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Added support for the Two index Symmetric and Antisymmetric representations
Tested for HMC convergence: OK Added also a test file showing an example for mixed representations
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Guido Cossu committed
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+1
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@@ -1,3 +1,3 @@
|
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HFILES=./tensors/Tensor_extract_merge.h ./tensors/Tensor_exp.h ./tensors/Tensor_index.h ./tensors/Tensor_arith_add.h ./tensors/Tensor_determinant.h ./tensors/Tensor_outer.h ./tensors/Tensor_trace.h ./tensors/Tensor_arith_mac.h ./tensors/Tensor_logical.h ./tensors/Tensor_reality.h ./tensors/Tensor_arith_sub.h ./tensors/Tensor_Ta.h ./tensors/Tensor_class.h ./tensors/Tensor_inner.h ./tensors/Tensor_arith_mul.h ./tensors/Tensor_transpose.h ./tensors/Tensor_arith.h ./tensors/Tensor_unary.h ./tensors/Tensor_arith_scalar.h ./tensors/Tensor_traits.h ./stencil/Lebesgue.h ./PerfCount.h ./FFT.h ./Communicator.h ./simd/Grid_vector_types.h ./simd/Grid_qpx.h ./simd/Grid_imci.h ./simd/Grid_avx.h ./simd/Intel512single.h ./simd/Grid_vector_unops.h ./simd/Grid_neon.h ./simd/Intel512common.h ./simd/Intel512wilson.h ./simd/Intel512imci.h ./simd/Intel512double.h ./simd/Grid_generic.h ./simd/Grid_avx512.h ./simd/Grid_sse4.h ./simd/Intel512avx.h ./Threads.h ./Timer.h ./algorithms/approx/bigfloat_double.h ./algorithms/approx/bigfloat.h ./algorithms/approx/Chebyshev.h ./algorithms/approx/Remez.h ./algorithms/approx/Zolotarev.h ./algorithms/approx/MultiShiftFunction.h ./algorithms/SparseMatrix.h ./algorithms/LinearOperator.h ./algorithms/Preconditioner.h ./algorithms/CoarsenedMatrix.h ./algorithms/iterative/AdefGeneric.h ./algorithms/iterative/ImplicitlyRestartedLanczos.h ./algorithms/iterative/ConjugateGradientMultiShift.h ./algorithms/iterative/DenseMatrix.h ./algorithms/iterative/ConjugateResidual.h ./algorithms/iterative/EigenSort.h ./algorithms/iterative/MatrixUtils.h ./algorithms/iterative/ConjugateGradientMixedPrec.h ./algorithms/iterative/PrecGeneralisedConjugateResidual.h ./algorithms/iterative/NormalEquations.h ./algorithms/iterative/Francis.h ./algorithms/iterative/SchurRedBlack.h ./algorithms/iterative/ConjugateGradient.h ./algorithms/iterative/Householder.h ./algorithms/iterative/PrecConjugateResidual.h ./algorithms/iterative/Matrix.h ./Algorithms.h ./fftw/fftw3.h ./lattice/Lattice_base.h ./lattice/Lattice_overload.h ./lattice/Lattice_ET.h ./lattice/Lattice_comparison_utils.h ./lattice/Lattice_trace.h ./lattice/Lattice_coordinate.h ./lattice/Lattice_arith.h ./lattice/Lattice_peekpoke.h ./lattice/Lattice_local.h ./lattice/Lattice_rng.h ./lattice/Lattice_comparison.h ./lattice/Lattice_reality.h ./lattice/Lattice_transpose.h ./lattice/Lattice_transfer.h ./lattice/Lattice_conformable.h ./lattice/Lattice_unary.h ./lattice/Lattice_where.h ./lattice/Lattice_reduction.h ./Cartesian.h ./Simd.h ./Init.h ./serialisation/TextIO.h ./serialisation/Serialisation.h ./serialisation/MacroMagic.h ./serialisation/BaseIO.h ./serialisation/XmlIO.h ./serialisation/BinaryIO.h ./communicator/Communicator_base.h ./Log.h ./Lattice.h ./cshift/Cshift_mpi.h ./cshift/Cshift_none.h ./cshift/Cshift_common.h ./Lexicographic.h ./Tensors.h ./Cshift.h ./parallelIO/NerscIO.h ./parallelIO/BinaryIO.h ./qcd/smearing/BaseSmearing.h ./qcd/smearing/GaugeConfiguration.h ./qcd/smearing/StoutSmearing.h ./qcd/smearing/APEsmearing.h ./qcd/smearing/Smearing.h ./qcd/hmc/HmcRunner.h ./qcd/hmc/NerscCheckpointer.h ./qcd/hmc/integrators/Integrator.h ./qcd/hmc/integrators/Integrator_algorithm.h ./qcd/hmc/HMC.h ./qcd/action/fermion/OverlapWilsonCayleyZolotarevFermion.h ./qcd/action/fermion/OverlapWilsonContfracZolotarevFermion.h ./qcd/action/fermion/WilsonFermion5D.h ./qcd/action/fermion/MobiusFermion.h ./qcd/action/fermion/MobiusZolotarevFermion.h ./qcd/action/fermion/OverlapWilsonPartialFractionZolotarevFermion.h ./qcd/action/fermion/DomainWallFermion.h ./qcd/action/fermion/ZMobiusFermion.h ./qcd/action/fermion/WilsonFermion.h ./qcd/action/fermion/OverlapWilsonCayleyTanhFermion.h ./qcd/action/fermion/FermionOperatorImpl.h ./qcd/action/fermion/g5HermitianLinop.h ./qcd/action/fermion/ContinuedFractionFermion5D.h ./qcd/action/fermion/WilsonTMFermion.h ./qcd/action/fermion/FermionOperator.h ./qcd/action/fermion/OverlapWilsonContfracTanhFermion.h ./qcd/action/fermion/PartialFractionFermion5D.h ./qcd/action/fermion/CayleyFermion5D.h ./qcd/action/fermion/OverlapWilsonPartialFractionTanhFermion.h ./qcd/action/fermion/ScaledShamirFermion.h ./qcd/action/fermion/ShamirZolotarevFermion.h ./qcd/action/fermion/WilsonKernels.h ./qcd/action/fermion/WilsonCompressor.h ./qcd/action/fermion/WilsonKernelsAsmBody.h ./qcd/action/ActionParams.h ./qcd/action/Actions.h ./qcd/action/pseudofermion/OneFlavourRationalRatio.h ./qcd/action/pseudofermion/OneFlavourEvenOddRational.h ./qcd/action/pseudofermion/TwoFlavourEvenOdd.h ./qcd/action/pseudofermion/OneFlavourEvenOddRationalRatio.h ./qcd/action/pseudofermion/TwoFlavourRatio.h ./qcd/action/pseudofermion/EvenOddSchurDifferentiable.h ./qcd/action/pseudofermion/TwoFlavour.h ./qcd/action/pseudofermion/TwoFlavourEvenOddRatio.h ./qcd/action/pseudofermion/OneFlavourRational.h ./qcd/action/gauge/WilsonGaugeAction.h ./qcd/action/gauge/PlaqPlusRectangleAction.h ./qcd/action/gauge/GaugeImpl.h ./qcd/action/ActionBase.h ./qcd/QCD.h ./qcd/spin/TwoSpinor.h ./qcd/spLine truncated
