root/applications/robust/robustlib.h @ 1396

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

#ifndef ROBUST_H
#define ROBUST_H

#include <stat/exp_family.h>
#include <itpp/itbase.h>
#include <itpp/base/random.h>
#include <map>
#include <limits>
#include <vector>
#include <list>
#include <set>
#include <algorithm>
        
using namespace bdm;
using namespace std;
using namespace itpp;

static Exponential_RNG ExpRNG;

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

/// An enumeration of possible actions performed on the polyhedrons. We can merge them or split them.
enum actions {MERGE, SPLIT};

// Forward declaration of polyhedron, vertex and emlig
class polyhedron;
class vertex;
class emlig;

/*
class t_simplex
{
public:
        set<vertex*> minima;

        set<vertex*> simplex;

        t_simplex(vertex* origin_vertex)
        {
                simplex.insert(origin_vertex);
                minima.insert(origin_vertex);
        }
};*/

/// A class representing a single condition that can be added to the emlig. A condition represents data entries in a statistical model.
class condition
{       
public:
        /// Value of the condition representing the data
        vec value;      

        /// Mulitplicity of the given condition may represent multiple occurences of same data entry.
        int multiplicity;

        /// Default constructor of condition class takes the value of data entry and creates a condition with multiplicity 1 (first occurence of the data).
        condition(vec value)
        {
                this->value = value;
                multiplicity = 1;
        }
};

class simplex
{
        

public:

        set<vertex*> vertices;

        double probability;

        double volume;

        vector<multimap<double,double>> positive_gamma_parameters;

        vector<multimap<double,double>> negative_gamma_parameters;

        double positive_gamma_sum;

        double negative_gamma_sum;

        double min_beta;
        

        simplex(set<vertex*> vertices)
        {
                this->vertices.insert(vertices.begin(),vertices.end());
                probability = 0;
        }

        simplex(vertex* vertex)
        {
                this->vertices.insert(vertex);
                probability = 0;
        }

        void clear_gammas()
        {
                positive_gamma_parameters.clear();
                negative_gamma_parameters.clear();              
                
                positive_gamma_sum = 0;
                negative_gamma_sum = 0;

                min_beta = numeric_limits<double>::max();
        }

        void insert_gamma(int order, double weight, double beta)
        {
                if(weight>=0)
                {
                        while(positive_gamma_parameters.size()<order+1)
                        {
                                multimap<double,double> map;
                                positive_gamma_parameters.push_back(map);
                        }

                        positive_gamma_sum += weight;

                        positive_gamma_parameters[order].insert(pair<double,double>(weight,beta));              
                }
                else
                {
                        while(negative_gamma_parameters.size()<order+1)
                        {
                                multimap<double,double> map;
                                negative_gamma_parameters.push_back(map);
                        }

                        negative_gamma_sum -= weight;

                        negative_gamma_parameters[order].insert(pair<double,double>(-weight,beta));
                }

                if(beta < min_beta)
                {
                        min_beta = beta;
                }
        }
};


/// 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;       

        /// A property representing the position of the polyhedron related to current condition with relation to which we
        /// are splitting the parameter space (new data has arrived). This property is setup within a classification procedure and
        /// is only valid while the new condition is being added. It has to be reset when new condition is added and new classification
        /// has to be performed.
        int split_state;

        /// A property representing the position of the polyhedron related to current condition with relation to which we
        /// are merging the parameter space (data is being deleted usually due to a moving window model which is more adaptive and 
        /// steps in for the forgetting in a classical Gaussian AR model). This property is setup within a classification procedure and
        /// is only valid while the new condition is being removed. It has to be reset when new condition is removed and new classification
        /// has to be performed.
        int merge_state;

                        

public:
        /// A pointer to the multi-Laplace inverse gamma distribution this polyhedron belongs to.
        emlig* my_emlig;

        /// 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
        set<vertex*> vertices;

        /// The conditions that gave birth to the polyhedron. If some of them is removed, the polyhedron ceases to exist.
        set<condition*> parentconditions;

        /// 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;

        /// A set of grandchildren of the polyhedron that when new condition is added lie exactly on the condition hyperplane. These grandchildren
        /// behave differently from other grandchildren, when the polyhedron is split. New grandchild is not necessarily created on the crossection of
        /// the polyhedron and new condition.
        set<polyhedron*> totallyneutralgrandchildren;

        /// A set of children of the polyhedron that when new condition is added lie exactly on the condition hyperplane. These children
        /// behave differently from other children, when the polyhedron is split. New child is not necessarily created on the crossection of
        /// the polyhedron and new condition.
        set<polyhedron*> totallyneutralchildren;

        /// Reverse relation to the totallyneutralgrandchildren set is needed for merging of already existing polyhedrons to keep 
        /// totallyneutralgrandchildren list up to date.
        set<polyhedron*> grandparents;

        /// Vertices of the polyhedron classified as positive related to an added condition. When the polyhderon is split by the new condition,
        /// these vertices will belong to the positive part of the splitted polyhedron.
        set<vertex*> positiveneutralvertices;

        /// Vertices of the polyhedron classified as negative related to an added condition. When the polyhderon is split by the new condition,
        /// these vertices will belong to the negative part of the splitted polyhedron.
        set<vertex*> negativeneutralvertices;

        /// A bool specifying if the polyhedron lies exactly on the newly added condition or not.
        bool totally_neutral;

        /// When two polyhedrons are merged, there always exists a child lying on the former border of the polyhedrons. This child manages the merge
        /// of the two polyhedrons. This property gives us the address of the mediator child.
        polyhedron* mergechild;

        /// If the polyhedron serves as a mergechild for two of its parents, we need to have the address of the parents to access them. This 
        /// is the pointer to the positive parent being merged.
        polyhedron* positiveparent;

        /// If the polyhedron serves as a mergechild for two of its parents, we need to have the address of the parents to access them. This 
        /// is the pointer to the negative parent being merged.
        polyhedron* negativeparent;     

        /// Adressing withing the statistic. Next_poly is a pointer to the next polyhedron in the statistic on the same level (if this is a point,
        /// next_poly will be a point etc.).
        polyhedron* next_poly;

        /// Adressing withing the statistic. Prev_poly is a pointer to the previous polyhedron in the statistic on the same level (if this is a point,
        /// next_poly will be a point etc.).
        polyhedron* prev_poly;

        /// A property counting the number of messages obtained from children within a classification procedure of position of the polyhedron related
        /// an added/removed condition. If the message counter reaches the number of children, we know the polyhedrons' position has been fully classified.
        int message_counter;

        /// List of triangulation polyhedrons of the polyhedron given by their relative vertices. 
        set<simplex*> triangulation;

        /// 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;

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

        /// Setter for lowering multiplicity
        void lower_multiplicity()
        {
                multiplicity--;
        }

        int get_multiplicity()
        {
                return 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;
        }

        
        /// A setter of state of current polyhedron relative to the action specified in the argument. The three possible states of the
        /// polyhedron are -1 - NEGATIVE, 0 - NEUTRAL, 1 - POSITIVE. Neutral state means that either the state has been reset or the polyhedron is
        /// ready to be split/merged.
        int set_state(double state_indicator, actions action)
        {
                switch(action)
                {
                        case MERGE:
                                merge_state = (int)sign(state_indicator);
                                return merge_state;                     
                        case SPLIT:
                                split_state = (int)sign(state_indicator);
                                return split_state;             
                }
        }

        /// A getter of state of current polyhedron relative to the action specified in the argument. The three possible states of the
        /// polyhedron are -1 - NEGATIVE, 0 - NEUTRAL, 1 - POSITIVE. Neutral state means that either the state has been reset or the polyhedron is
        /// ready to be split/merged.
        int get_state(actions action)
        {
                switch(action)
                {
                        case MERGE:
                                return merge_state;                     
                        break;
                        case SPLIT:
                                return split_state;
                        break;
                }
        }

        /// Method for obtaining the number of children of given polyhedron.
        int number_of_children()
        {
                return children.size();
        }

        /// A method for triangulation of given polyhedron.
        double triangulate(bool should_integrate);      
};


/// 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:
        /// A property specifying the value of the density (ted nevim, jestli je to jakoby log nebo ne) above the vertex.
        double function_value;

        /// Default constructor
        vertex();

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

                vertices.insert(this);

                simplex* vert_simplex = new simplex(vertices);          

                triangulation.insert(vert_simplex);
        }

        /// 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 differen   tiates
/// it from polyhedrons in other rows. 
class toprow : public polyhedron
{
        
public:
        double probability;

        vertex* minimal_vertex;

        /// A condition used for determining the function of a Laplace-Inverse-Gamma density resulting from Bayesian estimation
        vec condition_sum;

        int condition_order;

        /// Default constructor
        toprow(){};

        /// Constructor creating a toprow from the condition
        toprow(condition *condition, int condition_order)
        {
                this->condition_sum   = condition->value;
                this->condition_order = condition_order;
        }

        toprow(vec condition_sum, int condition_order)
        {
                this->condition_sum   = condition_sum;
                this->condition_order = condition_order;
        }

        double integrate_simplex(simplex* simplex, char c);

};







class c_statistic
{

public:
        polyhedron* end_poly;
        polyhedron* start_poly;

        vector<polyhedron*> rows;

        vector<polyhedron*> row_ends;

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

        ~c_statistic()
        {
                delete end_poly;
                delete start_poly;
        }

        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!");
                }
        }
};


class my_ivec : public ivec
{
public:
        my_ivec():ivec(){};

        my_ivec(ivec origin):ivec()
        {
                this->ins(0,origin);
        }

        bool operator>(const my_ivec &second) const
        {
                return max(*this)>max(second);          
        }
        
        bool operator==(const my_ivec &second) const
        {
                return max(*this)==max(second); 
        }

        bool operator<(const my_ivec &second) const
        {
                return !(((*this)>second)||((*this)==second));
        }

        bool operator!=(const my_ivec &second) const
        {
                return !((*this)==second);
        }

        bool operator<=(const my_ivec &second) const
        {
                return !((*this)>second);
        }

        bool operator>=(const my_ivec &second) const
        {
                return !((*this)<second);
        }

        my_ivec right(my_ivec original)
        {
                
        }
};







//! 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
        

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

        list<condition*> conditions;

        double normalization_factor;

        int condition_order;

        double last_log_nc;

        

        void alter_toprow_conditions(condition *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)
                {
                        set<vertex*>::iterator vertex_ref = horiz_ref->vertices.begin();

