Auxiliary fields

lib/qcd/hmc/GenericHMCrunner.h

@@ -144,7 +144,7 @@ class HMCWrapperTemplate: public HMCRunnerBase<ReaderClass> {
     LaplacianParams LapPar(0.0001, 1.0, 1000, 1e-8, 12, 64);
     RealD Kappa = 0.9;
 
-
+    // Better to pass the generalised momenta to the integrator
     LaplacianAdjointField<PeriodicGimplR> Laplacian(UGrid, CG, LapPar, Kappa);
     TheIntegrator MDynamics(UGrid, Parameters.MD, TheAction, Smearing, Laplacian);
 

lib/qcd/hmc/integrators/Integrator.h

@@ -128,17 +128,23 @@ class Integrator {
       Mom -= force * ep; 
     }
 
-
+    // Generalised momenta
     MomentaField MomDer(P.Mom._grid);
     P.M.ImportGauge(U);
     P.DerivativeU(P.Mom, MomDer);
     Mom -= MomDer * ep;
 
+    // Auxiliary fields
+    //P.update_auxiliary_momenta(ep*0.5);
+    //P.AuxiliaryFieldsDerivative(MomDer);
+    //Mom -= MomDer * ep;
+    //P.update_auxiliary_momenta(ep*0.5);
+
     // Force from the other representations
     as[level].apply(update_P_hireps, Representations, Mom, U, ep);
   }
 
-  void implicit_update_P(Field& U, int level, double ep) {
+  void implicit_update_P(Field& U, int level, double ep, bool intermediate = false) {
     t_P[level] += ep;
 
     std::cout << GridLogIntegrator << "[" << level << "] P "
@@ -170,16 +176,18 @@ class Integrator {
     P.M.ImportGauge(U);
     MomentaField MomDer(P.Mom._grid);
     MomentaField MomDer1(P.Mom._grid);
+    MomentaField AuxDer(P.Mom._grid);
     MomDer1 = zero;
     MomentaField diff(P.Mom._grid);
 
-    // be careful here, we need the first step
-    // in every trajectory
-    static int call = 0;
-    if (call == 1)
+    if (intermediate)
       P.DerivativeU(P.Mom, MomDer1);
 
-    call = 1;
+    // Auxiliary fields
+    //P.update_auxiliary_momenta(ep*0.5);
+    //P.AuxiliaryFieldsDerivative(AuxDer);
+    //Msum += AuxDer;
+    
 
     // Here run recursively
     int counter = 1;
@@ -194,7 +202,7 @@ class Integrator {
       std::cout << GridLogIntegrator << "|Force| laplacian site average: " << force_abs
                 << std::endl;
 
-      NewMom = P.Mom - ep* 0.5 * (2.0*Msum + MomDer + MomDer1);
+      NewMom = P.Mom - ep* 0.5 * (2.0*Msum + MomDer + MomDer1);// simplify
       diff = NewMom - OldMom;
       counter++;
       RelativeError = std::sqrt(norm2(diff))/std::sqrt(norm2(NewMom));
@@ -204,8 +212,8 @@ class Integrator {
 
     P.Mom = NewMom;
 
-    // update the auxiliary fields momenta
-    // todo
+    // update the auxiliary fields momenta    
+    //P.update_auxiliary_momenta(ep*0.5);
   }
 
 
@@ -239,7 +247,7 @@ class Integrator {
     Field diff(U._grid);
     Real threshold = 1e-6;
     int counter = 1;
-    int MaxCounter = 1000;
+    int MaxCounter = 100;
 
     Field OldU = U;
     Field NewU = U;
@@ -247,6 +255,10 @@ class Integrator {
     P.M.ImportGauge(U);
     P.DerivativeP(Mom1); // first term in the derivative 
 
+ 
+    //P.update_auxiliary_fields(ep*0.5);
+
+
     do {
       std::cout << GridLogIntegrator << "UpdateU implicit step "<< counter << std::endl;
       
@@ -271,6 +283,9 @@ class Integrator {
     } while (RelativeError > threshold && counter < MaxCounter);
 
     U = NewU;
+
+    //P.update_auxiliary_fields(ep*0.5);
+
   }
 
 

lib/qcd/hmc/integrators/Integrator_algorithm.h

@@ -344,7 +344,7 @@ class ImplicitLeapFrog : public Integrator<FieldImplementation, SmearingPolicy,
       if (last_step){
         this->update_P(U, level, eps / 2.0);
       } else {
-      this->implicit_update_P(U, level, eps);
+      this->implicit_update_P(U, level, eps, true);// intermediate step
       }
     }
   }

lib/qcd/utils/CovariantLaplacian.h

@@ -144,6 +144,25 @@ class LaplacianAdjointField: public Metric<typename Impl::Field> {
     } 
   }
 
