Added main program to reproduce 32ID ensemble with 240MeV pions and GPBC

Allowed EOFA to accept different solvers for the L and R operations in the heatbath step
Fixed EOFA Meofa operating on member Phi rather than input field
Added derived EOFA pseudofermion variant that allows for mixed prec CG to be used in the heatbath
Added forces/Test_mobius_gparity_eofa_mixed testing the above reproduces the regular EOFA
To Test_gamma, added checks for the various properties of the charge conjugation matrix C=-gamma2*gamma4 in Grid basis

tests/core/Test_gamma.cc

@@ -228,6 +228,59 @@ void checkGammaL(const Gamma::Algebra a, GridSerialRNG &rng)
   std::cout << std::endl;
 }
 
+void checkChargeConjMatrix(){
+  //Check the properties of the charge conjugation matrix
+  //In the Grid basis C = -\gamma^2 \gamma^4
+  SpinMatrix C = testAlgebra[Gamma::Algebra::MinusGammaY] * testAlgebra[Gamma::Algebra::GammaT];
+  SpinMatrix mC = -C;
+  SpinMatrix one = testAlgebra[Gamma::Algebra::Identity];
+
+  std::cout << "Testing properties of charge conjugation matrix C = -\\gamma^2 \\gamma^4 (in Grid's basis)" << std::endl;
+
+  //C^T = -C
+  SpinMatrix Ct = transpose(C);
+  std::cout << GridLogMessage << "C^T=-C ";
+  test(Ct, mC);
+  std::cout << std::endl;
+
+  //C^\dagger = -C
+  SpinMatrix Cdag = adj(C);
+  std::cout << GridLogMessage << "C^dag=-C ";
+  test(Cdag, mC);
+  std::cout << std::endl;
+
+  //C^* = C
+  SpinMatrix Cstar = conjugate(C);
+  std::cout << GridLogMessage << "C^*=C ";
+  test(Cstar, C);
+  std::cout << std::endl;
+
+  //C^{-1} = -C
+  SpinMatrix CinvC = mC * C;
+  std::cout << GridLogMessage << "C^{-1}=-C ";
+  test(CinvC, one);
+  std::cout << std::endl;
+
+  // C^{-1} \gamma^\mu C = -[\gamma^\mu]^T
+  Gamma::Algebra gmu_a[4] = { Gamma::Algebra::GammaX, Gamma::Algebra::GammaY, Gamma::Algebra::GammaZ, Gamma::Algebra::GammaT };
+  for(int mu=0;mu<4;mu++){
+    SpinMatrix gmu = testAlgebra[gmu_a[mu]];
+    SpinMatrix Cinv_gmu_C = mC * gmu * C;
+    SpinMatrix mgmu_T = -transpose(gmu);
+    std::cout << GridLogMessage << "C^{-1} \\gamma^" << mu << " C = -[\\gamma^" << mu << "]^T ";
+    test(Cinv_gmu_C, mgmu_T);
+    std::cout << std::endl;
+  }
+  
+  //[C, \gamma^5] = 0
+  SpinMatrix Cg5 = C * testAlgebra[Gamma::Algebra::Gamma5];
+  SpinMatrix g5C = testAlgebra[Gamma::Algebra::Gamma5] * C;
+  std::cout << GridLogMessage << "C \\gamma^5 = \\gamma^5 C";
+  test(Cg5, g5C);
+  std::cout << std::endl;
+}
+
+
 int main(int argc, char *argv[])
 {
   Grid_init(&argc,&argv);
@@ -270,6 +323,13 @@ int main(int argc, char *argv[])
   {
     checkGammaL(i, sRNG);
   }
+
+  std::cout << GridLogMessage << "======== Charge conjugation matrix check" << std::endl;
+  checkChargeConjMatrix();
+  std::cout << GridLogMessage << std::endl;
+  
+
+
   
   Grid_finalize();