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Added an RHMC pseudofermion action, GeneralEvenOddRatioRationalPseudoFermionAction, that works for an arbitrary fractional power, not just a square root

Browse Source 
Added a test evolution for the above, Test_rhmc_EOWilsonRatioPowQuarter, demonstrating conservation of Hamiltonian
Fixed HMC ignoring the MetropolisTest parameter of HMCparameters
This commit is contained in:
Christopher Kelly 2020-12-17 16:21:58 -05:00
parent 249b6e61ec
commit a0ca362690
6 changed files with 536 additions and 2 deletions
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41
Grid/qcd/action/ActionParams.h
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@ -36,7 +36,8 @@ NAMESPACE_BEGIN(Grid);
// These can move into a params header and be given MacroMagic serialisation // These can move into a params header and be given MacroMagic serialisation
struct GparityWilsonImplParams { struct GparityWilsonImplParams {
Coordinate twists; Coordinate twists; //Here the first Nd-1 directions are treated as "spatial", and a twist value of 1 indicates G-parity BCs in that direction.
//mu=Nd-1 is assumed to be the time direction and a twist value of 1 indicates antiperiodic BCs
GparityWilsonImplParams() : twists(Nd, 0) {}; GparityWilsonImplParams() : twists(Nd, 0) {};
}; };
@ -86,6 +87,44 @@ struct StaggeredImplParams {
BoundsCheckFreq(_BoundsCheckFreq){}; BoundsCheckFreq(_BoundsCheckFreq){};
}; };
/*Action parameters for the generalized rational action
The approximation is for (M^dag M)^{1/inv_pow}
where inv_pow is the denominator of the fractional power.
Default inv_pow=2 for square root, making this equivalent to
the OneFlavourRational action
*/
struct RationalActionParams : Serializable {
GRID_SERIALIZABLE_CLASS_MEMBERS(RationalActionParams,
int, inv_pow,
RealD, lo,
RealD, hi,
int, MaxIter,
RealD, tolerance,
int, degree,
int, precision,
int, BoundsCheckFreq);
// constructor
RationalActionParams(int _inv_pow = 2,
RealD _lo = 0.0,
RealD _hi = 1.0,
int _maxit = 1000,
RealD tol = 1.0e-8,
int _degree = 10,
int _precision = 64,
int _BoundsCheckFreq=20)
: inv_pow(_inv_pow),
lo(_lo),
hi(_hi),
MaxIter(_maxit),
tolerance(tol),
degree(_degree),
precision(_precision),
BoundsCheckFreq(_BoundsCheckFreq){};
};
NAMESPACE_END(Grid); NAMESPACE_END(Grid);
#endif #endif

51
Grid/qcd/action/pseudofermion/Bounds.h
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@ -48,5 +48,56 @@ NAMESPACE_BEGIN(Grid);
assert( (std::sqrt(Nd/Nx)<tol) && " InverseSqrtBoundsCheck "); assert( (std::sqrt(Nd/Nx)<tol) && " InverseSqrtBoundsCheck ");
} }
/* For a HermOp = M^dag M, check the approximation of HermOp^{-1/inv_pow}
by computing |X - HermOp * [ Hermop^{-1/inv_pow} ]^{inv_pow} X| < tol
for noise X (aka GaussNoise).
ApproxNegPow should be the rational approximation for X^{-1/inv_pow}
*/
template<class Field> void InversePowerBoundsCheck(int inv_pow,
int MaxIter,double tol,
LinearOperatorBase<Field> &HermOp,
Field &GaussNoise,
MultiShiftFunction &ApproxNegPow)
{
GridBase *FermionGrid = GaussNoise.Grid();
Field X(FermionGrid);
Field Y(FermionGrid);
Field Z(FermionGrid);
Field tmp1(FermionGrid), tmp2(FermionGrid);
X=GaussNoise;
RealD Nx = norm2(X);
ConjugateGradientMultiShift<Field> msCG(MaxIter,ApproxNegPow);
tmp1 = X;
Field* in = &tmp1;
Field* out = &tmp2;
for(int i=0;i<inv_pow;i++){ //apply [ Hermop^{-1/inv_pow} ]^{inv_pow} X = HermOp^{-1} X
msCG(HermOp, *in, *out); //backwards conventions!
