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better projection test
This commit is contained in:
Alessandro Lupo
parent
86b02c3cd8
commit
9b85bf9402
@ -212,7 +212,6 @@ accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg
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iMatrix<vtype,N> ret(arg);
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vtype nrm;
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vtype inner;
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vtype tmp;
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for(int c1=0;c1<N/2;c1++)
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{
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@ -250,20 +249,15 @@ accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg
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ret._internal[c1][c2]*= nrm;
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}
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for(int c2=0;c2<N/2;c2++)
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{
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tmp = conjugate(ret._internal[c1][c2]); // (up-left)* of the old matrix
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ret._internal[c1+N/2][c2+N/2] = tmp; // down right in the new matrix = (up-left)* of the old matrix
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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
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}
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for(int c2=N/2;c2<N;c2++)
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{
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tmp = conjugate(ret._internal[c1][c2]); // (up-right)* of the old
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ret._internal[c1+N/2][c2-N/2] = -tmp; // down left in the new matrix = -(up-right)* of the old
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ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);; // down left in the new matrix = -(up-right)* of the old
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}
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}
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return ret;
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}
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@ -2,11 +2,121 @@
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using namespace Grid;
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int SpGroupQuiz (const LatticeColourMatrixD Uin)
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{
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double vol = Uin.Grid()->gSites();
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const int nsp = Nc / 2;
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LatticeColourMatrixD Omega(Uin.Grid());
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Sp<Nc>::Omega(Omega);
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LatticeColourMatrixD aux(Uin.Grid());
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LatticeColourMatrixD identity(Uin.Grid());
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Complex i(0., 1.);
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identity = 1;
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std::cout << GridLogMessage << "Check matrix is non-zero " << std::endl;
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assert(norm2(Uin) > 1e-8);
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aux = Uin*adj(Uin) - identity;
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std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux)/vol << std::endl;
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assert(norm2(aux) < 1e-8);
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aux = Omega - (Uin * Omega * transpose(Uin));
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std::cout << GridLogMessage << "Omega - U Omega transpose(U) = " << norm2(aux)/vol << std::endl;
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assert(norm2(aux) < 1e-8);
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//Sp<Nc>::OmegaInvariance(Uin)
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std::cout << GridLogMessage << "Checking the structure is " << std::endl;
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std::cout << GridLogMessage << "U = ( W X ) " << std::endl;
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std::cout << GridLogMessage << " ( -X^* W^* ) " << std::endl;
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for (int c1 = 0; c1 < nsp; c1++) //check on W
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{
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for (int c2 = 0; c2 < nsp; c2++)
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{
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auto W = PeekIndex<ColourIndex>(Uin,c1,c2);
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auto Wstar = PeekIndex<ColourIndex>(Uin,c1+nsp,c2+nsp);
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auto Ww = conjugate( Wstar );
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auto amizero = sum(W - Ww);
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auto amizeroo = TensorRemove(amizero);
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assert( amizeroo.real() < 10e-6 );
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amizeroo *= i;
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assert( amizeroo.real() < 10e-6 );
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}
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}
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for (int c1 = 0; c1 < nsp ; c1++)
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{
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for (int c2 = 0; c2 < nsp; c2++)
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{
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auto X = PeekIndex<ColourIndex>(Uin,c1,c2+nsp);
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auto minusXstar = PeekIndex<ColourIndex>(Uin,c1+nsp,c2);
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auto minusXx = conjugate(minusXstar);
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auto amizero = sum (X + minusXx);
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auto amizeroo = TensorRemove(amizero);
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assert( amizeroo.real() < 10e-6 );
