From 046a23121e6c186d13b69ec52781aec0c48a1db0 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 5 Oct 2021 15:51:22 +0100
Subject: [PATCH 001/129] sp2n generators

---
 Grid/qcd/utils/Sp2n.h           | 396 ++++++++++++++++++++++++++++++++
 Grid/qcd/utils/Utils.h          |   1 +
 tests/core/test_sp2n_lie_gen.cc |  46 ++++
 3 files changed, 443 insertions(+)
 create mode 100644 Grid/qcd/utils/Sp2n.h
 create mode 100644 tests/core/test_sp2n_lie_gen.cc

diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.h
new file mode 100644
index 00000000..c8960383
--- /dev/null
+++ b/Grid/qcd/utils/Sp2n.h
@@ -0,0 +1,396 @@
+
+#ifndef QCD_UTIL_Sp2n_H
+#define QCD_UTIL_Sp2n_H
+
+NAMESPACE_BEGIN(Grid);
+
+// Sp(2N)
+// ncolour = N
+template <int ncolour>
+class Sp {
+public:
+    static const int Dimension = ncolour*2;
+    static const int AlgebraDimension = ncolour*(2*ncolour +1);
+    static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
+    
+    
+    template <typename vtype>
+    using iSp2nMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
+    template <typename vtype>
+    using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
+    template <typename vtype>
+    using iSp2nAlgebraVector = iScalar<iScalar<iVector<vtype, AlgebraDimension> > >;
+    
+    typedef iSp2nMatrix<Complex> Matrix;
+    
+    typedef iSp2nMatrix<vComplex> vMatrix;
+    
+    
+    typedef Lattice<vMatrix> LatticeMatrix;
+    // Sp(2N) has N(2N+1) = 2N^2+N generators
+    //
+    // normalise the generators such that
+    // Trace ( Ta Tb) = 1/2 delta_ab
+    //
+    // N generators in the cartan, 2N^2 off
+    // off diagonal:
+    //     there are 6 types named a,b,c,d and w,z
+    //     abcd are N(N-1)/2 each while wz are N each
+    
+    
+    
+    
+    template <class cplx>
+    static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
+        // map lie index into type of generators: diagonal, abcd type, wz type
+
+        int diagIndex;
+        int aIndex, bIndex, cIndex, dIndex;
+        int wIndex, zIndex; // a,b,c,d are N(N-1)/2 and w,z are N
+        int mod = ncolour * (ncolour-1) * 0.5;
+        int offdiag = 2*ncolour*ncolour; // number of generators not in the cartan subalgebra
+        int wmod = 4*mod;
+        int zmod = wmod+ncolour;
+        if (lieIndex >= offdiag) {
+            diagIndex = lieIndex - offdiag; // 0, ... ,N-1
+            //std::cout << GridLogMessage << "diag type " << std::endl;
+            generatorDiagtype(diagIndex, ta);
+            return;
+        }
+        if ( (lieIndex >= wmod) && (lieIndex < zmod) ) {
+            //std::cout << GridLogMessage << "w type " << std::endl;
+            wIndex = lieIndex- wmod;    // 0, ... ,N-1
+            generatorWtype(wIndex,ta);
+            return;
+        }
+        if ( (lieIndex >= zmod) && (lieIndex < offdiag) ) {
+            //std::cout << GridLogMessage << "z type " << std::endl;
+            //std::cout << GridLogMessage << "lie index " << lieIndex << std::endl;
+            //std::cout << GridLogMessage << "z mod " << zmod << std::endl;
+            zIndex = lieIndex - zmod;   // 0, ... ,N-1
+            generatorZtype(zIndex,ta);
+            return;
+        }
+        if (lieIndex < mod) { // atype 0, ... , N(N-1)/2=mod
+            //std::cout << GridLogMessage << "a type " << std::endl;
+            aIndex = lieIndex;
+            //std::cout << GridLogMessage << "a indx " << aIndex << std::endl;
+            generatorAtype(aIndex, ta);
+            return;
+        }
+        if ( (lieIndex >= mod) && lieIndex < 2*mod) { // btype mod, ... , 2mod-1
+            //std::cout << GridLogMessage << "b type " << std::endl;
+            bIndex = lieIndex - mod;
+            generatorBtype(bIndex, ta);
+            return;
+        }
+        if ( (lieIndex >= 2*mod) && lieIndex < 3*mod) { // ctype 2mod, ... , 3mod-1
+            //std::cout << GridLogMessage << "c type " << std::endl;
+            cIndex = lieIndex - 2*mod;
+            generatorCtype(cIndex, ta);
+            return;
+        }
+        if ( (lieIndex >= 3*mod) && lieIndex < wmod) { // ctype 3mod, ... , 4mod-1 = wmod-1
+             //std::cout << GridLogMessage << "d type " << std::endl;
+             dIndex = lieIndex - 3*mod;
+             generatorDtype(dIndex, ta);
+            return;
+         }
+            
+    } //end of generator
+    
+    template <class cplx>
+    static void generatorDiagtype(int diagIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan subalgebra
+        
+        ta = Zero();
+        RealD nrm = 1.0 / 2;
+
+        ta()()(diagIndex,diagIndex) = nrm;
+        ta()()(diagIndex+ncolour,diagIndex+ncolour) = -nrm;
+    }
+    
+    template <class cplx>
+    static void generatorAtype(int aIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,j) = ta(j,i) = -ta(i+N,j+N) = -ta(j+N,i+N) = 1 / 2 sqrt(2)
+        // with i<j and i=0,...,N-2
+        // follows that j=i+1, ... , N
+        int i1, i2;
+        ta = Zero();
+        RealD nrm = 1 / (2 * std::sqrt(2) );
+        
+        su2SubGroupIndex(i1, i2, aIndex);
+        ta()()(i1,i2) = 1;
+        ta()()(i2,i1) = 1;
+        ta()()(i1+ncolour,i2+ncolour) = -1;
+        ta()()(i2+ncolour,i1+ncolour) = -1;
+
+        ta = ta * nrm;
+    }
+    
+    template <class cplx>
+    static void generatorBtype(int bIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,j) = -ta(j,i) = ta(i+N,j+N) = -ta(j+N,i+N) = i / 1/ 2 sqrt(2)
+        // with i<j and i=0,...,N-2
+        // follows that j=i+1, ... , N-1
+        
+        int i1, i2;
+        ta = Zero();
+        cplx i(0.0, 1.0);
+        RealD nrm = 1 / (2 * std::sqrt(2));
+        su2SubGroupIndex(i1, i2, bIndex);
+        
+
+        ta()()(i1,i2) = i;
+        ta()()(i2,i1) = -i;
+        ta()()(i1+ncolour,i2+ncolour) = i;
+        ta()()(i2+ncolour,i1+ncolour) = -i;
+
+        ta = ta * nrm;
+    }
+    
+    template <class cplx>
+    static void generatorCtype(int cIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
+        
+        
+        int i1, i2;
+        ta = Zero();
+        RealD nrm = 1 / (2 * std::sqrt(2) );
+        su2SubGroupIndex(i1, i2, cIndex);
+        
+        ta()()(i1,i2+ncolour) = 1;
+        ta()()(i2,i1+ncolour) = 1;
+        ta()()(i1+ncolour,i2) = 1;
+        ta()()(i2+ncolour,i1) = 1;
+
+        ta = ta * nrm;
+    }
+    
+    template <class cplx>
+    static void generatorDtype(int dIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i /  2 sqrt(2)
+        
+        int i1, i2;
+        ta = Zero();
+        cplx i(0.0, 1.0);
+        RealD nrm = 1 / (2 * std::sqrt(2)  );
+        su2SubGroupIndex(i1, i2, dIndex);
+
+        ta()()(i1,i2+ncolour) = i;
+        ta()()(i2,i1+ncolour) = i;
+        ta()()(i1+ncolour,i2) = -i;
+        ta()()(i2+ncolour,i1) = -i;
+
+        ta = ta * nrm;
+    }
+    
+    template <class cplx>
+     static void generatorWtype(int wIndex, iSp2nMatrix<cplx> &ta) {
+         
+         // ta(i,i+N) =  ta(i+N,i) = 1/2
+         
+         ta = Zero();
+         RealD nrm = 1.0 / 2; //check
+
+         ta()()(wIndex,wIndex+ncolour) = 1;
+         ta()()(wIndex+ncolour,wIndex) = 1;
+         
+         ta = ta * nrm;
+     }
+    
+    template <class cplx>
+     static void generatorZtype(int zIndex, iSp2nMatrix<cplx> &ta) {
+         
+         // ta(i,i+N) = - ta(i+N,i) = i/2
+         
+         ta = Zero();
+         RealD nrm = 1.0 / 2; //check
+         cplx i(0.0, 1.0);
+         ta()()(zIndex,zIndex+ncolour) = i;
+         ta()()(zIndex+ncolour,zIndex) = -i;
+         
+         ta = ta * nrm;
+     }
+    
+    
+    ////////////////////////////////////////////////////////////////////////
+    // Map a su2 subgroup number to the pair of rows that are non zero
+    ////////////////////////////////////////////////////////////////////////
+    static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
+      assert((su2_index >= 0) && (su2_index < (ncolour * (ncolour - 1)) / 2));
+
+      int spare = su2_index;
+      for (i1 = 0; spare >= (ncolour - 1 - i1); i1++) {
+        spare = spare - (ncolour - 1 - i1);  // remove the Nc-1-i1 terms
+      }
+      i2 = i1 + 1 + spare;
+    }
+    
+    
+    
+    
+    
+    static void printGenerators(void) {
+        for (int gen = 0; gen < AlgebraDimension; gen++) {
+            Matrix ta;
+            generator(gen, ta);
+            std::cout << GridLogMessage << "Nc (2n) = " << 2*ncolour << std::endl;
+            std::cout << GridLogMessage << " t_" << gen << std::endl;
+            std::cout << GridLogMessage << ta << std::endl;
+        }
+    }
+    
+    
+    
+    static void testGenerators(void) {
+        Matrix ta;
+        Matrix tb;
+        std::cout << GridLogMessage << "Fundamental - Checking trace ta tb is 0.5 delta_ab " << std::endl;
+        for (int a = 0; a < AlgebraDimension; a++) {
+            for (int b = 0; b < AlgebraDimension; b++) {
+                generator(a,ta);
+                generator(b,tb);
+                Complex tr = TensorRemove(trace( ta * tb) );
+                std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
+                << std::endl;
+                if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
+                if (a != b) assert(abs(tr) < 1.0e-6);
+
+            }
+        }
+        std::cout << GridLogMessage << std::endl;
+        std::cout << GridLogMessage << "Fundamental - Checking if hermitian" << std::endl;
+        for (int a = 0; a < AlgebraDimension; a++) {
+            generator(a,ta);
+            std::cout << GridLogMessage << a << std::endl;
+            assert(norm2(ta - adj(ta)) < 1.0e-6);
+        }
+        std::cout << GridLogMessage << std::endl;
+        std::cout << GridLogMessage << "Fundamental - Checking if traceless" << std::endl;
+        for (int a = 0; a < AlgebraDimension; a++) {
+          generator(a, ta);
+          Complex tr = TensorRemove(trace(ta));
+          std::cout << GridLogMessage << a << std::endl;
+          assert(abs(tr) < 1.0e-6);
+        }
+        
+    }
+    
+    
+    static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG, //same as sun
+                                                    LatticeMatrix &out,
+                                                    Real scale = 1.0) {
+      GridBase *grid = out.Grid();
+      LatticeReal ca(grid);
+      LatticeMatrix la(grid);
+      Complex ci(0.0, scale);
+      Matrix ta;
+
+      out = Zero();
+      for (int a = 0; a < AlgebraDimension; a++) {
+        gaussian(pRNG, ca);
+        generator(a, ta);
+        la = toComplex(ca) * ta;
+        out += la;
+      }
+      out *= ci;
+    }
+    
+    
+    
+    template <typename LatticeMatrixType>
+    static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) { // same as sun
+      typedef typename LatticeMatrixType::scalar_type ComplexType;
+
+      LatticeMatrixType xn(x.Grid());
+      RealD nfac = 1.0;
+
+      xn = x;
+      ex = xn + ComplexType(1.0);  // 1+x
+
+      // Do a 12th order exponentiation
+      for (int i = 2; i <= 12; ++i) {
+        nfac = nfac / RealD(i);  // 1/2, 1/2.3 ...
+        xn = xn * x;             // x2, x3,x4....
+        ex = ex + xn * nfac;     // x2/2!, x3/3!....
+      }
+    }
+    
+    
+    
+    
+    
+}; // end of class Sp
+    
+    
+
+typedef Sp<2> Sp4;
+typedef Sp<3> Sp6;
+typedef Sp<4> Sp8;
+
+NAMESPACE_END(Grid);
+#endif
+
+
+    
+    
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+    
+    
+    
+/*     }
+     sigxy = lieIndex & 0x1;     // 1 if odd, 0 if even
+     su2Index = lieIndex >> 1 ;  // where to put the sigma_x(y)
+                                 //for the even(odd) lieindex, sigmax(y)
+     if (sigxy)
+         //put sigmay at su2index
+     else
+         //put sigmax    */
diff --git a/Grid/qcd/utils/Utils.h b/Grid/qcd/utils/Utils.h
index 8ce3df37..35594656 100644
--- a/Grid/qcd/utils/Utils.h
+++ b/Grid/qcd/utils/Utils.h
@@ -9,6 +9,7 @@
 
 // Include representations
 #include <Grid/qcd/utils/SUn.h>
+#include <Grid/qcd/utils/Sp2n.h>
 #include <Grid/qcd/utils/SUnAdjoint.h>
 #include <Grid/qcd/utils/SUnTwoIndex.h>
 
diff --git a/tests/core/test_sp2n_lie_gen.cc b/tests/core/test_sp2n_lie_gen.cc
new file mode 100644
index 00000000..5dbba9d3
--- /dev/null
+++ b/tests/core/test_sp2n_lie_gen.cc
@@ -0,0 +1,46 @@
+
+
+
+#include <Grid/Grid.h>
+#include <Grid/qcd/utils/SUn.h>
+
+using namespace Grid;
+
+int main(int argc, char** argv) {
+  Grid_init(&argc, &argv);
+    
+  //std::vector<int> latt({4, 4, 4, 8});
+  //GridCartesian* grid = SpaceTimeGrid::makeFourDimGrid(
+  //latt, GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
+  //GridRedBlackCartesian* rbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(grid);
+  
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(4)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+    
+  Sp4::printGenerators();
+  Sp4::testGenerators();
+    
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(6)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  
+  Sp6::printGenerators();
+  Sp6::testGenerators();
+    
+  std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(8)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+    
+  Sp8::printGenerators();
+  Sp8::testGenerators(); 
+    
+    
+  Grid_finalize();
+}

From 11fb943b1e756942e52cc24bda111df64b866a00 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Mon, 11 Oct 2021 16:21:25 +0100
Subject: [PATCH 002/129] gauge and fermion implementation for sp2n

---
 Grid/qcd/action/fermion/Fermion.h            |   5 +
 Grid/qcd/action/fermion/WilsonFermion.h      |   2 +
 Grid/qcd/action/fermion/WilsonImpl.h         |  10 +
 Grid/qcd/action/gauge/Gauge.h                |   3 +
 Grid/qcd/action/gauge/GaugeImplTypes.h       | 102 +++++++++--
 Grid/qcd/action/gauge/GaugeImplementations.h |   5 +
 Grid/qcd/representations/Representations.h   |   1 +
 Grid/qcd/representations/spfundamental.h     |  42 +++++
 Grid/qcd/utils/Sp2n.h                        | 181 +++++++++++++------
 tests/core/test_sp2n_lie_gen.cc              |  11 +-
 10 files changed, 292 insertions(+), 70 deletions(-)
 create mode 100644 Grid/qcd/representations/spfundamental.h

diff --git a/Grid/qcd/action/fermion/Fermion.h b/Grid/qcd/action/fermion/Fermion.h
index 59fc17d5..b988b306 100644
--- a/Grid/qcd/action/fermion/Fermion.h
+++ b/Grid/qcd/action/fermion/Fermion.h
@@ -115,6 +115,11 @@ typedef WilsonFermion<WilsonImplR> WilsonFermionR;
 typedef WilsonFermion<WilsonImplF> WilsonFermionF;
 typedef WilsonFermion<WilsonImplD> WilsonFermionD;
 
+
+typedef WilsonFermion<SpWilsonImplR> SpWilsonFermionR;
+typedef WilsonFermion<SpWilsonImplF> SpWilsonFermionF;
+typedef WilsonFermion<SpWilsonImplD> SpWilsonFermionD;
+
 //typedef WilsonFermion<WilsonImplRL> WilsonFermionRL;
 //typedef WilsonFermion<WilsonImplFH> WilsonFermionFH;
 //typedef WilsonFermion<WilsonImplDF> WilsonFermionDF;
diff --git a/Grid/qcd/action/fermion/WilsonFermion.h b/Grid/qcd/action/fermion/WilsonFermion.h
index bf8926d0..4a2d1ddd 100644
--- a/Grid/qcd/action/fermion/WilsonFermion.h
+++ b/Grid/qcd/action/fermion/WilsonFermion.h
@@ -208,5 +208,7 @@ public:
 
 typedef WilsonFermion<WilsonImplF> WilsonFermionF;
 typedef WilsonFermion<WilsonImplD> WilsonFermionD;
+//typedef WilsonFermion<SpWilsonImplF> SpWilsonFermionF;
+//typedef WilsonFermion<SpWilsonImplD> SpWilsonFermionD;
 
 NAMESPACE_END(Grid);
diff --git a/Grid/qcd/action/fermion/WilsonImpl.h b/Grid/qcd/action/fermion/WilsonImpl.h
index 2685796d..01545d3b 100644
--- a/Grid/qcd/action/fermion/WilsonImpl.h
+++ b/Grid/qcd/action/fermion/WilsonImpl.h
@@ -267,6 +267,16 @@ typedef WilsonImpl<vComplex,  TwoIndexAntiSymmetricRepresentation, CoeffReal > W
 typedef WilsonImpl<vComplexF, TwoIndexAntiSymmetricRepresentation, CoeffReal > WilsonTwoIndexAntiSymmetricImplF;  // Float
 typedef WilsonImpl<vComplexD, TwoIndexAntiSymmetricRepresentation, CoeffReal > WilsonTwoIndexAntiSymmetricImplD;  // Double
 
+//sp 2n
+
+typedef WilsonImpl<vComplex,  SpFundamentalRepresentation, CoeffReal > SpWilsonImplR;  // Real.. whichever prec
+typedef WilsonImpl<vComplexF, SpFundamentalRepresentation, CoeffReal > SpWilsonImplF;  // Float
+typedef WilsonImpl<vComplexD, SpFundamentalRepresentation, CoeffReal > SpWilsonImplD;  // Double
+
+//typedef WilsonImpl<vComplex,  SpFundamentalRepresentation, CoeffComplex > SpZWilsonImplR; // Real.. whichever prec
+//typedef WilsonImpl<vComplexF, SpFundamentalRepresentation, CoeffComplex > SpZWilsonImplF; // Float
+//typedef WilsonImpl<vComplexD, SpFundamentalRepresentation, CoeffComplex > SpZWilsonImplD; // Double
+
 
 NAMESPACE_END(Grid);
 
diff --git a/Grid/qcd/action/gauge/Gauge.h b/Grid/qcd/action/gauge/Gauge.h
index b3b34eba..535f0845 100644
--- a/Grid/qcd/action/gauge/Gauge.h
+++ b/Grid/qcd/action/gauge/Gauge.h
@@ -39,6 +39,9 @@ NAMESPACE_BEGIN(Grid);
 typedef WilsonGaugeAction<PeriodicGimplR>          WilsonGaugeActionR;
 typedef WilsonGaugeAction<PeriodicGimplF>          WilsonGaugeActionF;
 typedef WilsonGaugeAction<PeriodicGimplD>          WilsonGaugeActionD;
+typedef WilsonGaugeAction<SymplPeriodicGimplR>     SymplWilsonGaugeActionR;
+typedef WilsonGaugeAction<SymplPeriodicGimplF>     SymplWilsonGaugeActionF;
+typedef WilsonGaugeAction<SymplPeriodicGimplD>     SymplWilsonGaugeActionD;
 typedef PlaqPlusRectangleAction<PeriodicGimplR>    PlaqPlusRectangleActionR;
 typedef PlaqPlusRectangleAction<PeriodicGimplF>    PlaqPlusRectangleActionF;
 typedef PlaqPlusRectangleAction<PeriodicGimplD>    PlaqPlusRectangleActionD;
diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index 2499e0e9..2183d2e5 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -61,7 +61,8 @@ NAMESPACE_BEGIN(Grid);
   typedef typename Impl::Field Field;
 
 // hardcodes the exponential approximation in the template
-template <class S, int Nrepresentation = Nc, int Nexp = 12 > class GaugeImplTypes {
+//template <class S, int Nrepresentation = Nc, int Nexp = 12 > class GaugeImplTypes {
+template <class S, int Nrepresentation = Nc, int Nexp = 12, bool isSp2n = false > class GaugeImplTypes {
 public:
   typedef S Simd;
   typedef typename Simd::scalar_type scalar_type;
@@ -70,6 +71,7 @@ public:
   template <typename vtype> using iImplGaugeLink  = iScalar<iScalar<iMatrix<vtype, Nrepresentation> > >;
   template <typename vtype> using iImplGaugeField = iVector<iScalar<iMatrix<vtype, Nrepresentation> >, Nd>;
 
+
   typedef iImplScalar<Simd>     SiteComplex;
   typedef iImplGaugeLink<Simd>  SiteLink;
   typedef iImplGaugeField<Simd> SiteField;
@@ -117,8 +119,17 @@ public:
     //
     LinkField Pmu(P.Grid());
     Pmu = Zero();
-    for (int mu = 0; mu < Nd; mu++) {
-      SU<Nrepresentation>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
+    for (int mu = 0; mu < Nd; mu++)
+    {
+        if (isSp2n == true)
+        {
+            const int nSp = Nrepresentation/2;
+            Sp<nSp>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
+        } else
+        {
+        
+            SU<Nrepresentation>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
+        }
       RealD scale = ::sqrt(HMC_MOMENTUM_DENOMINATOR) ;
       Pmu = Pmu*scale;
       PokeIndex<LorentzIndex>(P, Pmu, mu);
@@ -135,14 +146,21 @@ public:
     autoView(P_v,P,AcceleratorRead);
     accelerator_for(ss, P.Grid()->oSites(),1,{
       for (int mu = 0; mu < Nd; mu++) {
-        U_v[ss](mu) = ProjectOnGroup(Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu));
+          if (isSp2n == true)
+          {
+              U_v[ss](mu) = ProjectOnSpGroup(Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu));
+          } else
+          {
+              U_v[ss](mu) = ProjectOnGroup(Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu));
+          }
+        
       }
     });
    //auto end = std::chrono::high_resolution_clock::now();
    // diff += end - start;
    // std::cout << "Time to exponentiate matrix " << diff.count() << " s\n";
   }
-
+    
   static inline RealD FieldSquareNorm(Field& U){
     LatticeComplex Hloc(U.Grid());
     Hloc = Zero();
@@ -154,21 +172,77 @@ public:
     return Hsum.real();
   }
 
-  static inline void Project(Field &U) {
-    ProjectSUn(U);
+  static inline void Project(Field &U)
+  {
+      if (isSp2n == true)
+      {
+          ProjectSp2n(U);
+      } else
+      {
+          ProjectSUn(U);
+      }
   }
 
-  static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U) {
-    SU<Nc>::HotConfiguration(pRNG, U);
+  static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U)
+  {
+      SU<Nc>::HotConfiguration(pRNG, U);
   }
 
   static inline void TepidConfiguration(GridParallelRNG &pRNG, Field &U) {
     SU<Nc>::TepidConfiguration(pRNG, U);
   }
 
-  static inline void ColdConfiguration(GridParallelRNG &pRNG, Field &U) {
-    SU<Nc>::ColdConfiguration(pRNG, U);
+  static inline void ColdConfiguration(GridParallelRNG &pRNG, Field &U)
+  {
+      if (isSp2n == true)
+      {
+          const int nSp = Nrepresentation/2;
+          Sp<nSp>::ColdConfiguration(pRNG, U);
+      } else
+      {
+          SU<Nc>::ColdConfiguration(pRNG, U);
+      }
   }
+    
+  //sp2n... see sp2n.h
+/*
+    static inline void generate_sp2n_momenta(Field &P, GridSerialRNG & sRNG, GridParallelRNG &pRNG)
+    {
+      
+      const int nSp = Nrepresentation/2;
+      LinkField Pmu(P.Grid());
+      Pmu = Zero();
+      for (int mu = 0; mu < Nd; mu++) {
+        
+        Sp<nSp>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
+        RealD scale = ::sqrt(HMC_MOMENTUM_DENOMINATOR) ;
+        Pmu = Pmu*scale;
+        PokeIndex<LorentzIndex>(P, Pmu, mu);
+      }
+    }
+    
+    static inline void update_sp2n_field(Field& P, Field& U, double ep){
+ 
+      autoView(U_v,U,AcceleratorWrite);
+      autoView(P_v,P,AcceleratorRead);
+      accelerator_for(ss, P.Grid()->oSites(),1,{
+        for (int mu = 0; mu < Nd; mu++) {
+          U_v[ss](mu) = ProjectOnSpGroup(Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu));
+        }
+      });
+    }
+    
+    static inline void SpProject(Field &U) {
+      ProjectSp2n(U);
+    }
+
+
+    static inline void ColdSpConfiguration(GridParallelRNG &pRNG, Field &U) {
+      const int nSp = Nrepresentation/2;
+      Sp<nSp>::ColdConfiguration(pRNG, U);
+    }
+*/
+
 };
 
 
@@ -176,10 +250,16 @@ typedef GaugeImplTypes<vComplex, Nc> GimplTypesR;
 typedef GaugeImplTypes<vComplexF, Nc> GimplTypesF;
 typedef GaugeImplTypes<vComplexD, Nc> GimplTypesD;
 
+typedef GaugeImplTypes<vComplex, Nc, 12, true> SymplGimplTypesR;
+typedef GaugeImplTypes<vComplexF, Nc, 12, true> SymplGimplTypesF;
+typedef GaugeImplTypes<vComplexD, Nc, 12, true> SymplGimplTypesD;
+
 typedef GaugeImplTypes<vComplex, SU<Nc>::AdjointDimension> GimplAdjointTypesR;
 typedef GaugeImplTypes<vComplexF, SU<Nc>::AdjointDimension> GimplAdjointTypesF;
 typedef GaugeImplTypes<vComplexD, SU<Nc>::AdjointDimension> GimplAdjointTypesD;
 
+
+
 NAMESPACE_END(Grid);
 
 #endif // GRID_GAUGE_IMPL_TYPES_H
diff --git a/Grid/qcd/action/gauge/GaugeImplementations.h b/Grid/qcd/action/gauge/GaugeImplementations.h
index 16147c77..bc056263 100644
--- a/Grid/qcd/action/gauge/GaugeImplementations.h
+++ b/Grid/qcd/action/gauge/GaugeImplementations.h
@@ -155,6 +155,11 @@ typedef ConjugateGaugeImpl<GimplTypesR> ConjugateGimplR; // Real.. whichever pre
 typedef ConjugateGaugeImpl<GimplTypesF> ConjugateGimplF; // Float
 typedef ConjugateGaugeImpl<GimplTypesD> ConjugateGimplD; // Double
 
+typedef PeriodicGaugeImpl<SymplGimplTypesR> SymplPeriodicGimplR; // Real.. whichever prec
+typedef PeriodicGaugeImpl<SymplGimplTypesF> SymplPeriodicGimplF; // Float
+typedef PeriodicGaugeImpl<SymplGimplTypesD> SymplPeriodicGimplD; // Double
+
+
 NAMESPACE_END(Grid);
 
 #endif
diff --git a/Grid/qcd/representations/Representations.h b/Grid/qcd/representations/Representations.h
index 22311be0..d408b22a 100644
--- a/Grid/qcd/representations/Representations.h
+++ b/Grid/qcd/representations/Representations.h
@@ -4,6 +4,7 @@
 #include <Grid/qcd/representations/adjoint.h>
 #include <Grid/qcd/representations/two_index.h>
 #include <Grid/qcd/representations/fundamental.h>
+#include <Grid/qcd/representations/spfundamental.h>
 #include <Grid/qcd/representations/hmc_types.h>
 
 #endif
diff --git a/Grid/qcd/representations/spfundamental.h b/Grid/qcd/representations/spfundamental.h
new file mode 100644
index 00000000..bab9a005
--- /dev/null
+++ b/Grid/qcd/representations/spfundamental.h
@@ -0,0 +1,42 @@
+
+
+#ifndef SPFUNDAMENTAL_H
+#define SPFUNDAMENTAL_H
+
+NAMESPACE_BEGIN(Grid);
+
+/*
+ * This is an helper class for the HMC
+ * Empty since HMC updates already the fundamental representation 
+ */
+
+template <int ncolour>
+class SpFundamentalRep {
+public:
+  static const int Dimension = ncolour;
+  static const int nSp = ncolour/2;
+  static const bool isFundamental = true;
+
+  // typdef to be used by the Representations class in HMC to get the
+  // types for the higher representation fields
+  typedef typename Sp<nSp>::LatticeMatrix LatticeMatrix;
+  typedef LatticeGaugeField LatticeField;
+  
+  explicit SpFundamentalRep(GridBase* grid) {} //do nothing
+  void update_representation(const LatticeGaugeField& Uin) {} // do nothing
+
+  LatticeField RtoFundamentalProject(const LatticeField& in, Real scale = 1.0) const{
+    return (scale * in);
+  }
+
+};
+
+
+    
+
+  
+typedef	 SpFundamentalRep<Nc> SpFundamentalRepresentation;
+
+NAMESPACE_END(Grid);  
+
+#endif
diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.h
index c8960383..51976146 100644
--- a/Grid/qcd/utils/Sp2n.h
+++ b/Grid/qcd/utils/Sp2n.h
@@ -6,6 +6,13 @@ NAMESPACE_BEGIN(Grid);
 
 // Sp(2N)
 // ncolour = N
+
+// need to be careful with n and 2n
+// I am defining the Sp class for Sp(2n) to be such that the template variable ncolour
+// is n inside 2n and the typedef at the end of the file should eliminate possible confusion.
+
+// the other routines, like projectOnSp2n, N will be the dimension of the actual number of colors for consistency with the sun routines
+
 template <int ncolour>
 class Sp {
 public:
@@ -22,11 +29,31 @@ public:
     using iSp2nAlgebraVector = iScalar<iScalar<iVector<vtype, AlgebraDimension> > >;
     
     typedef iSp2nMatrix<Complex> Matrix;
+    typedef iSp2nMatrix<ComplexF> MatrixF;
+    typedef iSp2nMatrix<ComplexD> MatrixD;
     
     typedef iSp2nMatrix<vComplex> vMatrix;
+    typedef iSp2nMatrix<vComplexF> vMatrixF;
+    typedef iSp2nMatrix<vComplexD> vMatrixD;
     
+    typedef iSp2nAlgebraVector<Complex> AlgebraVector;
+    typedef iSp2nAlgebraVector<ComplexF> AlgebraVectorF;
+    typedef iSp2nAlgebraVector<ComplexD> AlgebraVectorD;
+    
+    typedef iSp2nAlgebraVector<vComplex> vAlgebraVector;
+    typedef iSp2nAlgebraVector<vComplexF> vAlgebraVectorF;
+    typedef iSp2nAlgebraVector<vComplexD> vAlgebraVectorD;
     
     typedef Lattice<vMatrix> LatticeMatrix;
+    typedef Lattice<vMatrixF> LatticeMatrixF;
+    typedef Lattice<vMatrixD> LatticeMatrixD;
+    
+    typedef Lattice<vAlgebraVector> LatticeAlgebraVector;
+    typedef Lattice<vAlgebraVectorF> LatticeAlgebraVectorF;
+    typedef Lattice<vAlgebraVectorD> LatticeAlgebraVectorD;
+    
+    
+    
     // Sp(2N) has N(2N+1) = 2N^2+N generators
     //
     // normalise the generators such that
@@ -322,75 +349,113 @@ public:
       }
     }
     
+ 
     
     
+/*    template <typename GaugeField>
+    static void HotSpConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
+      typedef typename GaugeField::vector_type vector_type;
+      typedef iSp2nMatrix<vector_type> vMatrixType;
+      typedef Lattice<vMatrixType> LatticeMatrixType;
+
+      LatticeMatrixType Umu(out.Grid());
+      for (int mu = 0; mu < Nd; mu++) {
+        LieRandomize(pRNG, Umu, 1.0);   //def
+        PokeIndex<LorentzIndex>(out, Umu, mu);
+      }
+    }
+    template<typename GaugeField>
+    static void TepidSpConfiguration(GridParallelRNG &pRNG,GaugeField &out){
+      typedef typename GaugeField::vector_type vector_type;
+      typedef iSp2nMatrix<vector_type> vMatrixType;
+      typedef Lattice<vMatrixType> LatticeMatrixType;
+
+      LatticeMatrixType Umu(out.Grid());
+      for(int mu=0;mu<Nd;mu++){
+        LieRandomize(pRNG,Umu,0.01);    //def
+        PokeIndex<LorentzIndex>(out,Umu,mu);
+      }
+    } */
+    
+    template<typename GaugeField>
+    static void ColdConfiguration(GaugeField &out){
+      typedef typename GaugeField::vector_type vector_type;
+      typedef iSp2nMatrix<vector_type> vMatrixType;
+      typedef Lattice<vMatrixType> LatticeMatrixType;
+
+      LatticeMatrixType Umu(out.Grid());
+      Umu=1.0;
+      for(int mu=0;mu<Nd;mu++){
+        PokeIndex<LorentzIndex>(out,Umu,mu);
+      }
+    }
+    template<typename GaugeField>
+    static void ColdConfiguration(GridParallelRNG &pRNG,GaugeField &out){
+      ColdConfiguration(out);
+    }
+    
     
     
 }; // end of class Sp
     
     
 
+
+template<int N> //same of su
+ LatticeComplexD SpDeterminant(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
+ {
+   GridBase *grid=Umu.Grid();
+   auto lvol = grid->lSites();
+   LatticeComplexD ret(grid);
+
+   autoView(Umu_v,Umu,CpuRead);
+   autoView(ret_v,ret,CpuWrite);
+   thread_for(site,lvol,{
+     Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N,N);
+     Coordinate lcoor;
+     grid->LocalIndexToLocalCoor(site, lcoor);
+     iScalar<iScalar<iMatrix<ComplexD, N> > > Us;
+     peekLocalSite(Us, Umu_v, lcoor);
+     for(int i=0;i<N;i++){
+       for(int j=0;j<N;j++){
+     EigenU(i,j) = Us()()(i,j);
+       }}
+     ComplexD det = EigenU.determinant();
+     pokeLocalSite(det,ret_v,lcoor);
+   });
+   return ret;
+ }
+ 
+ template<int N>
+ static void ProjectSp2n(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
+ {
+   Umu      = ProjectOnSpGroup(Umu);
+   auto det = SpDeterminant(Umu); // ok ?
+
+   det = conjugate(det);
+
+   for(int i=0;i<N;i++){
+     auto element = PeekIndex<ColourIndex>(Umu,N-1,i);
+     element = element * det;
+     PokeIndex<ColourIndex>(Umu,element,Nc-1,i);
+   }
+ }
+ template<int N>
+ static void ProjectSp2n(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,Nd> > &U)
+ {
+   GridBase *grid=U.Grid();
+   for(int mu=0;mu<Nd;mu++){
+     auto Umu = PeekIndex<LorentzIndex>(U,mu);
+     Umu      = ProjectOnSpGroup(Umu);
+     ProjectSp2n(Umu);
+     PokeIndex<LorentzIndex>(U,Umu,mu);
+   }
+ }
+
+typedef Sp<1> Sp2;
 typedef Sp<2> Sp4;
 typedef Sp<3> Sp6;
 typedef Sp<4> Sp8;
 
 NAMESPACE_END(Grid);
 #endif
-
-
-    
-    
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-    
-    
-    
-/*     }
-     sigxy = lieIndex & 0x1;     // 1 if odd, 0 if even
-     su2Index = lieIndex >> 1 ;  // where to put the sigma_x(y)
-                                 //for the even(odd) lieindex, sigmax(y)
-     if (sigxy)
-         //put sigmay at su2index
-     else
-         //put sigmax    */
diff --git a/tests/core/test_sp2n_lie_gen.cc b/tests/core/test_sp2n_lie_gen.cc
index 5dbba9d3..6c3766e6 100644
--- a/tests/core/test_sp2n_lie_gen.cc
+++ b/tests/core/test_sp2n_lie_gen.cc
@@ -2,7 +2,7 @@
 
 
 #include <Grid/Grid.h>
-#include <Grid/qcd/utils/SUn.h>
+#include <Grid/qcd/utils/Sp2n.h>
 
 using namespace Grid;
 
@@ -13,6 +13,15 @@ int main(int argc, char** argv) {
   //GridCartesian* grid = SpaceTimeGrid::makeFourDimGrid(
   //latt, GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
   //GridRedBlackCartesian* rbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(grid);
+    
+    std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+    std::cout << GridLogMessage << "* Generators for Sp(2)" << std::endl;
+    std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+      
+    Sp2::printGenerators();
+    Sp2::testGenerators();
   
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;

From 4f5fe5792069c91c75ac68ff0569e5aa52787085 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Mon, 11 Oct 2021 16:28:15 +0100
Subject: [PATCH 003/129] project on sp2n

---
 Grid/lattice/Lattice_ET.h |   2 +
 Grid/tensors/Tensor_Ta.h  | 108 ++++++++++++++++++++++++++++++++++++++
 2 files changed, 110 insertions(+)

diff --git a/Grid/lattice/Lattice_ET.h b/Grid/lattice/Lattice_ET.h
index 4a8a7423..9042eb8f 100644
--- a/Grid/lattice/Lattice_ET.h
+++ b/Grid/lattice/Lattice_ET.h
@@ -346,6 +346,7 @@ GridUnopClass(UnaryTrace, trace(a));
 GridUnopClass(UnaryTranspose, transpose(a));
 GridUnopClass(UnaryTa, Ta(a));
 GridUnopClass(UnaryProjectOnGroup, ProjectOnGroup(a));
+GridUnopClass(UnaryProjectOnSpGroup, ProjectOnSpGroup(a));
 GridUnopClass(UnaryTimesI, timesI(a));
 GridUnopClass(UnaryTimesMinusI, timesMinusI(a));
 GridUnopClass(UnaryAbs, abs(a));
@@ -457,6 +458,7 @@ GRID_DEF_UNOP(trace, UnaryTrace);
 GRID_DEF_UNOP(transpose, UnaryTranspose);
 GRID_DEF_UNOP(Ta, UnaryTa);
 GRID_DEF_UNOP(ProjectOnGroup, UnaryProjectOnGroup);
+GRID_DEF_UNOP(ProjectOnSpGroup, UnaryProjectOnSpGroup);
 GRID_DEF_UNOP(timesI, UnaryTimesI);
 GRID_DEF_UNOP(timesMinusI, UnaryTimesMinusI);
 GRID_DEF_UNOP(abs, UnaryAbs);  // abs overloaded in cmath C++98; DON'T do the
diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index 90e57b2b..f53296bc 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -135,6 +135,114 @@ accelerator_inline iMatrix<vtype,N> ProjectOnGroup(const iMatrix<vtype,N> &arg)
   return ret;
 }
 
+// re-do for sp2n
+
+template<class vtype> accelerator_inline iScalar<vtype> ProjectOnSpGroup(const iScalar<vtype>&r)
+{
+  iScalar<vtype> ret;
+  ret._internal = ProjectOnSpGroup(r._internal);
+  return ret;
+}
+template<class vtype,int N> accelerator_inline iVector<vtype,N> ProjectOnSpGroup(const iVector<vtype,N>&r)
+{
+  iVector<vtype,N> ret;
+  for(int i=0;i<N;i++){
+    ret._internal[i] = ProjectOnSpGroup(r._internal[i]);
+  }
+  return ret;
+}
+
+
+// int N is 2n in Sp(2n)
+template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
+accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg)
+{
+  // need a check for the group type?
+  iMatrix<vtype,N> ret(arg);
+  vtype nrm;
+  vtype inner;
+  for(int c1=0;c1<N;c1++){
+
+       // Normalises row c1
+        zeroit(inner);
+        for(int c2=0;c2<N;c2++)
+          inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
+
+        nrm = sqrt(inner);
+        nrm = 1.0/nrm;
+        for(int c2=0;c2<N;c2++)
+          ret._internal[c1][c2]*= nrm;
+
+        // Compute row c1+N2/2: c1+N/2 = - \Omega c1*
+        for(int c2=0;c2<N/2;c2++)
+          //tmp = conjugate(ret._internal[c1][c2]);
+          //ret._internal[c1+N/2][c2+N/2] = tmp;
+            ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
+
+        for(int c2=N/2;c2<N;c2++)
+          //tmp = conjugate(ret._internal[c1][c2]);
+         // ret._internal[c1+N/2][c2-N/2] = -tmp;
+            ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
+
+        // Remove c1 from rows c1+1...N/2-1
+        for (int b=c1+1; b<N/2; ++b){
+          decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
+          zeroit(pr);
+          for(int c=0; c<N; ++c)
+            pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];
+
+          for(int c=0; c<N; ++c){
+            ret._internal[b][c] -= pr * ret._internal[c1][c];
+          }
+        }
+
+        // Remove c1+N/2 from rows c1+1...N/2-1
+        for (int b=c1+1; b<N; ++b){
+          decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
+          zeroit(pr);
+          for(int c=0; c<N; ++c)
+            pr += conjugate(ret._internal[c1+N/2][c])*ret._internal[b][c];
+
+          for(int c=0; c<N; ++c){
+            ret._internal[b][c] -= pr * ret._internal[c1+N/2][c];
+          }
+        }
+      } //end for loop over c1
+
+      // Compute the last row
+      {
+      // Normalise last row
+        int c1 = N/2-1;
+        zeroit(inner);
+        for(int c2=0;c2<N;c2++)
+        {
+          inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
+        }
+          
+        nrm = sqrt(inner);
+        nrm = 1.0/nrm;
+        for(int c2=0;c2<N;c2++)
+        {
+          ret._internal[c1][c2]*= nrm;
+        }
+      // Compute row cN-1+N2/2: cN-1+N/2 = - \Omega cN-1*
+        for(int c2=0;c2<N/2;c2++)
+        {
+          //tmp = conjugate(ret._internal[c1][c2]);
+          // ret._internal[c1+N/2][c2+N/2] = tmp;
+             ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
+        }
+        for(int c2=N/2;c2<N;c2++)
+        {
+          //tmp = conjugate(ret._internal[c1][c2]);
+          //ret._internal[c1+N/2][c2-N/2] = -tmp;
+            ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
+        }
+      }
+      // assuming the determinant is ok
+      return ret;
+  }
+
 NAMESPACE_END(Grid);
 
 #endif

From b6496b6cb50c70c0e30aa95ce2407e8beec19a9a Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Mon, 11 Oct 2021 16:32:10 +0100
Subject: [PATCH 004/129] sp fermion instantiation

---
 Grid/Makefile.am                                     |  1 +
 .../WilsonCloverFermionInstantiationSpWilsonImplD.cc |  1 +
 .../WilsonFermionInstantiationSpWilsonImplD.cc       |  1 +
 .../WilsonKernelsInstantiationSpWilsonImplD.cc       |  1 +
 .../WilsonTMFermionInstantiationSpWilsonImplD.cc     |  1 +
 .../fermion/instantiation/SpWilsonImplD/impl.h       |  1 +
 .../WilsonCloverFermionInstantiationSpWilsonImplF.cc |  1 +
 .../WilsonFermionInstantiationSpWilsonImplF.cc       |  1 +
 .../WilsonKernelsInstantiationSpWilsonImplF.cc       |  1 +
 .../WilsonTMFermionInstantiationSpWilsonImplF.cc     |  1 +
 .../fermion/instantiation/SpWilsonImplF/impl.h       |  1 +
 .../fermion/instantiation/generate_instantiations.sh |  2 ++
 Grid/qcd/hmc/GenericHMCrunner.h                      | 12 ++++++++++++
 scripts/filelist                                     |  2 ++
 14 files changed, 27 insertions(+)
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonCloverFermionInstantiationSpWilsonImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonFermionInstantiationSpWilsonImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonKernelsInstantiationSpWilsonImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonTMFermionInstantiationSpWilsonImplD.cc
 create mode 100644 Grid/qcd/action/fermion/instantiation/SpWilsonImplD/impl.h
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonCloverFermionInstantiationSpWilsonImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonFermionInstantiationSpWilsonImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonKernelsInstantiationSpWilsonImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonTMFermionInstantiationSpWilsonImplF.cc
 create mode 100644 Grid/qcd/action/fermion/instantiation/SpWilsonImplF/impl.h

diff --git a/Grid/Makefile.am b/Grid/Makefile.am
index 7c3c151b..fda92792 100644
--- a/Grid/Makefile.am
+++ b/Grid/Makefile.am
@@ -63,6 +63,7 @@ if BUILD_GPARITY
   extra_sources+=$(GP_FERMION_FILES)
 endif
 if BUILD_FERMION_REPS
+  extra_sources+=$(SP_FERMION_FILES)
   extra_sources+=$(ADJ_FERMION_FILES)
   extra_sources+=$(TWOIND_FERMION_FILES)
 endif
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonCloverFermionInstantiationSpWilsonImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonCloverFermionInstantiationSpWilsonImplD.cc
new file mode 120000
index 00000000..9cc05107
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonCloverFermionInstantiationSpWilsonImplD.cc
@@ -0,0 +1 @@
+../WilsonCloverFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonFermionInstantiationSpWilsonImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonFermionInstantiationSpWilsonImplD.cc
new file mode 120000
index 00000000..5f6ab65e
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonFermionInstantiationSpWilsonImplD.cc
@@ -0,0 +1 @@
+../WilsonFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonKernelsInstantiationSpWilsonImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonKernelsInstantiationSpWilsonImplD.cc
new file mode 120000
index 00000000..01c35e7b
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonKernelsInstantiationSpWilsonImplD.cc
@@ -0,0 +1 @@
+../WilsonKernelsInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonTMFermionInstantiationSpWilsonImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonTMFermionInstantiationSpWilsonImplD.cc
new file mode 120000
index 00000000..d5789bcf
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonTMFermionInstantiationSpWilsonImplD.cc
@@ -0,0 +1 @@
+../WilsonTMFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/impl.h b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/impl.h
new file mode 100644
index 00000000..5aa843dd
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/impl.h
@@ -0,0 +1 @@
+#define IMPLEMENTATION SpWilsonImplD
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonCloverFermionInstantiationSpWilsonImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonCloverFermionInstantiationSpWilsonImplF.cc
new file mode 120000
index 00000000..9cc05107
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonCloverFermionInstantiationSpWilsonImplF.cc
@@ -0,0 +1 @@
+../WilsonCloverFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonFermionInstantiationSpWilsonImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonFermionInstantiationSpWilsonImplF.cc
new file mode 120000
index 00000000..5f6ab65e
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonFermionInstantiationSpWilsonImplF.cc
@@ -0,0 +1 @@
+../WilsonFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonKernelsInstantiationSpWilsonImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonKernelsInstantiationSpWilsonImplF.cc
new file mode 120000
index 00000000..01c35e7b
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonKernelsInstantiationSpWilsonImplF.cc
@@ -0,0 +1 @@
+../WilsonKernelsInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonTMFermionInstantiationSpWilsonImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonTMFermionInstantiationSpWilsonImplF.cc
new file mode 120000
index 00000000..d5789bcf
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonTMFermionInstantiationSpWilsonImplF.cc
@@ -0,0 +1 @@
+../WilsonTMFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/impl.h b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/impl.h
new file mode 100644
index 00000000..761b0c82
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/impl.h
@@ -0,0 +1 @@
+#define IMPLEMENTATION SpWilsonImplF
diff --git a/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh b/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh
index d7553cdb..9c834f6e 100755
--- a/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh
+++ b/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh
@@ -9,6 +9,8 @@ STAG5_IMPL_LIST=""
 WILSON_IMPL_LIST=" \
 	   WilsonImplF \
 	   WilsonImplD \
+       SpWilsonImplF \
+       SpWilsonImplD \
 	   WilsonAdjImplF \
 	   WilsonAdjImplD \
 	   WilsonTwoIndexSymmetricImplF \
diff --git a/Grid/qcd/hmc/GenericHMCrunner.h b/Grid/qcd/hmc/GenericHMCrunner.h
index 98e8175a..16143455 100644
--- a/Grid/qcd/hmc/GenericHMCrunner.h
+++ b/Grid/qcd/hmc/GenericHMCrunner.h
@@ -204,6 +204,18 @@ template <class RepresentationsPolicy,
 using GenericHMCRunnerHirep =
 				     HMCWrapperTemplate<PeriodicGimplR, Integrator, RepresentationsPolicy>;
 
+// sp2n
+
+template <template <typename, typename, typename> class Integrator>
+using GenericSp2nHMCRunner = HMCWrapperTemplate<SymplPeriodicGimplR, Integrator>;
+
+template <class RepresentationsPolicy,
+          template <typename, typename, typename> class Integrator>
+using GenericSp2nHMCRunnerHirep =
+                     HMCWrapperTemplate<SymplPeriodicGimplR, Integrator, RepresentationsPolicy>;
+
+
+
 template <class Implementation, class RepresentationsPolicy, 
           template <typename, typename, typename> class Integrator>
 using GenericHMCRunnerTemplate = HMCWrapperTemplate<Implementation, Integrator, RepresentationsPolicy>;
diff --git a/scripts/filelist b/scripts/filelist
index c3f0cf3f..b117a87d 100755
--- a/scripts/filelist
+++ b/scripts/filelist
@@ -15,6 +15,7 @@ STAG_FERMION_FILES=`  find . -name '*.cc' -path '*/instantiation/*' -path '*/ins
 GP_FERMION_FILES=`    find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/Gparity*' `
 ADJ_FERMION_FILES=`   find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/WilsonAdj*' `
 TWOIND_FERMION_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/WilsonTwoIndex*'`
+SP_FERMION_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/SpWilsonImpl*'`
 
 HPPFILES=`find . -type f -name '*.hpp'`
 echo HFILES=$HFILES $HPPFILES > Make.inc
@@ -27,6 +28,7 @@ echo STAG_FERMION_FILES=$STAG_FERMION_FILES   >> Make.inc
 echo GP_FERMION_FILES=$GP_FERMION_FILES   >> Make.inc
 echo ADJ_FERMION_FILES=$ADJ_FERMION_FILES   >> Make.inc
 echo TWOIND_FERMION_FILES=$TWOIND_FERMION_FILES   >> Make.inc
+echo SP_FERMION_FILES=$SP_FERMION_FILES >> Make.inc
 
 # tests Make.inc
 cd $home/tests

From d4866157fe2f4a036be89dd031c44708eae9f497 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 12 Oct 2021 09:06:15 +0100
Subject: [PATCH 005/129] tests!

---
 configure.ac                     |  1 +
 tests/Makefile.am                |  2 +-
 tests/sp2n/Makefile.am           |  7 ++++
 tests/sp2n/Test_project_on_Sp.cc | 35 ++++++++++++++++++++
 tests/sp2n/Test_sp2n_lie_gen.cc  | 55 ++++++++++++++++++++++++++++++++
 5 files changed, 99 insertions(+), 1 deletion(-)
 create mode 100644 tests/sp2n/Makefile.am
 create mode 100644 tests/sp2n/Test_project_on_Sp.cc
 create mode 100644 tests/sp2n/Test_sp2n_lie_gen.cc

diff --git a/configure.ac b/configure.ac
index 406b0b74..aece85f9 100644
--- a/configure.ac
+++ b/configure.ac
@@ -815,6 +815,7 @@ AC_CONFIG_FILES(tests/lanczos/Makefile)
 AC_CONFIG_FILES(tests/smearing/Makefile)
 AC_CONFIG_FILES(tests/qdpxx/Makefile)
 AC_CONFIG_FILES(tests/testu01/Makefile)
+AC_CONFIG_FILES(tests/Sp2n/Makefile)
 AC_CONFIG_FILES(benchmarks/Makefile)
 AC_CONFIG_FILES(examples/Makefile)
 AC_OUTPUT
diff --git a/tests/Makefile.am b/tests/Makefile.am
index 7928a7fe..c6380cda 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -1,4 +1,4 @@
-SUBDIRS = . core forces hmc solver debug smearing IO lanczos
+SUBDIRS = . core forces hmc solver debug smearing IO lanczos sp2n
 
 if BUILD_CHROMA_REGRESSION
   SUBDIRS+= qdpxx
diff --git a/tests/sp2n/Makefile.am b/tests/sp2n/Makefile.am
new file mode 100644
index 00000000..0ee7421c
--- /dev/null
+++ b/tests/sp2n/Makefile.am
@@ -0,0 +1,7 @@
+.PHONY: check
+
+include Make.inc
+
+check: tests
+	./Test_project_on_Sp
+	./test_sp2n_lie_gen
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
new file mode 100644
index 00000000..61ec6d0c
--- /dev/null
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -0,0 +1,35 @@
+#include <Grid/Grid.h>
+
+using namespace Grid;
+
+int main (int argc, char **argv)
+{
+     Grid_init(&argc,&argv);
+    
+    
+    Coordinate latt_size   = GridDefaultLatt();
+    Coordinate simd_layout = GridDefaultSimd(Nd,vComplex::Nsimd());
+    Coordinate mpi_layout  = GridDefaultMpi();
+
+    GridCartesian             Grid(latt_size,simd_layout,mpi_layout);
+    GridRedBlackCartesian     RBGrid(&Grid);
+    
+    
+    LatticeGaugeField Umu(&Grid);
+    LatticeColourMatrixD U(&Grid);
+    
+    std::vector<int> pseeds({1,2,3,4,5});
+    std::vector<int> sseeds({6,7,8,9,10});
+    GridParallelRNG  pRNG(&Grid); pRNG.SeedFixedIntegers(pseeds);
+    GridSerialRNG    sRNG;       sRNG.SeedFixedIntegers(sseeds);
+    
+    SU<Nc>::HotConfiguration(pRNG,Umu);
+    U = PeekIndex<LorentzIndex>(Umu,0);
+    
+    
+    U = ProjectOnSpGroup(U);
+    
+    Grid_finalize();
+
+
+}
diff --git a/tests/sp2n/Test_sp2n_lie_gen.cc b/tests/sp2n/Test_sp2n_lie_gen.cc
new file mode 100644
index 00000000..6c3766e6
--- /dev/null
+++ b/tests/sp2n/Test_sp2n_lie_gen.cc
@@ -0,0 +1,55 @@
+
+
+
+#include <Grid/Grid.h>
+#include <Grid/qcd/utils/Sp2n.h>
+
+using namespace Grid;
+
+int main(int argc, char** argv) {
+  Grid_init(&argc, &argv);
+    
+  //std::vector<int> latt({4, 4, 4, 8});
+  //GridCartesian* grid = SpaceTimeGrid::makeFourDimGrid(
+  //latt, GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
+  //GridRedBlackCartesian* rbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(grid);
+    
+    std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+    std::cout << GridLogMessage << "* Generators for Sp(2)" << std::endl;
+    std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+      
+    Sp2::printGenerators();
+    Sp2::testGenerators();
+  
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(4)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+    
+  Sp4::printGenerators();
+  Sp4::testGenerators();
+    
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(6)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  
+  Sp6::printGenerators();
+  Sp6::testGenerators();
+    
+  std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(8)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+    
+  Sp8::printGenerators();
+  Sp8::testGenerators(); 
+    
+    
+  Grid_finalize();
+}

From 8c0fbcccaee341b135f12a14c080f3a32fe008ed Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 12 Oct 2021 12:12:16 +0100
Subject: [PATCH 006/129] fix sp2n projection

---
 Grid/tensors/Tensor_Ta.h         | 133 ++++++++++++++-----------------
 tests/sp2n/Test_project_on_Sp.cc | 122 +++++++++++++++++++++++++++-
 2 files changed, 181 insertions(+), 74 deletions(-)

diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index f53296bc..7b4bccca 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -161,88 +161,75 @@ accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg
   iMatrix<vtype,N> ret(arg);
   vtype nrm;
   vtype inner;
-  for(int c1=0;c1<N;c1++){
+  for(int c1=0;c1<N/2;c1++){
 
-       // Normalises row c1
-        zeroit(inner);
-        for(int c2=0;c2<N;c2++)
-          inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
+    // Normalises row c1
+    zeroit(inner);
+    for(int c2=0;c2<N;c2++)
+      inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
 
-        nrm = sqrt(inner);
-        nrm = 1.0/nrm;
-        for(int c2=0;c2<N;c2++)
-          ret._internal[c1][c2]*= nrm;
+    nrm = sqrt(inner);
+    nrm = 1.0/nrm;
+    for(int c2=0;c2<N;c2++)
+      ret._internal[c1][c2]*= nrm;
 
-        // Compute row c1+N2/2: c1+N/2 = - \Omega c1*
-        for(int c2=0;c2<N/2;c2++)
-          //tmp = conjugate(ret._internal[c1][c2]);
-          //ret._internal[c1+N/2][c2+N/2] = tmp;
-            ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
+    // Compute row c1+N2/2: c1+N/2 = - \Omega c1*
+    for(int c2=0;c2<N/2;c2++)
+      ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
 
-        for(int c2=N/2;c2<N;c2++)
-          //tmp = conjugate(ret._internal[c1][c2]);
-         // ret._internal[c1+N/2][c2-N/2] = -tmp;
-            ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
+    for(int c2=N/2;c2<N;c2++)
+      ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
 
-        // Remove c1 from rows c1+1...N/2-1
-        for (int b=c1+1; b<N/2; ++b){
-          decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
-          zeroit(pr);
-          for(int c=0; c<N; ++c)
-            pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];
+    // Remove c1 from rows c1+1...N/2-1
+    for (int b=c1+1; b<N/2; ++b){
+      decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
+      zeroit(pr);
+      for(int c=0; c<N; ++c)
+        pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];
 
-          for(int c=0; c<N; ++c){
-            ret._internal[b][c] -= pr * ret._internal[c1][c];
-          }
-        }
-
-        // Remove c1+N/2 from rows c1+1...N/2-1
-        for (int b=c1+1; b<N; ++b){
-          decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
-          zeroit(pr);
-          for(int c=0; c<N; ++c)
-            pr += conjugate(ret._internal[c1+N/2][c])*ret._internal[b][c];
-
-          for(int c=0; c<N; ++c){
-            ret._internal[b][c] -= pr * ret._internal[c1+N/2][c];
-          }
-        }
-      } //end for loop over c1
-
-      // Compute the last row
-      {
-      // Normalise last row
-        int c1 = N/2-1;
-        zeroit(inner);
-        for(int c2=0;c2<N;c2++)
-        {
-          inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
-        }
-          
-        nrm = sqrt(inner);
-        nrm = 1.0/nrm;
-        for(int c2=0;c2<N;c2++)
-        {
-          ret._internal[c1][c2]*= nrm;
-        }
-      // Compute row cN-1+N2/2: cN-1+N/2 = - \Omega cN-1*
-        for(int c2=0;c2<N/2;c2++)
-        {
-          //tmp = conjugate(ret._internal[c1][c2]);
-          // ret._internal[c1+N/2][c2+N/2] = tmp;
-             ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
-        }
-        for(int c2=N/2;c2<N;c2++)
-        {
-          //tmp = conjugate(ret._internal[c1][c2]);
-          //ret._internal[c1+N/2][c2-N/2] = -tmp;
-            ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
-        }
+      for(int c=0; c<N; ++c){
+        ret._internal[b][c] -= pr * ret._internal[c1][c];
       }
-      // assuming the determinant is ok
-      return ret;
+    }
+
+    // Remove c1+N/2 from rows c1+1...N/2-1
+    for (int b=c1+1; b<N; ++b){
+      decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
+      zeroit(pr);
+      for(int c=0; c<N; ++c)
+        pr += conjugate(ret._internal[c1+N/2][c])*ret._internal[b][c];
+
+      for(int c=0; c<N; ++c){
+        ret._internal[b][c] -= pr * ret._internal[c1+N/2][c];
+      }
+    }
   }
 
+  // Compute the last row
+  {
+  // Normalise last row
+    int c1 = N/2-1;
+    zeroit(inner);
+    for(int c2=0;c2<N;c2++)
+      inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
+
+    nrm = sqrt(inner);
+    nrm = 1.0/nrm;
+    for(int c2=0;c2<N;c2++)
+      ret._internal[c1][c2]*= nrm;
+
+  // Compute row cN-1+N2/2: cN-1+N/2 = - \Omega cN-1*
+    for(int c2=0;c2<N/2;c2++)
+      ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
+
+    for(int c2=N/2;c2<N;c2++)
+      ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
+  }
+  // assuming the determinant is ok
+  return ret;
+}
+
+
 NAMESPACE_END(Grid);
 
 #endif
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 61ec6d0c..d494d828 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -17,6 +17,14 @@ int main (int argc, char **argv)
     
     LatticeGaugeField Umu(&Grid);
     LatticeColourMatrixD U(&Grid);
+    LatticeColourMatrixD aux(&Grid);
+    LatticeColourMatrixD identity(&Grid);
+    
+    identity = 1.0;
+    RealD epsilon = 0.01;
+    Complex i(0., 1.);
+    RealD u = 0.;
+    double vol = Umu.Grid()->gSites();
     
     std::vector<int> pseeds({1,2,3,4,5});
     std::vector<int> sseeds({6,7,8,9,10});
@@ -24,10 +32,122 @@ int main (int argc, char **argv)
     GridSerialRNG    sRNG;       sRNG.SeedFixedIntegers(sseeds);
     
     SU<Nc>::HotConfiguration(pRNG,Umu);
-    U = PeekIndex<LorentzIndex>(Umu,0);
+    U = PeekIndex<LorentzIndex>(Umu,2);
     
+    // it is unitary
+    aux = U*adj(U) - identity;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout << GridLogMessage << "Unitary check of starting random SUn matrix " << std::endl;
+    std::cout <<GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout <<GridLogMessage << std::endl;
     
+    U = U + epsilon*identity;
+    aux = U*adj(U) - identity;
+    
+    std::cout << GridLogMessage << "Unitary matrix modified " << std::endl;
+    std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout << GridLogMessage << "Projecting on Sp2n " << std::endl;
+
     U = ProjectOnSpGroup(U);
+    aux = U*adj(U) - identity;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout << GridLogMessage << "Unitary check after Sp(2n) projection " << std::endl;
+    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+    assert( norm2(aux) < 1e-6);
+    std::cout <<GridLogMessage << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    
+    // checks on determinant
+    std::cout << GridLogMessage << "Det after Projection on Sp2n = " << norm2( Determinant(U) ) / vol << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    // checks on elements
+    // an Sp2n matrix is a block matrix of the type
+    //
+    //
+    //     U = (    W       X   )
+    //         (    -X^*    W^* )
+    //
+    // will check this
+    //
+    std::cout << GridLogMessage << "Checking that U[ i , j ] - conj U[ i+N/2, j+N/2 ] = 0 for i = 0, ... , N/2 " << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    const int nsp = Nc / 2;
+    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);
+            std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
+            assert(  amizeroo.real() < 10e-6 );
+            amizeroo *= i;
+            assert(  amizeroo.real() < 10e-6 );
+            std::cout << GridLogMessage << "ok " << std::endl;
+        }
+        
+    }
+    std::cout <<GridLogMessage << std::endl;
+    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;
+    std::cout <<GridLogMessage << std::endl;
+    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);
+            std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
+            assert(  amizeroo.real() < 10e-6 );
+            amizeroo *= i;
+            assert(  amizeroo.real() < 10e-6 );
+            std::cout << GridLogMessage << "ok " << std::endl;
+        }
+    }
+    
+    
+    // an explicit check for sp2
+    if (Nc == 2)
+    {
+        assert(Nc==2);
+        ColourMatrix A;
+        A = Zero();
+
+        Complex a(25041994., 12.);
+        Complex b(39., 0.22);
+        Complex d(10000., -2222.3333);
+    
+        A()()(0,0) = a;
+        A()()(0,1) = b;
+        A()()(1,0) = i;
+        A()()(1,1) = d;
+        std::cout <<GridLogMessage << std::endl;
+        std::cout <<GridLogMessage << std::endl;
+        std::cout << GridLogMessage << "An explicit check for Sp2" << std::endl;
+        std::cout <<GridLogMessage << std::endl;
+        std::cout << GridLogMessage << "Building a non unitary matrix by hand with funny entries " << std::endl;
+        std::cout << GridLogMessage << "A = " << A << std::endl;
+        std::cout << GridLogMessage << "Projecting on Sp2 " << std::endl;
+        A = ProjectOnSpGroup(A);
+        std::cout << GridLogMessage << "now A = " << A << std::endl;
+        std::cout << GridLogMessage << "A(0,0) - conjA(1,1) = " << A()()(0,0) - adj ( A()()(1,1) )<< std::endl;
+        std::cout << GridLogMessage << "A(0,1) + conjA(1,0) = " << A()()(0,1) + adj ( A()()(1,0) )<< std::endl;
+    }
+    
+    
+    
+    
+    
+    
     
     Grid_finalize();
 

From ed03bfd5555e490753acd9e20b356e8cf20898cb Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 12 Oct 2021 12:16:47 +0100
Subject: [PATCH 007/129] first hmc

---
 .../Test_hmc_Sp_WilsonFundFermionGauge.cc     | 78 +++++++++++++++++++
 1 file changed, 78 insertions(+)
 create mode 100644 tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc

diff --git a/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
new file mode 100644
index 00000000..d845c98f
--- /dev/null
+++ b/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
@@ -0,0 +1,78 @@
+#include <Grid/Grid.h>
+
+int main(int argc, char **argv) {
+  using namespace Grid;
+   
+  typedef Representations< SpFundamentalRepresentation > TheRepresentations;
+
+  Grid_init(&argc, &argv);
+    
+  typedef GenericSp2nHMCRunnerHirep<TheRepresentations, MinimumNorm2> HMCWrapper; // ok
+  typedef SpWilsonImplR FermionImplPolicy;                                    // ok
+  typedef SpWilsonFermionR FermionAction;                                     // ok
+  typedef typename FermionAction::FermionField FermionField;                  // ok?
+ 
+  //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+   
+  HMCWrapper TheHMC;
+    
+  TheHMC.Resources.AddFourDimGrid("gauge");
+    
+  // Checkpointer definition
+  CheckpointerParameters CPparams;
+  CPparams.config_prefix = "ckpoint_lat";
+  CPparams.rng_prefix = "ckpoint_rng";
+  CPparams.saveInterval = 5;
+  CPparams.format = "IEEE64BIG";
+    
+  TheHMC.Resources.LoadNerscCheckpointer(CPparams);
+
+  RNGModuleParameters RNGpar;
+  RNGpar.serial_seeds = "1 2 3 4 5";
+  RNGpar.parallel_seeds = "6 7 8 9 10";
+  TheHMC.Resources.SetRNGSeeds(RNGpar);
+
+  // Construct observables
+  typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
+  TheHMC.Resources.AddObservable<PlaqObs>();
+    
+  RealD beta = 2.25 ;
+    
+  SymplWilsonGaugeActionR Waction(beta);
+    
+  auto GridPtr = TheHMC.Resources.GetCartesian();
+  auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
+    
+    SpFundamentalRepresentation::LatticeField U(GridPtr);
+    //LatticeGaugeField U(GridPtr);
+    
+  RealD mass = -0.95;
+
+  FermionAction FermOp(U, *GridPtr, *GridRBPtr, mass);
+    
+ 
+  ConjugateGradient<FermionField> CG(1.0e-8, 2000, false);
+  
+  TwoFlavourPseudoFermionAction<FermionImplPolicy> Nf2(FermOp, CG, CG);
+    
+  Nf2.is_smeared = false;
+  
+    ActionLevel<HMCWrapper::Field, TheRepresentations > Level1(1);
+    Level1.push_back(&Nf2);
+    
+    ActionLevel<HMCWrapper::Field, TheRepresentations > Level2(4);
+    Level2.push_back(&Waction);
+    
+    TheHMC.TheAction.push_back(Level1);
+    TheHMC.TheAction.push_back(Level2);
+    
+    TheHMC.Parameters.MD.MDsteps = 20;
+    TheHMC.Parameters.MD.trajL   = 1.0;
+    
+    TheHMC.ReadCommandLine(argc, argv);
+    TheHMC.Run();
+    
+    
+  Grid_finalize();
+}
+

From 470d4dcc6db9fa41faceac54908bcd60a08bfd8a Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 12 Oct 2021 15:47:56 +0100
Subject: [PATCH 008/129] sp2n as config option

---
 configure.ac | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

diff --git a/configure.ac b/configure.ac
index aece85f9..b60c9148 100644
--- a/configure.ac
+++ b/configure.ac
@@ -128,6 +128,23 @@ case ${ac_LAPACK} in
         AC_DEFINE([USE_LAPACK],[1],[use LAPACK]);;
 esac
 
+
+############### Symplectic group
+AC_ARG_ENABLE([symplectic],
+    [AC_HELP_STRING([--enable-symplectic=yes|no], [enable gauge group Sp2n])],
+    [ac_ENABLE_SP=${enable_symplectic}], [ac_ENABLE_SP=no])
+
+AM_CONDITIONAL(BUILD_SP, [ test "${ac_ENABLE_SP}X" == "yesX" ])
+
+case ${ac_ENABLE_SP} in
+   yes)
+        AC_DEFINE([Sp2n_config],[1],[gauge group Sp2n], [have_sp2n=true]);;
+   no)
+        AC_DEFINE([Sp2n_config],[0],[gauge group SUn], [have_sp2n=false]);;
+    *)
+        AC_MSG_ERROR(["--enable-symplectic is either yes or no"]);;
+esac
+
 ############### fermions
 AC_ARG_ENABLE([fermion-reps],
      [AC_HELP_STRING([--enable-fermion-reps=yes|no], [enable extra fermion representation support])],
@@ -770,6 +787,7 @@ os (target)                 : $target_os
 compiler vendor             : ${ax_cv_cxx_compiler_vendor}
 compiler version            : ${ax_cv_gxx_version}
 ----- BUILD OPTIONS -----------------------------------
+gauge group                 : `if test "${ac_ENABLE_SP}x" == "yesx"; then echo Sp2n; else echo SUn; fi`
 Nc                          : ${ac_Nc}
 SIMD                        : ${ac_SIMD}${SIMD_GEN_WIDTH_MSG}
 Threading                   : ${ac_openmp}
@@ -787,6 +805,7 @@ FFTW                        : `if test "x$have_fftw" = xtrue; then echo yes; els
 LIME (ILDG support)         : `if test "x$have_lime" = xtrue; then echo yes; else echo no; fi`
 HDF5                        : `if test "x$have_hdf5" = xtrue; then echo yes; else echo no; fi`
 build DOXYGEN documentation : `if test "$DX_FLAG_doc" = '1'; then echo yes; else echo no; fi`
+Sp2n                        : ${ac_ENABLE_SP}
 ----- BUILD FLAGS -------------------------------------
 CXXFLAGS:
 `echo ${AM_CXXFLAGS} ${CXXFLAGS} | tr ' ' '\n' | sed 's/^-/    -/g'`

From 19eb51cf4185909c2c002590c3e59e25efa11dcb Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 5 Oct 2021 15:51:22 +0100
Subject: [PATCH 009/129] sp2n generators

---
 Grid/qcd/utils/Sp2n.h           | 396 ++++++++++++++++++++++++++++++++
 Grid/qcd/utils/Utils.h          |   1 +
 tests/core/test_sp2n_lie_gen.cc |  46 ++++
 3 files changed, 443 insertions(+)
 create mode 100644 Grid/qcd/utils/Sp2n.h
 create mode 100644 tests/core/test_sp2n_lie_gen.cc

diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.h
new file mode 100644
index 00000000..c8960383
--- /dev/null
+++ b/Grid/qcd/utils/Sp2n.h
@@ -0,0 +1,396 @@
+
+#ifndef QCD_UTIL_Sp2n_H
+#define QCD_UTIL_Sp2n_H
+
+NAMESPACE_BEGIN(Grid);
+
+// Sp(2N)
+// ncolour = N
+template <int ncolour>
+class Sp {
+public:
+    static const int Dimension = ncolour*2;
+    static const int AlgebraDimension = ncolour*(2*ncolour +1);
+    static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
+    
+    
+    template <typename vtype>
+    using iSp2nMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
+    template <typename vtype>
+    using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
+    template <typename vtype>
+    using iSp2nAlgebraVector = iScalar<iScalar<iVector<vtype, AlgebraDimension> > >;
+    
+    typedef iSp2nMatrix<Complex> Matrix;
+    
+    typedef iSp2nMatrix<vComplex> vMatrix;
+    
+    
+    typedef Lattice<vMatrix> LatticeMatrix;
+    // Sp(2N) has N(2N+1) = 2N^2+N generators
+    //
+    // normalise the generators such that
+    // Trace ( Ta Tb) = 1/2 delta_ab
+    //
+    // N generators in the cartan, 2N^2 off
+    // off diagonal:
+    //     there are 6 types named a,b,c,d and w,z
+    //     abcd are N(N-1)/2 each while wz are N each
+    
+    
+    
+    
+    template <class cplx>
+    static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
+        // map lie index into type of generators: diagonal, abcd type, wz type
+
+        int diagIndex;
+        int aIndex, bIndex, cIndex, dIndex;
+        int wIndex, zIndex; // a,b,c,d are N(N-1)/2 and w,z are N
+        int mod = ncolour * (ncolour-1) * 0.5;
+        int offdiag = 2*ncolour*ncolour; // number of generators not in the cartan subalgebra
+        int wmod = 4*mod;
+        int zmod = wmod+ncolour;
+        if (lieIndex >= offdiag) {
+            diagIndex = lieIndex - offdiag; // 0, ... ,N-1
+            //std::cout << GridLogMessage << "diag type " << std::endl;
+            generatorDiagtype(diagIndex, ta);
+            return;
+        }
+        if ( (lieIndex >= wmod) && (lieIndex < zmod) ) {
+            //std::cout << GridLogMessage << "w type " << std::endl;
+            wIndex = lieIndex- wmod;    // 0, ... ,N-1
+            generatorWtype(wIndex,ta);
+            return;
+        }
+        if ( (lieIndex >= zmod) && (lieIndex < offdiag) ) {
+            //std::cout << GridLogMessage << "z type " << std::endl;
+            //std::cout << GridLogMessage << "lie index " << lieIndex << std::endl;
+            //std::cout << GridLogMessage << "z mod " << zmod << std::endl;
+            zIndex = lieIndex - zmod;   // 0, ... ,N-1
+            generatorZtype(zIndex,ta);
+            return;
+        }
+        if (lieIndex < mod) { // atype 0, ... , N(N-1)/2=mod
+            //std::cout << GridLogMessage << "a type " << std::endl;
+            aIndex = lieIndex;
+            //std::cout << GridLogMessage << "a indx " << aIndex << std::endl;
+            generatorAtype(aIndex, ta);
+            return;
+        }
+        if ( (lieIndex >= mod) && lieIndex < 2*mod) { // btype mod, ... , 2mod-1
+            //std::cout << GridLogMessage << "b type " << std::endl;
+            bIndex = lieIndex - mod;
+            generatorBtype(bIndex, ta);
+            return;
+        }
+        if ( (lieIndex >= 2*mod) && lieIndex < 3*mod) { // ctype 2mod, ... , 3mod-1
+            //std::cout << GridLogMessage << "c type " << std::endl;
+            cIndex = lieIndex - 2*mod;
+            generatorCtype(cIndex, ta);
+            return;
+        }
+        if ( (lieIndex >= 3*mod) && lieIndex < wmod) { // ctype 3mod, ... , 4mod-1 = wmod-1
+             //std::cout << GridLogMessage << "d type " << std::endl;
+             dIndex = lieIndex - 3*mod;
+             generatorDtype(dIndex, ta);
+            return;
+         }
+            
+    } //end of generator
+    
+    template <class cplx>
+    static void generatorDiagtype(int diagIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan subalgebra
+        
+        ta = Zero();
+        RealD nrm = 1.0 / 2;
+
+        ta()()(diagIndex,diagIndex) = nrm;
+        ta()()(diagIndex+ncolour,diagIndex+ncolour) = -nrm;
+    }
+    
+    template <class cplx>
+    static void generatorAtype(int aIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,j) = ta(j,i) = -ta(i+N,j+N) = -ta(j+N,i+N) = 1 / 2 sqrt(2)
+        // with i<j and i=0,...,N-2
+        // follows that j=i+1, ... , N
+        int i1, i2;
+        ta = Zero();
+        RealD nrm = 1 / (2 * std::sqrt(2) );
+        
+        su2SubGroupIndex(i1, i2, aIndex);
+        ta()()(i1,i2) = 1;
+        ta()()(i2,i1) = 1;
+        ta()()(i1+ncolour,i2+ncolour) = -1;
+        ta()()(i2+ncolour,i1+ncolour) = -1;
+
+        ta = ta * nrm;
+    }
+    
+    template <class cplx>
+    static void generatorBtype(int bIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,j) = -ta(j,i) = ta(i+N,j+N) = -ta(j+N,i+N) = i / 1/ 2 sqrt(2)
+        // with i<j and i=0,...,N-2
+        // follows that j=i+1, ... , N-1
+        
+        int i1, i2;
+        ta = Zero();
+        cplx i(0.0, 1.0);
+        RealD nrm = 1 / (2 * std::sqrt(2));
+        su2SubGroupIndex(i1, i2, bIndex);
+        
+
+        ta()()(i1,i2) = i;
+        ta()()(i2,i1) = -i;
+        ta()()(i1+ncolour,i2+ncolour) = i;
+        ta()()(i2+ncolour,i1+ncolour) = -i;
+
+        ta = ta * nrm;
+    }
+    
+    template <class cplx>
+    static void generatorCtype(int cIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
+        
+        
+        int i1, i2;
+        ta = Zero();
+        RealD nrm = 1 / (2 * std::sqrt(2) );
+        su2SubGroupIndex(i1, i2, cIndex);
+        
+        ta()()(i1,i2+ncolour) = 1;
+        ta()()(i2,i1+ncolour) = 1;
+        ta()()(i1+ncolour,i2) = 1;
+        ta()()(i2+ncolour,i1) = 1;
+
+        ta = ta * nrm;
+    }
+    
+    template <class cplx>
+    static void generatorDtype(int dIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i /  2 sqrt(2)
+        
+        int i1, i2;
+        ta = Zero();
+        cplx i(0.0, 1.0);
+        RealD nrm = 1 / (2 * std::sqrt(2)  );
+        su2SubGroupIndex(i1, i2, dIndex);
+
+        ta()()(i1,i2+ncolour) = i;
+        ta()()(i2,i1+ncolour) = i;
+        ta()()(i1+ncolour,i2) = -i;
+        ta()()(i2+ncolour,i1) = -i;
+
+        ta = ta * nrm;
+    }
+    
+    template <class cplx>
+     static void generatorWtype(int wIndex, iSp2nMatrix<cplx> &ta) {
+         
+         // ta(i,i+N) =  ta(i+N,i) = 1/2
+         
+         ta = Zero();
+         RealD nrm = 1.0 / 2; //check
+
+         ta()()(wIndex,wIndex+ncolour) = 1;
+         ta()()(wIndex+ncolour,wIndex) = 1;
+         
+         ta = ta * nrm;
+     }
+    
+    template <class cplx>
+     static void generatorZtype(int zIndex, iSp2nMatrix<cplx> &ta) {
+         
+         // ta(i,i+N) = - ta(i+N,i) = i/2
+         
+         ta = Zero();
+         RealD nrm = 1.0 / 2; //check
+         cplx i(0.0, 1.0);
+         ta()()(zIndex,zIndex+ncolour) = i;
+         ta()()(zIndex+ncolour,zIndex) = -i;
+         
+         ta = ta * nrm;
+     }
+    
+    
+    ////////////////////////////////////////////////////////////////////////
+    // Map a su2 subgroup number to the pair of rows that are non zero
+    ////////////////////////////////////////////////////////////////////////
+    static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
+      assert((su2_index >= 0) && (su2_index < (ncolour * (ncolour - 1)) / 2));
+
+      int spare = su2_index;
+      for (i1 = 0; spare >= (ncolour - 1 - i1); i1++) {
+        spare = spare - (ncolour - 1 - i1);  // remove the Nc-1-i1 terms
+      }
+      i2 = i1 + 1 + spare;
+    }
+    
+    
+    
+    
+    
+    static void printGenerators(void) {
+        for (int gen = 0; gen < AlgebraDimension; gen++) {
+            Matrix ta;
+            generator(gen, ta);
+            std::cout << GridLogMessage << "Nc (2n) = " << 2*ncolour << std::endl;
+            std::cout << GridLogMessage << " t_" << gen << std::endl;
+            std::cout << GridLogMessage << ta << std::endl;
+        }
+    }
+    
+    
+    
+    static void testGenerators(void) {
+        Matrix ta;
+        Matrix tb;
+        std::cout << GridLogMessage << "Fundamental - Checking trace ta tb is 0.5 delta_ab " << std::endl;
+        for (int a = 0; a < AlgebraDimension; a++) {
+            for (int b = 0; b < AlgebraDimension; b++) {
+                generator(a,ta);
+                generator(b,tb);
+                Complex tr = TensorRemove(trace( ta * tb) );
+                std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
+                << std::endl;
+                if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
+                if (a != b) assert(abs(tr) < 1.0e-6);
+
+            }
+        }
+        std::cout << GridLogMessage << std::endl;
+        std::cout << GridLogMessage << "Fundamental - Checking if hermitian" << std::endl;
+        for (int a = 0; a < AlgebraDimension; a++) {
+            generator(a,ta);
+            std::cout << GridLogMessage << a << std::endl;
+            assert(norm2(ta - adj(ta)) < 1.0e-6);
+        }
+        std::cout << GridLogMessage << std::endl;
+        std::cout << GridLogMessage << "Fundamental - Checking if traceless" << std::endl;
+        for (int a = 0; a < AlgebraDimension; a++) {
+          generator(a, ta);
+          Complex tr = TensorRemove(trace(ta));
+          std::cout << GridLogMessage << a << std::endl;
+          assert(abs(tr) < 1.0e-6);
+        }
+        
+    }
+    
+    
+    static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG, //same as sun
+                                                    LatticeMatrix &out,
+                                                    Real scale = 1.0) {
+      GridBase *grid = out.Grid();
+      LatticeReal ca(grid);
+      LatticeMatrix la(grid);
+      Complex ci(0.0, scale);
+      Matrix ta;
+
+      out = Zero();
+      for (int a = 0; a < AlgebraDimension; a++) {
+        gaussian(pRNG, ca);
+        generator(a, ta);
+        la = toComplex(ca) * ta;
+        out += la;
+      }
+      out *= ci;
+    }
+    
+    
+    
+    template <typename LatticeMatrixType>
+    static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) { // same as sun
+      typedef typename LatticeMatrixType::scalar_type ComplexType;
+
+      LatticeMatrixType xn(x.Grid());
+      RealD nfac = 1.0;
+
+      xn = x;
+      ex = xn + ComplexType(1.0);  // 1+x
+
+      // Do a 12th order exponentiation
+      for (int i = 2; i <= 12; ++i) {
+        nfac = nfac / RealD(i);  // 1/2, 1/2.3 ...
+        xn = xn * x;             // x2, x3,x4....
+        ex = ex + xn * nfac;     // x2/2!, x3/3!....
+      }
+    }
+    
+    
+    
+    
+    
+}; // end of class Sp
+    
+    
+
+typedef Sp<2> Sp4;
+typedef Sp<3> Sp6;
+typedef Sp<4> Sp8;
+
+NAMESPACE_END(Grid);
+#endif
+
+
+    
+    
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+    
+    
+    
+/*     }
+     sigxy = lieIndex & 0x1;     // 1 if odd, 0 if even
+     su2Index = lieIndex >> 1 ;  // where to put the sigma_x(y)
+                                 //for the even(odd) lieindex, sigmax(y)
+     if (sigxy)
+         //put sigmay at su2index
+     else
+         //put sigmax    */
diff --git a/Grid/qcd/utils/Utils.h b/Grid/qcd/utils/Utils.h
index 8ce3df37..35594656 100644
--- a/Grid/qcd/utils/Utils.h
+++ b/Grid/qcd/utils/Utils.h
@@ -9,6 +9,7 @@
 
 // Include representations
 #include <Grid/qcd/utils/SUn.h>
+#include <Grid/qcd/utils/Sp2n.h>
 #include <Grid/qcd/utils/SUnAdjoint.h>
 #include <Grid/qcd/utils/SUnTwoIndex.h>
 
diff --git a/tests/core/test_sp2n_lie_gen.cc b/tests/core/test_sp2n_lie_gen.cc
new file mode 100644
index 00000000..5dbba9d3
--- /dev/null
+++ b/tests/core/test_sp2n_lie_gen.cc
@@ -0,0 +1,46 @@
+
+
+
+#include <Grid/Grid.h>
+#include <Grid/qcd/utils/SUn.h>
+
+using namespace Grid;
+
+int main(int argc, char** argv) {
+  Grid_init(&argc, &argv);
+    
+  //std::vector<int> latt({4, 4, 4, 8});
+  //GridCartesian* grid = SpaceTimeGrid::makeFourDimGrid(
+  //latt, GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
+  //GridRedBlackCartesian* rbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(grid);
+  
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(4)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+    
+  Sp4::printGenerators();
+  Sp4::testGenerators();
+    
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(6)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  
+  Sp6::printGenerators();
+  Sp6::testGenerators();
+    
+  std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(8)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+    
+  Sp8::printGenerators();
+  Sp8::testGenerators(); 
+    
+    
+  Grid_finalize();
+}

From 7ff3e5eed44a4ccdd79a2b2be15a92917ed3c231 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Mon, 11 Oct 2021 16:21:25 +0100
Subject: [PATCH 010/129] gauge and fermion implementation for sp2n

---
 Grid/qcd/action/fermion/Fermion.h            |   5 +
 Grid/qcd/action/fermion/WilsonFermion.h      |   2 +
 Grid/qcd/action/fermion/WilsonImpl.h         |  10 +
 Grid/qcd/action/gauge/Gauge.h                |   3 +
 Grid/qcd/action/gauge/GaugeImplTypes.h       |  75 ++++++--
 Grid/qcd/action/gauge/GaugeImplementations.h |   5 +
 Grid/qcd/representations/Representations.h   |   1 +
 Grid/qcd/representations/spfundamental.h     |  42 +++++
 Grid/qcd/utils/Sp2n.h                        | 181 +++++++++++++------
 tests/core/test_sp2n_lie_gen.cc              |  11 +-
 10 files changed, 262 insertions(+), 73 deletions(-)
 create mode 100644 Grid/qcd/representations/spfundamental.h

diff --git a/Grid/qcd/action/fermion/Fermion.h b/Grid/qcd/action/fermion/Fermion.h
index 59fc17d5..b988b306 100644
--- a/Grid/qcd/action/fermion/Fermion.h
+++ b/Grid/qcd/action/fermion/Fermion.h
@@ -115,6 +115,11 @@ typedef WilsonFermion<WilsonImplR> WilsonFermionR;
 typedef WilsonFermion<WilsonImplF> WilsonFermionF;
 typedef WilsonFermion<WilsonImplD> WilsonFermionD;
 
+
+typedef WilsonFermion<SpWilsonImplR> SpWilsonFermionR;
+typedef WilsonFermion<SpWilsonImplF> SpWilsonFermionF;
+typedef WilsonFermion<SpWilsonImplD> SpWilsonFermionD;
+
 //typedef WilsonFermion<WilsonImplRL> WilsonFermionRL;
 //typedef WilsonFermion<WilsonImplFH> WilsonFermionFH;
 //typedef WilsonFermion<WilsonImplDF> WilsonFermionDF;
diff --git a/Grid/qcd/action/fermion/WilsonFermion.h b/Grid/qcd/action/fermion/WilsonFermion.h
index bf8926d0..4a2d1ddd 100644
--- a/Grid/qcd/action/fermion/WilsonFermion.h
+++ b/Grid/qcd/action/fermion/WilsonFermion.h
@@ -208,5 +208,7 @@ public:
 
 typedef WilsonFermion<WilsonImplF> WilsonFermionF;
 typedef WilsonFermion<WilsonImplD> WilsonFermionD;
+//typedef WilsonFermion<SpWilsonImplF> SpWilsonFermionF;
+//typedef WilsonFermion<SpWilsonImplD> SpWilsonFermionD;
 
 NAMESPACE_END(Grid);
diff --git a/Grid/qcd/action/fermion/WilsonImpl.h b/Grid/qcd/action/fermion/WilsonImpl.h
index 2685796d..01545d3b 100644
--- a/Grid/qcd/action/fermion/WilsonImpl.h
+++ b/Grid/qcd/action/fermion/WilsonImpl.h
@@ -267,6 +267,16 @@ typedef WilsonImpl<vComplex,  TwoIndexAntiSymmetricRepresentation, CoeffReal > W
 typedef WilsonImpl<vComplexF, TwoIndexAntiSymmetricRepresentation, CoeffReal > WilsonTwoIndexAntiSymmetricImplF;  // Float
 typedef WilsonImpl<vComplexD, TwoIndexAntiSymmetricRepresentation, CoeffReal > WilsonTwoIndexAntiSymmetricImplD;  // Double
 
+//sp 2n
+
+typedef WilsonImpl<vComplex,  SpFundamentalRepresentation, CoeffReal > SpWilsonImplR;  // Real.. whichever prec
+typedef WilsonImpl<vComplexF, SpFundamentalRepresentation, CoeffReal > SpWilsonImplF;  // Float
+typedef WilsonImpl<vComplexD, SpFundamentalRepresentation, CoeffReal > SpWilsonImplD;  // Double
+
+//typedef WilsonImpl<vComplex,  SpFundamentalRepresentation, CoeffComplex > SpZWilsonImplR; // Real.. whichever prec
+//typedef WilsonImpl<vComplexF, SpFundamentalRepresentation, CoeffComplex > SpZWilsonImplF; // Float
+//typedef WilsonImpl<vComplexD, SpFundamentalRepresentation, CoeffComplex > SpZWilsonImplD; // Double
+
 
 NAMESPACE_END(Grid);
 
diff --git a/Grid/qcd/action/gauge/Gauge.h b/Grid/qcd/action/gauge/Gauge.h
index b3b34eba..535f0845 100644
--- a/Grid/qcd/action/gauge/Gauge.h
+++ b/Grid/qcd/action/gauge/Gauge.h
@@ -39,6 +39,9 @@ NAMESPACE_BEGIN(Grid);
 typedef WilsonGaugeAction<PeriodicGimplR>          WilsonGaugeActionR;
 typedef WilsonGaugeAction<PeriodicGimplF>          WilsonGaugeActionF;
 typedef WilsonGaugeAction<PeriodicGimplD>          WilsonGaugeActionD;
+typedef WilsonGaugeAction<SymplPeriodicGimplR>     SymplWilsonGaugeActionR;
+typedef WilsonGaugeAction<SymplPeriodicGimplF>     SymplWilsonGaugeActionF;
+typedef WilsonGaugeAction<SymplPeriodicGimplD>     SymplWilsonGaugeActionD;
 typedef PlaqPlusRectangleAction<PeriodicGimplR>    PlaqPlusRectangleActionR;
 typedef PlaqPlusRectangleAction<PeriodicGimplF>    PlaqPlusRectangleActionF;
 typedef PlaqPlusRectangleAction<PeriodicGimplD>    PlaqPlusRectangleActionD;
diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index 5c9405ab..64e32a7e 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -61,7 +61,8 @@ NAMESPACE_BEGIN(Grid);
   typedef typename Impl::Field Field;
 
 // hardcodes the exponential approximation in the template
-template <class S, int Nrepresentation = Nc, int Nexp = 12 > class GaugeImplTypes {
+//template <class S, int Nrepresentation = Nc, int Nexp = 12 > class GaugeImplTypes {
+template <class S, int Nrepresentation = Nc, int Nexp = 12, bool isSp2n = false > class GaugeImplTypes {
 public:
   typedef S Simd;
   typedef typename Simd::scalar_type scalar_type;
@@ -70,6 +71,7 @@ public:
   template <typename vtype> using iImplGaugeLink  = iScalar<iScalar<iMatrix<vtype, Nrepresentation> > >;
   template <typename vtype> using iImplGaugeField = iVector<iScalar<iMatrix<vtype, Nrepresentation> >, Nd>;
 
+
   typedef iImplScalar<Simd>     SiteComplex;
   typedef iImplGaugeLink<Simd>  SiteLink;
   typedef iImplGaugeField<Simd> SiteField;
@@ -119,8 +121,19 @@ public:
     //
     LinkField Pmu(P.Grid());
     Pmu = Zero();
-    for (int mu = 0; mu < Nd; mu++) {
-      Group::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
+
+    for (int mu = 0; mu < Nd; mu++)
+    {
+        if (isSp2n == true)
+        {
+            const int nSp = Nrepresentation/2;
+            Sp<nSp>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
+        } else
+        {
+        
+            Group::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
+        }
+
       RealD scale = ::sqrt(HMC_MOMENTUM_DENOMINATOR) ;
       Pmu = Pmu*scale;
       PokeIndex<LorentzIndex>(P, Pmu, mu);
@@ -137,14 +150,21 @@ public:
     autoView(P_v,P,AcceleratorRead);
     accelerator_for(ss, P.Grid()->oSites(),1,{
       for (int mu = 0; mu < Nd; mu++) {
-        U_v[ss](mu) = ProjectOnGroup(Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu));
+          if (isSp2n == true)
+          {
+              U_v[ss](mu) = ProjectOnSpGroup(Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu));
+          } else
+          {
+              U_v[ss](mu) = ProjectOnGroup(Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu));
+          }
+        
       }
     });
    //auto end = std::chrono::high_resolution_clock::now();
    // diff += end - start;
    // std::cout << "Time to exponentiate matrix " << diff.count() << " s\n";
   }
-
+    
   static inline RealD FieldSquareNorm(Field& U){
     LatticeComplex Hloc(U.Grid());
     Hloc = Zero();
@@ -156,21 +176,42 @@ public:
     return Hsum.real();
   }
 
-  static inline void Project(Field &U) {
-    ProjectSUn(U);
+  static inline void Project(Field &U)
+  {
+      if (isSp2n == true)
+      {
+          ProjectSp2n(U);
+      } else
+      {
+          ProjectSUn(U);
+      }
   }
 
-  static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U) {
-    Group::HotConfiguration(pRNG, U);
+
+
+  static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U)
+  {
+      Group::HotConfiguration(pRNG, U);
   }
 
   static inline void TepidConfiguration(GridParallelRNG &pRNG, Field &U) {
     Group::TepidConfiguration(pRNG, U);
   }
 
-  static inline void ColdConfiguration(GridParallelRNG &pRNG, Field &U) {
-    Group::ColdConfiguration(pRNG, U);
+
+  static inline void ColdConfiguration(GridParallelRNG &pRNG, Field &U)
+  {
+      if (isSp2n == true)
+      {
+          const int nSp = Nrepresentation/2;
+          Sp<nSp>::ColdConfiguration(pRNG, U);
+      } else
+      {
+          Group::ColdConfiguration(pRNG, U);
+      }
+
   }
+
 };
 
 
@@ -178,9 +219,15 @@ typedef GaugeImplTypes<vComplex, Nc> GimplTypesR;
 typedef GaugeImplTypes<vComplexF, Nc> GimplTypesF;
 typedef GaugeImplTypes<vComplexD, Nc> GimplTypesD;
 
-typedef GaugeImplTypes<vComplex, SU<Nc>::AdjointDimension> GimplAdjointTypesR;
-typedef GaugeImplTypes<vComplexF, SU<Nc>::AdjointDimension> GimplAdjointTypesF;
-typedef GaugeImplTypes<vComplexD, SU<Nc>::AdjointDimension> GimplAdjointTypesD;
+typedef GaugeImplTypes<vComplex, Nc, 12, true> SymplGimplTypesR;
+typedef GaugeImplTypes<vComplexF, Nc, 12, true> SymplGimplTypesF;
+typedef GaugeImplTypes<vComplexD, Nc, 12, true> SymplGimplTypesD;
+
+typedef GaugeImplTypes<vComplex, Group::AdjointDimension> GimplAdjointTypesR;
+typedef GaugeImplTypes<vComplexF, Group::AdjointDimension> GimplAdjointTypesF;
+typedef GaugeImplTypes<vComplexD, Group::AdjointDimension> GimplAdjointTypesD;
+
+
 
 NAMESPACE_END(Grid);
 
diff --git a/Grid/qcd/action/gauge/GaugeImplementations.h b/Grid/qcd/action/gauge/GaugeImplementations.h
index 16147c77..bc056263 100644
--- a/Grid/qcd/action/gauge/GaugeImplementations.h
+++ b/Grid/qcd/action/gauge/GaugeImplementations.h
@@ -155,6 +155,11 @@ typedef ConjugateGaugeImpl<GimplTypesR> ConjugateGimplR; // Real.. whichever pre
 typedef ConjugateGaugeImpl<GimplTypesF> ConjugateGimplF; // Float
 typedef ConjugateGaugeImpl<GimplTypesD> ConjugateGimplD; // Double
 
+typedef PeriodicGaugeImpl<SymplGimplTypesR> SymplPeriodicGimplR; // Real.. whichever prec
+typedef PeriodicGaugeImpl<SymplGimplTypesF> SymplPeriodicGimplF; // Float
+typedef PeriodicGaugeImpl<SymplGimplTypesD> SymplPeriodicGimplD; // Double
+
+
 NAMESPACE_END(Grid);
 
 #endif
diff --git a/Grid/qcd/representations/Representations.h b/Grid/qcd/representations/Representations.h
index 22311be0..d408b22a 100644
--- a/Grid/qcd/representations/Representations.h
+++ b/Grid/qcd/representations/Representations.h
@@ -4,6 +4,7 @@
 #include <Grid/qcd/representations/adjoint.h>
 #include <Grid/qcd/representations/two_index.h>
 #include <Grid/qcd/representations/fundamental.h>
+#include <Grid/qcd/representations/spfundamental.h>
 #include <Grid/qcd/representations/hmc_types.h>
 
