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Grid/Grid/qcd/utils/GaugeFix.h

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/*************************************************************************************
grid` physics library, www.github.com/paboyle/Grid
Copyright (C) 2015
Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
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 */
//#include <Grid/Grid.h>
#ifndef GRID_QCD_GAUGE_FIX_H
#define GRID_QCD_GAUGE_FIX_H
NAMESPACE_BEGIN(Grid);
template <class Gimpl>
class FourierAcceleratedGaugeFixer : public Gimpl {
public:
INHERIT_GIMPL_TYPES(Gimpl);
typedef typename Gimpl::GaugeLinkField GaugeMat;
typedef typename Gimpl::GaugeField GaugeLorentz;
//A_\mu(x) = -i Ta(U_\mu(x) ) where Ta(U) = 1/2( U - U^dag ) - 1/2N tr(U - U^dag) is the traceless antihermitian part. This is an O(A^3) approximation to the logarithm of U
static void GaugeLinkToLieAlgebraField(const GaugeMat &U, GaugeMat &A) {
Complex cmi(0.0,-1.0);
A = Ta(U) * cmi;
}
//The derivative of the Lie algebra field
static void DmuAmu(const std::vector<GaugeMat> &U, GaugeMat &dmuAmu,int orthog) {
GridBase* grid = U[0].Grid();
GaugeMat Ax(grid);
GaugeMat Axm1(grid);
GaugeMat Utmp(grid);
dmuAmu=Zero();
for(int mu=0;mu<Nd;mu++){
if ( mu != orthog ) {
//Rather than define functionality to work out how the BCs apply to A_\mu we simply use the BC-aware Cshift to the gauge links and compute A_\mu(x) and A_\mu(x-1) separately
//Ax = A_\mu(x)
GaugeLinkToLieAlgebraField(U[mu], Ax);
//Axm1 = A_\mu(x_\mu-1)
Utmp = Gimpl::CshiftLink(U[mu], mu, -1);
GaugeLinkToLieAlgebraField(Utmp, Axm1);
//Derivative
dmuAmu = dmuAmu + Ax - Axm1;
}
}
}
//Fix the gauge field Umu
//0 < alpha < 1 is related to the step size, cf https://arxiv.org/pdf/1405.5812.pdf
static void SteepestDescentGaugeFix(GaugeLorentz &Umu,Real & alpha,int maxiter,Real Omega_tol, Real Phi_tol,bool Fourier=false,int orthog=-1,bool err_on_no_converge=true) {
GridBase *grid = Umu.Grid();
GaugeMat xform(grid);
SteepestDescentGaugeFix(Umu,xform,alpha,maxiter,Omega_tol,Phi_tol,Fourier,orthog,err_on_no_converge);
}
static void SteepestDescentGaugeFix(GaugeLorentz &Umu,GaugeMat &xform,Real & alpha,int maxiter,Real Omega_tol, Real Phi_tol,bool Fourier=false,int orthog=-1,bool err_on_no_converge=true) {
//Fix the gauge field Umu and also return the gauge transformation from the original gauge field, xform
GridBase *grid = Umu.Grid();
Real org_plaq =WilsonLoops<Gimpl>::avgPlaquette(Umu);
Real org_link_trace=WilsonLoops<Gimpl>::linkTrace(Umu);
Real old_trace = org_link_trace;
Real trG;
xform=1.0;
std::vector<GaugeMat> U(Nd,grid);
GaugeMat dmuAmu(grid);
{
Real plaq =WilsonLoops<Gimpl>::avgPlaquette(Umu);
Real link_trace=WilsonLoops<Gimpl>::linkTrace(Umu);
if( (orthog>=0) && (orthog<Nd) ){
std::cout << GridLogMessage << " Gauge fixing to Coulomb gauge time="<<orthog<< " plaq= "<<plaq<<" link trace = "<<link_trace<< std::endl;
} else {
std::cout << GridLogMessage << " Gauge fixing to Landau gauge plaq= "<<plaq<<" link trace = "<<link_trace<< std::endl;
}
}
for(int i=0;i<maxiter;i++){
for(int mu=0;mu<Nd;mu++) U[mu]= PeekIndex<LorentzIndex>(Umu,mu);
if ( Fourier==false ) {
trG = SteepestDescentStep(U,xform,alpha,dmuAmu,orthog);
} else {
trG = FourierAccelSteepestDescentStep(U,xform,alpha,dmuAmu,orthog);
}
// std::cout << GridLogMessage << "trG "<< trG<< std::endl;
