166 lines
4.2 KiB
C++
166 lines
4.2 KiB
C++
/*
|
|
LA: linear algebra C++ interface library
|
|
Copyright (C) 2021 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
|
|
|
|
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 "polynomial.h"
|
|
#include <stdio.h>
|
|
#include <string.h>
|
|
|
|
|
|
namespace LA {
|
|
|
|
template <typename T>
|
|
void Polynomial<T>::polydiv(const Polynomial &rhs, Polynomial &q, Polynomial &r) const
|
|
{
|
|
if(rhs[rhs.degree()]==(T)0) laerror("division by a polynomial with zero leading coefficient - simplify it first");
|
|
if(rhs.degree()==0) //scalar division
|
|
{
|
|
q= *this/rhs[0];
|
|
r.resize(0,false);
|
|
r[0]=0;
|
|
return;
|
|
}
|
|
int rdegree= rhs.degree();
|
|
int qdegree= degree()-rdegree;
|
|
if(qdegree<0)
|
|
{
|
|
q.resize(0,false);
|
|
q[0]=0;
|
|
r= *this;
|
|
return;
|
|
}
|
|
//general case
|
|
q.resize(qdegree,false);
|
|
r= *this; r.copyonwrite();
|
|
for(int i=degree(); i>=rdegree; --i)
|
|
{
|
|
T tmp= r[i]/rhs[rdegree];
|
|
q[i-rdegree]= tmp;
|
|
r -= rhs.shifted(i-rdegree)*tmp;
|
|
}
|
|
r.resize(rhs.degree()-1,true);
|
|
}
|
|
|
|
|
|
template <typename T>
|
|
NRMat<T> Sylvester(const Polynomial<T> &p, const Polynomial<T> &q)
|
|
{
|
|
int nm=p.degree()+q.degree();
|
|
NRMat<T> a(nm,nm);
|
|
a.clear();
|
|
for(int i=0; i<q.degree(); ++i)
|
|
for(int j=p.degree(); j>=0; --j)
|
|
a(i,i+p.degree()-j)=p[j];
|
|
for(int i=0; i<p.degree(); ++i)
|
|
for(int j=q.degree(); j>=0; --j)
|
|
a(q.degree()+i,i+q.degree()-j)=q[j];
|
|
return a;
|
|
}
|
|
|
|
template <typename T>
|
|
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()];
|
|
return a;
|
|
}
|
|
|
|
template<>
|
|
NRVec<typename LA_traits<int>::complextype> Polynomial<int>::roots() const
|
|
{
|
|
laerror("roots not implemented for integer polynomials");
|
|
return NRVec<typename LA_traits<int>::complextype>(1);
|
|
}
|
|
|
|
template <typename T>
|
|
NRVec<typename LA_traits<T>::complextype> Polynomial<T>::roots() const
|
|
{
|
|
NRMat<T> a=this->companion();
|
|
NRVec<typename LA_traits<T>::complextype> r(degree());
|
|
gdiagonalize(a,r,NULL,NULL);
|
|
return r;
|
|
}
|
|
|
|
template <typename T>
|
|
NRVec<T> Polynomial<T>::realroots(const typename LA_traits<T>::normtype thr) const
|
|
{
|
|
NRVec<typename LA_traits<T>::complextype> r = roots();
|
|
NRVec<T> rr(degree());
|
|
int nr=0;
|
|
for(int i=0; i<degree(); ++i)
|
|
{
|
|
if(abs(r[i].imag())<thr)
|
|
{
|
|
rr[nr++] = r[i].real();
|
|
}
|
|
}
|
|
rr.resize(nr,true);
|
|
rr.sort();
|
|
return rr;
|
|
}
|
|
|
|
template <typename T>
|
|
Polynomial<T> lagrange_interpolation(const NRVec<T> &x, const NRVec<T> &y)
|
|
{
|
|
if(x.size()!=y.size()) laerror("vectors of different length in lagrange_interpolation");
|
|
if(x.size()<1) laerror("empty vector in lagrange_interpolation");
|
|
if(x.size()==1)
|
|
{
|
|
Polynomial<T> p(0);
|
|
p[0]=y[0];
|
|
return p;
|
|
}
|
|
int n=x.size()-1;
|
|
Polynomial<T> p(n);
|
|
p.clear();
|
|
for(int i=0; i<=n; ++i)
|
|
{
|
|
T prod=(T)1;
|
|
for(int j=0; j<=n; ++j) if(j!=i) prod *= (x[i]-x[j]);
|
|
if(prod==(T)0) laerror("repeated x-value in lagrange_interpolation");
|
|
Polynomial<T> tmp=polyfromroots(x,i);
|
|
p += tmp * y[i] / prod;
|
|
}
|
|
return p;
|
|
}
|
|
|
|
|
|
|
|
|
|
/***************************************************************************//**
|
|
* forced instantization in the corresponding object file
|
|
******************************************************************************/
|
|
template class Polynomial<int>;
|
|
template class Polynomial<double>;
|
|
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); \
|
|
|
|
|
|
INSTANTIZE(int)
|
|
INSTANTIZE(double)
|
|
INSTANTIZE(std::complex<double>)
|
|
|
|
|
|
|
|
}//namespace
|