FunctionData.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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*/

////////////////////////
// FunctionValueTable //
////////////////////////
template<class Real>
FunctionValueTable<Real>::FunctionValueTable(void){
    start=-1;
    size=0;
    values=NULL;
}
template<class Real>
FunctionValueTable<Real>::~FunctionValueTable(void){
    if(values){delete[] values;}
    start=-1;
    size=0;
    values=NULL;
}
template<class Real>
template<int Degree>
int FunctionValueTable<Real>::setValues(const PPolynomial<Degree>& ppoly,const int& res){
    int j;
    if(values){delete[] values;}
    start=-1;
    size=0;
    values=NULL;
    for(j=0;j<res;j++){
        double x=double(j)/(res-1);
        if(x>ppoly.polys[0].start && x<ppoly.polys[ppoly.polyCount-1].start){
            if(start==-1){start=j;}
            size=j+1-start;
        }
    }
    if(size){
        values=new Real[size];
        for(j=0;j<size;j++){
            double x=double(j+start)/(res-1);
            values[j]=Real(ppoly(x));
        }
    }
    return size;
}
template<class Real>
inline Real FunctionValueTable<Real>::operator [] (const int& idx){
    int i=idx-start;
    if(i<0 || i>=size){return 0;}
    else{return values[i];}
}

//////////////////
// FunctionData //
//////////////////
template<int Degree,class Real>
const int FunctionData<Degree,Real>::DOT_FLAG=1;
template<int Degree,class Real>
const int FunctionData<Degree,Real>::D_DOT_FLAG=2;
template<int Degree,class Real>
const int FunctionData<Degree,Real>::D2_DOT_FLAG=4;
template<int Degree,class Real>
const int FunctionData<Degree,Real>::VALUE_FLAG=1;
template<int Degree,class Real>
const int FunctionData<Degree,Real>::D_VALUE_FLAG=2;

template<int Degree,class Real>
FunctionData<Degree,Real>::FunctionData(void){
    dotTable=dDotTable=d2DotTable=NULL;
    valueTables=dValueTables=NULL;
    res=0;
}

template<int Degree,class Real>
FunctionData<Degree,Real>::~FunctionData(void){
    if(res){
        delete[] dotTable;
        delete[] dDotTable;
        delete[] d2DotTable;
        delete[] valueTables;
        delete[] dValueTables;
    }
    dotTable=dDotTable=d2DotTable=NULL;
    valueTables=dValueTables=NULL;
    res=0;
}

template<int Degree,class Real>
void FunctionData<Degree,Real>::set(const int& maxDepth,
                                    const PPolynomial<Degree>& F,
                                    const int& normalize,
                                    const int& useDotRatios){
    this->normalize=normalize;
    this->useDotRatios=useDotRatios;

    depth=maxDepth;
    res=BinaryNode<double>::CumulativeCenterCount(depth);
    res2=(1<<(depth+1))+1;
    baseFunctions=new PPolynomial<Degree+1>[res];
    // Scale the function so that it has:
    // 0] Value 1 at 0
    // 1] Integral equal to 1
    // 2] Square integral equal to 1
    switch(normalize){
        case 2:
            baseFunction=F/sqrt((F*F).integral(F.polys[0].start,F.polys[F.polyCount-1].start));
            break;
        case 1:
            baseFunction=F/F.integral(F.polys[0].start,F.polys[F.polyCount-1].start);
            break;
        default:
            baseFunction=F/F(0);
    }
    dBaseFunction=baseFunction.derivative();
    double c1,w1;
    for(int i=0;i<res;i++){
        BinaryNode<double>::CenterAndWidth(i,c1,w1);
//        printf("original start:%lf\n",baseFunction.polys[1].start);
//        baseFunction.printnl();
//        printf("%lf,%lf\n",c1,w1);
        baseFunctions[i]=baseFunction.scale(w1).shift(c1);
//        printf("next start:%lf\n",baseFunctions[i].polys[1].start);
//        baseFunctions[i].printnl();
        // Scale the function so that it has L2-norm equal to one
        switch(normalize){
            case 2:
                baseFunctions[i]/=sqrt(w1);
                break;
            case 1:
                baseFunctions[i]/=w1;
                break;
        }
    }
}
template<int Degree,class Real>
void FunctionData<Degree,Real>::setDotTables(const int& flags){
    clearDotTables(flags);
    if(flags & DOT_FLAG){
        dotTable=new double[res*res];
        memset(dotTable,0,sizeof(double)*res*res);
    }
    if(flags & D_DOT_FLAG){
        dDotTable=new double[res*res];
        memset(dDotTable,0,sizeof(double)*res*res);
    }
    if(flags & D2_DOT_FLAG){
        d2DotTable=new double[res*res];
        memset(d2DotTable,0,sizeof(double)*res*res);
    }

    double t1,t2;
    t1=baseFunction.polys[0].start;
    t2=baseFunction.polys[baseFunction.polyCount-1].start;
    for(int i=0;i<res;i++){
        double c1,c2,w1,w2;
        BinaryNode<double>::CenterAndWidth(i,c1,w1);
        // map the function centers at 0 to its real position
        double start1	=t1*w1+c1;
        double end1		=t2*w1+c1;
        for(int j=0;j<=i;j++){
            BinaryNode<double>::CenterAndWidth(j,c2,w2);
            int idx1=i+res*j;
            int idx2=j+res*i;

            double start	=t1*w2+c2;
            double end		=t2*w2+c2;

            if(start<start1){start=start1;}
            if(end>end1)	{end=end1;}
            if(start>=end){continue;}