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HFILES=./tensors/Tensor_extract_merge.h ./tensors/Tensor_exp.h ./tensors/Tensor_index.h ./tensors/Tensor_arith_add.h ./tensors/Tensor_determinant.h ./tensors/Tensor_outer.h ./tensors/Tensor_trace.h ./tensors/Tensor_arith_mac.h ./tensors/Tensor_logical.h ./tensors/Tensor_reality.h ./tensors/Tensor_arith_sub.h ./tensors/Tensor_Ta.h ./tensors/Tensor_class.h ./tensors/Tensor_inner.h ./tensors/Tensor_arith_mul.h ./tensors/Tensor_transpose.h ./tensors/Tensor_arith.h ./tensors/Tensor_unary.h ./tensors/Tensor_arith_scalar.h ./tensors/Tensor_traits.h ./stencil/Lebesgue.h ./PerfCount.h ./FFT.h ./Communicator.h ./simd/Grid_vector_types.h ./simd/Grid_qpx.h ./simd/Grid_imci.h ./simd/Grid_avx.h ./simd/Intel512single.h ./simd/Grid_vector_unops.h ./simd/Grid_neon.h ./simd/Intel512common.h ./simd/Intel512wilson.h ./simd/Intel512imci.h ./simd/Intel512double.h ./simd/Grid_generic.h ./simd/Grid_avx512.h ./simd/Grid_sse4.h ./simd/Intel512avx.h ./Threads.h ./Timer.h ./algorithms/approx/bigfloat_double.h ./algorithms/approx/bigfloat.h ./algorithms/approx/Chebyshev.h ./algorithms/approx/Remez.h ./algorithms/approx/Zolotarev.h ./algorithms/approx/MultiShiftFunction.h ./algorithms/SparseMatrix.h ./algorithms/LinearOperator.h ./algorithms/Preconditioner.h ./algorithms/CoarsenedMatrix.h ./algorithms/iterative/AdefGeneric.h ./algorithms/iterative/ImplicitlyRestartedLanczos.h ./algorithms/iterative/ConjugateGradientMultiShift.h ./algorithms/iterative/DenseMatrix.h ./algorithms/iterative/ConjugateResidual.h ./algorithms/iterative/EigenSort.h ./algorithms/iterative/MatrixUtils.h ./algorithms/iterative/ConjugateGradientMixedPrec.h ./algorithms/iterative/PrecGeneralisedConjugateResidual.h ./algorithms/iterative/NormalEquations.h ./algorithms/iterative/Francis.h ./algorithms/iterative/SchurRedBlack.h ./algorithms/iterative/ConjugateGradient.h ./algorithms/iterative/Householder.h ./algorithms/iterative/PrecConjugateResidual.h ./algorithms/iterative/Matrix.h ./Algorithms.h ./fftw/fftw3.h ./lattice/Lattice_base.h ./lattice/Lattice_overload.h ./lattice/Lattice_ET.h ./lattice/Lattice_comparison_utils.h ./lattice/Lattice_trace.h ./lattice/Lattice_coordinate.h ./lattice/Lattice_arith.h ./lattice/Lattice_peekpoke.h ./lattice/Lattice_local.h ./lattice/Lattice_rng.h ./lattice/Lattice_comparison.h ./lattice/Lattice_reality.h ./lattice/Lattice_transpose.h ./lattice/Lattice_transfer.h ./lattice/Lattice_conformable.h ./lattice/Lattice_unary.h ./lattice/Lattice_where.h ./lattice/Lattice_reduction.h ./Cartesian.h ./Simd.h ./Init.h ./serialisation/TextIO.h ./serialisation/Serialisation.h ./serialisation/MacroMagic.h ./serialisation/BaseIO.h ./serialisation/XmlIO.h ./serialisation/BinaryIO.h ./communicator/Communicator_base.h ./Log.h ./Lattice.h ./cshift/Cshift_mpi.h ./cshift/Cshift_none.h ./cshift/Cshift_common.h ./Lexicographic.h ./Tensors.h ./Cshift.h ./parallelIO/NerscIO.h ./parallelIO/BinaryIO.h ./qcd/smearing/BaseSmearing.h ./qcd/smearing/GaugeConfiguration.h ./qcd/smearing/StoutSmearing.h ./qcd/smearing/APEsmearing.h ./qcd/smearing/Smearing.h ./qcd/hmc/HmcRunner.h ./qcd/hmc/NerscCheckpointer.h ./qcd/hmc/integrators/Integrator.h ./qcd/hmc/integrators/Integrator_algorithm.h ./qcd/hmc/HMC.h ./qcd/action/fermion/OverlapWilsonCayleyZolotarevFermion.h ./qcd/action/fermion/OverlapWilsonContfracZolotarevFermion.h ./qcd/action/fermion/WilsonFermion5D.h ./qcd/action/fermion/MobiusFermion.h ./qcd/action/fermion/MobiusZolotarevFermion.h ./qcd/action/fermion/OverlapWilsonPartialFractionZolotarevFermion.h ./qcd/action/fermion/DomainWallFermion.h ./qcd/action/fermion/ZMobiusFermion.h ./qcd/action/fermion/WilsonFermion.h ./qcd/action/fermion/OverlapWilsonCayleyTanhFermion.h ./qcd/action/fermion/FermionOperatorImpl.h ./qcd/action/fermion/g5HermitianLinop.h ./qcd/action/fermion/ContinuedFractionFermion5D.h ./qcd/action/fermion/WilsonTMFermion.h ./qcd/action/fermion/FermionOperator.h ./qcd/action/fermion/OverlapWilsonContfracTanhFermion.h ./qcd/action/fermion/PartialFractionFermion5D.h ./qcd/action/fermion/CayleyFermion5D.h ./qcd/action/fermion/OverlapWilsonPartialFractionTanhFermion.h ./qcd/action/fermion/ScaledShamirFermion.h ./qcd/action/fermion/ShamirZolotarevFermion.h ./qcd/action/fermion/WilsonKernels.h ./qcd/action/fermion/WilsonCompressor.h ./qcd/action/fermion/WilsonKernelsAsmBody.h ./qcd/action/ActionParams.h ./qcd/action/Actions.h ./qcd/action/pseudofermion/OneFlavourRationalRatio.h ./qcd/action/pseudofermion/OneFlavourEvenOddRational.h ./qcd/action/pseudofermion/TwoFlavourEvenOdd.h ./qcd/action/pseudofermion/OneFlavourEvenOddRationalRatio.h ./qcd/action/pseudofermion/TwoFlavourRatio.h ./qcd/action/pseudofermion/EvenOddSchurDifferentiable.h ./qcd/action/pseudofermion/TwoFlavour.h ./qcd/action/pseudofermion/TwoFlavourEvenOddRatio.h ./qcd/action/pseudofermion/OneFlavourRational.h ./qcd/action/gauge/WilsonGaugeAction.h ./qcd/action/gauge/PlaqPlusRectangleAction.h ./qcd/action/gauge/GaugeImpl.h ./qcd/action/ActionBase.h ./qcd/QCD.h ./qcd/spin/TwoSpinor.h ./qcd/spLine truncated
