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b512ccbee6
Accepts and reproduces known results Check initial instability of inverters when starting from hot configurations
215 lines
8.0 KiB
C++
215 lines
8.0 KiB
C++
/*************************************************************************************
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Grid physics library, www.github.com/paboyle/Grid
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Source file: ./tests/Test_lie_generators.cc
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Copyright (C) 2015
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Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
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Author: Peter Boyle <paboyle@ph.ed.ac.uk>
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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
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directory
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*************************************************************************************/
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/* END LEGAL */
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#include <Grid.h>
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#include <qcd/utils/CovariantCshift.h>
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#include <qcd/utils/SUn.h>
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#include <qcd/utils/SUnAdjoint.h>
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#include <qcd/representations/adjoint.h>
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#include <qcd/utils/WilsonLoops.h>
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using namespace std;
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using namespace Grid;
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using namespace Grid::QCD;
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int main(int argc, char** argv) {
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Grid_init(&argc, &argv);
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std::vector<int> latt({4, 4, 4, 8});
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GridCartesian* grid = SpaceTimeGrid::makeFourDimGrid(
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latt, GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
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GridRedBlackCartesian* rbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(grid);
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std::cout << GridLogMessage << "*********************************************"
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<< std::endl;
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std::cout << GridLogMessage << "* Generators for SU(2)" << std::endl;
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std::cout << GridLogMessage << "*********************************************"
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<< std::endl;
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SU2::printGenerators();
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std::cout << "Dimension of adjoint representation: "<< SU2Adjoint::Dimension << std::endl;
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SU2Adjoint::printGenerators();
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SU2::testGenerators();
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SU2Adjoint::testGenerators();
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std::cout << GridLogMessage << "*********************************************"
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<< std::endl;
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std::cout << GridLogMessage << "* Generators for SU(3)" << std::endl;
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std::cout << GridLogMessage << "*********************************************"
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<< std::endl;
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SU3::printGenerators();
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std::cout << "Dimension of adjoint representation: "<< SU3Adjoint::Dimension << std::endl;
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SU3Adjoint::printGenerators();
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SU3::testGenerators();
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SU3Adjoint::testGenerators();
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std::cout<<GridLogMessage<<"*********************************************"<<std::endl;
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std::cout<<GridLogMessage<<"* Generators for SU(4)"<<std::endl;
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std::cout<<GridLogMessage<<"*********************************************"<<std::endl;
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SU4::printGenerators();
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std::cout << "Dimension of adjoint representation: "<< SU4Adjoint::Dimension << std::endl;
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SU4Adjoint::printGenerators();
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SU4::testGenerators();
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SU4Adjoint::testGenerators();
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// std::cout<<GridLogMessage<<"*********************************************"<<std::endl;
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// std::cout<<GridLogMessage<<"* Generators for SU(5)"<<std::endl;
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// std::cout<<GridLogMessage<<"*********************************************"<<std::endl;
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// SU5::printGenerators();
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// SU5::testGenerators();
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// Projectors
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GridParallelRNG gridRNG(grid);
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gridRNG.SeedRandomDevice();
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SU3Adjoint::LatticeAdjMatrix Gauss(grid);
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SU3::LatticeAlgebraVector ha(grid);
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SU3::LatticeAlgebraVector hb(grid);
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random(gridRNG,Gauss);
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std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
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SU3Adjoint::projectOnAlgebra(ha, Gauss);
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std::cout << GridLogMessage << "end projectOnAlgebra" << std::endl;
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std::cout << GridLogMessage << "Start projector" << std::endl;
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SU3Adjoint::projector(hb, Gauss);
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std::cout << GridLogMessage << "end projector" << std::endl;
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std::cout << GridLogMessage << "ReStart projector" << std::endl;
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SU3Adjoint::projector(hb, Gauss);
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std::cout << GridLogMessage << "end projector" << std::endl;
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SU3::LatticeAlgebraVector diff = ha -hb;
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std::cout << GridLogMessage << "Difference: " << norm2(diff) << std::endl;
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// Testing HMC representation classes
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AdjointRep<Nc> AdjRep(grid);