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amizeroo *= i;
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assert( amizeroo.real() < 10e-6 );
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}
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}
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std::cout << GridLogMessage << "|Det| = " << norm2( Determinant(Uin) ) / vol << std::endl;
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assert( norm2( Determinant(Uin) ) / vol - 1 < 1e-8);
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return 0;
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}
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int SpAntiHermitianAlgebraQuiz (const LatticeColourMatrixD Uin)
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{
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double vol = Uin.Grid()->gSites();
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const int nsp = Nc / 2;
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LatticeColourMatrixD Omega(Uin.Grid());
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Sp<Nc>::Omega(Omega);
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LatticeColourMatrixD aux(Uin.Grid());
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LatticeColourMatrixD identity(Uin.Grid());
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Complex i(0., 1.);
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identity = 1;
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std::cout << GridLogMessage << "Check matrix is non-zero " << std::endl;
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assert(norm2(Uin) > 1e-8);
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aux = Uin - adj(Uin);
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std::cout << GridLogMessage << "SpTa ::: T - Tda = " << norm2(aux)/vol << std::endl;
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aux = Uin + adj(Uin);
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std::cout << GridLogMessage << "SpTa ::: T + Tda = " << norm2(aux)/vol << std::endl;
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assert( norm2(aux) - 1 < 1e-8);
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std::cout << GridLogMessage << "Check that Omega T Omega + conj(T) = 0 " << std::endl;
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aux = Omega*Uin*Omega + conjugate(Uin);
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assert( norm2(aux) < 1e-8);
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std::cout << GridLogMessage << "Checking the structure is " << std::endl;
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std::cout << GridLogMessage << "U = ( W X ) " << std::endl;
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std::cout << GridLogMessage << " ( -X^* W^* ) " << std::endl;
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for (int c1 = 0; c1 < nsp; c1++) //check on W
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{
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for (int c2 = 0; c2 < nsp; c2++)
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{
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auto W = PeekIndex<ColourIndex>(Uin,c1,c2);
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auto Wstar = PeekIndex<ColourIndex>(Uin,c1+nsp,c2+nsp);
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auto Ww = conjugate( Wstar );
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auto amizero = sum(W - Ww);
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auto amizeroo = TensorRemove(amizero);
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assert( amizeroo.real() < 10e-6 );
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amizeroo *= i;
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assert( amizeroo.real() < 10e-6 );
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}
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}
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for (int c1 = 0; c1 < nsp ; c1++)
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{
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for (int c2 = 0; c2 < nsp; c2++)
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{
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auto X = PeekIndex<ColourIndex>(Uin,c1,c2+nsp);
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auto minusXstar = PeekIndex<ColourIndex>(Uin,c1+nsp,c2);
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auto minusXx = conjugate(minusXstar);
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auto amizero = sum (X + minusXx);
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auto amizeroo = TensorRemove(amizero);
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assert( amizeroo.real() < 10e-6 );
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amizeroo *= i;
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assert( amizeroo.real() < 10e-6 );
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}
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}
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return 0;
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}
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int main (int argc, char **argv)
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{
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Grid_init(&argc,&argv);
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Coordinate latt_size = GridDefaultLatt();
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Coordinate simd_layout = GridDefaultSimd(Nd,vComplex::Nsimd());
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Coordinate mpi_layout = GridDefaultMpi();
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@ -14,27 +124,18 @@ int main (int argc, char **argv)
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GridCartesian Grid(latt_size,simd_layout,mpi_layout);
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GridRedBlackCartesian RBGrid(&Grid);
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LatticeGaugeField Umu(&Grid);
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LatticeColourMatrixD U(&Grid);
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LatticeColourMatrixD Up(&Grid);
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LatticeColourMatrixD aux(&Grid);
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LatticeColourMatrixD identity(&Grid);
