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Add (mostly implemented) ExactOneFlavourRatio pseudofermion class and tests of Shamir heatbath and action

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David Murphy 2017-08-16 12:38:59 -04:00
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230
lib/qcd/action/pseudofermion/ExactOneFlavourRatio.h Normal file
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/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./lib/qcd/action/pseudofermion/ExactOneFlavourRatio.h
Copyright (C) 2017
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
Author: David Murphy <dmurphy@phys.columbia.edu>
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 */
/////////////////////////////////////////////////////////////////
// Implementation of exact one flavour algorithm (EOFA) //
// using fermion classes defined in: //
// Grid/qcd/action/fermion/DomainWallEOFAFermion.h (Shamir) //
// Grid/qcd/action/fermion/MobiusEOFAFermion.h (Mobius) //
// arXiv: 1403.1683, 1706.05843 //
/////////////////////////////////////////////////////////////////
#ifndef QCD_PSEUDOFERMION_EXACT_ONE_FLAVOUR_RATIO_H
#define QCD_PSEUDOFERMION_EXACT_ONE_FLAVOUR_RATIO_H
namespace Grid{
namespace QCD{
///////////////////////////////////////////////////////////////
// Exact one flavour implementation of DWF determinant ratio //
///////////////////////////////////////////////////////////////
template<class Impl>
class ExactOneFlavourRatioPseudoFermionAction : public Action<typename Impl::GaugeField>
{
public:
INHERIT_IMPL_TYPES(Impl);
typedef OneFlavourRationalParams Params;
Params param;
MultiShiftFunction PowerNegHalf;
private:
bool use_heatbath_forecasting;
AbstractEOFAFermion<Impl>& Lop; // the basic LH operator
AbstractEOFAFermion<Impl>& Rop; // the basic RH operator
SchurRedBlackDiagMooeeSolve<FermionField> Solver;
FermionField Phi; // the pseudofermion field for this trajectory
public:
ExactOneFlavourRatioPseudoFermionAction(AbstractEOFAFermion<Impl>& _Lop, AbstractEOFAFermion<Impl>& _Rop,
OperatorFunction<FermionField>& S, Params& p, bool use_fc=false) : Lop(_Lop), Rop(_Rop), Solver(S),
Phi(_Lop.FermionGrid()), param(p), use_heatbath_forecasting(use_fc)
{
AlgRemez remez(param.lo, param.hi, param.precision);
// MdagM^(+- 1/2)
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);
};
virtual std::string action_name() { return "ExactOneFlavourRatioPseudoFermionAction"; }
virtual std::string LogParameters() {
std::stringstream sstream;
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();
}
// Spin projection
void spProj(const FermionField& in, FermionField& out, int sign, int Ls)
{
if(sign == 1){ for(int s=0; s<Ls; ++s){ axpby_ssp_pplus(out, 0.0, in, 1.0, in, s, s); } }
else{ for(int s=0; s<Ls; ++s){ axpby_ssp_pminus(out, 0.0, in, 1.0, in, s, s); } }
}
// EOFA heatbath: see Eqn. (29) of arXiv:1706.05843
// We generate a Gaussian noise vector \eta, and then compute
// \Phi = M_{\rm EOFA}^{-1/2} * \eta
// using a rational approximation to the inverse square root
virtual void refresh(const GaugeField& U, GridParallelRNG& pRNG)
{
Lop.ImportGauge(U);
Rop.ImportGauge(U);
FermionField eta (Lop.FermionGrid());
FermionField CG_src (Lop.FermionGrid());
FermionField CG_soln (Lop.FermionGrid());
FermionField Forecast_src(Lop.FermionGrid());
std::vector<FermionField> tmp(2, Lop.FermionGrid());
// Use chronological inverter to forecast solutions across poles
std::vector<FermionField> prev_solns;
if(use_heatbath_forecasting){ prev_solns.reserve(param.degree); }
ChronoForecast<AbstractEOFAFermion<Impl>, FermionField> Forecast;
// Seed with Gaussian noise vector (var = 0.5)
RealD scale = std::sqrt(0.5);
gaussian(pRNG,eta);
eta = eta * scale;
printf("Heatbath source vector: <\eta|\eta> = %1.15e\n", norm2(eta));