                        do
                        {
                                vertex_ref++;

                                if(vertex_ref==horiz_ref->vertices.end())
                                {
                                        return;
                                }
                        }
                        while((*vertex_ref)->parentconditions.find(condition)!=(*vertex_ref)->parentconditions.end());

                        
                        
                        vec appended_coords = (*vertex_ref)->get_coordinates();
                        appended_coords.ins(0,-1.0);
                        
                        double product = appended_coords*condition->value;

                        if(should_be_added)
                        {
                                ((toprow*) horiz_ref)->condition_order++;

                                if(product>0)
                                {
                                        ((toprow*) horiz_ref)->condition_sum += condition->value;
                                }
                                else
                                {
                                        ((toprow*) horiz_ref)->condition_sum -= condition->value;
                                }
                        }
                        else
                        { 
                                ((toprow*) horiz_ref)->condition_order--;

                                if(product<0)                   
                                {
                                        ((toprow*) horiz_ref)->condition_sum += condition->value;
                                }
                                else
                                {
                                        ((toprow*) horiz_ref)->condition_sum -= condition->value;
                                }
                        }                               
                }
        }


        /// A method for recursive classification of polyhedrons with respect to SPLITting and MERGEing conditions.
        void send_state_message(polyhedron* sender, condition *toadd, condition *toremove, int level)
        {                       

                // We translate existence of toremove and toadd conditions to booleans for ease of manipulation
                bool shouldmerge    = (toremove != NULL);
                bool shouldsplit    = (toadd != NULL);
                
                // If such operation is desired, in the following cycle we send a message about polyhedrons classification
                // to all its parents. We loop through the parents and report the child sending its message.
                if(shouldsplit||shouldmerge)
                {
                        for(list<polyhedron*>::iterator parent_iterator = sender->parents.begin();parent_iterator!=sender->parents.end();parent_iterator++)
                        {
                                // We set an individual pointer to the value at parent_iterator for ease of use
                                polyhedron* current_parent = *parent_iterator;

                                // The message_counter counts the number of messages received by the parent
                                current_parent->message_counter++;

                                // If the child is the last one to send its message, the parent can as well be classified and
                                // send its message further up.
                                bool is_last  = (current_parent->message_counter == current_parent->number_of_children());

                                // Certain properties need to be set if this is the first message received by the parent
                                bool is_first = (current_parent->message_counter == 1);

                                // This boolean watches for polyhedrons that are already out of the game for further MERGEing
                                // and SPLITting purposes. This may seem quite straightforward at first, but because of all
                                // the operations involved it may be quite complicated. For example a polyhedron laying in the
                                // positive side of the MERGEing hyperplane should not be split, because it lays in the positive
                                // part of the location parameter space relative to the SPLITting hyperplane, but because it
                                // is merged with its MERGE negative counterpart, which is being SPLIT, the polyhedron itself
                                // will be SPLIT after it has been merged and needs to retain all properties needed for the
                                // purposes of SPLITting.
                                bool out_of_the_game = true;

                                if(shouldmerge)
                                {
                                        // get the MERGE state of the child
                                        int child_state  = sender->get_state(MERGE);
                                        // get the MERGE state of the parent so far, the parent can be partially classified
                                        int parent_state = current_parent->get_state(MERGE);

                                        // In case this is the first message received by the parent, its state has not been set yet
                                        // and therefore it inherits the MERGE state of the child. On the other hand if the state
                                        // of the parent is 0, all the children so far were neutral and if the next child isn't 
                                        // neutral the parent should be in state of the child again. 
                                        if(parent_state == 0||is_first)
                                        {
                                                parent_state = current_parent->set_state(child_state, MERGE);                                           
                                        }                                       

                                        // If a child is contained in the hyperplane of a condition that should be removed and it is
                                        // not of multiplicity higher than 1, it will later serve as a merger for two of its parents
                                        // each lying on one side of the removed hyperplane (one being classified MERGE positive, the
                                        // other MERGE negative). Here we set the possible merger candidates.
                                        if(child_state == 0)
                                        {
                                                if(current_parent->mergechild == NULL)
                                                {
                                                        current_parent->mergechild = sender;
                                                }                                                       
                                        }                                       

                                        // If the parent obtained a message from the last one of its children we have to classify it
                                        // with respect to the MERGE condition.
                                        if(is_last)
                                        {                                               
                                                // If the parent is a toprow from the top row of the Hasse diagram, we alter the condition
                                                // sum and condition order with respect to on which side of the cutting hyperplane the
                                                // toprow is located.
                                                if(level == number_of_parameters-1)
                                                {
                                                        // toprow on the positive side
                                                        if(parent_state == 1)
                                                        {
                                                                ((toprow*)current_parent)->condition_sum-=toremove->value;                                                      
                                                        }

                                                        // toprow on the negative side
                                                        if(parent_state == -1)
                                                        {
                                                                ((toprow*)current_parent)->condition_sum+=toremove->value;                                                      
                                                        }
                                                }

                                                // lowering the condition order. 
                                                // REMARK: This maybe could be done more globally for the whole statistic.
                                                ((toprow*)current_parent)->condition_order--;
                                                
                                                // If the parent is a candidate for being MERGEd
                                                if(current_parent->mergechild != NULL)
                                                {
                                                        // It might not be out of the game
                                                        out_of_the_game = false;

                                                        // If the mergechild multiplicity is 1 it will disappear after merging
                                                        if(current_parent->mergechild->get_multiplicity()==1)
                                                        {
                                                                // and because we need the child to have an address of the two parents it is
                                                                // supposed to merge, we assign the address of current parent to one of the
                                                                // two pointers existing in the child for this purpose regarding to its position
                                                                // in the location parameter space with respect to the MERGE hyperplane.
                                                                if(parent_state > 0)
                                                                {                                                       
                                                                        current_parent->mergechild->positiveparent = current_parent;                                                    
                                                                }

                                                                if(parent_state < 0)
                                                                {                                                       
                                                                        current_parent->mergechild->negativeparent = current_parent;                                                    
                                                                }
                                                        }
                                                        else
                                                        {
                                                                // If the mergechild has higher multiplicity, it will not disappear after the
                                                                // condition is removed and the parent will still be out of the game, because
                                                                // no MERGEing will occur.
                                                                out_of_the_game = true;
                                                        }
                                                }                                               
                                                
                                                // If so far the parent is out of the game, it is the toprow polyhedron and there will 
                                                // be no SPLITting, we compute its probability integral by summing all the integral
                                                // from the simplices contained in it.
                                                if(out_of_the_game)
                                                {
                                                        if((level == number_of_parameters - 1) && (!shouldsplit))
                                                        {
                                                                toprow* cur_par_toprow = ((toprow*)current_parent);
                                                                cur_par_toprow->probability = 0.0;                                                      

                                                                for(set<simplex*>::iterator s_ref = current_parent->triangulation.begin();s_ref!=current_parent->triangulation.end();s_ref++)
                                                                {
                                                                        double cur_prob = cur_par_toprow->integrate_simplex((*s_ref),'C');
                                                                        
                                                                        cur_par_toprow->probability += cur_prob;                                                                
                                                                }

                                                                normalization_factor += cur_par_toprow->probability;                                                            
                                                        }
                                                }

                                                // If the parent is classified MERGE neutral, it will serve as a merger for two of its
                                                // parents so we report it to the for_merging list.
                                                if(parent_state == 0)
                                                {
                                                        for_merging[level+1].push_back(current_parent);                                                                                                         
                                                }                                                                                               
                                        }                                       
                                }

                                // In the second part of the classification procedure, we will classify the parent polyhedron
                                // for the purposes of SPLITting. Since splitting comes from a parent that is being split by
                                // creating a neutral child that cuts the split polyhedron in two parts, the created child has
                                // to be connected to all the neutral grandchildren of the source parent. We therefore have to
                                // report all such grandchildren of the parent. More complication is brought in by grandchildren
                                // that have not been created in the process of splitting, but were classified SPLIT neutral
                                // already in the classification stage. Such grandchildren and children were already present
                                // in the Hasse diagram befor the SPLITting condition emerged. We call such object totallyneutral.
                                // They have to be watched and treated separately.
                                if(shouldsplit)
                                {
                                        // We report the totally neutral children of the message sending child into the totally neutral
                                        // grandchildren list of current parent.
                                        current_parent->totallyneutralgrandchildren.insert(sender->totallyneutralchildren.begin(),sender->totallyneutralchildren.end());
                                        
                                        // We need to have the pointers from grandchildren to grandparents as well, we therefore set
                                        // the opposite relation as well.
                                        for(set<polyhedron*>::iterator tot_child_ref = sender->totallyneutralchildren.begin();tot_child_ref!=sender->totallyneutralchildren.end();tot_child_ref++)
                                        {
                                                (*tot_child_ref)->grandparents.insert(current_parent);
                                        }

                                        // If this is the first child to report its total neutrality, the parent inherits its state.
                                        if(current_parent->totally_neutral == NULL)
                                        {
                                                current_parent->totally_neutral = sender->totally_neutral;
                                        }
                                        // else the parent is totally neutral only if all the children up to now are totally neutral.
                                        else
                                        {
                                                current_parent->totally_neutral = current_parent->totally_neutral && sender->totally_neutral;
                                        }

                                        // For splitting purposes, we have to mark all the children of the given parent by their SPLIT
                                        // state, because when we split the parent, we create its positive and negative offsprings and
                                        // its children have to be assigned accordingly.
                                        switch(sender->get_state(SPLIT))
                                        {
                                        case 1:
                                                // child classified positive
                                                current_parent->positivechildren.push_back(sender);

                                                // all the vertices of the positive child are assigned to the positive and neutral vertex
                                                // set
                                                current_parent->positiveneutralvertices.insert(sender->vertices.begin(),sender->vertices.end());
                                        break;
                                        case 0:
                                                // child classified neutral
                                                current_parent->neutralchildren.push_back(sender);

                                                // all the vertices of the neutral child are assigned to both negative and positive vertex
                                                // sets
                                                if(level!=0)
                                                {
                                                        current_parent->positiveneutralvertices.insert(sender->positiveneutralvertices.begin(),sender->positiveneutralvertices.end());
                                                        current_parent->negativeneutralvertices.insert(sender->negativeneutralvertices.begin(),sender->negativeneutralvertices.end());                                          
                                                }
                                                else
                                                {
                                                        current_parent->positiveneutralvertices.insert(*sender->vertices.begin());
                                                        current_parent->negativeneutralvertices.insert(*sender->vertices.begin());
                                                }

