Grid/tests/qdpxx/Test_qdpxx_munprec.cc

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

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

    Source file: ./tests/qdpxx/Test_qdpxx_munprec.cc

    Copyright (C) 2015

Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
Author: paboyle <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.h>

int    Ls=8;
double M5=1.6;
double mq=0.01;
double zolo_lo = 0.1;
double zolo_hi = 2.0;
double mobius_scale=2.0;

enum ChromaAction {
                 DWF,           // CPS style preconditioning
		 WilsonFermion, // Wilson
		 HwPartFracZolo, // KEK's approach
		 HwContFracZolo, // Edwards, Kennedy et al prefer this
		 HwPartFracTanh, // 
		 HwContFracTanh, // 
		 HwCayleyZolo, // Chiu Optimal
		 HtCayleyZolo, // 
		 HmCayleyZolo, // Scaled shamir 13
		 HwCayleyTanh, // Scaled shamir
		 HtCayleyTanh, // Plain old DWF.
		 HmCayleyTanh, // Scaled shamir 13
		 HtContFracTanh,
		 HtContFracZolo
};

void calc_grid      (ChromaAction action,Grid::QCD::LatticeGaugeField & lat, Grid::QCD::LatticeFermion &src, Grid::QCD::LatticeFermion &res,int dag);
void calc_chroma    (ChromaAction action,Grid::QCD::LatticeGaugeField & lat, Grid::QCD::LatticeFermion &src, Grid::QCD::LatticeFermion &res,int dag);

#include <chroma.h>
#include <actions/ferm/invert/syssolver_linop_cg_array.h>
#include <actions/ferm/invert/syssolver_linop_aggregate.h>



namespace Chroma { 

class ChromaWrapper {
public:

  
  typedef multi1d<LatticeColorMatrix> U;
  typedef LatticeFermion T4;
  typedef multi1d<LatticeFermion> T5;
  
  static void ImportGauge(Grid::QCD::LatticeGaugeField & gr,
			  QDP::multi1d<QDP::LatticeColorMatrix> & ch) 
  {
    Grid::QCD::LorentzColourMatrix LCM;
    Grid::Complex cc;
    QDP::ColorMatrix cm;
    QDP::Complex c;

    std::vector<int> x(4);
    QDP::multi1d<int> cx(4);
    std::vector<int> gd= gr._grid->GlobalDimensions();

    for (x[0]=0;x[0]<gd[0];x[0]++){
    for (x[1]=0;x[1]<gd[1];x[1]++){
    for (x[2]=0;x[2]<gd[2];x[2]++){
    for (x[3]=0;x[3]<gd[3];x[3]++){
      cx[0] = x[0];
      cx[1] = x[1];
      cx[2] = x[2];
      cx[3] = x[3];
      Grid::peekSite(LCM,gr,x);

      for(int mu=0;mu<4;mu++){
	for(int i=0;i<3;i++){
	for(int j=0;j<3;j++){
	  cc = LCM(mu)()(i,j);
	  c = QDP::cmplx(QDP::Real(real(cc)),QDP::Real(imag(cc)));
	  QDP::pokeColor(cm,c,i,j);
	}}
	QDP::pokeSite(ch[mu],cm,cx);
	/*
	std::cout << "("<<x[0]<<",";
	std::cout << x[1]<<",";
	std::cout << x[2]<<",";
	std::cout << x[3]<<") "<< Grid::norm2(LCM(mu)) << " " <<QDP::norm2(cm)<<std::endl ;
	*/
      }

    }}}}
  }
  
  static void ImportFermion(Grid::QCD::LatticeFermion & gr,
			    QDP::multi1d<QDP::LatticeFermion> & ch  ) 
  {
    Grid::QCD::SpinColourVector F;
    Grid::Complex c;