// \Phi = ( \alpha_{0} + \sum_{k=1}^{N_{p}} \alpha_{l} * \gamma_{l} ) * \eta
RealD N(PowerNegHalf.norm);
for(int k=0; k<param.degree; ++k){ N += PowerNegHalf.residues[k] / ( 1.0 + PowerNegHalf.poles[k] ); }
Phi = eta * N;
// LH terms:
// \Phi = \Phi + k \sum_{k=1}^{N_{p}} P_{-} \Omega_{-}^{\dagger} ( H(mf)
// - \gamma_{l} \Delta_{-}(mf,mb) P_{-} )^{-1} \Omega_{-} P_{-} \eta
RealD gamma_l(0.0);
spProj(eta, tmp[0], -1, Lop.Ls);
Lop.Omega(tmp[0], tmp[1], -1, 0);
G5R5(CG_src, tmp[1]);
tmp[1] = zero;
for(int k=0; k<param.degree; ++k){
gamma_l = 1.0 / ( 1.0 + PowerNegHalf.poles[k] );
Lop.RefreshShiftCoefficients(-gamma_l);
if(use_heatbath_forecasting){ // Forecast CG guess using solutions from previous poles
Lop.Mdag(CG_src, Forecast_src);
CG_soln = Forecast(Lop, Forecast_src, prev_solns);
Solver(Lop, CG_src, CG_soln);
prev_solns.push_back(CG_soln);
} else {
CG_soln = zero; // Just use zero as the initial guess
Solver(Lop, CG_src, CG_soln);
}
Lop.Dtilde(CG_soln, tmp[0]); // We actually solved Cayley preconditioned system: transform back
tmp[1] = tmp[1] + ( PowerNegHalf.residues[k]*gamma_l*gamma_l*Lop.k ) * tmp[0];
}
Lop.Omega(tmp[1], tmp[0], -1, 1);
spProj(tmp[0], tmp[1], -1, Lop.Ls);
Phi = Phi + tmp[1];
// RH terms:
// \Phi = \Phi - k \sum_{k=1}^{N_{p}} P_{+} \Omega_{+}^{\dagger} ( H(mb)
// + \gamma_{l} \Delta_{+}(mf,mb) P_{+} )^{-1} \Omega_{+} P_{+} \eta
spProj(eta, tmp[0], 1, Rop.Ls);
Rop.Omega(tmp[0], tmp[1], 1, 0);
G5R5(CG_src, tmp[1]);
tmp[1] = zero;
if(use_heatbath_forecasting){ prev_solns.clear(); } // empirically, LH solns don't help for RH solves
for(int k=0; k<param.degree; ++k){
gamma_l = 1.0 / ( 1.0 + PowerNegHalf.poles[k] );
Rop.RefreshShiftCoefficients(-gamma_l*PowerNegHalf.poles[k]);
if(use_heatbath_forecasting){
Rop.Mdag(CG_src, Forecast_src);
CG_soln = Forecast(Rop, Forecast_src, prev_solns);
Solver(Rop, CG_src, CG_soln);
prev_solns.push_back(CG_soln);
} else {
CG_soln = zero;
Solver(Rop, CG_src, CG_soln);
}
Rop.Dtilde(CG_soln, tmp[0]); // We actually solved Cayley preconditioned system: transform back
tmp[1] = tmp[1] - ( PowerNegHalf.residues[k]*gamma_l*gamma_l*Rop.k ) * tmp[0];
}
Rop.Omega(tmp[1], tmp[0], 1, 1);
spProj(tmp[0], tmp[1], 1, Rop.Ls);
Phi = Phi + tmp[1];
// Reset shift coefficients for energy and force evals
Lop.RefreshShiftCoefficients(0.0);
Rop.RefreshShiftCoefficients(-1.0);
};
// EOFA action: see Eqn. (10) of arXiv:1706.05843
virtual RealD S(const GaugeField& U)
{
Lop.ImportGauge(U);
Rop.ImportGauge(U);
FermionField spProj_Phi(Lop.FermionGrid());
std::vector<FermionField> tmp(2, Lop.FermionGrid());
// S = <\Phi|\Phi>
RealD action(norm2(Phi));
// LH term: S = S - k <\Phi| P_{-} \Omega_{-}^{\dagger} H(mf)^{-1} \Omega_{-} P_{-} |\Phi>
spProj(Phi, spProj_Phi, -1, Lop.Ls);
Lop.Omega(spProj_Phi, tmp[0], -1, 0);
G5R5(tmp[1], tmp[0]);
tmp[0] = zero;
Solver(Lop, tmp[1], tmp[0]);
Lop.Dtilde(tmp[0], tmp[1]); // We actually solved Cayley preconditioned system: transform back
Lop.Omega(tmp[1], tmp[0], -1, 1);
action -= Lop.k * innerProduct(spProj_Phi, tmp[0]).real();
// RH term: S = S + k <\Phi| P_{+} \Omega_{+}^{\dagger} ( H(mb)
// - \Delta_{+}(mf,mb) P_{+} )^{-1} \Omega_{-} P_{-} |\Phi>
spProj(Phi, spProj_Phi, 1, Rop.Ls);
Rop.Omega(spProj_Phi, tmp[0], 1, 0);
G5R5(tmp[1], tmp[0]);
tmp[0] = zero;
Solver(Rop, tmp[1], tmp[0]);
Rop.Dtilde(tmp[0], tmp[1]);
Rop.Omega(tmp[1], tmp[0], 1, 1);
action += Rop.k * innerProduct(spProj_Phi, tmp[0]).real();
return action;
};
// EOFA pseudofermion force: see Eqns. (34)-(36) of arXiv:1706.05843
virtual void deriv(const GaugeField& U, GaugeField& dSdU)
{
};
};
}}
#endif

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lib/qcd/action/pseudofermion/PseudoFermion.h
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#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/ExactOneFlavourRatio.h>
