temporal_gauge.cc

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/*! \file
 *  \brief Axial gauge fixing 
 */
 
#include "chromabase.h"
#include "meas/gfix/temporal_gauge.h"
 
namespace Chroma 
{
 
  //! Temporal gauge fixing
  /*!
   * \ingroup gfix
   *
   * Transfroms a gauge configuration, in place, into axial
   *            gauge with special direction decay_dir.
   *
   * Note: The non-unity time-like gauge fields from the last time slice
   *       will be copied to all other time slices.
   *
   * \param ug         gauge field and its axial gauge transform (Modify)
   * \param g          gauge rotation matrix (Write)
   * \param decay_dir  time direction (Read) 
   */
 
  void temporalGauge(multi1d<LatticeColorMatrix>& ug, LatticeColorMatrix& g, int decay_dir)
  {
    START_CODE();
 
    // Sanity check
    if (decay_dir < 0 || decay_dir >= ug.size())
    {
      QDPIO::cerr << __func__ << ": invalid decay_dir= " << decay_dir << std::endl;
      QDP_abort(1);
    }
 
    // Initialize
    int N_t = Layout::lattSize()[decay_dir];
    LatticeInteger t_coord = Layout::latticeCoordinate(decay_dir);
 
    {
      // Upcast to double precision
      LatticeColorMatrixD u = ug[decay_dir];
      LatticeColorMatrixD gt = 1; // Unitm matrix
 
      // U_prev holds U_{t-1}
      LatticeColorMatrixD U_prev = shift(u, BACKWARD, decay_dir);
      LatticeColorMatrixD G_prev = gt; // Not shifting becuse it is unit at this point
 
      for(int t = 1; t < N_t; ++t) {
        LatticeBoolean btmp = (t_coord == t); 
        LatticeColorMatrixD t1 = G_prev*U_prev ; // DO whole lattice... Sucks
        copymask(gt, btmp, t1);
        
        // Reuse t1, to compute G_prev for next t
        t1 = shift(gt, BACKWARD, decay_dir);
        G_prev = t1;
      }
 
      g=gt; // Save gauge transform matrix (downcast to base precision)
    }
 
    /* Now do the gauge transformation on all the links */
    for(int mu = 0; mu < Nd; ++mu) {
      LatticeColorMatrix tmp = ug[mu] * shift(adj(g), FORWARD, mu);
      ug[mu] = g * tmp;
    }
 
    // Check temporal links (except last timeslice are unit
    {
      // Take a copy
      LatticeColorMatrix u = ug[decay_dir];
      LatticeColorMatrix g_unit = 1; // For copying into the last timeslice
      
      // Blast last non-unit timeslice with a unit one...
      LatticeBoolean btmp  = (t_coord == (N_t-1) );
      copymask(u, btmp, g_unit); // Replace last timeslice with units...
 
      // U should now be indistinguishable from unit gauge
      QDPIO::cout << "Norm of Unit-Gauge violation / link = " << sqrt( norm2(u-g_unit) )/ Layout::vol() << std::endl;
 
    }
 
    END_CODE();
  }
 
}  // end namespace Chroma