PPolynomial.inl

/*
Copyright (c) 2006, Michael Kazhdan and Matthew Bolitho
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*/

#include "Factor.h"

////////////////////////
// StartingPolynomial //
////////////////////////
template<int Degree>
template<int Degree2>
inline StartingPolynomial<Degree+Degree2> StartingPolynomial<Degree>::operator * (const StartingPolynomial<Degree2>& iP) const
{
	StartingPolynomial<Degree+Degree2> sp;
	if(start>iP.start){sp.start=start;}
	else{sp.start=iP.start;}
	sp.p=this->p*iP.p;
	return sp;
}

template<int Degree>
inline StartingPolynomial<Degree> StartingPolynomial<Degree>::scale(const double& s) const
{
	StartingPolynomial q;
	q.start=start*s;
	q.p=p.scale(s);
	return q;
}

template<int Degree>
inline StartingPolynomial<Degree> StartingPolynomial<Degree>::shift(const double& s) const
{
	StartingPolynomial q;
	q.start=start+s;
	q.p=p.shift(s);
	return q;
}


template<int Degree>
inline int StartingPolynomial<Degree>::operator < (const StartingPolynomial<Degree>& sp) const
{
	if(start<sp.start)
    {
      return 1;
    }
	else
    {
      return 0;
    }
}

template<int Degree>
inline int StartingPolynomial<Degree>::Compare(const void* v1,const void* v2)
{
	double d=((StartingPolynomial*)(v1))->start-((StartingPolynomial*)(v2))->start;
	if		(d<0)	{return -1;}
	else if	(d>0)	{return  1;}
	else			{return  0;}
}

/////////////////
// PPolynomial //
/////////////////
template<int Degree>
inline PPolynomial<Degree>::PPolynomial(void)
{
	polyCount=0;
	polys=NULL;
}

template<int Degree>
inline PPolynomial<Degree>::PPolynomial(const PPolynomial<Degree>& p)
{
	polyCount=0;
	polys=NULL;
	set(p.polyCount);
	memcpy(polys,p.polys,sizeof(StartingPolynomial<Degree>)*p.polyCount);
}

template<int Degree>
inline PPolynomial<Degree>::~PPolynomial(void)
{
	if(polyCount){free(polys);}
	polyCount=0;
	polys=NULL;
}

template<int Degree>
inline void PPolynomial<Degree>::set(StartingPolynomial<Degree>* sps,const int& count)
{
	int i,c=0;
	set(count);
	qsort(sps,count,sizeof(StartingPolynomial<Degree>),StartingPolynomial<Degree>::Compare);
	for(i=0;i<count;i++){
		if(!c || sps[i].start!=polys[c-1].start){polys[c++]=sps[i];}
		else{polys[c-1].p+=sps[i].p;}
	}
	reset(c);
}

template <int Degree>
inline int PPolynomial<Degree>::size(void) const
{
  return int(sizeof(StartingPolynomial<Degree>)*polyCount);
}

template<int Degree>
inline void PPolynomial<Degree>::set(const size_t &iSize)
{
	if(polyCount){free(polys);}
	polyCount=0;
	polys=NULL;
	polyCount=iSize;
	if(iSize){
		polys=(StartingPolynomial<Degree>*)malloc(sizeof(StartingPolynomial<Degree>)*iSize);
		memset(polys,0,sizeof(StartingPolynomial<Degree>)*iSize);
	}
}

template<int Degree>
inline void PPolynomial<Degree>::reset(const size_t& newSize)
{
	polyCount=newSize;
	polys=(StartingPolynomial<Degree>*)realloc(polys,sizeof(StartingPolynomial<Degree>)*newSize);
}

template<int Degree>
inline PPolynomial<Degree>& PPolynomial<Degree>::operator = (const PPolynomial<Degree>& p)
{
	set(p.polyCount);
	memcpy(polys,p.polys,sizeof(StartingPolynomial<Degree>)*p.polyCount);
	return *this;
}

