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Correct implementation of SpTa

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This commit is contained in:
Alessandro Lupo
2023-04-27 18:17:06 +01:00
parent 5aabe074fe
commit 881b08a465
2 changed files with 30 additions and 120 deletions
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66
Grid/tensors/Tensor_Ta.h
View File

@@ -82,67 +82,39 @@ template<class vtype,int N> accelerator_inline iVector<vtype,N> SpTa(const iVect
} }
return ret; return ret;
} }
template<class vtype,int N> accelerator_inline iMatrix<vtype,N> SpTa(const iMatrix<vtype,N> &arg) template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr> accelerator_inline iMatrix<vtype,N> SpTa(const iMatrix<vtype,N> &arg)
{ {
// Generalises Ta to Sp2n
// Applies the following projections
// P_{antihermitian} P_{antihermitian-Sp-algebra} P_{traceless}
// where the ordering matters
// P_{traceless} subtracts the trace
// P_{antihermitian-Sp-algebra} provides the block structure of the algebra based on U = exp(T) i.e. anti-hermitian generators
// P_{antihermitian} does in-adj(in) / 2
iMatrix<vtype,N> ret(arg); iMatrix<vtype,N> ret(arg);
double factor = (1.0/(double)N);
vtype nrm; vtype nrm;
vtype inner; nrm = 0.5;
vtype tmp;
ret = arg - (trace(arg)*factor);
for(int c1=0;c1<N/2;c1++) for(int c1=0;c1<N/2;c1++)
{ {
for (int b=0; b<c1; b++) // remove the b-rows from U_c1
{
decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
decltype(ret._internal[b][b]*ret._internal[b][b]) prn;
zeroit(pr);
zeroit(prn);
for(int c=0; c<N; c++)
{
pr += conjugate(ret._internal[c1][c])*ret._internal[b][c]; // <U_c1 | U_b >
prn += conjugate(ret._internal[c1][c])*ret._internal[b+N/2][c]; // <U_c1 | U_{b+N} >
}
for(int c=0; c<N; c++)
{
ret._internal[c1][c] -= (conjugate(pr) * ret._internal[b][c] + conjugate(prn) * ret._internal[b+N/2][c] ); // U_c1 -= ( <U_c1 | U_b > U_b + <U_c1 | U_{b+N} > U_{b+N} )
}
}
zeroit(inner);
for(int c2=0;c2<N;c2++)
{
inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
}
nrm = sqrt(inner);
nrm = 1.0/nrm;
for(int c2=0;c2<N;c2++)
{
ret._internal[c1][c2]*= nrm;
}
for(int c2=0;c2<N/2;c2++) for(int c2=0;c2<N/2;c2++)
{ {
tmp = conjugate(ret._internal[c1][c2]); // (up-left)* of the old matrix ret._internal[c1][c2] = nrm*(conjugate(ret._internal[c1+N/2][c2+N/2]) + ret._internal[c1][c2]); // new[up-left] = old[up-left]+old*[down-right]
ret._internal[c1+N/2][c2+N/2] = -tmp; // down right in the new matrix = -(up-left)* of the old matrix ret._internal[c1][c2+N/2] = nrm*(ret._internal[c1][c2+N/2] - conjugate(ret._internal[c1+N/2][c2])); // new[up-right] = old[up-right]-old*[down-left]
} }
for(int c2=N/2;c2<N;c2++) for(int c2=N/2;c2<N;c2++)
{ {
tmp = conjugate(ret._internal[c1][c2]); // (up-right)* of the old ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]); // reconstructs lower blocks
ret._internal[c1+N/2][c2-N/2] = tmp; // down left in the new matrix = (up-right)* of the old ret._internal[c1+N/2][c2] = conjugate(ret._internal[c1][c2-N/2]); // from upper blocks
} }
} }
ret = (ret - adj(ret))*0.5;
return Ta(ret);
return ret;
} }

84
tests/sp2n/Test_project_on_Sp.cc
View File

@@ -117,6 +117,8 @@ int main (int argc, char **argv)
} }
} }
SU<Nc>::HotConfiguration(pRNG,Umu); //refresh
U = PeekIndex<LorentzIndex>(Umu,1);
std::cout << GridLogMessage << "Testing ProjectOnGaugeGroup" << std::endl; std::cout << GridLogMessage << "Testing ProjectOnGaugeGroup" << std::endl;
U = U + Delta*identity; U = U + Delta*identity;
@@ -214,7 +216,9 @@ int main (int argc, char **argv)
std::cout <<GridLogMessage << std::endl; std::cout <<GridLogMessage << std::endl;
std::cout << GridLogMessage << "Testing SpTa" << std::endl; std::cout << GridLogMessage << "Testing SpTa" << std::endl;
U = PeekIndex<LorentzIndex>(Umu,1); SU<Nc>::HotConfiguration(pRNG,Umu);//refresh
U = PeekIndex<LorentzIndex>(Umu,2);
U = U + Delta*identity; U = U + Delta*identity;
std::cout << GridLogMessage << "Matrix deformed " << std::endl; std::cout << GridLogMessage << "Matrix deformed " << std::endl;
std::cout << GridLogMessage << "Apply SpTa to deformed matrix" << std::endl; std::cout << GridLogMessage << "Apply SpTa to deformed matrix" << std::endl;
@@ -224,19 +228,19 @@ int main (int argc, char **argv)
std::cout << GridLogMessage << "SpTa ::: T - Tda = " << norm2(aux) << std::endl; std::cout << GridLogMessage << "SpTa ::: T - Tda = " << norm2(aux) << std::endl;
aux = U + adj(U); aux = U + adj(U);
std::cout << GridLogMessage << "SpTa ::: T + Tda = " << norm2(aux) << std::endl; std::cout << GridLogMessage << "SpTa ::: T + Tda = " << norm2(aux) << std::endl;
assert( norm2(aux) - 1 < 1e-8);
std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)" << std::endl; std::cout << GridLogMessage << "Check that Omega T Omega + conj(T) = 0 " << std::endl;
LatticeColourMatrixD Omega(&Grid); LatticeColourMatrixD Omega(&Grid);
Sp<Nc>::Omega(Omega); Sp<Nc>::Omega(Omega);
aux = Omega*U*Omega - conjugate(U); aux = Omega*U*Omega + conjugate(U);
std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
assert( norm2(aux) < 1e-8); assert( norm2(aux) < 1e-8);
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; 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
{ {
@@ -245,7 +249,7 @@ int main (int argc, char **argv)
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;
@@ -261,73 +265,7 @@ int main (int argc, char **argv)
auto X = PeekIndex<ColourIndex>(U,c1,c2+nsp); auto X = PeekIndex<ColourIndex>(U,c1,c2+nsp);
auto minusXstar = PeekIndex<ColourIndex>(U,c1+nsp,c2); auto minusXstar = PeekIndex<ColourIndex>(U,c1+nsp,c2);
auto minusXx = conjugate(minusXstar); auto minusXx = conjugate(minusXstar);
auto amizero = sum (X - minusXx); auto amizero = sum (X + minusXx);
auto amizeroo = TensorRemove(amizero);
assert( amizeroo.real() < 10e-6 );
amizeroo *= i;
assert( amizeroo.real() < 10e-6 );
}
}
//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 + Delta*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); auto amizeroo = TensorRemove(amizero);
assert( amizeroo.real() < 10e-6 ); assert( amizeroo.real() < 10e-6 );
amizeroo *= i; amizeroo *= i;