mirror of
https://github.com/paboyle/Grid.git
synced 2025-06-13 20:57:06 +01:00
Merge remote-tracking branch 'LupoA/develop' into LupoA-develop
This commit is contained in:
Peter Boyle
@ -218,9 +218,9 @@ void runBenchmark(int* argc, char*** argv) {
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int main(int argc, char** argv) {
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Grid_init(&argc, &argv);
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#if Nc==3
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runBenchmark<vComplexD>(&argc, &argv);
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runBenchmark<vComplexF>(&argc, &argv);
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#endif
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Grid_finalize();
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}
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@ -29,13 +29,14 @@ 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/Grid.h>
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#include <Grid/qcd/utils/CovariantCshift.h>
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#include <Grid/qcd/utils/SUn.h>
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#include <Grid/qcd/utils/GaugeGroup.h>
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#include <Grid/qcd/utils/SUnAdjoint.h>
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#include <Grid/qcd/utils/SUnTwoIndex.h>
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#include <Grid/qcd/utils/GaugeGroupTwoIndex.h>
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#include <Grid/qcd/representations/adjoint.h>
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#include <Grid/qcd/representations/two_index.h>
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@ -43,7 +44,6 @@ directory
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using namespace std;
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using namespace Grid;
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;
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int main(int argc, char** argv) {
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Grid_init(&argc, &argv);
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@ -62,20 +62,17 @@ int main(int argc, char** argv) {
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SU2::printGenerators();
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std::cout << "Dimension of adjoint representation: "<< SU2Adjoint::Dimension << std::endl;
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// guard as this code fails to compile for Nc != 3
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#if 1
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std::cout << " Printing Adjoint Generators"<< 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(Nc" << std::endl;
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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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<< 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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@ -94,22 +91,22 @@ int main(int argc, char** argv) {
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// Projectors
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GridParallelRNG gridRNG(grid);
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gridRNG.SeedFixedIntegers(std::vector<int>({45,12,81,9}));
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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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SU_Adjoint<Nc>::LatticeAdjMatrix Gauss(grid);
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SU<Nc>::LatticeAlgebraVector ha(grid);
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SU<Nc>::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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SU_Adjoint<Nc>::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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SU_Adjoint<Nc>::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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SU_Adjoint<Nc>::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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SU<Nc>::LatticeAlgebraVector diff = ha -hb;
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std::cout << GridLogMessage << "Difference: " << norm2(diff) << std::endl;
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@ -119,17 +116,17 @@ int main(int argc, char** argv) {
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// AdjointRepresentation has the predefined number of colours Nc
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// Representations<FundamentalRepresentation, AdjointRepresentation, TwoIndexSymmetricRepresentation> RepresentationTypes(grid);
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LatticeGaugeField U(grid), V(grid);
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SU3::HotConfiguration<LatticeGaugeField>(gridRNG, U);
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SU3::HotConfiguration<LatticeGaugeField>(gridRNG, V);
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SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, U);
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SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, V);
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// Adjoint representation
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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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SU3::LatticeMatrix Umu = peekLorentz(U,mu);
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SU3::LatticeMatrix Vmu = peekLorentz(V,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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@ -151,6 +148,7 @@ int main(int argc, char** argv) {
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pokeLorentz(UrVr,Urmu*Vrmu, mu);
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}
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#if Nc==3
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typedef typename SU_Adjoint<Nc>::AMatrix AdjointMatrix;
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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 (Adjoint representation) : " << norm2(Diff_check) << std::endl;
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@ -176,19 +174,19 @@ int main(int argc, char** argv) {
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assert(abs( (2.0*tr1-tr2) ) < 1.0e-7);
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std::cout << "------------------"<<std::endl;
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}}}
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#endif
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// Check correspondence of algebra and group transformations
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// Create a random vector
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SU3::LatticeAlgebraVector h_adj(grid);
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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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SU3::LatticeAlgebraVector h_adj2(grid);