template<int Degree>
template<int Degree2>
inline PPolynomial<Degree>& PPolynomial<Degree>::operator  = (const PPolynomial<Degree2>& p)
{
	set(p.polyCount);
	for(int i=0;i<int(polyCount);i++){
		polys[i].start=p.polys[i].start;
		polys[i].p=p.polys[i].p;
	}
	return *this;
}

template<int Degree>
inline double PPolynomial<Degree>::operator ()(const double& t) const
{
	double v=0;
	for(int i=0;i<int(polyCount) && t>polys[i].start;i++)
    {
      v+=polys[i].p(t);
    }
	return v;
}

template<int Degree>
inline double PPolynomial<Degree>::integral(const double& tMin,const double& tMax) const
{
	int m=1;
	double start,end,s,v=0;
	start=tMin;
	end=tMax;
	if(tMin>tMax){
		m=-1;
		start=tMax;
		end=tMin;
	}
	for(int i=0;i<int(polyCount) && polys[i].start<end;i++){
		if(start<polys[i].start){s=polys[i].start;}
		else{s=start;}
		v+=polys[i].p.integral(s,end);
	}
	return v*m;
}

template<int Degree>
inline double PPolynomial<Degree>::Integral(void) const
{
  return integral(polys[0].start,polys[polyCount-1].start);
}

template<int Degree>
inline PPolynomial<Degree> PPolynomial<Degree>::operator + (const PPolynomial<Degree>& p) const
{
	PPolynomial q;
	int i,j;
	size_t idx=0;
	q.set(polyCount+p.polyCount);
	i=j=-1;

	while(idx<q.polyCount){
		if		(j>=int(p.polyCount)-1)				{q.polys[idx]=  polys[++i];}
		else if	(i>=int(  polyCount)-1)				{q.polys[idx]=p.polys[++j];}
		else if(polys[i+1].start<p.polys[j+1].start){q.polys[idx]=  polys[++i];}
		else										{q.polys[idx]=p.polys[++j];}
//		if(idx && polys[idx].start==polys[idx-1].start)	{polys[idx-1].p+=polys[idx].p;}
//		else{idx++;}
		idx++;
	}
	return q;
}

template<int Degree>
inline PPolynomial<Degree> PPolynomial<Degree>::operator - (const PPolynomial<Degree>& p) const
{
	PPolynomial q;
	int i,j;
	size_t idx=0;
	q.set(polyCount+p.polyCount);
	i=j=-1;

	while(idx<q.polyCount){
		if		(j>=int(p.polyCount)-1)				{q.polys[idx]=  polys[++i];}
		else if	(i>=int(  polyCount)-1)				{q.polys[idx].start=p.polys[++j].start;q.polys[idx].p=p.polys[j].p*(-1.0);}
		else if(polys[i+1].start<p.polys[j+1].start){q.polys[idx]=  polys[++i];}
		else										{q.polys[idx].start=p.polys[++j].start;q.polys[idx].p=p.polys[j].p*(-1.0);}
//		if(idx && polys[idx].start==polys[idx-1].start)	{polys[idx-1].p+=polys[idx].p;}
//		else{idx++;}
		idx++;
	}
	return q;
}

template<int Degree>
inline PPolynomial<Degree>& PPolynomial<Degree>::addScaled(const PPolynomial<Degree>& p,const double& iScale)
{
	int i,j;
	StartingPolynomial<Degree>* oldPolys=polys;
	size_t idx=0,cnt=0,oldPolyCount=polyCount;
	polyCount=0;
	polys=NULL;
	set(oldPolyCount+p.polyCount);
	i=j=-1;
	while(cnt<polyCount){
		if		(j>=int( p.polyCount)-1)				{polys[idx]=oldPolys[++i];}
		else if	(i>=int(oldPolyCount)-1)				{polys[idx].start= p.polys[++j].start;polys[idx].p=p.polys[j].p*iScale;}
		else if	(oldPolys[i+1].start<p.polys[j+1].start){polys[idx]=oldPolys[++i];}
		else											{polys[idx].start= p.polys[++j].start;polys[idx].p=p.polys[j].p*iScale;}
		if(idx && polys[idx].start==polys[idx-1].start)	{polys[idx-1].p+=polys[idx].p;}
		else{idx++;}
		cnt++;
	}
	free(oldPolys);
	reset(idx);
	return *this;
}

