PPolynomial.inl

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

#include "Factor.h"

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


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

// PPolynomial //
template<int Degree>
PPolynomial<Degree>::PPolynomial(void){
  polyCount=0;
  polys=NULL;
}
template<int Degree>
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>
PPolynomial<Degree>::~PPolynomial(void){
  if(polyCount){free(polys);}
  polyCount=0;
  polys=NULL;
}
template<int Degree>
void PPolynomial<Degree>::set(StartingPolynomial<Degree>* sps,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>
int PPolynomial<Degree>::size(void) const{return int(sizeof(StartingPolynomial<Degree>)*polyCount);}

template<int Degree>
void PPolynomial<Degree>::set( size_t size )
{
  if(polyCount){free(polys);}
  polyCount=0;
  polys=NULL;
  polyCount=size;
  if(size){
    polys=static_cast<StartingPolynomial<Degree>*>(malloc(sizeof(StartingPolynomial<Degree>)*size));
    memset(polys,0,sizeof(StartingPolynomial<Degree>)*size);
  }
}
template<int Degree>
void PPolynomial<Degree>::reset( size_t newSize )
{
  polyCount=newSize;
  StartingPolynomial<Degree>* tmp = static_cast<StartingPolynomial<Degree>*>(realloc(polys,sizeof(StartingPolynomial<Degree>)*newSize));
  if (!tmp)
    free(polys);
  polys=tmp;
}

template<int Degree>
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>
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>
double PPolynomial<Degree>::operator ()( 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>
double PPolynomial<Degree>::integral( double tMin , 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>
double PPolynomial<Degree>::Integral(void) const{return integral(polys[0].start,polys[polyCount-1].start);}
template<int Degree>
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];}
    idx++;
  }
  return q;
}
template<int Degree>
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);}
    idx++;
  }
  return q;
}
template<int Degree>
PPolynomial<Degree>& PPolynomial<Degree>::addScaled(const PPolynomial<Degree>& p,double scale){
  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*scale;}
    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*scale;}
    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>
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>
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>
PPolynomial<Degree> PPolynomial<Degree>::scale( 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>
PPolynomial<Degree> PPolynomial<Degree>::shift( 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>
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>
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>
PPolynomial<Degree>& PPolynomial<Degree>::operator  += ( double s ) {polys[0].p+=s;}
template<int Degree>
PPolynomial<Degree>& PPolynomial<Degree>::operator  -= ( double s ) {polys[0].p-=s;}
template<int Degree>
PPolynomial<Degree>& PPolynomial<Degree>::operator  *= ( double s )
{
  for(int i=0;i<int(polyCount);i++){polys[i].p*=s;}
  return *this;
}
template<int Degree>
PPolynomial<Degree>& PPolynomial<Degree>::operator  /= ( double s )
{
  for(size_t i=0;i<polyCount;i++){polys[i].p/=s;}
  return *this;
}
template<int Degree>
PPolynomial<Degree> PPolynomial<Degree>::operator + ( double s ) const
{
  PPolynomial q=*this;
  q+=s;
  return q;
}
template<int Degree>
PPolynomial<Degree> PPolynomial<Degree>::operator - ( double s ) const
{
  PPolynomial q=*this;
  q-=s;
  return q;
}
template<int Degree>
PPolynomial<Degree> PPolynomial<Degree>::operator * ( double s ) const
{
  PPolynomial q=*this;
  q*=s;
  return q;
}
template<int Degree>
PPolynomial<Degree> PPolynomial<Degree>::operator / ( double s ) const
{
  PPolynomial q=*this;
  q/=s;
  return q;
}

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

  if(!polyCount){
    Polynomial<Degree> p;
    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< >
PPolynomial< 0 > PPolynomial< 0 >::BSpline( double radius )
{
  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<int Degree >
PPolynomial< Degree > PPolynomial<Degree>::BSpline( double radius )
{
  return PPolynomial< Degree-1 >::BSpline().MovingAverage( radius );
}
template<int Degree>
PPolynomial<Degree+1> PPolynomial<Degree>::MovingAverage( double radius )
{
  PPolynomial<Degree+1> A;
  Polynomial<Degree+1> p;
  StartingPolynomial<Degree+1>* sps;

  sps=static_cast<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>
void PPolynomial<Degree>::getSolutions(double c,std::vector<double>& roots,double EPS,double min,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>
void PPolynomial<Degree>::write(FILE* fp,int samples,double min,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);
  }
}