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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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SU3::LatticeAlgebraVector h_diff = h_adj - h_adj2;
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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 (Adjoint representation) : " << norm2(h_diff) << std::endl;
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// Exponentiate
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@ -210,14 +208,14 @@ int main(int argc, char** argv) {
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<< std::endl;
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// Construct the fundamental matrix in the group
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SU3::LatticeMatrix Af(grid);
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SU3::FundamentalLieAlgebraMatrix(h_adj,Af);
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SU3::LatticeMatrix Ufund(grid);
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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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SU3::LatticeMatrix uno_f(grid);
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SU<Nc>::LatticeMatrix uno_f(grid);
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uno_f = 1.0;
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SU3::LatticeMatrix UnitCheck(grid);
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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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@ -280,20 +278,20 @@ int main(int argc, char** argv) {
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std::cout << GridLogMessage << "Test for the Two Index Symmetric projectors"
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<< std::endl;
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// Projectors
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SU3TwoIndexSymm::LatticeTwoIndexMatrix Gauss2(grid);
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SU_TwoIndex<Nc, Symmetric>::LatticeTwoIndexMatrix Gauss2(grid);
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random(gridRNG,Gauss2);
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std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
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SU3TwoIndexSymm::projectOnAlgebra(ha, Gauss2);
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SU_TwoIndex<Nc, Symmetric>::projectOnAlgebra(ha, Gauss2);
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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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SU3TwoIndexSymm::projector(hb, Gauss2);
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SU_TwoIndex<Nc, Symmetric>::projector(hb, Gauss2);
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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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SU3TwoIndexSymm::projector(hb, Gauss2);
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SU_TwoIndex<Nc, Symmetric>::projector(hb, Gauss2);
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std::cout << GridLogMessage << "end projector" << std::endl;
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SU3::LatticeAlgebraVector diff2 = ha - hb;
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SU<Nc>::LatticeAlgebraVector diff2 = ha - hb;
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std::cout << GridLogMessage << "Difference: " << norm2(diff) << std::endl;
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std::cout << GridLogMessage << "*********************************************"
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<< std::endl;
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@ -304,20 +302,20 @@ int main(int argc, char** argv) {
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std::cout << GridLogMessage << "Test for the Two index anti-Symmetric projectors"
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<< std::endl;
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// Projectors
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SU3TwoIndexAntiSymm::LatticeTwoIndexMatrix Gauss2a(grid);
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SU_TwoIndex<Nc, AntiSymmetric>::LatticeTwoIndexMatrix Gauss2a(grid);
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random(gridRNG,Gauss2a);
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std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
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SU3TwoIndexAntiSymm::projectOnAlgebra(ha, Gauss2a);
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SU_TwoIndex<Nc, AntiSymmetric>::projectOnAlgebra(ha, Gauss2a);
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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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SU3TwoIndexAntiSymm::projector(hb, Gauss2a);
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SU_TwoIndex<Nc, AntiSymmetric>::projector(hb, Gauss2a);
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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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SU3TwoIndexAntiSymm::projector(hb, Gauss2a);
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SU_TwoIndex<Nc, AntiSymmetric>::projector(hb, Gauss2a);
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std::cout << GridLogMessage << "end projector" << std::endl;
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SU3::LatticeAlgebraVector diff2a = ha - hb;
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SU<Nc>::LatticeAlgebraVector diff2a = ha - hb;
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std::cout << GridLogMessage << "Difference: " << norm2(diff2a) << std::endl;
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std::cout << GridLogMessage << "*********************************************"
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<< std::endl;
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@ -326,55 +324,59 @@ int main(int argc, char** argv) {
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std::cout << GridLogMessage << "Two index Symmetric: Checking Group Structure"
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<< std::endl;
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// Testing HMC representation classes
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TwoIndexRep< Nc, Symmetric > TIndexRep(grid);
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TwoIndexRep< Nc, Symmetric> TIndexRep(grid);
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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 U2(grid), V2(grid);
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SU3::HotConfiguration<LatticeGaugeField>(gridRNG, U2);
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SU3::HotConfiguration<LatticeGaugeField>(gridRNG, V2);
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SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, U2);
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SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, V2);
