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265 lines
10 KiB
C++
265 lines
10 KiB
C++
/*************************************************************************************
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Grid physics library, www.github.com/paboyle/Grid
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Source file: ./lib/qcd/action/pseudofermion/ExactOneFlavourRatio.h
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Copyright (C) 2017
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Author: Peter Boyle <paboyle@ph.ed.ac.uk>
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Author: David Murphy <dmurphy@phys.columbia.edu>
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License along
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with this program; if not, write to the Free Software Foundation, Inc.,
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51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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See the full license in the file "LICENSE" in the top level distribution directory
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*************************************************************************************/
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/* END LEGAL */
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/////////////////////////////////////////////////////////////////
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// Implementation of exact one flavour algorithm (EOFA) //
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// using fermion classes defined in: //
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// Grid/qcd/action/fermion/DomainWallEOFAFermion.h (Shamir) //
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// Grid/qcd/action/fermion/MobiusEOFAFermion.h (Mobius) //
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// arXiv: 1403.1683, 1706.05843 //
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/////////////////////////////////////////////////////////////////
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#ifndef QCD_PSEUDOFERMION_EXACT_ONE_FLAVOUR_RATIO_H
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#define QCD_PSEUDOFERMION_EXACT_ONE_FLAVOUR_RATIO_H
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NAMESPACE_BEGIN(Grid);
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///////////////////////////////////////////////////////////////
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// Exact one flavour implementation of DWF determinant ratio //
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///////////////////////////////////////////////////////////////
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template<class Impl>
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class ExactOneFlavourRatioPseudoFermionAction : public Action<typename Impl::GaugeField>
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{
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public:
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INHERIT_IMPL_TYPES(Impl);
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typedef OneFlavourRationalParams Params;
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Params param;
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MultiShiftFunction PowerNegHalf;
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private:
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bool use_heatbath_forecasting;
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AbstractEOFAFermion<Impl>& Lop; // the basic LH operator
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AbstractEOFAFermion<Impl>& Rop; // the basic RH operator
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SchurRedBlackDiagMooeeSolve<FermionField> Solver;
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FermionField Phi; // the pseudofermion field for this trajectory
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public:
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ExactOneFlavourRatioPseudoFermionAction(AbstractEOFAFermion<Impl>& _Lop, AbstractEOFAFermion<Impl>& _Rop,
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OperatorFunction<FermionField>& S, Params& p, bool use_fc=false) : Lop(_Lop), Rop(_Rop), Solver(S),
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Phi(_Lop.FermionGrid()), param(p), use_heatbath_forecasting(use_fc)
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{
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AlgRemez remez(param.lo, param.hi, param.precision);
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// MdagM^(+- 1/2)
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std::cout << GridLogMessage << "Generating degree " << param.degree << " for x^(-1/2)" << std::endl;
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remez.generateApprox(param.degree, 1, 2);
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PowerNegHalf.Init(remez, param.tolerance, true);
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};
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virtual std::string action_name() { return "ExactOneFlavourRatioPseudoFermionAction"; }
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virtual std::string LogParameters() {
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std::stringstream sstream;
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sstream << GridLogMessage << "[" << action_name() << "] Low :" << param.lo << std::endl;
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sstream << GridLogMessage << "[" << action_name() << "] High :" << param.hi << std::endl;
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sstream << GridLogMessage << "[" << action_name() << "] Max iterations :" << param.MaxIter << std::endl;
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sstream << GridLogMessage << "[" << action_name() << "] Tolerance :" << param.tolerance << std::endl;
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sstream << GridLogMessage << "[" << action_name() << "] Degree :" << param.degree << std::endl;
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sstream << GridLogMessage << "[" << action_name() << "] Precision :" << param.precision << std::endl;
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return sstream.str();
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}
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// Spin projection
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void spProj(const FermionField& in, FermionField& out, int sign, int Ls)
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{
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if(sign == 1){ for(int s=0; s<Ls; ++s){ axpby_ssp_pplus(out, 0.0, in, 1.0, in, s, s); } }
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else{ for(int s=0; s<Ls; ++s){ axpby_ssp_pminus(out, 0.0, in, 1.0, in, s, s); } }