    QDP::Fermion cF;
    QDP::SpinVector cS;
    QDP::Complex cc;

    std::vector<int> x(5);
    QDP::multi1d<int> cx(4);
    std::vector<int> gd= gr._grid->GlobalDimensions();

    for (x[0]=0;x[0]<gd[0];x[0]++){
    for (x[1]=0;x[1]<gd[1];x[1]++){
    for (x[2]=0;x[2]<gd[2];x[2]++){
    for (x[3]=0;x[3]<gd[3];x[3]++){
    for (x[4]=0;x[4]<gd[4];x[4]++){
      int s = x[0];
      cx[0] = x[1];
      cx[1] = x[2];
      cx[2] = x[3];
      cx[3] = x[4];

      Grid::peekSite(F,gr,x);

      for(int j=0;j<3;j++){
	for(int sp=0;sp<4;sp++){

	  c= F()(sp)(j) ;

	  cc = QDP::cmplx(QDP::Real(real(c)),QDP::Real(imag(c)));

	  QDP::pokeSpin(cS,cc,sp);

	}
	QDP::pokeColor(cF,cS,j);
      }
      QDP::pokeSite(ch[s],cF,cx);
    }}}}}
  }
  static void ExportFermion(Grid::QCD::LatticeFermion & gr,
			    QDP::multi1d<QDP::LatticeFermion> & ch  ) 
  {
    Grid::QCD::SpinColourVector F;
    Grid::Complex c;

    QDP::Fermion cF;
    QDP::SpinVector cS;
    QDP::Complex cc;

    std::vector<int> x(5);
    QDP::multi1d<int> cx(4);
    std::vector<int> gd= gr._grid->GlobalDimensions();

    for (x[0]=0;x[0]<gd[0];x[0]++){
    for (x[1]=0;x[1]<gd[1];x[1]++){
    for (x[2]=0;x[2]<gd[2];x[2]++){
    for (x[3]=0;x[3]<gd[3];x[3]++){
    for (x[4]=0;x[4]<gd[4];x[4]++){
      int s = x[0];
      cx[0] = x[1];
      cx[1] = x[2];
      cx[2] = x[3];
      cx[3] = x[4];

      cF = QDP::peekSite(ch[s],cx);
      for(int sp=0;sp<4;sp++){
	for(int j=0;j<3;j++){
	  cS =QDP::peekColor(cF,j);
	  cc =QDP::peekSpin(cS,sp);
	  c = Grid::Complex(QDP::toDouble(QDP::real(cc)), 
			    QDP::toDouble(QDP::imag(cc)));
	  F()(sp)(j) = c;
	}
      }
      Grid::pokeSite(F,gr,x);
    }}}}}
  }

  static Handle< LinearOperatorArray<T4> >  GetLinOp (U &u, ChromaAction parms)
  {
    QDP::Real _mq(mq);
    QDP::Real eps_lo(zolo_lo);
    QDP::Real eps_hi(zolo_hi);
    QDP::Real scale(mobius_scale);

    QDP::multi1d<int> bcs(QDP::Nd);

    bcs[0] = bcs[1] = bcs[2] = bcs[3] = 1;

    Chroma::Handle<Chroma::FermBC<T4,U,U> > fbc(new Chroma::SimpleFermBC< T4, U, U >(bcs));
    Chroma::Handle<Chroma::CreateFermState<T4,U,U> > cfs( new Chroma::CreateSimpleFermState<T4,U,U>(fbc));


    Chroma::GroupXML_t invparm;
    invparm.xml=std::string(
"   <InvertParam>\n"
"   <invType>CG_INVERTER</invType>\n"
"   <RsdCG>1.0e-9</RsdCG>\n"
"   <MaxCG>3000</MaxCG>\n"
"   </InvertParam>"
);

    invparm.id=std::string("CG_INVERTER");
    invparm.path=std::string("/InvertParam");

