mirror of
https://github.com/paboyle/Grid.git
synced 2025-06-13 04:37:05 +01:00
Merge branch 'develop' into feature/feynman-rules
# Conflicts: # lib/Threads.h # lib/qcd/action/fermion/WilsonFermion.cc # lib/qcd/action/fermion/WilsonFermion.h # lib/qcd/utils/SUn.h # lib/simd/Grid_avx.h # lib/simd/Intel512common.h
This commit is contained in:
@ -1,76 +1,532 @@
|
||||
/*************************************************************************************
|
||||
/*************************************************************************************
|
||||
|
||||
Grid physics library, www.github.com/paboyle/Grid
|
||||
Grid physics library, www.github.com/paboyle/Grid
|
||||
|
||||
Source file: ./tests/Test_lie_generators.cc
|
||||
Source file: ./tests/Test_lie_generators.cc
|
||||
|
||||
Copyright (C) 2015
|
||||
Copyright (C) 2015
|
||||
|
||||
Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
|
||||
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
|
||||
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 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.
|
||||
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.
|
||||
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 */
|
||||
See the full license in the file "LICENSE" in the top level distribution
|
||||
directory
|
||||
*************************************************************************************/
|
||||
/* END LEGAL */
|
||||
#include <Grid/Grid.h>
|
||||
|
||||
#include <Grid/qcd/utils/CovariantCshift.h>
|
||||
|
||||
#include <Grid/qcd/utils/SUn.h>
|
||||
#include <Grid/qcd/utils/SUnAdjoint.h>
|
||||
#include <Grid/qcd/utils/SUnTwoIndex.h>
|
||||
|
||||
#include <Grid/qcd/representations/adjoint.h>
|
||||
#include <Grid/qcd/representations/two_index.h>
|
||||
#include <Grid/qcd/utils/WilsonLoops.h>
|
||||
|
||||
using namespace std;
|
||||
using namespace Grid;
|
||||
using namespace Grid::QCD;
|
||||
|
||||
int main(int argc, char** argv) {
|
||||
Grid_init(&argc, &argv);
|
||||
|
||||
int main (int argc, char ** argv)
|
||||
{
|
||||
Grid_init(&argc,&argv);
|
||||
std::vector<int> latt({4, 4, 4, 8});
|
||||
GridCartesian* grid = SpaceTimeGrid::makeFourDimGrid(
|
||||
latt, GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
|
||||
|
||||
std::vector<int> latt({4,4,4,8});
|
||||
GridCartesian * grid = SpaceTimeGrid::makeFourDimGrid(latt,
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||||
GridDefaultSimd(Nd,vComplex::Nsimd()),
|
||||
GridDefaultMpi());
|
||||
|
||||
GridRedBlackCartesian * rbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(grid);
|
||||
GridRedBlackCartesian* rbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(grid);
|
||||
|
||||
std::cout<<GridLogMessage<<"*********************************************"<<std::endl;
|
||||
std::cout<<GridLogMessage<<"* Generators for SU(2)"<<std::endl;
|
||||
std::cout<<GridLogMessage<<"*********************************************"<<std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for SU(2)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
SU2::printGenerators();
|
||||
std::cout << "Dimension of adjoint representation: "<< SU2Adjoint::Dimension << std::endl;
|
||||
SU2Adjoint::printGenerators();
|
||||
SU2::testGenerators();
|
||||
SU2Adjoint::testGenerators();
|
||||
|
||||
std::cout<<GridLogMessage<<"*********************************************"<<std::endl;
