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cleaner twoindex class, cleaner tests
This commit is contained in:
Alessandro Lupo
parent
e61a9ed2b4
commit
fe88a0c12f
@ -31,23 +31,7 @@ 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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template <int nc, TwoIndexSymmetry S, class group_name>
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struct DimensionHelper;
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template <int nc, TwoIndexSymmetry S>
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struct DimensionHelper<nc, S, GroupName::SU> {
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static const int Dimension = nc * (nc + S) / 2;
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};
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template <int nc>
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struct DimensionHelper<nc, Symmetric, GroupName::Sp> {
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static const int Dimension = nc * (nc + 1) / 2;
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};
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template <int nc>
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struct DimensionHelper<nc, AntiSymmetric, GroupName::Sp> {
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static const int Dimension = (nc / 2) * (nc - 1) - 1;
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};
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namespace detail {
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template <class cplx, int nc, TwoIndexSymmetry S>
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struct baseOffDiagonalSpHelper;
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@ -106,6 +90,8 @@ struct baseOffDiagonalSpHelper<cplx, nc, Symmetric> {
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}
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};
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} // closing detail namespace
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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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@ -117,7 +103,11 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
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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 =
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DimensionHelper<ncolour, S, group_name>::Dimension;
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(ncolour * (ncolour + S) / 2) + (std::is_same<group_name, GroupName::Sp>::value ? (S - 1) / 2 : 0);
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static const int DimensionAS =
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(ncolour * (ncolour - 1) / 2) + (std::is_same<group_name, GroupName::Sp>::value ? (- 1) : 0);
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static const int DimensionS =
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ncolour * (ncolour + 1) / 2;
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static const int NumGenerators =
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GaugeGroup<ncolour, group_name>::AlgebraDimension;
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@ -149,43 +139,9 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
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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, iGroupMatrix<cplx> &eij) {
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// returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
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base(Index, eij, group_name());
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}
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template <class cplx>
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static void base(int Index, iGroupMatrix<cplx> &eij, GroupName::SU) {
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// returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
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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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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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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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}
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filled = true;
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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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} 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 base(int Index, iGroupMatrix<cplx> &eij, GroupName::Sp) {
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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 < Dimension);
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eij = Zero();
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@ -197,24 +153,27 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
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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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a[counter][0] = i;
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if (j==0 && i==ngroup+j && S==-1) {
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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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if (std::is_same<group_name, GroupName::Sp>::value)
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{
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if (j==0 && i==ngroup+j && S==-1) {
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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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}
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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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}
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filled = true;
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}
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if (Index < DimensionHelper<ncolour, AntiSymmetric, GroupName::Sp>::Dimension + 1) { // +1 the singlet
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baseOffDiagonalSpHelper<cplx, ncolour, S>::baseOffDiagonalSp(a[Index][0], a[Index][1], eij);
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if (Index < ncolour*ncolour - DimensionS)
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{
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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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baseDiagonal(Index, eij);
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}
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}
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}
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template <class cplx>
