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expand ProjecOnGaugeGroup, change ProjectOnSp2nAlgebra into SpTa, fixing some of its issues

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This commit is contained in:
Alessandro Lupo
2023-04-04 17:48:13 +01:00
parent 026e736dfa
commit 778291230a
6 changed files with 202 additions and 26 deletions
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99
tests/sp2n/Test_project_on_Sp.cc
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@ -17,6 +17,7 @@ int main (int argc, char **argv)
LatticeGaugeField Umu(&Grid);
LatticeColourMatrixD U(&Grid);
LatticeColourMatrixD Up(&Grid);
LatticeColourMatrixD aux(&Grid);
LatticeColourMatrixD identity(&Grid);
@ -59,6 +60,11 @@ int main (int argc, char **argv)
std::cout << GridLogMessage << "Unitary matrix deformed " << std::endl;
std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl;
std::cout <<GridLogMessage << std::endl;
std::cout << GridLogMessage << "# # # #" << std::endl;
std::cout << GridLogMessage << "Group" << std::endl;
std::cout << GridLogMessage << "# # # #" << std::endl;
std::cout <<GridLogMessage << std::endl;
// Testing ProjectOnSpGroup
std::cout << GridLogMessage << "Testing ProjectOnSpGroup" << std::endl;
std::cout << GridLogMessage << "Apply ProjectOnSpGroup to deformed matrix" << std::endl;
@ -123,7 +129,7 @@ int main (int argc, char **argv)
std::cout << GridLogMessage << "Checking the structure is " << std::endl;
std::cout << GridLogMessage << "U = ( W X ) " << std::endl;
std::cout << GridLogMessage << " ( -X^* W^* ) " << std::endl;
std::cout <<GridLogMessage << std::endl;
for (int c1 = 0; c1 < nsp; c1++) //check on W
{
for (int c2 = 0; c2 < nsp; c2++)
@ -200,23 +206,27 @@ int main (int argc, char **argv)
assert( amizeroo.real() < 10e-6 );
}
}
std::cout << GridLogMessage << "Testing ProjectSp2nAlgebra" << std::endl;
std::cout <<GridLogMessage << std::endl;
std::cout << GridLogMessage << "# # # #" << std::endl;
std::cout << GridLogMessage << "Algebra" << std::endl;
std::cout << GridLogMessage << "# # # #" << std::endl;
std::cout <<GridLogMessage << std::endl;
std::cout << GridLogMessage << "Testing SpTa" << std::endl;
U = PeekIndex<LorentzIndex>(Umu,1);
U = U + 666.*identity;
aux = U*adj(U) - identity;
std::cout << GridLogMessage << "Matrix deformed " << std::endl;
std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
std::cout << GridLogMessage << "Apply ProjectSp2nAlgebra to deformed matrix" << std::endl;
U = ProjectSp2nAlgebra(U);
aux = U*adj(U) - identity;
std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
assert( norm2(aux) < 1e-8);
std::cout << GridLogMessage << "Apply SpTa to deformed matrix" << std::endl;
U = SpTa(U);
aux = U - adj(U);
std::cout << GridLogMessage << "SpTa ::: T - Tda = " << norm2(aux) << std::endl;
aux = U + adj(U);
std::cout << GridLogMessage << "SpTa ::: T + Tda = " << norm2(aux) << std::endl;
std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)" << std::endl;
LatticeColourMatrixD Omega(&Grid);
Sp<Nc>::Omega(Omega);
aux = Omega*U*Omega - conjugate(U);
std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
@ -258,6 +268,71 @@ int main (int argc, char **argv)
}
}
//test Ta
/*
U = U + 666.*identity;
Up = Ta(U);
aux = Up - adj(Up);
std::cout << GridLogMessage << "TA !!! T - Tda = " << norm2(aux) << std::endl;
aux = Up + adj(Up);
std::cout << GridLogMessage << "TA !!! T + Tda = " << norm2(aux) << std::endl;*/
// test taProj
std::cout << GridLogMessage << "Testing taProj" << std::endl;
U = U + 666.*identity;
std::cout << GridLogMessage << "Matrix deformed " << std::endl;
std::cout << GridLogMessage << "Apply taProj to deformed matrix" << std::endl;
Sp<Nc>::taProj(U, Up);
aux = Up - adj(Up);
std::cout << GridLogMessage << "taProj ::: T - Tda = " << norm2(aux) << std::endl;
aux = Up + adj(Up);
std::cout << GridLogMessage << "taProj ::: T + Tda = " << norm2(aux) << std::endl;
std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)" << std::endl;
Sp<Nc>::Omega(Omega);
aux = Omega*Up*Omega - conjugate(Up);
std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
assert( norm2(aux) < 1e-8);
// before it was
aux = Omega*U*Omega - conjugate(U);
std::cout << GridLogMessage << " before taProj Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
U = Up;
std::cout << GridLogMessage << "Checking the structure is " << std::endl;
std::cout << GridLogMessage << "U = ( W X ) " << std::endl;
std::cout << GridLogMessage << " ( X^* -W^* ) " << std::endl;
std::cout <<GridLogMessage << std::endl;
for (int c1 = 0; c1 < nsp; c1++) //check on W
{
for (int c2 = 0; c2 < nsp; c2++)
{
auto W = PeekIndex<ColourIndex>(U,c1,c2);
auto Wstar = PeekIndex<ColourIndex>(U,c1+nsp,c2+nsp);
auto Ww = conjugate( Wstar );
auto amizero = sum(W + Ww);
auto amizeroo = TensorRemove(amizero);
assert( amizeroo.real() < 10e-6 );
amizeroo *= i;
assert( amizeroo.real() < 10e-6 );
}
}
for (int c1 = 0; c1 < nsp ; c1++)
{
for (int c2 = 0; c2 < nsp; c2++)
{
auto X = PeekIndex<ColourIndex>(U,c1,c2+nsp);
auto minusXstar = PeekIndex<ColourIndex>(U,c1+nsp,c2);
auto minusXx = conjugate(minusXstar);
auto amizero = sum (X - minusXx);
auto amizeroo = TensorRemove(amizero);
assert( amizeroo.real() < 10e-6 );
amizeroo *= i;
assert( amizeroo.real() < 10e-6 );
}
}
Grid_finalize();