|
||||
std::cout<<GridLogMessage<<"* Generators for SU(3)"<<std::endl;
|
||||
std::cout<<GridLogMessage<<"*********************************************"<<std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for SU(3)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
SU3::printGenerators();
|
||||
std::cout << "Dimension of adjoint representation: "<< SU3Adjoint::Dimension << std::endl;
|
||||
SU3Adjoint::printGenerators();
|
||||
SU3::testGenerators();
|
||||
SU3Adjoint::testGenerators();
|
||||
|
||||
// std::cout<<GridLogMessage<<"*********************************************"<<std::endl;
|
||||
// std::cout<<GridLogMessage<<"* Generators for SU(4)"<<std::endl;
|
||||
// std::cout<<GridLogMessage<<"*********************************************"<<std::endl;
|
||||
// SU4::printGenerators();
|
||||
// SU4::testGenerators();
|
||||
std::cout<<GridLogMessage<<"*********************************************"<<std::endl;
|
||||
std::cout<<GridLogMessage<<"* Generators for SU(4)"<<std::endl;
|
||||
std::cout<<GridLogMessage<<"*********************************************"<<std::endl;
|
||||
SU4::printGenerators();
|
||||
std::cout << "Dimension of adjoint representation: "<< SU4Adjoint::Dimension << std::endl;
|
||||
SU4Adjoint::printGenerators();
|
||||
SU4::testGenerators();
|
||||
SU4Adjoint::testGenerators();
|
||||
|
||||
// std::cout<<GridLogMessage<<"*********************************************"<<std::endl;
|
||||
// std::cout<<GridLogMessage<<"* Generators for SU(5)"<<std::endl;
|
||||
// std::cout<<GridLogMessage<<"*********************************************"<<std::endl;
|
||||
// SU5::printGenerators();
|
||||
// SU5::testGenerators();
|
||||
// Projectors
|
||||
GridParallelRNG gridRNG(grid);
|
||||
gridRNG.SeedRandomDevice();
|
||||
SU3Adjoint::LatticeAdjMatrix Gauss(grid);
|
||||
SU3::LatticeAlgebraVector ha(grid);
|
||||
SU3::LatticeAlgebraVector hb(grid);
|
||||
random(gridRNG,Gauss);
|
||||
|
||||
std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
|
||||
SU3Adjoint::projectOnAlgebra(ha, Gauss);
|
||||
std::cout << GridLogMessage << "end projectOnAlgebra" << std::endl;
|
||||
std::cout << GridLogMessage << "Start projector" << std::endl;
|
||||
SU3Adjoint::projector(hb, Gauss);
|
||||
std::cout << GridLogMessage << "end projector" << std::endl;
|
||||
|
||||
std::cout << GridLogMessage << "ReStart projector" << std::endl;
|
||||
SU3Adjoint::projector(hb, Gauss);
|
||||
std::cout << GridLogMessage << "end projector" << std::endl;
|
||||
SU3::LatticeAlgebraVector diff = ha -hb;
|
||||
std::cout << GridLogMessage << "Difference: " << norm2(diff) << std::endl;
|
||||
|
||||
|
||||
Grid_finalize();
|
||||
// Testing HMC representation classes
|
||||
AdjointRep<Nc> AdjRep(grid);
|
||||
|
||||
// AdjointRepresentation has the predefined number of colours Nc
|
||||
Representations<FundamentalRepresentation, AdjointRepresentation, TwoIndexSymmetricRepresentation> RepresentationTypes(grid);
|
||||
|
||||
|
||||
LatticeGaugeField U(grid), V(grid);
|
||||
SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, U);
|
||||
SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, V);
|
||||
|
||||
// Adjoint representation
|
||||
// Test group structure
|
||||
// (U_f * V_f)_r = U_r * V_r
|
||||
LatticeGaugeField UV(grid);
|
||||
UV = zero;
|
||||
for (int mu = 0; mu < Nd; mu++) {
|
||||
