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realroot_doc 0.1.1
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realroot_doc 0.1.1
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#include <solver_ucf.hpp>
Definition at line 210 of file solver_ucf.hpp.
| solver_cffirst | ( | interval_rep< POL > | p | ) | [inline] |
Definition at line 215 of file solver_ucf.hpp.
References solver_cffirst< Real, POL >::eps, and solver_cffirst< Real, POL >::ir.
| Seq< interval_rep< POL > > all_roots | ( | ) |
Definition at line 321 of file solver_ucf.hpp.
References mmx::let::assign(), BOX, mmx::lower(), AkritasBound< RT >::lower_bound(), N_ITER, and POL.
{
typedef interval_rep<POL> BOX;
std::stack<BOX * > uboxes;
typedef typename POL::scalar_t C;
Real ev(0);
Seq<interval_rep<POL> > sols;
POL zero(0);
Interval<Real> mid(0);
BOX * b, * tmp;
POL p;
unsigned s, iters=0;
Interval<Real> I;
AkritasBound<C> lb;
//HongBound<C> lb;
//Kioustelidis<C> lb;
//NISP<C> lb;
//Cauchy<C> lb;
C lower;
b= new BOX(ir);
uboxes.push (b);
while ( !uboxes.empty() && iters++ < N_ITER )
{
b = uboxes.top() ;
p = b->poly() ;
uboxes.pop();
if ( p==zero && (!uboxes.empty()) ) {
sols<< *b;}
I = b->template domain<Real>();
// Interval<Real> ev= p( I ) ;
// if ( ev.m * ev.M > 0 ) continue;
s = b->sign_var() ;
if ( s==1 && (!uboxes.empty()) ) {
sols << *b; continue; }
if ( s > 0 )
{
if ( (!uboxes.empty()) && b->template width<Real>() < eps*.1 )
{std::cout<<
"all_roots: multiple root?"<<b->template domain<Real>() <<std::endl;
std::cout<< b->poly()<<" , "<<b->template width<Real>()<<std::endl;
std::cout<<"source: "<<ir.poly()<<std::endl;
}
else
{
lower= lb.lower_bound(p) ;
if ( lower!=0 )
{
let::assign(ev,lower);
if ( p(ev) == 0 )
sols<< *b;
tmp= new BOX( *b ) ;
free(b);
tmp->shift_box( lower );
uboxes.push (tmp);
}
else
{
// right box
tmp = new BOX( *b ) ;
tmp->shift_box( 1 );
uboxes.push ( tmp );
//middle if needed
ev=1;
if ( p( ev ) == Real(0) )
{ tmp = new BOX(zero, b->hom() ) ;
uboxes.push ( tmp ); }
//left
tmp = new BOX( *b ) ;
tmp->reverse_and_shift_box( 1 );
tmp->reverse_box( 1 );
uboxes.push ( tmp );
free(b);
}
}
}
}
return sols;
}
Definition at line 519 of file solver_ucf.hpp.
References POL, and Seq< C, R >::size().
Referenced by solver< Ring, CFdecide >::solve(), and solver< Ring, CFallIsolate >::solve().
{
Seq<interval_rep<POL> > a( all_roots() );
Seq<Interval<Real> > s;
typename POL::scalar_t t(1);
for ( unsigned i=0; i<a.size(); ++i)
if (a[i].poly()==POL(0) )
s<< Interval<Real>(a[i].template point<Real>(t) );
else
s<< a[i].template domain<Real>();
return s;
}
| Seq< Real > all_roots_separate | ( | ) |
Definition at line 535 of file solver_ucf.hpp.
References Seq< C, R >::size().
Referenced by solver< Ring, CFseparate >::solve().
{
Seq< Interval<Real> > ints;
Seq<Real> sep;
ints= all_roots_isolate();
for (unsigned i=1; i<ints.size(); ++i)
sep << (ints[i-1].M + ints[i].m)*Real(0.5) ;
return sep;
}
| interval_rep< POL > first_root | ( | ) |
Definition at line 235 of file solver_ucf.hpp.
References BOX, mmx::lower(), AkritasBound< RT >::lower_bound(), N_ITER, and POL.