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}
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// EOFA heatbath: see Eqn. (29) of arXiv:1706.05843
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// We generate a Gaussian noise vector \eta, and then compute
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// \Phi = M_{\rm EOFA}^{-1/2} * \eta
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// using a rational approximation to the inverse square root
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virtual void refresh(const GaugeField& U, GridParallelRNG& pRNG)
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{
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Lop.ImportGauge(U);
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Rop.ImportGauge(U);
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FermionField eta (Lop.FermionGrid());
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FermionField CG_src (Lop.FermionGrid());
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FermionField CG_soln (Lop.FermionGrid());
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FermionField Forecast_src(Lop.FermionGrid());
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std::vector<FermionField> tmp(2, Lop.FermionGrid());
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// Use chronological inverter to forecast solutions across poles
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std::vector<FermionField> prev_solns;
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if(use_heatbath_forecasting){ prev_solns.reserve(param.degree); }
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ChronoForecast<AbstractEOFAFermion<Impl>, FermionField> Forecast;
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// Seed with Gaussian noise vector (var = 0.5)
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RealD scale = std::sqrt(0.5);
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gaussian(pRNG,eta);
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eta = eta * scale;
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printf("Heatbath source vector: <\\eta|\\eta> = %1.15e\n", norm2(eta));
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// \Phi = ( \alpha_{0} + \sum_{k=1}^{N_{p}} \alpha_{l} * \gamma_{l} ) * \eta
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RealD N(PowerNegHalf.norm);
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for(int k=0; k<param.degree; ++k){ N += PowerNegHalf.residues[k] / ( 1.0 + PowerNegHalf.poles[k] ); }
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Phi = eta * N;
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// LH terms:
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// \Phi = \Phi + k \sum_{k=1}^{N_{p}} P_{-} \Omega_{-}^{\dagger} ( H(mf)
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// - \gamma_{l} \Delta_{-}(mf,mb) P_{-} )^{-1} \Omega_{-} P_{-} \eta
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RealD gamma_l(0.0);
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spProj(eta, tmp[0], -1, Lop.Ls);
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Lop.Omega(tmp[0], tmp[1], -1, 0);
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G5R5(CG_src, tmp[1]);
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tmp[1] = zero;
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for(int k=0; k<param.degree; ++k){
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gamma_l = 1.0 / ( 1.0 + PowerNegHalf.poles[k] );
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Lop.RefreshShiftCoefficients(-gamma_l);
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if(use_heatbath_forecasting){ // Forecast CG guess using solutions from previous poles
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Lop.Mdag(CG_src, Forecast_src);
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CG_soln = Forecast(Lop, Forecast_src, prev_solns);
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Solver(Lop, CG_src, CG_soln);
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prev_solns.push_back(CG_soln);
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} else {
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CG_soln = zero; // Just use zero as the initial guess
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Solver(Lop, CG_src, CG_soln);
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}
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Lop.Dtilde(CG_soln, tmp[0]); // We actually solved Cayley preconditioned system: transform back
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tmp[1] = tmp[1] + ( PowerNegHalf.residues[k]*gamma_l*gamma_l*Lop.k ) * tmp[0];
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}
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Lop.Omega(tmp[1], tmp[0], -1, 1);
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spProj(tmp[0], tmp[1], -1, Lop.Ls);
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Phi = Phi + tmp[1];
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// RH terms:
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// \Phi = \Phi - k \sum_{k=1}^{N_{p}} P_{+} \Omega_{+}^{\dagger} ( H(mb)
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// + \gamma_{l} \Delta_{+}(mf,mb) P_{+} )^{-1} \Omega_{+} P_{+} \eta
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spProj(eta, tmp[0], 1, Rop.Ls);
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Rop.Omega(tmp[0], tmp[1], 1, 0);
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G5R5(CG_src, tmp[1]);
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tmp[1] = zero;
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if(use_heatbath_forecasting){ prev_solns.clear(); } // empirically, LH solns don't help for RH solves
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for(int k=0; k<param.degree; ++k){
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gamma_l = 1.0 / ( 1.0 + PowerNegHalf.poles[k] );
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Rop.RefreshShiftCoefficients(-gamma_l*PowerNegHalf.poles[k]);
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if(use_heatbath_forecasting){
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Rop.Mdag(CG_src, Forecast_src);
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CG_soln = Forecast(Rop, Forecast_src, prev_solns);
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Solver(Rop, CG_src, CG_soln);
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prev_solns.push_back(CG_soln);
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} else {
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CG_soln = zero;
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Solver(Rop, CG_src, CG_soln);
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}
