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Adding metric and the implicit steps

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This commit is contained in:
Guido Cossu
2017-02-21 11:30:57 +00:00
parent 97a6b61551
commit 902afcfbaf
8 changed files with 287 additions and 59 deletions
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1
lib/qcd/action/Actions.h
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@@ -50,6 +50,7 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
////////////////////////////////////////////
#include <Grid/qcd/action/gauge/GaugeImplementations.h>
#include <Grid/qcd/utils/WilsonLoops.h>
#include <Grid/qcd/utils/Metric.h>
#include <Grid/qcd/utils/CovariantLaplacian.h>
#include <Grid/qcd/action/fermion/WilsonCompressor.h> //used by all wilson type fermions

6
lib/qcd/hmc/HMC_GridModules.h
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@@ -57,7 +57,7 @@ public:
}
template <class ReaderClass>
GridModuleParameters(Reader<ReaderClass>& Reader) {
GridModuleParameters(Reader<ReaderClass>& Reader, std::string n = "LatticeGrid"):name(n) {
read(Reader, name, *this);
check();
}
@@ -69,7 +69,7 @@ public:
write(Writer, name, *this);
}
private:
std::string name = "LatticeGrid";
std::string name;
};
// Lower level class
@@ -94,7 +94,7 @@ class GridModule {
////////////////////////////////////
// Classes for the user
////////////////////////////////////
// Note: the space time grid must be out of the QCD namespace
// Note: the space time grid should be out of the QCD namespace
template< class vector_type>
class GridFourDimModule : public GridModule {
public:

70
lib/qcd/hmc/integrators/Integrator.h
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@@ -77,7 +77,8 @@ class Integrator {
double t_U; // Track time passing on each level and for U and for P
std::vector<double> t_P;
MomentaField P;
//MomentaField P;
GeneralisedMomenta<FieldImplementation, TrivialMetric<MomentaField>> P;
SmearingPolicy& Smearer;
RepresentationPolicy Representations;
IntegratorParameters Params;
@@ -86,7 +87,7 @@ class Integrator {
void update_P(Field& U, int level, double ep) {
t_P[level] += ep;
update_P(P, U, level, ep);
update_P(P.Mom, U, level, ep);
std::cout << GridLogIntegrator << "[" << level << "] P "
<< " dt " << ep << " : t_P " << t_P[level] << std::endl;
@@ -131,51 +132,56 @@ class Integrator {
as[level].apply(update_P_hireps, Representations, Mom, U, ep);
}
void implicit_update_P(MomentaField& Mom, Field& U, int level, double ep) {
void implicit_update_P(Field& U, int level, double ep) {
t_P[level] += ep;
std::cout << GridLogIntegrator << "[" << level << "] P "
<< " dt " << ep << " : t_P " << t_P[level] << std::endl;
// Fundamental updates, include smearing
MomentaField Msum(Mom._grid);
MomentaField Msum(P.Mom._grid);
Msum = zero;
for (int a = 0; a < as[level].actions.size(); ++a) {
// Compute the force
// We need to compute the derivative of the actions
// only once
Field force(U._grid);
conformable(U._grid, Mom._grid);
conformable(U._grid, P.Mom._grid);
Field& Us = Smearer.get_U(as[level].actions.at(a)->is_smeared);