 #endif
diff --git a/Grid/qcd/representations/spfundamental.h b/Grid/qcd/representations/spfundamental.h
new file mode 100644
index 00000000..bab9a005
--- /dev/null
+++ b/Grid/qcd/representations/spfundamental.h
@@ -0,0 +1,42 @@
+
+
+#ifndef SPFUNDAMENTAL_H
+#define SPFUNDAMENTAL_H
+
+NAMESPACE_BEGIN(Grid);
+
+/*
+ * This is an helper class for the HMC
+ * Empty since HMC updates already the fundamental representation 
+ */
+
+template <int ncolour>
+class SpFundamentalRep {
+public:
+  static const int Dimension = ncolour;
+  static const int nSp = ncolour/2;
+  static const bool isFundamental = true;
+
+  // typdef to be used by the Representations class in HMC to get the
+  // types for the higher representation fields
+  typedef typename Sp<nSp>::LatticeMatrix LatticeMatrix;
+  typedef LatticeGaugeField LatticeField;
+  
+  explicit SpFundamentalRep(GridBase* grid) {} //do nothing
+  void update_representation(const LatticeGaugeField& Uin) {} // do nothing
+
+  LatticeField RtoFundamentalProject(const LatticeField& in, Real scale = 1.0) const{
+    return (scale * in);
+  }
+
+};
+
+
+    
+
+  
+typedef	 SpFundamentalRep<Nc> SpFundamentalRepresentation;
+
+NAMESPACE_END(Grid);  
+
+#endif
diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.h
index c8960383..51976146 100644
--- a/Grid/qcd/utils/Sp2n.h
+++ b/Grid/qcd/utils/Sp2n.h
@@ -6,6 +6,13 @@ NAMESPACE_BEGIN(Grid);
 
 // Sp(2N)
 // ncolour = N
+
+// need to be careful with n and 2n
+// I am defining the Sp class for Sp(2n) to be such that the template variable ncolour
+// is n inside 2n and the typedef at the end of the file should eliminate possible confusion.
+
+// the other routines, like projectOnSp2n, N will be the dimension of the actual number of colors for consistency with the sun routines
+
 template <int ncolour>
 class Sp {
 public:
@@ -22,11 +29,31 @@ public:
     using iSp2nAlgebraVector = iScalar<iScalar<iVector<vtype, AlgebraDimension> > >;
     
     typedef iSp2nMatrix<Complex> Matrix;
+    typedef iSp2nMatrix<ComplexF> MatrixF;
+    typedef iSp2nMatrix<ComplexD> MatrixD;
     
     typedef iSp2nMatrix<vComplex> vMatrix;
+    typedef iSp2nMatrix<vComplexF> vMatrixF;
+    typedef iSp2nMatrix<vComplexD> vMatrixD;
     
+    typedef iSp2nAlgebraVector<Complex> AlgebraVector;
+    typedef iSp2nAlgebraVector<ComplexF> AlgebraVectorF;
+    typedef iSp2nAlgebraVector<ComplexD> AlgebraVectorD;
+    
+    typedef iSp2nAlgebraVector<vComplex> vAlgebraVector;
+    typedef iSp2nAlgebraVector<vComplexF> vAlgebraVectorF;
+    typedef iSp2nAlgebraVector<vComplexD> vAlgebraVectorD;
     
     typedef Lattice<vMatrix> LatticeMatrix;
+    typedef Lattice<vMatrixF> LatticeMatrixF;
+    typedef Lattice<vMatrixD> LatticeMatrixD;
+    
+    typedef Lattice<vAlgebraVector> LatticeAlgebraVector;
+    typedef Lattice<vAlgebraVectorF> LatticeAlgebraVectorF;
+    typedef Lattice<vAlgebraVectorD> LatticeAlgebraVectorD;
+    
+    
+    
     // Sp(2N) has N(2N+1) = 2N^2+N generators
     //
     // normalise the generators such that
@@ -322,75 +349,113 @@ public:
       }
     }
     
+ 
     
     
+/*    template <typename GaugeField>
+    static void HotSpConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
+      typedef typename GaugeField::vector_type vector_type;
+      typedef iSp2nMatrix<vector_type> vMatrixType;
+      typedef Lattice<vMatrixType> LatticeMatrixType;
+
+      LatticeMatrixType Umu(out.Grid());
+      for (int mu = 0; mu < Nd; mu++) {
+        LieRandomize(pRNG, Umu, 1.0);   //def
+        PokeIndex<LorentzIndex>(out, Umu, mu);
+      }
+    }
+    template<typename GaugeField>
+    static void TepidSpConfiguration(GridParallelRNG &pRNG,GaugeField &out){
+      typedef typename GaugeField::vector_type vector_type;
+      typedef iSp2nMatrix<vector_type> vMatrixType;
+      typedef Lattice<vMatrixType> LatticeMatrixType;
+
+      LatticeMatrixType Umu(out.Grid());
+      for(int mu=0;mu<Nd;mu++){
+        LieRandomize(pRNG,Umu,0.01);    //def
+        PokeIndex<LorentzIndex>(out,Umu,mu);
+      }
+    } */
+    
+    template<typename GaugeField>
+    static void ColdConfiguration(GaugeField &out){
+      typedef typename GaugeField::vector_type vector_type;
+      typedef iSp2nMatrix<vector_type> vMatrixType;
+      typedef Lattice<vMatrixType> LatticeMatrixType;
+
+      LatticeMatrixType Umu(out.Grid());
+      Umu=1.0;
+      for(int mu=0;mu<Nd;mu++){
+        PokeIndex<LorentzIndex>(out,Umu,mu);
+      }
+    }
+    template<typename GaugeField>
+    static void ColdConfiguration(GridParallelRNG &pRNG,GaugeField &out){
+      ColdConfiguration(out);
+    }
+    
     
     
 }; // end of class Sp
     
     
 
+
+template<int N> //same of su
+ LatticeComplexD SpDeterminant(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
+ {
+   GridBase *grid=Umu.Grid();
+   auto lvol = grid->lSites();
+   LatticeComplexD ret(grid);
+
+   autoView(Umu_v,Umu,CpuRead);
+   autoView(ret_v,ret,CpuWrite);
+   thread_for(site,lvol,{
+     Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N,N);
+     Coordinate lcoor;
+     grid->LocalIndexToLocalCoor(site, lcoor);
+     iScalar<iScalar<iMatrix<ComplexD, N> > > Us;
+     peekLocalSite(Us, Umu_v, lcoor);
+     for(int i=0;i<N;i++){
+       for(int j=0;j<N;j++){
+     EigenU(i,j) = Us()()(i,j);
+       }}
+     ComplexD det = EigenU.determinant();
+     pokeLocalSite(det,ret_v,lcoor);
+   });
+   return ret;
+ }
+ 
+ template<int N>
+ static void ProjectSp2n(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
+ {
+   Umu      = ProjectOnSpGroup(Umu);
+   auto det = SpDeterminant(Umu); // ok ?
+
+   det = conjugate(det);
+
+   for(int i=0;i<N;i++){
+     auto element = PeekIndex<ColourIndex>(Umu,N-1,i);
+     element = element * det;
+     PokeIndex<ColourIndex>(Umu,element,Nc-1,i);
+   }
+ }
+ template<int N>
+ static void ProjectSp2n(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,Nd> > &U)
+ {
+   GridBase *grid=U.Grid();
+   for(int mu=0;mu<Nd;mu++){
+     auto Umu = PeekIndex<LorentzIndex>(U,mu);
+     Umu      = ProjectOnSpGroup(Umu);
+     ProjectSp2n(Umu);
+     PokeIndex<LorentzIndex>(U,Umu,mu);
+   }
+ }
+
+typedef Sp<1> Sp2;
 typedef Sp<2> Sp4;
 typedef Sp<3> Sp6;
 typedef Sp<4> Sp8;
 
 NAMESPACE_END(Grid);
 #endif
-
-
-    
-    
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-    
-    
-    
-/*     }
-     sigxy = lieIndex & 0x1;     // 1 if odd, 0 if even
-     su2Index = lieIndex >> 1 ;  // where to put the sigma_x(y)
-                                 //for the even(odd) lieindex, sigmax(y)
-     if (sigxy)
-         //put sigmay at su2index
-     else
-         //put sigmax    */
diff --git a/tests/core/test_sp2n_lie_gen.cc b/tests/core/test_sp2n_lie_gen.cc
index 5dbba9d3..6c3766e6 100644
--- a/tests/core/test_sp2n_lie_gen.cc
+++ b/tests/core/test_sp2n_lie_gen.cc
@@ -2,7 +2,7 @@
 
 
 #include <Grid/Grid.h>
-#include <Grid/qcd/utils/SUn.h>
+#include <Grid/qcd/utils/Sp2n.h>
 
 using namespace Grid;
 
@@ -13,6 +13,15 @@ int main(int argc, char** argv) {
   //GridCartesian* grid = SpaceTimeGrid::makeFourDimGrid(
   //latt, GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
   //GridRedBlackCartesian* rbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(grid);
+    
+    std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+    std::cout << GridLogMessage << "* Generators for Sp(2)" << std::endl;
+    std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+      
+    Sp2::printGenerators();
+    Sp2::testGenerators();
   
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;

From 7e3b298d3d712b5c8309454939cbf1cee2e82a33 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Mon, 11 Oct 2021 16:28:15 +0100
Subject: [PATCH 011/129] project on sp2n

---
 Grid/lattice/Lattice_ET.h |   2 +
 Grid/tensors/Tensor_Ta.h  | 108 ++++++++++++++++++++++++++++++++++++++
 2 files changed, 110 insertions(+)

diff --git a/Grid/lattice/Lattice_ET.h b/Grid/lattice/Lattice_ET.h
index 4a8a7423..9042eb8f 100644
--- a/Grid/lattice/Lattice_ET.h
+++ b/Grid/lattice/Lattice_ET.h
@@ -346,6 +346,7 @@ GridUnopClass(UnaryTrace, trace(a));
 GridUnopClass(UnaryTranspose, transpose(a));
 GridUnopClass(UnaryTa, Ta(a));
 GridUnopClass(UnaryProjectOnGroup, ProjectOnGroup(a));
+GridUnopClass(UnaryProjectOnSpGroup, ProjectOnSpGroup(a));
 GridUnopClass(UnaryTimesI, timesI(a));
 GridUnopClass(UnaryTimesMinusI, timesMinusI(a));
 GridUnopClass(UnaryAbs, abs(a));
@@ -457,6 +458,7 @@ GRID_DEF_UNOP(trace, UnaryTrace);
 GRID_DEF_UNOP(transpose, UnaryTranspose);
 GRID_DEF_UNOP(Ta, UnaryTa);
 GRID_DEF_UNOP(ProjectOnGroup, UnaryProjectOnGroup);
+GRID_DEF_UNOP(ProjectOnSpGroup, UnaryProjectOnSpGroup);
 GRID_DEF_UNOP(timesI, UnaryTimesI);
 GRID_DEF_UNOP(timesMinusI, UnaryTimesMinusI);
 GRID_DEF_UNOP(abs, UnaryAbs);  // abs overloaded in cmath C++98; DON'T do the
diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index 90e57b2b..f53296bc 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -135,6 +135,114 @@ accelerator_inline iMatrix<vtype,N> ProjectOnGroup(const iMatrix<vtype,N> &arg)
   return ret;
 }
 
+// re-do for sp2n
+
+template<class vtype> accelerator_inline iScalar<vtype> ProjectOnSpGroup(const iScalar<vtype>&r)
+{
+  iScalar<vtype> ret;
+  ret._internal = ProjectOnSpGroup(r._internal);
+  return ret;
+}
+template<class vtype,int N> accelerator_inline iVector<vtype,N> ProjectOnSpGroup(const iVector<vtype,N>&r)
+{
+  iVector<vtype,N> ret;
+  for(int i=0;i<N;i++){
+    ret._internal[i] = ProjectOnSpGroup(r._internal[i]);
+  }
+  return ret;
+}
+
+
+// int N is 2n in Sp(2n)
+template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
+accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg)
+{
+  // need a check for the group type?
+  iMatrix<vtype,N> ret(arg);
+  vtype nrm;
+  vtype inner;
+  for(int c1=0;c1<N;c1++){
+
+       // Normalises row c1
+        zeroit(inner);
+        for(int c2=0;c2<N;c2++)
+          inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
+
+        nrm = sqrt(inner);
+        nrm = 1.0/nrm;
+        for(int c2=0;c2<N;c2++)
+          ret._internal[c1][c2]*= nrm;
+
+        // Compute row c1+N2/2: c1+N/2 = - \Omega c1*
+        for(int c2=0;c2<N/2;c2++)
+          //tmp = conjugate(ret._internal[c1][c2]);
+          //ret._internal[c1+N/2][c2+N/2] = tmp;
+            ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
+
+        for(int c2=N/2;c2<N;c2++)
+          //tmp = conjugate(ret._internal[c1][c2]);
+         // ret._internal[c1+N/2][c2-N/2] = -tmp;
+            ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
+
+        // Remove c1 from rows c1+1...N/2-1
+        for (int b=c1+1; b<N/2; ++b){
+          decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
+          zeroit(pr);
+          for(int c=0; c<N; ++c)
+            pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];
+
+          for(int c=0; c<N; ++c){
+            ret._internal[b][c] -= pr * ret._internal[c1][c];
+          }
+        }
+
+        // Remove c1+N/2 from rows c1+1...N/2-1
+        for (int b=c1+1; b<N; ++b){
+          decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
+          zeroit(pr);
+          for(int c=0; c<N; ++c)
+            pr += conjugate(ret._internal[c1+N/2][c])*ret._internal[b][c];
+
+          for(int c=0; c<N; ++c){
+            ret._internal[b][c] -= pr * ret._internal[c1+N/2][c];
+          }
+        }
+      } //end for loop over c1
+
+      // Compute the last row
+      {
+      // Normalise last row
+        int c1 = N/2-1;
+        zeroit(inner);
+        for(int c2=0;c2<N;c2++)
+        {
+          inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
+        }
+          
+        nrm = sqrt(inner);
+        nrm = 1.0/nrm;
+        for(int c2=0;c2<N;c2++)
+        {
+          ret._internal[c1][c2]*= nrm;
+        }
+      // Compute row cN-1+N2/2: cN-1+N/2 = - \Omega cN-1*
+        for(int c2=0;c2<N/2;c2++)
+        {
+          //tmp = conjugate(ret._internal[c1][c2]);
+          // ret._internal[c1+N/2][c2+N/2] = tmp;
+             ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
+        }
+        for(int c2=N/2;c2<N;c2++)
+        {
+          //tmp = conjugate(ret._internal[c1][c2]);
+          //ret._internal[c1+N/2][c2-N/2] = -tmp;
+            ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
+        }
+      }
+      // assuming the determinant is ok
+      return ret;
+  }
+
 NAMESPACE_END(Grid);
 
 #endif

From 89457e25e37afe7ab21ccf45b9ee0175dc40a199 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Mon, 11 Oct 2021 16:32:10 +0100
Subject: [PATCH 012/129] sp fermion instantiation

---
 Grid/Makefile.am                                     |  1 +
 .../WilsonCloverFermionInstantiationSpWilsonImplD.cc |  1 +
 .../WilsonFermionInstantiationSpWilsonImplD.cc       |  1 +
 .../WilsonKernelsInstantiationSpWilsonImplD.cc       |  1 +
 .../WilsonTMFermionInstantiationSpWilsonImplD.cc     |  1 +
 .../fermion/instantiation/SpWilsonImplD/impl.h       |  1 +
 .../WilsonCloverFermionInstantiationSpWilsonImplF.cc |  1 +
 .../WilsonFermionInstantiationSpWilsonImplF.cc       |  1 +
 .../WilsonKernelsInstantiationSpWilsonImplF.cc       |  1 +
 .../WilsonTMFermionInstantiationSpWilsonImplF.cc     |  1 +
 .../fermion/instantiation/SpWilsonImplF/impl.h       |  1 +
 .../fermion/instantiation/generate_instantiations.sh |  2 ++
 Grid/qcd/hmc/GenericHMCrunner.h                      | 12 ++++++++++++
 scripts/filelist                                     |  2 ++
 14 files changed, 27 insertions(+)
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonCloverFermionInstantiationSpWilsonImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonFermionInstantiationSpWilsonImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonKernelsInstantiationSpWilsonImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonTMFermionInstantiationSpWilsonImplD.cc
 create mode 100644 Grid/qcd/action/fermion/instantiation/SpWilsonImplD/impl.h
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonCloverFermionInstantiationSpWilsonImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonFermionInstantiationSpWilsonImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonKernelsInstantiationSpWilsonImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonTMFermionInstantiationSpWilsonImplF.cc
 create mode 100644 Grid/qcd/action/fermion/instantiation/SpWilsonImplF/impl.h

diff --git a/Grid/Makefile.am b/Grid/Makefile.am
index 7c3c151b..fda92792 100644
--- a/Grid/Makefile.am
+++ b/Grid/Makefile.am
@@ -63,6 +63,7 @@ if BUILD_GPARITY
   extra_sources+=$(GP_FERMION_FILES)
 endif
 if BUILD_FERMION_REPS
+  extra_sources+=$(SP_FERMION_FILES)
   extra_sources+=$(ADJ_FERMION_FILES)
   extra_sources+=$(TWOIND_FERMION_FILES)
 endif
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonCloverFermionInstantiationSpWilsonImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonCloverFermionInstantiationSpWilsonImplD.cc
new file mode 120000
index 00000000..9cc05107
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonCloverFermionInstantiationSpWilsonImplD.cc
@@ -0,0 +1 @@
+../WilsonCloverFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonFermionInstantiationSpWilsonImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonFermionInstantiationSpWilsonImplD.cc
new file mode 120000
index 00000000..5f6ab65e
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonFermionInstantiationSpWilsonImplD.cc
@@ -0,0 +1 @@
+../WilsonFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonKernelsInstantiationSpWilsonImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonKernelsInstantiationSpWilsonImplD.cc
new file mode 120000
index 00000000..01c35e7b
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonKernelsInstantiationSpWilsonImplD.cc
@@ -0,0 +1 @@
+../WilsonKernelsInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonTMFermionInstantiationSpWilsonImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonTMFermionInstantiationSpWilsonImplD.cc
new file mode 120000
index 00000000..d5789bcf
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonTMFermionInstantiationSpWilsonImplD.cc
@@ -0,0 +1 @@
+../WilsonTMFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/impl.h b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/impl.h
new file mode 100644
index 00000000..5aa843dd
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplD/impl.h
@@ -0,0 +1 @@
+#define IMPLEMENTATION SpWilsonImplD
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonCloverFermionInstantiationSpWilsonImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonCloverFermionInstantiationSpWilsonImplF.cc
new file mode 120000
index 00000000..9cc05107
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonCloverFermionInstantiationSpWilsonImplF.cc
@@ -0,0 +1 @@
+../WilsonCloverFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonFermionInstantiationSpWilsonImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonFermionInstantiationSpWilsonImplF.cc
new file mode 120000
index 00000000..5f6ab65e
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonFermionInstantiationSpWilsonImplF.cc
@@ -0,0 +1 @@
+../WilsonFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonKernelsInstantiationSpWilsonImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonKernelsInstantiationSpWilsonImplF.cc
new file mode 120000
index 00000000..01c35e7b
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonKernelsInstantiationSpWilsonImplF.cc
@@ -0,0 +1 @@
+../WilsonKernelsInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonTMFermionInstantiationSpWilsonImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonTMFermionInstantiationSpWilsonImplF.cc
new file mode 120000
index 00000000..d5789bcf
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonTMFermionInstantiationSpWilsonImplF.cc
@@ -0,0 +1 @@
+../WilsonTMFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/impl.h b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/impl.h
new file mode 100644
index 00000000..761b0c82
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonImplF/impl.h
@@ -0,0 +1 @@
+#define IMPLEMENTATION SpWilsonImplF
diff --git a/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh b/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh
index d7553cdb..9c834f6e 100755
--- a/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh
+++ b/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh
@@ -9,6 +9,8 @@ STAG5_IMPL_LIST=""
 WILSON_IMPL_LIST=" \
 	   WilsonImplF \
 	   WilsonImplD \
+       SpWilsonImplF \
+       SpWilsonImplD \
 	   WilsonAdjImplF \
 	   WilsonAdjImplD \
 	   WilsonTwoIndexSymmetricImplF \
diff --git a/Grid/qcd/hmc/GenericHMCrunner.h b/Grid/qcd/hmc/GenericHMCrunner.h
index 98e8175a..16143455 100644
--- a/Grid/qcd/hmc/GenericHMCrunner.h
+++ b/Grid/qcd/hmc/GenericHMCrunner.h
@@ -204,6 +204,18 @@ template <class RepresentationsPolicy,
 using GenericHMCRunnerHirep =
 				     HMCWrapperTemplate<PeriodicGimplR, Integrator, RepresentationsPolicy>;
 
+// sp2n
+
+template <template <typename, typename, typename> class Integrator>
+using GenericSp2nHMCRunner = HMCWrapperTemplate<SymplPeriodicGimplR, Integrator>;
+
+template <class RepresentationsPolicy,
+          template <typename, typename, typename> class Integrator>
+using GenericSp2nHMCRunnerHirep =
+                     HMCWrapperTemplate<SymplPeriodicGimplR, Integrator, RepresentationsPolicy>;
+
+
+
 template <class Implementation, class RepresentationsPolicy, 
           template <typename, typename, typename> class Integrator>
 using GenericHMCRunnerTemplate = HMCWrapperTemplate<Implementation, Integrator, RepresentationsPolicy>;
diff --git a/scripts/filelist b/scripts/filelist
index c3f0cf3f..b117a87d 100755
--- a/scripts/filelist
+++ b/scripts/filelist
@@ -15,6 +15,7 @@ STAG_FERMION_FILES=`  find . -name '*.cc' -path '*/instantiation/*' -path '*/ins
 GP_FERMION_FILES=`    find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/Gparity*' `
 ADJ_FERMION_FILES=`   find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/WilsonAdj*' `
 TWOIND_FERMION_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/WilsonTwoIndex*'`
+SP_FERMION_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/SpWilsonImpl*'`
 
 HPPFILES=`find . -type f -name '*.hpp'`
 echo HFILES=$HFILES $HPPFILES > Make.inc
@@ -27,6 +28,7 @@ echo STAG_FERMION_FILES=$STAG_FERMION_FILES   >> Make.inc
 echo GP_FERMION_FILES=$GP_FERMION_FILES   >> Make.inc
 echo ADJ_FERMION_FILES=$ADJ_FERMION_FILES   >> Make.inc
 echo TWOIND_FERMION_FILES=$TWOIND_FERMION_FILES   >> Make.inc
+echo SP_FERMION_FILES=$SP_FERMION_FILES >> Make.inc
 
 # tests Make.inc
 cd $home/tests

From 1d6e708083221f48d8de2f7bc74fa0de6b97f679 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 12 Oct 2021 09:06:15 +0100
Subject: [PATCH 013/129] tests!

---
 configure.ac                     |  1 +
 tests/Makefile.am                |  2 +-
 tests/sp2n/Makefile.am           |  7 ++++
 tests/sp2n/Test_project_on_Sp.cc | 35 ++++++++++++++++++++
 tests/sp2n/Test_sp2n_lie_gen.cc  | 55 ++++++++++++++++++++++++++++++++
 5 files changed, 99 insertions(+), 1 deletion(-)
 create mode 100644 tests/sp2n/Makefile.am
 create mode 100644 tests/sp2n/Test_project_on_Sp.cc
 create mode 100644 tests/sp2n/Test_sp2n_lie_gen.cc

diff --git a/configure.ac b/configure.ac
index 406b0b74..aece85f9 100644
--- a/configure.ac
+++ b/configure.ac
@@ -815,6 +815,7 @@ AC_CONFIG_FILES(tests/lanczos/Makefile)
 AC_CONFIG_FILES(tests/smearing/Makefile)
 AC_CONFIG_FILES(tests/qdpxx/Makefile)
 AC_CONFIG_FILES(tests/testu01/Makefile)
+AC_CONFIG_FILES(tests/Sp2n/Makefile)
 AC_CONFIG_FILES(benchmarks/Makefile)
 AC_CONFIG_FILES(examples/Makefile)
 AC_OUTPUT
diff --git a/tests/Makefile.am b/tests/Makefile.am
index 7928a7fe..c6380cda 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -1,4 +1,4 @@
-SUBDIRS = . core forces hmc solver debug smearing IO lanczos
+SUBDIRS = . core forces hmc solver debug smearing IO lanczos sp2n
 
 if BUILD_CHROMA_REGRESSION
   SUBDIRS+= qdpxx
diff --git a/tests/sp2n/Makefile.am b/tests/sp2n/Makefile.am
new file mode 100644
index 00000000..0ee7421c
--- /dev/null
+++ b/tests/sp2n/Makefile.am
@@ -0,0 +1,7 @@
+.PHONY: check
+
+include Make.inc
+
+check: tests
+	./Test_project_on_Sp
+	./test_sp2n_lie_gen
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
new file mode 100644
index 00000000..61ec6d0c
--- /dev/null
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -0,0 +1,35 @@
+#include <Grid/Grid.h>
+
+using namespace Grid;
+
+int main (int argc, char **argv)
+{
+     Grid_init(&argc,&argv);
+    
+    
+    Coordinate latt_size   = GridDefaultLatt();
+    Coordinate simd_layout = GridDefaultSimd(Nd,vComplex::Nsimd());
+    Coordinate mpi_layout  = GridDefaultMpi();
+
+    GridCartesian             Grid(latt_size,simd_layout,mpi_layout);
+    GridRedBlackCartesian     RBGrid(&Grid);
+    
+    
+    LatticeGaugeField Umu(&Grid);
+    LatticeColourMatrixD U(&Grid);
+    
+    std::vector<int> pseeds({1,2,3,4,5});
+    std::vector<int> sseeds({6,7,8,9,10});
+    GridParallelRNG  pRNG(&Grid); pRNG.SeedFixedIntegers(pseeds);
+    GridSerialRNG    sRNG;       sRNG.SeedFixedIntegers(sseeds);
+    
+    SU<Nc>::HotConfiguration(pRNG,Umu);
+    U = PeekIndex<LorentzIndex>(Umu,0);
+    
+    
+    U = ProjectOnSpGroup(U);
+    
+    Grid_finalize();
+
+
+}
diff --git a/tests/sp2n/Test_sp2n_lie_gen.cc b/tests/sp2n/Test_sp2n_lie_gen.cc
new file mode 100644
index 00000000..6c3766e6
--- /dev/null
+++ b/tests/sp2n/Test_sp2n_lie_gen.cc
@@ -0,0 +1,55 @@
+
+
+
+#include <Grid/Grid.h>
+#include <Grid/qcd/utils/Sp2n.h>
+
+using namespace Grid;
+
+int main(int argc, char** argv) {
+  Grid_init(&argc, &argv);
+    
+  //std::vector<int> latt({4, 4, 4, 8});
+  //GridCartesian* grid = SpaceTimeGrid::makeFourDimGrid(
+  //latt, GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
+  //GridRedBlackCartesian* rbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(grid);
+    
+    std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+    std::cout << GridLogMessage << "* Generators for Sp(2)" << std::endl;
+    std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+      
+    Sp2::printGenerators();
+    Sp2::testGenerators();
+  
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(4)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+    
+  Sp4::printGenerators();
+  Sp4::testGenerators();
+    
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(6)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  
+  Sp6::printGenerators();
+  Sp6::testGenerators();
+    
+  std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(8)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+              << std::endl;
+    
+  Sp8::printGenerators();
+  Sp8::testGenerators(); 
+    
+    
+  Grid_finalize();
+}

From 283f14b7c1151538a5558bfb45fa3b18b52fef5b Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 12 Oct 2021 12:12:16 +0100
Subject: [PATCH 014/129] fix sp2n projection

---
 Grid/tensors/Tensor_Ta.h         | 133 ++++++++++++++-----------------
 tests/sp2n/Test_project_on_Sp.cc | 122 +++++++++++++++++++++++++++-
 2 files changed, 181 insertions(+), 74 deletions(-)

diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index f53296bc..7b4bccca 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -161,88 +161,75 @@ accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg
   iMatrix<vtype,N> ret(arg);
   vtype nrm;
   vtype inner;
-  for(int c1=0;c1<N;c1++){
+  for(int c1=0;c1<N/2;c1++){
 
-       // Normalises row c1
-        zeroit(inner);
-        for(int c2=0;c2<N;c2++)
-          inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
+    // Normalises row c1
+    zeroit(inner);
+    for(int c2=0;c2<N;c2++)
+      inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
 
-        nrm = sqrt(inner);
-        nrm = 1.0/nrm;
-        for(int c2=0;c2<N;c2++)
-          ret._internal[c1][c2]*= nrm;
+    nrm = sqrt(inner);
+    nrm = 1.0/nrm;
+    for(int c2=0;c2<N;c2++)
+      ret._internal[c1][c2]*= nrm;
 
-        // Compute row c1+N2/2: c1+N/2 = - \Omega c1*
-        for(int c2=0;c2<N/2;c2++)
-          //tmp = conjugate(ret._internal[c1][c2]);
-          //ret._internal[c1+N/2][c2+N/2] = tmp;
-            ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
+    // Compute row c1+N2/2: c1+N/2 = - \Omega c1*
+    for(int c2=0;c2<N/2;c2++)
+      ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
 
-        for(int c2=N/2;c2<N;c2++)
-          //tmp = conjugate(ret._internal[c1][c2]);
-         // ret._internal[c1+N/2][c2-N/2] = -tmp;
-            ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
+    for(int c2=N/2;c2<N;c2++)
+      ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
 
-        // Remove c1 from rows c1+1...N/2-1
-        for (int b=c1+1; b<N/2; ++b){
-          decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
-          zeroit(pr);
-          for(int c=0; c<N; ++c)
-            pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];
+    // Remove c1 from rows c1+1...N/2-1
+    for (int b=c1+1; b<N/2; ++b){
+      decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
+      zeroit(pr);
+      for(int c=0; c<N; ++c)
+        pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];
 
-          for(int c=0; c<N; ++c){
-            ret._internal[b][c] -= pr * ret._internal[c1][c];
-          }
-        }
-
-        // Remove c1+N/2 from rows c1+1...N/2-1
-        for (int b=c1+1; b<N; ++b){
-          decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
-          zeroit(pr);
-          for(int c=0; c<N; ++c)
-            pr += conjugate(ret._internal[c1+N/2][c])*ret._internal[b][c];
-
-          for(int c=0; c<N; ++c){
-            ret._internal[b][c] -= pr * ret._internal[c1+N/2][c];
-          }
-        }
-      } //end for loop over c1
-
-      // Compute the last row
-      {
-      // Normalise last row
-        int c1 = N/2-1;
-        zeroit(inner);
-        for(int c2=0;c2<N;c2++)
-        {
-          inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
-        }
-          
-        nrm = sqrt(inner);
-        nrm = 1.0/nrm;
-        for(int c2=0;c2<N;c2++)
-        {
-          ret._internal[c1][c2]*= nrm;
-        }
-      // Compute row cN-1+N2/2: cN-1+N/2 = - \Omega cN-1*
-        for(int c2=0;c2<N/2;c2++)
-        {
-          //tmp = conjugate(ret._internal[c1][c2]);
-          // ret._internal[c1+N/2][c2+N/2] = tmp;
-             ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
-        }
-        for(int c2=N/2;c2<N;c2++)
-        {
-          //tmp = conjugate(ret._internal[c1][c2]);
-          //ret._internal[c1+N/2][c2-N/2] = -tmp;
-            ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
-        }
+      for(int c=0; c<N; ++c){
+        ret._internal[b][c] -= pr * ret._internal[c1][c];
       }
-      // assuming the determinant is ok
-      return ret;
+    }
+
+    // Remove c1+N/2 from rows c1+1...N/2-1
+    for (int b=c1+1; b<N; ++b){
+      decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
+      zeroit(pr);
+      for(int c=0; c<N; ++c)
+        pr += conjugate(ret._internal[c1+N/2][c])*ret._internal[b][c];
+
+      for(int c=0; c<N; ++c){
+        ret._internal[b][c] -= pr * ret._internal[c1+N/2][c];
+      }
+    }
   }
 
+  // Compute the last row
+  {
+  // Normalise last row
+    int c1 = N/2-1;
+    zeroit(inner);
+    for(int c2=0;c2<N;c2++)
+      inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
+
+    nrm = sqrt(inner);
+    nrm = 1.0/nrm;
+    for(int c2=0;c2<N;c2++)
+      ret._internal[c1][c2]*= nrm;
+
+  // Compute row cN-1+N2/2: cN-1+N/2 = - \Omega cN-1*
+    for(int c2=0;c2<N/2;c2++)
+      ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
+
+    for(int c2=N/2;c2<N;c2++)
+      ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
+  }
+  // assuming the determinant is ok
+  return ret;
+}
+
+
 NAMESPACE_END(Grid);
 
 #endif
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 61ec6d0c..d494d828 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -17,6 +17,14 @@ int main (int argc, char **argv)
     
     LatticeGaugeField Umu(&Grid);
     LatticeColourMatrixD U(&Grid);
+    LatticeColourMatrixD aux(&Grid);
+    LatticeColourMatrixD identity(&Grid);
+    
+    identity = 1.0;
+    RealD epsilon = 0.01;
+    Complex i(0., 1.);
+    RealD u = 0.;
+    double vol = Umu.Grid()->gSites();
     
     std::vector<int> pseeds({1,2,3,4,5});
     std::vector<int> sseeds({6,7,8,9,10});
@@ -24,10 +32,122 @@ int main (int argc, char **argv)
     GridSerialRNG    sRNG;       sRNG.SeedFixedIntegers(sseeds);
     
     SU<Nc>::HotConfiguration(pRNG,Umu);
-    U = PeekIndex<LorentzIndex>(Umu,0);
+    U = PeekIndex<LorentzIndex>(Umu,2);
     
+    // it is unitary
+    aux = U*adj(U) - identity;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout << GridLogMessage << "Unitary check of starting random SUn matrix " << std::endl;
+    std::cout <<GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout <<GridLogMessage << std::endl;
     
+    U = U + epsilon*identity;
+    aux = U*adj(U) - identity;
+    
+    std::cout << GridLogMessage << "Unitary matrix modified " << std::endl;
+    std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout << GridLogMessage << "Projecting on Sp2n " << std::endl;
+
     U = ProjectOnSpGroup(U);
+    aux = U*adj(U) - identity;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout << GridLogMessage << "Unitary check after Sp(2n) projection " << std::endl;
+    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+    assert( norm2(aux) < 1e-6);
+    std::cout <<GridLogMessage << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    
+    // checks on determinant
+    std::cout << GridLogMessage << "Det after Projection on Sp2n = " << norm2( Determinant(U) ) / vol << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    // checks on elements
+    // an Sp2n matrix is a block matrix of the type
+    //
+    //
+    //     U = (    W       X   )
+    //         (    -X^*    W^* )
+    //
+    // will check this
+    //
+    std::cout << GridLogMessage << "Checking that U[ i , j ] - conj U[ i+N/2, j+N/2 ] = 0 for i = 0, ... , N/2 " << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    const int nsp = Nc / 2;
+    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);
+            std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
+            assert(  amizeroo.real() < 10e-6 );
+            amizeroo *= i;
+            assert(  amizeroo.real() < 10e-6 );
+            std::cout << GridLogMessage << "ok " << std::endl;
+        }
+        
+    }
+    std::cout <<GridLogMessage << std::endl;
+    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;
+    std::cout <<GridLogMessage << std::endl;
+    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);
+            std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
+            assert(  amizeroo.real() < 10e-6 );
+            amizeroo *= i;
+            assert(  amizeroo.real() < 10e-6 );
+            std::cout << GridLogMessage << "ok " << std::endl;
+        }
+    }
+    
+    
+    // an explicit check for sp2
+    if (Nc == 2)
+    {
+        assert(Nc==2);
+        ColourMatrix A;
+        A = Zero();
+
+        Complex a(25041994., 12.);
+        Complex b(39., 0.22);
+        Complex d(10000., -2222.3333);
+    
+        A()()(0,0) = a;
+        A()()(0,1) = b;
+        A()()(1,0) = i;
+        A()()(1,1) = d;
+        std::cout <<GridLogMessage << std::endl;
+        std::cout <<GridLogMessage << std::endl;
+        std::cout << GridLogMessage << "An explicit check for Sp2" << std::endl;
+        std::cout <<GridLogMessage << std::endl;
+        std::cout << GridLogMessage << "Building a non unitary matrix by hand with funny entries " << std::endl;
+        std::cout << GridLogMessage << "A = " << A << std::endl;
+        std::cout << GridLogMessage << "Projecting on Sp2 " << std::endl;
+        A = ProjectOnSpGroup(A);
+        std::cout << GridLogMessage << "now A = " << A << std::endl;
+        std::cout << GridLogMessage << "A(0,0) - conjA(1,1) = " << A()()(0,0) - adj ( A()()(1,1) )<< std::endl;
+        std::cout << GridLogMessage << "A(0,1) + conjA(1,0) = " << A()()(0,1) + adj ( A()()(1,0) )<< std::endl;
+    }
+    
+    
+    
+    
+    
+    
     
     Grid_finalize();
 

From 1ace5850ae22d1ad638c6696af8071f473a5e754 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 12 Oct 2021 12:16:47 +0100
Subject: [PATCH 015/129] first hmc

---
 .../Test_hmc_Sp_WilsonFundFermionGauge.cc     | 78 +++++++++++++++++++
 1 file changed, 78 insertions(+)
 create mode 100644 tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc

diff --git a/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
new file mode 100644
index 00000000..d845c98f
--- /dev/null
+++ b/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
@@ -0,0 +1,78 @@
+#include <Grid/Grid.h>
+
+int main(int argc, char **argv) {
+  using namespace Grid;
+   
+  typedef Representations< SpFundamentalRepresentation > TheRepresentations;
+
+  Grid_init(&argc, &argv);
+    
+  typedef GenericSp2nHMCRunnerHirep<TheRepresentations, MinimumNorm2> HMCWrapper; // ok
+  typedef SpWilsonImplR FermionImplPolicy;                                    // ok
+  typedef SpWilsonFermionR FermionAction;                                     // ok
+  typedef typename FermionAction::FermionField FermionField;                  // ok?
+ 
+  //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+   
+  HMCWrapper TheHMC;
+    
+  TheHMC.Resources.AddFourDimGrid("gauge");
+    
+  // Checkpointer definition
+  CheckpointerParameters CPparams;
+  CPparams.config_prefix = "ckpoint_lat";
+  CPparams.rng_prefix = "ckpoint_rng";
+  CPparams.saveInterval = 5;
+  CPparams.format = "IEEE64BIG";
+    
+  TheHMC.Resources.LoadNerscCheckpointer(CPparams);
+
+  RNGModuleParameters RNGpar;
+  RNGpar.serial_seeds = "1 2 3 4 5";
+  RNGpar.parallel_seeds = "6 7 8 9 10";
+  TheHMC.Resources.SetRNGSeeds(RNGpar);
+
+  // Construct observables
+  typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
+  TheHMC.Resources.AddObservable<PlaqObs>();
+    
+  RealD beta = 2.25 ;
+    
+  SymplWilsonGaugeActionR Waction(beta);
+    
+  auto GridPtr = TheHMC.Resources.GetCartesian();
+  auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
+    
+    SpFundamentalRepresentation::LatticeField U(GridPtr);
+    //LatticeGaugeField U(GridPtr);
+    
+  RealD mass = -0.95;
+
+  FermionAction FermOp(U, *GridPtr, *GridRBPtr, mass);
+    
+ 
+  ConjugateGradient<FermionField> CG(1.0e-8, 2000, false);
+  
+  TwoFlavourPseudoFermionAction<FermionImplPolicy> Nf2(FermOp, CG, CG);
+    
+  Nf2.is_smeared = false;
+  
+    ActionLevel<HMCWrapper::Field, TheRepresentations > Level1(1);
+    Level1.push_back(&Nf2);
+    
+    ActionLevel<HMCWrapper::Field, TheRepresentations > Level2(4);
+    Level2.push_back(&Waction);
+    
+    TheHMC.TheAction.push_back(Level1);
+    TheHMC.TheAction.push_back(Level2);
+    
+    TheHMC.Parameters.MD.MDsteps = 20;
+    TheHMC.Parameters.MD.trajL   = 1.0;
+    
+    TheHMC.ReadCommandLine(argc, argv);
+    TheHMC.Run();
+    
+    
+  Grid_finalize();
+}
+

From 291e80f88a6fdbca1966689de20d396750ae4f7f Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 12 Oct 2021 15:47:56 +0100
Subject: [PATCH 016/129] sp2n as config option

---
 configure.ac | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

diff --git a/configure.ac b/configure.ac
index aece85f9..b60c9148 100644
--- a/configure.ac
+++ b/configure.ac
@@ -128,6 +128,23 @@ case ${ac_LAPACK} in
         AC_DEFINE([USE_LAPACK],[1],[use LAPACK]);;
 esac
 
+
+############### Symplectic group
+AC_ARG_ENABLE([symplectic],
+    [AC_HELP_STRING([--enable-symplectic=yes|no], [enable gauge group Sp2n])],
+    [ac_ENABLE_SP=${enable_symplectic}], [ac_ENABLE_SP=no])
+
+AM_CONDITIONAL(BUILD_SP, [ test "${ac_ENABLE_SP}X" == "yesX" ])
+
+case ${ac_ENABLE_SP} in
+   yes)
+        AC_DEFINE([Sp2n_config],[1],[gauge group Sp2n], [have_sp2n=true]);;
+   no)
+        AC_DEFINE([Sp2n_config],[0],[gauge group SUn], [have_sp2n=false]);;
+    *)
+        AC_MSG_ERROR(["--enable-symplectic is either yes or no"]);;
+esac
+
 ############### fermions
 AC_ARG_ENABLE([fermion-reps],
      [AC_HELP_STRING([--enable-fermion-reps=yes|no], [enable extra fermion representation support])],
@@ -770,6 +787,7 @@ os (target)                 : $target_os
 compiler vendor             : ${ax_cv_cxx_compiler_vendor}
 compiler version            : ${ax_cv_gxx_version}
 ----- BUILD OPTIONS -----------------------------------
+gauge group                 : `if test "${ac_ENABLE_SP}x" == "yesx"; then echo Sp2n; else echo SUn; fi`
 Nc                          : ${ac_Nc}
 SIMD                        : ${ac_SIMD}${SIMD_GEN_WIDTH_MSG}
 Threading                   : ${ac_openmp}
@@ -787,6 +805,7 @@ FFTW                        : `if test "x$have_fftw" = xtrue; then echo yes; els
 LIME (ILDG support)         : `if test "x$have_lime" = xtrue; then echo yes; else echo no; fi`
 HDF5                        : `if test "x$have_hdf5" = xtrue; then echo yes; else echo no; fi`
 build DOXYGEN documentation : `if test "$DX_FLAG_doc" = '1'; then echo yes; else echo no; fi`
+Sp2n                        : ${ac_ENABLE_SP}
 ----- BUILD FLAGS -------------------------------------
 CXXFLAGS:
 `echo ${AM_CXXFLAGS} ${CXXFLAGS} | tr ' ' '\n' | sed 's/^-/    -/g'`

From b145fd4f5bb0e700013c36b83c565bddb9fe74fd Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 12 Oct 2021 17:08:46 +0100
Subject: [PATCH 017/129] necessary to merge

---
 Grid/qcd/action/gauge/GaugeImplTypes.h | 36 +++-----------------------
 1 file changed, 4 insertions(+), 32 deletions(-)

diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index 3f8db682..53f4f07e 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -121,10 +121,7 @@ public:
     //
     LinkField Pmu(P.Grid());
     Pmu = Zero();
-<<<<<<< HEAD
 
-=======
->>>>>>> 470d4dcc6db9fa41faceac54908bcd60a08bfd8a
     for (int mu = 0; mu < Nd; mu++)
     {
         if (isSp2n == true)
@@ -134,14 +131,10 @@ public:
         } else
         {
         
-<<<<<<< HEAD
+
             Group::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
         }
 
-=======
-            SU<Nrepresentation>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
-        }
->>>>>>> 470d4dcc6db9fa41faceac54908bcd60a08bfd8a
       RealD scale = ::sqrt(HMC_MOMENTUM_DENOMINATOR) ;
       Pmu = Pmu*scale;
       PokeIndex<LorentzIndex>(P, Pmu, mu);
@@ -195,27 +188,17 @@ public:
       }
   }
 
-<<<<<<< HEAD
-
 
   static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U)
   {
       Group::HotConfiguration(pRNG, U);
-=======
-  static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U)
-  {
-      SU<Nc>::HotConfiguration(pRNG, U);
->>>>>>> 470d4dcc6db9fa41faceac54908bcd60a08bfd8a
   }
 
   static inline void TepidConfiguration(GridParallelRNG &pRNG, Field &U) {
     Group::TepidConfiguration(pRNG, U);
   }
 
-<<<<<<< HEAD
 
-=======
->>>>>>> 470d4dcc6db9fa41faceac54908bcd60a08bfd8a
   static inline void ColdConfiguration(GridParallelRNG &pRNG, Field &U)
   {
       if (isSp2n == true)
@@ -224,15 +207,11 @@ public:
           Sp<nSp>::ColdConfiguration(pRNG, U);
       } else
       {
-<<<<<<< HEAD
           Group::ColdConfiguration(pRNG, U);
       }
 
   }
-=======
-          SU<Nc>::ColdConfiguration(pRNG, U);
-      }
-  }
+
     
   //sp2n... see sp2n.h
 /*
@@ -272,7 +251,7 @@ public:
       Sp<nSp>::ColdConfiguration(pRNG, U);
     }
 */
->>>>>>> 470d4dcc6db9fa41faceac54908bcd60a08bfd8a
+
 
 };
 
@@ -285,17 +264,10 @@ typedef GaugeImplTypes<vComplex, Nc, 12, true> SymplGimplTypesR;
 typedef GaugeImplTypes<vComplexF, Nc, 12, true> SymplGimplTypesF;
 typedef GaugeImplTypes<vComplexD, Nc, 12, true> SymplGimplTypesD;
 
-<<<<<<< HEAD
-typedef GaugeImplTypes<vComplex, Group::AdjointDimension> GimplAdjointTypesR;
-typedef GaugeImplTypes<vComplexF, Group::AdjointDimension> GimplAdjointTypesF;
-typedef GaugeImplTypes<vComplexD, Group::AdjointDimension> GimplAdjointTypesD;
-
-
-=======
 typedef GaugeImplTypes<vComplex, SU<Nc>::AdjointDimension> GimplAdjointTypesR;
 typedef GaugeImplTypes<vComplexF, SU<Nc>::AdjointDimension> GimplAdjointTypesF;
 typedef GaugeImplTypes<vComplexD, SU<Nc>::AdjointDimension> GimplAdjointTypesD;
->>>>>>> 470d4dcc6db9fa41faceac54908bcd60a08bfd8a
+
 
 
 

From 0d6674e489e3d043b223f25bba56856f5027b4c3 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 12 Oct 2021 18:53:54 +0100
Subject: [PATCH 018/129] hot start for sp2n

---
 Grid/qcd/QCD.h                         |   1 +
 Grid/qcd/action/gauge/GaugeImplTypes.h |  62 +++-------
 Grid/qcd/utils/Sp2n.h                  |  76 +++++++-----
 configure.ac                           |   2 +-
 tests/sp2n/Test_Sp_start.cc            | 158 +++++++++++++++++++++++++
 5 files changed, 222 insertions(+), 77 deletions(-)
 create mode 100644 tests/sp2n/Test_Sp_start.cc

diff --git a/Grid/qcd/QCD.h b/Grid/qcd/QCD.h
index 858aead7..90a78fce 100644
--- a/Grid/qcd/QCD.h
+++ b/Grid/qcd/QCD.h
@@ -47,6 +47,7 @@ static constexpr int Ym = 5;
 static constexpr int Zm = 6;
 static constexpr int Tm = 7;
 
+static constexpr int isSymplectic=Sp2n_config;
 static constexpr int Nc=Config_Nc;
 static constexpr int Ns=4;
 static constexpr int Nd=4;
diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index 53f4f07e..8e418209 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -191,11 +191,26 @@ public:
 
   static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U)
   {
-      Group::HotConfiguration(pRNG, U);
+      if (isSp2n == true)
+      {
+          const int nSp = Nrepresentation/2;
+          Sp<nSp>::HotConfiguration(pRNG, U);
+      } else
+      {
+          Group::HotConfiguration(pRNG, U);
+      }
   }
 
-  static inline void TepidConfiguration(GridParallelRNG &pRNG, Field &U) {
-    Group::TepidConfiguration(pRNG, U);
+  static inline void TepidConfiguration(GridParallelRNG &pRNG, Field &U)
+  {
+      if (isSp2n == true)
+    {
+        const int nSp = Nrepresentation/2;
+        Sp<nSp>::TepidConfiguration(pRNG, U);
+    } else
+    {
+        Group::TepidConfiguration(pRNG, U);
+    }
   }
 
 
@@ -212,47 +227,6 @@ public:
 
   }
 
-    
-  //sp2n... see sp2n.h
-/*
-    static inline void generate_sp2n_momenta(Field &P, GridSerialRNG & sRNG, GridParallelRNG &pRNG)
-    {
-      
-      const int nSp = Nrepresentation/2;
-      LinkField Pmu(P.Grid());
-      Pmu = Zero();
-      for (int mu = 0; mu < Nd; mu++) {
-        
-        Sp<nSp>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
-        RealD scale = ::sqrt(HMC_MOMENTUM_DENOMINATOR) ;
-        Pmu = Pmu*scale;
-        PokeIndex<LorentzIndex>(P, Pmu, mu);
-      }
-    }
-    
-    static inline void update_sp2n_field(Field& P, Field& U, double ep){
- 
-      autoView(U_v,U,AcceleratorWrite);
-      autoView(P_v,P,AcceleratorRead);
-      accelerator_for(ss, P.Grid()->oSites(),1,{
-        for (int mu = 0; mu < Nd; mu++) {
-          U_v[ss](mu) = ProjectOnSpGroup(Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu));
-        }
-      });
-    }
-    
-    static inline void SpProject(Field &U) {
-      ProjectSp2n(U);
-    }
-
-
-    static inline void ColdSpConfiguration(GridParallelRNG &pRNG, Field &U) {
-      const int nSp = Nrepresentation/2;
-      Sp<nSp>::ColdConfiguration(pRNG, U);
-    }
-*/
-
-
 };
 
 
diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.h
index 51976146..1dafd771 100644
--- a/Grid/qcd/utils/Sp2n.h
+++ b/Grid/qcd/utils/Sp2n.h
@@ -310,6 +310,45 @@ public:
     }
     
     
+    template <typename LatticeMatrixType>
+    static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out, double scale = 1.0)
+    {
+      GridBase *grid = out.Grid();
+
+      typedef typename LatticeMatrixType::vector_type vector_type;
+      typedef typename LatticeMatrixType::scalar_type scalar_type;
+
+      typedef iSinglet<vector_type> vTComplexType;
+
+      typedef Lattice<vTComplexType> LatticeComplexType;
+      typedef typename GridTypeMapper<typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
+
+      LatticeComplexType ca(grid);
+      LatticeMatrixType lie(grid);
+      LatticeMatrixType la(grid);
+      ComplexD ci(0.0, scale);
+      //    ComplexD cone(1.0, 0.0);
+      MatrixType ta;
+
+      lie = Zero();
+
+      for (int a = 0; a < AlgebraDimension; a++) {
+        random(pRNG, ca);
+
+        ca = (ca + conjugate(ca)) * 0.5;
+        ca = ca - 0.5;
+
+        generator(a, ta);
+
+        la = ci * ca * ta;
+
+        lie = lie + la;  // e^{i la ta}
+
+      }
+      taExp(lie, out);
+    }
+    
+    
     static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG, //same as sun
                                                     LatticeMatrix &out,
                                                     Real scale = 1.0) {
@@ -352,8 +391,8 @@ public:
  
     
     
-/*    template <typename GaugeField>
-    static void HotSpConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
+    template <typename GaugeField>
+    static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
       typedef typename GaugeField::vector_type vector_type;
       typedef iSp2nMatrix<vector_type> vMatrixType;
       typedef Lattice<vMatrixType> LatticeMatrixType;
@@ -365,7 +404,7 @@ public:
       }
     }
     template<typename GaugeField>
-    static void TepidSpConfiguration(GridParallelRNG &pRNG,GaugeField &out){
+    static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out){
       typedef typename GaugeField::vector_type vector_type;
       typedef iSp2nMatrix<vector_type> vMatrixType;
       typedef Lattice<vMatrixType> LatticeMatrixType;
@@ -375,7 +414,7 @@ public:
         LieRandomize(pRNG,Umu,0.01);    //def
         PokeIndex<LorentzIndex>(out,Umu,mu);
       }
-    } */
+    }
     
     template<typename GaugeField>
     static void ColdConfiguration(GaugeField &out){
@@ -398,39 +437,12 @@ public:
     
 }; // end of class Sp
     
-    
-
-
-template<int N> //same of su
- LatticeComplexD SpDeterminant(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
- {
-   GridBase *grid=Umu.Grid();
-   auto lvol = grid->lSites();
-   LatticeComplexD ret(grid);
-
-   autoView(Umu_v,Umu,CpuRead);
-   autoView(ret_v,ret,CpuWrite);
-   thread_for(site,lvol,{
-     Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N,N);
-     Coordinate lcoor;
-     grid->LocalIndexToLocalCoor(site, lcoor);
-     iScalar<iScalar<iMatrix<ComplexD, N> > > Us;
-     peekLocalSite(Us, Umu_v, lcoor);
-     for(int i=0;i<N;i++){
-       for(int j=0;j<N;j++){
-     EigenU(i,j) = Us()()(i,j);
-       }}
-     ComplexD det = EigenU.determinant();
-     pokeLocalSite(det,ret_v,lcoor);
-   });
-   return ret;
- }
  
  template<int N>
  static void ProjectSp2n(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
  {
    Umu      = ProjectOnSpGroup(Umu);
-   auto det = SpDeterminant(Umu); // ok ?
+   auto det = Determinant(Umu); // ok ?
 
    det = conjugate(det);
 
diff --git a/configure.ac b/configure.ac
index b60c9148..caadca41 100644
--- a/configure.ac
+++ b/configure.ac
@@ -787,7 +787,7 @@ os (target)                 : $target_os
 compiler vendor             : ${ax_cv_cxx_compiler_vendor}
 compiler version            : ${ax_cv_gxx_version}
 ----- BUILD OPTIONS -----------------------------------
-gauge group                 : `if test "${ac_ENABLE_SP}x" == "yesx"; then echo Sp2n; else echo SUn; fi`
+#gauge group                 : `if test "${ac_ENABLE_SP}x" == "yesx"; then echo Sp2n; else echo SUn; fi`
 Nc                          : ${ac_Nc}
 SIMD                        : ${ac_SIMD}${SIMD_GEN_WIDTH_MSG}
 Threading                   : ${ac_openmp}
diff --git a/tests/sp2n/Test_Sp_start.cc b/tests/sp2n/Test_Sp_start.cc
new file mode 100644
index 00000000..eaeb59f4
--- /dev/null
+++ b/tests/sp2n/Test_Sp_start.cc
@@ -0,0 +1,158 @@
+#include <Grid/Grid.h>
+
+using namespace Grid;
+
+int main (int argc, char **argv)
+{
+    Grid_init(&argc,&argv);
+    
+    Coordinate latt_size   = GridDefaultLatt();
+    Coordinate simd_layout = GridDefaultSimd(Nd,vComplex::Nsimd());
+    Coordinate mpi_layout  = GridDefaultMpi();
+
+    GridCartesian             Grid(latt_size,simd_layout,mpi_layout);
+    GridRedBlackCartesian     RBGrid(&Grid);
+    
+    LatticeGaugeField Umu(&Grid);
+    LatticeGaugeField identity(&Grid);
+    LatticeColourMatrixD U(&Grid);
+    LatticeColourMatrixD Cidentity(&Grid);
+    LatticeColourMatrixD aux(&Grid);
+    
+    identity = 1.0;
+    Cidentity = 1.0;
+    Complex i(0., 1.);
+    
+    double vol = Umu.Grid()->gSites();
+    
+    const int nsp = Nc / 2;
+    std::vector<int> pseeds({1,2,3,4,5});
+    std::vector<int> sseeds({6,7,8,9,10});
+    GridParallelRNG  pRNG(&Grid); pRNG.SeedFixedIntegers(pseeds);
+    GridSerialRNG    sRNG;       sRNG.SeedFixedIntegers(sseeds);
+    
+    std::cout << GridLogMessage << std::endl;
+    
+    
+    Sp<nsp>::ColdConfiguration(pRNG,Umu);
+    Umu = Umu - identity;
+    U = PeekIndex<LorentzIndex>(Umu,1);
+    
+    std::cout << GridLogMessage << "U - 1 = " << norm2(sum(U)) << std::endl;
+    assert ( norm2(sum(U)) < 1e-6);
+    std::cout << GridLogMessage << std::endl;
+    
+    std::cout << GridLogMessage << "Hot Start " << std::endl;
+    Sp<nsp>::HotConfiguration(pRNG,Umu);
+    U = PeekIndex<LorentzIndex>(Umu,1);
+    
+    std::cout << GridLogMessage << "Checking unitarity " << std::endl;
+    
+    aux = U*adj(U) - Cidentity;
+
+    assert( norm2(aux) < 1e-6 );
+    
+    std::cout << GridLogMessage << "ok" << std::endl;
+    std::cout << GridLogMessage << std::endl;
+    
+    std::cout << GridLogMessage << "Checking determinant " << std::endl;
+    std::cout << GridLogMessage << "Det = " <<  norm2( Determinant(U) )/vol << std::endl;
+    std::cout << GridLogMessage << std::endl;
+    
+    std::cout << GridLogMessage << "Checking the matrix is in Sp2n " << 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);
+            std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
+            assert(  amizeroo.real() < 10e-6 );
+            amizeroo *= i;
+            assert(  amizeroo.real() < 10e-6 );
+            std::cout << GridLogMessage << "ok " << std::endl;
+        }
+        
+    }
+    std::cout <<GridLogMessage << std::endl;
+    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;
+    std::cout <<GridLogMessage << std::endl;
+    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);
+            std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
+            assert(  amizeroo.real() < 10e-6 );
+            amizeroo *= i;
+            assert(  amizeroo.real() < 10e-6 );
+            std::cout << GridLogMessage << "ok " << std::endl;
+        }
+    }
+    
+    
+    std::vector<int> ppseeds({11,12,13,14,15});
+    std::vector<int> ssseeds({16,17,18,19,20});
+    GridParallelRNG  ppRNG(&Grid); pRNG.SeedFixedIntegers(ppseeds);
+    GridSerialRNG    ssRNG;       sRNG.SeedFixedIntegers(ssseeds);
+    
+    std::cout << GridLogMessage << std::endl;
+    std::cout << GridLogMessage << "Testing gauge implementation " << std::endl;
+    
+    SymplPeriodicGimplR::HotConfiguration(ppRNG, Umu);
+    
+    U = PeekIndex<LorentzIndex>(Umu,1);
+    
+    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);
+            std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
+            assert(  amizeroo.real() < 10e-6 );
+            amizeroo *= i;
+            assert(  amizeroo.real() < 10e-6 );
+            std::cout << GridLogMessage << "ok " << std::endl;
+        }
+        
+    }
+    std::cout <<GridLogMessage << std::endl;
+    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;
+    std::cout <<GridLogMessage << std::endl;
+    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);
+            std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
+            assert(  amizeroo.real() < 10e-6 );
+            amizeroo *= i;
+            assert(  amizeroo.real() < 10e-6 );
+            std::cout << GridLogMessage << "ok " << std::endl;
+        }
+    }
+    
+    
+    
+    Grid_finalize();
+
+
+    }
+

From 4e31e4e094530456653479f82b3990078eaa1e7d Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Wed, 13 Oct 2021 15:07:23 +0100
Subject: [PATCH 019/129] Better  tests

---
 Grid/qcd/utils/Sp2n.h            |  78 ++++++++++++++++++++++++
 configure.ac                     |   1 -
 tests/sp2n/Test_Sp_start.cc      | 100 +++++++++++++++++--------------
 tests/sp2n/Test_project_on_Sp.cc |  55 +++++++++--------
 4 files changed, 161 insertions(+), 73 deletions(-)

diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.h
index 1dafd771..ad6933e3 100644
--- a/Grid/qcd/utils/Sp2n.h
+++ b/Grid/qcd/utils/Sp2n.h
@@ -433,7 +433,85 @@ public:
       ColdConfiguration(out);
     }
     
+    static void OmegaInvariance(ColourMatrix &in)
+    {
+        
+        ColourMatrix Omega;
+        Omega = Zero();
+        
+        for (int i = 0; i < ncolour; i++)
+        {
+            Omega()()(i, 2*ncolour-1-i) = 1.;
+            Omega()()(2*ncolour-1-i, i) = -1;
+        }
+
+        auto diff = Omega - (in * Omega * transpose(in) );
+        auto sdiff = norm2(diff);
+        if (norm2(sdiff) < 1e-8)
+        {
+            std::cout << GridLogMessage << "Symplectic condition satisfied: Omega invariant" << std::endl;
+        } else {
+            std::cout << GridLogMessage << "WARNING!!!!!! Matrix Omega NOT left invariant by " << norm2(sdiff) << std::endl;
+        }
+        
+    }
     
+    template<typename GaugeField>
+    static void OmegaInvariance(GaugeField &in)
+    {
+        typedef typename GaugeField::vector_type vector_type;
+        typedef iSp2nMatrix<vector_type> vMatrixType;
+        typedef Lattice<vMatrixType> LatticeMatrixType;
+        
+        LatticeMatrixType U(in.Grid());
+        LatticeMatrixType OmegaLatt(in.Grid());
+        LatticeMatrixType identity(in.Grid());
+        RealD vol = in.Grid()->gSites();
+        ColourMatrix Omega;
+        
+        OmegaLatt = Zero();
+        Omega = Zero();
+        identity = 1.;
+        
+        U = PeekIndex<LorentzIndex>(in,1);
+        
+        OmegaInvariance(U);
+        
+    }
+    
+       static void OmegaInvariance(LatticeColourMatrixD &in)
+       {
+                      
+           LatticeColourMatrixD OmegaLatt(in.Grid());
+           LatticeColourMatrixD identity(in.Grid());
+           RealD vol = in.Grid()->gSites();
+           ColourMatrix Omega;
+           
+           OmegaLatt = Zero();
+           Omega = Zero();
+           identity = 1.;
+           
+           for (int i = 0; i < ncolour; i++)
+           {
+               Omega()()(i, 2*ncolour-1-i) = 1.;
+               Omega()()(2*ncolour-1-i, i) = -1;
+           }
+    
+           OmegaLatt = OmegaLatt + (identity*Omega);
+           
+           auto diff = OmegaLatt - (in*Omega*transpose(in));
+           auto sdiff = sum(diff);
+           //assert( norm2(sdiff) < 1e-8 );
+           if (norm2(sdiff) < 1e-8)
+           {
+               std::cout << GridLogMessage << "Symplectic condition satisfied: Omega invariant" << std::endl;
+           } else {
+               std::cout << GridLogMessage << "WARNING!!!!!! Matrix Omega NOT left invariant by " << norm2(sdiff) << std::endl;
+           }
+           
+           
+       }
+        
     
 }; // end of class Sp
     
diff --git a/configure.ac b/configure.ac
index caadca41..c6a85588 100644
--- a/configure.ac
+++ b/configure.ac
@@ -787,7 +787,6 @@ os (target)                 : $target_os
 compiler vendor             : ${ax_cv_cxx_compiler_vendor}
 compiler version            : ${ax_cv_gxx_version}
 ----- BUILD OPTIONS -----------------------------------
-#gauge group                 : `if test "${ac_ENABLE_SP}x" == "yesx"; then echo Sp2n; else echo SUn; fi`
 Nc                          : ${ac_Nc}
 SIMD                        : ${ac_SIMD}${SIMD_GEN_WIDTH_MSG}
 Threading                   : ${ac_openmp}
diff --git a/tests/sp2n/Test_Sp_start.cc b/tests/sp2n/Test_Sp_start.cc
index eaeb59f4..da19779f 100644
--- a/tests/sp2n/Test_Sp_start.cc
+++ b/tests/sp2n/Test_Sp_start.cc
@@ -14,54 +14,79 @@ int main (int argc, char **argv)
     GridRedBlackCartesian     RBGrid(&Grid);
     
     LatticeGaugeField Umu(&Grid);
-    LatticeGaugeField identity(&Grid);
     LatticeColourMatrixD U(&Grid);
-    LatticeColourMatrixD Cidentity(&Grid);
     LatticeColourMatrixD aux(&Grid);
-    
-    identity = 1.0;
-    Cidentity = 1.0;
-    Complex i(0., 1.);
+    LatticeGaugeField identity(&Grid);
+    LatticeColourMatrixD Cidentity(&Grid);
     
     double vol = Umu.Grid()->gSites();
-    
+
     const int nsp = Nc / 2;
+    identity = 1.;
+    Cidentity = 1.;
+    
     std::vector<int> pseeds({1,2,3,4,5});
     std::vector<int> sseeds({6,7,8,9,10});
     GridParallelRNG  pRNG(&Grid); pRNG.SeedFixedIntegers(pseeds);
     GridSerialRNG    sRNG;       sRNG.SeedFixedIntegers(sseeds);
     
     std::cout << GridLogMessage << std::endl;
-    
-    
+    std::cout << GridLogMessage << "-------" << std::endl;
+    std::cout << GridLogMessage << "Checking Cold Configuration " << std::endl;
+    std::cout << GridLogMessage << std::endl;
     Sp<nsp>::ColdConfiguration(pRNG,Umu);
+    Sp<nsp>::OmegaInvariance(Umu);
+    std::cout << GridLogMessage << std::endl;
+
     Umu = Umu - identity;
     U = PeekIndex<LorentzIndex>(Umu,1);
     
     std::cout << GridLogMessage << "U - 1 = " << norm2(sum(U)) << std::endl;
     assert ( norm2(sum(U)) < 1e-6);
     std::cout << GridLogMessage << std::endl;
-    
-    std::cout << GridLogMessage << "Hot Start " << std::endl;
+    std::cout << GridLogMessage << "-------" << std::endl;
+    std::cout << GridLogMessage << "Checking Hot Configuration" << std::endl;
+    std::cout << GridLogMessage << std::endl;
     Sp<nsp>::HotConfiguration(pRNG,Umu);
+    Sp<nsp>::OmegaInvariance(Umu);
+    std::cout << GridLogMessage << std::endl;
+    U = PeekIndex<LorentzIndex>(Umu,1);
+    std::cout << GridLogMessage << "Checking unitarity " << std::endl;
+    aux = U*adj(U) - Cidentity;
+    assert( norm2(aux) < 1e-6 );
+    std::cout << GridLogMessage << "ok" << std::endl;
+    std::cout << GridLogMessage << std::endl;
+    std::cout << GridLogMessage << "Checking determinant " << std::endl;
+    std::cout << GridLogMessage << "Det = " <<  norm2( Determinant(U) )/vol << std::endl;
+    std::cout << GridLogMessage << std::endl;
+    std::cout << GridLogMessage << "-------" << std::endl;
+    std::cout << GridLogMessage << "Checking Tepid Configuration" << std::endl;
+    std::cout << GridLogMessage << std::endl;
+    Sp<nsp>::TepidConfiguration(pRNG,Umu);
+    Sp<nsp>::OmegaInvariance(Umu);
+    std::cout << GridLogMessage << std::endl;
     U = PeekIndex<LorentzIndex>(Umu,1);
-    
     std::cout << GridLogMessage << "Checking unitarity " << std::endl;
-    
     aux = U*adj(U) - Cidentity;
-
     assert( norm2(aux) < 1e-6 );
-    
     std::cout << GridLogMessage << "ok" << std::endl;
     std::cout << GridLogMessage << std::endl;
-    
     std::cout << GridLogMessage << "Checking determinant " << std::endl;
     std::cout << GridLogMessage << "Det = " <<  norm2( Determinant(U) )/vol << std::endl;
     std::cout << GridLogMessage << std::endl;
     
-    std::cout << GridLogMessage << "Checking the matrix is in Sp2n " << std::endl;
-    std::cout << GridLogMessage << std::endl;
     
+     
+    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;
+    
+    Complex i(0., 1.);
+    
+    
+    Sp<nsp>::HotConfiguration(pRNG,Umu);
+    U = PeekIndex<LorentzIndex>(Umu,0);
     for (int c1 = 0; c1 < nsp; c1++) //check on W
     {
         for (int c2 = 0; c2 < nsp; c2++)
@@ -71,17 +96,14 @@ int main (int argc, char **argv)
             auto Ww = conjugate( Wstar );
             auto amizero = sum(W - Ww);
             auto amizeroo = TensorRemove(amizero);
-            std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
+            //std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
             assert(  amizeroo.real() < 10e-6 );
             amizeroo *= i;
             assert(  amizeroo.real() < 10e-6 );
-            std::cout << GridLogMessage << "ok " << std::endl;
+            //std::cout << GridLogMessage << "ok " << std::endl;
         }
         
     }
-    std::cout <<GridLogMessage << std::endl;
-    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;
-    std::cout <<GridLogMessage << std::endl;
     for (int c1 = 0; c1 < nsp ; c1++)
     {
         for (int c2 = 0; c2 < nsp; c2++)
@@ -91,27 +113,18 @@ int main (int argc, char **argv)
             auto minusXx = conjugate(minusXstar);
             auto amizero = sum (X + minusXx);
             auto amizeroo = TensorRemove(amizero);
-            std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
+            //std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
             assert(  amizeroo.real() < 10e-6 );
             amizeroo *= i;
             assert(  amizeroo.real() < 10e-6 );
-            std::cout << GridLogMessage << "ok " << std::endl;
+            //std::cout << GridLogMessage << "ok " << std::endl;
         }
     }
     
+    std::cout << GridLogMessage << "Hot start ok " << std::endl;
     
-    std::vector<int> ppseeds({11,12,13,14,15});
-    std::vector<int> ssseeds({16,17,18,19,20});
-    GridParallelRNG  ppRNG(&Grid); pRNG.SeedFixedIntegers(ppseeds);
-    GridSerialRNG    ssRNG;       sRNG.SeedFixedIntegers(ssseeds);
-    
-    std::cout << GridLogMessage << std::endl;
-    std::cout << GridLogMessage << "Testing gauge implementation " << std::endl;
-    
-    SymplPeriodicGimplR::HotConfiguration(ppRNG, Umu);
-    
-    U = PeekIndex<LorentzIndex>(Umu,1);
-    
+    Sp<nsp>::HotConfiguration(pRNG,Umu);
+    U = PeekIndex<LorentzIndex>(Umu,0);
     for (int c1 = 0; c1 < nsp; c1++) //check on W
     {
         for (int c2 = 0; c2 < nsp; c2++)
@@ -121,17 +134,14 @@ int main (int argc, char **argv)
             auto Ww = conjugate( Wstar );
             auto amizero = sum(W - Ww);
             auto amizeroo = TensorRemove(amizero);
-            std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
+            //std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
             assert(  amizeroo.real() < 10e-6 );
             amizeroo *= i;
             assert(  amizeroo.real() < 10e-6 );
-            std::cout << GridLogMessage << "ok " << std::endl;
+            //std::cout << GridLogMessage << "ok " << std::endl;
         }
         
     }
-    std::cout <<GridLogMessage << std::endl;
-    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;
-    std::cout <<GridLogMessage << std::endl;
     for (int c1 = 0; c1 < nsp ; c1++)
     {
         for (int c2 = 0; c2 < nsp; c2++)
@@ -141,15 +151,17 @@ int main (int argc, char **argv)
             auto minusXx = conjugate(minusXstar);
             auto amizero = sum (X + minusXx);
             auto amizeroo = TensorRemove(amizero);
-            std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
+            //std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
             assert(  amizeroo.real() < 10e-6 );
             amizeroo *= i;
             assert(  amizeroo.real() < 10e-6 );
-            std::cout << GridLogMessage << "ok " << std::endl;
+            //std::cout << GridLogMessage << "ok " << std::endl;
         }
     }
     
+    std::cout << GridLogMessage << "Tepid start ok " << std::endl;
     
+    std::cout << GridLogMessage << std::endl;
     
     Grid_finalize();
 
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index d494d828..4e14938e 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -4,7 +4,7 @@ using namespace Grid;
 
 int main (int argc, char **argv)
 {
-     Grid_init(&argc,&argv);
+    Grid_init(&argc,&argv);
     
     
     Coordinate latt_size   = GridDefaultLatt();
@@ -20,6 +20,8 @@ int main (int argc, char **argv)
     LatticeColourMatrixD aux(&Grid);
     LatticeColourMatrixD identity(&Grid);
     
+    const int nsp = Nc / 2;
+    
     identity = 1.0;
     RealD epsilon = 0.01;
     Complex i(0., 1.);
@@ -34,20 +36,28 @@ int main (int argc, char **argv)
     SU<Nc>::HotConfiguration(pRNG,Umu);
     U = PeekIndex<LorentzIndex>(Umu,2);
     
-    // it is unitary
     aux = U*adj(U) - identity;
     std::cout <<GridLogMessage << std::endl;
-    std::cout << GridLogMessage << "Unitary check of starting random SUn matrix " << std::endl;
+    std::cout << GridLogMessage << "Starting with random SUn matrix " << std::endl;
+    std::cout << GridLogMessage << "Unitary check " << std::endl;
     std::cout <<GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+    assert ( norm2(aux) < 1e-8 );
     std::cout <<GridLogMessage << std::endl;
+    if (Nc != 2)
+    {
+        std::cout << "This matrix should not leave Omega invariant, expect a warning" << std::endl;
+    }
+    Sp<nsp>::OmegaInvariance(U);
     std::cout <<GridLogMessage << std::endl;
     
     U = U + epsilon*identity;
     aux = U*adj(U) - identity;
     
-    std::cout << GridLogMessage << "Unitary matrix modified " << std::endl;
+    std::cout << GridLogMessage << "Unitary matrix deformed " << std::endl;
     std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl;
     std::cout <<GridLogMessage << std::endl;
+    std::cout << "This matrix should not leave Omega invariant, expect a warning" << std::endl;
+    Sp<nsp>::OmegaInvariance(U);
     std::cout <<GridLogMessage << std::endl;
     std::cout << GridLogMessage << "Projecting on Sp2n " << std::endl;
 
@@ -65,18 +75,17 @@ int main (int argc, char **argv)
     std::cout << GridLogMessage << "Det after Projection on Sp2n = " << norm2( Determinant(U) ) / vol << std::endl;
     std::cout <<GridLogMessage << std::endl;
     std::cout <<GridLogMessage << std::endl;
+    
+    // actual sp2n check
+    std::cout << GridLogMessage << "Checking invariance after projection "<< std::endl;
+    Sp<nsp>::OmegaInvariance(U);
+    
     // checks on elements
-    // an Sp2n matrix is a block matrix of the type
-    //
-    //
-    //     U = (    W       X   )
-    //         (    -X^*    W^* )
-    //
-    // will check this
-    //
-    std::cout << GridLogMessage << "Checking that U[ i , j ] - conj U[ i+N/2, j+N/2 ] = 0 for i = 0, ... , N/2 " << std::endl;
+
+    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;
-    const int nsp = Nc / 2;
     for (int c1 = 0; c1 < nsp; c1++) //check on W
     {
         for (int c2 = 0; c2 < nsp; c2++)
@@ -86,17 +95,13 @@ int main (int argc, char **argv)
             auto Ww = conjugate( Wstar );
             auto amizero = sum(W - Ww);
             auto amizeroo = TensorRemove(amizero);
-            std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
             assert(  amizeroo.real() < 10e-6 );
             amizeroo *= i;
             assert(  amizeroo.real() < 10e-6 );
-            std::cout << GridLogMessage << "ok " << std::endl;
         }
         
     }
-    std::cout <<GridLogMessage << std::endl;
-    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;
-    std::cout <<GridLogMessage << std::endl;
+
     for (int c1 = 0; c1 < nsp ; c1++)
     {
         for (int c2 = 0; c2 < nsp; c2++)
@@ -106,16 +111,16 @@ int main (int argc, char **argv)
             auto minusXx = conjugate(minusXstar);
             auto amizero = sum (X + minusXx);
             auto amizeroo = TensorRemove(amizero);
-            std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
             assert(  amizeroo.real() < 10e-6 );
             amizeroo *= i;
             assert(  amizeroo.real() < 10e-6 );
-            std::cout << GridLogMessage << "ok " << std::endl;
         }
     }
     
+    std::cout << GridLogMessage << "ok" << std::endl;
     
     // an explicit check for sp2
+    /*
     if (Nc == 2)
     {
         assert(Nc==2);
@@ -141,13 +146,7 @@ int main (int argc, char **argv)
         std::cout << GridLogMessage << "now A = " << A << std::endl;
         std::cout << GridLogMessage << "A(0,0) - conjA(1,1) = " << A()()(0,0) - adj ( A()()(1,1) )<< std::endl;
         std::cout << GridLogMessage << "A(0,1) + conjA(1,0) = " << A()()(0,1) + adj ( A()()(1,0) )<< std::endl;
-    }
-    
-    
-    
-    
-    
-    
+    }*/
     
     Grid_finalize();
 

From 4d8ae6221c37a55521c3f0307f43e41ae131ce62 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 22 Oct 2021 10:44:54 +0100
Subject: [PATCH 020/129] fix projection

---
 Grid/qcd/utils/Sp2n.h            |  9 ++--
 Grid/tensors/Tensor_Ta.h         | 75 ++++++++++++++++++++++++++++++--
 tests/sp2n/Test_project_on_Sp.cc | 12 ++---
 3 files changed, 84 insertions(+), 12 deletions(-)

diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.h
index ad6933e3..8b4a1a93 100644
--- a/Grid/qcd/utils/Sp2n.h
+++ b/Grid/qcd/utils/Sp2n.h
@@ -493,13 +493,14 @@ public:
            
            for (int i = 0; i < ncolour; i++)
            {
-               Omega()()(i, 2*ncolour-1-i) = 1.;
-               Omega()()(2*ncolour-1-i, i) = -1;
+               Omega()()(i, ncolour+i) = 1.;
+               Omega()()(ncolour+i, i) = -1;
            }
-    
+           
+           std::cout << GridLogMessage << "Omega = " << Omega()() << std::endl;
            OmegaLatt = OmegaLatt + (identity*Omega);
            
-           auto diff = OmegaLatt - (in*Omega*transpose(in));
+           auto diff = OmegaLatt - (in*OmegaLatt*transpose(in));
            auto sdiff = sum(diff);
            //assert( norm2(sdiff) < 1e-8 );
            if (norm2(sdiff) < 1e-8)
diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index 7b4bccca..a82fa7aa 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -156,6 +156,75 @@ template<class vtype,int N> accelerator_inline iVector<vtype,N> ProjectOnSpGroup
 // int N is 2n in Sp(2n)
 template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
 accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg)
+{
+  // need a check for the group type?
+  iMatrix<vtype,N> ret(arg);
+  vtype nrm;
+  vtype inner;
+  vtype tmp;
+  
+  for(int c1=0;c1<N/2;c1++)
+  {
+      
+      for (int b=0; b<c1; b++)                  // remove the b-rows from U_c1
+      {
+          decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
+          decltype(ret._internal[b][b]*ret._internal[b][b]) prn;
+          zeroit(pr);
+          zeroit(prn);
+          
+          for(int c=0; c<N; c++)
+          {
+              pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];        // <U_c1 | U_b >
+              prn += conjugate(ret._internal[c1][c])*ret._internal[b+N/2][c];   // <U_c1 | U_{b+N} >
+          }
+       
+
+          for(int c=0; c<N; c++)
+          {
+              ret._internal[c1][c] -= (conjugate(pr) * ret._internal[b][c] + conjugate(prn) * ret._internal[b+N/2][c] );    //  U_c1 -= (  <U_c1 | U_b > U_b + <U_c1 | U_{b+N} > U_{b+N}  )
+          }
+      }
+    
+      zeroit(inner);
+      for(int c2=0;c2<N;c2++)
+      {
+          inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
+      }
+      
+      nrm = sqrt(inner);
+      nrm = 1.0/nrm;
+      for(int c2=0;c2<N;c2++)
+      {
+          ret._internal[c1][c2]*= nrm;
+      }
+      
+
+      for(int c2=0;c2<N/2;c2++)
+      {
+          tmp = conjugate(ret._internal[c1][c2]);       // (up-left)* of the old matrix
+          ret._internal[c1+N/2][c2+N/2] = tmp;          // down right in the new matrix = (up-left)* of the old matrix
+      }
+         
+      for(int c2=N/2;c2<N;c2++)
+      {
+          tmp = conjugate(ret._internal[c1][c2]);   // (up-right)* of the old
+          ret._internal[c1+N/2][c2-N/2] = -tmp;     // down left in the new matrix = -(up-right)* of the old
+      }
+    
+      
+  }
+  return ret;
+}
+
+
+
+
+
+
+/*
+template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
+accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg)
 {
   // need a check for the group type?
   iMatrix<vtype,N> ret(arg);
@@ -175,7 +244,7 @@ accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg
 
     // Compute row c1+N2/2: c1+N/2 = - \Omega c1*
     for(int c2=0;c2<N/2;c2++)
-      ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
+      ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]); // lupo: c1,c2? dont we want c1 c2+N/2
 
     for(int c2=N/2;c2<N;c2++)
       ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
@@ -203,7 +272,7 @@ accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg
         ret._internal[b][c] -= pr * ret._internal[c1+N/2][c];
       }
     }
-  }
+  } //end c1 0, ... N/2-1 loop
 
   // Compute the last row
   {
@@ -227,7 +296,7 @@ accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg
   }
   // assuming the determinant is ok
   return ret;
-}
+}*/
 
 
 NAMESPACE_END(Grid);
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 4e14938e..71c6acc7 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -45,7 +45,7 @@ int main (int argc, char **argv)
     std::cout <<GridLogMessage << std::endl;
     if (Nc != 2)
     {
-        std::cout << "This matrix should not leave Omega invariant, expect a warning" << std::endl;
+        std::cout << GridLogMessage << "This matrix should not leave Omega invariant, expect a warning" << std::endl;
     }
     Sp<nsp>::OmegaInvariance(U);
     std::cout <<GridLogMessage << std::endl;
@@ -56,18 +56,18 @@ int main (int argc, char **argv)
     std::cout << GridLogMessage << "Unitary matrix deformed " << std::endl;
     std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl;
     std::cout <<GridLogMessage << std::endl;
-    std::cout << "This matrix should not leave Omega invariant, expect a warning" << std::endl;
-    Sp<nsp>::OmegaInvariance(U);
+
     std::cout <<GridLogMessage << std::endl;
     std::cout << GridLogMessage << "Projecting on Sp2n " << std::endl;
 
     U = ProjectOnSpGroup(U);
+    //U = ProjectOnGroup(U);
     aux = U*adj(U) - identity;
     std::cout <<GridLogMessage << std::endl;
     std::cout <<GridLogMessage << std::endl;
     std::cout << GridLogMessage << "Unitary check after Sp(2n) projection " << std::endl;
     std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-6);
+    assert( norm2(aux) < 1e-8);
     std::cout <<GridLogMessage << std::endl;
     std::cout <<GridLogMessage << std::endl;
     
@@ -81,7 +81,9 @@ int main (int argc, char **argv)
     Sp<nsp>::OmegaInvariance(U);
     
     // checks on elements
-
+    
+    std::cout <<GridLogMessage << std::endl;
+    std::cout <<GridLogMessage << std::endl;
     std::cout << GridLogMessage << "Checking the structure is " << std::endl;
     std::cout << GridLogMessage << "U  =  (   W    X   )  " << std::endl;
     std::cout << GridLogMessage << "      (  -X^*  W^* )  " << std::endl;

From 4044536eeab701bb49c2b233b9ef928de2492b7e Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 26 Oct 2021 10:20:44 +0100
Subject: [PATCH 021/129] add projection on sp2n algebra

---
 Grid/qcd/action/gauge/GaugeImplTypes.h    |  32 ++++++-
 Grid/tensors/Tensor_Ta.h                  |  85 +-----------------
 tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc | 100 ++++++++++++++++++++++
 3 files changed, 134 insertions(+), 83 deletions(-)
 create mode 100644 tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc

diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index 8e418209..dbab4386 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -140,8 +140,38 @@ public:
       PokeIndex<LorentzIndex>(P, Pmu, mu);
     }
   }
+    
+    
 
-  static inline Field projectForce(Field &P) { return Ta(P); }
+  static inline Field projectForce(Field &P)
+    {
+        if (isSp2n == true)
+        {
+            P = Ta(P);
+            const int nsp = Nc / 2;
+
+            Sp<nsp>::iSp2nMatrix<Complex> gen;
+            
+
+            auto Psum = P;
+
+            Psum = Zero();
+            
+            for (int a = 0; a < Sp<nsp>::AlgebraDimension; a++)
+            {
+                Sp<nsp>::generator(a, gen);
+
+                auto coeff = 2. * trace(P * gen);
+                Psum += coeff * gen;
+            }
+            
+            return Psum;
+            
+        } else
+        {
+            return Ta(P);
+        }
+    }
 
   static inline void update_field(Field& P, Field& U, double ep){
     //static std::chrono::duration<double> diff;
diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index a82fa7aa..2ee51fb4 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -137,6 +137,9 @@ accelerator_inline iMatrix<vtype,N> ProjectOnGroup(const iMatrix<vtype,N> &arg)
 
 // re-do for sp2n
 
+// Ta cannot be defined here for Sp2n because I need the generators from the Sp class
+// It is defined in gauge impl types
+
 template<class vtype> accelerator_inline iScalar<vtype> ProjectOnSpGroup(const iScalar<vtype>&r)
 {
   iScalar<vtype> ret;
@@ -217,88 +220,6 @@ accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg
   return ret;
 }
 
-
-
-
-
-
-/*
-template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
-accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg)
-{
-  // need a check for the group type?
-  iMatrix<vtype,N> ret(arg);
-  vtype nrm;
-  vtype inner;
-  for(int c1=0;c1<N/2;c1++){
-
-    // Normalises row c1
-    zeroit(inner);
-    for(int c2=0;c2<N;c2++)
-      inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
-
-    nrm = sqrt(inner);
-    nrm = 1.0/nrm;
-    for(int c2=0;c2<N;c2++)
-      ret._internal[c1][c2]*= nrm;
-
-    // Compute row c1+N2/2: c1+N/2 = - \Omega c1*
-    for(int c2=0;c2<N/2;c2++)
-      ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]); // lupo: c1,c2? dont we want c1 c2+N/2
-
-    for(int c2=N/2;c2<N;c2++)
-      ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
-
-    // Remove c1 from rows c1+1...N/2-1
-    for (int b=c1+1; b<N/2; ++b){
-      decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
-      zeroit(pr);
-      for(int c=0; c<N; ++c)
-        pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];
-
-      for(int c=0; c<N; ++c){
-        ret._internal[b][c] -= pr * ret._internal[c1][c];
-      }
-    }
-
-    // Remove c1+N/2 from rows c1+1...N/2-1
-    for (int b=c1+1; b<N; ++b){
-      decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
-      zeroit(pr);
-      for(int c=0; c<N; ++c)
-        pr += conjugate(ret._internal[c1+N/2][c])*ret._internal[b][c];
-
-      for(int c=0; c<N; ++c){
-        ret._internal[b][c] -= pr * ret._internal[c1+N/2][c];
-      }
-    }
-  } //end c1 0, ... N/2-1 loop
-
-  // Compute the last row
-  {
-  // Normalise last row
-    int c1 = N/2-1;
-    zeroit(inner);
-    for(int c2=0;c2<N;c2++)
-      inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
-
-    nrm = sqrt(inner);
-    nrm = 1.0/nrm;
-    for(int c2=0;c2<N;c2++)
-      ret._internal[c1][c2]*= nrm;
-
-  // Compute row cN-1+N2/2: cN-1+N/2 = - \Omega cN-1*
-    for(int c2=0;c2<N/2;c2++)
-      ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);
-
-    for(int c2=N/2;c2<N;c2++)
-      ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);
-  }
-  // assuming the determinant is ok
-  return ret;
-}*/
-
-
 NAMESPACE_END(Grid);
 
 #endif
diff --git a/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc b/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc
new file mode 100644
index 00000000..64049ec2
--- /dev/null
+++ b/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc
@@ -0,0 +1,100 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./tests/Test_hmc_WilsonFermionGauge.cc
+
+Copyright (C) 2015
+
+Author: Peter Boyle <pabobyle@ph.ed.ac.uk>
+Author: neo <cossu@post.kek.jp>
+Author: Guido Cossu <guido.cossu@ed.ac.uk>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#include <Grid/Grid.h>
+
+int main(int argc, char **argv) 
+{
+  using namespace Grid;
+
+  Grid_init(&argc, &argv);
+  GridLogLayout();
+
+  typedef GenericSp2nHMCRunner<MinimumNorm2> HMCWrapper;
+  HMCWrapper TheHMC;
+
+
+  TheHMC.Resources.AddFourDimGrid("gauge");
+
+
+
+  // Checkpointer definition
+  CheckpointerParameters CPparams;  
+  CPparams.config_prefix = "ckpoint_lat";
+  CPparams.rng_prefix = "ckpoint_rng";
+  CPparams.saveInterval = 5;
+  CPparams.format = "IEEE64BIG";
+  
+  TheHMC.Resources.LoadNerscCheckpointer(CPparams);
+
+  RNGModuleParameters RNGpar;
+  RNGpar.serial_seeds = "12 22 32 42 52";
+  RNGpar.parallel_seeds = "76 77 87 79 70";
+  TheHMC.Resources.SetRNGSeeds(RNGpar);
+
+  // Construct observables
+  // here there is too much indirection 
+  typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
+  typedef TopologicalChargeMod<HMCWrapper::ImplPolicy> QObs;
+  TheHMC.Resources.AddObservable<PlaqObs>();
+  TopologyObsParameters TopParams;
+  TopParams.interval = 5;
+  TopParams.do_smearing = true;
+  TopParams.Smearing.steps = 200;
+  TopParams.Smearing.step_size = 0.01;
+  TopParams.Smearing.meas_interval = 50;
+  TopParams.Smearing.maxTau = 2.0; 
+  TheHMC.Resources.AddObservable<QObs>(TopParams);
+  //////////////////////////////////////////////
+
+  /////////////////////////////////////////////////////////////
+  // Collect actions, here use more encapsulation
+  // need wrappers of the fermionic classes 
+  // that have a complex construction
+  // standard
+  RealD beta = 8.0 ;
+  SymplWilsonGaugeActionR Waction(beta);
+  
+  ActionLevel<HMCWrapper::Field> Level1(1);
+  Level1.push_back(&Waction);
+  //Level1.push_back(WGMod.getPtr());
+  TheHMC.TheAction.push_back(Level1);
+  /////////////////////////////////////////////////////////////
+
+  // HMC parameters are serialisable 
+  TheHMC.Parameters.MD.MDsteps = 10;
+  TheHMC.Parameters.MD.trajL   = 1.0;
+
+  TheHMC.ReadCommandLine(argc, argv); // these can be parameters from file
+  TheHMC.Run();  // no smearing
+
+  Grid_finalize();
+
+} // main

From 88bdd4344b8763214f3856c6e9b20bcca04afe20 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Thu, 4 Nov 2021 18:27:35 +0000
Subject: [PATCH 022/129] 2indx antisymm representation of sp2n

---
 Grid/Makefile.am                              |   1 +
 Grid/qcd/action/fermion/Fermion.h             |  13 +-
 Grid/qcd/action/fermion/WilsonImpl.h          |  10 +-
 ...ationSpWilsonTwoIndexAntiSymmetricImplD.cc |   1 +
 ...ationSpWilsonTwoIndexAntiSymmetricImplD.cc |   1 +
 ...ationSpWilsonTwoIndexAntiSymmetricImplD.cc |   1 +
 ...ationSpWilsonTwoIndexAntiSymmetricImplD.cc |   1 +
 .../SpWilsonTwoIndexAntiSymmetricImplD/impl.h |   1 +
 ...ationSpWilsonTwoIndexAntiSymmetricImplF.cc |   1 +
 ...ationSpWilsonTwoIndexAntiSymmetricImplF.cc |   1 +
 ...ationSpWilsonTwoIndexAntiSymmetricImplF.cc |   1 +
 ...ationSpWilsonTwoIndexAntiSymmetricImplF.cc |   1 +
 .../SpWilsonTwoIndexAntiSymmetricImplF/impl.h |   1 +
 ...antiationSpWilsonTwoIndexSymmetricImplD.cc |   1 +
 ...antiationSpWilsonTwoIndexSymmetricImplD.cc |   1 +
 ...antiationSpWilsonTwoIndexSymmetricImplD.cc |   1 +
 ...antiationSpWilsonTwoIndexSymmetricImplD.cc |   1 +
 .../SpWilsonTwoIndexSymmetricImplD/impl.h     |   1 +
 ...antiationSpWilsonTwoIndexSymmetricImplF.cc |   1 +
 ...antiationSpWilsonTwoIndexSymmetricImplF.cc |   1 +
 ...antiationSpWilsonTwoIndexSymmetricImplF.cc |   1 +
 ...antiationSpWilsonTwoIndexSymmetricImplF.cc |   1 +
 .../SpWilsonTwoIndexSymmetricImplF/impl.h     |   1 +
 .../instantiation/generate_instantiations.sh  |   4 +
 Grid/qcd/representations/Representations.h    |   1 +
 Grid/qcd/representations/hmc_types.h          |   2 +
 Grid/qcd/representations/sp_two_index.h       | 100 ++++++
 Grid/qcd/utils/Sp2n.h                         |  27 +-
 Grid/qcd/utils/Sp2nTwoIndex.h                 | 320 ++++++++++++++++++
 Grid/qcd/utils/Utils.h                        |   1 +
 configure.ac                                  |   9 +-
 scripts/filelist                              |   2 +
 tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc     | 102 ++++++
 .../sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc |  82 +++++
 34 files changed, 687 insertions(+), 7 deletions(-)
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc
 create mode 100644 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/impl.h
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc
 create mode 100644 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/impl.h
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
 create mode 100644 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
 create mode 100644 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h
 create mode 100644 Grid/qcd/representations/sp_two_index.h
 create mode 100644 Grid/qcd/utils/Sp2nTwoIndex.h
 create mode 100644 tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc
 create mode 100644 tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc

diff --git a/Grid/Makefile.am b/Grid/Makefile.am
index fda92792..fcb5670a 100644
--- a/Grid/Makefile.am
+++ b/Grid/Makefile.am
@@ -66,6 +66,7 @@ if BUILD_FERMION_REPS
   extra_sources+=$(SP_FERMION_FILES)
   extra_sources+=$(ADJ_FERMION_FILES)
   extra_sources+=$(TWOIND_FERMION_FILES)
+  extra_sources+=$(SP_TWOIND_FILES)
 endif
 
 lib_LIBRARIES = libGrid.a
diff --git a/Grid/qcd/action/fermion/Fermion.h b/Grid/qcd/action/fermion/Fermion.h
index b988b306..dac3478e 100644
--- a/Grid/qcd/action/fermion/Fermion.h
+++ b/Grid/qcd/action/fermion/Fermion.h
@@ -115,11 +115,22 @@ typedef WilsonFermion<WilsonImplR> WilsonFermionR;
 typedef WilsonFermion<WilsonImplF> WilsonFermionF;
 typedef WilsonFermion<WilsonImplD> WilsonFermionD;
 
-
+// sp
 typedef WilsonFermion<SpWilsonImplR> SpWilsonFermionR;
 typedef WilsonFermion<SpWilsonImplF> SpWilsonFermionF;
 typedef WilsonFermion<SpWilsonImplD> SpWilsonFermionD;
 
+typedef WilsonFermion<SpWilsonTwoIndexAntiSymmetricImplR> SpWilsonTwoIndexAntiSymmetricFermionR;
+typedef WilsonFermion<SpWilsonTwoIndexAntiSymmetricImplF> SpWilsonTwoIndexAntiSymmetricFermionF;
+typedef WilsonFermion<SpWilsonTwoIndexAntiSymmetricImplD> SpWilsonTwoIndexAntiSymmetricFermionD;
+
+typedef WilsonFermion<SpWilsonTwoIndexSymmetricImplR> SpWilsonTwoIndexSymmetricFermionR;
+typedef WilsonFermion<SpWilsonTwoIndexSymmetricImplF> SpWilsonTwoIndexSymmetricFermionF;
+typedef WilsonFermion<SpWilsonTwoIndexSymmetricImplD> SpWilsonTwoIndexSymmetricFermionD;
+
+// end sp
+
+
 //typedef WilsonFermion<WilsonImplRL> WilsonFermionRL;
 //typedef WilsonFermion<WilsonImplFH> WilsonFermionFH;
 //typedef WilsonFermion<WilsonImplDF> WilsonFermionDF;
diff --git a/Grid/qcd/action/fermion/WilsonImpl.h b/Grid/qcd/action/fermion/WilsonImpl.h
index 01545d3b..0a9ef773 100644
--- a/Grid/qcd/action/fermion/WilsonImpl.h
+++ b/Grid/qcd/action/fermion/WilsonImpl.h
@@ -273,9 +273,13 @@ typedef WilsonImpl<vComplex,  SpFundamentalRepresentation, CoeffReal > SpWilsonI
 typedef WilsonImpl<vComplexF, SpFundamentalRepresentation, CoeffReal > SpWilsonImplF;  // Float
 typedef WilsonImpl<vComplexD, SpFundamentalRepresentation, CoeffReal > SpWilsonImplD;  // Double
 
-//typedef WilsonImpl<vComplex,  SpFundamentalRepresentation, CoeffComplex > SpZWilsonImplR; // Real.. whichever prec
-//typedef WilsonImpl<vComplexF, SpFundamentalRepresentation, CoeffComplex > SpZWilsonImplF; // Float
-//typedef WilsonImpl<vComplexD, SpFundamentalRepresentation, CoeffComplex > SpZWilsonImplD; // Double
+typedef WilsonImpl<vComplex,  SpTwoIndexAntiSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexAntiSymmetricImplR;  // Real.. whichever prec
+typedef WilsonImpl<vComplexF, SpTwoIndexAntiSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexAntiSymmetricImplF;  // Float
+typedef WilsonImpl<vComplexD, SpTwoIndexAntiSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexAntiSymmetricImplD;  // Double
+
+typedef WilsonImpl<vComplex,  SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexSymmetricImplR;  // Real.. whichever prec
+typedef WilsonImpl<vComplexF, SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexSymmetricImplF;  // Float
+typedef WilsonImpl<vComplexD, SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexSymmetricImplD;  // Double
 
