Integrator works now

lib/qcd/hmc/GenericHMCrunner.h

@@ -138,7 +138,15 @@ class HMCWrapperTemplate: public HMCRunnerBase<ReaderClass> {
 
     // Can move this outside?
     typedef IntegratorType<SmearingPolicy> TheIntegrator;
-    TheIntegrator MDynamics(UGrid, Parameters.MD, TheAction, Smearing);
+    // Metric
+    //TrivialMetric<typename Implementation::Field> Mtr;
+    ConjugateGradient<LatticeGaugeField> CG(1.0e-8,10000);
+    LaplacianParams LapPar(0.0001, 1.0, 1000, 1e-8, 12, 64);
+    RealD Kappa = 0.9;
+
+
+    LaplacianAdjointField<PeriodicGimplR> Laplacian(UGrid, CG, LapPar, Kappa);
+    TheIntegrator MDynamics(UGrid, Parameters.MD, TheAction, Smearing, Laplacian);
 
     if (Parameters.StartingType == "HotStart") {
       // Hot start

lib/qcd/hmc/HMC.h

@@ -202,7 +202,7 @@ class HybridMonteCarlo {
     RealD H0 = TheIntegrator.S(U);  // initial state action
 
     std::streamsize current_precision = std::cout.precision();
-    std::cout.precision(17);
+    std::cout.precision(15);
     std::cout << GridLogMessage << "Total H before trajectory = " << H0 << "\n";
     std::cout.precision(current_precision);
 
@@ -210,7 +210,19 @@ class HybridMonteCarlo {
 
     RealD H1 = TheIntegrator.S(U);  // updated state action
 
-    std::cout.precision(17);
+    ///////////////////////////////////////////////////////////
+    if(0){
+      std::cout << "------------------------- Reversibility test" << std::endl;
+      TheIntegrator.reverse_momenta();
+      TheIntegrator.integrate(U);
+
+      H1 = TheIntegrator.S(U);  // updated state action
+      std::cout << "--------------------------------------------" << std::endl;
+    }
+    ///////////////////////////////////////////////////////////
+
+
+    std::cout.precision(15);
     std::cout << GridLogMessage << "Total H after trajectory  = " << H1
 	      << "  dH = " << H1 - H0 << "\n";
     std::cout.precision(current_precision);

lib/qcd/hmc/integrators/Integrator.h

@@ -78,7 +78,7 @@ class Integrator {
   std::vector<double> t_P;  
 
   //MomentaField P;
-  GeneralisedMomenta<FieldImplementation, TrivialMetric<MomentaField>> P;
+  GeneralisedMomenta<FieldImplementation > P;
   SmearingPolicy& Smearer;
   RepresentationPolicy Representations;
   IntegratorParameters Params;
@@ -125,9 +125,15 @@ class Integrator {
       force = FieldImplementation::projectForce(force); // Ta for gauge fields
       Real force_abs = std::sqrt(norm2(force)/U._grid->gSites());
       std::cout << GridLogIntegrator << "Force average: " << force_abs << std::endl;
-      Mom -= force * ep;
+      Mom -= force * ep; 
     }
 
