CovariantCshift.h

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/*************************************************************************************
 
    Grid physics library, www.github.com/paboyle/Grid 
 
    Source file: ./lib/qcd/utils/CovariantCshift.h
 
    Copyright (C) 2015
 
Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
Author: paboyle <paboyle@ph.ed.ac.uk>
 
    This program is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.
 
    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.
 
    You should have received a copy of the GNU General Public License along
    with this program; if not, write to the Free Software Foundation, Inc.,
    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 
    See the full license in the file "LICENSE" in the top level distribution directory
*************************************************************************************/
/*  END LEGAL */
#ifndef QCD_UTILS_COVARIANT_CSHIFT_H
#define QCD_UTILS_COVARIANT_CSHIFT_H
 
NAMESPACE_BEGIN(Grid);

// Low performance implementation of CovariantCshift API
// Make these members of an Impl class for BC's.
 
namespace PeriodicBC { 
  //Out(x) = Link(x)*field(x+mu)
  template<class covariant,class gauge> Lattice<covariant> CovShiftForward(const Lattice<gauge> &Link, 
                                       int mu,
                                       const Lattice<covariant> &field)
  {
    return Link*Cshift(field,mu,1);// moves towards negative mu
  }
  //Out(x) = Link^dag(x-mu)*field(x-mu)
  template<class covariant,class gauge> Lattice<covariant> CovShiftBackward(const Lattice<gauge> &Link, 
                                        int mu,
                                        const Lattice<covariant> &field)
  {
    Lattice<covariant> tmp(field.Grid());
    tmp = adj(Link)*field;
    return Cshift(tmp,mu,-1);// moves towards positive mu
  }
  //Out(x) = Link^dag(x-mu)
  template<class gauge> Lattice<gauge>
  CovShiftIdentityBackward(const Lattice<gauge> &Link, int mu) 
  {
    return Cshift(adj(Link), mu, -1);
  }
  //Out(x) = Link(x)
  template<class gauge> Lattice<gauge>
  CovShiftIdentityForward(const Lattice<gauge> &Link, int mu)
  {
    return Link;
  }
  //Link(x) = Link(x+mu)
  template<class gauge> Lattice<gauge>
  ShiftStaple(const Lattice<gauge> &Link, int mu)
  {
    return Cshift(Link, mu, 1);
  }
  
  template<class gauge,class Expr,typename std::enable_if<is_lattice_expr<Expr>::value,void>::type * = nullptr>
    auto  CovShiftForward(const Lattice<gauge> &Link, 
              int mu,
              const Expr &expr) -> decltype(closure(expr))
  {
    auto arg = closure(expr);
    return CovShiftForward(Link,mu,arg);
  }
  template<class gauge,class Expr,typename std::enable_if<is_lattice_expr<Expr>::value,void>::type * = nullptr>
    auto  CovShiftBackward(const Lattice<gauge> &Link, 
               int mu,
               const Expr &expr) -> decltype(closure(expr))
  {
    auto arg = closure(expr);
    return CovShiftBackward(Link,mu,arg);
  }
 
  //Boundary-aware C-shift of gauge links / gauge transformation matrices
  template<class gauge> Lattice<gauge>
  CshiftLink(const Lattice<gauge> &Link, int mu, int shift)
  {
    return Cshift(Link, mu, shift);
  }
 
}
 
 
namespace ConjugateBC { 
 
  // Must give right answers across boundary
  //     <----
  //       --    
  //      |  |              
  // xxxxxxxxxxxxxxxxxxxx
  //      |  | 
  //  
  //     Stap= Cshift(GImpl::CovShiftForward(U[nu],nu,
  //                  GImpl::CovShiftForward(U[nu],nu,
  //                  GImpl::CovShiftBackward(U[mu],mu,
  //                  GImpl::CovShiftBackward(U[nu],nu,
  //              GImpl::CovShiftIdentityBackward(U[nu],nu,-1))))) , mu, 1);
  //  
  //                      U  U^* U^* U^T U^adj =  U  (U U U^dag U^T )^*
  //                                           =  U  (U U U^dag)^* ( U^T )^*
  //
  // So covariant shift rule: Conjugate inward shifted plane when crossing boundary applies.
  //
  // This Conjugate should be applied to BOTH the link and the covariant field on backward shift
  // boundary wrap.
  // 
  //      |  |              
  // xxxxxxxxxxxxxxxxx         
  //      |  | <---- this link is Conjugated, and the path leading into it. Segment crossing in and out is double Conjugated.
  //       -- 
  //    ------->
  template<class covariant,class gauge> Lattice<covariant> CovShiftForward(const Lattice<gauge> &Link, 
                                       int mu,
                                       const Lattice<covariant> &field)
  {
    GridBase * grid = Link.Grid();
 
    int Lmu = grid->GlobalDimensions()[mu]-1;
 
    conformable(field,Link);
 
    Lattice<iScalar<vInteger> > coor(grid);    LatticeCoordinate(coor,mu);
 