SU<Nc>::LatticeMatrix Umu = peekLorentz(U,mu);
|
||||
SU<Nc>::LatticeMatrix Vmu = peekLorentz(V,mu);
|
||||
pokeLorentz(UV,Umu*Vmu, mu);
|
||||
}
|
||||
|
||||
AdjRep.update_representation(UV);
|
||||
typename AdjointRep<Nc>::LatticeField UVr = AdjRep.U; // (U_f * V_f)_r
|
||||
|
||||
|
||||
AdjRep.update_representation(U);
|
||||
typename AdjointRep<Nc>::LatticeField Ur = AdjRep.U; // U_r
|
||||
|
||||
AdjRep.update_representation(V);
|
||||
typename AdjointRep<Nc>::LatticeField Vr = AdjRep.U; // V_r
|
||||
|
||||
typename AdjointRep<Nc>::LatticeField UrVr(grid);
|
||||
UrVr = zero;
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||||
for (int mu = 0; mu < Nd; mu++) {
|
||||
typename AdjointRep<Nc>::LatticeMatrix Urmu = peekLorentz(Ur,mu);
|
||||
typename AdjointRep<Nc>::LatticeMatrix Vrmu = peekLorentz(Vr,mu);
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||||
pokeLorentz(UrVr,Urmu*Vrmu, mu);
|
||||
}
|
||||
|
||||
typename AdjointRep<Nc>::LatticeField Diff_check = UVr - UrVr;
|
||||
std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Adjoint representation) : " << norm2(Diff_check) << std::endl;
|
||||
|
||||
// Check correspondence of algebra and group transformations
|
||||
// Create a random vector
|
||||
SU<Nc>::LatticeAlgebraVector h_adj(grid);
|
||||
typename AdjointRep<Nc>::LatticeMatrix Ar(grid);
|
||||
random(gridRNG,h_adj);
|
||||
h_adj = real(h_adj);
|
||||
SU_Adjoint<Nc>::AdjointLieAlgebraMatrix(h_adj,Ar);
|
||||
|
||||
// Re-extract h_adj
|
||||
SU<Nc>::LatticeAlgebraVector h_adj2(grid);
|
||||
SU_Adjoint<Nc>::projectOnAlgebra(h_adj2, Ar);
|
||||
SU<Nc>::LatticeAlgebraVector h_diff = h_adj - h_adj2;
|
||||
std::cout << GridLogMessage << "Projections structure check vector difference (Adjoint representation) : " << norm2(h_diff) << std::endl;
|
||||
|
||||
// Exponentiate
|
||||
typename AdjointRep<Nc>::LatticeMatrix Uadj(grid);
|
||||
Uadj = expMat(Ar, 1.0, 16);
|
||||
|
||||
typename AdjointRep<Nc>::LatticeMatrix uno(grid);
|
||||
uno = 1.0;
|
||||
// Check matrix Uadj, must be real orthogonal
|
||||
typename AdjointRep<Nc>::LatticeMatrix Ucheck = Uadj - conjugate(Uadj);
|
||||
std::cout << GridLogMessage << "Reality check: " << norm2(Ucheck)
|
||||
<< std::endl;
|
||||
|
||||
Ucheck = Uadj * adj(Uadj) - uno;
|
||||
std::cout << GridLogMessage << "orthogonality check 1: " << norm2(Ucheck)
|
||||
<< std::endl;
|
||||
Ucheck = adj(Uadj) * Uadj - uno;
|
||||
std::cout << GridLogMessage << "orthogonality check 2: " << norm2(Ucheck)
|
||||
<< std::endl;
|
||||
|
||||
|
||||
// Construct the fundamental matrix in the group
|
||||
SU<Nc>::LatticeMatrix Af(grid);
|
||||
SU<Nc>::FundamentalLieAlgebraMatrix(h_adj,Af);
|
||||
SU<Nc>::LatticeMatrix Ufund(grid);
|
||||
Ufund = expMat(Af, 1.0, 16);
|
||||
// Check unitarity
|
||||
SU<Nc>::LatticeMatrix uno_f(grid);
|
||||
uno_f = 1.0;
|
||||
SU<Nc>::LatticeMatrix UnitCheck(grid);
|
||||
UnitCheck = Ufund * adj(Ufund) - uno_f;
|
||||
std::cout << GridLogMessage << "unitarity check 1: " << norm2(UnitCheck)
|
||||
<< std::endl;
|
||||
UnitCheck = adj(Ufund) * Ufund - uno_f;
|
||||
std::cout << GridLogMessage << "unitarity check 2: " << norm2(UnitCheck)
|
||||
<< std::endl;
|
||||
|
||||
|
||||
// Tranform to the adjoint representation
|
||||
U = zero; // fill this with only one direction
|
||||
pokeLorentz(U,Ufund,0); // the representation transf acts on full gauge fields