+
+    MomentaField MomDer(P.Mom._grid);
+    P.M.ImportGauge(U);
+    P.DerivativeU(P.Mom, MomDer);
+    Mom -= MomDer * ep;
+
     // Force from the other representations
     as[level].apply(update_P_hireps, Representations, Mom, U, ep);
   }
@@ -141,7 +147,7 @@ class Integrator {
     MomentaField Msum(P.Mom._grid);
     Msum = zero;
     for (int a = 0; a < as[level].actions.size(); ++a) {
-      // Compute the force
+      // Compute the force terms for the lagrangian part
       // We need to compute the derivative of the actions
       // only once
       Field force(U._grid);
@@ -153,7 +159,7 @@ class Integrator {
       if (as[level].actions.at(a)->is_smeared) Smearer.smeared_force(force);
       force = FieldImplementation::projectForce(force);  // Ta for gauge fields
       Real force_abs = std::sqrt(norm2(force) / U._grid->gSites());
-      std::cout << GridLogIntegrator << "Force average: " << force_abs
+      std::cout << GridLogIntegrator << "|Force| site average: " << force_abs
                 << std::endl;
       Msum += force;
     }
@@ -162,21 +168,44 @@ class Integrator {
     MomentaField OldMom = P.Mom;
     double threshold = 1e-6;
     P.M.ImportGauge(U);
+    MomentaField MomDer(P.Mom._grid);
+    MomentaField MomDer1(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)
+      P.DerivativeU(P.Mom, MomDer1);
+
+    call = 1;
+
     // Here run recursively
+    int counter = 1;
+    RealD RelativeError;
     do {
-      MomentaField MomDer(P.Mom._grid);
+      std::cout << GridLogIntegrator << "UpdateP implicit step "<< counter << std::endl;
-      MomentaField X(P.Mom._grid);
+
-      OldMom = NewMom;
       // Compute the derivative of the kinetic term
       // with respect to the gauge field
       P.DerivativeU(NewMom, MomDer);
-      NewMom = P.Mom - ep * (MomDer + Msum);
+      Real force_abs = std::sqrt(norm2(MomDer) / U._grid->gSites());
+      std::cout << GridLogIntegrator << "|Force| laplacian site average: " << force_abs
+                << std::endl;
 
-    } while (norm2(NewMom - OldMom) > threshold);
+      NewMom = P.Mom - ep* 0.5 * (2.0*Msum + MomDer + MomDer1);
+      diff = NewMom - OldMom;
+      counter++;
+      RelativeError = std::sqrt(norm2(diff))/std::sqrt(norm2(NewMom));
+      std::cout << GridLogIntegrator << "UpdateP RelativeError: " << RelativeError << std::endl;
+      OldMom = NewMom;
+    } while (RelativeError > threshold);
 
     P.Mom = NewMom;
 
     // update the auxiliary fields momenta
+    // todo
   }
 
 
@@ -204,19 +233,44 @@ class Integrator {
     int fl = levels - 1;
     std::cout << GridLogIntegrator << "   " << "[" << fl << "] U " << " dt " << ep << " : t_U " << t_U << std::endl;
 
-    Real threshold = 1e-6;
-    P.M.ImportGauge(U);
     MomentaField Mom1(P.Mom._grid);
     MomentaField Mom2(P.Mom._grid);
+    RealD RelativeError;
+    Field diff(U._grid);
+    Real threshold = 1e-6;
+    int counter = 1;
+    int MaxCounter = 1000;
+
     Field OldU = U;
     Field NewU = U;
+
+    P.M.ImportGauge(U);
     P.DerivativeP(Mom1); // first term in the derivative 
+
     do {
-      OldU = NewU; // some redundancy to be eliminated
+      std::cout << GridLogIntegrator << "UpdateU implicit step "<< counter << std::endl;
+      
       P.DerivativeP(Mom2); // second term in the derivative, on the updated U
-      FieldImplementation::update_field(Mom1 + Mom2, NewU, ep);
+      MomentaField sum = (Mom1 + Mom2);
+      //std::cout << GridLogMessage << "sum Norm " << norm2(sum) << std::endl;
+
+      for (int mu = 0; mu < Nd; mu++) {
+        auto Umu = PeekIndex<LorentzIndex>(U, mu);
+        auto Pmu = PeekIndex<LorentzIndex>(sum, mu);
+        Umu = expMat(Pmu, ep * 0.5, 12) * Umu;
+        PokeIndex<LorentzIndex>(NewU, ProjectOnGroup(Umu), mu);
+      }
+
+      diff = NewU - OldU;
+      RelativeError = std::sqrt(norm2(diff))/std::sqrt(norm2(NewU));
+      std::cout << GridLogIntegrator << "UpdateU RelativeError: " << RelativeError << std::endl;
+      
       P.M.ImportGauge(NewU);
-    } while (norm2(NewU - OldU) > threshold);
+      OldU = NewU; // some redundancy to be eliminated
+      counter++;
+    } while (RelativeError > threshold && counter < MaxCounter);
+
+    U = NewU;
   }
 