if(i!=inv_pow-1) std::swap(in, out);
}
Z = *out;
RealD Nz = norm2(Z);
HermOp.HermOp(Z,Y);
RealD Ny = norm2(Y);
X=X-Y;
RealD Nd = norm2(X);
std::cout << "************************* "<<std::endl;
std::cout << " noise = "<<Nx<<std::endl;
std::cout << " (MdagM^-1/" << inv_pow << ")^" << inv_pow << " noise = "<<Nz<<std::endl;
std::cout << " MdagM (MdagM^-1/" << inv_pow << ")^" << inv_pow << " noise = "<<Ny<<std::endl;
std::cout << " noise - MdagM (MdagM^-1/" << inv_pow << ")^" << inv_pow << " noise = "<<Nd<<std::endl;
std::cout << "************************* "<<std::endl;
assert( (std::sqrt(Nd/Nx)<tol) && " InversePowerBoundsCheck ");
}
NAMESPACE_END(Grid); NAMESPACE_END(Grid);

304
Grid/qcd/action/pseudofermion/GeneralEvenOddRationalRatio.h Normal file
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@ -0,0 +1,304 @@
/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./lib/qcd/action/pseudofermion/GeneralEvenOddRationalRatio.h
Copyright (C) 2015
Author: Christopher Kelly <ckelly@bnl.gov>
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 */
#ifndef QCD_PSEUDOFERMION_GENERAL_EVEN_ODD_RATIONAL_RATIO_H
#define QCD_PSEUDOFERMION_GENERAL_EVEN_ODD_RATIONAL_RATIO_H
NAMESPACE_BEGIN(Grid);
/////////////////////////////////////////////////////////
// Generic rational approximation for ratios of operators
/////////////////////////////////////////////////////////
/* S_f = -log( det( [M^dag M]/[V^dag V] )^{1/inv_pow} )
= chi^dag ( [M^dag M]/[V^dag V] )^{-1/inv_pow} chi\
= chi^dag ( [V^dag V]^{-1/2} [M^dag M] [V^dag V]^{-1/2} )^{-1/inv_pow} chi\
= chi^dag [V^dag V]^{1/(2*inv_pow)} [M^dag M]^{-1/inv_pow} [V^dag V]^{-1/(2*inv_pow)} chi\
S_f = chi^dag* P(V^dag*V)/Q(V^dag*V)* N(M^dag*M)/D(M^dag*M)* P(V^dag*V)/Q(V^dag*V)* chi
BIG WARNING:
Here V^dag V is referred to in this code as the "numerator" operator and M^dag M is the *denominator* operator.
this refers to their position in the pseudofermion action, which is the *inverse* of what appears in the determinant
Thus for DWF the numerator operator is the Pauli-Villars operator
Here P/Q \sim R_{1/(2*inv_pow)} ~ (V^dagV)^{1/(2*inv_pow)}
Here N/D \sim R_{-1/inv_pow} ~ (M^dagM)^{-1/inv_pow}
*/
template<class Impl>
class GeneralEvenOddRatioRationalPseudoFermionAction : public Action<typename Impl::GaugeField> {
public:
INHERIT_IMPL_TYPES(Impl);
typedef RationalActionParams Params;
Params param;
MultiShiftFunction ApproxPower ; //rational approx for X^{1/inv_pow}
MultiShiftFunction ApproxNegPower; //rational approx for X^{-1/inv_pow}
MultiShiftFunction ApproxHalfPower; //rational approx for X^{1/(2*inv_pow)}
MultiShiftFunction ApproxNegHalfPower; //rational approx for X^{-1/(2*inv_pow)}
