polynomial.hpp

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/*
Copyright (c) 2006, Michael Kazhdan and Matthew Bolitho
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#include <float.h>
#include <math.h>
#include <algorithm>
#include "factor.h"

// Polynomial //

namespace pcl
{
  namespace poisson
  {


    template<int Degree>
    Polynomial<Degree>::Polynomial(void){memset(coefficients,0,sizeof(double)*(Degree+1));}
    template<int Degree>
    template<int Degree2>
    Polynomial<Degree>::Polynomial(const Polynomial<Degree2>& P){
      memset(coefficients,0,sizeof(double)*(Degree+1));
      for(int i=0;i<=Degree && i<=Degree2;i++){coefficients[i]=P.coefficients[i];}
    }


    template<int Degree>
    template<int Degree2>
    Polynomial<Degree>& Polynomial<Degree>::operator  = (const Polynomial<Degree2> &p){
      int d=Degree<Degree2?Degree:Degree2;
      memset(coefficients,0,sizeof(double)*(Degree+1));
      memcpy(coefficients,p.coefficients,sizeof(double)*(d+1));
      return *this;
    }

    template<int Degree>
    Polynomial<Degree-1> Polynomial<Degree>::derivative(void) const{
      Polynomial<Degree-1> p;
      for(int i=0;i<Degree;i++){p.coefficients[i]=coefficients[i+1]*(i+1);}
      return p;
    }

    template<int Degree>
    Polynomial<Degree+1> Polynomial<Degree>::integral(void) const{
      Polynomial<Degree+1> p;
      p.coefficients[0]=0;
      for(int i=0;i<=Degree;i++){p.coefficients[i+1]=coefficients[i]/(i+1);}
      return p;
    }
    template<> double Polynomial< 0 >::operator() ( double t ) const { return coefficients[0]; }
    template<> double Polynomial< 1 >::operator() ( double t ) const { return coefficients[0]+coefficients[1]*t; }
    template<> double Polynomial< 2 >::operator() ( double t ) const { return coefficients[0]+(coefficients[1]+coefficients[2]*t)*t; }
    template<int Degree>
    double Polynomial<Degree>::operator() ( double t ) const{
      double v=coefficients[Degree];
      for( int d=Degree-1 ; d>=0 ; d-- ) v = v*t + coefficients[d];
      return v;
    }
    template<int Degree>
    double Polynomial<Degree>::integral( double tMin , double tMax ) const
    {
      double v=0;
      double t1,t2;
      t1=tMin;
      t2=tMax;
      for(int i=0;i<=Degree;i++){
        v+=coefficients[i]*(t2-t1)/(i+1);
        if(t1!=-DBL_MAX && t1!=DBL_MAX){t1*=tMin;}
        if(t2!=-DBL_MAX && t2!=DBL_MAX){t2*=tMax;}
      }
      return v;
    }
    template<int Degree>
    int Polynomial<Degree>::operator == (const Polynomial& p) const{
      for(int i=0;i<=Degree;i++){if(coefficients[i]!=p.coefficients[i]){return 0;}}
      return 1;
    }
    template<int Degree>
    int Polynomial<Degree>::operator != (const Polynomial& p) const{
      for(int i=0;i<=Degree;i++){if(coefficients[i]==p.coefficients[i]){return 0;}}
      return 1;
    }
    template<int Degree>
    int Polynomial<Degree>::isZero(void) const{
      for(int i=0;i<=Degree;i++){if(coefficients[i]!=0){return 0;}}
      return 1;
    }
    template<int Degree>
    void Polynomial<Degree>::setZero(void){memset(coefficients,0,sizeof(double)*(Degree+1));}

    template<int Degree>
    Polynomial<Degree>& Polynomial<Degree>::addScaled(const Polynomial& p,double s){
      for(int i=0;i<=Degree;i++){coefficients[i]+=p.coefficients[i]*s;}
      return *this;
    }
    template<int Degree>
    Polynomial<Degree>& Polynomial<Degree>::operator += (const Polynomial<Degree>& p){
      for(int i=0;i<=Degree;i++){coefficients[i]+=p.coefficients[i];}
      return *this;
    }
    template<int Degree>
    Polynomial<Degree>& Polynomial<Degree>::operator -= (const Polynomial<Degree>& p){
      for(int i=0;i<=Degree;i++){coefficients[i]-=p.coefficients[i];}
      return *this;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::operator + (const Polynomial<Degree>& p) const{
      Polynomial q;
      for(int i=0;i<=Degree;i++){q.coefficients[i]=(coefficients[i]+p.coefficients[i]);}
      return q;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::operator - (const Polynomial<Degree>& p) const{
      Polynomial q;
      for(int i=0;i<=Degree;i++)        {q.coefficients[i]=coefficients[i]-p.coefficients[i];}
      return q;
    }
    template<int Degree>
    void Polynomial<Degree>::Scale(const Polynomial& p,double w,Polynomial& q){
      for(int i=0;i<=Degree;i++){q.coefficients[i]=p.coefficients[i]*w;}
    }
    template<int Degree>
    void Polynomial<Degree>::AddScaled(const Polynomial& p1,double w1,const Polynomial& p2,double w2,Polynomial& q){
      for(int i=0;i<=Degree;i++){q.coefficients[i]=p1.coefficients[i]*w1+p2.coefficients[i]*w2;}
    }
    template<int Degree>
    void Polynomial<Degree>::AddScaled(const Polynomial& p1,double w1,const Polynomial& p2,Polynomial& q){
      for(int i=0;i<=Degree;i++){q.coefficients[i]=p1.coefficients[i]*w1+p2.coefficients[i];}
    }
    template<int Degree>
    void Polynomial<Degree>::AddScaled(const Polynomial& p1,const Polynomial& p2,double w2,Polynomial& q){
      for(int i=0;i<=Degree;i++){q.coefficients[i]=p1.coefficients[i]+p2.coefficients[i]*w2;}
    }