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// Will test resimplectification-related functionalities (from ProjectOnGaugeGroup, ProjectOnSpGroup, ProjectGn) and projection on the algebra (from ProjectSp2nAlgebra)
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// we work with matrices with positive determinant so detU = 1 even if in principle ProjectOnGaugeGroup and ProjectOnSpGroup allow for detU=-1
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// so the checks will be the same for the three functions
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// NB only ProjectGn is the proper simplectification function
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const int nsp = Nc / 2;
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LatticeColourMatrixD Omega(&Grid);
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Sp<Nc>::Omega(Omega);
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identity = 1.0;
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RealD epsilon = 0.01;
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RealD Delta = 666.;
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RealD epsilon = 0.1;
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Complex i(0., 1.);
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RealD u = 0.;
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double vol = Umu.Grid()->gSites();
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const int nsp = Nc / 2;
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std::vector<int> pseeds({1,2,3,4,5});
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GridParallelRNG pRNG(&Grid); pRNG.SeedFixedIntegers(pseeds);
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@ -42,236 +143,76 @@ int main (int argc, char **argv)
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SU<Nc>::HotConfiguration(pRNG,Umu);
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U = PeekIndex<LorentzIndex>(Umu,0);
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aux = U*adj(U) - identity;
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std::cout << GridLogMessage << "Starting with random SUn matrix " << std::endl;
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std::cout << GridLogMessage << "Unitary check " << std::endl;
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aux = U*adj(U) - identity;
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std::cout <<GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
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assert ( norm2(aux) < 1e-8 );
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std::cout <<GridLogMessage << std::endl;
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if (Nc != 2)
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if (Nc != 2) // Sp2 = SU2
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{
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std::cout << GridLogMessage << "This matrix should not leave Omega invariant, expect a warning" << std::endl;
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std::cout << GridLogMessage << "Checking matrix does NOT leave Omega invariant, to avoid a trivial test " << std::endl;
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aux = Omega - (U * Omega * transpose(U));
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assert ( norm2(aux) > 1e-8 );
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}
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Sp<Nc>::OmegaInvariance(U);
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std::cout <<GridLogMessage << std::endl;
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U = U + epsilon*identity;
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aux = U*adj(U) - identity;
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U = U + epsilon*identity - i*identity;
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std::cout << GridLogMessage << "Unitary matrix deformed " << std::endl;
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auto det = sum( Determinant(U) );
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std::cout << GridLogMessage << "Re(Det) = " << real(det) / vol << std::endl;
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det = det*i;
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std::cout << GridLogMessage << "Im(Det) = " << real(det) / vol << std::endl;
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aux = U*adj(U) - identity;
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std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl;
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std::cout <<GridLogMessage << std::endl;
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std::cout << GridLogMessage << "# # # #" << std::endl;
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std::cout << GridLogMessage << "Group" << std::endl;
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std::cout << GridLogMessage << "# # # #" << std::endl;
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std::cout <<GridLogMessage << std::endl;
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// Testing ProjectOnSpGroup
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// ProjectOnSpGroup
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std::cout << GridLogMessage << "Testing ProjectOnSpGroup" << std::endl;
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std::cout << GridLogMessage << "Apply ProjectOnSpGroup to deformed matrix" << std::endl;
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U = ProjectOnSpGroup(U);
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std::cout << GridLogMessage << "Run checks:" << std::endl;
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SpGroupQuiz(U);
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det = sum( Determinant(U) );
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std::cout << GridLogMessage << "Re(Det) after ProjectOnSpGroup (nothing to assert) = " << real(det) / vol << std::endl;
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det = det*i;
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std::cout << GridLogMessage << "Im(Det) after ProjectOnSpGroup (nothing to assert) = " << real(det) / vol << std::endl;
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aux = U*adj(U) - identity;
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std::cout << GridLogMessage << "Unitary check after ProjectOnSpGroup " << std::endl;
