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Check-in of working Mobius EOFA class and tests

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This commit is contained in:
David Murphy
2017-08-22 22:38:30 -04:00
parent 9d45fca8bc
commit 459f70e8d4
16 changed files with 2383 additions and 32 deletions
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tests/debug/Test_heatbath_mobius_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 b = 2.5;
const RealD c = 1.5;
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);
MobiusEOFAFermionR Lop(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mf, mf, mpv, 0.0, -1, M5, b, c);
MobiusEOFAFermionR Rop(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mpv, mf, mpv, -1.0, 1, M5, b, c);
// 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_mobius_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 GparityMobiusEOFAFermionR 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 b = 2.5;
const RealD c = 1.5;
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);
FermionAction::ImplParams params;
FermionAction Lop(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mf, mf, mpv, 0.0, -1, M5, b, c, params);
FermionAction Rop(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mpv, mf, mpv, -1.0, 1, M5, b, c, 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;
}

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tests/debug/Test_reweight_dwf_eofa_gparity.cc
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Grid physics library, www.github.com/paboyle/Grid
Source file: ./tests/debug/Test_reweight_dwf_eofa.cc
Source file: ./tests/debug/Test_reweight_dwf_eofa_gparity.cc
Copyright (C) 2017

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/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./tests/debug/Test_reweight_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 */
#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 Nhits = 10;
const int max_iter = 5000;
const RealD b = 2.5;
const RealD c = 1.5;
const RealD mf = 0.1;
const RealD mb = 0.11;
const RealD M5 = 1.8;
const RealD stop_tol = 1.0e-12;
RealD mean(const std::vector<RealD>& data)
{
int N = data.size();
RealD mean(0.0);
for(int i=0; i<N; ++i){ mean += data[i]; }
return mean/RealD(N);
}
RealD jack_mean(const std::vector<RealD>& data, int sample)
{
int N = data.size();
RealD mean(0.0);
for(int i=0; i<N; ++i){ if(i != sample){ mean += data[i]; } }
return mean/RealD(N-1);
}
RealD jack_std(const std::vector<RealD>& jacks, RealD mean)
{
int N = jacks.size();
RealD std(0.0);
for(int i=0; i<N; ++i){ std += std::pow(jacks[i]-mean, 2.0); }
return std::sqrt(RealD(N-1)/RealD(N)*std);
}
std::vector<RealD> jack_stats(const std::vector<RealD>& data)
{
int N = data.size();
std::vector<RealD> jack_samples(N);
std::vector<RealD> jack_stats(2);
jack_stats[0] = mean(data);
for(int i=0; i<N; i++){ jack_samples[i] = jack_mean(data,i); }
jack_stats[1] = jack_std(jack_samples, jack_stats[0]);
return jack_stats;
}
int main(int argc, char **argv)
{
Grid_init(&argc, &argv);
// 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);
// Initialize RHMC fermion operators
MobiusFermionR Ddwf_f(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mf, M5, b, c);
MobiusFermionR Ddwf_b(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mb, M5, b, c);