 
 NAMESPACE_END(Grid);
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc
new file mode 120000
index 00000000..9cc05107
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc
@@ -0,0 +1 @@
+../WilsonCloverFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc
new file mode 120000
index 00000000..5f6ab65e
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc
@@ -0,0 +1 @@
+../WilsonFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc
new file mode 120000
index 00000000..01c35e7b
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc
@@ -0,0 +1 @@
+../WilsonKernelsInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc
new file mode 120000
index 00000000..d5789bcf
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc
@@ -0,0 +1 @@
+../WilsonTMFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/impl.h b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/impl.h
new file mode 100644
index 00000000..4c546322
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/impl.h
@@ -0,0 +1 @@
+#define IMPLEMENTATION SpWilsonTwoIndexAntiSymmetricImplD
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc
new file mode 120000
index 00000000..9cc05107
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc
@@ -0,0 +1 @@
+../WilsonCloverFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc
new file mode 120000
index 00000000..5f6ab65e
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc
@@ -0,0 +1 @@
+../WilsonFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc
new file mode 120000
index 00000000..01c35e7b
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc
@@ -0,0 +1 @@
+../WilsonKernelsInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc
new file mode 120000
index 00000000..d5789bcf
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc
@@ -0,0 +1 @@
+../WilsonTMFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/impl.h b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/impl.h
new file mode 100644
index 00000000..8425236e
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/impl.h
@@ -0,0 +1 @@
+#define IMPLEMENTATION SpWilsonTwoIndexAntiSymmetricImplF
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
new file mode 120000
index 00000000..9cc05107
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
@@ -0,0 +1 @@
+../WilsonCloverFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
new file mode 120000
index 00000000..5f6ab65e
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
@@ -0,0 +1 @@
+../WilsonFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc
new file mode 120000
index 00000000..01c35e7b
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc
@@ -0,0 +1 @@
+../WilsonKernelsInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
new file mode 120000
index 00000000..d5789bcf
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
@@ -0,0 +1 @@
+../WilsonTMFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h
new file mode 100644
index 00000000..ac5babca
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h
@@ -0,0 +1 @@
+#define IMPLEMENTATION SpWilsonTwoIndexSymmetricImplD
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
new file mode 120000
index 00000000..9cc05107
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
@@ -0,0 +1 @@
+../WilsonCloverFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
new file mode 120000
index 00000000..5f6ab65e
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
@@ -0,0 +1 @@
+../WilsonFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc
new file mode 120000
index 00000000..01c35e7b
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc
@@ -0,0 +1 @@
+../WilsonKernelsInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
new file mode 120000
index 00000000..d5789bcf
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
@@ -0,0 +1 @@
+../WilsonTMFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h
new file mode 100644
index 00000000..bea7dce7
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h
@@ -0,0 +1 @@
+#define IMPLEMENTATION SpWilsonTwoIndexSymmetricImplF
diff --git a/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh b/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh
index 9c834f6e..ef280054 100755
--- a/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh
+++ b/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh
@@ -17,6 +17,10 @@ WILSON_IMPL_LIST=" \
 	   WilsonTwoIndexSymmetricImplD \
 	   WilsonTwoIndexAntiSymmetricImplF \
 	   WilsonTwoIndexAntiSymmetricImplD \
+       SpWilsonTwoIndexAntiSymmetricImplF \
+       SpWilsonTwoIndexAntiSymmetricImplD \
+       SpWilsonTwoIndexSymmetricImplF \
+       SpWilsonTwoIndexSymmetricImplD \
 	   GparityWilsonImplF \
 	   GparityWilsonImplD "
 
diff --git a/Grid/qcd/representations/Representations.h b/Grid/qcd/representations/Representations.h
index d408b22a..8791f653 100644
--- a/Grid/qcd/representations/Representations.h
+++ b/Grid/qcd/representations/Representations.h
@@ -5,6 +5,7 @@
 #include <Grid/qcd/representations/two_index.h>
 #include <Grid/qcd/representations/fundamental.h>
 #include <Grid/qcd/representations/spfundamental.h>
+#include <Grid/qcd/representations/sp_two_index.h>
 #include <Grid/qcd/representations/hmc_types.h>
 
 #endif
diff --git a/Grid/qcd/representations/hmc_types.h b/Grid/qcd/representations/hmc_types.h
index 5e4ab020..a24d5752 100644
--- a/Grid/qcd/representations/hmc_types.h
+++ b/Grid/qcd/representations/hmc_types.h
@@ -4,6 +4,8 @@
 #include <Grid/qcd/representations/adjoint.h>
 #include <Grid/qcd/representations/two_index.h>
 #include <Grid/qcd/representations/fundamental.h>
+#include <Grid/qcd/representations/spfundamental.h>
+#include <Grid/qcd/representations/sp_two_index.h>
 #include <Grid/qcd/action/scalar/ScalarImpl.h>
 
 #include <tuple>
diff --git a/Grid/qcd/representations/sp_two_index.h b/Grid/qcd/representations/sp_two_index.h
new file mode 100644
index 00000000..d6884736
--- /dev/null
+++ b/Grid/qcd/representations/sp_two_index.h
@@ -0,0 +1,100 @@
+/*
+ *  Policy classes for the HMC
+ *  Authors: Guido Cossu, David Preti
+ */
+
+#ifndef SP2N2INDEX_H_H
+#define SP2N2INDEX_H_H
+
+NAMESPACE_BEGIN(Grid);
+
+/*
+ * This is an helper class for the HMC
+ * Should contain only the data for the two index representations
+ * and the facility to convert from the fundamental -> two index
+ * The templated parameter TwoIndexSymmetry choses between the 
+ * symmetric and antisymmetric representations
+ * 
+ * There is an 
+ * enum TwoIndexSymmetry { Symmetric = 1, AntiSymmetric = -1 };
+ * in the SUnTwoIndex.h file
+ */
+
+template <int ncolour, TwoIndexSymmetry S>
+class SpTwoIndexRep {
+public:
+  // typdef to be used by the Representations class in HMC to get the
+  // types for the higher representation fields
+  typedef typename Sp_TwoIndex<ncolour, S>::LatticeTwoIndexMatrix LatticeMatrix;
+  typedef typename Sp_TwoIndex<ncolour, S>::LatticeTwoIndexField LatticeField;
+  static const int Dimension = (ncolour * (ncolour + S) / 2) - 1;
+  static const bool isFundamental = false;
+  static const int nsp = Nc / 2;
+  LatticeField U;
+
+  explicit SpTwoIndexRep(GridBase *grid) : U(grid) {}
+
+  void update_representation(const LatticeGaugeField &Uin) {
+    std::cout << GridLogDebug << "Updating TwoIndex representation\n";
+    // Uin is in the fundamental representation
+    // get the U in TwoIndexRep
+    // (U)_{(ij)(lk)} = tr [ adj(e^(ij)) U e^(lk) transpose(U) ]
+    conformable(U, Uin);
+    U = Zero();
+    LatticeColourMatrix tmp(Uin.Grid());
+
+    Vector<typename Sp<nsp>::Matrix> eij(Dimension);
+
+    for (int a = 0; a < Dimension; a++)
+      Sp_TwoIndex<ncolour, S>::base(a, eij[a]);
+
+    for (int mu = 0; mu < Nd; mu++) {
+      auto Uin_mu = peekLorentz(Uin, mu);
+      auto U_mu = peekLorentz(U, mu);
+      for (int a = 0; a < Dimension; a++) {
+        tmp = transpose(Uin_mu) * adj(eij[a]) * Uin_mu;
+        for (int b = 0; b < Dimension; b++)
+          pokeColour(U_mu, trace(tmp * eij[b]), a, b);
+      }
+      pokeLorentz(U, U_mu, mu);
+    }
+  }
+
+  LatticeGaugeField RtoFundamentalProject(const LatticeField &in,
+                                          Real scale = 1.0) const {
+    LatticeGaugeField out(in.Grid());
+    out = Zero();
+
+    for (int mu = 0; mu < Nd; mu++) {
+      LatticeColourMatrix out_mu(in.Grid());  // fundamental representation
+      LatticeMatrix in_mu = peekLorentz(in, mu);
+
+      out_mu = Zero();
+
+      typename Sp<nsp>::LatticeAlgebraVector h(in.Grid());
+      projectOnAlgebra(h, in_mu, double(Nc + 2 * S));  // factor T(r)/T(fund)
+      FundamentalLieAlgebraMatrix(h, out_mu);          // apply scale only once
+      pokeLorentz(out, out_mu, mu);                     // should be 2 for sp4 as. ok
+    }
+    return out;
+  }
+
+private:
+  void projectOnAlgebra(typename Sp<nsp>::LatticeAlgebraVector &h_out,
+                        const LatticeMatrix &in, Real scale = 1.0) const {
+    Sp_TwoIndex<ncolour, S>::projectOnAlgebra(h_out, in, scale);
+  }
+
+  void FundamentalLieAlgebraMatrix(
+				   typename Sp<nsp>::LatticeAlgebraVector &h,
+				   typename Sp<nsp>::LatticeMatrix &out, Real scale = 1.0) const {
+    Sp<nsp>::FundamentalLieAlgebraMatrix(h, out, scale);
+  }
+};
+
+typedef SpTwoIndexRep<Nc, Symmetric> SpTwoIndexSymmetricRepresentation;
+typedef SpTwoIndexRep<Nc, AntiSymmetric> SpTwoIndexAntiSymmetricRepresentation;
+
+NAMESPACE_END(Grid);
+
+#endif
diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.h
index 8b4a1a93..53ce3d5c 100644
--- a/Grid/qcd/utils/Sp2n.h
+++ b/Grid/qcd/utils/Sp2n.h
@@ -19,6 +19,7 @@ public:
     static const int Dimension = ncolour*2;
     static const int AlgebraDimension = ncolour*(2*ncolour +1);
     static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
+    static const int nnsp = ncolour;
     
     
     template <typename vtype>
@@ -368,6 +369,21 @@ public:
       out *= ci;
     }
     
+    static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
+                                            LatticeMatrix &out,
+                                            Real scale = 1.0) {
+      conformable(h, out);
+      GridBase *grid = out.Grid();
+      LatticeMatrix la(grid);
+      Matrix ta;
+
+      out = Zero();
+      for (int a = 0; a < AlgebraDimension; a++) {
+        generator(a, ta);
+        la = peekColour(h, a) * timesI(ta) * scale;
+        out += la;
+      }
+    }
     
     
     template <typename LatticeMatrixType>
@@ -388,7 +404,16 @@ public:
       }
     }
     
- 
+ static void projectOnAlgebra(LatticeAlgebraVector &h_out, const LatticeMatrix &in, Real scale = 1.0) {
+   conformable(h_out, in);
+   h_out = Zero();
+   Matrix Ta;
+
+   for (int a = 0; a < AlgebraDimension; a++) {
+     generator(a, Ta);
+     pokeColour(h_out, - 2.0 * (trace(timesI(Ta) * in)) * scale, a);
+   }
+ }
     
     
     template <typename GaugeField>
diff --git a/Grid/qcd/utils/Sp2nTwoIndex.h b/Grid/qcd/utils/Sp2nTwoIndex.h
new file mode 100644
index 00000000..60739551
--- /dev/null
+++ b/Grid/qcd/utils/Sp2nTwoIndex.h
@@ -0,0 +1,320 @@
+////////////////////////////////////////////////////////////////////////
+//
+// * Two index representation generators
+//
+// * Normalisation for the fundamental generators:
+//   trace ta tb = 1/2 delta_ab = T_F delta_ab
+//   T_F = 1/2  for SU(N) groups
+//
+//
+//   base for NxN two index (anti-symmetric) matrices
+//   normalized to 1 (d_ij is the kroenecker delta)
+//
+//   (e^(ij)_{kl} = 1 / sqrt(2) (d_ik d_jl +/- d_jk d_il)
+//
+//   Then the generators are written as
+//
+//   (iT_a)^(ij)(lk) = i * ( tr[e^(ij)^dag e^(lk) T^trasp_a] +
+//   tr[e^(lk)e^(ij)^dag T_a] )  //
+//   
+//
+////////////////////////////////////////////////////////////////////////
+
+// Authors: David Preti, Guido Cossu
+
+#ifndef QCD_UTIL_SP2N2INDEX_H
+#define QCD_UTIL_SP2N2INDEX_H
+
+
+NAMESPACE_BEGIN(Grid);
+
+//enum SpTwoIndexSymmetry { S = 1, AS = -1 };
+
+//inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
+
+template <int ncolour, TwoIndexSymmetry S>
+class Sp_TwoIndex : public Sp<Config_nsp> {
+public:
+  static const int nsp = ncolour/2;
+  static const int Dimension = nsp * (ncolour + S) - 1 ;
+  static const int NumGenerators = Sp<nsp>::AlgebraDimension;
+
+  template <typename vtype>
+  using iSp2nTwoIndexMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
+
+  typedef iSp2nTwoIndexMatrix<Complex> TIMatrix;
+  typedef iSp2nTwoIndexMatrix<ComplexF> TIMatrixF;
+  typedef iSp2nTwoIndexMatrix<ComplexD> TIMatrixD;
+
+  typedef iSp2nTwoIndexMatrix<vComplex> vTIMatrix;
+  typedef iSp2nTwoIndexMatrix<vComplexF> vTIMatrixF;
+  typedef iSp2nTwoIndexMatrix<vComplexD> vTIMatrixD;
+
+  typedef Lattice<vTIMatrix> LatticeTwoIndexMatrix;
+  typedef Lattice<vTIMatrixF> LatticeTwoIndexMatrixF;
+  typedef Lattice<vTIMatrixD> LatticeTwoIndexMatrixD;
+
+  typedef Lattice<iVector<iScalar<iMatrix<vComplex, Dimension> >, Nd> >
+  LatticeTwoIndexField;
+  typedef Lattice<iVector<iScalar<iMatrix<vComplexF, Dimension> >, Nd> >
+  LatticeTwoIndexFieldF;
+  typedef Lattice<iVector<iScalar<iMatrix<vComplexD, Dimension> >, Nd> >
+  LatticeTwoIndexFieldD;
+
+  template <typename vtype>
+  using iSp2nMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
+
+  typedef iSp2nMatrix<Complex> Matrix;
+  typedef iSp2nMatrix<ComplexF> MatrixF;
+  typedef iSp2nMatrix<ComplexD> MatrixD;
+
+  template <class cplx>
+  static void base(int Index, iSp2nMatrix<cplx> &eij) {
+    // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
+    assert(Index < NumGenerators);
+    eij = Zero();
+
+    // for the linearisation of the 2 indexes 
+    static int a[ncolour * (ncolour - 1) / 2][2]; // store the a <-> i,j
+    static bool filled = false;
+    if (!filled) {
+      int counter = 0;
+      for (int i = 1; i < ncolour; i++) {
+        for (int j = 0; j < i; j++) {
+           
+            if (i==nsp)
+            {
+                j = j+1;
+            }
+          a[counter][0] = i;
+          a[counter][1] = j;
+          counter++;
+        }
+      }
+      filled = true;
+    }
+
+    if (Index < ncolour * (ncolour - 1) / 2) {
+      baseOffDiagonal(a[Index][0], a[Index][1], eij);
+    } else {
+      baseDiagonal(Index, eij);
+    }
+  }
+    
+
+
+  template <class cplx>
+  static void baseDiagonal(int Index, iSp2nMatrix<cplx> &eij) {
+    eij = Zero();
+    eij()()(Index - ncolour * (ncolour - 1) / 2,
+            Index - ncolour * (ncolour - 1) / 2) = 1.0;
+  }
+
+  template <class cplx>
+  static void baseOffDiagonal(int i, int j, iSp2nMatrix<cplx> &eij) {
+    eij = Zero();
+    //std::cout << GridLogMessage << " doing i j = " << i << j << std::endl;
+      RealD tmp;
+
+    if ( (i == nsp + j) && (1 <= j) && (j < nsp) )
+        {
+            for (int k = 0; k < nsp; k++)
+            {
+                if (k < j)
+                {
+                    //std::cout << GridLogMessage << "b=N+a 1"<< std::endl;
+                    //std::cout << GridLogMessage << "j i "<< j << i << std::endl;
+                    tmp = sqrt( 2*j*(j+1)  );
+                    tmp = 1/tmp;
+                    tmp *= std::sqrt(2.0);
+                    eij()()(k,k+nsp) =  tmp;
+                    eij()()(k+nsp,k) =  - tmp;
+                }
+                if (k == j)
+                {
+                    //std::cout << GridLogMessage << "b=N+a 2"<< std::endl;
+                    //std::cout << GridLogMessage << "j i "<< j << i << std::endl;
+                    tmp = sqrt(2*j*(j+1)  );
+                    tmp = -j/tmp;
+                    tmp *= std::sqrt(2.0);
+                    eij()()(k,k+nsp) = tmp ;
+                    eij()()(k+nsp,k) = - tmp ;
+                 }
+            }
+            
+        }
+      
+      
+        else if (i != nsp+j)
+        {
+            for (int k = 0; k < ncolour; k++)
+                for (int l = 0; l < ncolour; l++)
+                {
+                    eij()()(l, k) = delta(i, k) * delta(j, l) + S * delta(j, k) * delta(i, l);
+                }
+            
+        }
+      
+          
+    
+        
+
+    RealD nrm = 1. / std::sqrt(2.0);
+    eij = eij * nrm;
+  }
+
+  static void printBase(void) {
+    for (int gen = 0; gen < Dimension; gen++) {
+      Matrix tmp;
+      base(gen, tmp);
+      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
+                << std::endl;
+      std::cout << GridLogMessage << tmp << std::endl;
+    }
+  }
+
+  template <class cplx>
+  static void generator(int Index, iSp2nTwoIndexMatrix<cplx> &i2indTa) {
+    Vector<typename Sp<nsp>::template iSp2nMatrix<cplx> > ta(
+								NumGenerators);
+    Vector<typename Sp<nsp>::template iSp2nMatrix<cplx> > eij(Dimension);
+    typename Sp<nsp>::template iSp2nMatrix<cplx> tmp;
+    i2indTa = Zero();
+    
+    for (int a = 0; a < NumGenerators; a++)
+      Sp<nsp>::generator(a, ta[a]);
+    
+    for (int a = 0; a < Dimension; a++) base(a, eij[a]);
+
+    for (int a = 0; a < Dimension; a++) {
+      tmp = transpose(ta[Index]) * adj(eij[a]) + adj(eij[a]) * ta[Index];
+      for (int b = 0; b < Dimension; b++) {
+        typename Sp<nsp>::template iSp2nMatrix<cplx> tmp1 =
+	  tmp * eij[b]; 
+        Complex iTr = TensorRemove(timesI(trace(tmp1)));
+        i2indTa()()(a, b) = iTr;
+      }
+    }
+  }
+
+  static void printGenerators(void) {
+    for (int gen = 0; gen < NumGenerators; gen++) {
+      TIMatrix i2indTa;
+      generator(gen, i2indTa);
+      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
+                << std::endl;
+      std::cout << GridLogMessage << i2indTa << std::endl;
+    }
+  }
+
+  static void testGenerators(void) {
+    TIMatrix i2indTa, i2indTb;
+    std::cout << GridLogMessage << "2IndexRep - Checking if traceless"
+              << std::endl;
+    for (int a = 0; a < NumGenerators; a++) {
+      generator(a, i2indTa);
+      std::cout << GridLogMessage << a << std::endl;
+      assert(norm2(trace(i2indTa)) < 1.0e-6);
+    }
+    std::cout << GridLogMessage << std::endl;
+
+    std::cout << GridLogMessage << "2IndexRep - Checking if antihermitean"
+              << std::endl;
+    for (int a = 0; a < NumGenerators; a++) {
+      generator(a, i2indTa);
+      std::cout << GridLogMessage << a << std::endl;
+      assert(norm2(adj(i2indTa) + i2indTa) < 1.0e-6);
+    }
+
+    std::cout << GridLogMessage << std::endl;
+    std::cout << GridLogMessage
+              << "2IndexRep - Checking Tr[Ta*Tb]=delta(a,b)*(N +- 2)/2"
+              << std::endl;
+    for (int a = 0; a < NumGenerators; a++) {
+      for (int b = 0; b < NumGenerators; b++) {
+        generator(a, i2indTa);
+        generator(b, i2indTb);
+
+        // generator returns iTa, so we need a minus sign here
+        Complex Tr = -TensorRemove(trace(i2indTa * i2indTb));
+        std::cout << GridLogMessage << "a=" << a << "b=" << b << "Tr=" << Tr
+                  << std::endl;
+      }
+    }
+    std::cout << GridLogMessage << std::endl;
+  }
+
+  static void TwoIndexLieAlgebraMatrix(
+				       const typename Sp<nsp>::LatticeAlgebraVector &h,
+				       LatticeTwoIndexMatrix &out, Real scale = 1.0) {
+    conformable(h, out);
+    GridBase *grid = out.Grid();
+    LatticeTwoIndexMatrix la(grid);
+    TIMatrix i2indTa;
+
+    out = Zero();
+    for (int a = 0; a < NumGenerators; a++) {
+      generator(a, i2indTa);
+      la = peekColour(h, a) * i2indTa;
+      out += la;
+    }
+    out *= scale;
+  }
+
+  // Projects the algebra components 
+  // of a lattice matrix ( of dimension ncol*ncol -1 )
+  static void projectOnAlgebra(
+			       typename Sp<nsp>::LatticeAlgebraVector &h_out,
+			       const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
+    conformable(h_out, in);
+    h_out = Zero();
+    TIMatrix i2indTa;
+    Real coefficient = -2.0 / (ncolour + 2 * S) * scale;
+    // 2/(Nc +/- 2) for the normalization of the trace in the two index rep
+    for (int a = 0; a < NumGenerators; a++) {
+      generator(a, i2indTa);
+      auto tmp = real(trace(i2indTa * in)) * coefficient;
+      pokeColour(h_out, tmp, a);
+    }
+  }
+
+  // a projector that keeps the generators stored to avoid the overhead of
+  // recomputing them
+  static void projector(typename Sp<nsp>::LatticeAlgebraVector &h_out,
+                        const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
+    conformable(h_out, in);
+    // to store the generators
+    static std::vector<TIMatrix> i2indTa(NumGenerators);
+    h_out = Zero();
+    static bool precalculated = false;
+    if (!precalculated) {
+      precalculated = true;
+      for (int a = 0; a < NumGenerators; a++) generator(a, i2indTa[a]);
+    }
+
+    Real coefficient =
+      -2.0 / (ncolour + 2 * S) * scale;  // 2/(Nc +/- 2) for the normalization
+    // of the trace in the two index rep
+
+    for (int a = 0; a < NumGenerators; a++) {
+      auto tmp = real(trace(i2indTa[a] * in)) * coefficient;
+      pokeColour(h_out, tmp, a);
+    }
+  }
+};
+
+
+// Some useful type names
+typedef Sp_TwoIndex<Nc, Symmetric> SpTwoIndexSymmMatrices;
+typedef Sp_TwoIndex<Nc, AntiSymmetric> SpTwoIndexAntiSymmMatrices;
+
+typedef Sp_TwoIndex<2, Symmetric> Sp2TwoIndexSymm;
+typedef Sp_TwoIndex<4, Symmetric> Sp4TwoIndexSymm;
+
+typedef Sp_TwoIndex<2, AntiSymmetric> Sp2TwoIndexAntiSymm;
+typedef Sp_TwoIndex<4, AntiSymmetric> Sp4TwoIndexAntiSymm;
+
+
+NAMESPACE_END(Grid);
+
+#endif
diff --git a/Grid/qcd/utils/Utils.h b/Grid/qcd/utils/Utils.h
index 35594656..c654ce18 100644
--- a/Grid/qcd/utils/Utils.h
+++ b/Grid/qcd/utils/Utils.h
@@ -12,6 +12,7 @@
 #include <Grid/qcd/utils/Sp2n.h>
 #include <Grid/qcd/utils/SUnAdjoint.h>
 #include <Grid/qcd/utils/SUnTwoIndex.h>
+#include <Grid/qcd/utils/Sp2nTwoIndex.h>
 
 // All-to-all contraction kernels that touch the 
 // internal lattice structure
diff --git a/configure.ac b/configure.ac
index c6a85588..3a4ed469 100644
--- a/configure.ac
+++ b/configure.ac
@@ -181,13 +181,18 @@ AC_ARG_ENABLE([Nc],
 
 case ${ac_Nc} in
     2)
-        AC_DEFINE([Config_Nc],[2],[Gauge group Nc]);;
+        AC_DEFINE([Config_Nc],[2],[Gauge group Nc])
+        AC_DEFINE([Config_nsp],[1],[n of Sp2n]);;
     3)
         AC_DEFINE([Config_Nc],[3],[Gauge group Nc]);;
     4)
-        AC_DEFINE([Config_Nc],[4],[Gauge group Nc]);;
+        AC_DEFINE([Config_Nc],[4],[Gauge group Nc])
+        AC_DEFINE([Config_nsp],[2],[n of Sp2n]);;
     5)
         AC_DEFINE([Config_Nc],[5],[Gauge group Nc]);;
+    8)
+        AC_DEFINE([Config_Nc],[8],[Gauge group Nc])
+        AC_DEFINE([Config_nsp],[4],[n of Sp2n]);;
     *)
       AC_MSG_ERROR(["Unsupport gauge group choice Nc = ${ac_Nc}"]);;
 esac
diff --git a/scripts/filelist b/scripts/filelist
index b117a87d..4e64cd62 100755
--- a/scripts/filelist
+++ b/scripts/filelist
@@ -16,6 +16,7 @@ GP_FERMION_FILES=`    find . -name '*.cc' -path '*/instantiation/*' -path '*/ins
 ADJ_FERMION_FILES=`   find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/WilsonAdj*' `
 TWOIND_FERMION_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/WilsonTwoIndex*'`
 SP_FERMION_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/SpWilsonImpl*'`
+SP_TWOIND_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/SpWilsonTwo*'`
 
 HPPFILES=`find . -type f -name '*.hpp'`
 echo HFILES=$HFILES $HPPFILES > Make.inc
@@ -29,6 +30,7 @@ echo GP_FERMION_FILES=$GP_FERMION_FILES   >> Make.inc
 echo ADJ_FERMION_FILES=$ADJ_FERMION_FILES   >> Make.inc
 echo TWOIND_FERMION_FILES=$TWOIND_FERMION_FILES   >> Make.inc
 echo SP_FERMION_FILES=$SP_FERMION_FILES >> Make.inc
+echo SP_TWOIND_FILES=$SP_TWOIND_FILES >> Make.inc
 
 # tests Make.inc
 cd $home/tests
diff --git a/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc b/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc
new file mode 100644
index 00000000..3943cd29
--- /dev/null
+++ b/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc
@@ -0,0 +1,102 @@
+#include <Grid/Grid.h>
+
+int main(int argc, char **argv) {
+  using namespace Grid;
+   
+  typedef Representations< SpFundamentalRepresentation, SpTwoIndexAntiSymmetricRepresentation > TheRepresentations;
+
+  Grid_init(&argc, &argv);
+    
+  typedef GenericSp2nHMCRunnerHirep<TheRepresentations, MinimumNorm2> HMCWrapper;
+    
+  typedef SpWilsonTwoIndexAntiSymmetricImplR TwoIndexFermionImplPolicy;
+  typedef SpWilsonTwoIndexAntiSymmetricFermionR TwoIndexFermionAction;
+  typedef typename TwoIndexFermionAction::FermionField TwoIndexFermionField;
+    
+  typedef SpWilsonImplR FundFermionImplPolicy;                                    // ok
+  typedef SpWilsonFermionR FundFermionAction;                                     // ok
+  typedef typename FundFermionAction::FermionField FundFermionField;
+ 
+  //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+   
+  HMCWrapper TheHMC;
+    
+  TheHMC.Resources.AddFourDimGrid("gauge");
+    
+  // Checkpointer definition
+  CheckpointerParameters CPparams;
+  CPparams.config_prefix = "ckpoint_lat";
+  CPparams.rng_prefix = "ckpoint_rng";
+  CPparams.saveInterval = 5;
+  CPparams.format = "IEEE64BIG";
+    
+  TheHMC.Resources.LoadNerscCheckpointer(CPparams);
+
+  RNGModuleParameters RNGpar;
+  RNGpar.serial_seeds = "1 2 3 4 5";
+  RNGpar.parallel_seeds = "6 7 8 9 10";
+  TheHMC.Resources.SetRNGSeeds(RNGpar);
+
+  // Construct observables
+  typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
+  TheHMC.Resources.AddObservable<PlaqObs>();
+    
+      typedef PolyakovMod<HMCWrapper::ImplPolicy> PolyakovObs;
+      TheHMC.Resources.AddObservable<PolyakovObs>();
+    
+
+    
+  RealD beta = 6 ;
+    
+  SymplWilsonGaugeActionR Waction(beta);
+    
+  auto GridPtr = TheHMC.Resources.GetCartesian();
+  auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
+    
+  SpFundamentalRepresentation::LatticeField fundU(GridPtr);
+  SpTwoIndexAntiSymmetricRepresentation::LatticeField asU(GridPtr);
+    //LatticeGaugeField U(GridPtr);
+    
+  RealD Fundmass = -0.71;
+  RealD ASmass = -0.71;
+  std::vector<Complex> boundary = {-1,-1,-1,-1};
+
+  FundFermionAction::ImplParams bc(boundary);
+  TwoIndexFermionAction::ImplParams bbc(boundary);
+    
+  FundFermionAction FundFermOp(fundU, *GridPtr, *GridRBPtr, Fundmass, bbc);
+  TwoIndexFermionAction TwoIndexFermOp(asU, *GridPtr, *GridRBPtr, ASmass, bbc);
+  ConjugateGradient<FundFermionField> fCG(1.0e-8, 2000, false);
+  ConjugateGradient<TwoIndexFermionField> asCG(1.0e-8, 2000, false);
+  OneFlavourRationalParams Params(1.0e-6, 64.0, 2000, 1.0e-6, 16);
+    
+    
+  TwoFlavourPseudoFermionAction<FundFermionImplPolicy> fundNf2(FundFermOp, fCG, fCG);
+  TwoFlavourPseudoFermionAction<TwoIndexFermionImplPolicy> asNf2(TwoIndexFermOp, asCG, asCG);
+  OneFlavourRationalPseudoFermionAction<TwoIndexFermionImplPolicy> asNf1(TwoIndexFermOp,Params);
+    
+  fundNf2.is_smeared = false;
+  asNf2.is_smeared = false;
+  asNf1.is_smeared = false;
+  
+    ActionLevel<HMCWrapper::Field, TheRepresentations > Level1(1);
+    Level1.push_back(&fundNf2);
+    Level1.push_back(&asNf2);
+    Level1.push_back(&asNf1);
+    
+    ActionLevel<HMCWrapper::Field, TheRepresentations > Level2(4);
+    Level2.push_back(&Waction);
+    
+    TheHMC.TheAction.push_back(Level1);
+    TheHMC.TheAction.push_back(Level2);
+    
+    TheHMC.Parameters.MD.MDsteps = 28;
+    TheHMC.Parameters.MD.trajL   = 1.0;
+    
+    TheHMC.ReadCommandLine(argc, argv);
+    TheHMC.Run();
+    
+    
+  Grid_finalize();
+}
+
diff --git a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
new file mode 100644
index 00000000..c5eb94d0
--- /dev/null
+++ b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
@@ -0,0 +1,82 @@
+#include <Grid/Grid.h>
+
+int main(int argc, char **argv) {
+  using namespace Grid;
+   
+  typedef Representations< SpFundamentalRepresentation, SpTwoIndexAntiSymmetricRepresentation > TheRepresentations;
+
+  Grid_init(&argc, &argv);
+    
+  typedef GenericSp2nHMCRunnerHirep<TheRepresentations, MinimumNorm2> HMCWrapper;
+  typedef SpWilsonTwoIndexAntiSymmetricImplR FermionImplPolicy;
+  typedef SpWilsonTwoIndexAntiSymmetricFermionR FermionAction;
+  typedef typename FermionAction::FermionField FermionField;
+ 
+  //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+   
+  HMCWrapper TheHMC;
+    
+  TheHMC.Resources.AddFourDimGrid("gauge");
+    
+  // Checkpointer definition
+  CheckpointerParameters CPparams;
+  CPparams.config_prefix = "ckpoint_lat";
+  CPparams.rng_prefix = "ckpoint_rng";
+  CPparams.saveInterval = 5;
+  CPparams.format = "IEEE64BIG";
+    
+  TheHMC.Resources.LoadNerscCheckpointer(CPparams);
+
+  RNGModuleParameters RNGpar;
+  RNGpar.serial_seeds = "1 2 3 4 5";
+  RNGpar.parallel_seeds = "6 7 8 9 10";
+  TheHMC.Resources.SetRNGSeeds(RNGpar);
+
+  // Construct observables
+  typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
+  TheHMC.Resources.AddObservable<PlaqObs>();
+    
+  RealD beta = 6.7 ;
+    
+  SymplWilsonGaugeActionR Waction(beta);
+    
+  auto GridPtr = TheHMC.Resources.GetCartesian();
+  auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
+    
+   SpTwoIndexAntiSymmetricRepresentation::LatticeField U(GridPtr);
+    //LatticeGaugeField U(GridPtr);
+    
+  RealD mass = -0.85;
+  
+
+  std::vector<Complex> boundary = {-1,-1,-1,-1};
+  FermionAction::ImplParams bc(boundary);
+  FermionAction FermOp(U, *GridPtr, *GridRBPtr, mass, bc);
+    
+  
+  ConjugateGradient<FermionField> CG(1.0e-8, 2000, false);
+  
+  TwoFlavourPseudoFermionAction<FermionImplPolicy> Nf2(FermOp, CG, CG);
+    
+  Nf2.is_smeared = false;
+  std::cout << GridLogMessage << "mass " << mass << std::endl;
+    
+    ActionLevel<HMCWrapper::Field, TheRepresentations > Level1(1);
+    Level1.push_back(&Nf2);
+    
+    ActionLevel<HMCWrapper::Field, TheRepresentations > Level2(4);
+    Level2.push_back(&Waction);
+    
+    TheHMC.TheAction.push_back(Level1);
+    TheHMC.TheAction.push_back(Level2);
+    
+    TheHMC.Parameters.MD.MDsteps = 16;
+    TheHMC.Parameters.MD.trajL   = 1.0;
+    
+    TheHMC.ReadCommandLine(argc, argv);
+    TheHMC.Run();
+    
+    
+  Grid_finalize();
+}
+

From 1ba429345bda00f277455611bb4c8142588bf558 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Wed, 23 Nov 2022 18:45:01 +0000
Subject: [PATCH 023/129] Fixing issue #11: consistent use of ncolour and nsp

---
 Grid/qcd/action/gauge/GaugeImplTypes.h | 24 +++----
 Grid/qcd/utils/Sp2n.h                  | 99 +++++++++++++-------------
 tests/sp2n/Test_Sp_start.cc            | 18 ++---
 tests/sp2n/Test_project_on_Sp.cc       |  7 +-
 4 files changed, 76 insertions(+), 72 deletions(-)

diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index dbab4386..dc39c30b 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -126,8 +126,8 @@ public:
     {
         if (isSp2n == true)
         {
-            const int nSp = Nrepresentation/2;
-            Sp<nSp>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
+            //const int nSp = Nrepresentation/2;
+            Sp<Nrepresentation>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
         } else
         {
         
@@ -148,18 +148,18 @@ public:
         if (isSp2n == true)
         {
             P = Ta(P);
-            const int nsp = Nc / 2;
+            //const int nsp = Nc / 2;
 
-            Sp<nsp>::iSp2nMatrix<Complex> gen;
+            Sp<Nc>::iSp2nMatrix<Complex> gen;
             
 
             auto Psum = P;
 
             Psum = Zero();
             
-            for (int a = 0; a < Sp<nsp>::AlgebraDimension; a++)
+            for (int a = 0; a < Sp<Nrepresentation>::AlgebraDimension; a++)
             {
-                Sp<nsp>::generator(a, gen);
+                Sp<Nrepresentation>::generator(a, gen);
 
                 auto coeff = 2. * trace(P * gen);
                 Psum += coeff * gen;
@@ -223,8 +223,8 @@ public:
   {
       if (isSp2n == true)
       {
-          const int nSp = Nrepresentation/2;
-          Sp<nSp>::HotConfiguration(pRNG, U);
+          //const int nSp = Nrepresentation/2;
+          Sp<Nrepresentation>::HotConfiguration(pRNG, U);
       } else
       {
           Group::HotConfiguration(pRNG, U);
@@ -235,8 +235,8 @@ public:
   {
       if (isSp2n == true)
     {
-        const int nSp = Nrepresentation/2;
-        Sp<nSp>::TepidConfiguration(pRNG, U);
+        //const int nSp = Nrepresentation/2;
+        Sp<Nrepresentation>::TepidConfiguration(pRNG, U);
     } else
     {
         Group::TepidConfiguration(pRNG, U);
@@ -248,8 +248,8 @@ public:
   {
       if (isSp2n == true)
       {
-          const int nSp = Nrepresentation/2;
-          Sp<nSp>::ColdConfiguration(pRNG, U);
+          //const int nSp = Nrepresentation/2;
+          Sp<Nrepresentation>::ColdConfiguration(pRNG, U);
       } else
       {
           Group::ColdConfiguration(pRNG, U);
diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.h
index 53ce3d5c..19e30568 100644
--- a/Grid/qcd/utils/Sp2n.h
+++ b/Grid/qcd/utils/Sp2n.h
@@ -5,21 +5,16 @@
 NAMESPACE_BEGIN(Grid);
 
 // Sp(2N)
-// ncolour = N
+// ncolour = 2N
 
-// need to be careful with n and 2n
-// I am defining the Sp class for Sp(2n) to be such that the template variable ncolour
-// is n inside 2n and the typedef at the end of the file should eliminate possible confusion.
-
-// the other routines, like projectOnSp2n, N will be the dimension of the actual number of colors for consistency with the sun routines
 
 template <int ncolour>
 class Sp {
 public:
-    static const int Dimension = ncolour*2;
-    static const int AlgebraDimension = ncolour*(2*ncolour +1);
-    static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
-    static const int nnsp = ncolour;
+    static const int nsp = ncolour/2;
+    static const int Dimension = ncolour;
+    static const int AlgebraDimension = nsp*(2*nsp +1);
+    static int su2subgroups(void) { return (nsp * (nsp - 1)) / 2; }
     
     
     template <typename vtype>
@@ -65,20 +60,17 @@ public:
     //     there are 6 types named a,b,c,d and w,z
     //     abcd are N(N-1)/2 each while wz are N each
     
-    
-    
-    
-    template <class cplx>
+ template <class cplx>
     static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
         // map lie index into type of generators: diagonal, abcd type, wz type
 
         int diagIndex;
         int aIndex, bIndex, cIndex, dIndex;
         int wIndex, zIndex; // a,b,c,d are N(N-1)/2 and w,z are N
-        int mod = ncolour * (ncolour-1) * 0.5;
-        int offdiag = 2*ncolour*ncolour; // number of generators not in the cartan subalgebra
+        int mod = nsp * (nsp-1) * 0.5;
+        int offdiag = 2*nsp*nsp; // number of generators not in the cartan subalgebra
         int wmod = 4*mod;
-        int zmod = wmod+ncolour;
+        int zmod = wmod+nsp;
         if (lieIndex >= offdiag) {
             diagIndex = lieIndex - offdiag; // 0, ... ,N-1
             //std::cout << GridLogMessage << "diag type " << std::endl;
@@ -136,7 +128,7 @@ public:
         RealD nrm = 1.0 / 2;
 
         ta()()(diagIndex,diagIndex) = nrm;
-        ta()()(diagIndex+ncolour,diagIndex+ncolour) = -nrm;
+        ta()()(diagIndex+nsp,diagIndex+nsp) = -nrm;
     }
     
     template <class cplx>
@@ -152,8 +144,8 @@ public:
         su2SubGroupIndex(i1, i2, aIndex);
         ta()()(i1,i2) = 1;
         ta()()(i2,i1) = 1;
-        ta()()(i1+ncolour,i2+ncolour) = -1;
-        ta()()(i2+ncolour,i1+ncolour) = -1;
+        ta()()(i1+nsp,i2+nsp) = -1;
+        ta()()(i2+nsp,i1+nsp) = -1;
 
         ta = ta * nrm;
     }
@@ -174,8 +166,8 @@ public:
 
         ta()()(i1,i2) = i;
         ta()()(i2,i1) = -i;
-        ta()()(i1+ncolour,i2+ncolour) = i;
-        ta()()(i2+ncolour,i1+ncolour) = -i;
+        ta()()(i1+nsp,i2+nsp) = i;
+        ta()()(i2+nsp,i1+nsp) = -i;
 
         ta = ta * nrm;
     }
@@ -191,10 +183,10 @@ public:
         RealD nrm = 1 / (2 * std::sqrt(2) );
         su2SubGroupIndex(i1, i2, cIndex);
         
-        ta()()(i1,i2+ncolour) = 1;
-        ta()()(i2,i1+ncolour) = 1;
-        ta()()(i1+ncolour,i2) = 1;
-        ta()()(i2+ncolour,i1) = 1;
+        ta()()(i1,i2+nsp) = 1;
+        ta()()(i2,i1+nsp) = 1;
+        ta()()(i1+nsp,i2) = 1;
+        ta()()(i2+nsp,i1) = 1;
 
         ta = ta * nrm;
     }
@@ -210,10 +202,10 @@ public:
         RealD nrm = 1 / (2 * std::sqrt(2)  );
         su2SubGroupIndex(i1, i2, dIndex);
 
-        ta()()(i1,i2+ncolour) = i;
-        ta()()(i2,i1+ncolour) = i;
-        ta()()(i1+ncolour,i2) = -i;
-        ta()()(i2+ncolour,i1) = -i;
+        ta()()(i1,i2+nsp) = i;
+        ta()()(i2,i1+nsp) = i;
+        ta()()(i1+nsp,i2) = -i;
+        ta()()(i2+nsp,i1) = -i;
 
         ta = ta * nrm;
     }
@@ -226,8 +218,8 @@ public:
          ta = Zero();
          RealD nrm = 1.0 / 2; //check
 
-         ta()()(wIndex,wIndex+ncolour) = 1;
-         ta()()(wIndex+ncolour,wIndex) = 1;
+         ta()()(wIndex,wIndex+nsp) = 1;
+         ta()()(wIndex+nsp,wIndex) = 1;
          
          ta = ta * nrm;
      }
@@ -240,8 +232,8 @@ public:
          ta = Zero();
          RealD nrm = 1.0 / 2; //check
          cplx i(0.0, 1.0);
-         ta()()(zIndex,zIndex+ncolour) = i;
-         ta()()(zIndex+ncolour,zIndex) = -i;
+         ta()()(zIndex,zIndex+nsp) = i;
+         ta()()(zIndex+nsp,zIndex) = -i;
          
          ta = ta * nrm;
      }
@@ -251,11 +243,11 @@ public:
     // Map a su2 subgroup number to the pair of rows that are non zero
     ////////////////////////////////////////////////////////////////////////
     static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
-      assert((su2_index >= 0) && (su2_index < (ncolour * (ncolour - 1)) / 2));
+      assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
 
       int spare = su2_index;
-      for (i1 = 0; spare >= (ncolour - 1 - i1); i1++) {
-        spare = spare - (ncolour - 1 - i1);  // remove the Nc-1-i1 terms
+      for (i1 = 0; spare >= (nsp - 1 - i1); i1++) {
+        spare = spare - (nsp - 1 - i1);  // remove the Nc-1-i1 terms
       }
       i2 = i1 + 1 + spare;
     }
@@ -268,7 +260,7 @@ public:
         for (int gen = 0; gen < AlgebraDimension; gen++) {
             Matrix ta;
             generator(gen, ta);
-            std::cout << GridLogMessage << "Nc (2n) = " << 2*ncolour << std::endl;
+            std::cout << GridLogMessage << "Nc = " << ncolour << std::endl;
             std::cout << GridLogMessage << " t_" << gen << std::endl;
             std::cout << GridLogMessage << ta << std::endl;
         }
@@ -464,10 +456,17 @@ public:
         ColourMatrix Omega;
         Omega = Zero();
         
-        for (int i = 0; i < ncolour; i++)
+        std::cout << GridLogMessage << "I am a ColourMatrix" << std::endl;
+        
+        //for (int i = 0; i < ncolour; i++)         wrong?!
+        //{
+        //    Omega()()(i, 2*ncolour-1-i) = 1.;
+        //    Omega()()(2*ncolour-1-i, i) = -1;
+        //}
+        for (int i = 0; i < nsp; i++)
         {
-            Omega()()(i, 2*ncolour-1-i) = 1.;
-            Omega()()(2*ncolour-1-i, i) = -1;
+            Omega()()(i, nsp+i) = 1.;
+            Omega()()(nsp+i, i) = -1;
         }
 
         auto diff = Omega - (in * Omega * transpose(in) );
@@ -498,6 +497,8 @@ public:
         Omega = Zero();
         identity = 1.;
         
+        std::cout << GridLogMessage << "I am a GaugeField " << std::endl;
+        
         U = PeekIndex<LorentzIndex>(in,1);
         
         OmegaInvariance(U);
@@ -516,10 +517,12 @@ public:
            Omega = Zero();
            identity = 1.;
            
-           for (int i = 0; i < ncolour; i++)
+           std::cout << GridLogMessage << "I am a LatticeColourMatrix " << std::endl;
+           
+           for (int i = 0; i < nsp; i++)
            {
-               Omega()()(i, ncolour+i) = 1.;
-               Omega()()(ncolour+i, i) = -1;
+               Omega()()(i, nsp+i) = 1.;
+               Omega()()(nsp+i, i) = -1;
            }
            
            std::cout << GridLogMessage << "Omega = " << Omega()() << std::endl;
@@ -568,10 +571,10 @@ public:
    }
  }
 
-typedef Sp<1> Sp2;
-typedef Sp<2> Sp4;
-typedef Sp<3> Sp6;
-typedef Sp<4> Sp8;
+typedef Sp<2> Sp2;
+typedef Sp<4> Sp4;
+typedef Sp<6> Sp6;
+typedef Sp<8> Sp8;
 
 NAMESPACE_END(Grid);
 #endif
diff --git a/tests/sp2n/Test_Sp_start.cc b/tests/sp2n/Test_Sp_start.cc
index da19779f..16a66367 100644
--- a/tests/sp2n/Test_Sp_start.cc
+++ b/tests/sp2n/Test_Sp_start.cc
@@ -21,7 +21,7 @@ int main (int argc, char **argv)
     
     double vol = Umu.Grid()->gSites();
 
-    const int nsp = Nc / 2;
+    const int nsp = Sp<Nc>::nsp;
     identity = 1.;
     Cidentity = 1.;
     
@@ -34,8 +34,8 @@ int main (int argc, char **argv)
     std::cout << GridLogMessage << "-------" << std::endl;
     std::cout << GridLogMessage << "Checking Cold Configuration " << std::endl;
     std::cout << GridLogMessage << std::endl;
-    Sp<nsp>::ColdConfiguration(pRNG,Umu);
-    Sp<nsp>::OmegaInvariance(Umu);
+    Sp<Nc>::ColdConfiguration(pRNG,Umu);
+    Sp<Nc>::OmegaInvariance(Umu);
     std::cout << GridLogMessage << std::endl;
 
     Umu = Umu - identity;
@@ -47,8 +47,8 @@ int main (int argc, char **argv)
     std::cout << GridLogMessage << "-------" << std::endl;
     std::cout << GridLogMessage << "Checking Hot Configuration" << std::endl;
     std::cout << GridLogMessage << std::endl;
-    Sp<nsp>::HotConfiguration(pRNG,Umu);
-    Sp<nsp>::OmegaInvariance(Umu);
+    Sp<Nc>::HotConfiguration(pRNG,Umu);
+    Sp<Nc>::OmegaInvariance(Umu);
     std::cout << GridLogMessage << std::endl;
     U = PeekIndex<LorentzIndex>(Umu,1);
     std::cout << GridLogMessage << "Checking unitarity " << std::endl;
@@ -62,8 +62,8 @@ int main (int argc, char **argv)
     std::cout << GridLogMessage << "-------" << std::endl;
     std::cout << GridLogMessage << "Checking Tepid Configuration" << std::endl;
     std::cout << GridLogMessage << std::endl;
-    Sp<nsp>::TepidConfiguration(pRNG,Umu);
-    Sp<nsp>::OmegaInvariance(Umu);
+    Sp<Nc>::TepidConfiguration(pRNG,Umu);
+    Sp<Nc>::OmegaInvariance(Umu);
     std::cout << GridLogMessage << std::endl;
     U = PeekIndex<LorentzIndex>(Umu,1);
     std::cout << GridLogMessage << "Checking unitarity " << std::endl;
@@ -85,7 +85,7 @@ int main (int argc, char **argv)
     Complex i(0., 1.);
     
     
-    Sp<nsp>::HotConfiguration(pRNG,Umu);
+    Sp<Nc>::HotConfiguration(pRNG,Umu);
     U = PeekIndex<LorentzIndex>(Umu,0);
     for (int c1 = 0; c1 < nsp; c1++) //check on W
     {
@@ -123,7 +123,7 @@ int main (int argc, char **argv)
     
     std::cout << GridLogMessage << "Hot start ok " << std::endl;
     
-    Sp<nsp>::HotConfiguration(pRNG,Umu);
+    Sp<Nc>::HotConfiguration(pRNG,Umu);
     U = PeekIndex<LorentzIndex>(Umu,0);
     for (int c1 = 0; c1 < nsp; c1++) //check on W
     {
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 71c6acc7..d1cf33bd 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -20,7 +20,8 @@ int main (int argc, char **argv)
     LatticeColourMatrixD aux(&Grid);
     LatticeColourMatrixD identity(&Grid);
     
-    const int nsp = Nc / 2;
+    //const int nsp = Nc / 2;
+    const int nsp = Sp<Nc>::nsp;
     
     identity = 1.0;
     RealD epsilon = 0.01;
@@ -47,7 +48,7 @@ int main (int argc, char **argv)
     {
         std::cout << GridLogMessage << "This matrix should not leave Omega invariant, expect a warning" << std::endl;
     }
-    Sp<nsp>::OmegaInvariance(U);
+    Sp<Nc>::OmegaInvariance(U);
     std::cout <<GridLogMessage << std::endl;
     
     U = U + epsilon*identity;
@@ -78,7 +79,7 @@ int main (int argc, char **argv)
     
     // actual sp2n check
     std::cout << GridLogMessage << "Checking invariance after projection "<< std::endl;
-    Sp<nsp>::OmegaInvariance(U);
+    Sp<Nc>::OmegaInvariance(U);
     
     // checks on elements
     

From 3af4929ddab4caee9f561f835de30a2c8bc527c5 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Wed, 23 Nov 2022 19:34:59 +0000
Subject: [PATCH 024/129] Revert "Fixing issue #11: consistent use of ncolour
 and nsp"

This reverts commit 1ba429345bda00f277455611bb4c8142588bf558.
---
 Grid/qcd/action/gauge/GaugeImplTypes.h | 24 +++----
 Grid/qcd/utils/Sp2n.h                  | 99 +++++++++++++-------------
 tests/sp2n/Test_Sp_start.cc            | 18 ++---
 tests/sp2n/Test_project_on_Sp.cc       |  7 +-
 4 files changed, 72 insertions(+), 76 deletions(-)

diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index dc39c30b..dbab4386 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -126,8 +126,8 @@ public:
     {
         if (isSp2n == true)
         {
-            //const int nSp = Nrepresentation/2;
-            Sp<Nrepresentation>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
+            const int nSp = Nrepresentation/2;
+            Sp<nSp>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
         } else
         {
         
@@ -148,18 +148,18 @@ public:
         if (isSp2n == true)
         {
             P = Ta(P);
-            //const int nsp = Nc / 2;
+            const int nsp = Nc / 2;
 
-            Sp<Nc>::iSp2nMatrix<Complex> gen;
+            Sp<nsp>::iSp2nMatrix<Complex> gen;
             
 
             auto Psum = P;
 
             Psum = Zero();
             
-            for (int a = 0; a < Sp<Nrepresentation>::AlgebraDimension; a++)
+            for (int a = 0; a < Sp<nsp>::AlgebraDimension; a++)
             {
-                Sp<Nrepresentation>::generator(a, gen);
+                Sp<nsp>::generator(a, gen);
 
                 auto coeff = 2. * trace(P * gen);
                 Psum += coeff * gen;
@@ -223,8 +223,8 @@ public:
   {
       if (isSp2n == true)
       {
-          //const int nSp = Nrepresentation/2;
-          Sp<Nrepresentation>::HotConfiguration(pRNG, U);
+          const int nSp = Nrepresentation/2;
+          Sp<nSp>::HotConfiguration(pRNG, U);
       } else
       {
           Group::HotConfiguration(pRNG, U);
@@ -235,8 +235,8 @@ public:
   {
       if (isSp2n == true)
     {
-        //const int nSp = Nrepresentation/2;
-        Sp<Nrepresentation>::TepidConfiguration(pRNG, U);
+        const int nSp = Nrepresentation/2;
+        Sp<nSp>::TepidConfiguration(pRNG, U);
     } else
     {
         Group::TepidConfiguration(pRNG, U);
@@ -248,8 +248,8 @@ public:
   {
       if (isSp2n == true)
       {
-          //const int nSp = Nrepresentation/2;
-          Sp<Nrepresentation>::ColdConfiguration(pRNG, U);
+          const int nSp = Nrepresentation/2;
+          Sp<nSp>::ColdConfiguration(pRNG, U);
       } else
       {
           Group::ColdConfiguration(pRNG, U);
diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.h
index 19e30568..53ce3d5c 100644
--- a/Grid/qcd/utils/Sp2n.h
+++ b/Grid/qcd/utils/Sp2n.h
@@ -5,16 +5,21 @@
 NAMESPACE_BEGIN(Grid);
 
 // Sp(2N)
-// ncolour = 2N
+// ncolour = N
 
+// need to be careful with n and 2n
+// I am defining the Sp class for Sp(2n) to be such that the template variable ncolour
+// is n inside 2n and the typedef at the end of the file should eliminate possible confusion.
+
+// the other routines, like projectOnSp2n, N will be the dimension of the actual number of colors for consistency with the sun routines
 
 template <int ncolour>
 class Sp {
 public:
-    static const int nsp = ncolour/2;
-    static const int Dimension = ncolour;
-    static const int AlgebraDimension = nsp*(2*nsp +1);
-    static int su2subgroups(void) { return (nsp * (nsp - 1)) / 2; }
+    static const int Dimension = ncolour*2;
+    static const int AlgebraDimension = ncolour*(2*ncolour +1);
+    static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
+    static const int nnsp = ncolour;
     
     
     template <typename vtype>
@@ -60,17 +65,20 @@ public:
     //     there are 6 types named a,b,c,d and w,z
     //     abcd are N(N-1)/2 each while wz are N each
     
- template <class cplx>
+    
+    
+    
+    template <class cplx>
     static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
         // map lie index into type of generators: diagonal, abcd type, wz type
 
         int diagIndex;
         int aIndex, bIndex, cIndex, dIndex;
         int wIndex, zIndex; // a,b,c,d are N(N-1)/2 and w,z are N
-        int mod = nsp * (nsp-1) * 0.5;
-        int offdiag = 2*nsp*nsp; // number of generators not in the cartan subalgebra
+        int mod = ncolour * (ncolour-1) * 0.5;
+        int offdiag = 2*ncolour*ncolour; // number of generators not in the cartan subalgebra
         int wmod = 4*mod;
-        int zmod = wmod+nsp;
+        int zmod = wmod+ncolour;
         if (lieIndex >= offdiag) {
             diagIndex = lieIndex - offdiag; // 0, ... ,N-1
             //std::cout << GridLogMessage << "diag type " << std::endl;
@@ -128,7 +136,7 @@ public:
         RealD nrm = 1.0 / 2;
 
         ta()()(diagIndex,diagIndex) = nrm;
-        ta()()(diagIndex+nsp,diagIndex+nsp) = -nrm;
+        ta()()(diagIndex+ncolour,diagIndex+ncolour) = -nrm;
     }
     
     template <class cplx>
@@ -144,8 +152,8 @@ public:
         su2SubGroupIndex(i1, i2, aIndex);
         ta()()(i1,i2) = 1;
         ta()()(i2,i1) = 1;
-        ta()()(i1+nsp,i2+nsp) = -1;
-        ta()()(i2+nsp,i1+nsp) = -1;
+        ta()()(i1+ncolour,i2+ncolour) = -1;
+        ta()()(i2+ncolour,i1+ncolour) = -1;
 
         ta = ta * nrm;
     }
@@ -166,8 +174,8 @@ public:
 
         ta()()(i1,i2) = i;
         ta()()(i2,i1) = -i;
-        ta()()(i1+nsp,i2+nsp) = i;
-        ta()()(i2+nsp,i1+nsp) = -i;
+        ta()()(i1+ncolour,i2+ncolour) = i;
+        ta()()(i2+ncolour,i1+ncolour) = -i;
 
         ta = ta * nrm;
     }
@@ -183,10 +191,10 @@ public:
         RealD nrm = 1 / (2 * std::sqrt(2) );
         su2SubGroupIndex(i1, i2, cIndex);
         
-        ta()()(i1,i2+nsp) = 1;
-        ta()()(i2,i1+nsp) = 1;
-        ta()()(i1+nsp,i2) = 1;
-        ta()()(i2+nsp,i1) = 1;
+        ta()()(i1,i2+ncolour) = 1;
+        ta()()(i2,i1+ncolour) = 1;
+        ta()()(i1+ncolour,i2) = 1;
+        ta()()(i2+ncolour,i1) = 1;
 
         ta = ta * nrm;
     }
@@ -202,10 +210,10 @@ public:
         RealD nrm = 1 / (2 * std::sqrt(2)  );
         su2SubGroupIndex(i1, i2, dIndex);
 
-        ta()()(i1,i2+nsp) = i;
-        ta()()(i2,i1+nsp) = i;
-        ta()()(i1+nsp,i2) = -i;
-        ta()()(i2+nsp,i1) = -i;
+        ta()()(i1,i2+ncolour) = i;
+        ta()()(i2,i1+ncolour) = i;
+        ta()()(i1+ncolour,i2) = -i;
+        ta()()(i2+ncolour,i1) = -i;
 
         ta = ta * nrm;
     }
@@ -218,8 +226,8 @@ public:
          ta = Zero();
          RealD nrm = 1.0 / 2; //check
 
-         ta()()(wIndex,wIndex+nsp) = 1;
-         ta()()(wIndex+nsp,wIndex) = 1;
+         ta()()(wIndex,wIndex+ncolour) = 1;
+         ta()()(wIndex+ncolour,wIndex) = 1;
          
          ta = ta * nrm;
      }
@@ -232,8 +240,8 @@ public:
          ta = Zero();
          RealD nrm = 1.0 / 2; //check
          cplx i(0.0, 1.0);
-         ta()()(zIndex,zIndex+nsp) = i;
-         ta()()(zIndex+nsp,zIndex) = -i;
+         ta()()(zIndex,zIndex+ncolour) = i;
+         ta()()(zIndex+ncolour,zIndex) = -i;
          
          ta = ta * nrm;
      }
@@ -243,11 +251,11 @@ public:
     // Map a su2 subgroup number to the pair of rows that are non zero
     ////////////////////////////////////////////////////////////////////////
     static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
-      assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
+      assert((su2_index >= 0) && (su2_index < (ncolour * (ncolour - 1)) / 2));
 
       int spare = su2_index;
-      for (i1 = 0; spare >= (nsp - 1 - i1); i1++) {
-        spare = spare - (nsp - 1 - i1);  // remove the Nc-1-i1 terms
+      for (i1 = 0; spare >= (ncolour - 1 - i1); i1++) {
+        spare = spare - (ncolour - 1 - i1);  // remove the Nc-1-i1 terms
       }
       i2 = i1 + 1 + spare;
     }
@@ -260,7 +268,7 @@ public:
         for (int gen = 0; gen < AlgebraDimension; gen++) {
             Matrix ta;
             generator(gen, ta);
-            std::cout << GridLogMessage << "Nc = " << ncolour << std::endl;
+            std::cout << GridLogMessage << "Nc (2n) = " << 2*ncolour << std::endl;
             std::cout << GridLogMessage << " t_" << gen << std::endl;
             std::cout << GridLogMessage << ta << std::endl;
         }
@@ -456,17 +464,10 @@ public:
         ColourMatrix Omega;
         Omega = Zero();
         
-        std::cout << GridLogMessage << "I am a ColourMatrix" << std::endl;
-        
-        //for (int i = 0; i < ncolour; i++)         wrong?!
-        //{
-        //    Omega()()(i, 2*ncolour-1-i) = 1.;
-        //    Omega()()(2*ncolour-1-i, i) = -1;
-        //}
-        for (int i = 0; i < nsp; i++)
+        for (int i = 0; i < ncolour; i++)
         {
-            Omega()()(i, nsp+i) = 1.;
-            Omega()()(nsp+i, i) = -1;
+            Omega()()(i, 2*ncolour-1-i) = 1.;
+            Omega()()(2*ncolour-1-i, i) = -1;
         }
 
         auto diff = Omega - (in * Omega * transpose(in) );
@@ -497,8 +498,6 @@ public:
         Omega = Zero();
         identity = 1.;
         
-        std::cout << GridLogMessage << "I am a GaugeField " << std::endl;
-        
         U = PeekIndex<LorentzIndex>(in,1);
         
         OmegaInvariance(U);
@@ -517,12 +516,10 @@ public:
            Omega = Zero();
            identity = 1.;
            
-           std::cout << GridLogMessage << "I am a LatticeColourMatrix " << std::endl;
-           
-           for (int i = 0; i < nsp; i++)
+           for (int i = 0; i < ncolour; i++)
            {
-               Omega()()(i, nsp+i) = 1.;
-               Omega()()(nsp+i, i) = -1;
+               Omega()()(i, ncolour+i) = 1.;
+               Omega()()(ncolour+i, i) = -1;
            }
            
            std::cout << GridLogMessage << "Omega = " << Omega()() << std::endl;
@@ -571,10 +568,10 @@ public:
    }
  }
 
-typedef Sp<2> Sp2;
-typedef Sp<4> Sp4;
-typedef Sp<6> Sp6;
-typedef Sp<8> Sp8;
+typedef Sp<1> Sp2;
+typedef Sp<2> Sp4;
+typedef Sp<3> Sp6;
+typedef Sp<4> Sp8;
 
 NAMESPACE_END(Grid);
 #endif
diff --git a/tests/sp2n/Test_Sp_start.cc b/tests/sp2n/Test_Sp_start.cc
index 16a66367..da19779f 100644
--- a/tests/sp2n/Test_Sp_start.cc
+++ b/tests/sp2n/Test_Sp_start.cc
@@ -21,7 +21,7 @@ int main (int argc, char **argv)
     
     double vol = Umu.Grid()->gSites();
 
-    const int nsp = Sp<Nc>::nsp;
+    const int nsp = Nc / 2;
     identity = 1.;
     Cidentity = 1.;
     
@@ -34,8 +34,8 @@ int main (int argc, char **argv)
     std::cout << GridLogMessage << "-------" << std::endl;
     std::cout << GridLogMessage << "Checking Cold Configuration " << std::endl;
     std::cout << GridLogMessage << std::endl;
-    Sp<Nc>::ColdConfiguration(pRNG,Umu);
-    Sp<Nc>::OmegaInvariance(Umu);
+    Sp<nsp>::ColdConfiguration(pRNG,Umu);
+    Sp<nsp>::OmegaInvariance(Umu);
     std::cout << GridLogMessage << std::endl;
 
     Umu = Umu - identity;
@@ -47,8 +47,8 @@ int main (int argc, char **argv)
     std::cout << GridLogMessage << "-------" << std::endl;
     std::cout << GridLogMessage << "Checking Hot Configuration" << std::endl;
     std::cout << GridLogMessage << std::endl;
-    Sp<Nc>::HotConfiguration(pRNG,Umu);
-    Sp<Nc>::OmegaInvariance(Umu);
+    Sp<nsp>::HotConfiguration(pRNG,Umu);
+    Sp<nsp>::OmegaInvariance(Umu);
     std::cout << GridLogMessage << std::endl;
     U = PeekIndex<LorentzIndex>(Umu,1);
     std::cout << GridLogMessage << "Checking unitarity " << std::endl;
@@ -62,8 +62,8 @@ int main (int argc, char **argv)
     std::cout << GridLogMessage << "-------" << std::endl;
     std::cout << GridLogMessage << "Checking Tepid Configuration" << std::endl;
     std::cout << GridLogMessage << std::endl;
-    Sp<Nc>::TepidConfiguration(pRNG,Umu);
-    Sp<Nc>::OmegaInvariance(Umu);
+    Sp<nsp>::TepidConfiguration(pRNG,Umu);
+    Sp<nsp>::OmegaInvariance(Umu);
     std::cout << GridLogMessage << std::endl;
     U = PeekIndex<LorentzIndex>(Umu,1);
     std::cout << GridLogMessage << "Checking unitarity " << std::endl;
@@ -85,7 +85,7 @@ int main (int argc, char **argv)
     Complex i(0., 1.);
     
     
-    Sp<Nc>::HotConfiguration(pRNG,Umu);
+    Sp<nsp>::HotConfiguration(pRNG,Umu);
     U = PeekIndex<LorentzIndex>(Umu,0);
     for (int c1 = 0; c1 < nsp; c1++) //check on W
     {
@@ -123,7 +123,7 @@ int main (int argc, char **argv)
     
     std::cout << GridLogMessage << "Hot start ok " << std::endl;
     
-    Sp<Nc>::HotConfiguration(pRNG,Umu);
+    Sp<nsp>::HotConfiguration(pRNG,Umu);
     U = PeekIndex<LorentzIndex>(Umu,0);
     for (int c1 = 0; c1 < nsp; c1++) //check on W
     {
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index d1cf33bd..71c6acc7 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -20,8 +20,7 @@ int main (int argc, char **argv)
     LatticeColourMatrixD aux(&Grid);
     LatticeColourMatrixD identity(&Grid);
     
-    //const int nsp = Nc / 2;
-    const int nsp = Sp<Nc>::nsp;
+    const int nsp = Nc / 2;
     
     identity = 1.0;
     RealD epsilon = 0.01;
@@ -48,7 +47,7 @@ int main (int argc, char **argv)
     {
         std::cout << GridLogMessage << "This matrix should not leave Omega invariant, expect a warning" << std::endl;
     }
-    Sp<Nc>::OmegaInvariance(U);
+    Sp<nsp>::OmegaInvariance(U);
     std::cout <<GridLogMessage << std::endl;
     
     U = U + epsilon*identity;
@@ -79,7 +78,7 @@ int main (int argc, char **argv)
     
     // actual sp2n check
     std::cout << GridLogMessage << "Checking invariance after projection "<< std::endl;
-    Sp<Nc>::OmegaInvariance(U);
+    Sp<nsp>::OmegaInvariance(U);
     
     // checks on elements
     

From 2de03e5172d2a6f4b83e47acd0503c969ce303d0 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Wed, 23 Nov 2022 19:40:28 +0000
Subject: [PATCH 025/129] Revert "Revert "Fixing issue #11: consistent use of
 ncolour and nsp""

This reverts commit 3af4929ddab4caee9f561f835de30a2c8bc527c5.
---
 Grid/qcd/action/gauge/GaugeImplTypes.h | 24 +++----
 Grid/qcd/utils/Sp2n.h                  | 99 +++++++++++++-------------
 tests/sp2n/Test_Sp_start.cc            | 18 ++---
 tests/sp2n/Test_project_on_Sp.cc       |  7 +-
 4 files changed, 76 insertions(+), 72 deletions(-)

diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index dbab4386..dc39c30b 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -126,8 +126,8 @@ public:
     {
         if (isSp2n == true)
         {
-            const int nSp = Nrepresentation/2;
-            Sp<nSp>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
+            //const int nSp = Nrepresentation/2;
+            Sp<Nrepresentation>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
         } else
         {
         
@@ -148,18 +148,18 @@ public:
         if (isSp2n == true)
         {
             P = Ta(P);
-            const int nsp = Nc / 2;
+            //const int nsp = Nc / 2;
 
-            Sp<nsp>::iSp2nMatrix<Complex> gen;
+            Sp<Nc>::iSp2nMatrix<Complex> gen;
             
 
             auto Psum = P;
 
             Psum = Zero();
             
-            for (int a = 0; a < Sp<nsp>::AlgebraDimension; a++)
+            for (int a = 0; a < Sp<Nrepresentation>::AlgebraDimension; a++)
             {
-                Sp<nsp>::generator(a, gen);
+                Sp<Nrepresentation>::generator(a, gen);
 
                 auto coeff = 2. * trace(P * gen);
                 Psum += coeff * gen;
@@ -223,8 +223,8 @@ public:
   {
       if (isSp2n == true)
       {
-          const int nSp = Nrepresentation/2;
-          Sp<nSp>::HotConfiguration(pRNG, U);
+          //const int nSp = Nrepresentation/2;
+          Sp<Nrepresentation>::HotConfiguration(pRNG, U);
       } else
       {
           Group::HotConfiguration(pRNG, U);
@@ -235,8 +235,8 @@ public:
   {
       if (isSp2n == true)
     {
-        const int nSp = Nrepresentation/2;
-        Sp<nSp>::TepidConfiguration(pRNG, U);
+        //const int nSp = Nrepresentation/2;
+        Sp<Nrepresentation>::TepidConfiguration(pRNG, U);
     } else
     {
         Group::TepidConfiguration(pRNG, U);
@@ -248,8 +248,8 @@ public:
   {
       if (isSp2n == true)
       {
-          const int nSp = Nrepresentation/2;
-          Sp<nSp>::ColdConfiguration(pRNG, U);
+          //const int nSp = Nrepresentation/2;
+          Sp<Nrepresentation>::ColdConfiguration(pRNG, U);
       } else
       {
           Group::ColdConfiguration(pRNG, U);
diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.h
index 53ce3d5c..19e30568 100644
--- a/Grid/qcd/utils/Sp2n.h
+++ b/Grid/qcd/utils/Sp2n.h
@@ -5,21 +5,16 @@
 NAMESPACE_BEGIN(Grid);
 
 // Sp(2N)
-// ncolour = N
+// ncolour = 2N
 
-// need to be careful with n and 2n
-// I am defining the Sp class for Sp(2n) to be such that the template variable ncolour
-// is n inside 2n and the typedef at the end of the file should eliminate possible confusion.
-
-// the other routines, like projectOnSp2n, N will be the dimension of the actual number of colors for consistency with the sun routines
 
 template <int ncolour>
 class Sp {
 public:
-    static const int Dimension = ncolour*2;
-    static const int AlgebraDimension = ncolour*(2*ncolour +1);
-    static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
-    static const int nnsp = ncolour;
+    static const int nsp = ncolour/2;
+    static const int Dimension = ncolour;
+    static const int AlgebraDimension = nsp*(2*nsp +1);
+    static int su2subgroups(void) { return (nsp * (nsp - 1)) / 2; }
     
     
     template <typename vtype>
@@ -65,20 +60,17 @@ public:
     //     there are 6 types named a,b,c,d and w,z
     //     abcd are N(N-1)/2 each while wz are N each
     
-    
-    
-    
-    template <class cplx>
+ template <class cplx>
     static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
         // map lie index into type of generators: diagonal, abcd type, wz type
 
         int diagIndex;
         int aIndex, bIndex, cIndex, dIndex;
         int wIndex, zIndex; // a,b,c,d are N(N-1)/2 and w,z are N
-        int mod = ncolour * (ncolour-1) * 0.5;
-        int offdiag = 2*ncolour*ncolour; // number of generators not in the cartan subalgebra
+        int mod = nsp * (nsp-1) * 0.5;
+        int offdiag = 2*nsp*nsp; // number of generators not in the cartan subalgebra
         int wmod = 4*mod;
-        int zmod = wmod+ncolour;
+        int zmod = wmod+nsp;
         if (lieIndex >= offdiag) {
             diagIndex = lieIndex - offdiag; // 0, ... ,N-1
             //std::cout << GridLogMessage << "diag type " << std::endl;
@@ -136,7 +128,7 @@ public:
         RealD nrm = 1.0 / 2;
 
         ta()()(diagIndex,diagIndex) = nrm;
-        ta()()(diagIndex+ncolour,diagIndex+ncolour) = -nrm;
+        ta()()(diagIndex+nsp,diagIndex+nsp) = -nrm;
     }
     
     template <class cplx>
@@ -152,8 +144,8 @@ public:
         su2SubGroupIndex(i1, i2, aIndex);
         ta()()(i1,i2) = 1;
         ta()()(i2,i1) = 1;
-        ta()()(i1+ncolour,i2+ncolour) = -1;
-        ta()()(i2+ncolour,i1+ncolour) = -1;
+        ta()()(i1+nsp,i2+nsp) = -1;
+        ta()()(i2+nsp,i1+nsp) = -1;
 
         ta = ta * nrm;
     }
@@ -174,8 +166,8 @@ public:
 
         ta()()(i1,i2) = i;
         ta()()(i2,i1) = -i;
-        ta()()(i1+ncolour,i2+ncolour) = i;
-        ta()()(i2+ncolour,i1+ncolour) = -i;
+        ta()()(i1+nsp,i2+nsp) = i;
+        ta()()(i2+nsp,i1+nsp) = -i;
 
         ta = ta * nrm;
     }
@@ -191,10 +183,10 @@ public:
         RealD nrm = 1 / (2 * std::sqrt(2) );
         su2SubGroupIndex(i1, i2, cIndex);
         
-        ta()()(i1,i2+ncolour) = 1;
-        ta()()(i2,i1+ncolour) = 1;
-        ta()()(i1+ncolour,i2) = 1;
-        ta()()(i2+ncolour,i1) = 1;
+        ta()()(i1,i2+nsp) = 1;
+        ta()()(i2,i1+nsp) = 1;
+        ta()()(i1+nsp,i2) = 1;
+        ta()()(i2+nsp,i1) = 1;
 
         ta = ta * nrm;
     }
@@ -210,10 +202,10 @@ public:
         RealD nrm = 1 / (2 * std::sqrt(2)  );
         su2SubGroupIndex(i1, i2, dIndex);
 
-        ta()()(i1,i2+ncolour) = i;
-        ta()()(i2,i1+ncolour) = i;
-        ta()()(i1+ncolour,i2) = -i;
-        ta()()(i2+ncolour,i1) = -i;
+        ta()()(i1,i2+nsp) = i;
+        ta()()(i2,i1+nsp) = i;
+        ta()()(i1+nsp,i2) = -i;
+        ta()()(i2+nsp,i1) = -i;
 
         ta = ta * nrm;
     }
@@ -226,8 +218,8 @@ public:
          ta = Zero();
          RealD nrm = 1.0 / 2; //check
 
-         ta()()(wIndex,wIndex+ncolour) = 1;
-         ta()()(wIndex+ncolour,wIndex) = 1;
+         ta()()(wIndex,wIndex+nsp) = 1;
+         ta()()(wIndex+nsp,wIndex) = 1;
          
          ta = ta * nrm;
      }
@@ -240,8 +232,8 @@ public:
          ta = Zero();
          RealD nrm = 1.0 / 2; //check
          cplx i(0.0, 1.0);
-         ta()()(zIndex,zIndex+ncolour) = i;
-         ta()()(zIndex+ncolour,zIndex) = -i;
+         ta()()(zIndex,zIndex+nsp) = i;
+         ta()()(zIndex+nsp,zIndex) = -i;
          
          ta = ta * nrm;
      }
@@ -251,11 +243,11 @@ public:
     // Map a su2 subgroup number to the pair of rows that are non zero
     ////////////////////////////////////////////////////////////////////////
     static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
-      assert((su2_index >= 0) && (su2_index < (ncolour * (ncolour - 1)) / 2));
+      assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
 
       int spare = su2_index;
-      for (i1 = 0; spare >= (ncolour - 1 - i1); i1++) {
-        spare = spare - (ncolour - 1 - i1);  // remove the Nc-1-i1 terms
+      for (i1 = 0; spare >= (nsp - 1 - i1); i1++) {
+        spare = spare - (nsp - 1 - i1);  // remove the Nc-1-i1 terms
       }
       i2 = i1 + 1 + spare;
     }
@@ -268,7 +260,7 @@ public:
         for (int gen = 0; gen < AlgebraDimension; gen++) {
             Matrix ta;
             generator(gen, ta);
-            std::cout << GridLogMessage << "Nc (2n) = " << 2*ncolour << std::endl;
+            std::cout << GridLogMessage << "Nc = " << ncolour << std::endl;
             std::cout << GridLogMessage << " t_" << gen << std::endl;
             std::cout << GridLogMessage << ta << std::endl;
         }
@@ -464,10 +456,17 @@ public:
         ColourMatrix Omega;
         Omega = Zero();
         
-        for (int i = 0; i < ncolour; i++)
+        std::cout << GridLogMessage << "I am a ColourMatrix" << std::endl;
+        
+        //for (int i = 0; i < ncolour; i++)         wrong?!
+        //{
+        //    Omega()()(i, 2*ncolour-1-i) = 1.;
+        //    Omega()()(2*ncolour-1-i, i) = -1;
+        //}
+        for (int i = 0; i < nsp; i++)
         {
-            Omega()()(i, 2*ncolour-1-i) = 1.;
-            Omega()()(2*ncolour-1-i, i) = -1;
+            Omega()()(i, nsp+i) = 1.;
+            Omega()()(nsp+i, i) = -1;
         }
 
         auto diff = Omega - (in * Omega * transpose(in) );
@@ -498,6 +497,8 @@ public:
         Omega = Zero();
         identity = 1.;
         
+        std::cout << GridLogMessage << "I am a GaugeField " << std::endl;
+        
         U = PeekIndex<LorentzIndex>(in,1);
         
         OmegaInvariance(U);
@@ -516,10 +517,12 @@ public:
            Omega = Zero();
            identity = 1.;
            
-           for (int i = 0; i < ncolour; i++)
+           std::cout << GridLogMessage << "I am a LatticeColourMatrix " << std::endl;
+           
+           for (int i = 0; i < nsp; i++)
            {
-               Omega()()(i, ncolour+i) = 1.;
-               Omega()()(ncolour+i, i) = -1;
+               Omega()()(i, nsp+i) = 1.;
+               Omega()()(nsp+i, i) = -1;
            }
            
            std::cout << GridLogMessage << "Omega = " << Omega()() << std::endl;
@@ -568,10 +571,10 @@ public:
    }
  }
 
-typedef Sp<1> Sp2;
-typedef Sp<2> Sp4;
-typedef Sp<3> Sp6;
-typedef Sp<4> Sp8;
+typedef Sp<2> Sp2;
+typedef Sp<4> Sp4;
+typedef Sp<6> Sp6;
+typedef Sp<8> Sp8;
 
 NAMESPACE_END(Grid);
 #endif
diff --git a/tests/sp2n/Test_Sp_start.cc b/tests/sp2n/Test_Sp_start.cc
index da19779f..16a66367 100644
--- a/tests/sp2n/Test_Sp_start.cc
+++ b/tests/sp2n/Test_Sp_start.cc
@@ -21,7 +21,7 @@ int main (int argc, char **argv)
     
     double vol = Umu.Grid()->gSites();
 
-    const int nsp = Nc / 2;
+    const int nsp = Sp<Nc>::nsp;
     identity = 1.;
     Cidentity = 1.;
     
@@ -34,8 +34,8 @@ int main (int argc, char **argv)
     std::cout << GridLogMessage << "-------" << std::endl;
     std::cout << GridLogMessage << "Checking Cold Configuration " << std::endl;
     std::cout << GridLogMessage << std::endl;
-    Sp<nsp>::ColdConfiguration(pRNG,Umu);
-    Sp<nsp>::OmegaInvariance(Umu);
+    Sp<Nc>::ColdConfiguration(pRNG,Umu);
+    Sp<Nc>::OmegaInvariance(Umu);
     std::cout << GridLogMessage << std::endl;
 
     Umu = Umu - identity;
@@ -47,8 +47,8 @@ int main (int argc, char **argv)
     std::cout << GridLogMessage << "-------" << std::endl;
     std::cout << GridLogMessage << "Checking Hot Configuration" << std::endl;
     std::cout << GridLogMessage << std::endl;
-    Sp<nsp>::HotConfiguration(pRNG,Umu);
-    Sp<nsp>::OmegaInvariance(Umu);
+    Sp<Nc>::HotConfiguration(pRNG,Umu);
+    Sp<Nc>::OmegaInvariance(Umu);
     std::cout << GridLogMessage << std::endl;
     U = PeekIndex<LorentzIndex>(Umu,1);
     std::cout << GridLogMessage << "Checking unitarity " << std::endl;
@@ -62,8 +62,8 @@ int main (int argc, char **argv)
     std::cout << GridLogMessage << "-------" << std::endl;
     std::cout << GridLogMessage << "Checking Tepid Configuration" << std::endl;
     std::cout << GridLogMessage << std::endl;
-    Sp<nsp>::TepidConfiguration(pRNG,Umu);
-    Sp<nsp>::OmegaInvariance(Umu);
+    Sp<Nc>::TepidConfiguration(pRNG,Umu);
+    Sp<Nc>::OmegaInvariance(Umu);
     std::cout << GridLogMessage << std::endl;
     U = PeekIndex<LorentzIndex>(Umu,1);
     std::cout << GridLogMessage << "Checking unitarity " << std::endl;
@@ -85,7 +85,7 @@ int main (int argc, char **argv)
     Complex i(0., 1.);
     
     
-    Sp<nsp>::HotConfiguration(pRNG,Umu);
+    Sp<Nc>::HotConfiguration(pRNG,Umu);
     U = PeekIndex<LorentzIndex>(Umu,0);
     for (int c1 = 0; c1 < nsp; c1++) //check on W
     {
@@ -123,7 +123,7 @@ int main (int argc, char **argv)
     
     std::cout << GridLogMessage << "Hot start ok " << std::endl;
     
-    Sp<nsp>::HotConfiguration(pRNG,Umu);
+    Sp<Nc>::HotConfiguration(pRNG,Umu);
     U = PeekIndex<LorentzIndex>(Umu,0);
     for (int c1 = 0; c1 < nsp; c1++) //check on W
     {
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 71c6acc7..d1cf33bd 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -20,7 +20,8 @@ int main (int argc, char **argv)
     LatticeColourMatrixD aux(&Grid);
     LatticeColourMatrixD identity(&Grid);
     
-    const int nsp = Nc / 2;
+    //const int nsp = Nc / 2;
+    const int nsp = Sp<Nc>::nsp;
     
     identity = 1.0;
     RealD epsilon = 0.01;
@@ -47,7 +48,7 @@ int main (int argc, char **argv)
     {
         std::cout << GridLogMessage << "This matrix should not leave Omega invariant, expect a warning" << std::endl;
     }
-    Sp<nsp>::OmegaInvariance(U);
+    Sp<Nc>::OmegaInvariance(U);
     std::cout <<GridLogMessage << std::endl;
     
     U = U + epsilon*identity;
@@ -78,7 +79,7 @@ int main (int argc, char **argv)
     
     // actual sp2n check
     std::cout << GridLogMessage << "Checking invariance after projection "<< std::endl;
-    Sp<nsp>::OmegaInvariance(U);
+    Sp<Nc>::OmegaInvariance(U);
     
     // checks on elements
     

From 22064c7e4c1c737fa8a1296f70b1f491f2925eac Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 25 Nov 2022 13:10:29 +0000
Subject: [PATCH 026/129] Fixing #11

---
 Grid/qcd/representations/sp_two_index.h       | 14 ++++++-------
 Grid/qcd/representations/spfundamental.h      |  4 ++--
 Grid/qcd/utils/Sp2nTwoIndex.h                 | 20 +++++++++----------
 .../sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc |  4 ++--
 .../Test_hmc_Sp_WilsonFundFermionGauge.cc     |  8 ++++----
 5 files changed, 25 insertions(+), 25 deletions(-)

diff --git a/Grid/qcd/representations/sp_two_index.h b/Grid/qcd/representations/sp_two_index.h
index d6884736..ec0663b4 100644
--- a/Grid/qcd/representations/sp_two_index.h
+++ b/Grid/qcd/representations/sp_two_index.h
@@ -29,7 +29,7 @@ public:
   typedef typename Sp_TwoIndex<ncolour, S>::LatticeTwoIndexField LatticeField;
   static const int Dimension = (ncolour * (ncolour + S) / 2) - 1;
   static const bool isFundamental = false;
-  static const int nsp = Nc / 2;
+  //static const int nsp = Nc / 2;
   LatticeField U;
 
   explicit SpTwoIndexRep(GridBase *grid) : U(grid) {}
@@ -43,7 +43,7 @@ public:
     U = Zero();
     LatticeColourMatrix tmp(Uin.Grid());
 
-    Vector<typename Sp<nsp>::Matrix> eij(Dimension);
+    Vector<typename Sp<ncolour>::Matrix> eij(Dimension);
 
     for (int a = 0; a < Dimension; a++)
       Sp_TwoIndex<ncolour, S>::base(a, eij[a]);
@@ -71,7 +71,7 @@ public:
 
       out_mu = Zero();
 
-      typename Sp<nsp>::LatticeAlgebraVector h(in.Grid());
+      typename Sp<ncolour>::LatticeAlgebraVector h(in.Grid());
       projectOnAlgebra(h, in_mu, double(Nc + 2 * S));  // factor T(r)/T(fund)
       FundamentalLieAlgebraMatrix(h, out_mu);          // apply scale only once
       pokeLorentz(out, out_mu, mu);                     // should be 2 for sp4 as. ok
@@ -80,15 +80,15 @@ public:
   }
 
 private:
-  void projectOnAlgebra(typename Sp<nsp>::LatticeAlgebraVector &h_out,
+  void projectOnAlgebra(typename Sp<ncolour>::LatticeAlgebraVector &h_out,
                         const LatticeMatrix &in, Real scale = 1.0) const {
     Sp_TwoIndex<ncolour, S>::projectOnAlgebra(h_out, in, scale);
   }
 
   void FundamentalLieAlgebraMatrix(
-				   typename Sp<nsp>::LatticeAlgebraVector &h,
-				   typename Sp<nsp>::LatticeMatrix &out, Real scale = 1.0) const {
-    Sp<nsp>::FundamentalLieAlgebraMatrix(h, out, scale);
+				   typename Sp<ncolour>::LatticeAlgebraVector &h,
+				   typename Sp<ncolour>::LatticeMatrix &out, Real scale = 1.0) const {
+    Sp<ncolour>::FundamentalLieAlgebraMatrix(h, out, scale);
   }
 };
 
diff --git a/Grid/qcd/representations/spfundamental.h b/Grid/qcd/representations/spfundamental.h
index bab9a005..df6b6fed 100644
--- a/Grid/qcd/representations/spfundamental.h
+++ b/Grid/qcd/representations/spfundamental.h
@@ -14,12 +14,12 @@ template <int ncolour>
 class SpFundamentalRep {
 public:
   static const int Dimension = ncolour;
-  static const int nSp = ncolour/2;
+  //static const int nSp = ncolour/2;
   static const bool isFundamental = true;
 
   // typdef to be used by the Representations class in HMC to get the
   // types for the higher representation fields
-  typedef typename Sp<nSp>::LatticeMatrix LatticeMatrix;
+  typedef typename Sp<ncolour>::LatticeMatrix LatticeMatrix;
   typedef LatticeGaugeField LatticeField;
   
   explicit SpFundamentalRep(GridBase* grid) {} //do nothing
diff --git a/Grid/qcd/utils/Sp2nTwoIndex.h b/Grid/qcd/utils/Sp2nTwoIndex.h
index 60739551..3b685802 100644
--- a/Grid/qcd/utils/Sp2nTwoIndex.h
+++ b/Grid/qcd/utils/Sp2nTwoIndex.h
@@ -33,11 +33,11 @@ NAMESPACE_BEGIN(Grid);
 //inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
 
 template <int ncolour, TwoIndexSymmetry S>
-class Sp_TwoIndex : public Sp<Config_nsp> {
+class Sp_TwoIndex : public Sp<ncolour> {
 public:
   static const int nsp = ncolour/2;
   static const int Dimension = nsp * (ncolour + S) - 1 ;
-  static const int NumGenerators = Sp<nsp>::AlgebraDimension;
+  static const int NumGenerators = Sp<ncolour>::AlgebraDimension;
 
   template <typename vtype>
   using iSp2nTwoIndexMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
@@ -175,21 +175,21 @@ public:
 
   template <class cplx>
   static void generator(int Index, iSp2nTwoIndexMatrix<cplx> &i2indTa) {
-    Vector<typename Sp<nsp>::template iSp2nMatrix<cplx> > ta(
+    Vector<typename Sp<ncolour>::template iSp2nMatrix<cplx> > ta(
 								NumGenerators);
-    Vector<typename Sp<nsp>::template iSp2nMatrix<cplx> > eij(Dimension);
-    typename Sp<nsp>::template iSp2nMatrix<cplx> tmp;
+    Vector<typename Sp<ncolour>::template iSp2nMatrix<cplx> > eij(Dimension);
+    typename Sp<ncolour>::template iSp2nMatrix<cplx> tmp;
     i2indTa = Zero();
     
     for (int a = 0; a < NumGenerators; a++)
-      Sp<nsp>::generator(a, ta[a]);
+      Sp<ncolour>::generator(a, ta[a]);
     
     for (int a = 0; a < Dimension; a++) base(a, eij[a]);
 
     for (int a = 0; a < Dimension; a++) {
       tmp = transpose(ta[Index]) * adj(eij[a]) + adj(eij[a]) * ta[Index];
       for (int b = 0; b < Dimension; b++) {
-        typename Sp<nsp>::template iSp2nMatrix<cplx> tmp1 =
+        typename Sp<ncolour>::template iSp2nMatrix<cplx> tmp1 =
 	  tmp * eij[b]; 
         Complex iTr = TensorRemove(timesI(trace(tmp1)));
         i2indTa()()(a, b) = iTr;
@@ -245,7 +245,7 @@ public:
   }
 
   static void TwoIndexLieAlgebraMatrix(
-				       const typename Sp<nsp>::LatticeAlgebraVector &h,
+				       const typename Sp<ncolour>::LatticeAlgebraVector &h,
 				       LatticeTwoIndexMatrix &out, Real scale = 1.0) {
     conformable(h, out);
     GridBase *grid = out.Grid();
@@ -264,7 +264,7 @@ public:
   // Projects the algebra components 
   // of a lattice matrix ( of dimension ncol*ncol -1 )
   static void projectOnAlgebra(
-			       typename Sp<nsp>::LatticeAlgebraVector &h_out,
+			       typename Sp<ncolour>::LatticeAlgebraVector &h_out,
 			       const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
     conformable(h_out, in);
     h_out = Zero();
@@ -280,7 +280,7 @@ public:
 
   // a projector that keeps the generators stored to avoid the overhead of
   // recomputing them
-  static void projector(typename Sp<nsp>::LatticeAlgebraVector &h_out,
+  static void projector(typename Sp<ncolour>::LatticeAlgebraVector &h_out,
                         const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
     conformable(h_out, in);
     // to store the generators
diff --git a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
index c5eb94d0..72fae3f4 100644
--- a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
+++ b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
@@ -22,7 +22,7 @@ int main(int argc, char **argv) {
   CheckpointerParameters CPparams;
   CPparams.config_prefix = "ckpoint_lat";
   CPparams.rng_prefix = "ckpoint_rng";
-  CPparams.saveInterval = 5;
+  CPparams.saveInterval = 100;
   CPparams.format = "IEEE64BIG";
     
   TheHMC.Resources.LoadNerscCheckpointer(CPparams);
@@ -46,7 +46,7 @@ int main(int argc, char **argv) {
    SpTwoIndexAntiSymmetricRepresentation::LatticeField U(GridPtr);
     //LatticeGaugeField U(GridPtr);
     
-  RealD mass = -0.85;
+  RealD mass = -0.115;
   
 
   std::vector<Complex> boundary = {-1,-1,-1,-1};
diff --git a/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
index d845c98f..45f86ba8 100644
--- a/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
+++ b/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
@@ -22,7 +22,7 @@ int main(int argc, char **argv) {
   CheckpointerParameters CPparams;
   CPparams.config_prefix = "ckpoint_lat";
   CPparams.rng_prefix = "ckpoint_rng";
-  CPparams.saveInterval = 5;
+  CPparams.saveInterval = 100;
   CPparams.format = "IEEE64BIG";
     
   TheHMC.Resources.LoadNerscCheckpointer(CPparams);
@@ -36,7 +36,7 @@ int main(int argc, char **argv) {
   typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
   TheHMC.Resources.AddObservable<PlaqObs>();
     
-  RealD beta = 2.25 ;
+  RealD beta = 7.2 ;
     
   SymplWilsonGaugeActionR Waction(beta);
     
@@ -46,7 +46,7 @@ int main(int argc, char **argv) {
     SpFundamentalRepresentation::LatticeField U(GridPtr);
     //LatticeGaugeField U(GridPtr);
     
-  RealD mass = -0.95;
+  RealD mass = -0.76;
 
   FermionAction FermOp(U, *GridPtr, *GridRBPtr, mass);
     
@@ -66,7 +66,7 @@ int main(int argc, char **argv) {
     TheHMC.TheAction.push_back(Level1);
     TheHMC.TheAction.push_back(Level2);
     
-    TheHMC.Parameters.MD.MDsteps = 20;
+    TheHMC.Parameters.MD.MDsteps = 36;
     TheHMC.Parameters.MD.trajL   = 1.0;
     
     TheHMC.ReadCommandLine(argc, argv);

From 03235d63686dac3b369fd5208c2bb1ef50c0dbb1 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Fri, 25 Nov 2022 16:57:40 +0000
Subject: [PATCH 027/129] Fixed type in configure.ac

---
 configure.ac | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/configure.ac b/configure.ac
index 3a4ed469..04a3cdf4 100644
--- a/configure.ac
+++ b/configure.ac
@@ -838,7 +838,7 @@ AC_CONFIG_FILES(tests/lanczos/Makefile)
 AC_CONFIG_FILES(tests/smearing/Makefile)
 AC_CONFIG_FILES(tests/qdpxx/Makefile)
 AC_CONFIG_FILES(tests/testu01/Makefile)
-AC_CONFIG_FILES(tests/Sp2n/Makefile)
+AC_CONFIG_FILES(tests/sp2n/Makefile)
 AC_CONFIG_FILES(benchmarks/Makefile)
 AC_CONFIG_FILES(examples/Makefile)
 AC_OUTPUT

From 629cb2987ad4293f4cc79aac713a0a6fd8c50fe2 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Fri, 25 Nov 2022 17:40:21 +0000
Subject: [PATCH 028/129] Fix typo in Makefile.am

---
 tests/sp2n/Makefile.am | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tests/sp2n/Makefile.am b/tests/sp2n/Makefile.am
index 0ee7421c..164fce52 100644
--- a/tests/sp2n/Makefile.am
+++ b/tests/sp2n/Makefile.am
@@ -4,4 +4,4 @@ include Make.inc
 
 check: tests
 	./Test_project_on_Sp
-	./test_sp2n_lie_gen
+	./Test_sp2n_lie_gen

From 1aa28b47ae31c32e8a885c2d8c183ab231dc0a6f Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Fri, 25 Nov 2022 17:40:40 +0000
Subject: [PATCH 029/129] Add existing test to check

---
 tests/sp2n/Makefile.am | 1 +
 1 file changed, 1 insertion(+)

diff --git a/tests/sp2n/Makefile.am b/tests/sp2n/Makefile.am
index 164fce52..346c8ad0 100644
--- a/tests/sp2n/Makefile.am
+++ b/tests/sp2n/Makefile.am
@@ -5,3 +5,4 @@ include Make.inc
 check: tests
 	./Test_project_on_Sp
 	./Test_sp2n_lie_gen
+	./Test_Sp_start

From 9273f2937c3322c2fd33dfe06088a2d1566939ca Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Fri, 25 Nov 2022 17:44:08 +0000
Subject: [PATCH 030/129] Autoformat google style

---
 Grid/qcd/utils/SUn.h | 281 +++++++++++++++++++++----------------------
 1 file changed, 138 insertions(+), 143 deletions(-)

diff --git a/Grid/qcd/utils/SUn.h b/Grid/qcd/utils/SUn.h
index 675493b3..0f7482ae 100644
--- a/Grid/qcd/utils/SUn.h
+++ b/Grid/qcd/utils/SUn.h
@@ -28,7 +28,7 @@ with this program; if not, write to the Free Software Foundation, Inc.,
 See the full license in the file "LICENSE" in the top level distribution
 directory
 *************************************************************************************/
-			   /*  END LEGAL */
+/*  END LEGAL */
 #ifndef QCD_UTIL_SUN_H
 #define QCD_UTIL_SUN_H
 
@@ -36,7 +36,7 @@ NAMESPACE_BEGIN(Grid);
 
 template <int ncolour>
 class SU {
-public:
+ public:
   static const int Dimension = ncolour;
   static const int AdjointDimension = ncolour * ncolour - 1;
   static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
@@ -47,7 +47,7 @@ public:
   using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
   template <typename vtype>
   using iSUnAlgebraVector =
-    iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
+      iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
 
   //////////////////////////////////////////////////////////////////////////////////////////////////
   // Types can be accessed as SU<2>::Matrix , SU<2>::vSUnMatrix,
@@ -159,7 +159,7 @@ public:
     else
       generatorSigmaX(su2Index, ta);
   }
-  
+
   template <class cplx>
   static void generatorSigmaY(int su2Index, iSUnMatrix<cplx> &ta) {
     ta = Zero();
@@ -169,7 +169,7 @@ public:
     ta()()(i2, i1) = 1.0;
     ta = ta * 0.5;
   }
-  
+
   template <class cplx>
   static void generatorSigmaX(int su2Index, iSUnMatrix<cplx> &ta) {
     ta = Zero();
@@ -194,8 +194,6 @@ public:
     ta = ta * nrm;
   }
 
-
-
   ////////////////////////////////////////////////////////////////////////
   // Map a su2 subgroup number to the pair of rows that are non zero
   ////////////////////////////////////////////////////////////////////////
@@ -223,11 +221,10 @@ public:
     int i0, i1;
     su2SubGroupIndex(i0, i1, su2_index);
 
-    autoView( subgroup_v , subgroup,AcceleratorWrite);
-    autoView( source_v   , source,AcceleratorRead);
-    autoView( Determinant_v , Determinant,AcceleratorWrite);
+    autoView(subgroup_v, subgroup, AcceleratorWrite);
+    autoView(source_v, source, AcceleratorRead);
+    autoView(Determinant_v, Determinant, AcceleratorWrite);
     accelerator_for(ss, grid->oSites(), 1, {
-
       subgroup_v[ss]()()(0, 0) = source_v[ss]()()(i0, i0);
       subgroup_v[ss]()()(0, 1) = source_v[ss]()()(i0, i1);
       subgroup_v[ss]()()(1, 0) = source_v[ss]()()(i1, i0);
@@ -241,7 +238,7 @@ public:
 
       // this should be purely real
       Determinant_v[ss] =
-	Sigma()()(0, 0) * Sigma()()(1, 1) - Sigma()()(0, 1) * Sigma()()(1, 0);
+          Sigma()()(0, 0) * Sigma()()(1, 1) - Sigma()()(0, 1) * Sigma()()(1, 0);
     });
   }
 
