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cleaner twoindex class, cleaner tests
This commit is contained in:
Alessandro Lupo
@ -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
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std::cout << GridLogMessage << "Orthonormality for (ab) = " << a << std::endl;
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if (a==b) {
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assert(real(d_ab)+1 < 1e-8);
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assert(imag(d_ab) < 1e-8);
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} else {
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assert(real(d_ab) < 1e-8);
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assert(imag(d_ab) < 1e-8);
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}
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}
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}
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int sum = 0;
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int sum_im = 0;
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Vector<Matrix> ta_fund(this_algebra_dim);
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Vector<Matrix> eij(this_irrep_dim);
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Matrix tmp_l;
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Matrix tmp_r;
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for (int n = 0; n < this_algebra_dim; n++)
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{
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Sp<this_nc>::generator(n, ta_fund[n]);
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}
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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[a]);
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}
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for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
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{
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Complex iTr;
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sum = 0;
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sum_im = 0;
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std::cout << GridLogMessage << "generator number " << gen_id << std::endl;
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for (int a = 0; a < this_irrep_dim; a++)
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{
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tmp_l = adj(eij[a])*ta_fund[gen_id]*eij[a];
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tmp_r = adj(eij[a])*eij[a]*transpose(ta_fund[gen_id]);
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#if verbose
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std::cout << GridLogMessage << " as_indx = " << a << " eDag T_F e = " << std::endl << tmp_l << std::endl;
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std::cout << GridLogMessage << " as_indx = " << a << " eDag e T_F^T = " << std::endl << tmp_r << std::endl;
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#endif
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std::cout << GridLogMessage << " as_indx = " << a << " Tr(sum) = " << TensorRemove(trace(tmp_l+tmp_r)) << std::endl;
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sum += real(TensorRemove(trace(tmp_l+tmp_r)));
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sum_im += imag(TensorRemove(trace(tmp_l+tmp_r)));
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}
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std::cout << GridLogMessage << "re-evaluated trace of the generator " << gen_id << " is " << sum << " " << sum_im << std::endl;
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assert ( sum < 1e-8) ;
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assert ( sum_im < 1e-8) ;
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}
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template<int this_nc>
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static void check_dimensions() {
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const int this_n = this_nc/2;
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const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
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RealD realA;
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std::cout << GridLogMessage << "Nc = " << this_n << " 2as dimension is " << Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension << std::endl;
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std::cout << GridLogMessage << "Nc = " << this_n << " 2s dimension is " << Sp_TwoIndex<this_nc, Symmetric>::Dimension << std::endl;
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std::cout << GridLogMessage << "Nc = " << this_n << " 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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std::cout << GridLogMessage << "Checking dim(2AS) + dim(AS) + 1 = Nc * Nc " << this_algebra_dim << std::endl;
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assert ( realA == this_nc * this_nc - 1); // Nc x Nc = dim(2indxS) + dim(2indxAS) + dim(singlet)
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}
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static void symm_base() {
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template<int this_nc, TwoIndexSymmetry S>
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static void S_checks() {
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std::cout << S << std::endl;
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std::cout << 1 + S * 3 << std::endl;
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}
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template<int this_nc, TwoIndexSymmetry S>
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static void run_base_checks() {
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std::cout << GridLogMessage << " ****** " << std::endl;
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std::cout << GridLogMessage << "Running checks for Nc = " << this_nc << " TwoIndex Symmetry = " << S << std::endl;
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const int this_n = this_nc/2;
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const int this_irrep_dim = Sp_TwoIndex<this_nc, S>::Dimension;
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const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
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typedef typename Sp_TwoIndex<this_nc, S>::template iGroupMatrix<Complex> Matrix;
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typedef typename Sp_TwoIndex<this_nc, S>::template iGroupTwoIndexMatrix<Complex> ASMatrix;
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RealD realS = S;
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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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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, Symmetric>::Dimension;
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const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
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typedef Sp_TwoIndex<this_nc, Symmetric>::iGroupMatrix<Complex> Matrix;