+  // separating this temporarily
+  void MDeriv(const GaugeField& left, const GaugeField& right,
+              GaugeField& der) {
+    // in is anti-hermitian
+    RealD factor = -kappa / (double(4 * Nd));
+
+    for (int mu = 0; mu < Nd; mu++) {
+      GaugeLinkField der_mu(der._grid);
+      der_mu = zero;
+      for (int nu = 0; nu < Nd; nu++) {
+        GaugeLinkField left_nu = PeekIndex<LorentzIndex>(left, nu);
+        GaugeLinkField right_nu = PeekIndex<LorentzIndex>(right, nu);
+        der_mu += U[mu] * Cshift(left_nu, mu, 1) * adj(U[mu]) * right_nu;
+        der_mu += U[mu] * Cshift(right_nu, mu, 1) * adj(U[mu]) * left_nu;
+      }
+      PokeIndex<LorentzIndex>(der, -factor * der_mu, mu);
+    }
+  }
+
   void Minv(const GaugeField& in, GaugeField& inverted){
     HermitianLinearOperator<LaplacianAdjointField<Impl>,GaugeField> HermOp(*this);
     Solver(HermOp, in, inverted);
@@ -157,6 +176,14 @@ class LaplacianAdjointField: public Metric<typename Impl::Field> {
     P = Gp; 
   }
 
+  void MInvSquareRoot(GaugeField& P){
+    GaugeField Gp(P._grid);
+    HermitianLinearOperator<LaplacianAdjointField<Impl>,GaugeField> HermOp(*this);
+    ConjugateGradientMultiShift<GaugeField> msCG(param.MaxIter,PowerInvHalf);
+    msCG(HermOp,P,Gp);
+    P = Gp; 
+  }
+
 
 
  private:

lib/qcd/utils/Metric.h

@@ -40,7 +40,9 @@ public:
   virtual void M(const Field&, Field&)     = 0;
   virtual void Minv(const Field&, Field&)  = 0;
   virtual void MSquareRoot(Field&) = 0;
+  virtual void MInvSquareRoot(Field&) = 0;
   virtual void MDeriv(const Field&, Field&) = 0;
+  virtual void MDeriv(const Field&, const Field&, Field&) = 0;
 };
 
 
@@ -58,9 +60,15 @@ public:
   virtual void MSquareRoot(Field& P){
     // do nothing
   }
+  virtual void MInvSquareRoot(Field& P){
+    // do nothing
+  }
   virtual void MDeriv(const Field& in, Field& out){
     out = zero;
   }
+  virtual void MDeriv(const Field& left, const Field& right, Field& out){
+    out = zero;
+  }
 
 };
 
@@ -76,18 +84,37 @@ public:
   Metric<MomentaField>& M;
   MomentaField Mom;
 
-  GeneralisedMomenta(GridBase* grid, Metric<MomentaField>& M): M(M), Mom(grid){}
+  // Auxiliary fields
+  // not hard coded but inherit the type from the metric
+  // created Nd new fields
+  // hide these in the metric?
+  //typedef Lattice<iVector<iScalar<iMatrix<vComplex, Nc> >, Nd/2 > > AuxiliaryMomentaType;
+  MomentaField AuxMom;
+  MomentaField AuxField;
+
+  GeneralisedMomenta(GridBase* grid, Metric<MomentaField>& M): M(M), Mom(grid), AuxMom(grid), AuxField(grid){}
 
   // Correct
   void MomentaDistribution(GridParallelRNG& pRNG){
     // Generate a distribution for
-    // 1/2 P^dag G P
+    // P^dag G P
     // where G = M^-1
 
     // Generate gaussian momenta
     Implementation::generate_momenta(Mom, pRNG);
     // Modify the distribution with the metric
     M.MSquareRoot(Mom);
+
+    if (0) {
+      // Auxiliary momenta
+      // do nothing if trivial, so hide in the metric
+      MomentaField AuxMomTemp(Mom._grid);
+      Implementation::generate_momenta(AuxMom, pRNG);
+      Implementation::generate_momenta(AuxField, pRNG);
+      // Modify the distribution with the metric
+      // Aux^dag M Aux
+      M.MInvSquareRoot(AuxMom);  // AuxMom = M^{-1/2} AuxMomTemp
+    }
   }
 
