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fix sp2n projection

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This commit is contained in:
Alessandro Lupo 2021-10-12 12:12:16 +01:00
parent 1d6e708083
commit 283f14b7c1
2 changed files with 181 additions and 74 deletions
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133
Grid/tensors/Tensor_Ta.h
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@ -161,88 +161,75 @@ accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg
iMatrix<vtype,N> ret(arg); iMatrix<vtype,N> ret(arg);
vtype nrm; vtype nrm;
vtype inner; vtype inner;
for(int c1=0;c1<N;c1++){ for(int c1=0;c1<N/2;c1++){
// Normalises row c1 // Normalises row c1
zeroit(inner); zeroit(inner);
for(int c2=0;c2<N;c2++) for(int c2=0;c2<N;c2++)
inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]); inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
nrm = sqrt(inner); nrm = sqrt(inner);
nrm = 1.0/nrm; nrm = 1.0/nrm;
for(int c2=0;c2<N;c2++) for(int c2=0;c2<N;c2++)
ret._internal[c1][c2]*= nrm; ret._internal[c1][c2]*= nrm;
// Compute row c1+N2/2: c1+N/2 = - \Omega c1* // Compute row c1+N2/2: c1+N/2 = - \Omega c1*
for(int c2=0;c2<N/2;c2++) for(int c2=0;c2<N/2;c2++)
//tmp = conjugate(ret._internal[c1][c2]); ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
//ret._internal[c1+N/2][c2+N/2] = tmp;
ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
for(int c2=N/2;c2<N;c2++) for(int c2=N/2;c2<N;c2++)
//tmp = conjugate(ret._internal[c1][c2]); ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
// ret._internal[c1+N/2][c2-N/2] = -tmp;
ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
// Remove c1 from rows c1+1...N/2-1 // Remove c1 from rows c1+1...N/2-1
for (int b=c1+1; b<N/2; ++b){ for (int b=c1+1; b<N/2; ++b){
decltype(ret._internal[b][b]*ret._internal[b][b]) pr; decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
zeroit(pr); zeroit(pr);
for(int c=0; c<N; ++c) for(int c=0; c<N; ++c)
pr += conjugate(ret._internal[c1][c])*ret._internal[b][c]; pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];
for(int c=0; c<N; ++c){ for(int c=0; c<N; ++c){
ret._internal[b][c] -= pr * ret._internal[c1][c]; ret._internal[b][c] -= pr * ret._internal[c1][c];
}
}
// Remove c1+N/2 from rows c1+1...N/2-1
for (int b=c1+1; b<N; ++b){
decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
zeroit(pr);
for(int c=0; c<N; ++c)
pr += conjugate(ret._internal[c1+N/2][c])*ret._internal[b][c];
for(int c=0; c<N; ++c){
ret._internal[b][c] -= pr * ret._internal[c1+N/2][c];
}
}
} //end for loop over c1
// Compute the last row
{
// Normalise last row
int c1 = N/2-1;
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;
}
// Compute row cN-1+N2/2: cN-1+N/2 = - \Omega cN-1*
for(int c2=0;c2<N/2;c2++)
{
//tmp = conjugate(ret._internal[c1][c2]);
// ret._internal[c1+N/2][c2+N/2] = tmp;
ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
}
for(int c2=N/2;c2<N;c2++)
{
//tmp = conjugate(ret._internal[c1][c2]);
//ret._internal[c1+N/2][c2-N/2] = -tmp;
ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
}
} }
// assuming the determinant is ok }
return ret;
// Remove c1+N/2 from rows c1+1...N/2-1
for (int b=c1+1; b<N; ++b){
decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
zeroit(pr);
for(int c=0; c<N; ++c)
pr += conjugate(ret._internal[c1+N/2][c])*ret._internal[b][c];
for(int c=0; c<N; ++c){
ret._internal[b][c] -= pr * ret._internal[c1+N/2][c];
}
}
} }
// Compute the last row
{
// Normalise last row
int c1 = N/2-1;
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;
// Compute row cN-1+N2/2: cN-1+N/2 = - \Omega cN-1*
for(int c2=0;c2<N/2;c2++)
ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
for(int c2=N/2;c2<N;c2++)
ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
}
// assuming the determinant is ok
return ret;
}
NAMESPACE_END(Grid); NAMESPACE_END(Grid);
#endif #endif