SchurDiagMooeeOperator<MobiusFermionR, LatticeFermion> MdagM(Ddwf_f);
SchurDiagMooeeOperator<MobiusFermionR, LatticeFermion> VdagV(Ddwf_b);
// Degree 12 rational approximations to x^(1/4) and x^(-1/4)
double lo = 0.0001;
double hi = 95.0;
int precision = 64;
int degree = 12;
AlgRemez remez(lo, hi, precision);
std::cout << GridLogMessage << "Generating degree " << degree << " for x^(1/4)" << std::endl;
remez.generateApprox(degree, 1, 4);
MultiShiftFunction PowerQuarter(remez, stop_tol, false);
MultiShiftFunction PowerNegQuarter(remez, stop_tol, true);
// Stochastically estimate reweighting factor via RHMC
RealD scale = std::sqrt(0.5);
std::vector<RealD> rw_rhmc(Nhits);
ConjugateGradientMultiShift<LatticeFermion> msCG_V(max_iter, PowerQuarter);
ConjugateGradientMultiShift<LatticeFermion> msCG_M(max_iter, PowerNegQuarter);
std::cout.precision(12);
for(int hit=0; hit<Nhits; hit++){
// Gaussian source
LatticeFermion Phi (Ddwf_f.FermionGrid());
LatticeFermion PhiOdd (Ddwf_f.FermionRedBlackGrid());
std::vector<LatticeFermion> tmp(2, Ddwf_f.FermionRedBlackGrid());
gaussian(RNG5, Phi);
Phi = Phi*scale;
pickCheckerboard(Odd, PhiOdd, Phi);
// evaluate -log(rw)
msCG_V(VdagV, PhiOdd, tmp[0]);
msCG_M(MdagM, tmp[0], tmp[1]);
rw_rhmc[hit] = norm2(tmp[1]) - norm2(PhiOdd);
std::cout << std::endl << "==================================================" << std::endl;
std::cout << " --- RHMC: Hit " << hit << ": rw = " << rw_rhmc[hit];
std::cout << std::endl << "==================================================" << std::endl << std::endl;
}
// Initialize EOFA fermion operators
RealD shift_L = 0.0;
RealD shift_R = -1.0;
int pm = 1;
MobiusEOFAFermionR Deofa_L(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mf, mf, mb, shift_L, pm, M5, b, c);
MobiusEOFAFermionR Deofa_R(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mb, mf, mb, shift_R, pm, M5, b, c);
MdagMLinearOperator<MobiusEOFAFermionR, LatticeFermion> LdagL(Deofa_L);
MdagMLinearOperator<MobiusEOFAFermionR, LatticeFermion> RdagR(Deofa_R);
// Stochastically estimate reweighting factor via EOFA
RealD k = Deofa_L.k;
std::vector<RealD> rw_eofa(Nhits);
ConjugateGradient<LatticeFermion> CG(stop_tol, max_iter);
SchurRedBlackDiagMooeeSolve<LatticeFermion> SchurSolver(CG);
// Compute -log(Z), where: ( RHMC det ratio ) = Z * ( EOFA det ratio )
RealD Z = std::pow(b+c+1.0,Ls) + mf*std::pow(b+c-1.0,Ls);
Z /= std::pow(b+c+1.0,Ls) + mb*std::pow(b+c-1.0,Ls);
Z = -12.0*grid_dim[0]*grid_dim[1]*grid_dim[2]*grid_dim[3]*std::log(Z);
for(int hit=0; hit<Nhits; hit++){
// Gaussian source
LatticeFermion Phi (Deofa_L.FermionGrid());
LatticeFermion spProj_Phi(Deofa_L.FermionGrid());
std::vector<LatticeFermion> tmp(2, Deofa_L.FermionGrid());
gaussian(RNG5, Phi);
Phi = Phi*scale;
// evaluate -log(rw)
// LH term
for(int s=0; s<Ls; ++s){ axpby_ssp_pminus(spProj_Phi, 0.0, Phi, 1.0, Phi, s, s); }
Deofa_L.Omega(spProj_Phi, tmp[0], -1, 0);
G5R5(tmp[1], tmp[0]);
tmp[0] = zero;
SchurSolver(Deofa_L, tmp[1], tmp[0]);
Deofa_L.Dtilde(tmp[0], tmp[1]);
Deofa_L.Omega(tmp[1], tmp[0], -1, 1);
rw_eofa[hit] = Z - k*innerProduct(spProj_Phi,tmp[0]).real();
// RH term
for(int s=0; s<Ls; ++s){ axpby_ssp_pplus(spProj_Phi, 0.0, Phi, 1.0, Phi, s, s); }
Deofa_R.Omega(spProj_Phi, tmp[0], 1, 0);
G5R5(tmp[1], tmp[0]);
tmp[0] = zero;
SchurSolver(Deofa_R, tmp[1], tmp[0]);
Deofa_R.Dtilde(tmp[0], tmp[1]);
