22 | | // cout << "C:" << condition_order << " N:" << my_emlig->number_of_parameters << " C+N:" << condition_order-my_emlig->number_of_parameters << endl; |
23 | | // pause(0.1); |
24 | | if(should_integrate && condition_order-my_emlig->number_of_parameters >= 0) |
| 32 | |
| 33 | double toprow::integrate_simplex(set<vertex*> simplex, char c) |
| 34 | { |
| 35 | int condition_order = ((toprow*)this)->condition_order-1; |
| 36 | |
| 37 | // cout << "C:" << condition_order << " N:" << my_emlig->number_of_parameters << " C+N:" << condition_order-my_emlig->number_of_parameters << endl; |
| 38 | // pause(0.1); |
| 39 | |
| 40 | if(condition_order-my_emlig->number_of_parameters >= 0) |
| 41 | { |
| 42 | emlig* current_emlig; |
| 43 | |
| 44 | if(this->my_emlig!=NULL) |
| 45 | { |
| 46 | current_emlig = this->my_emlig; |
| 47 | } |
| 48 | else |
| 49 | { |
| 50 | throw exception("The statistic of the polyhedron you are trying to integrate over doesn't belong to any emlig!"); |
| 51 | } |
| 52 | |
| 53 | toprow* as_toprow = (toprow*)this; |
| 54 | |
| 55 | vec cur_condition = as_toprow->condition.get(1,as_toprow->condition.size()-1); |
| 56 | |
| 57 | vertex* base_vertex = (*simplex.begin()); |
| 58 | |
| 59 | int dimension = simplex.size()-1; |
| 60 | |
| 61 | mat jacobian(dimension,dimension); |
| 62 | |
| 63 | double a_0 = base_vertex->get_coordinates()*cur_condition+as_toprow->condition[0]; |
| 64 | map<double,int> as; |
| 65 | |
| 66 | int row_count = 0; |
| 67 | for(set<vertex*>::iterator vert_ref = (++simplex.begin()); vert_ref!=simplex.end();vert_ref++) |
| 68 | { |
| 69 | vec relative_coords = (*vert_ref)->get_coordinates()-base_vertex->get_coordinates(); |
| 70 | |
| 71 | // cout << relative_coords << endl; |
| 72 | |
| 73 | jacobian.set_row(row_count,relative_coords); |
| 74 | |
| 75 | double new_a = relative_coords*cur_condition; |
| 76 | |
| 77 | pair<map<double,int>::iterator,bool> returned = as.insert(pair<double,int>(new_a,1)); |
| 78 | if(returned.second == false) |
| 79 | { |
| 80 | (*returned.first).second++; |
| 81 | } |
| 82 | else |
| 83 | { |
| 84 | cout << "a[" << row_count << "] = " << new_a << endl; |
| 85 | } |
| 86 | //as.ins(as.size(),new_a); |
| 87 | |
| 88 | row_count++; |
| 89 | } |
| 90 | |
| 91 | // cout << endl; |
| 92 | |
| 93 | double int_value = 0; |
| 94 | |
| 95 | // cout << jacobian << endl; |
| 96 | |
| 97 | double det_jacobian = det(jacobian); |
| 98 | for(map<double,int>::iterator as_ref = as.begin();as_ref!=as.end();as_ref++) |
| 99 | { |
| 100 | double multiplier = det_jacobian; |
| 101 | if(a_0!=(*as_ref).first) |
| 102 | { |
| 103 | int as1_order = (*as_ref).second; |
| 104 | |
| 105 | current_emlig->set_correction_factors(as1_order); |
| 106 | |
| 107 | vector<double> factors; |
| 108 | int number_of_factors = 0; |
| 109 | for(map<double,int>::iterator as2_ref = as.begin();as2_ref!=as.end();as2_ref++) |
39 | | vec cur_condition = as_toprow->condition.get(1,as_toprow->condition.size()-1); |
| 131 | double bracket = fact(condition_order-number_of_factors)/fact(as1_order-1)/pow((*as_ref).first-a_0,condition_order-number_of_factors); |
