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fix sp2n projection
This commit is contained in:
Alessandro Lupo
parent
1d6e708083
commit
283f14b7c1
@ -161,88 +161,75 @@ 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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for(int c1=0;c1<N;c1++){
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for(int c1=0;c1<N/2;c1++){
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// Normalises row c1
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zeroit(inner);
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for(int c2=0;c2<N;c2++)
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inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
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// Normalises row c1
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zeroit(inner);
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for(int c2=0;c2<N;c2++)
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inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
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nrm = sqrt(inner);
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nrm = 1.0/nrm;
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for(int c2=0;c2<N;c2++)
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ret._internal[c1][c2]*= nrm;
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nrm = sqrt(inner);
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nrm = 1.0/nrm;
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for(int c2=0;c2<N;c2++)
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ret._internal[c1][c2]*= nrm;
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// Compute row c1+N2/2: c1+N/2 = - \Omega c1*
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for(int c2=0;c2<N/2;c2++)
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//tmp = conjugate(ret._internal[c1][c2]);
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//ret._internal[c1+N/2][c2+N/2] = tmp;
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ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
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// Compute row c1+N2/2: c1+N/2 = - \Omega c1*
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for(int c2=0;c2<N/2;c2++)
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ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
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for(int c2=N/2;c2<N;c2++)
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//tmp = conjugate(ret._internal[c1][c2]);
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// ret._internal[c1+N/2][c2-N/2] = -tmp;
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ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
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for(int c2=N/2;c2<N;c2++)
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ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
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// Remove c1 from rows c1+1...N/2-1
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for (int b=c1+1; b<N/2; ++b){
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decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
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zeroit(pr);
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for(int c=0; c<N; ++c)
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pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];
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// Remove c1 from rows c1+1...N/2-1
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for (int b=c1+1; b<N/2; ++b){
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decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
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zeroit(pr);
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for(int c=0; c<N; ++c)
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pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];
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for(int c=0; c<N; ++c){
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ret._internal[b][c] -= pr * ret._internal[c1][c];
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}
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}
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// Remove c1+N/2 from rows c1+1...N/2-1
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for (int b=c1+1; b<N; ++b){
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decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
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zeroit(pr);
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for(int c=0; c<N; ++c)
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pr += conjugate(ret._internal[c1+N/2][c])*ret._internal[b][c];
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for(int c=0; c<N; ++c){
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ret._internal[b][c] -= pr * ret._internal[c1+N/2][c];
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}
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}
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} //end for loop over c1
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// Compute the last row
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{
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// Normalise last row
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int c1 = N/2-1;
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zeroit(inner);
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for(int c2=0;c2<N;c2++)
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{
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inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
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}
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nrm = sqrt(inner);
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nrm = 1.0/nrm;
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for(int c2=0;c2<N;c2++)
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{
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ret._internal[c1][c2]*= nrm;
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}
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// Compute row cN-1+N2/2: cN-1+N/2 = - \Omega cN-1*
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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]);
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// ret._internal[c1+N/2][c2+N/2] = tmp;
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ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
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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]);
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//ret._internal[c1+N/2][c2-N/2] = -tmp;
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ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
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}
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for(int c=0; c<N; ++c){
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ret._internal[b][c] -= pr * ret._internal[c1][c];
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}
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// assuming the determinant is ok
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return ret;
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}
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// Remove c1+N/2 from rows c1+1...N/2-1
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for (int b=c1+1; b<N; ++b){
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decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
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zeroit(pr);
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for(int c=0; c<N; ++c)
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pr += conjugate(ret._internal[c1+N/2][c])*ret._internal[b][c];
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for(int c=0; c<N; ++c){
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ret._internal[b][c] -= pr * ret._internal[c1+N/2][c];
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}
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}
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}
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// Compute the last row
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{
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// Normalise last row
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int c1 = N/2-1;
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zeroit(inner);
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for(int c2=0;c2<N;c2++)
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inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
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nrm = sqrt(inner);
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nrm = 1.0/nrm;