as[level].actions.at(a)->deriv(Us, force); // deriv should NOT include Ta
std::cout << GridLogIntegrator << "Smearing (on/off): " << as[level].actions.at(a)->is_smeared << std::endl;
if (as[level].actions.at(a)->is_smeared) Smearer.smeared_force(force);
force = FieldImplementation::projectForce(force); // Ta for gauge fields
Real force_abs = std::sqrt(norm2(force)/U._grid->gSites());
std::cout << GridLogIntegrator << "Force average: " << force_abs << std::endl;
force = FieldImplementation::projectForce(force); // Ta for gauge fields
Real force_abs = std::sqrt(norm2(force) / U._grid->gSites());
std::cout << GridLogIntegrator << "Force average: " << force_abs
<< std::endl;
Msum += force;
}
MomentaField NewMom = Mom;
MomentaField OldMom = Mom;
MomentaField NewMom = P.Mom;
MomentaField OldMom = P.Mom;
double threshold = 1e-6;
P.M.ImportGauge(U);
// Here run recursively
do{
MomentaField MomDer(Mom._grid);
do {
MomentaField MomDer(P.Mom._grid);
MomentaField X(P.Mom._grid);
OldMom = NewMom;
// Compute the derivative of the kinetic term
// with respect to the gauge field
// Laplacian.Mder(NewMom, MomDer);
// NewMom = Mom - ep*(MomDer + Msum);
P.DerivativeU(NewMom, MomDer);
NewMom = P.Mom - ep * (MomDer + Msum);
} while (norm2(NewMom - OldMom) > threshold);
Mom = NewMom;
P.Mom = NewMom;
// update the auxiliary fields momenta
}
void update_U(Field& U, double ep) {
update_U(P, U, ep);
update_U(P.Mom, U, ep);
t_U += ep;
int fl = levels - 1;
@@ -193,6 +199,27 @@ class Integrator {
Representations.update(U); // void functions if fundamental representation
}
void implicit_update_U(Field&U, double ep){
t_U += ep;
int fl = levels - 1;
std::cout << GridLogIntegrator << " " << "[" << fl << "] U " << " dt " << ep << " : t_U " << t_U << std::endl;
Real threshold = 1e-6;
P.M.ImportGauge(U);
MomentaField Mom1(P.Mom._grid);
MomentaField Mom2(P.Mom._grid);
Field OldU = U;
Field NewU = U;
P.DerivativeP(Mom1); // first term in the derivative
do {
OldU = NewU; // some redundancy to be eliminated
P.DerivativeP(Mom2); // second term in the derivative, on the updated U
FieldImplementation::update_field(Mom1 + Mom2, NewU, ep);
P.M.ImportGauge(NewU);
} while (norm2(NewU - OldU) > threshold);
}
virtual void step(Field& U, int level, int first, int last) = 0;
public:
@@ -249,9 +276,10 @@ class Integrator {
// Initialization of momenta and actions
void refresh(Field& U, GridParallelRNG& pRNG) {
assert(P._grid == U._grid);
assert(P.Mom._grid == U._grid);
std::cout << GridLogIntegrator << "Integrator refresh\n";
FieldImplementation::generate_momenta(P, pRNG);
//FieldImplementation::generate_momenta(P, pRNG);
P.MomentaDistribution(pRNG);
// Update the smeared fields, can be implemented as observer
// necessary to keep the fields updated even after a reject
@@ -297,7 +325,7 @@ class Integrator {
// Calculate action
RealD S(Field& U) { // here also U not used
RealD H = - FieldImplementation::FieldSquareNorm(P); // - trace (P*P)
RealD H = - FieldImplementation::FieldSquareNorm(P.Mom); // - trace (P*P)
RealD Hterm;
std::cout << GridLogMessage << "Momentum action H_p = " << H << "\n";

