root/applications/robust/robustlib.cpp @ 1273

#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);

                        // cout << as_toprow->condition << endl;

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

                        int dimension = simplex.size()-1;

                        mat jacobian(dimension,dimension);

                        // cout << base_vertex->get_coordinates() << endl;

                        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 << (*vert_ref)->get_coordinates() << endl;
                                // 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++;
                        }

                        

                        double int_value = 0;

                        // cout << jacobian << endl;

                        double det_jacobian    = abs(det(jacobian));
                        double correction_term = 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;
                                        
                                        correction_term /= -pow((*as_ref).first,as1_order);                                     
                                        
                                        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(a_0+(*as_ref).first,condition_order-number_of_factors+1);
                                        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(a_0+(*as_ref).first,condition_order-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)");
                                }                                                                                                               
                        }

                        
                        correction_term *= fact(condition_order-my_emlig->number_of_parameters)/pow(a_0,condition_order-my_emlig->number_of_parameters+1);

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

                        int_value += correction_term;

                        // cout << int_value << endl;

                        // cout  << "***************************"  << endl << endl;

                        return int_value;
                        
                }
                else
                {
                        return 0.0;
                }
        }