@@ -257,16 +254,14 @@ public:
     su2SubGroupIndex(i0, i1, su2_index);
 
     dest = 1.0;  // start out with identity
-    autoView( dest_v , dest, AcceleratorWrite);
-    autoView( subgroup_v, subgroup, AcceleratorRead);
-    accelerator_for(ss, grid->oSites(),1,
-    {
+    autoView(dest_v, dest, AcceleratorWrite);
+    autoView(subgroup_v, subgroup, AcceleratorRead);
+    accelerator_for(ss, grid->oSites(), 1, {
       dest_v[ss]()()(i0, i0) = subgroup_v[ss]()()(0, 0);
       dest_v[ss]()()(i0, i1) = subgroup_v[ss]()()(0, 1);
       dest_v[ss]()()(i1, i0) = subgroup_v[ss]()()(1, 0);
       dest_v[ss]()()(i1, i1) = subgroup_v[ss]()()(1, 1);
     });
-
   }
 
   ///////////////////////////////////////////////
@@ -279,12 +274,12 @@ public:
   // in action.
   //
   ///////////////////////////////////////////////
-  static void SubGroupHeatBath(GridSerialRNG &sRNG, GridParallelRNG &pRNG,
-			       RealD beta,  // coeff multiplying staple in action (with no 1/Nc)
-			       LatticeMatrix &link,
-			       const LatticeMatrix &barestaple,  // multiplied by action coeffs so th
-			       int su2_subgroup, int nheatbath, LatticeInteger &wheremask) 
-  {
+  static void SubGroupHeatBath(
+      GridSerialRNG &sRNG, GridParallelRNG &pRNG,
+      RealD beta,  // coeff multiplying staple in action (with no 1/Nc)
+      LatticeMatrix &link,
+      const LatticeMatrix &barestaple,  // multiplied by action coeffs so th
+      int su2_subgroup, int nheatbath, LatticeInteger &wheremask) {
     GridBase *grid = link.Grid();
 
     const RealD twopi = 2.0 * M_PI;
@@ -297,7 +292,8 @@ public:
     V = link * staple;
 
     // Subgroup manipulation in the lie algebra space
-    LatticeSU2Matrix u(grid);  // Kennedy pendleton "u" real projected normalised Sigma
+    LatticeSU2Matrix u(
+        grid);  // Kennedy pendleton "u" real projected normalised Sigma
     LatticeSU2Matrix uinv(grid);
     LatticeSU2Matrix ua(grid);  // a in pauli form
     LatticeSU2Matrix b(grid);   // rotated matrix after hb
@@ -390,7 +386,7 @@ public:
 
     xi = 0.5 * sqrt(udet);  // 4xi^2 = Det [ Sig - Sig^dag  + 1 Tr Sigdag]
     u = 0.5 * u *
-      pow(xi, -1.0);  //  u   = 1/2xi [ Sig - Sig^dag  + 1 Tr Sigdag]
+        pow(xi, -1.0);  //  u   = 1/2xi [ Sig - Sig^dag  + 1 Tr Sigdag]
 
     // Debug test for sanity
     uinv = adj(u);
@@ -405,29 +401,24 @@ public:
       r) )
       = da0 r/2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r) )
 
-      Action factor Q(h) dh  = e^-S[h]  dh =  e^{  xi Tr uh} dh    // beta enters
-      through xi
-      =  e^{2 xi (h.u)} dh
-      =  e^{2 xi h0u0}.e^{2 xi h1u1}.e^{2 xi
-      h2u2}.e^{2 xi h3u3} dh
+      Action factor Q(h) dh  = e^-S[h]  dh =  e^{  xi Tr uh} dh    // beta
+      enters through xi =  e^{2 xi (h.u)} dh =  e^{2 xi h0u0}.e^{2 xi h1u1}.e^{2
+      xi h2u2}.e^{2 xi h3u3} dh
 
       Therefore for each site, take xi for that site
       i) generate  |a0|<1 with dist
       (1-a0^2)^0.5 e^{2 xi a0 } da0
 
-      Take alpha = 2 xi  = 2 xi [ recall 2 beta/Nc unmod staple norm]; hence 2.0/Nc
-      factor in Chroma ]
-      A. Generate two uniformly distributed pseudo-random numbers R and R', R'',
-      R''' in the unit interval;
-      B. Set X = -(ln R)/alpha, X' =-(ln R')/alpha;
-      C. Set C = cos^2(2pi R"), with R" another uniform random number in [0,1] ;
-      D. Set A = XC;
-      E. Let d  = X'+A;
+      Take alpha = 2 xi  = 2 xi [ recall 2 beta/Nc unmod staple norm];
+      hence 2.0/Nc factor in Chroma ] A. Generate two uniformly distributed
+      pseudo-random numbers R and R', R'', R''' in the unit interval; B. Set X =
+      -(ln R)/alpha, X' =-(ln R')/alpha; C. Set C = cos^2(2pi R"), with R"
+      another uniform random number in [0,1] ; D. Set A = XC; E. Let d  = X'+A;
       F. If R'''^2 :> 1 - 0.5 d,  go back to A;
       G. Set a0 = 1 - d;
 
-      Note that in step D setting B ~ X - A and using B in place of A in step E will
-      generate a second independent a 0 value.
+      Note that in step D setting B ~ X - A and using B in place of A in step E
+      will generate a second independent a 0 value.
     */
 
     /////////////////////////////////////////////////////////
@@ -449,7 +440,7 @@ public:
     LatticeReal alpha(grid);
 
     //    std::cout<<GridLogMessage<<"xi "<<xi <<std::endl;
-    xi = 2.0 *xi;
+    xi = 2.0 * xi;
     alpha = toReal(xi);
 
     do {
@@ -522,7 +513,7 @@ public:
     a[2] = a123mag * sin_theta * sin(phi);
     a[3] = a123mag * cos_theta;
 
-    ua = toComplex(a[0]) * ident  + toComplex(a[1]) * pauli1 +
+    ua = toComplex(a[0]) * ident + toComplex(a[1]) * pauli1 +
          toComplex(a[2]) * pauli2 + toComplex(a[3]) * pauli3;
 
     b = 1.0;
@@ -568,8 +559,6 @@ public:
     }
   }
 
-
-
   static void testGenerators(void) {
     Matrix ta;
     Matrix tb;
@@ -610,8 +599,8 @@ public:
 
   // reunitarise??
   template <typename LatticeMatrixType>
-  static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out, double scale = 1.0) 
-  {
+  static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out,
+                           double scale = 1.0) {
     GridBase *grid = out.Grid();
 
     typedef typename LatticeMatrixType::vector_type vector_type;
@@ -620,7 +609,8 @@ public:
     typedef iSinglet<vector_type> vTComplexType;
 
     typedef Lattice<vTComplexType> LatticeComplexType;
-    typedef typename GridTypeMapper<typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
+    typedef typename GridTypeMapper<
+        typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
 
     LatticeComplexType ca(grid);
     LatticeMatrixType lie(grid);
@@ -642,7 +632,6 @@ public:
       la = ci * ca * ta;
 
       lie = lie + la;  // e^{i la ta}
-
     }
     taExp(lie, out);
   }
@@ -681,57 +670,61 @@ public:
       out += la;
     }
   }
-/*
- * Fundamental rep gauge xform
- */
-  template<typename Fundamental,typename GaugeMat>
-  static void GaugeTransformFundamental( Fundamental &ferm, GaugeMat &g){
+  /*
+   * Fundamental rep gauge xform
+   */
+  template <typename Fundamental, typename GaugeMat>
+  static void GaugeTransformFundamental(Fundamental &ferm, GaugeMat &g) {
     GridBase *grid = ferm._grid;
-    conformable(grid,g._grid);
-    ferm = g*ferm;
+    conformable(grid, g._grid);
+    ferm = g * ferm;
   }
-/*
- * Adjoint rep gauge xform
- */
+  /*
+   * Adjoint rep gauge xform
+   */
 
-  template<typename GaugeField,typename GaugeMat>
-  static void GaugeTransform( GaugeField &Umu, GaugeMat &g){
+  template <typename GaugeField, typename GaugeMat>
+  static void GaugeTransform(GaugeField &Umu, GaugeMat &g) {
     GridBase *grid = Umu.Grid();
-    conformable(grid,g.Grid());
+    conformable(grid, g.Grid());
 
     GaugeMat U(grid);
-    GaugeMat ag(grid); ag = adj(g);
+    GaugeMat ag(grid);
+    ag = adj(g);
 
-    for(int mu=0;mu<Nd;mu++){
-      U= PeekIndex<LorentzIndex>(Umu,mu);
-      U = g*U*Cshift(ag, mu, 1);
-      PokeIndex<LorentzIndex>(Umu,U,mu);
+    for (int mu = 0; mu < Nd; mu++) {
+      U = PeekIndex<LorentzIndex>(Umu, mu);
+      U = g * U * Cshift(ag, mu, 1);
+      PokeIndex<LorentzIndex>(Umu, U, mu);
     }
   }
-  template<typename GaugeMat>
-  static void GaugeTransform( std::vector<GaugeMat> &U, GaugeMat &g){
+  template <typename GaugeMat>
+  static void GaugeTransform(std::vector<GaugeMat> &U, GaugeMat &g) {
     GridBase *grid = g.Grid();
-    GaugeMat ag(grid); ag = adj(g);
-    for(int mu=0;mu<Nd;mu++){
-      U[mu] = g*U[mu]*Cshift(ag, mu, 1);
+    GaugeMat ag(grid);
+    ag = adj(g);
+    for (int mu = 0; mu < Nd; mu++) {
+      U[mu] = g * U[mu] * Cshift(ag, mu, 1);
     }
   }
-  template<typename GaugeField,typename GaugeMat>
-  static void RandomGaugeTransform(GridParallelRNG &pRNG, GaugeField &Umu, GaugeMat &g){
-    LieRandomize(pRNG,g,1.0);
-    GaugeTransform(Umu,g);
+  template <typename GaugeField, typename GaugeMat>
+  static void RandomGaugeTransform(GridParallelRNG &pRNG, GaugeField &Umu,
+                                   GaugeMat &g) {
+    LieRandomize(pRNG, g, 1.0);
+    GaugeTransform(Umu, g);
   }
 
-  // Projects the algebra components a lattice matrix (of dimension ncol*ncol -1 )
-  // inverse operation: FundamentalLieAlgebraMatrix
-  static void projectOnAlgebra(LatticeAlgebraVector &h_out, const LatticeMatrix &in, Real scale = 1.0) {
+  // Projects the algebra components a lattice matrix (of dimension ncol*ncol -1
+  // ) inverse operation: FundamentalLieAlgebraMatrix
+  static void projectOnAlgebra(LatticeAlgebraVector &h_out,
+                               const LatticeMatrix &in, Real scale = 1.0) {
     conformable(h_out, in);
     h_out = Zero();
     Matrix Ta;
 
     for (int a = 0; a < AdjointDimension; a++) {
       generator(a, Ta);
-      pokeColour(h_out, - 2.0 * (trace(timesI(Ta) * in)) * scale, a);
+      pokeColour(h_out, -2.0 * (trace(timesI(Ta) * in)) * scale, a);
     }
   }
 
@@ -747,37 +740,37 @@ public:
       PokeIndex<LorentzIndex>(out, Umu, mu);
     }
   }
-  template<typename GaugeField>
-  static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out){
+  template <typename GaugeField>
+  static void TepidConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
     typedef typename GaugeField::vector_type vector_type;
     typedef iSUnMatrix<vector_type> vMatrixType;
     typedef Lattice<vMatrixType> LatticeMatrixType;
 
     LatticeMatrixType Umu(out.Grid());
-    for(int mu=0;mu<Nd;mu++){
-      LieRandomize(pRNG,Umu,0.01);
-      PokeIndex<LorentzIndex>(out,Umu,mu);
+    for (int mu = 0; mu < Nd; mu++) {
+      LieRandomize(pRNG, Umu, 0.01);
+      PokeIndex<LorentzIndex>(out, Umu, mu);
     }
   }
-  template<typename GaugeField>
-  static void ColdConfiguration(GaugeField &out){
+  template <typename GaugeField>
+  static void ColdConfiguration(GaugeField &out) {
     typedef typename GaugeField::vector_type vector_type;
     typedef iSUnMatrix<vector_type> vMatrixType;
     typedef Lattice<vMatrixType> LatticeMatrixType;
 
     LatticeMatrixType Umu(out.Grid());
-    Umu=1.0;
-    for(int mu=0;mu<Nd;mu++){
-      PokeIndex<LorentzIndex>(out,Umu,mu);
+    Umu = 1.0;
+    for (int mu = 0; mu < Nd; mu++) {
+      PokeIndex<LorentzIndex>(out, Umu, mu);
     }
   }
-  template<typename GaugeField>
-  static void ColdConfiguration(GridParallelRNG &pRNG,GaugeField &out){
+  template <typename GaugeField>
+  static void ColdConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
     ColdConfiguration(out);
   }
 
-  template<typename LatticeMatrixType>
-  static void taProj( const LatticeMatrixType &in,  LatticeMatrixType &out){
+  template <typename LatticeMatrixType>
+  static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out) {
     out = Ta(in);
   }
   template <typename LatticeMatrixType>
@@ -799,85 +792,88 @@ public:
   }
 };
 
-template<int N>
-LatticeComplexD Determinant(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
-{
-  GridBase *grid=Umu.Grid();
+template <int N>
+LatticeComplexD Determinant(
+    const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
+  GridBase *grid = Umu.Grid();
   auto lvol = grid->lSites();
   LatticeComplexD ret(grid);
 
-  autoView(Umu_v,Umu,CpuRead);
-  autoView(ret_v,ret,CpuWrite);
-  thread_for(site,lvol,{
-    Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N,N);
+  autoView(Umu_v, Umu, CpuRead);
+  autoView(ret_v, ret, CpuWrite);
+  thread_for(site, lvol, {
+    Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N, N);
     Coordinate lcoor;
     grid->LocalIndexToLocalCoor(site, lcoor);
     iScalar<iScalar<iMatrix<ComplexD, N> > > Us;
     peekLocalSite(Us, Umu_v, lcoor);
-    for(int i=0;i<N;i++){
-      for(int j=0;j<N;j++){
-	EigenU(i,j) = Us()()(i,j);
-      }}
+    for (int i = 0; i < N; i++) {
+      for (int j = 0; j < N; j++) {
+        EigenU(i, j) = Us()()(i, j);
+      }
+    }
     ComplexD det = EigenU.determinant();
-    pokeLocalSite(det,ret_v,lcoor);
+    pokeLocalSite(det, ret_v, lcoor);
   });
   return ret;
 }
-template<int N>
-static void ProjectSUn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
-{
-  Umu      = ProjectOnGroup(Umu);
+template <int N>
+static void ProjectSUn(
+    Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
+  Umu = ProjectOnGroup(Umu);
   auto det = Determinant(Umu);
 
   det = conjugate(det);
 
-  for(int i=0;i<N;i++){
-    auto element = PeekIndex<ColourIndex>(Umu,N-1,i);
+  for (int i = 0; i < N; i++) {
+    auto element = PeekIndex<ColourIndex>(Umu, N - 1, i);
     element = element * det;
-    PokeIndex<ColourIndex>(Umu,element,Nc-1,i);
+    PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
   }
 }
-template<int N>
-static void ProjectSUn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,Nd> > &U)
-{
-  GridBase *grid=U.Grid();
+template <int N>
+static void ProjectSUn(
+    Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
+  GridBase *grid = U.Grid();
   // Reunitarise
-  for(int mu=0;mu<Nd;mu++){
-    auto Umu = PeekIndex<LorentzIndex>(U,mu);
-    Umu      = ProjectOnGroup(Umu);
+  for (int mu = 0; mu < Nd; mu++) {
+    auto Umu = PeekIndex<LorentzIndex>(U, mu);
+    Umu = ProjectOnGroup(Umu);
     ProjectSUn(Umu);
-    PokeIndex<LorentzIndex>(U,Umu,mu);
+    PokeIndex<LorentzIndex>(U, Umu, mu);
   }
 }
 // Explicit specialisation for SU(3).
 // Explicit specialisation for SU(3).
-static void
-ProjectSU3 (Lattice<iScalar<iScalar<iMatrix<vComplexD, 3> > > > &Umu)
-{
-  GridBase *grid=Umu.Grid();
-  const int x=0;
-  const int y=1;
-  const int z=2;
+static void ProjectSU3(
+    Lattice<iScalar<iScalar<iMatrix<vComplexD, 3> > > > &Umu) {
+  GridBase *grid = Umu.Grid();
+  const int x = 0;
+  const int y = 1;
+  const int z = 2;
   // Reunitarise
   Umu = ProjectOnGroup(Umu);
-  autoView(Umu_v,Umu,CpuWrite);
-  thread_for(ss,grid->oSites(),{
-      auto cm = Umu_v[ss];
-      cm()()(2,x) = adj(cm()()(0,y)*cm()()(1,z)-cm()()(0,z)*cm()()(1,y)); //x= yz-zy
-      cm()()(2,y) = adj(cm()()(0,z)*cm()()(1,x)-cm()()(0,x)*cm()()(1,z)); //y= zx-xz
-      cm()()(2,z) = adj(cm()()(0,x)*cm()()(1,y)-cm()()(0,y)*cm()()(1,x)); //z= xy-yx
-      Umu_v[ss]=cm;
+  autoView(Umu_v, Umu, CpuWrite);
+  thread_for(ss, grid->oSites(), {
+    auto cm = Umu_v[ss];
+    cm()()(2, x) = adj(cm()()(0, y) * cm()()(1, z) -
+                       cm()()(0, z) * cm()()(1, y));  // x= yz-zy
+    cm()()(2, y) = adj(cm()()(0, z) * cm()()(1, x) -
+                       cm()()(0, x) * cm()()(1, z));  // y= zx-xz
+    cm()()(2, z) = adj(cm()()(0, x) * cm()()(1, y) -
+                       cm()()(0, y) * cm()()(1, x));  // z= xy-yx
+    Umu_v[ss] = cm;
   });
 }
-static void ProjectSU3(Lattice<iVector<iScalar<iMatrix<vComplexD, 3> >,Nd> > &U)
-{
-  GridBase *grid=U.Grid();
+static void ProjectSU3(
+    Lattice<iVector<iScalar<iMatrix<vComplexD, 3> >, Nd> > &U) {
+  GridBase *grid = U.Grid();
   // Reunitarise
-  for(int mu=0;mu<Nd;mu++){
-    auto Umu = PeekIndex<LorentzIndex>(U,mu);
-    Umu      = ProjectOnGroup(Umu);
+  for (int mu = 0; mu < Nd; mu++) {
+    auto Umu = PeekIndex<LorentzIndex>(U, mu);
+    Umu = ProjectOnGroup(Umu);
     ProjectSU3(Umu);
-    PokeIndex<LorentzIndex>(U,Umu,mu);
+    PokeIndex<LorentzIndex>(U, Umu, mu);
   }
 }
 
@@ -886,7 +882,6 @@ typedef SU<3> SU3;
 typedef SU<4> SU4;
 typedef SU<5> SU5;
 
-
 typedef SU<Nc> FundamentalMatrices;
 
 NAMESPACE_END(Grid);

From b8f1f5d2a3e164007b6901aa40b0cdc1d42bcf56 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Fri, 25 Nov 2022 17:45:32 +0000
Subject: [PATCH 031/129] Introduce GaugeGroup

---
 Grid/qcd/utils/SUn.h | 11 ++++++++++-
 1 file changed, 10 insertions(+), 1 deletion(-)

diff --git a/Grid/qcd/utils/SUn.h b/Grid/qcd/utils/SUn.h
index 0f7482ae..50a035d4 100644
--- a/Grid/qcd/utils/SUn.h
+++ b/Grid/qcd/utils/SUn.h
@@ -33,9 +33,18 @@ directory
 #define QCD_UTIL_SUN_H
 
 NAMESPACE_BEGIN(Grid);
+namespace GroupName {
+class SU {};
+}  // namespace GroupName
+
+template <int ncolour, class group_name = GroupName::SU>
+class GaugeGroup;
 
 template <int ncolour>
-class SU {
+using SU = GaugeGroup<ncolour, GroupName::SU>;
+
+template <int ncolour, class group_name>
+class GaugeGroup {
  public:
   static const int Dimension = ncolour;
   static const int AdjointDimension = ncolour * ncolour - 1;

From 6e750ecb0edc01e633be65f8ddc4bb7cf4932a1d Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Mon, 28 Nov 2022 16:33:46 +0000
Subject: [PATCH 032/129] Remove apparently forgotten file

---
 tests/core/test_sp2n_lie_gen.cc | 55 ---------------------------------
 1 file changed, 55 deletions(-)
 delete mode 100644 tests/core/test_sp2n_lie_gen.cc

diff --git a/tests/core/test_sp2n_lie_gen.cc b/tests/core/test_sp2n_lie_gen.cc
deleted file mode 100644
index 6c3766e6..00000000
--- a/tests/core/test_sp2n_lie_gen.cc
+++ /dev/null
@@ -1,55 +0,0 @@
-
-
-
-#include <Grid/Grid.h>
-#include <Grid/qcd/utils/Sp2n.h>
-
-using namespace Grid;
-
-int main(int argc, char** argv) {
-  Grid_init(&argc, &argv);
-    
-  //std::vector<int> latt({4, 4, 4, 8});
-  //GridCartesian* grid = SpaceTimeGrid::makeFourDimGrid(
-  //latt, GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
-  //GridRedBlackCartesian* rbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(grid);
-    
-    std::cout << GridLogMessage << "*********************************************"
-              << std::endl;
-    std::cout << GridLogMessage << "* Generators for Sp(2)" << std::endl;
-    std::cout << GridLogMessage << "*********************************************"
-              << std::endl;
-      
-    Sp2::printGenerators();
-    Sp2::testGenerators();
-  
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(4)" << std::endl;
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-    
-  Sp4::printGenerators();
-  Sp4::testGenerators();
-    
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(6)" << std::endl;
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-  
-  Sp6::printGenerators();
-  Sp6::testGenerators();
-    
-  std::cout << GridLogMessage << "*********************************************"
-              << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(8)" << std::endl;
-  std::cout << GridLogMessage << "*********************************************"
-              << std::endl;
-    
-  Sp8::printGenerators();
-  Sp8::testGenerators(); 
-    
-    
-  Grid_finalize();
-}

From 921e23e83ce252044932e7d0455e4dbf904b716c Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Mon, 28 Nov 2022 17:47:50 +0000
Subject: [PATCH 033/129] Separated out everything SU specific

---
 Grid/qcd/utils/SUn.h      | 591 +++-----------------------------------
 Grid/qcd/utils/SUn_impl.h | 552 +++++++++++++++++++++++++++++++++++
 2 files changed, 586 insertions(+), 557 deletions(-)
 create mode 100644 Grid/qcd/utils/SUn_impl.h

diff --git a/Grid/qcd/utils/SUn.h b/Grid/qcd/utils/SUn.h
index 50a035d4..4a7148e9 100644
--- a/Grid/qcd/utils/SUn.h
+++ b/Grid/qcd/utils/SUn.h
@@ -32,11 +32,25 @@ directory
 #ifndef QCD_UTIL_SUN_H
 #define QCD_UTIL_SUN_H
 
+#define ONLY_IF_SU                  \
+  typename dummy_name = group_name, \
+           typename = std::enable_if_t<is_su<dummy_name>::value>
+
 NAMESPACE_BEGIN(Grid);
 namespace GroupName {
 class SU {};
 }  // namespace GroupName
 
+template <typename group_name>
+struct is_su {
+  static const bool value = false;
+};
+
+template <>
+struct is_su<GroupName::SU> {
+  static const bool value = true;
+};
+
 template <int ncolour, class group_name = GroupName::SU>
 class GaugeGroup;
 
@@ -50,36 +64,35 @@ class GaugeGroup {
   static const int AdjointDimension = ncolour * ncolour - 1;
   static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
 
-  template <typename vtype>
-  using iSUnMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
   template <typename vtype>
   using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
   template <typename vtype>
-  using iSUnAlgebraVector =
-      iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
+  using iGroupMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
+  template <typename vtype>
+  using iAlgebraVector = iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
 
   //////////////////////////////////////////////////////////////////////////////////////////////////
   // Types can be accessed as SU<2>::Matrix , SU<2>::vSUnMatrix,
   // SU<2>::LatticeMatrix etc...
   //////////////////////////////////////////////////////////////////////////////////////////////////
-  typedef iSUnMatrix<Complex> Matrix;
-  typedef iSUnMatrix<ComplexF> MatrixF;
-  typedef iSUnMatrix<ComplexD> MatrixD;
+  typedef iGroupMatrix<Complex> Matrix;
+  typedef iGroupMatrix<ComplexF> MatrixF;
+  typedef iGroupMatrix<ComplexD> MatrixD;
 
-  typedef iSUnMatrix<vComplex> vMatrix;
-  typedef iSUnMatrix<vComplexF> vMatrixF;
-  typedef iSUnMatrix<vComplexD> vMatrixD;
+  typedef iGroupMatrix<vComplex> vMatrix;
+  typedef iGroupMatrix<vComplexF> vMatrixF;
+  typedef iGroupMatrix<vComplexD> vMatrixD;
 
   // For the projectors to the algebra
   // these should be real...
   // keeping complex for consistency with the SIMD vector types
-  typedef iSUnAlgebraVector<Complex> AlgebraVector;
-  typedef iSUnAlgebraVector<ComplexF> AlgebraVectorF;
-  typedef iSUnAlgebraVector<ComplexD> AlgebraVectorD;
+  typedef iAlgebraVector<Complex> AlgebraVector;
+  typedef iAlgebraVector<ComplexF> AlgebraVectorF;
+  typedef iAlgebraVector<ComplexD> AlgebraVectorD;
 
-  typedef iSUnAlgebraVector<vComplex> vAlgebraVector;
-  typedef iSUnAlgebraVector<vComplexF> vAlgebraVectorF;
-  typedef iSUnAlgebraVector<vComplexD> vAlgebraVectorD;
+  typedef iAlgebraVector<vComplex> vAlgebraVector;
+  typedef iAlgebraVector<vComplexF> vAlgebraVectorF;
+  typedef iAlgebraVector<vComplexD> vAlgebraVectorD;
 
   typedef Lattice<vMatrix> LatticeMatrix;
   typedef Lattice<vMatrixF> LatticeMatrixF;
@@ -101,462 +114,7 @@ class GaugeGroup {
   typedef Lattice<vSU2MatrixF> LatticeSU2MatrixF;
   typedef Lattice<vSU2MatrixD> LatticeSU2MatrixD;
 
-  ////////////////////////////////////////////////////////////////////////
-  // There are N^2-1 generators for SU(N).
-  //
-  // We take a traceless hermitian generator basis as follows
-  //
-  // * Normalisation: trace ta tb = 1/2 delta_ab = T_F delta_ab
-  //   T_F = 1/2  for SU(N) groups
-  //
-  // * Off diagonal
-  //    - pairs of rows i1,i2 behaving like pauli matrices signma_x, sigma_y
-  //
-  //    - there are (Nc-1-i1) slots for i2 on each row [ x  0  x ]
-  //      direct count off each row
-  //
-  //    - Sum of all pairs is Nc(Nc-1)/2: proof arithmetic series
-  //
-  //      (Nc-1) + (Nc-2)+...  1      ==> Nc*(Nc-1)/2
-  //      1+ 2+          +   + Nc-1
-  //
-  //    - There are 2 x Nc (Nc-1)/ 2 of these = Nc^2 - Nc
-  //
-  //    - We enumerate the row-col pairs.
-  //    - for each row col pair there is a (sigma_x) and a (sigma_y) like
-  //    generator
-  //
-  //
-  //   t^a_ij = { in 0.. Nc(Nc-1)/2 -1} =>  1/2(delta_{i,i1} delta_{j,i2} +
-  //   delta_{i,i1} delta_{j,i2})
-  //   t^a_ij = { in Nc(Nc-1)/2 ... Nc(Nc-1) - 1} =>  i/2( delta_{i,i1}
-  //   delta_{j,i2} - i delta_{i,i1} delta_{j,i2})
-  //
-  // * Diagonal; must be traceless and normalised
-  //   - Sequence is
-  //   N  (1,-1,0,0...)
-  //   N  (1, 1,-2,0...)
-  //   N  (1, 1, 1,-3,0...)
-  //   N  (1, 1, 1, 1,-4,0...)
-  //
-  //   where 1/2 = N^2 (1+.. m^2)etc.... for the m-th diagonal generator
-  //   NB this gives the famous SU3 result for su2 index 8
-  //
-  //   N= sqrt(1/2 . 1/6 ) = 1/2 . 1/sqrt(3)
-  //
-  //   ( 1      )
-  //   (    1   ) / sqrt(3) /2  = 1/2 lambda_8
-  //   (      -2)
-  //
-  ////////////////////////////////////////////////////////////////////////
-  template <class cplx>
-  static void generator(int lieIndex, iSUnMatrix<cplx> &ta) {
-    // map lie index to which type of generator
-    int diagIndex;
-    int su2Index;
-    int sigxy;
-    int NNm1 = ncolour * (ncolour - 1);
-    if (lieIndex >= NNm1) {
-      diagIndex = lieIndex - NNm1;
-      generatorDiagonal(diagIndex, ta);
-      return;
-    }
-    sigxy = lieIndex & 0x1;  // even or odd
-    su2Index = lieIndex >> 1;
-    if (sigxy)
-      generatorSigmaY(su2Index, ta);
-    else
-      generatorSigmaX(su2Index, ta);
-  }
-
-  template <class cplx>
-  static void generatorSigmaY(int su2Index, iSUnMatrix<cplx> &ta) {
-    ta = Zero();
-    int i1, i2;
-    su2SubGroupIndex(i1, i2, su2Index);
-    ta()()(i1, i2) = 1.0;
-    ta()()(i2, i1) = 1.0;
-    ta = ta * 0.5;
-  }
-
-  template <class cplx>
-  static void generatorSigmaX(int su2Index, iSUnMatrix<cplx> &ta) {
-    ta = Zero();
-    cplx i(0.0, 1.0);
-    int i1, i2;
-    su2SubGroupIndex(i1, i2, su2Index);
-    ta()()(i1, i2) = i;
-    ta()()(i2, i1) = -i;
-    ta = ta * 0.5;
-  }
-
-  template <class cplx>
-  static void generatorDiagonal(int diagIndex, iSUnMatrix<cplx> &ta) {
-    // diag ({1, 1, ..., 1}(k-times), -k, 0, 0, ...)
-    ta = Zero();
-    int k = diagIndex + 1;                  // diagIndex starts from 0
-    for (int i = 0; i <= diagIndex; i++) {  // k iterations
-      ta()()(i, i) = 1.0;
-    }
-    ta()()(k, k) = -k;  // indexing starts from 0
-    RealD nrm = 1.0 / std::sqrt(2.0 * k * (k + 1));
-    ta = ta * nrm;
-  }
-
-  ////////////////////////////////////////////////////////////////////////
-  // Map a su2 subgroup number to the pair of rows that are non zero
-  ////////////////////////////////////////////////////////////////////////
-  static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
-    assert((su2_index >= 0) && (su2_index < (ncolour * (ncolour - 1)) / 2));
-
-    int spare = su2_index;
-    for (i1 = 0; spare >= (ncolour - 1 - i1); i1++) {
-      spare = spare - (ncolour - 1 - i1);  // remove the Nc-1-i1 terms
-    }
-    i2 = i1 + 1 + spare;
-  }
-
-  //////////////////////////////////////////////////////////////////////////////////////////
-  // Pull out a subgroup and project on to real coeffs x pauli basis
-  //////////////////////////////////////////////////////////////////////////////////////////
-  template <class vcplx>
-  static void su2Extract(Lattice<iSinglet<vcplx> > &Determinant,
-                         Lattice<iSU2Matrix<vcplx> > &subgroup,
-                         const Lattice<iSUnMatrix<vcplx> > &source,
-                         int su2_index) {
-    GridBase *grid(source.Grid());
-    conformable(subgroup, source);
-    conformable(subgroup, Determinant);
-    int i0, i1;
-    su2SubGroupIndex(i0, i1, su2_index);
-
-    autoView(subgroup_v, subgroup, AcceleratorWrite);
-    autoView(source_v, source, AcceleratorRead);
-    autoView(Determinant_v, Determinant, AcceleratorWrite);
-    accelerator_for(ss, grid->oSites(), 1, {
-      subgroup_v[ss]()()(0, 0) = source_v[ss]()()(i0, i0);
-      subgroup_v[ss]()()(0, 1) = source_v[ss]()()(i0, i1);
-      subgroup_v[ss]()()(1, 0) = source_v[ss]()()(i1, i0);
-      subgroup_v[ss]()()(1, 1) = source_v[ss]()()(i1, i1);
-
-      iSU2Matrix<vcplx> Sigma = subgroup_v[ss];
-
-      Sigma = Sigma - adj(Sigma) + trace(adj(Sigma));
-
-      subgroup_v[ss] = Sigma;
-
-      // this should be purely real
-      Determinant_v[ss] =
-          Sigma()()(0, 0) * Sigma()()(1, 1) - Sigma()()(0, 1) * Sigma()()(1, 0);
-    });
-  }
-
-  //////////////////////////////////////////////////////////////////////////////////////////
-  // Set matrix to one and insert a pauli subgroup
-  //////////////////////////////////////////////////////////////////////////////////////////
-  template <class vcplx>
-  static void su2Insert(const Lattice<iSU2Matrix<vcplx> > &subgroup,
-                        Lattice<iSUnMatrix<vcplx> > &dest, int su2_index) {
-    GridBase *grid(dest.Grid());
-    conformable(subgroup, dest);
-    int i0, i1;
-    su2SubGroupIndex(i0, i1, su2_index);
-
-    dest = 1.0;  // start out with identity
-    autoView(dest_v, dest, AcceleratorWrite);
-    autoView(subgroup_v, subgroup, AcceleratorRead);
-    accelerator_for(ss, grid->oSites(), 1, {
-      dest_v[ss]()()(i0, i0) = subgroup_v[ss]()()(0, 0);
-      dest_v[ss]()()(i0, i1) = subgroup_v[ss]()()(0, 1);
-      dest_v[ss]()()(i1, i0) = subgroup_v[ss]()()(1, 0);
-      dest_v[ss]()()(i1, i1) = subgroup_v[ss]()()(1, 1);
-    });
-  }
-
-  ///////////////////////////////////////////////
-  // Generate e^{ Re Tr Staple Link} dlink
-  //
-  // *** Note Staple should be appropriate linear compbination between all
-  // staples.
-  // *** If already by beta pass coefficient 1.0.
-  // *** This routine applies the additional 1/Nc factor that comes after trace
-  // in action.
-  //
-  ///////////////////////////////////////////////
-  static void SubGroupHeatBath(
-      GridSerialRNG &sRNG, GridParallelRNG &pRNG,
-      RealD beta,  // coeff multiplying staple in action (with no 1/Nc)
-      LatticeMatrix &link,
-      const LatticeMatrix &barestaple,  // multiplied by action coeffs so th
-      int su2_subgroup, int nheatbath, LatticeInteger &wheremask) {
-    GridBase *grid = link.Grid();
-
-    const RealD twopi = 2.0 * M_PI;
-
-    LatticeMatrix staple(grid);
-
-    staple = barestaple * (beta / ncolour);
-
-    LatticeMatrix V(grid);
-    V = link * staple;
-
-    // Subgroup manipulation in the lie algebra space
-    LatticeSU2Matrix u(
-        grid);  // Kennedy pendleton "u" real projected normalised Sigma
-    LatticeSU2Matrix uinv(grid);
-    LatticeSU2Matrix ua(grid);  // a in pauli form
-    LatticeSU2Matrix b(grid);   // rotated matrix after hb
-
-    // Some handy constant fields
-    LatticeComplex ones(grid);
-    ones = 1.0;
-    LatticeComplex zeros(grid);
-    zeros = Zero();
-    LatticeReal rones(grid);
-    rones = 1.0;
-    LatticeReal rzeros(grid);
-    rzeros = Zero();
-    LatticeComplex udet(grid);  // determinant of real(staple)
-    LatticeInteger mask_true(grid);
-    mask_true = 1;
-    LatticeInteger mask_false(grid);
-    mask_false = 0;
-
-    /*
-      PLB 156 P393 (1985) (Kennedy and Pendleton)
-
-      Note: absorb "beta" into the def of sigma compared to KP paper; staple
-      passed to this routine has "beta" already multiplied in
-
-      Action linear in links h and of form:
-
-      beta S = beta  Sum_p (1 - 1/Nc Re Tr Plaq )
-
-      Writing Sigma = 1/Nc (beta Sigma') where sum over staples is "Sigma' "
-
-      beta S = const - beta/Nc Re Tr h Sigma'
-      = const - Re Tr h Sigma
-
-      Decompose h and Sigma into (1, sigma_j) ; h_i real, h^2=1, Sigma_i complex
-      arbitrary.
-
-      Tr h Sigma = h_i Sigma_j Tr (sigma_i sigma_j)  = h_i Sigma_j 2 delta_ij
-      Re Tr h Sigma = 2 h_j Re Sigma_j
-
-      Normalised re Sigma_j = xi u_j
-
-      With u_j a unit vector and U can be in SU(2);
-
-      Re Tr h Sigma = 2 h_j Re Sigma_j = 2 xi (h.u)
-
-      4xi^2 = Det [ Sig - Sig^dag  + 1 Tr Sigdag]
-      u   = 1/2xi [ Sig - Sig^dag  + 1 Tr Sigdag]
-
-      xi = sqrt(Det)/2;
-
-      Write a= u h in SU(2); a has pauli decomp a_j;
-
-      Note: Product b' xi is unvariant because scaling Sigma leaves
-      normalised vector "u" fixed; Can rescale Sigma so b' = 1.
-    */
-
-    ////////////////////////////////////////////////////////
-    // Real part of Pauli decomposition
-    // Note a subgroup can project to zero in cold start
-    ////////////////////////////////////////////////////////
-    su2Extract(udet, u, V, su2_subgroup);
-
-    //////////////////////////////////////////////////////
-    // Normalising this vector if possible; else identity
-    //////////////////////////////////////////////////////
-    LatticeComplex xi(grid);
-
-    LatticeSU2Matrix lident(grid);
-
-    SU2Matrix ident = Complex(1.0);
-    SU2Matrix pauli1;
-    SU<2>::generator(0, pauli1);
-    SU2Matrix pauli2;
-    SU<2>::generator(1, pauli2);
-    SU2Matrix pauli3;
-    SU<2>::generator(2, pauli3);
-    pauli1 = timesI(pauli1) * 2.0;
-    pauli2 = timesI(pauli2) * 2.0;
-    pauli3 = timesI(pauli3) * 2.0;
-
-    LatticeComplex cone(grid);
-    LatticeReal adet(grid);
-    adet = abs(toReal(udet));
-    lident = Complex(1.0);
-    cone = Complex(1.0);
-    Real machine_epsilon = 1.0e-7;
-    u = where(adet > machine_epsilon, u, lident);
-    udet = where(adet > machine_epsilon, udet, cone);
-
-    xi = 0.5 * sqrt(udet);  // 4xi^2 = Det [ Sig - Sig^dag  + 1 Tr Sigdag]
-    u = 0.5 * u *
-        pow(xi, -1.0);  //  u   = 1/2xi [ Sig - Sig^dag  + 1 Tr Sigdag]
-
-    // Debug test for sanity
-    uinv = adj(u);
-    b = u * uinv - 1.0;
-    assert(norm2(b) < 1.0e-4);
-
-    /*
-      Measure: Haar measure dh has d^4a delta(1-|a^2|)
-      In polars:
-      da = da0 r^2 sin theta dr dtheta dphi delta( 1 - r^2 -a0^2)
-      = da0 r^2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r)(sqrt(1-a0^) +
-      r) )
-      = da0 r/2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r) )
-
-      Action factor Q(h) dh  = e^-S[h]  dh =  e^{  xi Tr uh} dh    // beta
-      enters through xi =  e^{2 xi (h.u)} dh =  e^{2 xi h0u0}.e^{2 xi h1u1}.e^{2
-      xi h2u2}.e^{2 xi h3u3} dh
-
-      Therefore for each site, take xi for that site
-      i) generate  |a0|<1 with dist
-      (1-a0^2)^0.5 e^{2 xi a0 } da0
-
-      Take alpha = 2 xi  = 2 xi [ recall 2 beta/Nc unmod staple norm];
-      hence 2.0/Nc factor in Chroma ] A. Generate two uniformly distributed
-      pseudo-random numbers R and R', R'', R''' in the unit interval; B. Set X =
-      -(ln R)/alpha, X' =-(ln R')/alpha; C. Set C = cos^2(2pi R"), with R"
-      another uniform random number in [0,1] ; D. Set A = XC; E. Let d  = X'+A;
-      F. If R'''^2 :> 1 - 0.5 d,  go back to A;
-      G. Set a0 = 1 - d;
-
-      Note that in step D setting B ~ X - A and using B in place of A in step E
-      will generate a second independent a 0 value.
-    */
-
-    /////////////////////////////////////////////////////////
-    // count the number of sites by picking "1"'s out of hat
-    /////////////////////////////////////////////////////////
-    Integer hit = 0;
-    LatticeReal rtmp(grid);
-    rtmp = where(wheremask, rones, rzeros);
-    RealD numSites = sum(rtmp);
-    RealD numAccepted;
-    LatticeInteger Accepted(grid);
-    Accepted = Zero();
-    LatticeInteger newlyAccepted(grid);
-
-    std::vector<LatticeReal> xr(4, grid);
-    std::vector<LatticeReal> a(4, grid);
-    LatticeReal d(grid);
-    d = Zero();
-    LatticeReal alpha(grid);
-
-    //    std::cout<<GridLogMessage<<"xi "<<xi <<std::endl;
-    xi = 2.0 * xi;
-    alpha = toReal(xi);
-
-    do {
-      // A. Generate two uniformly distributed pseudo-random numbers R and R',
-      // R'', R''' in the unit interval;
-      random(pRNG, xr[0]);
-      random(pRNG, xr[1]);
-      random(pRNG, xr[2]);
-      random(pRNG, xr[3]);
-
-      // B. Set X = - ln R/alpha, X' = -ln R'/alpha
-      xr[1] = -log(xr[1]) / alpha;
-      xr[2] = -log(xr[2]) / alpha;
-
-      // C. Set C = cos^2(2piR'')
-      xr[3] = cos(xr[3] * twopi);
-      xr[3] = xr[3] * xr[3];
-
-      LatticeReal xrsq(grid);
-
-      // D. Set A = XC;
-      // E. Let d  = X'+A;
-      xrsq = xr[2] + xr[1] * xr[3];
-
-      d = where(Accepted, d, xr[2] + xr[1] * xr[3]);
-
-      // F. If R'''^2 :> 1 - 0.5 d,  go back to A;
-      LatticeReal thresh(grid);
-      thresh = 1.0 - d * 0.5;
-      xrsq = xr[0] * xr[0];
-      LatticeInteger ione(grid);
-      ione = 1;
-      LatticeInteger izero(grid);
-      izero = Zero();
-
-      newlyAccepted = where(xrsq < thresh, ione, izero);
-      Accepted = where(newlyAccepted, newlyAccepted, Accepted);
-      Accepted = where(wheremask, Accepted, izero);
-
-      // FIXME need an iSum for integer to avoid overload on return type??
-      rtmp = where(Accepted, rones, rzeros);
-      numAccepted = sum(rtmp);
-
-      hit++;
-
-    } while ((numAccepted < numSites) && (hit < nheatbath));
-
-    // G. Set a0 = 1 - d;
-    a[0] = Zero();
-    a[0] = where(wheremask, 1.0 - d, a[0]);
-
-    //////////////////////////////////////////
-    //    ii) generate a_i uniform on two sphere radius (1-a0^2)^0.5
-    //////////////////////////////////////////
-
-    LatticeReal a123mag(grid);
-    a123mag = sqrt(abs(1.0 - a[0] * a[0]));
-
-    LatticeReal cos_theta(grid);
-    LatticeReal sin_theta(grid);
-    LatticeReal phi(grid);
-
-    random(pRNG, phi);
-    phi = phi * twopi;  // uniform in [0,2pi]
-    random(pRNG, cos_theta);
-    cos_theta = (cos_theta * 2.0) - 1.0;  // uniform in [-1,1]
-    sin_theta = sqrt(abs(1.0 - cos_theta * cos_theta));
-
-    a[1] = a123mag * sin_theta * cos(phi);
-    a[2] = a123mag * sin_theta * sin(phi);
-    a[3] = a123mag * cos_theta;
-
-    ua = toComplex(a[0]) * ident + toComplex(a[1]) * pauli1 +
-         toComplex(a[2]) * pauli2 + toComplex(a[3]) * pauli3;
-
-    b = 1.0;
-    b = where(wheremask, uinv * ua, b);
-    su2Insert(b, V, su2_subgroup);
-
-    // mask the assignment back based on Accptance
-    link = where(Accepted, V * link, link);
-
-    //////////////////////////////
-    // Debug Checks
-    // SU2 check
-    LatticeSU2Matrix check(grid);  // rotated matrix after hb
-    u = Zero();
-    check = ua * adj(ua) - 1.0;
-    check = where(Accepted, check, u);
-    assert(norm2(check) < 1.0e-4);
-
-    check = b * adj(b) - 1.0;
-    check = where(Accepted, check, u);
-    assert(norm2(check) < 1.0e-4);
-
-    LatticeMatrix Vcheck(grid);
-    Vcheck = Zero();
-    Vcheck = where(Accepted, V * adj(V) - 1.0, Vcheck);
-    //    std::cout<<GridLogMessage << "SU3 check " <<norm2(Vcheck)<<std::endl;
-    assert(norm2(Vcheck) < 1.0e-4);
-
-    // Verify the link stays in SU(3)
-    //    std::cout<<GridLogMessage <<"Checking the modified link"<<std::endl;
-    Vcheck = link * adj(link) - 1.0;
-    assert(norm2(Vcheck) < 1.0e-4);
-    /////////////////////////////////
-  }
+#include "Grid/qcd/utils/SUn_impl.h"
 
   static void printGenerators(void) {
     for (int gen = 0; gen < AdjointDimension; gen++) {
@@ -568,44 +126,6 @@ class GaugeGroup {
     }
   }
 
-  static void testGenerators(void) {
-    Matrix ta;
-    Matrix tb;
-    std::cout << GridLogMessage
-              << "Fundamental - Checking trace ta tb is 0.5 delta_ab"
-              << std::endl;
-    for (int a = 0; a < AdjointDimension; a++) {
-      for (int b = 0; b < AdjointDimension; b++) {
-        generator(a, ta);
-        generator(b, tb);
-        Complex tr = TensorRemove(trace(ta * tb));
-        std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
-                  << std::endl;
-        if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
-        if (a != b) assert(abs(tr) < 1.0e-6);
-      }
-      std::cout << GridLogMessage << std::endl;
-    }
-    std::cout << GridLogMessage << "Fundamental - Checking if hermitian"
-              << std::endl;
-    for (int a = 0; a < AdjointDimension; a++) {
-      generator(a, ta);
-      std::cout << GridLogMessage << a << std::endl;
-      assert(norm2(ta - adj(ta)) < 1.0e-6);
-    }
-    std::cout << GridLogMessage << std::endl;
-
-    std::cout << GridLogMessage << "Fundamental - Checking if traceless"
-              << std::endl;
-    for (int a = 0; a < AdjointDimension; a++) {
-      generator(a, ta);
-      Complex tr = TensorRemove(trace(ta));
-      std::cout << GridLogMessage << a << " " << std::endl;
-      assert(abs(tr) < 1.0e-6);
-    }
-    std::cout << GridLogMessage << std::endl;
-  }
-
   // reunitarise??
   template <typename LatticeMatrixType>
   static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out,
@@ -679,49 +199,6 @@ class GaugeGroup {
       out += la;
     }
   }
-  /*
-   * Fundamental rep gauge xform
-   */
-  template <typename Fundamental, typename GaugeMat>
-  static void GaugeTransformFundamental(Fundamental &ferm, GaugeMat &g) {
-    GridBase *grid = ferm._grid;
-    conformable(grid, g._grid);
-    ferm = g * ferm;
-  }
-  /*
-   * Adjoint rep gauge xform
-   */
-
-  template <typename GaugeField, typename GaugeMat>
-  static void GaugeTransform(GaugeField &Umu, GaugeMat &g) {
-    GridBase *grid = Umu.Grid();
-    conformable(grid, g.Grid());
-
-    GaugeMat U(grid);
-    GaugeMat ag(grid);
-    ag = adj(g);
-
-    for (int mu = 0; mu < Nd; mu++) {
-      U = PeekIndex<LorentzIndex>(Umu, mu);
-      U = g * U * Cshift(ag, mu, 1);
-      PokeIndex<LorentzIndex>(Umu, U, mu);
-    }
-  }
-  template <typename GaugeMat>
-  static void GaugeTransform(std::vector<GaugeMat> &U, GaugeMat &g) {
-    GridBase *grid = g.Grid();
-    GaugeMat ag(grid);
-    ag = adj(g);
-    for (int mu = 0; mu < Nd; mu++) {
-      U[mu] = g * U[mu] * Cshift(ag, mu, 1);
-    }
-  }
-  template <typename GaugeField, typename GaugeMat>
-  static void RandomGaugeTransform(GridParallelRNG &pRNG, GaugeField &Umu,
-                                   GaugeMat &g) {
-    LieRandomize(pRNG, g, 1.0);
-    GaugeTransform(Umu, g);
-  }
 
   // Projects the algebra components a lattice matrix (of dimension ncol*ncol -1
   // ) inverse operation: FundamentalLieAlgebraMatrix
@@ -740,7 +217,7 @@ class GaugeGroup {
   template <typename GaugeField>
   static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
     typedef typename GaugeField::vector_type vector_type;
-    typedef iSUnMatrix<vector_type> vMatrixType;
+    typedef iGroupMatrix<vector_type> vMatrixType;
     typedef Lattice<vMatrixType> LatticeMatrixType;
 
     LatticeMatrixType Umu(out.Grid());
@@ -752,7 +229,7 @@ class GaugeGroup {
   template <typename GaugeField>
   static void TepidConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
     typedef typename GaugeField::vector_type vector_type;
-    typedef iSUnMatrix<vector_type> vMatrixType;
+    typedef iGroupMatrix<vector_type> vMatrixType;
     typedef Lattice<vMatrixType> LatticeMatrixType;
 
     LatticeMatrixType Umu(out.Grid());
@@ -764,7 +241,7 @@ class GaugeGroup {
   template <typename GaugeField>
   static void ColdConfiguration(GaugeField &out) {
     typedef typename GaugeField::vector_type vector_type;
-    typedef iSUnMatrix<vector_type> vMatrixType;
+    typedef iGroupMatrix<vector_type> vMatrixType;
     typedef Lattice<vMatrixType> LatticeMatrixType;
 
     LatticeMatrixType Umu(out.Grid());
@@ -778,7 +255,7 @@ class GaugeGroup {
     ColdConfiguration(out);
   }
 
-  template <typename LatticeMatrixType>
+  template <typename LatticeMatrixType, ONLY_IF_SU>
   static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out) {
     out = Ta(in);
   }
diff --git a/Grid/qcd/utils/SUn_impl.h b/Grid/qcd/utils/SUn_impl.h
new file mode 100644
index 00000000..e7b972ef
--- /dev/null
+++ b/Grid/qcd/utils/SUn_impl.h
@@ -0,0 +1,552 @@
+// This file is #included into the body of the class template definition of
+// GaugeGroup. So, image there to be
+//
+// template <int ncolour, class group_name>
+// class GaugeGroup {
+//
+// around it.
+
+template <typename vtype, ONLY_IF_SU>
+using iSUnMatrix = iGroupMatrix<vtype>;
+template <typename vtype, ONLY_IF_SU>
+using iSUnAlgebraVector = iAlgebraVector<vtype>;
+////////////////////////////////////////////////////////////////////////
+// There are N^2-1 generators for SU(N).
+//
+// We take a traceless hermitian generator basis as follows
+//
+// * Normalisation: trace ta tb = 1/2 delta_ab = T_F delta_ab
+//   T_F = 1/2  for SU(N) groups
+//
+// * Off diagonal
+//    - pairs of rows i1,i2 behaving like pauli matrices signma_x, sigma_y
+//
+//    - there are (Nc-1-i1) slots for i2 on each row [ x  0  x ]
+//      direct count off each row
+//
+//    - Sum of all pairs is Nc(Nc-1)/2: proof arithmetic series
+//
+//      (Nc-1) + (Nc-2)+...  1      ==> Nc*(Nc-1)/2
+//      1+ 2+          +   + Nc-1
+//
+//    - There are 2 x Nc (Nc-1)/ 2 of these = Nc^2 - Nc
+//
+//    - We enumerate the row-col pairs.
+//    - for each row col pair there is a (sigma_x) and a (sigma_y) like
+//    generator
+//
+//
+//   t^a_ij = { in 0.. Nc(Nc-1)/2 -1} =>  1/2(delta_{i,i1} delta_{j,i2} +
+//   delta_{i,i1} delta_{j,i2})
+//   t^a_ij = { in Nc(Nc-1)/2 ... Nc(Nc-1) - 1} =>  i/2( delta_{i,i1}
+//   delta_{j,i2} - i delta_{i,i1} delta_{j,i2})
+//
+// * Diagonal; must be traceless and normalised
+//   - Sequence is
+//   N  (1,-1,0,0...)
+//   N  (1, 1,-2,0...)
+//   N  (1, 1, 1,-3,0...)
+//   N  (1, 1, 1, 1,-4,0...)
+//
+//   where 1/2 = N^2 (1+.. m^2)etc.... for the m-th diagonal generator
+//   NB this gives the famous SU3 result for su2 index 8
+//
+//   N= sqrt(1/2 . 1/6 ) = 1/2 . 1/sqrt(3)
+//
+//   ( 1      )
+//   (    1   ) / sqrt(3) /2  = 1/2 lambda_8
+//   (      -2)
+//
+////////////////////////////////////////////////////////////////////////
+template <class cplx, ONLY_IF_SU>
+static void generator(int lieIndex, iSUnMatrix<cplx> &ta) {
+  // map lie index to which type of generator
+  int diagIndex;
+  int su2Index;
+  int sigxy;
+  int NNm1 = ncolour * (ncolour - 1);
+  if (lieIndex >= NNm1) {
+    diagIndex = lieIndex - NNm1;
+    generatorDiagonal(diagIndex, ta);
+    return;
+  }
+  sigxy = lieIndex & 0x1;  // even or odd
+  su2Index = lieIndex >> 1;
+  if (sigxy)
+    generatorSigmaY(su2Index, ta);
+  else
+    generatorSigmaX(su2Index, ta);
+}
+
+template <class cplx, ONLY_IF_SU>
+static void generatorSigmaY(int su2Index, iSUnMatrix<cplx> &ta) {
+  ta = Zero();
+  int i1, i2;
+  su2SubGroupIndex(i1, i2, su2Index);
+  ta()()(i1, i2) = 1.0;
+  ta()()(i2, i1) = 1.0;
+  ta = ta * 0.5;
+}
+
+template <class cplx, ONLY_IF_SU>
+static void generatorSigmaX(int su2Index, iSUnMatrix<cplx> &ta) {
+  ta = Zero();
+  cplx i(0.0, 1.0);
+  int i1, i2;
+  su2SubGroupIndex(i1, i2, su2Index);
+  ta()()(i1, i2) = i;
+  ta()()(i2, i1) = -i;
+  ta = ta * 0.5;
+}
+
+template <class cplx, ONLY_IF_SU>
+static void generatorDiagonal(int diagIndex, iSUnMatrix<cplx> &ta) {
+  // diag ({1, 1, ..., 1}(k-times), -k, 0, 0, ...)
+  ta = Zero();
+  int k = diagIndex + 1;                  // diagIndex starts from 0
+  for (int i = 0; i <= diagIndex; i++) {  // k iterations
+    ta()()(i, i) = 1.0;
+  }
+  ta()()(k, k) = -k;  // indexing starts from 0
+  RealD nrm = 1.0 / std::sqrt(2.0 * k * (k + 1));
+  ta = ta * nrm;
+}
+
+////////////////////////////////////////////////////////////////////////
+// Map a su2 subgroup number to the pair of rows that are non zero
+////////////////////////////////////////////////////////////////////////
+template <ONLY_IF_SU>
+static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
+  assert((su2_index >= 0) && (su2_index < (ncolour * (ncolour - 1)) / 2));
+
+  int spare = su2_index;
+  for (i1 = 0; spare >= (ncolour - 1 - i1); i1++) {
+    spare = spare - (ncolour - 1 - i1);  // remove the Nc-1-i1 terms
+  }
+  i2 = i1 + 1 + spare;
+}
+
+//////////////////////////////////////////////////////////////////////////////////////////
+// Pull out a subgroup and project on to real coeffs x pauli basis
+//////////////////////////////////////////////////////////////////////////////////////////
+template <class vcplx, ONLY_IF_SU>
+static void su2Extract(Lattice<iSinglet<vcplx> > &Determinant,
+                       Lattice<iSU2Matrix<vcplx> > &subgroup,
+                       const Lattice<iSUnMatrix<vcplx> > &source,
+                       int su2_index) {
+  GridBase *grid(source.Grid());
+  conformable(subgroup, source);
+  conformable(subgroup, Determinant);
+  int i0, i1;
+  su2SubGroupIndex(i0, i1, su2_index);
+
+  autoView(subgroup_v, subgroup, AcceleratorWrite);
+  autoView(source_v, source, AcceleratorRead);
+  autoView(Determinant_v, Determinant, AcceleratorWrite);
+  accelerator_for(ss, grid->oSites(), 1, {
+    subgroup_v[ss]()()(0, 0) = source_v[ss]()()(i0, i0);
+    subgroup_v[ss]()()(0, 1) = source_v[ss]()()(i0, i1);
+    subgroup_v[ss]()()(1, 0) = source_v[ss]()()(i1, i0);
+    subgroup_v[ss]()()(1, 1) = source_v[ss]()()(i1, i1);
+
+    iSU2Matrix<vcplx> Sigma = subgroup_v[ss];
+
+    Sigma = Sigma - adj(Sigma) + trace(adj(Sigma));
+
+    subgroup_v[ss] = Sigma;
+
+    // this should be purely real
+    Determinant_v[ss] =
+        Sigma()()(0, 0) * Sigma()()(1, 1) - Sigma()()(0, 1) * Sigma()()(1, 0);
+  });
+}
+
+//////////////////////////////////////////////////////////////////////////////////////////
+// Set matrix to one and insert a pauli subgroup
+//////////////////////////////////////////////////////////////////////////////////////////
+template <class vcplx, ONLY_IF_SU>
+static void su2Insert(const Lattice<iSU2Matrix<vcplx> > &subgroup,
+                      Lattice<iSUnMatrix<vcplx> > &dest, int su2_index) {
+  GridBase *grid(dest.Grid());
+  conformable(subgroup, dest);
+  int i0, i1;
+  su2SubGroupIndex(i0, i1, su2_index);
+
+  dest = 1.0;  // start out with identity
+  autoView(dest_v, dest, AcceleratorWrite);
+  autoView(subgroup_v, subgroup, AcceleratorRead);
+  accelerator_for(ss, grid->oSites(), 1, {
+    dest_v[ss]()()(i0, i0) = subgroup_v[ss]()()(0, 0);
+    dest_v[ss]()()(i0, i1) = subgroup_v[ss]()()(0, 1);
+    dest_v[ss]()()(i1, i0) = subgroup_v[ss]()()(1, 0);
+    dest_v[ss]()()(i1, i1) = subgroup_v[ss]()()(1, 1);
+  });
+}
+
+///////////////////////////////////////////////
+// Generate e^{ Re Tr Staple Link} dlink
+//
+// *** Note Staple should be appropriate linear compbination between all
+// staples.
+// *** If already by beta pass coefficient 1.0.
+// *** This routine applies the additional 1/Nc factor that comes after trace
+// in action.
+//
+///////////////////////////////////////////////
+template <ONLY_IF_SU>
+static void SubGroupHeatBath(
+    GridSerialRNG &sRNG, GridParallelRNG &pRNG,
+    RealD beta,  // coeff multiplying staple in action (with no 1/Nc)
+    LatticeMatrix &link,
+    const LatticeMatrix &barestaple,  // multiplied by action coeffs so th
+    int su2_subgroup, int nheatbath, LatticeInteger &wheremask) {
+  GridBase *grid = link.Grid();
+
+  const RealD twopi = 2.0 * M_PI;
+
+  LatticeMatrix staple(grid);
+
+  staple = barestaple * (beta / ncolour);
+
+  LatticeMatrix V(grid);
+  V = link * staple;
+
+  // Subgroup manipulation in the lie algebra space
+  LatticeSU2Matrix u(
+      grid);  // Kennedy pendleton "u" real projected normalised Sigma
+  LatticeSU2Matrix uinv(grid);
+  LatticeSU2Matrix ua(grid);  // a in pauli form
+  LatticeSU2Matrix b(grid);   // rotated matrix after hb
+
+  // Some handy constant fields
+  LatticeComplex ones(grid);
+  ones = 1.0;
+  LatticeComplex zeros(grid);
+  zeros = Zero();
+  LatticeReal rones(grid);
+  rones = 1.0;
+  LatticeReal rzeros(grid);
+  rzeros = Zero();
+  LatticeComplex udet(grid);  // determinant of real(staple)
+  LatticeInteger mask_true(grid);
+  mask_true = 1;
+  LatticeInteger mask_false(grid);
+  mask_false = 0;
+
+  /*
+    PLB 156 P393 (1985) (Kennedy and Pendleton)
+
+    Note: absorb "beta" into the def of sigma compared to KP paper; staple
+    passed to this routine has "beta" already multiplied in
+
+    Action linear in links h and of form:
+
+    beta S = beta  Sum_p (1 - 1/Nc Re Tr Plaq )
+
+    Writing Sigma = 1/Nc (beta Sigma') where sum over staples is "Sigma' "
+
+    beta S = const - beta/Nc Re Tr h Sigma'
+    = const - Re Tr h Sigma
+
+    Decompose h and Sigma into (1, sigma_j) ; h_i real, h^2=1, Sigma_i complex
+    arbitrary.
+
+    Tr h Sigma = h_i Sigma_j Tr (sigma_i sigma_j)  = h_i Sigma_j 2 delta_ij
+    Re Tr h Sigma = 2 h_j Re Sigma_j
+
+    Normalised re Sigma_j = xi u_j
+
+    With u_j a unit vector and U can be in SU(2);
+
+    Re Tr h Sigma = 2 h_j Re Sigma_j = 2 xi (h.u)
+
+    4xi^2 = Det [ Sig - Sig^dag  + 1 Tr Sigdag]
+    u   = 1/2xi [ Sig - Sig^dag  + 1 Tr Sigdag]
+
+    xi = sqrt(Det)/2;
+
+    Write a= u h in SU(2); a has pauli decomp a_j;
+
+    Note: Product b' xi is unvariant because scaling Sigma leaves
+    normalised vector "u" fixed; Can rescale Sigma so b' = 1.
+  */
+
+  ////////////////////////////////////////////////////////
+  // Real part of Pauli decomposition
+  // Note a subgroup can project to zero in cold start
+  ////////////////////////////////////////////////////////
+  su2Extract(udet, u, V, su2_subgroup);
+
+  //////////////////////////////////////////////////////
+  // Normalising this vector if possible; else identity
+  //////////////////////////////////////////////////////
+  LatticeComplex xi(grid);
+
+  LatticeSU2Matrix lident(grid);
+
+  SU2Matrix ident = Complex(1.0);
+  SU2Matrix pauli1;
+  SU<2>::generator(0, pauli1);
+  SU2Matrix pauli2;
+  SU<2>::generator(1, pauli2);
+  SU2Matrix pauli3;
+  SU<2>::generator(2, pauli3);
+  pauli1 = timesI(pauli1) * 2.0;
+  pauli2 = timesI(pauli2) * 2.0;
+  pauli3 = timesI(pauli3) * 2.0;
+
+  LatticeComplex cone(grid);
+  LatticeReal adet(grid);
+  adet = abs(toReal(udet));
+  lident = Complex(1.0);
+  cone = Complex(1.0);
+  Real machine_epsilon = 1.0e-7;
+  u = where(adet > machine_epsilon, u, lident);
+  udet = where(adet > machine_epsilon, udet, cone);
+
+  xi = 0.5 * sqrt(udet);        // 4xi^2 = Det [ Sig - Sig^dag  + 1 Tr Sigdag]
+  u = 0.5 * u * pow(xi, -1.0);  //  u   = 1/2xi [ Sig - Sig^dag  + 1 Tr Sigdag]
+
+  // Debug test for sanity
+  uinv = adj(u);
+  b = u * uinv - 1.0;
+  assert(norm2(b) < 1.0e-4);
+
+  /*
+    Measure: Haar measure dh has d^4a delta(1-|a^2|)
+    In polars:
+    da = da0 r^2 sin theta dr dtheta dphi delta( 1 - r^2 -a0^2)
+    = da0 r^2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r)(sqrt(1-a0^) +
+    r) )
+    = da0 r/2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r) )
+
+    Action factor Q(h) dh  = e^-S[h]  dh =  e^{  xi Tr uh} dh    // beta
+    enters through xi =  e^{2 xi (h.u)} dh =  e^{2 xi h0u0}.e^{2 xi h1u1}.e^{2
+    xi h2u2}.e^{2 xi h3u3} dh
+
+    Therefore for each site, take xi for that site
+    i) generate  |a0|<1 with dist
+    (1-a0^2)^0.5 e^{2 xi a0 } da0
+
+    Take alpha = 2 xi  = 2 xi [ recall 2 beta/Nc unmod staple norm];
+    hence 2.0/Nc factor in Chroma ] A. Generate two uniformly distributed
+    pseudo-random numbers R and R', R'', R''' in the unit interval; B. Set X =
+    -(ln R)/alpha, X' =-(ln R')/alpha; C. Set C = cos^2(2pi R"), with R"
+    another uniform random number in [0,1] ; D. Set A = XC; E. Let d  = X'+A;
+    F. If R'''^2 :> 1 - 0.5 d,  go back to A;
+    G. Set a0 = 1 - d;
+
+    Note that in step D setting B ~ X - A and using B in place of A in step E
+    will generate a second independent a 0 value.
+  */
+
+  /////////////////////////////////////////////////////////
+  // count the number of sites by picking "1"'s out of hat
+  /////////////////////////////////////////////////////////
+  Integer hit = 0;
+  LatticeReal rtmp(grid);
+  rtmp = where(wheremask, rones, rzeros);
+  RealD numSites = sum(rtmp);
+  RealD numAccepted;
+  LatticeInteger Accepted(grid);
+  Accepted = Zero();
+  LatticeInteger newlyAccepted(grid);
+
+  std::vector<LatticeReal> xr(4, grid);
+  std::vector<LatticeReal> a(4, grid);
+  LatticeReal d(grid);
+  d = Zero();
+  LatticeReal alpha(grid);
+
+  //    std::cout<<GridLogMessage<<"xi "<<xi <<std::endl;
+  xi = 2.0 * xi;
+  alpha = toReal(xi);
+
+  do {
+    // A. Generate two uniformly distributed pseudo-random numbers R and R',
+    // R'', R''' in the unit interval;
+    random(pRNG, xr[0]);
+    random(pRNG, xr[1]);
+    random(pRNG, xr[2]);
+    random(pRNG, xr[3]);
+
+    // B. Set X = - ln R/alpha, X' = -ln R'/alpha
+    xr[1] = -log(xr[1]) / alpha;
+    xr[2] = -log(xr[2]) / alpha;
+
+    // C. Set C = cos^2(2piR'')
+    xr[3] = cos(xr[3] * twopi);
+    xr[3] = xr[3] * xr[3];
+
+    LatticeReal xrsq(grid);
+
+    // D. Set A = XC;
+    // E. Let d  = X'+A;
+    xrsq = xr[2] + xr[1] * xr[3];
+
+    d = where(Accepted, d, xr[2] + xr[1] * xr[3]);
+
+    // F. If R'''^2 :> 1 - 0.5 d,  go back to A;
+    LatticeReal thresh(grid);
+    thresh = 1.0 - d * 0.5;
+    xrsq = xr[0] * xr[0];
+    LatticeInteger ione(grid);
+    ione = 1;
+    LatticeInteger izero(grid);
+    izero = Zero();
+
+    newlyAccepted = where(xrsq < thresh, ione, izero);
+    Accepted = where(newlyAccepted, newlyAccepted, Accepted);
+    Accepted = where(wheremask, Accepted, izero);
+
+    // FIXME need an iSum for integer to avoid overload on return type??
+    rtmp = where(Accepted, rones, rzeros);
+    numAccepted = sum(rtmp);
+
+    hit++;
+
+  } while ((numAccepted < numSites) && (hit < nheatbath));
+
+  // G. Set a0 = 1 - d;
+  a[0] = Zero();
+  a[0] = where(wheremask, 1.0 - d, a[0]);
+
+  //////////////////////////////////////////
+  //    ii) generate a_i uniform on two sphere radius (1-a0^2)^0.5
+  //////////////////////////////////////////
+
+  LatticeReal a123mag(grid);
+  a123mag = sqrt(abs(1.0 - a[0] * a[0]));
+
+  LatticeReal cos_theta(grid);
+  LatticeReal sin_theta(grid);
+  LatticeReal phi(grid);
+
+  random(pRNG, phi);
+  phi = phi * twopi;  // uniform in [0,2pi]
+  random(pRNG, cos_theta);
+  cos_theta = (cos_theta * 2.0) - 1.0;  // uniform in [-1,1]
+  sin_theta = sqrt(abs(1.0 - cos_theta * cos_theta));
+
+  a[1] = a123mag * sin_theta * cos(phi);
+  a[2] = a123mag * sin_theta * sin(phi);
+  a[3] = a123mag * cos_theta;
+
+  ua = toComplex(a[0]) * ident + toComplex(a[1]) * pauli1 +
+       toComplex(a[2]) * pauli2 + toComplex(a[3]) * pauli3;
+
+  b = 1.0;
+  b = where(wheremask, uinv * ua, b);
+  su2Insert(b, V, su2_subgroup);
+
+  // mask the assignment back based on Accptance
+  link = where(Accepted, V * link, link);
+
+  //////////////////////////////
+  // Debug Checks
+  // SU2 check
+  LatticeSU2Matrix check(grid);  // rotated matrix after hb
+  u = Zero();
+  check = ua * adj(ua) - 1.0;
+  check = where(Accepted, check, u);
+  assert(norm2(check) < 1.0e-4);
+
+  check = b * adj(b) - 1.0;
+  check = where(Accepted, check, u);
+  assert(norm2(check) < 1.0e-4);
+
+  LatticeMatrix Vcheck(grid);
+  Vcheck = Zero();
+  Vcheck = where(Accepted, V * adj(V) - 1.0, Vcheck);
+  //    std::cout<<GridLogMessage << "SU3 check " <<norm2(Vcheck)<<std::endl;
+  assert(norm2(Vcheck) < 1.0e-4);
+
+  // Verify the link stays in SU(3)
+  //    std::cout<<GridLogMessage <<"Checking the modified link"<<std::endl;
+  Vcheck = link * adj(link) - 1.0;
+  assert(norm2(Vcheck) < 1.0e-4);
+  /////////////////////////////////
+}
+
+template <ONLY_IF_SU>
+static void testGenerators(void) {
+  Matrix ta;
+  Matrix tb;
+  std::cout << GridLogMessage
+            << "Fundamental - Checking trace ta tb is 0.5 delta_ab"
+            << std::endl;
+  for (int a = 0; a < AdjointDimension; a++) {
+    for (int b = 0; b < AdjointDimension; b++) {
+      generator(a, ta);
+      generator(b, tb);
+      Complex tr = TensorRemove(trace(ta * tb));
+      std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
+                << std::endl;
+      if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
+      if (a != b) assert(abs(tr) < 1.0e-6);
+    }
+    std::cout << GridLogMessage << std::endl;
+  }
+  std::cout << GridLogMessage << "Fundamental - Checking if hermitian"
+            << std::endl;
+  for (int a = 0; a < AdjointDimension; a++) {
+    generator(a, ta);
+    std::cout << GridLogMessage << a << std::endl;
+    assert(norm2(ta - adj(ta)) < 1.0e-6);
+  }
+  std::cout << GridLogMessage << std::endl;
+
+  std::cout << GridLogMessage << "Fundamental - Checking if traceless"
+            << std::endl;
+  for (int a = 0; a < AdjointDimension; a++) {
+    generator(a, ta);
+    Complex tr = TensorRemove(trace(ta));
+    std::cout << GridLogMessage << a << " " << std::endl;
+    assert(abs(tr) < 1.0e-6);
+  }
+  std::cout << GridLogMessage << std::endl;
+}
+
+/*
+ * Fundamental rep gauge xform
+ */
+template <typename Fundamental, typename GaugeMat, ONLY_IF_SU>
+static void GaugeTransformFundamental(Fundamental &ferm, GaugeMat &g) {
+  GridBase *grid = ferm._grid;
+  conformable(grid, g._grid);
+  ferm = g * ferm;
+}
+/*
+ * Adjoint rep gauge xform
+ */
+
+template <typename GaugeField, typename GaugeMat, ONLY_IF_SU>
+static void GaugeTransform(GaugeField &Umu, GaugeMat &g) {
+  GridBase *grid = Umu.Grid();
+  conformable(grid, g.Grid());
+
+  GaugeMat U(grid);
+  GaugeMat ag(grid);
+  ag = adj(g);
+
+  for (int mu = 0; mu < Nd; mu++) {
+    U = PeekIndex<LorentzIndex>(Umu, mu);
+    U = g * U * Cshift(ag, mu, 1);
+    PokeIndex<LorentzIndex>(Umu, U, mu);
+  }
+}
+template <typename GaugeMat, ONLY_IF_SU>
+static void GaugeTransform(std::vector<GaugeMat> &U, GaugeMat &g) {
+  GridBase *grid = g.Grid();
+  GaugeMat ag(grid);
+  ag = adj(g);
+  for (int mu = 0; mu < Nd; mu++) {
+    U[mu] = g * U[mu] * Cshift(ag, mu, 1);
+  }
+}
+template <typename GaugeField, typename GaugeMat, ONLY_IF_SU>
+static void RandomGaugeTransform(GridParallelRNG &pRNG, GaugeField &Umu,
+                                 GaugeMat &g) {
+  LieRandomize(pRNG, g, 1.0);
+  GaugeTransform(Umu, g);
+}

From 54c8025aad0263b8258d8e6b2a683689f6ec9260 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Mon, 28 Nov 2022 17:50:38 +0000
Subject: [PATCH 034/129] Remove unnecessary pwd in scripts/filelist

---
 scripts/filelist | 1 -
 1 file changed, 1 deletion(-)

diff --git a/scripts/filelist b/scripts/filelist
index 4e64cd62..d91da5f1 100755
--- a/scripts/filelist
+++ b/scripts/filelist
@@ -37,7 +37,6 @@ cd $home/tests
 dirs=`find . -type d -not -path '*/\.*'`
 for subdir in $dirs; do
     cd $home/tests/$subdir
-    pwd
     TESTS=`ls T*.cc`
     TESTLIST=`echo ${TESTS} | sed s/.cc//g `
     PREF=`[ $subdir = '.' ] && echo noinst || echo EXTRA`

From 7c2ad4f8c8c42aee5fc8aba0dd3be0d970776b3c Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 30 Nov 2022 11:57:39 +0000
Subject: [PATCH 035/129] Attempt with SFINAE (failed)

---
 Grid/qcd/utils/SUn.h       |   42 +-
 Grid/qcd/utils/SUn_impl.h  |    2 +
 Grid/qcd/utils/Sp2n.h      | 1161 ++++++++++++++++++------------------
 Grid/qcd/utils/Sp2n_impl.h |  245 ++++++++
 4 files changed, 866 insertions(+), 584 deletions(-)
 create mode 100644 Grid/qcd/utils/Sp2n_impl.h

diff --git a/Grid/qcd/utils/SUn.h b/Grid/qcd/utils/SUn.h
index 4a7148e9..0c961ab4 100644
--- a/Grid/qcd/utils/SUn.h
+++ b/Grid/qcd/utils/SUn.h
@@ -33,12 +33,19 @@ directory
 #define QCD_UTIL_SUN_H
 
 #define ONLY_IF_SU                  \
-  typename dummy_name = group_name, \
-           typename = std::enable_if_t<is_su<dummy_name>::value>
+  typename \
+    typename std::enable_if_t<is_su<group_name>::value, dummy_name> ,\
+    dummy_name = group_name, 
+
+#define ONLY_IF_Sp                  \
+  typename \
+    typename std::enable_if_t<is_sp<group_name>::value, dummy_name> ,\
+    dummy_name =group_name, 
 
 NAMESPACE_BEGIN(Grid);
 namespace GroupName {
 class SU {};
+class Sp {};
 }  // namespace GroupName
 
 template <typename group_name>
@@ -51,18 +58,44 @@ struct is_su<GroupName::SU> {
   static const bool value = true;
 };
 
+template <typename group_name>
+struct is_sp {
+  static const bool value = false;
+};
+
+template <>
+struct is_sp<GroupName::Sp> {
+  static const bool value = true;
+};
+
+template<typename group_name>
+constexpr int compute_adjoint_dimension(int ncolour);
+
+template<>
+constexpr int compute_adjoint_dimension<GroupName::SU>(int ncolour) { return ncolour * ncolour - 1;}
+
+template<>
+constexpr int compute_adjoint_dimension<GroupName::Sp>(int ncolour) { return ncolour/2*(ncolour+1);}
+
+
 template <int ncolour, class group_name = GroupName::SU>
 class GaugeGroup;
 
 template <int ncolour>
 using SU = GaugeGroup<ncolour, GroupName::SU>;
 
+template <int ncolour>
+using Sp = GaugeGroup<ncolour, GroupName::Sp>;
+
 template <int ncolour, class group_name>
 class GaugeGroup {
  public:
   static const int Dimension = ncolour;
-  static const int AdjointDimension = ncolour * ncolour - 1;
-  static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
+  static const int AdjointDimension = compute_adjoint_dimension<group_name>(ncolour);
+  static const int AlgebraDimension = compute_adjoint_dimension<group_name>(ncolour);
+  // Don't know how to only enable this for Sp:
+  static const int nsp = ncolour/2;
+
 
   template <typename vtype>
   using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
@@ -115,6 +148,7 @@ class GaugeGroup {
   typedef Lattice<vSU2MatrixD> LatticeSU2MatrixD;
 
 #include "Grid/qcd/utils/SUn_impl.h"
+#include "Grid/qcd/utils/Sp2n_impl.h"
 
   static void printGenerators(void) {
     for (int gen = 0; gen < AdjointDimension; gen++) {
diff --git a/Grid/qcd/utils/SUn_impl.h b/Grid/qcd/utils/SUn_impl.h
index e7b972ef..30d8ff14 100644
--- a/Grid/qcd/utils/SUn_impl.h
+++ b/Grid/qcd/utils/SUn_impl.h
@@ -6,6 +6,8 @@
 //
 // around it.
 