private:
FermionOperator<Impl> & NumOp;// the basic operator
FermionOperator<Impl> & DenOp;// the basic operator
FermionField PhiEven; // the pseudo fermion field for this trajectory
FermionField PhiOdd; // the pseudo fermion field for this trajectory
public:
GeneralEvenOddRatioRationalPseudoFermionAction(FermionOperator<Impl> &_NumOp,
FermionOperator<Impl> &_DenOp,
Params & p
) :
NumOp(_NumOp),
DenOp(_DenOp),
PhiOdd (_NumOp.FermionRedBlackGrid()),
PhiEven(_NumOp.FermionRedBlackGrid()),
param(p)
{
AlgRemez remez(param.lo,param.hi,param.precision);
int inv_pow = param.inv_pow;
int _2_inv_pow = 2*inv_pow;
// MdagM^(+- 1/inv_pow)
std::cout<<GridLogMessage << "Generating degree "<<param.degree<<" for x^(1/" << inv_pow << ")"<<std::endl;
remez.generateApprox(param.degree,1,inv_pow);
ApproxPower.Init(remez,param.tolerance,false);
ApproxNegPower.Init(remez,param.tolerance,true);
// VdagV^(+- 1/(2*inv_pow))
std::cout<<GridLogMessage << "Generating degree "<<param.degree<<" for x^(1/" << _2_inv_pow << ")"<<std::endl;
remez.generateApprox(param.degree,1,_2_inv_pow);
ApproxHalfPower.Init(remez,param.tolerance,false);
ApproxNegHalfPower.Init(remez,param.tolerance,true);
};
virtual std::string action_name(){return "GeneralEvenOddRatioRationalPseudoFermionAction";}
virtual std::string LogParameters(){
std::stringstream sstream;
sstream << GridLogMessage << "["<<action_name()<<"] Power : 1/" << param.inv_pow << std::endl;
sstream << GridLogMessage << "["<<action_name()<<"] Low :" << param.lo << std::endl;
sstream << GridLogMessage << "["<<action_name()<<"] High :" << param.hi << std::endl;
sstream << GridLogMessage << "["<<action_name()<<"] Max iterations :" << param.MaxIter << std::endl;
sstream << GridLogMessage << "["<<action_name()<<"] Tolerance :" << param.tolerance << std::endl;
sstream << GridLogMessage << "["<<action_name()<<"] Degree :" << param.degree << std::endl;
sstream << GridLogMessage << "["<<action_name()<<"] Precision :" << param.precision << std::endl;
return sstream.str();
}
virtual void refresh(const GaugeField &U, GridParallelRNG& pRNG) {
// S_f = chi^dag* P(V^dag*V)/Q(V^dag*V)* N(M^dag*M)/D(M^dag*M)* P(V^dag*V)/Q(V^dag*V)* chi
//
// P(phi) = e^{- phi^dag (VdagV)^1/(2*inv_pow) (MdagM)^-1/inv_pow (VdagV)^1/(2*inv_pow) phi}
// = e^{- phi^dag (VdagV)^1/(2*inv_pow) (MdagM)^-1/(2*inv_pow) (MdagM)^-1/(2*inv_pow) (VdagV)^1/(2*inv_pow) phi}
//
// Phi = (VdagV)^-1/(2*inv_pow) Mdag^{1/(2*inv_pow)} eta
//
// P(eta) = e^{- eta^dag eta}
//
// General gaussian random draws from e^{x^2/(2 sig^2)} => sig^2 = 0.5.
//
// So eta should be of width sig = 1/sqrt(2).