 
@@ -225,10 +279,10 @@ class Integrator {
  public:
   Integrator(GridBase* grid, IntegratorParameters Par,
              ActionSet<Field, RepresentationPolicy>& Aset,
-             SmearingPolicy& Sm)
+             SmearingPolicy& Sm, Metric<MomentaField>& M)
       : Params(Par),
         as(Aset),
-        P(grid),
+        P(grid, M),
         levels(Aset.size()),
         Smearer(Sm),
         Representations(grid) {
@@ -260,6 +314,10 @@ class Integrator {
 
   }
 
+  void reverse_momenta(){
+    P.Mom *= 1.0;
+  }
+
   // to be used by the actionlevel class to iterate
   // over the representations
   struct _refresh {
@@ -278,7 +336,10 @@ class Integrator {
   void refresh(Field& U, GridParallelRNG& pRNG) {
     assert(P.Mom._grid == U._grid);
     std::cout << GridLogIntegrator << "Integrator refresh\n";
+
     //FieldImplementation::generate_momenta(P, pRNG);
+
+    P.M.ImportGauge(U);
     P.MomentaDistribution(pRNG);
 
     // Update the smeared fields, can be implemented as observer
@@ -325,7 +386,9 @@ class Integrator {
   // Calculate action
   RealD S(Field& U) {  // here also U not used
 
-    RealD H = - FieldImplementation::FieldSquareNorm(P.Mom); // - trace (P*P)
+    //RealD H = - FieldImplementation::FieldSquareNorm(P.Mom); // - trace (P*P)
+    P.M.ImportGauge(U);
+    RealD H = - P.MomentaAction();
     RealD Hterm;
     std::cout << GridLogMessage << "Momentum action H_p = " << H << "\n";
 
@@ -369,6 +432,7 @@ class Integrator {
 
     // and that we indeed got to the end of the trajectory
     assert(fabs(t_U - Params.trajL) < 1.0e-6);
+
   }
 
 

lib/qcd/hmc/integrators/Integrator_algorithm.h

@@ -294,7 +294,7 @@ class ForceGradient : public Integrator<FieldImplementation, SmearingPolicy,
 
 
 
-
+// correct
 template <class FieldImplementation, class SmearingPolicy,
           class RepresentationPolicy =
               Representations<FundamentalRepresentation> >
@@ -311,9 +311,9 @@ class ImplicitLeapFrog : public Integrator<FieldImplementation, SmearingPolicy,
   std::string integrator_name(){return "ImplicitLeapFrog";}
 
   ImplicitLeapFrog(GridBase* grid, IntegratorParameters Par,
-           ActionSet<Field, RepresentationPolicy>& Aset, SmearingPolicy& Sm)
+           ActionSet<Field, RepresentationPolicy>& Aset, SmearingPolicy& Sm, Metric<Field>& M)
       : Integrator<FieldImplementation, SmearingPolicy, RepresentationPolicy>(
-            grid, Par, Aset, Sm){};
+            grid, Par, Aset, Sm, M){};
 
   void step(Field& U, int level, int _first, int _last) {
     int fl = this->as.size() - 1;
@@ -335,19 +335,89 @@ class ImplicitLeapFrog : public Integrator<FieldImplementation, SmearingPolicy,
       }
 
       if (level == fl) {  // lowest level
-        this->implicit_update_U(U, eps / 2.0);
+        this->implicit_update_U(U, eps);
       } else {  // recursive function call
         this->step(U, level + 1, first_step, last_step);
       }
 
-      int mm = last_step ? 1 : 2;
+      //int mm = last_step ? 1 : 2;
-      this->update_P(U, level, mm * eps / 2.0);
+      if (last_step){
+        this->update_P(U, level, eps / 2.0);
+      } else {
+      this->implicit_update_P(U, level, eps);
+      }
     }
   }
 };
 