#endif #endif

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tests/debug/Test_heatbath_dwf_eofa.cc Normal file
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/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./tests/debug/Test_heatbath_dwf_eofa.cc
Copyright (C) 2017
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
Author: paboyle <paboyle@ph.ed.ac.uk>
Author: David Murphy <dmurphy@phys.columbia.edu>
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 */
//////////////////////////////////////////////////////////////////////////////////////////
// This program sets up the initial pseudofermion field |Phi> = Meofa^{-1/2}*|eta>, and
// then uses this Phi to compute the action <Phi|Meofa|Phi>.
// If all is working, one should find that <eta|eta> = <Phi|Meofa|Phi>.
//////////////////////////////////////////////////////////////////////////////////////////
#include <Grid/Grid.h>
using namespace std;
using namespace Grid;
using namespace Grid::QCD;
// Parameters for test
const std::vector<int> grid_dim = { 8, 8, 8, 8 };
const int Ls = 8;
const int Npoles = 12;
const RealD mf = 0.01;
const RealD mpv = 1.0;
const RealD M5 = 1.8;
int main(int argc, char** argv)
{
Grid_init(&argc, &argv);
int threads = GridThread::GetThreads();
std::cout << GridLogMessage << "Grid is set up to use " << threads << " threads" << std::endl;
// Initialize spacetime grid
std::cout << GridLogMessage << "Lattice dimensions: " << grid_dim << " Ls: " << Ls << std::endl;
GridCartesian* UGrid = SpaceTimeGrid::makeFourDimGrid(grid_dim,
GridDefaultSimd(Nd,vComplex::Nsimd()), GridDefaultMpi());
GridRedBlackCartesian* UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
GridCartesian* FGrid = SpaceTimeGrid::makeFiveDimGrid(Ls, UGrid);
GridRedBlackCartesian* FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls, UGrid);
// Set up RNGs
std::vector<int> seeds4({1, 2, 3, 4});
std::vector<int> seeds5({5, 6, 7, 8});
GridParallelRNG RNG5(FGrid);
RNG5.SeedFixedIntegers(seeds5);
GridParallelRNG RNG4(UGrid);
RNG4.SeedFixedIntegers(seeds4);
// Random gauge field
LatticeGaugeField Umu(UGrid);
SU3::HotConfiguration(RNG4, Umu);
DomainWallEOFAFermionR Lop(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mf, mf, mpv, 0.0, -1, M5);
DomainWallEOFAFermionR Rop(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mpv, mf, mpv, -1.0, 1, M5);
// Construct the action and test the heatbath (zero initial guess)
{
OneFlavourRationalParams Params(0.95, 100.0, 5000, 1.0e-12, Npoles);
ConjugateGradient<LatticeFermion> CG(1.0e-12, 5000);
ExactOneFlavourRatioPseudoFermionAction<WilsonImplR> Meofa(Lop, Rop, CG, Params, false);
Meofa.refresh(Umu, RNG5);
printf("<Phi|Meofa|Phi> = %1.15e\n", Meofa.S(Umu));
}
// Construct the action and test the heatbath (forecasted initial guesses)
{
OneFlavourRationalParams Params(0.95, 100.0, 5000, 1.0e-12, Npoles);
ConjugateGradient<LatticeFermion> CG(1.0e-12, 5000);
ExactOneFlavourRatioPseudoFermionAction<WilsonImplR> Meofa(Lop, Rop, CG, Params, true);
Meofa.refresh(Umu, RNG5);
printf("<Phi|Meofa|Phi> = %1.15e\n", Meofa.S(Umu));
}
return 0;
}

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tests/debug/Test_heatbath_dwf_eofa_gparity.cc Normal file
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/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./tests/debug/Test_heatbath_dwf_eofa.cc
Copyright (C) 2017
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
Author: paboyle <paboyle@ph.ed.ac.uk>
Author: David Murphy <dmurphy@phys.columbia.edu>
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 */
//////////////////////////////////////////////////////////////////////////////////////////
// This program sets up the initial pseudofermion field |Phi> = Meofa^{-1/2}*|eta>, and
// then uses this Phi to compute the action <Phi|Meofa|Phi>.
