Lattice_trace.h

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/*************************************************************************************
 
    Grid physics library, www.github.com/paboyle/Grid 
 
    Source file: ./lib/lattice/Lattice_trace.h
 
    Copyright (C) 2015
 
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 
    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_LATTICE_TRACE_H
#define GRID_LATTICE_TRACE_H

// Tracing, transposing, peeking, poking
 
NAMESPACE_BEGIN(Grid);

// Trace
/*
template<class vobj>
inline auto trace(const Lattice<vobj> &lhs)  -> Lattice<decltype(trace(vobj()))>
{
  Lattice<decltype(trace(vobj()))> ret(lhs.Grid());
  autoView(ret_v , ret, AcceleratorWrite);
  autoView(lhs_v , lhs, AcceleratorRead);
  accelerator_for( ss, lhs_v.size(), vobj::Nsimd(), {
    coalescedWrite(ret_v[ss], trace(lhs_v(ss)));
  });
  return ret;
};
*/
    
// Trace Index level dependent operation
template<int Index,class vobj>
inline auto TraceIndex(const Lattice<vobj> &lhs) -> Lattice<decltype(traceIndex<Index>(vobj()))>
{
  Lattice<decltype(traceIndex<Index>(vobj()))> ret(lhs.Grid());
  autoView( ret_v , ret, AcceleratorWrite);
  autoView( lhs_v , lhs, AcceleratorRead);
  accelerator_for( ss, lhs_v.size(), vobj::Nsimd(), {
    coalescedWrite(ret_v[ss], traceIndex<Index>(lhs_v(ss)));
  });
  return ret;
};
 
template<int N, class Vec>
Lattice<iScalar<iScalar<iScalar<Vec> > > > Determinant(const Lattice<iScalar<iScalar<iMatrix<Vec, N> > > > &Umu)
{
  GridBase *grid=Umu.Grid();
  auto lvol = grid->lSites();
  Lattice<iScalar<iScalar<iScalar<Vec> > > > ret(grid);
  typedef typename Vec::scalar_type scalar;
  autoView(Umu_v,Umu,CpuRead);
  autoView(ret_v,ret,CpuWrite);
  thread_for(site,lvol,{
    Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N,N);
    Coordinate lcoor;
    grid->LocalIndexToLocalCoor(site, lcoor);
    iScalar<iScalar<iMatrix<scalar, N> > > Us;
    peekLocalSite(Us, Umu_v, lcoor);
    for(int i=0;i<N;i++){
      for(int j=0;j<N;j++){
    scalar tmp= Us()()(i,j);
    ComplexD ztmp(real(tmp),imag(tmp));
    EigenU(i,j)=ztmp;
      }}
    ComplexD detD  = EigenU.determinant();
    typename Vec::scalar_type det(detD.real(),detD.imag());
    pokeLocalSite(det,ret_v,lcoor);
  });
  return ret;
}
 
template<int N>
Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > Inverse(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
{
  GridBase *grid=Umu.Grid();
  auto lvol = grid->lSites();
  Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > ret(grid);
  
  autoView(Umu_v,Umu,CpuRead);
  autoView(ret_v,ret,CpuWrite);
  thread_for(site,lvol,{
    Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N,N);
    Coordinate lcoor;
    grid->LocalIndexToLocalCoor(site, lcoor);
    iScalar<iScalar<iMatrix<ComplexD, N> > > Us;
    iScalar<iScalar<iMatrix<ComplexD, N> > > Ui;
    peekLocalSite(Us, Umu_v, lcoor);
    for(int i=0;i<N;i++){
      for(int j=0;j<N;j++){
    EigenU(i,j) = Us()()(i,j);
      }}
    Eigen::MatrixXcd EigenUinv = EigenU.inverse();
    for(int i=0;i<N;i++){
      for(int j=0;j<N;j++){
    Ui()()(i,j) = EigenUinv(i,j);
      }}
    pokeLocalSite(Ui,ret_v,lcoor);
  });
  return ret;
}
 
 
NAMESPACE_END(Grid);
#endif