Grid/lib/qcd/action/fermion/ContinuedFractionFermion5D.cc

#include <Grid.h>

namespace Grid {
  namespace QCD {

    void ContinuedFractionFermion5D::SetCoefficientsTanh(Approx::zolotarev_data *zdata,RealD b,RealD c)
    {
      SetCoefficientsZolotarev(1.0,zdata,b,c);
    }
    void ContinuedFractionFermion5D::SetCoefficientsZolotarev(RealD zolo_hi,Approx::zolotarev_data *zdata,RealD b,RealD c)
    {
      R=(1+this->mass)/(1-this->mass);

      Beta.resize(Ls);
      cc.resize(Ls);
      cc_d.resize(Ls);
      sqrt_cc.resize(Ls);
      for(int i=0; i < Ls ; i++){
	Beta[i] = zdata -> beta[i];
	cc[i] = 1.0/Beta[i];
	cc_d[i]=sqrt(cc[i]);
      }
    
      cc_d[Ls-1]=1.0;
      for(int i=0; i < Ls-1 ; i++){
	sqrt_cc[i]= sqrt(cc[i]*cc[i+1]);
      }    
      sqrt_cc[Ls-2]=sqrt(cc[Ls-2]);


      ZoloHiInv =1.0/zolo_hi;
      double dw_diag = (4.0-M5)*ZoloHiInv;
    
      See.resize(Ls);
      Aee.resize(Ls);
      int sign=1;
      for(int s=0;s<Ls;s++){
	Aee[s] = sign * Beta[s] * dw_diag;
	sign   = - sign;
      }
      Aee[Ls-1] += R;
    
      See[0] = Aee[0];
      for(int s=1;s<Ls;s++){
	See[s] = Aee[s] - 1.0/See[s-1];
      }
      for(int s=0;s<Ls;s++){
	std::cout <<"s = "<<s<<" Beta "<<Beta[s]<<" Aee "<<Aee[s] <<" See "<<See[s] <<std::endl;
      }
    }



    RealD  ContinuedFractionFermion5D::M           (const LatticeFermion &psi, LatticeFermion &chi)
    {
      LatticeFermion D(psi._grid);

      DW(psi,D,DaggerNo); 

      int sign=1;
      for(int s=0;s<Ls;s++){
	if ( s==0 ) {
	  ag5xpby_ssp(chi,cc[0]*Beta[0]*sign*ZoloHiInv,D,sqrt_cc[0],psi,s,s+1); // Multiplies Dw by G5 so Hw
	} else if ( s==(Ls-1) ){
	  RealD R=(1.0+mass)/(1.0-mass);
	  ag5xpby_ssp(chi,Beta[s]*ZoloHiInv,D,sqrt_cc[s-1],psi,s,s-1);
	  ag5xpby_ssp(chi,R,psi,1.0,chi,s,s);
	} else {
	  ag5xpby_ssp(chi,cc[s]*Beta[s]*sign*ZoloHiInv,D,sqrt_cc[s],psi,s,s+1);
  	  axpby_ssp(chi,1.0,chi,sqrt_cc[s-1],psi,s,s-1);
	}
	sign=-sign; 
      }
      return norm2(chi);
    }
    RealD  ContinuedFractionFermion5D::Mdag        (const LatticeFermion &psi, LatticeFermion &chi)
    {
      // This matrix is already hermitian. (g5 Dw) = Dw dag g5 = (g5 Dw)dag
      // The rest of matrix is symmetric.
      // Can ignore "dag"
      return M(psi,chi);
    }
    void   ContinuedFractionFermion5D::Meooe       (const LatticeFermion &psi, LatticeFermion &chi)
    {
      // Apply 4d dslash
      if ( psi.checkerboard == Odd ) {
	DhopEO(psi,chi,DaggerNo); // Dslash on diagonal. g5 Dslash is hermitian
      } else {
	DhopOE(psi,chi,DaggerNo); // Dslash on diagonal. g5 Dslash is hermitian
      }
      
