#ifndef GRID_QCD_H
#define GRID_QCD_H
namespace Grid{
namespace QCD {

    static const int Nc=3;
    static const int Ns=4;
    static const int CbRed  =0;
    static const int CbBlack=1;

    // QCD iMatrix types
    template<typename vtype> using iSinglet          = iScalar<iScalar<vtype> > ;
    template<typename vtype> using iSpinMatrix       = iMatrix<iScalar<vtype>, Ns>;
    template<typename vtype> using iSpinColourMatrix = iMatrix<iMatrix<vtype, Nc>, Ns>;

    template<typename vtype> using iColourMatrix     = iScalar<iMatrix<vtype, Nc>> ;

    template<typename vtype> using iSpinVector       = iVector<iScalar<vtype>, Ns>;
    template<typename vtype> using iColourVector     = iScalar<iVector<vtype, Nc> >;
    template<typename vtype> using iSpinColourVector = iVector<iVector<vtype, Nc>, Ns>;

    typedef iSinglet<Complex >          TComplex;    // This is painful. Tensor singlet complex type.
    typedef iSinglet<vComplex >         vTComplex;
    typedef iSinglet<Real >             TReal;    // This is painful. Tensor singlet complex type.


    typedef iSinglet<vIntegerF >         vTIntegerF;
    typedef iSinglet<vIntegerD >         vTIntegerD;
    typedef iSinglet<vIntegerC >         vTIntegerC;
    typedef iSinglet<vIntegerZ >         vTIntegerZ;

    typedef iSpinMatrix<Complex >       SpinMatrix;
    typedef iColourMatrix<Complex >     ColourMatrix;
    typedef iSpinColourMatrix<Complex > SpinColourMatrix;

    typedef iSpinVector<Complex >       SpinVector;
    typedef iColourVector<Complex >     ColourVector;
    typedef iSpinColourVector<Complex > SpinColourVector;

    
    typedef iSpinMatrix<vComplex >       vSpinMatrix;
    typedef iColourMatrix<vComplex >     vColourMatrix;
    typedef iSpinColourMatrix<vComplex > vSpinColourMatrix;
    
    typedef iSpinVector<vComplex >       vSpinVector;
    typedef iColourVector<vComplex >     vColourVector;
    typedef iSpinColourVector<vComplex > vSpinColourVector;
    
    typedef Lattice<vTComplex>         LatticeComplex;

    typedef Lattice<vTIntegerF>            LatticeIntegerF; // Predicates for "where"
    typedef Lattice<vTIntegerD>            LatticeIntegerD; 
    typedef Lattice<vTIntegerC>            LatticeIntegerC;
    typedef Lattice<vTIntegerZ>            LatticeIntegerZ;
    
    typedef Lattice<vColourMatrix>     LatticeColourMatrix;
    typedef Lattice<vSpinMatrix>       LatticeSpinMatrix;
    typedef Lattice<vSpinColourMatrix> LatticePropagator;
    typedef LatticePropagator LatticeSpinColourMatrix;

    typedef Lattice<vSpinColourVector> LatticeFermion;
    typedef Lattice<vSpinColourVector> LatticeSpinColourVector;
    typedef Lattice<vSpinVector>       LatticeSpinVector;
    typedef Lattice<vColourVector>     LatticeColourVector;

    // localNorm2,
    template<class tt>
    inline LatticeComplex localNorm2 (const Lattice<tt> &rhs)
    {
        LatticeComplex ret(rhs._grid);
#pragma omp parallel for
        for(int ss=0;ss<rhs._grid->oSites(); ss++){
            ret._odata[ss]=trace(adj(rhs)*rhs);
        }
        return ret;
    }
    // localInnerProduct
    template<class tt>
    inline LatticeComplex localInnerProduct (const Lattice<tt> &lhs,const Lattice<tt> &rhs)
    {
        LatticeComplex ret(rhs._grid);
#pragma omp parallel for
        for(int ss=0;ss<rhs._grid->oSites(); ss++){
            ret._odata[ss]=localInnerProduct(lhs._odata[ss],rhs._odata[ss]);
        }
        return ret;
    }
    
    // outerProduct Scalar x Scalar -> Scalar
    //              Vector x Vector -> Matrix
    template<class ll,class rr>
    inline auto outerProduct (const Lattice<ll> &lhs,const Lattice<rr> &rhs) -> Lattice<decltype(outerProduct(lhs._odata[0],rhs._odata[0]))>
    {
        Lattice<decltype(outerProduct(lhs._odata[0],rhs._odata[0]))> ret(rhs._grid);
#pragma omp parallel for
        for(int ss=0;ss<rhs._grid->oSites(); ss++){
            ret._odata[ss]=outerProduct(lhs._odata[ss],rhs._odata[ss]);
        }
        return ret;
     }
}   //namespace QCD
} // Grid
#endif