#include "robustlib.h"

void polyhedron::triangulate(bool should_integrate)
	{		
		if(should_integrate)
		{
			((toprow *)this)->probability = 0.0;
		}		
		
		for(list<polyhedron*>::iterator child_ref = children.begin();child_ref!=children.end();child_ref++)
		{			
			for(list<set<vertex*>>::iterator t_ref = (*child_ref)->triangulation.begin();t_ref!=(*child_ref)->triangulation.end();t_ref++)
			{
				set<vertex*> new_simplex;
				new_simplex.insert((*t_ref).begin(),(*t_ref).end());				

				pair<set<vertex*>::iterator,bool> ret_val = new_simplex.insert(*vertices.begin());

				if(ret_val.second == true)
				{
					triangulation.push_back(new_simplex);

					if(should_integrate)
					{
						((toprow *)this)->probability += ((toprow *)this)->integrate_simplex(new_simplex, 'S');
					}
				} 
			}	
		}		
	}


	double toprow::integrate_simplex(set<vertex*> simplex, char c)
	{
		int condition_order = ((toprow*)this)->condition_order-1;

		// cout << "C:" << condition_order << "  N:" << my_emlig->number_of_parameters << "  C+N:" << condition_order-my_emlig->number_of_parameters << endl;
		// pause(0.1);

		if(condition_order-my_emlig->number_of_parameters >= 0)
		{
			emlig* current_emlig;

			if(this->my_emlig!=NULL)
			{
				current_emlig = this->my_emlig;
			}
			else
			{
				throw exception("The statistic of the polyhedron you are trying to integrate over doesn't belong to any emlig!");
			}						

			toprow* as_toprow = (toprow*)this;

			vec cur_condition = as_toprow->condition.get(1,as_toprow->condition.size()-1);

			vertex* base_vertex = (*simplex.begin());

			int dimension = simplex.size()-1;

			mat jacobian(dimension,dimension);

			double a_0 = base_vertex->get_coordinates()*cur_condition+as_toprow->condition[0];
			map<double,int> as;

			int row_count = 0;
			for(set<vertex*>::iterator vert_ref = (++simplex.begin()); vert_ref!=simplex.end();vert_ref++)
			{
				vec relative_coords = (*vert_ref)->get_coordinates()-base_vertex->get_coordinates();

				// cout << relative_coords << endl;

				jacobian.set_row(row_count,relative_coords);

				double new_a = relative_coords*cur_condition;							
				
				pair<map<double,int>::iterator,bool> returned = as.insert(pair<double,int>(new_a,1));
				if(returned.second == false)
				{
					(*returned.first).second++;
				}
				else
				{
					cout << "a[" << row_count << "] = " << new_a << endl;
				}
				//as.ins(as.size(),new_a);							
				
				row_count++;
			}

			// cout << endl;

			double int_value = 0;

			// cout << jacobian << endl;

			double det_jacobian = det(jacobian);
			for(map<double,int>::iterator as_ref = as.begin();as_ref!=as.end();as_ref++)
			{
				double multiplier = det_jacobian;
				if(a_0!=(*as_ref).first)
				{								
					int as1_order = (*as_ref).second;

					current_emlig->set_correction_factors(as1_order);

					vector<double> factors;
					int number_of_factors = 0;								
					for(map<double,int>::iterator as2_ref = as.begin();as2_ref!=as.end();as2_ref++)
					{
						
						if(as2_ref!=as_ref)
						{										
							for(int k = 0;k<(*as2_ref).second;k++)
							{
								factors.push_back((*as_ref).first-(*as2_ref).first);
							}

							multiplier        /= pow((*as_ref).first-(*as2_ref).first,(*as2_ref).second);
							number_of_factors += (*as2_ref).second;
						}
						else
						{
							factors.push_back((*as_ref).first);

							multiplier        /= (*as_ref).first;
							number_of_factors += 1;
						}									
					}					

					double bracket = fact(condition_order-number_of_factors)/fact(as1_order-1)/pow((*as_ref).first-a_0,condition_order-number_of_factors);
					for(int k = 0;k < as1_order-1;k++)
					{
						double bracket_factor = pow((double)-1,k+1)*fact(condition_order-1-number_of_factors-k)/fact(as1_order-2-k)/pow((*as_ref).first-a_0,condition_order-1-number_of_factors-k);
						
						for(set<my_ivec>::iterator combi_ref = this->my_emlig->correction_factors[k].begin();combi_ref!=this->my_emlig->correction_factors[k].end();combi_ref++)
						{
							double bracket_combination = 1;
							for(int j = 0;j<(*combi_ref).size();j++)
							{
								bracket_combination /= factors[(*combi_ref)[j]];
							}

							bracket+=bracket_factor*bracket_combination;									
						}									
					}								

					int_value += multiplier*bracket;	

				}
				else
				{
					throw new exception("Should this happen? a_i=a_0 in the formula for integrating over a simplex! I think it can happen with 0 probability(when phi*2*v_0=phi*v_i)");
				}

				// cout << c << int_value << endl;

				return int_value;										
			}
			
		}
		else
		{
			return 0.0;
		}
	}