 
+// This is not completely tested
+template <class FieldImplementation, class SmearingPolicy,
+          class RepresentationPolicy =
+              Representations<FundamentalRepresentation> >
+class ImplicitMinimumNorm2 : public Integrator<FieldImplementation, SmearingPolicy,
+                                       RepresentationPolicy> {
+ private:
+  const RealD lambda = 0.1931833275037836;
 
+ public:
+  INHERIT_FIELD_TYPES(FieldImplementation);
+
+  ImplicitMinimumNorm2(GridBase* grid, IntegratorParameters Par,
+               ActionSet<Field, RepresentationPolicy>& Aset, SmearingPolicy& Sm, Metric<Field>& M)
+      : Integrator<FieldImplementation, SmearingPolicy, RepresentationPolicy>(
+            grid, Par, Aset, Sm, M){};
+
+  std::string integrator_name(){return "ImplicitMininumNorm2";}
+
+  void step(Field& U, int level, int _first, int _last) {
+    // level  : current level
+    // fl     : final level
+    // eps    : current step size
+
+    int fl = this->as.size() - 1;
+
+    RealD eps = this->Params.trajL/this->Params.MDsteps * 2.0;
+    for (int l = 0; l <= level; ++l) eps /= 2.0 * this->as[l].multiplier;
+
+    // Nesting:  2xupdate_U of size eps/2
+    // Next level is eps/2/multiplier
+
+    int multiplier = this->as[level].multiplier;
+    for (int e = 0; e < multiplier; ++e) {  // steps per step
+
+      int first_step = _first && (e == 0);
+      int last_step = _last && (e == multiplier - 1);
+
+      if (first_step) {  // initial half step
+        this->implicit_update_P(U, level, lambda * eps);
+      }
+
+      if (level == fl) {  // lowest level
+        this->implicit_update_U(U, 0.5 * eps);
+      } else {  // recursive function call
+        this->step(U, level + 1, first_step, 0);
+      }
+
+      this->implicit_update_P(U, level, (1.0 - 2.0 * lambda) * eps);
+
+      if (level == fl) {  // lowest level
+        this->implicit_update_U(U, 0.5 * eps);
+      } else {  // recursive function call
+        this->step(U, level + 1, 0, last_step);
+      }
+
+      //int mm = (last_step) ? 1 : 2;
+      //this->update_P(U, level, lambda * eps * mm);
+
+      if (last_step) {
+        this->update_P(U, level, eps * lambda);
+      } else {
+        this->implicit_update_P(U, level, lambda * eps*2.0);
+      }
+    }
+  }
+};
 
 
 

lib/qcd/utils/CovariantLaplacian.h

@@ -77,7 +77,8 @@ template <class Impl>
 class LaplacianAdjointField: public Metric<typename Impl::Field> {
   OperatorFunction<typename Impl::Field> &Solver;
   LaplacianParams param;
-  MultiShiftFunction PowerNegHalf;    
+  MultiShiftFunction PowerHalf;    
+  MultiShiftFunction PowerInvHalf;    
 
  public:
   INHERIT_GIMPL_TYPES(Impl);
@@ -87,10 +88,15 @@ class LaplacianAdjointField: public Metric<typename Impl::Field> {
         AlgRemez remez(param.lo,param.hi,param.precision);
         std::cout<<GridLogMessage << "Generating degree "<<param.degree<<" for x^(1/2)"<<std::endl;
         remez.generateApprox(param.degree,1,2);
-        PowerNegHalf.Init(remez,param.tolerance,true);
+        PowerHalf.Init(remez,param.tolerance,false);
+        PowerInvHalf.Init(remez,param.tolerance,true);
+        
 
       };
 
+  void Mdir(const GaugeField&, GaugeField&, int, int){ assert(0);}
+  void Mdiag(const GaugeField&, GaugeField&){ assert(0);}
+
   void ImportGauge(const GaugeField& _U) {
     for (int mu = 0; mu < Nd; mu++) {
       U[mu] = PeekIndex<LorentzIndex>(_U, mu);
@@ -98,6 +104,11 @@ class LaplacianAdjointField: public Metric<typename Impl::Field> {
   }
 
   void M(const GaugeField& in, GaugeField& out) {
+    // in is an antihermitian matrix
+    // test
+    //GaugeField herm = in + adj(in);
+    //std::cout << "AHermiticity: " << norm2(herm) << std::endl;
+
     GaugeLinkField tmp(in._grid);
     GaugeLinkField tmp2(in._grid);
     GaugeLinkField sum(in._grid);
@@ -116,17 +127,21 @@ class LaplacianAdjointField: public Metric<typename Impl::Field> {
     }
   }
 
