RMHMC implementation, originaly from Guido Cossu

Grid/qcd/hmc/GenericHMCrunner.h

@@ -140,7 +140,17 @@ private:
 
     // 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, 10000, 1e-8, 12, 64);
+//    RealD Kappa = 1.2;
+    RealD Kappa = Parameters.Kappa;
+    std::cout << GridLogMessage << "Kappa = " << Kappa << std::endl;
+
+    // Better to pass the generalised momenta to the integrator
+    LaplacianAdjointField<PeriodicGimplR> Laplacian(UGrid, CG, LapPar, Kappa);
+    TheIntegrator MDynamics(UGrid, Parameters.MD, TheAction, Smearing, Laplacian);
 
     if (Parameters.StartingType == "HotStart") {
       // Hot start

Grid/qcd/hmc/HMC.h

@@ -53,6 +53,7 @@ struct HMCparameters: Serializable {
                                   bool, MetropolisTest,
                                   Integer, NoMetropolisUntil,
                                   std::string, StartingType,
+				  RealD, Kappa,
                                   IntegratorParameters, MD)
 
   HMCparameters() {

Grid/qcd/hmc/integrators/Integrator.h

@@ -137,6 +137,80 @@ protected:
     as[level].apply(update_P_hireps, Representations, Mom, U, ep);
   }
 
+  void implicit_update_P(Field& U, int level, double ep, bool intermediate = false) {
+    t_P[level] += ep;
+
+    std::cout << GridLogIntegrator << "[" << level << "] P "
+              << " dt " << ep << " : t_P " << t_P[level] << std::endl;
+    // Fundamental updates, include smearing
+    MomentaField Msum(P.Mom._grid);
+    Msum = Zero();
+    for (int a = 0; a < as[level].actions.size(); ++a) {
+      // Compute the force terms for the lagrangian part
+      // We need to compute the derivative of the actions
+      // only once
+      Field force(U._grid);
+      conformable(U._grid, P.Mom._grid);
+      Field& Us = Smearer.get_U(as[level].actions.at(a)->is_smeared);
+      as[level].actions.at(a)->deriv(Us, force);  // deriv should NOT include Ta
+
+      std::cout << GridLogIntegrator << "Smearing (on/off): " << as[level].actions.at(a)->is_smeared << std::endl;
+      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| site average: " << force_abs
+                << std::endl;
+      Msum += force;
+    }
+
+    MomentaField NewMom = P.Mom;
+    MomentaField OldMom = P.Mom;
+    double threshold = 1e-8;
+    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);
+    double factor = 2.0;
+    if (intermediate){
+      P.DerivativeU(P.Mom, MomDer1);
+      factor = 1.0;
+    }
+
+    // Auxiliary fields
+    P.update_auxiliary_momenta(ep*0.5);
+    P.AuxiliaryFieldsDerivative(AuxDer);
+    Msum += AuxDer;
+    
+
+    // Here run recursively
+    int counter = 1;
+    RealD RelativeError;
+    do {
+      std::cout << GridLogIntegrator << "UpdateP implicit step "<< counter << std::endl;
+
+      // Compute the derivative of the kinetic term
+      // with respect to the gauge field
+      P.DerivativeU(NewMom, MomDer);
+      Real force_abs = std::sqrt(norm2(MomDer) / U._grid->gSites());
+      std::cout << GridLogIntegrator << "|Force| laplacian site average: " << force_abs
+                << std::endl;
+
+      NewMom = P.Mom - ep* 0.5 * (2.0*Msum + factor*MomDer + MomDer1);// simplify
+      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    
+    P.update_auxiliary_momenta(ep*0.5);
+  }
+
   void update_U(Field& U, double ep) 
   {
     update_U(P, U, ep);
@@ -158,6 +232,55 @@ protected:
     Representations.update(U);  // void functions if fundamental representation
   }
 