|
||||
|
||||
AdjRep.update_representation(U);
|
||||
Ur = AdjRep.U; // U_r
|
||||
typename AdjointRep<Nc>::LatticeMatrix Ur0 = peekLorentz(Ur,0); // this should be the same as Uadj
|
||||
|
||||
typename AdjointRep<Nc>::LatticeMatrix Diff_check_mat = Ur0 - Uadj;
|
||||
std::cout << GridLogMessage << "Projections structure check group difference : " << norm2(Diff_check_mat) << std::endl;
|
||||
|
||||
|
||||
|
||||
|
||||
// TwoIndexRep tests
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
|
||||
|
||||
std::cout << GridLogMessage << "* eS^{ij} base for SU(2)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "Dimension of Two Index Symmetric representation: "<< SU2TwoIndexSymm::Dimension << std::endl;
|
||||
SU2TwoIndexSymm::printBase();
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "Generators of Two Index Symmetric representation: "<< SU2TwoIndexSymm::Dimension << std::endl;
|
||||
SU2TwoIndexSymm::printGenerators();
|
||||
std::cout << GridLogMessage << "Test of Two Index Symmetric Generators: "<< SU2TwoIndexSymm::Dimension << std::endl;
|
||||
SU2TwoIndexSymm::testGenerators();
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* eAS^{ij} base for SU(2)" << std::endl;
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "Dimension of Two Index anti-Symmetric representation: "<< SU2TwoIndexAntiSymm::Dimension << std::endl;
|
||||
SU2TwoIndexAntiSymm::printBase();
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "Dimension of Two Index anti-Symmetric representation: "<< SU2TwoIndexAntiSymm::Dimension << std::endl;
|
||||
SU2TwoIndexAntiSymm::printGenerators();
|
||||
std::cout << GridLogMessage << "Test of Two Index anti-Symmetric Generators: "<< SU2TwoIndexAntiSymm::Dimension << std::endl;
|
||||
SU2TwoIndexAntiSymm::testGenerators();
|
||||
|
||||
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "Test for the Two Index Symmetric projectors"
|
||||
<< std::endl;
|
||||
// Projectors
|
||||
SU3TwoIndexSymm::LatticeTwoIndexMatrix Gauss2(grid);
|
||||
random(gridRNG,Gauss2);
|
||||
|
||||
std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
|
||||
SU3TwoIndexSymm::projectOnAlgebra(ha, Gauss2);
|
||||
std::cout << GridLogMessage << "end projectOnAlgebra" << std::endl;
|
||||
std::cout << GridLogMessage << "Start projector" << std::endl;
|
||||
SU3TwoIndexSymm::projector(hb, Gauss2);
|
||||
std::cout << GridLogMessage << "end projector" << std::endl;
|
||||
|
||||
std::cout << GridLogMessage << "ReStart projector" << std::endl;
|
||||
SU3TwoIndexSymm::projector(hb, Gauss2);
|
||||
std::cout << GridLogMessage << "end projector" << std::endl;
|
||||
SU3::LatticeAlgebraVector diff2 = ha - hb;
|
||||
std::cout << GridLogMessage << "Difference: " << norm2(diff) << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "Test for the Two index anti-Symmetric projectors"
|
||||
<< std::endl;
|
||||
// Projectors
|
||||
SU3TwoIndexAntiSymm::LatticeTwoIndexMatrix Gauss2a(grid);
|
||||
random(gridRNG,Gauss2a);
|
||||
|
||||
std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
|
||||
SU3TwoIndexAntiSymm::projectOnAlgebra(ha, Gauss2a);
|
||||
std::cout << GridLogMessage << "end projectOnAlgebra" << std::endl;
|
||||
std::cout << GridLogMessage << "Start projector" << std::endl;
|
||||
SU3TwoIndexAntiSymm::projector(hb, Gauss2a);
|
||||
std::cout << GridLogMessage << "end projector" << std::endl;
|
||||
|
