/*!
  \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;

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;	

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;

	/// 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;	
	}
	
	/// Setter for raising multiplicity
	void RaiseMultiplicity()
	{
		multiplicity++;
	}

	/// Setter for lowering multiplicity
	void LowerMultiplicity()
	{
		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 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
	vector<double> coordinates;

public:

	/// Default constructor
	vertex();

	/// Constructor of a vertex from a set of coordinates
	vertex(vector<double> 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.push_back(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).
	vector<double> get_coordinates()
	{
		vector<double> returned_vec;

		for(int i = 0;i<coordinates.size();i++)
		{
			returned_vec.push_back(coordinates[i]);
		}

		return returned_vec;
	}
};

/// 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
{
	/// A condition used for determining the function of a Laplace-Inverse-Gamma density resulting from Bayesian estimation
	vector<double> condition;

public:

	/// Default constructor
	toprow();

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

};




//! 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;
	
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);
	}

	/// 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;
	}

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.
		vector<double> 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
			vector<double> origin_coord1 = origin->get_coordinates();
			vector<double> origin_coord2 = origin->get_coordinates();			

			// And we incorporate the nonzero coordinates into the new cooordinate vectors
			origin_coord1.push_back(max_range);
			origin_coord2.push_back(-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.
					vector<double> vec1(i+2,0);
					vector<double> vec2(i+2,0);

					// 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 BMEF{
};


#endif //TRAGE_H