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CCFILES=./stencil/Stencil_common.cc ./stencil/Lebesgue.cc ./algorithms/approx/MultiShiftFunction.cc ./algorithms/approx/Remez.cc ./algorithms/approx/Zolotarev.cc ./PerfCount.cc ./serialisation/BinaryIO.cc ./serialisation/XmlIO.cc ./serialisation/TextIO.cc ./qcd/hmc/HMC.cc ./qcd/action/fermion/CayleyFermion5D.cc ./qcd/action/fermion/ContinuedFractionFermion5D.cc ./qcd/action/fermion/CayleyFermion5Ddense.cc ./qcd/action/fermion/WilsonKernelsHand.cc ./qcd/action/fermion/WilsonTMFermion.cc ./qcd/action/fermion/WilsonFermion.cc ./qcd/action/fermion/CayleyFermion5Dcache.cc ./qcd/action/fermion/WilsonKernelsAsm.cc ./qcd/action/fermion/CayleyFermion5Dssp.cc ./qcd/action/fermion/WilsonKernels.cc ./qcd/action/fermion/WilsonFermion5D.cc ./qcd/action/fermion/PartialFractionFermion5D.cc ./qcd/action/fermion/CayleyFermion5Dvec.cc ./qcd/spin/Dirac.cc ./qcd/utils/SpaceTimeGrid.cc ./Init.cc ./pugixml/pugixml.cc ./Log.cc
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+5
-4
@@ -45,7 +45,7 @@ namespace QCD {
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static const int Zm = 6;
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static const int Tm = 7;
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static const int Nc=3;
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static const int Nc=2;
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static const int Ns=4;
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static const int Nd=4;
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static const int Nhs=2; // half spinor
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@@ -499,12 +499,13 @@ namespace QCD {
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#include <Grid/qcd/spin/TwoSpinor.h>
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#include <Grid/qcd/utils/LinalgUtils.h>
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#include <Grid/qcd/utils/CovariantCshift.h>
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// Include representations
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#include <Grid/qcd/utils/SUn.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/representations/hmc_types.h>
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#include <Grid/qcd/action/Actions.h>
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#include <Grid/qcd/smearing/Smearing.h>
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@@ -120,6 +120,10 @@ typedef SymanzikGaugeAction<ConjugateGimplD> ConjugateSymanzikGaugeAction
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template class A<WilsonAdjImplF>; \
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template class A<WilsonAdjImplD>;
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#define TwoIndexFermOpTemplateInstantiate(A) \
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template class A<WilsonTwoIndexSymmetricImplF>; \
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template class A<WilsonTwoIndexSymmetricImplD>;
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#define FermOp5dVecTemplateInstantiate(A) \
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template class A<DomainWallVec5dImplF>; \
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template class A<DomainWallVec5dImplD>; \
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@@ -180,6 +184,10 @@ typedef WilsonFermion<WilsonAdjImplR> WilsonAdjFermionR;
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typedef WilsonFermion<WilsonAdjImplF> WilsonAdjFermionF;
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typedef WilsonFermion<WilsonAdjImplD> WilsonAdjFermionD;
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typedef WilsonFermion<WilsonTwoIndexSymmetricImplR> WilsonTwoIndexSymmetricFermionR;
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typedef WilsonFermion<WilsonTwoIndexSymmetricImplF> WilsonTwoIndexSymmetricFermionF;
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typedef WilsonFermion<WilsonTwoIndexSymmetricImplD> WilsonTwoIndexSymmetricFermionD;
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typedef WilsonTMFermion<WilsonImplR> WilsonTMFermionR;
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typedef WilsonTMFermion<WilsonImplF> WilsonTMFermionF;
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typedef WilsonTMFermion<WilsonImplD> WilsonTMFermionD;
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@@ -522,7 +522,11 @@ namespace Grid {
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typedef WilsonImpl<vComplex, AdjointRepresentation > WilsonAdjImplR; // Real.. whichever prec