-  void MDeriv(const GaugeField& in, GaugeField& der, bool dag) {
+  void MDeriv(const GaugeField& in, GaugeField& der) {
+    // in is anti-hermitian
     RealD factor = -kappa / (double(4 * Nd));
-    for (int mu = 0; mu < Nd; mu++) {
+    
-      GaugeLinkField in_mu = PeekIndex<LorentzIndex>(in, mu);
+    for (int mu = 0; mu < Nd; mu++){
       GaugeLinkField der_mu(der._grid);
-      if (!dag)
+      der_mu = zero;
-        der_mu =
+      for (int nu = 0; nu < Nd; nu++){
-            factor * Cshift(in_mu, mu, +1) * adj(U[mu]) + adj(U[mu]) * in_mu;
+        GaugeLinkField in_nu = PeekIndex<LorentzIndex>(in, nu);
-      else
+        der_mu += U[mu] * Cshift(in_nu, mu, 1) * adj(U[mu]) * in_nu;
-        der_mu = factor * U[mu] * Cshift(in_mu, mu, +1) + in_mu * U[mu];
+      }
-    }
+      // the minus sign comes by using the in_nu instead of the
+      // adjoint in the last multiplication
+      PokeIndex<LorentzIndex>(der,  -2.0 * factor * der_mu, mu);
+    } 
   }
 
   void Minv(const GaugeField& in, GaugeField& inverted){
@@ -134,14 +149,12 @@ class LaplacianAdjointField: public Metric<typename Impl::Field> {
     Solver(HermOp, in, inverted);
   }
 
-  void MInvSquareRoot(GaugeField& P){
+  void MSquareRoot(GaugeField& P){
-    // Takes a gaussian gauge field and multiplies by the metric
-    // need the rational approximation for the square root 
     GaugeField Gp(P._grid);
     HermitianLinearOperator<LaplacianAdjointField<Impl>,GaugeField> HermOp(*this);
-    ConjugateGradientMultiShift<GaugeField> msCG(param.MaxIter,PowerNegHalf);
+    ConjugateGradientMultiShift<GaugeField> msCG(param.MaxIter,PowerHalf);
     msCG(HermOp,P,Gp);
-    P = Gp; // now P has the correct distribution
+    P = Gp; 
   }
 
 

lib/qcd/utils/Metric.h

@@ -39,7 +39,8 @@ public:
   virtual void ImportGauge(const Field&)   = 0;
   virtual void M(const Field&, Field&)     = 0;
   virtual void Minv(const Field&, Field&)  = 0;
-  virtual void MInvSquareRoot(Field&) = 0;
+  virtual void MSquareRoot(Field&) = 0;
+  virtual void MDeriv(const Field&, Field&) = 0;
 };
 
 
@@ -54,9 +55,12 @@ public:
   virtual void Minv(const Field& in, Field& out){
     out = in;
   }
-  virtual void MInvSquareRoot(Field& P){
+  virtual void MSquareRoot(Field& P){
     // do nothing
   }
+  virtual void MDeriv(const Field& in, Field& out){
+    out = zero;
+  }
 
 };
 
@@ -64,17 +68,17 @@ public:
 // Generalised momenta
 ///////////////////////////////
 
-template <typename Implementation, typename Metric>
+template <typename Implementation>
 class GeneralisedMomenta{
 public:
   typedef typename Implementation::Field MomentaField;  //for readability
-
+  typedef typename Implementation::GaugeLinkField MomentaLinkField;  //for readability
-  Metric M;
+  Metric<MomentaField>& M;
   MomentaField Mom;
 
