Grid/lib/algorithms/approx/Chebyshev.h

#ifndef GRID_CHEBYSHEV_H
#define GRID_CHEBYSHEV_H

#include<Grid.h>
#include<algorithms/LinearOperator.h>

namespace Grid {

  ////////////////////////////////////////////////////////////////////////////////////////////
  // Simple general polynomial with user supplied coefficients
  ////////////////////////////////////////////////////////////////////////////////////////////
  template<class Field>
  class Polynomial : public OperatorFunction<Field> {
  private:
    std::vector<double> Coeffs;
  public:
    Polynomial(std::vector<double> &_Coeffs) : Coeffs(_Coeffs) {};

    // Implement the required interface
    void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {

      Field AtoN = in;
      out = AtoN*Coeffs[0];

      for(int n=1;n<Coeffs.size();n++){
	Field Mtmp=AtoN;
	Linop.Op(Mtmp,AtoN);
	out=out+AtoN*Coeffs[n];
      }
    };
  };

  ////////////////////////////////////////////////////////////////////////////////////////////
  // Generic Chebyshev approximations
  ////////////////////////////////////////////////////////////////////////////////////////////
  template<class Field>
  class Chebyshev : public OperatorFunction<Field> {
  private:
    std::vector<double> Coeffs;
    int order;
    double hi;
    double lo;

  public:
    void csv(std::ostream &out){
      for (double x=lo; x<hi; x+=(hi-lo)/1000) {
	double f = approx(x);
	out<< x<<" "<<f<<std::endl;
      }
      return;
    }

    // Convenience for plotting the approximation
    void   PlotApprox(std::ostream &out) {
      out<<"Polynomial approx ["<<lo<<","<<hi<<"]"<<std::endl;
      for(double x=lo;x<hi;x+=(hi-lo)/50.0){
	out <<x<<"\t"<<approx(x)<<std::endl;
      }
    };

    
    // c.f. numerical recipes "chebft"/"chebev". This is sec 5.8 "Chebyshev approximation".
    //
    Chebyshev(double _lo,double _hi,int _order, double (* func)(double) ){
      lo=_lo;
      hi=_hi;
      order=_order;
      
      if(order < 2) exit(-1);
      Coeffs.resize(order);
      for(int j=0;j<order;j++){
	double s=0;
	for(int k=0;k<order;k++){
	  double y=std::cos(M_PI*(k+0.5)/order);
	  double x=0.5*(y*(hi-lo)+(hi+lo));
	  double f=func(x);
	  s=s+f*std::cos( j*M_PI*(k+0.5)/order );
	}
	Coeffs[j] = s * 2.0/order;
      }
    };
    void JacksonSmooth(void){
      double M=order;
      double alpha = M_PI/(M+2);
      double lmax = std::cos(alpha);
      double sumUsq =0;
      std::vector<double> U(M);
      std::vector<double> a(M);
      std::vector<double> g(M);
      for(int n=0;n<=M;n++){
	U[n] = std::sin((n+1)*std::acos(lmax))/std::sin(std::acos(lmax));
	sumUsq += U[n]*U[n];
      }      
      sumUsq = std::sqrt(sumUsq);

      for(int i=1;i<=M;i++){
	a[i] = U[i]/sumUsq;
      }
      g[0] = 1.0;
      for(int m=1;m<=M;m++){
	g[m] = 0;
	for(int i=0;i<=M-m;i++){
	  g[m]+= a[i]*a[m+i];
	}
      }
      for(int m=1;m<=M;m++){
	Coeffs[m]*=g[m];
      }
    }
    double approx(double x) // Convenience for plotting the approximation
    {
      double Tn;
      double Tnm;
      double Tnp;
      
      double y=( x-0.5*(hi+lo))/(0.5*(hi-lo));
      
      double T0=1;
      double T1=y;
      
      double sum;
      sum = 0.5*Coeffs[0]*T0;
      sum+= Coeffs[1]*T1;
      
      Tn =T1;
      Tnm=T0;
      for(int i=2;i<order;i++){
	Tnp=2*y*Tn-Tnm;
	Tnm=Tn;
	Tn =Tnp;
	sum+= Tn*Coeffs[i];
      }
      return sum;
    };

    // Implement the required interface
    void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {

      GridBase *grid=in._grid;

      int vol=grid->gSites();

      Field T0(grid); T0 = in;  
      Field T1(grid); 
      Field T2(grid);
      Field y(grid);
      
      Field *Tnm = &T0;
      Field *Tn  = &T1;
      Field *Tnp = &T2;

      std::cout<<GridLogMessage << "Chebyshev ["<<lo<<","<<hi<<"]"<< " order "<<order <<std::endl;
      // Tn=T1 = (xscale M + mscale)in
      double xscale = 2.0/(hi-lo);
      double mscale = -(hi+lo)/(hi-lo);
      Linop.HermOp(T0,y);
      T1=y*xscale+in*mscale;

      // sum = .5 c[0] T0 + c[1] T1
      out = (0.5*Coeffs[0])*T0 + Coeffs[1]*T1;
      for(int n=2;n<order;n++){
	
	Linop.HermOp(*Tn,y);

	y=xscale*y+mscale*(*Tn);

	*Tnp=2.0*y-(*Tnm);

	out=out+Coeffs[n]* (*Tnp);

	// Cycle pointers to avoid copies
	Field *swizzle = Tnm;
	Tnm    =Tn;
	Tn     =Tnp;
	Tnp    =swizzle;
	  
      }
    }
  };


}
#endif