    Lattice<covariant> field_bc = Cshift(field,mu,1);// moves towards negative mu;
 
    field_bc = where(coor==Lmu,conjugate(field_bc),field_bc);
    //    std::cout<<"Gparity::CovCshiftForward mu="<<mu<<std::endl;
    return Link*field_bc;
  }
 
  template<class covariant,class gauge> Lattice<covariant> CovShiftBackward(const Lattice<gauge> &Link, 
                                        int mu,
                                        const Lattice<covariant> &field)
  {
    GridBase * grid = field.Grid();
 
    int Lmu = grid->GlobalDimensions()[mu]-1;
 
    conformable(field,Link);
 
    Lattice<iScalar<vInteger> > coor(grid);    LatticeCoordinate(coor,mu);
 
    Lattice<covariant> tmp(grid);
 
    tmp = adj(Link)*field;
    tmp = where(coor==Lmu,conjugate(tmp),tmp);
    //    std::cout<<"Gparity::CovCshiftBackward mu="<<mu<<std::endl;
    return Cshift(tmp,mu,-1);// moves towards positive mu
  }
 
  //Out(x) = U^dag_\mu(x-mu)  | x_\mu != 0
  //       = U^T_\mu(L-1)  | x_\mu == 0
  template<class gauge> Lattice<gauge>
  CovShiftIdentityBackward(const Lattice<gauge> &Link, int mu) {
    GridBase *grid = Link.Grid();
    int Lmu = grid->GlobalDimensions()[mu] - 1;
 
    Lattice<iScalar<vInteger>> coor(grid);
    LatticeCoordinate(coor, mu);
 
    Lattice<gauge> tmp(grid);
    tmp = adj(Link);
    tmp = where(coor == Lmu, conjugate(tmp), tmp);
    return Cshift(tmp, mu, -1); // moves towards positive mu
  }
  template<class gauge> Lattice<gauge>
  CovShiftIdentityForward(const Lattice<gauge> &Link, int mu) {
    return Link;
  }
 
  //Out(x) = S_\mu(x+\hat\mu)  | x_\mu != L-1
  //       = S*_\mu(0)  | x_\mu == L-1
  //Note: While this is used for Staples it is also applicable for shifting gauge links or gauge transformation matrices
  template<class gauge> Lattice<gauge>
  ShiftStaple(const Lattice<gauge> &Link, int mu)
  {
    GridBase *grid = Link.Grid();
    int Lmu = grid->GlobalDimensions()[mu] - 1;
 
    Lattice<iScalar<vInteger>> coor(grid);
    LatticeCoordinate(coor, mu);
 
    Lattice<gauge> tmp(grid);
    tmp = Cshift(Link, mu, 1);
    tmp = where(coor == Lmu, conjugate(tmp), tmp);
    return tmp;
  }
 
  template<class gauge,class Expr,typename std::enable_if<is_lattice_expr<Expr>::value,void>::type * = nullptr>
    auto  CovShiftForward(const Lattice<gauge> &Link, 
              int mu,
              const Expr &expr) -> decltype(closure(expr))
  {
    auto arg = closure(expr);
    return CovShiftForward(Link,mu,arg);
  }
  template<class gauge,class Expr,typename std::enable_if<is_lattice_expr<Expr>::value,void>::type * = nullptr>
    auto  CovShiftBackward(const Lattice<gauge> &Link, 
               int mu,
               const Expr &expr)  -> decltype(closure(expr))
  {
    auto arg = closure(expr);
    return CovShiftBackward(Link,mu,arg);
  }
 
  //Boundary-aware C-shift of gauge links / gauge transformation matrices
  //shift = 1
  //Out(x) = U_\mu(x+\hat\mu)  | x_\mu != L-1
  //       = U*_\mu(0)  | x_\mu == L-1
  //shift = -1
  //Out(x) = U_\mu(x-mu)  | x_\mu != 0
  //       = U*_\mu(L-1)  | x_\mu == 0
  //shift = 2
  //Out(x) = U_\mu(x+2\hat\mu)  | x_\mu < L-2
  //       = U*_\mu(1)  | x_\mu == L-1
  //       = U*_\mu(0)  | x_\mu == L-2
  //shift = -2
  //Out(x) = U_\mu(x-2mu)  | x_\mu > 1
  //       = U*_\mu(L-2)  | x_\mu == 0
  //       = U*_\mu(L-1)  | x_\mu == 1
  //etc
  template<class gauge> Lattice<gauge>
  CshiftLink(const Lattice<gauge> &Link, int mu, int shift)
  {
    GridBase *grid = Link.Grid();
    int Lmu = grid->GlobalDimensions()[mu];
    assert(abs(shift) < Lmu && "Invalid shift value");
 
    Lattice<iScalar<vInteger>> coor(grid);
    LatticeCoordinate(coor, mu);
 
    Lattice<gauge> tmp(grid);
    if(shift > 0){
      tmp = Cshift(Link, mu, shift);
      tmp = where(coor >= Lmu-shift, conjugate(tmp), tmp);
      return tmp;
    }else if(shift < 0){
      tmp = Link;
      tmp = where(coor >= Lmu+shift, conjugate(tmp), tmp);
      return Cshift(tmp, mu, shift);
    }
    
    //shift == 0
    return Link;
  }
 
}
 
 
NAMESPACE_END(Grid);
#endif