jiri/LA_library
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

implemented polynomial gcd

Browse Source
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
Download Patch File Download Diff File Expand all files Collapse all files

51
polynomial.cc
View File

@@ -19,6 +19,7 @@
#include "polynomial.h"
#include <stdio.h>
#include <string.h>
#include <math.h>
namespace LA {
@@ -77,8 +78,8 @@ NRMat<T> Polynomial<T>::companion() const
if((*this)[degree()]==(T)0) laerror("zero coefficient at highest degree - simplify first");
NRMat<T> a(degree(),degree());
a.clear();
for(int i=0; i<degree(); ++i) a(degree()-1,i) = -(*this)[i];
for(int i=0; i<degree()-1; ++i) a(i,i+1) = (*this)[degree()];
for(int i=0; i<degree(); ++i) a(degree()-1,i) = -(*this)[i]/(*this)[degree()];
for(int i=0; i<degree()-1; ++i) a(i,i+1) = (T)1;
return a;
}
@@ -158,6 +159,49 @@ return x;
}
template <typename T>
Polynomial<T> poly_gcd(const Polynomial<T> &p, const Polynomial<T> &q, const typename LA_traits<T>::normtype thr, const int d)
{
Polynomial<T> big,small;
if(p.degree() < q.degree()) {big=q; small=p;} else {big=p; small=q;}
small.simplify(thr);
if(small.degree()==0) return small;
Polynomial<T> help;
do {
help=small;
small= big%small;
big=help;
small.simplify(thr);
}
while((d<0 && small.degree() != 0) || (d>=0 && small.degree()>=d));
return big;
}
template <>
Polynomial<int> svd_gcd(const Polynomial<int> &p, const Polynomial<int> &q, const typename LA_traits<int>::normtype thr)
{
laerror("SVD gcd only for floating point numbers");
return p;
}
template <typename T>
Polynomial<T> svd_gcd(const Polynomial<T> &p, const Polynomial<T> &q, const typename LA_traits<T>::normtype thr)
{
Polynomial<T> big,small;
if(p.degree() < q.degree()) {big=q; small=p;} else {big=p; small=q;}
small.simplify(thr);
if(small.degree()==0) return small;
NRMat<T> s = Sylvester(p,q);
NRMat<T> u(s.nrows(),s.nrows()),v(s.ncols(),s.ncols());
NRVec<typename LA_traits<T>::normtype> w(s.nrows());
singular_decomposition(s,&u,w,&v,0);
int rank=0;
for(int i=0; i<w.size(); ++i) if(w[i]>thr*::sqrt((double)big.degree()*small.degree())) ++rank;
int d=big.degree()+small.degree()-rank;
return poly_gcd(big,small,thr,d);
}
/***************************************************************************//**
@@ -170,6 +214,9 @@ template class Polynomial<std::complex<double> >;
#define INSTANTIZE(T) \
template NRMat<T> Sylvester(const Polynomial<T> &p, const Polynomial<T> &q); \
template Polynomial<T> lagrange_interpolation(const NRVec<T> &x, const NRVec<T> &y); \
template Polynomial<T> poly_gcd(const Polynomial<T> &p, const Polynomial<T> &q, const typename LA_traits<T>::normtype thr,const int d); \
template Polynomial<T> svd_gcd(const Polynomial<T> &p, const Polynomial<T> &q, const typename LA_traits<T>::normtype thr); \
INSTANTIZE(int)