Grid/lib/qcd/smearing/APEsmearing.h

/*!
  @brief Declaration of Smear_APE class for APE smearing
*/

#ifndef APE_SMEAR_
#define APE_SMEAR_

  namespace Grid {
  	namespace QCD {


    /*!  @brief APE type smearing of link variables. */
    template <class Gimpl> 
  		class Smear_APE: public Smear<Gimpl>{
  		private:
      	const std::vector<double> rho;/*!< Array of weights */

//This member must be private - we do not want to control from outside 
  			std::vector<double> set_rho(const double common_rho) const {
  				std::vector<double> res;

  				for(int mn=0; mn<Nd*Nd; ++mn) res.push_back(common_rho);
  					for(int mu=0; mu<Nd; ++mu) res[mu + mu*Nd] = 0.0;
  						return res;
  				}

  			public:
      // Defines the gauge field types
  				INHERIT_GIMPL_TYPES(Gimpl)


      // Constructors and destructors
  				Smear_APE(const std::vector<double>& rho_):rho(rho_){} // check vector size
  				Smear_APE(double rho_val):rho(set_rho(rho_val)){}
  				Smear_APE():rho(set_rho(1.0)){}
  				~Smear_APE(){}

      ///////////////////////////////////////////////////////////////////////////////
  				void smear(GaugeField& u_smr, const GaugeField& U)const{
  					GridBase *grid = U._grid;
  					GaugeLinkField Cup(grid), tmp_stpl(grid);
  					WilsonLoops<Gimpl> WL;
  					u_smr = zero; 

  					for(int mu=0; mu<Nd; ++mu){
  						Cup = zero;
  						for(int nu=0; nu<Nd; ++nu){
  							if (nu != mu) {
  								// get the staple in direction mu, nu
	      						WL.Staple(tmp_stpl, U, mu, nu);  //nb staple conventions of IroIro and Grid differ by a dagger
	      						Cup += tmp_stpl*rho[mu + Nd * nu];
	      					}
	      				}
	  					// save the Cup link-field on the u_smr gauge-field
	  					pokeLorentz(u_smr, adj(Cup), mu); // u_smr[mu] = Cup^dag   see conventions for Staple
	  				}
	  			}

////////////////////////////////////////////////////////////////////////////////
	  			void derivative(GaugeField& SigmaTerm,
	  				const GaugeField& iLambda,
	  				const GaugeField& U)const{

	// Reference 
	// Morningstar, Peardon, Phys.Rev.D69,054501(2004)
	// Equation 75
    // Computing Sigma_mu, derivative of S[fat links] with respect to the thin links
    // Output SigmaTerm

	  				GridBase *grid = U._grid;

	  				WilsonLoops<Gimpl> WL;
	  				GaugeLinkField staple(grid), u_tmp(grid);
	  				GaugeLinkField iLambda_mu(grid), iLambda_nu(grid);
	  				GaugeLinkField U_mu(grid), U_nu(grid);
	  				GaugeLinkField sh_field(grid), temp_Sigma(grid);
	  				Real rho_munu, rho_numu;

	  				for(int mu = 0; mu < Nd; ++mu){
	  					U_mu       = peekLorentz(      U, mu);
	  					iLambda_mu = peekLorentz(iLambda, mu);

	  					for(int nu = 0; nu < Nd; ++nu){
	  						if(nu==mu) continue;
	  						U_nu       = peekLorentz(      U, nu);
	  						iLambda_nu = peekLorentz(iLambda, nu);

	  						rho_munu = rho[mu + Nd * nu];
	  						rho_numu = rho[nu + Nd * mu];

	  						WL.StapleUpper(staple, U, mu, nu);

	  						temp_Sigma = -rho_numu*staple*iLambda_nu;  //ok
	        				//-r_numu*U_nu(x+mu)*Udag_mu(x+nu)*Udag_nu(x)*Lambda_nu(x)
	  						Gimpl::AddLink(SigmaTerm, temp_Sigma, mu);

	    					sh_field = Cshift(iLambda_nu, mu, 1);// general also for Gparity?

	    					temp_Sigma = rho_numu*sh_field*staple; //ok
	    					//r_numu*Lambda_nu(mu)*U_nu(x+mu)*Udag_mu(x+nu)*Udag_nu(x)
	    					Gimpl::AddLink(SigmaTerm, temp_Sigma, mu);

	    					sh_field = Cshift(iLambda_mu, nu, 1);

	    					temp_Sigma = -rho_munu*staple*U_nu*sh_field*adj(U_nu); //ok
	    					//-r_munu*U_nu(x+mu)*Udag_mu(x+nu)*Lambda_mu(x+nu)*Udag_nu(x)
	    					Gimpl::AddLink(SigmaTerm, temp_Sigma, mu);

	    					staple = zero;
	    					sh_field = Cshift(U_nu, mu, 1);

	    					temp_Sigma = -rho_munu*adj(sh_field)*adj(U_mu)*iLambda_mu*U_nu;
	    					temp_Sigma += rho_numu*adj(sh_field)*adj(U_mu)*iLambda_nu*U_nu;

	    					u_tmp = adj(U_nu)*iLambda_nu;
	    					sh_field = Cshift(u_tmp, mu, 1);
	    					temp_Sigma += -rho_numu*sh_field*adj(U_mu)*U_nu;
	    					sh_field = Cshift(temp_Sigma, nu, -1);
	    					Gimpl::AddLink(SigmaTerm, sh_field, mu);

	    				}
	    			}
	    		}
	    	};



  }// namespace QCD
}//namespace Grid
#endif