    if ( (parms == HtCayleyTanh)|| (parms==DWF) ) {
      Chroma::UnprecDWFermActArray  S_f(cfs, M5, _mq, Ls);
      Chroma::Handle< Chroma::FermState<T4,U,U> > fs( S_f.createState(u) );
      Chroma::Handle< Chroma::LinearOperatorArray<T4> > M(S_f.unprecLinOp(fs,_mq));
     return  M;
    }
    if ( parms == HwCayleyTanh ) {
      QDP::Real b5 = 0.5;
      QDP::Real c5 = 0.5;
      Chroma::UnprecNEFFermActArray  S_f(cfs, M5,b5,c5, _mq, Ls);
      Chroma::Handle< Chroma::FermState<T4,U,U> > fs( S_f.createState(u) );
      Chroma::Handle< Chroma::LinearOperatorArray<T4> > M(S_f.unprecLinOp(fs,_mq));
      return  M;
    }
    if ( parms == HmCayleyTanh ) {
      Real b5 = 0.5*(scale +1.0);
      Real c5 = 0.5*(scale -1.0);
      UnprecNEFFermActArray  S_f(cfs, M5,b5,c5, _mq, Ls);
      Handle< FermState<T4,U,U> > fs( S_f.createState(u) );
      Handle< LinearOperatorArray<T4> > M(S_f.unprecLinOp(fs,_mq));
      return  M;
    }
   if ( parms == HwCayleyZolo ) {
     UnprecZoloNEFFermActArrayParams params;
     params.OverMass=M5;
     params.Mass=_mq;
     params.b5=0.5;
     params.c5=0.5;
     params.N5=Ls;
     params.approximation_type = COEFF_TYPE_ZOLOTAREV;
     params.ApproxMin=eps_lo;
     params.ApproxMax=eps_hi;
     UnprecZoloNEFFermActArray  S_f(cfs, params);
     Handle< FermState<T4,U,U> > fs( S_f.createState(u) );
     Handle< LinearOperatorArray<T4> > M(S_f.unprecLinOp(fs,_mq));
     return  M;
   }
   if ( parms == HtCayleyZolo ) {
     UnprecZoloNEFFermActArrayParams params;
     params.OverMass=M5;
     params.Mass=_mq;
     params.b5=1.0;
     params.c5=0.0;
     params.N5=Ls;
     params.approximation_type = COEFF_TYPE_ZOLOTAREV;
     params.ApproxMin=eps_lo;
     params.ApproxMax=eps_hi;
     UnprecZoloNEFFermActArray  S_f(cfs, params);
     Handle< FermState<T4,U,U> > fs( S_f.createState(u) );
     Handle< LinearOperatorArray<T4> > M(S_f.unprecLinOp(fs,_mq));
     return M;
   }
   if ( parms == HmCayleyZolo ) {
     UnprecZoloNEFFermActArrayParams params;
     params.OverMass=M5;
     params.Mass=_mq;
     params.b5= 0.5*(mobius_scale +1.0);
     params.c5= 0.5*(mobius_scale -1.0);
     params.N5=Ls;
     params.approximation_type = COEFF_TYPE_ZOLOTAREV;
     params.ApproxMin=eps_lo;
     params.ApproxMax=eps_hi;
     UnprecZoloNEFFermActArray  S_f(cfs, params);
     Handle< FermState<T4,U,U> > fs( S_f.createState(u) );
     Handle< LinearOperatorArray<T4> > M(S_f.unprecLinOp(fs,_mq));
     return M;
   }
   if ( parms == HwPartFracZolo ) {
     if ( Ls%2 == 0 ) { 
       printf("Ls is not odd\n");
       exit(-1);
     }
     UnprecOvExtFermActArrayParams param;
     param.OverMass=M5; 
     param.Mass=_mq;
     param.RatPolyDeg = Ls;
     param.ApproxMin =eps_lo;
     param.ApproxMax =eps_hi;
     param.b5 =1.0;
     param.c5 =1.0;
     param.approximation_type=COEFF_TYPE_ZOLOTAREV;
     //     param.approximation_type=COEFF_TYPE_TANH_UNSCALED;
     //     param.approximation_type=COEFF_TYPE_TANH;
     param.tuning_strategy_xml=
"<TuningStrategy><Name>OVEXT_CONSTANT_STRATEGY</Name></TuningStrategy>\n";
     UnprecOvExtFermActArray S_f(cfs,param);
     Handle< FermState<T4,U,U> > fs( S_f.createState(u) );
     Handle< LinearOperatorArray<T4> > M(S_f.linOp(fs));
     return M;
   }
   if ( parms == HwContFracZolo ) {
     UnprecOvlapContFrac5DFermActParams param;
     param.Mass=_mq; // How is M5 set? Wilson mass In AuxFermAct
     param.ApproxMin=eps_lo;
     param.ApproxMax=eps_hi;
     param.approximation_type=COEFF_TYPE_ZOLOTAREV;
     param.RatPolyDeg=Ls;
     // The following is why I think Chroma made some directional errors:
     param.AuxFermAct= std::string(
"<AuxFermAct>\n"
"  <FermAct>UNPRECONDITIONED_WILSON</FermAct>\n"
"  <Mass>-1.8</Mass>\n"
"  <b5>1</b5>\n"
"  <c5>0</c5>\n"
"  <MaxCG>1000</MaxCG>\n"
"  <RsdCG>1.0e-9</RsdCG>\n"
"  <FermionBC>\n"
"      <FermBC>SIMPLE_FERMBC</FermBC>\n"
"      <boundary>1 1 1 1</boundary>\n"
"   </FermionBC> \n"
"</AuxFermAct>"
);
     param.AuxFermActGrp= std::string("");
     UnprecOvlapContFrac5DFermActArray S_f(fbc,param);
     Handle< FermState<T4,U,U> > fs( S_f.createState(u) );
     Handle< LinearOperatorArray<T4> > M(S_f.linOp(fs));
     return  M;
   }
   assert(0);
  }

