Grid/lib/tensors/Tensor_Ta.h

#ifndef GRID_MATH_TA_H
#define GRID_MATH_TA_H


namespace Grid {

  /////////////////////////////////////////////// 
  // Ta function for scalar, vector, matrix
  /////////////////////////////////////////////// 
  /*
  inline ComplexF Ta( const ComplexF &arg){    return arg;}
  inline ComplexD Ta( const ComplexD &arg){    return arg;}
  inline RealF Ta( const RealF &arg){    return arg;}
  inline RealD Ta( const RealD &arg){    return arg;}
  */

  template<class vtype> inline iScalar<vtype> Ta(const iScalar<vtype>&r)
    {
      iScalar<vtype> ret;
      ret._internal = Ta(r._internal);
      return ret;
    }
  template<class vtype,int N> inline iVector<vtype,N> Ta(const iVector<vtype,N>&r)
    {
      iVector<vtype,N> ret;
      for(int i=0;i<N;i++){
        ret._internal[i] = Ta(r._internal[i]);
      }
      return ret;
    }
  template<class vtype,int N> inline iMatrix<vtype,N> Ta(const iMatrix<vtype,N> &arg)
    {
      iMatrix<vtype,N> ret;

      double factor = (1.0/(double)N);
      ret= (arg - adj(arg))*0.5;
      ret=ret - (trace(ret)*factor);
      return ret;
    }


  /////////////////////////////////////////////// 
  // ProjectOnGroup function for scalar, vector, matrix 
  // Projects on orthogonal, unitary group
  /////////////////////////////////////////////// 


  template<class vtype> inline iScalar<vtype> ProjectOnGroup(const iScalar<vtype>&r)
    {
      iScalar<vtype> ret;
      ret._internal = ProjectOnGroup(r._internal);
      return ret;
    }
  template<class vtype,int N> inline iVector<vtype,N> ProjectOnGroup(const iVector<vtype,N>&r)
    {
      iVector<vtype,N> ret;
      for(int i=0;i<N;i++){
        ret._internal[i] = ProjectOnGroup(r._internal[i]);
      }
      return ret;
    }
  template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr> 
    inline iMatrix<vtype,N> ProjectOnGroup(const iMatrix<vtype,N> &arg)
    {
      // need a check for the group type?
      iMatrix<vtype,N> ret(arg);
      vtype nrm;
      vtype inner;
      for(int c1=0;c1<N;c1++){
	zeroit(inner);	
	for(int c2=0;c2<N;c2++)
	  inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);

	nrm = rsqrt(inner);
	for(int c2=0;c2<N;c2++)
	  ret._internal[c1][c2]*= nrm;
      
	for (int b=c1+1; b<N; ++b){
	  decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
	  zeroit(pr);
	  for(int c=0; c<N; ++c)
	    pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];
	  
	  for(int c=0; c<N; ++c){
	    ret._internal[b][c] -= pr * ret._internal[c1][c];
	  }
	}
	  
      }
      // assuming the determinant is ok
      return ret;
    }



}
#endif