||||
std::cout << GridLogMessage << "ReStart projector" << std::endl;
|
||||
SU3TwoIndexAntiSymm::projector(hb, Gauss2a);
|
||||
std::cout << GridLogMessage << "end projector" << std::endl;
|
||||
SU3::LatticeAlgebraVector diff2a = ha - hb;
|
||||
std::cout << GridLogMessage << "Difference: " << norm2(diff2a) << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
|
||||
std::cout << GridLogMessage << "Two index Symmetric: Checking Group Structure"
|
||||
<< std::endl;
|
||||
// Testing HMC representation classes
|
||||
TwoIndexRep< Nc, Symmetric > TIndexRep(grid);
|
||||
|
||||
// Test group structure
|
||||
// (U_f * V_f)_r = U_r * V_r
|
||||
LatticeGaugeField U2(grid), V2(grid);
|
||||
SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, U2);
|
||||
SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, V2);
|
||||
|
||||
LatticeGaugeField UV2(grid);
|
||||
UV2 = zero;
|
||||
for (int mu = 0; mu < Nd; mu++) {
|
||||
SU<Nc>::LatticeMatrix Umu2 = peekLorentz(U2,mu);
|
||||
SU<Nc>::LatticeMatrix Vmu2 = peekLorentz(V2,mu);
|
||||
pokeLorentz(UV2,Umu2*Vmu2, mu);
|
||||
}
|
||||
|
||||
TIndexRep.update_representation(UV2);
|
||||
typename TwoIndexRep< Nc, Symmetric >::LatticeField UVr2 = TIndexRep.U; // (U_f * V_f)_r
|
||||
|
||||
TIndexRep.update_representation(U2);
|
||||
typename TwoIndexRep< Nc, Symmetric >::LatticeField Ur2 = TIndexRep.U; // U_r
|
||||
|
||||
TIndexRep.update_representation(V2);
|
||||
typename TwoIndexRep< Nc, Symmetric >::LatticeField Vr2 = TIndexRep.U; // V_r
|
||||
|
||||
typename TwoIndexRep< Nc, Symmetric >::LatticeField Ur2Vr2(grid);
|
||||
Ur2Vr2 = zero;
|
||||
for (int mu = 0; mu < Nd; mu++) {
|
||||
typename TwoIndexRep< Nc, Symmetric >::LatticeMatrix Urmu2 = peekLorentz(Ur2,mu);
|
||||
typename TwoIndexRep< Nc, Symmetric >::LatticeMatrix Vrmu2 = peekLorentz(Vr2,mu);
|
||||
pokeLorentz(Ur2Vr2,Urmu2*Vrmu2, mu);
|
||||
}
|
||||
|
||||
typename TwoIndexRep< Nc, Symmetric >::LatticeField Diff_check2 = UVr2 - Ur2Vr2;
|
||||
std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Two Index Symmetric): " << norm2(Diff_check2) << std::endl;
|
||||
|
||||
|
||||
// Check correspondence of algebra and group transformations
|
||||
// Create a random vector
|
||||
SU<Nc>::LatticeAlgebraVector h_sym(grid);
|
||||
typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ar_sym(grid);
|
||||
random(gridRNG,h_sym);
|
||||
h_sym = real(h_sym);
|
||||
SU_TwoIndex<Nc,Symmetric>::TwoIndexLieAlgebraMatrix(h_sym,Ar_sym);
|
||||
|
||||
// Re-extract h_sym
|
||||
SU<Nc>::LatticeAlgebraVector h_sym2(grid);
|
||||
SU_TwoIndex< Nc, Symmetric>::projectOnAlgebra(h_sym2, Ar_sym);
|
||||
SU<Nc>::LatticeAlgebraVector h_diff_sym = h_sym - h_sym2;
|
||||
std::cout << GridLogMessage << "Projections structure check vector difference (Two Index Symmetric): " << norm2(h_diff_sym) << std::endl;
|
||||
|
||||
|
||||
// Exponentiate
|
||||
typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix U2iS(grid);
|
||||
U2iS = expMat(Ar_sym, 1.0, 16);
|
||||
|
||||
typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix uno2iS(grid);
|
||||
uno2iS = 1.0;
|
||||
// Check matrix U2iS, must be real orthogonal
|
||||
typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ucheck2iS = U2iS - conjugate(U2iS);
|
||||
std::cout << GridLogMessage << "Reality check: " << norm2(Ucheck2iS)
|
||||
<< std::endl;
|
||||
|
||||
