libgofigure-dev 0.9.0-3 / usr / include / gofigure2 / Polynomial.inl

/*=========================================================================
 Authors: Michael Kazhdan and Matthew Bolitho
 at Johns Hopkins University, 2006-10

 Copyright (c) 2006-10, Michael Kazhdan and Matthew Bolitho, 
 Johns Hopkins University.
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#include <float.h>
#include <cmath>
#include <algorithm>
#include "Factor.h"

////////////////
// Polynomial //
////////////////
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<int Degree>
double Polynomial<Degree>::operator() (const double& t) const{
	double temp=1;
	double v=0;
	for(int i=0;i<=Degree;i++){
		v+=temp*coefficients[i];
		temp*=t;
	}
	return v;
}
template<int Degree>
double Polynomial<Degree>::integral(const double& tMin,const 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,const 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,const 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,const double& w1,const Polynomial& p2,const 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,const 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,const 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 += (const double& s){
	coefficients[0]+=s;
	return *this;
}
template<int Degree>
Polynomial<Degree>& Polynomial<Degree>::operator -= (const double& s){
	coefficients[0]-=s;
	return *this;
}
template<int Degree>
Polynomial<Degree>& Polynomial<Degree>::operator *= (const double& s){
	for(int i=0;i<=Degree;i++){coefficients[i]*=s;}
	return *this;
}
template<int Degree>
Polynomial<Degree>& Polynomial<Degree>::operator /= (const double& s){
	for(int i=0;i<=Degree;i++){coefficients[i]/=s;}
	return *this;
}
template<int Degree>
Polynomial<Degree> Polynomial<Degree>::operator + (const double& s) const{
	Polynomial<Degree> q=*this;
	q.coefficients[0]+=s;
	return q;
}
template<int Degree>
Polynomial<Degree> Polynomial<Degree>::operator - (const double& s) const{
	Polynomial q=*this;
	q.coefficients[0]-=s;
	return q;
}
template<int Degree>
Polynomial<Degree> Polynomial<Degree>::operator * (const 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 / (const double& s) const{
	Polynomial q(this->degree());
	for(int i=0;i<=Degree;i++){q.coefficients[i]=coefficients[i]/s;}
	return q;
}
template<int Degree>
Polynomial<Degree> Polynomial<Degree>::scale(const 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(const 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(const double& c,std::vector<double>& roots,const 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]);
//printf("%d] %f\t%f\n",i,r[i][0],(*this)(r[i][0])-c);
		}
	}
}