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std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
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assert( norm2(aux) < 1e-8);
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// actual sp2n check
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std::cout << GridLogMessage << "Checking Omega invariance after ProjectOnSpGroup" << std::endl;
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Sp<Nc>::OmegaInvariance(U); // no assertion here, but the next check will kill us if we are not simplectic
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// checks on elements
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std::cout << GridLogMessage << "Checking the structure is " << std::endl;
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std::cout << GridLogMessage << "U = ( W X ) " << std::endl;
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std::cout << GridLogMessage << " ( -X^* W^* ) " << std::endl;
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std::cout <<GridLogMessage << std::endl;
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for (int c1 = 0; c1 < nsp; c1++) //check on W
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{
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for (int c2 = 0; c2 < nsp; c2++)
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{
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auto W = PeekIndex<ColourIndex>(U,c1,c2);
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auto Wstar = PeekIndex<ColourIndex>(U,c1+nsp,c2+nsp);
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auto Ww = conjugate( Wstar );
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auto amizero = sum(W - Ww);
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auto amizeroo = TensorRemove(amizero);
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assert( amizeroo.real() < 10e-6 );
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amizeroo *= i;
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assert( amizeroo.real() < 10e-6 );
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}
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}
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for (int c1 = 0; c1 < nsp ; c1++)
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{
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for (int c2 = 0; c2 < nsp; c2++)
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{
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auto X = PeekIndex<ColourIndex>(U,c1,c2+nsp);
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auto minusXstar = PeekIndex<ColourIndex>(U,c1+nsp,c2);
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auto minusXx = conjugate(minusXstar);
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auto amizero = sum (X + minusXx);
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auto amizeroo = TensorRemove(amizero);
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assert( amizeroo.real() < 10e-6 );
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amizeroo *= i;
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assert( amizeroo.real() < 10e-6 );
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}
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}
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// ProjectOnGaugeGroup
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SU<Nc>::HotConfiguration(pRNG,Umu); //refresh
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U = PeekIndex<LorentzIndex>(Umu,1);
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U = PeekIndex<LorentzIndex>(Umu,0);
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std::cout << GridLogMessage << "Testing ProjectOnGaugeGroup" << std::endl;
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U = U + Delta*identity;
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U = U + epsilon*identity - i*identity;
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std::cout << GridLogMessage << "Apply ProjectOnGaugeGroup to deformed matrix" << std::endl;
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Sp<Nc>::ProjectOnGaugeGroup(U);
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aux = U*adj(U) - identity;
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std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
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assert( norm2(aux) < 1e-8);
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Sp<Nc>::OmegaInvariance(U);
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std::cout << GridLogMessage << "Checking the structure is " << std::endl;
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std::cout << GridLogMessage << "U = ( W X ) " << std::endl;
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std::cout << GridLogMessage << " ( -X^* W^* ) " << std::endl;
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for (int c1 = 0; c1 < nsp; c1++) //check on W
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{
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for (int c2 = 0; c2 < nsp; c2++)
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{
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auto W = PeekIndex<ColourIndex>(U,c1,c2);
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auto Wstar = PeekIndex<ColourIndex>(U,c1+nsp,c2+nsp);
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auto Ww = conjugate( Wstar );
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auto amizero = sum(W - Ww);
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auto amizeroo = TensorRemove(amizero);
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assert( amizeroo.real() < 10e-6 );
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amizeroo *= i;
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assert( amizeroo.real() < 10e-6 );
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}
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}
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for (int c1 = 0; c1 < nsp ; c1++)
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{
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for (int c2 = 0; c2 < nsp; c2++)
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{
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auto X = PeekIndex<ColourIndex>(U,c1,c2+nsp);
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auto minusXstar = PeekIndex<ColourIndex>(U,c1+nsp,c2);