122
tests/sp2n/Test_project_on_Sp.cc
View File

@ -17,6 +17,14 @@ int main (int argc, char **argv)
LatticeGaugeField Umu(&Grid); LatticeGaugeField Umu(&Grid);
LatticeColourMatrixD U(&Grid); LatticeColourMatrixD U(&Grid);
LatticeColourMatrixD aux(&Grid);
LatticeColourMatrixD identity(&Grid);
identity = 1.0;
RealD epsilon = 0.01;
Complex i(0., 1.);
RealD u = 0.;
double vol = Umu.Grid()->gSites();
std::vector<int> pseeds({1,2,3,4,5}); std::vector<int> pseeds({1,2,3,4,5});
std::vector<int> sseeds({6,7,8,9,10}); std::vector<int> sseeds({6,7,8,9,10});
@ -24,10 +32,122 @@ int main (int argc, char **argv)
GridSerialRNG sRNG; sRNG.SeedFixedIntegers(sseeds); GridSerialRNG sRNG; sRNG.SeedFixedIntegers(sseeds);
SU<Nc>::HotConfiguration(pRNG,Umu); SU<Nc>::HotConfiguration(pRNG,Umu);
U = PeekIndex<LorentzIndex>(Umu,0); U = PeekIndex<LorentzIndex>(Umu,2);
// it is unitary
aux = U*adj(U) - identity;
std::cout <<GridLogMessage << std::endl;
std::cout << GridLogMessage << "Unitary check of starting random SUn matrix " << std::endl;
std::cout <<GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
std::cout <<GridLogMessage << std::endl;
std::cout <<GridLogMessage << std::endl;
U = U + epsilon*identity;
aux = U*adj(U) - identity;
std::cout << GridLogMessage << "Unitary matrix modified " << 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 << "Projecting on Sp2n " << std::endl;
U = ProjectOnSpGroup(U); U = ProjectOnSpGroup(U);
aux = U*adj(U) - identity;
std::cout <<GridLogMessage << std::endl;
std::cout <<GridLogMessage << std::endl;
std::cout << GridLogMessage << "Unitary check after Sp(2n) projection " << std::endl;
std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
assert( norm2(aux) < 1e-6);
std::cout <<GridLogMessage << std::endl;
std::cout <<GridLogMessage << std::endl;
// checks on determinant
std::cout << GridLogMessage << "Det after Projection on Sp2n = " << norm2( Determinant(U) ) / vol << std::endl;
std::cout <<GridLogMessage << std::endl;
std::cout <<GridLogMessage << std::endl;
// checks on elements
// an Sp2n matrix is a block matrix of the type
//
//
// U = ( W X )
// ( -X^* W^* )
//
// will check this
//
std::cout << GridLogMessage << "Checking that U[ i , j ] - conj U[ i+N/2, j+N/2 ] = 0 for i = 0, ... , N/2 " << std::endl;
std::cout <<GridLogMessage << std::endl;
const int nsp = Nc / 2;
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);
std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
assert( amizeroo.real() < 10e-6 );
amizeroo *= i;
assert( amizeroo.real() < 10e-6 );
std::cout << GridLogMessage << "ok " << std::endl;
}
}
std::cout <<GridLogMessage << std::endl;
std::cout << GridLogMessage << "Checking that U [ i , j+N/2 ] + conj U [ i+N/2, j+N/2 ] = 0 for i = 0, ... , N/2 " << std::endl;
std::cout <<GridLogMessage << std::endl;
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);
std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
assert( amizeroo.real() < 10e-6 );
amizeroo *= i;
assert( amizeroo.real() < 10e-6 );
std::cout << GridLogMessage << "ok " << std::endl;
}
}
// an explicit check for sp2
if (Nc == 2)
{
assert(Nc==2);
ColourMatrix A;
A = Zero();
Complex a(25041994., 12.);
Complex b(39., 0.22);
Complex d(10000., -2222.3333);
A()()(0,0) = a;
A()()(0,1) = b;
A()()(1,0) = i;
A()()(1,1) = d;
std::cout <<GridLogMessage << std::endl;
std::cout <<GridLogMessage << std::endl;
std::cout << GridLogMessage << "An explicit check for Sp2" << std::endl;
std::cout <<GridLogMessage << std::endl;
std::cout << GridLogMessage << "Building a non unitary matrix by hand with funny entries " << std::endl;
std::cout << GridLogMessage << "A = " << A << std::endl;
std::cout << GridLogMessage << "Projecting on Sp2 " << std::endl;
A = ProjectOnSpGroup(A);
std::cout << GridLogMessage << "now A = " << A << std::endl;
std::cout << GridLogMessage << "A(0,0) - conjA(1,1) = " << A()()(0,0) - adj ( A()()(1,1) )<< std::endl;
std::cout << GridLogMessage << "A(0,1) + conjA(1,0) = " << A()()(0,1) + adj ( A()()(1,0) )<< std::endl;
}
Grid_finalize(); Grid_finalize();