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static void baseDiagonal(int Index, iGroupMatrix<cplx> &eij) {
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@ -224,7 +183,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
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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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static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij, 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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@ -236,8 +195,8 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
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}
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template <class cplx>
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static void baseOffDiagonalSp(int i, int j, iGroupMatrix<cplx> &eij) {
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baseOffDiagonalSpHelper<cplx, ncolour, S>::baseOffDiagonalSp(i, j, eij);
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static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij, GroupName::Sp) {
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detail::baseOffDiagonalSpHelper<cplx, ncolour, S>::baseOffDiagonalSp(i, j, eij);
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}
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static void printBase(void) {
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@ -324,30 +324,30 @@ int main(int argc, char** argv) {
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}
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TIndexRep.update_representation(UV2);
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typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField UVr2 = TIndexRep.U; // (U_f * V_f)_r
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typename TwoIndexRep< Nc, Symmetric>::LatticeField UVr2 = TIndexRep.U; // (U_f * V_f)_r
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TIndexRep.update_representation(U2);
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typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField Ur2 = TIndexRep.U; // U_r
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typename TwoIndexRep< Nc, Symmetric>::LatticeField Ur2 = TIndexRep.U; // U_r
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TIndexRep.update_representation(V2);
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typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField Vr2 = TIndexRep.U; // V_r
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typename TwoIndexRep< Nc, Symmetric>::LatticeField Vr2 = TIndexRep.U; // V_r
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typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField Ur2Vr2(grid);
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typename TwoIndexRep< Nc, Symmetric>::LatticeField Ur2Vr2(grid);
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Ur2Vr2 = Zero();
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for (int mu = 0; mu < Nd; mu++) {
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typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeMatrix Urmu2 = peekLorentz(Ur2,mu);
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typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeMatrix Vrmu2 = peekLorentz(Vr2,mu);
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typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Urmu2 = peekLorentz(Ur2,mu);
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typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Vrmu2 = peekLorentz(Vr2,mu);
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pokeLorentz(Ur2Vr2,Urmu2*Vrmu2, mu);
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}
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typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField Diff_check2 = UVr2 - Ur2Vr2;
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typename TwoIndexRep< Nc, Symmetric>::LatticeField Diff_check2 = UVr2 - Ur2Vr2;
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std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Two Index Symmetric): " << norm2(Diff_check2) << std::endl;
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// Check correspondence of algebra and group transformations
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// Create a random vector
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SU<Nc>::LatticeAlgebraVector h_sym(grid);
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typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix Ar_sym(grid);
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typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ar_sym(grid);
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random(gridRNG,h_sym);
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h_sym = real(h_sym);
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SU_TwoIndex<Nc,Symmetric>::TwoIndexLieAlgebraMatrix(h_sym,Ar_sym);
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@ -360,13 +360,13 @@ int main(int argc, char** argv) {
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// Exponentiate
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typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix U2iS(grid);
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typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix U2iS(grid);
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U2iS = expMat(Ar_sym, 1.0, 16);
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typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix uno2iS(grid);
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typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix uno2iS(grid);
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uno2iS = 1.0;
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// Check matrix U2iS, must be real orthogonal
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typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix Ucheck2iS = U2iS - conjugate(U2iS);
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typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ucheck2iS = U2iS - conjugate(U2iS);
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std::cout << GridLogMessage << "Reality check: " << norm2(Ucheck2iS)
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<< std::endl;
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@ -399,15 +399,15 @@ int main(int argc, char** argv) {
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TIndexRep.update_representation(U);
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Ur2 = TIndexRep.U; // U_r
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typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix Ur02 = peekLorentz(Ur2,0); // this should be the same as U2iS
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typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ur02 = peekLorentz(Ur2,0); // this should be the same as U2iS