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auto minusXx = conjugate(minusXstar);
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auto amizero = sum (X + minusXx);
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auto amizeroo = TensorRemove(amizero);
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assert( amizeroo.real() < 10e-6 );
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amizeroo *= i;
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assert( amizeroo.real() < 10e-6 );
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}
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}
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std::cout << GridLogMessage <<"Run checks:" << std::endl;
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SpGroupQuiz(U);
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det = sum( Determinant(U) );
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std::cout << GridLogMessage << "Re(Det) after ProjectOnGaugeGroup (nothing to assert) = " << real(det) / vol << std::endl;
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det = det*i;
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std::cout << GridLogMessage << "Im(Det) after ProjectOnGaugeGroup (nothing to assert) = " << real(det) / vol << std::endl;
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// ProjectGn
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SU<Nc>::HotConfiguration(pRNG,Umu); //refresh
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U = PeekIndex<LorentzIndex>(Umu,0);
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std::cout << GridLogMessage << "Testing ProjectGn" << std::endl;
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U = U + Delta*identity;
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U = U + epsilon*identity - i*identity;
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std::cout << GridLogMessage << "Apply ProjectGn to deformed matrix" << std::endl;
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Sp<Nc>::ProjectGn(U);
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aux = U*adj(U) - identity;
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std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
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assert( norm2(aux) < 1e-8);
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std::cout << GridLogMessage << "Det after ProjectGn = " << norm2( Determinant(U) ) / vol << std::endl;
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assert( norm2(aux) - 1 < 1e-8);
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Sp<Nc>::OmegaInvariance(U);
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std::cout << GridLogMessage << "Checking the structure is " << std::endl;
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std::cout << GridLogMessage << "U = ( W X ) " << std::endl;
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std::cout << GridLogMessage << " ( -X^* W^* ) " << std::endl;
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std::cout <<GridLogMessage << std::endl;
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for (int c1 = 0; c1 < nsp; c1++) //check on W
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{
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for (int c2 = 0; c2 < nsp; c2++)
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{
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auto W = PeekIndex<ColourIndex>(U,c1,c2);
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auto Wstar = PeekIndex<ColourIndex>(U,c1+nsp,c2+nsp);
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auto Ww = conjugate( Wstar );
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auto amizero = sum(W - Ww);
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auto amizeroo = TensorRemove(amizero);
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assert( amizeroo.real() < 10e-6 );
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amizeroo *= i;
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assert( amizeroo.real() < 10e-6 );
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}
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}
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for (int c1 = 0; c1 < nsp ; c1++)
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{
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for (int c2 = 0; c2 < nsp; c2++)
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{
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auto X = PeekIndex<ColourIndex>(U,c1,c2+nsp);
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auto minusXstar = PeekIndex<ColourIndex>(U,c1+nsp,c2);
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auto minusXx = conjugate(minusXstar);
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auto amizero = sum (X + minusXx);
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auto amizeroo = TensorRemove(amizero);
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assert( amizeroo.real() < 10e-6 );
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amizeroo *= i;
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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;
|
||||
std::cout << GridLogMessage << "Run checks:" << std::endl;
|
||||
SpGroupQuiz(U);
|
||||
det = sum( Determinant(U) );
|
||||
std::cout << GridLogMessage << "Re(Det) after ProjectGn (constrained) = " << real(det) / vol << std::endl;
|
||||
assert ( (real(det) / vol) - 1 < 1e-8 );
|
||||
det = det*i;
|
||||
std::cout << GridLogMessage << "Im(Det) after ProjectGn (constrained) = " << real(det) / vol << std::endl;
|
||||
assert ( real(det) / vol < 1e-8 );
|
||||
|
||||
// SpTa
|
||||
SU<Nc>::HotConfiguration(pRNG,Umu);//refresh
|
||||
U = PeekIndex<LorentzIndex>(Umu,2);
|
||||
|
||||
U = U + Delta*identity;
|
||||
std::cout << GridLogMessage << "Matrix deformed " << std::endl;
|
||||
U = PeekIndex<LorentzIndex>(Umu,0);
|
||||
std::cout << GridLogMessage << "Testing SpTa" << std::endl;
|
||||
U = U + epsilon*identity - i*identity;
|
||||
std::cout << GridLogMessage << "Apply SpTa to deformed matrix" << std::endl;
|
||||
U = SpTa(U);
|
||||
|
||||
aux = U - adj(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 );
|
||||
}
|
||||
}
|
||||
std::cout << GridLogMessage << "Run checks:" << std::endl;
|
||||
SpAntiHermitianAlgebraQuiz(U);
|
||||
|
||||
Grid_finalize();
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user