+template<ONLY_IF_SU>
+  static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
 template <typename vtype, ONLY_IF_SU>
 using iSUnMatrix = iGroupMatrix<vtype>;
 template <typename vtype, ONLY_IF_SU>
diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.h
index 19e30568..1f7009e3 100644
--- a/Grid/qcd/utils/Sp2n.h
+++ b/Grid/qcd/utils/Sp2n.h
@@ -1,580 +1,581 @@
-
-#ifndef QCD_UTIL_Sp2n_H
-#define QCD_UTIL_Sp2n_H
-
-NAMESPACE_BEGIN(Grid);
-
-// Sp(2N)
-// ncolour = 2N
-
-
-template <int ncolour>
-class Sp {
-public:
-    static const int nsp = ncolour/2;
-    static const int Dimension = ncolour;
-    static const int AlgebraDimension = nsp*(2*nsp +1);
-    static int su2subgroups(void) { return (nsp * (nsp - 1)) / 2; }
-    
-    
-    template <typename vtype>
-    using iSp2nMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
-    template <typename vtype>
-    using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
-    template <typename vtype>
-    using iSp2nAlgebraVector = iScalar<iScalar<iVector<vtype, AlgebraDimension> > >;
-    
-    typedef iSp2nMatrix<Complex> Matrix;
-    typedef iSp2nMatrix<ComplexF> MatrixF;
-    typedef iSp2nMatrix<ComplexD> MatrixD;
-    
-    typedef iSp2nMatrix<vComplex> vMatrix;
-    typedef iSp2nMatrix<vComplexF> vMatrixF;
-    typedef iSp2nMatrix<vComplexD> vMatrixD;
-    
-    typedef iSp2nAlgebraVector<Complex> AlgebraVector;
-    typedef iSp2nAlgebraVector<ComplexF> AlgebraVectorF;
-    typedef iSp2nAlgebraVector<ComplexD> AlgebraVectorD;
-    
-    typedef iSp2nAlgebraVector<vComplex> vAlgebraVector;
-    typedef iSp2nAlgebraVector<vComplexF> vAlgebraVectorF;
-    typedef iSp2nAlgebraVector<vComplexD> vAlgebraVectorD;
-    
-    typedef Lattice<vMatrix> LatticeMatrix;
-    typedef Lattice<vMatrixF> LatticeMatrixF;
-    typedef Lattice<vMatrixD> LatticeMatrixD;
-    
-    typedef Lattice<vAlgebraVector> LatticeAlgebraVector;
-    typedef Lattice<vAlgebraVectorF> LatticeAlgebraVectorF;
-    typedef Lattice<vAlgebraVectorD> LatticeAlgebraVectorD;
-    
-    
-    
-    // Sp(2N) has N(2N+1) = 2N^2+N generators
-    //
-    // normalise the generators such that
-    // Trace ( Ta Tb) = 1/2 delta_ab
-    //
-    // N generators in the cartan, 2N^2 off
-    // off diagonal:
-    //     there are 6 types named a,b,c,d and w,z
-    //     abcd are N(N-1)/2 each while wz are N each
-    
- template <class cplx>
-    static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
-        // map lie index into type of generators: diagonal, abcd type, wz type
-
-        int diagIndex;
-        int aIndex, bIndex, cIndex, dIndex;
-        int wIndex, zIndex; // a,b,c,d are N(N-1)/2 and w,z are N
-        int mod = nsp * (nsp-1) * 0.5;
-        int offdiag = 2*nsp*nsp; // number of generators not in the cartan subalgebra
-        int wmod = 4*mod;
-        int zmod = wmod+nsp;
-        if (lieIndex >= offdiag) {
-            diagIndex = lieIndex - offdiag; // 0, ... ,N-1
-            //std::cout << GridLogMessage << "diag type " << std::endl;
-            generatorDiagtype(diagIndex, ta);
-            return;
-        }
-        if ( (lieIndex >= wmod) && (lieIndex < zmod) ) {
-            //std::cout << GridLogMessage << "w type " << std::endl;
-            wIndex = lieIndex- wmod;    // 0, ... ,N-1
-            generatorWtype(wIndex,ta);
-            return;
-        }
-        if ( (lieIndex >= zmod) && (lieIndex < offdiag) ) {
-            //std::cout << GridLogMessage << "z type " << std::endl;
-            //std::cout << GridLogMessage << "lie index " << lieIndex << std::endl;
-            //std::cout << GridLogMessage << "z mod " << zmod << std::endl;
-            zIndex = lieIndex - zmod;   // 0, ... ,N-1
-            generatorZtype(zIndex,ta);
-            return;
-        }
-        if (lieIndex < mod) { // atype 0, ... , N(N-1)/2=mod
-            //std::cout << GridLogMessage << "a type " << std::endl;
-            aIndex = lieIndex;
-            //std::cout << GridLogMessage << "a indx " << aIndex << std::endl;
-            generatorAtype(aIndex, ta);
-            return;
-        }
-        if ( (lieIndex >= mod) && lieIndex < 2*mod) { // btype mod, ... , 2mod-1
-            //std::cout << GridLogMessage << "b type " << std::endl;
-            bIndex = lieIndex - mod;
-            generatorBtype(bIndex, ta);
-            return;
-        }
-        if ( (lieIndex >= 2*mod) && lieIndex < 3*mod) { // ctype 2mod, ... , 3mod-1
-            //std::cout << GridLogMessage << "c type " << std::endl;
-            cIndex = lieIndex - 2*mod;
-            generatorCtype(cIndex, ta);
-            return;
-        }
-        if ( (lieIndex >= 3*mod) && lieIndex < wmod) { // ctype 3mod, ... , 4mod-1 = wmod-1
-             //std::cout << GridLogMessage << "d type " << std::endl;
-             dIndex = lieIndex - 3*mod;
-             generatorDtype(dIndex, ta);
-            return;
-         }
-            
-    } //end of generator
-    
-    template <class cplx>
-    static void generatorDiagtype(int diagIndex, iSp2nMatrix<cplx> &ta) {
-        
-        // ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan subalgebra
-        
-        ta = Zero();
-        RealD nrm = 1.0 / 2;
-
-        ta()()(diagIndex,diagIndex) = nrm;
-        ta()()(diagIndex+nsp,diagIndex+nsp) = -nrm;
-    }
-    
-    template <class cplx>
-    static void generatorAtype(int aIndex, iSp2nMatrix<cplx> &ta) {
-        
-        // ta(i,j) = ta(j,i) = -ta(i+N,j+N) = -ta(j+N,i+N) = 1 / 2 sqrt(2)
-        // with i<j and i=0,...,N-2
-        // follows that j=i+1, ... , N
-        int i1, i2;
-        ta = Zero();
-        RealD nrm = 1 / (2 * std::sqrt(2) );
-        
-        su2SubGroupIndex(i1, i2, aIndex);
-        ta()()(i1,i2) = 1;
-        ta()()(i2,i1) = 1;
-        ta()()(i1+nsp,i2+nsp) = -1;
-        ta()()(i2+nsp,i1+nsp) = -1;
-
-        ta = ta * nrm;
-    }
-    
-    template <class cplx>
-    static void generatorBtype(int bIndex, iSp2nMatrix<cplx> &ta) {
-        
-        // ta(i,j) = -ta(j,i) = ta(i+N,j+N) = -ta(j+N,i+N) = i / 1/ 2 sqrt(2)
-        // with i<j and i=0,...,N-2
-        // follows that j=i+1, ... , N-1
-        
-        int i1, i2;
-        ta = Zero();
-        cplx i(0.0, 1.0);
-        RealD nrm = 1 / (2 * std::sqrt(2));
-        su2SubGroupIndex(i1, i2, bIndex);
-        
-
-        ta()()(i1,i2) = i;
-        ta()()(i2,i1) = -i;
-        ta()()(i1+nsp,i2+nsp) = i;
-        ta()()(i2+nsp,i1+nsp) = -i;
-
-        ta = ta * nrm;
-    }
-    
-    template <class cplx>
-    static void generatorCtype(int cIndex, iSp2nMatrix<cplx> &ta) {
-        
-        // ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
-        
-        
-        int i1, i2;
-        ta = Zero();
-        RealD nrm = 1 / (2 * std::sqrt(2) );
-        su2SubGroupIndex(i1, i2, cIndex);
-        
-        ta()()(i1,i2+nsp) = 1;
-        ta()()(i2,i1+nsp) = 1;
-        ta()()(i1+nsp,i2) = 1;
-        ta()()(i2+nsp,i1) = 1;
-
-        ta = ta * nrm;
-    }
-    
-    template <class cplx>
-    static void generatorDtype(int dIndex, iSp2nMatrix<cplx> &ta) {
-        
-        // ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i /  2 sqrt(2)
-        
-        int i1, i2;
-        ta = Zero();
-        cplx i(0.0, 1.0);
-        RealD nrm = 1 / (2 * std::sqrt(2)  );
-        su2SubGroupIndex(i1, i2, dIndex);
-
-        ta()()(i1,i2+nsp) = i;
-        ta()()(i2,i1+nsp) = i;
-        ta()()(i1+nsp,i2) = -i;
-        ta()()(i2+nsp,i1) = -i;
-
-        ta = ta * nrm;
-    }
-    
-    template <class cplx>
-     static void generatorWtype(int wIndex, iSp2nMatrix<cplx> &ta) {
-         
-         // ta(i,i+N) =  ta(i+N,i) = 1/2
-         
-         ta = Zero();
-         RealD nrm = 1.0 / 2; //check
-
-         ta()()(wIndex,wIndex+nsp) = 1;
-         ta()()(wIndex+nsp,wIndex) = 1;
-         
-         ta = ta * nrm;
-     }
-    
-    template <class cplx>
-     static void generatorZtype(int zIndex, iSp2nMatrix<cplx> &ta) {
-         
-         // ta(i,i+N) = - ta(i+N,i) = i/2
-         
-         ta = Zero();
-         RealD nrm = 1.0 / 2; //check
-         cplx i(0.0, 1.0);
-         ta()()(zIndex,zIndex+nsp) = i;
-         ta()()(zIndex+nsp,zIndex) = -i;
-         
-         ta = ta * nrm;
-     }
-    
-    
-    ////////////////////////////////////////////////////////////////////////
-    // Map a su2 subgroup number to the pair of rows that are non zero
-    ////////////////////////////////////////////////////////////////////////
-    static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
-      assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
-
-      int spare = su2_index;
-      for (i1 = 0; spare >= (nsp - 1 - i1); i1++) {
-        spare = spare - (nsp - 1 - i1);  // remove the Nc-1-i1 terms
-      }
-      i2 = i1 + 1 + spare;
-    }
-    
-    
-    
-    
-    
-    static void printGenerators(void) {
-        for (int gen = 0; gen < AlgebraDimension; gen++) {
-            Matrix ta;
-            generator(gen, ta);
-            std::cout << GridLogMessage << "Nc = " << ncolour << std::endl;
-            std::cout << GridLogMessage << " t_" << gen << std::endl;
-            std::cout << GridLogMessage << ta << std::endl;
-        }
-    }
-    
-    
-    
-    static void testGenerators(void) {
-        Matrix ta;
-        Matrix tb;
-        std::cout << GridLogMessage << "Fundamental - Checking trace ta tb is 0.5 delta_ab " << std::endl;
-        for (int a = 0; a < AlgebraDimension; a++) {
-            for (int b = 0; b < AlgebraDimension; b++) {
-                generator(a,ta);
-                generator(b,tb);
-                Complex tr = TensorRemove(trace( ta * tb) );
-                std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
-                << std::endl;
-                if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
-                if (a != b) assert(abs(tr) < 1.0e-6);
-
-            }
-        }
-        std::cout << GridLogMessage << std::endl;
-        std::cout << GridLogMessage << "Fundamental - Checking if hermitian" << std::endl;
-        for (int a = 0; a < AlgebraDimension; a++) {
-            generator(a,ta);
-            std::cout << GridLogMessage << a << std::endl;
-            assert(norm2(ta - adj(ta)) < 1.0e-6);
-        }
-        std::cout << GridLogMessage << std::endl;
-        std::cout << GridLogMessage << "Fundamental - Checking if traceless" << std::endl;
-        for (int a = 0; a < AlgebraDimension; a++) {
-          generator(a, ta);
-          Complex tr = TensorRemove(trace(ta));
-          std::cout << GridLogMessage << a << std::endl;
-          assert(abs(tr) < 1.0e-6);
-        }
-        
-    }
-    
-    
-    template <typename LatticeMatrixType>
-    static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out, double scale = 1.0)
-    {
-      GridBase *grid = out.Grid();
-
-      typedef typename LatticeMatrixType::vector_type vector_type;
-      typedef typename LatticeMatrixType::scalar_type scalar_type;
-
-      typedef iSinglet<vector_type> vTComplexType;
-
-      typedef Lattice<vTComplexType> LatticeComplexType;
-      typedef typename GridTypeMapper<typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
-
-      LatticeComplexType ca(grid);
-      LatticeMatrixType lie(grid);
-      LatticeMatrixType la(grid);
-      ComplexD ci(0.0, scale);
-      //    ComplexD cone(1.0, 0.0);
-      MatrixType ta;
-
-      lie = Zero();
-
-      for (int a = 0; a < AlgebraDimension; a++) {
-        random(pRNG, ca);
-
-        ca = (ca + conjugate(ca)) * 0.5;
-        ca = ca - 0.5;
-
-        generator(a, ta);
-
-        la = ci * ca * ta;
-
-        lie = lie + la;  // e^{i la ta}
-
-      }
-      taExp(lie, out);
-    }
-    
-    
-    static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG, //same as sun
-                                                    LatticeMatrix &out,
-                                                    Real scale = 1.0) {
-      GridBase *grid = out.Grid();
-      LatticeReal ca(grid);
-      LatticeMatrix la(grid);
-      Complex ci(0.0, scale);
-      Matrix ta;
-
-      out = Zero();
-      for (int a = 0; a < AlgebraDimension; a++) {
-        gaussian(pRNG, ca);
-        generator(a, ta);
-        la = toComplex(ca) * ta;
-        out += la;
-      }
-      out *= ci;
-    }
-    
-    static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
-                                            LatticeMatrix &out,
-                                            Real scale = 1.0) {
-      conformable(h, out);
-      GridBase *grid = out.Grid();
-      LatticeMatrix la(grid);
-      Matrix ta;
-
-      out = Zero();
-      for (int a = 0; a < AlgebraDimension; a++) {
-        generator(a, ta);
-        la = peekColour(h, a) * timesI(ta) * scale;
-        out += la;
-      }
-    }
-    
-    
-    template <typename LatticeMatrixType>
-    static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) { // same as sun
-      typedef typename LatticeMatrixType::scalar_type ComplexType;
-
-      LatticeMatrixType xn(x.Grid());
-      RealD nfac = 1.0;
-
-      xn = x;
-      ex = xn + ComplexType(1.0);  // 1+x
-
-      // Do a 12th order exponentiation
-      for (int i = 2; i <= 12; ++i) {
-        nfac = nfac / RealD(i);  // 1/2, 1/2.3 ...
-        xn = xn * x;             // x2, x3,x4....
-        ex = ex + xn * nfac;     // x2/2!, x3/3!....
-      }
-    }
-    
- static void projectOnAlgebra(LatticeAlgebraVector &h_out, const LatticeMatrix &in, Real scale = 1.0) {
-   conformable(h_out, in);
-   h_out = Zero();
-   Matrix Ta;
-
-   for (int a = 0; a < AlgebraDimension; a++) {
-     generator(a, Ta);
-     pokeColour(h_out, - 2.0 * (trace(timesI(Ta) * in)) * scale, a);
-   }
- }
-    
-    
-    template <typename GaugeField>
-    static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
-      typedef typename GaugeField::vector_type vector_type;
-      typedef iSp2nMatrix<vector_type> vMatrixType;
-      typedef Lattice<vMatrixType> LatticeMatrixType;
-
-      LatticeMatrixType Umu(out.Grid());
-      for (int mu = 0; mu < Nd; mu++) {
-        LieRandomize(pRNG, Umu, 1.0);   //def
-        PokeIndex<LorentzIndex>(out, Umu, mu);
-      }
-    }
-    template<typename GaugeField>
-    static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out){
-      typedef typename GaugeField::vector_type vector_type;
-      typedef iSp2nMatrix<vector_type> vMatrixType;
-      typedef Lattice<vMatrixType> LatticeMatrixType;
-
-      LatticeMatrixType Umu(out.Grid());
-      for(int mu=0;mu<Nd;mu++){
-        LieRandomize(pRNG,Umu,0.01);    //def
-        PokeIndex<LorentzIndex>(out,Umu,mu);
-      }
-    }
-    
-    template<typename GaugeField>
-    static void ColdConfiguration(GaugeField &out){
-      typedef typename GaugeField::vector_type vector_type;
-      typedef iSp2nMatrix<vector_type> vMatrixType;
-      typedef Lattice<vMatrixType> LatticeMatrixType;
-
-      LatticeMatrixType Umu(out.Grid());
-      Umu=1.0;
-      for(int mu=0;mu<Nd;mu++){
-        PokeIndex<LorentzIndex>(out,Umu,mu);
-      }
-    }
-    template<typename GaugeField>
-    static void ColdConfiguration(GridParallelRNG &pRNG,GaugeField &out){
-      ColdConfiguration(out);
-    }
-    
-    static void OmegaInvariance(ColourMatrix &in)
-    {
-        
-        ColourMatrix Omega;
-        Omega = Zero();
-        
-        std::cout << GridLogMessage << "I am a ColourMatrix" << std::endl;
-        
-        //for (int i = 0; i < ncolour; i++)         wrong?!
-        //{
-        //    Omega()()(i, 2*ncolour-1-i) = 1.;
-        //    Omega()()(2*ncolour-1-i, i) = -1;
-        //}
-        for (int i = 0; i < nsp; i++)
-        {
-            Omega()()(i, nsp+i) = 1.;
-            Omega()()(nsp+i, i) = -1;
-        }
-
-        auto diff = Omega - (in * Omega * transpose(in) );
-        auto sdiff = norm2(diff);
-        if (norm2(sdiff) < 1e-8)
-        {
-            std::cout << GridLogMessage << "Symplectic condition satisfied: Omega invariant" << std::endl;
-        } else {
-            std::cout << GridLogMessage << "WARNING!!!!!! Matrix Omega NOT left invariant by " << norm2(sdiff) << std::endl;
-        }
-        
-    }
-    
-    template<typename GaugeField>
-    static void OmegaInvariance(GaugeField &in)
-    {
-        typedef typename GaugeField::vector_type vector_type;
-        typedef iSp2nMatrix<vector_type> vMatrixType;
-        typedef Lattice<vMatrixType> LatticeMatrixType;
-        
-        LatticeMatrixType U(in.Grid());
-        LatticeMatrixType OmegaLatt(in.Grid());
-        LatticeMatrixType identity(in.Grid());
-        RealD vol = in.Grid()->gSites();
-        ColourMatrix Omega;
-        
-        OmegaLatt = Zero();
-        Omega = Zero();
-        identity = 1.;
-        
-        std::cout << GridLogMessage << "I am a GaugeField " << std::endl;
-        
-        U = PeekIndex<LorentzIndex>(in,1);
-        
-        OmegaInvariance(U);
-        
-    }
-    
-       static void OmegaInvariance(LatticeColourMatrixD &in)
-       {
-                      
-           LatticeColourMatrixD OmegaLatt(in.Grid());
-           LatticeColourMatrixD identity(in.Grid());
-           RealD vol = in.Grid()->gSites();
-           ColourMatrix Omega;
-           
-           OmegaLatt = Zero();
-           Omega = Zero();
-           identity = 1.;
-           
-           std::cout << GridLogMessage << "I am a LatticeColourMatrix " << std::endl;
-           
-           for (int i = 0; i < nsp; i++)
-           {
-               Omega()()(i, nsp+i) = 1.;
-               Omega()()(nsp+i, i) = -1;
-           }
-           
-           std::cout << GridLogMessage << "Omega = " << Omega()() << std::endl;
-           OmegaLatt = OmegaLatt + (identity*Omega);
-           
-           auto diff = OmegaLatt - (in*OmegaLatt*transpose(in));
-           auto sdiff = sum(diff);
-           //assert( norm2(sdiff) < 1e-8 );
-           if (norm2(sdiff) < 1e-8)
-           {
-               std::cout << GridLogMessage << "Symplectic condition satisfied: Omega invariant" << std::endl;
-           } else {
-               std::cout << GridLogMessage << "WARNING!!!!!! Matrix Omega NOT left invariant by " << norm2(sdiff) << std::endl;
-           }
-           
-           
-       }
-        
-    
-}; // end of class Sp
-    
- 
- template<int N>
- static void ProjectSp2n(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
- {
-   Umu      = ProjectOnSpGroup(Umu);
-   auto det = Determinant(Umu); // ok ?
-
-   det = conjugate(det);
-
-   for(int i=0;i<N;i++){
-     auto element = PeekIndex<ColourIndex>(Umu,N-1,i);
-     element = element * det;
-     PokeIndex<ColourIndex>(Umu,element,Nc-1,i);
-   }
- }
- template<int N>
- static void ProjectSp2n(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,Nd> > &U)
- {
-   GridBase *grid=U.Grid();
-   for(int mu=0;mu<Nd;mu++){
-     auto Umu = PeekIndex<LorentzIndex>(U,mu);
-     Umu      = ProjectOnSpGroup(Umu);
-     ProjectSp2n(Umu);
-     PokeIndex<LorentzIndex>(U,Umu,mu);
-   }
- }
-
-typedef Sp<2> Sp2;
-typedef Sp<4> Sp4;
-typedef Sp<6> Sp6;
-typedef Sp<8> Sp8;
-
-NAMESPACE_END(Grid);
-#endif
+#include "Grid/qcd/utils/SUn.h"
+// 
+// #ifndef QCD_UTIL_Sp2n_H
+// #define QCD_UTIL_Sp2n_H
+// 
+// NAMESPACE_BEGIN(Grid);
+// 
+// // Sp(2N)
+// // ncolour = 2N
+// 
+// 
+// template <int ncolour>
+// class Sp {
+// public:
+//     static const int nsp = ncolour/2;
+//     static const int Dimension = ncolour;
+//     static const int AlgebraDimension = nsp*(2*nsp +1);
+//     static int su2subgroups(void) { return (nsp * (nsp - 1)) / 2; }
+//     
+//     
+//     template <typename vtype>
+//     using iSp2nMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
+//     template <typename vtype>
+//     using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
+//     template <typename vtype>
+//     using iSp2nAlgebraVector = iScalar<iScalar<iVector<vtype, AlgebraDimension> > >;
+//     
+//     typedef iSp2nMatrix<Complex> Matrix;
+//     typedef iSp2nMatrix<ComplexF> MatrixF;
+//     typedef iSp2nMatrix<ComplexD> MatrixD;
+//     
+//     typedef iSp2nMatrix<vComplex> vMatrix;
+//     typedef iSp2nMatrix<vComplexF> vMatrixF;
+//     typedef iSp2nMatrix<vComplexD> vMatrixD;
+//     
+//     typedef iSp2nAlgebraVector<Complex> AlgebraVector;
+//     typedef iSp2nAlgebraVector<ComplexF> AlgebraVectorF;
+//     typedef iSp2nAlgebraVector<ComplexD> AlgebraVectorD;
+//     
+//     typedef iSp2nAlgebraVector<vComplex> vAlgebraVector;
+//     typedef iSp2nAlgebraVector<vComplexF> vAlgebraVectorF;
+//     typedef iSp2nAlgebraVector<vComplexD> vAlgebraVectorD;
+//     
+//     typedef Lattice<vMatrix> LatticeMatrix;
+//     typedef Lattice<vMatrixF> LatticeMatrixF;
+//     typedef Lattice<vMatrixD> LatticeMatrixD;
+//     
+//     typedef Lattice<vAlgebraVector> LatticeAlgebraVector;
+//     typedef Lattice<vAlgebraVectorF> LatticeAlgebraVectorF;
+//     typedef Lattice<vAlgebraVectorD> LatticeAlgebraVectorD;
+//     
+//     
+//     
+//     // Sp(2N) has N(2N+1) = 2N^2+N generators
+//     //
+//     // normalise the generators such that
+//     // Trace ( Ta Tb) = 1/2 delta_ab
+//     //
+//     // N generators in the cartan, 2N^2 off
+//     // off diagonal:
+//     //     there are 6 types named a,b,c,d and w,z
+//     //     abcd are N(N-1)/2 each while wz are N each
+//     
+//  template <class cplx>
+//     static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
+//         // map lie index into type of generators: diagonal, abcd type, wz type
+// 
+//         int diagIndex;
+//         int aIndex, bIndex, cIndex, dIndex;
+//         int wIndex, zIndex; // a,b,c,d are N(N-1)/2 and w,z are N
+//         int mod = nsp * (nsp-1) * 0.5;
+//         int offdiag = 2*nsp*nsp; // number of generators not in the cartan subalgebra
+//         int wmod = 4*mod;
+//         int zmod = wmod+nsp;
+//         if (lieIndex >= offdiag) {
+//             diagIndex = lieIndex - offdiag; // 0, ... ,N-1
+//             //std::cout << GridLogMessage << "diag type " << std::endl;
+//             generatorDiagtype(diagIndex, ta);
+//             return;
+//         }
+//         if ( (lieIndex >= wmod) && (lieIndex < zmod) ) {
+//             //std::cout << GridLogMessage << "w type " << std::endl;
+//             wIndex = lieIndex- wmod;    // 0, ... ,N-1
+//             generatorWtype(wIndex,ta);
+//             return;
+//         }
+//         if ( (lieIndex >= zmod) && (lieIndex < offdiag) ) {
+//             //std::cout << GridLogMessage << "z type " << std::endl;
+//             //std::cout << GridLogMessage << "lie index " << lieIndex << std::endl;
+//             //std::cout << GridLogMessage << "z mod " << zmod << std::endl;
+//             zIndex = lieIndex - zmod;   // 0, ... ,N-1
+//             generatorZtype(zIndex,ta);
+//             return;
+//         }
+//         if (lieIndex < mod) { // atype 0, ... , N(N-1)/2=mod
+//             //std::cout << GridLogMessage << "a type " << std::endl;
+//             aIndex = lieIndex;
+//             //std::cout << GridLogMessage << "a indx " << aIndex << std::endl;
+//             generatorAtype(aIndex, ta);
+//             return;
+//         }
+//         if ( (lieIndex >= mod) && lieIndex < 2*mod) { // btype mod, ... , 2mod-1
+//             //std::cout << GridLogMessage << "b type " << std::endl;
+//             bIndex = lieIndex - mod;
+//             generatorBtype(bIndex, ta);
+//             return;
+//         }
+//         if ( (lieIndex >= 2*mod) && lieIndex < 3*mod) { // ctype 2mod, ... , 3mod-1
+//             //std::cout << GridLogMessage << "c type " << std::endl;
+//             cIndex = lieIndex - 2*mod;
+//             generatorCtype(cIndex, ta);
+//             return;
+//         }
+//         if ( (lieIndex >= 3*mod) && lieIndex < wmod) { // ctype 3mod, ... , 4mod-1 = wmod-1
+//              //std::cout << GridLogMessage << "d type " << std::endl;
+//              dIndex = lieIndex - 3*mod;
+//              generatorDtype(dIndex, ta);
+//             return;
+//          }
+//             
+//     } //end of generator
+//     
+//     template <class cplx>
+//     static void generatorDiagtype(int diagIndex, iSp2nMatrix<cplx> &ta) {
+//         
+//         // ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan subalgebra
+//         
+//         ta = Zero();
+//         RealD nrm = 1.0 / 2;
+// 
+//         ta()()(diagIndex,diagIndex) = nrm;
+//         ta()()(diagIndex+nsp,diagIndex+nsp) = -nrm;
+//     }
+//     
+//     template <class cplx>
+//     static void generatorAtype(int aIndex, iSp2nMatrix<cplx> &ta) {
+//         
+//         // ta(i,j) = ta(j,i) = -ta(i+N,j+N) = -ta(j+N,i+N) = 1 / 2 sqrt(2)
+//         // with i<j and i=0,...,N-2
+//         // follows that j=i+1, ... , N
+//         int i1, i2;
+//         ta = Zero();
+//         RealD nrm = 1 / (2 * std::sqrt(2) );
+//         
+//         su2SubGroupIndex(i1, i2, aIndex);
+//         ta()()(i1,i2) = 1;
+//         ta()()(i2,i1) = 1;
+//         ta()()(i1+nsp,i2+nsp) = -1;
+//         ta()()(i2+nsp,i1+nsp) = -1;
+// 
+//         ta = ta * nrm;
+//     }
+//     
+//     template <class cplx>
+//     static void generatorBtype(int bIndex, iSp2nMatrix<cplx> &ta) {
+//         
+//         // ta(i,j) = -ta(j,i) = ta(i+N,j+N) = -ta(j+N,i+N) = i / 1/ 2 sqrt(2)
+//         // with i<j and i=0,...,N-2
+//         // follows that j=i+1, ... , N-1
+//         
+//         int i1, i2;
+//         ta = Zero();
+//         cplx i(0.0, 1.0);
+//         RealD nrm = 1 / (2 * std::sqrt(2));
+//         su2SubGroupIndex(i1, i2, bIndex);
+//         
+// 
+//         ta()()(i1,i2) = i;
+//         ta()()(i2,i1) = -i;
+//         ta()()(i1+nsp,i2+nsp) = i;
+//         ta()()(i2+nsp,i1+nsp) = -i;
+// 
+//         ta = ta * nrm;
+//     }
+//     
+//     template <class cplx>
+//     static void generatorCtype(int cIndex, iSp2nMatrix<cplx> &ta) {
+//         
+//         // ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
+//         
+//         
+//         int i1, i2;
+//         ta = Zero();
+//         RealD nrm = 1 / (2 * std::sqrt(2) );
+//         su2SubGroupIndex(i1, i2, cIndex);
+//         
+//         ta()()(i1,i2+nsp) = 1;
+//         ta()()(i2,i1+nsp) = 1;
+//         ta()()(i1+nsp,i2) = 1;
+//         ta()()(i2+nsp,i1) = 1;
+// 
+//         ta = ta * nrm;
+//     }
+//     
+//     template <class cplx>
+//     static void generatorDtype(int dIndex, iSp2nMatrix<cplx> &ta) {
+//         
+//         // ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i /  2 sqrt(2)
+//         
+//         int i1, i2;
+//         ta = Zero();
+//         cplx i(0.0, 1.0);
+//         RealD nrm = 1 / (2 * std::sqrt(2)  );
+//         su2SubGroupIndex(i1, i2, dIndex);
+// 
+//         ta()()(i1,i2+nsp) = i;
+//         ta()()(i2,i1+nsp) = i;
+//         ta()()(i1+nsp,i2) = -i;
+//         ta()()(i2+nsp,i1) = -i;
+// 
+//         ta = ta * nrm;
+//     }
+//     
+//     template <class cplx>
+//      static void generatorWtype(int wIndex, iSp2nMatrix<cplx> &ta) {
+//          
+//          // ta(i,i+N) =  ta(i+N,i) = 1/2
+//          
+//          ta = Zero();
+//          RealD nrm = 1.0 / 2; //check
+// 
+//          ta()()(wIndex,wIndex+nsp) = 1;
+//          ta()()(wIndex+nsp,wIndex) = 1;
+//          
+//          ta = ta * nrm;
+//      }
+//     
+//     template <class cplx>
+//      static void generatorZtype(int zIndex, iSp2nMatrix<cplx> &ta) {
+//          
+//          // ta(i,i+N) = - ta(i+N,i) = i/2
+//          
+//          ta = Zero();
+//          RealD nrm = 1.0 / 2; //check
+//          cplx i(0.0, 1.0);
+//          ta()()(zIndex,zIndex+nsp) = i;
+//          ta()()(zIndex+nsp,zIndex) = -i;
+//          
+//          ta = ta * nrm;
+//      }
+//     
+//     
+//     ////////////////////////////////////////////////////////////////////////
+//     // Map a su2 subgroup number to the pair of rows that are non zero
+//     ////////////////////////////////////////////////////////////////////////
+//     static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
+//       assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
+// 
+//       int spare = su2_index;
+//       for (i1 = 0; spare >= (nsp - 1 - i1); i1++) {
+//         spare = spare - (nsp - 1 - i1);  // remove the Nc-1-i1 terms
+//       }
+//       i2 = i1 + 1 + spare;
+//     }
+//     
+//     
+//     
+//     
+//     
+//     static void printGenerators(void) {
+//         for (int gen = 0; gen < AlgebraDimension; gen++) {
+//             Matrix ta;
+//             generator(gen, ta);
+//             std::cout << GridLogMessage << "Nc = " << ncolour << std::endl;
+//             std::cout << GridLogMessage << " t_" << gen << std::endl;
+//             std::cout << GridLogMessage << ta << std::endl;
+//         }
+//     }
+//     
+//     
+//     
+//     static void testGenerators(void) {
+//         Matrix ta;
+//         Matrix tb;
+//         std::cout << GridLogMessage << "Fundamental - Checking trace ta tb is 0.5 delta_ab " << std::endl;
+//         for (int a = 0; a < AlgebraDimension; a++) {
+//             for (int b = 0; b < AlgebraDimension; b++) {
+//                 generator(a,ta);
+//                 generator(b,tb);
+//                 Complex tr = TensorRemove(trace( ta * tb) );
+//                 std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
+//                 << std::endl;
+//                 if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
+//                 if (a != b) assert(abs(tr) < 1.0e-6);
+// 
+//             }
+//         }
+//         std::cout << GridLogMessage << std::endl;
+//         std::cout << GridLogMessage << "Fundamental - Checking if hermitian" << std::endl;
+//         for (int a = 0; a < AlgebraDimension; a++) {
+//             generator(a,ta);
+//             std::cout << GridLogMessage << a << std::endl;
+//             assert(norm2(ta - adj(ta)) < 1.0e-6);
+//         }
+//         std::cout << GridLogMessage << std::endl;
+//         std::cout << GridLogMessage << "Fundamental - Checking if traceless" << std::endl;
+//         for (int a = 0; a < AlgebraDimension; a++) {
+//           generator(a, ta);
+//           Complex tr = TensorRemove(trace(ta));
+//           std::cout << GridLogMessage << a << std::endl;
+//           assert(abs(tr) < 1.0e-6);
+//         }
+//         
+//     }
+//     
+//     
+//     template <typename LatticeMatrixType>
+//     static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out, double scale = 1.0)
+//     {
+//       GridBase *grid = out.Grid();
+// 
+//       typedef typename LatticeMatrixType::vector_type vector_type;
+//       typedef typename LatticeMatrixType::scalar_type scalar_type;
+// 
+//       typedef iSinglet<vector_type> vTComplexType;
+// 
+//       typedef Lattice<vTComplexType> LatticeComplexType;
+//       typedef typename GridTypeMapper<typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
+// 
+//       LatticeComplexType ca(grid);
+//       LatticeMatrixType lie(grid);
+//       LatticeMatrixType la(grid);
+//       ComplexD ci(0.0, scale);
+//       //    ComplexD cone(1.0, 0.0);
+//       MatrixType ta;
+// 
+//       lie = Zero();
+// 
+//       for (int a = 0; a < AlgebraDimension; a++) {
+//         random(pRNG, ca);
+// 
+//         ca = (ca + conjugate(ca)) * 0.5;
+//         ca = ca - 0.5;
+// 
+//         generator(a, ta);
+// 
+//         la = ci * ca * ta;
+// 
+//         lie = lie + la;  // e^{i la ta}
+// 
+//       }
+//       taExp(lie, out);
+//     }
+//     
+//     
+//     static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG, //same as sun
+//                                                     LatticeMatrix &out,
+//                                                     Real scale = 1.0) {
+//       GridBase *grid = out.Grid();
+//       LatticeReal ca(grid);
+//       LatticeMatrix la(grid);
+//       Complex ci(0.0, scale);
+//       Matrix ta;
+// 
+//       out = Zero();
+//       for (int a = 0; a < AlgebraDimension; a++) {
+//         gaussian(pRNG, ca);
+//         generator(a, ta);
+//         la = toComplex(ca) * ta;
+//         out += la;
+//       }
+//       out *= ci;
+//     }
+//     
+//     static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
+//                                             LatticeMatrix &out,
+//                                             Real scale = 1.0) {
+//       conformable(h, out);
+//       GridBase *grid = out.Grid();
+//       LatticeMatrix la(grid);
+//       Matrix ta;
+// 
+//       out = Zero();
+//       for (int a = 0; a < AlgebraDimension; a++) {
+//         generator(a, ta);
+//         la = peekColour(h, a) * timesI(ta) * scale;
+//         out += la;
+//       }
+//     }
+//     
+//     
+//     template <typename LatticeMatrixType>
+//     static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) { // same as sun
+//       typedef typename LatticeMatrixType::scalar_type ComplexType;
+// 
+//       LatticeMatrixType xn(x.Grid());
+//       RealD nfac = 1.0;
+// 
+//       xn = x;
+//       ex = xn + ComplexType(1.0);  // 1+x
+// 
+//       // Do a 12th order exponentiation
+//       for (int i = 2; i <= 12; ++i) {
+//         nfac = nfac / RealD(i);  // 1/2, 1/2.3 ...
+//         xn = xn * x;             // x2, x3,x4....
+//         ex = ex + xn * nfac;     // x2/2!, x3/3!....
+//       }
+//     }
+//     
+//  static void projectOnAlgebra(LatticeAlgebraVector &h_out, const LatticeMatrix &in, Real scale = 1.0) {
+//    conformable(h_out, in);
+//    h_out = Zero();
+//    Matrix Ta;
+// 
+//    for (int a = 0; a < AlgebraDimension; a++) {
+//      generator(a, Ta);
+//      pokeColour(h_out, - 2.0 * (trace(timesI(Ta) * in)) * scale, a);
+//    }
+//  }
+//     
+//     
+//     template <typename GaugeField>
+//     static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
+//       typedef typename GaugeField::vector_type vector_type;
+//       typedef iSp2nMatrix<vector_type> vMatrixType;
+//       typedef Lattice<vMatrixType> LatticeMatrixType;
+// 
+//       LatticeMatrixType Umu(out.Grid());
+//       for (int mu = 0; mu < Nd; mu++) {
+//         LieRandomize(pRNG, Umu, 1.0);   //def
+//         PokeIndex<LorentzIndex>(out, Umu, mu);
+//       }
+//     }
+//     template<typename GaugeField>
+//     static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out){
+//       typedef typename GaugeField::vector_type vector_type;
+//       typedef iSp2nMatrix<vector_type> vMatrixType;
+//       typedef Lattice<vMatrixType> LatticeMatrixType;
+// 
+//       LatticeMatrixType Umu(out.Grid());
+//       for(int mu=0;mu<Nd;mu++){
+//         LieRandomize(pRNG,Umu,0.01);    //def
+//         PokeIndex<LorentzIndex>(out,Umu,mu);
+//       }
+//     }
+//     
+//     template<typename GaugeField>
+//     static void ColdConfiguration(GaugeField &out){
+//       typedef typename GaugeField::vector_type vector_type;
+//       typedef iSp2nMatrix<vector_type> vMatrixType;
+//       typedef Lattice<vMatrixType> LatticeMatrixType;
+// 
+//       LatticeMatrixType Umu(out.Grid());
+//       Umu=1.0;
+//       for(int mu=0;mu<Nd;mu++){
+//         PokeIndex<LorentzIndex>(out,Umu,mu);
+//       }
+//     }
+//     template<typename GaugeField>
+//     static void ColdConfiguration(GridParallelRNG &pRNG,GaugeField &out){
+//       ColdConfiguration(out);
+//     }
+//     
+//     static void OmegaInvariance(ColourMatrix &in)
+//     {
+//         
+//         ColourMatrix Omega;
+//         Omega = Zero();
+//         
+//         std::cout << GridLogMessage << "I am a ColourMatrix" << std::endl;
+//         
+//         //for (int i = 0; i < ncolour; i++)         wrong?!
+//         //{
+//         //    Omega()()(i, 2*ncolour-1-i) = 1.;
+//         //    Omega()()(2*ncolour-1-i, i) = -1;
+//         //}
+//         for (int i = 0; i < nsp; i++)
+//         {
+//             Omega()()(i, nsp+i) = 1.;
+//             Omega()()(nsp+i, i) = -1;
+//         }
+// 
+//         auto diff = Omega - (in * Omega * transpose(in) );
+//         auto sdiff = norm2(diff);
+//         if (norm2(sdiff) < 1e-8)
+//         {
+//             std::cout << GridLogMessage << "Symplectic condition satisfied: Omega invariant" << std::endl;
+//         } else {
+//             std::cout << GridLogMessage << "WARNING!!!!!! Matrix Omega NOT left invariant by " << norm2(sdiff) << std::endl;
+//         }
+//         
+//     }
+//     
+//     template<typename GaugeField>
+//     static void OmegaInvariance(GaugeField &in)
+//     {
+//         typedef typename GaugeField::vector_type vector_type;
+//         typedef iSp2nMatrix<vector_type> vMatrixType;
+//         typedef Lattice<vMatrixType> LatticeMatrixType;
+//         
+//         LatticeMatrixType U(in.Grid());
+//         LatticeMatrixType OmegaLatt(in.Grid());
+//         LatticeMatrixType identity(in.Grid());
+//         RealD vol = in.Grid()->gSites();
+//         ColourMatrix Omega;
+//         
+//         OmegaLatt = Zero();
+//         Omega = Zero();
+//         identity = 1.;
+//         
+//         std::cout << GridLogMessage << "I am a GaugeField " << std::endl;
+//         
+//         U = PeekIndex<LorentzIndex>(in,1);
+//         
+//         OmegaInvariance(U);
+//         
+//     }
+//     
+//        static void OmegaInvariance(LatticeColourMatrixD &in)
+//        {
+//                       
+//            LatticeColourMatrixD OmegaLatt(in.Grid());
+//            LatticeColourMatrixD identity(in.Grid());
+//            RealD vol = in.Grid()->gSites();
+//            ColourMatrix Omega;
+//            
+//            OmegaLatt = Zero();
+//            Omega = Zero();
+//            identity = 1.;
+//            
+//            std::cout << GridLogMessage << "I am a LatticeColourMatrix " << std::endl;
+//            
+//            for (int i = 0; i < nsp; i++)
+//            {
+//                Omega()()(i, nsp+i) = 1.;
+//                Omega()()(nsp+i, i) = -1;
+//            }
+//            
+//            std::cout << GridLogMessage << "Omega = " << Omega()() << std::endl;
+//            OmegaLatt = OmegaLatt + (identity*Omega);
+//            
+//            auto diff = OmegaLatt - (in*OmegaLatt*transpose(in));
+//            auto sdiff = sum(diff);
+//            //assert( norm2(sdiff) < 1e-8 );
+//            if (norm2(sdiff) < 1e-8)
+//            {
+//                std::cout << GridLogMessage << "Symplectic condition satisfied: Omega invariant" << std::endl;
+//            } else {
+//                std::cout << GridLogMessage << "WARNING!!!!!! Matrix Omega NOT left invariant by " << norm2(sdiff) << std::endl;
+//            }
+//            
+//            
+//        }
+//         
+//     
+// }; // end of class Sp
+//     
+//  
+//  template<int N>
+//  static void ProjectSp2n(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
+//  {
+//    Umu      = ProjectOnSpGroup(Umu);
+//    auto det = Determinant(Umu); // ok ?
+// 
+//    det = conjugate(det);
+// 
+//    for(int i=0;i<N;i++){
+//      auto element = PeekIndex<ColourIndex>(Umu,N-1,i);
+//      element = element * det;
+//      PokeIndex<ColourIndex>(Umu,element,Nc-1,i);
+//    }
+//  }
+//  template<int N>
+//  static void ProjectSp2n(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,Nd> > &U)
+//  {
+//    GridBase *grid=U.Grid();
+//    for(int mu=0;mu<Nd;mu++){
+//      auto Umu = PeekIndex<LorentzIndex>(U,mu);
+//      Umu      = ProjectOnSpGroup(Umu);
+//      ProjectSp2n(Umu);
+//      PokeIndex<LorentzIndex>(U,Umu,mu);
+//    }
+//  }
+// 
+// typedef Sp<2> Sp2;
+// typedef Sp<4> Sp4;
+// typedef Sp<6> Sp6;
+// typedef Sp<8> Sp8;
+// 
+// NAMESPACE_END(Grid);
+// #endif
diff --git a/Grid/qcd/utils/Sp2n_impl.h b/Grid/qcd/utils/Sp2n_impl.h
new file mode 100644
index 00000000..03a42d70
--- /dev/null
+++ b/Grid/qcd/utils/Sp2n_impl.h
@@ -0,0 +1,245 @@
+
+template<ONLY_IF_Sp>
+    static int su2subgroups(void) { return (nsp * (nsp - 1)) / 2; }
+template <typename vtype, ONLY_IF_Sp>
+using iSp2nMatrix = iGroupMatrix<vtype>;
+template <typename vtype, ONLY_IF_Sp>
+using iSp2nAlgebraVector = iAlgebraVector<vtype>;
+
+    // Sp(2N) has N(2N+1) = 2N^2+N generators
+    //
+    // normalise the generators such that
+    // Trace ( Ta Tb) = 1/2 delta_ab
+    //
+    // N generators in the cartan, 2N^2 off
+    // off diagonal:
+    //     there are 6 types named a,b,c,d and w,z
+    //     abcd are N(N-1)/2 each while wz are N each
+    
+ template <class cplx, ONLY_IF_Sp>
+    static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
+        // map lie index into type of generators: diagonal, abcd type, wz type
+
+        int diagIndex;
+        int aIndex, bIndex, cIndex, dIndex;
+        int wIndex, zIndex; // a,b,c,d are N(N-1)/2 and w,z are N
+        int mod = nsp * (nsp-1) * 0.5;
+        int offdiag = 2*nsp*nsp; // number of generators not in the cartan subalgebra
+        int wmod = 4*mod;
+        int zmod = wmod+nsp;
+        if (lieIndex >= offdiag) {
+            diagIndex = lieIndex - offdiag; // 0, ... ,N-1
+            //std::cout << GridLogMessage << "diag type " << std::endl;
+            generatorDiagtype(diagIndex, ta);
+            return;
+        }
+        if ( (lieIndex >= wmod) && (lieIndex < zmod) ) {
+            //std::cout << GridLogMessage << "w type " << std::endl;
+            wIndex = lieIndex- wmod;    // 0, ... ,N-1
+            generatorWtype(wIndex,ta);
+            return;
+        }
+        if ( (lieIndex >= zmod) && (lieIndex < offdiag) ) {
+            //std::cout << GridLogMessage << "z type " << std::endl;
+            //std::cout << GridLogMessage << "lie index " << lieIndex << std::endl;
+            //std::cout << GridLogMessage << "z mod " << zmod << std::endl;
+            zIndex = lieIndex - zmod;   // 0, ... ,N-1
+            generatorZtype(zIndex,ta);
+            return;
+        }
+        if (lieIndex < mod) { // atype 0, ... , N(N-1)/2=mod
+            //std::cout << GridLogMessage << "a type " << std::endl;
+            aIndex = lieIndex;
+            //std::cout << GridLogMessage << "a indx " << aIndex << std::endl;
+            generatorAtype(aIndex, ta);
+            return;
+        }
+        if ( (lieIndex >= mod) && lieIndex < 2*mod) { // btype mod, ... , 2mod-1
+            //std::cout << GridLogMessage << "b type " << std::endl;
+            bIndex = lieIndex - mod;
+            generatorBtype(bIndex, ta);
+            return;
+        }
+        if ( (lieIndex >= 2*mod) && lieIndex < 3*mod) { // ctype 2mod, ... , 3mod-1
+            //std::cout << GridLogMessage << "c type " << std::endl;
+            cIndex = lieIndex - 2*mod;
+            generatorCtype(cIndex, ta);
+            return;
+        }
+        if ( (lieIndex >= 3*mod) && lieIndex < wmod) { // ctype 3mod, ... , 4mod-1 = wmod-1
+             //std::cout << GridLogMessage << "d type " << std::endl;
+             dIndex = lieIndex - 3*mod;
+             generatorDtype(dIndex, ta);
+            return;
+         }
+            
+    } //end of generator
+    
+    template <class cplx, ONLY_IF_Sp>
+    static void generatorDiagtype(int diagIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan subalgebra
+        
+        ta = Zero();
+        RealD nrm = 1.0 / 2;
+
+        ta()()(diagIndex,diagIndex) = nrm;
+        ta()()(diagIndex+nsp,diagIndex+nsp) = -nrm;
+    }
+    
+    template <class cplx, ONLY_IF_Sp>
+    static void generatorAtype(int aIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,j) = ta(j,i) = -ta(i+N,j+N) = -ta(j+N,i+N) = 1 / 2 sqrt(2)
+        // with i<j and i=0,...,N-2
+        // follows that j=i+1, ... , N
+        int i1, i2;
+        ta = Zero();
+        RealD nrm = 1 / (2 * std::sqrt(2) );
+        
+        su2SubGroupIndex(i1, i2, aIndex);
+        ta()()(i1,i2) = 1;
+        ta()()(i2,i1) = 1;
+        ta()()(i1+nsp,i2+nsp) = -1;
+        ta()()(i2+nsp,i1+nsp) = -1;
+
+        ta = ta * nrm;
+    }
+    
+    template <class cplx, ONLY_IF_Sp>
+    static void generatorBtype(int bIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,j) = -ta(j,i) = ta(i+N,j+N) = -ta(j+N,i+N) = i / 1/ 2 sqrt(2)
+        // with i<j and i=0,...,N-2
+        // follows that j=i+1, ... , N-1
+        
+        int i1, i2;
+        ta = Zero();
+        cplx i(0.0, 1.0);
+        RealD nrm = 1 / (2 * std::sqrt(2));
+        su2SubGroupIndex(i1, i2, bIndex);
+        
+
+        ta()()(i1,i2) = i;
+        ta()()(i2,i1) = -i;
+        ta()()(i1+nsp,i2+nsp) = i;
+        ta()()(i2+nsp,i1+nsp) = -i;
+
+        ta = ta * nrm;
+    }
+    
+    template <class cplx, ONLY_IF_Sp>
+    static void generatorCtype(int cIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
+        
+        
+        int i1, i2;
+        ta = Zero();
+        RealD nrm = 1 / (2 * std::sqrt(2) );
+        su2SubGroupIndex(i1, i2, cIndex);
+        
+        ta()()(i1,i2+nsp) = 1;
+        ta()()(i2,i1+nsp) = 1;
+        ta()()(i1+nsp,i2) = 1;
+        ta()()(i2+nsp,i1) = 1;
+
+        ta = ta * nrm;
+    }
+    
+    template <class cplx, ONLY_IF_Sp>
+    static void generatorDtype(int dIndex, iSp2nMatrix<cplx> &ta) {
+        
+        // ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i /  2 sqrt(2)
+        
+        int i1, i2;
+        ta = Zero();
+        cplx i(0.0, 1.0);
+        RealD nrm = 1 / (2 * std::sqrt(2)  );
+        su2SubGroupIndex(i1, i2, dIndex);
+
+        ta()()(i1,i2+nsp) = i;
+        ta()()(i2,i1+nsp) = i;
+        ta()()(i1+nsp,i2) = -i;
+        ta()()(i2+nsp,i1) = -i;
+
+        ta = ta * nrm;
+    }
+    
+    template <class cplx, ONLY_IF_Sp>
+     static void generatorWtype(int wIndex, iSp2nMatrix<cplx> &ta) {
+         
+         // ta(i,i+N) =  ta(i+N,i) = 1/2
+         
+         ta = Zero();
+         RealD nrm = 1.0 / 2; //check
+
+         ta()()(wIndex,wIndex+nsp) = 1;
+         ta()()(wIndex+nsp,wIndex) = 1;
+         
+         ta = ta * nrm;
+     }
+    
+    template <class cplx, ONLY_IF_Sp>
+     static void generatorZtype(int zIndex, iSp2nMatrix<cplx> &ta) {
+         
+         // ta(i,i+N) = - ta(i+N,i) = i/2
+         
+         ta = Zero();
+         RealD nrm = 1.0 / 2; //check
+         cplx i(0.0, 1.0);
+         ta()()(zIndex,zIndex+nsp) = i;
+         ta()()(zIndex+nsp,zIndex) = -i;
+         
+         ta = ta * nrm;
+     }
+    
+    ////////////////////////////////////////////////////////////////////////
+    // Map a su2 subgroup number to the pair of rows that are non zero
+    ////////////////////////////////////////////////////////////////////////
+    template<ONLY_IF_Sp>
+    static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
+      assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
+
+      int spare = su2_index;
+      for (i1 = 0; spare >= (nsp - 1 - i1); i1++) {
+        spare = spare - (nsp - 1 - i1);  // remove the Nc-1-i1 terms
+      }
+      i2 = i1 + 1 + spare;
+    }
+    
+    template<ONLY_IF_Sp>
+    static void testGenerators(void) {
+        Matrix ta;
+        Matrix tb;
+        std::cout << GridLogMessage << "Fundamental - Checking trace ta tb is 0.5 delta_ab " << std::endl;
+        for (int a = 0; a < AlgebraDimension; a++) {
+            for (int b = 0; b < AlgebraDimension; b++) {
+                generator(a,ta);
+                generator(b,tb);
+                Complex tr = TensorRemove(trace( ta * tb) );
+                std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
+                << std::endl;
+                if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
+                if (a != b) assert(abs(tr) < 1.0e-6);
+
+            }
+        }
+        std::cout << GridLogMessage << std::endl;
+        std::cout << GridLogMessage << "Fundamental - Checking if hermitian" << std::endl;
+        for (int a = 0; a < AlgebraDimension; a++) {
+            generator(a,ta);
+            std::cout << GridLogMessage << a << std::endl;
+            assert(norm2(ta - adj(ta)) < 1.0e-6);
+        }
+        std::cout << GridLogMessage << std::endl;
+        std::cout << GridLogMessage << "Fundamental - Checking if traceless" << std::endl;
+        for (int a = 0; a < AlgebraDimension; a++) {
+          generator(a, ta);
+          Complex tr = TensorRemove(trace(ta));
+          std::cout << GridLogMessage << a << std::endl;
+          assert(abs(tr) < 1.0e-6);
+        }
+        
+    }
+

From 2507606bd0771fc14e8b859615d6ecce9af494b7 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 30 Nov 2022 12:52:33 +0000
Subject: [PATCH 036/129] With function overloading (still dirty).

---
 Grid/qcd/utils/SUn.h       |  62 +++--
 Grid/qcd/utils/SUn_impl.h  |  16 +-
 Grid/qcd/utils/Sp2n.h      | 400 ++++++++++++++-------------
 Grid/qcd/utils/Sp2n_impl.h | 536 +++++++++++++++++++++----------------
 4 files changed, 563 insertions(+), 451 deletions(-)

diff --git a/Grid/qcd/utils/SUn.h b/Grid/qcd/utils/SUn.h
index 0c961ab4..6b7e9079 100644
--- a/Grid/qcd/utils/SUn.h
+++ b/Grid/qcd/utils/SUn.h
@@ -32,15 +32,17 @@ directory
 #ifndef QCD_UTIL_SUN_H
 #define QCD_UTIL_SUN_H
 
-#define ONLY_IF_SU                  \
-  typename \
-    typename std::enable_if_t<is_su<group_name>::value, dummy_name> ,\
-    dummy_name = group_name, 
+#define ONLY_IF_SU                                                       \
+  typename dummy_name = group_name,                                      \
+           typename = std::enable_if_t <                                 \
+                          std::is_same<dummy_name, group_name>::value && \
+                      is_su<dummy_name>::value >
 
-#define ONLY_IF_Sp                  \
-  typename \
-    typename std::enable_if_t<is_sp<group_name>::value, dummy_name> ,\
-    dummy_name =group_name, 
+#define ONLY_IF_Sp                                                       \
+  typename dummy_name = group_name,                                      \
+           typename = std::enable_if_t <                                 \
+                          std::is_same<dummy_name, group_name>::value && \
+                      is_sp<dummy_name>::value >
 
 NAMESPACE_BEGIN(Grid);
 namespace GroupName {
@@ -68,15 +70,18 @@ struct is_sp<GroupName::Sp> {
   static const bool value = true;
 };
 
-template<typename group_name>
+template <typename group_name>
 constexpr int compute_adjoint_dimension(int ncolour);
 
-template<>
-constexpr int compute_adjoint_dimension<GroupName::SU>(int ncolour) { return ncolour * ncolour - 1;}
-
-template<>
-constexpr int compute_adjoint_dimension<GroupName::Sp>(int ncolour) { return ncolour/2*(ncolour+1);}
+template <>
+constexpr int compute_adjoint_dimension<GroupName::SU>(int ncolour) {
+  return ncolour * ncolour - 1;
+}
 
+template <>
+constexpr int compute_adjoint_dimension<GroupName::Sp>(int ncolour) {
+  return ncolour / 2 * (ncolour + 1);
+}
 
 template <int ncolour, class group_name = GroupName::SU>
 class GaugeGroup;
@@ -91,11 +96,12 @@ template <int ncolour, class group_name>
 class GaugeGroup {
  public:
   static const int Dimension = ncolour;
-  static const int AdjointDimension = compute_adjoint_dimension<group_name>(ncolour);
-  static const int AlgebraDimension = compute_adjoint_dimension<group_name>(ncolour);
+  static const int AdjointDimension =
+      compute_adjoint_dimension<group_name>(ncolour);
+  static const int AlgebraDimension =
+      compute_adjoint_dimension<group_name>(ncolour);
   // Don't know how to only enable this for Sp:
-  static const int nsp = ncolour/2;
-
+  static const int nsp = ncolour / 2;
 
   template <typename vtype>
   using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
@@ -103,6 +109,15 @@ class GaugeGroup {
   using iGroupMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
   template <typename vtype>
   using iAlgebraVector = iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
+  static int su2subgroups(void) { return su2subgroups(group_name()); }
+  template <typename vtype>
+  using iSUnMatrix = iGroupMatrix<vtype>;
+  template <typename vtype>
+  using iSUnAlgebraVector = iAlgebraVector<vtype>;
+  template <typename vtype>
+  using iSp2nMatrix = iGroupMatrix<vtype>;
+  template <typename vtype>
+  using iSp2nAlgebraVector = iAlgebraVector<vtype>;
 
   //////////////////////////////////////////////////////////////////////////////////////////////////
   // Types can be accessed as SU<2>::Matrix , SU<2>::vSUnMatrix,
@@ -150,6 +165,17 @@ class GaugeGroup {
 #include "Grid/qcd/utils/SUn_impl.h"
 #include "Grid/qcd/utils/Sp2n_impl.h"
 
+  template <class cplx>
+  static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
+    return generator(lieIndex, ta, group_name());
+  }
+
+  static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
+    return su2SubGroupIndex(i1, i2, su2_index, group_name());
+  }
+
+  static void testGenerators(void) { testGenerators(group_name()); }
+
   static void printGenerators(void) {
     for (int gen = 0; gen < AdjointDimension; gen++) {
       Matrix ta;
diff --git a/Grid/qcd/utils/SUn_impl.h b/Grid/qcd/utils/SUn_impl.h
index 30d8ff14..2d97dc17 100644
--- a/Grid/qcd/utils/SUn_impl.h
+++ b/Grid/qcd/utils/SUn_impl.h
@@ -6,12 +6,7 @@
 //
 // around it.
 
-template<ONLY_IF_SU>
-  static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
-template <typename vtype, ONLY_IF_SU>
-using iSUnMatrix = iGroupMatrix<vtype>;
-template <typename vtype, ONLY_IF_SU>
-using iSUnAlgebraVector = iAlgebraVector<vtype>;
+static int su2subgroups(GroupName::SU) { return (ncolour * (ncolour - 1)) / 2; }
 ////////////////////////////////////////////////////////////////////////
 // There are N^2-1 generators for SU(N).
 //
@@ -60,8 +55,8 @@ using iSUnAlgebraVector = iAlgebraVector<vtype>;
 //   (      -2)
 //
 ////////////////////////////////////////////////////////////////////////
-template <class cplx, ONLY_IF_SU>
-static void generator(int lieIndex, iSUnMatrix<cplx> &ta) {
+template <class cplx>
+static void generator(int lieIndex, iSUnMatrix<cplx> &ta, GroupName::SU) {
   // map lie index to which type of generator
   int diagIndex;
   int su2Index;
@@ -117,8 +112,7 @@ static void generatorDiagonal(int diagIndex, iSUnMatrix<cplx> &ta) {
 ////////////////////////////////////////////////////////////////////////
 // Map a su2 subgroup number to the pair of rows that are non zero
 ////////////////////////////////////////////////////////////////////////
-template <ONLY_IF_SU>
-static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
+static void su2SubGroupIndex(int &i1, int &i2, int su2_index, GroupName::SU) {
   assert((su2_index >= 0) && (su2_index < (ncolour * (ncolour - 1)) / 2));
 
   int spare = su2_index;
@@ -471,7 +465,7 @@ static void SubGroupHeatBath(
 }
 
 template <ONLY_IF_SU>
-static void testGenerators(void) {
+static void testGenerators(GroupName::SU) {
   Matrix ta;
   Matrix tb;
   std::cout << GridLogMessage
diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.h
index 1f7009e3..201e1e7c 100644
--- a/Grid/qcd/utils/Sp2n.h
+++ b/Grid/qcd/utils/Sp2n.h
@@ -1,14 +1,14 @@
+
+#ifndef QCD_UTIL_Sp2n_H
+#define QCD_UTIL_Sp2n_H
+
 #include "Grid/qcd/utils/SUn.h"
-// 
-// #ifndef QCD_UTIL_Sp2n_H
-// #define QCD_UTIL_Sp2n_H
-// 
-// NAMESPACE_BEGIN(Grid);
-// 
+NAMESPACE_BEGIN(Grid);
+//
 // // Sp(2N)
 // // ncolour = 2N
-// 
-// 
+//
+//
 // template <int ncolour>
 // class Sp {
 // public:
@@ -16,41 +16,42 @@
 //     static const int Dimension = ncolour;
 //     static const int AlgebraDimension = nsp*(2*nsp +1);
 //     static int su2subgroups(void) { return (nsp * (nsp - 1)) / 2; }
-//     
-//     
+//
+//
 //     template <typename vtype>
 //     using iSp2nMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
 //     template <typename vtype>
 //     using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
 //     template <typename vtype>
-//     using iSp2nAlgebraVector = iScalar<iScalar<iVector<vtype, AlgebraDimension> > >;
-//     
+//     using iSp2nAlgebraVector = iScalar<iScalar<iVector<vtype,
+//     AlgebraDimension> > >;
+//
 //     typedef iSp2nMatrix<Complex> Matrix;
 //     typedef iSp2nMatrix<ComplexF> MatrixF;
 //     typedef iSp2nMatrix<ComplexD> MatrixD;
-//     
+//
 //     typedef iSp2nMatrix<vComplex> vMatrix;
 //     typedef iSp2nMatrix<vComplexF> vMatrixF;
 //     typedef iSp2nMatrix<vComplexD> vMatrixD;
-//     
+//
 //     typedef iSp2nAlgebraVector<Complex> AlgebraVector;
 //     typedef iSp2nAlgebraVector<ComplexF> AlgebraVectorF;
 //     typedef iSp2nAlgebraVector<ComplexD> AlgebraVectorD;
-//     
+//
 //     typedef iSp2nAlgebraVector<vComplex> vAlgebraVector;
 //     typedef iSp2nAlgebraVector<vComplexF> vAlgebraVectorF;
 //     typedef iSp2nAlgebraVector<vComplexD> vAlgebraVectorD;
-//     
+//
 //     typedef Lattice<vMatrix> LatticeMatrix;
 //     typedef Lattice<vMatrixF> LatticeMatrixF;
 //     typedef Lattice<vMatrixD> LatticeMatrixD;
-//     
+//
 //     typedef Lattice<vAlgebraVector> LatticeAlgebraVector;
 //     typedef Lattice<vAlgebraVectorF> LatticeAlgebraVectorF;
 //     typedef Lattice<vAlgebraVectorD> LatticeAlgebraVectorD;
-//     
-//     
-//     
+//
+//
+//
 //     // Sp(2N) has N(2N+1) = 2N^2+N generators
 //     //
 //     // normalise the generators such that
@@ -60,19 +61,19 @@
 //     // off diagonal:
 //     //     there are 6 types named a,b,c,d and w,z
 //     //     abcd are N(N-1)/2 each while wz are N each
-//     
+//
 //  template <class cplx>
 //     static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
-//         // map lie index into type of generators: diagonal, abcd type, wz type
-// 
+//         // map lie index into type of generators: diagonal, abcd type, wz
+//         type
+//
 //         int diagIndex;
 //         int aIndex, bIndex, cIndex, dIndex;
 //         int wIndex, zIndex; // a,b,c,d are N(N-1)/2 and w,z are N
 //         int mod = nsp * (nsp-1) * 0.5;
-//         int offdiag = 2*nsp*nsp; // number of generators not in the cartan subalgebra
-//         int wmod = 4*mod;
-//         int zmod = wmod+nsp;
-//         if (lieIndex >= offdiag) {
+//         int offdiag = 2*nsp*nsp; // number of generators not in the cartan
+//         subalgebra int wmod = 4*mod; int zmod = wmod+nsp; if (lieIndex >=
+//         offdiag) {
 //             diagIndex = lieIndex - offdiag; // 0, ... ,N-1
 //             //std::cout << GridLogMessage << "diag type " << std::endl;
 //             generatorDiagtype(diagIndex, ta);
@@ -86,7 +87,8 @@
 //         }
 //         if ( (lieIndex >= zmod) && (lieIndex < offdiag) ) {
 //             //std::cout << GridLogMessage << "z type " << std::endl;
-//             //std::cout << GridLogMessage << "lie index " << lieIndex << std::endl;
+//             //std::cout << GridLogMessage << "lie index " << lieIndex <<
+//             std::endl;
 //             //std::cout << GridLogMessage << "z mod " << zmod << std::endl;
 //             zIndex = lieIndex - zmod;   // 0, ... ,N-1
 //             generatorZtype(zIndex,ta);
@@ -95,168 +97,171 @@
 //         if (lieIndex < mod) { // atype 0, ... , N(N-1)/2=mod
 //             //std::cout << GridLogMessage << "a type " << std::endl;
 //             aIndex = lieIndex;
-//             //std::cout << GridLogMessage << "a indx " << aIndex << std::endl;
-//             generatorAtype(aIndex, ta);
-//             return;
+//             //std::cout << GridLogMessage << "a indx " << aIndex <<
+//             std::endl; generatorAtype(aIndex, ta); return;
 //         }
-//         if ( (lieIndex >= mod) && lieIndex < 2*mod) { // btype mod, ... , 2mod-1
+//         if ( (lieIndex >= mod) && lieIndex < 2*mod) { // btype mod, ... ,
+//         2mod-1
 //             //std::cout << GridLogMessage << "b type " << std::endl;
 //             bIndex = lieIndex - mod;
 //             generatorBtype(bIndex, ta);
 //             return;
 //         }
-//         if ( (lieIndex >= 2*mod) && lieIndex < 3*mod) { // ctype 2mod, ... , 3mod-1
+//         if ( (lieIndex >= 2*mod) && lieIndex < 3*mod) { // ctype 2mod, ... ,
+//         3mod-1
 //             //std::cout << GridLogMessage << "c type " << std::endl;
 //             cIndex = lieIndex - 2*mod;
 //             generatorCtype(cIndex, ta);
 //             return;
 //         }
-//         if ( (lieIndex >= 3*mod) && lieIndex < wmod) { // ctype 3mod, ... , 4mod-1 = wmod-1
+//         if ( (lieIndex >= 3*mod) && lieIndex < wmod) { // ctype 3mod, ... ,
+//         4mod-1 = wmod-1
 //              //std::cout << GridLogMessage << "d type " << std::endl;
 //              dIndex = lieIndex - 3*mod;
 //              generatorDtype(dIndex, ta);
 //             return;
 //          }
-//             
+//
 //     } //end of generator
-//     
+//
 //     template <class cplx>
 //     static void generatorDiagtype(int diagIndex, iSp2nMatrix<cplx> &ta) {
-//         
-//         // ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan subalgebra
-//         
+//
+//         // ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan
+//         subalgebra
+//
 //         ta = Zero();
 //         RealD nrm = 1.0 / 2;
-// 
+//
 //         ta()()(diagIndex,diagIndex) = nrm;
 //         ta()()(diagIndex+nsp,diagIndex+nsp) = -nrm;
 //     }
-//     
+//
 //     template <class cplx>
 //     static void generatorAtype(int aIndex, iSp2nMatrix<cplx> &ta) {
-//         
+//
 //         // ta(i,j) = ta(j,i) = -ta(i+N,j+N) = -ta(j+N,i+N) = 1 / 2 sqrt(2)
 //         // with i<j and i=0,...,N-2
 //         // follows that j=i+1, ... , N
 //         int i1, i2;
 //         ta = Zero();
 //         RealD nrm = 1 / (2 * std::sqrt(2) );
-//         
+//
 //         su2SubGroupIndex(i1, i2, aIndex);
 //         ta()()(i1,i2) = 1;
 //         ta()()(i2,i1) = 1;
 //         ta()()(i1+nsp,i2+nsp) = -1;
 //         ta()()(i2+nsp,i1+nsp) = -1;
-// 
+//
 //         ta = ta * nrm;
 //     }
-//     
+//
 //     template <class cplx>
 //     static void generatorBtype(int bIndex, iSp2nMatrix<cplx> &ta) {
-//         
+//
 //         // ta(i,j) = -ta(j,i) = ta(i+N,j+N) = -ta(j+N,i+N) = i / 1/ 2 sqrt(2)
 //         // with i<j and i=0,...,N-2
 //         // follows that j=i+1, ... , N-1
-//         
+//
 //         int i1, i2;
 //         ta = Zero();
 //         cplx i(0.0, 1.0);
 //         RealD nrm = 1 / (2 * std::sqrt(2));
 //         su2SubGroupIndex(i1, i2, bIndex);
-//         
-// 
+//
+//
 //         ta()()(i1,i2) = i;
 //         ta()()(i2,i1) = -i;
 //         ta()()(i1+nsp,i2+nsp) = i;
 //         ta()()(i2+nsp,i1+nsp) = -i;
-// 
+//
 //         ta = ta * nrm;
 //     }
-//     
+//
 //     template <class cplx>
 //     static void generatorCtype(int cIndex, iSp2nMatrix<cplx> &ta) {
-//         
+//
 //         // ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
-//         
-//         
+//
+//
 //         int i1, i2;
 //         ta = Zero();
 //         RealD nrm = 1 / (2 * std::sqrt(2) );
 //         su2SubGroupIndex(i1, i2, cIndex);
-//         
+//
 //         ta()()(i1,i2+nsp) = 1;
 //         ta()()(i2,i1+nsp) = 1;
 //         ta()()(i1+nsp,i2) = 1;
 //         ta()()(i2+nsp,i1) = 1;
-// 
+//
 //         ta = ta * nrm;
 //     }
-//     
+//
 //     template <class cplx>
 //     static void generatorDtype(int dIndex, iSp2nMatrix<cplx> &ta) {
-//         
+//
 //         // ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i /  2 sqrt(2)
-//         
+//
 //         int i1, i2;
 //         ta = Zero();
 //         cplx i(0.0, 1.0);
 //         RealD nrm = 1 / (2 * std::sqrt(2)  );
 //         su2SubGroupIndex(i1, i2, dIndex);
-// 
+//
 //         ta()()(i1,i2+nsp) = i;
 //         ta()()(i2,i1+nsp) = i;
 //         ta()()(i1+nsp,i2) = -i;
 //         ta()()(i2+nsp,i1) = -i;
-// 
+//
 //         ta = ta * nrm;
 //     }
-//     
+//
 //     template <class cplx>
 //      static void generatorWtype(int wIndex, iSp2nMatrix<cplx> &ta) {
-//          
+//
 //          // ta(i,i+N) =  ta(i+N,i) = 1/2
-//          
+//
 //          ta = Zero();
 //          RealD nrm = 1.0 / 2; //check
-// 
+//
 //          ta()()(wIndex,wIndex+nsp) = 1;
 //          ta()()(wIndex+nsp,wIndex) = 1;
-//          
+//
 //          ta = ta * nrm;
 //      }
-//     
+//
 //     template <class cplx>
 //      static void generatorZtype(int zIndex, iSp2nMatrix<cplx> &ta) {
-//          
+//
 //          // ta(i,i+N) = - ta(i+N,i) = i/2
-//          
+//
 //          ta = Zero();
 //          RealD nrm = 1.0 / 2; //check
 //          cplx i(0.0, 1.0);
 //          ta()()(zIndex,zIndex+nsp) = i;
 //          ta()()(zIndex+nsp,zIndex) = -i;
-//          
+//
 //          ta = ta * nrm;
 //      }
-//     
-//     
+//
+//
 //     ////////////////////////////////////////////////////////////////////////
 //     // Map a su2 subgroup number to the pair of rows that are non zero
 //     ////////////////////////////////////////////////////////////////////////
 //     static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
 //       assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
-// 
+//
 //       int spare = su2_index;
 //       for (i1 = 0; spare >= (nsp - 1 - i1); i1++) {
 //         spare = spare - (nsp - 1 - i1);  // remove the Nc-1-i1 terms
 //       }
 //       i2 = i1 + 1 + spare;
 //     }
-//     
-//     
-//     
-//     
-//     
+//
+//
+//
+//
+//
 //     static void printGenerators(void) {
 //         for (int gen = 0; gen < AlgebraDimension; gen++) {
 //             Matrix ta;
@@ -266,84 +271,89 @@
 //             std::cout << GridLogMessage << ta << std::endl;
 //         }
 //     }
-//     
-//     
-//     
+//
+//
+//
 //     static void testGenerators(void) {
 //         Matrix ta;
 //         Matrix tb;
-//         std::cout << GridLogMessage << "Fundamental - Checking trace ta tb is 0.5 delta_ab " << std::endl;
-//         for (int a = 0; a < AlgebraDimension; a++) {
+//         std::cout << GridLogMessage << "Fundamental - Checking trace ta tb is
+//         0.5 delta_ab " << std::endl; for (int a = 0; a < AlgebraDimension;
+//         a++) {
 //             for (int b = 0; b < AlgebraDimension; b++) {
 //                 generator(a,ta);
 //                 generator(b,tb);
 //                 Complex tr = TensorRemove(trace( ta * tb) );
-//                 std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
+//                 std::cout << GridLogMessage << "(" << a << "," << b << ") =
+//                 " << tr
 //                 << std::endl;
 //                 if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
 //                 if (a != b) assert(abs(tr) < 1.0e-6);
-// 
+//
 //             }
 //         }
 //         std::cout << GridLogMessage << std::endl;
-//         std::cout << GridLogMessage << "Fundamental - Checking if hermitian" << std::endl;
-//         for (int a = 0; a < AlgebraDimension; a++) {
+//         std::cout << GridLogMessage << "Fundamental - Checking if hermitian"
+//         << std::endl; for (int a = 0; a < AlgebraDimension; a++) {
 //             generator(a,ta);
 //             std::cout << GridLogMessage << a << std::endl;
 //             assert(norm2(ta - adj(ta)) < 1.0e-6);
 //         }
 //         std::cout << GridLogMessage << std::endl;
-//         std::cout << GridLogMessage << "Fundamental - Checking if traceless" << std::endl;
-//         for (int a = 0; a < AlgebraDimension; a++) {
+//         std::cout << GridLogMessage << "Fundamental - Checking if traceless"
+//         << std::endl; for (int a = 0; a < AlgebraDimension; a++) {
 //           generator(a, ta);
 //           Complex tr = TensorRemove(trace(ta));
 //           std::cout << GridLogMessage << a << std::endl;
 //           assert(abs(tr) < 1.0e-6);
 //         }
-//         
+//
 //     }
-//     
-//     
+//
+//
 //     template <typename LatticeMatrixType>
-//     static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out, double scale = 1.0)
+//     static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out,
+//     double scale = 1.0)
 //     {
 //       GridBase *grid = out.Grid();
-// 
+//
 //       typedef typename LatticeMatrixType::vector_type vector_type;
 //       typedef typename LatticeMatrixType::scalar_type scalar_type;
-// 
+//
 //       typedef iSinglet<vector_type> vTComplexType;
-// 
+//
 //       typedef Lattice<vTComplexType> LatticeComplexType;
-//       typedef typename GridTypeMapper<typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
-// 
+//       typedef typename GridTypeMapper<typename
+//       LatticeMatrixType::vector_object>::scalar_object MatrixType;
+//
 //       LatticeComplexType ca(grid);
 //       LatticeMatrixType lie(grid);
 //       LatticeMatrixType la(grid);
 //       ComplexD ci(0.0, scale);
 //       //    ComplexD cone(1.0, 0.0);
 //       MatrixType ta;
-// 
+//
 //       lie = Zero();
-// 
+//
 //       for (int a = 0; a < AlgebraDimension; a++) {
 //         random(pRNG, ca);
-// 
+//
 //         ca = (ca + conjugate(ca)) * 0.5;
 //         ca = ca - 0.5;
-// 
+//
 //         generator(a, ta);
-// 
+//
 //         la = ci * ca * ta;
-// 
+//
 //         lie = lie + la;  // e^{i la ta}
-// 
+//
 //       }
 //       taExp(lie, out);
 //     }
-//     
-//     
-//     static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG, //same as sun
+//
+//
+//     static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
+//     //same as sun
 //                                                     LatticeMatrix &out,
 //                                                     Real scale = 1.0) {
 //       GridBase *grid = out.Grid();
@@ -351,7 +361,7 @@
 //       LatticeMatrix la(grid);
 //       Complex ci(0.0, scale);
 //       Matrix ta;
-// 
+//
 //       out = Zero();
 //       for (int a = 0; a < AlgebraDimension; a++) {
 //         gaussian(pRNG, ca);
@@ -361,7 +371,7 @@
 //       }
 //       out *= ci;
 //     }
-//     
+//
 //     static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
 //                                             LatticeMatrix &out,
 //                                             Real scale = 1.0) {
@@ -369,7 +379,7 @@
 //       GridBase *grid = out.Grid();
 //       LatticeMatrix la(grid);
 //       Matrix ta;
-// 
+//
 //       out = Zero();
 //       for (int a = 0; a < AlgebraDimension; a++) {
 //         generator(a, ta);
@@ -377,18 +387,19 @@
 //         out += la;
 //       }
 //     }
-//     
-//     
+//
+//
 //     template <typename LatticeMatrixType>
-//     static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) { // same as sun
+//     static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) { //
+//     same as sun
 //       typedef typename LatticeMatrixType::scalar_type ComplexType;
-// 
+//
 //       LatticeMatrixType xn(x.Grid());
 //       RealD nfac = 1.0;
-// 
+//
 //       xn = x;
 //       ex = xn + ComplexType(1.0);  // 1+x
-// 
+//
 //       // Do a 12th order exponentiation
 //       for (int i = 2; i <= 12; ++i) {
 //         nfac = nfac / RealD(i);  // 1/2, 1/2.3 ...
@@ -396,25 +407,26 @@
 //         ex = ex + xn * nfac;     // x2/2!, x3/3!....
 //       }
 //     }
-//     
-//  static void projectOnAlgebra(LatticeAlgebraVector &h_out, const LatticeMatrix &in, Real scale = 1.0) {
+//
+//  static void projectOnAlgebra(LatticeAlgebraVector &h_out, const
+//  LatticeMatrix &in, Real scale = 1.0) {
 //    conformable(h_out, in);
 //    h_out = Zero();
 //    Matrix Ta;
-// 
+//
 //    for (int a = 0; a < AlgebraDimension; a++) {
 //      generator(a, Ta);
 //      pokeColour(h_out, - 2.0 * (trace(timesI(Ta) * in)) * scale, a);
 //    }
 //  }
-//     
-//     
+//
+//
 //     template <typename GaugeField>
 //     static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
 //       typedef typename GaugeField::vector_type vector_type;
 //       typedef iSp2nMatrix<vector_type> vMatrixType;
 //       typedef Lattice<vMatrixType> LatticeMatrixType;
-// 
+//
 //       LatticeMatrixType Umu(out.Grid());
 //       for (int mu = 0; mu < Nd; mu++) {
 //         LieRandomize(pRNG, Umu, 1.0);   //def
@@ -426,20 +438,20 @@
 //       typedef typename GaugeField::vector_type vector_type;
 //       typedef iSp2nMatrix<vector_type> vMatrixType;
 //       typedef Lattice<vMatrixType> LatticeMatrixType;
-// 
+//
 //       LatticeMatrixType Umu(out.Grid());
 //       for(int mu=0;mu<Nd;mu++){
 //         LieRandomize(pRNG,Umu,0.01);    //def
 //         PokeIndex<LorentzIndex>(out,Umu,mu);
 //       }
 //     }
-//     
+//
 //     template<typename GaugeField>
 //     static void ColdConfiguration(GaugeField &out){
 //       typedef typename GaugeField::vector_type vector_type;
 //       typedef iSp2nMatrix<vector_type> vMatrixType;
 //       typedef Lattice<vMatrixType> LatticeMatrixType;
-// 
+//
 //       LatticeMatrixType Umu(out.Grid());
 //       Umu=1.0;
 //       for(int mu=0;mu<Nd;mu++){
@@ -450,15 +462,15 @@
 //     static void ColdConfiguration(GridParallelRNG &pRNG,GaugeField &out){
 //       ColdConfiguration(out);
 //     }
-//     
+//
 //     static void OmegaInvariance(ColourMatrix &in)
 //     {
-//         
+//
 //         ColourMatrix Omega;
 //         Omega = Zero();
-//         
+//
 //         std::cout << GridLogMessage << "I am a ColourMatrix" << std::endl;
-//         
+//
 //         //for (int i = 0; i < ncolour; i++)         wrong?!
 //         //{
 //         //    Omega()()(i, 2*ncolour-1-i) = 1.;
@@ -469,113 +481,117 @@
 //             Omega()()(i, nsp+i) = 1.;
 //             Omega()()(nsp+i, i) = -1;
 //         }
-// 
+//
 //         auto diff = Omega - (in * Omega * transpose(in) );
 //         auto sdiff = norm2(diff);
 //         if (norm2(sdiff) < 1e-8)
 //         {
-//             std::cout << GridLogMessage << "Symplectic condition satisfied: Omega invariant" << std::endl;
+//             std::cout << GridLogMessage << "Symplectic condition satisfied:
+//             Omega invariant" << std::endl;
 //         } else {
-//             std::cout << GridLogMessage << "WARNING!!!!!! Matrix Omega NOT left invariant by " << norm2(sdiff) << std::endl;
+//             std::cout << GridLogMessage << "WARNING!!!!!! Matrix Omega NOT
+//             left invariant by " << norm2(sdiff) << std::endl;
 //         }
-//         
+//
 //     }
-//     
+//
 //     template<typename GaugeField>
 //     static void OmegaInvariance(GaugeField &in)
 //     {
 //         typedef typename GaugeField::vector_type vector_type;
 //         typedef iSp2nMatrix<vector_type> vMatrixType;
 //         typedef Lattice<vMatrixType> LatticeMatrixType;
-//         
+//
 //         LatticeMatrixType U(in.Grid());
 //         LatticeMatrixType OmegaLatt(in.Grid());
 //         LatticeMatrixType identity(in.Grid());
 //         RealD vol = in.Grid()->gSites();
 //         ColourMatrix Omega;
-//         
+//
 //         OmegaLatt = Zero();
 //         Omega = Zero();
 //         identity = 1.;
-//         
+//
 //         std::cout << GridLogMessage << "I am a GaugeField " << std::endl;
-//         
+//
 //         U = PeekIndex<LorentzIndex>(in,1);
-//         
+//
 //         OmegaInvariance(U);
-//         
+//
 //     }
-//     
+//
 //        static void OmegaInvariance(LatticeColourMatrixD &in)
 //        {
-//                       
+//
 //            LatticeColourMatrixD OmegaLatt(in.Grid());
 //            LatticeColourMatrixD identity(in.Grid());
 //            RealD vol = in.Grid()->gSites();
 //            ColourMatrix Omega;
-//            
+//
 //            OmegaLatt = Zero();
 //            Omega = Zero();
 //            identity = 1.;
-//            
-//            std::cout << GridLogMessage << "I am a LatticeColourMatrix " << std::endl;
-//            
+//
+//            std::cout << GridLogMessage << "I am a LatticeColourMatrix " <<
+//            std::endl;
+//
 //            for (int i = 0; i < nsp; i++)
 //            {
 //                Omega()()(i, nsp+i) = 1.;
 //                Omega()()(nsp+i, i) = -1;
 //            }
-//            
-//            std::cout << GridLogMessage << "Omega = " << Omega()() << std::endl;
-//            OmegaLatt = OmegaLatt + (identity*Omega);
-//            
+//
+//            std::cout << GridLogMessage << "Omega = " << Omega()() <<
+//            std::endl; OmegaLatt = OmegaLatt + (identity*Omega);
+//
 //            auto diff = OmegaLatt - (in*OmegaLatt*transpose(in));
 //            auto sdiff = sum(diff);
 //            //assert( norm2(sdiff) < 1e-8 );
 //            if (norm2(sdiff) < 1e-8)
 //            {
-//                std::cout << GridLogMessage << "Symplectic condition satisfied: Omega invariant" << std::endl;
+//                std::cout << GridLogMessage << "Symplectic condition
+//                satisfied: Omega invariant" << std::endl;
 //            } else {
-//                std::cout << GridLogMessage << "WARNING!!!!!! Matrix Omega NOT left invariant by " << norm2(sdiff) << std::endl;
+//                std::cout << GridLogMessage << "WARNING!!!!!! Matrix Omega NOT
+//                left invariant by " << norm2(sdiff) << std::endl;
 //            }
-//            
-//            
+//
+//
 //        }
-//         
-//     
+//
+//
 // }; // end of class Sp
-//     
-//  
-//  template<int N>
-//  static void ProjectSp2n(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
-//  {
-//    Umu      = ProjectOnSpGroup(Umu);
-//    auto det = Determinant(Umu); // ok ?
-// 
-//    det = conjugate(det);
-// 
-//    for(int i=0;i<N;i++){
-//      auto element = PeekIndex<ColourIndex>(Umu,N-1,i);
-//      element = element * det;
-//      PokeIndex<ColourIndex>(Umu,element,Nc-1,i);
-//    }
-//  }
-//  template<int N>
-//  static void ProjectSp2n(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,Nd> > &U)
-//  {
-//    GridBase *grid=U.Grid();
-//    for(int mu=0;mu<Nd;mu++){
-//      auto Umu = PeekIndex<LorentzIndex>(U,mu);
-//      Umu      = ProjectOnSpGroup(Umu);
-//      ProjectSp2n(Umu);
-//      PokeIndex<LorentzIndex>(U,Umu,mu);
-//    }
-//  }
-// 
-// typedef Sp<2> Sp2;
-// typedef Sp<4> Sp4;
-// typedef Sp<6> Sp6;
-// typedef Sp<8> Sp8;
-// 
-// NAMESPACE_END(Grid);
-// #endif
+
+template <int N>
+static void ProjectSp2n(
+    Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
+  Umu = ProjectOnSpGroup(Umu);
+  auto det = Determinant(Umu);  // ok ?
+
+  det = conjugate(det);
+
+  for (int i = 0; i < N; i++) {
+    auto element = PeekIndex<ColourIndex>(Umu, N - 1, i);
+    element = element * det;
+    PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
+  }
+}
+template <int N>
+static void ProjectSp2n(
+    Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
+  GridBase *grid = U.Grid();
+  for (int mu = 0; mu < Nd; mu++) {
+    auto Umu = PeekIndex<LorentzIndex>(U, mu);
+    Umu = ProjectOnSpGroup(Umu);
+    ProjectSp2n(Umu);
+    PokeIndex<LorentzIndex>(U, Umu, mu);
+  }
+}
+
+typedef Sp<2> Sp2;
+typedef Sp<4> Sp4;
+typedef Sp<6> Sp6;
+typedef Sp<8> Sp8;
+
+NAMESPACE_END(Grid);
+#endif
diff --git a/Grid/qcd/utils/Sp2n_impl.h b/Grid/qcd/utils/Sp2n_impl.h
index 03a42d70..9399d5b2 100644
--- a/Grid/qcd/utils/Sp2n_impl.h
+++ b/Grid/qcd/utils/Sp2n_impl.h
@@ -1,245 +1,321 @@
 
-template<ONLY_IF_Sp>
-    static int su2subgroups(void) { return (nsp * (nsp - 1)) / 2; }
-template <typename vtype, ONLY_IF_Sp>
-using iSp2nMatrix = iGroupMatrix<vtype>;
-template <typename vtype, ONLY_IF_Sp>
-using iSp2nAlgebraVector = iAlgebraVector<vtype>;
+static int su2subgroups(GroupName::Sp) { return (nsp * (nsp - 1)) / 2; }
 
-    // Sp(2N) has N(2N+1) = 2N^2+N generators
-    //
-    // normalise the generators such that
-    // Trace ( Ta Tb) = 1/2 delta_ab
-    //
-    // N generators in the cartan, 2N^2 off
-    // off diagonal:
-    //     there are 6 types named a,b,c,d and w,z
-    //     abcd are N(N-1)/2 each while wz are N each
-    
- template <class cplx, ONLY_IF_Sp>
-    static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
-        // map lie index into type of generators: diagonal, abcd type, wz type
+// Sp(2N) has N(2N+1) = 2N^2+N generators
+//
+// normalise the generators such that
+// Trace ( Ta Tb) = 1/2 delta_ab
+//
+// N generators in the cartan, 2N^2 off
+// off diagonal:
+//     there are 6 types named a,b,c,d and w,z
+//     abcd are N(N-1)/2 each while wz are N each
 
-        int diagIndex;
-        int aIndex, bIndex, cIndex, dIndex;
-        int wIndex, zIndex; // a,b,c,d are N(N-1)/2 and w,z are N
-        int mod = nsp * (nsp-1) * 0.5;
-        int offdiag = 2*nsp*nsp; // number of generators not in the cartan subalgebra
-        int wmod = 4*mod;
-        int zmod = wmod+nsp;
-        if (lieIndex >= offdiag) {
-            diagIndex = lieIndex - offdiag; // 0, ... ,N-1
-            //std::cout << GridLogMessage << "diag type " << std::endl;
-            generatorDiagtype(diagIndex, ta);
-            return;
-        }
-        if ( (lieIndex >= wmod) && (lieIndex < zmod) ) {
-            //std::cout << GridLogMessage << "w type " << std::endl;
-            wIndex = lieIndex- wmod;    // 0, ... ,N-1
-            generatorWtype(wIndex,ta);
-            return;
-        }
-        if ( (lieIndex >= zmod) && (lieIndex < offdiag) ) {
-            //std::cout << GridLogMessage << "z type " << std::endl;
-            //std::cout << GridLogMessage << "lie index " << lieIndex << std::endl;
-            //std::cout << GridLogMessage << "z mod " << zmod << std::endl;
-            zIndex = lieIndex - zmod;   // 0, ... ,N-1
-            generatorZtype(zIndex,ta);
-            return;
-        }
-        if (lieIndex < mod) { // atype 0, ... , N(N-1)/2=mod
-            //std::cout << GridLogMessage << "a type " << std::endl;
-            aIndex = lieIndex;
-            //std::cout << GridLogMessage << "a indx " << aIndex << std::endl;
-            generatorAtype(aIndex, ta);
-            return;
-        }
-        if ( (lieIndex >= mod) && lieIndex < 2*mod) { // btype mod, ... , 2mod-1
-            //std::cout << GridLogMessage << "b type " << std::endl;
-            bIndex = lieIndex - mod;
-            generatorBtype(bIndex, ta);
-            return;
-        }
-        if ( (lieIndex >= 2*mod) && lieIndex < 3*mod) { // ctype 2mod, ... , 3mod-1
-            //std::cout << GridLogMessage << "c type " << std::endl;
-            cIndex = lieIndex - 2*mod;
-            generatorCtype(cIndex, ta);
-            return;
-        }
-        if ( (lieIndex >= 3*mod) && lieIndex < wmod) { // ctype 3mod, ... , 4mod-1 = wmod-1
-             //std::cout << GridLogMessage << "d type " << std::endl;
-             dIndex = lieIndex - 3*mod;
-             generatorDtype(dIndex, ta);
-            return;
-         }
-            
-    } //end of generator
-    
-    template <class cplx, ONLY_IF_Sp>
-    static void generatorDiagtype(int diagIndex, iSp2nMatrix<cplx> &ta) {
-        
-        // ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan subalgebra
-        
-        ta = Zero();
-        RealD nrm = 1.0 / 2;
+template <class cplx, ONLY_IF_Sp>
+static void generator(int lieIndex, iSp2nMatrix<cplx> &ta, GroupName::Sp) {
+  // map lie index into type of generators: diagonal, abcd type, wz type
 
-        ta()()(diagIndex,diagIndex) = nrm;
-        ta()()(diagIndex+nsp,diagIndex+nsp) = -nrm;
-    }
-    
-    template <class cplx, ONLY_IF_Sp>
-    static void generatorAtype(int aIndex, iSp2nMatrix<cplx> &ta) {
-        
-        // ta(i,j) = ta(j,i) = -ta(i+N,j+N) = -ta(j+N,i+N) = 1 / 2 sqrt(2)
-        // with i<j and i=0,...,N-2
-        // follows that j=i+1, ... , N
-        int i1, i2;
-        ta = Zero();
-        RealD nrm = 1 / (2 * std::sqrt(2) );
-        
-        su2SubGroupIndex(i1, i2, aIndex);
-        ta()()(i1,i2) = 1;
-        ta()()(i2,i1) = 1;
-        ta()()(i1+nsp,i2+nsp) = -1;
-        ta()()(i2+nsp,i1+nsp) = -1;
+  int diagIndex;
+  int aIndex, bIndex, cIndex, dIndex;
+  int wIndex, zIndex;  // a,b,c,d are N(N-1)/2 and w,z are N
+  int mod = nsp * (nsp - 1) * 0.5;
+  int offdiag =
+      2 * nsp * nsp;  // number of generators not in the cartan subalgebra
+  int wmod = 4 * mod;
+  int zmod = wmod + nsp;
+  if (lieIndex >= offdiag) {
+    diagIndex = lieIndex - offdiag;  // 0, ... ,N-1
+    // std::cout << GridLogMessage << "diag type " << std::endl;
+    generatorDiagtype(diagIndex, ta);
+    return;
+  }
+  if ((lieIndex >= wmod) && (lieIndex < zmod)) {
+    // std::cout << GridLogMessage << "w type " << std::endl;
+    wIndex = lieIndex - wmod;  // 0, ... ,N-1
+    generatorWtype(wIndex, ta);
+    return;
+  }
+  if ((lieIndex >= zmod) && (lieIndex < offdiag)) {
+    // std::cout << GridLogMessage << "z type " << std::endl;
+    // std::cout << GridLogMessage << "lie index " << lieIndex << std::endl;
+    // std::cout << GridLogMessage << "z mod " << zmod << std::endl;
+    zIndex = lieIndex - zmod;  // 0, ... ,N-1
+    generatorZtype(zIndex, ta);
+    return;
+  }
+  if (lieIndex < mod) {  // atype 0, ... , N(N-1)/2=mod
+    // std::cout << GridLogMessage << "a type " << std::endl;
+    aIndex = lieIndex;
+    // std::cout << GridLogMessage << "a indx " << aIndex << std::endl;
+    generatorAtype(aIndex, ta);
+    return;
+  }
+  if ((lieIndex >= mod) && lieIndex < 2 * mod) {  // btype mod, ... , 2mod-1
+    // std::cout << GridLogMessage << "b type " << std::endl;
+    bIndex = lieIndex - mod;
+    generatorBtype(bIndex, ta);
+    return;
+  }
+  if ((lieIndex >= 2 * mod) &&
+      lieIndex < 3 * mod) {  // ctype 2mod, ... , 3mod-1
+    // std::cout << GridLogMessage << "c type " << std::endl;
+    cIndex = lieIndex - 2 * mod;
+    generatorCtype(cIndex, ta);
+    return;
+  }
+  if ((lieIndex >= 3 * mod) &&
+      lieIndex < wmod) {  // ctype 3mod, ... , 4mod-1 = wmod-1
+    // std::cout << GridLogMessage << "d type " << std::endl;
+    dIndex = lieIndex - 3 * mod;
+    generatorDtype(dIndex, ta);
+    return;
+  }
 
-        ta = ta * nrm;
-    }
-    
-    template <class cplx, ONLY_IF_Sp>
-    static void generatorBtype(int bIndex, iSp2nMatrix<cplx> &ta) {
-        
-        // ta(i,j) = -ta(j,i) = ta(i+N,j+N) = -ta(j+N,i+N) = i / 1/ 2 sqrt(2)
-        // with i<j and i=0,...,N-2
-        // follows that j=i+1, ... , N-1
-        
-        int i1, i2;
-        ta = Zero();
-        cplx i(0.0, 1.0);
-        RealD nrm = 1 / (2 * std::sqrt(2));
-        su2SubGroupIndex(i1, i2, bIndex);
-        
+}  // end of generator
 
-        ta()()(i1,i2) = i;
-        ta()()(i2,i1) = -i;
-        ta()()(i1+nsp,i2+nsp) = i;
-        ta()()(i2+nsp,i1+nsp) = -i;
+template <class cplx, ONLY_IF_Sp>
+static void generatorDiagtype(int diagIndex, iSp2nMatrix<cplx> &ta) {
+  // ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan subalgebra
 
-        ta = ta * nrm;
-    }
-    
-    template <class cplx, ONLY_IF_Sp>
-    static void generatorCtype(int cIndex, iSp2nMatrix<cplx> &ta) {
-        
-        // ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
-        
-        
-        int i1, i2;
-        ta = Zero();
-        RealD nrm = 1 / (2 * std::sqrt(2) );
-        su2SubGroupIndex(i1, i2, cIndex);
-        
-        ta()()(i1,i2+nsp) = 1;
-        ta()()(i2,i1+nsp) = 1;
-        ta()()(i1+nsp,i2) = 1;
-        ta()()(i2+nsp,i1) = 1;
+  ta = Zero();
+  RealD nrm = 1.0 / 2;
 
-        ta = ta * nrm;
-    }
-    
-    template <class cplx, ONLY_IF_Sp>
-    static void generatorDtype(int dIndex, iSp2nMatrix<cplx> &ta) {
-        
-        // ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i /  2 sqrt(2)
-        
-        int i1, i2;
-        ta = Zero();
-        cplx i(0.0, 1.0);
-        RealD nrm = 1 / (2 * std::sqrt(2)  );
-        su2SubGroupIndex(i1, i2, dIndex);
+  ta()()(diagIndex, diagIndex) = nrm;
+  ta()()(diagIndex + nsp, diagIndex + nsp) = -nrm;
+}
 
-        ta()()(i1,i2+nsp) = i;
-        ta()()(i2,i1+nsp) = i;
-        ta()()(i1+nsp,i2) = -i;
-        ta()()(i2+nsp,i1) = -i;
+template <class cplx, ONLY_IF_Sp>
+static void generatorAtype(int aIndex, iSp2nMatrix<cplx> &ta) {
+  // ta(i,j) = ta(j,i) = -ta(i+N,j+N) = -ta(j+N,i+N) = 1 / 2 sqrt(2)
+  // with i<j and i=0,...,N-2
+  // follows that j=i+1, ... , N
+  int i1, i2;
+  ta = Zero();
+  RealD nrm = 1 / (2 * std::sqrt(2));
 
-        ta = ta * nrm;
-    }
-    
-    template <class cplx, ONLY_IF_Sp>
-     static void generatorWtype(int wIndex, iSp2nMatrix<cplx> &ta) {
-         
-         // ta(i,i+N) =  ta(i+N,i) = 1/2
-         
-         ta = Zero();
-         RealD nrm = 1.0 / 2; //check
+  su2SubGroupIndex(i1, i2, aIndex);
+  ta()()(i1, i2) = 1;
+  ta()()(i2, i1) = 1;
+  ta()()(i1 + nsp, i2 + nsp) = -1;
+  ta()()(i2 + nsp, i1 + nsp) = -1;
 
-         ta()()(wIndex,wIndex+nsp) = 1;
-         ta()()(wIndex+nsp,wIndex) = 1;
-         
-         ta = ta * nrm;
-     }
-    
-    template <class cplx, ONLY_IF_Sp>
-     static void generatorZtype(int zIndex, iSp2nMatrix<cplx> &ta) {
-         
-         // ta(i,i+N) = - ta(i+N,i) = i/2
-         
-         ta = Zero();
-         RealD nrm = 1.0 / 2; //check
-         cplx i(0.0, 1.0);
-         ta()()(zIndex,zIndex+nsp) = i;
-         ta()()(zIndex+nsp,zIndex) = -i;
-         
-         ta = ta * nrm;
-     }
-    
-    ////////////////////////////////////////////////////////////////////////
-    // Map a su2 subgroup number to the pair of rows that are non zero
-    ////////////////////////////////////////////////////////////////////////
-    template<ONLY_IF_Sp>
-    static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
-      assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
+  ta = ta * nrm;
+}
 
-      int spare = su2_index;
-      for (i1 = 0; spare >= (nsp - 1 - i1); i1++) {
-        spare = spare - (nsp - 1 - i1);  // remove the Nc-1-i1 terms
-      }
-      i2 = i1 + 1 + spare;
-    }
-    
-    template<ONLY_IF_Sp>
-    static void testGenerators(void) {
-        Matrix ta;
-        Matrix tb;
-        std::cout << GridLogMessage << "Fundamental - Checking trace ta tb is 0.5 delta_ab " << std::endl;
-        for (int a = 0; a < AlgebraDimension; a++) {
-            for (int b = 0; b < AlgebraDimension; b++) {
-                generator(a,ta);
-                generator(b,tb);
-                Complex tr = TensorRemove(trace( ta * tb) );
-                std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
+template <class cplx, ONLY_IF_Sp>
+static void generatorBtype(int bIndex, iSp2nMatrix<cplx> &ta) {
+  // ta(i,j) = -ta(j,i) = ta(i+N,j+N) = -ta(j+N,i+N) = i / 1/ 2 sqrt(2)
+  // with i<j and i=0,...,N-2
+  // follows that j=i+1, ... , N-1
+
+  int i1, i2;
+  ta = Zero();
+  cplx i(0.0, 1.0);
+  RealD nrm = 1 / (2 * std::sqrt(2));
+  su2SubGroupIndex(i1, i2, bIndex);
+
+  ta()()(i1, i2) = i;
+  ta()()(i2, i1) = -i;
+  ta()()(i1 + nsp, i2 + nsp) = i;
+  ta()()(i2 + nsp, i1 + nsp) = -i;
+
+  ta = ta * nrm;
+}
+
+template <class cplx, ONLY_IF_Sp>
+static void generatorCtype(int cIndex, iSp2nMatrix<cplx> &ta) {
+  // ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
+
+  int i1, i2;
+  ta = Zero();
+  RealD nrm = 1 / (2 * std::sqrt(2));
+  su2SubGroupIndex(i1, i2, cIndex);
+
+  ta()()(i1, i2 + nsp) = 1;
+  ta()()(i2, i1 + nsp) = 1;
+  ta()()(i1 + nsp, i2) = 1;
+  ta()()(i2 + nsp, i1) = 1;
+
+  ta = ta * nrm;
+}
+
+template <class cplx, ONLY_IF_Sp>
+static void generatorDtype(int dIndex, iSp2nMatrix<cplx> &ta) {
+  // ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i /  2 sqrt(2)
+
+  int i1, i2;
+  ta = Zero();
+  cplx i(0.0, 1.0);
+  RealD nrm = 1 / (2 * std::sqrt(2));
+  su2SubGroupIndex(i1, i2, dIndex);
+
+  ta()()(i1, i2 + nsp) = i;
+  ta()()(i2, i1 + nsp) = i;
+  ta()()(i1 + nsp, i2) = -i;
+  ta()()(i2 + nsp, i1) = -i;
+
+  ta = ta * nrm;
+}
+
+template <class cplx, ONLY_IF_Sp>
+static void generatorWtype(int wIndex, iSp2nMatrix<cplx> &ta) {
+  // ta(i,i+N) =  ta(i+N,i) = 1/2
+
+  ta = Zero();
+  RealD nrm = 1.0 / 2;  // check
+
+  ta()()(wIndex, wIndex + nsp) = 1;
+  ta()()(wIndex + nsp, wIndex) = 1;
+
+  ta = ta * nrm;
+}
+
+template <class cplx, ONLY_IF_Sp>
+static void generatorZtype(int zIndex, iSp2nMatrix<cplx> &ta) {
+  // ta(i,i+N) = - ta(i+N,i) = i/2
+
+  ta = Zero();
+  RealD nrm = 1.0 / 2;  // check
+  cplx i(0.0, 1.0);
+  ta()()(zIndex, zIndex + nsp) = i;
+  ta()()(zIndex + nsp, zIndex) = -i;
+
+  ta = ta * nrm;
+}
+
+////////////////////////////////////////////////////////////////////////
+// Map a su2 subgroup number to the pair of rows that are non zero
+////////////////////////////////////////////////////////////////////////
+template <ONLY_IF_Sp>
+static void su2SubGroupIndex(int &i1, int &i2, int su2_index, GroupName::Sp) {
+  assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
+
+  int spare = su2_index;
+  for (i1 = 0; spare >= (nsp - 1 - i1); i1++) {
+    spare = spare - (nsp - 1 - i1);  // remove the Nc-1-i1 terms
+  }
+  i2 = i1 + 1 + spare;
+}
+
+static void testGenerators(GroupName::Sp) {
+  Matrix ta;
+  Matrix tb;
+  std::cout << GridLogMessage
+            << "Fundamental - Checking trace ta tb is 0.5 delta_ab "
+            << std::endl;
+  for (int a = 0; a < AlgebraDimension; a++) {
+    for (int b = 0; b < AlgebraDimension; b++) {
+      generator(a, ta);
+      generator(b, tb);
+      Complex tr = TensorRemove(trace(ta * tb));
+      std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
                 << std::endl;
-                if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
-                if (a != b) assert(abs(tr) < 1.0e-6);
-
-            }
-        }
-        std::cout << GridLogMessage << std::endl;
-        std::cout << GridLogMessage << "Fundamental - Checking if hermitian" << std::endl;
-        for (int a = 0; a < AlgebraDimension; a++) {
-            generator(a,ta);
-            std::cout << GridLogMessage << a << std::endl;
-            assert(norm2(ta - adj(ta)) < 1.0e-6);
-        }
-        std::cout << GridLogMessage << std::endl;
-        std::cout << GridLogMessage << "Fundamental - Checking if traceless" << std::endl;
-        for (int a = 0; a < AlgebraDimension; a++) {
-          generator(a, ta);
-          Complex tr = TensorRemove(trace(ta));
-          std::cout << GridLogMessage << a << std::endl;
-          assert(abs(tr) < 1.0e-6);
-        }
-        
+      if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
+      if (a != b) assert(abs(tr) < 1.0e-6);
     }
+  }
+  std::cout << GridLogMessage << std::endl;
+  std::cout << GridLogMessage << "Fundamental - Checking if hermitian"
+            << std::endl;
+  for (int a = 0; a < AlgebraDimension; a++) {
+    generator(a, ta);
+    std::cout << GridLogMessage << a << std::endl;
+    assert(norm2(ta - adj(ta)) < 1.0e-6);
+  }
+  std::cout << GridLogMessage << std::endl;
+  std::cout << GridLogMessage << "Fundamental - Checking if traceless"
+            << std::endl;
+  for (int a = 0; a < AlgebraDimension; a++) {
+    generator(a, ta);
+    Complex tr = TensorRemove(trace(ta));
+    std::cout << GridLogMessage << a << std::endl;
+    assert(abs(tr) < 1.0e-6);
+  }
+}
+
+template <ONLY_IF_Sp>
+static void OmegaInvariance(ColourMatrix &in) {
+  ColourMatrix Omega;
+  Omega = Zero();
+
+  std::cout << GridLogMessage << "I am a ColourMatrix" << std::endl;
+
+  // for (int i = 0; i < ncolour; i++)         wrong?!
+  //{
+  //     Omega()()(i, 2*ncolour-1-i) = 1.;
+  //     Omega()()(2*ncolour-1-i, i) = -1;
+  // }
+  for (int i = 0; i < nsp; i++) {
+    Omega()()(i, nsp + i) = 1.;
+    Omega()()(nsp + i, i) = -1;
+  }
+
+  auto diff = Omega - (in * Omega * transpose(in));
+  auto sdiff = norm2(diff);
+  if (norm2(sdiff) < 1e-8) {
+    std::cout << GridLogMessage
+              << "Symplectic condition satisfied: Omega invariant" << std::endl;
+  } else {
+    std::cout << GridLogMessage
+              << "WARNING!!!!!! Matrix Omega NOT left invariant by "
+              << norm2(sdiff) << std::endl;
+  }
+}
+
+template <typename GaugeField, ONLY_IF_Sp>
+static void OmegaInvariance(GaugeField &in) {
+  typedef typename GaugeField::vector_type vector_type;
+  typedef iSp2nMatrix<vector_type> vMatrixType;
+  typedef Lattice<vMatrixType> LatticeMatrixType;
+
+  LatticeMatrixType U(in.Grid());
+  LatticeMatrixType OmegaLatt(in.Grid());
+  LatticeMatrixType identity(in.Grid());
+  RealD vol = in.Grid()->gSites();
+  ColourMatrix Omega;
+
+  OmegaLatt = Zero();
+  Omega = Zero();
+  identity = 1.;
+
+  std::cout << GridLogMessage << "I am a GaugeField " << std::endl;
+
+  U = PeekIndex<LorentzIndex>(in, 1);
+
+  OmegaInvariance(U);
+}
+
+template <ONLY_IF_Sp>
+static void OmegaInvariance(LatticeColourMatrixD &in) {
+  LatticeColourMatrixD OmegaLatt(in.Grid());
+  LatticeColourMatrixD identity(in.Grid());
+  RealD vol = in.Grid()->gSites();
+  ColourMatrix Omega;
+
+  OmegaLatt = Zero();
+  Omega = Zero();
+  identity = 1.;
+
+  std::cout << GridLogMessage << "I am a LatticeColourMatrix " << std::endl;
+
+  for (int i = 0; i < nsp; i++) {
+    Omega()()(i, nsp + i) = 1.;
+    Omega()()(nsp + i, i) = -1;
+  }
+
+  std::cout << GridLogMessage << "Omega = " << Omega()() << std::endl;
+  OmegaLatt = OmegaLatt + (identity * Omega);
+
+  auto diff = OmegaLatt - (in * OmegaLatt * transpose(in));
+  auto sdiff = sum(diff);
+  // assert( norm2(sdiff) < 1e-8 );
+  if (norm2(sdiff) < 1e-8) {
+    std::cout << GridLogMessage
+              << "Symplectic condition satisfied: Omega invariant" << std::endl;
+  } else {
+    std::cout << GridLogMessage
+              << "WARNING!!!!!! Matrix Omega NOT left invariant by "
+              << norm2(sdiff) << std::endl;
+  }
+}
 

From 55c008da21be79c5d1d41c69be0aed1f0570be0e Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 30 Nov 2022 13:12:21 +0000
Subject: [PATCH 037/129] Removed forward declaration

---
 Grid/qcd/utils/SUn.h      | 15 ++++++---------
 Grid/qcd/utils/SUn_impl.h |  6 +++---
 2 files changed, 9 insertions(+), 12 deletions(-)

diff --git a/Grid/qcd/utils/SUn.h b/Grid/qcd/utils/SUn.h
index 6b7e9079..30ac36a3 100644
--- a/Grid/qcd/utils/SUn.h
+++ b/Grid/qcd/utils/SUn.h
@@ -83,15 +83,6 @@ constexpr int compute_adjoint_dimension<GroupName::Sp>(int ncolour) {
   return ncolour / 2 * (ncolour + 1);
 }
 
-template <int ncolour, class group_name = GroupName::SU>
-class GaugeGroup;
-
-template <int ncolour>
-using SU = GaugeGroup<ncolour, GroupName::SU>;
-
-template <int ncolour>
-using Sp = GaugeGroup<ncolour, GroupName::Sp>;
-
 template <int ncolour, class group_name>
 class GaugeGroup {
  public:
@@ -423,6 +414,12 @@ static void ProjectSU3(
   }
 }
 
+template <int ncolour>
+using SU = GaugeGroup<ncolour, GroupName::SU>;
+
+template <int ncolour>
+using Sp = GaugeGroup<ncolour, GroupName::Sp>;
+
 typedef SU<2> SU2;
 typedef SU<3> SU3;
 typedef SU<4> SU4;
diff --git a/Grid/qcd/utils/SUn_impl.h b/Grid/qcd/utils/SUn_impl.h
index 2d97dc17..be0eb42d 100644
--- a/Grid/qcd/utils/SUn_impl.h
+++ b/Grid/qcd/utils/SUn_impl.h
@@ -282,11 +282,11 @@ static void SubGroupHeatBath(
 
   SU2Matrix ident = Complex(1.0);
   SU2Matrix pauli1;
-  SU<2>::generator(0, pauli1);
+  GaugeGroup<2, GroupName::SU>::generator(0, pauli1);
   SU2Matrix pauli2;
-  SU<2>::generator(1, pauli2);
+  GaugeGroup<2, GroupName::SU>::generator(1, pauli2);
   SU2Matrix pauli3;
-  SU<2>::generator(2, pauli3);
+  GaugeGroup<2, GroupName::SU>::generator(2, pauli3);
   pauli1 = timesI(pauli1) * 2.0;
   pauli2 = timesI(pauli2) * 2.0;
   pauli3 = timesI(pauli3) * 2.0;

From b8b3ae6ac14bad667a02078c205a38cb83144026 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 30 Nov 2022 13:28:09 +0000
Subject: [PATCH 038/129] Make helper functions private

---
 Grid/qcd/utils/SUn.h       | 1 +
 Grid/qcd/utils/SUn_impl.h  | 2 ++
 Grid/qcd/utils/Sp2n_impl.h | 2 ++
 3 files changed, 5 insertions(+)

diff --git a/Grid/qcd/utils/SUn.h b/Grid/qcd/utils/SUn.h
index 30ac36a3..a6e6c36c 100644
--- a/Grid/qcd/utils/SUn.h
+++ b/Grid/qcd/utils/SUn.h
@@ -156,6 +156,7 @@ class GaugeGroup {
 #include "Grid/qcd/utils/SUn_impl.h"
 #include "Grid/qcd/utils/Sp2n_impl.h"
 
+ public:
   template <class cplx>
   static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
     return generator(lieIndex, ta, group_name());
diff --git a/Grid/qcd/utils/SUn_impl.h b/Grid/qcd/utils/SUn_impl.h
index be0eb42d..6081f79c 100644
--- a/Grid/qcd/utils/SUn_impl.h
+++ b/Grid/qcd/utils/SUn_impl.h
@@ -6,6 +6,7 @@
 //
 // around it.
 