            BinaryNode<double>::CenterAndWidth(j,c2,w2);
            double dot=dotProduct(c1,w1,c2,w2);
            if(fabs(dot)<1e-15){continue;}
            if(flags & DOT_FLAG){dotTable[idx1]=dotTable[idx2]=dot;}
            if(useDotRatios){
                if(flags & D_DOT_FLAG){
                    dDotTable [idx1]= dDotProduct(c1,w1,c2,w2)/dot;
                    dDotTable [idx2]=-dDotTable[idx1];
                }
                if(flags & D2_DOT_FLAG){d2DotTable[idx1]=d2DotTable[idx2]=d2DotProduct(c1,w1,c2,w2)/dot;}
            }
            else{
                if(flags & D_DOT_FLAG){
                    dDotTable[idx1]= dDotProduct(c1,w1,c2,w2);
                    dDotTable[idx2]=-dDotTable[idx1];
                }
                if(flags & D2_DOT_FLAG){d2DotTable[idx1]=d2DotTable[idx2]=d2DotProduct(c1,w1,c2,w2);}
            }
        }
    }
}
template<int Degree,class Real>
void FunctionData<Degree,Real>::clearDotTables(const int& flags){
    if((flags & DOT_FLAG) && dotTable){
        delete[] dotTable;
        dotTable=NULL;
    }
    if((flags & D_DOT_FLAG) && dDotTable){
        delete[] dDotTable;
        dDotTable=NULL;
    }
    if((flags & D2_DOT_FLAG) && d2DotTable){
        delete[] d2DotTable;
        d2DotTable=NULL;
    }
}
template<int Degree,class Real>
void FunctionData<Degree,Real>::setValueTables(const int& flags,const double& smooth){
    clearValueTables();
    if(flags &   VALUE_FLAG){ valueTables=new double[res*res2];}
    if(flags & D_VALUE_FLAG){dValueTables=new double[res*res2];}
    PPolynomial<Degree+1> function;
    PPolynomial<Degree>  dFunction;
    for(int i=0;i<res;i++){
        if(smooth>0){
            function=baseFunctions[i].MovingAverage(smooth);
            dFunction=baseFunctions[i].derivative().MovingAverage(smooth);
        }
        else{
            function=baseFunctions[i];
            dFunction=baseFunctions[i].derivative();
        }
        for(int j=0;j<res2;j++){
            double x=double(j)/(res2-1);
            if(flags &   VALUE_FLAG){ valueTables[i*res2+j]= function(x);}
            if(flags & D_VALUE_FLAG){dValueTables[i*res2+j]=dFunction(x);}
        }
    }
}
template<int Degree,class Real>
void FunctionData<Degree,Real>::clearValueTables(void){
    if(valueTables){
        delete[] valueTables;
        valueTables=NULL;
    }
    if(dValueTables){
        delete[] dValueTables;
        dValueTables=NULL;
    }
}
template<int Degree,class Real>
double FunctionData<Degree,Real>::dotProduct(const double& center1,const double& width1,const double& center2,const double& width2) const{
    double r=fabs(baseFunction.polys[0].start);
    switch(normalize){
        case 2:
            return (baseFunction*baseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)*width1/sqrt(width1*width2);
        case 1:
            return (baseFunction*baseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)*width1/(width1*width2);
        default:
            return (baseFunction*baseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)*width1;
    }
}
template<int Degree,class Real>
double FunctionData<Degree,Real>::dDotProduct(const double& center1,const double& width1,const double& center2,const double& width2) const{
    double r=fabs(baseFunction.polys[0].start);
    switch(normalize){
        case 2:
            return (dBaseFunction*baseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)/sqrt(width1*width2);
        case 1:
            return (dBaseFunction*baseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)/(width1*width2);
        default:
            return (dBaseFunction*baseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r);
    }
}
template<int Degree,class Real>
double FunctionData<Degree,Real>::d2DotProduct(const double& center1,const double& width1,const double& center2,const double& width2) const{
    double r=fabs(baseFunction.polys[0].start);
    switch(normalize){
        case 2:
            return (dBaseFunction*dBaseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)/width2/sqrt(width1*width2);
        case 1:
            return (dBaseFunction*dBaseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)/width2/(width1*width2);
        default:
            return (dBaseFunction*dBaseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)/width2;
    }
}