  static Chroma::Handle< Chroma::SystemSolver<QDP::LatticeFermion> > GetSolver(QDP::multi1d<QDP::LatticeColorMatrix> &u, ChromaAction parms)
  {
    QDP::multi1d<int> bcs(Nd);
    bcs[0] = bcs[1] = bcs[2] = bcs[3] = 1;
    Chroma::Handle<Chroma::FermBC<T4,U,U> > fbc(new Chroma::SimpleFermBC< T4, U, U >(bcs));
    Chroma::Handle<Chroma::CreateFermState<T4,U,U> > cfs( new Chroma::CreateSimpleFermState<T4,U,U>(fbc));
    
    Chroma::GroupXML_t invparm;
    invparm.xml=std::string(
			    "   <InvertParam>\n"
			    "   <invType>CG_INVERTER</invType>\n"
			    "   <RsdCG>1.0e-10</RsdCG>\n"
			    "   <MaxCG>3000</MaxCG>\n"
			    "   </InvertParam>"
			    );
    invparm.id=std::string("CG_INVERTER");
    invparm.path=std::string("/InvertParam");
    
    Chroma::UnprecDWFermActArray  S_f(cfs, M5, mq, Ls);
    std::cout << "GetSolver: DWF 4d prec "<<std::endl;
    std::cout << "GetSolver: M5 "<<M5<<std::endl;
    std::cout << "GetSolver: mq "<<mq<<std::endl;
    std::cout << "GetSolver: Ls "<<Ls<<std::endl;
    Chroma::Handle< Chroma::FermState<T4,U,U> > fs( S_f.createState(u) );
    Chroma::Handle< LinearOperatorArray<T4> > M(S_f.unprecLinOp(fs,mq));
    return  S_f.qprop(fs,invparm);
  }
};
}

int main (int argc,char **argv )
{

  /********************************************************
   * Setup QDP
   *********************************************************/
  Chroma::initialize(&argc,&argv);
  Chroma::WilsonTypeFermActs4DEnv::registerAll(); 

  /********************************************************
   * Setup Grid
   *********************************************************/
  Grid::Grid_init(&argc,&argv);
  Grid::GridCartesian * UGrid   = Grid::QCD::SpaceTimeGrid::makeFourDimGrid(Grid::GridDefaultLatt(), 
									    Grid::GridDefaultSimd(Grid::QCD::Nd,Grid::vComplex::Nsimd()),
									    Grid::GridDefaultMpi());
  
  std::vector<int> gd = UGrid->GlobalDimensions();
  QDP::multi1d<int> nrow(QDP::Nd);
  for(int mu=0;mu<4;mu++) nrow[mu] = gd[mu];

