static bool is_small(Interval r) {
return r.sup()- r.inf() < .001;
}
Interval LDB::operator ()(const LDB::ipolynomial_type *poly_ptr,
const LDB::additional_var_data *data_ptr ) const
{
unsigned int data_size = data_ptr->size();
/*
Abspalten der linearen Terme. Die Konstante wird den hoeheren Termen zugerechnet.
Gleichzeitig werden die hoeheren Terme eingeschlossen.
*/
Interval rest(0.0);
std::vector<Interval> arguments( data_ptr->size() );
for(unsigned int i = 0; i < data_size; i++)
if( (*data_ptr)[ i ].operator ->() != 0 )
arguments[ i ] = ((*data_ptr)[ i ])->domain_ - ((*data_ptr)[ i ])->devel_point_;
std::vector<Interval> linear_coeffs(data_size, Interval(0.0));
std::vector<unsigned int> var_codes; var_codes.reserve(data_size); //Codes of Vars with linear term.
LDB::ipolynomial_type::const_iterator
curr = poly_ptr->begin(),
last = poly_ptr->end();
while( curr != last )
{
if( curr->key().expnt_sum() == 0 ) //Konstanter Term.
{
rest += curr->value();
}
else if( curr->key().expnt_sum() == 1 ) //Linearer Term.
{
unsigned int i = curr->key().min_var_code();
var_codes.push_back(i-1);
linear_coeffs[i-1] = curr->value();
}
else //Nonlinear term.
{
Interval prod(1.0);
//Evaluate the current monomial.
for(unsigned int i = curr->key().min_var_code(); i <= curr->key().max_var_code(); i++)
{
unsigned int e = curr->key().expnt_of_var(i);
if( e != 0 )
{
prod *= power( arguments[i-1], e );
}
}
//Multiply with coefficient.
prod *= curr->value();
//Add enclosure to bound interval.
rest += prod;
}
++curr;
}
if( var_codes.size() == 0 ) return rest; //No linear terms in polynomial. So return with enclosure of
//higher order terms.
/*
Lokale Kopien der 'Domains' anlegen, da diese im weiteren Verlauf unter Umstaenden
veraendert werden.
*/
std::vector<Interval> domain_of_max(data_size,Interval(0.0));
std::vector<Interval> domain_of_min(data_size,Interval(0.0));
for(unsigned int i = 0; i < data_size; i++)
{
if( (*data_ptr)[i].operator ->() ) //There is information.
{
domain_of_max[i] = domain_of_min[i] = ((*data_ptr)[i])->domain_;
}
}
/*
Jetzt beginnt der Algorithmus des LDB range bounders.
*/
Interval idelta(rest.diam());
for(unsigned int i = 0; i < var_codes.size(); i++)
{
unsigned int k = var_codes[i];
Interval b = linear_coeffs[k];
idelta += b.diam() * abs( ((*data_ptr)[k])->domain_ - ((*data_ptr)[k])->devel_point_ );
}
double delta = idelta.sup();
bool resizing = false;
for(unsigned int i = 0; i < var_codes.size(); i++)
{
unsigned int k = var_codes[i];
double mid_b = linear_coeffs[k].mid();
Interval abs_b = Interval( std::abs(mid_b) );
Interval domain = ((*data_ptr)[k])->domain_;
Interval upper = abs_b * domain.diam();
if( upper.inf() > delta )
{
Interval tmp = delta / abs_b;
if( mid_b > 0 )
{
domain_of_min[k] = domain_of_min[k].inf() + Interval(0,tmp.sup());
domain_of_max[k] = domain_of_max[k].sup() - Interval(0,tmp.sup());
}
else
{
domain_of_min[k] = domain_of_min[k].sup() - Interval(0,tmp.sup());
domain_of_max[k] = domain_of_max[k].inf() + Interval(0,tmp.sup());
}
resizing = true;
}
}
for(unsigned int i = 0; i < data_size; i++)
{
if( (*data_ptr)[i].operator ->() ) //There is information.
{
domain_of_min[i] -= ((*data_ptr)[i])->devel_point_;
domain_of_max[i] -= ((*data_ptr)[i])->devel_point_;
}
}
if( resizing ) //Die Domains wurden verändert.
{
Interval min(0.0),max(0.0);
curr = poly_ptr->begin();
while( curr != last ) //Walk trough the polynomial.
{
Interval prod1(1.0),prod2(1.0);
//Evaluate the current monomial.
for(unsigned int i = (*curr).key().min_var_code(); i <= (*curr).key().max_var_code(); i++)
{
unsigned int e = (*curr).key().expnt_of_var(i);
if( e != 0 )
{
prod1 *= power( domain_of_min[ i - 1 ], e );
prod2 *= power( domain_of_max[ i - 1 ], e );
}
}
//Multiply with coefficient.
prod1 *= (*curr).value(); // <---- Multiply with double value.
prod2 *= (*curr).value(); // <---- Multiply with double value.
//Add enclosure to interval.
min += prod1;
max += prod2;
++curr;
}
return Interval( min.inf(), max.sup() );
}
else
{
for(unsigned int i = 0; i < var_codes.size(); i++)
{
unsigned int k = var_codes[i];
rest += linear_coeffs[k] * domain_of_min[k];
}
return rest;
}
}
static bool is_unknown_sign(Interval rv) {
return rv.inf() <=0 && rv.sup() >=0;
}