template<int Degree>
template<int Degree2>
inline PPolynomial<Degree+Degree2> PPolynomial<Degree>::operator * (const PPolynomial<Degree2>& p) const
{
	PPolynomial<Degree+Degree2> q;
	StartingPolynomial<Degree+Degree2> *sp;
	int i,j,spCount=int(polyCount*p.polyCount);

	sp=(StartingPolynomial<Degree+Degree2>*)malloc(sizeof(StartingPolynomial<Degree+Degree2>)*spCount);
	for(i=0;i<int(polyCount);i++){
		for(j=0;j<int(p.polyCount);j++){
			sp[i*p.polyCount+j]=polys[i]*p.polys[j];
		}
	}
	q.set(sp,spCount);
	free(sp);
	return q;
}

template<int Degree>
template<int Degree2>
inline PPolynomial<Degree+Degree2> PPolynomial<Degree>::operator * (const Polynomial<Degree2>& p) const
{
	PPolynomial<Degree+Degree2> q;
	q.set(polyCount);
	for(int i=0;i<int(polyCount);i++){
		q.polys[i].start=polys[i].start;
		q.polys[i].p=polys[i].p*p;
	}
	return q;
}

template<int Degree>
inline PPolynomial<Degree> PPolynomial<Degree>::scale(const double& s) const
{
	PPolynomial q;
	q.set(polyCount);
	for(size_t i=0;i<polyCount;i++){q.polys[i]=polys[i].scale(s);}
	return q;
}

template<int Degree>
inline PPolynomial<Degree> PPolynomial<Degree>::shift(const double& s) const
{
	PPolynomial q;
	q.set(polyCount);
	for(size_t i=0;i<polyCount;i++){q.polys[i]=polys[i].shift(s);}
	return q;
}

template<int Degree>
inline PPolynomial<Degree-1> PPolynomial<Degree>::derivative(void) const
{
	PPolynomial<Degree-1> q;
	q.set(polyCount);
	for(size_t i=0;i<polyCount;i++){
		q.polys[i].start=polys[i].start;
		q.polys[i].p=polys[i].p.derivative();
	}
	return q;
}

template<int Degree>
inline PPolynomial<Degree+1> PPolynomial<Degree>::integral(void) const
{
	int i;
	PPolynomial<Degree+1> q;
	q.set(polyCount);
	for(i=0;i<int(polyCount);i++){
		q.polys[i].start=polys[i].start;
		q.polys[i].p=polys[i].p.integral();
		q.polys[i].p-=q.polys[i].p(q.polys[i].start);
	}
	return q;
}

template<int Degree>
inline PPolynomial<Degree>& PPolynomial<Degree>::operator  += (const double &s)
{
  polys[0].p+=s;
}

template<int Degree>
inline PPolynomial<Degree>& PPolynomial<Degree>::operator  -= (const double &s)
{
  polys[0].p-=s;
}

template<int Degree>
inline PPolynomial<Degree>& PPolynomial<Degree>::operator  *= (const double &s)
{
	for(int i=0;i<int(polyCount);i++)
    {
      polys[i].p*=s;
    }
	return *this;
}

template<int Degree>
inline PPolynomial<Degree>& PPolynomial<Degree>::operator  /= (const double &s)
{
	for(size_t i=0;i<polyCount;i++)
    {
      polys[i].p/=s;
    }
	return *this;
}

template<int Degree>
inline PPolynomial<Degree> PPolynomial<Degree>::operator + (const double& s) const
{
	PPolynomial q=*this;
	q+=s;
	return q;
}

template<int Degree>
inline PPolynomial<Degree> PPolynomial<Degree>::operator - (const double& s) const
{
	PPolynomial q=*this;
	q-=s;
	return q;
}

template<int Degree>
inline PPolynomial<Degree> PPolynomial<Degree>::operator * (const double& s) const
{
	PPolynomial q=*this;
	q*=s;
	return q;
}

