mirror of
https://github.com/paboyle/Grid.git
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chillenzer
GitHub
commit
d169c275b6
@ -1 +0,0 @@
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../WilsonCloverFermionInstantiation.cc.master
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@ -1 +0,0 @@
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../WilsonFermionInstantiation.cc.master
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@ -1 +0,0 @@
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../WilsonKernelsInstantiation.cc.master
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@ -1 +0,0 @@
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../WilsonTMFermionInstantiation.cc.master
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@ -1 +0,0 @@
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#define IMPLEMENTATION SpWilsonTwoIndexSymmetricImplD
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@ -1 +0,0 @@
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../WilsonCloverFermionInstantiation.cc.master
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@ -1 +0,0 @@
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../WilsonFermionInstantiation.cc.master
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@ -1 +0,0 @@
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../WilsonKernelsInstantiation.cc.master
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@ -1 +0,0 @@
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../WilsonTMFermionInstantiation.cc.master
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@ -1 +0,0 @@
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#define IMPLEMENTATION SpWilsonTwoIndexSymmetricImplF
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@ -27,7 +27,7 @@ public:
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// types for the higher representation fields
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typedef typename Sp_TwoIndex<ncolour, S>::LatticeTwoIndexMatrix LatticeMatrix;
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typedef typename Sp_TwoIndex<ncolour, S>::LatticeTwoIndexField LatticeField;
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static const int Dimension = (ncolour * (ncolour + S) / 2) - 1;
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static const int Dimension = (ncolour * (ncolour + S) / 2) + S;
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static const bool isFundamental = false;
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//static const int nsp = Nc / 2;
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LatticeField U;
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@ -16,77 +16,90 @@
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//
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// (iT_a)^(ij)(lk) = i * ( tr[e^(ij)^dag e^(lk) T^trasp_a] +
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// tr[e^(lk)e^(ij)^dag T_a] ) //
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//
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//
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//
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////////////////////////////////////////////////////////////////////////
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// Authors: David Preti, Guido Cossu
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#ifndef QCD_UTIL_SP2N2INDEX_H
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#define QCD_UTIL_SP2N2INDEX_H
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#ifndef QCD_UTIL_SUN2INDEX_H
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#define QCD_UTIL_SUN2INDEX_H
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NAMESPACE_BEGIN(Grid);
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//enum SpTwoIndexSymmetry { S = 1, AS = -1 };
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enum TwoIndexSymmetry { Symmetric = 1, AntiSymmetric = -1 };
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//inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
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inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
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template <int ncolour, TwoIndexSymmetry S>
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class Sp_TwoIndex : public Sp<ncolour> {
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public:
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static const int nsp = ncolour/2;
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static const int Dimension = nsp * (ncolour + S) - 1 ;
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static const int NumGenerators = Sp<ncolour>::AlgebraDimension;
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template <int ncolour, TwoIndexSymmetry S, class group_name>
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class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
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public:
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static_assert(
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std::is_same<group_name, GroupName::Sp>::value ? S != Symmetric : true,
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"The symmetric two-index representation of Sp(2N) does not work "
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"currently. If you want to use it, you need to implement the equivalent "
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"of Eq. (27) and (28) from https://doi.org/10.48550/arXiv.2202.05516.");
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// The chosen convention is that we are taking ncolour to be N in SU<N> but 2N
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// in Sp(2N). ngroup is equal to N for SU but 2N/2 = N for Sp(2N).