                                                // if the child is totally neutral it is also assigned to the totallyneutralchildren
                                                if(sender->totally_neutral)
                                                {
                                                        current_parent->totallyneutralchildren.insert(sender);
                                                }
                                                        
                                        break;
                                        case -1:
                                                // child classified negative
                                                current_parent->negativechildren.push_back(sender);
                                                current_parent->negativeneutralvertices.insert(sender->vertices.begin(),sender->vertices.end());
                                        break;
                                        }

                                        // If the last child has sent its message to the parent, we have to decide if the polyhedron
                                        // needs to be split. 
                                        if(is_last)
                                        {                                               
                                                // If the polyhedron extends to both sides of the cutting hyperplane it needs to be SPLIT. Such
                                                // situation occurs if either the polyhedron has negative and also positive children or
                                                // if the polyhedron contains neutral children that cross the cutting hyperplane. Such
                                                // neutral children cannot be totally neutral, since totally neutral children lay within
                                                // the cutting hyperplane. If the polyhedron is to be cut its state is set to SPLIT neutral
                                                if((current_parent->negativechildren.size()>0&&current_parent->positivechildren.size()>0)
                                                                                                        ||(current_parent->neutralchildren.size()>0&&current_parent->totallyneutralchildren.empty()))
                                                {
                                                        for_splitting[level+1].push_back(current_parent);                                                       
                                                        current_parent->set_state(0, SPLIT);
                                                }
                                                else
                                                {
                                                        // Else if the polyhedron has a positive number of negative children we set its state
                                                        // to SPLIT negative. In such a case we subtract current condition from the overall
                                                        // condition sum
                                                        if(current_parent->negativechildren.size()>0)
                                                        {
                                                                // set the state
                                                                current_parent->set_state(-1, SPLIT);

                                                                // alter the condition sum
                                                                if(level == number_of_parameters-1)
                                                                {
                                                                        ((toprow*)current_parent)->condition_sum-=toadd->value;
                                                                }                                                                       
                                                        }
                                                        // If the polyhedron has a positive number of positive children we set its state
                                                        // to SPLIT positive. In such a case we add current condition to the overall
                                                        // condition sum
                                                        else if(current_parent->positivechildren.size()>0)
                                                        {
                                                                // set the state 
                                                                current_parent->set_state(1, SPLIT);

                                                                // alter the condition sum
                                                                if(level == number_of_parameters-1)
                                                                {
                                                                        ((toprow*)current_parent)->condition_sum+=toadd->value;                                                                 
                                                                }
                                                        }
                                                        // Else the polyhedron only has children that are totally neutral. In such a case,
                                                        // we mark it totally neutral as well and insert the SPLIT condition into the 
                                                        // parent conditions of the polyhedron. No addition or subtraction is needed in 
                                                        // this case.
                                                        else
                                                        {
                                                                current_parent->raise_multiplicity();
                                                                current_parent->totally_neutral = true;
                                                                current_parent->parentconditions.insert(toadd);
                                                        }

                                                        // In either case we raise the condition order (statistical condition sum significance)
                                                        ((toprow*)current_parent)->condition_order++;

                                                        // In case the polyhedron is a toprow and it will not be SPLIT, we compute its probability
                                                        // integral with the altered condition.
                                                        if(level == number_of_parameters - 1 && current_parent->mergechild == NULL)
                                                        {
                                                                toprow* cur_par_toprow = ((toprow*)current_parent);
                                                                cur_par_toprow->probability = 0.0;                                                              
                                                                
                                                                // We compute the integral as a sum over all simplices contained within the
                                                                // polyhedron.
                                                                for(set<simplex*>::iterator s_ref = current_parent->triangulation.begin();s_ref!=current_parent->triangulation.end();s_ref++)
                                                                {
                                                                        double cur_prob = cur_par_toprow->integrate_simplex((*s_ref),'C');
                                                                        
                                                                        cur_par_toprow->probability += cur_prob;
                                                                }

                                                                normalization_factor += cur_par_toprow->probability;
                                                        }

                                                        // If the parent polyhedron is out of the game, so that it will not be MERGEd or
                                                        // SPLIT any more, we will reset the lists specifying its relation with respect
                                                        // to the SPLITting condition, so that they will be clear for future use.
                                                        if(out_of_the_game)
                                                        {
                                                                current_parent->positivechildren.clear();
                                                                current_parent->negativechildren.clear();
                                                                current_parent->neutralchildren.clear();                                                                
                                                                current_parent->totallyneutralgrandchildren.clear();                                                            
                                                                current_parent->positiveneutralvertices.clear();
                                                                current_parent->negativeneutralvertices.clear();
                                                                current_parent->totally_neutral = NULL;
                                                                current_parent->kids_rel_addresses.clear();
                                                        }                                                       
                                                }
                                        }
                                }

                                // Finally if the the parent polyhedron has been SPLIT and MERGE classified, we will send a message
                                // about its classification to its parents.
                                if(is_last)
                                {
                                        current_parent->mergechild = NULL;
                                        current_parent->message_counter = 0;

                                        send_state_message(current_parent,toadd,toremove,level+1);
                                }
                        
                        }

                        // We clear the totally neutral children of the child here, because we needed them to be assigned as
                        // totally neutral grandchildren to all its parents.
                        sender->totallyneutralchildren.clear();                 
                }               
        }
        
public: 
        c_statistic statistic;

        vertex* minimal_vertex;

        double min_ll;

        double log_nc;

        

        vector<multiset<my_ivec>> correction_factors;

        int number_of_parameters;

        /// 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, double alpha_deviation, double sigma_deviation, int nu)
        {       
                this->number_of_parameters = number_of_parameters;

                condition_order = nu;
                                                
                create_statistic(number_of_parameters, alpha_deviation, sigma_deviation);

                //step_me(10);

                min_ll = numeric_limits<double>::max();         

                
                double normalization_factor = 0;
                int counter = 0;
                for(polyhedron* top_ref = statistic.rows[number_of_parameters];top_ref!=statistic.get_end();top_ref=top_ref->next_poly)
                {
                        counter++;
                        toprow* cur_toprow = (toprow*)top_ref;
                                
                        set<simplex*>::iterator cur_simplex = cur_toprow->triangulation.begin();
                        normalization_factor += cur_toprow->integrate_simplex(*cur_simplex,'X');
                }

                last_log_nc = NULL;
                log_nc = log(normalization_factor);             
                
                cout << "Prior constructed." << endl;
        }

        /// 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, int condition_order)
        {
                this->statistic = statistic;    

                min_ll = numeric_limits<double>::max();

                this->condition_order = condition_order;
        }


        void step_me(int marker)
        {
                set<int> orders;

                for(int i = 0;i<statistic.size();i++)
                {
                        //int zero = 0;
                        //int one  = 0;
                        //int two  = 0;

                        for(polyhedron* horiz_ref = statistic.rows[i];horiz_ref!=statistic.get_end();horiz_ref=horiz_ref->next_poly)
                        {
                                
                                
                                if(i==statistic.size()-1)
                                {
                                        orders.insert(((toprow*)horiz_ref)->condition_order);
                                        
                                        /*
                                        cout << ((toprow*)horiz_ref)->condition_sum << "   " << ((toprow*)horiz_ref)->probability << endl;
                                        cout << "Condition: " << ((toprow*)horiz_ref)->condition_sum << endl;
                                        cout << "Order:" << ((toprow*)horiz_ref)->condition_order << endl;*/
                                }
                                

                                // cout << "Stepped." << endl;

                                if(marker==101)
                                {
                                        if(!(*horiz_ref).negativechildren.empty()||!(*horiz_ref).positivechildren.empty()||!(*horiz_ref).neutralchildren.empty()||!(*horiz_ref).kids_rel_addresses.empty()||!(*horiz_ref).mergechild==NULL||!(*horiz_ref).negativeneutralvertices.empty())
                                        {
                                                cout << "Cleaning error!" << endl;
                                        }
                                
                                }

                                /*
                                for(set<simplex*>::iterator sim_ref = (*horiz_ref).triangulation.begin();sim_ref!=(*horiz_ref).triangulation.end();sim_ref++)
                                {
                                        if((*sim_ref)->vertices.size()!=i+1)
                                        {
                                                cout << "Something is wrong." << endl;
                                        }
                                }
                                */
                                
                                /*
                                if(i==0)
                                {
                                        cout << ((vertex*)horiz_ref)->get_coordinates() << endl;
                                }
                                */

                                /*
                                char* string = "Checkpoint";


                                if((*horiz_ref).parentconditions.size()==0)
                                {
                                        zero++;
                                }
                                else if((*horiz_ref).parentconditions.size()==1)
                                {
                                        one++;                                  
                                }
                                else
                                {
                                        two++;
                                }
                                */
                                
                        }
                }
                

                /*
                list<vec> table_entries;
                for(polyhedron* horiz_ref = statistic.rows[statistic.size()-1];horiz_ref!=statistic.row_ends[statistic.size()-1];horiz_ref=horiz_ref->next_poly)
                {
                        toprow *current_toprow = (toprow*)(horiz_ref);
                        for(list<set<vertex*>>::iterator tri_ref = current_toprow->triangulation.begin();tri_ref!=current_toprow->triangulation.end();tri_ref++)
                        {
                                for(set<vertex*>::iterator vert_ref = (*tri_ref).begin();vert_ref!=(*tri_ref).end();vert_ref++)
                                {
                                        vec table_entry = vec();
                                        
                                        table_entry.ins(0,(*vert_ref)->get_coordinates()*current_toprow->condition.get(1,current_toprow->condition.size()-1)-current_toprow->condition.get(0,0));
                                        
                                        table_entry.ins(0,(*vert_ref)->get_coordinates());

                                        table_entries.push_back(table_entry);
                                }
                        }                       
                }

                unique(table_entries.begin(),table_entries.end());

                                
                
                for(list<vec>::iterator entry_ref = table_entries.begin();entry_ref!=table_entries.end();entry_ref++)
                {
                        ofstream myfile;
                        myfile.open("robust_data.txt", ios::out | ios::app);
                        if (myfile.is_open())
                        {
                                for(int i = 0;i<(*entry_ref).size();i++)
                                {
                                        myfile << (*entry_ref)[i] << ";";
                                }
                                myfile << endl;
                        
                                myfile.close();
                        }
                        else
                        {
                                cout << "File problem." << endl;
                        }
                }
                */
                

                return;
        }

        int statistic_rowsize(int row)
        {
                return statistic.row_size(row);
        }

        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)
        {

                // New condition arrived (new data are available). Here we will perform the Bayesian data update
                // step by splitting the location parameter space with respect to the new condition and computing
                // normalization integrals for each polyhedron in the location parameter space.
                
