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

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

    Source file: ./tests/Test_dwf_force.cc

    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 */
#include <Grid/Grid.h>

using namespace std;
using namespace Grid;


int main (int argc, char ** argv)
{
  Grid_init(&argc,&argv);

  Coordinate latt_size   = GridDefaultLatt();
  Coordinate simd_layout = GridDefaultSimd(Nd,vComplex::Nsimd());
  Coordinate mpi_layout  = GridDefaultMpi();

  const int Ls=8;

  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(), GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
  
  std::vector<int> seeds4({1,2,3,5});
  std::vector<int> seeds5({5,6,7,8});
  GridParallelRNG          RNG5(FGrid);  RNG5.SeedFixedIntegers(seeds5);
  GridParallelRNG          RNG4(UGrid);  RNG4.SeedFixedIntegers(seeds4);

  int threads = GridThread::GetThreads();
  std::cout<<GridLogMessage << "Grid is setup to use "<<threads<<" threads"<<std::endl;

  LatticeFermion phi        (FGrid); gaussian(RNG5,phi);
  LatticeFermion Mphi       (FGrid); 
  LatticeFermion MphiPrime  (FGrid); 

  LatticeGaugeField U(UGrid);

  SU<Nc>::HotConfiguration(RNG4,U);
  
  ////////////////////////////////////
  // Unmodified matrix element
  ////////////////////////////////////
  RealD mass=0.01; 
  RealD M5=1.8; 
  DomainWallFermionD Ddwf(U,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5);
  Ddwf.M   (phi,Mphi);

  ComplexD S    = innerProduct(Mphi,Mphi); // pdag MdagM p

  // get the deriv of phidag MdagM phi with respect to "U"
  LatticeGaugeField UdSdU(UGrid);
  LatticeGaugeField tmp(UGrid);
  

  Ddwf.MDeriv(tmp , Mphi,  phi,DaggerNo );  UdSdU=tmp;
  Ddwf.MDeriv(tmp , phi,  Mphi,DaggerYes ); UdSdU=(UdSdU+tmp);  
  
  LatticeFermion Ftmp      (FGrid);

  ////////////////////////////////////
  // Modify the gauge field a little 
  ////////////////////////////////////
  RealD dt = 0.0001;

  LatticeColourMatrix mommu(UGrid); 
  LatticeColourMatrix forcemu(UGrid); 
  LatticeGaugeField mom(UGrid); 
  LatticeGaugeField Uprime(UGrid); 

  for(int mu=0;mu<Nd;mu++){

    SU<Nc>::GaussianFundamentalLieAlgebraMatrix(RNG4, mommu); // Traceless antihermitian momentum; gaussian in lie alg

    PokeIndex<LorentzIndex>(mom,mommu,mu);

    // fourth order exponential approx

    autoView( mom_v, mom, CpuRead);
    autoView( U_v , U, CpuRead);
    autoView(Uprime_v, Uprime, CpuWrite);

    thread_foreach( i,mom_v,{
      Uprime_v[i](mu) =	  U_v[i](mu)
	+ mom_v[i](mu)*U_v[i](mu)*dt 
	+ mom_v[i](mu) *mom_v[i](mu) *U_v[i](mu)*(dt*dt/2.0)
	+ mom_v[i](mu) *mom_v[i](mu) *mom_v[i](mu) *U_v[i](mu)*(dt*dt*dt/6.0)
	+ mom_v[i](mu) *mom_v[i](mu) *mom_v[i](mu) *mom_v[i](mu) *U_v[i](mu)*(dt*dt*dt*dt/24.0)
	+ mom_v[i](mu) *mom_v[i](mu) *mom_v[i](mu) *mom_v[i](mu) *mom_v[i](mu) *U_v[i](mu)*(dt*dt*dt*dt*dt/120.0)
	+ mom_v[i](mu) *mom_v[i](mu) *mom_v[i](mu) *mom_v[i](mu) *mom_v[i](mu) *mom_v[i](mu) *U_v[i](mu)*(dt*dt*dt*dt*dt*dt/720.0)
	;
    });
  }
  
  Ddwf.ImportGauge(Uprime);
  Ddwf.M          (phi,MphiPrime);

  ComplexD Sprime    = innerProduct(MphiPrime   ,MphiPrime);

  //////////////////////////////////////////////
  // Use derivative to estimate dS
  //////////////////////////////////////////////


  LatticeComplex dS(UGrid); dS = Zero();
  for(int mu=0;mu<Nd;mu++){
    mommu   = PeekIndex<LorentzIndex>(UdSdU,mu);
    mommu=Ta(mommu)*2.0;
    PokeIndex<LorentzIndex>(UdSdU,mommu,mu);
  }

  for(int mu=0;mu<Nd;mu++){
    forcemu = PeekIndex<LorentzIndex>(UdSdU,mu);
    mommu   = PeekIndex<LorentzIndex>(mom,mu);

    // Update PF action density
    dS = dS+trace(mommu*forcemu)*dt;

  }

  ComplexD dSpred    = sum(dS);

  std::cout << std::setprecision(14);
  std::cout << GridLogMessage << " S      "<<S<<std::endl;
  std::cout << GridLogMessage << " Sprime "<<Sprime<<std::endl;
  std::cout << GridLogMessage << "dS      "<<Sprime-S<<std::endl;
  std::cout << GridLogMessage << "predict dS    "<< dSpred <<std::endl;

  GRID_ASSERT( fabs(real(Sprime-S-dSpred)) < 1.0 ) ;

  std::cout<< GridLogMessage << "Done" <<std::endl;
  Grid_finalize();
}