2
lib/qcd/hmc/integrators/Integrator_algorithm.h
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@@ -335,7 +335,7 @@ class ImplicitLeapFrog : public Integrator<FieldImplementation, SmearingPolicy,
}
if (level == fl) { // lowest level
this->update_U(U, eps);
this->implicit_update_U(U, eps / 2.0);
} else { // recursive function call
this->step(U, level + 1, first_step, last_step);
}

106
lib/qcd/utils/CovariantLaplacian.h
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@@ -33,6 +33,32 @@ directory
namespace Grid {
namespace QCD {
struct LaplacianParams : Serializable {
GRID_SERIALIZABLE_CLASS_MEMBERS(LaplacianParams,
RealD, lo,
RealD, hi,
int, MaxIter,
RealD, tolerance,
int, degree,
int, precision);
// constructor
LaplacianParams(RealD lo = 0.0,
RealD hi = 1.0,
int maxit = 1000,
RealD tol = 1.0e-8,
int degree = 10,
int precision = 64)
: lo(lo),
hi(hi),
MaxIter(maxit),
tolerance(tol),
degree(degree),
precision(precision){};
};
////////////////////////////////////////////////////////////
// Laplacian operator L on adjoint fields
//
@@ -48,12 +74,22 @@ namespace QCD {
////////////////////////////////////////////////////////////
template <class Impl>
class LaplacianAdjointField {
class LaplacianAdjointField: public Metric<typename Impl::Field> {
OperatorFunction<typename Impl::Field> &Solver;
LaplacianParams param;
MultiShiftFunction PowerNegHalf;
public:
INHERIT_GIMPL_TYPES(Impl);
LaplacianAdjointField(GridBase* grid, const RealD k = 1.0) :
U(Nd, grid), kappa(k){};
LaplacianAdjointField(GridBase* grid, OperatorFunction<GaugeField>& S, LaplacianParams& p, const RealD k = 1.0)
: U(Nd, grid), Solver(S), param(p), kappa(k){
AlgRemez remez(param.lo,param.hi,param.precision);
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);
};
void ImportGauge(const GaugeField& _U) {
for (int mu = 0; mu < Nd; mu++) {
@@ -61,41 +97,63 @@ class LaplacianAdjointField {
}
}
void Mdiag(const GaugeLinkField& in, GaugeLinkField& out) { assert(0); }
void Mdir(const GaugeLinkField& in, GaugeLinkField& out, int dir, int disp) {
assert(0);
}
void M(const GaugeLinkField& in, GaugeLinkField& out) {
void M(const GaugeField& in, GaugeField& out) {
GaugeLinkField tmp(in._grid);
GaugeLinkField tmp2(in._grid);
GaugeLinkField sum(in._grid);
sum = zero;
for (int mu = 0; mu < Nd; mu++) {
tmp = U[mu] * Cshift(in, mu, +1) * adj(U[mu]);
tmp2 = adj(U[mu]) * in * U[mu];
sum += tmp + Cshift(tmp2, mu, -1) - 2.0 * in;
for (int nu = 0; nu < Nd; nu++) {
sum = zero;
GaugeLinkField in_nu = PeekIndex<LorentzIndex>(in, nu);
GaugeLinkField out_nu(out._grid);
for (int mu = 0; mu < Nd; mu++) {
tmp = U[mu] * Cshift(in_nu, mu, +1) * adj(U[mu]);
tmp2 = adj(U[mu]) * in_nu * U[mu];
sum += tmp + Cshift(tmp2, mu, -1) - 2.0 * in_nu;
}
out_nu = (1.0 - kappa) * in_nu - kappa / (double(4 * Nd)) * sum;
PokeIndex<LorentzIndex>(out, out_nu, nu);
}
out = (1.0 - kappa) * in - kappa / (double(4 * Nd)) * sum;
}
void MDeriv(const GaugeLinkField& in, GaugeLinkField& out, bool dag){
RealD factor = - kappa / (double(4 * Nd))
if (!dag)
out = factor * Cshift(in, mu, +1) * adj(U[mu]) + adj(U[mu]) * in;
else
out = factor * U[mu] * Cshift(in, mu, +1) + in * U[mu];
void MDeriv(const GaugeField& in, GaugeField& der, bool dag) {
RealD factor = -kappa / (double(4 * Nd));
for (int mu = 0; mu < Nd; mu++) {
GaugeLinkField in_mu = PeekIndex<LorentzIndex>(in, mu);
GaugeLinkField der_mu(der._grid);
if (!dag)
der_mu =
factor * Cshift(in_mu, mu, +1) * adj(U[mu]) + adj(U[mu]) * in_mu;
else
der_mu = factor * U[mu] * Cshift(in_mu, mu, +1) + in_mu * U[mu];
}
}
void Minv(const GaugeField& in, GaugeField& inverted){
HermitianLinearOperator<LaplacianAdjointField<Impl>,GaugeField> HermOp(*this);
Solver(HermOp, in, inverted);
}
void MInvSquareRoot(GaugeField& P){
// Takes a gaussian gauge field and multiplies by the metric
// need the rational approximation for the square root
GaugeField Gp(P._grid);
HermitianLinearOperator<LaplacianAdjointField<Impl>,GaugeField> HermOp(*this);
ConjugateGradientMultiShift<GaugeField> msCG(param.MaxIter,PowerNegHalf);
msCG(HermOp,P,Gp);
P = Gp; // now P has the correct distribution
}
private:
RealD kappa;
std::vector<GaugeLinkField> U;
};
// This is just a debug tests
// not meant to be used
// This is just for debuggin purposes
// not meant to be used by the final users
template <class Impl>
class LaplacianAlgebraField {

