Polynomial.inl

/*
Copyright (c) 2006, Michael Kazhdan and Matthew Bolitho
All rights reserved.

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are permitted provided that the following conditions are met:

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the above copyright notice, this list of conditions and the following disclaimer
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may be used to endorse or promote products derived from this software without specific
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*/

#include <float.h>
#include <math.h>
#include <algorithm>
#include "Factor.cuh"

////////////////
// Polynomial //
////////////////
template<int Degree>
__host__ __device__ Polynomial<Degree>::Polynomial(void){
#if !defined(__CUDA_ARCH__)
    memset(coefficients,0,sizeof(float)*(Degree+1));
#endif
}
template<int Degree>
template<int Degree2>
Polynomial<Degree>::Polynomial(const Polynomial<Degree2>& P){
    memset(coefficients,0,sizeof(float)*(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(float)*(Degree+1));
    memcpy(coefficients,p.coefficients,sizeof(float)*(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>
__host__ __device__ float Polynomial<Degree>::operator() (const float& t) const{
    float temp=1;
    float v=0;
    for(int i=0;i<=Degree;i++){
        v+=temp*coefficients[i];
        temp*=t;
    }
    return v;
}
template<int Degree>
float Polynomial<Degree>::integral(const float& tMin,const float& tMax) const{
    float v=0;
    float 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(float)*(Degree+1));}

template<int Degree>
Polynomial<Degree>& Polynomial<Degree>::addScaled(const Polynomial& p,const float& 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 float& 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 float& w1,const Polynomial& p2,const float& 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 float& 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 float& 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>
__host__ __device__ 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 float& s){
    coefficients[0]+=s;
    return *this;
}
template<int Degree>
Polynomial<Degree>& Polynomial<Degree>::operator -= (const float& s){
    coefficients[0]-=s;
    return *this;
}
template<int Degree>
Polynomial<Degree>& Polynomial<Degree>::operator *= (const float& s){
    for(int i=0;i<=Degree;i++){coefficients[i]*=s;}
    return *this;
}
template<int Degree>
Polynomial<Degree>& Polynomial<Degree>::operator /= (const float& s){
    for(int i=0;i<=Degree;i++){coefficients[i]/=s;}
    return *this;
}
template<int Degree>
Polynomial<Degree> Polynomial<Degree>::operator + (const float& s) const{
    Polynomial<Degree> q=*this;
    q.coefficients[0]+=s;
    return q;
}
template<int Degree>
Polynomial<Degree> Polynomial<Degree>::operator - (const float& s) const{
    Polynomial q=*this;
    q.coefficients[0]-=s;
    return q;
}
template<int Degree>
Polynomial<Degree> Polynomial<Degree>::operator * (const float& 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 float& s) const{
    Polynomial q(Degree);
    for(int i=0;i<=Degree;i++){q.coefficients[i]=coefficients[i]/s;}
    return q;
}
template<int Degree>
__host__ __device__ Polynomial<Degree> Polynomial<Degree>::scale(const float& s) const{
    Polynomial q=*this;
    float s2=1.0;
    for(int i=0;i<=Degree;i++){
        q.coefficients[i]*=s2;
        s2/=s;
    }
    return q;
}
template<int Degree>
__host__ __device__ Polynomial<Degree> Polynomial<Degree>::shift(const float& t) const{
    Polynomial<Degree> q;
    for(int i=0;i<=Degree;i++){
        float 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 float& c,std::vector<float>& roots,const float& EPS) const {
    float 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);
        }
    }
}