                // First we reset previous value of normalization factor and maximum value of the log likelihood.
                // Because there is a minus sign in the exponent of the likelihood, we really search for a minimum
                // and here we set min_ll to a high value.
                normalization_factor = 0;
                min_ll = numeric_limits<double>::max();

                // We translate the presence of a condition to add to a boolean. Also, if moving window version of
                // data update is used, we check for the presence of a condition to be removed from consideration.
                // To take care of addition and deletion of a condition in one method is computationally better than 
                // treating both cases separately.
                bool should_remove = (toremove.size() != 0);
                bool should_add    = (toadd.size() != 0);

                // We lower the number of conditions so far considered if we remove one.
                if(should_remove)
                {
                        condition_order--;
                }

                // We raise the number of conditions so far considered if we add one.
                if(should_add)
                {
                        condition_order++;
                }

                // We erase the support lists used in splitting/merging operations later on to keep track of the
                // split/merged polyhedrons.
                for_splitting.clear();
                for_merging.clear();

                // This is a somewhat stupid operation, where we fill the vector of lists by empty lists, so that
                // we can extend the lists contained in the vector later on.
                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);
                }

                // We set`the iterator in the conditions list to a blind end() iterator
                list<condition*>::iterator toremove_ref = conditions.end();             

                // We search the list of conditions for existence of toremove and toadd conditions and check their
                // possible multiplicity. 
                for(list<condition*>::iterator ref = conditions.begin();ref!=conditions.end();ref++)
                {
                        // If condition should be removed..
                        if(should_remove)
                        {
                                // if it exists in the list
                                if((*ref)->value == toremove)
                                {
                                        // if it has multiplicity higher than 1
                                        if((*ref)->multiplicity>1)
                                        {
                                                // we just lower the multiplicity
                                                (*ref)->multiplicity--;

                                                // In this case the parameter space remains unchanged (we have to process no merging),
                                                // so we only alter the condition sums in all the cells and compute the integrals
                                                // over the cells with the subtracted condition
                                                alter_toprow_conditions(*ref,false);

                                                // By altering the condition sums in each individual unchanged cell, we have finished
                                                // all the tasks of this method related to merging and removing given condition. Therefore
                                                // we switch the should_remove switch to false.
                                                should_remove = false;
                                        }
                                        else
                                        {
                                                // In case the condition to be removed has a multiplicity of 1, we mark its position in
                                                // the vector of conditions by assigning its iterator to toremove_ref variable.
                                                toremove_ref = ref;                                                     
                                        }                                       
                                }
                        }

                        // If a condition should be added..
                        if(should_add)
                        {
                                // We search the vector of conditions if a condition with the same value already exists.
                                if((*ref)->value == toadd)
                                {
                                        // If it does, there will be no further splitting necessary. We have to raise its multiplicity..
                                        (*ref)->multiplicity++;

                                        // Again as with the condition to be removed, if no splitting is performed, we only have to
                                        // perform the computations in the individual cells in the top row of Hasse diagram of the
                                        // complex of polyhedrons by changing the condition sums in individual cells and computing
                                        // integrals with changed condition sum. 
                                        alter_toprow_conditions(*ref,true);

                                        // We switch off any further operations on the complex by switching the should_add variable
                                        // to false.
                                        should_add = false;                                     
                                }                               
                        }
                }       

                // Here we erase the removed condition from the conditions vector and assign a pointer to the
                // condition object of the removed condition, if there is such, else the pointer remains NULL.
                condition* condition_to_remove = NULL;
                if(should_remove)
                {
                        if(toremove_ref!=conditions.end())
                        {
                                condition_to_remove = *toremove_ref;
                                conditions.erase(toremove_ref);                 
                        }
                }

                // Here we create the condition object for a condition value to be added and we insert it in
                // the list of conditions in case new condition should be added, else the pointer is set to NULL.
                condition* condition_to_add = NULL;
                if(should_add)
                {
                        condition_to_add = new condition(toadd);                        
                        conditions.push_back(condition_to_add);                 
                }               
                
                //**********************************************************************************************
                //             Classification of points related to added and removed conditions
                //**********************************************************************************************
                // Here the preliminary and preparation part ends and we begin classifying individual vertices in
                // the bottom row of the representing Hasse diagram relative to the condition to be removed and the
                // one to be added. This classification proceeds further in a recursive manner. Each classified
                // polyhedron sends an information about its classification to its parent, when all the children of
                // given parents are classified, the parent can be itself classified and send information further to
                // its parent and so on.

                // We loop through all ther vertices
                for(polyhedron* horizontal_position = statistic.rows[0];horizontal_position!=statistic.get_end();horizontal_position=horizontal_position->next_poly)
                {               
                        // Cast from general polyhedron to a vertex
                        vertex* current_vertex = (vertex*)horizontal_position;
                        
                        // If a condition should be added or removed..
                        if(should_add||should_remove)
                        {
                                // The coordinates are extended by a -1 representing there is no parameter multiplying the
                                // regressor in the autoregressive model. The condition is passed to the method as a vector
                                // (y_t,psi_{t-1}), where y_t is the value of regressor and psi_t is the vector of regressands.
                                // Minus sign is needed, because the AR model equation reads y_t = theta*psi_{t-1}+e_t, which 
                                // can be rewriten as (y_t, psi_{t-1})*(-1,theta)', where ' stands for transposition and * for
                                // scalar product
                                vec appended_coords = current_vertex->get_coordinates();
                                appended_coords.ins(0,-1.0);                            

                                if(should_add)
                                {
                                        // We compute the position of the vertex relative to the added condition
                                        double local_condition = appended_coords*toadd;// = toadd*(appended_coords.first/=appended_coords.second);

                                        // The method set_state classifies the SPLIT state of the vertex as positive, negative or
                                        // neutral
                                        current_vertex->set_state(local_condition,SPLIT);

                                        /// \TODO There should be a rounding error tolerance used here to insure we are not having too many points because of rounding error.
                                        // If the vertex lays on the hyperplane related to the condition cutting the location parameter
                                        // space in half, we say it is totally neutral. This way it will be different than the later
                                        // newly created vertices appearing on the cuts of line segments. In an environment, where
                                        // the data variables are continuous (they don't have positive probability mass at any point
                                        // in the data space) the occurence of a point on the cutting hyperplane has probability 0.
                                        // In real world application, where data are often discrete, we have to take such situation
                                        // into account.
                                        if(local_condition == 0)
                                        {
                                                // In certain scenarios this situation is rather rare. We might then want to know about
                                                // occurence of a point laying on the cutting hyperplane (Programmers note:Also such 
                                                // scenarios were not so well tested and computation errors may occur!)
                                                cout << "Condition to add: " << toadd << endl;
                                                cout << "Vertex coords: " << appended_coords << endl;

                                                // We classify the vertex totally neutral
                                                current_vertex->totally_neutral = true;

                                                // We raise its multiplicity and set current splitting condition as a parent condition
                                                // of the vertex, since if we later remove the original parent condition, the vertex 
                                                // has to have a parent condition its right to exist.
                                                current_vertex->raise_multiplicity();
                                                current_vertex->parentconditions.insert(condition_to_add);                                              
                                        }
                                        else
                                        {
                                                // If the vertex lays off the cutting hyperplane, we set its totally_neutral property
                                                // to false.
                                                current_vertex->totally_neutral = false;
                                        }
                                }
                        
                                // Now we classify the vertex with respect to the MERGEing condition..
                                if(should_remove)
                                {                                       
                                        // We search the condition to be removed in the list of vertice's parent conditions
                                        set<condition*>::iterator cond_ref;                                     
                                        for(cond_ref = current_vertex->parentconditions.begin();cond_ref!=current_vertex->parentconditions.end();cond_ref++)
                                        {
                                                if(*cond_ref == condition_to_remove)
                                                {
                                                        break;
                                                }
                                        }

                                        // If the list of parent conditions of the given vertex contain the condition that is being
                                        // removed, we erase it from the list, we set the vertice's MERGE state to neutral and we
                                        // insert the vertex into the set of polyhedrons that are supposed to be used for merging 
                                        // (themselves possibly being deleted). 

                                        // REMARK: One may think it would be easier to check the condition again computationally. 
                                        // Such design has been used before in the software, but due to rounding errors it was 
                                        // very unreliable. These rounding errors are avoided using current design.
                                        if(cond_ref!=current_vertex->parentconditions.end())
                                        {
                                                current_vertex->parentconditions.erase(cond_ref);
                                                current_vertex->set_state(0,MERGE);
                                                for_merging[0].push_back(current_vertex);
                                        }
                                        else
                                        {
                                                // If parent conditions of the vertex don't contain the condition to be removed, we
                                                // check in which halfspace it is located and set its MERGE state accordingly.
                                                double local_condition = toremove*appended_coords;
                                                current_vertex->set_state(local_condition,MERGE);
                                        }
                                }                               
                        }

                        // Once classified we proceed recursively by calling the send_state_message method
                        send_state_message(current_vertex, condition_to_add, condition_to_remove, 0);           
                        
                }

                // step_me(1);
                
                if(should_remove)
                {
                        /*
                        for(int i = 0;i<for_merging.size();i++)
                        {
                                for(list<polyhedron*>::iterator merge_ref = for_merging[i].begin();merge_ref!=for_merging[i].end();merge_ref++)
                                {
                                        
                                        for(list<polyhedron*>::iterator par_ref = (*merge_ref)->children.begin();par_ref!=(*merge_ref)->children.end();par_ref++)
                                        {
                                                if(find((*par_ref)->parents.begin(),(*par_ref)->parents.end(),(*merge_ref))==(*par_ref)->parents.end())
                                                {
                                                        cout << "Parent/child relations are not matched!" << endl;
                                                }
                                        }
                                        
                                        //cout << (*merge_ref)->get_state(MERGE) << ",";
                                }

                                // cout << endl;
                        }
                        */              


                        // Here we have finished the classification part and we have at hand two sets of polyhedrons used for
                        // further operation on the location parameter space. The first operation will be merging of polyhedrons
                        // with respect to the MERGE condition. For that purpose, we have a set of mergers in a list called
                        // for_merging. After we are finished merging, we need to split the polyhedrons cut by the SPLIT
                        // condition. These polyhedrons are gathered in the for_splitting list. As can be seen, the MERGE
                        // operation is done from below, in the terms of the Hasse diagram and therefore we start to merge
                        // from the very bottom row, from the vertices. On the other hand splitting is done from the top
                        // and we therefore start with the segments that need to be split.