+private:
 static int su2subgroups(GroupName::SU) { return (ncolour * (ncolour - 1)) / 2; }
 ////////////////////////////////////////////////////////////////////////
 // There are N^2-1 generators for SU(N).
@@ -122,6 +123,7 @@ static void su2SubGroupIndex(int &i1, int &i2, int su2_index, GroupName::SU) {
   i2 = i1 + 1 + spare;
 }
 
+public:
 //////////////////////////////////////////////////////////////////////////////////////////
 // Pull out a subgroup and project on to real coeffs x pauli basis
 //////////////////////////////////////////////////////////////////////////////////////////
diff --git a/Grid/qcd/utils/Sp2n_impl.h b/Grid/qcd/utils/Sp2n_impl.h
index 9399d5b2..addbd118 100644
--- a/Grid/qcd/utils/Sp2n_impl.h
+++ b/Grid/qcd/utils/Sp2n_impl.h
@@ -1,4 +1,5 @@
 
+private:
 static int su2subgroups(GroupName::Sp) { return (nsp * (nsp - 1)) / 2; }
 
 // Sp(2N) has N(2N+1) = 2N^2+N generators
@@ -233,6 +234,7 @@ static void testGenerators(GroupName::Sp) {
   }
 }
 
+public:
 template <ONLY_IF_Sp>
 static void OmegaInvariance(ColourMatrix &in) {
   ColourMatrix Omega;

From fa71b46a41c4cc6455c223aab12b9a2c324c084a Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 30 Nov 2022 14:27:19 +0000
Subject: [PATCH 039/129] Hide nsp

---
 Grid/qcd/utils/SUn.h             |  2 --
 Grid/qcd/utils/Sp2n_impl.h       | 21 ++++++++++++++++-----
 tests/sp2n/Test_Sp_start.cc      |  2 +-
 tests/sp2n/Test_project_on_Sp.cc |  3 +--
 4 files changed, 18 insertions(+), 10 deletions(-)

diff --git a/Grid/qcd/utils/SUn.h b/Grid/qcd/utils/SUn.h
index a6e6c36c..2cedf67d 100644
--- a/Grid/qcd/utils/SUn.h
+++ b/Grid/qcd/utils/SUn.h
@@ -91,8 +91,6 @@ class GaugeGroup {
       compute_adjoint_dimension<group_name>(ncolour);
   static const int AlgebraDimension =
       compute_adjoint_dimension<group_name>(ncolour);
-  // Don't know how to only enable this for Sp:
-  static const int nsp = ncolour / 2;
 
   template <typename vtype>
   using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
diff --git a/Grid/qcd/utils/Sp2n_impl.h b/Grid/qcd/utils/Sp2n_impl.h
index addbd118..28dac5f8 100644
--- a/Grid/qcd/utils/Sp2n_impl.h
+++ b/Grid/qcd/utils/Sp2n_impl.h
@@ -1,6 +1,6 @@
 
 private:
-static int su2subgroups(GroupName::Sp) { return (nsp * (nsp - 1)) / 2; }
+static int su2subgroups(GroupName::Sp) { return (ncolour/2 * (ncolour/2 - 1)) / 2; }
 
 // Sp(2N) has N(2N+1) = 2N^2+N generators
 //
@@ -16,14 +16,15 @@ template <class cplx, ONLY_IF_Sp>
 static void generator(int lieIndex, iSp2nMatrix<cplx> &ta, GroupName::Sp) {
   // map lie index into type of generators: diagonal, abcd type, wz type
 
+  const int nsp = ncolour/2;
   int diagIndex;
   int aIndex, bIndex, cIndex, dIndex;
   int wIndex, zIndex;  // a,b,c,d are N(N-1)/2 and w,z are N
-  int mod = nsp * (nsp - 1) * 0.5;
-  int offdiag =
+  const int mod = nsp * (nsp - 1) * 0.5;
+  const int offdiag =
       2 * nsp * nsp;  // number of generators not in the cartan subalgebra
-  int wmod = 4 * mod;
-  int zmod = wmod + nsp;
+  const int wmod = 4 * mod;
+  const int zmod = wmod + nsp;
   if (lieIndex >= offdiag) {
     diagIndex = lieIndex - offdiag;  // 0, ... ,N-1
     // std::cout << GridLogMessage << "diag type " << std::endl;
@@ -78,6 +79,7 @@ template <class cplx, ONLY_IF_Sp>
 static void generatorDiagtype(int diagIndex, iSp2nMatrix<cplx> &ta) {
   // ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan subalgebra
 
+  const int nsp=ncolour/2;
   ta = Zero();
   RealD nrm = 1.0 / 2;
 
@@ -91,6 +93,7 @@ static void generatorAtype(int aIndex, iSp2nMatrix<cplx> &ta) {
   // with i<j and i=0,...,N-2
   // follows that j=i+1, ... , N
   int i1, i2;
+  const int nsp=ncolour/2;
   ta = Zero();
   RealD nrm = 1 / (2 * std::sqrt(2));
 
@@ -109,6 +112,7 @@ static void generatorBtype(int bIndex, iSp2nMatrix<cplx> &ta) {
   // with i<j and i=0,...,N-2
   // follows that j=i+1, ... , N-1
 
+  const int nsp=ncolour/2;
   int i1, i2;
   ta = Zero();
   cplx i(0.0, 1.0);
@@ -127,6 +131,7 @@ template <class cplx, ONLY_IF_Sp>
 static void generatorCtype(int cIndex, iSp2nMatrix<cplx> &ta) {
   // ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
 
+  const int nsp=ncolour/2;
   int i1, i2;
   ta = Zero();
   RealD nrm = 1 / (2 * std::sqrt(2));
@@ -144,6 +149,7 @@ template <class cplx, ONLY_IF_Sp>
 static void generatorDtype(int dIndex, iSp2nMatrix<cplx> &ta) {
   // ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i /  2 sqrt(2)
 
+  const int nsp=ncolour/2;
   int i1, i2;
   ta = Zero();
   cplx i(0.0, 1.0);
@@ -162,6 +168,7 @@ template <class cplx, ONLY_IF_Sp>
 static void generatorWtype(int wIndex, iSp2nMatrix<cplx> &ta) {
   // ta(i,i+N) =  ta(i+N,i) = 1/2
 
+  const int nsp=ncolour/2;
   ta = Zero();
   RealD nrm = 1.0 / 2;  // check
 
@@ -175,6 +182,7 @@ template <class cplx, ONLY_IF_Sp>
 static void generatorZtype(int zIndex, iSp2nMatrix<cplx> &ta) {
   // ta(i,i+N) = - ta(i+N,i) = i/2
 
+  const int nsp=ncolour/2;
   ta = Zero();
   RealD nrm = 1.0 / 2;  // check
   cplx i(0.0, 1.0);
@@ -189,6 +197,7 @@ static void generatorZtype(int zIndex, iSp2nMatrix<cplx> &ta) {
 ////////////////////////////////////////////////////////////////////////
 template <ONLY_IF_Sp>
 static void su2SubGroupIndex(int &i1, int &i2, int su2_index, GroupName::Sp) {
+  const int nsp=ncolour/2;
   assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
 
   int spare = su2_index;
@@ -239,6 +248,7 @@ template <ONLY_IF_Sp>
 static void OmegaInvariance(ColourMatrix &in) {
   ColourMatrix Omega;
   Omega = Zero();
+  const int nsp=ncolour/2;
 
   std::cout << GridLogMessage << "I am a ColourMatrix" << std::endl;
 
@@ -289,6 +299,7 @@ static void OmegaInvariance(GaugeField &in) {
 
 template <ONLY_IF_Sp>
 static void OmegaInvariance(LatticeColourMatrixD &in) {
+  const int nsp=ncolour/2;
   LatticeColourMatrixD OmegaLatt(in.Grid());
   LatticeColourMatrixD identity(in.Grid());
   RealD vol = in.Grid()->gSites();
diff --git a/tests/sp2n/Test_Sp_start.cc b/tests/sp2n/Test_Sp_start.cc
index 16a66367..061acbcc 100644
--- a/tests/sp2n/Test_Sp_start.cc
+++ b/tests/sp2n/Test_Sp_start.cc
@@ -21,7 +21,7 @@ int main (int argc, char **argv)
     
     double vol = Umu.Grid()->gSites();
 
-    const int nsp = Sp<Nc>::nsp;
+    const int nsp = Nc/2;
     identity = 1.;
     Cidentity = 1.;
     
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index d1cf33bd..36b95cf4 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -20,8 +20,7 @@ int main (int argc, char **argv)
     LatticeColourMatrixD aux(&Grid);
     LatticeColourMatrixD identity(&Grid);
     
-    //const int nsp = Nc / 2;
-    const int nsp = Sp<Nc>::nsp;
+    const int nsp = Nc / 2;
     
     identity = 1.0;
     RealD epsilon = 0.01;

From a13820656a03cca25f74cc0300d0cc8c66cdf6a2 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 30 Nov 2022 15:09:03 +0000
Subject: [PATCH 040/129] Removed iSUnMatrix, etc.

---
 Grid/qcd/action/gauge/GaugeImplTypes.h |  2 +-
 Grid/qcd/utils/SUn.h                   | 10 +---------
 Grid/qcd/utils/SUn_impl.h              | 12 ++++++------
 Grid/qcd/utils/Sp2nTwoIndex.h          |  8 ++++----
 Grid/qcd/utils/Sp2n_impl.h             | 18 +++++++++---------
 5 files changed, 21 insertions(+), 29 deletions(-)

diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index dc39c30b..5a8887f2 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -150,7 +150,7 @@ public:
             P = Ta(P);
             //const int nsp = Nc / 2;
 
-            Sp<Nc>::iSp2nMatrix<Complex> gen;
+            Sp<Nc>::iGroupMatrix<Complex> gen;
             
 
             auto Psum = P;
diff --git a/Grid/qcd/utils/SUn.h b/Grid/qcd/utils/SUn.h
index 2cedf67d..7a096df2 100644
--- a/Grid/qcd/utils/SUn.h
+++ b/Grid/qcd/utils/SUn.h
@@ -99,14 +99,6 @@ class GaugeGroup {
   template <typename vtype>
   using iAlgebraVector = iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
   static int su2subgroups(void) { return su2subgroups(group_name()); }
-  template <typename vtype>
-  using iSUnMatrix = iGroupMatrix<vtype>;
-  template <typename vtype>
-  using iSUnAlgebraVector = iAlgebraVector<vtype>;
-  template <typename vtype>
-  using iSp2nMatrix = iGroupMatrix<vtype>;
-  template <typename vtype>
-  using iSp2nAlgebraVector = iAlgebraVector<vtype>;
 
   //////////////////////////////////////////////////////////////////////////////////////////////////
   // Types can be accessed as SU<2>::Matrix , SU<2>::vSUnMatrix,
@@ -156,7 +148,7 @@ class GaugeGroup {
 
  public:
   template <class cplx>
-  static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
+  static void generator(int lieIndex, iGroupMatrix<cplx> &ta) {
     return generator(lieIndex, ta, group_name());
   }
 
diff --git a/Grid/qcd/utils/SUn_impl.h b/Grid/qcd/utils/SUn_impl.h
index 6081f79c..61b19fbc 100644
--- a/Grid/qcd/utils/SUn_impl.h
+++ b/Grid/qcd/utils/SUn_impl.h
@@ -57,7 +57,7 @@ static int su2subgroups(GroupName::SU) { return (ncolour * (ncolour - 1)) / 2; }
 //
 ////////////////////////////////////////////////////////////////////////
 template <class cplx>
-static void generator(int lieIndex, iSUnMatrix<cplx> &ta, GroupName::SU) {
+static void generator(int lieIndex, iGroupMatrix<cplx> &ta, GroupName::SU) {
   // map lie index to which type of generator
   int diagIndex;
   int su2Index;
@@ -77,7 +77,7 @@ static void generator(int lieIndex, iSUnMatrix<cplx> &ta, GroupName::SU) {
 }
 
 template <class cplx, ONLY_IF_SU>
-static void generatorSigmaY(int su2Index, iSUnMatrix<cplx> &ta) {
+static void generatorSigmaY(int su2Index, iGroupMatrix<cplx> &ta) {
   ta = Zero();
   int i1, i2;
   su2SubGroupIndex(i1, i2, su2Index);
@@ -87,7 +87,7 @@ static void generatorSigmaY(int su2Index, iSUnMatrix<cplx> &ta) {
 }
 
 template <class cplx, ONLY_IF_SU>
-static void generatorSigmaX(int su2Index, iSUnMatrix<cplx> &ta) {
+static void generatorSigmaX(int su2Index, iGroupMatrix<cplx> &ta) {
   ta = Zero();
   cplx i(0.0, 1.0);
   int i1, i2;
@@ -98,7 +98,7 @@ static void generatorSigmaX(int su2Index, iSUnMatrix<cplx> &ta) {
 }
 
 template <class cplx, ONLY_IF_SU>
-static void generatorDiagonal(int diagIndex, iSUnMatrix<cplx> &ta) {
+static void generatorDiagonal(int diagIndex, iGroupMatrix<cplx> &ta) {
   // diag ({1, 1, ..., 1}(k-times), -k, 0, 0, ...)
   ta = Zero();
   int k = diagIndex + 1;                  // diagIndex starts from 0
@@ -130,7 +130,7 @@ public:
 template <class vcplx, ONLY_IF_SU>
 static void su2Extract(Lattice<iSinglet<vcplx> > &Determinant,
                        Lattice<iSU2Matrix<vcplx> > &subgroup,
-                       const Lattice<iSUnMatrix<vcplx> > &source,
+                       const Lattice<iGroupMatrix<vcplx> > &source,
                        int su2_index) {
   GridBase *grid(source.Grid());
   conformable(subgroup, source);
@@ -164,7 +164,7 @@ static void su2Extract(Lattice<iSinglet<vcplx> > &Determinant,
 //////////////////////////////////////////////////////////////////////////////////////////
 template <class vcplx, ONLY_IF_SU>
 static void su2Insert(const Lattice<iSU2Matrix<vcplx> > &subgroup,
-                      Lattice<iSUnMatrix<vcplx> > &dest, int su2_index) {
+                      Lattice<iGroupMatrix<vcplx> > &dest, int su2_index) {
   GridBase *grid(dest.Grid());
   conformable(subgroup, dest);
   int i0, i1;
diff --git a/Grid/qcd/utils/Sp2nTwoIndex.h b/Grid/qcd/utils/Sp2nTwoIndex.h
index 3b685802..98306970 100644
--- a/Grid/qcd/utils/Sp2nTwoIndex.h
+++ b/Grid/qcd/utils/Sp2nTwoIndex.h
@@ -175,10 +175,10 @@ public:
 
   template <class cplx>
   static void generator(int Index, iSp2nTwoIndexMatrix<cplx> &i2indTa) {
-    Vector<typename Sp<ncolour>::template iSp2nMatrix<cplx> > ta(
+    Vector<iSp2nMatrix<cplx> > ta(
 								NumGenerators);
-    Vector<typename Sp<ncolour>::template iSp2nMatrix<cplx> > eij(Dimension);
-    typename Sp<ncolour>::template iSp2nMatrix<cplx> tmp;
+    Vector<iSp2nMatrix<cplx> > eij(Dimension);
+    iSp2nMatrix<cplx> tmp;
     i2indTa = Zero();
     
     for (int a = 0; a < NumGenerators; a++)
@@ -189,7 +189,7 @@ public:
     for (int a = 0; a < Dimension; a++) {
       tmp = transpose(ta[Index]) * adj(eij[a]) + adj(eij[a]) * ta[Index];
       for (int b = 0; b < Dimension; b++) {
-        typename Sp<ncolour>::template iSp2nMatrix<cplx> tmp1 =
+        iSp2nMatrix<cplx> tmp1 =
 	  tmp * eij[b]; 
         Complex iTr = TensorRemove(timesI(trace(tmp1)));
         i2indTa()()(a, b) = iTr;
diff --git a/Grid/qcd/utils/Sp2n_impl.h b/Grid/qcd/utils/Sp2n_impl.h
index 28dac5f8..6d559c0a 100644
--- a/Grid/qcd/utils/Sp2n_impl.h
+++ b/Grid/qcd/utils/Sp2n_impl.h
@@ -13,7 +13,7 @@ static int su2subgroups(GroupName::Sp) { return (ncolour/2 * (ncolour/2 - 1)) /
 //     abcd are N(N-1)/2 each while wz are N each
 
 template <class cplx, ONLY_IF_Sp>
-static void generator(int lieIndex, iSp2nMatrix<cplx> &ta, GroupName::Sp) {
+static void generator(int lieIndex, iGroupMatrix<cplx> &ta, GroupName::Sp) {
   // map lie index into type of generators: diagonal, abcd type, wz type
 
   const int nsp = ncolour/2;
@@ -76,7 +76,7 @@ static void generator(int lieIndex, iSp2nMatrix<cplx> &ta, GroupName::Sp) {
 }  // end of generator
 
 template <class cplx, ONLY_IF_Sp>
-static void generatorDiagtype(int diagIndex, iSp2nMatrix<cplx> &ta) {
+static void generatorDiagtype(int diagIndex, iGroupMatrix<cplx> &ta) {
   // ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan subalgebra
 
   const int nsp=ncolour/2;
@@ -88,7 +88,7 @@ static void generatorDiagtype(int diagIndex, iSp2nMatrix<cplx> &ta) {
 }
 
 template <class cplx, ONLY_IF_Sp>
-static void generatorAtype(int aIndex, iSp2nMatrix<cplx> &ta) {
+static void generatorAtype(int aIndex, iGroupMatrix<cplx> &ta) {
   // ta(i,j) = ta(j,i) = -ta(i+N,j+N) = -ta(j+N,i+N) = 1 / 2 sqrt(2)
   // with i<j and i=0,...,N-2
   // follows that j=i+1, ... , N
@@ -107,7 +107,7 @@ static void generatorAtype(int aIndex, iSp2nMatrix<cplx> &ta) {
 }
 
 template <class cplx, ONLY_IF_Sp>
-static void generatorBtype(int bIndex, iSp2nMatrix<cplx> &ta) {
+static void generatorBtype(int bIndex, iGroupMatrix<cplx> &ta) {
   // ta(i,j) = -ta(j,i) = ta(i+N,j+N) = -ta(j+N,i+N) = i / 1/ 2 sqrt(2)
   // with i<j and i=0,...,N-2
   // follows that j=i+1, ... , N-1
@@ -128,7 +128,7 @@ static void generatorBtype(int bIndex, iSp2nMatrix<cplx> &ta) {
 }
 
 template <class cplx, ONLY_IF_Sp>
-static void generatorCtype(int cIndex, iSp2nMatrix<cplx> &ta) {
+static void generatorCtype(int cIndex, iGroupMatrix<cplx> &ta) {
   // ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
 
   const int nsp=ncolour/2;
@@ -146,7 +146,7 @@ static void generatorCtype(int cIndex, iSp2nMatrix<cplx> &ta) {
 }
 
 template <class cplx, ONLY_IF_Sp>
-static void generatorDtype(int dIndex, iSp2nMatrix<cplx> &ta) {
+static void generatorDtype(int dIndex, iGroupMatrix<cplx> &ta) {
   // ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i /  2 sqrt(2)
 
   const int nsp=ncolour/2;
@@ -165,7 +165,7 @@ static void generatorDtype(int dIndex, iSp2nMatrix<cplx> &ta) {
 }
 
 template <class cplx, ONLY_IF_Sp>
-static void generatorWtype(int wIndex, iSp2nMatrix<cplx> &ta) {
+static void generatorWtype(int wIndex, iGroupMatrix<cplx> &ta) {
   // ta(i,i+N) =  ta(i+N,i) = 1/2
 
   const int nsp=ncolour/2;
@@ -179,7 +179,7 @@ static void generatorWtype(int wIndex, iSp2nMatrix<cplx> &ta) {
 }
 
 template <class cplx, ONLY_IF_Sp>
-static void generatorZtype(int zIndex, iSp2nMatrix<cplx> &ta) {
+static void generatorZtype(int zIndex, iGroupMatrix<cplx> &ta) {
   // ta(i,i+N) = - ta(i+N,i) = i/2
 
   const int nsp=ncolour/2;
@@ -277,7 +277,7 @@ static void OmegaInvariance(ColourMatrix &in) {
 template <typename GaugeField, ONLY_IF_Sp>
 static void OmegaInvariance(GaugeField &in) {
   typedef typename GaugeField::vector_type vector_type;
-  typedef iSp2nMatrix<vector_type> vMatrixType;
+  typedef iGroupMatrix<vector_type> vMatrixType;
   typedef Lattice<vMatrixType> LatticeMatrixType;
 
   LatticeMatrixType U(in.Grid());

From 7bcf33def98cced5bcfe5ee70527c1671617539a Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 30 Nov 2022 16:59:46 +0000
Subject: [PATCH 041/129] Removed Sp2n.h

---
 Grid/qcd/utils/SUn.h            |  32 ++
 Grid/qcd/utils/Sp2n.h           | 597 --------------------------------
 Grid/qcd/utils/Utils.h          |   1 -
 tests/sp2n/Test_sp2n_lie_gen.cc |   4 -
 4 files changed, 32 insertions(+), 602 deletions(-)
 delete mode 100644 Grid/qcd/utils/Sp2n.h

diff --git a/Grid/qcd/utils/SUn.h b/Grid/qcd/utils/SUn.h
index 7a096df2..88476f47 100644
--- a/Grid/qcd/utils/SUn.h
+++ b/Grid/qcd/utils/SUn.h
@@ -418,5 +418,37 @@ typedef SU<5> SU5;
 
 typedef SU<Nc> FundamentalMatrices;
 
+template <int N>
+static void ProjectSp2n(
+    Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
+  Umu = ProjectOnSpGroup(Umu);
+  auto det = Determinant(Umu);  // ok ?
+
+  det = conjugate(det);
+
+  for (int i = 0; i < N; i++) {
+    auto element = PeekIndex<ColourIndex>(Umu, N - 1, i);
+    element = element * det;
+    PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
+  }
+}
+template <int N>
+static void ProjectSp2n(
+    Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
+  GridBase *grid = U.Grid();
+  for (int mu = 0; mu < Nd; mu++) {
+    auto Umu = PeekIndex<LorentzIndex>(U, mu);
+    Umu = ProjectOnSpGroup(Umu);
+    ProjectSp2n(Umu);
+    PokeIndex<LorentzIndex>(U, Umu, mu);
+  }
+}
+
+typedef Sp<2> Sp2;
+typedef Sp<4> Sp4;
+typedef Sp<6> Sp6;
+typedef Sp<8> Sp8;
+
+
 NAMESPACE_END(Grid);
 #endif
diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.h
deleted file mode 100644
index 201e1e7c..00000000
--- a/Grid/qcd/utils/Sp2n.h
+++ /dev/null
@@ -1,597 +0,0 @@
-
-#ifndef QCD_UTIL_Sp2n_H
-#define QCD_UTIL_Sp2n_H
-
-#include "Grid/qcd/utils/SUn.h"
-NAMESPACE_BEGIN(Grid);
-//
-// // Sp(2N)
-// // ncolour = 2N
-//
-//
-// template <int ncolour>
-// class Sp {
-// public:
-//     static const int nsp = ncolour/2;
-//     static const int Dimension = ncolour;
-//     static const int AlgebraDimension = nsp*(2*nsp +1);
-//     static int su2subgroups(void) { return (nsp * (nsp - 1)) / 2; }
-//
-//
-//     template <typename vtype>
-//     using iSp2nMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
-//     template <typename vtype>
-//     using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
-//     template <typename vtype>
-//     using iSp2nAlgebraVector = iScalar<iScalar<iVector<vtype,
-//     AlgebraDimension> > >;
-//
-//     typedef iSp2nMatrix<Complex> Matrix;
-//     typedef iSp2nMatrix<ComplexF> MatrixF;
-//     typedef iSp2nMatrix<ComplexD> MatrixD;
-//
-//     typedef iSp2nMatrix<vComplex> vMatrix;
-//     typedef iSp2nMatrix<vComplexF> vMatrixF;
-//     typedef iSp2nMatrix<vComplexD> vMatrixD;
-//
-//     typedef iSp2nAlgebraVector<Complex> AlgebraVector;
-//     typedef iSp2nAlgebraVector<ComplexF> AlgebraVectorF;
-//     typedef iSp2nAlgebraVector<ComplexD> AlgebraVectorD;
-//
-//     typedef iSp2nAlgebraVector<vComplex> vAlgebraVector;
-//     typedef iSp2nAlgebraVector<vComplexF> vAlgebraVectorF;
-//     typedef iSp2nAlgebraVector<vComplexD> vAlgebraVectorD;
-//
-//     typedef Lattice<vMatrix> LatticeMatrix;
-//     typedef Lattice<vMatrixF> LatticeMatrixF;
-//     typedef Lattice<vMatrixD> LatticeMatrixD;
-//
-//     typedef Lattice<vAlgebraVector> LatticeAlgebraVector;
-//     typedef Lattice<vAlgebraVectorF> LatticeAlgebraVectorF;
-//     typedef Lattice<vAlgebraVectorD> LatticeAlgebraVectorD;
-//
-//
-//
-//     // Sp(2N) has N(2N+1) = 2N^2+N generators
-//     //
-//     // normalise the generators such that
-//     // Trace ( Ta Tb) = 1/2 delta_ab
-//     //
-//     // N generators in the cartan, 2N^2 off
-//     // off diagonal:
-//     //     there are 6 types named a,b,c,d and w,z
-//     //     abcd are N(N-1)/2 each while wz are N each
-//
-//  template <class cplx>
-//     static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
-//         // map lie index into type of generators: diagonal, abcd type, wz
-//         type
-//
-//         int diagIndex;
-//         int aIndex, bIndex, cIndex, dIndex;
-//         int wIndex, zIndex; // a,b,c,d are N(N-1)/2 and w,z are N
-//         int mod = nsp * (nsp-1) * 0.5;
-//         int offdiag = 2*nsp*nsp; // number of generators not in the cartan
-//         subalgebra int wmod = 4*mod; int zmod = wmod+nsp; if (lieIndex >=
-//         offdiag) {
-//             diagIndex = lieIndex - offdiag; // 0, ... ,N-1
-//             //std::cout << GridLogMessage << "diag type " << std::endl;
-//             generatorDiagtype(diagIndex, ta);
-//             return;
-//         }
-//         if ( (lieIndex >= wmod) && (lieIndex < zmod) ) {
-//             //std::cout << GridLogMessage << "w type " << std::endl;
-//             wIndex = lieIndex- wmod;    // 0, ... ,N-1
-//             generatorWtype(wIndex,ta);
-//             return;
-//         }
-//         if ( (lieIndex >= zmod) && (lieIndex < offdiag) ) {
-//             //std::cout << GridLogMessage << "z type " << std::endl;
-//             //std::cout << GridLogMessage << "lie index " << lieIndex <<
-//             std::endl;
-//             //std::cout << GridLogMessage << "z mod " << zmod << std::endl;
-//             zIndex = lieIndex - zmod;   // 0, ... ,N-1
-//             generatorZtype(zIndex,ta);
-//             return;
-//         }
-//         if (lieIndex < mod) { // atype 0, ... , N(N-1)/2=mod
-//             //std::cout << GridLogMessage << "a type " << std::endl;
-//             aIndex = lieIndex;
-//             //std::cout << GridLogMessage << "a indx " << aIndex <<
-//             std::endl; generatorAtype(aIndex, ta); return;
-//         }
-//         if ( (lieIndex >= mod) && lieIndex < 2*mod) { // btype mod, ... ,
-//         2mod-1
-//             //std::cout << GridLogMessage << "b type " << std::endl;
-//             bIndex = lieIndex - mod;
-//             generatorBtype(bIndex, ta);
-//             return;
-//         }
-//         if ( (lieIndex >= 2*mod) && lieIndex < 3*mod) { // ctype 2mod, ... ,
-//         3mod-1
-//             //std::cout << GridLogMessage << "c type " << std::endl;
-//             cIndex = lieIndex - 2*mod;
-//             generatorCtype(cIndex, ta);
-//             return;
-//         }
-//         if ( (lieIndex >= 3*mod) && lieIndex < wmod) { // ctype 3mod, ... ,
-//         4mod-1 = wmod-1
-//              //std::cout << GridLogMessage << "d type " << std::endl;
-//              dIndex = lieIndex - 3*mod;
-//              generatorDtype(dIndex, ta);
-//             return;
-//          }
-//
-//     } //end of generator
-//
-//     template <class cplx>
-//     static void generatorDiagtype(int diagIndex, iSp2nMatrix<cplx> &ta) {
-//
-//         // ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan
-//         subalgebra
-//
-//         ta = Zero();
-//         RealD nrm = 1.0 / 2;
-//
-//         ta()()(diagIndex,diagIndex) = nrm;
-//         ta()()(diagIndex+nsp,diagIndex+nsp) = -nrm;
-//     }
-//
-//     template <class cplx>
-//     static void generatorAtype(int aIndex, iSp2nMatrix<cplx> &ta) {
-//
-//         // ta(i,j) = ta(j,i) = -ta(i+N,j+N) = -ta(j+N,i+N) = 1 / 2 sqrt(2)
-//         // with i<j and i=0,...,N-2
-//         // follows that j=i+1, ... , N
-//         int i1, i2;
-//         ta = Zero();
-//         RealD nrm = 1 / (2 * std::sqrt(2) );
-//
-//         su2SubGroupIndex(i1, i2, aIndex);
-//         ta()()(i1,i2) = 1;
-//         ta()()(i2,i1) = 1;
-//         ta()()(i1+nsp,i2+nsp) = -1;
-//         ta()()(i2+nsp,i1+nsp) = -1;
-//
-//         ta = ta * nrm;
-//     }
-//
-//     template <class cplx>
-//     static void generatorBtype(int bIndex, iSp2nMatrix<cplx> &ta) {
-//
-//         // ta(i,j) = -ta(j,i) = ta(i+N,j+N) = -ta(j+N,i+N) = i / 1/ 2 sqrt(2)
-//         // with i<j and i=0,...,N-2
-//         // follows that j=i+1, ... , N-1
-//
-//         int i1, i2;
-//         ta = Zero();
-//         cplx i(0.0, 1.0);
-//         RealD nrm = 1 / (2 * std::sqrt(2));
-//         su2SubGroupIndex(i1, i2, bIndex);
-//
-//
-//         ta()()(i1,i2) = i;
-//         ta()()(i2,i1) = -i;
-//         ta()()(i1+nsp,i2+nsp) = i;
-//         ta()()(i2+nsp,i1+nsp) = -i;
-//
-//         ta = ta * nrm;
-//     }
-//
-//     template <class cplx>
-//     static void generatorCtype(int cIndex, iSp2nMatrix<cplx> &ta) {
-//
-//         // ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
-//
-//
-//         int i1, i2;
-//         ta = Zero();
-//         RealD nrm = 1 / (2 * std::sqrt(2) );
-//         su2SubGroupIndex(i1, i2, cIndex);
-//
-//         ta()()(i1,i2+nsp) = 1;
-//         ta()()(i2,i1+nsp) = 1;
-//         ta()()(i1+nsp,i2) = 1;
-//         ta()()(i2+nsp,i1) = 1;
-//
-//         ta = ta * nrm;
-//     }
-//
-//     template <class cplx>
-//     static void generatorDtype(int dIndex, iSp2nMatrix<cplx> &ta) {
-//
-//         // ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i /  2 sqrt(2)
-//
-//         int i1, i2;
-//         ta = Zero();
-//         cplx i(0.0, 1.0);
-//         RealD nrm = 1 / (2 * std::sqrt(2)  );
-//         su2SubGroupIndex(i1, i2, dIndex);
-//
-//         ta()()(i1,i2+nsp) = i;
-//         ta()()(i2,i1+nsp) = i;
-//         ta()()(i1+nsp,i2) = -i;
-//         ta()()(i2+nsp,i1) = -i;
-//
-//         ta = ta * nrm;
-//     }
-//
-//     template <class cplx>
-//      static void generatorWtype(int wIndex, iSp2nMatrix<cplx> &ta) {
-//
-//          // ta(i,i+N) =  ta(i+N,i) = 1/2
-//
-//          ta = Zero();
-//          RealD nrm = 1.0 / 2; //check
-//
-//          ta()()(wIndex,wIndex+nsp) = 1;
-//          ta()()(wIndex+nsp,wIndex) = 1;
-//
-//          ta = ta * nrm;
-//      }
-//
-//     template <class cplx>
-//      static void generatorZtype(int zIndex, iSp2nMatrix<cplx> &ta) {
-//
-//          // ta(i,i+N) = - ta(i+N,i) = i/2
-//
-//          ta = Zero();
-//          RealD nrm = 1.0 / 2; //check
-//          cplx i(0.0, 1.0);
-//          ta()()(zIndex,zIndex+nsp) = i;
-//          ta()()(zIndex+nsp,zIndex) = -i;
-//
-//          ta = ta * nrm;
-//      }
-//
-//
-//     ////////////////////////////////////////////////////////////////////////
-//     // Map a su2 subgroup number to the pair of rows that are non zero
-//     ////////////////////////////////////////////////////////////////////////
-//     static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
-//       assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
-//
-//       int spare = su2_index;
-//       for (i1 = 0; spare >= (nsp - 1 - i1); i1++) {
-//         spare = spare - (nsp - 1 - i1);  // remove the Nc-1-i1 terms
-//       }
-//       i2 = i1 + 1 + spare;
-//     }
-//
-//
-//
-//
-//
-//     static void printGenerators(void) {
-//         for (int gen = 0; gen < AlgebraDimension; gen++) {
-//             Matrix ta;
-//             generator(gen, ta);
-//             std::cout << GridLogMessage << "Nc = " << ncolour << std::endl;
-//             std::cout << GridLogMessage << " t_" << gen << std::endl;
-//             std::cout << GridLogMessage << ta << std::endl;
-//         }
-//     }
-//
-//
-//
-//     static void testGenerators(void) {
-//         Matrix ta;
-//         Matrix tb;
-//         std::cout << GridLogMessage << "Fundamental - Checking trace ta tb is
-//         0.5 delta_ab " << std::endl; for (int a = 0; a < AlgebraDimension;
-//         a++) {
-//             for (int b = 0; b < AlgebraDimension; b++) {
-//                 generator(a,ta);
-//                 generator(b,tb);
-//                 Complex tr = TensorRemove(trace( ta * tb) );
-//                 std::cout << GridLogMessage << "(" << a << "," << b << ") =
-//                 " << tr
-//                 << std::endl;
-//                 if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
-//                 if (a != b) assert(abs(tr) < 1.0e-6);
-//
-//             }
-//         }
-//         std::cout << GridLogMessage << std::endl;
-//         std::cout << GridLogMessage << "Fundamental - Checking if hermitian"
-//         << std::endl; for (int a = 0; a < AlgebraDimension; a++) {
-//             generator(a,ta);
-//             std::cout << GridLogMessage << a << std::endl;
-//             assert(norm2(ta - adj(ta)) < 1.0e-6);
-//         }
-//         std::cout << GridLogMessage << std::endl;
-//         std::cout << GridLogMessage << "Fundamental - Checking if traceless"
-//         << std::endl; for (int a = 0; a < AlgebraDimension; a++) {
-//           generator(a, ta);
-//           Complex tr = TensorRemove(trace(ta));
-//           std::cout << GridLogMessage << a << std::endl;
-//           assert(abs(tr) < 1.0e-6);
-//         }
-//
-//     }
-//
-//
-//     template <typename LatticeMatrixType>
-//     static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out,
-//     double scale = 1.0)
-//     {
-//       GridBase *grid = out.Grid();
-//
-//       typedef typename LatticeMatrixType::vector_type vector_type;
-//       typedef typename LatticeMatrixType::scalar_type scalar_type;
-//
-//       typedef iSinglet<vector_type> vTComplexType;
-//
-//       typedef Lattice<vTComplexType> LatticeComplexType;
-//       typedef typename GridTypeMapper<typename
-//       LatticeMatrixType::vector_object>::scalar_object MatrixType;
-//
-//       LatticeComplexType ca(grid);
-//       LatticeMatrixType lie(grid);
-//       LatticeMatrixType la(grid);
-//       ComplexD ci(0.0, scale);
-//       //    ComplexD cone(1.0, 0.0);
-//       MatrixType ta;
-//
-//       lie = Zero();
-//
-//       for (int a = 0; a < AlgebraDimension; a++) {
-//         random(pRNG, ca);
-//
-//         ca = (ca + conjugate(ca)) * 0.5;
-//         ca = ca - 0.5;
-//
-//         generator(a, ta);
-//
-//         la = ci * ca * ta;
-//
-//         lie = lie + la;  // e^{i la ta}
-//
-//       }
-//       taExp(lie, out);
-//     }
-//
-//
-//     static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
-//     //same as sun
-//                                                     LatticeMatrix &out,
-//                                                     Real scale = 1.0) {
-//       GridBase *grid = out.Grid();
-//       LatticeReal ca(grid);
-//       LatticeMatrix la(grid);
-//       Complex ci(0.0, scale);
-//       Matrix ta;
-//
-//       out = Zero();
-//       for (int a = 0; a < AlgebraDimension; a++) {
-//         gaussian(pRNG, ca);
-//         generator(a, ta);
-//         la = toComplex(ca) * ta;
-//         out += la;
-//       }
-//       out *= ci;
-//     }
-//
-//     static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
-//                                             LatticeMatrix &out,
-//                                             Real scale = 1.0) {
-//       conformable(h, out);
-//       GridBase *grid = out.Grid();
-//       LatticeMatrix la(grid);
-//       Matrix ta;
-//
-//       out = Zero();
-//       for (int a = 0; a < AlgebraDimension; a++) {
-//         generator(a, ta);
-//         la = peekColour(h, a) * timesI(ta) * scale;
-//         out += la;
-//       }
-//     }
-//
-//
-//     template <typename LatticeMatrixType>
-//     static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) { //
-//     same as sun
-//       typedef typename LatticeMatrixType::scalar_type ComplexType;
-//
-//       LatticeMatrixType xn(x.Grid());
-//       RealD nfac = 1.0;
-//
-//       xn = x;
-//       ex = xn + ComplexType(1.0);  // 1+x
-//
-//       // Do a 12th order exponentiation
-//       for (int i = 2; i <= 12; ++i) {
-//         nfac = nfac / RealD(i);  // 1/2, 1/2.3 ...
-//         xn = xn * x;             // x2, x3,x4....
-//         ex = ex + xn * nfac;     // x2/2!, x3/3!....
-//       }
-//     }
-//
-//  static void projectOnAlgebra(LatticeAlgebraVector &h_out, const
-//  LatticeMatrix &in, Real scale = 1.0) {
-//    conformable(h_out, in);
-//    h_out = Zero();
-//    Matrix Ta;
-//
-//    for (int a = 0; a < AlgebraDimension; a++) {
-//      generator(a, Ta);
-//      pokeColour(h_out, - 2.0 * (trace(timesI(Ta) * in)) * scale, a);
-//    }
-//  }
-//
-//
-//     template <typename GaugeField>
-//     static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
-//       typedef typename GaugeField::vector_type vector_type;
-//       typedef iSp2nMatrix<vector_type> vMatrixType;
-//       typedef Lattice<vMatrixType> LatticeMatrixType;
-//
-//       LatticeMatrixType Umu(out.Grid());
-//       for (int mu = 0; mu < Nd; mu++) {
-//         LieRandomize(pRNG, Umu, 1.0);   //def
-//         PokeIndex<LorentzIndex>(out, Umu, mu);
-//       }
-//     }
-//     template<typename GaugeField>
-//     static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out){
-//       typedef typename GaugeField::vector_type vector_type;
-//       typedef iSp2nMatrix<vector_type> vMatrixType;
-//       typedef Lattice<vMatrixType> LatticeMatrixType;
-//
-//       LatticeMatrixType Umu(out.Grid());
-//       for(int mu=0;mu<Nd;mu++){
-//         LieRandomize(pRNG,Umu,0.01);    //def
-//         PokeIndex<LorentzIndex>(out,Umu,mu);
-//       }
-//     }
-//
-//     template<typename GaugeField>
-//     static void ColdConfiguration(GaugeField &out){
-//       typedef typename GaugeField::vector_type vector_type;
-//       typedef iSp2nMatrix<vector_type> vMatrixType;
-//       typedef Lattice<vMatrixType> LatticeMatrixType;
-//
-//       LatticeMatrixType Umu(out.Grid());
-//       Umu=1.0;
-//       for(int mu=0;mu<Nd;mu++){
-//         PokeIndex<LorentzIndex>(out,Umu,mu);
-//       }
-//     }
-//     template<typename GaugeField>
-//     static void ColdConfiguration(GridParallelRNG &pRNG,GaugeField &out){
-//       ColdConfiguration(out);
-//     }
-//
-//     static void OmegaInvariance(ColourMatrix &in)
-//     {
-//
-//         ColourMatrix Omega;
-//         Omega = Zero();
-//
-//         std::cout << GridLogMessage << "I am a ColourMatrix" << std::endl;
-//
-//         //for (int i = 0; i < ncolour; i++)         wrong?!
-//         //{
-//         //    Omega()()(i, 2*ncolour-1-i) = 1.;
-//         //    Omega()()(2*ncolour-1-i, i) = -1;
-//         //}
-//         for (int i = 0; i < nsp; i++)
-//         {
-//             Omega()()(i, nsp+i) = 1.;
-//             Omega()()(nsp+i, i) = -1;
-//         }
-//
-//         auto diff = Omega - (in * Omega * transpose(in) );
-//         auto sdiff = norm2(diff);
-//         if (norm2(sdiff) < 1e-8)
-//         {
-//             std::cout << GridLogMessage << "Symplectic condition satisfied:
-//             Omega invariant" << std::endl;
-//         } else {
-//             std::cout << GridLogMessage << "WARNING!!!!!! Matrix Omega NOT
-//             left invariant by " << norm2(sdiff) << std::endl;
-//         }
-//
-//     }
-//
-//     template<typename GaugeField>
-//     static void OmegaInvariance(GaugeField &in)
-//     {
-//         typedef typename GaugeField::vector_type vector_type;
-//         typedef iSp2nMatrix<vector_type> vMatrixType;
-//         typedef Lattice<vMatrixType> LatticeMatrixType;
-//
-//         LatticeMatrixType U(in.Grid());
-//         LatticeMatrixType OmegaLatt(in.Grid());
-//         LatticeMatrixType identity(in.Grid());
-//         RealD vol = in.Grid()->gSites();
-//         ColourMatrix Omega;
-//
-//         OmegaLatt = Zero();
-//         Omega = Zero();
-//         identity = 1.;
-//
-//         std::cout << GridLogMessage << "I am a GaugeField " << std::endl;
-//
-//         U = PeekIndex<LorentzIndex>(in,1);
-//
-//         OmegaInvariance(U);
-//
-//     }
-//
-//        static void OmegaInvariance(LatticeColourMatrixD &in)
-//        {
-//
-//            LatticeColourMatrixD OmegaLatt(in.Grid());
-//            LatticeColourMatrixD identity(in.Grid());
-//            RealD vol = in.Grid()->gSites();
-//            ColourMatrix Omega;
-//
-//            OmegaLatt = Zero();
-//            Omega = Zero();
-//            identity = 1.;
-//
-//            std::cout << GridLogMessage << "I am a LatticeColourMatrix " <<
-//            std::endl;
-//
-//            for (int i = 0; i < nsp; i++)
-//            {
-//                Omega()()(i, nsp+i) = 1.;
-//                Omega()()(nsp+i, i) = -1;
-//            }
-//
-//            std::cout << GridLogMessage << "Omega = " << Omega()() <<
-//            std::endl; OmegaLatt = OmegaLatt + (identity*Omega);
-//
-//            auto diff = OmegaLatt - (in*OmegaLatt*transpose(in));
-//            auto sdiff = sum(diff);
-//            //assert( norm2(sdiff) < 1e-8 );
-//            if (norm2(sdiff) < 1e-8)
-//            {
-//                std::cout << GridLogMessage << "Symplectic condition
-//                satisfied: Omega invariant" << std::endl;
-//            } else {
-//                std::cout << GridLogMessage << "WARNING!!!!!! Matrix Omega NOT
-//                left invariant by " << norm2(sdiff) << std::endl;
-//            }
-//
-//
-//        }
-//
-//
-// }; // end of class Sp
-
-template <int N>
-static void ProjectSp2n(
-    Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
-  Umu = ProjectOnSpGroup(Umu);
-  auto det = Determinant(Umu);  // ok ?
-
-  det = conjugate(det);
-
-  for (int i = 0; i < N; i++) {
-    auto element = PeekIndex<ColourIndex>(Umu, N - 1, i);
-    element = element * det;
-    PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
-  }
-}
-template <int N>
-static void ProjectSp2n(
-    Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
-  GridBase *grid = U.Grid();
-  for (int mu = 0; mu < Nd; mu++) {
-    auto Umu = PeekIndex<LorentzIndex>(U, mu);
-    Umu = ProjectOnSpGroup(Umu);
-    ProjectSp2n(Umu);
-    PokeIndex<LorentzIndex>(U, Umu, mu);
-  }
-}
-
-typedef Sp<2> Sp2;
-typedef Sp<4> Sp4;
-typedef Sp<6> Sp6;
-typedef Sp<8> Sp8;
-
-NAMESPACE_END(Grid);
-#endif
diff --git a/Grid/qcd/utils/Utils.h b/Grid/qcd/utils/Utils.h
index c654ce18..256fd18e 100644
--- a/Grid/qcd/utils/Utils.h
+++ b/Grid/qcd/utils/Utils.h
@@ -9,7 +9,6 @@
 
 // Include representations
 #include <Grid/qcd/utils/SUn.h>
-#include <Grid/qcd/utils/Sp2n.h>
 #include <Grid/qcd/utils/SUnAdjoint.h>
 #include <Grid/qcd/utils/SUnTwoIndex.h>
 #include <Grid/qcd/utils/Sp2nTwoIndex.h>
diff --git a/tests/sp2n/Test_sp2n_lie_gen.cc b/tests/sp2n/Test_sp2n_lie_gen.cc
index 6c3766e6..5c6430a3 100644
--- a/tests/sp2n/Test_sp2n_lie_gen.cc
+++ b/tests/sp2n/Test_sp2n_lie_gen.cc
@@ -1,8 +1,4 @@
-
-
-
 #include <Grid/Grid.h>
-#include <Grid/qcd/utils/Sp2n.h>
 
 using namespace Grid;
 

From 505fa49983c6745d1819a3f49da6ebd9e63e9511 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 30 Nov 2022 17:09:48 +0000
Subject: [PATCH 042/129] Renamed SUn.h -> GaugeGroup.h

---
 Grid/qcd/utils/{SUn.h => GaugeGroup.h} | 0
 Grid/qcd/utils/Utils.h                 | 2 +-
 tests/core/Test_lie_generators.cc      | 2 +-
 3 files changed, 2 insertions(+), 2 deletions(-)
 rename Grid/qcd/utils/{SUn.h => GaugeGroup.h} (100%)

diff --git a/Grid/qcd/utils/SUn.h b/Grid/qcd/utils/GaugeGroup.h
similarity index 100%
rename from Grid/qcd/utils/SUn.h
rename to Grid/qcd/utils/GaugeGroup.h
diff --git a/Grid/qcd/utils/Utils.h b/Grid/qcd/utils/Utils.h
index 256fd18e..87196cdc 100644
--- a/Grid/qcd/utils/Utils.h
+++ b/Grid/qcd/utils/Utils.h
@@ -8,7 +8,7 @@
 #include <Grid/qcd/utils/ScalarObjs.h>
 
 // Include representations
-#include <Grid/qcd/utils/SUn.h>
+#include <Grid/qcd/utils/GaugeGroup.h>
 #include <Grid/qcd/utils/SUnAdjoint.h>
 #include <Grid/qcd/utils/SUnTwoIndex.h>
 #include <Grid/qcd/utils/Sp2nTwoIndex.h>
diff --git a/tests/core/Test_lie_generators.cc b/tests/core/Test_lie_generators.cc
index e044378c..372e1408 100644
--- a/tests/core/Test_lie_generators.cc
+++ b/tests/core/Test_lie_generators.cc
@@ -32,7 +32,7 @@ directory
 
 #include <Grid/qcd/utils/CovariantCshift.h>
 
-#include <Grid/qcd/utils/SUn.h>
+#include <Grid/qcd/utils/GaugeGroup.h>
 #include <Grid/qcd/utils/SUnAdjoint.h>
 #include <Grid/qcd/utils/SUnTwoIndex.h>
 

From 0af7d5a793f7052a95e716ecbc5e8f125ac12101 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 30 Nov 2022 17:12:00 +0000
Subject: [PATCH 043/129] Rename Grid/qcd/utils/<Group>_impl.h ->
 Grid/qcd/utils/<Group>.h

---
 Grid/qcd/utils/GaugeGroup.h            | 4 ++--
 Grid/qcd/utils/{SUn_impl.h => SUn.h}   | 0
 Grid/qcd/utils/{Sp2n_impl.h => Sp2n.h} | 0
 3 files changed, 2 insertions(+), 2 deletions(-)
 rename Grid/qcd/utils/{SUn_impl.h => SUn.h} (100%)
 rename Grid/qcd/utils/{Sp2n_impl.h => Sp2n.h} (100%)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index 88476f47..24b89945 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -143,8 +143,8 @@ class GaugeGroup {
   typedef Lattice<vSU2MatrixF> LatticeSU2MatrixF;
   typedef Lattice<vSU2MatrixD> LatticeSU2MatrixD;
 
-#include "Grid/qcd/utils/SUn_impl.h"
-#include "Grid/qcd/utils/Sp2n_impl.h"
+#include "Grid/qcd/utils/SUn.h"
+#include "Grid/qcd/utils/Sp2n.h"
 
  public:
   template <class cplx>
diff --git a/Grid/qcd/utils/SUn_impl.h b/Grid/qcd/utils/SUn.h
similarity index 100%
rename from Grid/qcd/utils/SUn_impl.h
rename to Grid/qcd/utils/SUn.h
diff --git a/Grid/qcd/utils/Sp2n_impl.h b/Grid/qcd/utils/Sp2n.h
similarity index 100%
rename from Grid/qcd/utils/Sp2n_impl.h
rename to Grid/qcd/utils/Sp2n.h

From 92ad5b8f74448959c40780ab8d0608f8693aaa9b Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Sun, 18 Dec 2022 15:50:19 +0000
Subject: [PATCH 044/129] Compiler error fix: NVCC requires names for templ.
 par.

---
 Grid/qcd/utils/GaugeGroup.h | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index 24b89945..dc2c99c1 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -32,15 +32,17 @@ directory
 #ifndef QCD_UTIL_SUN_H
 #define QCD_UTIL_SUN_H
 
+// Important detail: nvcc requires all template parameters to have names.
+// This is the only reason why the second template parameter has a name.
 #define ONLY_IF_SU                                                       \
   typename dummy_name = group_name,                                      \
-           typename = std::enable_if_t <                                 \
+           typename named_dummy = std::enable_if_t <                                 \
                           std::is_same<dummy_name, group_name>::value && \
                       is_su<dummy_name>::value >
 
 #define ONLY_IF_Sp                                                       \
   typename dummy_name = group_name,                                      \
-           typename = std::enable_if_t <                                 \
+           typename named_dummy = std::enable_if_t <                                 \
                           std::is_same<dummy_name, group_name>::value && \
                       is_sp<dummy_name>::value >
 

From 37b6b82869f9b1a86fae5c3e592076a56e91a841 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Sun, 18 Dec 2022 16:12:56 +0000
Subject: [PATCH 045/129] Fix file extensions

---
 Grid/qcd/utils/GaugeGroup.h          |  6 +++---
 Grid/qcd/utils/{SUn.h => SUn.impl}   |  3 +++
 Grid/qcd/utils/{Sp2n.h => Sp2n.impl} | 10 ++++++++++
 3 files changed, 16 insertions(+), 3 deletions(-)
 rename Grid/qcd/utils/{SUn.h => SUn.impl} (99%)
 rename Grid/qcd/utils/{Sp2n.h => Sp2n.impl} (96%)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index dc2c99c1..ecd92780 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -2,7 +2,7 @@
 
 Grid physics library, www.github.com/paboyle/Grid
 
-Source file: ./lib/qcd/utils/SUn.h
+Source file: ./lib/qcd/utils/GaugeGroup.h
 
 Copyright (C) 2015
 
@@ -145,8 +145,8 @@ class GaugeGroup {
   typedef Lattice<vSU2MatrixF> LatticeSU2MatrixF;
   typedef Lattice<vSU2MatrixD> LatticeSU2MatrixD;
 
-#include "Grid/qcd/utils/SUn.h"
-#include "Grid/qcd/utils/Sp2n.h"
+#include "Grid/qcd/utils/SUn.impl"
+#include "Grid/qcd/utils/Sp2n.impl"
 
  public:
   template <class cplx>
diff --git a/Grid/qcd/utils/SUn.h b/Grid/qcd/utils/SUn.impl
similarity index 99%
rename from Grid/qcd/utils/SUn.h
rename to Grid/qcd/utils/SUn.impl
index 61b19fbc..eaf82877 100644
--- a/Grid/qcd/utils/SUn.h
+++ b/Grid/qcd/utils/SUn.impl
@@ -5,6 +5,9 @@
 // class GaugeGroup {
 //
 // around it.
+//
+// Please note that the unconventional file extension makes sure that it
+// doesn't get found by the scripts/filelist during bootstrapping.
 
 private:
 static int su2subgroups(GroupName::SU) { return (ncolour * (ncolour - 1)) / 2; }
diff --git a/Grid/qcd/utils/Sp2n.h b/Grid/qcd/utils/Sp2n.impl
similarity index 96%
rename from Grid/qcd/utils/Sp2n.h
rename to Grid/qcd/utils/Sp2n.impl
index 6d559c0a..c8ed2ddc 100644
--- a/Grid/qcd/utils/Sp2n.h
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -1,3 +1,13 @@
+// This file is #included into the body of the class template definition of
+// GaugeGroup. So, image there to be
+//
+// template <int ncolour, class group_name>
+// class GaugeGroup {
+//
+// around it.
+//
+// Please note that the unconventional file extension makes sure that it
+// doesn't get found by the scripts/filelist during bootstrapping.
 
 private:
 static int su2subgroups(GroupName::Sp) { return (ncolour/2 * (ncolour/2 - 1)) / 2; }

From b10e1b7bc8bec809f874e9e48a3ccc7b2619c9d1 Mon Sep 17 00:00:00 2001
From: Niccolo Forzano <s.2227764@sl2.sunbird.supercomputingwales.ac.uk>
Date: Wed, 18 Jan 2023 18:04:47 +0000
Subject: [PATCH 046/129] Fixed files giving zero force computation on GPU,
 issue #8

---
 Grid/qcd/utils/SUnAdjoint.h   | 3 +--
 Grid/qcd/utils/SUnTwoIndex.h  | 3 +--
 Grid/qcd/utils/Sp2nTwoIndex.h | 3 +--
 3 files changed, 3 insertions(+), 6 deletions(-)

diff --git a/Grid/qcd/utils/SUnAdjoint.h b/Grid/qcd/utils/SUnAdjoint.h
index 18d6b875..c03036ef 100644
--- a/Grid/qcd/utils/SUnAdjoint.h
+++ b/Grid/qcd/utils/SUnAdjoint.h
@@ -133,8 +133,7 @@ public:
 
     for (int a = 0; a < Dimension; a++) {
       generator(a, iTa);
-      LatticeComplex tmp = real(trace(iTa * in)) * coefficient;
-      pokeColour(h_out, tmp, a);
+      pokeColour(h_out, real(trace(iTa * in)) * coefficient, a);
     }
   }
 
diff --git a/Grid/qcd/utils/SUnTwoIndex.h b/Grid/qcd/utils/SUnTwoIndex.h
index cd440c26..50ddf5c1 100644
--- a/Grid/qcd/utils/SUnTwoIndex.h
+++ b/Grid/qcd/utils/SUnTwoIndex.h
@@ -224,8 +224,7 @@ public:
     // 2/(Nc +/- 2) for the normalization of the trace in the two index rep
     for (int a = 0; a < ncolour * ncolour - 1; a++) {
       generator(a, i2indTa);
-      auto tmp = real(trace(i2indTa * in)) * coefficient;
-      pokeColour(h_out, tmp, a);
+      pokeColour(h_out, real(trace(i2indTa * in)) * coefficient, a);
     }
   }
 
diff --git a/Grid/qcd/utils/Sp2nTwoIndex.h b/Grid/qcd/utils/Sp2nTwoIndex.h
index 60739551..474c7794 100644
--- a/Grid/qcd/utils/Sp2nTwoIndex.h
+++ b/Grid/qcd/utils/Sp2nTwoIndex.h
@@ -273,8 +273,7 @@ public:
     // 2/(Nc +/- 2) for the normalization of the trace in the two index rep
     for (int a = 0; a < NumGenerators; a++) {
       generator(a, i2indTa);
-      auto tmp = real(trace(i2indTa * in)) * coefficient;
-      pokeColour(h_out, tmp, a);
+     pokeColour(h_out, real(trace(i2indTa * in)) * coefficient, a);
     }
   }
 

From f51222086c3cc795808a0adaa820db0245d6c48b Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Thu, 9 Mar 2023 16:22:20 +0000
Subject: [PATCH 047/129] Move functions from GaugeGroup to group specific
 implementations

---
 Grid/qcd/utils/GaugeGroup.h |  94 +++---------------------------
 Grid/qcd/utils/SUn.impl     | 113 ++++++++++++++++++++++++++++++++++++
 Grid/qcd/utils/Sp2n.impl    | 113 ++++++++++++++++++++++++++++++++++++
 3 files changed, 235 insertions(+), 85 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index ecd92780..f0442e2f 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -170,118 +170,40 @@ class GaugeGroup {
     }
   }
 
-  // reunitarise??
   template <typename LatticeMatrixType>
   static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out,
                            double scale = 1.0) {
-    GridBase *grid = out.Grid();
-
-    typedef typename LatticeMatrixType::vector_type vector_type;
-    typedef typename LatticeMatrixType::scalar_type scalar_type;
-
-    typedef iSinglet<vector_type> vTComplexType;
-
-    typedef Lattice<vTComplexType> LatticeComplexType;
-    typedef typename GridTypeMapper<
-        typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
-
-    LatticeComplexType ca(grid);
-    LatticeMatrixType lie(grid);
-    LatticeMatrixType la(grid);
-    ComplexD ci(0.0, scale);
-    //    ComplexD cone(1.0, 0.0);
-    MatrixType ta;
-
-    lie = Zero();
-
-    for (int a = 0; a < AdjointDimension; a++) {
-      random(pRNG, ca);
-
-      ca = (ca + conjugate(ca)) * 0.5;
-      ca = ca - 0.5;
-
-      generator(a, ta);
-
-      la = ci * ca * ta;
-
-      lie = lie + la;  // e^{i la ta}
-    }
-    taExp(lie, out);
+    LieRandomize(pRNG, out, group_name(), scale);
   }
 
   static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
                                                   LatticeMatrix &out,
                                                   Real scale = 1.0) {
-    GridBase *grid = out.Grid();
-    LatticeReal ca(grid);
-    LatticeMatrix la(grid);
-    Complex ci(0.0, scale);
-    Matrix ta;
-
-    out = Zero();
-    for (int a = 0; a < AdjointDimension; a++) {
-      gaussian(pRNG, ca);
-      generator(a, ta);
-      la = toComplex(ca) * ta;
-      out += la;
-    }
-    out *= ci;
+      GaussianFundamentalLieAlgebraMatrix(pRNG, out, group_name(), scale);
   }
 
   static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
                                           LatticeMatrix &out,
                                           Real scale = 1.0) {
-    conformable(h, out);
-    GridBase *grid = out.Grid();
-    LatticeMatrix la(grid);
-    Matrix ta;
-
-    out = Zero();
-    for (int a = 0; a < AdjointDimension; a++) {
-      generator(a, ta);
-      la = peekColour(h, a) * timesI(ta) * scale;
-      out += la;
-    }
+      FundamentalLieAlgebraMatrix(h, out, group_name(), scale);
   }
 
   // Projects the algebra components a lattice matrix (of dimension ncol*ncol -1
   // ) inverse operation: FundamentalLieAlgebraMatrix
   static void projectOnAlgebra(LatticeAlgebraVector &h_out,
                                const LatticeMatrix &in, Real scale = 1.0) {
-    conformable(h_out, in);
-    h_out = Zero();
-    Matrix Ta;
-
-    for (int a = 0; a < AdjointDimension; a++) {
-      generator(a, Ta);
-      pokeColour(h_out, -2.0 * (trace(timesI(Ta) * in)) * scale, a);
-    }
+      projectOnAlgebra(h_out, in, group_name(), scale);
   }
 
   template <typename GaugeField>
   static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
-    typedef typename GaugeField::vector_type vector_type;
-    typedef iGroupMatrix<vector_type> vMatrixType;
-    typedef Lattice<vMatrixType> LatticeMatrixType;
-
-    LatticeMatrixType Umu(out.Grid());
-    for (int mu = 0; mu < Nd; mu++) {
-      LieRandomize(pRNG, Umu, 1.0);
-      PokeIndex<LorentzIndex>(out, Umu, mu);
-    }
+      HotConfiguration(pRNG, out, group_name());
   }
   template <typename GaugeField>
   static void TepidConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
-    typedef typename GaugeField::vector_type vector_type;
-    typedef iGroupMatrix<vector_type> vMatrixType;
-    typedef Lattice<vMatrixType> LatticeMatrixType;
-
-    LatticeMatrixType Umu(out.Grid());
-    for (int mu = 0; mu < Nd; mu++) {
-      LieRandomize(pRNG, Umu, 0.01);
-      PokeIndex<LorentzIndex>(out, Umu, mu);
-    }
+      TepidConfiguration(pRNG, out, group_name());
   }
+    
   template <typename GaugeField>
   static void ColdConfiguration(GaugeField &out) {
     typedef typename GaugeField::vector_type vector_type;
@@ -294,6 +216,7 @@ class GaugeGroup {
       PokeIndex<LorentzIndex>(out, Umu, mu);
     }
   }
+    
   template <typename GaugeField>
   static void ColdConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
     ColdConfiguration(out);
@@ -303,6 +226,7 @@ class GaugeGroup {
   static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out) {
     out = Ta(in);
   }
+    
   template <typename LatticeMatrixType>
   static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) {
     typedef typename LatticeMatrixType::scalar_type ComplexType;
diff --git a/Grid/qcd/utils/SUn.impl b/Grid/qcd/utils/SUn.impl
index eaf82877..eef039c7 100644
--- a/Grid/qcd/utils/SUn.impl
+++ b/Grid/qcd/utils/SUn.impl
@@ -508,6 +508,119 @@ static void testGenerators(GroupName::SU) {
   std::cout << GridLogMessage << std::endl;
 }
 
+template <typename LatticeMatrixType>
+static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out, GroupName::SU,
+                         double scale = 1.0) {
+  GridBase *grid = out.Grid();
+
+  typedef typename LatticeMatrixType::vector_type vector_type;
+  typedef typename LatticeMatrixType::scalar_type scalar_type;
+
+  typedef iSinglet<vector_type> vTComplexType;
+
+  typedef Lattice<vTComplexType> LatticeComplexType;
+  typedef typename GridTypeMapper<
+      typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
+
+  LatticeComplexType ca(grid);
+  LatticeMatrixType lie(grid);
+  LatticeMatrixType la(grid);
+  ComplexD ci(0.0, scale);
+  //    ComplexD cone(1.0, 0.0);
+  MatrixType ta;
+
+  lie = Zero();
+
+  for (int a = 0; a < AdjointDimension; a++) {
+    random(pRNG, ca);
+
+    ca = (ca + conjugate(ca)) * 0.5;
+    ca = ca - 0.5;
+
+    generator(a, ta);
+
+    la = ci * ca * ta;
+
+    lie = lie + la;  // e^{i la ta}
+  }
+  taExp(lie, out);
+}
+
+static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
+                                                LatticeMatrix &out, GroupName::SU,
+                                                Real scale = 1.0) {
+  GridBase *grid = out.Grid();
+  LatticeReal ca(grid);
+  LatticeMatrix la(grid);
+  Complex ci(0.0, scale);
+  Matrix ta;
+
+  out = Zero();
+  for (int a = 0; a < AdjointDimension; a++) {
+    gaussian(pRNG, ca);
+    generator(a, ta);
+    la = toComplex(ca) * ta;
+    out += la;
+  }
+  out *= ci;
+}
+
+static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
+                                        LatticeMatrix &out, GroupName::SU,
+                                        Real scale = 1.0) {
+  conformable(h, out);
+  GridBase *grid = out.Grid();
+  LatticeMatrix la(grid);
+  Matrix ta;
+
+  out = Zero();
+  for (int a = 0; a < AdjointDimension; a++) {
+    generator(a, ta);
+    la = peekColour(h, a) * timesI(ta) * scale;
+    out += la;
+  }
+}
+
+template <typename GaugeField>
+static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out, GroupName::SU) {
+  typedef typename GaugeField::vector_type vector_type;
+  typedef iGroupMatrix<vector_type> vMatrixType;
+  typedef Lattice<vMatrixType> LatticeMatrixType;
+
+  LatticeMatrixType Umu(out.Grid());
+  for (int mu = 0; mu < Nd; mu++) {
+    LieRandomize(pRNG, Umu, 1.0);
+    PokeIndex<LorentzIndex>(out, Umu, mu);
+  }
+}
+
+template <typename GaugeField>
+static void TepidConfiguration(GridParallelRNG &pRNG, GaugeField &out, GroupName::SU) {
+  typedef typename GaugeField::vector_type vector_type;
+  typedef iGroupMatrix<vector_type> vMatrixType;
+  typedef Lattice<vMatrixType> LatticeMatrixType;
+
+  LatticeMatrixType Umu(out.Grid());
+  for (int mu = 0; mu < Nd; mu++) {
+    LieRandomize(pRNG, Umu, 0.01);
+    PokeIndex<LorentzIndex>(out, Umu, mu);
+  }
+}
+
+// Projects the algebra components a lattice matrix (of dimension ncol*ncol -1
+// ) inverse operation: FundamentalLieAlgebraMatrix
+static void projectOnAlgebra(LatticeAlgebraVector &h_out,
+                             const LatticeMatrix &in, GroupName::SU, Real scale = 1.0) {
+  conformable(h_out, in);
+  h_out = Zero();
+  Matrix Ta;
+
+  for (int a = 0; a < AdjointDimension; a++) {
+    generator(a, Ta);
+    pokeColour(h_out, -2.0 * (trace(timesI(Ta) * in)) * scale, a);
+  }
+}
+
 /*
  * Fundamental rep gauge xform
  */
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index c8ed2ddc..411235ec 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -253,6 +253,119 @@ static void testGenerators(GroupName::Sp) {
   }
 }
 
+template <typename LatticeMatrixType>
+ static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out, GroupName::Sp,
+                          double scale = 1.0) {
+   GridBase *grid = out.Grid();
+
+   typedef typename LatticeMatrixType::vector_type vector_type;
+   typedef typename LatticeMatrixType::scalar_type scalar_type;
+
+   typedef iSinglet<vector_type> vTComplexType;
+
+   typedef Lattice<vTComplexType> LatticeComplexType;
+   typedef typename GridTypeMapper<
+       typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
+
+   LatticeComplexType ca(grid);
+   LatticeMatrixType lie(grid);
+   LatticeMatrixType la(grid);
+   ComplexD ci(0.0, scale);
+   //    ComplexD cone(1.0, 0.0);
+   MatrixType ta;
+
+   lie = Zero();
+
+   for (int a = 0; a < AdjointDimension; a++) {
+     random(pRNG, ca);
+
+     ca = (ca + conjugate(ca)) * 0.5;
+     ca = ca - 0.5;
+
+     generator(a, ta);
+
+     la = ci * ca * ta;
+
+     lie = lie + la;  // e^{i la ta}
+   }
+   taExp(lie, out);
+ }
+
+static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
+                                                LatticeMatrix &out, GroupName::Sp,
+                                                Real scale = 1.0) {
+  GridBase *grid = out.Grid();
+  LatticeReal ca(grid);
+  LatticeMatrix la(grid);
+  Complex ci(0.0, scale);
+  Matrix ta;
+
+  out = Zero();
+  for (int a = 0; a < AdjointDimension; a++) {
+    gaussian(pRNG, ca);
+    generator(a, ta);
+    la = toComplex(ca) * ta;
+    out += la;
+  }
+  out *= ci;
+}
+
+static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
+                                        LatticeMatrix &out, GroupName::Sp,
+                                        Real scale = 1.0) {
+  conformable(h, out);
+  GridBase *grid = out.Grid();
+  LatticeMatrix la(grid);
+  Matrix ta;
+
+  out = Zero();
+  for (int a = 0; a < AdjointDimension; a++) {
+    generator(a, ta);
+    la = peekColour(h, a) * timesI(ta) * scale;
+    out += la;
+  }
+}
+
+// Projects the algebra components a lattice matrix (of dimension ncol*ncol -1
+// ) inverse operation: FundamentalLieAlgebraMatrix
+static void projectOnAlgebra(LatticeAlgebraVector &h_out,
+                             const LatticeMatrix &in, GroupName::Sp, Real scale = 1.0) {
+  conformable(h_out, in);
+  h_out = Zero();
+  Matrix Ta;
+
+  for (int a = 0; a < AdjointDimension; a++) {
+    generator(a, Ta);
+    pokeColour(h_out, -2.0 * (trace(timesI(Ta) * in)) * scale, a);
+  }
+}
+
+template <typename GaugeField>
+static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out, GroupName::Sp) {
+  typedef typename GaugeField::vector_type vector_type;
+  typedef iGroupMatrix<vector_type> vMatrixType;
+  typedef Lattice<vMatrixType> LatticeMatrixType;
+
+  LatticeMatrixType Umu(out.Grid());
+  for (int mu = 0; mu < Nd; mu++) {
+    LieRandomize(pRNG, Umu, 1.0);
+    PokeIndex<LorentzIndex>(out, Umu, mu);
+  }
+}
+
+template <typename GaugeField>
+static void TepidConfiguration(GridParallelRNG &pRNG, GaugeField &out, GroupName::Sp) {
+  typedef typename GaugeField::vector_type vector_type;
+  typedef iGroupMatrix<vector_type> vMatrixType;
+  typedef Lattice<vMatrixType> LatticeMatrixType;
+
+  LatticeMatrixType Umu(out.Grid());
+  for (int mu = 0; mu < Nd; mu++) {
+    LieRandomize(pRNG, Umu, 0.01);
+    PokeIndex<LorentzIndex>(out, Umu, mu);
+  }
+}
+
 public:
 template <ONLY_IF_Sp>
 static void OmegaInvariance(ColourMatrix &in) {

From fd057c838f4788f809b49ce137b33acd6b3a4377 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 10 Mar 2023 12:10:46 +0000
Subject: [PATCH 048/129] add ProjectOnGaugeGroup and ProjectGn to allow future
 templating in GaugeImplTypes

---
 Grid/qcd/utils/GaugeGroup.h | 27 ++++++++++++++++++++++++
 Grid/qcd/utils/SUn.impl     | 41 +++++++++++++++++++++++++++++++++++++
 Grid/qcd/utils/Sp2n.impl    | 41 +++++++++++++++++++++++++++++++++++++
 3 files changed, 109 insertions(+)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index f0442e2f..dea8f985 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -244,6 +244,29 @@ class GaugeGroup {
       ex = ex + xn * nfac;     // x2/2!, x3/3!....
     }
   }
+    
+  template <int N>        // reunitarise, resimplectify...
+  static void ProjectOnGaugeGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
+      ProjectOnGaugeGroup(U, group_name());
+  }
+       
+  template <int N>        // reunitarise, resimplectify...
+  static void ProjectOnGaugeGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
+      ProjectOnGaugeGroup(Umu, group_name());
+  }
+    
+    
+  template <int N>        // reunitarise, resimplectify... previously ProjectSUn
+  static void ProjectGn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
+      ProjectGn(Umu, group_name());
+  }
+
+  template <int N>        // reunitarise, resimplectify... previously ProjectSUn
+  static void ProjectGn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
+      ProjectGn(U, group_name());
+      
+  }
+
 };
 
 template <int N>
@@ -271,6 +294,8 @@ LatticeComplexD Determinant(
   });
   return ret;
 }
+
+
 template <int N>
 static void ProjectSUn(
     Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
@@ -285,6 +310,7 @@ static void ProjectSUn(
     PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
   }
 }
+
 template <int N>
 static void ProjectSUn(
     Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
@@ -297,6 +323,7 @@ static void ProjectSUn(
     PokeIndex<LorentzIndex>(U, Umu, mu);
   }
 }
+
 // Explicit specialisation for SU(3).
 // Explicit specialisation for SU(3).
 static void ProjectSU3(
diff --git a/Grid/qcd/utils/SUn.impl b/Grid/qcd/utils/SUn.impl
index eef039c7..18be96b1 100644
--- a/Grid/qcd/utils/SUn.impl
+++ b/Grid/qcd/utils/SUn.impl
@@ -621,6 +621,47 @@ static void projectOnAlgebra(LatticeAlgebraVector &h_out,
   }
 }
 
+template <int N>
+static void ProjectOnGaugeGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::SU) {
+  Umu = ProjectOnGroup(Umu);
+ }
+
+template <int N>
+static void ProjectOnGaugeGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U, GroupName::SU) {
+  GridBase *grid = U.Grid();
+  // Reunitarise
+  for (int mu = 0; mu < Nd; mu++) {
+    auto Umu = PeekIndex<LorentzIndex>(U, mu);
+    Umu = ProjectOnGroup(Umu);
+  }
+}
+
+template <int N>
+static void ProjectGn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::SU) {
+  Umu = ProjectOnGroup(Umu);
+  auto det = Determinant(Umu);
+
+  det = conjugate(det);
+
+  for (int i = 0; i < N; i++) {
+    auto element = PeekIndex<ColourIndex>(Umu, N - 1, i);
+    element = element * det;
+    PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
+  }
+}
+
+template <int N>
+static void ProjectGn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U, GroupName::SU) {
+  GridBase *grid = U.Grid();
+  // Reunitarise
+  for (int mu = 0; mu < Nd; mu++) {
+    auto Umu = PeekIndex<LorentzIndex>(U, mu);
+    Umu = ProjectOnGroup(Umu);
+    ProjectSUn(Umu);
+    PokeIndex<LorentzIndex>(U, Umu, mu);
+  }
+}
+
 /*
  * Fundamental rep gauge xform
  */
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index 411235ec..44771a14 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -366,6 +366,47 @@ static void TepidConfiguration(GridParallelRNG &pRNG, GaugeField &out, GroupName
   }
 }
 
+template <int N>
+static void ProjectOnGaugeGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::Sp) {
+  Umu = ProjectOnSpGroup(Umu);
+ }
+
+template <int N>
+static void ProjectOnGaugeGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U, GroupName::Sp) {
+  GridBase *grid = U.Grid();
+  // Reunitarise
+  for (int mu = 0; mu < Nd; mu++) {
+    auto Umu = PeekIndex<LorentzIndex>(U, mu);
+    Umu = ProjectOnSpGroup(Umu);
+  }
+}
+
+template <int N>
+static void ProjectGn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::Sp) {
+  Umu = ProjectOnSpGroup(Umu);
+  auto det = Determinant(Umu);
+
+  det = conjugate(det);
+
+  for (int i = 0; i < N; i++) {
+    auto element = PeekIndex<ColourIndex>(Umu, N - 1, i);
+    element = element * det;
+    PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
+  }
+}
+
+template <int N>
+static void ProjectGn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U, GroupName::Sp) {
+  GridBase *grid = U.Grid();
+  // Reunitarise
+  for (int mu = 0; mu < Nd; mu++) {
+    auto Umu = PeekIndex<LorentzIndex>(U, mu);
+    Umu = ProjectOnSpGroup(Umu);
+    ProjectSUn(Umu);
+    PokeIndex<LorentzIndex>(U, Umu, mu);
+  }
+}
+
 public:
 template <ONLY_IF_Sp>
 static void OmegaInvariance(ColourMatrix &in) {

From 29586f6b5ee09bc21b61f00230ec16d9b881e83a Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Mon, 13 Mar 2023 08:17:14 +0000
Subject: [PATCH 049/129] Deactivate some tests for Nc!=3

---
 tests/core/Test_lie_generators.cc | 2 ++
 tests/core/Test_reunitarise.cc    | 2 ++
 2 files changed, 4 insertions(+)

diff --git a/tests/core/Test_lie_generators.cc b/tests/core/Test_lie_generators.cc
index 372e1408..a49dbca1 100644
--- a/tests/core/Test_lie_generators.cc
+++ b/tests/core/Test_lie_generators.cc
@@ -28,6 +28,7 @@ See the full license in the file "LICENSE" in the top level distribution
 directory
 *************************************************************************************/
 /*  END LEGAL */
+#if Nc==3
 #include <Grid/Grid.h>
 
 #include <Grid/qcd/utils/CovariantCshift.h>
@@ -530,3 +531,4 @@ int main(int argc, char** argv) {
   
   Grid_finalize();
 }
+#endif
diff --git a/tests/core/Test_reunitarise.cc b/tests/core/Test_reunitarise.cc
index 6644be1a..0ff8ec7e 100644
--- a/tests/core/Test_reunitarise.cc
+++ b/tests/core/Test_reunitarise.cc
@@ -26,6 +26,7 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     See the full license in the file "LICENSE" in the top level distribution directory
     *************************************************************************************/
     /*  END LEGAL */
+#if Nc==3
 #include <Grid/Grid.h>
 
 using namespace std;
@@ -143,3 +144,4 @@ int main (int argc, char ** argv)
 
 
 
+#endif

From d6ff644aab51e0e33a8efbfc3b7a862622fd2598 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 14 Mar 2023 10:43:25 +0000
Subject: [PATCH 050/129] Towards the day all tests compile

---
 tests/core/Test_lie_generators.cc    | 113 +++++++++++++--------------
 tests/core/Test_reunitarise.cc       |  10 +--
 tests/solver/Test_coarse_even_odd.cc |   2 +-
 3 files changed, 62 insertions(+), 63 deletions(-)

diff --git a/tests/core/Test_lie_generators.cc b/tests/core/Test_lie_generators.cc
index a49dbca1..5b044061 100644
--- a/tests/core/Test_lie_generators.cc
+++ b/tests/core/Test_lie_generators.cc
@@ -28,7 +28,7 @@ See the full license in the file "LICENSE" in the top level distribution
 directory
 *************************************************************************************/
 /*  END LEGAL */
-#if Nc==3
+
 #include <Grid/Grid.h>
 
 #include <Grid/qcd/utils/CovariantCshift.h>
@@ -43,11 +43,11 @@ directory
 
 using namespace std;
 using namespace Grid;
- ;
+
 
 int main(int argc, char** argv) {
   Grid_init(&argc, &argv);
-
+    
   std::vector<int> latt({4, 4, 4, 8});
   GridCartesian* grid = SpaceTimeGrid::makeFourDimGrid(
       latt, GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
@@ -67,7 +67,7 @@ int main(int argc, char** argv) {
 
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
-  std::cout << GridLogMessage << "* Generators for SU(Nc" << std::endl;
+  std::cout << GridLogMessage << "* Generators for SU(3)" << std::endl;
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
   SU3::printGenerators();
@@ -88,22 +88,22 @@ int main(int argc, char** argv) {
   // Projectors 
   GridParallelRNG gridRNG(grid);
   gridRNG.SeedFixedIntegers(std::vector<int>({45,12,81,9}));
-  SU3Adjoint::LatticeAdjMatrix Gauss(grid);
-  SU3::LatticeAlgebraVector ha(grid);
-  SU3::LatticeAlgebraVector hb(grid);
+  SU_Adjoint<Nc>::LatticeAdjMatrix Gauss(grid);
+  SU<Nc>::LatticeAlgebraVector ha(grid);
+  SU<Nc>::LatticeAlgebraVector hb(grid);
   random(gridRNG,Gauss);
 
   std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
-  SU3Adjoint::projectOnAlgebra(ha, Gauss);
+  SU_Adjoint<Nc>::projectOnAlgebra(ha, Gauss);
   std::cout << GridLogMessage << "end projectOnAlgebra" << std::endl;
   std::cout << GridLogMessage << "Start projector" << std::endl;
-  SU3Adjoint::projector(hb, Gauss);
+  SU_Adjoint<Nc>::projector(hb, Gauss);
   std::cout << GridLogMessage << "end projector" << std::endl;
 
   std::cout << GridLogMessage << "ReStart projector" << std::endl;
-  SU3Adjoint::projector(hb, Gauss);
+  SU_Adjoint<Nc>::projector(hb, Gauss);
   std::cout << GridLogMessage << "end projector" << std::endl;
-  SU3::LatticeAlgebraVector diff = ha -hb;
+  SU<Nc>::LatticeAlgebraVector diff = ha -hb;
   std::cout << GridLogMessage << "Difference: " << norm2(diff) << std::endl;
 
 
@@ -115,8 +115,8 @@ int main(int argc, char** argv) {
 
   
   LatticeGaugeField U(grid), V(grid);
-  SU3::HotConfiguration<LatticeGaugeField>(gridRNG, U);
-  SU3::HotConfiguration<LatticeGaugeField>(gridRNG, V);
+  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, U);
+  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, V);
 
   // Adjoint representation
   // Test group structure
@@ -124,8 +124,8 @@ int main(int argc, char** argv) {
   LatticeGaugeField UV(grid);
   UV = Zero();
   for (int mu = 0; mu < Nd; mu++) {
-    SU3::LatticeMatrix Umu = peekLorentz(U,mu);
-    SU3::LatticeMatrix Vmu = peekLorentz(V,mu);
+    SU<Nc>::LatticeMatrix Umu = peekLorentz(U,mu);
+    SU<Nc>::LatticeMatrix Vmu = peekLorentz(V,mu);
     pokeLorentz(UV,Umu*Vmu, mu);
   }
 
@@ -152,16 +152,16 @@ int main(int argc, char** argv) {
 
   // Check correspondence of algebra and group transformations
   // Create a random vector
-  SU3::LatticeAlgebraVector h_adj(grid);
+  SU<Nc>::LatticeAlgebraVector h_adj(grid);
   typename AdjointRep<Nc>::LatticeMatrix Ar(grid);
   random(gridRNG,h_adj);
   h_adj = real(h_adj);
   SU_Adjoint<Nc>::AdjointLieAlgebraMatrix(h_adj,Ar);
 
   // Re-extract h_adj
-  SU3::LatticeAlgebraVector h_adj2(grid);
+  SU<Nc>::LatticeAlgebraVector h_adj2(grid);
   SU_Adjoint<Nc>::projectOnAlgebra(h_adj2, Ar);
-  SU3::LatticeAlgebraVector h_diff = h_adj - h_adj2;
+  SU<Nc>::LatticeAlgebraVector h_diff = h_adj - h_adj2;
   std::cout << GridLogMessage << "Projections structure check vector difference (Adjoint representation) : " << norm2(h_diff) << std::endl;
 
   // Exponentiate
@@ -184,14 +184,14 @@ int main(int argc, char** argv) {
       
 
   // Construct the fundamental matrix in the group
-  SU3::LatticeMatrix Af(grid);
-  SU3::FundamentalLieAlgebraMatrix(h_adj,Af);
-  SU3::LatticeMatrix Ufund(grid);
+  SU<Nc>::LatticeMatrix Af(grid);
+  SU<Nc>::FundamentalLieAlgebraMatrix(h_adj,Af);
+  SU<Nc>::LatticeMatrix Ufund(grid);
   Ufund  = expMat(Af, 1.0, 16);
   // Check unitarity
-  SU3::LatticeMatrix uno_f(grid);
+  SU<Nc>::LatticeMatrix uno_f(grid);
   uno_f = 1.0;
-  SU3::LatticeMatrix UnitCheck(grid);
+  SU<Nc>::LatticeMatrix UnitCheck(grid);
   UnitCheck = Ufund * adj(Ufund) - uno_f;
   std::cout << GridLogMessage << "unitarity check 1: " << norm2(UnitCheck)
             << std::endl;
@@ -261,20 +261,20 @@ int main(int argc, char** argv) {
   std::cout << GridLogMessage << "Test for the Two Index Symmetric projectors"
       << std::endl;
   // Projectors 
-  SU3TwoIndexSymm::LatticeTwoIndexMatrix Gauss2(grid);
+  SU_TwoIndex<Nc, Symmetric>::LatticeTwoIndexMatrix Gauss2(grid);
   random(gridRNG,Gauss2);
   
   std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
-  SU3TwoIndexSymm::projectOnAlgebra(ha, Gauss2);
+  SU_TwoIndex<Nc, Symmetric>::projectOnAlgebra(ha, Gauss2);
   std::cout << GridLogMessage << "end projectOnAlgebra" << std::endl;
   std::cout << GridLogMessage << "Start projector" << std::endl;
-  SU3TwoIndexSymm::projector(hb, Gauss2);
+  SU_TwoIndex<Nc, Symmetric>::projector(hb, Gauss2);
   std::cout << GridLogMessage << "end projector" << std::endl;
   
   std::cout << GridLogMessage << "ReStart projector" << std::endl;
-  SU3TwoIndexSymm::projector(hb, Gauss2);
+  SU_TwoIndex<Nc, Symmetric>::projector(hb, Gauss2);
   std::cout << GridLogMessage << "end projector" << std::endl;
-  SU3::LatticeAlgebraVector diff2 = ha - hb;
+  SU<Nc>::LatticeAlgebraVector diff2 = ha - hb;
   std::cout << GridLogMessage << "Difference: " << norm2(diff) << std::endl;
   std::cout << GridLogMessage << "*********************************************"
       << std::endl;
@@ -285,20 +285,20 @@ int main(int argc, char** argv) {
   std::cout << GridLogMessage << "Test for the Two index anti-Symmetric projectors"
       << std::endl;
   // Projectors
-  SU3TwoIndexAntiSymm::LatticeTwoIndexMatrix Gauss2a(grid);
+  SU_TwoIndex<Nc, AntiSymmetric>::LatticeTwoIndexMatrix Gauss2a(grid);
   random(gridRNG,Gauss2a);
   
   std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
-  SU3TwoIndexAntiSymm::projectOnAlgebra(ha, Gauss2a);
+  SU_TwoIndex<Nc, AntiSymmetric>::projectOnAlgebra(ha, Gauss2a);
   std::cout << GridLogMessage << "end projectOnAlgebra" << std::endl;
   std::cout << GridLogMessage << "Start projector" << std::endl;
-  SU3TwoIndexAntiSymm::projector(hb, Gauss2a);
+  SU_TwoIndex<Nc, AntiSymmetric>::projector(hb, Gauss2a);
   std::cout << GridLogMessage << "end projector" << std::endl;
   
   std::cout << GridLogMessage << "ReStart projector" << std::endl;
-  SU3TwoIndexAntiSymm::projector(hb, Gauss2a);
+  SU_TwoIndex<Nc, AntiSymmetric>::projector(hb, Gauss2a);
   std::cout << GridLogMessage << "end projector" << std::endl;
-  SU3::LatticeAlgebraVector diff2a = ha - hb;
+  SU<Nc>::LatticeAlgebraVector diff2a = ha - hb;
   std::cout << GridLogMessage << "Difference: " << norm2(diff2a) << std::endl;
   std::cout << GridLogMessage << "*********************************************"
       << std::endl;
@@ -312,14 +312,14 @@ int main(int argc, char** argv) {
   // Test group structure
   // (U_f * V_f)_r = U_r * V_r
   LatticeGaugeField U2(grid), V2(grid);
-  SU3::HotConfiguration<LatticeGaugeField>(gridRNG, U2);
-  SU3::HotConfiguration<LatticeGaugeField>(gridRNG, V2);
+  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, U2);
+  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, V2);
   
   LatticeGaugeField UV2(grid);
   UV2 = Zero();
   for (int mu = 0; mu < Nd; mu++) {
-    SU3::LatticeMatrix Umu2 = peekLorentz(U2,mu);
-    SU3::LatticeMatrix Vmu2 = peekLorentz(V2,mu);
+    SU<Nc>::LatticeMatrix Umu2 = peekLorentz(U2,mu);
+    SU<Nc>::LatticeMatrix Vmu2 = peekLorentz(V2,mu);
     pokeLorentz(UV2,Umu2*Vmu2, mu);
   }
   
@@ -346,16 +346,16 @@ int main(int argc, char** argv) {
   
   // Check correspondence of algebra and group transformations
   // Create a random vector
-  SU3::LatticeAlgebraVector h_sym(grid);
+  SU<Nc>::LatticeAlgebraVector h_sym(grid);
   typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ar_sym(grid);
   random(gridRNG,h_sym);
   h_sym = real(h_sym);
   SU_TwoIndex<Nc,Symmetric>::TwoIndexLieAlgebraMatrix(h_sym,Ar_sym);
   
   // Re-extract h_sym
-  SU3::LatticeAlgebraVector h_sym2(grid);
+  SU<Nc>::LatticeAlgebraVector h_sym2(grid);
   SU_TwoIndex< Nc, Symmetric>::projectOnAlgebra(h_sym2, Ar_sym);
-  SU3::LatticeAlgebraVector h_diff_sym = h_sym - h_sym2;
+  SU<Nc>::LatticeAlgebraVector h_diff_sym = h_sym - h_sym2;
   std::cout << GridLogMessage << "Projections structure check vector difference (Two Index Symmetric): " << norm2(h_diff_sym) << std::endl;
 
   
@@ -380,11 +380,11 @@ int main(int argc, char** argv) {
   
   
   // Construct the fundamental matrix in the group
-  SU3::LatticeMatrix Af_sym(grid);
-  SU3::FundamentalLieAlgebraMatrix(h_sym,Af_sym);
-  SU3::LatticeMatrix Ufund2(grid);
+  SU<Nc>::LatticeMatrix Af_sym(grid);
+  SU<Nc>::FundamentalLieAlgebraMatrix(h_sym,Af_sym);
+  SU<Nc>::LatticeMatrix Ufund2(grid);
   Ufund2  = expMat(Af_sym, 1.0, 16);
-  SU3::LatticeMatrix UnitCheck2(grid);
+  SU<Nc>::LatticeMatrix UnitCheck2(grid);
   UnitCheck2 = Ufund2 * adj(Ufund2) - uno_f;
   std::cout << GridLogMessage << "unitarity check 1: " << norm2(UnitCheck2)
       << std::endl;
@@ -422,14 +422,14 @@ int main(int argc, char** argv) {
   // Test group structure
   // (U_f * V_f)_r = U_r * V_r
   LatticeGaugeField U2A(grid), V2A(grid);
-  SU3::HotConfiguration<LatticeGaugeField>(gridRNG, U2A);
-  SU3::HotConfiguration<LatticeGaugeField>(gridRNG, V2A);
+  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, U2A);
+  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, V2A);
   
   LatticeGaugeField UV2A(grid);
   UV2A = Zero();
   for (int mu = 0; mu < Nd; mu++) {
-    SU3::LatticeMatrix Umu2A = peekLorentz(U2,mu);
-    SU3::LatticeMatrix Vmu2A = peekLorentz(V2,mu);
+    SU<Nc>::LatticeMatrix Umu2A = peekLorentz(U2,mu);
+    SU<Nc>::LatticeMatrix Vmu2A = peekLorentz(V2,mu);
     pokeLorentz(UV2A,Umu2A*Vmu2A, mu);
   }
   
@@ -456,16 +456,16 @@ int main(int argc, char** argv) {
   
   // Check correspondence of algebra and group transformations
   // Create a random vector
-  SU3::LatticeAlgebraVector h_Asym(grid);
+  SU<Nc>::LatticeAlgebraVector h_Asym(grid);
   typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ar_Asym(grid);
   random(gridRNG,h_Asym);
   h_Asym = real(h_Asym);
   SU_TwoIndex< Nc, AntiSymmetric>::TwoIndexLieAlgebraMatrix(h_Asym,Ar_Asym);
   
   // Re-extract h_sym
-  SU3::LatticeAlgebraVector h_Asym2(grid);
+  SU<Nc>::LatticeAlgebraVector h_Asym2(grid);
   SU_TwoIndex< Nc, AntiSymmetric>::projectOnAlgebra(h_Asym2, Ar_Asym);
-  SU3::LatticeAlgebraVector h_diff_Asym = h_Asym - h_Asym2;
+  SU<Nc>::LatticeAlgebraVector h_diff_Asym = h_Asym - h_Asym2;
   std::cout << GridLogMessage << "Projections structure check vector difference (Two Index anti-Symmetric): " << norm2(h_diff_Asym) << std::endl;
 
   
@@ -490,11 +490,11 @@ int main(int argc, char** argv) {
   
   
   // Construct the fundamental matrix in the group
-  SU3::LatticeMatrix Af_Asym(grid);
-  SU3::FundamentalLieAlgebraMatrix(h_Asym,Af_Asym);
-  SU3::LatticeMatrix Ufund2A(grid);
+  SU<Nc>::LatticeMatrix Af_Asym(grid);
+  SU<Nc>::FundamentalLieAlgebraMatrix(h_Asym,Af_Asym);
+  SU<Nc>::LatticeMatrix Ufund2A(grid);
   Ufund2A  = expMat(Af_Asym, 1.0, 16);
-  SU3::LatticeMatrix UnitCheck2A(grid);
+  SU<Nc>::LatticeMatrix UnitCheck2A(grid);
   UnitCheck2A = Ufund2A * adj(Ufund2A) - uno_f;
   std::cout << GridLogMessage << "unitarity check 1: " << norm2(UnitCheck2A)
       << std::endl;
@@ -527,8 +527,7 @@ int main(int argc, char** argv) {
 
 
 
-
   
   Grid_finalize();
 }
-#endif
+
diff --git a/tests/core/Test_reunitarise.cc b/tests/core/Test_reunitarise.cc
index 0ff8ec7e..e421a2a8 100644
--- a/tests/core/Test_reunitarise.cc
+++ b/tests/core/Test_reunitarise.cc
@@ -26,7 +26,7 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     See the full license in the file "LICENSE" in the top level distribution directory
     *************************************************************************************/
     /*  END LEGAL */
-#if Nc==3
+
 #include <Grid/Grid.h>
 
 using namespace std;
@@ -36,7 +36,7 @@ using namespace Grid;
 int main (int argc, char ** argv)
 {
   Grid_init(&argc,&argv);
-
+    
   std::vector<int> latt({8,8,8,8});
   GridCartesian * grid = SpaceTimeGrid::makeFourDimGrid(latt, 
 							GridDefaultSimd(Nd,vComplexD::Nsimd()),
@@ -123,14 +123,14 @@ int main (int argc, char ** argv)
   std::cout << "Determinant defect before projection " <<norm2(detU)<<std::endl;
   tmp = U*adj(U) - ident;
   std::cout << "Unitarity check before projection    " << norm2(tmp)<<std::endl; 
-  
+  #if Nc==3
   ProjectSU3(U);
   detU= Determinant(U) ;
   detU= detU -1.0;
   std::cout << "Determinant ProjectSU3 defect " <<norm2(detU)<<std::endl;
   tmp = U*adj(U) - ident;
   std::cout << "Unitarity check after projection    " << norm2(tmp)<<std::endl; 
-
+  #endif
   ProjectSUn(UU);
   detUU= Determinant(UU);
   detUU= detUU -1.0;
@@ -144,4 +144,4 @@ int main (int argc, char ** argv)
 
 
 
-#endif
+
diff --git a/tests/solver/Test_coarse_even_odd.cc b/tests/solver/Test_coarse_even_odd.cc
index dfbab747..3c8f65a2 100644
--- a/tests/solver/Test_coarse_even_odd.cc
+++ b/tests/solver/Test_coarse_even_odd.cc
@@ -93,7 +93,7 @@ int main(int argc, char** argv) {
   //                    Setup of Dirac Matrix and Operator                   //
   /////////////////////////////////////////////////////////////////////////////
 
-  LatticeGaugeField Umu(Grid_f); SU3::HotConfiguration(pRNG_f, Umu);
+  LatticeGaugeField Umu(Grid_f); SU<Nc>::HotConfiguration(pRNG_f, Umu);
 
   RealD checkTolerance = (getPrecision<LatticeFermion>::value == 1) ? 1e-7 : 1e-15;
 

From 371fd123fb5ddf7da5f151e9b2fcb41829b0f7e0 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 14 Mar 2023 10:47:07 +0000
Subject: [PATCH 051/129] consequence of iSUnMatrix being no longer a member of
 the SU class

---
 Grid/qcd/utils/SUnAdjoint.h  | 8 +++++---
 Grid/qcd/utils/SUnTwoIndex.h | 8 ++++----
 2 files changed, 9 insertions(+), 7 deletions(-)

diff --git a/Grid/qcd/utils/SUnAdjoint.h b/Grid/qcd/utils/SUnAdjoint.h
index c03036ef..3a5954ca 100644
--- a/Grid/qcd/utils/SUnAdjoint.h
+++ b/Grid/qcd/utils/SUnAdjoint.h
@@ -51,14 +51,16 @@ public:
   typedef Lattice<iVector<iScalar<iMatrix<vComplexF, Dimension> >, Nd> > LatticeAdjFieldF;
   typedef Lattice<iVector<iScalar<iMatrix<vComplexD, Dimension> >, Nd> > LatticeAdjFieldD;
 
+  template <typename vtype>
+  using iSUnMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
 
   template <class cplx>
   static void generator(int Index, iSUnAdjointMatrix<cplx> &iAdjTa) {
     // returns i(T_Adj)^index necessary for the projectors
     // see definitions above
     iAdjTa = Zero();
-    Vector<typename SU<ncolour>::template iSUnMatrix<cplx> > ta(ncolour * ncolour - 1);
-    typename SU<ncolour>::template iSUnMatrix<cplx> tmp;
+    Vector<iSUnMatrix<cplx> > ta(ncolour * ncolour - 1);
+    iSUnMatrix<cplx> tmp;
 
     // FIXME not very efficient to get all the generators everytime
     for (int a = 0; a < Dimension; a++) SU<ncolour>::generator(a, ta[a]);
@@ -66,7 +68,7 @@ public:
     for (int a = 0; a < Dimension; a++) {
       tmp = ta[a] * ta[Index] - ta[Index] * ta[a];
       for (int b = 0; b < (ncolour * ncolour - 1); b++) {
-        typename SU<ncolour>::template iSUnMatrix<cplx> tmp1 =
+        iSUnMatrix<cplx> tmp1 =
 	  2.0 * tmp * ta[b];  // 2.0 from the normalization
         Complex iTr = TensorRemove(timesI(trace(tmp1)));
         //iAdjTa()()(b, a) = iTr;
diff --git a/Grid/qcd/utils/SUnTwoIndex.h b/Grid/qcd/utils/SUnTwoIndex.h
index 50ddf5c1..5e283de7 100644
--- a/Grid/qcd/utils/SUnTwoIndex.h
+++ b/Grid/qcd/utils/SUnTwoIndex.h
@@ -126,10 +126,10 @@ public:
 
   template <class cplx>
   static void generator(int Index, iSUnTwoIndexMatrix<cplx> &i2indTa) {
-    Vector<typename SU<ncolour>::template iSUnMatrix<cplx> > ta(
+    Vector<iSUnMatrix<cplx> > ta(
 								ncolour * ncolour - 1);
-    Vector<typename SU<ncolour>::template iSUnMatrix<cplx> > eij(Dimension);
-    typename SU<ncolour>::template iSUnMatrix<cplx> tmp;
+    Vector<iSUnMatrix<cplx> > eij(Dimension);
+    iSUnMatrix<cplx> tmp;
     i2indTa = Zero();
     
     for (int a = 0; a < ncolour * ncolour - 1; a++)
@@ -140,7 +140,7 @@ public:
     for (int a = 0; a < Dimension; a++) {
       tmp = transpose(ta[Index]) * adj(eij[a]) + adj(eij[a]) * ta[Index];
       for (int b = 0; b < Dimension; b++) {
-        typename SU<ncolour>::template iSUnMatrix<cplx> tmp1 =
+        iSUnMatrix<cplx> tmp1 =
 	  tmp * eij[b]; 
         Complex iTr = TensorRemove(timesI(trace(tmp1)));
         i2indTa()()(a, b) = iTr;

From ba7f9d7b70321613497f1cbd68197d0f4df08552 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Wed, 15 Mar 2023 15:55:12 +0000
Subject: [PATCH 052/129] projection on Sp2n algebra, to be used instead of Ta

---
 Grid/lattice/Lattice_ET.h        |   2 +
 Grid/qcd/utils/Sp2n.impl         |  29 +++---
 Grid/tensors/Tensor_Ta.h         |  84 ++++++++++++++++-
 tests/sp2n/Test_project_on_Sp.cc | 157 ++++++++++++++++++++++---------
 4 files changed, 214 insertions(+), 58 deletions(-)

diff --git a/Grid/lattice/Lattice_ET.h b/Grid/lattice/Lattice_ET.h
index 9042eb8f..661d7441 100644
--- a/Grid/lattice/Lattice_ET.h
+++ b/Grid/lattice/Lattice_ET.h
@@ -345,6 +345,7 @@ GridUnopClass(UnaryNot, Not(a));
 GridUnopClass(UnaryTrace, trace(a));
 GridUnopClass(UnaryTranspose, transpose(a));
 GridUnopClass(UnaryTa, Ta(a));
+GridUnopClass(UnaryProjectSp2nAlgebra, ProjectSp2nAlgebra(a));
 GridUnopClass(UnaryProjectOnGroup, ProjectOnGroup(a));
 GridUnopClass(UnaryProjectOnSpGroup, ProjectOnSpGroup(a));
 GridUnopClass(UnaryTimesI, timesI(a));
@@ -457,6 +458,7 @@ GRID_DEF_UNOP(operator!, UnaryNot);
 GRID_DEF_UNOP(trace, UnaryTrace);
 GRID_DEF_UNOP(transpose, UnaryTranspose);
 GRID_DEF_UNOP(Ta, UnaryTa);
+GRID_DEF_UNOP(ProjectSp2nAlgebra, UnaryProjectSp2nAlgebra);
 GRID_DEF_UNOP(ProjectOnGroup, UnaryProjectOnGroup);
 GRID_DEF_UNOP(ProjectOnSpGroup, UnaryProjectOnSpGroup);
 GRID_DEF_UNOP(timesI, UnaryTimesI);
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index 44771a14..0bad3d79 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -414,13 +414,6 @@ static void OmegaInvariance(ColourMatrix &in) {
   Omega = Zero();
   const int nsp=ncolour/2;
 