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static_assert(std::is_same<group_name, GroupName::SU>::value or
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std::is_same<group_name, GroupName::Sp>::value,
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"ngroup is only implemented for SU and Sp currently.");
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static const int ngroup =
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std::is_same<group_name, GroupName::SU>::value ? ncolour : ncolour / 2;
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static const int Dimension = std::is_same<group_name, GroupName::SU>::value
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? ncolour * (ncolour + S) / 2
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: ngroup * (ncolour + S) + S;
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static const int NumGenerators =
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GaugeGroup<ncolour, group_name>::AlgebraDimension;
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template <typename vtype>
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using iSp2nTwoIndexMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
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using iGroupTwoIndexMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
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typedef iSp2nTwoIndexMatrix<Complex> TIMatrix;
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typedef iSp2nTwoIndexMatrix<ComplexF> TIMatrixF;
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typedef iSp2nTwoIndexMatrix<ComplexD> TIMatrixD;
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typedef iGroupTwoIndexMatrix<Complex> TIMatrix;
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typedef iGroupTwoIndexMatrix<ComplexF> TIMatrixF;
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typedef iGroupTwoIndexMatrix<ComplexD> TIMatrixD;
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typedef iSp2nTwoIndexMatrix<vComplex> vTIMatrix;
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typedef iSp2nTwoIndexMatrix<vComplexF> vTIMatrixF;
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typedef iSp2nTwoIndexMatrix<vComplexD> vTIMatrixD;
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typedef iGroupTwoIndexMatrix<vComplex> vTIMatrix;
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typedef iGroupTwoIndexMatrix<vComplexF> vTIMatrixF;
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typedef iGroupTwoIndexMatrix<vComplexD> vTIMatrixD;
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typedef Lattice<vTIMatrix> LatticeTwoIndexMatrix;
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typedef Lattice<vTIMatrixF> LatticeTwoIndexMatrixF;
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typedef Lattice<vTIMatrixD> LatticeTwoIndexMatrixD;
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typedef Lattice<iVector<iScalar<iMatrix<vComplex, Dimension> >, Nd> >
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LatticeTwoIndexField;
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LatticeTwoIndexField;
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typedef Lattice<iVector<iScalar<iMatrix<vComplexF, Dimension> >, Nd> >
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LatticeTwoIndexFieldF;
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LatticeTwoIndexFieldF;
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typedef Lattice<iVector<iScalar<iMatrix<vComplexD, Dimension> >, Nd> >
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LatticeTwoIndexFieldD;
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LatticeTwoIndexFieldD;
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template <typename vtype>
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using iSp2nMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
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using iGroupMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
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typedef iSp2nMatrix<Complex> Matrix;
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typedef iSp2nMatrix<ComplexF> MatrixF;
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typedef iSp2nMatrix<ComplexD> MatrixD;
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typedef iGroupMatrix<Complex> Matrix;
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typedef iGroupMatrix<ComplexF> MatrixF;
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typedef iGroupMatrix<ComplexD> MatrixD;
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template <class cplx>
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static void base(int Index, iSp2nMatrix<cplx> &eij) {
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static void base(int Index, iGroupMatrix<cplx> &eij) {
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// returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
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assert(Index < NumGenerators);
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assert(Index < Dimension);
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eij = Zero();
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// for the linearisation of the 2 indexes
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static int a[ncolour * (ncolour - 1) / 2][2]; // store the a <-> i,j
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// for the linearisation of the 2 indexes
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static int a[ncolour * (ncolour - 1) / 2][2]; // store the a <-> i,j
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static bool filled = false;
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if (!filled) {
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int counter = 0;
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for (int i = 1; i < ncolour; i++) {
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for (int j = 0; j < i; j++) {
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if (i==nsp)
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{
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a[counter][0] = i;
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if (j==0 && ngroup == ncolour/2 && i==ngroup+j) {
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//std::cout << "skipping" << std::endl; // for Sp2n this vanishes identically.