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// AdjointRepresentation has the predefined number of colours Nc
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Representations<FundamentalRepresentation, AdjointRepresentation> RepresentationTypes(grid);
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LatticeGaugeField U(grid), V(grid);
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SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, U);
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SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, V);
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// Test group structure
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// (U_f * V_f)_r = U_r * V_r
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LatticeGaugeField UV(grid);
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UV = zero;
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for (int mu = 0; mu < Nd; mu++) {
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SU<Nc>::LatticeMatrix Umu = peekLorentz(U,mu);
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SU<Nc>::LatticeMatrix Vmu = peekLorentz(V,mu);
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pokeLorentz(UV,Umu*Vmu, mu);
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}
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AdjRep.update_representation(UV);
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typename AdjointRep<Nc>::LatticeField UVr = AdjRep.U; // (U_f * V_f)_r
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AdjRep.update_representation(U);
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typename AdjointRep<Nc>::LatticeField Ur = AdjRep.U; // U_r
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AdjRep.update_representation(V);
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typename AdjointRep<Nc>::LatticeField Vr = AdjRep.U; // V_r
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typename AdjointRep<Nc>::LatticeField UrVr(grid);
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UrVr = zero;
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for (int mu = 0; mu < Nd; mu++) {
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typename AdjointRep<Nc>::LatticeMatrix Urmu = peekLorentz(Ur,mu);
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typename AdjointRep<Nc>::LatticeMatrix Vrmu = peekLorentz(Vr,mu);
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pokeLorentz(UrVr,Urmu*Vrmu, mu);
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}
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typename AdjointRep<Nc>::LatticeField Diff_check = UVr - UrVr;
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std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference : " << norm2(Diff_check) << std::endl;
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// Check correspondence of algebra and group transformations
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// Create a random vector
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SU<Nc>::LatticeAlgebraVector h_adj(grid);
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typename AdjointRep<Nc>::LatticeMatrix Ar(grid);
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random(gridRNG,h_adj);
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h_adj = real(h_adj);
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SU_Adjoint<Nc>::AdjointLieAlgebraMatrix(h_adj,Ar);
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// Re-extract h_adj
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SU<Nc>::LatticeAlgebraVector h_adj2(grid);
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SU_Adjoint<Nc>::projectOnAlgebra(h_adj2, Ar);
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SU<Nc>::LatticeAlgebraVector h_diff = h_adj - h_adj2;
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std::cout << GridLogMessage << "Projections structure check vector difference : " << norm2(h_diff) << std::endl;
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// Exponentiate
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typename AdjointRep<Nc>::LatticeMatrix Uadj(grid);
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Uadj = expMat(Ar, 1.0, 16);
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typename AdjointRep<Nc>::LatticeMatrix uno(grid);
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uno = 1.0;
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// Check matrix Uadj, must be real orthogonal
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typename AdjointRep<Nc>::LatticeMatrix Ucheck = Uadj - conjugate(Uadj);
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std::cout << GridLogMessage << "Reality check: " << norm2(Ucheck)
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<< std::endl;
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Ucheck = Uadj * adj(Uadj) - uno;
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std::cout << GridLogMessage << "orthogonality check 1: " << norm2(Ucheck)
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<< std::endl;
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Ucheck = adj(Uadj) * Uadj - uno;
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std::cout << GridLogMessage << "orthogonality check 2: " << norm2(Ucheck)
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<< std::endl;
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// Construct the fundamental matrix in the group
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SU<Nc>::LatticeMatrix Af(grid);
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SU<Nc>::FundamentalLieAlgebraMatrix(h_adj,Af);
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SU<Nc>::LatticeMatrix Ufund(grid);
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Ufund = expMat(Af, 1.0, 16);
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// Check unitarity
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SU<Nc>::LatticeMatrix uno_f(grid);
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uno_f = 1.0;
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SU<Nc>::LatticeMatrix UnitCheck(grid);
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UnitCheck = Ufund * adj(Ufund) - uno_f;
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std::cout << GridLogMessage << "unitarity check 1: " << norm2(UnitCheck)
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<< std::endl;
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UnitCheck = adj(Ufund) * Ufund - uno_f;
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std::cout << GridLogMessage << "unitarity check 2: " << norm2(UnitCheck)
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<< std::endl;
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// Tranform to the adjoint representation
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U = zero; // fill this with only one direction
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pokeLorentz(U,Ufund,0); // the representation transf acts on full gauge fields
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AdjRep.update_representation(U);
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Ur = AdjRep.U; // U_r
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typename AdjointRep<Nc>::LatticeMatrix Ur0 = peekLorentz(Ur,0); // this should be the same as Uadj
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typename AdjointRep<Nc>::LatticeMatrix Diff_check_mat = Ur0 - Uadj;
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std::cout << GridLogMessage << "Projections structure check group difference : " << norm2(Diff_check_mat) << std::endl;
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Grid_finalize();
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}
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