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better projection test

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This commit is contained in:
Alessandro Lupo 2023-05-02 15:42:20 +01:00
parent 86b02c3cd8
commit 9b85bf9402
2 changed files with 195 additions and 260 deletions
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74
Grid/tensors/Tensor_Ta.h
View File

@ -212,58 +212,52 @@ 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;
vtype tmp;
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 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]) pr;
decltype(ret._internal[b][b]*ret._internal[b][b]) prn; decltype(ret._internal[b][b]*ret._internal[b][b]) prn;
zeroit(pr); zeroit(pr);
zeroit(prn); zeroit(prn);
for(int c=0; c<N; c++) for(int c=0; c<N; c++)
{ {
pr += conjugate(ret._internal[c1][c])*ret._internal[b][c]; // <U_c1 | U_b > 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} > prn += conjugate(ret._internal[c1][c])*ret._internal[b+N/2][c]; // <U_c1 | U_{b+N} >
} }
for(int c=0; c<N; c++) 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} ) 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); 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;
} }
for(int c2=0;c2<N/2;c2++)
for(int c2=0;c2<N/2;c2++) {
{ ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]); // down right in the new matrix = (up-left)* of the old matrix
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
}
for(int c2=N/2;c2<N;c2++)
{
ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);; // down left in the new matrix = -(up-right)* of the old
}
} }
return ret; return ret;
} }

381
tests/sp2n/Test_project_on_Sp.cc
View File

@ -2,11 +2,121 @@
using namespace Grid; using namespace Grid;
int SpGroupQuiz (const LatticeColourMatrixD Uin)
{
double vol = Uin.Grid()->gSites();
const int nsp = Nc / 2;
LatticeColourMatrixD Omega(Uin.Grid());
Sp<Nc>::Omega(Omega);
LatticeColourMatrixD aux(Uin.Grid());
LatticeColourMatrixD identity(Uin.Grid());
Complex i(0., 1.);
identity = 1;
std::cout << GridLogMessage << "Check matrix is non-zero " << std::endl;
assert(norm2(Uin) > 1e-8);
aux = Uin*adj(Uin) - identity;
std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux)/vol << std::endl;
assert(norm2(aux) < 1e-8);
aux = Omega - (Uin * Omega * transpose(Uin));
std::cout << GridLogMessage << "Omega - U Omega transpose(U) = " << norm2(aux)/vol << std::endl;
assert(norm2(aux) < 1e-8);
//Sp<Nc>::OmegaInvariance(Uin)
std::cout << GridLogMessage << "Checking the structure is " << std::endl;
std::cout << GridLogMessage << "U = ( W X ) " << std::endl;
std::cout << GridLogMessage << " ( -X^* W^* ) " << std::endl;
for (int c1 = 0; c1 < nsp; c1++) //check on W
{
for (int c2 = 0; c2 < nsp; c2++)
{
auto W = PeekIndex<ColourIndex>(Uin,c1,c2);
auto Wstar = PeekIndex<ColourIndex>(Uin,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>(Uin,c1,c2+nsp);
auto minusXstar = PeekIndex<ColourIndex>(Uin,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 );
}
}
std::cout << GridLogMessage << "|Det| = " << norm2( Determinant(Uin) ) / vol << std::endl;
assert( norm2( Determinant(Uin) ) / vol - 1 < 1e-8);
return 0;
}
int SpAntiHermitianAlgebraQuiz (const LatticeColourMatrixD Uin)
{
double vol = Uin.Grid()->gSites();
const int nsp = Nc / 2;
LatticeColourMatrixD Omega(Uin.Grid());
Sp<Nc>::Omega(Omega);
LatticeColourMatrixD aux(Uin.Grid());
LatticeColourMatrixD identity(Uin.Grid());
Complex i(0., 1.);
identity = 1;
std::cout << GridLogMessage << "Check matrix is non-zero " << std::endl;
assert(norm2(Uin) > 1e-8);
aux = Uin - adj(Uin);
std::cout << GridLogMessage << "SpTa ::: T - Tda = " << norm2(aux)/vol << std::endl;
aux = Uin + adj(Uin);
std::cout << GridLogMessage << "SpTa ::: T + Tda = " << norm2(aux)/vol << std::endl;
assert( norm2(aux) - 1 < 1e-8);
std::cout << GridLogMessage << "Check that Omega T Omega + conj(T) = 0 " << std::endl;
aux = Omega*Uin*Omega + conjugate(Uin);
assert( norm2(aux) < 1e-8);
std::cout << GridLogMessage << "Checking the structure is " << std::endl;
std::cout << GridLogMessage << "U = ( W X ) " << std::endl;
std::cout << GridLogMessage << " ( -X^* W^* ) " << std::endl;
for (int c1 = 0; c1 < nsp; c1++) //check on W
{
for (int c2 = 0; c2 < nsp; c2++)
{
auto W = PeekIndex<ColourIndex>(Uin,c1,c2);