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j = j+1;
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}
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a[counter][0] = i;
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a[counter][1] = j;
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counter++;
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}
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@ -95,69 +108,65 @@ public:
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}
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if (Index < ncolour * (ncolour - 1) / 2) {
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baseOffDiagonal(a[Index][0], a[Index][1], eij);
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baseOffDiagonal(a[Index][0], a[Index][1], eij, group_name());
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} else {
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baseDiagonal(Index, eij);
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}
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}
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template <class cplx>
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static void baseDiagonal(int Index, iSp2nMatrix<cplx> &eij) {
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static void baseDiagonal(int Index, iGroupMatrix<cplx> &eij) {
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eij = Zero();
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eij()()(Index - ncolour * (ncolour - 1) / 2,
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Index - ncolour * (ncolour - 1) / 2) = 1.0;
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}
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template <class cplx>
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static void baseOffDiagonal(int i, int j, iSp2nMatrix<cplx> &eij) {
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static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij,
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GroupName::Sp) {
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eij = Zero();
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//std::cout << GridLogMessage << " doing i j = " << i << j << std::endl;
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RealD tmp;
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RealD tmp;
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if ( (i == nsp + j) && (1 <= j) && (j < nsp) )
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{
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for (int k = 0; k < nsp; k++)
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{
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if (k < j)
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{
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//std::cout << GridLogMessage << "b=N+a 1"<< std::endl;
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//std::cout << GridLogMessage << "j i "<< j << i << std::endl;
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tmp = sqrt( 2*j*(j+1) );
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tmp = 1/tmp;
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tmp *= std::sqrt(2.0);
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eij()()(k,k+nsp) = tmp;
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eij()()(k+nsp,k) = - tmp;
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}
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if (k == j)
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{
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//std::cout << GridLogMessage << "b=N+a 2"<< std::endl;
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//std::cout << GridLogMessage << "j i "<< j << i << std::endl;
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tmp = sqrt(2*j*(j+1) );
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tmp = -j/tmp;
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tmp *= std::sqrt(2.0);
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eij()()(k,k+nsp) = tmp ;
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eij()()(k+nsp,k) = - tmp ;
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}
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}
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if ((i == ngroup + j) && (1 <= j) && (j < ngroup)) {
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for (int k = 0; k < ngroup; k++) {
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if (k < j) {
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tmp = sqrt(2 * j * (j + 1));
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tmp = 1 / tmp;
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tmp *= std::sqrt(2.0);
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eij()()(k, k + ngroup) = tmp;
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eij()()(k + ngroup, k) = -tmp;
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}