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typedef WilsonImpl<vComplexF, AdjointRepresentation > WilsonAdjImplF; // Float
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typedef WilsonImpl<vComplexD, AdjointRepresentation > WilsonAdjImplD; // Double
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typedef WilsonImpl<vComplex, TwoIndexSymmetricRepresentation > WilsonTwoIndexSymmetricImplR; // Real.. whichever prec
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typedef WilsonImpl<vComplexF, TwoIndexSymmetricRepresentation > WilsonTwoIndexSymmetricImplF; // Float
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typedef WilsonImpl<vComplexD, TwoIndexSymmetricRepresentation > WilsonTwoIndexSymmetricImplD; // Double
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typedef DomainWallVec5dImpl<vComplex ,Nc> DomainWallVec5dImplR; // Real.. whichever prec
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typedef DomainWallVec5dImpl<vComplexF,Nc> DomainWallVec5dImplF; // Float
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typedef DomainWallVec5dImpl<vComplexD,Nc> DomainWallVec5dImplD; // Double
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@@ -309,6 +309,7 @@ void WilsonFermion<Impl>::DhopInternal(StencilImpl &st, LebesgueOrder &lo,
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FermOpTemplateInstantiate(WilsonFermion);
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AdjointFermOpTemplateInstantiate(WilsonFermion);
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TwoIndexFermOpTemplateInstantiate(WilsonFermion);
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GparityFermOpTemplateInstantiate(WilsonFermion);
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}
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}
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@@ -526,6 +526,7 @@ void WilsonKernels<Impl>::DiracOptDhopDir(
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FermOpTemplateInstantiate(WilsonKernels);
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AdjointFermOpTemplateInstantiate(WilsonKernels);
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TwoIndexFermOpTemplateInstantiate(WilsonKernels);
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}}
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@@ -2,6 +2,7 @@
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#define HMC_TYPES_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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#include <Grid/qcd/representations/fundamental.h>
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#include <tuple>
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#include <utility>
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+33
-25
@@ -1,53 +1,62 @@
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/*
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* Policy classes for the HMC
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* Author: Guido Cossu
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* Authors: Guido Cossu, David Preti
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*/
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#ifndef ADJOINT_H
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#define ADJOINT_H
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#ifndef SUN2INDEX_H_H
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#define SUN2INDEX_H_H
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namespace Grid {
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namespace QCD {
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/*
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* This is an helper class for the HMC
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* Should contain only the data for the adjoint representation
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* and the facility to convert from the fundamental -> adjoint
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*/
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* This is an helper class for the HMC
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* Should contain only the data for the two index representations
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* and the facility to convert from the fundamental -> two index
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* The templated parameter TwoIndexSymmetry choses between the
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* symmetric and antisymmetric representations
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*
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* There is an
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* enum TwoIndexSymmetry { Symmetric = 1, AntiSymmetric = -1 };
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* in the SUnTwoIndex.h file
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*/
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template <int ncolour, TwoIndexSymmetry S>
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class TwoIndexSymmetricRep {