| 132 | for(int k = 0;k < as1_order-1;k++) |
| 133 | { |
| 134 | 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); |
| 135 | |
| 136 | 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++) |
| 137 | { |
| 138 | double bracket_combination = 1; |
| 139 | for(int j = 0;j<(*combi_ref).size();j++) |
| 140 | { |
| 141 | bracket_combination /= factors[(*combi_ref)[j]]; |
| 142 | } |
50 | | int row_count = 0; |
51 | | |
52 | | for(set<vertex*>::iterator vert_ref = (++new_simplex.begin()); vert_ref!=new_simplex.end();vert_ref++) |
53 | | { |
54 | | vec relative_coords = (*vert_ref)->get_coordinates()-base_vertex->get_coordinates(); |
55 | | jacobian.set_row(row_count,relative_coords); |
56 | | |
57 | | double new_a = relative_coords*cur_condition; |
58 | | |
59 | | pair<map<double,int>::iterator,bool> returned = as.insert(pair<double,int>(new_a,1)); |
60 | | if(returned.second == false) |
61 | | { |
62 | | (*returned.first).second++; |
63 | | } |
64 | | //as.ins(as.size(),new_a); |
65 | | |
66 | | row_count++; |
67 | | } |
68 | | |
69 | | double int_value = 0; |
70 | | double det_jacobian = det(jacobian); |
71 | | for(map<double,int>::iterator as_ref = as.begin();as_ref!=as.end();as_ref++) |
72 | | { |
73 | | double multiplier = det_jacobian; |
74 | | if(a_0!=(*as_ref).first) |
75 | | { |
76 | | int as1_order = (*as_ref).second; |
77 | | |
78 | | current_emlig->set_correction_factors(as1_order); |
79 | | |
80 | | vector<double> factors; |
81 | | int number_of_factors = 0; |
82 | | for(map<double,int>::iterator as2_ref = as.begin();as2_ref!=as.end();as2_ref++) |
83 | | { |
84 | | |
85 | | if(as2_ref!=as_ref) |
86 | | { |
87 | | for(int k = 0;k<(*as2_ref).second;k++) |
88 | | { |
89 | | factors.push_back((*as_ref).first-(*as2_ref).first); |
90 | | } |
91 | | |
92 | | multiplier /= pow((*as_ref).first-(*as2_ref).first,(*as2_ref).second); |
93 | | number_of_factors += (*as2_ref).second; |
94 | | } |
95 | | else |
96 | | { |
97 | | factors.push_back((*as_ref).first); |
98 | | |
99 | | multiplier /= (*as_ref).first; |
100 | | number_of_factors += 1; |
101 | | } |
102 | | } |
103 | | |
104 | | double facti = fact(0); |
105 | | |
106 | | double bracket = fact(condition_order-number_of_factors)/fact(as1_order-1)/pow((*as_ref).first-a_0,condition_order-number_of_factors); |
107 | | for(int k = 0;k < as1_order-1;k++) |
108 | | { |
109 | | 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); |
110 | | |
111 | | 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++) |
112 | | { |
113 | | double bracket_combination = 1; |
114 | | for(int j = 0;j<(*combi_ref).size();j++) |
115 | | { |
116 | | bracket_combination /= factors[(*combi_ref)[j]]; |
117 | | } |
118 | | |
119 | | bracket+=bracket_factor*bracket_combination; |
120 | | } |
121 | | } |
122 | | |
123 | | int_value += multiplier*bracket; |
124 | | |
125 | | } |
126 | | else |
127 | | { |
128 | | 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)"); |
129 | | } |
130 | | |
131 | | } |
132 | | |
133 | | cout << int_value << endl; |
134 | | pause(0.1); |
135 | | |
136 | | |
137 | | simplex_integrals.insert(int_value); |
138 | | } |
139 | | } |
| 158 | return int_value; |