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else if (i != nsp+j)
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{
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for (int k = 0; k < ncolour; k++)
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for (int l = 0; l < ncolour; l++)
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{
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eij()()(l, k) = delta(i, k) * delta(j, l) + S * delta(j, k) * delta(i, l);
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}
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if (k == j) {
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tmp = sqrt(2 * j * (j + 1));
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tmp = -j / tmp;
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tmp *= std::sqrt(2.0);
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eij()()(k, k + ngroup) = tmp;
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eij()()(k + ngroup, k) = -tmp;
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}
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}
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}
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else if (i != ngroup + j) {
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for (int k = 0; k < ncolour; k++)
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for (int l = 0; l < ncolour; l++) {
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eij()()(l, k) =
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delta(i, k) * delta(j, l) + S * delta(j, k) * delta(i, l);
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}
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}
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RealD nrm = 1. / std::sqrt(2.0);
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eij = eij * nrm;
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}
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template <class cplx>
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static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij,
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GroupName::SU) {
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eij = Zero();
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for (int k = 0; k < ncolour; k++)
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for (int l = 0; l < ncolour; l++)
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eij()()(l, k) =
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delta(i, k) * delta(j, l) + S * delta(j, k) * delta(i, l);
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RealD nrm = 1. / std::sqrt(2.0);
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eij = eij * nrm;
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@ -174,23 +183,21 @@ public:
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}
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template <class cplx>
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static void generator(int Index, iSp2nTwoIndexMatrix<cplx> &i2indTa) {
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Vector<iSp2nMatrix<cplx> > ta(
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NumGenerators);
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Vector<iSp2nMatrix<cplx> > eij(Dimension);
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iSp2nMatrix<cplx> tmp;
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static void generator(int Index, iGroupTwoIndexMatrix<cplx> &i2indTa) {
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Vector<iGroupMatrix<cplx> > ta(NumGenerators);
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Vector<iGroupMatrix<cplx> > eij(Dimension);
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iGroupMatrix<cplx> tmp;
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i2indTa = Zero();
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for (int a = 0; a < NumGenerators; a++)
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Sp<ncolour>::generator(a, ta[a]);
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GaugeGroup<ncolour, group_name>::generator(a, ta[a]);
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for (int a = 0; a < Dimension; a++) base(a, eij[a]);
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for (int a = 0; a < Dimension; a++) {
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tmp = transpose(ta[Index]) * adj(eij[a]) + adj(eij[a]) * ta[Index];
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for (int b = 0; b < Dimension; b++) {
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iSp2nMatrix<cplx> tmp1 =
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tmp * eij[b];
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iGroupMatrix<cplx> tmp1 = tmp * eij[b];
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Complex iTr = TensorRemove(timesI(trace(tmp1)));
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i2indTa()()(a, b) = iTr;
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}
