Grid/tests/sp2n/Test_2as_base.cc

#include <Grid/Grid.h>

#define verbose 0

using namespace Grid;

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)
}

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;
      }

      RealD realA;

      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, S>::base(a, eij[a]);
      }
      for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
      {
          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) ;
      }
}

int main(int argc, char** argv) {
    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>();
}