                        // We start the MERGE operation here. Some of the vertices will disappear from the Hasse diagram. 
                        // Because they are part of polyhedrons in the Hasse diagram above the segments, we need to remember
                        // them in the separate set and get rid of them only after the process of merging all the polyhedrons
                        // has been finished.
                        cout << "Merging." << endl;
                        set<vertex*> vertices_to_be_reduced;                    
                        
                        // We loop through the vector list of polyhedrons for merging from the bottom row up. We keep track
                        // of the number of the processed row.
                        int k = 1;
                        for(vector<list<polyhedron*>>::iterator vert_ref = for_merging.begin();vert_ref<for_merging.end();vert_ref++)
                        {
                                // Within a row we loop through all the polyhedrons that we use as mergers.
                                for(list<polyhedron*>::iterator merge_ref = (*vert_ref).begin();merge_ref!=(*vert_ref).end();merge_ref++)
                                {
                                        // ***************************************************
                                        //   First we treat the case of a multiple merger.
                                        // ***************************************************

                                        // If the multiplicity of the merger is greater than one, the merger will remain in the Hasse
                                        // diagram and its parents will remain split.
                                        if((*merge_ref)->get_multiplicity()>1)
                                        {
                                                // We remove the condition to be removed (the MERGE condition) from the list of merger's
                                                // parents.
                                                (*merge_ref)->parentconditions.erase(condition_to_remove);

                                                // If the merger is a vertex..
                                                if(k==1)
                                                {
                                                        // ..we will later reduce its multiplicity (this is to prevent multiple reduction of
                                                        // the same vertex) 
                                                        vertices_to_be_reduced.insert((vertex*)(*merge_ref));
                                                }
                                                // If the merger is not a vertex..
                                                else
                                                {
                                                        // lower the multiplicity of the merger
                                                        (*merge_ref)->lower_multiplicity();
                                                }       

                                                // If the merger will not be split and it is not totally neutral with respect to SPLIT
                                                // condition (it doesn't lay in the hyperplane defined by the condition), we will not
                                                // need it for splitting purposes and we can therefore clean all the splitting related
                                                // properties, to be able to reuse them when new data arrive. A merger is never a toprow
                                                // so we do not need to integrate.
                                                if((*merge_ref)->get_state(SPLIT)!=0||(*merge_ref)->totally_neutral)
                                                {
                                                        (*merge_ref)->positivechildren.clear();
                                                        (*merge_ref)->negativechildren.clear();
                                                        (*merge_ref)->neutralchildren.clear();                                          
                                                        (*merge_ref)->totallyneutralgrandchildren.clear();                                              
                                                        (*merge_ref)->positiveneutralvertices.clear();
                                                        (*merge_ref)->negativeneutralvertices.clear();
                                                        (*merge_ref)->totally_neutral = NULL;
                                                        (*merge_ref)->kids_rel_addresses.clear();
                                                }
                                        }                                                                       
                                        // Else, if the multiplicity of the merger is equal to 1, we proceed with the merging part of
                                        // the algorithm.
                                        else
                                        {
                                                // A boolean that will be true, if after being merged, the new polyhedron should be split
                                                // in the next step of the algorithm.
                                                bool will_be_split = false;
                                                
                                                // The newly created polyhedron will be merged of a negative and positive part specified
                                                // by its merger.
                                                toprow* current_positive = (toprow*)(*merge_ref)->positiveparent;
                                                toprow* current_negative = (toprow*)(*merge_ref)->negativeparent;
                                                
                                                // An error check for situation that should not occur.
                                                if(current_positive->totally_neutral!=current_negative->totally_neutral)
                                                {
                                                        throw new exception("Both polyhedrons must be totally neutral if they should be merged!");
                                                }                                               

                                                // *************************************************************************************
                                                //    Now we rewire the Hasse properties of the MERGE negative part of the merged
                                                //    polyhedron to the MERGE positive part - it will be used as the merged polyhedron
                                                // *************************************************************************************
                                                
                                                // Instead of establishing a new polyhedron and filling in all the necessary connections
                                                // and thus adding it into the Hasse diagram, we use the positive polyhedron with its
                                                // connections and we merge it with all the connections from the negative side so that
                                                // the positive polyhedron becomes the merged one.

                                                // We remove the MERGE condition from parent conditions.
                                                current_positive->parentconditions.erase(condition_to_remove);
                                                
                                                // We add the children from the negative part into the children list and remove from it the
                                                // merger.
                                                current_positive->children.insert(current_positive->children.end(),current_negative->children.begin(),current_negative->children.end());
                                                current_positive->children.remove(*merge_ref);

                                                // We reconnect the reciprocal addresses from children to parents.
                                                for(list<polyhedron*>::iterator child_ref = current_negative->children.begin();child_ref!=current_negative->children.end();child_ref++)
                                                {
                                                        (*child_ref)->parents.remove(current_negative);
                                                        (*child_ref)->parents.push_back(current_positive);                                                                                                      
                                                }

                                                // We loop through the parents of the negative polyhedron.
                                                for(list<polyhedron*>::iterator parent_ref = current_negative->parents.begin();parent_ref!=current_negative->parents.end();parent_ref++)
                                                {
                                                        // Remove the negative polyhedron from its children
                                                        (*parent_ref)->children.remove(current_negative);                                                       

                                                        // Remove it from the according list with respect to the negative polyhedron's
                                                        // SPLIT state.
                                                        switch(current_negative->get_state(SPLIT))
                                                        {
                                                        case -1:
                                                                (*parent_ref)->negativechildren.remove(current_negative);
                                                                break;
                                                        case 0:
                                                                (*parent_ref)->neutralchildren.remove(current_negative);                                                                
                                                                break;
                                                        case 1:
                                                                (*parent_ref)->positivechildren.remove(current_negative);
                                                                break;
                                                        }                                                       
                                                }

                                                // We merge the vertices of the negative and positive part
                                                current_positive->vertices.insert(current_negative->vertices.begin(),current_negative->vertices.end());                                                                                         

                                                // **************************************************************************
                                                //       Now we treat the situation that one of the MERGEd polyhedrons is to be
                                                //   SPLIT. 
                                                // **************************************************************************

                                                if(!current_positive->totally_neutral)
                                                {
                                                        // If the positive polyhedron was not to be SPLIT and the negative polyhedron was..
                                                        if(current_positive->get_state(SPLIT)!=0&&current_negative->get_state(SPLIT)==0)
                                                        {
                                                                //..we loop through the parents of the positive polyhedron..
                                                                for(list<polyhedron*>::iterator parent_ref = current_positive->parents.begin();parent_ref!=current_positive->parents.end();parent_ref++)
                                                                {
                                                                        //..and if the MERGE positive polyhedron is SPLIT positive, we remove it
                                                                        //from the list of SPLIT positive children..
                                                                        if(current_positive->get_state(SPLIT)==1)
                                                                        {
                                                                                (*parent_ref)->positivechildren.remove(current_positive);
                                                                        }
                                                                        //..or if the MERGE positive polyhedron is SPLIT negative, we remove it
                                                                        //from the list of SPLIT positive children..
                                                                        else
                                                                        {
                                                                                (*parent_ref)->negativechildren.remove(current_positive);
                                                                        }
                                                                        //..and we add it to the SPLIT neutral children, because the MERGE negative polyhedron
                                                                        //that is being MERGEd with it causes it to be SPLIT neutral (the hyperplane runs
                                                                        //through the merged polyhedron)
                                                                        (*parent_ref)->neutralchildren.push_back(current_positive);
                                                                }

                                                                // Because of the above mentioned reason, we set the SPLIT state of the MERGE positive
                                                                // polyhedron to neutral
                                                                current_positive->set_state(0,SPLIT);

                                                                for_splitting[k].remove(current_negative);
                                                                // and we add it to the list of polyhedrons to be SPLIT
                                                                for_splitting[k].push_back(current_positive);                                                   
                                                        }
                                                
                                                
                                                        // If the MERGEd polyhedron is to be split..
                                                        if(current_positive->get_state(SPLIT)==0)
                                                        {
                                                                // We need to fill the lists related to split with correct values, adding the SPLIT
                                                                // positive, negative and neutral children to according list in the MERGE positive,
                                                                // or future MERGEd polyhedron
                                                                current_positive->negativechildren.insert(current_positive->negativechildren.end(),current_negative->negativechildren.begin(),current_negative->negativechildren.end());                                                
                                                                current_positive->positivechildren.insert(current_positive->positivechildren.end(),current_negative->positivechildren.begin(),current_negative->positivechildren.end());                                                                                                
                                                                current_positive->neutralchildren.insert(current_positive->neutralchildren.end(),current_negative->neutralchildren.begin(),current_negative->neutralchildren.end());
                                                        
                                                                // and remove the merger, which will be later deleted from the lists of SPLIT classified
                                                                // children.
                                                                switch((*merge_ref)->get_state(SPLIT))
                                                                {
                                                                case -1:
                                                                        current_positive->negativechildren.remove(*merge_ref);
                                                                        break;
                                                                case 0:
                                                                        current_positive->neutralchildren.remove(*merge_ref);
                                                                        break;
                                                                case 1:
                                                                        current_positive->positivechildren.remove(*merge_ref);
                                                                        break;
                                                                }                                                       

                                                                // We also have to merge the lists of totally neutral children laying in the SPLIT related
                                                                // cutting hyperpalne and the lists of positive+neutral and negative+neutral vertices. 
                                                                current_positive->totallyneutralgrandchildren.insert(current_negative->totallyneutralgrandchildren.begin(),current_negative->totallyneutralgrandchildren.end());
                                                                // Because a vertex cannot be SPLIT, we don't need to remove the merger from the 
                                                                // positive+neutral and negative+neutral lists
                                                                current_positive->negativeneutralvertices.insert(current_negative->negativeneutralvertices.begin(),current_negative->negativeneutralvertices.end());                                                    
                                                                current_positive->positiveneutralvertices.insert(current_negative->positiveneutralvertices.begin(),current_negative->positiveneutralvertices.end());

