ref++)
                        {                       

                                for(list<polyhedron*>::reverse_iterator split_ref = vert_ref->rbegin();split_ref != vert_ref->rend();split_ref++)
                                {
                                        polyhedron* new_totally_neutral_child;

                                        polyhedron* current_polyhedron = (*split_ref);
                                        
                                        if(vert_ref == beginning_ref)
                                        {
                                                vec coordinates1 = ((vertex*)(*(current_polyhedron->children.begin())))->get_coordinates();                                             
                                                vec coordinates2 = ((vertex*)(*(current_polyhedron->children.begin()++)))->get_coordinates();
                                                coordinates2.ins(0,-1.0);
                                                
                                                double t = (-toadd*coordinates2)/(toadd(1,toadd.size()-1)*coordinates1)+1;

                                                vec new_coordinates = coordinates1*t+(coordinates2(1,coordinates2.size()-1)-coordinates1);                                      

                                                vertex* neutral_vertex = new vertex(new_coordinates);

                                                new_totally_neutral_child = neutral_vertex;
                                        }
                                        else
                                        {
                                                toprow* neutral_toprow = new toprow();

                                                new_totally_neutral_child = neutral_toprow;
                                        }
                                        
                                        new_totally_neutral_child->children.insert(new_totally_neutral_child->children.end(),
                                                                                                                current_polyhedron->totallyneutralgrandchildren.begin(),
                                                                                                                                current_polyhedron->totallyneutralgrandchildren.end());

                                        toprow* positive_poly = new toprow(((toprow*)current_polyhedron)->condition+toadd);
                                        toprow* negative_poly = new toprow(((toprow*)current_polyhedron)->condition-toadd);

                                        positive_poly->children.push_back(new_totally_neutral_child);
                                        negative_poly->children.push_back(new_totally_neutral_child);

                                        positive_poly->parents.insert(positive_poly->parents.end(),
                                                                                                current_polyhedron->parents.begin(),
                                                                                                                current_polyhedron->parents.end());

                                        negative_poly->parents.insert(negative_poly->parents.end(),
                                                                                                current_polyhedron->parents.begin(),
                                                                                                                current_polyhedron->parents.end());

                                        positive_poly->children.insert(positive_poly->children.end(),
                                                                                                current_polyhedron->positivechildren.begin(),
                                                                                                                        current_polyhedron->positivechildren.end());

                                        negative_poly->children.insert(negative_poly->children.end(),
                                                                                                current_polyhedron->negativechildren.begin(),
                                                                                                                        current_polyhedron->negativechildren.end());

                                        statistic.append_polyhedron(k-1, new_totally_neutral_child);
                                        
                                        statistic.insert_polyhedron(k, positive_poly, current_polyhedron);
                                        statistic.insert_polyhedron(k, negative_poly, current_polyhedron);                                      

                                        statistic.delete_polyhedron(k, current_polyhedron);                             
                                }

                                k++;
                        }
                }

                vector<int> sizevector;
                for(int s = 0;s<statistic.size();s++)
                {
                        sizevector.push_back(statistic.row_size(s));
                }
        }

protected:

        /// A method for creating plain default statistic representing only the range of the parameter space.
    void create_statistic(int number_of_parameters)
        {
                // An empty vector of coordinates.
                vec origin_coord;       

                // We create an origin - this point will have all the coordinates zero, but now it has an empty vector of coords.
                vertex *origin = new vertex(origin_coord);

                // It has itself as a vertex. There will be a nice use for this when the vertices of its parents are searched in
                // the recursive creation procedure below.
                origin->vertices.push_back(origin);

                /*
                // As a statistic, we have to create a vector of vectors of polyhedron pointers. It will then represent the Hasse
                // diagram. First we create a vector of polyhedrons..
                list<polyhedron*> origin_vec;

                // ..we fill it with the origin..
                origin_vec.push_back(origin);

                // ..and we fill the statistic with the created vector.
                statistic.push_back(origin_vec);
                */

                statistic = *(new c_statistic());

                statistic.append_polyhedron(0, origin);

                // Now we have a statistic for a zero dimensional space. Regarding to how many dimensional space we need to 
                // describe, we have to widen the descriptional default statistic. We use an iterative procedure as follows:
                for(int i=0;i<number_of_parameters;i++)
                {
                        // We first will create two new vertices. These will be the borders of the parameter space in the dimension
                        // of newly added parameter. Therefore they will have all coordinates except the last one zero. We get the 
                        // right amount of zero cooridnates by reading them from the origin
                        vec origin_coord = origin->get_coordinates();                                           

                        // And we incorporate the nonzero coordinates into the new cooordinate vectors
                        vec origin_coord1 = concat(origin_coord,max_range);
                        vec origin_coord2 = concat(origin_coord,-max_range);

                        // Now we create the points
                        vertex *new_point1 = new vertex(origin_coord1);
                        vertex *new_point2 = new vertex(origin_coord2);
                        
