integralii.cpp
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/*
* <one line to give the library's name and an idea of what it does.>
* Copyright (C) 2019 mullier <email>
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include "integralii.h"
std::list<ibex::Interval *>& IntegralII::compute_list_of_zeros(ibex::Interval searchdomain)
{
//ATTENTION pas de preuve d'unicité
std::list<ibex::Interval *>* res = new std::list<ibex::Interval *>();
ibex::CtcNewton newton(*_f);
ibex::CtcFwdBwd fb (*_f);
ibex::RoundRobin bisector(0);
ibex::CellStack buff;
ibex::CtcCompo comp( fb, newton);
ibex::CtcFixPoint fix(comp, 1e-7);
ibex::Solver s(fix, bisector, buff);
ibex::IntervalVector inf(1);
inf[0] = searchdomain;
std::vector<ibex::IntervalVector> sols = s.solve(inf);
unsigned int i;
for (i = 0; i < sols.size(); i++){
//ATTENTION detection foireuse de la pente dans la cas ou [f(temp)] contient 0
ibex::Interval * current = new ibex::Interval(sols[i][0]);
res->push_back(current);
}
return *res;
}
std::list<ibex::Interval *>& IntegralII::compute_list_of_zeros_inf()
{
std::list<ibex::Interval *>& res = compute_list_of_zeros(_inf_endpoint);
res.sort();
return res;
}
std::list<ibex::Interval *>& IntegralII::compute_list_of_zeros_sup()
{
return compute_list_of_zeros(_sup_endpoint);
}
void IntegralII::compute_integral()
{
std::list<IntegralRR> res_temp;
std::list<IntegralRR>::iterator it_sols;
ibex::Interval *current = new ibex::Interval(_inf_endpoint.lb());
IntegralRR min, max;
//=======================================================================
//Computation of the integrals in the _inf_endpoint
std::list<ibex::Interval *> list_of_zeros_inf = compute_list_of_zeros_inf();
if (list_of_zeros_inf.size()>0){
std::list<ibex::Interval *>::iterator it_zeros_inf = list_of_zeros_inf.begin();
while (it_zeros_inf != list_of_zeros_inf.end()){//calcul des intégrales entre chaque zéro de f
IntegralRR current_integral(current->mid(), (*it_zeros_inf)->mid(), _f);
it_sols = res_temp.begin();
while (it_sols != res_temp.end()){//On ajoute l'intégrale courante aux autres intégrales
*it_sols += current_integral;
it_sols++;
}
res_temp.push_back(current_integral);
current = *it_zeros_inf;
it_zeros_inf++;
}
//Dernière intégrale du dernier zéro vers la borne inf de l'intervalle
IntegralRR current_integral(current->mid(), _inf_endpoint.ub(), _f);
it_sols = res_temp.begin();
while (it_sols != res_temp.end()){//On ajoute l'intégrale courante aux autres intégrales
*it_sols += current_integral;
it_sols++;
}
res_temp.push_back(current_integral);
} else {
IntegralRR whole_integral(_inf_endpoint.lb(), _inf_endpoint.ub(), _f);
res_temp.push_back(whole_integral);
res_temp.push_back(IntegralRR(_inf_endpoint.ub(), _inf_endpoint.ub(), _f, 0.));
}
it_sols = res_temp.begin();
min = *it_sols;
max = *it_sols;
it_sols++;
while (it_sols != res_temp.end()){//On recherche le min et le max
if (max < *it_sols){
max = *it_sols;
}
if (*it_sols < min){
min = *it_sols;
}
it_sols ++;
}
delete current;
//Calcul de l'intégrale entre les intervalles
IntegralRR integrale_milieu(_inf_endpoint.ub(), _sup_endpoint.lb(), _f);
_solution.first = min + integrale_milieu;
_solution.second = max + integrale_milieu;
//=======================================================================
current = new ibex::Interval(_sup_endpoint.ub());
res_temp.clear();
std::list<ibex::Interval *> list_of_zeros_sup = compute_list_of_zeros_sup();
if (list_of_zeros_sup.size()>0){
std::list<ibex::Interval *>::iterator it_zeros_sup = list_of_zeros_sup.begin();
while (it_zeros_sup != list_of_zeros_sup.end()){//calcul des intégrales entre chaque zéro de f
IntegralRR current_integral((*it_zeros_sup)->mid(), current->mid(), _f);
it_sols = res_temp.begin();
while (it_sols != res_temp.end()){//On ajoute l'intégrale courante aux autres intégrales
*it_sols += current_integral;
it_sols++;
}
res_temp.push_back(current_integral);
current = *it_zeros_sup;
it_zeros_sup++;
}
//Dernière intégrale du dernier zéro vers la borne inf de l'intervalle
IntegralRR current_integral(_sup_endpoint.lb(), current->mid(), _f);
it_sols = res_temp.begin();
while (it_sols != res_temp.end()){//On ajoute l'intégrale courante aux autres intégrales
*it_sols += current_integral;
it_sols++;
}
res_temp.push_back(current_integral);
} else {
IntegralRR whole_integral(_sup_endpoint.lb(), _sup_endpoint.ub(), _f);
res_temp.push_back(whole_integral);
res_temp.push_back(IntegralRR(_sup_endpoint.lb(), _sup_endpoint.lb(), _f, 0.));
}
it_sols = res_temp.begin();
min = *it_sols;
max = *it_sols;
it_sols++;
while (it_sols != res_temp.end()){//On recherche le min et le max
if (max < *it_sols){
max = *it_sols;
}
if (*it_sols < min){
min = *it_sols;
}
it_sols ++;
}
_solution.first += min;
_solution.second += max;
}
std::ostream& operator<<(std::ostream& os, const IntegralII& integral){
os << "Integrale from " << integral.get_inf_endpoint() << " to " << integral.get_sup_endpoint();
os << " of the function " << *integral.get_f() << " : " << endl << "minimum : " << integral.get_solution().first << endl << "maximum : " << integral.get_solution().second;
return os;
}