  QDP::Layout::setLattSize(nrow);
  QDP::Layout::create();

  Grid::GridCartesian         * FGrid   = Grid::QCD::SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
  Grid::QCD::LatticeGaugeField lat(UGrid);
  Grid::QCD::LatticeFermion    src(FGrid);
  Grid::QCD::LatticeFermion    res_chroma(FGrid);
  Grid::QCD::LatticeFermion    res_grid  (FGrid);
  
  std::vector<ChromaAction> ActionList({
		 HtCayleyTanh, // Plain old DWF.
		 HmCayleyTanh,
		 HwCayleyTanh,
		 HtCayleyZolo, // Plain old DWF.
		 HmCayleyZolo,
		 HwCayleyZolo
  });
  std::vector<std::string> ActionName({
        "HtCayleyTanh",
	"HmCayleyTanh",
	"HwCayleyTanh",
	"HtCayleyZolo",
	"HmCayleyZolo",
        "HwCayleyZolo"
  });

  for(int i=0;i<ActionList.size();i++) {
    std::cout << "*****************************"<<std::endl;
    std::cout << "Action "<<ActionName[i]<<std::endl;
    std::cout << "*****************************"<<std::endl;
    for(int dag=0;dag<2;dag++) {


      std::cout << "Dag =  "<<dag<<std::endl;
      
      calc_grid  (ActionList[i],lat,src,res_grid,dag);
      
      std::cout << "Norm of Grid DWF multiply "<<Grid::norm2(res_grid)<<std::endl;
      
      calc_chroma(ActionList[i],lat,src,res_chroma,dag);
      
      std::cout << "Norm of chroma DWF multiply "<<Grid::norm2(res_chroma)<<std::endl;
      
      res_chroma=res_chroma - res_grid;
      
      std::cout << "Norm of difference "<<Grid::norm2(res_chroma)<<std::endl;
    }
  }

  std::cout << "Finished test "<<std::endl;

  Chroma::finalize();
}

void calc_chroma(ChromaAction action,Grid::QCD::LatticeGaugeField & lat, Grid::QCD::LatticeFermion &src, Grid::QCD::LatticeFermion &res,int dag)
{
  QDP::multi1d<QDP::LatticeColorMatrix> u(4);

  //  Chroma::HotSt(u);
  Chroma::ChromaWrapper::ImportGauge(lat,u) ;

  QDP::multi1d<QDP::LatticeFermion>  check(Ls);
  QDP::multi1d<QDP::LatticeFermion> result(Ls);
  QDP::multi1d<QDP::LatticeFermion>  psi(Ls);

  Chroma::ChromaWrapper::ImportFermion(src,psi);

  for(int mu=0;mu<4;mu++){
    std::cout <<"Imported Gauge norm ["<<mu<<"] "<< QDP::norm2(u[mu])<<std::endl;
  }
  std::cout <<"Imported Fermion norm "<< QDP::norm2(psi)<<std::endl;

  typedef QDP::LatticeFermion T;
  typedef QDP::multi1d<QDP::LatticeColorMatrix> U;
  
  auto linop =Chroma::ChromaWrapper::GetLinOp(u, action);

  printf("Calling Chroma Linop\n"); fflush(stdout);

  if ( dag ) 
    (*linop)(check,psi,Chroma::MINUS);
  else
    (*linop)(check,psi,Chroma::PLUS);

  printf("Called Chroma Linop\n"); fflush(stdout);

  Chroma::ChromaWrapper::ExportFermion(res,check) ;
}



void calc_grid(ChromaAction action,Grid::QCD::LatticeGaugeField & Umu, Grid::QCD::LatticeFermion &src, Grid::QCD::LatticeFermion &res,int dag)
{
  using namespace Grid;
  using namespace Grid::QCD;

  std::vector<int> seeds4({1,2,3,4});
  std::vector<int> seeds5({5,6,7,8});