                        //*********************************************************************************************************
                        // The algorithm for recursive build of a new Hasse diagram representing the space structure from the old
                        // diagram works so that you create two copies of the old Hasse diagram, you shift them up one level (points
                        // will be segments, segments will be areas etc.) and you connect each one of the original copied polyhedrons
                        // with its offspring by a parent-child relation. Also each of the segments in the first (second) copy is
                        // connected to the first (second) newly created vertex by a parent-child relation.
                        //*********************************************************************************************************


                        /*
                        // Create the vectors of vectors of pointers to polyhedrons to hold the copies of the old Hasse diagram
                        vector<vector<polyhedron*>> new_statistic1;
                        vector<vector<polyhedron*>> new_statistic2;
                        */

                        c_statistic* new_statistic1 = new c_statistic();
                        c_statistic* new_statistic2 = new c_statistic();

                        
                        // Copy the statistic by rows                   
                        for(int j=0;j<statistic.size();j++)
                        {
                                

                                // an element counter
                                int element_number = 0;

                                /*
                                vector<polyhedron*> supportnew_1;
                                vector<polyhedron*> supportnew_2;

                                new_statistic1.push_back(supportnew_1);
                                new_statistic2.push_back(supportnew_2);
                                */

                                // for each polyhedron in the given row
                                for(polyhedron* horiz_ref = statistic.rows[j];horiz_ref!=statistic.get_end();horiz_ref=horiz_ref->next_poly)
                                {       
                                        // Append an extra zero coordinate to each of the vertices for the new dimension
                                        // If vert_ref is at the first index => we loop through vertices
                                        if(j == 0)
                                        {
                                                // cast the polyhedron pointer to a vertex pointer and push a zero to its vector of coordinates
                                                ((vertex*) horiz_ref)->push_coordinate(0);
                                        }
                                        /*
                                        else
                                        {
                                                ((toprow*) (*horiz_ref))->condition.ins(0,0);
                                        }*/

                                        // if it has parents
                                        if(!horiz_ref->parents.empty())
                                        {
                                                // save the relative address of this child in a vector kids_rel_addresses of all its parents.
                                                // This information will later be used for copying the whole Hasse diagram with each of the
                                                // relations contained within.
                                                for(list<polyhedron*>::iterator parent_ref = horiz_ref->parents.begin();parent_ref != horiz_ref->parents.end();parent_ref++)
                                                {
                                                        (*parent_ref)->kids_rel_addresses.push_back(element_number);                                                    
                                                }                                               
                                        }

                                        // **************************************************************************************************
                                        // Here we begin creating a new polyhedron, which will be a copy of the old one. Each such polyhedron
                                        // will be created as a toprow, but this information will be later forgotten and only the polyhedrons
                                        // in the top row of the Hasse diagram will be considered toprow for later use.
                                        // **************************************************************************************************

                                        // First we create vectors specifying a toprow condition. In the case of a preconstructed statistic
                                        // this condition will be a vector of zeros. There are two vectors, because we need two copies of 
                                        // the original Hasse diagram.
                                        vec vec1(number_of_parameters+1);
                                        vec1.zeros();

                                        vec vec2(number_of_parameters+1);
                                        vec2.zeros();

                                        // We create a new toprow with the previously specified condition.
                                        toprow* current_copy1 = new toprow(vec1);
                                        toprow* current_copy2 = new toprow(vec2);                                       

                                        // The vertices of the copies will be inherited, because there will be a parent/child relation
                                        // between each polyhedron and its offspring (comming from the copy) and a parent has all the
                                        // vertices of its child plus more.
                                        for(list<vertex*>::iterator vertex_ref = horiz_ref->vertices.begin();vertex_ref!=horiz_ref->vertices.end();vertex_ref++)
                                        {
                                                current_copy1->vertices.push_back(*vertex_ref);
                                                current_copy2->vertices.push_back(*vertex_ref);                                         
                                        }
                                        
                                        // The only new vertex of the offspring should be the newly created point.
                                        current_copy1->vertices.push_back(new_point1);
                                        current_copy2->vertices.push_back(new_point2);
                                        
                                        // This method guarantees that each polyhedron is already triangulated, therefore its triangulation
                                        // is only one set of vertices and it is the set of all its vertices.
                                        current_copy1->triangulations.push_back(current_copy1->vertices);
                                        current_copy2->triangulations.push_back(current_copy2->vertices);
                                        
                                        // Now we have copied the polyhedron and we have to copy all of its relations. Because we are copying
                                        // in the Hasse diagram from bottom up, we always have to copy the parent/child relations to all the
                                        // kids and when we do that and know the child, in the child we will remember the parent we came from.
                                        // This way all the parents/children relations are saved in both the parent and the child.
                                        if(!horiz_ref->kids_rel_addresses.empty())
                                        {
                                                for(list<int>::iterator kid_ref = horiz_ref->kids_rel_addresses.begin();kid_ref!=horiz_ref->kids_rel_addresses.end();kid_ref++)
                                                {       
                                                        polyhedron* new_kid1 = new_statistic1->rows[j-1];
                                                        polyhedron* new_kid2 = new_statistic2->rows[j-1];