auto Wstar = PeekIndex<ColourIndex>(Uin,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>(Uin,c1,c2+nsp);
auto minusXstar = PeekIndex<ColourIndex>(Uin,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 0;
}
int main (int argc, char **argv) int main (int argc, char **argv)
{ {
Grid_init(&argc,&argv); Grid_init(&argc,&argv);
Coordinate latt_size = GridDefaultLatt(); Coordinate latt_size = GridDefaultLatt();
Coordinate simd_layout = GridDefaultSimd(Nd,vComplex::Nsimd()); Coordinate simd_layout = GridDefaultSimd(Nd,vComplex::Nsimd());
Coordinate mpi_layout = GridDefaultMpi(); Coordinate mpi_layout = GridDefaultMpi();
@ -14,27 +124,18 @@ int main (int argc, char **argv)
GridCartesian Grid(latt_size,simd_layout,mpi_layout); GridCartesian Grid(latt_size,simd_layout,mpi_layout);
GridRedBlackCartesian RBGrid(&Grid); GridRedBlackCartesian RBGrid(&Grid);
LatticeGaugeField Umu(&Grid); LatticeGaugeField Umu(&Grid);
LatticeColourMatrixD U(&Grid); LatticeColourMatrixD U(&Grid);
LatticeColourMatrixD Up(&Grid);
LatticeColourMatrixD aux(&Grid); LatticeColourMatrixD aux(&Grid);
LatticeColourMatrixD identity(&Grid); LatticeColourMatrixD identity(&Grid);
LatticeColourMatrixD Omega(&Grid);
// Will test resimplectification-related functionalities (from ProjectOnGaugeGroup, ProjectOnSpGroup, ProjectGn) and projection on the algebra (from ProjectSp2nAlgebra) Sp<Nc>::Omega(Omega);
// we work with matrices with positive determinant so detU = 1 even if in principle ProjectOnGaugeGroup and ProjectOnSpGroup allow for detU=-1
// so the checks will be the same for the three functions
// NB only ProjectGn is the proper simplectification function
const int nsp = Nc / 2;
identity = 1.0; identity = 1.0;
RealD epsilon = 0.01; RealD epsilon = 0.1;
RealD Delta = 666.;
Complex i(0., 1.); Complex i(0., 1.);
RealD u = 0.;
double vol = Umu.Grid()->gSites(); double vol = Umu.Grid()->gSites();
const int nsp = Nc / 2;
std::vector<int> pseeds({1,2,3,4,5}); std::vector<int> pseeds({1,2,3,4,5});
GridParallelRNG pRNG(&Grid); pRNG.SeedFixedIntegers(pseeds); GridParallelRNG pRNG(&Grid); pRNG.SeedFixedIntegers(pseeds);
@ -42,236 +143,76 @@ int main (int argc, char **argv)
SU<Nc>::HotConfiguration(pRNG,Umu); SU<Nc>::HotConfiguration(pRNG,Umu);
U = PeekIndex<LorentzIndex>(Umu,0); U = PeekIndex<LorentzIndex>(Umu,0);
aux = U*adj(U) - identity;
std::cout << GridLogMessage << "Starting with random SUn matrix " << std::endl; std::cout << GridLogMessage << "Starting with random SUn matrix " << std::endl;
std::cout << GridLogMessage << "Unitary check " << std::endl; aux = U*adj(U) - identity;
std::cout <<GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl; std::cout <<GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
assert ( norm2(aux) < 1e-8 ); assert ( norm2(aux) < 1e-8 );
std::cout <<GridLogMessage << std::endl; if (Nc != 2) // Sp2 = SU2
if (Nc != 2)
{ {
std::cout << GridLogMessage << "This matrix should not leave Omega invariant, expect a warning" << std::endl; std::cout << GridLogMessage << "Checking matrix does NOT leave Omega invariant, to avoid a trivial test " << std::endl;
aux = Omega - (U * Omega * transpose(U));
assert ( norm2(aux) > 1e-8 );
} }
Sp<Nc>::OmegaInvariance(U);
std::cout <<GridLogMessage << std::endl;
U = U + epsilon*identity;
aux = U*adj(U) - identity;
U = U + epsilon*identity - i*identity;
std::cout << GridLogMessage << "Unitary matrix deformed " << std::endl; std::cout << GridLogMessage << "Unitary matrix deformed " << std::endl;
auto det = sum( Determinant(U) );
std::cout << GridLogMessage << "Re(Det) = " << real(det) / vol << std::endl;
det = det*i;
std::cout << GridLogMessage << "Im(Det) = " << real(det) / vol << std::endl;
aux = U*adj(U) - identity;
std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl; std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl;
std::cout <<GridLogMessage << std::endl; // ProjectOnSpGroup
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 << "Testing ProjectOnSpGroup" << std::endl;
std::cout << GridLogMessage << "Apply ProjectOnSpGroup to deformed matrix" << std::endl; std::cout << GridLogMessage << "Apply ProjectOnSpGroup to deformed matrix" << std::endl;
U = ProjectOnSpGroup(U); U = ProjectOnSpGroup(U);
std::cout << GridLogMessage << "Run checks:" << std::endl;
aux = U*adj(U) - identity; SpGroupQuiz(U);