Ucheck2iS = U2iS * adj(U2iS) - uno2iS;
|
||||
std::cout << GridLogMessage << "orthogonality check 1: " << norm2(Ucheck2iS)
|
||||
<< std::endl;
|
||||
Ucheck2iS = adj(U2iS) * U2iS - uno2iS;
|
||||
std::cout << GridLogMessage << "orthogonality check 2: " << norm2(Ucheck2iS)
|
||||
<< std::endl;
|
||||
|
||||
|
||||
|
||||
// Construct the fundamental matrix in the group
|
||||
SU<Nc>::LatticeMatrix Af_sym(grid);
|
||||
SU<Nc>::FundamentalLieAlgebraMatrix(h_sym,Af_sym);
|
||||
SU<Nc>::LatticeMatrix Ufund2(grid);
|
||||
Ufund2 = expMat(Af_sym, 1.0, 16);
|
||||
SU<Nc>::LatticeMatrix UnitCheck2(grid);
|
||||
UnitCheck2 = Ufund2 * adj(Ufund2) - uno_f;
|
||||
std::cout << GridLogMessage << "unitarity check 1: " << norm2(UnitCheck2)
|
||||
<< std::endl;
|
||||
UnitCheck2 = adj(Ufund2) * Ufund2 - uno_f;
|
||||
std::cout << GridLogMessage << "unitarity check 2: " << norm2(UnitCheck2)
|
||||
<< std::endl;
|
||||
|
||||
|
||||
// Tranform to the 2Index Sym representation
|
||||
U = zero; // fill this with only one direction
|
||||
pokeLorentz(U,Ufund2,0); // the representation transf acts on full gauge fields
|
||||
|
||||
TIndexRep.update_representation(U);
|
||||
Ur2 = TIndexRep.U; // U_r
|
||||
typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ur02 = peekLorentz(Ur2,0); // this should be the same as U2iS
|
||||
|
||||
typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Diff_check_mat2 = Ur02 - U2iS;
|
||||
std::cout << GridLogMessage << "Projections structure check group difference (Two Index Symmetric): " << norm2(Diff_check_mat2) << std::endl;
|
||||
|
||||
|
||||
|
||||
|
||||
if (TwoIndexRep<Nc, AntiSymmetric >::Dimension != 1){
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
|
||||
std::cout << GridLogMessage << "Two Index anti-Symmetric: Check Group Structure"
|
||||
<< std::endl;
|
||||
// Testing HMC representation classes
|
||||
TwoIndexRep< Nc, AntiSymmetric > TIndexRepA(grid);
|
||||
|
||||
|
||||
// Test group structure
|
||||
// (U_f * V_f)_r = U_r * V_r
|
||||
LatticeGaugeField U2A(grid), V2A(grid);
|
||||
SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, U2A);
|
||||
SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, V2A);
|
||||
|
||||
LatticeGaugeField UV2A(grid);
|
||||
UV2A = zero;
|
||||
for (int mu = 0; mu < Nd; mu++) {
|
||||
SU<Nc>::LatticeMatrix Umu2A = peekLorentz(U2,mu);
|
||||
SU<Nc>::LatticeMatrix Vmu2A = peekLorentz(V2,mu);
|
||||
pokeLorentz(UV2A,Umu2A*Vmu2A, mu);
|
||||
}
|
||||
|
||||
TIndexRep.update_representation(UV2A);
|
||||
typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField UVr2A = TIndexRepA.U; // (U_f * V_f)_r
|
||||
|
||||
TIndexRep.update_representation(U2A);
|
||||
typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField Ur2A = TIndexRepA.U; // U_r
|
||||
|
||||
TIndexRep.update_representation(V2A);
|
||||
typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField Vr2A = TIndexRepA.U; // V_r
|
||||
|
||||
typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField Ur2Vr2A(grid);
|
||||
Ur2Vr2A = zero;
|
||||
for (int mu = 0; mu < Nd; mu++) {
|
||||
typename TwoIndexRep< Nc, AntiSymmetric >::LatticeMatrix Urmu2A = peekLorentz(Ur2A,mu);
|
||||
typename TwoIndexRep< Nc, AntiSymmetric >::LatticeMatrix Vrmu2A = peekLorentz(Vr2A,mu);
|
||||
pokeLorentz(Ur2Vr2A,Urmu2A*Vrmu2A, mu);
|
||||
}
|
||||
|
||||
typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField Diff_check2A = UVr2A - Ur2Vr2A;
