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implemented polynomial gcd

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This commit is contained in:
Jiri Pittner
2021-06-12 21:42:31 +02:00
parent 73aed62650
commit cc65575536
3 changed files with 96 additions and 7 deletions
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38
t.cc
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@@ -2203,18 +2203,23 @@ cout << (value(p,u)*value(q,u) -value(r,u)).norm()<<endl;
}
if(1)
if(0)
{
int n;
cin >>n ;
NRVec<double> r(n);
r.randomize(1.);
//r.randomize(1.);
//wilkinson's ill-conditionel polynomial
for(int i=0; i<n;++i) r[i]=i+1;
double x0=r[0]*0.8+r[1]*0.2;
r.sort(0);
Polynomial<double> p=polyfromroots(r);
cout <<p;
cout <<r;
cout <<p.realroots(1e-10);
NRVec<double> rr= p.realroots(1e-10);
rr.resize(n,true);
cout <<rr;
cout <<"root error = "<<(r-rr).norm()<<endl;
double x=p.newton(x0);
double xdif=1e10;
for(int i=0; i<n; ++i) if(abs(x-r[i])<xdif) xdif=abs(x-r[i]);
@@ -2237,4 +2242,31 @@ Polynomial<double>pp=q.derivative(2);
cout<<"test deriv. "<<(pp-p).norm()<<endl;
}
if(1)
{
int n;
cin >>n;
NRVec<double> rr(n);
rr.randomize(1.);
rr.sort(0);
if(rr.size()>2) rr[1]=rr[0];//make a degenerate root
NRVec<double> pr(2*n);
NRVec<double> qr(2*n);
pr.randomize(1.);
qr.randomize(1.);
for(int i=0; i<n; ++i) {pr[i]=qr[i]=rr[i];}
Polynomial<double> p=polyfromroots(pr);
Polynomial<double> q=polyfromroots(qr);
Polynomial<double> g=poly_gcd(p,q,1e-8);
cout <<"GCD ="<<g;
Polynomial<double> gg=svd_gcd(p,q,1e-13);
cout <<"SVDGCD ="<<gg;
NRVec<double> rrr=g.realroots(1e-5);
NRVec<double> rrrr=gg.realroots(1e-5);
cout <<rr<<rrr<<rrrr;
cout <<"test gcd "<<(rr-rrr).norm()<<endl;
cout <<"test svdgcd "<<(rr-rrrr).norm()<<endl;
}
}