      int sign=1;
      for(int s=0;s<Ls;s++){
	if ( s==(Ls-1) ){
	  ag5xpby_ssp(chi,Beta[s]*ZoloHiInv,chi,0.0,chi,s,s);
	} else {
	  ag5xpby_ssp(chi,cc[s]*Beta[s]*sign*ZoloHiInv,chi,0.0,chi,s,s);
	}
	sign=-sign; 
      }
    }
    void   ContinuedFractionFermion5D::MeooeDag    (const LatticeFermion &psi, LatticeFermion &chi)
    {
      Meooe(psi,chi);
    }
    void   ContinuedFractionFermion5D::Mooee       (const LatticeFermion &psi, LatticeFermion &chi)
    {
      double dw_diag = (4.0-M5)*ZoloHiInv;
    
      int sign=1;
      for(int s=0;s<Ls;s++){
	if ( s==0 ) {
	  ag5xpby_ssp(chi,cc[0]*Beta[0]*sign*dw_diag,psi,sqrt_cc[0],psi,s,s+1); // Multiplies Dw by G5 so Hw
	} else if ( s==(Ls-1) ){
	  // Drop the CC here.
	  double R=(1+mass)/(1-mass);
	  ag5xpby_ssp(chi,Beta[s]*dw_diag,psi,sqrt_cc[s-1],psi,s,s-1);
	  ag5xpby_ssp(chi,R,psi,1.0,chi,s,s);
	} else {
	  ag5xpby_ssp(chi,cc[s]*Beta[s]*sign*dw_diag,psi,sqrt_cc[s],psi,s,s+1);
	  axpby_ssp(chi,1.0,chi,sqrt_cc[s-1],psi,s,s-1);
	}
	sign=-sign; 
      }
    }

    void   ContinuedFractionFermion5D::MooeeDag    (const LatticeFermion &psi, LatticeFermion &chi)
    {
      Mooee(psi,chi);
    }
    void   ContinuedFractionFermion5D::MooeeInv    (const LatticeFermion &psi, LatticeFermion &chi)
    {
      // Apply Linv
      axpby_ssp(chi,1.0/cc_d[0],psi,0.0,psi,0,0); 
      for(int s=1;s<Ls;s++){
	axpbg5y_ssp(chi,1.0/cc_d[s],psi,-1.0/See[s-1],chi,s,s-1);
      }
      // Apply Dinv
      for(int s=0;s<Ls;s++){
	ag5xpby_ssp(chi,1.0/See[s],chi,0.0,chi,s,s); //only appearance of See[0]
      }
      // Apply Uinv = (Linv)^T
      axpby_ssp(chi,1.0/cc_d[Ls-1],chi,0.0,chi,Ls-1,Ls-1);
      for(int s=Ls-2;s>=0;s--){
	axpbg5y_ssp(chi,1.0/cc_d[s],chi,-1.0*cc_d[s+1]/See[s]/cc_d[s],chi,s,s+1);
      }
    }
    void   ContinuedFractionFermion5D::MooeeInvDag (const LatticeFermion &psi, LatticeFermion &chi)
    {
      MooeeInv(psi,chi);
    }
    
    // Constructors
    ContinuedFractionFermion5D::ContinuedFractionFermion5D(
							   LatticeGaugeField &_Umu,
							   GridCartesian         &FiveDimGrid,
							   GridRedBlackCartesian &FiveDimRedBlackGrid,
							   GridCartesian         &FourDimGrid,
							   GridRedBlackCartesian &FourDimRedBlackGrid,
							   RealD _mass,RealD M5) :
      WilsonFermion5D(_Umu,
		      FiveDimGrid, FiveDimRedBlackGrid,
		      FourDimGrid, FourDimRedBlackGrid,M5),
      mass(_mass)
    {
      assert((Ls&0x1)==1); // Odd Ls required
      int nrational=Ls-1;// Even rational order
      zdata = Approx::grid_higham(1.0,nrational);// eps is ignored for higham
      SetCoefficientsTanh(zdata,1.0,0.0);
    }

  }
}