-  std::cout << GridLogMessage << "I am a ColourMatrix" << std::endl;
-
-  // for (int i = 0; i < ncolour; i++)         wrong?!
-  //{
-  //     Omega()()(i, 2*ncolour-1-i) = 1.;
-  //     Omega()()(2*ncolour-1-i, i) = -1;
-  // }
   for (int i = 0; i < nsp; i++) {
     Omega()()(i, nsp + i) = 1.;
     Omega()()(nsp + i, i) = -1;
@@ -454,8 +447,6 @@ static void OmegaInvariance(GaugeField &in) {
   Omega = Zero();
   identity = 1.;
 
-  std::cout << GridLogMessage << "I am a GaugeField " << std::endl;
-
   U = PeekIndex<LorentzIndex>(in, 1);
 
   OmegaInvariance(U);
@@ -473,8 +464,6 @@ static void OmegaInvariance(LatticeColourMatrixD &in) {
   Omega = Zero();
   identity = 1.;
 
-  std::cout << GridLogMessage << "I am a LatticeColourMatrix " << std::endl;
-
   for (int i = 0; i < nsp; i++) {
     Omega()()(i, nsp + i) = 1.;
     Omega()()(nsp + i, i) = -1;
@@ -496,3 +485,21 @@ static void OmegaInvariance(LatticeColourMatrixD &in) {
   }
 }
 
+template <ONLY_IF_Sp>
+static void Omega(LatticeColourMatrixD &in) {
+  const int nsp=ncolour/2;
+  LatticeColourMatrixD OmegaLatt(in.Grid());
+  LatticeColourMatrixD identity(in.Grid());
+  ColourMatrix Omega;
+
+  OmegaLatt = Zero();
+  Omega = Zero();
+  identity = 1.;
+
+  for (int i = 0; i < nsp; i++) {
+    Omega()()(i, nsp + i) = 1.;
+    Omega()()(nsp + i, i) = -1;
+  }
+  OmegaLatt = OmegaLatt + (identity * Omega);
+  in = OmegaLatt;
+}
diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index 2ee51fb4..7ceeabba 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -66,6 +66,88 @@ template<class vtype,int N> accelerator_inline iMatrix<vtype,N> Ta(const iMatrix
   return ret;
 }
 
+// for sp2n can't do something as simple as Ta
+
+template<class vtype> accelerator_inline iScalar<vtype> ProjectSp2nAlgebra(const iScalar<vtype>&r)
+{
+  iScalar<vtype> ret;
+  ret._internal = ProjectSp2nAlgebra(r._internal);
+  return ret;
+}
+template<class vtype,int N> accelerator_inline iVector<vtype,N> ProjectSp2nAlgebra(const iVector<vtype,N>&r)
+{
+  iVector<vtype,N> ret;
+  for(int i=0;i<N;i++){
+    ret._internal[i] = ProjectSp2nAlgebra(r._internal[i]);
+  }
+  return ret;
+}
+template<class vtype,int N> accelerator_inline iMatrix<vtype,N> ProjectSp2nAlgebra(const iMatrix<vtype,N> &arg)
+{
+  iMatrix<vtype,N> ret;
+    // following HiRep's suN_utils.c does a sort of Gram-Schmidt
+    vtype nrm;
+    vtype inner;
+    vtype tmp;
+    
+    for(int c1=0;c1<N/2;c1++)
+    {
+        
+        for (int b=0; b<c1; b++)                  // remove the b-rows from U_c1
+        {
+            decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
+            decltype(ret._internal[b][b]*ret._internal[b][b]) prn;
+            zeroit(pr);
+            zeroit(prn);
+            
+            for(int c=0; c<N; c++)
+            {
+                pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];        // <U_c1 | U_b >
+                prn += conjugate(ret._internal[c1][c])*ret._internal[b+N/2][c];   // <U_c1 | U_{b+N} >
+            }
+         
+
+            for(int c=0; c<N; c++)
+            {
+                ret._internal[c1][c] -= (conjugate(pr) * ret._internal[b][c] + conjugate(prn) * ret._internal[b+N/2][c] );    //  U_c1 -= (  <U_c1 | U_b > U_b + <U_c1 | U_{b+N} > U_{b+N}  )
+            }
+        }
+      
+        zeroit(inner);
+        for(int c2=0;c2<N;c2++)
+        {
+            inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
+        }
+        
+        nrm = sqrt(inner);
+        nrm = 1.0/nrm;
+        for(int c2=0;c2<N;c2++)
+        {
+            ret._internal[c1][c2]*= nrm;
+        }
+        
+
+        for(int c2=0;c2<N/2;c2++)
+        {
+            tmp = conjugate(ret._internal[c1][c2]);       // (up-left)* of the old matrix
+            ret._internal[c1+N/2][c2+N/2] = -tmp;          // down right in the new matrix = -(up-left)* of the old matrix
+        }
+           
+        for(int c2=N/2;c2<N;c2++)
+        {
+            tmp = conjugate(ret._internal[c1][c2]);   // (up-right)* of the old
+            ret._internal[c1+N/2][c2-N/2] = tmp;     // down left in the new matrix = (up-right)* of the old
+        }
+      
+        
+    }
+    
+  
+  return ret;
+}
+
+
+
 
 /////////////////////////////////////////////// 
 // ProjectOnGroup function for scalar, vector, matrix 
@@ -137,8 +219,6 @@ accelerator_inline iMatrix<vtype,N> ProjectOnGroup(const iMatrix<vtype,N> &arg)
 
 // re-do for sp2n
 
-// Ta cannot be defined here for Sp2n because I need the generators from the Sp class
-// It is defined in gauge impl types
 
 template<class vtype> accelerator_inline iScalar<vtype> ProjectOnSpGroup(const iScalar<vtype>&r)
 {
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 36b95cf4..320ab230 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -20,6 +20,8 @@ int main (int argc, char **argv)
     LatticeColourMatrixD aux(&Grid);
     LatticeColourMatrixD identity(&Grid);
     
+    // Will test resimplectification (from ProjectOnGaugeGroup, ProjectOnSpGroup) and projection on the algebra (from ProjectSp2nAlgebra)
+    
     const int nsp = Nc / 2;
     
     identity = 1.0;
@@ -29,15 +31,12 @@ int main (int argc, char **argv)
     double vol = Umu.Grid()->gSites();
     
     std::vector<int> pseeds({1,2,3,4,5});
-    std::vector<int> sseeds({6,7,8,9,10});
     GridParallelRNG  pRNG(&Grid); pRNG.SeedFixedIntegers(pseeds);
-    GridSerialRNG    sRNG;       sRNG.SeedFixedIntegers(sseeds);
     
     SU<Nc>::HotConfiguration(pRNG,Umu);
-    U = PeekIndex<LorentzIndex>(Umu,2);
+    U = PeekIndex<LorentzIndex>(Umu,0);
     
     aux = U*adj(U) - identity;
-    std::cout <<GridLogMessage << std::endl;
     std::cout << GridLogMessage << "Starting with random SUn matrix " << std::endl;
     std::cout << GridLogMessage << "Unitary check " << std::endl;
     std::cout <<GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
@@ -55,35 +54,27 @@ int main (int argc, char **argv)
     
     std::cout << GridLogMessage << "Unitary matrix deformed " << std::endl;
     std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl;
-    std::cout <<GridLogMessage << std::endl;
-
-    std::cout <<GridLogMessage << std::endl;
-    std::cout << GridLogMessage << "Projecting on Sp2n " << std::endl;
+    std::cout << GridLogMessage << "Simplectify" << std::endl;
 
     U = ProjectOnSpGroup(U);
-    //U = ProjectOnGroup(U);
+
     aux = U*adj(U) - identity;
     std::cout <<GridLogMessage << std::endl;
     std::cout <<GridLogMessage << std::endl;
-    std::cout << GridLogMessage << "Unitary check after Sp(2n) projection " << std::endl;
+    std::cout << GridLogMessage << "Unitary check after simplectification " << std::endl;
     std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
     assert( norm2(aux) < 1e-8);
-    std::cout <<GridLogMessage << std::endl;
-    std::cout <<GridLogMessage << std::endl;
     
     // checks on determinant
-    std::cout << GridLogMessage << "Det after Projection on Sp2n = " << norm2( Determinant(U) ) / vol << std::endl;
-    std::cout <<GridLogMessage << std::endl;
-    std::cout <<GridLogMessage << std::endl;
+    std::cout << GridLogMessage << "Det after simplectification = " << norm2( Determinant(U) ) / vol << std::endl;
+    assert( norm2(aux) - 1 < 1e-8);
     
     // actual sp2n check
-    std::cout << GridLogMessage << "Checking invariance after projection "<< std::endl;
+    std::cout << GridLogMessage << "Checking invariance after simplectification. Will not kill if it fails, but the next check will " << std::endl;
     Sp<Nc>::OmegaInvariance(U);
     
     // checks on elements
     
-    std::cout <<GridLogMessage << std::endl;
-    std::cout <<GridLogMessage << std::endl;
     std::cout << GridLogMessage << "Checking the structure is " << std::endl;
     std::cout << GridLogMessage << "U  =  (   W    X   )  " << std::endl;
     std::cout << GridLogMessage << "      (  -X^*  W^* )  " << std::endl;
@@ -121,34 +112,110 @@ int main (int argc, char **argv)
     
     std::cout << GridLogMessage << "ok" << std::endl;
     
-    // an explicit check for sp2
-    /*
-    if (Nc == 2)
-    {
-        assert(Nc==2);
-        ColourMatrix A;
-        A = Zero();
-
-        Complex a(25041994., 12.);
-        Complex b(39., 0.22);
-        Complex d(10000., -2222.3333);
+    std::cout << GridLogMessage << "Check the ProjectOnGaugeGroup function to simplectify" << std::endl;
+    U = U + 2932.111*identity;
+    std::cout << GridLogMessage << "Resimplectify deformed matrix" << std::endl;
+    Sp<Nc>::ProjectOnGaugeGroup(U);
+    aux = U*adj(U) - identity;
+    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+    assert( norm2(aux) < 1e-8);
+    Sp<Nc>::OmegaInvariance(U);
+    
+    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 << "ok" << std::endl;
+    
+    std::cout << GridLogMessage << "Now check projection on the algebra" << std::endl;
+    
+    U = PeekIndex<LorentzIndex>(Umu,1);
+    U = U + 666.*identity;
+    aux = U*adj(U) - identity;
+    std::cout << GridLogMessage << "Matrix deformed " << std::endl;
+    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+    std::cout << GridLogMessage << "Project on sp2n algebra" << std::endl;
+    U = ProjectSp2nAlgebra(U);
+    aux = U*adj(U) - identity;
+    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+    assert( norm2(aux) < 1e-8);
+    std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)" << std::endl;
+    
+    LatticeColourMatrixD Omega(&Grid);
+    
+    Sp<Nc>::Omega(Omega);
+    aux = Omega*U*Omega - conjugate(U);
+    std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
+    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 );
+        }
+    }
+    
     
-        A()()(0,0) = a;
-        A()()(0,1) = b;
-        A()()(1,0) = i;
-        A()()(1,1) = d;
-        std::cout <<GridLogMessage << std::endl;
-        std::cout <<GridLogMessage << std::endl;
-        std::cout << GridLogMessage << "An explicit check for Sp2" << std::endl;
-        std::cout <<GridLogMessage << std::endl;
-        std::cout << GridLogMessage << "Building a non unitary matrix by hand with funny entries " << std::endl;
-        std::cout << GridLogMessage << "A = " << A << std::endl;
-        std::cout << GridLogMessage << "Projecting on Sp2 " << std::endl;
-        A = ProjectOnSpGroup(A);
-        std::cout << GridLogMessage << "now A = " << A << std::endl;
-        std::cout << GridLogMessage << "A(0,0) - conjA(1,1) = " << A()()(0,0) - adj ( A()()(1,1) )<< std::endl;
-        std::cout << GridLogMessage << "A(0,1) + conjA(1,0) = " << A()()(0,1) + adj ( A()()(1,0) )<< std::endl;
-    }*/
     
     Grid_finalize();
 

From cbc053c3dba5592016aadcd8b0a1fb8f0ce9b159 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 17 Mar 2023 11:36:58 +0000
Subject: [PATCH 053/129] Revert "projection on Sp2n algebra, to be used
 instead of Ta"

This reverts commit ba7f9d7b70321613497f1cbd68197d0f4df08552.
---
 Grid/lattice/Lattice_ET.h        |   2 -
 Grid/qcd/utils/Sp2n.impl         |  29 +++---
 Grid/tensors/Tensor_Ta.h         |  84 +----------------
 tests/sp2n/Test_project_on_Sp.cc | 153 +++++++++----------------------
 4 files changed, 56 insertions(+), 212 deletions(-)

diff --git a/Grid/lattice/Lattice_ET.h b/Grid/lattice/Lattice_ET.h
index 661d7441..9042eb8f 100644
--- a/Grid/lattice/Lattice_ET.h
+++ b/Grid/lattice/Lattice_ET.h
@@ -345,7 +345,6 @@ GridUnopClass(UnaryNot, Not(a));
 GridUnopClass(UnaryTrace, trace(a));
 GridUnopClass(UnaryTranspose, transpose(a));
 GridUnopClass(UnaryTa, Ta(a));
-GridUnopClass(UnaryProjectSp2nAlgebra, ProjectSp2nAlgebra(a));
 GridUnopClass(UnaryProjectOnGroup, ProjectOnGroup(a));
 GridUnopClass(UnaryProjectOnSpGroup, ProjectOnSpGroup(a));
 GridUnopClass(UnaryTimesI, timesI(a));
@@ -458,7 +457,6 @@ GRID_DEF_UNOP(operator!, UnaryNot);
 GRID_DEF_UNOP(trace, UnaryTrace);
 GRID_DEF_UNOP(transpose, UnaryTranspose);
 GRID_DEF_UNOP(Ta, UnaryTa);
-GRID_DEF_UNOP(ProjectSp2nAlgebra, UnaryProjectSp2nAlgebra);
 GRID_DEF_UNOP(ProjectOnGroup, UnaryProjectOnGroup);
 GRID_DEF_UNOP(ProjectOnSpGroup, UnaryProjectOnSpGroup);
 GRID_DEF_UNOP(timesI, UnaryTimesI);
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index 0bad3d79..44771a14 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -414,6 +414,13 @@ static void OmegaInvariance(ColourMatrix &in) {
   Omega = Zero();
   const int nsp=ncolour/2;
 
+  std::cout << GridLogMessage << "I am a ColourMatrix" << std::endl;
+
+  // for (int i = 0; i < ncolour; i++)         wrong?!
+  //{
+  //     Omega()()(i, 2*ncolour-1-i) = 1.;
+  //     Omega()()(2*ncolour-1-i, i) = -1;
+  // }
   for (int i = 0; i < nsp; i++) {
     Omega()()(i, nsp + i) = 1.;
     Omega()()(nsp + i, i) = -1;
@@ -447,6 +454,8 @@ static void OmegaInvariance(GaugeField &in) {
   Omega = Zero();
   identity = 1.;
 
+  std::cout << GridLogMessage << "I am a GaugeField " << std::endl;
+
   U = PeekIndex<LorentzIndex>(in, 1);
 
   OmegaInvariance(U);
@@ -464,6 +473,8 @@ static void OmegaInvariance(LatticeColourMatrixD &in) {
   Omega = Zero();
   identity = 1.;
 
+  std::cout << GridLogMessage << "I am a LatticeColourMatrix " << std::endl;
+
   for (int i = 0; i < nsp; i++) {
     Omega()()(i, nsp + i) = 1.;
     Omega()()(nsp + i, i) = -1;
@@ -485,21 +496,3 @@ static void OmegaInvariance(LatticeColourMatrixD &in) {
   }
 }
 
-template <ONLY_IF_Sp>
-static void Omega(LatticeColourMatrixD &in) {
-  const int nsp=ncolour/2;
-  LatticeColourMatrixD OmegaLatt(in.Grid());
-  LatticeColourMatrixD identity(in.Grid());
-  ColourMatrix Omega;
-
-  OmegaLatt = Zero();
-  Omega = Zero();
-  identity = 1.;
-
-  for (int i = 0; i < nsp; i++) {
-    Omega()()(i, nsp + i) = 1.;
-    Omega()()(nsp + i, i) = -1;
-  }
-  OmegaLatt = OmegaLatt + (identity * Omega);
-  in = OmegaLatt;
-}
diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index 7ceeabba..2ee51fb4 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -66,88 +66,6 @@ template<class vtype,int N> accelerator_inline iMatrix<vtype,N> Ta(const iMatrix
   return ret;
 }
 
-// for sp2n can't do something as simple as Ta
-
-template<class vtype> accelerator_inline iScalar<vtype> ProjectSp2nAlgebra(const iScalar<vtype>&r)
-{
-  iScalar<vtype> ret;
-  ret._internal = ProjectSp2nAlgebra(r._internal);
-  return ret;
-}
-template<class vtype,int N> accelerator_inline iVector<vtype,N> ProjectSp2nAlgebra(const iVector<vtype,N>&r)
-{
-  iVector<vtype,N> ret;
-  for(int i=0;i<N;i++){
-    ret._internal[i] = ProjectSp2nAlgebra(r._internal[i]);
-  }
-  return ret;
-}
-template<class vtype,int N> accelerator_inline iMatrix<vtype,N> ProjectSp2nAlgebra(const iMatrix<vtype,N> &arg)
-{
-  iMatrix<vtype,N> ret;
-    // following HiRep's suN_utils.c does a sort of Gram-Schmidt
-    vtype nrm;
-    vtype inner;
-    vtype tmp;
-    
-    for(int c1=0;c1<N/2;c1++)
-    {
-        
-        for (int b=0; b<c1; b++)                  // remove the b-rows from U_c1
-        {
-            decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
-            decltype(ret._internal[b][b]*ret._internal[b][b]) prn;
-            zeroit(pr);
-            zeroit(prn);
-            
-            for(int c=0; c<N; c++)
-            {
-                pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];        // <U_c1 | U_b >
-                prn += conjugate(ret._internal[c1][c])*ret._internal[b+N/2][c];   // <U_c1 | U_{b+N} >
-            }
-         
-
-            for(int c=0; c<N; c++)
-            {
-                ret._internal[c1][c] -= (conjugate(pr) * ret._internal[b][c] + conjugate(prn) * ret._internal[b+N/2][c] );    //  U_c1 -= (  <U_c1 | U_b > U_b + <U_c1 | U_{b+N} > U_{b+N}  )
-            }
-        }
-      
-        zeroit(inner);
-        for(int c2=0;c2<N;c2++)
-        {
-            inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
-        }
-        
-        nrm = sqrt(inner);
-        nrm = 1.0/nrm;
-        for(int c2=0;c2<N;c2++)
-        {
-            ret._internal[c1][c2]*= nrm;
-        }
-        
-
-        for(int c2=0;c2<N/2;c2++)
-        {
-            tmp = conjugate(ret._internal[c1][c2]);       // (up-left)* of the old matrix
-            ret._internal[c1+N/2][c2+N/2] = -tmp;          // down right in the new matrix = -(up-left)* of the old matrix
-        }
-           
-        for(int c2=N/2;c2<N;c2++)
-        {
-            tmp = conjugate(ret._internal[c1][c2]);   // (up-right)* of the old
-            ret._internal[c1+N/2][c2-N/2] = tmp;     // down left in the new matrix = (up-right)* of the old
-        }
-      
-        
-    }
-    
-  
-  return ret;
-}
-
-
-
 
 /////////////////////////////////////////////// 
 // ProjectOnGroup function for scalar, vector, matrix 
@@ -219,6 +137,8 @@ accelerator_inline iMatrix<vtype,N> ProjectOnGroup(const iMatrix<vtype,N> &arg)
 
 // re-do for sp2n
 
+// Ta cannot be defined here for Sp2n because I need the generators from the Sp class
+// It is defined in gauge impl types
 
 template<class vtype> accelerator_inline iScalar<vtype> ProjectOnSpGroup(const iScalar<vtype>&r)
 {
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 320ab230..36b95cf4 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -20,8 +20,6 @@ int main (int argc, char **argv)
     LatticeColourMatrixD aux(&Grid);
     LatticeColourMatrixD identity(&Grid);
     
-    // Will test resimplectification (from ProjectOnGaugeGroup, ProjectOnSpGroup) and projection on the algebra (from ProjectSp2nAlgebra)
-    
     const int nsp = Nc / 2;
     
     identity = 1.0;
@@ -31,12 +29,15 @@ int main (int argc, char **argv)
     double vol = Umu.Grid()->gSites();
     
     std::vector<int> pseeds({1,2,3,4,5});
+    std::vector<int> sseeds({6,7,8,9,10});
     GridParallelRNG  pRNG(&Grid); pRNG.SeedFixedIntegers(pseeds);
+    GridSerialRNG    sRNG;       sRNG.SeedFixedIntegers(sseeds);
     
     SU<Nc>::HotConfiguration(pRNG,Umu);
-    U = PeekIndex<LorentzIndex>(Umu,0);
+    U = PeekIndex<LorentzIndex>(Umu,2);
     
     aux = U*adj(U) - identity;
+    std::cout <<GridLogMessage << std::endl;
     std::cout << GridLogMessage << "Starting with random SUn matrix " << std::endl;
     std::cout << GridLogMessage << "Unitary check " << std::endl;
     std::cout <<GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
@@ -54,27 +55,35 @@ int main (int argc, char **argv)
     
     std::cout << GridLogMessage << "Unitary matrix deformed " << std::endl;
     std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl;
-    std::cout << GridLogMessage << "Simplectify" << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+
+    std::cout <<GridLogMessage << std::endl;
+    std::cout << GridLogMessage << "Projecting on Sp2n " << std::endl;
 
     U = ProjectOnSpGroup(U);
-
+    //U = ProjectOnGroup(U);
     aux = U*adj(U) - identity;
     std::cout <<GridLogMessage << std::endl;
     std::cout <<GridLogMessage << std::endl;
-    std::cout << GridLogMessage << "Unitary check after simplectification " << std::endl;
+    std::cout << GridLogMessage << "Unitary check after Sp(2n) projection " << std::endl;
     std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
     assert( norm2(aux) < 1e-8);
+    std::cout <<GridLogMessage << std::endl;
+    std::cout <<GridLogMessage << std::endl;
     
     // checks on determinant
-    std::cout << GridLogMessage << "Det after simplectification = " << norm2( Determinant(U) ) / vol << std::endl;
-    assert( norm2(aux) - 1 < 1e-8);
+    std::cout << GridLogMessage << "Det after Projection on Sp2n = " << norm2( Determinant(U) ) / vol << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+    std::cout <<GridLogMessage << std::endl;
     
     // actual sp2n check
-    std::cout << GridLogMessage << "Checking invariance after simplectification. Will not kill if it fails, but the next check will " << std::endl;
+    std::cout << GridLogMessage << "Checking invariance after projection "<< std::endl;
     Sp<Nc>::OmegaInvariance(U);
     
     // checks on elements
     
+    std::cout <<GridLogMessage << std::endl;
+    std::cout <<GridLogMessage << std::endl;
     std::cout << GridLogMessage << "Checking the structure is " << std::endl;
     std::cout << GridLogMessage << "U  =  (   W    X   )  " << std::endl;
     std::cout << GridLogMessage << "      (  -X^*  W^* )  " << std::endl;
@@ -112,110 +121,34 @@ int main (int argc, char **argv)
     
     std::cout << GridLogMessage << "ok" << std::endl;
     
-    std::cout << GridLogMessage << "Check the ProjectOnGaugeGroup function to simplectify" << std::endl;
-    U = U + 2932.111*identity;
-    std::cout << GridLogMessage << "Resimplectify deformed matrix" << std::endl;
-    Sp<Nc>::ProjectOnGaugeGroup(U);
-    aux = U*adj(U) - identity;
-    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
-    Sp<Nc>::OmegaInvariance(U);
-    
-    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
+    // an explicit check for sp2
+    /*
+    if (Nc == 2)
     {
-        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 );
-        }
-        
-    }
+        assert(Nc==2);
+        ColourMatrix A;
+        A = Zero();
 
-    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 << "ok" << std::endl;
-    
-    std::cout << GridLogMessage << "Now check projection on the algebra" << std::endl;
-    
-    U = PeekIndex<LorentzIndex>(Umu,1);
-    U = U + 666.*identity;
-    aux = U*adj(U) - identity;
-    std::cout << GridLogMessage << "Matrix deformed " << std::endl;
-    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
-    std::cout << GridLogMessage << "Project on sp2n algebra" << std::endl;
-    U = ProjectSp2nAlgebra(U);
-    aux = U*adj(U) - identity;
-    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
-    std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)" << std::endl;
-    
-    LatticeColourMatrixD Omega(&Grid);
-    
-    Sp<Nc>::Omega(Omega);
-    aux = Omega*U*Omega - conjugate(U);
-    std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
-    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 );
-        }
-    }
-    
+        Complex a(25041994., 12.);
+        Complex b(39., 0.22);
+        Complex d(10000., -2222.3333);
     
+        A()()(0,0) = a;
+        A()()(0,1) = b;
+        A()()(1,0) = i;
+        A()()(1,1) = d;
+        std::cout <<GridLogMessage << std::endl;
+        std::cout <<GridLogMessage << std::endl;
+        std::cout << GridLogMessage << "An explicit check for Sp2" << std::endl;
+        std::cout <<GridLogMessage << std::endl;
+        std::cout << GridLogMessage << "Building a non unitary matrix by hand with funny entries " << std::endl;
+        std::cout << GridLogMessage << "A = " << A << std::endl;
+        std::cout << GridLogMessage << "Projecting on Sp2 " << std::endl;
+        A = ProjectOnSpGroup(A);
+        std::cout << GridLogMessage << "now A = " << A << std::endl;
+        std::cout << GridLogMessage << "A(0,0) - conjA(1,1) = " << A()()(0,0) - adj ( A()()(1,1) )<< std::endl;
+        std::cout << GridLogMessage << "A(0,1) + conjA(1,0) = " << A()()(0,1) + adj ( A()()(1,0) )<< std::endl;
+    }*/
     
     Grid_finalize();
 

From 1b8176e2c098ce01046ff0322bb322d2ed6ac9d3 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 17 Mar 2023 14:58:00 +0000
Subject: [PATCH 054/129] fix code duplication

---
 Grid/qcd/utils/GaugeGroup.h | 126 +++++++++++++++++++++++++++-----
 Grid/qcd/utils/SUn.impl     | 139 ------------------------------------
 Grid/qcd/utils/Sp2n.impl    | 139 ------------------------------------
 3 files changed, 109 insertions(+), 295 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index dea8f985..6a407706 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -170,38 +170,116 @@ class GaugeGroup {
     }
   }
 
-  template <typename LatticeMatrixType>
+ template <typename LatticeMatrixType>
   static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out,
                            double scale = 1.0) {
-    LieRandomize(pRNG, out, group_name(), scale);
+    GridBase *grid = out.Grid();
+
+    typedef typename LatticeMatrixType::vector_type vector_type;
+    typedef typename LatticeMatrixType::scalar_type scalar_type;
+
+    typedef iSinglet<vector_type> vTComplexType;
+
+    typedef Lattice<vTComplexType> LatticeComplexType;
+    typedef typename GridTypeMapper<
+        typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
+
+    LatticeComplexType ca(grid);
+    LatticeMatrixType lie(grid);
+    LatticeMatrixType la(grid);
+    ComplexD ci(0.0, scale);
+    //    ComplexD cone(1.0, 0.0);
+    MatrixType ta;
+
+    lie = Zero();
+
+    for (int a = 0; a < AdjointDimension; a++) {
+      random(pRNG, ca);
+
+      ca = (ca + conjugate(ca)) * 0.5;
+      ca = ca - 0.5;
+
+      generator(a, ta);
+
+      la = ci * ca * ta;
+
+      lie = lie + la;  // e^{i la ta}
+    }
+    taExp(lie, out);
   }
 
   static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
                                                   LatticeMatrix &out,
                                                   Real scale = 1.0) {
-      GaussianFundamentalLieAlgebraMatrix(pRNG, out, group_name(), scale);
+    GridBase *grid = out.Grid();
+    LatticeReal ca(grid);
+    LatticeMatrix la(grid);
+    Complex ci(0.0, scale);
+    Matrix ta;
+
+    out = Zero();
+    for (int a = 0; a < AdjointDimension; a++) {
+      gaussian(pRNG, ca);
+      generator(a, ta);
+      la = toComplex(ca) * ta;
+      out += la;
+    }
+    out *= ci;
   }
 
   static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
                                           LatticeMatrix &out,
                                           Real scale = 1.0) {
-      FundamentalLieAlgebraMatrix(h, out, group_name(), scale);
+    conformable(h, out);
+    GridBase *grid = out.Grid();
+    LatticeMatrix la(grid);
+    Matrix ta;
+
+    out = Zero();
+    for (int a = 0; a < AdjointDimension; a++) {
+      generator(a, ta);
+      la = peekColour(h, a) * timesI(ta) * scale;
+      out += la;
+    }
   }
 
   // Projects the algebra components a lattice matrix (of dimension ncol*ncol -1
   // ) inverse operation: FundamentalLieAlgebraMatrix
   static void projectOnAlgebra(LatticeAlgebraVector &h_out,
                                const LatticeMatrix &in, Real scale = 1.0) {
-      projectOnAlgebra(h_out, in, group_name(), scale);
+    conformable(h_out, in);
+    h_out = Zero();
+    Matrix Ta;
+
+    for (int a = 0; a < AdjointDimension; a++) {
+      generator(a, Ta);
+      pokeColour(h_out, -2.0 * (trace(timesI(Ta) * in)) * scale, a);
+    }
   }
 
   template <typename GaugeField>
   static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
-      HotConfiguration(pRNG, out, group_name());
+    typedef typename GaugeField::vector_type vector_type;
+    typedef iGroupMatrix<vector_type> vMatrixType;
+    typedef Lattice<vMatrixType> LatticeMatrixType;
+
+    LatticeMatrixType Umu(out.Grid());
+    for (int mu = 0; mu < Nd; mu++) {
+      LieRandomize(pRNG, Umu, 1.0);
+      PokeIndex<LorentzIndex>(out, Umu, mu);
+    }
   }
   template <typename GaugeField>
   static void TepidConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
-      TepidConfiguration(pRNG, out, group_name());
+    typedef typename GaugeField::vector_type vector_type;
+    typedef iGroupMatrix<vector_type> vMatrixType;
+    typedef Lattice<vMatrixType> LatticeMatrixType;
+
+    LatticeMatrixType Umu(out.Grid());
+    for (int mu = 0; mu < Nd; mu++) {
+      LieRandomize(pRNG, Umu, 0.01);
+      PokeIndex<LorentzIndex>(out, Umu, mu);
+    }
   }
     
   template <typename GaugeField>
@@ -255,17 +333,31 @@ class GaugeGroup {
       ProjectOnGaugeGroup(Umu, group_name());
   }
     
-    
-  template <int N>        // reunitarise, resimplectify... previously ProjectSUn
-  static void ProjectGn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
-      ProjectGn(Umu, group_name());
-  }
 
-  template <int N>        // reunitarise, resimplectify... previously ProjectSUn
-  static void ProjectGn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
-      ProjectGn(U, group_name());
-      
-  }
+  template <int N>       // reunitarise, resimplectify... previously ProjectSUn
+  static void ProjectGn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
+       ProjectOnGaugeGroup(Umu);
+       auto det = Determinant(Umu);
+
+       det = conjugate(det);
+
+       for (int i = 0; i < N; i++) {
+           auto element = PeekIndex<ColourIndex>(Umu, N - 1, i);
+           element = element * det;
+           PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
+       }
+   }
+
+    template <int N>    // reunitarise, resimplectify... previously ProjectSUn
+    static void ProjectGn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U, GroupName::SU) {
+      GridBase *grid = U.Grid();
+      // Reunitarise
+      for (int mu = 0; mu < Nd; mu++) {
+        auto Umu = PeekIndex<LorentzIndex>(U, mu);
+        ProjectOnGaugeGroup(Umu);
+        PokeIndex<LorentzIndex>(U, Umu, mu);
+      }
+    }
 
 };
 
diff --git a/Grid/qcd/utils/SUn.impl b/Grid/qcd/utils/SUn.impl
index 18be96b1..a8a5210b 100644
--- a/Grid/qcd/utils/SUn.impl
+++ b/Grid/qcd/utils/SUn.impl
@@ -508,119 +508,6 @@ static void testGenerators(GroupName::SU) {
   std::cout << GridLogMessage << std::endl;
 }
 
-template <typename LatticeMatrixType>
-static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out, GroupName::SU,
-                         double scale = 1.0) {
-  GridBase *grid = out.Grid();
-
-  typedef typename LatticeMatrixType::vector_type vector_type;
-  typedef typename LatticeMatrixType::scalar_type scalar_type;
-
-  typedef iSinglet<vector_type> vTComplexType;
-
-  typedef Lattice<vTComplexType> LatticeComplexType;
-  typedef typename GridTypeMapper<
-      typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
-
-  LatticeComplexType ca(grid);
-  LatticeMatrixType lie(grid);
-  LatticeMatrixType la(grid);
-  ComplexD ci(0.0, scale);
-  //    ComplexD cone(1.0, 0.0);
-  MatrixType ta;
-
-  lie = Zero();
-
-  for (int a = 0; a < AdjointDimension; a++) {
-    random(pRNG, ca);
-
-    ca = (ca + conjugate(ca)) * 0.5;
-    ca = ca - 0.5;
-
-    generator(a, ta);
-
-    la = ci * ca * ta;
-
-    lie = lie + la;  // e^{i la ta}
-  }
-  taExp(lie, out);
-}
-
-static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
-                                                LatticeMatrix &out, GroupName::SU,
-                                                Real scale = 1.0) {
-  GridBase *grid = out.Grid();
-  LatticeReal ca(grid);
-  LatticeMatrix la(grid);
-  Complex ci(0.0, scale);
-  Matrix ta;
-
-  out = Zero();
-  for (int a = 0; a < AdjointDimension; a++) {
-    gaussian(pRNG, ca);
-    generator(a, ta);
-    la = toComplex(ca) * ta;
-    out += la;
-  }
-  out *= ci;
-}
-
-static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
-                                        LatticeMatrix &out, GroupName::SU,
-                                        Real scale = 1.0) {
-  conformable(h, out);
-  GridBase *grid = out.Grid();
-  LatticeMatrix la(grid);
-  Matrix ta;
-
-  out = Zero();
-  for (int a = 0; a < AdjointDimension; a++) {
-    generator(a, ta);
-    la = peekColour(h, a) * timesI(ta) * scale;
-    out += la;
-  }
-}
-
-template <typename GaugeField>
-static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out, GroupName::SU) {
-  typedef typename GaugeField::vector_type vector_type;
-  typedef iGroupMatrix<vector_type> vMatrixType;
-  typedef Lattice<vMatrixType> LatticeMatrixType;
-
-  LatticeMatrixType Umu(out.Grid());
-  for (int mu = 0; mu < Nd; mu++) {
-    LieRandomize(pRNG, Umu, 1.0);
-    PokeIndex<LorentzIndex>(out, Umu, mu);
-  }
-}
-
-template <typename GaugeField>
-static void TepidConfiguration(GridParallelRNG &pRNG, GaugeField &out, GroupName::SU) {
-  typedef typename GaugeField::vector_type vector_type;
-  typedef iGroupMatrix<vector_type> vMatrixType;
-  typedef Lattice<vMatrixType> LatticeMatrixType;
-
-  LatticeMatrixType Umu(out.Grid());
-  for (int mu = 0; mu < Nd; mu++) {
-    LieRandomize(pRNG, Umu, 0.01);
-    PokeIndex<LorentzIndex>(out, Umu, mu);
-  }
-}
-
-// Projects the algebra components a lattice matrix (of dimension ncol*ncol -1
-// ) inverse operation: FundamentalLieAlgebraMatrix
-static void projectOnAlgebra(LatticeAlgebraVector &h_out,
-                             const LatticeMatrix &in, GroupName::SU, Real scale = 1.0) {
-  conformable(h_out, in);
-  h_out = Zero();
-  Matrix Ta;
-
-  for (int a = 0; a < AdjointDimension; a++) {
-    generator(a, Ta);
-    pokeColour(h_out, -2.0 * (trace(timesI(Ta) * in)) * scale, a);
-  }
-}
-
 template <int N>
 static void ProjectOnGaugeGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::SU) {
   Umu = ProjectOnGroup(Umu);
@@ -636,32 +523,6 @@ static void ProjectOnGaugeGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,
   }
 }
 
-template <int N>
-static void ProjectGn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::SU) {
-  Umu = ProjectOnGroup(Umu);
-  auto det = Determinant(Umu);
-
-  det = conjugate(det);
-
-  for (int i = 0; i < N; i++) {
-    auto element = PeekIndex<ColourIndex>(Umu, N - 1, i);
-    element = element * det;
-    PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
-  }
-}
-
-template <int N>
-static void ProjectGn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U, GroupName::SU) {
-  GridBase *grid = U.Grid();
-  // Reunitarise
-  for (int mu = 0; mu < Nd; mu++) {
-    auto Umu = PeekIndex<LorentzIndex>(U, mu);
-    Umu = ProjectOnGroup(Umu);
-    ProjectSUn(Umu);
-    PokeIndex<LorentzIndex>(U, Umu, mu);
-  }
-}
-
 /*
  * Fundamental rep gauge xform
  */
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index 44771a14..75a1af17 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -253,119 +253,6 @@ static void testGenerators(GroupName::Sp) {
   }
 }
 
-template <typename LatticeMatrixType>
- static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out, GroupName::Sp,
-                          double scale = 1.0) {
-   GridBase *grid = out.Grid();
-
-   typedef typename LatticeMatrixType::vector_type vector_type;
-   typedef typename LatticeMatrixType::scalar_type scalar_type;
-
-   typedef iSinglet<vector_type> vTComplexType;
-
-   typedef Lattice<vTComplexType> LatticeComplexType;
-   typedef typename GridTypeMapper<
-       typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
-
-   LatticeComplexType ca(grid);
-   LatticeMatrixType lie(grid);
-   LatticeMatrixType la(grid);
-   ComplexD ci(0.0, scale);
-   //    ComplexD cone(1.0, 0.0);
-   MatrixType ta;
-
-   lie = Zero();
-
-   for (int a = 0; a < AdjointDimension; a++) {
-     random(pRNG, ca);
-
-     ca = (ca + conjugate(ca)) * 0.5;
-     ca = ca - 0.5;
-
-     generator(a, ta);
-
-     la = ci * ca * ta;
-
-     lie = lie + la;  // e^{i la ta}
-   }
-   taExp(lie, out);
- }
-
-static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
-                                                LatticeMatrix &out, GroupName::Sp,
-                                                Real scale = 1.0) {
-  GridBase *grid = out.Grid();
-  LatticeReal ca(grid);
-  LatticeMatrix la(grid);
-  Complex ci(0.0, scale);
-  Matrix ta;
-
-  out = Zero();
-  for (int a = 0; a < AdjointDimension; a++) {
-    gaussian(pRNG, ca);
-    generator(a, ta);
-    la = toComplex(ca) * ta;
-    out += la;
-  }
-  out *= ci;
-}
-
-static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
-                                        LatticeMatrix &out, GroupName::Sp,
-                                        Real scale = 1.0) {
-  conformable(h, out);
-  GridBase *grid = out.Grid();
-  LatticeMatrix la(grid);
-  Matrix ta;
-
-  out = Zero();
-  for (int a = 0; a < AdjointDimension; a++) {
-    generator(a, ta);
-    la = peekColour(h, a) * timesI(ta) * scale;
-    out += la;
-  }
-}
-
-// Projects the algebra components a lattice matrix (of dimension ncol*ncol -1
-// ) inverse operation: FundamentalLieAlgebraMatrix
-static void projectOnAlgebra(LatticeAlgebraVector &h_out,
-                             const LatticeMatrix &in, GroupName::Sp, Real scale = 1.0) {
-  conformable(h_out, in);
-  h_out = Zero();
-  Matrix Ta;
-
-  for (int a = 0; a < AdjointDimension; a++) {
-    generator(a, Ta);
-    pokeColour(h_out, -2.0 * (trace(timesI(Ta) * in)) * scale, a);
-  }
-}
-
-template <typename GaugeField>
-static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out, GroupName::Sp) {
-  typedef typename GaugeField::vector_type vector_type;
-  typedef iGroupMatrix<vector_type> vMatrixType;
-  typedef Lattice<vMatrixType> LatticeMatrixType;
-
-  LatticeMatrixType Umu(out.Grid());
-  for (int mu = 0; mu < Nd; mu++) {
-    LieRandomize(pRNG, Umu, 1.0);
-    PokeIndex<LorentzIndex>(out, Umu, mu);
-  }
-}
-
-template <typename GaugeField>
-static void TepidConfiguration(GridParallelRNG &pRNG, GaugeField &out, GroupName::Sp) {
-  typedef typename GaugeField::vector_type vector_type;
-  typedef iGroupMatrix<vector_type> vMatrixType;
-  typedef Lattice<vMatrixType> LatticeMatrixType;
-
-  LatticeMatrixType Umu(out.Grid());
-  for (int mu = 0; mu < Nd; mu++) {
-    LieRandomize(pRNG, Umu, 0.01);
-    PokeIndex<LorentzIndex>(out, Umu, mu);
-  }
-}
-
 template <int N>
 static void ProjectOnGaugeGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::Sp) {
   Umu = ProjectOnSpGroup(Umu);
@@ -381,32 +268,6 @@ static void ProjectOnGaugeGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,
   }
 }
 
-template <int N>
-static void ProjectGn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::Sp) {
-  Umu = ProjectOnSpGroup(Umu);
-  auto det = Determinant(Umu);
-
-  det = conjugate(det);
-
-  for (int i = 0; i < N; i++) {
-    auto element = PeekIndex<ColourIndex>(Umu, N - 1, i);
-    element = element * det;
-    PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
-  }
-}
-
-template <int N>
-static void ProjectGn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U, GroupName::Sp) {
-  GridBase *grid = U.Grid();
-  // Reunitarise
-  for (int mu = 0; mu < Nd; mu++) {
-    auto Umu = PeekIndex<LorentzIndex>(U, mu);
-    Umu = ProjectOnSpGroup(Umu);
-    ProjectSUn(Umu);
-    PokeIndex<LorentzIndex>(U, Umu, mu);
-  }
-}
-
 public:
 template <ONLY_IF_Sp>
 static void OmegaInvariance(ColourMatrix &in) {

From 4275b3f4313f365ac4d4996738d4ec8f1689eb13 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Mon, 3 Apr 2023 12:01:52 +0100
Subject: [PATCH 055/129] Fix typo and remove unnecessary lines

---
 Grid/qcd/utils/GaugeGroup.h | 3 +--
 Grid/qcd/utils/SUn.impl     | 1 -
 Grid/qcd/utils/Sp2n.impl    | 1 -
 3 files changed, 1 insertion(+), 4 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index 6a407706..d0cdec17 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -350,11 +350,10 @@ class GaugeGroup {
 
     template <int N>    // reunitarise, resimplectify... previously ProjectSUn
     static void ProjectGn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U, GroupName::SU) {
-      GridBase *grid = U.Grid();
       // Reunitarise
       for (int mu = 0; mu < Nd; mu++) {
         auto Umu = PeekIndex<LorentzIndex>(U, mu);
-        ProjectOnGaugeGroup(Umu);
+        ProjectGn(Umu);
         PokeIndex<LorentzIndex>(U, Umu, mu);
       }
     }
diff --git a/Grid/qcd/utils/SUn.impl b/Grid/qcd/utils/SUn.impl
index a8a5210b..0e4b6124 100644
--- a/Grid/qcd/utils/SUn.impl
+++ b/Grid/qcd/utils/SUn.impl
@@ -515,7 +515,6 @@ static void ProjectOnGaugeGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> >
 
 template <int N>
 static void ProjectOnGaugeGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U, GroupName::SU) {
-  GridBase *grid = U.Grid();
   // Reunitarise
   for (int mu = 0; mu < Nd; mu++) {
     auto Umu = PeekIndex<LorentzIndex>(U, mu);
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index 75a1af17..77da9ad0 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -260,7 +260,6 @@ static void ProjectOnGaugeGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> >
 
 template <int N>
 static void ProjectOnGaugeGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U, GroupName::Sp) {
-  GridBase *grid = U.Grid();
   // Reunitarise
   for (int mu = 0; mu < Nd; mu++) {
     auto Umu = PeekIndex<LorentzIndex>(U, mu);

From 026e736dfabdb256056a5fc6dc31d443556a5bfc Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Mon, 3 Apr 2023 16:31:19 +0100
Subject: [PATCH 056/129] Projection on algebra can now be templated. Fix #12

---
 Grid/lattice/Lattice_ET.h        |   2 +
 Grid/qcd/utils/Sp2n.impl         |  24 +++-
 Grid/tensors/Tensor_Ta.h         |  80 ++++++++++++
 tests/sp2n/Test_project_on_Sp.cc | 211 +++++++++++++++++++++++--------
 4 files changed, 261 insertions(+), 56 deletions(-)

diff --git a/Grid/lattice/Lattice_ET.h b/Grid/lattice/Lattice_ET.h
index 9042eb8f..661d7441 100644
--- a/Grid/lattice/Lattice_ET.h
+++ b/Grid/lattice/Lattice_ET.h
@@ -345,6 +345,7 @@ GridUnopClass(UnaryNot, Not(a));
 GridUnopClass(UnaryTrace, trace(a));
 GridUnopClass(UnaryTranspose, transpose(a));
 GridUnopClass(UnaryTa, Ta(a));
+GridUnopClass(UnaryProjectSp2nAlgebra, ProjectSp2nAlgebra(a));
 GridUnopClass(UnaryProjectOnGroup, ProjectOnGroup(a));
 GridUnopClass(UnaryProjectOnSpGroup, ProjectOnSpGroup(a));
 GridUnopClass(UnaryTimesI, timesI(a));
@@ -457,6 +458,7 @@ GRID_DEF_UNOP(operator!, UnaryNot);
 GRID_DEF_UNOP(trace, UnaryTrace);
 GRID_DEF_UNOP(transpose, UnaryTranspose);
 GRID_DEF_UNOP(Ta, UnaryTa);
+GRID_DEF_UNOP(ProjectSp2nAlgebra, UnaryProjectSp2nAlgebra);
 GRID_DEF_UNOP(ProjectOnGroup, UnaryProjectOnGroup);
 GRID_DEF_UNOP(ProjectOnSpGroup, UnaryProjectOnSpGroup);
 GRID_DEF_UNOP(timesI, UnaryTimesI);
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index 77da9ad0..347eb3ce 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -274,8 +274,6 @@ static void OmegaInvariance(ColourMatrix &in) {
   Omega = Zero();
   const int nsp=ncolour/2;
 
-  std::cout << GridLogMessage << "I am a ColourMatrix" << std::endl;
-
   // for (int i = 0; i < ncolour; i++)         wrong?!
   //{
   //     Omega()()(i, 2*ncolour-1-i) = 1.;
@@ -314,8 +312,6 @@ static void OmegaInvariance(GaugeField &in) {
   Omega = Zero();
   identity = 1.;
 
-  std::cout << GridLogMessage << "I am a GaugeField " << std::endl;
-
   U = PeekIndex<LorentzIndex>(in, 1);
 
   OmegaInvariance(U);
@@ -333,8 +329,6 @@ static void OmegaInvariance(LatticeColourMatrixD &in) {
   Omega = Zero();
   identity = 1.;
 
-  std::cout << GridLogMessage << "I am a LatticeColourMatrix " << std::endl;
-
   for (int i = 0; i < nsp; i++) {
     Omega()()(i, nsp + i) = 1.;
     Omega()()(nsp + i, i) = -1;
@@ -356,3 +350,21 @@ static void OmegaInvariance(LatticeColourMatrixD &in) {
   }
 }
 
+template <ONLY_IF_Sp>
+static void Omega(LatticeColourMatrixD &in) {
+  const int nsp=ncolour/2;
+  LatticeColourMatrixD OmegaLatt(in.Grid());
+  LatticeColourMatrixD identity(in.Grid());
+  ColourMatrix Omega;
+
+  OmegaLatt = Zero();
+  Omega = Zero();
+  identity = 1.;
+
+  for (int i = 0; i < nsp; i++) {
+    Omega()()(i, nsp + i) = 1.;
+    Omega()()(nsp + i, i) = -1;
+  }
+  OmegaLatt = OmegaLatt + (identity * Omega);
+  in = OmegaLatt;
+}
diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index 2ee51fb4..87169ffc 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -66,6 +66,86 @@ template<class vtype,int N> accelerator_inline iMatrix<vtype,N> Ta(const iMatrix
   return ret;
 }
 
+// for sp2n can't do something as simple as Ta. We do a Gram-Schmidt
+
+template<class vtype> accelerator_inline iScalar<vtype> ProjectSp2nAlgebra(const iScalar<vtype>&r)
+{
+  iScalar<vtype> ret;
+  ret._internal = ProjectSp2nAlgebra(r._internal);
+  return ret;
+}
+template<class vtype,int N> accelerator_inline iVector<vtype,N> ProjectSp2nAlgebra(const iVector<vtype,N>&r)
+{
+  iVector<vtype,N> ret;
+  for(int i=0;i<N;i++){
+    ret._internal[i] = ProjectSp2nAlgebra(r._internal[i]);
+  }
+  return ret;
+}
+template<class vtype,int N> accelerator_inline iMatrix<vtype,N> ProjectSp2nAlgebra(const iMatrix<vtype,N> &arg)
+{
+    iMatrix<vtype,N> ret;
+    vtype nrm;
+    vtype inner;
+    vtype tmp;
+    
+    for(int c1=0;c1<N/2;c1++)
+    {
+        
+        for (int b=0; b<c1; b++)                  // remove the b-rows from U_c1
+        {
+            decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
+            decltype(ret._internal[b][b]*ret._internal[b][b]) prn;
+            zeroit(pr);
+            zeroit(prn);
+            
+            for(int c=0; c<N; c++)
+            {
+                pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];        // <U_c1 | U_b >
+                prn += conjugate(ret._internal[c1][c])*ret._internal[b+N/2][c];   // <U_c1 | U_{b+N} >
+            }
+         
+
+            for(int c=0; c<N; c++)
+            {
+                ret._internal[c1][c] -= (conjugate(pr) * ret._internal[b][c] + conjugate(prn) * ret._internal[b+N/2][c] );    //  U_c1 -= (  <U_c1 | U_b > U_b + <U_c1 | U_{b+N} > U_{b+N}  )
+            }
+        }
+      
+        zeroit(inner);
+        for(int c2=0;c2<N;c2++)
+        {
+            inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
+        }
+        
+        nrm = sqrt(inner);
+        nrm = 1.0/nrm;
+        for(int c2=0;c2<N;c2++)
+        {
+            ret._internal[c1][c2]*= nrm;
+        }
+        
+
+        for(int c2=0;c2<N/2;c2++)
+        {
+            tmp = conjugate(ret._internal[c1][c2]);       // (up-left)* of the old matrix
+            ret._internal[c1+N/2][c2+N/2] = -tmp;          // down right in the new matrix = -(up-left)* of the old matrix
+        }
+           
+        for(int c2=N/2;c2<N;c2++)
+        {
+            tmp = conjugate(ret._internal[c1][c2]);   // (up-right)* of the old
+            ret._internal[c1+N/2][c2-N/2] = tmp;     // down left in the new matrix = (up-right)* of the old
+        }
+      
+        
+    }
+    
+  
+  return ret;
+}
+
+
 
 /////////////////////////////////////////////// 
 // ProjectOnGroup function for scalar, vector, matrix 
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 36b95cf4..eefee4f8 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -20,6 +20,12 @@ int main (int argc, char **argv)
     LatticeColourMatrixD aux(&Grid);
     LatticeColourMatrixD identity(&Grid);
     
+    // Will test resimplectification-related functionalities (from ProjectOnGaugeGroup, ProjectOnSpGroup, ProjectGn) and projection on the algebra (from ProjectSp2nAlgebra)
+    // we work with matrices with positive determinant so detU = 1 even if in principle ProjectOnGaugeGroup and ProjectOnSpGroup allow for detU=-1
+    // so the checks will be the same for the three functions
+    // NB only ProjectGn is the proper simplectification function
+    
+    
     const int nsp = Nc / 2;
     
     identity = 1.0;
@@ -29,15 +35,12 @@ int main (int argc, char **argv)
     double vol = Umu.Grid()->gSites();
     
     std::vector<int> pseeds({1,2,3,4,5});
-    std::vector<int> sseeds({6,7,8,9,10});
     GridParallelRNG  pRNG(&Grid); pRNG.SeedFixedIntegers(pseeds);
-    GridSerialRNG    sRNG;       sRNG.SeedFixedIntegers(sseeds);
     
     SU<Nc>::HotConfiguration(pRNG,Umu);
-    U = PeekIndex<LorentzIndex>(Umu,2);
+    U = PeekIndex<LorentzIndex>(Umu,0);
     
     aux = U*adj(U) - identity;
-    std::cout <<GridLogMessage << std::endl;
     std::cout << GridLogMessage << "Starting with random SUn matrix " << std::endl;
     std::cout << GridLogMessage << "Unitary check " << std::endl;
     std::cout <<GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
@@ -55,35 +58,23 @@ int main (int argc, char **argv)
     
     std::cout << GridLogMessage << "Unitary matrix deformed " << std::endl;
     std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl;
-    std::cout <<GridLogMessage << std::endl;
-
-    std::cout <<GridLogMessage << std::endl;
-    std::cout << GridLogMessage << "Projecting on Sp2n " << std::endl;
-
+    
+    //  Testing ProjectOnSpGroup
+    std::cout << GridLogMessage << "Testing ProjectOnSpGroup" << std::endl;
+    std::cout << GridLogMessage << "Apply ProjectOnSpGroup to deformed matrix" << std::endl;
     U = ProjectOnSpGroup(U);
-    //U = ProjectOnGroup(U);
+
     aux = U*adj(U) - identity;
-    std::cout <<GridLogMessage << std::endl;
-    std::cout <<GridLogMessage << std::endl;
-    std::cout << GridLogMessage << "Unitary check after Sp(2n) projection " << std::endl;
+    std::cout << GridLogMessage << "Unitary check after ProjectOnSpGroup " << std::endl;
     std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
     assert( norm2(aux) < 1e-8);
-    std::cout <<GridLogMessage << std::endl;
-    std::cout <<GridLogMessage << std::endl;
-    
-    // checks on determinant
-    std::cout << GridLogMessage << "Det after Projection on Sp2n = " << norm2( Determinant(U) ) / vol << std::endl;
-    std::cout <<GridLogMessage << std::endl;
-    std::cout <<GridLogMessage << std::endl;
     
     // actual sp2n check
-    std::cout << GridLogMessage << "Checking invariance after projection "<< std::endl;
-    Sp<Nc>::OmegaInvariance(U);
+    std::cout << GridLogMessage << "Checking Omega invariance after ProjectOnSpGroup" << std::endl;
+    Sp<Nc>::OmegaInvariance(U);     // no assertion here, but the next check will kill us if we are not simplectic
     
     // checks on elements
     
-    std::cout <<GridLogMessage << std::endl;
-    std::cout <<GridLogMessage << std::endl;
     std::cout << GridLogMessage << "Checking the structure is " << std::endl;
     std::cout << GridLogMessage << "U  =  (   W    X   )  " << std::endl;
     std::cout << GridLogMessage << "      (  -X^*  W^* )  " << std::endl;
@@ -119,38 +110,158 @@ int main (int argc, char **argv)
         }
     }
     
-    std::cout << GridLogMessage << "ok" << std::endl;
     
-    // an explicit check for sp2
-    /*
-    if (Nc == 2)
+    std::cout << GridLogMessage << "Testing ProjectOnGaugeGroup" << std::endl;
+    U = U + 2932.111*identity;
+    std::cout << GridLogMessage << "Apply ProjectOnGaugeGroup to deformed matrix" << std::endl;
+    Sp<Nc>::ProjectOnGaugeGroup(U);
+    aux = U*adj(U) - identity;
+    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+    assert( norm2(aux) < 1e-8);
+    Sp<Nc>::OmegaInvariance(U);
+    
+    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
     {
-        assert(Nc==2);
-        ColourMatrix A;
-        A = Zero();
+        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 );
+        }
+        
+    }
 
-        Complex a(25041994., 12.);
-        Complex b(39., 0.22);
-        Complex d(10000., -2222.3333);
+    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 << "Testing ProjectGn" << std::endl;
+    U = U + 2932.111*identity;
+    std::cout << GridLogMessage << "Apply ProjectGn to deformed matrix" << std::endl;
+    Sp<Nc>::ProjectGn(U);
+    aux = U*adj(U) - identity;
+    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+    assert( norm2(aux) < 1e-8);
+    std::cout << GridLogMessage << "Det after ProjectGn = " << norm2( Determinant(U) ) / vol << std::endl;
+    assert( norm2(aux) - 1 < 1e-8);
+    Sp<Nc>::OmegaInvariance(U);
+    
+    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 << "Testing ProjectSp2nAlgebra" << std::endl;
+    
+    U = PeekIndex<LorentzIndex>(Umu,1);
+    U = U + 666.*identity;
+    aux = U*adj(U) - identity;
+    std::cout << GridLogMessage << "Matrix deformed " << std::endl;
+    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+    std::cout << GridLogMessage << "Apply ProjectSp2nAlgebra to deformed matrix" << std::endl;
+    U = ProjectSp2nAlgebra(U);
+    aux = U*adj(U) - identity;
+    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+    assert( norm2(aux) < 1e-8);
+    std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)" << std::endl;
+    
+    LatticeColourMatrixD Omega(&Grid);
+    
+    Sp<Nc>::Omega(Omega);
+    aux = Omega*U*Omega - conjugate(U);
+    std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
+    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 );
+        }
+    }
+    
     
-        A()()(0,0) = a;
-        A()()(0,1) = b;
-        A()()(1,0) = i;
-        A()()(1,1) = d;
-        std::cout <<GridLogMessage << std::endl;
-        std::cout <<GridLogMessage << std::endl;
-        std::cout << GridLogMessage << "An explicit check for Sp2" << std::endl;
-        std::cout <<GridLogMessage << std::endl;
-        std::cout << GridLogMessage << "Building a non unitary matrix by hand with funny entries " << std::endl;
-        std::cout << GridLogMessage << "A = " << A << std::endl;
-        std::cout << GridLogMessage << "Projecting on Sp2 " << std::endl;
-        A = ProjectOnSpGroup(A);
-        std::cout << GridLogMessage << "now A = " << A << std::endl;
-        std::cout << GridLogMessage << "A(0,0) - conjA(1,1) = " << A()()(0,0) - adj ( A()()(1,1) )<< std::endl;
-        std::cout << GridLogMessage << "A(0,1) + conjA(1,0) = " << A()()(0,1) + adj ( A()()(1,0) )<< std::endl;
-    }*/
     
     Grid_finalize();
 
 
 }
+

From 778291230a9adc61dc8da161a521bf0ffb37fc39 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 4 Apr 2023 17:48:13 +0100
Subject: [PATCH 057/129] expand ProjecOnGaugeGroup, change
 ProjectOnSp2nAlgebra into SpTa, fixing some of its issues

---
 Grid/lattice/Lattice_ET.h        |  4 +-
 Grid/qcd/utils/GaugeGroup.h      | 33 ++++++++++-
 Grid/qcd/utils/SUn.impl          | 39 +++++++++++++
 Grid/qcd/utils/Sp2n.impl         | 35 +++++++++++
 Grid/tensors/Tensor_Ta.h         | 18 +++---
 tests/sp2n/Test_project_on_Sp.cc | 99 ++++++++++++++++++++++++++++----
 6 files changed, 202 insertions(+), 26 deletions(-)

diff --git a/Grid/lattice/Lattice_ET.h b/Grid/lattice/Lattice_ET.h
index 661d7441..c7f8382c 100644
--- a/Grid/lattice/Lattice_ET.h
+++ b/Grid/lattice/Lattice_ET.h
@@ -345,7 +345,7 @@ GridUnopClass(UnaryNot, Not(a));
 GridUnopClass(UnaryTrace, trace(a));
 GridUnopClass(UnaryTranspose, transpose(a));
 GridUnopClass(UnaryTa, Ta(a));
-GridUnopClass(UnaryProjectSp2nAlgebra, ProjectSp2nAlgebra(a));
+GridUnopClass(UnarySpTa, SpTa(a));
 GridUnopClass(UnaryProjectOnGroup, ProjectOnGroup(a));
 GridUnopClass(UnaryProjectOnSpGroup, ProjectOnSpGroup(a));
 GridUnopClass(UnaryTimesI, timesI(a));
@@ -458,7 +458,7 @@ GRID_DEF_UNOP(operator!, UnaryNot);
 GRID_DEF_UNOP(trace, UnaryTrace);
 GRID_DEF_UNOP(transpose, UnaryTranspose);
 GRID_DEF_UNOP(Ta, UnaryTa);
-GRID_DEF_UNOP(ProjectSp2nAlgebra, UnaryProjectSp2nAlgebra);
+GRID_DEF_UNOP(SpTa, UnarySpTa);
 GRID_DEF_UNOP(ProjectOnGroup, UnaryProjectOnGroup);
 GRID_DEF_UNOP(ProjectOnSpGroup, UnaryProjectOnSpGroup);
 GRID_DEF_UNOP(timesI, UnaryTimesI);
diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index d0cdec17..8e6c5ee4 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -300,9 +300,10 @@ class GaugeGroup {
     ColdConfiguration(out);
   }
 
-  template <typename LatticeMatrixType, ONLY_IF_SU>
+  template <typename LatticeMatrixType>
   static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out) {
-    out = Ta(in);
+    taProj(in, out, group_name());
+    //out = Ta(in);
   }
     
   template <typename LatticeMatrixType>
@@ -333,6 +334,32 @@ class GaugeGroup {
       ProjectOnGaugeGroup(Umu, group_name());
   }
     
+    template <class vtype>
+    static void ProjectOnGaugeGroup(iScalar<vtype> &r) {
+      ProjectOnGaugeGroup(r, group_name());
+    }
+
+    template <class vtype, int N>
+    static void ProjectOnGaugeGroup(iVector<vtype,N> &r) {
+      r = ProjectOnGaugeGroup(r, group_name());
+    }
+
+    template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
+    static void ProjectOnGaugeGroup(iMatrix<vtype,N> &arg) {
+      arg = ProjectOnGaugeGroup(arg, group_name());
+    }
+
+    
+/*
+  template <int N>        // reunitarise, resimplectify...
+  static void ProjectOnGaugeGroup(iVector<iScalar<iMatrix<vComplexD, N> >, Nd> &U) {
+      ProjectOnGaugeGroup(U, group_name());
+  }
+         
+  template <int N>        // reunitarise, resimplectify...
+  static void ProjectOnGaugeGroup(iScalar<iScalar<iMatrix<vComplexD, N> > > &Umu) {
+      ProjectOnGaugeGroup(Umu, group_name());
+  }*/
 
   template <int N>       // reunitarise, resimplectify... previously ProjectSUn
   static void ProjectGn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
@@ -349,7 +376,7 @@ class GaugeGroup {
    }
 
     template <int N>    // reunitarise, resimplectify... previously ProjectSUn
-    static void ProjectGn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U, GroupName::SU) {
+    static void ProjectGn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
       // Reunitarise
       for (int mu = 0; mu < Nd; mu++) {
         auto Umu = PeekIndex<LorentzIndex>(U, mu);
diff --git a/Grid/qcd/utils/SUn.impl b/Grid/qcd/utils/SUn.impl
index 0e4b6124..a5d2e2f1 100644
--- a/Grid/qcd/utils/SUn.impl
+++ b/Grid/qcd/utils/SUn.impl
@@ -508,6 +508,7 @@ static void testGenerators(GroupName::SU) {
   std::cout << GridLogMessage << std::endl;
 }
 
+
 template <int N>
 static void ProjectOnGaugeGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::SU) {
   Umu = ProjectOnGroup(Umu);
@@ -522,6 +523,44 @@ static void ProjectOnGaugeGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,
   }
 }
 
+template <class vtype>
+static void ProjectOnGaugeGroup(iScalar<vtype> &r, GroupName::SU) {
+  r = ProjectOnGroup(r);
+}
+
+template <class vtype, int N>
+static void ProjectOnGaugeGroup(iVector<vtype,N> &r, GroupName::SU) {
+  r = ProjectOnGroup(r);
+}
+
+template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
+static void ProjectOnGaugeGroup(iMatrix<vtype,N> &arg, GroupName::SU) {
+  arg = ProjectOnGroup(arg);
+}
+
+
+
+
+/*
+template <int N>    // non-lattice objects
+static void ProjectOnGaugeGroup(iScalar<iScalar<iMatrix<vComplexD, N> > >  &Umu, GroupName::SU) {
+  Umu = ProjectOnGroup(Umu);
+ }
+
+template <int N>
+static void ProjectOnGaugeGroup(iVector<iScalar<iMatrix<vComplexD, N> >, Nd>  &U, GroupName::SU) {
+  // Reunitarise
+  for (int mu = 0; mu < Nd; mu++) {
+    auto Umu = PeekIndex<LorentzIndex>(U, mu);
+    Umu = ProjectOnGroup(Umu);
+  }
+}*/
+
+template <typename LatticeMatrixType>
+static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::SU) {
+  out = Ta(in);
+}
+
 /*
  * Fundamental rep gauge xform
  */
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index 347eb3ce..59b56b1f 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -267,6 +267,41 @@ static void ProjectOnGaugeGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,
   }
 }
 
+template <class vtype>
+static void ProjectOnGaugeGroup(iScalar<vtype> &r, GroupName::Sp) {
+  r = ProjectOnSpGroup(r);
+}
+
+template <class vtype, int N>
+static void ProjectOnGaugeGroup(iVector<vtype,N> &r, GroupName::Sp) {
+  r = ProjectOnSpGroup(r);
+}
+
+template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
+static void ProjectOnGaugeGroup(iMatrix<vtype,N> &arg, GroupName::Sp) {
+  arg = ProjectOnSpGroup(arg);
+}
+
+/*
+template <int N>    // non-lattice objects
+static void ProjectOnGaugeGroup(iScalar<iScalar<iMatrix<vComplexD, N> > >  &Umu, GroupName::Sp) {
+  Umu = ProjectOnSpGroup(Umu);
+ }
+
+template <int N>
+static void ProjectOnGaugeGroup(iVector<iScalar<iMatrix<vComplexD, N> >, Nd>  &U, GroupName::Sp) {
+  // Reunitarise
+  for (int mu = 0; mu < Nd; mu++) {
+    auto Umu = PeekIndex<LorentzIndex>(U, mu);
+    Umu = ProjectOnSpGroup(Umu);
+  }
+}*/
+
+template <typename LatticeMatrixType>   
+static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::Sp) {
+  out = SpTa(in);
+}
+
 public:
 template <ONLY_IF_Sp>
 static void OmegaInvariance(ColourMatrix &in) {
diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index 87169ffc..a7103343 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -66,23 +66,23 @@ template<class vtype,int N> accelerator_inline iMatrix<vtype,N> Ta(const iMatrix
   return ret;
 }
 
-// for sp2n can't do something as simple as Ta. We do a Gram-Schmidt
+// for sp2n can't be as simple as Ta. We do a Gram-Schmidt
 
-template<class vtype> accelerator_inline iScalar<vtype> ProjectSp2nAlgebra(const iScalar<vtype>&r)
+template<class vtype> accelerator_inline iScalar<vtype> SpTa(const iScalar<vtype>&r)
 {
   iScalar<vtype> ret;
-  ret._internal = ProjectSp2nAlgebra(r._internal);
-  return ret;
+  ret._internal = SpTa(r._internal);
+  return Ta(ret);
 }
-template<class vtype,int N> accelerator_inline iVector<vtype,N> ProjectSp2nAlgebra(const iVector<vtype,N>&r)
+template<class vtype,int N> accelerator_inline iVector<vtype,N> SpTa(const iVector<vtype,N>&r)
 {
   iVector<vtype,N> ret;
   for(int i=0;i<N;i++){
-    ret._internal[i] = ProjectSp2nAlgebra(r._internal[i]);
+    ret._internal[i] = SpTa(r._internal[i]);
   }
-  return ret;
+  return Ta(ret);
 }
-template<class vtype,int N> accelerator_inline iMatrix<vtype,N> ProjectSp2nAlgebra(const iMatrix<vtype,N> &arg)
+template<class vtype,int N> accelerator_inline iMatrix<vtype,N> SpTa(const iMatrix<vtype,N> &arg)
 {
     iMatrix<vtype,N> ret;
     vtype nrm;
@@ -142,7 +142,7 @@ template<class vtype,int N> accelerator_inline iMatrix<vtype,N> ProjectSp2nAlgeb
     }
     
   
-  return ret;
+  return Ta(ret);
 }
 
 
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index eefee4f8..516a7f93 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -17,6 +17,7 @@ int main (int argc, char **argv)
     
     LatticeGaugeField Umu(&Grid);
     LatticeColourMatrixD U(&Grid);
+    LatticeColourMatrixD Up(&Grid);
     LatticeColourMatrixD aux(&Grid);
     LatticeColourMatrixD identity(&Grid);
     
@@ -59,6 +60,11 @@ int main (int argc, char **argv)
     std::cout << GridLogMessage << "Unitary matrix deformed " << std::endl;
     std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl;
     
+    std::cout <<GridLogMessage << std::endl;
+    std::cout << GridLogMessage << "#   #   #   #" << std::endl;
+    std::cout << GridLogMessage << "Group" << std::endl;
+    std::cout << GridLogMessage << "#   #   #   #" << std::endl;
+    std::cout <<GridLogMessage << std::endl;
     //  Testing ProjectOnSpGroup
     std::cout << GridLogMessage << "Testing ProjectOnSpGroup" << std::endl;
     std::cout << GridLogMessage << "Apply ProjectOnSpGroup to deformed matrix" << std::endl;
@@ -123,7 +129,7 @@ int main (int argc, char **argv)
     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++)
@@ -200,23 +206,27 @@ int main (int argc, char **argv)
             assert(  amizeroo.real() < 10e-6 );
         }
     }
-    
-    std::cout << GridLogMessage << "Testing ProjectSp2nAlgebra" << std::endl;
+    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;
     
     U = PeekIndex<LorentzIndex>(Umu,1);
     U = U + 666.*identity;
-    aux = U*adj(U) - identity;
     std::cout << GridLogMessage << "Matrix deformed " << std::endl;
-    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
-    std::cout << GridLogMessage << "Apply ProjectSp2nAlgebra to deformed matrix" << std::endl;
-    U = ProjectSp2nAlgebra(U);
-    aux = U*adj(U) - identity;
-    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
+    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;
+    
     std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)" << std::endl;
-    
+
     LatticeColourMatrixD Omega(&Grid);
-    
     Sp<Nc>::Omega(Omega);
     aux = Omega*U*Omega - conjugate(U);
     std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
@@ -258,6 +268,71 @@ int main (int argc, char **argv)
         }
     }
     
+    //test Ta
+    /*
+    U = U + 666.*identity;
+    Up = Ta(U);
+    aux = Up - adj(Up);
+    std::cout << GridLogMessage << "TA !!! T - Tda = " << norm2(aux) << std::endl;
+    aux = Up + adj(Up);
+    std::cout << GridLogMessage << "TA !!! T + Tda = " << norm2(aux) << std::endl;*/
+    
+    // test taProj
+    std::cout << GridLogMessage << "Testing taProj" << std::endl;
+    U = U + 666.*identity;
+    std::cout << GridLogMessage << "Matrix deformed " << std::endl;
+    std::cout << GridLogMessage << "Apply taProj to deformed matrix" << std::endl;
+    Sp<Nc>::taProj(U, Up);
+    aux = Up - adj(Up);
+    std::cout << GridLogMessage << "taProj ::: T - Tda = " << norm2(aux) << std::endl;
+    aux = Up + adj(Up);
+    std::cout << GridLogMessage << "taProj ::: T + Tda = " << norm2(aux) << std::endl;
+    
+    std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)" << std::endl;
+    Sp<Nc>::Omega(Omega);
+    aux = Omega*Up*Omega - conjugate(Up);
+    std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
+    assert( norm2(aux) < 1e-8);
+    // before it was
+    aux = Omega*U*Omega - conjugate(U);
+    std::cout << GridLogMessage << " before taProj Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
+
+    U = Up;
+    
+    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 );
+        }
+    }
     
     
     Grid_finalize();

From 4ea29b8f0f1c619bebe1853b9b2dd39ced8f4762 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 4 Apr 2023 17:49:28 +0100
Subject: [PATCH 058/129] Template group into GaugeImplTypes. Closing #2

---
 Grid/qcd/action/gauge/GaugeImplTypes.h | 106 ++++++-------------------
 1 file changed, 24 insertions(+), 82 deletions(-)

diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index 5a8887f2..17bee86a 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -62,7 +62,7 @@ NAMESPACE_BEGIN(Grid);
 
 // hardcodes the exponential approximation in the template
 //template <class S, int Nrepresentation = Nc, int Nexp = 12 > class GaugeImplTypes {
-template <class S, int Nrepresentation = Nc, int Nexp = 12, bool isSp2n = false > class GaugeImplTypes {
+template <class S, int Nrepresentation = Nc, int Nexp = 12, class Group = SU<Nc> > class GaugeImplTypes {
 public:
   typedef S Simd;
   typedef typename Simd::scalar_type scalar_type;
@@ -80,7 +80,7 @@ public:
   typedef Lattice<SiteLink>    LinkField; 
   typedef Lattice<SiteField>   Field;
 
-  typedef SU<Nrepresentation> Group;
+  //typedef SU<Nrepresentation> Group;
 
   // Guido: we can probably separate the types from the HMC functions
   // this will create 2 kind of implementations
@@ -124,53 +124,31 @@ public:
 
     for (int mu = 0; mu < Nd; mu++)
     {
-        if (isSp2n == true)
-        {
-            //const int nSp = Nrepresentation/2;
-            Sp<Nrepresentation>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
-        } else
-        {
-        
-
-            Group::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
-        }
-
+      Group::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
       RealD scale = ::sqrt(HMC_MOMENTUM_DENOMINATOR) ;
       Pmu = Pmu*scale;
       PokeIndex<LorentzIndex>(P, Pmu, mu);
     }
   }
     
-    
-
   static inline Field projectForce(Field &P)
     {
-        if (isSp2n == true)
-        {
-            P = Ta(P);
-            //const int nsp = Nc / 2;
-
-            Sp<Nc>::iGroupMatrix<Complex> gen;
-            
-
-            auto Psum = P;
-
-            Psum = Zero();
-            
-            for (int a = 0; a < Sp<Nrepresentation>::AlgebraDimension; a++)
+        /*  // this works
+        iScalar<iScalar<iMatrix<Complex, Nc> > > gen;
+        auto Psum = P;
+        Psum = Zero();
+        for (int a = 0; a < Group::AlgebraDimension; a++)
             {
-                Sp<Nrepresentation>::generator(a, gen);
-
+                Group::generator(a, gen);
                 auto coeff = 2. * trace(P * gen);
                 Psum += coeff * gen;
-            }
             
-            return Psum;
-            
-        } else
-        {
-            return Ta(P);
-        }
+                   
+        return Psum;}*/
+        //this doesnt
+        Field ret(P.Grid());
+        Group::taProj(P, ret);
+        return ret;
     }
 
   static inline void update_field(Field& P, Field& U, double ep){
@@ -181,14 +159,8 @@ public:
     autoView(P_v,P,AcceleratorRead);
     accelerator_for(ss, P.Grid()->oSites(),1,{
       for (int mu = 0; mu < Nd; mu++) {
-          if (isSp2n == true)
-          {
-              U_v[ss](mu) = ProjectOnSpGroup(Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu));
-          } else
-          {
-              U_v[ss](mu) = ProjectOnGroup(Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu));
-          }
-        
+          U_v[ss](mu) = Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu);  //
+          Group::ProjectOnGaugeGroup(U_v[ss](mu));
       }
     });
    //auto end = std::chrono::high_resolution_clock::now();
@@ -209,52 +181,22 @@ public:
 
   static inline void Project(Field &U)
   {
-      if (isSp2n == true)
-      {
-          ProjectSp2n(U);
-      } else
-      {
-          ProjectSUn(U);
-      }
+      Group::ProjectGn(U);
   }
 
-
   static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U)
   {
-      if (isSp2n == true)
-      {
-          //const int nSp = Nrepresentation/2;
-          Sp<Nrepresentation>::HotConfiguration(pRNG, U);
-      } else
-      {
-          Group::HotConfiguration(pRNG, U);
-      }
+      Group::HotConfiguration(pRNG, U);
   }
 
   static inline void TepidConfiguration(GridParallelRNG &pRNG, Field &U)
   {
-      if (isSp2n == true)
-    {
-        //const int nSp = Nrepresentation/2;
-        Sp<Nrepresentation>::TepidConfiguration(pRNG, U);
-    } else
-    {
-        Group::TepidConfiguration(pRNG, U);
-    }
+    Group::TepidConfiguration(pRNG, U);
   }
 
-
   static inline void ColdConfiguration(GridParallelRNG &pRNG, Field &U)
   {
-      if (isSp2n == true)
-      {
-          //const int nSp = Nrepresentation/2;
-          Sp<Nrepresentation>::ColdConfiguration(pRNG, U);
-      } else
-      {
-          Group::ColdConfiguration(pRNG, U);
-      }
-
+    Group::ColdConfiguration(pRNG, U);
   }
 
 };
@@ -264,9 +206,9 @@ typedef GaugeImplTypes<vComplex, Nc> GimplTypesR;
 typedef GaugeImplTypes<vComplexF, Nc> GimplTypesF;
 typedef GaugeImplTypes<vComplexD, Nc> GimplTypesD;
 
-typedef GaugeImplTypes<vComplex, Nc, 12, true> SymplGimplTypesR;
-typedef GaugeImplTypes<vComplexF, Nc, 12, true> SymplGimplTypesF;
-typedef GaugeImplTypes<vComplexD, Nc, 12, true> SymplGimplTypesD;
+typedef GaugeImplTypes<vComplex, Nc, 12, Sp<Nc>> SymplGimplTypesR;
+typedef GaugeImplTypes<vComplexF, Nc, 12, Sp<Nc>> SymplGimplTypesF;
+typedef GaugeImplTypes<vComplexD, Nc, 12, Sp<Nc>> SymplGimplTypesD;
 
 typedef GaugeImplTypes<vComplex, SU<Nc>::AdjointDimension> GimplAdjointTypesR;
 typedef GaugeImplTypes<vComplexF, SU<Nc>::AdjointDimension> GimplAdjointTypesF;

From 178376f24bb99a99f268573a0239f88cd897e3b1 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Thu, 6 Apr 2023 12:08:17 +0100
Subject: [PATCH 059/129] minor stylistic changes

---
 Grid/qcd/action/gauge/GaugeImplTypes.h | 21 ++++-----------------
 Grid/qcd/utils/GaugeGroup.h            |  2 +-
 tests/core/Test_reunitarise.cc         | 12 ++++--------
 tests/sp2n/Test_project_on_Sp.cc       | 14 ++++++--------
 4 files changed, 15 insertions(+), 34 deletions(-)

diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index 17bee86a..e2d98b85 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -133,19 +133,6 @@ public:
     
   static inline Field projectForce(Field &P)
     {
-        /*  // this works
-        iScalar<iScalar<iMatrix<Complex, Nc> > > gen;
-        auto Psum = P;
-        Psum = Zero();
-        for (int a = 0; a < Group::AlgebraDimension; a++)
-            {
-                Group::generator(a, gen);
-                auto coeff = 2. * trace(P * gen);
-                Psum += coeff * gen;
-            
-                   
-        return Psum;}*/
-        //this doesnt
         Field ret(P.Grid());
         Group::taProj(P, ret);
         return ret;
@@ -159,7 +146,7 @@ public:
     autoView(P_v,P,AcceleratorRead);
     accelerator_for(ss, P.Grid()->oSites(),1,{
       for (int mu = 0; mu < Nd; mu++) {
-          U_v[ss](mu) = Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu);  //
+          U_v[ss](mu) = Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu);
           Group::ProjectOnGaugeGroup(U_v[ss](mu));
       }
     });
@@ -206,9 +193,9 @@ typedef GaugeImplTypes<vComplex, Nc> GimplTypesR;
 typedef GaugeImplTypes<vComplexF, Nc> GimplTypesF;
 typedef GaugeImplTypes<vComplexD, Nc> GimplTypesD;
 
-typedef GaugeImplTypes<vComplex, Nc, 12, Sp<Nc>> SymplGimplTypesR;
-typedef GaugeImplTypes<vComplexF, Nc, 12, Sp<Nc>> SymplGimplTypesF;
-typedef GaugeImplTypes<vComplexD, Nc, 12, Sp<Nc>> SymplGimplTypesD;
+typedef GaugeImplTypes<vComplex, Nc, 12, Sp<Nc> > SymplGimplTypesR;
+typedef GaugeImplTypes<vComplexF, Nc, 12, Sp<Nc> > SymplGimplTypesF;
+typedef GaugeImplTypes<vComplexD, Nc, 12, Sp<Nc> > SymplGimplTypesD;
 
 typedef GaugeImplTypes<vComplex, SU<Nc>::AdjointDimension> GimplAdjointTypesR;
 typedef GaugeImplTypes<vComplexF, SU<Nc>::AdjointDimension> GimplAdjointTypesF;
diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index 8e6c5ee4..0e8fbabe 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -170,7 +170,7 @@ class GaugeGroup {
     }
   }
 
- template <typename LatticeMatrixType>
+  template <typename LatticeMatrixType>
   static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out,
                            double scale = 1.0) {
     GridBase *grid = out.Grid();
diff --git a/tests/core/Test_reunitarise.cc b/tests/core/Test_reunitarise.cc
index e421a2a8..110ebabf 100644
--- a/tests/core/Test_reunitarise.cc
+++ b/tests/core/Test_reunitarise.cc
@@ -122,15 +122,16 @@ int main (int argc, char ** argv)
   detU=detU-1.0;
   std::cout << "Determinant defect before projection " <<norm2(detU)<<std::endl;
   tmp = U*adj(U) - ident;
-  std::cout << "Unitarity check before projection    " << norm2(tmp)<<std::endl; 
-  #if Nc==3
+  std::cout << "Unitarity check before projection    " << norm2(tmp)<<std::endl;
+    
+#if Nc==3
   ProjectSU3(U);
   detU= Determinant(U) ;
   detU= detU -1.0;
   std::cout << "Determinant ProjectSU3 defect " <<norm2(detU)<<std::endl;
   tmp = U*adj(U) - ident;
   std::cout << "Unitarity check after projection    " << norm2(tmp)<<std::endl; 
-  #endif
+#endif
   ProjectSUn(UU);
   detUU= Determinant(UU);
   detUU= detUU -1.0;
@@ -140,8 +141,3 @@ int main (int argc, char ** argv)
   
   Grid_finalize();
 }
-
-
-
-
-
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 516a7f93..13c2bc17 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -31,6 +31,7 @@ int main (int argc, char **argv)
     
     identity = 1.0;
     RealD epsilon = 0.01;
+    RealD Delta = 666.;
     Complex i(0., 1.);
     RealD u = 0.;
     double vol = Umu.Grid()->gSites();
@@ -118,7 +119,7 @@ int main (int argc, char **argv)
     
     
     std::cout << GridLogMessage << "Testing ProjectOnGaugeGroup" << std::endl;
-    U = U + 2932.111*identity;
+    U = U + Delta*identity;
     std::cout << GridLogMessage << "Apply ProjectOnGaugeGroup to deformed matrix" << std::endl;
     Sp<Nc>::ProjectOnGaugeGroup(U);
     aux = U*adj(U) - identity;
@@ -162,7 +163,7 @@ int main (int argc, char **argv)
     }
     
     std::cout << GridLogMessage << "Testing ProjectGn" << std::endl;
-    U = U + 2932.111*identity;
+    U = U + Delta*identity;
     std::cout << GridLogMessage << "Apply ProjectGn to deformed matrix" << std::endl;
     Sp<Nc>::ProjectGn(U);
     aux = U*adj(U) - identity;
@@ -214,7 +215,7 @@ int main (int argc, char **argv)
     std::cout << GridLogMessage << "Testing SpTa" << std::endl;
     
     U = PeekIndex<LorentzIndex>(Umu,1);
-    U = U + 666.*identity;
+    U = U + Delta*identity;
     std::cout << GridLogMessage << "Matrix deformed " << std::endl;
     std::cout << GridLogMessage << "Apply SpTa to deformed matrix" << std::endl;
     U = SpTa(U);
@@ -279,7 +280,7 @@ int main (int argc, char **argv)
     
     // test taProj
     std::cout << GridLogMessage << "Testing taProj" << std::endl;
-    U = U + 666.*identity;
+    U = U + Delta*identity;
     std::cout << GridLogMessage << "Matrix deformed " << std::endl;
     std::cout << GridLogMessage << "Apply taProj to deformed matrix" << std::endl;
     Sp<Nc>::taProj(U, Up);
@@ -333,10 +334,7 @@ int main (int argc, char **argv)
             assert(  amizeroo.real() < 10e-6 );
         }
     }
-    
-    
+        
     Grid_finalize();
 
-
 }
-

From be98d26610822bc39b847f18e52547978c54e79b Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Thu, 13 Apr 2023 17:48:43 +0100
Subject: [PATCH 060/129] small change I missed in previous commit

---
 Grid/qcd/action/gauge/GaugeImplTypes.h | 2 --
 1 file changed, 2 deletions(-)

diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index e2d98b85..036d93ef 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -80,8 +80,6 @@ public:
   typedef Lattice<SiteLink>    LinkField; 
   typedef Lattice<SiteField>   Field;
 
-  //typedef SU<Nrepresentation> Group;
-
   // Guido: we can probably separate the types from the HMC functions
   // this will create 2 kind of implementations
   // probably confusing the users

From dace904c10c32d9513a0298313dfe17e1f064457 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 14 Apr 2023 18:06:18 +0100
Subject: [PATCH 061/129] fix typo

---
 Grid/tensors/Tensor_Ta.h | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index a7103343..c9132854 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -72,7 +72,7 @@ template<class vtype> accelerator_inline iScalar<vtype> SpTa(const iScalar<vtype
 {
   iScalar<vtype> ret;
   ret._internal = SpTa(r._internal);
-  return Ta(ret);
+  return ret;
 }
 template<class vtype,int N> accelerator_inline iVector<vtype,N> SpTa(const iVector<vtype,N>&r)
 {
@@ -80,11 +80,11 @@ template<class vtype,int N> accelerator_inline iVector<vtype,N> SpTa(const iVect
   for(int i=0;i<N;i++){
     ret._internal[i] = SpTa(r._internal[i]);
   }
-  return Ta(ret);
+  return ret;
 }
 template<class vtype,int N> accelerator_inline iMatrix<vtype,N> SpTa(const iMatrix<vtype,N> &arg)
 {
-    iMatrix<vtype,N> ret;
+    iMatrix<vtype,N> ret(arg);
     vtype nrm;
     vtype inner;
     vtype tmp;

From 5aabe074fe36f24a18ef8933f10c14281f7e1318 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 18 Apr 2023 11:50:20 +0100
Subject: [PATCH 062/129] Rename Sympl* to Sp*

---
 Grid/qcd/action/gauge/Gauge.h                    | 6 +++---
 Grid/qcd/action/gauge/GaugeImplTypes.h           | 6 +++---
 Grid/qcd/action/gauge/GaugeImplementations.h     | 6 +++---
 Grid/qcd/hmc/GenericHMCrunner.h                  | 4 ++--
 tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc        | 2 +-
 tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc  | 2 +-
 tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc | 2 +-
 tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc        | 2 +-
 8 files changed, 15 insertions(+), 15 deletions(-)

diff --git a/Grid/qcd/action/gauge/Gauge.h b/Grid/qcd/action/gauge/Gauge.h
index 535f0845..7a72d087 100644
--- a/Grid/qcd/action/gauge/Gauge.h
+++ b/Grid/qcd/action/gauge/Gauge.h
@@ -39,9 +39,9 @@ NAMESPACE_BEGIN(Grid);
 typedef WilsonGaugeAction<PeriodicGimplR>          WilsonGaugeActionR;
 typedef WilsonGaugeAction<PeriodicGimplF>          WilsonGaugeActionF;
 typedef WilsonGaugeAction<PeriodicGimplD>          WilsonGaugeActionD;
-typedef WilsonGaugeAction<SymplPeriodicGimplR>     SymplWilsonGaugeActionR;
-typedef WilsonGaugeAction<SymplPeriodicGimplF>     SymplWilsonGaugeActionF;
-typedef WilsonGaugeAction<SymplPeriodicGimplD>     SymplWilsonGaugeActionD;
+typedef WilsonGaugeAction<SpPeriodicGimplR>        SpWilsonGaugeActionR;
+typedef WilsonGaugeAction<SpPeriodicGimplF>        SpWilsonGaugeActionF;
+typedef WilsonGaugeAction<SpPeriodicGimplD>        SpWilsonGaugeActionD;
 typedef PlaqPlusRectangleAction<PeriodicGimplR>    PlaqPlusRectangleActionR;
 typedef PlaqPlusRectangleAction<PeriodicGimplF>    PlaqPlusRectangleActionF;
 typedef PlaqPlusRectangleAction<PeriodicGimplD>    PlaqPlusRectangleActionD;
diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index 036d93ef..c3e42f80 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -191,9 +191,9 @@ typedef GaugeImplTypes<vComplex, Nc> GimplTypesR;
 typedef GaugeImplTypes<vComplexF, Nc> GimplTypesF;
 typedef GaugeImplTypes<vComplexD, Nc> GimplTypesD;
 
-typedef GaugeImplTypes<vComplex, Nc, 12, Sp<Nc> > SymplGimplTypesR;
-typedef GaugeImplTypes<vComplexF, Nc, 12, Sp<Nc> > SymplGimplTypesF;
-typedef GaugeImplTypes<vComplexD, Nc, 12, Sp<Nc> > SymplGimplTypesD;
+typedef GaugeImplTypes<vComplex, Nc, 12, Sp<Nc> > SpGimplTypesR;
+typedef GaugeImplTypes<vComplexF, Nc, 12, Sp<Nc> > SpGimplTypesF;
+typedef GaugeImplTypes<vComplexD, Nc, 12, Sp<Nc> > SpGimplTypesD;
 
 typedef GaugeImplTypes<vComplex, SU<Nc>::AdjointDimension> GimplAdjointTypesR;
 typedef GaugeImplTypes<vComplexF, SU<Nc>::AdjointDimension> GimplAdjointTypesF;
diff --git a/Grid/qcd/action/gauge/GaugeImplementations.h b/Grid/qcd/action/gauge/GaugeImplementations.h
index bc056263..4a5a6651 100644
--- a/Grid/qcd/action/gauge/GaugeImplementations.h
+++ b/Grid/qcd/action/gauge/GaugeImplementations.h
@@ -155,9 +155,9 @@ typedef ConjugateGaugeImpl<GimplTypesR> ConjugateGimplR; // Real.. whichever pre
 typedef ConjugateGaugeImpl<GimplTypesF> ConjugateGimplF; // Float
 typedef ConjugateGaugeImpl<GimplTypesD> ConjugateGimplD; // Double
 
-typedef PeriodicGaugeImpl<SymplGimplTypesR> SymplPeriodicGimplR; // Real.. whichever prec
-typedef PeriodicGaugeImpl<SymplGimplTypesF> SymplPeriodicGimplF; // Float
-typedef PeriodicGaugeImpl<SymplGimplTypesD> SymplPeriodicGimplD; // Double
+typedef PeriodicGaugeImpl<SpGimplTypesR> SpPeriodicGimplR; // Real.. whichever prec
+typedef PeriodicGaugeImpl<SpGimplTypesF> SpPeriodicGimplF; // Float
+typedef PeriodicGaugeImpl<SpGimplTypesD> SpPeriodicGimplD; // Double
 
 
 NAMESPACE_END(Grid);
diff --git a/Grid/qcd/hmc/GenericHMCrunner.h b/Grid/qcd/hmc/GenericHMCrunner.h
index 16143455..a9b51a4d 100644
--- a/Grid/qcd/hmc/GenericHMCrunner.h
+++ b/Grid/qcd/hmc/GenericHMCrunner.h
@@ -207,12 +207,12 @@ using GenericHMCRunnerHirep =
 // sp2n
 
 template <template <typename, typename, typename> class Integrator>
-using GenericSp2nHMCRunner = HMCWrapperTemplate<SymplPeriodicGimplR, Integrator>;
+using GenericSp2nHMCRunner = HMCWrapperTemplate<SpPeriodicGimplR, Integrator>;
 
 template <class RepresentationsPolicy,
           template <typename, typename, typename> class Integrator>
 using GenericSp2nHMCRunnerHirep =
-                     HMCWrapperTemplate<SymplPeriodicGimplR, Integrator, RepresentationsPolicy>;
+                     HMCWrapperTemplate<SpPeriodicGimplR, Integrator, RepresentationsPolicy>;
 
 
 
diff --git a/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc b/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc
index 3943cd29..cd83faec 100644
--- a/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc
+++ b/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc
@@ -48,7 +48,7 @@ int main(int argc, char **argv) {
     
   RealD beta = 6 ;
     
-  SymplWilsonGaugeActionR Waction(beta);
+  SpWilsonGaugeActionR Waction(beta);
     
   auto GridPtr = TheHMC.Resources.GetCartesian();
   auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
diff --git a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
index 72fae3f4..8f293e72 100644
--- a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
+++ b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
@@ -38,7 +38,7 @@ int main(int argc, char **argv) {
     
   RealD beta = 6.7 ;
     
-  SymplWilsonGaugeActionR Waction(beta);
+  SpWilsonGaugeActionR Waction(beta);
     
   auto GridPtr = TheHMC.Resources.GetCartesian();
   auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
diff --git a/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
index 45f86ba8..e7e6120e 100644
--- a/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
+++ b/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
@@ -38,7 +38,7 @@ int main(int argc, char **argv) {
     
   RealD beta = 7.2 ;
     
-  SymplWilsonGaugeActionR Waction(beta);
+  SpWilsonGaugeActionR Waction(beta);
     
   auto GridPtr = TheHMC.Resources.GetCartesian();
   auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
diff --git a/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc b/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc
index 64049ec2..cda76860 100644
--- a/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc
+++ b/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc
@@ -80,7 +80,7 @@ int main(int argc, char **argv)
   // that have a complex construction
   // standard
   RealD beta = 8.0 ;
-  SymplWilsonGaugeActionR Waction(beta);
+  SpWilsonGaugeActionR Waction(beta);
   
   ActionLevel<HMCWrapper::Field> Level1(1);
   Level1.push_back(&Waction);

From 5e28fe56d2bc971318a37e5b7d274d018ca02d64 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Fri, 21 Apr 2023 08:08:06 +0100
Subject: [PATCH 063/129] Remove code duplication: Iterating through vectors

---
 Grid/qcd/utils/GaugeGroup.h |  5 ++++-
 Grid/qcd/utils/SUn.impl     | 10 ----------
 Grid/qcd/utils/Sp2n.impl    |  9 ---------
 3 files changed, 4 insertions(+), 20 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index 0e8fbabe..d4636292 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -326,7 +326,10 @@ class GaugeGroup {
     
   template <int N>        // reunitarise, resimplectify...
   static void ProjectOnGaugeGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
-      ProjectOnGaugeGroup(U, group_name());
+    for (int mu = 0; mu < Nd; mu++) {
+      auto Umu = PeekIndex<LorentzIndex>(U, mu);
+      ProjectOnGaugeGroup(Umu);
+    }
   }
        
   template <int N>        // reunitarise, resimplectify...
diff --git a/Grid/qcd/utils/SUn.impl b/Grid/qcd/utils/SUn.impl
index a5d2e2f1..1fc7ccd5 100644
--- a/Grid/qcd/utils/SUn.impl
+++ b/Grid/qcd/utils/SUn.impl
@@ -508,19 +508,9 @@ static void testGenerators(GroupName::SU) {
   std::cout << GridLogMessage << std::endl;
 }
 
-
 template <int N>
 static void ProjectOnGaugeGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::SU) {
   Umu = ProjectOnGroup(Umu);
- }
-
-template <int N>
-static void ProjectOnGaugeGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U, GroupName::SU) {
-  // Reunitarise
-  for (int mu = 0; mu < Nd; mu++) {
-    auto Umu = PeekIndex<LorentzIndex>(U, mu);
-    Umu = ProjectOnGroup(Umu);
-  }
 }
 
 template <class vtype>
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index 59b56b1f..e18bb519 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -256,15 +256,6 @@ static void testGenerators(GroupName::Sp) {
 template <int N>
 static void ProjectOnGaugeGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::Sp) {
   Umu = ProjectOnSpGroup(Umu);
- }
-
-template <int N>
-static void ProjectOnGaugeGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U, GroupName::Sp) {
-  // Reunitarise
-  for (int mu = 0; mu < Nd; mu++) {
-    auto Umu = PeekIndex<LorentzIndex>(U, mu);
-    Umu = ProjectOnSpGroup(Umu);
-  }
 }
 
 template <class vtype>

From 3ee5444c69523545995c46c2ec5b6223760bea0e Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Fri, 21 Apr 2023 08:08:18 +0100
Subject: [PATCH 064/129] Remove commented out stuff

---
 Grid/qcd/utils/SUn.impl  | 18 ------------------
 Grid/qcd/utils/Sp2n.impl | 20 --------------------
 2 files changed, 38 deletions(-)

diff --git a/Grid/qcd/utils/SUn.impl b/Grid/qcd/utils/SUn.impl
index 1fc7ccd5..38337305 100644
--- a/Grid/qcd/utils/SUn.impl
+++ b/Grid/qcd/utils/SUn.impl
@@ -528,24 +528,6 @@ static void ProjectOnGaugeGroup(iMatrix<vtype,N> &arg, GroupName::SU) {
   arg = ProjectOnGroup(arg);
 }
 
-
-
-
-/*
-template <int N>    // non-lattice objects
-static void ProjectOnGaugeGroup(iScalar<iScalar<iMatrix<vComplexD, N> > >  &Umu, GroupName::SU) {
-  Umu = ProjectOnGroup(Umu);
- }
-
-template <int N>
-static void ProjectOnGaugeGroup(iVector<iScalar<iMatrix<vComplexD, N> >, Nd>  &U, GroupName::SU) {
-  // Reunitarise
-  for (int mu = 0; mu < Nd; mu++) {
-    auto Umu = PeekIndex<LorentzIndex>(U, mu);
-    Umu = ProjectOnGroup(Umu);
-  }
-}*/
-
 template <typename LatticeMatrixType>
 static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::SU) {
   out = Ta(in);
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index e18bb519..2ffb79ad 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -273,21 +273,6 @@ static void ProjectOnGaugeGroup(iMatrix<vtype,N> &arg, GroupName::Sp) {
   arg = ProjectOnSpGroup(arg);
 }
 