{
typedef interval_rep<POL> BOX;
std::stack<BOX * > uboxes;
typedef typename POL::scalar_t C;
POL zero(0);
Interval<Real> mid(0);
BOX * b, * tmp;
POL p;
unsigned s, iters=0;
Interval<Real> I;
AkritasBound<C> lb;
//HongBound<C> lb;
//Kioustelidis<C> lb;
//NISP<C> lb;
//Cauchy<C> lb;
C lower;
b= new BOX(ir);
uboxes.push (b);
while ( !uboxes.empty() && iters++ < N_ITER )
{
b = uboxes.top() ;
p = b->poly() ;
uboxes.pop();
if ( p==zero && (!uboxes.empty()) ) {
return *b;}
s = b->sign_var() ;
I = b->template domain<Real>();
if ( s==1 && (!uboxes.empty()) ) {
return *b;}
if ( s > 0 )
{
if ( b->template width<Real>() < eps )
{std::cout<< "first_root: multiple root?"<<b->template domain<Real>() <<std::endl;}
else
{
lower= lb.lower_bound(p) ;
if ( lower!=0 )
{
if ( p( lower ) == 0 )
return *b;
tmp= new BOX( *b ) ;
free(b);
tmp->shift_box( lower );
uboxes.push (tmp);
}
else
{
// right box
tmp = new BOX( *b ) ;
tmp->shift_box( 1 );
uboxes.push ( tmp );
//middle if needed
if ( p( Real(1) ) == Real(0) )
{ tmp = new BOX(zero, b->hom() ) ;
uboxes.push ( tmp ); }
//left
tmp = new BOX( *b ) ;
tmp->reverse_and_shift_box( 1 );
tmp->reverse_box( 1 );
uboxes.push ( tmp );
free(b);
}
}
}
}
/* -1 = No positive root */
return BOX(-1);
}
| Real first_root_approximate | ( | ) |
Definition at line 430 of file solver_ucf.hpp.
Referenced by solver< Ring, CFfirstApproximate >::solve().
{
typedef interval_rep<POL> BOX;
typedef typename POL::scalar_t C;
BOX * l, * r= new BOX( first_root() ) ;
C t(1);
if ( r->poly()== POL(-1) )
return (0);
else
if (r->poly()==POL(0) )
return( r->template point<Real>(t) );
else
{
/* Approximate */
while ( r->template width<Real>() > eps )
{
t= r->middle();
if ( r->poly()( t ) == 0 ) return( r->template point<Real>(t) );
l= new BOX( *r) ;
l->shift_box( t );
if ( l->sign_var() )
{
free(r);
r=l;
continue;
}
else
{
free(l);
r->contract_box(t);
r->reverse_and_shift_box(1);
r->reverse_box(1);
}
}
return ( r->template domain<Real>() );
}
}
| Real first_root_floor | ( | ) |
Definition at line 473 of file solver_ucf.hpp.
References BOX, Interval< T, r >::M, Interval< T, r >::m, POL, and mmx::rfloor().
Referenced by solver< Ring, CFfirstFloor >::solve().
{
typedef interval_rep<POL> BOX;
typedef typename POL::scalar_t C;
BOX * l, * r= new BOX( first_root() ) ;
Interval<Real> I;
C t(1);
if ( r->poly()== POL(-1) )
return (0);
else
if (r->poly()==POL(0) )
return( r->template point<Real>(t) );
else
{
I= r->template domain<Real>();
if ( r->poly() == POL(0) ) return as<Real> (floor(as<double>(r->template point<Real>(t))) );
while ( rfloor(I.m)!=rfloor(I.M) )
{
t= r->middle();
if ( r->poly()( t ) == 0 ) return as<Real>( floor(as<double>(r->template point<Real>(t))) );
l= new BOX( *r) ;
l->shift_box( t );
if ( l->sign_var() )
{
free(r);
r=l;
I= r->template domain<Real>();
continue;
}
else
{
free(l);
r->reverse_and_shift_box();
r->reverse_box();
I= r->template domain<Real>();
}
}
}
return as<Real>( floor(as<double>(I.m)) );
}/*first_root_floor*/
| Interval< Real > first_root_isolate | ( | ) |
Definition at line 415 of file solver_ucf.hpp.
References POL, and interval_rep< POL >::poly().
Referenced by solver< Ring, CFfirstIsolate >::solve().
{
interval_rep<POL> a( first_root() );
typename POL::scalar_t t(1);
if ( a.poly()== POL(-1) )
return (0);
else
if (a.poly()==POL(0) )
return( a.template point<Real>(t) );
else
return ( a.template domain<Real>() );
}
| Real eps |
Definition at line 213 of file solver_ucf.hpp.
Referenced by solver_cffirst< Real, POL >::solver_cffirst().
| interval_rep<POL> ir |
Definition at line 212 of file solver_ucf.hpp.
Referenced by solver_cffirst< Real, POL >::solver_cffirst().