-  GeneralisedMomenta(GridBase* grid): Mom(grid){}
+  GeneralisedMomenta(GridBase* grid, Metric<MomentaField>& M): M(M), Mom(grid){}
-
 
+  // Correct
   void MomentaDistribution(GridParallelRNG& pRNG){
     // Generate a distribution for
     // 1/2 P^dag G P
@@ -83,26 +87,45 @@ public:
     // Generate gaussian momenta
     Implementation::generate_momenta(Mom, pRNG);
     // Modify the distribution with the metric
-    M.MInvSquareRoot(Mom);
+    M.MSquareRoot(Mom);
   }
 
-  void Derivative(MomentaField& in, MomentaField& der){
+  // Correct
+  RealD MomentaAction(){
+    MomentaField inv(Mom._grid);
+    inv = zero;
+    M.Minv(Mom, inv);
+    LatticeComplex Hloc(Mom._grid);
+    Hloc = zero;
+    for (int mu = 0; mu < Nd; mu++) {
+      // This is not very general
+      // hide in the operators
+      auto Mom_mu = PeekIndex<LorentzIndex>(Mom, mu);
+      auto inv_mu = PeekIndex<LorentzIndex>(inv, mu);
+      Hloc += trace(Mom_mu * inv_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 MomDer(in._grid);
+    MomentaField MDer(in._grid);
     MomentaField X(in._grid);
-
+    X = zero;
-    M.Minv(in, X); // X = G in
+    M.Minv(in, X);  // X = G in
-    M.MDeriv(X, MomDer, DaggerNo); // MomDer = dM/dU X
+    M.MDeriv(X, MDer);  // MDer = U * dS/dU
-    // MomDer is just the derivative
+    der = Implementation::projectForce(MDer);  // Ta if gauge fields
-    MomDer = adj(X)* MomDer;
-    // Traceless Antihermitian
-    // assuming we are in the algebra
-    der = Implementation::projectForce(MomDer);
   }
 
+
+  //   
   void DerivativeP(MomentaField& der){
+    der = zero;
     M.Minv(Mom, der);
+    der = Implementation::projectForce(der); 
   }
 
 };