                                                                // And we set the will be split property to true
                                                                will_be_split = true;
                                                        }
                                                }
                                                
                                                // If the polyhedron will not be split (both parts are totally neutral or neither of them
                                                // was classified SPLIT neutral), we clear all the lists holding the SPLIT information for
                                                // them to be ready to reuse.
                                                if(!will_be_split)
                                                {                                                       
                                                        current_positive->positivechildren.clear();
                                                        current_positive->negativechildren.clear();
                                                        current_positive->neutralchildren.clear();                                                      
                                                        current_positive->totallyneutralgrandchildren.clear();                                                          
                                                        current_positive->positiveneutralvertices.clear();
                                                        current_positive->negativeneutralvertices.clear();
                                                        current_positive->totally_neutral = NULL;
                                                        current_positive->kids_rel_addresses.clear();                                           
                                                }                                                                               
                                                
                                                // If both the merged polyhedrons are totally neutral, we have to rewire the addressing
                                                // in the grandparents from the negative to the positive (merged) polyhedron.
                                                if(current_positive->totally_neutral)
                                                {
                                                        for(set<polyhedron*>::iterator grand_ref = current_negative->grandparents.begin();grand_ref!=current_negative->grandparents.end();grand_ref++)
                                                        {
                                                                (*grand_ref)->totallyneutralgrandchildren.erase(current_negative);
                                                                (*grand_ref)->totallyneutralgrandchildren.insert(current_positive);
                                                        }                                                       
                                                }                                       

                                                // We clear the grandparents list for further reuse.
                                                current_positive->grandparents.clear();
                                
                                                // Triangulate the newly created polyhedron and compute its normalization integral if the
                                                // polyhedron is a toprow.
                                                normalization_factor += current_positive->triangulate(k==for_splitting.size()-1 && !will_be_split);
                                                
                                                // Delete the negative polyhedron from the Hasse diagram (rewire all the connections)
                                                statistic.delete_polyhedron(k,current_negative);

                                                // Delete the negative polyhedron object
                                                delete current_negative;

                                                // *********************************************
                                                //   Here we treat the deletion of the merger. 
                                                // *********************************************
                                                
                                                // We erase the vertices of the merger from all the respective lists.
                                                for(set<vertex*>::iterator vert_ref = (*merge_ref)->vertices.begin();vert_ref!=(*merge_ref)->vertices.end();vert_ref++)
                                                {
                                                        if((*vert_ref)->get_multiplicity()==1)
                                                        {
                                                                current_positive->vertices.erase(*vert_ref);

                                                                if(will_be_split)
                                                                {
                                                                        current_positive->negativeneutralvertices.erase(*vert_ref);
                                                                        current_positive->positiveneutralvertices.erase(*vert_ref);                                                             
                                                                }
                                                        }
                                                }
                                                
                                                // We remove the connection to the merger from the merger's children
                                                for(list<polyhedron*>::iterator child_ref = (*merge_ref)->children.begin();child_ref!=(*merge_ref)->children.end();child_ref++)
                                                {
                                                        (*child_ref)->parents.remove(*merge_ref);
                                                }                               

                                                // We remove the connection to the merger from the merger's grandchildren
                                                for(set<polyhedron*>::iterator grand_ch_ref = (*merge_ref)->totallyneutralgrandchildren.begin();grand_ch_ref!=(*merge_ref)->totallyneutralgrandchildren.end();grand_ch_ref++)
                                                {
                                                        (*grand_ch_ref)->grandparents.erase(*merge_ref);
                                                }
                                                
                                                // We remove the connection to the merger from the merger's grandparents
                                                for(set<polyhedron*>::iterator grand_p_ref = (*merge_ref)->grandparents.begin();grand_p_ref!=(*merge_ref)->grandparents.end();grand_p_ref++)
                                                {
                                                        (*grand_p_ref)->totallyneutralgrandchildren.erase(*merge_ref);
                                                }                               

                                                // We remove the merger from the Hasse diagram
                                                statistic.delete_polyhedron(k-1,*merge_ref);                                            
                                                // And we delete the merger from the list of polyhedrons to be split
                                                for_splitting[k-1].remove(*merge_ref);                                          
                                                // If the merger is a vertex with multiplicity 1, we add it to the list of vertices to get
                                                // rid of at the end of the merging procedure.
                                                if(k==1)
                                                {                                                       
                                                        vertices_to_be_reduced.insert((vertex*)(*merge_ref));                                                   
                                                }                                                                                               
                                        }
                                }                       
                        
                                // And we go to the next row
                                k++;

                        }

                        // At the end of the merging procedure, we delete all the merger's objects. These should now be already
                        // disconnected from the Hasse diagram.
                        for(int i = 1;i<for_merging.size();i++)
                        {
                                for(list<polyhedron*>::iterator merge_ref = for_merging[i].begin();merge_ref!=for_merging[i].end();merge_ref++)
                                {
                                        delete (*merge_ref);
                                }
                        }
                        
                        // We also treat the vertices that we called to be reduced by either lowering their multiplicity or
                        // deleting them in case the already have multiplicity 1.
                        for(set<vertex*>::iterator vert_ref = vertices_to_be_reduced.begin();vert_ref!=vertices_to_be_reduced.end();vert_ref++)
                        {
                                if((*vert_ref)->get_multiplicity()>1)
                                {
                                        (*vert_ref)->lower_multiplicity();
                                }
                                else
                                {
                                        delete (*vert_ref);
                                }
                        }

                        // Finally we delete the condition object
                        delete condition_to_remove;
                }
                
                // This is a control check for errors in the merging procedure.
                /*
                vector<int> sizevector;
                for(int s = 0;s<statistic.size();s++)
                {
                        sizevector.push_back(statistic.row_size(s));
                        cout << statistic.row_size(s) << ", ";
                }
                cout << endl;
                */

                // After the merging is finished or if there is no condition to be removed from the conditions list,
                // we split the location parameter space with respect to the condition to be added or SPLIT condition.
                if(should_add)
                {
                        cout << "Splitting." << endl;

                        // We reset the row counter
                        int k = 1;                      

                        // Since the bottom row of the for_splitting list is empty - we can't split vertices, we start from
                        // the second row from the bottom - the row containing segments
                        vector<list<polyhedron*>>::iterator beginning_ref = ++for_splitting.begin();

                        // We loop through the rows
                        for(vector<list<polyhedron*>>::iterator vert_ref = beginning_ref;vert_ref<for_splitting.end();vert_ref++)
                        {                       

                                // and we loop through the polyhedrons in each row
                                for(list<polyhedron*>::reverse_iterator split_ref = vert_ref->rbegin();split_ref != vert_ref->rend();split_ref++)
                                {
                                        // If we split a polyhedron by a SPLIT condition hyperplane, in the crossection of the two a
                                        // new polyhedron is created. It is totally neutral, because it lays in the condition hyperplane.
                                        polyhedron* new_totally_neutral_child;

                                        // For clear notation we rename the value referenced by split_ref iterator
                                        polyhedron* current_polyhedron = (*split_ref);
                                        
                                        // If the current polyhedron is a segment, the new totally neutral child will be a vertex and
                                        // we have to assign coordinates to it.
                                        if(vert_ref == beginning_ref)
                                        {
                                                // The coordinates will be computed from the equation of the straight line containing the
                                                // segment, obtained from the coordinates of the endpoints of the segment
                                                vec coordinates1 = ((vertex*)(*(current_polyhedron->children.begin())))->get_coordinates();                                             
                                                vec coordinates2 = ((vertex*)(*(++current_polyhedron->children.begin())))->get_coordinates();
                                                
                                                // For computation of the scalar product with the SPLIT condition, we need extended coordinates
                                                vec extended_coord2 = coordinates2;
                                                extended_coord2.ins(0,-1.0);                                            

                                                // We compute the parameter t an element of (0,1) describing where the segment is cut
                                                double t = (-toadd*extended_coord2)/(toadd(1,toadd.size()-1)*(coordinates1-coordinates2));                                              

                                                // And compute the coordinates as convex sum of the coordinates
                                                vec new_coordinates = (1-t)*coordinates2+t*coordinates1;                                                

                                                // cout << "c1:" << coordinates1 << endl << "c2:" << coordinates2 << endl << "nc:" << new_coordinates << endl;

                                                // We create a new vertex object
                                                vertex* neutral_vertex = new vertex(new_coordinates);                                           

                                                // and assign it to the new totally neutral child
                                                new_totally_neutral_child = neutral_vertex;
                                        }
                                        else
                                        {
                                                // If the split polyhedron isn't a segment, the totally neutral child will be a general
                                                // polyhedron. Because a toprow inherits from polyhedron, we make it a toprow for further
                                                // universality \TODO: is this really needed?
                                                toprow* neutral_toprow = new toprow();
                                                
                                                // A toprow needs a valid condition
                                                neutral_toprow->condition_sum   = ((toprow*)current_polyhedron)->condition_sum; // tohle tu bylo driv: zeros(number_of_parameters+1);
                                                neutral_toprow->condition_order = ((toprow*)current_polyhedron)->condition_order+1;

                                                // We assign it to the totally neutral child variable
                                                new_totally_neutral_child = neutral_toprow;
                                        }

                                        // We assign current SPLIT condition as a parent condition of the totally neutral child and also
                                        // the child inherits all the parent conditions of the split polyhedron
                                        new_totally_neutral_child->parentconditions.insert(current_polyhedron->parentconditions.begin(),current_polyhedron->parentconditions.end());
                                        new_totally_neutral_child->parentconditions.insert(condition_to_add);

                                        // The totally neutral child is a polyhedron belonging to my_emlig distribution
                                        new_totally_neutral_child->my_emlig = this;
                                        
                                        // We connect the totally neutral child to all totally neutral grandchildren of the polyhedron
                                        // being split. This is what we need the totally neutral grandchildren for. It complicates the
                                        // algorithm, because it is a second level dependence (opposed to the children <-> parents 
                                        // relations, but it is needed.)
                                        new_totally_neutral_child->children.insert(new_totally_neutral_child->children.end(),
                                                                                                                current_polyhedron->totallyneutralgrandchildren.begin(),
                                                                                                                                current_polyhedron->totallyneutralgrandchildren.end());