  Grid::GridCartesian         * UGrid   = (Grid::GridCartesian *) Umu._grid;
  Grid::GridCartesian         * FGrid   = (Grid::GridCartesian *) src._grid;
  Grid::GridRedBlackCartesian * UrbGrid = Grid::QCD::SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
  Grid::GridRedBlackCartesian * FrbGrid = Grid::QCD::SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);

  Grid::GridParallelRNG          RNG4(UGrid);  RNG4.SeedFixedIntegers(seeds4);
  Grid::GridParallelRNG          RNG5(FGrid);  RNG5.SeedFixedIntegers(seeds5);

  Grid::gaussian(RNG5,src);
  Grid::gaussian(RNG5,res);

  Grid::QCD::SU3::HotConfiguration(RNG4,Umu);

  /*
  Grid::QCD::LatticeColourMatrix U(UGrid);
  U=Grid::zero;
  for(int nn=0;nn<Grid::QCD::Nd;nn++){
    if ( nn>=4 ) {
      Grid::PokeIndex<LorentzIndex>(Umu,U,nn);
    }
  }
  */

  Grid::RealD _mass=mq;
  Grid::RealD _M5  =M5;

  if ( action == HtCayleyTanh ) { 

    Grid::QCD::DomainWallFermionR Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,_mass,_M5);

    std::cout << Grid::GridLogMessage <<" Calling domain wall multiply "<<std::endl;

    if ( dag ) 
      Ddwf.Mdag(src,res);  
    else 
      Ddwf.M(src,res);  
    return;

  } 

  if ( action == HmCayleyZolo ) {

    Grid::Real _b = 0.5*(mobius_scale +1.0);
    Grid::Real _c = 0.5*(mobius_scale -1.0);
    Grid::QCD::MobiusZolotarevFermionR D(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,_mass,_M5,_b,_c,zolo_lo,zolo_hi);

    std::cout << Grid::GridLogMessage <<" Calling mobius zolo multiply "<<std::endl;

    if ( dag ) 
      D.Mdag(src,res);  
    else 
      D.M(src,res);  

    return;
  }

  if ( action == HtCayleyZolo ) {

    Grid::QCD::ShamirZolotarevFermionR D(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,_mass,_M5,zolo_lo,zolo_hi);

    std::cout << Grid::GridLogMessage <<" Calling shamir zolo multiply "<<std::endl;

    if ( dag ) 
      D.Mdag(src,res);  
    else 
      D.M(src,res);  

    return;
  }

  /*
  if ( action == HmCayleyTanh ) {
    Grid::Real _b = 0.5*(mobius_scale +1.0);
    Grid::Real _c = 0.5*(mobius_scale -1.0);
    Grid::QCD::MobiusFermionR D(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,_mass,_M5,_b,_c);

    std::cout << Grid::GridLogMessage <<" Calling mobius tanh multiply "<<std::endl;

    if ( dag ) 
      D.Mdag(src,res);  
    else 
      D.M(src,res);  

    return;

  }
  */

  if ( action == HmCayleyTanh ) {

    Grid::QCD::ScaledShamirFermionR D(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,_mass,_M5,mobius_scale);

    std::cout << Grid::GridLogMessage <<" Calling scaled shamir multiply "<<std::endl;

    if ( dag ) 
      D.Mdag(src,res);  
    else 
      D.M(src,res);  

    return;
  }

  if ( action == HwCayleyTanh ) {

    Grid::QCD::OverlapWilsonCayleyTanhFermionR D(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,_mass,_M5,1.0);

    if ( dag ) 
      D.Mdag(src,res);  
    else 
      D.M(src,res);  

    return;
  }

  if ( action == HwCayleyZolo ) {

    Grid::QCD::OverlapWilsonCayleyZolotarevFermionR D(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,_mass,_M5,zolo_lo,zolo_hi);

    if ( dag ) 
      D.Mdag(src,res);  
    else 
      D.M(src,res);  

    return;
  }
  
  assert(0);
}