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typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix Diff_check_mat2 = Ur02 - U2iS;
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typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Diff_check_mat2 = Ur02 - U2iS;
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std::cout << GridLogMessage << "Projections structure check group difference (Two Index Symmetric): " << norm2(Diff_check_mat2) << std::endl;
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if (TwoIndexRep<Nc, AntiSymmetric , GroupName::SU>::Dimension != 1){
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if (TwoIndexRep<Nc, AntiSymmetric>::Dimension != 1){
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std::cout << GridLogMessage << "*********************************************"
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<< std::endl;
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@ -416,7 +416,7 @@ int main(int argc, char** argv) {
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std::cout << GridLogMessage << "Two Index anti-Symmetric: Check Group Structure"
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<< std::endl;
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// Testing HMC representation classes
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TwoIndexRep< Nc, AntiSymmetric, GroupName::SU > TIndexRepA(grid);
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TwoIndexRep< Nc, AntiSymmetric> TIndexRepA(grid);
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// Test group structure
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@ -434,30 +434,30 @@ int main(int argc, char** argv) {
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}
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TIndexRep.update_representation(UV2A);
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typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField UVr2A = TIndexRepA.U; // (U_f * V_f)_r
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typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField UVr2A = TIndexRepA.U; // (U_f * V_f)_r
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TIndexRep.update_representation(U2A);
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typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField Ur2A = TIndexRepA.U; // U_r
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typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField Ur2A = TIndexRepA.U; // U_r
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TIndexRep.update_representation(V2A);
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typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField Vr2A = TIndexRepA.U; // V_r
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typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField Vr2A = TIndexRepA.U; // V_r
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typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField Ur2Vr2A(grid);
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typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField Ur2Vr2A(grid);
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Ur2Vr2A = Zero();
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for (int mu = 0; mu < Nd; mu++) {
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typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeMatrix Urmu2A = peekLorentz(Ur2A,mu);
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typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeMatrix Vrmu2A = peekLorentz(Vr2A,mu);
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typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Urmu2A = peekLorentz(Ur2A,mu);
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typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Vrmu2A = peekLorentz(Vr2A,mu);
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pokeLorentz(Ur2Vr2A,Urmu2A*Vrmu2A, mu);
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}
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typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField Diff_check2A = UVr2A - Ur2Vr2A;
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typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField Diff_check2A = UVr2A - Ur2Vr2A;
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std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Two Index anti-Symmetric): " << norm2(Diff_check2A) << std::endl;
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// Check correspondence of algebra and group transformations
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// Create a random vector
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SU<Nc>::LatticeAlgebraVector h_Asym(grid);
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typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix Ar_Asym(grid);
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typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ar_Asym(grid);
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random(gridRNG,h_Asym);
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h_Asym = real(h_Asym);
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SU_TwoIndex< Nc, AntiSymmetric>::TwoIndexLieAlgebraMatrix(h_Asym,Ar_Asym);
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@ -470,13 +470,13 @@ int main(int argc, char** argv) {
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// Exponentiate
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typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix U2iAS(grid);
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typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix U2iAS(grid);
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U2iAS = expMat(Ar_Asym, 1.0, 16);
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typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix uno2iAS(grid);
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typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix uno2iAS(grid);
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uno2iAS = 1.0;
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// Check matrix U2iS, must be real orthogonal
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typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix Ucheck2iAS = U2iAS - conjugate(U2iAS);
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typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ucheck2iAS = U2iAS - conjugate(U2iAS);
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std::cout << GridLogMessage << "Reality check: " << norm2(Ucheck2iAS)
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<< std::endl;
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@ -509,9 +509,9 @@ int main(int argc, char** argv) {
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TIndexRepA.update_representation(U);
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Ur2A = TIndexRepA.U; // U_r
