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Extracted is_element_of Sp2n
This commit is contained in:
Julian Lenz
parent
3ee5444c69
commit
339c4fda79
@ -2,6 +2,109 @@
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using namespace Grid;
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template <typename T>
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bool has_correct_block_structure(T U){
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// checks on elements
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const int nsp = Nc / 2;
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Complex i(0., 1.);
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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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return true;
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};
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template <typename T>
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bool is_element_of_Sp2n(T U) {
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LatticeColourMatrixD aux(U.Grid());
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LatticeColourMatrixD identity(U.Grid());
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identity = 1.0;
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double vol = U.Grid()->gSites();
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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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// actual sp2n check
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std::cout << GridLogMessage << "Checking Omega invariance" << 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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return has_correct_block_structure(U);
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}
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template<typename T>
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void test_group_projections(T U) {
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RealD Delta = 666.;
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LatticeColourMatrixD identity(U.Grid());
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identity = 1.0;
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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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std::string name="ProjectOnSpGroup";
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std::cout << GridLogMessage << "Testing "<< name << std::endl;
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std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
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U = ProjectOnSpGroup(U);
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assert(is_element_of_Sp2n(U));
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name = "ProjectOnGaugeGroup";
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std::cout << GridLogMessage << "Testing "<< name << std::endl;
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std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
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U = U + Delta*identity;
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Sp<Nc>::ProjectOnGaugeGroup(U);
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assert(is_element_of_Sp2n(U));
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name = "ProjectGn";
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std::cout << GridLogMessage << "Testing "<< name << std::endl;
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std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
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U = U + Delta*identity;
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Sp<Nc>::ProjectGn(U);
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assert(is_element_of_Sp2n(U));
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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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@ -61,152 +164,8 @@ int main (int argc, char **argv)
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std::cout << GridLogMessage << "Unitary matrix deformed " << 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 << "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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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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test_group_projections(U);
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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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std::cout << GridLogMessage << "Testing ProjectOnGaugeGroup" << std::endl;
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U = U + Delta*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 << "Testing ProjectGn" << std::endl;
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U = U + Delta*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 );
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}
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}
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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 << "Algebra" << std::endl;
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