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Take over additional algebra tests from Alessandro

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This commit is contained in:
Julian Lenz 2023-05-03 16:02:02 +01:00
parent c7fba9aace
commit 6a7bdca53b
1 changed files with 46 additions and 41 deletions
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87
tests/sp2n/Test_project_on_Sp.cc
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@ -107,62 +107,67 @@ void test_group_projections(T U) {
template <typename T> template <typename T>
bool has_correct_algebra_block_structure(const T& U) { bool has_correct_algebra_block_structure(const T& U) {
// this only checks for the anti-hermitian part of the algebra
const int nsp = Nc / 2; const int nsp = Nc / 2;
Complex i(0., 1.); Complex i(0., 1.);
std::cout << GridLogMessage << "Checking the structure is " << std::endl; std::cout << GridLogMessage << "Checking the structure is " << std::endl;
std::cout << GridLogMessage << "U = ( W X ) " << std::endl; std::cout << GridLogMessage << "U = ( W X ) " << std::endl;
std::cout << GridLogMessage << " ( X^* -W^* ) " << 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 c1 = 0; c1 < nsp; c1++) // check on W {
{ for (int c2 = 0; c2 < nsp; c2++)
for (int c2 = 0; c2 < nsp; c2++) { {
auto W = PeekIndex<ColourIndex>(U, c1, c2); auto W = PeekIndex<ColourIndex>(U,c1,c2);
auto Wstar = PeekIndex<ColourIndex>(U, c1 + nsp, c2 + nsp); auto Wstar = PeekIndex<ColourIndex>(U,c1+nsp,c2+nsp);
auto Ww = conjugate(Wstar); auto Ww = conjugate( Wstar );
auto amizero = sum(W + Ww); auto amizero = sum(W - Ww);
auto amizeroo = TensorRemove(amizero); auto amizeroo = TensorRemove(amizero);
assert(amizeroo.real() < 10e-6); assert( amizeroo.real() < 10e-6 );
amizeroo *= i; amizeroo *= i;
assert(amizeroo.real() < 10e-6); 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 );
}
} }
}
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);
}
}
return true; return true;
} }
template <typename T> template <typename T>
bool is_element_of_sp2n_algebra(T U) { bool is_element_of_sp2n_algebra(const T& U) {
// does explicitly take a copy in order to not spoil the matrix for further
// use
LatticeColourMatrixD aux(U.Grid()); LatticeColourMatrixD aux(U.Grid());
LatticeColourMatrixD identity(U.Grid()); LatticeColourMatrixD identity(U.Grid());
identity = 1.0; identity = 1.0;
aux = U - adj(U);
std::cout << GridLogMessage << "T - Tda = " << norm2(aux) << std::endl;
aux = U + adj(U);
std::cout << GridLogMessage << "T + Tda = " << norm2(aux) << std::endl;
std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)"
<< std::endl;
LatticeColourMatrixD Omega(U.Grid()); LatticeColourMatrixD Omega(U.Grid());
Sp<Nc>::Omega(Omega); Sp<Nc>::Omega(Omega);
aux = Omega * U * Omega - conjugate(U);
std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) std::cout << GridLogMessage << "Check matrix is non-zero " << std::endl;
assert(norm2(U) > 1e-8);
aux = U - adj(U);
std::cout << GridLogMessage << "T - Tda = " << norm2(aux)
<< " (not supposed to vanish)" << std::endl;
aux = U + adj(U);
std::cout << GridLogMessage << "T + Tda = " << norm2(aux)
<< " (supposed to vanish)" << std::endl;
assert(norm2(aux) - 1 < 1e-8);
std::cout << GridLogMessage << "Check that Omega T Omega + conj(T) = 0 "
<< std::endl; << std::endl;
aux = Omega * U * Omega + conjugate(U);
assert(norm2(aux) < 1e-8); assert(norm2(aux) < 1e-8);
return has_correct_algebra_block_structure(U); return has_correct_algebra_block_structure(U);