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LatticeGaugeField UV2(grid);
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UV2 = Zero();
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for (int mu = 0; mu < Nd; mu++) {
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SU3::LatticeMatrix Umu2 = peekLorentz(U2,mu);
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SU3::LatticeMatrix Vmu2 = peekLorentz(V2,mu);
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SU<Nc>::LatticeMatrix Umu2 = peekLorentz(U2,mu);
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SU<Nc>::LatticeMatrix Vmu2 = peekLorentz(V2,mu);
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pokeLorentz(UV2,Umu2*Vmu2, mu);
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}
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TIndexRep.update_representation(UV2);
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typename TwoIndexRep< Nc, Symmetric >::LatticeField UVr2 = TIndexRep.U; // (U_f * V_f)_r
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TIndexRep.update_representation(U2);
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typename TwoIndexRep< Nc, Symmetric >::LatticeField Ur2 = TIndexRep.U; // U_r
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TIndexRep.update_representation(V2);
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typename TwoIndexRep< Nc, Symmetric >::LatticeField Vr2 = TIndexRep.U; // V_r
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typename TwoIndexRep< Nc, Symmetric >::LatticeField Ur2Vr2(grid);
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Ur2Vr2 = Zero();
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for (int mu = 0; mu < Nd; mu++) {
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typename TwoIndexRep< Nc, Symmetric >::LatticeMatrix Urmu2 = peekLorentz(Ur2,mu);
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typename TwoIndexRep< Nc, Symmetric >::LatticeMatrix Vrmu2 = peekLorentz(Vr2,mu);
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typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Urmu2 = peekLorentz(Ur2,mu);
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typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Vrmu2 = peekLorentz(Vr2,mu);
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pokeLorentz(Ur2Vr2,Urmu2*Vrmu2, mu);
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||||
}
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typename TwoIndexRep< Nc, Symmetric >::LatticeField Diff_check2 = UVr2 - Ur2Vr2;
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std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Two Index Symmetric): " << norm2(Diff_check2) << std::endl;
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||||
|
||||
|
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// Check correspondence of algebra and group transformations
|
||||
// Create a random vector
|
||||
SU3::LatticeAlgebraVector h_sym(grid);
|
||||
SU<Nc>::LatticeAlgebraVector h_sym(grid);
|
||||
typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ar_sym(grid);
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||||
random(gridRNG,h_sym);
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||||
h_sym = real(h_sym);
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||||
SU_TwoIndex<Nc,Symmetric>::TwoIndexLieAlgebraMatrix(h_sym,Ar_sym);
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||||
|
||||
// Re-extract h_sym
|
||||
SU3::LatticeAlgebraVector h_sym2(grid);
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||||
SU<Nc>::LatticeAlgebraVector h_sym2(grid);
|
||||
SU_TwoIndex< Nc, Symmetric>::projectOnAlgebra(h_sym2, Ar_sym);
|
||||
SU3::LatticeAlgebraVector h_diff_sym = h_sym - h_sym2;
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||||
SU<Nc>::LatticeAlgebraVector h_diff_sym = h_sym - h_sym2;
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||||
std::cout << GridLogMessage << "Projections structure check vector difference (Two Index Symmetric): " << norm2(h_diff_sym) << std::endl;
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||||
|
||||
// Exponentiate
|
||||
@ -396,11 +398,11 @@ int main(int argc, char** argv) {
|
||||
<< std::endl;
|
||||
|
||||
// Construct the fundamental matrix in the group
|
||||
SU3::LatticeMatrix Af_sym(grid);
|
||||
SU3::FundamentalLieAlgebraMatrix(h_sym,Af_sym);
|
||||
SU3::LatticeMatrix Ufund2(grid);
|
||||
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);
|
||||
SU3::LatticeMatrix UnitCheck2(grid);
|
||||
SU<Nc>::LatticeMatrix UnitCheck2(grid);
|
||||
UnitCheck2 = Ufund2 * adj(Ufund2) - uno_f;
|
||||
std::cout << GridLogMessage << "unitarity check 1: " << norm2(UnitCheck2)
|
||||
<< std::endl;
|
||||
@ -425,115 +427,113 @@ int main(int argc, char** argv) {
|
||||
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);
|
||||
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);
|
||||
SU3::HotConfiguration<LatticeGaugeField>(gridRNG, U2A);
|
||||
SU3::HotConfiguration<LatticeGaugeField>(gridRNG, V2A);
|
||||
// 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++) {
|
||||
SU3::LatticeMatrix Umu2A = peekLorentz(U2,mu);
|
||||
SU3::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
|
||||
SU3::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
|
||||
SU3::LatticeAlgebraVector h_Asym2(grid);
|
||||
SU_TwoIndex< Nc, AntiSymmetric>::projectOnAlgebra(h_Asym2, Ar_Asym);
|
||||
SU3::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
|
||||
SU3::LatticeMatrix Af_Asym(grid);
|
||||
SU3::FundamentalLieAlgebraMatrix(h_Asym,Af_Asym);
|
||||
SU3::LatticeMatrix Ufund2A(grid);
|
||||
Ufund2A = expMat(Af_Asym, 1.0, 16);
|
||||
SU3::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;
|
||||
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;
|
||||
|
||||
#endif
|
||||
|
||||
// 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();
|
||||
}
|
||||
|
||||
|
||||
@ -26,6 +26,7 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
|
||||
See the full license in the file "LICENSE" in the top level distribution directory
|
||||
*************************************************************************************/
|
||||
/* END LEGAL */
|
||||
|
||||
#include <Grid/Grid.h>
|
||||
|
||||
using namespace std;
|
||||
@ -121,8 +122,9 @@ int main (int argc, char ** argv)
|
||||
detU=detU-1.0;
|
||||
std::cout << "Determinant defect before projection " <<norm2(detU)<<std::endl;
|
||||
tmp = U*adj(U) - ident;
|
||||
std::cout << "Unitarity check before projection " << norm2(tmp)<<std::endl;
|
||||
#if (Nc == 3)
|
||||
std::cout << "Unitarity check before projection " << norm2(tmp)<<std::endl;
|
||||
|
||||
#if Nc==3
|
||||
ProjectSU3(U);
|
||||
detU= Determinant(U) ;
|
||||
detU= detU -1.0;
|
||||
@ -130,7 +132,7 @@ int main (int argc, char ** argv)
|
||||
tmp = U*adj(U) - ident;
|
||||
std::cout << "Unitarity check after projection " << norm2(tmp)<<std::endl;
|
||||
#endif
|
||||
|
||||
|
||||
ProjectSUn(UU);
|
||||
detUU= Determinant(UU);
|
||||
detUU= detUU -1.0;
|
||||
@ -140,7 +142,3 @@ int main (int argc, char ** argv)
|
||||
|
||||
Grid_finalize();
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user