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typedef Sp_TwoIndex<this_nc, Symmetric>::iGroupTwoIndexMatrix<Complex> SMatrix;
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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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RealD realA;
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RealD realB;
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std::cout << GridLogMessage << "symm 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 symmetric " << 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, Symmetric>::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, Symmetric>::Dimension; a++) {
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Sp_TwoIndex<this_nc, Symmetric>::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, Symmetric>::Dimension; b++) {
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Sp_TwoIndex<this_nc, Symmetric>::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
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std::cout << GridLogMessage << "Orthonormality for (ab) = " << a << std::endl;
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if (a==b) {
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assert(real(d_ab)-1 < 1e-8);
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assert(imag(d_ab) < 1e-8);
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} else {
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assert(real(d_ab) < 1e-8);
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assert(imag(d_ab) < 1e-8);
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std::cout << GridLogMessage << "checking base has symmetry " << S << 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, S>::base(a, eij_c);
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e_sum = eij_c - realS * transpose(eij_c);
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std::cout << GridLogMessage << "e_ab - (" << S << " * 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, S>::Dimension; a++) {
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Sp_TwoIndex<this_nc, S>::base(a, eij_a);
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realA = norm2(trace(Omega*eij_a));
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std::cout << GridLogMessage << "Checkig Omega-trace for e_{ab=" << a << "} " << std::endl;
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//std::cout << GridLogMessage << "Tr ( Omega e_{ab=" << a << "} ) = " << realA << std::endl;
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assert(realA < 1e-8);
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for (int b=0; b < Sp_TwoIndex<this_nc, S>::Dimension; b++) {
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Sp_TwoIndex<this_nc, S>::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
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std::cout << GridLogMessage << "Checking orthonormality for e_{ab = " << a << "} " << std::endl;
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if (a==b) {
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assert(real(d_ab) - realS < 1e-8);
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assert(imag(d_ab) < 1e-8);
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} else {
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assert(real(d_ab) < 1e-8);
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assert(imag(d_ab) < 1e-8);
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}
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}
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}
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}
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int sum = 0;
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int sum_im = 0;
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Vector<Matrix> ta_fund(this_algebra_dim);
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Vector<Matrix> eij(this_irrep_dim);
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Matrix tmp_l;
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Matrix tmp_r;
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for (int n = 0; n < this_algebra_dim; n++)
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{
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Sp<this_nc>::generator(n, ta_fund[n]);
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}
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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, Symmetric>::base(a, eij[a]);
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}
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for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
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{
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Complex iTr;
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sum = 0;
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sum_im = 0;
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std::cout << GridLogMessage << "generator number " << gen_id << std::endl;
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int sum = 0;
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int sum_im = 0;
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Vector<Matrix> ta_fund(this_algebra_dim);
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Vector<Matrix> eij(this_irrep_dim);
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Matrix tmp_l;
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Matrix tmp_r;
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for (int n = 0; n < this_algebra_dim; n++)
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{
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Sp<this_nc>::generator(n, ta_fund[n]);
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}
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for (int a = 0; a < this_irrep_dim; a++)
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{
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tmp_l = adj(eij[a])*ta_fund[gen_id]*eij[a];
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tmp_r = adj(eij[a])*eij[a]*transpose(ta_fund[gen_id]);
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#if verbose
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std::cout << GridLogMessage << " as_indx = " << a << " eDag T_F e = " << std::endl << tmp_l << std::endl;
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std::cout << GridLogMessage << " as_indx = " << a << " eDag e T_F^T = " << std::endl << tmp_r << std::endl;
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#endif
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std::cout << GridLogMessage << " as_indx = " << a << " Tr(sum) = " << TensorRemove(trace(tmp_l+tmp_r)) << std::endl;
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sum += real(TensorRemove(trace(tmp_l+tmp_r)));
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sum_im += imag(TensorRemove(trace(tmp_l+tmp_r)));
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Sp_TwoIndex<this_nc, S>::base(a, eij[a]);
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}
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for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
