To PeriodicBC and ConjugateBC, added a new function "CshiftLink" which performs a boundary-aware C-shift of links or products of links. For the latter, the links crossing the global boundary are complex-conjugated.

To the gauge implementations, added CshiftLink functions calling into the appropriate operation for the BC in a given direction.
GaugeTransform, FourierAcceleratedGaugeFixer and WilsonLoops::FieldStrength no longer implicitly assume periodic boundary conditions; instead the shifted link is obtained using CshiftLink and is aware of the gauge implementation.
Added an assert-check to ensure that the gauge fixing converges within the specified number of steps.
Added functionality to compute the timeslice averaged plaquette
Added functionality to compute the 5LI topological charge and timeslice topological charge
Added a check of the properties of the charge conjugation matrix C=-gamma_2 gamma_4 to Test_gamma
Fixed const correctness for Replicate
Modified Test_fft_gfix to support either conjugate or periodic BCs, optionally disabling Fourier-accelerated gauge fixing, and tuning of alpha using cmdline options

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();