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for(int c2=0;c2<N;c2++)
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ret._internal[c1][c2]*= nrm;
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// Compute row cN-1+N2/2: cN-1+N/2 = - \Omega cN-1*
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for(int c2=0;c2<N/2;c2++)
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ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
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for(int c2=N/2;c2<N;c2++)
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ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
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}
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// assuming the determinant is ok
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return ret;
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}
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NAMESPACE_END(Grid);
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#endif
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@ -17,6 +17,14 @@ int main (int argc, char **argv)
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LatticeGaugeField Umu(&Grid);
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LatticeColourMatrixD U(&Grid);
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LatticeColourMatrixD aux(&Grid);
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LatticeColourMatrixD identity(&Grid);
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identity = 1.0;
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RealD epsilon = 0.01;
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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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std::vector<int> pseeds({1,2,3,4,5});
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std::vector<int> sseeds({6,7,8,9,10});
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@ -24,10 +32,122 @@ int main (int argc, char **argv)
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GridSerialRNG sRNG; sRNG.SeedFixedIntegers(sseeds);
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SU<Nc>::HotConfiguration(pRNG,Umu);
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U = PeekIndex<LorentzIndex>(Umu,0);
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U = PeekIndex<LorentzIndex>(Umu,2);
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// it is unitary
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aux = U*adj(U) - identity;
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std::cout <<GridLogMessage << std::endl;
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std::cout << GridLogMessage << "Unitary check of starting random SUn matrix " << std::endl;
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std::cout <<GridLogMessage << "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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U = U + epsilon*identity;
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aux = U*adj(U) - identity;
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std::cout << GridLogMessage << "Unitary matrix modified " << std::endl;
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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 << "Projecting on Sp2n " << std::endl;
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U = ProjectOnSpGroup(U);
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aux = U*adj(U) - identity;
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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 << "Unitary check after Sp(2n) projection " << std::endl;
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std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
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assert( norm2(aux) < 1e-6);
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std::cout <<GridLogMessage << std::endl;
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std::cout <<GridLogMessage << std::endl;
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// checks on determinant
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std::cout << GridLogMessage << "Det after Projection on Sp2n = " << norm2( Determinant(U) ) / vol << std::endl;
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std::cout <<GridLogMessage << std::endl;
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std::cout <<GridLogMessage << std::endl;
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// checks on elements
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// an Sp2n matrix is a block matrix of the type
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//
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//
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// U = ( W X )
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// ( -X^* W^* )
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//
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// will check this
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//
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std::cout << GridLogMessage << "Checking that U[ i , j ] - conj U[ i+N/2, j+N/2 ] = 0 for i = 0, ... , N/2 " << std::endl;
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std::cout <<GridLogMessage << std::endl;
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const int nsp = Nc / 2;
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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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std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
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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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std::cout << GridLogMessage << "ok " << std::endl;
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}
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}
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std::cout <<GridLogMessage << std::endl;
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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;
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std::cout <<GridLogMessage << std::endl;
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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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std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
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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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std::cout << GridLogMessage << "ok " << std::endl;
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}
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}
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// an explicit check for sp2
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if (Nc == 2)
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{
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assert(Nc==2);
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ColourMatrix A;
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A = Zero();
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Complex a(25041994., 12.);
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Complex b(39., 0.22);
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Complex d(10000., -2222.3333);
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A()()(0,0) = a;
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A()()(0,1) = b;
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A()()(1,0) = i;
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A()()(1,1) = d;
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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 << "An explicit check for Sp2" << std::endl;
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std::cout <<GridLogMessage << std::endl;
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std::cout << GridLogMessage << "Building a non unitary matrix by hand with funny entries " << std::endl;
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std::cout << GridLogMessage << "A = " << A << std::endl;
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std::cout << GridLogMessage << "Projecting on Sp2 " << std::endl;
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A = ProjectOnSpGroup(A);
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std::cout << GridLogMessage << "now A = " << A << std::endl;
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std::cout << GridLogMessage << "A(0,0) - conjA(1,1) = " << A()()(0,0) - adj ( A()()(1,1) )<< std::endl;
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std::cout << GridLogMessage << "A(0,1) + conjA(1,0) = " << A()()(0,1) + adj ( A()()(1,0) )<< std::endl;
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}
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Grid_finalize();
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