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class TwoIndexRep {
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public:
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// typdef to be used by the Representations class in HMC to get the
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// types for the higher representation fields
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typedef typename SU_TwoIndex<ncolour,S>::LatticeTwoIndexMatrix LatticeMatrix;
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typedef typename SU_TwoIndex<ncolour,S>::LatticeTwoIndexField LatticeField;
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typedef typename SU_TwoIndex<ncolour, S>::LatticeTwoIndexMatrix LatticeMatrix;
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typedef typename SU_TwoIndex<ncolour, S>::LatticeTwoIndexField LatticeField;
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static const int Dimension = ncolour * (ncolour + S) / 2;
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LatticeField U;
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explicit TwoIndexSymmetricRep(GridBase *grid) : U(grid) {}
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explicit TwoIndexRep(GridBase *grid) : U(grid) {}
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void update_representation(const LatticeGaugeField &Uin) {
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std::cout << GridLogDebug << "Updating TwoIndex representation\n";
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// Uin is in the fundamental representation
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// get the U in AdjointRep
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// (U)(ij)_(lk) =
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// e^a =
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// get the U in TwoIndexRep
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// (U)_{(ij)(lk)} = tr [ adj(e^(ij)) U e^(lk) transpose(U) ]
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conformable(U, Uin);
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U = zero;
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LatticeColourMatrix tmp(Uin._grid);
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Vector<typename SU<ncolour>::Matrix> ta(Dimension);
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Vector<typename SU<ncolour>::Matrix> eij(Dimension);
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// FIXME probably not very efficient to get all the generators
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// everytime
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for (int a = 0; a < Dimension; a++) SU<ncolour>::generator(a, ta[a]);
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for (int a = 0; a < Dimension; a++)
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SU_TwoIndex<ncolour, S>::base(a, eij[a]);
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for (int mu = 0; mu < Nd; mu++) {
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auto Uin_mu = peekLorentz(Uin, mu);
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auto U_mu = peekLorentz(U, mu);
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for (int a = 0; a < Dimension; a++) {
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tmp = transpose(Uin_mu) * adj(eij[a]) * Uin_mu;
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for (int b = 0; b < Dimension; b++)
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pokeColour(U_mu, trace(tmp * eij[b]), a, b);
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}
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pokeLorentz(U, U_mu, mu);
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}
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}
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@@ -63,8 +72,8 @@ class TwoIndexSymmetricRep {
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out_mu = zero;
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typename SU<ncolour>::LatticeAlgebraVector h(in._grid);
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projectOnAlgebra(h, in_mu, double(Nc + 2*S) ); // factor T(r)/T(fund)
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FundamentalLieAlgebraMatrix(h, out_mu); // apply scale only once
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projectOnAlgebra(h, in_mu, double(Nc + 2 * S)); // factor T(r)/T(fund)
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FundamentalLieAlgebraMatrix(h, out_mu); // apply scale only once
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pokeLorentz(out, out_mu, mu);
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}
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return out;
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@@ -73,7 +82,7 @@ class TwoIndexSymmetricRep {
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private:
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void projectOnAlgebra(typename SU<ncolour>::LatticeAlgebraVector &h_out,