   // Correct
@@ -99,17 +126,34 @@ public:
     Hloc = zero;
     for (int mu = 0; mu < Nd; mu++) {
       // This is not very general
-      // hide in the operators
+      // hide in the metric
       auto Mom_mu = PeekIndex<LorentzIndex>(Mom, mu);
       auto inv_mu = PeekIndex<LorentzIndex>(inv, mu);
       Hloc += trace(Mom_mu * inv_mu);
     }
+
+    if (0) {
+      // Auxiliary Fields
+      // hide in the metric
+      M.M(AuxMom, inv);
+      for (int mu = 0; mu < Nd; mu++) {
+        // This is not very general
+        // hide in the operators
+        auto inv_mu = PeekIndex<LorentzIndex>(inv, mu);
+        auto am_mu = PeekIndex<LorentzIndex>(AuxMom, mu);
+        auto af_mu = PeekIndex<LorentzIndex>(AuxField, mu);
+        Hloc += trace(am_mu * inv_mu);// p M p
+        Hloc += trace(af_mu * af_mu);
+      }
+    }
+
     Complex Hsum = sum(Hloc);
     return Hsum.real();
   }
 
   // Correct
   void DerivativeU(MomentaField& in, MomentaField& der){
+
     // Compute the derivative of the kinetic term
     // with respect to the gauge field
     MomentaField MDer(in._grid);
@@ -118,16 +162,54 @@ public:
     M.Minv(in, X);  // X = G in
     M.MDeriv(X, MDer);  // MDer = U * dS/dU
     der = Implementation::projectForce(MDer);  // Ta if gauge fields
+    
   }
 
+  void AuxiliaryFieldsDerivative(MomentaField& der){
+    der = zero;
+    if (0){
+    // Auxiliary fields
+    MomentaField der_temp(der._grid);
+    MomentaField X(der._grid);
+    X=zero;
+    //M.M(AuxMom, X); // X = M Aux
+    // Two derivative terms
+    // the Mderiv need separation of left and right terms
+    M.MDeriv(AuxMom, der); 
+
+
+    // this one should not be necessary (identical to the previous one)
+    //M.MDeriv(X, AuxMom, der_temp); der += der_temp;
+
+    der = -1.0*Implementation::projectForce(der);
+    }
+  }
 
-  //   
   void DerivativeP(MomentaField& der){
     der = zero;
     M.Minv(Mom, der);
+    // is the projection necessary here?
+    // no for fields in the algebra
     der = Implementation::projectForce(der); 
   }
 
+  void update_auxiliary_momenta(RealD ep){
+    if(0){
+      AuxMom -= ep * AuxField;
+    }
+  }
+
+  void update_auxiliary_fields(RealD ep){
+    if (0) {
+      MomentaField tmp(AuxMom._grid);
+      MomentaField tmp2(AuxMom._grid);
+      M.M(AuxMom, tmp);
+      // M.M(tmp, tmp2);
+      AuxField += ep * tmp;  // M^2 AuxMom
+      // factor of 2?
+    }
+  }
+
 };
 
 

tests/forces/Test_laplacian_force.cc

@@ -79,14 +79,16 @@ int main (int argc, char ** argv)
 
   // get the deriv with respect to "U"
   LatticeGaugeField UdSdU(&Grid);
+  LatticeGaugeField AuxDer(&Grid);
   std::cout << GridLogMessage<< "DerivativeU" << std::endl;
   LaplacianMomenta.DerivativeU(LaplacianMomenta.Mom, UdSdU);
-
+  LaplacianMomenta.AuxiliaryFieldsDerivative(AuxDer);
+  UdSdU += AuxDer;
 
   ////////////////////////////////////
   // Modify the gauge field a little 
   ////////////////////////////////////
-  RealD dt = 0.001;
+  RealD dt = 0.0001;
 
   LatticeColourMatrix mommu(&Grid); 
   LatticeColourMatrix forcemu(&Grid); 

tests/hmc/Test_hmc_WilsonGauge_Implicit.cc

@@ -76,7 +76,7 @@ int main(int argc, char **argv) {
   // need wrappers of the fermionic classes 
   // that have a complex construction
   // standard
-  RealD beta = 5.6;
+  RealD beta = 0.0;
   WilsonGaugeActionR Waction(beta);
   
   ActionLevel<HMCWrapper::Field> Level1(1);