+  void implicit_update_U(Field&U, double ep){
+    t_U += ep;
+    int fl = levels - 1;
+    std::cout << GridLogIntegrator << "   " << "[" << fl << "] U " << " dt " << ep << " : t_U " << t_U << std::endl;
+
+    MomentaField Mom1(P.Mom._grid);
+    MomentaField Mom2(P.Mom._grid);
+    RealD RelativeError;
+    Field diff(U._grid);
+    Real threshold = 1e-8;
+    int counter = 1;
+    int MaxCounter = 100;
+
+    Field OldU = U;
+    Field NewU = U;
+
+    P.M.ImportGauge(U);
+    P.DerivativeP(Mom1); // first term in the derivative 
+
+    P.update_auxiliary_fields(ep*0.5);
+
+
+    MomentaField sum=Mom1;
+    do {
+      std::cout << GridLogIntegrator << "UpdateU implicit step "<< counter << std::endl;
+      
+      P.DerivativeP(Mom2); // second term in the derivative, on the updated U
+      sum = (Mom1 + Mom2);
+
+      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);
+      OldU = NewU; // some redundancy to be eliminated
+      counter++;
+    } while (RelativeError > threshold && counter < MaxCounter);
+
+    U = NewU;
+    P.update_auxiliary_fields(ep*0.5);
+  }
+
   virtual void step(Field& U, int level, int first, int last) = 0;
 
 public:

Grid/qcd/hmc/integrators/Integrator_algorithm.h

@@ -101,7 +101,7 @@ public:
 
   std::string integrator_name(){return "LeapFrog";}
 
-  LeapFrog(GridBase* grid, IntegratorParameters Par, ActionSet<Field, RepresentationPolicy>& Aset, SmearingPolicy& Sm)
+  LeapFrog(GridBase* grid, IntegratorParameters Par, ActionSet<Field, RepresentationPolicy>& Aset, SmearingPolicy& Sm, Metric<Field>& M)
     : Integrator<FieldImplementation, SmearingPolicy, RepresentationPolicy>(grid, Par, Aset, Sm){};
 
   void step(Field& U, int level, int _first, int _last) {
@@ -144,7 +144,7 @@ private:
 public:
   INHERIT_FIELD_TYPES(FieldImplementation);
 
-  MinimumNorm2(GridBase* grid, IntegratorParameters Par, ActionSet<Field, RepresentationPolicy>& Aset, SmearingPolicy& Sm)
+  MinimumNorm2(GridBase* grid, IntegratorParameters Par, ActionSet<Field, RepresentationPolicy>& Aset, SmearingPolicy& Sm, Metric<Field>& M)
     : Integrator<FieldImplementation, SmearingPolicy, RepresentationPolicy>(grid, Par, Aset, Sm){};
 
   std::string integrator_name(){return "MininumNorm2";}
@@ -207,7 +207,7 @@ public:
   // Looks like dH scales as dt^4. tested wilson/wilson 2 level.
   ForceGradient(GridBase* grid, IntegratorParameters Par,
                 ActionSet<Field, RepresentationPolicy>& Aset,
-                SmearingPolicy& Sm)
+                SmearingPolicy& Sm, Metric<Field>& M)
     : Integrator<FieldImplementation, SmearingPolicy, RepresentationPolicy>(
 									    grid, Par, Aset, Sm){};
 
@@ -271,6 +271,139 @@ public:
   }
 };
 
+////////////////////////////////
+// Riemannian Manifold HMC
+// Girolami et al
+////////////////////////////////
+
+
+
+// correct
+template <class FieldImplementation, class SmearingPolicy,
+          class RepresentationPolicy =
+              Representations<FundamentalRepresentation> >
+class ImplicitLeapFrog : public Integrator<FieldImplementation, SmearingPolicy,
+                                           RepresentationPolicy> {
+ public:
+  typedef ImplicitLeapFrog<FieldImplementation, SmearingPolicy, RepresentationPolicy>
+      Algorithm;
+  INHERIT_FIELD_TYPES(FieldImplementation);
+
+  // Riemannian manifold metric operator
+  // Hermitian operator Fisher
+
+  std::string integrator_name(){return "ImplicitLeapFrog";}
+
+  ImplicitLeapFrog(GridBase* grid, IntegratorParameters Par,
+           ActionSet<Field, RepresentationPolicy>& Aset, SmearingPolicy& Sm, Metric<Field>& M)
+      : Integrator<FieldImplementation, SmearingPolicy, RepresentationPolicy>(
+            grid, Par, Aset, Sm, M){};
+
+  void step(Field& U, int level, int _first, int _last) {
+    int fl = this->as.size() - 1;
+    // level  : current level
+    // fl     : final level
+    // eps    : current step size
+
+    // Get current level step size
+    RealD eps = this->Params.trajL/this->Params.MDsteps;
+    for (int l = 0; l <= level; ++l) eps /= this->as[l].multiplier;
+
+    int multiplier = this->as[level].multiplier;
+    for (int e = 0; e < multiplier; ++e) {
+      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, eps / 2.0);
+      }
+
+      if (level == fl) {  // lowest level
+        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;
+      if (last_step){
+        this->update_P(U, level, eps / 2.0);
+      } else {
+      this->implicit_update_P(U, level, eps, true);// works intermediate step
+      //  this->update_P(U, level, eps); // looks not reversible
+      }
+    }
+  }
+};
+
+
+// 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, true);
+
+      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, true);
+      }
+    }
+  }
+};
+
 NAMESPACE_END(Grid);
 