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typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix Ur02A = peekLorentz(Ur2A,0); // this should be the same as U2iS
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typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ur02A = peekLorentz(Ur2A,0); // this should be the same as U2iS
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typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix Diff_check_mat2A = Ur02A - U2iAS;
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typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Diff_check_mat2A = Ur02A - U2iAS;
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std::cout << GridLogMessage << "Projections structure check group difference (Two Index anti-Symmetric): " << norm2(Diff_check_mat2A) << std::endl;
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} else {
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@ -1,212 +1,141 @@
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#include <Grid/Grid.h>
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#define verbose 1
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#define verbose 0
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using namespace Grid;
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static void antisymm_base() {
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const int this_nc = 6;
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const int this_n = this_nc/2;
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const int this_irrep_dim = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension;
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const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
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typedef Sp_TwoIndex<this_nc, AntiSymmetric>::iGroupMatrix<Complex> Matrix;
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typedef Sp_TwoIndex<this_nc, AntiSymmetric>::iGroupTwoIndexMatrix<Complex> ASMatrix;
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Matrix Omega;
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Matrix eij_a;
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Matrix eij_b;
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Matrix eij_c;
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Matrix e_sum;
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Omega = Zero();
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for (int i = 0; i < this_n; i++)
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{
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Omega()()(i, this_n + i) = 1.;
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Omega()()(this_n + i, i) = -1;
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}
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RealD realA;
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RealD realB;
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std::cout << GridLogMessage << "2as dimension is " << this_irrep_dim << std::endl;
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std::cout << GridLogMessage << "algebra dimension is " << this_algebra_dim << std::endl;
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realA = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension + Sp_TwoIndex<this_nc, Symmetric>::Dimension;
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assert ( realA == this_nc * this_nc - 1); // Nc x Nc = dim(2indxS) + dim(2indxAS) + dim(singlet)
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std::cout << GridLogMessage << "checking base is antisymmetric " << std::endl;
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for (int a=0; a < this_irrep_dim; a++)
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{
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Sp_TwoIndex<this_nc, AntiSymmetric>::base(a, eij_c);
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e_sum = eij_c + transpose(eij_c);
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std::cout << GridLogMessage << "e_ab + e_ab^T " << norm2(e_sum) << std::endl;
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assert(norm2(e_sum) < 1e-8);
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}
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std::cout << GridLogMessage << "Checking Tr (e^(ab) Omega ) = 0 and Tr (e^(ab) e^(cd) = delta^((ab)(cd)) ) " << std::endl;
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for (int a=0; a < Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension; a++) {
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Sp_TwoIndex<this_nc, AntiSymmetric>::base(a, eij_a);
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realA = norm2(trace(Omega*eij_a));
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std::cout << GridLogMessage << "Omega trace for (ab) = " << a << std::endl;
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assert(realA == 0);
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for (int b=0; b < Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension; b++) {
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Sp_TwoIndex<this_nc, AntiSymmetric>::base(b, eij_b);
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auto d_ab = TensorRemove(trace(eij_a * eij_b));
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#if verbose
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std::cout << GridLogMessage << "Tr( e_{ab=" << a << "} e_{cd=" << b << "} ) = " << d_ab << std::endl;
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#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) ;
|
||||
}
|
||||
template<int this_nc>
|
||||
static void check_dimensions() {
|
||||
|
||||
const int this_n = this_nc/2;
|
||||
const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
|
||||
|
||||
RealD realA;
|
||||
std::cout << GridLogMessage << "Nc = " << this_n << " 2as dimension is " << Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension << std::endl;
|
||||
std::cout << GridLogMessage << "Nc = " << this_n << " 2s dimension is " << Sp_TwoIndex<this_nc, Symmetric>::Dimension << std::endl;
|
||||
std::cout << GridLogMessage << "Nc = " << this_n << " algebra dimension is " << this_algebra_dim << std::endl;
|
||||
realA = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension + Sp_TwoIndex<this_nc, Symmetric>::Dimension;
|
||||
std::cout << GridLogMessage << "Checking dim(2AS) + dim(AS) + 1 = Nc * Nc " << this_algebra_dim << std::endl;
|
||||
assert ( realA == this_nc * this_nc - 1); // Nc x Nc = dim(2indxS) + dim(2indxAS) + dim(singlet)
|
||||
}
|
||||
|
||||
static void symm_base() {
|
||||
template<int this_nc, TwoIndexSymmetry S>
|
||||
static void S_checks() {
|
||||
std::cout << S << std::endl;
|
||||
std::cout << 1 + S * 3 << std::endl;
|
||||
}
|
||||
|
||||
|
||||
template<int this_nc, TwoIndexSymmetry S>
|
||||
static void run_base_checks() {
|
||||
std::cout << GridLogMessage << " ****** " << std::endl;
|
||||
std::cout << GridLogMessage << "Running checks for Nc = " << this_nc << " TwoIndex Symmetry = " << S << std::endl;