tests/forces/Test_laplacian_force.cc

@@ -0,0 +1,178 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./tests/Test_rect_force.cc
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.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;
+using namespace Grid::QCD;
+
+#define parallel_for PARALLEL_FOR_LOOP for
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  std::vector<int> latt_size   = GridDefaultLatt();
+  std::vector<int> simd_layout = GridDefaultSimd(Nd,vComplex::Nsimd());
+  std::vector<int> mpi_layout  = GridDefaultMpi();
+
+  GridCartesian               Grid(latt_size,simd_layout,mpi_layout);
+  GridRedBlackCartesian     RBGrid(latt_size,simd_layout,mpi_layout);
+
+  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);
+  pRNG.SeedRandomDevice();
+
+  LatticeGaugeField U(&Grid);
+  LatticeGaugeField P(&Grid);
+  LatticeColourMatrix P_mu(&Grid);
+  // Matrix in the algebra
+  for (int mu = 0; mu < Nd; mu++) {
+    SU<Nc>::GaussianFundamentalLieAlgebraMatrix(pRNG, P_mu);
+    PokeIndex<LorentzIndex>(P, P_mu, mu);
+  }
+
+  SU3::HotConfiguration(pRNG,U);
+  
+
+  ConjugateGradient<LatticeGaugeField> CG(1.0e-8, 10000);
+  LaplacianParams LapPar(0.001, 1.0, 1000, 1e-8, 10, 64);
+  RealD Kappa = 0.99;
+  LaplacianAdjointField<PeriodicGimplR> Laplacian(&Grid, CG, LapPar, Kappa);
+  GeneralisedMomenta<PeriodicGimplR> LaplacianMomenta(&Grid, Laplacian);
+  LaplacianMomenta.M.ImportGauge(U);
+  LaplacianMomenta.MomentaDistribution(pRNG);// fills the Momenta with the correct distr
+  
+
+  std::cout << std::setprecision(15);
+  std::cout << GridLogMessage << "MomentaAction" << std::endl;
+  ComplexD S    = LaplacianMomenta.MomentaAction();
+
+  // get the deriv with respect to "U"
+  LatticeGaugeField UdSdU(&Grid);
+  std::cout << GridLogMessage<< "DerivativeU" << std::endl;
+  LaplacianMomenta.DerivativeU(LaplacianMomenta.Mom, UdSdU);
+
+
+  ////////////////////////////////////
+  // Modify the gauge field a little 
+  ////////////////////////////////////
+  RealD dt = 0.001;
+
+  LatticeColourMatrix mommu(&Grid); 
+  LatticeColourMatrix forcemu(&Grid); 
+  LatticeGaugeField mom(&Grid); 
+  LatticeGaugeField Uprime(&Grid); 
+
+  std::cout << GridLogMessage << "Update the U " << std::endl;
+  for(int mu=0;mu<Nd;mu++){
+  // Traceless antihermitian momentum; gaussian in lie algebra
+    SU3::GaussianFundamentalLieAlgebraMatrix(pRNG, mommu); 
+    auto Umu = PeekIndex<LorentzIndex>(U, mu);
+    PokeIndex<LorentzIndex>(mom,mommu,mu);
+    Umu = expMat(mommu, dt, 12) * Umu;
+    PokeIndex<LorentzIndex>(Uprime, ProjectOnGroup(Umu), mu);
+  
+  }
+
+  std::cout << GridLogMessage << "New action " << std::endl;
+  LaplacianMomenta.M.ImportGauge(Uprime);
+  ComplexD Sprime    = LaplacianMomenta.MomentaAction();
+
+  //////////////////////////////////////////////
+  // Use derivative to estimate dS
+  //////////////////////////////////////////////
+
+  LatticeComplex dS(&Grid); dS = zero;
+
+  for(int mu=0;mu<Nd;mu++){
+    auto UdSdUmu = PeekIndex<LorentzIndex>(UdSdU,mu);
+         mommu   = PeekIndex<LorentzIndex>(mom,mu);
+
+    // Update gauge action density
+    // U = exp(p dt) U
+    // dU/dt = p U
+    // so dSdt = trace( dUdt dSdU) = trace( p UdSdUmu ) 
+
+    dS = dS + trace(mommu*UdSdUmu)*dt*2.0;
+  }
+
+  Complex dSpred    = sum(dS);
+
+  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 << "pred dS "<< dSpred <<std::endl;
+
+
+  // P derivative
+  // Increment p 
+  dt = 0.0001;
+  LaplacianMomenta.M.ImportGauge(U);
+  LatticeGaugeField UdSdP(&Grid);
+  LaplacianMomenta.DerivativeP(UdSdP);
+
+
+  LaplacianMomenta.Mom += dt*P;
+  
+  Sprime    = LaplacianMomenta.MomentaAction();
+
+  // Prediciton
+
+  dS = zero;
+   for(int mu=0;mu<Nd;mu++){
+    auto dSdPmu = PeekIndex<LorentzIndex>(UdSdP,mu);
+    auto Pmu = PeekIndex<LorentzIndex>(P,mu);
+    // Update gauge action density
+    // 
+    // dMom/dt = P
+    // so dSdt = trace( dPdt dSdP) = trace( P dSdP ) 
+
+    dS = dS + trace(Pmu*dSdPmu)*dt*2.0;
+  } 
+  dSpred    = sum(dS);
+
+  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 << "pred dS "<< dSpred <<std::endl; 
+
+
+
+
+
+
+
+
+  std::cout<< GridLogMessage << "Done" <<std::endl;
+  Grid_finalize();
+}

