Grid/lib/tensors/Tensor_Ta.h

/*************************************************************************************

    Grid physics library, www.github.com/paboyle/Grid 

    Source file: ./lib/tensors/Tensor_Ta.h

    Copyright (C) 2015

Author: Peter Boyle <paboyle@ph.ed.ac.uk>
Author: neo <cossu@post.kek.jp>

    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 GRID_MATH_TA_H
#define GRID_MATH_TA_H


NAMESPACE_BEGIN(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;
}

NAMESPACE_END(Grid);

#endif