 #endif  // INTEGRATOR_INCLUDED

tests/hmc/Test_hmc_WilsonGauge_Implicit.cc

@@ -0,0 +1,154 @@
+/*************************************************************************************
+
+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>
+
+namespace Grid{
+struct RMHMCActionParameters: Serializable {
+  GRID_SERIALIZABLE_CLASS_MEMBERS(RMHMCActionParameters,
+				  double, gauge_beta)
+
+  template <class ReaderClass >
+  RMHMCActionParameters(Reader<ReaderClass>& Reader){
+    read(Reader, "Action", *this);
+  }
+};
+}
+
+int main(int argc, char **argv) {
+  using namespace Grid;
+  using namespace Grid::QCD;
+
+  Grid_init(&argc, &argv);
+  GridLogIntegrator.Active(1);
+  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<ImplicitMinimumNorm2> HMCWrapper;  // Uses the default minimum norm
+   // Serialiser
+  typedef Grid::JSONReader       Serialiser;
+
+
+  HMCWrapper TheHMC;
+  TheHMC.ReadCommandLine(argc, argv); // these can be parameters from file
+  
+  // Reader, file should come from command line
+  if (TheHMC.ParameterFile.empty()){
+    std::cout << "Input file not specified."
+              << "Use --ParameterFile option in the command line.\nAborting" 
+              << std::endl;
+    exit(1);
+  }
+  Serialiser Reader(TheHMC.ParameterFile);
+
+  RMHMCActionParameters ActionParams(Reader);  
+
+  // Grid from the command line
+  TheHMC.Resources.AddFourDimGrid("gauge");
+ 
+
+  // Checkpointer definition
+  CheckpointerParameters CPparams(Reader);
+//  TheHMC.Resources.LoadBinaryCheckpointer(CPparams);
+  TheHMC.Resources.LoadNerscCheckpointer(CPparams);
+
+  RNGModuleParameters RNGpar(Reader);
+  TheHMC.Resources.SetRNGSeeds(RNGpar);
+
+  // Construct observables
+  typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
+  typedef TopologicalChargeMod<HMCWrapper::ImplPolicy> QObs;
+  TheHMC.Resources.AddObservable<PlaqObs>();
+  TopologyObsParameters TopParams(Reader);
+  TheHMC.Resources.AddObservable<QObs>(TopParams);
+  /////////////////////////////////////////////////////////////
+  // Collect actions
+  WilsonGaugeActionR Waction(ActionParams.gauge_beta);
+
+  
+  ActionLevel<HMCWrapper::Field> Level1(1);
+  Level1.push_back(&Waction);
+  TheHMC.TheAction.push_back(Level1);
+  /////////////////////////////////////////////////////////////
+  TheHMC.Parameters.initialize(Reader);
+  TheHMC.Run(); 
+
+  Grid_finalize();
+
+} // main
+
+/* Examples for input files
+
+JSON
+
+{
+    "Checkpointer": {
+	"config_prefix": "ckpoint_json_lat",
+	"rng_prefix": "ckpoint_json_rng",
+	"saveInterval": 10,
+	"format": "IEEE64BIG"
+    },
+    "RandomNumberGenerator": {
+	"serial_seeds": "1 2 3 4 6",
+	"parallel_seeds": "55 7 8 9 11"
+    },
+    "Action":{
+	"gauge_beta": 5.8
+    },
+    "TopologyMeasurement":{
+	"interval": 1,
+	"do_smearing": true,
+	"Smearing":{
+	    "steps": 200,
+	    "step_size": 0.01,
+	    "meas_interval": 50,
+	    "maxTau": 2.0
+	}
+    },
+    "HMC":{
+	"StartTrajectory": 0,
+	"Trajectories": 10,
+	"MetropolisTest": true,
+	"NoMetropolisUntil": 10,
+	"StartingType": "HotStart",
+	"MD":{
+	    "name": "MinimumNorm2",
+	    "MDsteps": 40,
+	    "trajL": 1.0
+	}
+    }
+}
+
+
+XML example not provided yet
+
+*/