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@ -239,14 +246,21 @@ public:
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Complex Tr = -TensorRemove(trace(i2indTa * i2indTb));
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std::cout << GridLogMessage << "a=" << a << "b=" << b << "Tr=" << Tr
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<< std::endl;
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if (a == b) {
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assert(imag(Tr) < 1e-8);
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assert(real(Tr) - ((ncolour + S * 2) * 0.5) < 1e-8);
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} else {
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assert(imag(Tr) < 1e-8);
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assert(real(Tr) < 1e-8);
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}
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}
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}
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std::cout << GridLogMessage << std::endl;
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}
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static void TwoIndexLieAlgebraMatrix(
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const typename Sp<ncolour>::LatticeAlgebraVector &h,
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LatticeTwoIndexMatrix &out, Real scale = 1.0) {
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const typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h,
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LatticeTwoIndexMatrix &out, Real scale = 1.0) {
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conformable(h, out);
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GridBase *grid = out.Grid();
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LatticeTwoIndexMatrix la(grid);
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@ -261,11 +275,11 @@ public:
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out *= scale;
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}
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// Projects the algebra components
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// Projects the algebra components
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// of a lattice matrix ( of dimension ncol*ncol -1 )
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static void projectOnAlgebra(
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typename Sp<ncolour>::LatticeAlgebraVector &h_out,
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const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
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typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
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const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
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conformable(h_out, in);
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h_out = Zero();
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TIMatrix i2indTa;
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@ -273,14 +287,15 @@ public:
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// 2/(Nc +/- 2) for the normalization of the trace in the two index rep
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for (int a = 0; a < NumGenerators; a++) {
|
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generator(a, i2indTa);
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pokeColour(h_out, real(trace(i2indTa * in)) * coefficient, a);
|
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pokeColour(h_out, real(trace(i2indTa * in)) * coefficient, a);
|
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}
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}
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// a projector that keeps the generators stored to avoid the overhead of
|
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// recomputing them
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static void projector(typename Sp<ncolour>::LatticeAlgebraVector &h_out,
|
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const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
|
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static void projector(
|
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typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
|
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const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
|
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conformable(h_out, in);
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// to store the generators
|
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static std::vector<TIMatrix> i2indTa(NumGenerators);
|
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@ -292,7 +307,7 @@ public:
|
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}
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Real coefficient =