tests/hmc/Test_hmc_WilsonGauge_Implicit.cc

@@ -0,0 +1,97 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./tests/Test_hmc_WilsonFermionGauge.cc
+
+Copyright (C) 2015
+
+Author: Peter Boyle <pabobyle@ph.ed.ac.uk>
+Author: neo <cossu@post.kek.jp>
+Author: Guido Cossu <guido.cossu@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>
+
+int main(int argc, char **argv) {
+  using namespace Grid;
+  using namespace Grid::QCD;
+
+  Grid_init(&argc, &argv);
+  int threads = GridThread::GetThreads();
+  // here make a routine to print all the relevant information on the run
+  std::cout << GridLogMessage << "Grid is setup to use " << threads << " threads" << std::endl;
+
+   // Typedefs to simplify notation
+  typedef GenericHMCRunner<ImplicitLeapFrog> HMCWrapper;  // Uses the default minimum norm
+  HMCWrapper TheHMC;
+
+  // Grid from the command line
+  TheHMC.Resources.AddFourDimGrid("gauge");
+  // Possibile to create the module by hand 
+  // hardcoding parameters or using a Reader
+
+
+  // Checkpointer definition
+  CheckpointerParameters CPparams;  
+  CPparams.config_prefix = "ckpoint_lat";
+  CPparams.rng_prefix = "ckpoint_rng";
+  CPparams.saveInterval = 20;
+  CPparams.format = "IEEE64BIG";
+  
+  TheHMC.Resources.LoadBinaryCheckpointer(CPparams);
+
+  RNGModuleParameters RNGpar;
+  RNGpar.serial_seeds = "1 2 3 4 5";
+  RNGpar.parallel_seeds = "6 7 8 9 10 12";
+  TheHMC.Resources.SetRNGSeeds(RNGpar);
+
+  // Construct observables
+  // here there is too much indirection 
+  PlaquetteObsParameters PlPar;
+  PlPar.output_prefix = "Plaquette";
+  PlaquetteMod<HMCWrapper::ImplPolicy> PlaqModule(PlPar);
+  TheHMC.Resources.AddObservable(&PlaqModule);
+  //////////////////////////////////////////////
+
+  /////////////////////////////////////////////////////////////
+  // Collect actions, here use more encapsulation
+  // need wrappers of the fermionic classes 
+  // that have a complex construction
+  // standard
+  RealD beta = 5.6;
+  WilsonGaugeActionR Waction(beta);
+  
+  ActionLevel<HMCWrapper::Field> Level1(1);
+  Level1.push_back(&Waction);
+  //Level1.push_back(WGMod.getPtr());
+  TheHMC.TheAction.push_back(Level1);
+  /////////////////////////////////////////////////////////////
+
+  // HMC parameters are serialisable 
+  TheHMC.Parameters.MD.MDsteps = 60;
+  TheHMC.Parameters.MD.trajL   = 1.0;
+
+  TheHMC.ReadCommandLine(argc, argv); // these can be parameters from file
+  TheHMC.Run();  // no smearing
+
+  Grid_finalize();
+
+} // main

tests/solver/Test_laplacian.cc

@@ -70,13 +70,13 @@ int main (int argc, char ** argv)
   LatticeColourMatrix src_mu(&Grid);
   for (int mu = 0; mu < Nd; mu++) {
     SU<Nc>::GaussianFundamentalLieAlgebraMatrix(pRNG, src_mu);
-    PokeIndex<LorentzIndex>(src_f, src_mu, mu);
+    PokeIndex<LorentzIndex>(src_f, timesI(src_mu), mu);
   }
   LatticeGaugeField result_f(&Grid);
 
   // Definition of the Laplacian operator
   ConjugateGradient<LatticeGaugeField> CG(1.0e-8,10000);
-  LaplacianParams LapPar(0.001, 1.0, 1000, 1e-8, 10, 64);
+  LaplacianParams LapPar(0.00001, 1.0, 1000, 1e-8, 10, 64);
   LaplacianAdjointField<PeriodicGimplR> Laplacian(&Grid, CG, LapPar, Kappa);
   Laplacian.ImportGauge(Umu);
   std::cout << GridLogMessage << "Testing the Laplacian using the full matrix" <<std::endl;
@@ -84,7 +84,7 @@ int main (int argc, char ** argv)
   
 
 
-  Laplacian.MomentaDistribution(src_f);
+  Laplacian.MSquareRoot(src_f);
 
 
   // Tests also the version using the algebra decomposition