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

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

    Source file: ./tests/Test_wilson_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();

  GridCartesian               Grid(latt_size,simd_layout,mpi_layout);
  GridRedBlackCartesian     RBGrid(&Grid);

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

  std::vector<int> seeds({1,2,3,4});

  GridParallelRNG          pRNG(&Grid);
  std::vector<int> vrand(4);
  std::srand(std::time(0));
  std::generate(vrand.begin(), vrand.end(), std::rand);
  std::cout << GridLogMessage << vrand << std::endl;
  pRNG.SeedFixedIntegers(vrand);
  //pRNG.SeedFixedIntegers(std::vector<int>({45,12,81,9}));

  LatticeFermion phi        (&Grid); gaussian(pRNG,phi);
  LatticeFermion Mphi       (&Grid); 
  LatticeFermion MphiPrime  (&Grid); 

  LatticeGaugeField U(&Grid);

  //SU2::HotConfiguration(pRNG,U);
  SU<Nc>::ColdConfiguration(pRNG,U);
  
  ////////////////////////////////////
  // Unmodified matrix element
  ////////////////////////////////////
  RealD mass=-4.0; //kills the diagonal term
  WilsonFermionD Dw     (U,     Grid,RBGrid,mass);
  Dw.M   (phi,Mphi);

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

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

  Dw.MDeriv(tmp , Mphi,  phi,DaggerNo );  UdSdU=tmp;
  Dw.MDeriv(tmp , phi,  Mphi,DaggerYes ); UdSdU=(UdSdU+tmp);

  // Take the trace
  UdSdU = Ta(UdSdU);
  
  LatticeFermion Ftmp      (&Grid);

  ////////////////////////////////////
  // Modify the gauge field a little 
  ////////////////////////////////////
  RealD dt = 0.0001;
  RealD Hmom = 0.0;
  RealD Hmomprime = 0.0;
  LatticeColourMatrix mommu(&Grid); 
  LatticeColourMatrix forcemu(&Grid); 
  LatticeGaugeField mom(&Grid); 
  LatticeGaugeField Uprime(&Grid); 

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

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

    Hmom -= real(sum(trace(mommu*mommu)));

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

    // fourth order exponential approx
    autoView( U_v , U, CpuRead);
    autoView( mom_v, mom, CpuRead);
    autoView(Uprime_v, Uprime, CpuWrite);
    thread_foreach( i,mom_v,{
      Uprime_v[i](mu)  =	  U_v[i](mu);
      Uprime_v[i](mu) += mom_v[i](mu)*U_v[i](mu)*dt ;
      Uprime_v[i](mu) += mom_v[i](mu) *mom_v[i](mu) *U_v[i](mu)*(dt*dt/2.0);
      Uprime_v[i](mu) += mom_v[i](mu) *mom_v[i](mu) *mom_v[i](mu) *U_v[i](mu)*(dt*dt*dt/6.0);
      Uprime_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/24.0);
      Uprime_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/120.0);
      Uprime_v[i](mu) += 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);
    });
  }

  std::cout << GridLogMessage <<"Initial mom hamiltonian is "<< Hmom <<std::endl;
  Dw.ImportGauge(Uprime);
  Dw.M          (phi,MphiPrime);

  ComplexD Sprime    = innerProduct(MphiPrime   ,MphiPrime);

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

  for(int mu=0;mu<Nd;mu++){
    std::cout << "" <<std::endl;
    mommu   = PeekIndex<LorentzIndex>(mom,mu);
    std::cout << GridLogMessage<< " Mommu  " << norm2(mommu)<<std::endl;
    mommu   = mommu+adj(mommu);
    std::cout << GridLogMessage<< " Mommu + Mommudag " << norm2(mommu)<<std::endl;
    mommu   = PeekIndex<LorentzIndex>(UdSdU,mu);
    std::cout << GridLogMessage<< " dsdumu  " << norm2(mommu)<<std::endl;
    mommu   = mommu+adj(mommu);
    std::cout << GridLogMessage<< " dsdumu + dag  " << norm2(mommu)<<std::endl;
  }

  LatticeComplex dS(&Grid); dS = Zero();
  LatticeComplex dSmom(&Grid); dSmom = Zero();
  LatticeComplex dSmom2(&Grid); dSmom2 = 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++){
    mommu   = PeekIndex<LorentzIndex>(mom,mu);
    std::cout << GridLogMessage<< " Mommu  " << norm2(mommu)<<std::endl;
    mommu   = mommu+adj(mommu);
    std::cout << GridLogMessage<< " Mommu + Mommudag " << norm2(mommu)<<std::endl;
    mommu   = PeekIndex<LorentzIndex>(UdSdU,mu);
    std::cout << GridLogMessage<< " dsdumu  " << norm2(mommu)<<std::endl;
    mommu   = mommu+adj(mommu);
    std::cout << GridLogMessage<< " dsdumu + dag  " << norm2(mommu)<<std::endl;
  }

  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;

    // Smom = - P^2 ;
    //  dSmom = trace ( (mom+f/2dt)(mom+f/2dt) ) - trace mom*mom
    //        = trace(mom*f) dt  + 0.25*dt*dt * trace(f*f).
    //
    // can we improve on this in HMC???
    //
    // 
    dSmom  = dSmom  - trace(mommu*forcemu) * dt;
    dSmom2 = dSmom2 - trace(forcemu*forcemu) *(0.25* dt*dt);

    // Update mom action density
    mommu = mommu + forcemu*(dt * 0.5);

    Hmomprime -= real(sum(trace(mommu*mommu)));

  }

  ComplexD dSpred    = sum(dS);
  ComplexD dSm       = sum(dSmom);
  ComplexD dSm2      = sum(dSmom2);


  std::cout << GridLogMessage <<"Initial mom hamiltonian is "<< Hmom <<std::endl;
  std::cout << GridLogMessage <<"Final   mom hamiltonian is "<< Hmomprime <<std::endl;
  std::cout << GridLogMessage <<"Delta   mom hamiltonian is "<< Hmomprime-Hmom <<std::endl;

  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;
  std::cout << GridLogMessage <<"dSm "<< dSm<<std::endl;
  std::cout << GridLogMessage <<"dSm2"<< dSm2<<std::endl;

  std::cout << GridLogMessage << "Total dS    "<< Hmomprime - Hmom + Sprime - S <<std::endl;

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

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