                                        // We also create the reciprocal connection from the totally neutral grandchildren to the
                                        // new totally neutral child and add all the vertices of the totally neutral grandchildren
                                        // to the set of vertices of the new totally neutral child.
                                        for(set<polyhedron*>::iterator grand_ref = current_polyhedron->totallyneutralgrandchildren.begin(); grand_ref != current_polyhedron->totallyneutralgrandchildren.end();grand_ref++)
                                        {
                                                // parent connection
                                                (*grand_ref)->parents.push_back(new_totally_neutral_child);                                             

                                                // vertices
                                                new_totally_neutral_child->vertices.insert((*grand_ref)->vertices.begin(),(*grand_ref)->vertices.end());
                                        }
                                        
                                        // We create a condition sum for the split parts of the split polyhedron
                                        vec cur_pos_condition = ((toprow*)current_polyhedron)->condition_sum;
                                        vec cur_neg_condition = ((toprow*)current_polyhedron)->condition_sum;
                                        
                                        // If the split polyhedron is a toprow, we update the condition sum with the use of the SPLIT
                                        // condition. The classification of the intermediate row polyhedrons as toprows probably isn't
                                        // necessary and it could be changed for more elegance, but it is here for historical reasons.
                                        if(k == number_of_parameters)
                                        {
                                                cur_pos_condition = cur_pos_condition + toadd;
                                                cur_neg_condition = cur_neg_condition - toadd;
                                        }

                                        // We create the positive and negative parts of the split polyhedron completely from scratch,
                                        // using the condition sum constructed earlier. This is different from the merging part, where
                                        // we have reused one of the parts to create the merged entity. This way, we don't have to
                                        // clean up old information from the split parts and the operation will be more symetrical.
                                        toprow* positive_poly = new toprow(cur_pos_condition, ((toprow*)current_polyhedron)->condition_order+1);
                                        toprow* negative_poly = new toprow(cur_neg_condition, ((toprow*)current_polyhedron)->condition_order+1);

                                        // Set the new SPLIT positive and negative parts of the split polyhedrons as parents of the new
                                        // totally neutral child
                                        new_totally_neutral_child->parents.push_back(positive_poly);
                                        new_totally_neutral_child->parents.push_back(negative_poly);

                                        // and the new totally neutral child as a child of the SPLIT positive and negative parts
                                        // of the split polyhedron
                                        positive_poly->children.push_back(new_totally_neutral_child);
                                        negative_poly->children.push_back(new_totally_neutral_child);
                                        
                                        // The new polyhedrons belong to my_emlig
                                        positive_poly->my_emlig = this;
                                        negative_poly->my_emlig = this;

                                        // Parent conditions of the new polyhedrons are the same as parent conditions of the split polyhedron
                                        positive_poly->parentconditions.insert(current_polyhedron->parentconditions.begin(),current_polyhedron->parentconditions.end());
                                        negative_poly->parentconditions.insert(current_polyhedron->parentconditions.begin(),current_polyhedron->parentconditions.end());

                                        // We loop through the parents of the split polyhedron
                                        for(list<polyhedron*>::iterator parent_ref = current_polyhedron->parents.begin();parent_ref!=current_polyhedron->parents.end();parent_ref++)
                                        {
                                                // We set the new totally neutral child to be a totally neutral grandchild of the parent
                                                (*parent_ref)->totallyneutralgrandchildren.insert(new_totally_neutral_child);                                           

                                                // We remove the split polyhedron from both lists, where it should be present
                                                (*parent_ref)->neutralchildren.remove(current_polyhedron);
                                                (*parent_ref)->children.remove(current_polyhedron);

                                                // And instead set the newly created SPLIT negative and positive parts as children of 
                                                // the parent (maybe the parent will be split once we get to treating its row, but that
                                                // should be taken care of later) and we add it to the classified positive and negative
                                                // children list accordingly.
                                                (*parent_ref)->children.push_back(positive_poly);
                                                (*parent_ref)->children.push_back(negative_poly);
                                                (*parent_ref)->positivechildren.push_back(positive_poly);
                                                (*parent_ref)->negativechildren.push_back(negative_poly);
                                        }

                                        // Here we set the reciprocal connections to the ones set in the previous list. All the parents
                                        // of currently split polyhedron are added as parents of the SPLIT negative and positive parts.
                                        
                                        // for positive part..
                                        positive_poly->parents.insert(positive_poly->parents.end(),
                                                                                                current_polyhedron->parents.begin(),
                                                                                                                current_polyhedron->parents.end());
                                        // for negative part..
                                        negative_poly->parents.insert(negative_poly->parents.end(),
                                                                                                current_polyhedron->parents.begin(),
                                                                                                                current_polyhedron->parents.end());                                     

                                        // We loop through the positive children of the split polyhedron, remove it from their parents
                                        // lists and add the SPLIT positive part as their parent.
                                        for(list<polyhedron*>::iterator child_ref = current_polyhedron->positivechildren.begin();child_ref!=current_polyhedron->positivechildren.end();child_ref++)
                                        {
                                                (*child_ref)->parents.remove(current_polyhedron);
                                                (*child_ref)->parents.push_back(positive_poly);                                         
                                        }                                       

                                        // And again we set the reciprocal connections from the SPLIT positive part by adding
                                        // all the positive children of the split polyhedron to its list of children.
                                        positive_poly->children.insert(positive_poly->children.end(),
                                                                                                current_polyhedron->positivechildren.begin(),
                                                                                                                        current_polyhedron->positivechildren.end());

                                        // We loop through the negative children of the split polyhedron, remove it from their parents
                                        // lists and add the SPLIT negative part as their parent.
                                        for(list<polyhedron*>::iterator child_ref = current_polyhedron->negativechildren.begin();child_ref!=current_polyhedron->negativechildren.end();child_ref++)
                                        {
                                                (*child_ref)->parents.remove(current_polyhedron);
                                                (*child_ref)->parents.push_back(negative_poly);
                                        }

                                        // And again we set the reciprocal connections from the SPLIT negative part by adding
                                        // all the negative children of the split polyhedron to its list of children.
                                        negative_poly->children.insert(negative_poly->children.end(),
                                                                                                current_polyhedron->negativechildren.begin(),
                                                                                                                        current_polyhedron->negativechildren.end());

                                        // The vertices of the SPLIT positive part are the union of positive and neutral vertices of
                                        // the split polyhedron and vertices of the new neutral child
                                        positive_poly->vertices.insert(current_polyhedron->positiveneutralvertices.begin(),current_polyhedron->positiveneutralvertices.end());
                                        positive_poly->vertices.insert(new_totally_neutral_child->vertices.begin(),new_totally_neutral_child->vertices.end());

                                        // The vertices of the SPLIT negative part are the union of negative and neutral vertices of
                                        // the split polyhedron and vertices of the new neutral child
                                        negative_poly->vertices.insert(current_polyhedron->negativeneutralvertices.begin(),current_polyhedron->negativeneutralvertices.end());
                                        negative_poly->vertices.insert(new_totally_neutral_child->vertices.begin(),new_totally_neutral_child->vertices.end());
                                                                
                                        // Triangulate the new totally neutral child without computing its normalization intergral 
                                        // (because the child is never a toprow polyhedron)
                                        new_totally_neutral_child->triangulate(false);

                                        // Triangulate the new SPLIT positive and negative parts of the split polyhedron and compute
                                        // their normalization integral if they are toprow polyhedrons
                                        normalization_factor += positive_poly->triangulate(k==for_splitting.size()-1);
                                        normalization_factor += negative_poly->triangulate(k==for_splitting.size()-1);
                                        
                                        // Insert all the newly created polyhedrons into the Hasse diagram
                                        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);                                      

                                        // and delete the split polyhedron from the diagram
                                        statistic.delete_polyhedron(k, current_polyhedron);

                                        // and also delete its object from the memory
                                        delete current_polyhedron;
                                }

                                // Goto a higher row of the for_splitting list
                                k++;
                        }
                }

                /*
                vector<int> sizevector;
                //sizevector.clear();
                for(int s = 0;s<statistic.size();s++)
                {
                        sizevector.push_back(statistic.row_size(s));
                        cout << statistic.row_size(s) << ", ";
                }
                
                cout << endl;
                */

                // cout << "Normalization factor: " << normalization_factor << endl;    

                last_log_nc = log_nc;
                log_nc = log(normalization_factor); 

                /*
                for(polyhedron* topr_ref = statistic.rows[statistic.size()-1];topr_ref!=statistic.row_ends[statistic.size()-1]->next_poly;topr_ref=topr_ref->next_poly)
                {
                        cout << ((toprow*)topr_ref)->condition << endl;
                }
                */

                // step_me(101);
        }

        double _ll()
        {
                if(last_log_nc!=NULL)
                {
                        return log_nc - last_log_nc;
                }
                else
                {
                        throw new exception("You can not ask for log likelihood difference for a prior!");
                }
        }

        void set_correction_factors(int order)
                {
                        for(int remaining_order = correction_factors.size();remaining_order<order;remaining_order++)
                        {
                                multiset<my_ivec> factor_templates;
                                multiset<my_ivec> final_factors;                                

                                my_ivec orig_template = my_ivec();                              

                                for(int i = 1;i<number_of_parameters-remaining_order+1;i++)
                                {                                       
                                        bool in_cycle = false;
                                        for(int j = 0;j<=remaining_order;j++)                                   {
                                                
                                                multiset<my_ivec>::iterator fac_ref = factor_templates.begin();

                                                do
                                                {
                                                        my_ivec current_template;
                                                        if(!in_cycle)
                                                        {
                                                                current_template = orig_template;
                                                                in_cycle = true;
                                                        }
                                                        else
                                                        {
                                                                current_template = (*fac_ref);
                                                                fac_ref++;
                                                        }                                                       
                                                        
                                                        current_template.ins(current_template.size(),i);

                                                        // cout << "template:" << current_template << endl;
                                                        
                                                        if(current_template.size()==remaining_order+1)
                                                        {
                                                                final_factors.insert(current_template);
                                                        }
                                                        else
                                                        {
                                                                factor_templates.insert(current_template);
                                                        }
                                                }
                                                while(fac_ref!=factor_templates.end());
                                        }
                                }       

                                correction_factors.push_back(final_factors);                    