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{
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Complex iTr;
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sum = 0;
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sum_im = 0;
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std::cout << GridLogMessage << "generator number " << gen_id << std::endl;
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for (int a = 0; a < this_irrep_dim; a++)
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{
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tmp_l = adj(eij[a])*ta_fund[gen_id]*eij[a];
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tmp_r = adj(eij[a])*eij[a]*transpose(ta_fund[gen_id]);
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#if verbose
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std::cout << GridLogMessage << " as_indx = " << a << " eDag T_F e = " << std::endl << tmp_l << std::endl;
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std::cout << GridLogMessage << " as_indx = " << a << " eDag e T_F^T = " << std::endl << tmp_r << std::endl;
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#endif
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//std::cout << GridLogMessage << " as_indx = " << a << " Tr(eDag T_F e + eDag e T_F^T) = " << TensorRemove(trace(tmp_l+tmp_r)) << std::endl;
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sum += real(TensorRemove(trace(tmp_l+tmp_r)));
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sum_im += imag(TensorRemove(trace(tmp_l+tmp_r)));
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}
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std::cout << GridLogMessage << "re-evaluated trace of the generator " << gen_id << " is " << sum << " " << sum_im << std::endl;
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assert ( sum < 1e-8) ;
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assert ( sum_im < 1e-8) ;
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}
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std::cout << GridLogMessage << "re-evaluated trace of the generator " << gen_id << " is " << sum << " " << sum_im << std::endl;
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assert ( sum < 1e-8) ;
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assert ( sum_im < 1e-8) ;
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}
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}
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int main(int argc, char** argv) {
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std::cout << GridLogMessage << "Checking AntiSymmetric base " << std::endl;
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antisymm_base();
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std::cout << GridLogMessage << "*************** " << std::endl;
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std::cout << GridLogMessage << "Checking Symmetric base " << std::endl;
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symm_base();
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check_dimensions<2>();
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check_dimensions<4>();
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check_dimensions<6>();
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check_dimensions<8>();
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run_base_checks<2, Symmetric>();
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run_base_checks<4, Symmetric>();
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run_base_checks<4, AntiSymmetric>();
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run_base_checks<6, Symmetric>();
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run_base_checks<6, AntiSymmetric>();
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run_base_checks<8, Symmetric>();
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run_base_checks<8, AntiSymmetric>();
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}
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@ -2,99 +2,52 @@
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using namespace Grid;
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template<int ncolour>
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void run_checks(bool print_generators = 0) {
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std::cout << GridLogMessage << "*********************************************"
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<< std::endl;
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std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")" << "Fundamental" << std::endl;
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std::cout << GridLogMessage << "*********************************************"
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<< std::endl;
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if (print_generators)
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{
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Sp<ncolour>::printGenerators();
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}
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Sp<ncolour>::testGenerators();
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if (Sp_TwoIndex<ncolour, Symmetric>::Dimension > 1) {
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std::cout << GridLogMessage << "*********************************************"
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<< std::endl;
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std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")" << "TwoIndex Symmetric: " << std::endl;
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std::cout << GridLogMessage << "*********************************************"
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<< std::endl;
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if (print_generators) {
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Sp_TwoIndex<ncolour, Symmetric>::printGenerators();
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}
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Sp_TwoIndex<ncolour, Symmetric>::testGenerators();
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}
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if (Sp_TwoIndex<ncolour, AntiSymmetric>::Dimension > 1) {
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std::cout << GridLogMessage << "*********************************************"
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<< std::endl;
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std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")" << "TwoIndex AntiSymmetric: " << std::endl;
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std::cout << GridLogMessage << "*********************************************"
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<< std::endl;
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if (print_generators) {
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Sp_TwoIndex<ncolour, AntiSymmetric>::printGenerators();
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}
|
||||
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();
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user