|
||||
std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Two Index anti-Symmetric): " << norm2(Diff_check2A) << std::endl;
|
||||
|
||||
|
||||
// Check correspondence of algebra and group transformations
|
||||
// Create a random vector
|
||||
SU<Nc>::LatticeAlgebraVector h_Asym(grid);
|
||||
typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ar_Asym(grid);
|
||||
random(gridRNG,h_Asym);
|
||||
h_Asym = real(h_Asym);
|
||||
SU_TwoIndex< Nc, AntiSymmetric>::TwoIndexLieAlgebraMatrix(h_Asym,Ar_Asym);
|
||||
|
||||
// Re-extract h_sym
|
||||
SU<Nc>::LatticeAlgebraVector h_Asym2(grid);
|
||||
SU_TwoIndex< Nc, AntiSymmetric>::projectOnAlgebra(h_Asym2, Ar_Asym);
|
||||
SU<Nc>::LatticeAlgebraVector h_diff_Asym = h_Asym - h_Asym2;
|
||||
std::cout << GridLogMessage << "Projections structure check vector difference (Two Index anti-Symmetric): " << norm2(h_diff_Asym) << std::endl;
|
||||
|
||||
|
||||
// Exponentiate
|
||||
typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix U2iAS(grid);
|
||||
U2iAS = expMat(Ar_Asym, 1.0, 16);
|
||||
|
||||
typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix uno2iAS(grid);
|
||||
uno2iAS = 1.0;
|
||||
// Check matrix U2iS, must be real orthogonal
|
||||
typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ucheck2iAS = U2iAS - conjugate(U2iAS);
|
||||
std::cout << GridLogMessage << "Reality check: " << norm2(Ucheck2iAS)
|
||||
<< std::endl;
|
||||
|
||||
Ucheck2iAS = U2iAS * adj(U2iAS) - uno2iAS;
|
||||
std::cout << GridLogMessage << "orthogonality check 1: " << norm2(Ucheck2iAS)
|
||||
<< std::endl;
|
||||
Ucheck2iAS = adj(U2iAS) * U2iAS - uno2iAS;
|
||||
std::cout << GridLogMessage << "orthogonality check 2: " << norm2(Ucheck2iAS)
|
||||
<< std::endl;
|
||||
|
||||
|
||||
|
||||
// Construct the fundamental matrix in the group
|
||||
SU<Nc>::LatticeMatrix Af_Asym(grid);
|
||||
SU<Nc>::FundamentalLieAlgebraMatrix(h_Asym,Af_Asym);
|
||||
SU<Nc>::LatticeMatrix Ufund2A(grid);
|
||||
Ufund2A = expMat(Af_Asym, 1.0, 16);
|
||||
SU<Nc>::LatticeMatrix UnitCheck2A(grid);
|
||||
UnitCheck2A = Ufund2A * adj(Ufund2A) - uno_f;
|
||||
std::cout << GridLogMessage << "unitarity check 1: " << norm2(UnitCheck2A)
|
||||
<< std::endl;
|
||||
UnitCheck2A = adj(Ufund2A) * Ufund2A - uno_f;
|
||||
std::cout << GridLogMessage << "unitarity check 2: " << norm2(UnitCheck2A)
|
||||
<< std::endl;
|
||||
|
||||
|
||||
// Tranform to the 2Index Sym representation
|
||||
U = zero; // fill this with only one direction
|
||||
pokeLorentz(U,Ufund2A,0); // the representation transf acts on full gauge fields
|
||||
|
||||
TIndexRepA.update_representation(U);
|
||||
Ur2A = TIndexRepA.U; // U_r
|
||||
typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ur02A = peekLorentz(Ur2A,0); // this should be the same as U2iS
|
||||
|
||||
typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Diff_check_mat2A = Ur02A - U2iAS;
|
||||
std::cout << GridLogMessage << "Projections structure check group difference (Two Index anti-Symmetric): " << norm2(Diff_check_mat2A) << std::endl;
|
||||
|
||||
} else {
|
||||
std::cout << GridLogMessage << "Skipping Two Index anti-Symmetric tests "
|
||||
"because representation is trivial (dim = 1)"
|
||||
<< std::endl;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Grid_finalize();
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user