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-2.0 / (ncolour + 2 * S) * scale; // 2/(Nc +/- 2) for the normalization
|
||||
-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 < NumGenerators; a++) {
|
||||
@ -302,18 +317,34 @@ public:
|
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}
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||||
};
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||||
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template <int ncolour, TwoIndexSymmetry S>
|
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using SU_TwoIndex = GaugeGroupTwoIndex<ncolour, S, GroupName::SU>;
|
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|
||||
// Some useful type names
|
||||
typedef SU_TwoIndex<Nc, Symmetric> TwoIndexSymmMatrices;
|
||||
typedef SU_TwoIndex<Nc, AntiSymmetric> TwoIndexAntiSymmMatrices;
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||||
typedef SU_TwoIndex<2, Symmetric> SU2TwoIndexSymm;
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typedef SU_TwoIndex<3, Symmetric> SU3TwoIndexSymm;
|
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typedef SU_TwoIndex<4, Symmetric> SU4TwoIndexSymm;
|
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typedef SU_TwoIndex<5, Symmetric> SU5TwoIndexSymm;
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typedef SU_TwoIndex<2, AntiSymmetric> SU2TwoIndexAntiSymm;
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typedef SU_TwoIndex<3, AntiSymmetric> SU3TwoIndexAntiSymm;
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typedef SU_TwoIndex<4, AntiSymmetric> SU4TwoIndexAntiSymm;
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typedef SU_TwoIndex<5, AntiSymmetric> SU5TwoIndexAntiSymm;
|
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template <int ncolour, TwoIndexSymmetry S>
|
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using Sp_TwoIndex = GaugeGroupTwoIndex<ncolour, S, GroupName::Sp>;
|
||||
|
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typedef Sp_TwoIndex<Nc, Symmetric> SpTwoIndexSymmMatrices;
|
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typedef Sp_TwoIndex<Nc, AntiSymmetric> SpTwoIndexAntiSymmMatrices;
|
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typedef Sp_TwoIndex<2, Symmetric> Sp2TwoIndexSymm;
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typedef Sp_TwoIndex<4, Symmetric> Sp4TwoIndexSymm;
|
||||
|
||||
typedef Sp_TwoIndex<2, AntiSymmetric> Sp2TwoIndexAntiSymm;
|
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typedef Sp_TwoIndex<4, AntiSymmetric> Sp4TwoIndexAntiSymm;
|
||||
|
||||
|
||||
NAMESPACE_END(Grid);
|
||||
|
||||
#endif
|
||||
@ -1,271 +0,0 @@
|
||||
////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// * Two index representation 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
|
||||
//
|
||||
//
|
||||
// base for NxN two index (anti-symmetric) matrices
|
||||
// normalized to 1 (d_ij is the kroenecker delta)
|
||||
//
|
||||
// (e^(ij)_{kl} = 1 / sqrt(2) (d_ik d_jl +/- d_jk d_il)
|
||||
//
|
||||
// Then the generators are written as
|
||||
//
|
||||
// (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_BEGIN(Grid);
|
||||
|
||||
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> >
|
||||
LatticeTwoIndexFieldF;
|
||||
typedef Lattice<iVector<iScalar<iMatrix<vComplexD, Dimension> >, Nd> >
|
||||
LatticeTwoIndexFieldD;
|
||||
|
||||
template <typename vtype>
|
||||
using iSUnMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
|
||||
|
||||
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 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;
|
||||
counter++;
|
||||
}
|
||||
}
|
||||
filled = true;
|
||||
}
|
||||
|
||||
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<iSUnMatrix<cplx> > ta(ncolour * ncolour - 1);
|
||||
Vector<iSUnMatrix<cplx> > eij(Dimension);
|
||||
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++) {
|
||||
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);
|
||||
pokeColour(h_out, real(trace(i2indTa * in)) * coefficient, 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;
|
||||
|
||||
NAMESPACE_END(Grid);
|
||||
|
||||
#endif
|
||||
@ -10,8 +10,7 @@
|
||||
// Include representations
|
||||
#include <Grid/qcd/utils/GaugeGroup.h>
|
||||
#include <Grid/qcd/utils/SUnAdjoint.h>
|
||||
#include <Grid/qcd/utils/SUnTwoIndex.h>
|
||||
#include <Grid/qcd/utils/Sp2nTwoIndex.h>
|
||||
#include <Grid/qcd/utils/GaugeGroupTwoIndex.h>
|
||||
|
||||
// All-to-all contraction kernels that touch the
|
||||
// internal lattice structure
|
||||
|
||||
@ -35,7 +35,7 @@ directory
|
||||
|
||||
#include <Grid/qcd/utils/GaugeGroup.h>
|
||||
#include <Grid/qcd/utils/SUnAdjoint.h>
|
||||
#include <Grid/qcd/utils/SUnTwoIndex.h>
|
||||
#include <Grid/qcd/utils/GaugeGroupTwoIndex.h>
|
||||
|
||||
#include <Grid/qcd/representations/adjoint.h>
|
||||
#include <Grid/qcd/representations/two_index.h>
|
||||
|
||||
110
tests/sp2n/Test_2as_base.cc
Normal file
110
tests/sp2n/Test_2as_base.cc
Normal file