121
lib/qcd/utils/Metric.h Normal file
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@@ -0,0 +1,121 @@
/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./lib/qcd/hmc/integrators/Integrator.h
Copyright (C) 2015
Author: Guido Cossu <guido.cossu@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 METRIC_H
#define METRIC_H
namespace Grid{
namespace QCD{
template <typename Field>
class Metric{
public:
virtual void ImportGauge(const Field&) = 0;
virtual void M(const Field&, Field&) = 0;
virtual void Minv(const Field&, Field&) = 0;
virtual void MInvSquareRoot(Field&) = 0;
};
// Need a trivial operator
template <typename Field>
class TrivialMetric : public Metric<Field>{
public:
virtual void ImportGauge(const Field&){};
virtual void M(const Field& in, Field& out){
out = in;
}
virtual void Minv(const Field& in, Field& out){
out = in;
}
virtual void MInvSquareRoot(Field& P){
// do nothing
}
};
///////////////////////////////
// Generalised momenta
///////////////////////////////
template <typename Implementation, typename Metric>
class GeneralisedMomenta{
public:
typedef typename Implementation::Field MomentaField; //for readability
Metric M;
MomentaField Mom;
GeneralisedMomenta(GridBase* grid): Mom(grid){}
void MomentaDistribution(GridParallelRNG& pRNG){
// Generate a distribution for
// 1/2 P^dag G P
// where G = M^-1
// Generate gaussian momenta
Implementation::generate_momenta(Mom, pRNG);
// Modify the distribution with the metric
M.MInvSquareRoot(Mom);
}
void Derivative(MomentaField& in, MomentaField& der){
// Compute the derivative of the kinetic term
// with respect to the gauge field
MomentaField MomDer(in._grid);
MomentaField X(in._grid);
M.Minv(in, X); // X = G in
M.MDeriv(X, MomDer, DaggerNo); // MomDer = dM/dU X
// MomDer is just the derivative
MomDer = adj(X)* MomDer;
// Traceless Antihermitian
// assuming we are in the algebra
der = Implementation::projectForce(MomDer);
}
void DerivativeP(MomentaField& der){
M.Minv(Mom, der);
}
};
}
}
#endif //METRIC_H

32
tests/solver/Test_laplacian.cc
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@@ -50,8 +50,11 @@ int main (int argc, char ** argv)
double Kappa = 0.9999;
std::cout << GridLogMessage << "Running with kappa: " << Kappa << std::endl;
typedef SU<Nc>::LatticeAlgebraVector AVector;
// Source and result in the algebra
// needed for the second test
AVector src_vec(&Grid); random(pRNG, src_vec);
AVector result_vec(&Grid); result_vec = zero;
@@ -59,16 +62,33 @@ int main (int argc, char ** argv)
SU<Nc>::FundamentalLieAlgebraMatrix(src_vec, src);
LatticeColourMatrix result(&Grid); result=zero;
LaplacianAdjointField<PeriodicGimplR> Laplacian(&Grid, Kappa);
Laplacian.ImportGauge(Umu);
HermitianLinearOperator<LaplacianAdjointField<PeriodicGimplR>,LatticeColourMatrix> HermOp(Laplacian);
ConjugateGradient<LatticeColourMatrix> CG(1.0e-8,10000);
// Generate a field of adjoint matrices
LatticeGaugeField src_f(&Grid);
// A matrix in the adjoint
LatticeColourMatrix src_mu(&Grid);
for (int mu = 0; mu < Nd; mu++) {
SU<Nc>::GaussianFundamentalLieAlgebraMatrix(pRNG, src_mu);
PokeIndex<LorentzIndex>(src_f, src_mu, mu);
}
LatticeGaugeField result_f(&Grid);
// Definition of the Laplacian operator
ConjugateGradient<LatticeGaugeField> CG(1.0e-8,10000);
LaplacianParams LapPar(0.001, 1.0, 1000, 1e-8, 10, 64);
LaplacianAdjointField<PeriodicGimplR> Laplacian(&Grid, CG, LapPar, Kappa);
Laplacian.ImportGauge(Umu);
std::cout << GridLogMessage << "Testing the Laplacian using the full matrix" <<std::endl;
CG(HermOp,src,result); // fastest
Laplacian.Minv(src_f, result_f);
Laplacian.MomentaDistribution(src_f);
// Tests also the version using the algebra decomposition
/*
LaplacianAlgebraField<PeriodicGimplR> LaplacianAlgebra(&Grid, Kappa);
LaplacianAlgebra.ImportGauge(Umu);
@@ -82,7 +102,7 @@ int main (int argc, char ** argv)
result2 -= result;
std::cout << GridLogMessage << "Results difference " << norm2(result2) << std::endl;
*/
Grid_finalize();
}