// If all is working, one should find that <eta|eta> = <Phi|Meofa|Phi>.
//////////////////////////////////////////////////////////////////////////////////////////
#include <Grid/Grid.h>
using namespace std;
using namespace Grid;
using namespace Grid::QCD;
typedef GparityWilsonImplR FermionImplPolicy;
typedef GparityDomainWallEOFAFermionR FermionAction;
typedef typename FermionAction::FermionField FermionField;
// Parameters for test
const std::vector<int> grid_dim = { 8, 8, 8, 8 };
const int Ls = 8;
const int Npoles = 12;
const RealD mf = 0.01;
const RealD mpv = 1.0;
const RealD M5 = 1.8;
int main(int argc, char** argv)
{
Grid_init(&argc, &argv);
int threads = GridThread::GetThreads();
std::cout << GridLogMessage << "Grid is set up to use " << threads << " threads" << std::endl;
// Initialize spacetime grid
std::cout << GridLogMessage << "Lattice dimensions: " << grid_dim << " Ls: " << Ls << std::endl;
GridCartesian* UGrid = SpaceTimeGrid::makeFourDimGrid(grid_dim,
GridDefaultSimd(Nd,vComplex::Nsimd()), GridDefaultMpi());
GridRedBlackCartesian* UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
GridCartesian* FGrid = SpaceTimeGrid::makeFiveDimGrid(Ls, UGrid);
GridRedBlackCartesian* FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls, UGrid);
// Set up RNGs
std::vector<int> seeds4({1, 2, 3, 4});
std::vector<int> seeds5({5, 6, 7, 8});
GridParallelRNG RNG5(FGrid);
RNG5.SeedFixedIntegers(seeds5);
GridParallelRNG RNG4(UGrid);
RNG4.SeedFixedIntegers(seeds4);
// Random gauge field
LatticeGaugeField Umu(UGrid);
SU3::HotConfiguration(RNG4, Umu);
// GparityDomainWallFermionR::ImplParams params;
FermionAction::ImplParams params;
FermionAction Lop(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mf, mf, mpv, 0.0, -1, M5, params);
FermionAction Rop(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mpv, mf, mpv, -1.0, 1, M5, params);
// Construct the action and test the heatbath (zero initial guess)
{
OneFlavourRationalParams Params(0.95, 100.0, 5000, 1.0e-12, Npoles);
ConjugateGradient<FermionField> CG(1.0e-12, 5000);
ExactOneFlavourRatioPseudoFermionAction<FermionImplPolicy> Meofa(Lop, Rop, CG, Params, false);
Meofa.refresh(Umu, RNG5);
printf("<Phi|Meofa|Phi> = %1.15e\n", Meofa.S(Umu));
}
// Construct the action and test the heatbath (forecasted initial guesses)
{
OneFlavourRationalParams Params(0.95, 100.0, 5000, 1.0e-12, Npoles);
ConjugateGradient<FermionField> CG(1.0e-12, 5000);
ExactOneFlavourRatioPseudoFermionAction<FermionImplPolicy> Meofa(Lop, Rop, CG, Params, true);
Meofa.refresh(Umu, RNG5);
printf("<Phi|Meofa|Phi> = %1.15e\n", Meofa.S(Umu));
}
return 0;
}