|
||||
const int this_n = this_nc/2;
|
||||
const int this_irrep_dim = Sp_TwoIndex<this_nc, S>::Dimension;
|
||||
const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
|
||||
typedef typename Sp_TwoIndex<this_nc, S>::template iGroupMatrix<Complex> Matrix;
|
||||
typedef typename Sp_TwoIndex<this_nc, S>::template iGroupTwoIndexMatrix<Complex> ASMatrix;
|
||||
RealD realS = S;
|
||||
|
||||
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;
|
||||
}
|
||||
|
||||
const int this_nc = 6;
|
||||
const int this_n = this_nc/2;
|
||||
const int this_irrep_dim = Sp_TwoIndex<this_nc, Symmetric>::Dimension;
|
||||
const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
|
||||
typedef Sp_TwoIndex<this_nc, Symmetric>::iGroupMatrix<Complex> Matrix;
|
||||
typedef Sp_TwoIndex<this_nc, Symmetric>::iGroupTwoIndexMatrix<Complex> SMatrix;
|
||||
|
||||
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;
|
||||
}
|
||||
RealD realA;
|
||||
RealD realB;
|
||||
|
||||
RealD realA;
|
||||
RealD realB;
|
||||
std::cout << GridLogMessage << "symm 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;
|
||||
assert ( realA == this_nc * this_nc - 1); // Nc x Nc = dim(2indxS) + dim(2indxAS) + dim(singlet)
|
||||
|
||||
std::cout << GridLogMessage << "checking base is symmetric " << std::endl;
|
||||
for (int a=0; a < this_irrep_dim; a++)
|
||||
{
|
||||
Sp_TwoIndex<this_nc, Symmetric>::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, Symmetric>::Dimension; a++) {
|
||||
Sp_TwoIndex<this_nc, Symmetric>::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, Symmetric>::Dimension; b++) {
|
||||
Sp_TwoIndex<this_nc, Symmetric>::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);
|
||||
std::cout << GridLogMessage << "checking base has symmetry " << S << std::endl;
|
||||
for (int a=0; a < this_irrep_dim; a++)
|
||||
{
|
||||
Sp_TwoIndex<this_nc, S>::base(a, eij_c);
|
||||
e_sum = eij_c - realS * transpose(eij_c);
|
||||
std::cout << GridLogMessage << "e_ab - (" << S << " * 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, S>::Dimension; a++) {
|
||||
Sp_TwoIndex<this_nc, S>::base(a, eij_a);
|
||||
realA = norm2(trace(Omega*eij_a));
|
||||
std::cout << GridLogMessage << "Checkig Omega-trace for e_{ab=" << a << "} " << std::endl;
|
||||
//std::cout << GridLogMessage << "Tr ( Omega e_{ab=" << a << "} ) = " << realA << std::endl;
|
||||
assert(realA < 1e-8);
|
||||
for (int b=0; b < Sp_TwoIndex<this_nc, S>::Dimension; b++) {
|
||||
Sp_TwoIndex<this_nc, S>::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 << "Checking orthonormality for e_{ab = " << a << "} " << std::endl;
|
||||
if (a==b) {
|
||||
assert(real(d_ab) - realS < 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, Symmetric>::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;
|
||||
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++)
|
||||
{
|
||||
|
||||
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)));
|
||||
Sp_TwoIndex<this_nc, S>::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(eDag T_F e + eDag e T_F^T) = " << 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) ;
|
||||
}
|
||||
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) ;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
int main(int argc, char** argv) {
|
||||
std::cout << GridLogMessage << "Checking AntiSymmetric base " << std::endl;
|
||||
antisymm_base();
|
||||
std::cout << GridLogMessage << "*************** " << std::endl;
|
||||
std::cout << GridLogMessage << "Checking Symmetric base " << std::endl;
|
||||
symm_base();
|
||||
check_dimensions<2>();
|
||||
check_dimensions<4>();
|
||||
check_dimensions<6>();
|
||||
check_dimensions<8>();
|
||||
|
||||
run_base_checks<2, Symmetric>();
|
||||
run_base_checks<4, Symmetric>();
|
||||
run_base_checks<4, AntiSymmetric>();
|
||||
run_base_checks<6, Symmetric>();
|
||||
run_base_checks<6, AntiSymmetric>();
|
||||
run_base_checks<8, Symmetric>();
|
||||
run_base_checks<8, AntiSymmetric>();
|
||||
}
|
||||
|
||||
|
||||
@ -2,99 +2,52 @@
|
||||
|
||||
using namespace Grid;
|
||||
|
||||
template<int ncolour>
|
||||
void run_checks(bool print_generators = 0) {
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")" << "Fundamental" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
if (print_generators)
|
||||
{
|
||||
Sp<ncolour>::printGenerators();
|
||||
}
|
||||
Sp<ncolour>::testGenerators();
|
||||
|
||||
if (Sp_TwoIndex<ncolour, Symmetric>::Dimension > 1) {
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")" << "TwoIndex Symmetric: " << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
if (print_generators) {
|
||||
Sp_TwoIndex<ncolour, Symmetric>::printGenerators();
|
||||
}
|
||||
Sp_TwoIndex<ncolour, Symmetric>::testGenerators();
|
||||
}
|
||||
|
||||
if (Sp_TwoIndex<ncolour, AntiSymmetric>::Dimension > 1) {
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")" << "TwoIndex AntiSymmetric: " << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
if (print_generators) {
|
||||
Sp_TwoIndex<ncolour, AntiSymmetric>::printGenerators();
|
||||
}
|
||||
Sp_TwoIndex<ncolour, AntiSymmetric>::testGenerators();
|
||||
}
|
||||
}
|
||||
|
||||
int main(int argc, char** argv) {
|
||||
Grid_init(&argc, &argv);
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(2) (print and test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
Sp2::printGenerators();
|
||||
Sp2::testGenerators();
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(4) (print and test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
Sp4::printGenerators();
|
||||
Sp4::testGenerators();
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(6) (test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
Sp6::testGenerators();
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(8) (test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
Sp8::testGenerators();
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(2) TwoIndexS (print & test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
Sp_TwoIndex<2, Symmetric>::printGenerators();
|
||||
Sp_TwoIndex<2, Symmetric>::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(4) TwoIndexS (test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
Sp_TwoIndex<4, Symmetric>::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(6) TwoIndexS (test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
Sp_TwoIndex<6, Symmetric>::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();
|
||||
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
std::cout << GridLogMessage << "* Generators for Sp(8) TwoIndexS (test)" << std::endl;
|
||||
std::cout << GridLogMessage << "*********************************************"
|
||||
<< std::endl;
|
||||
|
||||
Sp_TwoIndex<8, Symmetric>::testGenerators();
|
||||
run_checks<2>(1); // check and print Nc=2
|
||||
run_checks<4>(1); // check and print Nc=4
|
||||
run_checks<6>(); // check Nc=6
|
||||
run_checks<8>(); // check Nc=8
|
||||
|
||||
Grid_finalize();
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user