    template<int Degree>
    void Polynomial<Degree>::Subtract(const Polynomial &p1,const Polynomial& p2,Polynomial& q){
      for(int i=0;i<=Degree;i++){q.coefficients[i]=p1.coefficients[i]-p2.coefficients[i];}
    }
    template<int Degree>
    void Polynomial<Degree>::Negate(const Polynomial& in,Polynomial& out){
      out=in;
      for(int i=0;i<=Degree;i++){out.coefficients[i]=-out.coefficients[i];}
    }

    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::operator - (void) const{
      Polynomial q=*this;
      for(int i=0;i<=Degree;i++){q.coefficients[i]=-q.coefficients[i];}
      return q;
    }
    template<int Degree>
    template<int Degree2>
    Polynomial<Degree+Degree2> Polynomial<Degree>::operator * (const Polynomial<Degree2>& p) const{
      Polynomial<Degree+Degree2> q;
      for(int i=0;i<=Degree;i++){for(int j=0;j<=Degree2;j++){q.coefficients[i+j]+=coefficients[i]*p.coefficients[j];}}
      return q;
    }

    template<int Degree>
    Polynomial<Degree>& Polynomial<Degree>::operator += ( double s )
    {
      coefficients[0]+=s;
      return *this;
    }
    template<int Degree>
    Polynomial<Degree>& Polynomial<Degree>::operator -= ( double s )
    {
      coefficients[0]-=s;
      return *this;
    }
    template<int Degree>
    Polynomial<Degree>& Polynomial<Degree>::operator *= ( double s )
    {
      for(int i=0;i<=Degree;i++){coefficients[i]*=s;}
      return *this;
    }
    template<int Degree>
    Polynomial<Degree>& Polynomial<Degree>::operator /= ( double s )
    {
      for(int i=0;i<=Degree;i++){coefficients[i]/=s;}
      return *this;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::operator + ( double s ) const
    {
      Polynomial<Degree> q=*this;
      q.coefficients[0]+=s;
      return q;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::operator - ( double s ) const
    {
      Polynomial q=*this;
      q.coefficients[0]-=s;
      return q;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::operator * ( double s ) const
    {
      Polynomial q;
      for(int i=0;i<=Degree;i++){q.coefficients[i]=coefficients[i]*s;}
      return q;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::operator / ( double s ) const
    {
      Polynomial q;
      for( int i=0 ; i<=Degree ; i++ ) q.coefficients[i] = coefficients[i]/s;
      return q;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::scale( double s ) const
    {
      Polynomial q=*this;
      double s2=1.0;
      for(int i=0;i<=Degree;i++){
        q.coefficients[i]*=s2;
        s2/=s;
      }
      return q;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::shift( double t ) const
    {
      Polynomial<Degree> q;
      for(int i=0;i<=Degree;i++){
        double temp=1;
        for(int j=i;j>=0;j--){
          q.coefficients[j]+=coefficients[i]*temp;
          temp*=-t*j;
          temp/=(i-j+1);
        }
      }
      return q;
    }
    template<int Degree>
    void Polynomial<Degree>::printnl(void) const{
      for(int j=0;j<=Degree;j++){
        printf("%6.4f x^%d ",coefficients[j],j);
        if(j<Degree && coefficients[j+1]>=0){printf("+");}
      }
      printf("\n");
    }
    template<int Degree>
    void Polynomial<Degree>::getSolutions(double c,std::vector<double>& roots,double EPS) const
    {
      double r[4][2];
      int rCount=0;
      roots.clear();
      switch(Degree){
      case 1:
        rCount=Factor(coefficients[1],coefficients[0]-c,r,EPS);
        break;
      case 2:
        rCount=Factor(coefficients[2],coefficients[1],coefficients[0]-c,r,EPS);
        break;
      case 3:
        rCount=Factor(coefficients[3],coefficients[2],coefficients[1],coefficients[0]-c,r,EPS);
        break;
        //      case 4:
        //              rCount=Factor(coefficients[4],coefficients[3],coefficients[2],coefficients[1],coefficients[0]-c,r,EPS);
        //              break;
      default:
        printf("Can't solve polynomial of degree: %d\n",Degree);
      }
      for(int i=0;i<rCount;i++){
        if(fabs(r[i][1])<=EPS){
          roots.push_back(r[i][0]);
        }
      }
    }
    template< >
    Polynomial< 0 > Polynomial< 0 >::BSplineComponent( int i )
    {
      Polynomial p;
      p.coefficients[0] = 1.;
      return p;
    }
    template< int Degree >
    Polynomial< Degree > Polynomial< Degree >::BSplineComponent( int i )
    {
      Polynomial p;
      if( i>0 )
      {
        Polynomial< Degree > _p = Polynomial< Degree-1 >::BSplineComponent( i-1 ).integral();
        p -= _p;
        p.coefficients[0] += _p(1);
      }
      if( i<Degree )
      {
        Polynomial< Degree > _p = Polynomial< Degree-1 >::BSplineComponent( i ).integral();
        p += _p;
      }
      return p;
    }

  }
}