                        }
                }

        pair<vec,simplex*> choose_simplex()
        {
                double rnumber = randu();

                // cout << "RND:" << rnumber << endl;

                // This could be more efficient (log n), but map::upper_bound() doesn't let me dereference returned iterator
                double  prob_sum     = 0;       
                toprow* sampled_toprow;                         
                for(polyhedron* top_ref = statistic.rows[number_of_parameters];top_ref!=statistic.end_poly;top_ref=top_ref->next_poly)
                {
                        // cout << "CDF:"<< (*top_ref).first << endl;

                        toprow* current_toprow = ((toprow*)top_ref);

                        prob_sum += current_toprow->probability;

                        if(prob_sum >= rnumber*normalization_factor)
                        {
                                sampled_toprow = (toprow*)top_ref;
                                break;
                        }
                        else
                        {
                                if(top_ref->next_poly==statistic.end_poly)
                                {
                                        cout << "Error.";
                                }
                        }
                }                               

                //// cout << "Toprow/Count: " << toprow_count << "/" << ordered_toprows.size() << endl;
                // cout << &sampled_toprow << ";";

                rnumber = randu();                              

                set<simplex*>::iterator s_ref;
                prob_sum = 0;           
                for(s_ref = sampled_toprow->triangulation.begin();s_ref!=sampled_toprow->triangulation.end();s_ref++)
                {               
                        prob_sum += (*s_ref)->probability;

                        if(prob_sum/sampled_toprow->probability >= rnumber)
                                break;
                }

                return pair<vec,simplex*>(sampled_toprow->condition_sum,*s_ref);        
        }

        pair<double,double> choose_sigma(simplex* sampled_simplex)
        {
                double sigma = 0;
                double pg_sum;                                  
                double rnumber = randu();                       
                                        
                double sum_g = 0;
                for(int i = 0;i<sampled_simplex->positive_gamma_parameters.size();i++)
                {
                        for(multimap<double,double>::iterator g_ref = sampled_simplex->positive_gamma_parameters[i].begin();g_ref != sampled_simplex->positive_gamma_parameters[i].end();g_ref++)
                        {
                                sum_g += (*g_ref).first/sampled_simplex->positive_gamma_sum;

                                                        
                                if(sum_g>rnumber)
                                {                                       
                                        // tady je mozna chyba ve vaskove kodu
                                        GamRNG.setup(condition_order-number_of_parameters-1+i,(*g_ref).second);
                                                                                                                                
                                        sigma = 1/GamRNG();
                                        // cout << "Sigma mean:   " << (*g_ref).second/(conditions.size()-number_of_parameters-1) << endl;                                                              

                                        break;
                                }                                                       
                        }

                        if(sigma!=0)
                        {
                                break;
                        }
                }       

                pg_sum = 0;
                int i = 0;
                for(vector<multimap<double,double>>::iterator v_ref = sampled_simplex->positive_gamma_parameters.begin();v_ref!=sampled_simplex->positive_gamma_parameters.end();v_ref++)
                {
                        for(multimap<double,double>::iterator pg_ref = (*v_ref).begin();pg_ref!=(*v_ref).end();pg_ref++)
                        {
                                pg_sum += exp(-(*pg_ref).second/sigma)*pow((*pg_ref).second/sigma,condition_order-number_of_parameters-1+i)/sigma/fact(condition_order-number_of_parameters-2+i)*(*pg_ref).first;  // pg_sum += exp((sampled_simplex->min_beta-(*pg_ref).second)/sigma)*pow((*pg_ref).second/sigma,(int)conditions.size())*(*pg_ref).second/fact(conditions.size())*(*pg_ref).first;
                        }

                        i++;
                }       

                return pair<double,double>(sampled_simplex->positive_gamma_sum/pg_sum,sigma);
        }

        pair<vec,mat> sample(int n, bool rejection)
        {
                vec probabilities;
                mat samples;            
                
                while(samples.cols()<n)
                {
                        pair<vec,simplex*> condition_and_simplex = choose_simplex();

                        pair<double,double> probability_and_sigma = choose_sigma(condition_and_simplex.second);

                        int dimension = condition_and_simplex.second->vertices.size();

                        mat jacobian(dimension,dimension-1);
                        vec gradient = condition_and_simplex.first;
                                
                        int row_count = 0;

                        for(set<vertex*>::iterator vert_ref = condition_and_simplex.second->vertices.begin();vert_ref!=condition_and_simplex.second->vertices.end();vert_ref++)
                        {
                                jacobian.set_row(row_count,(*vert_ref)->get_coordinates());
                                row_count++;
                        }               
                        
                        ExpRNG.setup(1);

                        vec sample_coords;
                        double sample_sum = 0;
                        for(int j = 0;j<dimension;j++)
                        {
                                double rnumber = ExpRNG();

                                sample_sum += rnumber;

                                sample_coords.ins(0,rnumber);                           
                        }

                        sample_coords /= sample_sum;

                        sample_coords = jacobian.T()*sample_coords;

                        vec extended_coords = sample_coords;
                        extended_coords.ins(0,-1.0);

                        double exponent = extended_coords*condition_and_simplex.first;
                        double sample_prob = 1*condition_and_simplex.second->volume/condition_and_simplex.second->probability/pow(2*probability_and_sigma.second,condition_order)*exp(-exponent/probability_and_sigma.second);//*probability_and_sigma.first;                   

                        sample_coords.ins(sample_coords.size(),probability_and_sigma.second);
                        
                        samples.ins_col(0,sample_coords);
                        probabilities.ins(0,sample_prob);

                        

                        //cout << "C:" << sample_coords << "   p:" << sample_prob << endl;
                        //pause(1);
                }

                if(rejection)
                {
                        double max_prob = max(probabilities);

                        set<int> indices;
                        for(int i = 0;i<n;i++)
                        {
                                double randn = randu();

                                if(probabilities.get(i)<randn*max_prob)
                                {
                                        indices.insert(i);
                                }
                        }

                        for(set<int>::reverse_iterator ind_ref = indices.rbegin();ind_ref!=indices.rend();ind_ref++)
                        {
                                samples.del_col(*ind_ref);                              
                        }

                        return pair<vec,mat>(ones(samples.cols()),samples);
                }
                else
                {       
                        return pair<vec,mat>(probabilities,samples);
                }
        }

        int logfact(int factor)
        {
                if(factor>1)
                {
                        return log((double)factor)+logfact(factor-1);
                }
                else
                {
                        return 0;
                }
        }
protected:

        /// A method for creating plain default statistic representing only the range of the parameter space.
    void create_statistic(int number_of_parameters, double alpha_deviation, double sigma_deviation)
        {
                /*
                for(int i = 0;i<number_of_parameters;i++)
                {
                        vec condition_vec = zeros(number_of_parameters+1);
                        condition_vec[i+1]  = 1;

                        condition* new_condition = new condition(condition_vec);
                        
                        conditions.push_back(new_condition);
                }
                */

                // 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);

                origin->my_emlig = this;
                
                /*
                // 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);

                        new_point1->my_emlig = this;
                        new_point2->my_emlig = this;
                        
                        //*********************************************************************************************************
                        // 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;
                                        vec vec2;
                                        if(!horiz_ref->kids_rel_addresses.empty())
                                        {                                       
                                                vec1 = ((toprow*)horiz_ref)->condition_sum;
                                                vec1.ins(vec1.size(),-alpha_deviation);

                                                vec2 = ((toprow*)horiz_ref)->condition_sum;
                                                vec2.ins(vec2.size(),alpha_deviation);
                                        }
                                        else
                                        {                                               
                                                vec1.ins(0,-alpha_deviation);
                                                vec2.ins(0,alpha_deviation);

                                                vec1.ins(0,-sigma_deviation);
                                                vec2.ins(0,-sigma_deviation);
                                        }
                                        
                                        // cout << vec1 << endl;
                                        // cout << vec2 << endl;


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

                                        current_copy1->my_emlig = this;
                                        current_copy2->my_emlig = this;

                                        // 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(set<vertex*>::iterator vertex_ref = horiz_ref->vertices.begin();vertex_ref!=horiz_ref->vertices.end();vertex_ref++)
                                        {
                                                current_copy1->vertices.insert(*vertex_ref);
                                                current_copy2->vertices.insert(*vertex_ref);                                            
                                        }
                                        
                                        // The only new vertex of the offspring should be the newly created point.
                                        current_copy1->vertices.insert(new_point1);
                                        current_copy2->vertices.insert(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.
                                        simplex* t_simplex1 = new simplex(current_copy1->vertices);
                                        simplex* t_simplex2 = new simplex(current_copy2->vertices);                                     
                                        
                                        current_copy1->triangulation.insert(t_simplex1);
                                        current_copy2->triangulation.insert(t_simplex2);                                        
                                        
                                        // 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:
        bool has_constant;

        int window_size;        

        list<vec> conditions;

public:
        emlig* posterior;

        RARX(int number_of_parameters, const int window_size, bool has_constant, double alpha_deviation, double sigma_deviation, int nu)//:BM()
        {
                this->has_constant = has_constant;
                
                posterior = new emlig(number_of_parameters,alpha_deviation,sigma_deviation,nu);

                this->window_size = window_size;                
        };
        
        RARX(int number_of_parameters, const int window_size, bool has_constant)//:BM()
        {
                this->has_constant = has_constant;
                
                posterior = new emlig(number_of_parameters,1.0,1.0,number_of_parameters+3);

                this->window_size = window_size;                
        };

        void bayes(itpp::vec yt)
        {
                if(has_constant)
                {
                        int c_size = yt.size();
                        
                        yt.ins(c_size,1.0);
                }               

                if(yt.size() == posterior->number_of_parameters+1)
                {
                        conditions.push_back(yt);               
                }
                else
                {
                        throw new exception("Wrong condition size for bayesian data update!");
                }

                //posterior->step_me(0);
                
                cout << "*************************************" << endl << "Current condition:" << yt << endl << "*************************************" << endl;

                /// \TODO tohle je spatne, tady musi byt jiny vypocet poctu podminek, kdyby nejaka byla multiplicitni, tak tohle bude spatne
                if(conditions.size()>window_size && window_size!=0)
                {
                        posterior->add_and_remove_condition(yt,conditions.front());
                        conditions.pop_front();

                        //posterior->step_me(1);
                }
                else
                {
                        posterior->add_condition(yt);
                }

                
                                
        }

};



#endif //TRAGE_H