template<int Degree>
inline PPolynomial<Degree> PPolynomial<Degree>::operator / (const double& s) const
{
	PPolynomial q=*this;
	q/=s;
	return q;
}

template<int Degree>
inline void PPolynomial<Degree>::printnl(void) const
{
	Polynomial<Degree> p;

	if(!polyCount){
		printf("[-Infinity,Infinity]\n");
	}
	else{
		for(size_t i=0;i<polyCount;i++){
			printf("[");
			if		(polys[i  ].start== DBL_MAX){printf("Infinity,");}
			else if	(polys[i  ].start==-DBL_MAX){printf("-Infinity,");}
			else								{printf("%f,",polys[i].start);}
			if(i+1==polyCount)					{printf("Infinity]\t");}
			else if (polys[i+1].start== DBL_MAX){printf("Infinity]\t");}
			else if	(polys[i+1].start==-DBL_MAX){printf("-Infinity]\t");}
			else								{printf("%f]\t",polys[i+1].start);}
			p=p+polys[i].p;
			p.printnl();
		}
	}
	printf("\n");
}

template<int Degree>
inline PPolynomial<Degree> PPolynomial<Degree>::ConstantFunction(const double& radius)
{
	if(Degree<0){
		fprintf(stderr,"Could not set degree %d polynomial as constant\n",Degree);
		exit(0);
	}
	PPolynomial q;
	q.set(2);

	q.polys[0].start=-radius;
	q.polys[1].start= radius;

	q.polys[0].p.coefficients[0]= 1.0;
	q.polys[1].p.coefficients[0]=-1.0;
	return q;
}

template<>
inline PPolynomial<0> PPolynomial<0>::GaussianApproximation(const double& width)
{
	return ConstantFunction(width);
}

template<int Degree>
inline PPolynomial<Degree> PPolynomial<Degree>::GaussianApproximation(const double& width)
{
  return PPolynomial<Degree-1>::GaussianApproximation().MovingAverage(width);
}

template<int Degree>
inline PPolynomial<Degree+1> PPolynomial<Degree>::MovingAverage(const double& radius)
{
	PPolynomial<Degree+1> A;
	Polynomial<Degree+1> p;
	StartingPolynomial<Degree+1>* sps;

	sps=(StartingPolynomial<Degree+1>*)malloc(sizeof(StartingPolynomial<Degree+1>)*polyCount*2);

	for(int i=0;i<int(polyCount);i++){
		sps[2*i  ].start=polys[i].start-radius;
		sps[2*i+1].start=polys[i].start+radius;
		p=polys[i].p.integral()-polys[i].p.integral()(polys[i].start);
		sps[2*i  ].p=p.shift(-radius);
		sps[2*i+1].p=p.shift( radius)*-1;
	}
	A.set(sps,int(polyCount*2));
	free(sps);
	return A*1.0/(2*radius);
}

template<int Degree>
inline void PPolynomial<Degree>::getSolutions(const double& c,std::vector<double>& roots,const double& EPS,const double& min,const double& max) const
{
	Polynomial<Degree> p;
	std::vector<double> tempRoots;

	p.setZero();
	for(size_t i=0;i<polyCount;i++){
		p+=polys[i].p;
		if(polys[i].start>max){break;}
		if(i<polyCount-1 && polys[i+1].start<min){continue;}
		p.getSolutions(c,tempRoots,EPS);
		for(size_t j=0;j<tempRoots.size();j++){
			if(tempRoots[j]>polys[i].start && (i+1==polyCount || tempRoots[j]<=polys[i+1].start)){
				if(tempRoots[j]>min && tempRoots[j]<max){roots.push_back(tempRoots[j]);}
			}
		}
	}
}

template<int Degree>
inline void PPolynomial<Degree>::write(FILE* fp,const int& samples,const double& min,const double& max) const
{
	fwrite(&samples,sizeof(int),1,fp);
	for(int i=0;i<samples;i++){
		double x=min+i*(max-min)/(samples-1);
		float v=(*this)(x);
		fwrite(&v,sizeof(float),1,fp);
	}
}