                                                        // THIS IS NOT EFFECTIVE: It could be improved by having the list indexed for new_statistic, but
                                                        // not indexed for statistic. Hopefully this will not cause a big slowdown - happens only offline.
                                                        if(*kid_ref)
                                                        {
                                                                for(int k = 1;k<=(*kid_ref);k++)
                                                                {
                                                                        new_kid1=new_kid1->next_poly;
                                                                        new_kid2=new_kid2->next_poly;
                                                                }
                                                        }
                                                        
                                                        // find the child and save the relation to the parent
                                                        current_copy1->children.push_back(new_kid1);
                                                        current_copy2->children.push_back(new_kid2);

                                                        // in the child save the parents' address
                                                        new_kid1->parents.push_back(current_copy1);
                                                        new_kid2->parents.push_back(current_copy2);
                                                }                                               

                                                // Here we clear the parents kids_rel_addresses vector for later use (when we need to widen the
                                                // Hasse diagram again)
                                                horiz_ref->kids_rel_addresses.clear();
                                        }
                                        // If there were no children previously, we are copying a polyhedron that has been a vertex before.
                                        // In this case it is a segment now and it will have a relation to its mother (copywise) and to the
                                        // newly created point. Here we create the connection to the new point, again from both sides.
                                        else
                                        {
                                                // Add the address of the new point in the former vertex
                                                current_copy1->children.push_back(new_point1);
                                                current_copy2->children.push_back(new_point2);

                                                // Add the address of the former vertex in the new point
                                                new_point1->parents.push_back(current_copy1);
                                                new_point2->parents.push_back(current_copy2);
                                        }

                                        // Save the mother in its offspring
                                        current_copy1->children.push_back(horiz_ref);
                                        current_copy2->children.push_back(horiz_ref);

                                        // Save the offspring in its mother
                                        horiz_ref->parents.push_back(current_copy1);
                                        horiz_ref->parents.push_back(current_copy2);    
                                                                
                                        
                                        // Add the copies into the relevant statistic. The statistic will later be appended to the previous
                                        // Hasse diagram
                                        new_statistic1->append_polyhedron(j,current_copy1);
                                        new_statistic2->append_polyhedron(j,current_copy2);
                                        
                                        // Raise the count in the vector of polyhedrons
                                        element_number++;                       
                                        
                                }
                                
                        }

                        /*
                        statistic.begin()->push_back(new_point1);
                        statistic.begin()->push_back(new_point2);
                        */

                        statistic.append_polyhedron(0, new_point1);
                        statistic.append_polyhedron(0, new_point2);

                        // Merge the new statistics into the old one. This will either be the final statistic or we will
                        // reenter the widening loop. 
                        for(int j=0;j<new_statistic1->size();j++)
                        {
                                /*
                                if(j+1==statistic.size())
                                {
                                        list<polyhedron*> support;
                                        statistic.push_back(support);
                                }
                                
                                (statistic.begin()+j+1)->insert((statistic.begin()+j+1)->end(),new_statistic1[j].begin(),new_statistic1[j].end());
                                (statistic.begin()+j+1)->insert((statistic.begin()+j+1)->end(),new_statistic2[j].begin(),new_statistic2[j].end());
                                */
                                statistic.append_polyhedron(j+1,new_statistic1->rows[j],new_statistic1->row_ends[j]);
                                statistic.append_polyhedron(j+1,new_statistic2->rows[j],new_statistic2->row_ends[j]);
                        }

                
                }

                /*
                vector<list<toprow*>> toprow_statistic;
                int line_count = 0;

                for(vector<list<polyhedron*>>::iterator polyhedron_ref = ++statistic.begin(); polyhedron_ref!=statistic.end();polyhedron_ref++)
                {
                        list<toprow*> support_list;
                        toprow_statistic.push_back(support_list);                                               

                        for(list<polyhedron*>::iterator polyhedron_ref2 = polyhedron_ref->begin(); polyhedron_ref2 != polyhedron_ref->end(); polyhedron_ref2++)
                        {
                                toprow* support_top = (toprow*)(*polyhedron_ref2);

                                toprow_statistic[line_count].push_back(support_top);
                        }

                        line_count++;
                }*/

                
                vector<int> sizevector;
                for(int s = 0;s<statistic.size();s++)
                {
                        sizevector.push_back(statistic.row_size(s));
                }
                
        }


        
        
};

/*

//! Robust Bayesian AR model for Multicriteria-Laplace-Inverse-Gamma density
class RARX : public BM
{
private:

        emlig posterior;

public:
        RARX():BM()
        {
        };

        void bayes(const itpp::vec &yt, const itpp::vec &cond = empty_vec)
        {
                
        }

};*/



#endif //TRAGE_H