std::cout << GridLogMessage << "Unitary check after ProjectOnSpGroup " << std::endl; det = sum( Determinant(U) );
std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl; std::cout << GridLogMessage << "Re(Det) after ProjectOnSpGroup (nothing to assert) = " << real(det) / vol << std::endl;
assert( norm2(aux) < 1e-8); det = det*i;
std::cout << GridLogMessage << "Im(Det) after ProjectOnSpGroup (nothing to assert) = " << real(det) / vol << std::endl;
// actual sp2n check
std::cout << GridLogMessage << "Checking Omega invariance after ProjectOnSpGroup" << std::endl;
Sp<Nc>::OmegaInvariance(U); // no assertion here, but the next check will kill us if we are not simplectic
// checks on elements
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 );
}
}
// ProjectOnGaugeGroup
SU<Nc>::HotConfiguration(pRNG,Umu); //refresh SU<Nc>::HotConfiguration(pRNG,Umu); //refresh
U = PeekIndex<LorentzIndex>(Umu,1); U = PeekIndex<LorentzIndex>(Umu,0);
std::cout << GridLogMessage << "Testing ProjectOnGaugeGroup" << std::endl; std::cout << GridLogMessage << "Testing ProjectOnGaugeGroup" << std::endl;
U = U + Delta*identity; U = U + epsilon*identity - i*identity;
std::cout << GridLogMessage << "Apply ProjectOnGaugeGroup to deformed matrix" << std::endl; std::cout << GridLogMessage << "Apply ProjectOnGaugeGroup to deformed matrix" << std::endl;
Sp<Nc>::ProjectOnGaugeGroup(U); Sp<Nc>::ProjectOnGaugeGroup(U);
aux = U*adj(U) - identity; std::cout << GridLogMessage <<"Run checks:" << std::endl;
std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl; SpGroupQuiz(U);
assert( norm2(aux) < 1e-8); det = sum( Determinant(U) );
Sp<Nc>::OmegaInvariance(U); std::cout << GridLogMessage << "Re(Det) after ProjectOnGaugeGroup (nothing to assert) = " << real(det) / vol << std::endl;
det = det*i;
std::cout << GridLogMessage << "Checking the structure is " << std::endl; std::cout << GridLogMessage << "Im(Det) after ProjectOnGaugeGroup (nothing to assert) = " << real(det) / vol << std::endl;
std::cout << GridLogMessage << "U = ( W X ) " << std::endl;
std::cout << GridLogMessage << " ( -X^* W^* ) " << 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 );
}
}
// ProjectGn
SU<Nc>::HotConfiguration(pRNG,Umu); //refresh
U = PeekIndex<LorentzIndex>(Umu,0);
std::cout << GridLogMessage << "Testing ProjectGn" << std::endl; std::cout << GridLogMessage << "Testing ProjectGn" << std::endl;
U = U + Delta*identity; U = U + epsilon*identity - i*identity;
std::cout << GridLogMessage << "Apply ProjectGn to deformed matrix" << std::endl; std::cout << GridLogMessage << "Apply ProjectGn to deformed matrix" << std::endl;
Sp<Nc>::ProjectGn(U); Sp<Nc>::ProjectGn(U);
aux = U*adj(U) - identity; std::cout << GridLogMessage << "Run checks:" << std::endl;
std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl; SpGroupQuiz(U);
assert( norm2(aux) < 1e-8); det = sum( Determinant(U) );
std::cout << GridLogMessage << "Det after ProjectGn = " << norm2( Determinant(U) ) / vol << std::endl; std::cout << GridLogMessage << "Re(Det) after ProjectGn (constrained) = " << real(det) / vol << std::endl;
assert( norm2(aux) - 1 < 1e-8); assert ( (real(det) / vol) - 1 < 1e-8 );
Sp<Nc>::OmegaInvariance(U); det = det*i;
std::cout << GridLogMessage << "Im(Det) after ProjectGn (constrained) = " << real(det) / vol << std::endl;
std::cout << GridLogMessage << "Checking the structure is " << std::endl; assert ( real(det) / vol < 1e-8 );
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 );
}
}
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;
// SpTa
SU<Nc>::HotConfiguration(pRNG,Umu);//refresh SU<Nc>::HotConfiguration(pRNG,Umu);//refresh
U = PeekIndex<LorentzIndex>(Umu,2); U = PeekIndex<LorentzIndex>(Umu,0);
std::cout << GridLogMessage << "Testing SpTa" << std::endl;
U = U + Delta*identity; U = U + epsilon*identity - i*identity;
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;
U = SpTa(U); U = SpTa(U);
std::cout << GridLogMessage << "Run checks:" << std::endl;
aux = U - adj(U); SpAntiHermitianAlgebraQuiz(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;
assert( norm2(aux) - 1 < 1e-8);
std::cout << GridLogMessage << "Check that Omega T Omega + conj(T) = 0 " << std::endl;
LatticeColourMatrixD Omega(&Grid);
Sp<Nc>::Omega(Omega);
aux = Omega*U*Omega + conjugate(U);
assert( norm2(aux) < 1e-8);
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(); Grid_finalize();