RealD scale = std::sqrt(0.5);
FermionField eta(NumOp.FermionGrid());
FermionField etaOdd (NumOp.FermionRedBlackGrid());
FermionField etaEven(NumOp.FermionRedBlackGrid());
FermionField tmp(NumOp.FermionRedBlackGrid());
gaussian(pRNG,eta); eta=eta*scale;
pickCheckerboard(Even,etaEven,eta);
pickCheckerboard(Odd,etaOdd,eta);
NumOp.ImportGauge(U);
DenOp.ImportGauge(U);
// MdagM^1/(2*inv_pow) eta
SchurDifferentiableOperator<Impl> MdagM(DenOp);
ConjugateGradientMultiShift<FermionField> msCG_M(param.MaxIter,ApproxHalfPower);
msCG_M(MdagM,etaOdd,tmp);
// VdagV^-1/(2*inv_pow) MdagM^1/(2*inv_pow) eta
SchurDifferentiableOperator<Impl> VdagV(NumOp);
ConjugateGradientMultiShift<FermionField> msCG_V(param.MaxIter,ApproxNegHalfPower);
msCG_V(VdagV,tmp,PhiOdd);
assert(NumOp.ConstEE() == 1);
assert(DenOp.ConstEE() == 1);
PhiEven = Zero();
};
//////////////////////////////////////////////////////
// S_f = chi^dag* P(V^dag*V)/Q(V^dag*V)* N(M^dag*M)/D(M^dag*M)* P(V^dag*V)/Q(V^dag*V)* chi
//////////////////////////////////////////////////////
virtual RealD S(const GaugeField &U) {
NumOp.ImportGauge(U);
DenOp.ImportGauge(U);
FermionField X(NumOp.FermionRedBlackGrid());
FermionField Y(NumOp.FermionRedBlackGrid());
// VdagV^1/(2*inv_pow) Phi
SchurDifferentiableOperator<Impl> VdagV(NumOp);
ConjugateGradientMultiShift<FermionField> msCG_V(param.MaxIter,ApproxHalfPower);
msCG_V(VdagV,PhiOdd,X);
// MdagM^-1/(2*inv_pow) VdagV^1/(2*inv_pow) Phi
SchurDifferentiableOperator<Impl> MdagM(DenOp);
ConjugateGradientMultiShift<FermionField> msCG_M(param.MaxIter,ApproxNegHalfPower);
msCG_M(MdagM,X,Y);
// Randomly apply rational bounds checks.
if ( (rand()%param.BoundsCheckFreq)==0 ) {
FermionField gauss(NumOp.FermionRedBlackGrid());
gauss = PhiOdd;
HighBoundCheck(MdagM,gauss,param.hi);
InversePowerBoundsCheck(param.inv_pow,param.MaxIter,param.tolerance*100,MdagM,gauss,ApproxNegPower);
}
// Phidag VdagV^1/(2*inv_pow) MdagM^-1/(2*inv_pow) MdagM^-1/(2*inv_pow) VdagV^1/(2*inv_pow) Phi
RealD action = norm2(Y);
return action;
};
// S_f = chi^dag* P(V^dag*V)/Q(V^dag*V)* N(M^dag*M)/D(M^dag*M)* P(V^dag*V)/Q(V^dag*V)* chi
//
// Here, M is some 5D operator and V is the Pauli-Villars field
// N and D makeup the rat. poly of the M term and P and & makeup the rat.poly of the denom term
//
// Need
// dS_f/dU = chi^dag d[P/Q] N/D P/Q chi
// + chi^dag P/Q d[N/D] P/Q chi
// + chi^dag P/Q N/D d[P/Q] chi
//
// P/Q is expressed as partial fraction expansion:
//
// a0 + \sum_k ak/(V^dagV + bk)
//
// d[P/Q] is then
//
// \sum_k -ak [V^dagV+bk]^{-1} [ dV^dag V + V^dag dV ] [V^dag V + bk]^{-1}
//
// and similar for N/D.
