taproj.cc

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// TAPROJ
 
/*! \file
 *  \brief Take the traceless antihermitian projection of a color matrix
 */
 
#include "chromabase.h"
#include "util/gauge/taproj.h"
 
namespace Chroma 
{
 
  namespace TaprojEnv {
    static double time_spent =0;
    double getTime() { return time_spent; }
  }
 
  //! Take the traceless antihermitian projection of a color matrix
  /*!
   * \ingroup gauge
   *
   *  a = (1/2)[a - a_dag] - Tr[(1/2)*(a - a_dag)]/Nc
   *
   * that is the anti-hermitian traceless part of a 
   *
   * Arguments:
   *
   *  \param a        LatticeColorMatrix          (Modify)
   */
 
  void taproj(LatticeColorMatrix& a)
  {
    START_CODE();
    QDP::StopWatch swatch;
    swatch.reset();
    swatch.start();
 
    // a = a - a_dagger  --- a -> antihermitian matrix
    LatticeColorMatrix aux_1 = a;
    a -= adj(aux_1);
 
    if (Nc > 1) {
      // tmp = Im Tr[ a ]
      LatticeReal tmp = imag(trace(a));
    
      // a = a - (1/Nc) * Im Tr[ a] = a - (1/Nc)*tmp
      tmp *= (Real(1)/Real(Nc));
 
      // Is this a fill or a UnitMatrix*I?
      LatticeColorMatrix aux = cmplx(0, tmp);
      a -= aux;
    }
 
    // Normalisation to make taproj idempotent
    a *= (Real(1)/Real(2));
 
    swatch.stop();
    TaprojEnv::time_spent+=swatch.getTimeInSeconds();
    END_CODE();
  }
 
}  // end namespace Chroma