@ -0,0 +1,110 @@
|
||||
#include <Grid/Grid.h>
|
||||
|
||||
#define verbose 0
|
||||
|
||||
using namespace Grid;
|
||||
|
||||
int main(int argc, char** argv) {
|
||||
Grid_init(&argc, &argv);
|
||||
|
||||
const int this_nc = 4;
|
||||
const int this_n = this_nc/2;
|
||||
const int this_irrep_dim = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension;
|
||||
const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
|
||||
typedef Sp_TwoIndex<this_nc, AntiSymmetric>::iGroupMatrix<Complex> Matrix;
|
||||
typedef Sp_TwoIndex<this_nc, AntiSymmetric>::iGroupTwoIndexMatrix<Complex> ASMatrix;
|
||||
|
||||
Matrix Omega;
|
||||
Matrix eij_a;
|
||||
Matrix eij_b;
|
||||
Matrix eij_c;
|
||||
Matrix e_sum;
|
||||
Omega = Zero();
|
||||
for (int i = 0; i < this_n; i++)
|
||||
{
|
||||
Omega()()(i, this_n + i) = 1.;
|
||||
Omega()()(this_n + i, i) = -1;
|
||||
}
|
||||
std::cout << "Omega " << Omega << std::endl;
|
||||
|
||||
RealD realA;
|
||||
RealD realB;
|
||||
std::cout << GridLogMessage << "2as dimension is " << this_irrep_dim << std::endl;
|
||||
std::cout << GridLogMessage << "algebra dimension is " << this_algebra_dim << std::endl;
|
||||
realA = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension + Sp_TwoIndex<this_nc, Symmetric>::Dimension;
|
||||
realB = Sp<this_nc>::Dimension*Sp<this_nc>::Dimension;
|
||||
assert ( realA == realB);
|
||||
|
||||
std::cout << GridLogMessage << "checking base is antisymmetric " << std::endl;
|
||||
for (int a=0; a < this_irrep_dim; a++)
|
||||
{
|
||||
Sp_TwoIndex<this_nc, AntiSymmetric>::base(a, eij_c);
|
||||
e_sum = eij_c + transpose(eij_c);
|
||||
std::cout << GridLogMessage << "e_ab + e_ab^T " << norm2(e_sum) << std::endl;
|
||||
assert(norm2(e_sum) < 1e-8);
|
||||
|
||||
}
|
||||
std::cout << GridLogMessage << "Checking Tr (e^(ab) Omega ) = 0 and Tr (e^(ab) e^(cd) = delta^((ab)(cd)) ) " << std::endl;
|
||||
for (int a=0; a < Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension; a++) {
|
||||
Sp_TwoIndex<this_nc, AntiSymmetric>::base(a, eij_a);
|
||||
realA = norm2(trace(Omega*eij_a));
|
||||
std::cout << GridLogMessage << "Omega trace for (ab) = " << a << std::endl;
|
||||
assert(realA == 0);
|
||||
for (int b=0; b < Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension; b++) {
|
||||
Sp_TwoIndex<this_nc, AntiSymmetric>::base(b, eij_b);
|
||||
auto d_ab = TensorRemove(trace(eij_a * eij_b));
|
||||
#if verbose
|
||||
std::cout << GridLogMessage << "Tr( e_{ab=" << a << "} e_{cd=" << b << "} ) = " << d_ab << std::endl;
|
||||
#endif
|
||||
std::cout << GridLogMessage << "Orthonormality for (ab) = " << a << std::endl;
|
||||
if (a==b) {
|
||||
assert(real(d_ab)+1 < 1e-8);
|
||||
assert(imag(d_ab) < 1e-8);
|
||||
} else {
|
||||
assert(real(d_ab) < 1e-8);
|
||||
assert(imag(d_ab) < 1e-8);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
int sum = 0;
|
||||
int sum_im = 0;
|
||||
Vector<Matrix> ta_fund(this_algebra_dim);
|
||||
Vector<Matrix> eij(this_irrep_dim);
|
||||
Matrix tmp_l;
|
||||
Matrix tmp_r;
|
||||
for (int n = 0; n < this_algebra_dim; n++)
|
||||
{
|
||||
Sp<this_nc>::generator(n, ta_fund[n]);
|
||||
}
|
||||
for (int a = 0; a < this_irrep_dim; a++)
|
||||
{
|
||||
Sp_TwoIndex<this_nc, AntiSymmetric>::base(a, eij[a]);
|
||||
}
|
||||
for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
|
||||
{
|
||||
Complex iTr;
|
||||
sum = 0;
|
||||
sum_im = 0;
|
||||
std::cout << GridLogMessage << "generator number " << gen_id << std::endl;
|
||||
for (int a = 0; a < this_irrep_dim; a++)
|
||||
{
|
||||
|
||||
tmp_l = adj(eij[a])*ta_fund[gen_id]*eij[a];
|
||||
tmp_r = adj(eij[a])*eij[a]*transpose(ta_fund[gen_id]);
|
||||
#if verbose
|
||||
std::cout << GridLogMessage << " as_indx = " << a << " eDag T_F e = " << std::endl << tmp_l << std::endl;
|
||||
std::cout << GridLogMessage << " as_indx = " << a << " eDag e T_F^T = " << std::endl << tmp_r << std::endl;
|
||||
#endif
|
||||
std::cout << GridLogMessage << " as_indx = " << a << " Tr(sum) = " << TensorRemove(trace(tmp_l+tmp_r)) << std::endl;
|
||||
sum += real(TensorRemove(trace(tmp_l+tmp_r)));
|
||||
sum_im += imag(TensorRemove(trace(tmp_l+tmp_r)));
|
||||
}
|
||||
std::cout << GridLogMessage << "re-evaluated trace of the generator " << gen_id << " is " << sum << " " << sum_im << std::endl;
|
||||
assert ( sum < 1e-8) ;
|
||||
assert ( sum_im < 1e-8) ;
|
||||
|
||||
}
|
||||
|
||||
Grid_finalize();
|
||||
}
|
||||
@ -2,29 +2,32 @@
|
||||
|
||||
int main(int argc, char **argv) {
|
||||
using namespace Grid;
|
||||
|
||||
typedef Representations< SpFundamentalRepresentation, SpTwoIndexAntiSymmetricRepresentation > TheRepresentations;
|
||||
|
||||
typedef Representations<SpFundamentalRepresentation,
|
||||
SpTwoIndexAntiSymmetricRepresentation>
|
||||
TheRepresentations;
|
||||
|
||||
Grid_init(&argc, &argv);
|
||||
|
||||
typedef GenericSp2nHMCRunnerHirep<TheRepresentations, MinimumNorm2> HMCWrapper;
|
||||
|
||||
typedef GenericSp2nHMCRunnerHirep<TheRepresentations, MinimumNorm2>
|
||||
HMCWrapper;
|
||||