// std::cout << GridLogMessage << "xform "<< norm2(xform)<< std::endl;
// std::cout << GridLogMessage << "dmuAmu "<< norm2(dmuAmu)<< std::endl;
for(int mu=0;mu<Nd;mu++) PokeIndex<LorentzIndex>(Umu,U[mu],mu);
// Monitor progress and convergence test
// infrequently to minimise cost overhead
if ( i %20 == 0 ) {
Real plaq =WilsonLoops<Gimpl>::avgPlaquette(Umu);
Real link_trace=WilsonLoops<Gimpl>::linkTrace(Umu);
if (Fourier)
std::cout << GridLogMessage << "Fourier Iteration "<<i<< " plaq= "<<plaq<< " dmuAmu " << norm2(dmuAmu)<< std::endl;
else
std::cout << GridLogMessage << " Iteration "<<i<< " plaq= "<<plaq<< " dmuAmu " << norm2(dmuAmu)<< std::endl;
Real Phi = 1.0 - old_trace / link_trace ;
Real Omega= 1.0 - trG;
std::cout << GridLogMessage << " Iteration "<<i<< " Phi= "<<Phi<< " Omega= " << Omega<< " trG " << trG <<std::endl;
if ( (Omega < Omega_tol) && ( ::fabs(Phi) < Phi_tol) ) {
std::cout << GridLogMessage << "Converged ! "<<std::endl;
return;
}
old_trace = link_trace;
}
}
std::cout << GridLogError << "Gauge fixing did not converge in " << maxiter << " iterations." << std::endl;
if (err_on_no_converge)
assert(0 && "Gauge fixing did not converge within the specified number of iterations");
};
static Real SteepestDescentStep(std::vector<GaugeMat> &U,GaugeMat &xform, Real alpha, GaugeMat & dmuAmu,int orthog) {
GridBase *grid = U[0].Grid();
GaugeMat g(grid);
ExpiAlphaDmuAmu(U,g,alpha,dmuAmu,orthog);
Real vol = grid->gSites();
Real trG = TensorRemove(sum(trace(g))).real()/vol/Nc;
xform = g*xform ;
SU<Nc>::GaugeTransform<Gimpl>(U,g);
return trG;
}
static Real FourierAccelSteepestDescentStep(std::vector<GaugeMat> &U,GaugeMat &xform, Real alpha, GaugeMat & dmuAmu,int orthog) {
GridBase *grid = U[0].Grid();
Real vol = grid->gSites();
FFT theFFT((GridCartesian *)grid);
LatticeComplex Fp(grid);
LatticeComplex psq(grid); psq=Zero();
LatticeComplex pmu(grid);
LatticeComplex one(grid); one = Complex(1.0,0.0);
GaugeMat g(grid);
GaugeMat dmuAmu_p(grid);
DmuAmu(U,dmuAmu,orthog);
std::vector<int> mask(Nd,1);
for(int mu=0;mu<Nd;mu++) if (mu==orthog) mask[mu]=0;
theFFT.FFT_dim_mask(dmuAmu_p,dmuAmu,mask,FFT::forward);
//////////////////////////////////
// Work out Fp = psq_max/ psq...
// Avoid singularities in Fp
//////////////////////////////////
Coordinate latt_size = grid->GlobalDimensions();
Coordinate coor(grid->_ndimension,0);
for(int mu=0;mu<Nd;mu++) {
if ( mu != orthog ) {
Real TwoPiL = M_PI * 2.0/ latt_size[mu];
LatticeCoordinate(pmu,mu);
pmu = TwoPiL * pmu ;
psq = psq + 4.0*sin(pmu*0.5)*sin(pmu*0.5);
}
}
Complex psqMax(16.0);
Fp = psqMax*one/psq;
pokeSite(TComplex(16.0),Fp,coor);
if( (orthog>=0) && (orthog<Nd) ){
for(int t=0;t<grid->GlobalDimensions()[orthog];t++){
coor[orthog]=t;
pokeSite(TComplex(16.0),Fp,coor);
}
}
dmuAmu_p = dmuAmu_p * Fp;
theFFT.FFT_dim_mask(dmuAmu,dmuAmu_p,mask,FFT::backward);
GaugeMat ciadmam(grid);
Complex cialpha(0.0,-alpha);
ciadmam = dmuAmu*cialpha;
SU<Nc>::taExp(ciadmam,g);
Real trG = TensorRemove(sum(trace(g))).real()/vol/Nc;
xform = g*xform ;
SU<Nc>::GaugeTransform<Gimpl>(U,g);
return trG;
}
static void ExpiAlphaDmuAmu(const std::vector<GaugeMat> &U,GaugeMat &g, Real alpha, GaugeMat &dmuAmu,int orthog) {
GridBase *grid = g.Grid();
Complex cialpha(0.0,-alpha);
GaugeMat ciadmam(grid);
DmuAmu(U,dmuAmu,orthog);
ciadmam = dmuAmu*cialpha;
SU<Nc>::taExp(ciadmam,g);
}
};
NAMESPACE_END(Grid);
#endif
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