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const LatticeMatrix &in, Real scale = 1.0) const {
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SU_TwoIndex<ncolour,S>::projectOnAlgebra(h_out, in, scale);
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SU_TwoIndex<ncolour, S>::projectOnAlgebra(h_out, in, scale);
|
||||
}
|
||||
|
||||
void FundamentalLieAlgebraMatrix(
|
||||
@@ -83,9 +92,8 @@ class TwoIndexSymmetricRep {
|
||||
}
|
||||
};
|
||||
|
||||
typedef TwoIndexRep< Nc, Symmetric > TwoIndexSymmetricRepresentation;
|
||||
typedef TwoIndexRep< Nc, AntiSymmetric > TwoIndexAntiSymmetricRepresentation;
|
||||
typedef TwoIndexRep<Nc, Symmetric> TwoIndexSymmetricRepresentation;
|
||||
typedef TwoIndexRep<Nc, AntiSymmetric> TwoIndexAntiSymmetricRepresentation;
|
||||
}
|
||||
}
|
||||
|
||||
#endif
|
||||
+242
-130
@@ -1,11 +1,8 @@
|
||||
#ifndef QCD_UTIL_SUNADJOINT_H
|
||||
#define QCD_UTIL_SUNADJOINT_H
|
||||
|
||||
////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// * Two index representation generators
|
||||
//
|
||||
// * Normalisation for the fundamental generators:
|
||||
// * Normalisation for the fundamental generators:
|
||||
// trace ta tb = 1/2 delta_ab = T_F delta_ab
|
||||
// T_F = 1/2 for SU(N) groups
|
||||
//
|
||||
@@ -17,147 +14,262 @@
|
||||
//
|
||||
// Then the generators are written as
|
||||
//
|
||||
// (iT^(ij))_lk = i
|
||||
// (iT_a)^(ij)(lk) = i * ( tr[e^(ij)^dag e^(lk) T^trasp_a] +
|
||||
// tr[e^(lk)e^(ij)^dag T_a] ) //
|
||||
//
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////
|
||||
|
||||
// Authors: David Preti, Guido Cossu
|
||||
|
||||
#ifndef QCD_UTIL_SUN2INDEX_H
|
||||
#define QCD_UTIL_SUN2INDEX_H
|
||||
|
||||
|
||||
namespace Grid {
|
||||
namespace QCD {
|
||||
namespace QCD {
|
||||
|
||||
enum TwoIndexSymmetry {Symmetric = 1, AntiSymmetric = -1};
|
||||
|
||||
template <int ncolour, TwoIndexSymmetry S>
|
||||
class SU_TwoIndex : public SU<ncolour> {
|
||||
public:
|
||||
static const int Dimension = ncolour * (ncolour + S) / 2;
|
||||
|
||||
template <typename vtype>
|
||||
using iSUnTwoIndexMatrix =
|
||||
iScalar<iScalar<iMatrix<vtype, Dimension > > >;
|
||||
|
||||
typedef iSUnTwoIndexMatrix<Complex> TIMatrix;
|
||||
typedef iSUnTwoIndexMatrix<ComplexF> TIMatrixF;
|
||||
typedef iSUnTwoIndexMatrix<ComplexD> TIMatrixD;
|
||||
|
||||
typedef iSUnTwoIndexMatrix<vComplex> vTIMatrix;
|
||||
typedef iSUnTwoIndexMatrix<vComplexF> vTIMatrixF;
|
||||
typedef iSUnTwoIndexMatrix<vComplexD> vTIMatrixD;
|
||||
|
||||
typedef Lattice<vAMatrix> LatticeTwoIndexMatrix;
|
||||
typedef Lattice<vAMatrixF> LatticeTwoIndexMatrixF;
|
||||
typedef Lattice<vAMatrixD> LatticeTwoIndexMatrixD;
|
||||
|
||||
typedef Lattice<iVector<iScalar<iMatrix<vComplex, Dimension> >, Nd> >
|
||||
enum TwoIndexSymmetry { Symmetric = 1, AntiSymmetric = -1 };
|
||||
|
||||
inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
|
||||
|
||||
template <int ncolour, TwoIndexSymmetry S>
|
||||
class SU_TwoIndex : public SU<ncolour> {
|
||||
public:
|
||||
static const int Dimension = ncolour * (ncolour + S) / 2;
|
||||
static const int NumGenerators = SU<ncolour>::AdjointDimension;
|
||||
|
||||
template <typename vtype>
|
||||
using iSUnTwoIndexMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
|
||||
|
||||
typedef iSUnTwoIndexMatrix<Complex> TIMatrix;
|
||||
typedef iSUnTwoIndexMatrix<ComplexF> TIMatrixF;
|
||||
typedef iSUnTwoIndexMatrix<ComplexD> TIMatrixD;
|
||||
|
||||
typedef iSUnTwoIndexMatrix<vComplex> vTIMatrix;
|
||||
typedef iSUnTwoIndexMatrix<vComplexF> vTIMatrixF;
|
||||
typedef iSUnTwoIndexMatrix<vComplexD> vTIMatrixD;
|
||||
|
||||
typedef Lattice<vTIMatrix> LatticeTwoIndexMatrix;
|
||||
typedef Lattice<vTIMatrixF> LatticeTwoIndexMatrixF;
|
||||
typedef Lattice<vTIMatrixD> LatticeTwoIndexMatrixD;
|
||||
|
||||
typedef Lattice<iVector<iScalar<iMatrix<vComplex, Dimension> >, Nd> >
|
||||
LatticeTwoIndexField;
|
||||
typedef Lattice<iVector<iScalar<iMatrix<vComplexF, Dimension> >, Nd> >
|
||||
typedef Lattice<iVector<iScalar<iMatrix<vComplexF, Dimension> >, Nd> >
|
||||
LatticeTwoIndexFieldF;
|
||||
typedef Lattice<iVector<iScalar<iMatrix<vComplexD, Dimension> >, Nd> >
|
||||
typedef Lattice<iVector<iScalar<iMatrix<vComplexD, Dimension> >, Nd> >
|
||||
LatticeTwoIndexFieldD;
|
||||
|
||||
|
||||
|
||||
template <typename vtype>
|
||||
using iSUnMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
|
||||
|
||||
template <class cplx>
|
||||
static void generator(int Index, iSUnTwoIndexMatrix<cplx> &iTwoIdxTa) {
|
||||
// returns i(T)^(ij) necessary for the projectors
|
||||
// see definitions above
|
||||
iTwoIdxTa = zero;
|
||||
Vector<typename SU<ncolour>::template iSUnMatrix<cplx> > tij(Dimension);
|
||||
typename SU<ncolour>::template iSUnMatrix<cplx> tmp;
|
||||
typedef iSUnMatrix<Complex> Matrix;
|
||||
typedef iSUnMatrix<ComplexF> MatrixF;
|
||||
typedef iSUnMatrix<ComplexD> MatrixD;
|
||||
|
||||
template <class cplx>
|
||||
static void base(int Index, iSUnMatrix<cplx> &eij) {
|
||||
// returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
|
||||
assert(Index < NumGenerators);
|
||||
eij = zero;
|
||||
|
||||
for (int a = 0; a < Dimension; a++) {
|
||||
|
||||
}
|
||||
// for the linearisation of the 2 indexes
|
||||
static int a[ncolour * (ncolour - 1) / 2][2]; // store the a <-> i,j
|
||||
static bool filled = false;
|
||||
if (!filled) {
|
||||
int counter = 0;
|
||||
for (int i = 1; i < ncolour; i++) {
|
||||
for (int j = 0; j < i; j++) {
|
||||
a[counter++][0] = i;
|
||||
a[counter++][1] = j;
|
||||
}
|
||||
}
|
||||
filled = true;
|
||||
}
|
||||
|
||||
static void printGenerators(void) {
|
||||
for (int gen = 0; gen < Dimension; gen++) {
|
||||
AMatrix ta;
|
||||
generator(gen, ta);
|
||||
std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << ta << std::endl;
|
||||
}
|
||||
}
|
||||
|
||||
static void testGenerators(void) {
|
||||
TIMatrix TwoIndexTa;
|
||||
|
||||
}
|
||||
|
||||
static void TwoIndexLieAlgebraMatrix(const typename SU<ncolour>::LatticeAlgebraVector &h,
|
||||
LatticeTwoIndexMatrix &out, Real scale = 1.0) {
|
||||
conformable(h, out);
|
||||
GridBase *grid = out._grid;
|
||||
LatticeAdjMatrix la(grid);
|
||||
TIMatrix iTa;
|
||||
|
||||
out = zero;
|
||||
for (int a = 0; a < Dimension; a++) {
|
||||
generator(a, iTa);
|
||||
la = peekColour(h, a) * iTa;
|
||||
out += la;
|
||||
}
|
||||
out *= scale;
|
||||
}
|
||||
|
||||
// Projects the algebra components a lattice matrix (of dimension ncol*ncol -1 )
|
||||
static void projectOnAlgebra(typename SU<ncolour>::LatticeAlgebraVector &h_out, const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
|
||||
conformable(h_out, in);
|
||||
h_out = zero;
|
||||
TIMatrix iTa;
|
||||
Real coefficient = - 2.0/(ncolour + 2*S) * scale;// 2/(Nc +/- 2) for the normalization of the trace in the two index rep
|
||||
|
||||
for (int a = 0; a < Dimension; a++) {
|
||||
generator(a, iTa);
|
||||
auto tmp = real(trace(iTa * in)) * coefficient;
|
||||
pokeColour(h_out, tmp, a);
|
||||
}
|
||||
}
|
||||
|
||||
// a projector that keeps the generators stored to avoid the overhead of recomputing them
|
||||
static void projector(typename SU<ncolour>::LatticeAlgebraVector &h_out, const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
|
||||
conformable(h_out, in);
|
||||
static std::vector<TIMatrix> iTa(Dimension); // to store the generators
|
||||
h_out = zero;
|
||||
static bool precalculated = false;
|
||||
if (!precalculated){
|
||||
precalculated = true;
|
||||
for (int a = 0; a < Dimension; a++) generator(a, iTa[a]);
|
||||
}
|
||||
|
||||
Real coefficient = - 2.0/(ncolour + 2*S) * scale; // 2/(Nc +/- 2) for the normalization of the trace in the two index rep
|
||||
|
||||
for (int a = 0; a < Dimension; a++) {
|
||||
auto tmp = real(trace(iTa[a] * in)) * coefficient;
|
||||
pokeColour(h_out, tmp, a);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
};
|
||||
|
||||
|
||||
|
||||
|
||||
// Some useful type names
|
||||
typedef SU_TwoIndex<2, Symmetric> SU2TwoIndexSymm;
|
||||
typedef SU_TwoIndex<3, Symmetric> SU3TwoIndexSymm;
|
||||
typedef SU_TwoIndex<4, Symmetric> SU4TwoIndexSymm;
|
||||
typedef SU_TwoIndex<5, Symmetric> SU5TwoIndexSymm;
|
||||
|
||||
typedef SU_TwoIndex<Nc, Symmetric> TwoIndexSymmMatrices;
|
||||
|
||||
typedef SU_TwoIndex<2, AntiSymmetric> SU2TwoIndexAntiSymm;
|
||||
typedef SU_TwoIndex<3, AntiSymmetric> SU3TwoIndexAntiSymm;
|
||||
typedef SU_TwoIndex<4, AntiSymmetric> SU4TwoIndexAntiSymm;
|
||||
typedef SU_TwoIndex<5, AntiSymmetric> SU5TwoIndexAntiSymm;
|
||||
|
||||
typedef SU_TwoIndex<Nc, AntiSymmetric> TwoIndexAntiSymmMatrices;
|
||||
|
||||
|
||||
if (Index < ncolour * (ncolour - 1) / 2) {
|
||||
baseOffDiagonal(a[Index][0], a[Index][1], eij);
|
||||
} else {
|
||||
baseDiagonal(Index, eij);
|
||||
}
|
||||
}
|
||||
|
||||
template <class cplx>
|
||||
static void baseDiagonal(int Index, iSUnMatrix<cplx> &eij) {
|
||||
eij = zero;
|
||||
eij()()(Index - ncolour * (ncolour - 1) / 2,
|
||||
Index - ncolour * (ncolour - 1) / 2) = 1.0;
|
||||
}
|
||||
|
||||
template <class cplx>
|
||||
static void baseOffDiagonal(int i, int j, iSUnMatrix<cplx> &eij) {
|
||||
eij = zero;
|
||||
for (int k = 0; k < ncolour; k++)
|
||||
for (int l = 0; l < ncolour; l++)
|
||||
eij()()(l, k) = delta(i, k) * delta(j, l) +
|
||||
S * delta(j, k) * delta(i, l);
|
||||
|
||||
RealD nrm = 1. / std::sqrt(2.0);
|
||||
eij = eij * nrm;
|
||||
}
|
||||
|
||||
static void printBase(void) {
|
||||
for (int gen = 0; gen < Dimension; gen++) {
|
||||
Matrix tmp;
|
||||
base(gen, tmp);
|
||||
std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << tmp << std::endl;
|
||||
}
|
||||
}
|
||||
|
||||
template <class cplx>
|
||||
static void generator(int Index, iSUnTwoIndexMatrix<cplx> &i2indTa) {
|
||||
Vector<typename SU<ncolour>::template iSUnMatrix<cplx> > ta(
|
||||
ncolour * ncolour - 1);
|
||||
Vector<typename SU<ncolour>::template iSUnMatrix<cplx> > eij(Dimension);
|
||||
typename SU<ncolour>::template iSUnMatrix<cplx> tmp;
|
||||
i2indTa = zero;
|
||||
|
||||
for (int a = 0; a < ncolour * ncolour - 1; a++)
|
||||
