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fix projection

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This commit is contained in:
Alessandro Lupo 2021-10-22 10:44:54 +01:00
parent 4e31e4e094
commit 4d8ae6221c
3 changed files with 84 additions and 12 deletions
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9
Grid/qcd/utils/Sp2n.h
View File

@ -493,13 +493,14 @@ public:
for (int i = 0; i < ncolour; i++)
{
Omega()()(i, 2*ncolour-1-i) = 1.;
Omega()()(2*ncolour-1-i, i) = -1;
Omega()()(i, ncolour+i) = 1.;
Omega()()(ncolour+i, i) = -1;
}
std::cout << GridLogMessage << "Omega = " << Omega()() << std::endl;
OmegaLatt = OmegaLatt + (identity*Omega);
auto diff = OmegaLatt - (in*Omega*transpose(in));
auto diff = OmegaLatt - (in*OmegaLatt*transpose(in));
auto sdiff = sum(diff);
//assert( norm2(sdiff) < 1e-8 );
if (norm2(sdiff) < 1e-8)

75
Grid/tensors/Tensor_Ta.h
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@ -156,6 +156,75 @@ template<class vtype,int N> accelerator_inline iVector<vtype,N> ProjectOnSpGroup
// int N is 2n in Sp(2n)
template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg)
{
// need a check for the group type?
iMatrix<vtype,N> ret(arg);
vtype nrm;
vtype inner;
vtype tmp;
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++)
{
tmp = conjugate(ret._internal[c1][c2]); // (up-left)* of the old matrix
ret._internal[c1+N/2][c2+N/2] = tmp; // down right in the new matrix = (up-left)* of the old matrix
}
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] = -tmp; // down left in the new matrix = -(up-right)* of the old
}
}
return ret;
}
/*
template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg)
{
// need a check for the group type?
iMatrix<vtype,N> ret(arg);
@ -175,7 +244,7 @@ accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg
// Compute row c1+N2/2: c1+N/2 = - \Omega c1*
for(int c2=0;c2<N/2;c2++)
ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]); // lupo: c1,c2? dont we want c1 c2+N/2
for(int c2=N/2;c2<N;c2++)
ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
@ -203,7 +272,7 @@ accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg
ret._internal[b][c] -= pr * ret._internal[c1+N/2][c];
}
}
}
} //end c1 0, ... N/2-1 loop
// Compute the last row
{
@ -227,7 +296,7 @@ accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg
}
// assuming the determinant is ok
return ret;
}
}*/
NAMESPACE_END(Grid);

12
tests/sp2n/Test_project_on_Sp.cc
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@ -45,7 +45,7 @@ int main (int argc, char **argv)
std::cout <<GridLogMessage << std::endl;
if (Nc != 2)
{
std::cout << "This matrix should not leave Omega invariant, expect a warning" << std::endl;
std::cout << GridLogMessage << "This matrix should not leave Omega invariant, expect a warning" << std::endl;
}
Sp<nsp>::OmegaInvariance(U);
std::cout <<GridLogMessage << std::endl;
@ -56,18 +56,18 @@ 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 << "This matrix should not leave Omega invariant, expect a warning" << std::endl;
Sp<nsp>::OmegaInvariance(U);
std::cout <<GridLogMessage << std::endl;
std::cout << GridLogMessage << "Projecting on Sp2n " << std::endl;
U = ProjectOnSpGroup(U);
//U = ProjectOnGroup(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);
assert( norm2(aux) < 1e-8);
std::cout <<GridLogMessage << std::endl;
std::cout <<GridLogMessage << std::endl;
@ -81,7 +81,9 @@ int main (int argc, char **argv)
Sp<nsp>::OmegaInvariance(U);
// checks on elements
std::cout <<GridLogMessage << std::endl;
std::cout <<GridLogMessage << std::endl;
std::cout << GridLogMessage << "Checking the structure is " << std::endl;
std::cout << GridLogMessage << "U = ( W X ) " << std::endl;
std::cout << GridLogMessage << " ( -X^* W^* ) " << std::endl;