Deofa_R.Omega(tmp[1], tmp[0], 1, 1);
rw_eofa[hit] += k*innerProduct(spProj_Phi,tmp[0]).real();
std::cout << std::endl << "==================================================" << std::endl;
std::cout << " --- EOFA: Hit " << hit << ": rw = " << rw_eofa[hit];
std::cout << std::endl << "==================================================" << std::endl << std::endl;
}
std::vector<RealD> rhmc_result = jack_stats(rw_rhmc);
std::vector<RealD> eofa_result = jack_stats(rw_eofa);
std::cout << std::endl << "RHMC: rw = " << rhmc_result[0] << " +/- " << rhmc_result[1] << std::endl;
std::cout << std::endl << "EOFA: rw = " << eofa_result[0] << " +/- " << eofa_result[1] << std::endl;
Grid_finalize();
}

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/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./tests/debug/Test_reweight_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 */
#include <Grid/Grid.h>
using namespace std;
using namespace Grid;
using namespace Grid::QCD;
typedef typename GparityDomainWallFermionR::FermionField FermionField;
// parameters for test
const std::vector<int> grid_dim = { 8, 8, 8, 8 };
const int Ls = 8;
const int Nhits = 10;
const int max_iter = 5000;
const RealD b = 2.5;
const RealD c = 1.5;
const RealD mf = 0.1;
const RealD mb = 0.11;
const RealD M5 = 1.8;
const RealD stop_tol = 1.0e-12;
RealD mean(const std::vector<RealD>& data)
{
int N = data.size();
RealD mean(0.0);
for(int i=0; i<N; ++i){ mean += data[i]; }
return mean/RealD(N);
}
RealD jack_mean(const std::vector<RealD>& data, int sample)
{
int N = data.size();
RealD mean(0.0);
for(int i=0; i<N; ++i){ if(i != sample){ mean += data[i]; } }
return mean/RealD(N-1);
}
RealD jack_std(const std::vector<RealD>& jacks, RealD mean)
{
int N = jacks.size();
RealD std(0.0);
for(int i=0; i<N; ++i){ std += std::pow(jacks[i]-mean, 2.0); }
return std::sqrt(RealD(N-1)/RealD(N)*std);
}
std::vector<RealD> jack_stats(const std::vector<RealD>& data)
{
int N = data.size();
std::vector<RealD> jack_samples(N);
std::vector<RealD> jack_stats(2);
jack_stats[0] = mean(data);
for(int i=0; i<N; i++){ jack_samples[i] = jack_mean(data,i); }
jack_stats[1] = jack_std(jack_samples, jack_stats[0]);
return jack_stats;
}
int main(int argc, char **argv)
{
Grid_init(&argc, &argv);
// 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);
// Initialize RHMC fermion operators
GparityDomainWallFermionR::ImplParams params;
GparityMobiusFermionR Ddwf_f(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mf, M5, b, c, params);
GparityMobiusFermionR Ddwf_b(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mb, M5, b, c, params);
SchurDiagMooeeOperator<GparityMobiusFermionR, FermionField> MdagM(Ddwf_f);
SchurDiagMooeeOperator<GparityMobiusFermionR, FermionField> VdagV(Ddwf_b);
// Degree 12 rational approximations to x^(1/4) and x^(-1/4)
double lo = 0.0001;
double hi = 95.0;
int precision = 64;
int degree = 12;
AlgRemez remez(lo, hi, precision);
std::cout << GridLogMessage << "Generating degree " << degree << " for x^(1/4)" << std::endl;
remez.generateApprox(degree, 1, 4);
MultiShiftFunction PowerQuarter(remez, stop_tol, false);
MultiShiftFunction PowerNegQuarter(remez, stop_tol, true);
// Stochastically estimate reweighting factor via RHMC
RealD scale = std::sqrt(0.5);
std::vector<RealD> rw_rhmc(Nhits);
ConjugateGradientMultiShift<FermionField> msCG_V(max_iter, PowerQuarter);