SU<ncolour>::generator(a, ta[a]);
|
||||
|
||||
for (int a = 0; a < Dimension; a++) base(a, eij[a]);
|
||||
|
||||
for (int a = 0; a < Dimension; a++) {
|
||||
tmp = transpose(ta[Index]) * adj(eij[a]) + adj(eij[a]) * ta[Index];
|
||||
for (int b = 0; b < Dimension; b++) {
|
||||
typename SU<ncolour>::template iSUnMatrix<cplx> tmp1 =
|
||||
tmp * eij[b];
|
||||
Complex iTr = TensorRemove(timesI(trace(tmp1)));
|
||||
i2indTa()()(a, b) = iTr;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
static void printGenerators(void) {
|
||||
for (int gen = 0; gen < ncolour * ncolour - 1; gen++) {
|
||||
TIMatrix i2indTa;
|
||||
generator(gen, i2indTa);
|
||||
std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << i2indTa << std::endl;
|
||||
}
|
||||
}
|
||||
|
||||
static void testGenerators(void) {
|
||||
TIMatrix i2indTa, i2indTb;
|
||||
std::cout << GridLogMessage << "2IndexRep - Checking if traceless"
|
||||
<< std::endl;
|
||||
for (int a = 0; a < ncolour * ncolour - 1; a++) {
|
||||
generator(a, i2indTa);
|
||||
std::cout << GridLogMessage << a << std::endl;
|
||||
assert(norm2(trace(i2indTa)) < 1.0e-6);
|
||||
}
|
||||
std::cout << GridLogMessage << std::endl;
|
||||
|
||||
std::cout << GridLogMessage << "2IndexRep - Checking if antihermitean"
|
||||
<< std::endl;
|
||||
for (int a = 0; a < ncolour * ncolour - 1; a++) {
|
||||
generator(a, i2indTa);
|
||||
std::cout << GridLogMessage << a << std::endl;
|
||||
assert(norm2(adj(i2indTa) + i2indTa) < 1.0e-6);
|
||||
}
|
||||
|
||||
std::cout << GridLogMessage << std::endl;
|
||||
std::cout << GridLogMessage
|
||||
<< "2IndexRep - Checking Tr[Ta*Tb]=delta(a,b)*(N +- 2)/2"
|
||||
<< std::endl;
|
||||
for (int a = 0; a < ncolour * ncolour - 1; a++) {
|
||||
for (int b = 0; b < ncolour * ncolour - 1; b++) {
|
||||
generator(a, i2indTa);
|
||||
generator(b, i2indTb);
|
||||
|
||||
// generator returns iTa, so we need a minus sign here
|
||||
Complex Tr = -TensorRemove(trace(i2indTa * i2indTb));
|
||||
std::cout << GridLogMessage << "a=" << a << "b=" << b << "Tr=" << Tr
|
||||
<< std::endl;
|
||||
}
|
||||
}
|
||||
std::cout << GridLogMessage << std::endl;
|
||||
}
|
||||
|
||||
static void TwoIndexLieAlgebraMatrix(
|
||||
const typename SU<ncolour>::LatticeAlgebraVector &h,
|
||||
LatticeTwoIndexMatrix &out, Real scale = 1.0) {
|
||||
conformable(h, out);
|
||||
GridBase *grid = out._grid;
|
||||
LatticeTwoIndexMatrix la(grid);
|
||||
TIMatrix i2indTa;
|
||||
|
||||
out = zero;
|
||||
for (int a = 0; a < ncolour * ncolour - 1; a++) {
|
||||
generator(a, i2indTa);
|
||||
la = peekColour(h, a) * i2indTa;
|
||||
out += la;
|
||||
}
|
||||
out *= scale;
|
||||
}
|
||||
|
||||
// Projects the algebra components
|
||||
// of a lattice matrix ( of dimension ncol*ncol -1 )
|
||||
static void projectOnAlgebra(
|
||||
typename SU<ncolour>::LatticeAlgebraVector &h_out,
|
||||
const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
|
||||
conformable(h_out, in);
|
||||
h_out = zero;
|
||||
TIMatrix i2indTa;
|
||||
Real coefficient = -2.0 / (ncolour + 2 * S) * scale;
|
||||
// 2/(Nc +/- 2) for the normalization of the trace in the two index rep
|
||||
for (int a = 0; a < ncolour * ncolour - 1; a++) {
|
||||
generator(a, i2indTa);
|
||||
auto tmp = real(trace(i2indTa * in)) * coefficient;
|
||||
pokeColour(h_out, tmp, a);
|
||||
}
|
||||
}
|
||||
|
||||
// a projector that keeps the generators stored to avoid the overhead of
|
||||
// recomputing them
|
||||
static void projector(typename SU<ncolour>::LatticeAlgebraVector &h_out,
|
||||
const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
|
||||
conformable(h_out, in);
|
||||
// to store the generators
|
||||
static std::vector<TIMatrix> i2indTa(ncolour * ncolour -1);
|
||||
h_out = zero;
|
||||
static bool precalculated = false;
|
||||
if (!precalculated) {
|
||||
precalculated = true;
|
||||
for (int a = 0; a < ncolour * ncolour - 1; a++) generator(a, i2indTa[a]);
|
||||
}
|
||||
|
||||
Real coefficient =
|
||||
-2.0 / (ncolour + 2 * S) * scale; // 2/(Nc +/- 2) for the normalization
|
||||
// of the trace in the two index rep
|
||||
|
||||
for (int a = 0; a < ncolour * ncolour - 1; a++) {
|
||||
auto tmp = real(trace(i2indTa[a] * in)) * coefficient;
|
||||
pokeColour(h_out, tmp, a);
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
// Some useful type names
|
||||
typedef SU_TwoIndex<Nc, Symmetric> TwoIndexSymmMatrices;
|
||||
typedef SU_TwoIndex<Nc, AntiSymmetric> TwoIndexAntiSymmMatrices;
|
||||
|
||||
typedef SU_TwoIndex<2, Symmetric> SU2TwoIndexSymm;
|
||||
typedef SU_TwoIndex<3, Symmetric> SU3TwoIndexSymm;
|
||||
typedef SU_TwoIndex<4, Symmetric> SU4TwoIndexSymm;
|
||||
typedef SU_TwoIndex<5, Symmetric> SU5TwoIndexSymm;
|
||||
|
||||
typedef SU_TwoIndex<2, AntiSymmetric> SU2TwoIndexAntiSymm;
|
||||
typedef SU_TwoIndex<3, AntiSymmetric> SU3TwoIndexAntiSymm;
|
||||
typedef SU_TwoIndex<4, AntiSymmetric> SU4TwoIndexAntiSymm;
|
||||
typedef SU_TwoIndex<5, AntiSymmetric> SU5TwoIndexAntiSymm;
|
||||
|
||||
|
||||
}
|
||||
}
|
||||
|
||||
#endif
|
||||
Reference in new issue
Block a user