//
// Need
// MpvPhi_k = [Vdag V + bk]^{-1} chi
// MpvPhi = {a0 + \sum_k ak [Vdag V + bk]^{-1} }chi
//
// MfMpvPhi_k = [MdagM+bk]^{-1} MpvPhi
// MfMpvPhi = {a0 + \sum_k ak [Mdag M + bk]^{-1} } MpvPhi
//
// MpvMfMpvPhi_k = [Vdag V + bk]^{-1} MfMpvchi
//
virtual void deriv(const GaugeField &U,GaugeField & dSdU) {
const int n_f = ApproxNegPower.poles.size();
const int n_pv = ApproxHalfPower.poles.size();
std::vector<FermionField> MpvPhi_k (n_pv,NumOp.FermionRedBlackGrid());
std::vector<FermionField> MpvMfMpvPhi_k(n_pv,NumOp.FermionRedBlackGrid());
std::vector<FermionField> MfMpvPhi_k (n_f ,NumOp.FermionRedBlackGrid());
FermionField MpvPhi(NumOp.FermionRedBlackGrid());
FermionField MfMpvPhi(NumOp.FermionRedBlackGrid());
FermionField MpvMfMpvPhi(NumOp.FermionRedBlackGrid());
FermionField Y(NumOp.FermionRedBlackGrid());
GaugeField tmp(NumOp.GaugeGrid());
NumOp.ImportGauge(U);
DenOp.ImportGauge(U);
SchurDifferentiableOperator<Impl> VdagV(NumOp);
SchurDifferentiableOperator<Impl> MdagM(DenOp);
ConjugateGradientMultiShift<FermionField> msCG_V(param.MaxIter,ApproxHalfPower);
ConjugateGradientMultiShift<FermionField> msCG_M(param.MaxIter,ApproxNegPower);
msCG_V(VdagV,PhiOdd,MpvPhi_k,MpvPhi);
msCG_M(MdagM,MpvPhi,MfMpvPhi_k,MfMpvPhi);
msCG_V(VdagV,MfMpvPhi,MpvMfMpvPhi_k,MpvMfMpvPhi);
RealD ak;
dSdU = Zero();
// With these building blocks
//
// dS/dU =
// \sum_k -ak MfMpvPhi_k^dag [ dM^dag M + M^dag dM ] MfMpvPhi_k (1)
// + \sum_k -ak MpvMfMpvPhi_k^\dag [ dV^dag V + V^dag dV ] MpvPhi_k (2)
// -ak MpvPhi_k^dag [ dV^dag V + V^dag dV ] MpvMfMpvPhi_k (3)
//(1)
for(int k=0;k<n_f;k++){
ak = ApproxNegPower.residues[k];
MdagM.Mpc(MfMpvPhi_k[k],Y);
MdagM.MpcDagDeriv(tmp , MfMpvPhi_k[k], Y ); dSdU=dSdU+ak*tmp;
MdagM.MpcDeriv(tmp , Y, MfMpvPhi_k[k] ); dSdU=dSdU+ak*tmp;
}
//(2)
//(3)
for(int k=0;k<n_pv;k++){
ak = ApproxHalfPower.residues[k];
VdagV.Mpc(MpvPhi_k[k],Y);
VdagV.MpcDagDeriv(tmp,MpvMfMpvPhi_k[k],Y); dSdU=dSdU+ak*tmp;
VdagV.MpcDeriv (tmp,Y,MpvMfMpvPhi_k[k]); dSdU=dSdU+ak*tmp;
VdagV.Mpc(MpvMfMpvPhi_k[k],Y); // V as we take Ydag
VdagV.MpcDeriv (tmp,Y, MpvPhi_k[k]); dSdU=dSdU+ak*tmp;
VdagV.MpcDagDeriv(tmp,MpvPhi_k[k], Y); dSdU=dSdU+ak*tmp;
}
//dSdU = Ta(dSdU);
};
};
NAMESPACE_END(Grid);
#endif

1
Grid/qcd/action/pseudofermion/PseudoFermion.h
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@ -41,6 +41,7 @@ directory
#include <Grid/qcd/action/pseudofermion/OneFlavourRationalRatio.h> #include <Grid/qcd/action/pseudofermion/OneFlavourRationalRatio.h>
#include <Grid/qcd/action/pseudofermion/OneFlavourEvenOddRational.h> #include <Grid/qcd/action/pseudofermion/OneFlavourEvenOddRational.h>
#include <Grid/qcd/action/pseudofermion/OneFlavourEvenOddRationalRatio.h> #include <Grid/qcd/action/pseudofermion/OneFlavourEvenOddRationalRatio.h>
#include <Grid/qcd/action/pseudofermion/GeneralEvenOddRationalRatio.h>
#include <Grid/qcd/action/pseudofermion/ExactOneFlavourRatio.h> #include <Grid/qcd/action/pseudofermion/ExactOneFlavourRatio.h>
#endif #endif

2
Grid/qcd/hmc/HMC.h
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@ -207,7 +207,7 @@ public:
DeltaH = evolve_hmc_step(Ucopy); DeltaH = evolve_hmc_step(Ucopy);
// Metropolis-Hastings test // Metropolis-Hastings test
bool accept = true; bool accept = true;