ConjugateGradientMultiShift<FermionField> msCG_M(max_iter, PowerNegQuarter);
std::cout.precision(12);
for(int hit=0; hit<Nhits; hit++){
// Gaussian source
FermionField Phi (Ddwf_f.FermionGrid());
FermionField PhiOdd (Ddwf_f.FermionRedBlackGrid());
std::vector<FermionField> tmp(2, Ddwf_f.FermionRedBlackGrid());
gaussian(RNG5, Phi);
Phi = Phi*scale;
pickCheckerboard(Odd, PhiOdd, Phi);
// evaluate -log(rw)
msCG_V(VdagV, PhiOdd, tmp[0]);
msCG_M(MdagM, tmp[0], tmp[1]);
rw_rhmc[hit] = norm2(tmp[1]) - norm2(PhiOdd);
std::cout << std::endl << "==================================================" << std::endl;
std::cout << " --- RHMC: Hit " << hit << ": rw = " << rw_rhmc[hit];
std::cout << std::endl << "==================================================" << std::endl << std::endl;
}
// Initialize EOFA fermion operators
RealD shift_L = 0.0;
RealD shift_R = -1.0;
int pm = 1;
GparityMobiusEOFAFermionR Deofa_L(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mf, mf, mb, shift_L, pm, M5, b, c, params);
GparityMobiusEOFAFermionR Deofa_R(Umu, *FGrid, *FrbGrid, *UGrid, *UrbGrid, mb, mf, mb, shift_R, pm, M5, b, c, params);
MdagMLinearOperator<GparityMobiusEOFAFermionR, FermionField> LdagL(Deofa_L);
MdagMLinearOperator<GparityMobiusEOFAFermionR, FermionField> RdagR(Deofa_R);
// Stochastically estimate reweighting factor via EOFA
RealD k = Deofa_L.k;
std::vector<RealD> rw_eofa(Nhits);
ConjugateGradient<FermionField> CG(stop_tol, max_iter);
SchurRedBlackDiagMooeeSolve<FermionField> SchurSolver(CG);
// Compute -log(Z), where: ( RHMC det ratio ) = Z * ( EOFA det ratio )
RealD Z = std::pow(b+c+1.0,Ls) + mf*std::pow(b+c-1.0,Ls);
Z /= std::pow(b+c+1.0,Ls) + mb*std::pow(b+c-1.0,Ls);
Z = -12.0*grid_dim[0]*grid_dim[1]*grid_dim[2]*grid_dim[3]*std::log(Z);
for(int hit=0; hit<Nhits; hit++){
// Gaussian source
FermionField Phi (Deofa_L.FermionGrid());
FermionField spProj_Phi(Deofa_L.FermionGrid());
std::vector<FermionField> tmp(2, Deofa_L.FermionGrid());
gaussian(RNG5, Phi);
Phi = Phi*scale;
// evaluate -log(rw)
// LH term
for(int s=0; s<Ls; ++s){ axpby_ssp_pminus(spProj_Phi, 0.0, Phi, 1.0, Phi, s, s); }
Deofa_L.Omega(spProj_Phi, tmp[0], -1, 0);
G5R5(tmp[1], tmp[0]);
tmp[0] = zero;
SchurSolver(Deofa_L, tmp[1], tmp[0]);
Deofa_L.Dtilde(tmp[0], tmp[1]);
Deofa_L.Omega(tmp[1], tmp[0], -1, 1);
rw_eofa[hit] = 2.0*Z - k*innerProduct(spProj_Phi,tmp[0]).real();
// RH term
for(int s=0; s<Ls; ++s){ axpby_ssp_pplus(spProj_Phi, 0.0, Phi, 1.0, Phi, s, s); }
Deofa_R.Omega(spProj_Phi, tmp[0], 1, 0);
G5R5(tmp[1], tmp[0]);
tmp[0] = zero;
SchurSolver(Deofa_R, tmp[1], tmp[0]);
Deofa_R.Dtilde(tmp[0], tmp[1]);
Deofa_R.Omega(tmp[1], tmp[0], 1, 1);
rw_eofa[hit] += k*innerProduct(spProj_Phi,tmp[0]).real();
std::cout << std::endl << "==================================================" << std::endl;
std::cout << " --- EOFA: Hit " << hit << ": rw = " << rw_eofa[hit];
std::cout << std::endl << "==================================================" << std::endl << std::endl;
}
std::vector<RealD> rhmc_result = jack_stats(rw_rhmc);
std::vector<RealD> eofa_result = jack_stats(rw_eofa);
std::cout << std::endl << "RHMC: rw = " << rhmc_result[0] << " +/- " << rhmc_result[1] << std::endl;
std::cout << std::endl << "EOFA: rw = " << eofa_result[0] << " +/- " << eofa_result[1] << std::endl;
Grid_finalize();
}