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Rop.Dtilde(CG_soln, tmp[0]); // We actually solved Cayley preconditioned system: transform back
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tmp[1] = tmp[1] - ( PowerNegHalf.residues[k]*gamma_l*gamma_l*Rop.k ) * tmp[0];
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}
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Rop.Omega(tmp[1], tmp[0], 1, 1);
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spProj(tmp[0], tmp[1], 1, Rop.Ls);
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Phi = Phi + tmp[1];
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// Reset shift coefficients for energy and force evals
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Lop.RefreshShiftCoefficients(0.0);
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Rop.RefreshShiftCoefficients(-1.0);
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};
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// EOFA action: see Eqn. (10) of arXiv:1706.05843
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virtual RealD S(const GaugeField& U)
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{
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Lop.ImportGauge(U);
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Rop.ImportGauge(U);
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FermionField spProj_Phi(Lop.FermionGrid());
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std::vector<FermionField> tmp(2, Lop.FermionGrid());
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// S = <\Phi|\Phi>
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RealD action(norm2(Phi));
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// LH term: S = S - k <\Phi| P_{-} \Omega_{-}^{\dagger} H(mf)^{-1} \Omega_{-} P_{-} |\Phi>
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spProj(Phi, spProj_Phi, -1, Lop.Ls);
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Lop.Omega(spProj_Phi, tmp[0], -1, 0);
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G5R5(tmp[1], tmp[0]);
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tmp[0] = zero;
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Solver(Lop, tmp[1], tmp[0]);
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Lop.Dtilde(tmp[0], tmp[1]); // We actually solved Cayley preconditioned system: transform back
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Lop.Omega(tmp[1], tmp[0], -1, 1);
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action -= Lop.k * innerProduct(spProj_Phi, tmp[0]).real();
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// RH term: S = S + k <\Phi| P_{+} \Omega_{+}^{\dagger} ( H(mb)
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// - \Delta_{+}(mf,mb) P_{+} )^{-1} \Omega_{-} P_{-} |\Phi>
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spProj(Phi, spProj_Phi, 1, Rop.Ls);
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Rop.Omega(spProj_Phi, tmp[0], 1, 0);
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G5R5(tmp[1], tmp[0]);
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tmp[0] = zero;
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Solver(Rop, tmp[1], tmp[0]);
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Rop.Dtilde(tmp[0], tmp[1]);
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Rop.Omega(tmp[1], tmp[0], 1, 1);
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action += Rop.k * innerProduct(spProj_Phi, tmp[0]).real();
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return action;
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};
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// EOFA pseudofermion force: see Eqns. (34)-(36) of arXiv:1706.05843
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virtual void deriv(const GaugeField& U, GaugeField& dSdU)
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{
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Lop.ImportGauge(U);
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Rop.ImportGauge(U);
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FermionField spProj_Phi (Lop.FermionGrid());
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FermionField Omega_spProj_Phi(Lop.FermionGrid());
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FermionField CG_src (Lop.FermionGrid());
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FermionField Chi (Lop.FermionGrid());
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FermionField g5_R5_Chi (Lop.FermionGrid());
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GaugeField force(Lop.GaugeGrid());
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// LH: dSdU = k \chi_{L}^{\dagger} \gamma_{5} R_{5} ( \partial_{x,\mu} D_{w} ) \chi_{L}
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// \chi_{L} = H(mf)^{-1} \Omega_{-} P_{-} \Phi
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spProj(Phi, spProj_Phi, -1, Lop.Ls);
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Lop.Omega(spProj_Phi, Omega_spProj_Phi, -1, 0);
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G5R5(CG_src, Omega_spProj_Phi);
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spProj_Phi = zero;
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Solver(Lop, CG_src, spProj_Phi);
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Lop.Dtilde(spProj_Phi, Chi);
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G5R5(g5_R5_Chi, Chi);
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Lop.MDeriv(force, g5_R5_Chi, Chi, DaggerNo);
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dSdU = Lop.k * force;
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// RH: dSdU = dSdU - k \chi_{R}^{\dagger} \gamma_{5} R_{5} ( \partial_{x,\mu} D_{w} ) \chi_{}
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// \chi_{R} = ( H(mb) - \Delta_{+}(mf,mb) P_{+} )^{-1} \Omega_{+} P_{+} \Phi
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spProj(Phi, spProj_Phi, 1, Rop.Ls);
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Rop.Omega(spProj_Phi, Omega_spProj_Phi, 1, 0);
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G5R5(CG_src, Omega_spProj_Phi);
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spProj_Phi = zero;
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Solver(Rop, CG_src, spProj_Phi);
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Rop.Dtilde(spProj_Phi, Chi);
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G5R5(g5_R5_Chi, Chi);
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Lop.MDeriv(force, g5_R5_Chi, Chi, DaggerNo);
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dSdU = dSdU - Rop.k * force;
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};
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};
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NAMESPACE_END(Grid);
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#endif
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