if (traj >= Params.StartTrajectory + Params.NoMetropolisUntil) { if (Params.MetropolisTest && traj >= Params.StartTrajectory + Params.NoMetropolisUntil) {
accept = metropolis_test(DeltaH); accept = metropolis_test(DeltaH);
} else { } else {
std::cout << GridLogMessage << "Skipping Metropolis test" << std::endl; std::cout << GridLogMessage << "Skipping Metropolis test" << std::endl;

139
tests/hmc/Test_rhmc_EOWilsonRatioPowQuarter.cc Normal file
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@ -0,0 +1,139 @@
/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./tests/Test_rhmc_EOWilsonRatio.cc
Copyright (C) 2015
Author: Peter Boyle <paboyle@ph.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/Grid.h>
//This test is for the Wilson action with the determinant det( M^dag M)^1/4
//testing the generic RHMC
int main(int argc, char **argv) {
using namespace Grid;
;
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<MinimumNorm2> HMCWrapper; // Uses the default minimum norm
typedef WilsonImplR FermionImplPolicy;
typedef WilsonFermionR FermionAction;
typedef typename FermionAction::FermionField FermionField;
//::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
HMCWrapper TheHMC;
// Grid from the command line
TheHMC.Resources.AddFourDimGrid("gauge");
// Checkpointer definition
CheckpointerParameters CPparams;
CPparams.config_prefix = "ckpoint_lat";
CPparams.rng_prefix = "ckpoint_rng";
CPparams.saveInterval = 5;
CPparams.format = "IEEE64BIG";
TheHMC.Resources.LoadNerscCheckpointer(CPparams);
RNGModuleParameters RNGpar;
RNGpar.serial_seeds = "1 2 3 4 5";
RNGpar.parallel_seeds = "6 7 8 9 10";
TheHMC.Resources.SetRNGSeeds(RNGpar);
// Construct observables
typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
TheHMC.Resources.AddObservable<PlaqObs>();
//////////////////////////////////////////////
/////////////////////////////////////////////////////////////
// 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);
auto GridPtr = TheHMC.Resources.GetCartesian();
auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
// temporarily need a gauge field
LatticeGaugeField U(GridPtr);
Real mass = -0.77;
Real pv = 0.0;
// Can we define an overloaded operator that does not need U and initialises
// it with zeroes?
FermionAction DenOp(U, *GridPtr, *GridRBPtr, mass);
FermionAction NumOp(U, *GridPtr, *GridRBPtr, pv);
// 1/2+1/2 flavour
// RationalActionParams(int _inv_pow = 2,
// RealD _lo = 0.0,
// RealD _hi = 1.0,
// int _maxit = 1000,
// RealD tol = 1.0e-8,
// int _degree = 10,
// int _precision = 64,
// int _BoundsCheckFreq=20)
int inv_pow = 4;
RationalActionParams Params(inv_pow,1.0e-2,64.0,1000,1.0e-6,14,64,1);
GeneralEvenOddRatioRationalPseudoFermionAction<FermionImplPolicy> RHMC(NumOp,DenOp,Params);
// Collect actions
ActionLevel<HMCWrapper::Field> Level1(1);
Level1.push_back(&RHMC);
ActionLevel<HMCWrapper::Field> Level2(4);
Level2.push_back(&Waction);
TheHMC.TheAction.push_back(Level1);
TheHMC.TheAction.push_back(Level2);
/////////////////////////////////////////////////////////////
// HMC parameters are serialisable
TheHMC.Parameters.MD.MDsteps = 20;
TheHMC.Parameters.MD.trajL = 1.0;
TheHMC.ReadCommandLine(argc, argv); // these can be parameters from file
TheHMC.Run();
Grid_finalize();
} // main