root/applications/robust/robustlib.h @ 1207

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

#ifndef ROBUST_H
#define ROBUST_H

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

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

class polyhedron;
class vertex;

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

        int split_state;

        int merge_state;

        

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

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

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

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

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

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

        vector<polyhedron*> mergechildren;

        polyhedron* positiveparent;

        polyhedron* negativeparent;

        int message_counter;

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

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

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

                message_counter = 0;
        }
        
        /// Setter for raising multiplicity
        void raise_multiplicity()
        {
                multiplicity++;
        }

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

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

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

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

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

        
};

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

        enum actions {MERGE, SPLIT};

public:



        /// Default constructor
        vertex();

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

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

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

                
};

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

        /// Default constructor
        toprow();

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

};

class condition
{       
public:
        vec value;      

        int multiplicity;

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


//! 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<vector<polyhedron*>> statistic;

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

        vector<condition*> conditions;

        double normalization_factor;

        void alter_toprow_conditions(vec condition, bool should_be_added)
        {
                for(vector<polyhedron*>::iterator horiz_ref = statistic[statistic.size()-1].begin();horiz_ref<statistic[statistic.size()-1].end();horiz_ref++)
                {
                        double product = 0;

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

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

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


        void send_state_message(polyhedron* sender, bool shouldsplit, bool shouldmerge, int level)
        {
                if(shouldsplit||shouldmerge)
                {
                        for(vector<polyhedron*>::iterator parent_iterator = sender->parents.begin();parent_iterator<sender->parents.end();parent_iterator++)
                        {
                                polyhedron* current_parent = *parent_iterator;

                                current_parent->message_counter++;

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

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

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

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

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

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

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

                                                current_parent->mergechildren.clear();
                                        }

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

                                                if(is_last)
                                                {
                                                        if(current_parent->negativechildren.size()>0) 
                                                        {                                                               
                                                                if(current_parent->positivechildren.size()>0)
                                                                {
                                                                        for_splitting[level+1].push_back(current_parent);
                                                                
                                                                        current_parent->set_state(0, SPLIT);
                                                                }
                                                                else 
                                                                {
                                                                        current_parent->set_state(-1, SPLIT);

                                                                        current_parent->negativechildren.clear();
                                                                        current_parent->neutralchildren.clear();
                                                                }
                                                        }
                                                        else if(current_parent->positivechildren.size()>0)
                                                        {
                                                                current_parent->set_state(1, SPLIT);

                                                                current_parent->positivechildren.clear();
                                                                current_parent->neutralchildren.clear();
                                                        }
                                                        else
                                                        {
                                                                current_parent->raise_multiplicity();

                                                                current_parent->neutralchildren.clear();
                                                        }
                                                }
                                        }

                                        if(is_last)
                                        {
                                                send_state_message(current_parent,shouldsplit,shouldmerge,level+1);
                                        }
                                }                       
                        
                        }
                        
                }               
        }
        
public: 

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

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

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

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

        void add_and_remove_condition(vec toremove, vec toadd)
        {
                vector<condition*>::iterator toremove_ref = conditions.end();
                bool condition_should_be_added = false;

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

                                                alter_toprow_conditions(toremove,false);

                                                toremove = NULL;
                                        }
                                        else
                                        {
                                                toremove_ref = ref;                                                     
                                        }
                                }
                        }

                        if(toadd != NULL)
                        {
                                if((*iterator)->value == toadd)
                                {
                                        (*iterator)->multiplicity++;

                                        alter_toprow_conditions(toadd,true);

                                        toadd = NULL;
                                }
                                else
                                {
                                        condition_should_be_added = true;
                                }
                        }
                }

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

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

                

                for(vector<polyhedron*>::iterator horizontal_position = statistic[0].begin();horizontal_position<statistic[0].end();horizontal_position++)
                {               
                        vertex* current_vertex = (vertex*)horizontal_position;
                        
                        if(toadd != NULL)
                        {
                                current_vertex->set_state(toadd*current_vertex->coordinates,SPLIT);
                        }
                        
                        if(toremove != NULL)
                        {
                                current_vertex->set_state(toremove*current_vertex->coordinates,MERGE);

                                if(current_vertex->get_state(MERGE) == 0)
                                {
                                        for_merging[0].push_back(current_vertex);
                                }
                        }

                        send_state_message(current_vertex, toadd != NULL, toremove != NULL, 0);

                        
                }
        }

protected:

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

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

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

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

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

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

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


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

                        // 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(vector<polyhedron*>::iterator horiz_ref = statistic[j].begin();horiz_ref<statistic[j].end();horiz_ref++)
                                {       
                                        // Append an extra zero coordinate to each of the vertices for the new dimension
                                        // If j==0 => 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);
                                        }

                                        // 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(vector<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(i+2);
                                        vec1.zeros();

                                        vec vec2(i+2);
                                        vec2.zeros();

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

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

                                                        // in the child save the parents' address
                                                        new_statistic1[j-1][(*kid_ref)]->parents.push_back(current_copy1);
                                                        new_statistic2[j-1][(*kid_ref)]->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[j].push_back(current_copy1);
                                        new_statistic2[j].push_back(current_copy2);
                                        
                                        // Raise the count in the vector of polyhedrons
                                        element_number++;
                                        
                                }                               
                        }

                        statistic[0].push_back(new_point1);
                        statistic[0].push_back(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())
                                {
                                        vector<polyhedron*> support;
                                        statistic.push_back(support);
                                }
                                
                                statistic[j+1].insert(statistic[j+1].end(),new_statistic1[j].begin(),new_statistic1[j].end());
                                statistic[j+1].insert(statistic[j+1].end(),new_statistic2[j].begin(),new_statistic2[j].end());
                        }
                }
        }


        
        
};

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

        emlig posterior;

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

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

};


#endif //TRAGE_H