/*!
  \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;

enum actions {MERGE, SPLIT};

class polyhedron;
class vertex;

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

	int split_state;

	int merge_state;

	

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

	vector<polyhedron*> totallyneutralchildren;

	bool totally_neutral;

	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;

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

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

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

	

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

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

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

	
};

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

	

public:



	/// Default constructor
	vertex();

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

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

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

		
};

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

	/// Default constructor
	toprow();

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

};

class condition
{	
public:
	vec value;	

	int multiplicity;

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


//! 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)->get_coordinates()*condition;
			}
			while(product == 0);

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


	void send_state_message(polyhedron* sender, 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)
					{
						current_parent->totallyneutralgrandchildren.insert(current_parent->totallyneutralgrandchildren.end(),sender->totallyneutralchildren.begin(),sender->totallyneutralchildren.end());

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

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

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

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

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

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

					if(is_last)
					{
						send_state_message(current_parent,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_condition(vec toadd)
	{
		vec null_vector = "";

		add_and_remove_condition(toadd, null_vector);
	}

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

		add_and_remove_condition(null_vector, toremove);
	
	}

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

		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(should_remove)
			{
				if((*ref)->value == toremove)
				{
					if((*ref)->multiplicity>1)
					{
						(*ref)->multiplicity--;

						alter_toprow_conditions(toremove,false);

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

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

					alter_toprow_conditions(toadd,true);

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

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

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

		

		for(vector<polyhedron*>::iterator horizontal_position = statistic[0].begin();horizontal_position<statistic[0].end();horizontal_position++)
		{		
			vertex* current_vertex = (vertex*)(*horizontal_position);
			
			if(should_add||should_remove)
			{
				vec appended_vec = current_vertex->get_coordinates();
				appended_vec.ins(0,1.0);

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

					current_vertex->set_state(local_condition,SPLIT);

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

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

					current_vertex->set_state(local_condition,MERGE);

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

			send_state_message(current_vertex, should_add, should_remove, 0);			
		}

		for(vector<vector<polyhedron*>>::iterator vert_ref = for_splitting.begin();vert_ref<for_splitting.end();vert_ref++)
		{
			int original_size = (*vert_ref).size();

			for(int split_counter = 0;split_counter<original_size;split_counter++)
			{
				polyhedron* current_polyhedron = (*vert_ref)[original_size-1-split_counter];

				
			}
		}


	}

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