typedef SpWilsonTwoIndexAntiSymmetricImplR FermionImplPolicy;
|
||||
typedef SpWilsonTwoIndexAntiSymmetricFermionR FermionAction;
|
||||
typedef typename FermionAction::FermionField FermionField;
|
||||
|
||||
|
||||
//::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
|
||||
|
||||
|
||||
HMCWrapper TheHMC;
|
||||
|
||||
|
||||
TheHMC.Resources.AddFourDimGrid("gauge");
|
||||
|
||||
|
||||
// Checkpointer definition
|
||||
CheckpointerParameters CPparams;
|
||||
CPparams.config_prefix = "ckpoint_lat";
|
||||
CPparams.rng_prefix = "ckpoint_rng";
|
||||
CPparams.saveInterval = 100;
|
||||
CPparams.format = "IEEE64BIG";
|
||||
|
||||
|
||||
TheHMC.Resources.LoadNerscCheckpointer(CPparams);
|
||||
|
||||
RNGModuleParameters RNGpar;
|
||||
@ -35,48 +38,45 @@ int main(int argc, char **argv) {
|
||||
// Construct observables
|
||||
typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
|
||||
TheHMC.Resources.AddObservable<PlaqObs>();
|
||||
|
||||
RealD beta = 6.7 ;
|
||||
|
||||
|
||||
RealD beta = 6.7;
|
||||
|
||||
SpWilsonGaugeActionR Waction(beta);
|
||||
|
||||
|
||||
auto GridPtr = TheHMC.Resources.GetCartesian();
|
||||
auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
|
||||
|
||||
SpTwoIndexAntiSymmetricRepresentation::LatticeField U(GridPtr);
|
||||
//LatticeGaugeField U(GridPtr);
|
||||
|
||||
RealD mass = -0.115;
|
||||
|
||||
|
||||
std::vector<Complex> boundary = {-1,-1,-1,-1};
|
||||
SpTwoIndexAntiSymmetricRepresentation::LatticeField U(GridPtr);
|
||||
// LatticeGaugeField U(GridPtr);
|
||||
|
||||
RealD mass = -0.115;
|
||||
|
||||
std::vector<Complex> boundary = {-1, -1, -1, -1};
|
||||
FermionAction::ImplParams bc(boundary);
|
||||
FermionAction FermOp(U, *GridPtr, *GridRBPtr, mass, bc);
|
||||
|
||||
|
||||
|
||||
ConjugateGradient<FermionField> CG(1.0e-8, 2000, false);
|
||||
|
||||
|
||||
TwoFlavourPseudoFermionAction<FermionImplPolicy> Nf2(FermOp, CG, CG);
|
||||
|
||||
|
||||
Nf2.is_smeared = false;
|
||||
std::cout << GridLogMessage << "mass " << mass << std::endl;
|
||||
|
||||
ActionLevel<HMCWrapper::Field, TheRepresentations > Level1(1);
|
||||
Level1.push_back(&Nf2);
|
||||
|
||||
ActionLevel<HMCWrapper::Field, TheRepresentations > Level2(4);
|
||||
Level2.push_back(&Waction);
|
||||
|
||||
TheHMC.TheAction.push_back(Level1);
|
||||
TheHMC.TheAction.push_back(Level2);
|
||||
|
||||
TheHMC.Parameters.MD.MDsteps = 16;
|
||||
TheHMC.Parameters.MD.trajL = 1.0;
|
||||
|
||||
TheHMC.ReadCommandLine(argc, argv);
|
||||
TheHMC.Run();
|
||||
|
||||
|
||||
|
||||
ActionLevel<HMCWrapper::Field, TheRepresentations> Level1(1);
|
||||
Level1.push_back(&Nf2);
|
||||
|
||||
ActionLevel<HMCWrapper::Field, TheRepresentations> Level2(4);
|
||||
Level2.push_back(&Waction);
|
||||
|
||||
TheHMC.TheAction.push_back(Level1);
|
||||
TheHMC.TheAction.push_back(Level2);
|
||||
|
||||
TheHMC.Parameters.MD.MDsteps = 16;
|
||||
TheHMC.Parameters.MD.trajL = 1.0;
|
||||
|
||||
TheHMC.ReadCommandLine(argc, argv);
|
||||
TheHMC.Run();
|
||||
|
||||
Grid_finalize();
|
||||
}
|
||||
|
||||
|
||||
@ -4,15 +4,10 @@ using namespace Grid;
|
||||
|
||||
int main(int argc, char** argv) {
|
||||
Grid_init(&argc, &argv);
|
||||
|
||||
//std::vector<int> latt({4, 4, 4, 8});
|
||||
//GridCartesian* grid = SpaceTimeGrid::makeFourDimGrid(
|
||||
//latt, GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
|
||||
//GridRedBlackCartesian* rbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(grid);
|
||||
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(2)" << std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(2) (print and test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
@ -21,7 +16,7 @@ int main(int argc, char** argv) {
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(4)" << std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(4) (print and test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
@ -30,21 +25,43 @@ int main(int argc, char** argv) {
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(6)" << std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(6) (test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
Sp6::printGenerators();
|
||||
|
||||
Sp6::testGenerators();
|
||||
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(8)" << std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(8) (test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
Sp8::printGenerators();
|
||||
Sp8::testGenerators();
|
||||
Sp8::testGenerators();
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(4) TwoIndexAS (test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
Sp_TwoIndex<4, AntiSymmetric>::testGenerators();
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(6) TwoIndexAS (test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
Sp_TwoIndex<6, AntiSymmetric>::testGenerators();
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(8) TwoIndexAS (test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
Sp_TwoIndex<8, AntiSymmetric>::testGenerators();
|
||||
|
||||
Grid_finalize();
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user