-/*
-template <int N>    // non-lattice objects
-static void ProjectOnGaugeGroup(iScalar<iScalar<iMatrix<vComplexD, N> > >  &Umu, GroupName::Sp) {
-  Umu = ProjectOnSpGroup(Umu);
- }
-
-template <int N>
-static void ProjectOnGaugeGroup(iVector<iScalar<iMatrix<vComplexD, N> >, Nd>  &U, GroupName::Sp) {
-  // Reunitarise
-  for (int mu = 0; mu < Nd; mu++) {
-    auto Umu = PeekIndex<LorentzIndex>(U, mu);
-    Umu = ProjectOnSpGroup(Umu);
-  }
-}*/
-
 template <typename LatticeMatrixType>   
 static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::Sp) {
   out = SpTa(in);
@@ -300,11 +285,6 @@ static void OmegaInvariance(ColourMatrix &in) {
   Omega = Zero();
   const int nsp=ncolour/2;
 
-  // for (int i = 0; i < ncolour; i++)         wrong?!
-  //{
-  //     Omega()()(i, 2*ncolour-1-i) = 1.;
-  //     Omega()()(2*ncolour-1-i, i) = -1;
-  // }
   for (int i = 0; i < nsp; i++) {
     Omega()()(i, nsp + i) = 1.;
     Omega()()(nsp + i, i) = -1;

From 881b08a465ee5a8ea11bbb5f068a458155c8e08a Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Thu, 27 Apr 2023 18:17:06 +0100
Subject: [PATCH 065/129] Correct implementation of SpTa

---
 Grid/tensors/Tensor_Ta.h         | 66 ++++++++-----------------
 tests/sp2n/Test_project_on_Sp.cc | 84 +++++---------------------------
 2 files changed, 30 insertions(+), 120 deletions(-)

diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index c9132854..c4e7a840 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -82,67 +82,39 @@ template<class vtype,int N> accelerator_inline iVector<vtype,N> SpTa(const iVect
   }
   return ret;
 }
-template<class vtype,int N> accelerator_inline iMatrix<vtype,N> SpTa(const iMatrix<vtype,N> &arg)
+template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr> accelerator_inline iMatrix<vtype,N> SpTa(const iMatrix<vtype,N> &arg)
 {
+    // Generalises Ta to Sp2n
+    // Applies the following projections
+    // P_{antihermitian} P_{antihermitian-Sp-algebra} P_{traceless}
+    // where the ordering matters
+    // P_{traceless} subtracts the trace
+    // P_{antihermitian-Sp-algebra} provides the block structure of the algebra based on U = exp(T) i.e. anti-hermitian generators
+    // P_{antihermitian} does in-adj(in) / 2
     iMatrix<vtype,N> ret(arg);
+    double factor = (1.0/(double)N);
     vtype nrm;
-    vtype inner;
-    vtype tmp;
+    nrm = 0.5;
+    
+    ret = arg - (trace(arg)*factor);
     
     for(int c1=0;c1<N/2;c1++)
     {
-        
-        for (int b=0; b<c1; b++)                  // remove the b-rows from U_c1
-        {
-            decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
-            decltype(ret._internal[b][b]*ret._internal[b][b]) prn;
-            zeroit(pr);
-            zeroit(prn);
-            
-            for(int c=0; c<N; c++)
-            {
-                pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];        // <U_c1 | U_b >
-                prn += conjugate(ret._internal[c1][c])*ret._internal[b+N/2][c];   // <U_c1 | U_{b+N} >
-            }
-         
-
-            for(int c=0; c<N; c++)
-            {
-                ret._internal[c1][c] -= (conjugate(pr) * ret._internal[b][c] + conjugate(prn) * ret._internal[b+N/2][c] );    //  U_c1 -= (  <U_c1 | U_b > U_b + <U_c1 | U_{b+N} > U_{b+N}  )
-            }
-        }
-      
-        zeroit(inner);
-        for(int c2=0;c2<N;c2++)
-        {
-            inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
-        }
-        
-        nrm = sqrt(inner);
-        nrm = 1.0/nrm;
-        for(int c2=0;c2<N;c2++)
-        {
-            ret._internal[c1][c2]*= nrm;
-        }
-        
-
         for(int c2=0;c2<N/2;c2++)
         {
-            tmp = conjugate(ret._internal[c1][c2]);       // (up-left)* of the old matrix
-            ret._internal[c1+N/2][c2+N/2] = -tmp;          // down right in the new matrix = -(up-left)* of the old matrix
+            ret._internal[c1][c2] = nrm*(conjugate(ret._internal[c1+N/2][c2+N/2]) + ret._internal[c1][c2]); // new[up-left] = old[up-left]+old*[down-right]
+            ret._internal[c1][c2+N/2] = nrm*(ret._internal[c1][c2+N/2] - conjugate(ret._internal[c1+N/2][c2])); // new[up-right] = old[up-right]-old*[down-left]
         }
-           
         for(int c2=N/2;c2<N;c2++)
         {
-            tmp = conjugate(ret._internal[c1][c2]);   // (up-right)* of the old
-            ret._internal[c1+N/2][c2-N/2] = tmp;     // down left in the new matrix = (up-right)* of the old
+            ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);  //  reconstructs lower blocks
+            ret._internal[c1+N/2][c2] = conjugate(ret._internal[c1][c2-N/2]);   //  from upper blocks
         }
-      
-        
     }
     
-  
-  return Ta(ret);
+    ret = (ret - adj(ret))*0.5;
+
+    return ret;
 }
 
 
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 13c2bc17..e514106f 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -117,6 +117,8 @@ int main (int argc, char **argv)
         }
     }
     
+    SU<Nc>::HotConfiguration(pRNG,Umu); //refresh
+    U = PeekIndex<LorentzIndex>(Umu,1);
     
     std::cout << GridLogMessage << "Testing ProjectOnGaugeGroup" << std::endl;
     U = U + Delta*identity;
@@ -214,7 +216,9 @@ int main (int argc, char **argv)
     std::cout <<GridLogMessage << std::endl;
     std::cout << GridLogMessage << "Testing SpTa" << std::endl;
     
-    U = PeekIndex<LorentzIndex>(Umu,1);
+    SU<Nc>::HotConfiguration(pRNG,Umu);//refresh
+    U = PeekIndex<LorentzIndex>(Umu,2);
+
     U = U + Delta*identity;
     std::cout << GridLogMessage << "Matrix deformed " << std::endl;
     std::cout << GridLogMessage << "Apply SpTa to deformed matrix" << std::endl;
@@ -224,19 +228,19 @@ int main (int argc, char **argv)
     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 U Omega = conj(U)" << std::endl;
+    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);
-    std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
+    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 << "      (  -X^*  W^* )  " << std::endl;
     std::cout <<GridLogMessage << std::endl;
     for (int c1 = 0; c1 < nsp; c1++) //check on W
     {
@@ -245,7 +249,7 @@ int main (int argc, char **argv)
             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 amizero = sum(W - Ww);
             auto amizeroo = TensorRemove(amizero);
             assert(  amizeroo.real() < 10e-6 );
             amizeroo *= i;
@@ -261,73 +265,7 @@ int main (int argc, char **argv)
             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 );
-        }
-    }
-    
-    //test Ta
-    /*
-    U = U + 666.*identity;
-    Up = Ta(U);
-    aux = Up - adj(Up);
-    std::cout << GridLogMessage << "TA !!! T - Tda = " << norm2(aux) << std::endl;
-    aux = Up + adj(Up);
-    std::cout << GridLogMessage << "TA !!! T + Tda = " << norm2(aux) << std::endl;*/
-    
-    // test taProj
-    std::cout << GridLogMessage << "Testing taProj" << std::endl;
-    U = U + Delta*identity;
-    std::cout << GridLogMessage << "Matrix deformed " << std::endl;
-    std::cout << GridLogMessage << "Apply taProj to deformed matrix" << std::endl;
-    Sp<Nc>::taProj(U, Up);
-    aux = Up - adj(Up);
-    std::cout << GridLogMessage << "taProj ::: T - Tda = " << norm2(aux) << std::endl;
-    aux = Up + adj(Up);
-    std::cout << GridLogMessage << "taProj ::: T + Tda = " << norm2(aux) << std::endl;
-    
-    std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)" << std::endl;
-    Sp<Nc>::Omega(Omega);
-    aux = Omega*Up*Omega - conjugate(Up);
-    std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
-    // before it was
-    aux = Omega*U*Omega - conjugate(U);
-    std::cout << GridLogMessage << " before taProj Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
-
-    U = Up;
-    
-    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 amizero = sum (X + minusXx);
             auto amizeroo = TensorRemove(amizero);
             assert(  amizeroo.real() < 10e-6 );
             amizeroo *= i;

From 7b3b7093fa1d0c1ec9768d9b461392c4a6200541 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 2 May 2023 12:50:57 +0100
Subject: [PATCH 066/129] cleaning up requested by Ed

---
 Grid/qcd/utils/GaugeGroup.h       | 38 +++++++--------------
 Grid/qcd/utils/SUn.impl           | 18 ----------
 Grid/qcd/utils/Sp2n.impl          | 15 --------
 Grid/tensors/Tensor_Ta.h          | 57 +++++++++++++++----------------
 tests/core/Test_lie_generators.cc |  2 +-
 tests/core/Test_reunitarise.cc    |  2 +-
 tests/sp2n/Test_sp2n_lie_gen.cc   | 11 +++---
 7 files changed, 46 insertions(+), 97 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index 0e8fbabe..22e124c6 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -303,7 +303,6 @@ class GaugeGroup {
   template <typename LatticeMatrixType>
   static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out) {
     taProj(in, out, group_name());
-    //out = Ta(in);
   }
     
   template <typename LatticeMatrixType>
@@ -334,32 +333,20 @@ class GaugeGroup {
       ProjectOnGaugeGroup(Umu, group_name());
   }
     
-    template <class vtype>
-    static void ProjectOnGaugeGroup(iScalar<vtype> &r) {
+  template <class vtype>
+  static void ProjectOnGaugeGroup(iScalar<vtype> &r) {
       ProjectOnGaugeGroup(r, group_name());
-    }
-
-    template <class vtype, int N>
-    static void ProjectOnGaugeGroup(iVector<vtype,N> &r) {
-      r = ProjectOnGaugeGroup(r, group_name());
-    }
-
-    template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
-    static void ProjectOnGaugeGroup(iMatrix<vtype,N> &arg) {
-      arg = ProjectOnGaugeGroup(arg, group_name());
-    }
-
-    
-/*
-  template <int N>        // reunitarise, resimplectify...
-  static void ProjectOnGaugeGroup(iVector<iScalar<iMatrix<vComplexD, N> >, Nd> &U) {
-      ProjectOnGaugeGroup(U, group_name());
   }
-         
-  template <int N>        // reunitarise, resimplectify...
-  static void ProjectOnGaugeGroup(iScalar<iScalar<iMatrix<vComplexD, N> > > &Umu) {
-      ProjectOnGaugeGroup(Umu, group_name());
-  }*/
+
+  template <class vtype, int N>
+  static void ProjectOnGaugeGroup(iVector<vtype,N> &r) {
+      r = ProjectOnGaugeGroup(r, group_name());
+  }
+
+  template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
+  static void ProjectOnGaugeGroup(iMatrix<vtype,N> &arg) {
+      arg = ProjectOnGaugeGroup(arg, group_name());
+  }
 
   template <int N>       // reunitarise, resimplectify... previously ProjectSUn
   static void ProjectGn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
@@ -413,7 +400,6 @@ LatticeComplexD Determinant(
   return ret;
 }
 
-
 template <int N>
 static void ProjectSUn(
     Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
diff --git a/Grid/qcd/utils/SUn.impl b/Grid/qcd/utils/SUn.impl
index a5d2e2f1..3d2c3ec0 100644
--- a/Grid/qcd/utils/SUn.impl
+++ b/Grid/qcd/utils/SUn.impl
@@ -538,24 +538,6 @@ static void ProjectOnGaugeGroup(iMatrix<vtype,N> &arg, GroupName::SU) {
   arg = ProjectOnGroup(arg);
 }
 
-
-
-
-/*
-template <int N>    // non-lattice objects
-static void ProjectOnGaugeGroup(iScalar<iScalar<iMatrix<vComplexD, N> > >  &Umu, GroupName::SU) {
-  Umu = ProjectOnGroup(Umu);
- }
-
-template <int N>
-static void ProjectOnGaugeGroup(iVector<iScalar<iMatrix<vComplexD, N> >, Nd>  &U, GroupName::SU) {
-  // Reunitarise
-  for (int mu = 0; mu < Nd; mu++) {
-    auto Umu = PeekIndex<LorentzIndex>(U, mu);
-    Umu = ProjectOnGroup(Umu);
-  }
-}*/
-
 template <typename LatticeMatrixType>
 static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::SU) {
   out = Ta(in);
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index 59b56b1f..d862b2b7 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -282,21 +282,6 @@ static void ProjectOnGaugeGroup(iMatrix<vtype,N> &arg, GroupName::Sp) {
   arg = ProjectOnSpGroup(arg);
 }
 
-/*
-template <int N>    // non-lattice objects
-static void ProjectOnGaugeGroup(iScalar<iScalar<iMatrix<vComplexD, N> > >  &Umu, GroupName::Sp) {
-  Umu = ProjectOnSpGroup(Umu);
- }
-
-template <int N>
-static void ProjectOnGaugeGroup(iVector<iScalar<iMatrix<vComplexD, N> >, Nd>  &U, GroupName::Sp) {
-  // Reunitarise
-  for (int mu = 0; mu < Nd; mu++) {
-    auto Umu = PeekIndex<LorentzIndex>(U, mu);
-    Umu = ProjectOnSpGroup(Umu);
-  }
-}*/
-
 template <typename LatticeMatrixType>   
 static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::Sp) {
   out = SpTa(in);
diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index c4e7a840..01b58adb 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -84,47 +84,44 @@ template<class vtype,int N> accelerator_inline iVector<vtype,N> SpTa(const iVect
 }
 template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr> accelerator_inline iMatrix<vtype,N> SpTa(const iMatrix<vtype,N> &arg)
 {
-    // Generalises Ta to Sp2n
-    // Applies the following projections
-    // P_{antihermitian} P_{antihermitian-Sp-algebra} P_{traceless}
-    // where the ordering matters
-    // P_{traceless} subtracts the trace
-    // P_{antihermitian-Sp-algebra} provides the block structure of the algebra based on U = exp(T) i.e. anti-hermitian generators
-    // P_{antihermitian} does in-adj(in) / 2
-    iMatrix<vtype,N> ret(arg);
-    double factor = (1.0/(double)N);
-    vtype nrm;
-    nrm = 0.5;
+  // Generalises Ta to Sp2n
+  // Applies the following projections
+  // P_{antihermitian} P_{antihermitian-Sp-algebra} P_{traceless}
+  // where the ordering matters
+  // P_{traceless} subtracts the trace
+  // P_{antihermitian-Sp-algebra} provides the block structure of the algebra based on U = exp(T) i.e. anti-hermitian generators
+  // P_{antihermitian} does in-adj(in) / 2
+  iMatrix<vtype,N> ret(arg);
+  double factor = (1.0/(double)N);
+  vtype nrm;
+  nrm = 0.5;
     
-    ret = arg - (trace(arg)*factor);
+  ret = arg - (trace(arg)*factor);
     
-    for(int c1=0;c1<N/2;c1++)
-    {
-        for(int c2=0;c2<N/2;c2++)
-        {
-            ret._internal[c1][c2] = nrm*(conjugate(ret._internal[c1+N/2][c2+N/2]) + ret._internal[c1][c2]); // new[up-left] = old[up-left]+old*[down-right]
-            ret._internal[c1][c2+N/2] = nrm*(ret._internal[c1][c2+N/2] - conjugate(ret._internal[c1+N/2][c2])); // new[up-right] = old[up-right]-old*[down-left]
-        }
-        for(int c2=N/2;c2<N;c2++)
-        {
-            ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);  //  reconstructs lower blocks
-            ret._internal[c1+N/2][c2] = conjugate(ret._internal[c1][c2-N/2]);   //  from upper blocks
-        }
-    }
+  for(int c1=0;c1<N/2;c1++)
+  {
+      for(int c2=0;c2<N/2;c2++)
+      {
+          ret._internal[c1][c2] = nrm*(conjugate(ret._internal[c1+N/2][c2+N/2]) + ret._internal[c1][c2]); // new[up-left] = old[up-left]+old*[down-right]
+          ret._internal[c1][c2+N/2] = nrm*(ret._internal[c1][c2+N/2] - conjugate(ret._internal[c1+N/2][c2])); // new[up-right] = old[up-right]-old*[down-left]
+      }
+      for(int c2=N/2;c2<N;c2++)
+      {
+          ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);  //  reconstructs lower blocks
+          ret._internal[c1+N/2][c2] = conjugate(ret._internal[c1][c2-N/2]);   //  from upper blocks
+      }
+  }
     
-    ret = (ret - adj(ret))*0.5;
+  ret = (ret - adj(ret))*0.5;
 
-    return ret;
+  return ret;
 }
 
-
-
 /////////////////////////////////////////////// 
 // ProjectOnGroup function for scalar, vector, matrix 
 // Projects on orthogonal, unitary group
 /////////////////////////////////////////////// 
 
-
 template<class vtype> accelerator_inline iScalar<vtype> ProjectOnGroup(const iScalar<vtype>&r)
 {
   iScalar<vtype> ret;
diff --git a/tests/core/Test_lie_generators.cc b/tests/core/Test_lie_generators.cc
index 5b044061..7a86fd6a 100644
--- a/tests/core/Test_lie_generators.cc
+++ b/tests/core/Test_lie_generators.cc
@@ -47,7 +47,7 @@ using namespace Grid;
 
 int main(int argc, char** argv) {
   Grid_init(&argc, &argv);
-    
+
   std::vector<int> latt({4, 4, 4, 8});
   GridCartesian* grid = SpaceTimeGrid::makeFourDimGrid(
       latt, GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
diff --git a/tests/core/Test_reunitarise.cc b/tests/core/Test_reunitarise.cc
index 110ebabf..dd2f2041 100644
--- a/tests/core/Test_reunitarise.cc
+++ b/tests/core/Test_reunitarise.cc
@@ -36,7 +36,7 @@ using namespace Grid;
 int main (int argc, char ** argv)
 {
   Grid_init(&argc,&argv);
-    
+
   std::vector<int> latt({8,8,8,8});
   GridCartesian * grid = SpaceTimeGrid::makeFourDimGrid(latt, 
 							GridDefaultSimd(Nd,vComplexD::Nsimd()),
diff --git a/tests/sp2n/Test_sp2n_lie_gen.cc b/tests/sp2n/Test_sp2n_lie_gen.cc
index 5c6430a3..bac7d084 100644
--- a/tests/sp2n/Test_sp2n_lie_gen.cc
+++ b/tests/sp2n/Test_sp2n_lie_gen.cc
@@ -10,14 +10,14 @@ int main(int argc, char** argv) {
   //latt, GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
   //GridRedBlackCartesian* rbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(grid);
     
-    std::cout << GridLogMessage << "*********************************************"
+  std::cout << GridLogMessage << "*********************************************"
               << std::endl;
-    std::cout << GridLogMessage << "* Generators for Sp(2)" << std::endl;
-    std::cout << GridLogMessage << "*********************************************"
+  std::cout << GridLogMessage << "* Generators for Sp(2)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
               << std::endl;
       
-    Sp2::printGenerators();
-    Sp2::testGenerators();
+  Sp2::printGenerators();
+  Sp2::testGenerators();
   
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
@@ -46,6 +46,5 @@ int main(int argc, char** argv) {
   Sp8::printGenerators();
   Sp8::testGenerators(); 
     
-    
   Grid_finalize();
 }

From 86b02c3cd8d1b023e60bc55d69fd11f565d7e3a8 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 2 May 2023 13:31:17 +0100
Subject: [PATCH 067/129] cleaning up requested by Julian

---
 Grid/qcd/utils/GaugeGroup.h  | 5 ++---
 Grid/qcd/utils/SUnAdjoint.h  | 3 +--
 Grid/qcd/utils/SUnTwoIndex.h | 3 +--
 Grid/tensors/Tensor_Ta.h     | 5 ++---
 4 files changed, 6 insertions(+), 10 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index 22e124c6..d04488de 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -340,12 +340,12 @@ class GaugeGroup {
 
   template <class vtype, int N>
   static void ProjectOnGaugeGroup(iVector<vtype,N> &r) {
-      r = ProjectOnGaugeGroup(r, group_name());
+      ProjectOnGaugeGroup(r, group_name());
   }
 
   template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
   static void ProjectOnGaugeGroup(iMatrix<vtype,N> &arg) {
-      arg = ProjectOnGaugeGroup(arg, group_name());
+      ProjectOnGaugeGroup(arg, group_name());
   }
 
   template <int N>       // reunitarise, resimplectify... previously ProjectSUn
@@ -428,7 +428,6 @@ static void ProjectSUn(
   }
 }
 
-// Explicit specialisation for SU(3).
 // Explicit specialisation for SU(3).
 static void ProjectSU3(
     Lattice<iScalar<iScalar<iMatrix<vComplexD, 3> > > > &Umu) {
diff --git a/Grid/qcd/utils/SUnAdjoint.h b/Grid/qcd/utils/SUnAdjoint.h
index 3a5954ca..acbb9da3 100644
--- a/Grid/qcd/utils/SUnAdjoint.h
+++ b/Grid/qcd/utils/SUnAdjoint.h
@@ -68,8 +68,7 @@ public:
     for (int a = 0; a < Dimension; a++) {
       tmp = ta[a] * ta[Index] - ta[Index] * ta[a];
       for (int b = 0; b < (ncolour * ncolour - 1); b++) {
-        iSUnMatrix<cplx> tmp1 =
-	  2.0 * tmp * ta[b];  // 2.0 from the normalization
+        iSUnMatrix<cplx> tmp1 = 2.0 * tmp * ta[b];  // 2.0 from the normalization
         Complex iTr = TensorRemove(timesI(trace(tmp1)));
         //iAdjTa()()(b, a) = iTr;
         iAdjTa()()(a, b) = iTr;
diff --git a/Grid/qcd/utils/SUnTwoIndex.h b/Grid/qcd/utils/SUnTwoIndex.h
index 5e283de7..a7640d65 100644
--- a/Grid/qcd/utils/SUnTwoIndex.h
+++ b/Grid/qcd/utils/SUnTwoIndex.h
@@ -126,8 +126,7 @@ public:
 
   template <class cplx>
   static void generator(int Index, iSUnTwoIndexMatrix<cplx> &i2indTa) {
-    Vector<iSUnMatrix<cplx> > ta(
-								ncolour * ncolour - 1);
+    Vector<iSUnMatrix<cplx> > ta(ncolour * ncolour - 1);
     Vector<iSUnMatrix<cplx> > eij(Dimension);
     iSUnMatrix<cplx> tmp;
     i2indTa = Zero();
diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index 01b58adb..15120ffd 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -66,8 +66,6 @@ template<class vtype,int N> accelerator_inline iMatrix<vtype,N> Ta(const iMatrix
   return ret;
 }
 
-// for sp2n can't be as simple as Ta. We do a Gram-Schmidt
-
 template<class vtype> accelerator_inline iScalar<vtype> SpTa(const iScalar<vtype>&r)
 {
   iScalar<vtype> ret;
@@ -82,7 +80,8 @@ template<class vtype,int N> accelerator_inline iVector<vtype,N> SpTa(const iVect
   }
   return ret;
 }
-template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr> accelerator_inline iMatrix<vtype,N> SpTa(const iMatrix<vtype,N> &arg)
+template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
+accelerator_inline iMatrix<vtype,N> SpTa(const iMatrix<vtype,N> &arg)
 {
   // Generalises Ta to Sp2n
   // Applies the following projections

From 9b85bf940210e064333a2c258d90f221609fe995 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 2 May 2023 15:42:20 +0100
Subject: [PATCH 068/129] better projection test

---
 Grid/tensors/Tensor_Ta.h         |  74 +++---
 tests/sp2n/Test_project_on_Sp.cc | 381 +++++++++++++------------------
 2 files changed, 195 insertions(+), 260 deletions(-)

diff --git a/Grid/tensors/Tensor_Ta.h b/Grid/tensors/Tensor_Ta.h
index 15120ffd..cc21378e 100644
--- a/Grid/tensors/Tensor_Ta.h
+++ b/Grid/tensors/Tensor_Ta.h
@@ -212,58 +212,52 @@ accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg
   iMatrix<vtype,N> ret(arg);
   vtype nrm;
   vtype inner;
-  vtype tmp;
   
   for(int c1=0;c1<N/2;c1++)
   {
       
-      for (int b=0; b<c1; b++)                  // remove the b-rows from U_c1
-      {
-          decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
-          decltype(ret._internal[b][b]*ret._internal[b][b]) prn;
-          zeroit(pr);
-          zeroit(prn);
+    for (int b=0; b<c1; b++)                  // remove the b-rows from U_c1
+    {
+      decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
+      decltype(ret._internal[b][b]*ret._internal[b][b]) prn;
+      zeroit(pr);
+      zeroit(prn);
           
-          for(int c=0; c<N; c++)
-          {
-              pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];        // <U_c1 | U_b >
-              prn += conjugate(ret._internal[c1][c])*ret._internal[b+N/2][c];   // <U_c1 | U_{b+N} >
-          }
+      for(int c=0; c<N; c++)
+      {
+        pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];        // <U_c1 | U_b >
+        prn += conjugate(ret._internal[c1][c])*ret._internal[b+N/2][c];   // <U_c1 | U_{b+N} >
+      }
        
 
-          for(int c=0; c<N; c++)
-          {
-              ret._internal[c1][c] -= (conjugate(pr) * ret._internal[b][c] + conjugate(prn) * ret._internal[b+N/2][c] );    //  U_c1 -= (  <U_c1 | U_b > U_b + <U_c1 | U_{b+N} > U_{b+N}  )
-          }
+      for(int c=0; c<N; c++)
+      {
+        ret._internal[c1][c] -= (conjugate(pr) * ret._internal[b][c] + conjugate(prn) * ret._internal[b+N/2][c] );    //  U_c1 -= (  <U_c1 | U_b > U_b + <U_c1 | U_{b+N} > U_{b+N}  )
       }
+    }
     
-      zeroit(inner);
-      for(int c2=0;c2<N;c2++)
-      {
-          inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
-      }
+    zeroit(inner);
+    for(int c2=0;c2<N;c2++)
+    {
+      inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
+    }
       
-      nrm = sqrt(inner);
-      nrm = 1.0/nrm;
-      for(int c2=0;c2<N;c2++)
-      {
-          ret._internal[c1][c2]*= nrm;
-      }
+    nrm = sqrt(inner);
+    nrm = 1.0/nrm;
+    for(int c2=0;c2<N;c2++)
+    {
+      ret._internal[c1][c2]*= nrm;
+    }
       
-
-      for(int c2=0;c2<N/2;c2++)
-      {
-          tmp = conjugate(ret._internal[c1][c2]);       // (up-left)* of the old matrix
-          ret._internal[c1+N/2][c2+N/2] = tmp;          // down right in the new matrix = (up-left)* of the old matrix
-      }
-         
-      for(int c2=N/2;c2<N;c2++)
-      {
-          tmp = conjugate(ret._internal[c1][c2]);   // (up-right)* of the old
-          ret._internal[c1+N/2][c2-N/2] = -tmp;     // down left in the new matrix = -(up-right)* of the old
-      }
-    
+    for(int c2=0;c2<N/2;c2++)
+    {
+      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
+    }
       
+    for(int c2=N/2;c2<N;c2++)
+    {
+      ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);;     // down left in the new matrix = -(up-right)* of the old
+    }
   }
   return ret;
 }
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index e514106f..2f8dd32b 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -2,11 +2,121 @@
 
 using namespace Grid;
 
+int SpGroupQuiz (const LatticeColourMatrixD Uin)
+{
+    double vol = Uin.Grid()->gSites();
+    const int nsp = Nc / 2;
+    LatticeColourMatrixD Omega(Uin.Grid());
+    Sp<Nc>::Omega(Omega);
+    LatticeColourMatrixD aux(Uin.Grid());
+    LatticeColourMatrixD identity(Uin.Grid());
+    Complex i(0., 1.);
+    identity = 1;
+    
+    std::cout << GridLogMessage << "Check matrix is non-zero " << std::endl;
+    assert(norm2(Uin) > 1e-8);
+    aux = Uin*adj(Uin) - identity;
+    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux)/vol << std::endl;
+    assert(norm2(aux) < 1e-8);
+    aux = Omega - (Uin * Omega * transpose(Uin));
+    std::cout << GridLogMessage << "Omega - U Omega transpose(U) = " << norm2(aux)/vol << std::endl;
+    assert(norm2(aux) < 1e-8);
+    //Sp<Nc>::OmegaInvariance(Uin)
+    std::cout << GridLogMessage << "Checking the structure is " << std::endl;
+    std::cout << GridLogMessage << "U  =  (   W    X   )  " << std::endl;
+    std::cout << GridLogMessage << "      (  -X^*  W^* )  " << std::endl;
+    for (int c1 = 0; c1 < nsp; c1++) //check on W
+    {
+        for (int c2 = 0; c2 < nsp; c2++)
+        {
+            auto W = PeekIndex<ColourIndex>(Uin,c1,c2);
+            auto Wstar =  PeekIndex<ColourIndex>(Uin,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>(Uin,c1,c2+nsp);
+            auto minusXstar = PeekIndex<ColourIndex>(Uin,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 << "|Det| = " << norm2( Determinant(Uin) ) / vol << std::endl;
+    assert( norm2( Determinant(Uin) ) / vol - 1 < 1e-8);
+    return 0;
+}
+
+int SpAntiHermitianAlgebraQuiz (const LatticeColourMatrixD Uin)
+{
+    double vol = Uin.Grid()->gSites();
+    const int nsp = Nc / 2;
+    LatticeColourMatrixD Omega(Uin.Grid());
+    Sp<Nc>::Omega(Omega);
+    LatticeColourMatrixD aux(Uin.Grid());
+    LatticeColourMatrixD identity(Uin.Grid());
+    Complex i(0., 1.);
+    identity = 1;
+    
+    std::cout << GridLogMessage << "Check matrix is non-zero " << std::endl;
+    assert(norm2(Uin) > 1e-8);
+    aux = Uin - adj(Uin);
+    std::cout << GridLogMessage << "SpTa ::: T - Tda = " << norm2(aux)/vol << std::endl;
+    aux = Uin + adj(Uin);
+    std::cout << GridLogMessage << "SpTa ::: T + Tda = " << norm2(aux)/vol << std::endl;
+    assert( norm2(aux) - 1 < 1e-8);
+    std::cout << GridLogMessage << "Check that Omega T Omega + conj(T) = 0 " << std::endl;
+    aux = Omega*Uin*Omega + conjugate(Uin);
+    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;
+    for (int c1 = 0; c1 < nsp; c1++) //check on W
+    {
+        for (int c2 = 0; c2 < nsp; c2++)
+        {
+            auto W = PeekIndex<ColourIndex>(Uin,c1,c2);
+            auto Wstar =  PeekIndex<ColourIndex>(Uin,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>(Uin,c1,c2+nsp);
+            auto minusXstar = PeekIndex<ColourIndex>(Uin,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 );
+        }
+    }
+    return 0;
+}
+
 int main (int argc, char **argv)
 {
     Grid_init(&argc,&argv);
     
-    
     Coordinate latt_size   = GridDefaultLatt();
     Coordinate simd_layout = GridDefaultSimd(Nd,vComplex::Nsimd());
     Coordinate mpi_layout  = GridDefaultMpi();
@@ -14,27 +124,18 @@ int main (int argc, char **argv)
     GridCartesian             Grid(latt_size,simd_layout,mpi_layout);
     GridRedBlackCartesian     RBGrid(&Grid);
     
-    
     LatticeGaugeField Umu(&Grid);
     LatticeColourMatrixD U(&Grid);
-    LatticeColourMatrixD Up(&Grid);
     LatticeColourMatrixD aux(&Grid);
     LatticeColourMatrixD identity(&Grid);
-    
-    // Will test resimplectification-related functionalities (from ProjectOnGaugeGroup, ProjectOnSpGroup, ProjectGn) and projection on the algebra (from ProjectSp2nAlgebra)
-    // we work with matrices with positive determinant so detU = 1 even if in principle ProjectOnGaugeGroup and ProjectOnSpGroup allow for detU=-1
-    // so the checks will be the same for the three functions
-    // NB only ProjectGn is the proper simplectification function
-    
-    
-    const int nsp = Nc / 2;
-    
+    LatticeColourMatrixD Omega(&Grid);
+    Sp<Nc>::Omega(Omega);
+
     identity = 1.0;
-    RealD epsilon = 0.01;
-    RealD Delta = 666.;
+    RealD epsilon = 0.1;
     Complex i(0., 1.);
-    RealD u = 0.;
     double vol = Umu.Grid()->gSites();
+    const int nsp = Nc / 2;
     
     std::vector<int> pseeds({1,2,3,4,5});
     GridParallelRNG  pRNG(&Grid); pRNG.SeedFixedIntegers(pseeds);
@@ -42,236 +143,76 @@ int main (int argc, char **argv)
     SU<Nc>::HotConfiguration(pRNG,Umu);
     U = PeekIndex<LorentzIndex>(Umu,0);
     
-    aux = U*adj(U) - identity;
     std::cout << GridLogMessage << "Starting with random SUn matrix " << std::endl;
-    std::cout << GridLogMessage << "Unitary check " << std::endl;
+    aux = U*adj(U) - identity;
     std::cout <<GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
     assert ( norm2(aux) < 1e-8 );
-    std::cout <<GridLogMessage << std::endl;
-    if (Nc != 2)
+    if (Nc != 2)    // Sp2 = SU2
     {
-        std::cout << GridLogMessage << "This matrix should not leave Omega invariant, expect a warning" << std::endl;
+        std::cout << GridLogMessage <<  "Checking matrix does NOT leave Omega invariant, to avoid a trivial test " << std::endl;
+        aux = Omega - (U * Omega * transpose(U));
+        assert ( norm2(aux) > 1e-8 );
     }
-    Sp<Nc>::OmegaInvariance(U);
-    std::cout <<GridLogMessage << std::endl;
-    
-    U = U + epsilon*identity;
-    aux = U*adj(U) - identity;
     
+    U = U + epsilon*identity - i*identity;
     std::cout << GridLogMessage << "Unitary matrix deformed " << std::endl;
+    auto det =  sum( Determinant(U) );
+    std::cout << GridLogMessage << "Re(Det) = " << real(det) / vol << std::endl;
+    det = det*i;
+    std::cout << GridLogMessage << "Im(Det) = " << real(det) / vol << std::endl;
+    aux = U*adj(U) - identity;
     std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl;
     
-    std::cout <<GridLogMessage << std::endl;
-    std::cout << GridLogMessage << "#   #   #   #" << std::endl;
-    std::cout << GridLogMessage << "Group" << std::endl;
-    std::cout << GridLogMessage << "#   #   #   #" << std::endl;
-    std::cout <<GridLogMessage << std::endl;
-    //  Testing ProjectOnSpGroup
+    //  ProjectOnSpGroup
     std::cout << GridLogMessage << "Testing ProjectOnSpGroup" << std::endl;
     std::cout << GridLogMessage << "Apply ProjectOnSpGroup to deformed matrix" << std::endl;
     U = ProjectOnSpGroup(U);
-
-    aux = U*adj(U) - identity;
-    std::cout << GridLogMessage << "Unitary check after ProjectOnSpGroup " << std::endl;
-    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
-    
-    // actual sp2n check
-    std::cout << GridLogMessage << "Checking Omega invariance after ProjectOnSpGroup" << std::endl;
-    Sp<Nc>::OmegaInvariance(U);     // no assertion here, but the next check will kill us if we are not simplectic
-    
-    // checks on elements
-    
-    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;
+    SpGroupQuiz(U);
+    det =  sum( Determinant(U) );
+    std::cout << GridLogMessage << "Re(Det) after ProjectOnSpGroup (nothing to assert) = " << real(det) / vol << std::endl;
+    det = det*i;
+    std::cout << GridLogMessage << "Im(Det) after ProjectOnSpGroup (nothing to assert) = " << real(det) / vol << std::endl;
     
+    //  ProjectOnGaugeGroup
     SU<Nc>::HotConfiguration(pRNG,Umu); //refresh
-    U = PeekIndex<LorentzIndex>(Umu,1);
-    
+    U = PeekIndex<LorentzIndex>(Umu,0);
     std::cout << GridLogMessage << "Testing ProjectOnGaugeGroup" << std::endl;
-    U = U + Delta*identity;
+    U = U + epsilon*identity - i*identity;
     std::cout << GridLogMessage << "Apply ProjectOnGaugeGroup to deformed matrix" << std::endl;
     Sp<Nc>::ProjectOnGaugeGroup(U);
-    aux = U*adj(U) - identity;
-    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
-    Sp<Nc>::OmegaInvariance(U);
-    
-    std::cout << GridLogMessage << "Checking the structure is " << std::endl;
-    std::cout << GridLogMessage << "U  =  (   W    X   )  " << std::endl;
-    std::cout << GridLogMessage << "      (  -X^*  W^* )  " << 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;
+    SpGroupQuiz(U);
+    det =  sum( Determinant(U) );
+    std::cout << GridLogMessage << "Re(Det) after ProjectOnGaugeGroup (nothing to assert) = " << real(det) / vol << std::endl;
+    det = det*i;
+    std::cout << GridLogMessage << "Im(Det) after ProjectOnGaugeGroup (nothing to assert) = " << real(det) / vol << std::endl;
     
+    //  ProjectGn
+    SU<Nc>::HotConfiguration(pRNG,Umu); //refresh
+    U = PeekIndex<LorentzIndex>(Umu,0);
     std::cout << GridLogMessage << "Testing ProjectGn" << std::endl;
-    U = U + Delta*identity;
+    U = U + epsilon*identity - i*identity;
     std::cout << GridLogMessage << "Apply ProjectGn to deformed matrix" << std::endl;
     Sp<Nc>::ProjectGn(U);
-    aux = U*adj(U) - identity;
-    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
-    std::cout << GridLogMessage << "Det after ProjectGn = " << norm2( Determinant(U) ) / vol << std::endl;
-    assert( norm2(aux) - 1 < 1e-8);
-    Sp<Nc>::OmegaInvariance(U);
-    
-    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 << 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();
 

From 339c4fda79f23c46e28ee42394e26892c7eb01d0 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Tue, 2 May 2023 15:44:34 +0100
Subject: [PATCH 069/129] Extracted is_element_of Sp2n

---
 tests/sp2n/Test_project_on_Sp.cc | 249 +++++++++++++------------------
 1 file changed, 104 insertions(+), 145 deletions(-)

diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 13c2bc17..52b6debf 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -2,6 +2,109 @@
 
 using namespace Grid;
 
+template <typename T>
+bool has_correct_block_structure(T U){
+    // checks on elements
+    
+    const int nsp = Nc / 2;
+    Complex i(0., 1.);
+
+    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 );
+        }
+    }
+    return true;
+};
+
+template <typename T>
+bool is_element_of_Sp2n(T U) {
+ 
+    LatticeColourMatrixD aux(U.Grid());
+    LatticeColourMatrixD identity(U.Grid());
+    
+    identity = 1.0;
+    double vol = U.Grid()->gSites();
+    
+    std::cout << GridLogMessage << "Unitary check" << std::endl;
+    aux = U*adj(U) - identity;
+    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+    assert( norm2(aux) < 1e-8);
+    
+    // actual sp2n check
+    std::cout << GridLogMessage << "Checking Omega invariance" << std::endl;
+    Sp<Nc>::OmegaInvariance(U);     // no assertion here, but the next check will kill us if we are not simplectic
+    
+  return has_correct_block_structure(U);
+}
+
+template<typename T>
+void test_group_projections(T U) {
+    RealD Delta = 666.;
+    LatticeColourMatrixD identity(U.Grid());
+    identity = 1.0;
+
+    std::cout <<GridLogMessage << std::endl;
+    std::cout << GridLogMessage << "#   #   #   #" << std::endl;
+    std::cout << GridLogMessage << "Group" << std::endl;
+    std::cout << GridLogMessage << "#   #   #   #" << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+
+    std::string name="ProjectOnSpGroup";
+    std::cout << GridLogMessage << "Testing "<< name << std::endl;
+    std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+
+    U = ProjectOnSpGroup(U);
+    assert(is_element_of_Sp2n(U));
+   
+    name = "ProjectOnGaugeGroup";
+    std::cout << GridLogMessage << "Testing "<< name << std::endl;
+    std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+
+    U = U + Delta*identity;
+    Sp<Nc>::ProjectOnGaugeGroup(U);
+    assert(is_element_of_Sp2n(U));
+   
+    name = "ProjectGn";
+    std::cout << GridLogMessage << "Testing "<< name << std::endl;
+    std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+
+    U = U + Delta*identity;
+    Sp<Nc>::ProjectGn(U);
+    assert(is_element_of_Sp2n(U));
+}
+
+
+
 int main (int argc, char **argv)
 {
     Grid_init(&argc,&argv);
@@ -61,152 +164,8 @@ int main (int argc, char **argv)
     std::cout << GridLogMessage << "Unitary matrix deformed " << std::endl;
     std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl;
     
-    std::cout <<GridLogMessage << std::endl;
-    std::cout << GridLogMessage << "#   #   #   #" << std::endl;
-    std::cout << GridLogMessage << "Group" << std::endl;
-    std::cout << GridLogMessage << "#   #   #   #" << std::endl;
-    std::cout <<GridLogMessage << std::endl;
-    //  Testing ProjectOnSpGroup
-    std::cout << GridLogMessage << "Testing ProjectOnSpGroup" << std::endl;
-    std::cout << GridLogMessage << "Apply ProjectOnSpGroup to deformed matrix" << std::endl;
-    U = ProjectOnSpGroup(U);
+    test_group_projections(U);
 
-    aux = U*adj(U) - identity;
-    std::cout << GridLogMessage << "Unitary check after ProjectOnSpGroup " << std::endl;
-    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
-    
-    // actual sp2n check
-    std::cout << GridLogMessage << "Checking Omega invariance after ProjectOnSpGroup" << std::endl;
-    Sp<Nc>::OmegaInvariance(U);     // no assertion here, but the next check will kill us if we are not simplectic
-    
-    // checks on elements
-    
-    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 << "Testing ProjectOnGaugeGroup" << std::endl;
-    U = U + Delta*identity;
-    std::cout << GridLogMessage << "Apply ProjectOnGaugeGroup to deformed matrix" << std::endl;
-    Sp<Nc>::ProjectOnGaugeGroup(U);
-    aux = U*adj(U) - identity;
-    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
-    Sp<Nc>::OmegaInvariance(U);
-    
-    std::cout << GridLogMessage << "Checking the structure is " << std::endl;
-    std::cout << GridLogMessage << "U  =  (   W    X   )  " << std::endl;
-    std::cout << GridLogMessage << "      (  -X^*  W^* )  " << 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 << "Testing ProjectGn" << std::endl;
-    U = U + Delta*identity;
-    std::cout << GridLogMessage << "Apply ProjectGn to deformed matrix" << std::endl;
-    Sp<Nc>::ProjectGn(U);
-    aux = U*adj(U) - identity;
-    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
-    std::cout << GridLogMessage << "Det after ProjectGn = " << norm2( Determinant(U) ) / vol << std::endl;
-    assert( norm2(aux) - 1 < 1e-8);
-    Sp<Nc>::OmegaInvariance(U);
-    
-    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 << std::endl;
     std::cout << GridLogMessage << "#   #   #   #" << std::endl;
     std::cout << GridLogMessage << "Algebra" << std::endl;

From 42b0e1125de5dfac2ad2805950f4b93f54a84ff4 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 3 May 2023 01:51:46 +0100
Subject: [PATCH 070/129] Naming and argument types

---
 tests/sp2n/Test_project_on_Sp.cc | 25 ++++++++++---------------
 1 file changed, 10 insertions(+), 15 deletions(-)

diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 52b6debf..4c2e7b76 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -3,16 +3,14 @@
 using namespace Grid;
 
 template <typename T>
-bool has_correct_block_structure(T U){
-    // checks on elements
-    
-    const int nsp = Nc / 2;
-    Complex i(0., 1.);
-
+bool has_correct_group_block_structure(const T& U){
     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;
+
+    const int nsp = Nc / 2;
+    Complex i(0., 1.);
     for (int c1 = 0; c1 < nsp; c1++) //check on W
     {
         for (int c2 = 0; c2 < nsp; c2++)
@@ -47,24 +45,21 @@ bool has_correct_block_structure(T U){
 };
 
 template <typename T>
-bool is_element_of_Sp2n(T U) {
+bool is_element_of_sp2n_group(T U) {// does explicitly take a copy in order to not spoil the matrix for further use
  
     LatticeColourMatrixD aux(U.Grid());
     LatticeColourMatrixD identity(U.Grid());
-    
     identity = 1.0;
-    double vol = U.Grid()->gSites();
     
     std::cout << GridLogMessage << "Unitary check" << std::endl;
     aux = U*adj(U) - identity;
     std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
     assert( norm2(aux) < 1e-8);
     
-    // actual sp2n check
     std::cout << GridLogMessage << "Checking Omega invariance" << std::endl;
     Sp<Nc>::OmegaInvariance(U);     // no assertion here, but the next check will kill us if we are not simplectic
     
-  return has_correct_block_structure(U);
+  return has_correct_group_block_structure(U);
 }
 
 template<typename T>
@@ -83,8 +78,9 @@ void test_group_projections(T U) {
     std::cout << GridLogMessage << "Testing "<< name << std::endl;
     std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
 
+    U = U + Delta*identity;
     U = ProjectOnSpGroup(U);
-    assert(is_element_of_Sp2n(U));
+    assert(is_element_of_sp2n_group(U));
    
     name = "ProjectOnGaugeGroup";
     std::cout << GridLogMessage << "Testing "<< name << std::endl;
@@ -92,7 +88,7 @@ void test_group_projections(T U) {
 
     U = U + Delta*identity;
     Sp<Nc>::ProjectOnGaugeGroup(U);
-    assert(is_element_of_Sp2n(U));
+    assert(is_element_of_sp2n_group(U));
    
     name = "ProjectGn";
     std::cout << GridLogMessage << "Testing "<< name << std::endl;
@@ -100,7 +96,7 @@ void test_group_projections(T U) {
 
     U = U + Delta*identity;
     Sp<Nc>::ProjectGn(U);
-    assert(is_element_of_Sp2n(U));
+    assert(is_element_of_sp2n_group(U));
 }
 
 
@@ -115,7 +111,6 @@ int main (int argc, char **argv)
     Coordinate mpi_layout  = GridDefaultMpi();
 
     GridCartesian             Grid(latt_size,simd_layout,mpi_layout);
-    GridRedBlackCartesian     RBGrid(&Grid);
     
     
     LatticeGaugeField Umu(&Grid);

From ac0a74be0dc1acf7d16de49f05e6ab6874cfceec Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 3 May 2023 02:32:42 +0100
Subject: [PATCH 071/129] Taken care of algebra tests

---
 tests/sp2n/Test_project_on_Sp.cc | 245 ++++++++++++-------------------
 1 file changed, 97 insertions(+), 148 deletions(-)

diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 4c2e7b76..046db4bb 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -68,7 +68,6 @@ void test_group_projections(T U) {
     LatticeColourMatrixD identity(U.Grid());
     identity = 1.0;
 
-    std::cout <<GridLogMessage << std::endl;
     std::cout << GridLogMessage << "#   #   #   #" << std::endl;
     std::cout << GridLogMessage << "Group" << std::endl;
     std::cout << GridLogMessage << "#   #   #   #" << std::endl;
@@ -99,6 +98,102 @@ void test_group_projections(T U) {
     assert(is_element_of_sp2n_group(U));
 }
 
+template<typename T>
+bool has_correct_algebra_block_structure(const T& U) {
+    const int nsp = Nc / 2;
+    Complex i(0., 1.);
+  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 );
+        }
+    }
+    return true;
+}
+
+template<typename T>
+bool is_element_of_sp2n_algebra(T U) {
+ 
+    LatticeColourMatrixD aux(U.Grid());
+    LatticeColourMatrixD identity(U.Grid());
+    identity = 1.0;
+
+    aux = U - adj(U);
+    std::cout << GridLogMessage << "T - Tda = " << norm2(aux) << std::endl;
+    assert( norm2(aux) < 1e-8);
+    aux = U + adj(U);
+    std::cout << GridLogMessage << "T + Tda = " << norm2(aux) << std::endl;
+    assert( norm2(aux) < 1e-8);
+    
+    std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)" << std::endl;
+
+    LatticeColourMatrixD Omega(U.Grid());
+    Sp<Nc>::Omega(Omega);
+    aux = Omega*U*Omega - conjugate(U);
+    std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
+    assert( norm2(aux) < 1e-8);
+
+   return has_correct_algebra_block_structure(U); 
+}
+
+
+template< typename T>
+void test_algebra_projections(T U) {
+    RealD Delta = 666.;
+    LatticeColourMatrixD tmp(U.Grid());
+    LatticeColourMatrixD identity(U.Grid());
+    identity = 1.0;
+
+    std::cout << GridLogMessage << "#   #   #   #" << std::endl;
+    std::cout << GridLogMessage << "Algebra" << std::endl;
+    std::cout << GridLogMessage << "#   #   #   #" << std::endl;
+    std::cout <<GridLogMessage << std::endl;
+
+    std::string name="SpTa";
+    std::cout << GridLogMessage << "Testing "<< name << std::endl;
+    std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+
+     U = U + Delta*identity;
+    U = SpTa(U);
+    assert(is_element_of_sp2n_algebra(U));
+    
+name="TaProj";
+    std::cout << GridLogMessage << "Testing "<< name << std::endl;
+    std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+
+     U = U + Delta*identity;
+    Sp<Nc>::taProj(U, tmp);
+    U = tmp;
+    assert(is_element_of_sp2n_algebra(U));
+}    
 
 
 int main (int argc, char **argv)
@@ -139,155 +234,9 @@ int main (int argc, char **argv)
     
     SU<Nc>::HotConfiguration(pRNG,Umu);
     U = PeekIndex<LorentzIndex>(Umu,0);
-    
-    aux = U*adj(U) - identity;
-    std::cout << GridLogMessage << "Starting with random SUn matrix " << std::endl;
-    std::cout << GridLogMessage << "Unitary check " << std::endl;
-    std::cout <<GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
-    assert ( norm2(aux) < 1e-8 );
-    std::cout <<GridLogMessage << std::endl;
-    if (Nc != 2)
-    {
-        std::cout << GridLogMessage << "This matrix should not leave Omega invariant, expect a warning" << std::endl;
-    }
-    Sp<Nc>::OmegaInvariance(U);
-    std::cout <<GridLogMessage << std::endl;
-    
-    U = U + epsilon*identity;
-    aux = U*adj(U) - identity;
-    
-    std::cout << GridLogMessage << "Unitary matrix deformed " << std::endl;
-    std::cout << GridLogMessage << "now U adjU - 1 = " << norm2(aux) << std::endl;
-    
     test_group_projections(U);
-
-    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;
-    
     U = PeekIndex<LorentzIndex>(Umu,1);
-    U = U + Delta*identity;
-    std::cout << GridLogMessage << "Matrix deformed " << std::endl;
-    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;
-    
-    std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)" << std::endl;
-
-    LatticeColourMatrixD Omega(&Grid);
-    Sp<Nc>::Omega(Omega);
-    aux = Omega*U*Omega - conjugate(U);
-    std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
-    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 );
-        }
-    }
-    
-    //test Ta
-    /*
-    U = U + 666.*identity;
-    Up = Ta(U);
-    aux = Up - adj(Up);
-    std::cout << GridLogMessage << "TA !!! T - Tda = " << norm2(aux) << std::endl;
-    aux = Up + adj(Up);
-    std::cout << GridLogMessage << "TA !!! T + Tda = " << norm2(aux) << std::endl;*/
-    
-    // test taProj
-    std::cout << GridLogMessage << "Testing taProj" << std::endl;
-    U = U + Delta*identity;
-    std::cout << GridLogMessage << "Matrix deformed " << std::endl;
-    std::cout << GridLogMessage << "Apply taProj to deformed matrix" << std::endl;
-    Sp<Nc>::taProj(U, Up);
-    aux = Up - adj(Up);
-    std::cout << GridLogMessage << "taProj ::: T - Tda = " << norm2(aux) << std::endl;
-    aux = Up + adj(Up);
-    std::cout << GridLogMessage << "taProj ::: T + Tda = " << norm2(aux) << std::endl;
-    
-    std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)" << std::endl;
-    Sp<Nc>::Omega(Omega);
-    aux = Omega*Up*Omega - conjugate(Up);
-    std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
-    // before it was
-    aux = Omega*U*Omega - conjugate(U);
-    std::cout << GridLogMessage << " before taProj Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
-
-    U = Up;
-    
-    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 );
-        }
-    }
+    test_algebra_projections(U);
         
     Grid_finalize();
 

From c5924833a16b9a6fb35330ddf6bd7c15238a6cf3 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 3 May 2023 02:39:36 +0100
Subject: [PATCH 072/129] ClangFormat

---
 tests/sp2n/Test_project_on_Sp.cc | 382 +++++++++++++++----------------
 1 file changed, 182 insertions(+), 200 deletions(-)

diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 046db4bb..e5c2ed05 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -3,241 +3,223 @@
 using namespace Grid;
 
 template <typename T>
-bool has_correct_group_block_structure(const T& U){
-    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;
+bool has_correct_group_block_structure(const T& U) {
+  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;
 
-    const int nsp = Nc / 2;
-    Complex i(0., 1.);
-    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 );
-        }
-        
+  const int nsp = Nc / 2;
+  Complex i(0., 1.);
+  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 );
-        }
+  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);
     }
-    return true;
+  }
+  return true;
 };
 
 template <typename T>
-bool is_element_of_sp2n_group(T U) {// does explicitly take a copy in order to not spoil the matrix for further use
- 
-    LatticeColourMatrixD aux(U.Grid());
-    LatticeColourMatrixD identity(U.Grid());
-    identity = 1.0;
-    
-    std::cout << GridLogMessage << "Unitary check" << std::endl;
-    aux = U*adj(U) - identity;
-    std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
-    
-    std::cout << GridLogMessage << "Checking Omega invariance" << std::endl;
-    Sp<Nc>::OmegaInvariance(U);     // no assertion here, but the next check will kill us if we are not simplectic
-    
+bool is_element_of_sp2n_group(T U) {
+  // does explicitly take a copy in order to not spoil the matrix for further
+  // use
+
+  LatticeColourMatrixD aux(U.Grid());
+  LatticeColourMatrixD identity(U.Grid());
+  identity = 1.0;
+
+  std::cout << GridLogMessage << "Unitary check" << std::endl;
+  aux = U * adj(U) - identity;
+  std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+  assert(norm2(aux) < 1e-8);
+
+  std::cout << GridLogMessage << "Checking Omega invariance" << std::endl;
+  Sp<Nc>::OmegaInvariance(U);  // no assertion here, but the next check will
+                               // kill us if we are not simplectic
+
   return has_correct_group_block_structure(U);
 }
 
-template<typename T>
+template <typename T>
 void test_group_projections(T U) {
-    RealD Delta = 666.;
-    LatticeColourMatrixD identity(U.Grid());
-    identity = 1.0;
+  RealD Delta = 666.;
+  LatticeColourMatrixD identity(U.Grid());
+  identity = 1.0;
 
-    std::cout << GridLogMessage << "#   #   #   #" << std::endl;
-    std::cout << GridLogMessage << "Group" << std::endl;
-    std::cout << GridLogMessage << "#   #   #   #" << std::endl;
-    std::cout <<GridLogMessage << std::endl;
+  std::cout << GridLogMessage << "#   #   #   #" << std::endl;
+  std::cout << GridLogMessage << "Group" << std::endl;
+  std::cout << GridLogMessage << "#   #   #   #" << std::endl;
+  std::cout << GridLogMessage << std::endl;
 
-    std::string name="ProjectOnSpGroup";
-    std::cout << GridLogMessage << "Testing "<< name << std::endl;
-    std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+  std::string name = "ProjectOnSpGroup";
+  std::cout << GridLogMessage << "Testing " << name << std::endl;
+  std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
 
-    U = U + Delta*identity;
-    U = ProjectOnSpGroup(U);
-    assert(is_element_of_sp2n_group(U));
-   
-    name = "ProjectOnGaugeGroup";
-    std::cout << GridLogMessage << "Testing "<< name << std::endl;
-    std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+  U = U + Delta * identity;
+  U = ProjectOnSpGroup(U);
+  assert(is_element_of_sp2n_group(U));
 
-    U = U + Delta*identity;
-    Sp<Nc>::ProjectOnGaugeGroup(U);
-    assert(is_element_of_sp2n_group(U));
-   
-    name = "ProjectGn";
-    std::cout << GridLogMessage << "Testing "<< name << std::endl;
-    std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+  name = "ProjectOnGaugeGroup";
+  std::cout << GridLogMessage << "Testing " << name << std::endl;
+  std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
 
-    U = U + Delta*identity;
-    Sp<Nc>::ProjectGn(U);
-    assert(is_element_of_sp2n_group(U));
+  U = U + Delta * identity;
+  Sp<Nc>::ProjectOnGaugeGroup(U);
+  assert(is_element_of_sp2n_group(U));
+
+  name = "ProjectGn";
+  std::cout << GridLogMessage << "Testing " << name << std::endl;
+  std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+
+  U = U + Delta * identity;
+  Sp<Nc>::ProjectGn(U);
+  assert(is_element_of_sp2n_group(U));
 }
 
-template<typename T>
+template <typename T>
 bool has_correct_algebra_block_structure(const T& U) {
-    const int nsp = Nc / 2;
-    Complex i(0., 1.);
+  const int nsp = Nc / 2;
+  Complex i(0., 1.);
   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 );
-        }
-        
+  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 );
-        }
+  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);
     }
-    return true;
+  }
+  return true;
 }
 
-template<typename T>
+template <typename T>
 bool is_element_of_sp2n_algebra(T U) {
- 
-    LatticeColourMatrixD aux(U.Grid());
-    LatticeColourMatrixD identity(U.Grid());
-    identity = 1.0;
+  // does explicitly take a copy in order to not spoil the matrix for further
+  // use
+  LatticeColourMatrixD aux(U.Grid());
+  LatticeColourMatrixD identity(U.Grid());
+  identity = 1.0;
 
-    aux = U - adj(U);
-    std::cout << GridLogMessage << "T - Tda = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
-    aux = U + adj(U);
-    std::cout << GridLogMessage << "T + Tda = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
-    
-    std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)" << std::endl;
+  aux = U - adj(U);
+  std::cout << GridLogMessage << "T - Tda = " << norm2(aux) << std::endl;
+  assert(norm2(aux) < 1e-8);
+  aux = U + adj(U);
+  std::cout << GridLogMessage << "T + Tda = " << norm2(aux) << std::endl;
+  assert(norm2(aux) < 1e-8);
 
-    LatticeColourMatrixD Omega(U.Grid());
-    Sp<Nc>::Omega(Omega);
-    aux = Omega*U*Omega - conjugate(U);
-    std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux) << std::endl;
-    assert( norm2(aux) < 1e-8);
+  std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)"
+            << std::endl;
 
-   return has_correct_algebra_block_structure(U); 
+  LatticeColourMatrixD Omega(U.Grid());
+  Sp<Nc>::Omega(Omega);
+  aux = Omega * U * Omega - conjugate(U);
+  std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux)
+            << std::endl;
+  assert(norm2(aux) < 1e-8);
+
+  return has_correct_algebra_block_structure(U);
 }
 
-
-template< typename T>
+template <typename T>
 void test_algebra_projections(T U) {
-    RealD Delta = 666.;
-    LatticeColourMatrixD tmp(U.Grid());
-    LatticeColourMatrixD identity(U.Grid());
-    identity = 1.0;
+  RealD Delta = 666.;
+  LatticeColourMatrixD tmp(U.Grid());
+  LatticeColourMatrixD identity(U.Grid());
+  identity = 1.0;
 
-    std::cout << GridLogMessage << "#   #   #   #" << std::endl;
-    std::cout << GridLogMessage << "Algebra" << std::endl;
-    std::cout << GridLogMessage << "#   #   #   #" << std::endl;
-    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::string name="SpTa";
-    std::cout << GridLogMessage << "Testing "<< name << std::endl;
-    std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+  std::string name = "SpTa";
+  std::cout << GridLogMessage << "Testing " << name << std::endl;
+  std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
 
-     U = U + Delta*identity;
-    U = SpTa(U);
-    assert(is_element_of_sp2n_algebra(U));
-    
-name="TaProj";
-    std::cout << GridLogMessage << "Testing "<< name << std::endl;
-    std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+  U = U + Delta * identity;
+  U = SpTa(U);
+  assert(is_element_of_sp2n_algebra(U));
 
-     U = U + Delta*identity;
-    Sp<Nc>::taProj(U, tmp);
-    U = tmp;
-    assert(is_element_of_sp2n_algebra(U));
-}    
-
-
-int main (int argc, char **argv)
-{
-    Grid_init(&argc,&argv);
-    
-    
-    Coordinate latt_size   = GridDefaultLatt();
-    Coordinate simd_layout = GridDefaultSimd(Nd,vComplex::Nsimd());
-    Coordinate mpi_layout  = GridDefaultMpi();
-
-    GridCartesian             Grid(latt_size,simd_layout,mpi_layout);
-    
-    
-    LatticeGaugeField Umu(&Grid);
-    LatticeColourMatrixD U(&Grid);
-    LatticeColourMatrixD Up(&Grid);
-    LatticeColourMatrixD aux(&Grid);
-    LatticeColourMatrixD identity(&Grid);
-    
-    // Will test resimplectification-related functionalities (from ProjectOnGaugeGroup, ProjectOnSpGroup, ProjectGn) and projection on the algebra (from ProjectSp2nAlgebra)
-    // we work with matrices with positive determinant so detU = 1 even if in principle ProjectOnGaugeGroup and ProjectOnSpGroup allow for detU=-1
-    // so the checks will be the same for the three functions
-    // NB only ProjectGn is the proper simplectification function
-    
-    
-    const int nsp = Nc / 2;
-    
-    identity = 1.0;
-    RealD epsilon = 0.01;
-    RealD Delta = 666.;
-    Complex i(0., 1.);
-    RealD u = 0.;
-    double vol = Umu.Grid()->gSites();
-    
-    std::vector<int> pseeds({1,2,3,4,5});
-    GridParallelRNG  pRNG(&Grid); pRNG.SeedFixedIntegers(pseeds);
-    
-    SU<Nc>::HotConfiguration(pRNG,Umu);
-    U = PeekIndex<LorentzIndex>(Umu,0);
-    test_group_projections(U);
-    U = PeekIndex<LorentzIndex>(Umu,1);
-    test_algebra_projections(U);
-        
-    Grid_finalize();
+  name = "TaProj";
+  std::cout << GridLogMessage << "Testing " << name << std::endl;
+  std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
 
+  U = U + Delta * identity;
+  Sp<Nc>::taProj(U, tmp);
+  U = tmp;
+  assert(is_element_of_sp2n_algebra(U));
+}
+
+int main(int argc, char** argv) {
+  Grid_init(&argc, &argv);
+
+  Coordinate latt_size = GridDefaultLatt();
+  Coordinate simd_layout = GridDefaultSimd(Nd, vComplex::Nsimd());
+  Coordinate mpi_layout = GridDefaultMpi();
+
+  GridCartesian Grid(latt_size, simd_layout, mpi_layout);
+
+  LatticeGaugeField Umu(&Grid);
+  LatticeColourMatrixD U(&Grid);
+
+  // Will test resimplectification-related functionalities (from
+  // ProjectOnGaugeGroup, ProjectOnSpGroup, ProjectGn) and projection on the
+  // algebra (from ProjectSp2nAlgebra) we work with matrices with positive
+  // determinant so detU = 1 even if in principle ProjectOnGaugeGroup and
+  // ProjectOnSpGroup allow for detU=-1 so the checks will be the same for the
+  // three functions NB only ProjectGn is the proper simplectification function
+
+  std::vector<int> pseeds({1, 2, 3, 4, 5});
+  GridParallelRNG pRNG(&Grid);
+  pRNG.SeedFixedIntegers(pseeds);
+
+  SU<Nc>::HotConfiguration(pRNG, Umu);
+  U = PeekIndex<LorentzIndex>(Umu, 0);
+  test_group_projections(U);
+  U = PeekIndex<LorentzIndex>(Umu, 1);
+  test_algebra_projections(U);
+
+  Grid_finalize();
 }

From c7fba9aaced5eb9ee07b89fda140650aa2b3d071 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 3 May 2023 13:54:01 +0100
Subject: [PATCH 073/129] Take over additional group tests from Alessandro

---
 tests/sp2n/Test_project_on_Sp.cc | 22 +++++++++++++++-------
 1 file changed, 15 insertions(+), 7 deletions(-)

diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 10d989e0..4560714d 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -41,22 +41,30 @@ bool has_correct_group_block_structure(const T& U) {
 };
 
 template <typename T>
-bool is_element_of_sp2n_group(T U) {
-  // does explicitly take a copy in order to not spoil the matrix for further
-  // use
-
+bool is_element_of_sp2n_group(const T& U) {
   LatticeColourMatrixD aux(U.Grid());
   LatticeColourMatrixD identity(U.Grid());
   identity = 1.0;
+  LatticeColourMatrixD Omega(U.Grid());
+  Sp<Nc>::Omega(Omega);
+
+  std::cout << GridLogMessage << "Check matrix is non-zero " << std::endl;
+  assert(norm2(U) > 1e-8);
 
   std::cout << GridLogMessage << "Unitary check" << std::endl;
   aux = U * adj(U) - identity;
   std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
   assert(norm2(aux) < 1e-8);
 
-  std::cout << GridLogMessage << "Checking Omega invariance" << std::endl;
-  Sp<Nc>::OmegaInvariance(U);  // no assertion here, but the next check will
-                               // kill us if we are not simplectic
+  aux = Omega - (U * Omega * transpose(U));
+  std::cout << GridLogMessage << "Omega - U Omega transpose(U) = " << norm2(aux)
+            << std::endl;
+  assert(norm2(aux) < 1e-8);
+
+  std::cout << GridLogMessage
+            << "|Det| = " << norm2(Determinant(U)) / U.Grid()->gSites()
+            << std::endl;
+  assert(norm2(Determinant(U)) / U.Grid()->gSites() - 1 < 1e-8);
 
   return has_correct_group_block_structure(U);
 }

From 6a7bdca53b0565360bd491d9a76aa07d277eaa21 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 3 May 2023 16:02:02 +0100
Subject: [PATCH 074/129] Take over additional algebra tests from Alessandro

---
 tests/sp2n/Test_project_on_Sp.cc | 87 +++++++++++++++++---------------
 1 file changed, 46 insertions(+), 41 deletions(-)

diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 4560714d..e56c918a 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -107,62 +107,67 @@ void test_group_projections(T U) {
 
 template <typename T>
 bool has_correct_algebra_block_structure(const T& U) {
+  // this only checks for the anti-hermitian part of the algebra
   const int nsp = Nc / 2;
   Complex i(0., 1.);
   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);
+    std::cout << GridLogMessage << "U  =  (   W    X   )  " << std::endl;
+    std::cout << GridLogMessage << "      (  -X^*  W^* )  " << 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 );
+        }
     }
-  }
 
-  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);
-    }
-  }
   return true;
 }
 
 template <typename T>
-bool is_element_of_sp2n_algebra(T U) {
-  // does explicitly take a copy in order to not spoil the matrix for further
-  // use
+bool is_element_of_sp2n_algebra(const T& U) {
   LatticeColourMatrixD aux(U.Grid());
   LatticeColourMatrixD identity(U.Grid());
   identity = 1.0;
-
-  aux = U - adj(U);
-  std::cout << GridLogMessage << "T - Tda = " << norm2(aux) << std::endl;
-  aux = U + adj(U);
-  std::cout << GridLogMessage << "T + Tda = " << norm2(aux) << std::endl;
-
-  std::cout << GridLogMessage << "Check that Omega U Omega = conj(U)"
-            << std::endl;
-
   LatticeColourMatrixD Omega(U.Grid());
   Sp<Nc>::Omega(Omega);
-  aux = Omega * U * Omega - conjugate(U);
-  std::cout << GridLogMessage << "Omega U Omega - conj(U) = " << norm2(aux)
+
+  std::cout << GridLogMessage << "Check matrix is non-zero " << std::endl;
+  assert(norm2(U) > 1e-8);
+
+  aux = U - adj(U);
+  std::cout << GridLogMessage << "T - Tda = " << norm2(aux)
+            << " (not supposed to vanish)" << std::endl;
+
+  aux = U + adj(U);
+  std::cout << GridLogMessage << "T + Tda = " << norm2(aux)
+            << " (supposed to vanish)" << std::endl;
+  assert(norm2(aux) - 1 < 1e-8);
+
+  std::cout << GridLogMessage << "Check that Omega T Omega + conj(T) = 0 "
             << std::endl;
+  aux = Omega * U * Omega + conjugate(U);
   assert(norm2(aux) < 1e-8);
 
   return has_correct_algebra_block_structure(U);

From 6e62f4f616c1a2e2a85619ffc732763b2492e42c Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 3 May 2023 16:15:12 +0100
Subject: [PATCH 075/129] ClangFormat

---
 tests/sp2n/Test_project_on_Sp.cc | 53 +++++++++++++++-----------------
 1 file changed, 25 insertions(+), 28 deletions(-)

diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index e56c918a..9f42610f 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -111,36 +111,33 @@ bool has_correct_algebra_block_structure(const T& U) {
   const int nsp = Nc / 2;
   Complex i(0., 1.);
   std::cout << GridLogMessage << "Checking the structure is " << std::endl;
-    std::cout << GridLogMessage << "U  =  (   W    X   )  " << std::endl;
-    std::cout << GridLogMessage << "      (  -X^*  W^* )  " << 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 );
-        }
+  std::cout << GridLogMessage << "U  =  (   W    X   )  " << std::endl;
+  std::cout << GridLogMessage << "      (  -X^*  W^* )  " << 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 );
-        }
+  }
+  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);
     }
+  }
 
   return true;
 }

From aa9df63a05d9c7c4513236c2fb4a86aee825a85c Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Wed, 10 May 2023 14:50:52 +0100
Subject: [PATCH 076/129] rename group projections based on determinants

---
 Grid/qcd/action/gauge/GaugeImplTypes.h |  4 +--
 Grid/qcd/utils/GaugeGroup.h            | 34 +++++++++++++-------------
 Grid/qcd/utils/SUn.impl                |  8 +++---
 Grid/qcd/utils/Sp2n.impl               |  8 +++---
 tests/sp2n/Test_project_on_Sp.cc       | 17 ++++++-------
 5 files changed, 35 insertions(+), 36 deletions(-)

diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index c3e42f80..1cc5ef05 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -145,7 +145,7 @@ public:
     accelerator_for(ss, P.Grid()->oSites(),1,{
       for (int mu = 0; mu < Nd; mu++) {
           U_v[ss](mu) = Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu);
-          Group::ProjectOnGaugeGroup(U_v[ss](mu));
+          Group::ProjectOnGeneralGroup(U_v[ss](mu));
       }
     });
    //auto end = std::chrono::high_resolution_clock::now();
@@ -166,7 +166,7 @@ public:
 
   static inline void Project(Field &U)
   {
-      Group::ProjectGn(U);
+      Group::ProjectOnSpecialGroup(U);
   }
 
   static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U)
diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index 5a8f51c2..825881e2 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -323,37 +323,37 @@ class GaugeGroup {
     }
   }
     
-  template <int N>        // reunitarise, resimplectify...
-  static void ProjectOnGaugeGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
+  template <int N>                  // Projects on the general groups U(N), Sp(2N)xZ2 i.e. determinant il allowed a complex phase.
+  static void ProjectOnGeneralGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
     for (int mu = 0; mu < Nd; mu++) {
       auto Umu = PeekIndex<LorentzIndex>(U, mu);
-      ProjectOnGaugeGroup(Umu);
+      ProjectOnGeneralGroup(Umu);
     }
   }
        
-  template <int N>        // reunitarise, resimplectify...
-  static void ProjectOnGaugeGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
-      ProjectOnGaugeGroup(Umu, group_name());
+  template <int N>
+  static void ProjectOnGeneralGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
+      ProjectOnGeneralGroup(Umu, group_name());
   }
     
   template <class vtype>
-  static void ProjectOnGaugeGroup(iScalar<vtype> &r) {
-      ProjectOnGaugeGroup(r, group_name());
+  static void ProjectOnGeneralGroup(iScalar<vtype> &r) {
+      ProjectOnGeneralGroup(r, group_name());
   }
 
   template <class vtype, int N>
-  static void ProjectOnGaugeGroup(iVector<vtype,N> &r) {
-      ProjectOnGaugeGroup(r, group_name());
+  static void ProjectOnGeneralGroup(iVector<vtype,N> &r) {
+      ProjectOnGeneralGroup(r, group_name());
   }
 
   template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
-  static void ProjectOnGaugeGroup(iMatrix<vtype,N> &arg) {
-      ProjectOnGaugeGroup(arg, group_name());
+  static void ProjectOnGeneralGroup(iMatrix<vtype,N> &arg) {
+      ProjectOnGeneralGroup(arg, group_name());
   }
 
-  template <int N>       // reunitarise, resimplectify... previously ProjectSUn
-  static void ProjectGn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
-       ProjectOnGaugeGroup(Umu);
+  template <int N>       // Projects on SU(N), Sp(2N)
+  static void ProjectOnSpecialGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
+       ProjectOnGeneralGroup(Umu);
        auto det = Determinant(Umu);
 
        det = conjugate(det);
@@ -366,11 +366,11 @@ class GaugeGroup {
    }
 
     template <int N>    // reunitarise, resimplectify... previously ProjectSUn
-    static void ProjectGn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
+    static void ProjectOnSpecialGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
       // Reunitarise
       for (int mu = 0; mu < Nd; mu++) {
         auto Umu = PeekIndex<LorentzIndex>(U, mu);
-        ProjectGn(Umu);
+        ProjectOnSpecialGroup(Umu);
         PokeIndex<LorentzIndex>(U, Umu, mu);
       }
     }
diff --git a/Grid/qcd/utils/SUn.impl b/Grid/qcd/utils/SUn.impl
index 38337305..07bfc6e7 100644
--- a/Grid/qcd/utils/SUn.impl
+++ b/Grid/qcd/utils/SUn.impl
@@ -509,22 +509,22 @@ static void testGenerators(GroupName::SU) {
 }
 
 template <int N>
-static void ProjectOnGaugeGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::SU) {
+static void ProjectOnGeneralGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::SU) {
   Umu = ProjectOnGroup(Umu);
 }
 
 template <class vtype>
-static void ProjectOnGaugeGroup(iScalar<vtype> &r, GroupName::SU) {
+static void ProjectOnGeneralGroup(iScalar<vtype> &r, GroupName::SU) {
   r = ProjectOnGroup(r);
 }
 
 template <class vtype, int N>
-static void ProjectOnGaugeGroup(iVector<vtype,N> &r, GroupName::SU) {
+static void ProjectOnGeneralGroup(iVector<vtype,N> &r, GroupName::SU) {
   r = ProjectOnGroup(r);
 }
 
 template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
-static void ProjectOnGaugeGroup(iMatrix<vtype,N> &arg, GroupName::SU) {
+static void ProjectOnGeneralGroup(iMatrix<vtype,N> &arg, GroupName::SU) {
   arg = ProjectOnGroup(arg);
 }
 
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index 2ffb79ad..9cca5d49 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -254,22 +254,22 @@ static void testGenerators(GroupName::Sp) {
 }
 
 template <int N>
-static void ProjectOnGaugeGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::Sp) {
+static void ProjectOnGeneralGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::Sp) {
   Umu = ProjectOnSpGroup(Umu);
 }
 
 template <class vtype>
-static void ProjectOnGaugeGroup(iScalar<vtype> &r, GroupName::Sp) {
+static void ProjectOnGeneralGroup(iScalar<vtype> &r, GroupName::Sp) {
   r = ProjectOnSpGroup(r);
 }
 
 template <class vtype, int N>
-static void ProjectOnGaugeGroup(iVector<vtype,N> &r, GroupName::Sp) {
+static void ProjectOnGeneralGroup(iVector<vtype,N> &r, GroupName::Sp) {
   r = ProjectOnSpGroup(r);
 }
 
 template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
-static void ProjectOnGaugeGroup(iMatrix<vtype,N> &arg, GroupName::Sp) {
+static void ProjectOnGeneralGroup(iMatrix<vtype,N> &arg, GroupName::Sp) {
   arg = ProjectOnSpGroup(arg);
 }
 
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 9f42610f..7737bc09 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -88,20 +88,20 @@ void test_group_projections(T U) {
   U = ProjectOnSpGroup(U);
   assert(is_element_of_sp2n_group(U));
 
-  name = "ProjectOnGaugeGroup";
+  name = "ProjectOnGeneralGroup";
   std::cout << GridLogMessage << "Testing " << name << std::endl;
   std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
 
   U = U + Delta * identity;
-  Sp<Nc>::ProjectOnGaugeGroup(U);
+  Sp<Nc>::ProjectOnGeneralGroup(U);
   assert(is_element_of_sp2n_group(U));
 
-  name = "ProjectGn";
+  name = "ProjectOnSpecialGroup";
   std::cout << GridLogMessage << "Testing " << name << std::endl;
   std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
 
   U = U + Delta * identity;
-  Sp<Nc>::ProjectGn(U);
+  Sp<Nc>::ProjectOnSpecialGroup(U);
   assert(is_element_of_sp2n_group(U));
 }
 
@@ -213,11 +213,10 @@ int main(int argc, char** argv) {
   LatticeColourMatrixD U(&Grid);
 
   // Will test resimplectification-related functionalities (from
-  // ProjectOnGaugeGroup, ProjectOnSpGroup, ProjectGn) and projection on the
-  // algebra (from ProjectSp2nAlgebra) we work with matrices with positive
-  // determinant so detU = 1 even if in principle ProjectOnGaugeGroup and
-  // ProjectOnSpGroup allow for detU=-1 so the checks will be the same for the
-  // three functions NB only ProjectGn is the proper simplectification function
+  // ProjectOnGeneralGroup, ProjectOnSpGroup, ProjectOnSpecialGroup) and projection on the
+  // algebra (from SpTa)
+  // ProjectOnGeneralGroup, ProjectOnSpGroup project on the non-special group allowi for complex determinants of module 1
+  // ProjectOnSpecialGroup projects on the full gauge group providing a determinant equals to 1
 
   std::vector<int> pseeds({1, 2, 3, 4, 5});
   GridParallelRNG pRNG(&Grid);

From e8ad1fef5323d945a121b3bb0cb8547a9cfa8c43 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Fri, 12 May 2023 14:35:50 +0100
Subject: [PATCH 077/129] Unify TwoIndex

---
 .../{SUnTwoIndex.h => GaugeGroupTwoIndex.h}   | 156 ++++++---
 Grid/qcd/utils/Sp2nTwoIndex.h                 | 319 ------------------
 Grid/qcd/utils/Utils.h                        |   3 +-
 tests/core/Test_lie_generators.cc             |   2 +-
 4 files changed, 112 insertions(+), 368 deletions(-)
 rename Grid/qcd/utils/{SUnTwoIndex.h => GaugeGroupTwoIndex.h} (60%)
 delete mode 100644 Grid/qcd/utils/Sp2nTwoIndex.h

diff --git a/Grid/qcd/utils/SUnTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
similarity index 60%
rename from Grid/qcd/utils/SUnTwoIndex.h
rename to Grid/qcd/utils/GaugeGroupTwoIndex.h
index a7640d65..02ec245a 100644
--- a/Grid/qcd/utils/SUnTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -16,7 +16,7 @@
 //
 //   (iT_a)^(ij)(lk) = i * ( tr[e^(ij)^dag e^(lk) T^trasp_a] +
 //   tr[e^(lk)e^(ij)^dag T_a] )  //
-//   
+//
 //
 ////////////////////////////////////////////////////////////////////////
 
@@ -25,63 +25,73 @@
 #ifndef QCD_UTIL_SUN2INDEX_H
 #define QCD_UTIL_SUN2INDEX_H
 
-
 NAMESPACE_BEGIN(Grid);
 
 enum TwoIndexSymmetry { Symmetric = 1, AntiSymmetric = -1 };
 
 inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
 
-template <int ncolour, TwoIndexSymmetry S>
-class SU_TwoIndex : public SU<ncolour> {
-public:
-  static const int Dimension = ncolour * (ncolour + S) / 2;
-  static const int NumGenerators = SU<ncolour>::AdjointDimension;
+template <int ncolour, TwoIndexSymmetry S, class group_name>
+class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
+ public:
+  // The chosen convention is that we are taking ncolour to be N in SU<N> but 2N
+  // in Sp(2N). ngroup is equal to N for SU but 2N/2 = N for Sp(2N).
+  static_assert(std::is_same<group_name, GroupName::SU>::value or
+                    std::is_same<group_name, GroupName::Sp>::value,
+                "ngroup is only implemented for SU and Sp currently.");
+  static const int ngroup =
+      std::is_same<group_name, GroupName::SU>::value ? ncolour : ncolour / 2;
+  static const int Dimension = ngroup * (ncolour + S) / 2;
+  static const int NumGenerators =
+      GaugeGroup<ncolour, group_name>::AlgebraDimension;
 
   template <typename vtype>
-  using iSUnTwoIndexMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
+  using iGroupTwoIndexMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
 
-  typedef iSUnTwoIndexMatrix<Complex> TIMatrix;
-  typedef iSUnTwoIndexMatrix<ComplexF> TIMatrixF;
-  typedef iSUnTwoIndexMatrix<ComplexD> TIMatrixD;
+  typedef iGroupTwoIndexMatrix<Complex> TIMatrix;
+  typedef iGroupTwoIndexMatrix<ComplexF> TIMatrixF;
+  typedef iGroupTwoIndexMatrix<ComplexD> TIMatrixD;
 
-  typedef iSUnTwoIndexMatrix<vComplex> vTIMatrix;
-  typedef iSUnTwoIndexMatrix<vComplexF> vTIMatrixF;
-  typedef iSUnTwoIndexMatrix<vComplexD> vTIMatrixD;
+  typedef iGroupTwoIndexMatrix<vComplex> vTIMatrix;
+  typedef iGroupTwoIndexMatrix<vComplexF> vTIMatrixF;
+  typedef iGroupTwoIndexMatrix<vComplexD> vTIMatrixD;
 
   typedef Lattice<vTIMatrix> LatticeTwoIndexMatrix;
   typedef Lattice<vTIMatrixF> LatticeTwoIndexMatrixF;
   typedef Lattice<vTIMatrixD> LatticeTwoIndexMatrixD;
 
   typedef Lattice<iVector<iScalar<iMatrix<vComplex, Dimension> >, Nd> >
-  LatticeTwoIndexField;
+      LatticeTwoIndexField;
   typedef Lattice<iVector<iScalar<iMatrix<vComplexF, Dimension> >, Nd> >
-  LatticeTwoIndexFieldF;
+      LatticeTwoIndexFieldF;
   typedef Lattice<iVector<iScalar<iMatrix<vComplexD, Dimension> >, Nd> >
-  LatticeTwoIndexFieldD;
+      LatticeTwoIndexFieldD;
 
   template <typename vtype>
-  using iSUnMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
+  using iGroupMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
 
-  typedef iSUnMatrix<Complex> Matrix;
-  typedef iSUnMatrix<ComplexF> MatrixF;
-  typedef iSUnMatrix<ComplexD> MatrixD;
+  typedef iGroupMatrix<Complex> Matrix;
+  typedef iGroupMatrix<ComplexF> MatrixF;
+  typedef iGroupMatrix<ComplexD> MatrixD;
 
   template <class cplx>
-  static void base(int Index, iSUnMatrix<cplx> &eij) {
+  static void base(int Index, iGroupMatrix<cplx> &eij) {
     // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
     assert(Index < NumGenerators);
     eij = Zero();
 
-    // for the linearisation of the 2 indexes 
-    static int a[ncolour * (ncolour - 1) / 2][2]; // store the a <-> i,j
+    // for the linearisation of the 2 indexes
+    static int a[ncolour * (ncolour - 1) / 2][2];  // store the a <-> i,j
     static bool filled = false;
     if (!filled) {
       int counter = 0;
       for (int i = 1; i < ncolour; i++) {
         for (int j = 0; j < i; j++) {
           a[counter][0] = i;
-          a[counter][1] = j;
+          a[counter][1] =
+              i == ngroup ? j + 1
+                          : j;  // this will only ever trigger for Sp because
+                                // ngroup == ncolour is out of range for SU
           counter++;
         }
       }
@@ -89,26 +99,65 @@ public:
     }
 
     if (Index < ncolour * (ncolour - 1) / 2) {
-      baseOffDiagonal(a[Index][0], a[Index][1], eij);
+      baseOffDiagonal(a[Index][0], a[Index][1], eij, group_name());
     } else {
       baseDiagonal(Index, eij);
     }
   }
 
   template <class cplx>
-  static void baseDiagonal(int Index, iSUnMatrix<cplx> &eij) {
+  static void baseDiagonal(int Index, iGroupMatrix<cplx> &eij) {
     eij = Zero();
     eij()()(Index - ncolour * (ncolour - 1) / 2,
             Index - ncolour * (ncolour - 1) / 2) = 1.0;
   }
 
   template <class cplx>
-  static void baseOffDiagonal(int i, int j, iSUnMatrix<cplx> &eij) {
+  static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij,
+                              GroupName::Sp) {
+    eij = Zero();
+    RealD tmp;
+
+    if ((i == ngroup + j) && (1 <= j) && (j < ngroup)) {
+      for (int k = 0; k < ngroup; k++) {
+        if (k < j) {
+          tmp = sqrt(2 * j * (j + 1));
+          tmp = 1 / tmp;
+          tmp *= std::sqrt(2.0);
+          eij()()(k, k + ngroup) = tmp;
+          eij()()(k + ngroup, k) = -tmp;
+        }
+        if (k == j) {
+          tmp = sqrt(2 * j * (j + 1));
+          tmp = -j / tmp;
+          tmp *= std::sqrt(2.0);
+          eij()()(k, k + ngroup) = tmp;
+          eij()()(k + ngroup, k) = -tmp;
+        }
+      }
+
+    }
+
+    else if (i != ngroup + j) {
+      for (int k = 0; k < ncolour; k++)
+        for (int l = 0; l < ncolour; l++) {
+          eij()()(l, k) =
+              delta(i, k) * delta(j, l) + S * delta(j, k) * delta(i, l);
+        }
+    }
+
+    RealD nrm = 1. / std::sqrt(2.0);
+    eij = eij * nrm;
+  }
+
+  template <class cplx>
+  static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij,
+                              GroupName::SU) {
     eij = Zero();
     for (int k = 0; k < ncolour; k++)
       for (int l = 0; l < ncolour; l++)
-        eij()()(l, k) = delta(i, k) * delta(j, l) +
-	  S * delta(j, k) * delta(i, l);
+        eij()()(l, k) =
+            delta(i, k) * delta(j, l) + S * delta(j, k) * delta(i, l);
 
     RealD nrm = 1. / std::sqrt(2.0);
     eij = eij * nrm;
@@ -125,22 +174,21 @@ public:
   }
 
   template <class cplx>
-  static void generator(int Index, iSUnTwoIndexMatrix<cplx> &i2indTa) {
-    Vector<iSUnMatrix<cplx> > ta(ncolour * ncolour - 1);
-    Vector<iSUnMatrix<cplx> > eij(Dimension);
-    iSUnMatrix<cplx> tmp;
+  static void generator(int Index, iGroupTwoIndexMatrix<cplx> &i2indTa) {
+    Vector<iGroupMatrix<cplx> > ta(NumGenerators);
+    Vector<iGroupMatrix<cplx> > eij(Dimension);
+    iGroupMatrix<cplx> tmp;
     i2indTa = Zero();
-    
+
     for (int a = 0; a < ncolour * ncolour - 1; a++)
-      SU<ncolour>::generator(a, ta[a]);
-    
+      GaugeGroup<ncolour, group_name>::generator(a, ta[a]);
+
     for (int a = 0; a < Dimension; a++) base(a, eij[a]);
 
     for (int a = 0; a < Dimension; a++) {
       tmp = transpose(ta[Index]) * adj(eij[a]) + adj(eij[a]) * ta[Index];
       for (int b = 0; b < Dimension; b++) {
-        iSUnMatrix<cplx> tmp1 =
-	  tmp * eij[b]; 
+        iGroupMatrix<cplx> tmp1 = tmp * eij[b];
         Complex iTr = TensorRemove(timesI(trace(tmp1)));
         i2indTa()()(a, b) = iTr;
       }
@@ -195,8 +243,8 @@ public:
   }
 
   static void TwoIndexLieAlgebraMatrix(
-				       const typename SU<ncolour>::LatticeAlgebraVector &h,
-				       LatticeTwoIndexMatrix &out, Real scale = 1.0) {
+      const typename SU<ncolour>::LatticeAlgebraVector &h,
+      LatticeTwoIndexMatrix &out, Real scale = 1.0) {
     conformable(h, out);
     GridBase *grid = out.Grid();
     LatticeTwoIndexMatrix la(grid);
@@ -211,11 +259,11 @@ public:
     out *= scale;
   }
 
-  // Projects the algebra components 
+  // Projects the algebra components
   // of a lattice matrix ( of dimension ncol*ncol -1 )
   static void projectOnAlgebra(
-			       typename SU<ncolour>::LatticeAlgebraVector &h_out,
-			       const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
+      typename SU<ncolour>::LatticeAlgebraVector &h_out,
+      const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
     conformable(h_out, in);
     h_out = Zero();
     TIMatrix i2indTa;
@@ -233,7 +281,7 @@ public:
                         const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
     conformable(h_out, in);
     // to store the generators
-    static std::vector<TIMatrix> i2indTa(ncolour * ncolour -1); 
+    static std::vector<TIMatrix> i2indTa(ncolour * ncolour - 1);
     h_out = Zero();
     static bool precalculated = false;
     if (!precalculated) {
@@ -242,7 +290,7 @@ public:
     }
 
     Real coefficient =
-      -2.0 / (ncolour + 2 * S) * scale;  // 2/(Nc +/- 2) for the normalization
+        -2.0 / (ncolour + 2 * S) * scale;  // 2/(Nc +/- 2) for the normalization
     // of the trace in the two index rep
 
     for (int a = 0; a < ncolour * ncolour - 1; a++) {
@@ -252,6 +300,9 @@ public:
   }
 };
 
+template <int ncolour, TwoIndexSymmetry S>
+using SU_TwoIndex = GaugeGroupTwoIndex<ncolour, S, GroupName::SU>;
+
 // Some useful type names
 typedef SU_TwoIndex<Nc, Symmetric> TwoIndexSymmMatrices;
 typedef SU_TwoIndex<Nc, AntiSymmetric> TwoIndexAntiSymmMatrices;
@@ -266,6 +317,19 @@ typedef SU_TwoIndex<3, AntiSymmetric> SU3TwoIndexAntiSymm;
 typedef SU_TwoIndex<4, AntiSymmetric> SU4TwoIndexAntiSymm;
 typedef SU_TwoIndex<5, AntiSymmetric> SU5TwoIndexAntiSymm;
 
+template <int ncolour, TwoIndexSymmetry S>
+using Sp_TwoIndex = GaugeGroupTwoIndex<ncolour, S, GroupName::Sp>;
+
+typedef Sp_TwoIndex<Nc, Symmetric> SpTwoIndexSymmMatrices;
+typedef Sp_TwoIndex<Nc, AntiSymmetric> SpTwoIndexAntiSymmMatrices;
+
+typedef Sp_TwoIndex<2, Symmetric> Sp2TwoIndexSymm;
+typedef Sp_TwoIndex<4, Symmetric> Sp4TwoIndexSymm;
+
+typedef Sp_TwoIndex<2, AntiSymmetric> Sp2TwoIndexAntiSymm;
+typedef Sp_TwoIndex<4, AntiSymmetric> Sp4TwoIndexAntiSymm;
+
+
 NAMESPACE_END(Grid);
 
 #endif
diff --git a/Grid/qcd/utils/Sp2nTwoIndex.h b/Grid/qcd/utils/Sp2nTwoIndex.h
deleted file mode 100644
index 3535fb4d..00000000
--- a/Grid/qcd/utils/Sp2nTwoIndex.h
+++ /dev/null
@@ -1,319 +0,0 @@
-////////////////////////////////////////////////////////////////////////
-//
-// * Two index representation generators
-//
-// * Normalisation for the fundamental generators:
-//   trace ta tb = 1/2 delta_ab = T_F delta_ab
-//   T_F = 1/2  for SU(N) groups
-//
-//
-//   base for NxN two index (anti-symmetric) matrices
-//   normalized to 1 (d_ij is the kroenecker delta)
-//
-//   (e^(ij)_{kl} = 1 / sqrt(2) (d_ik d_jl +/- d_jk d_il)
-//
-//   Then the generators are written as
-//
-//   (iT_a)^(ij)(lk) = i * ( tr[e^(ij)^dag e^(lk) T^trasp_a] +
-//   tr[e^(lk)e^(ij)^dag T_a] )  //
-//   
-//
-////////////////////////////////////////////////////////////////////////
-
-// Authors: David Preti, Guido Cossu
-
-#ifndef QCD_UTIL_SP2N2INDEX_H
-#define QCD_UTIL_SP2N2INDEX_H
-
-
-NAMESPACE_BEGIN(Grid);
-
-//enum SpTwoIndexSymmetry { S = 1, AS = -1 };
-
-//inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
-
-template <int ncolour, TwoIndexSymmetry S>
-class Sp_TwoIndex : public Sp<ncolour> {
-public:
-  static const int nsp = ncolour/2;
-  static const int Dimension = nsp * (ncolour + S) - 1 ;
-  static const int NumGenerators = Sp<ncolour>::AlgebraDimension;
-
-  template <typename vtype>
-  using iSp2nTwoIndexMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
-
-  typedef iSp2nTwoIndexMatrix<Complex> TIMatrix;
-  typedef iSp2nTwoIndexMatrix<ComplexF> TIMatrixF;
-  typedef iSp2nTwoIndexMatrix<ComplexD> TIMatrixD;
-
-  typedef iSp2nTwoIndexMatrix<vComplex> vTIMatrix;
-  typedef iSp2nTwoIndexMatrix<vComplexF> vTIMatrixF;
-  typedef iSp2nTwoIndexMatrix<vComplexD> vTIMatrixD;
-
-  typedef Lattice<vTIMatrix> LatticeTwoIndexMatrix;
-  typedef Lattice<vTIMatrixF> LatticeTwoIndexMatrixF;
-  typedef Lattice<vTIMatrixD> LatticeTwoIndexMatrixD;
-
-  typedef Lattice<iVector<iScalar<iMatrix<vComplex, Dimension> >, Nd> >
-  LatticeTwoIndexField;
-  typedef Lattice<iVector<iScalar<iMatrix<vComplexF, Dimension> >, Nd> >
-  LatticeTwoIndexFieldF;
-  typedef Lattice<iVector<iScalar<iMatrix<vComplexD, Dimension> >, Nd> >
-  LatticeTwoIndexFieldD;
-
-  template <typename vtype>
-  using iSp2nMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
-
-  typedef iSp2nMatrix<Complex> Matrix;
-  typedef iSp2nMatrix<ComplexF> MatrixF;
-  typedef iSp2nMatrix<ComplexD> MatrixD;
-
-  template <class cplx>
-  static void base(int Index, iSp2nMatrix<cplx> &eij) {
-    // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
-    assert(Index < NumGenerators);
-    eij = Zero();
-
-    // for the linearisation of the 2 indexes 
-    static int a[ncolour * (ncolour - 1) / 2][2]; // store the a <-> i,j
-    static bool filled = false;
-    if (!filled) {
-      int counter = 0;
-      for (int i = 1; i < ncolour; i++) {
-        for (int j = 0; j < i; j++) {
-           
-            if (i==nsp)
-            {
-                j = j+1;
-            }
-          a[counter][0] = i;
-          a[counter][1] = j;
-          counter++;
-        }
-      }
-      filled = true;
-    }
-
-    if (Index < ncolour * (ncolour - 1) / 2) {
-      baseOffDiagonal(a[Index][0], a[Index][1], eij);
-    } else {
-      baseDiagonal(Index, eij);
-    }
-  }
-    
-
-
-  template <class cplx>
-  static void baseDiagonal(int Index, iSp2nMatrix<cplx> &eij) {
-    eij = Zero();
-    eij()()(Index - ncolour * (ncolour - 1) / 2,
-            Index - ncolour * (ncolour - 1) / 2) = 1.0;
-  }
-
-  template <class cplx>
-  static void baseOffDiagonal(int i, int j, iSp2nMatrix<cplx> &eij) {
-    eij = Zero();
-    //std::cout << GridLogMessage << " doing i j = " << i << j << std::endl;
-      RealD tmp;
-
-    if ( (i == nsp + j) && (1 <= j) && (j < nsp) )
-        {
-            for (int k = 0; k < nsp; k++)
-            {
-                if (k < j)
-                {
-                    //std::cout << GridLogMessage << "b=N+a 1"<< std::endl;
-                    //std::cout << GridLogMessage << "j i "<< j << i << std::endl;
-                    tmp = sqrt( 2*j*(j+1)  );
-                    tmp = 1/tmp;
-                    tmp *= std::sqrt(2.0);
-                    eij()()(k,k+nsp) =  tmp;
-                    eij()()(k+nsp,k) =  - tmp;
-                }
-                if (k == j)
-                {
-                    //std::cout << GridLogMessage << "b=N+a 2"<< std::endl;
-                    //std::cout << GridLogMessage << "j i "<< j << i << std::endl;
-                    tmp = sqrt(2*j*(j+1)  );
-                    tmp = -j/tmp;
-                    tmp *= std::sqrt(2.0);
-                    eij()()(k,k+nsp) = tmp ;
-                    eij()()(k+nsp,k) = - tmp ;
-                 }
-            }
-            
-        }
-      
-      
-        else if (i != nsp+j)
-        {
-            for (int k = 0; k < ncolour; k++)
-                for (int l = 0; l < ncolour; l++)
-                {
-                    eij()()(l, k) = delta(i, k) * delta(j, l) + S * delta(j, k) * delta(i, l);
-                }
-            
-        }
-      
-          
-    
-        
-
-    RealD nrm = 1. / std::sqrt(2.0);
-    eij = eij * nrm;
-  }
-
-  static void printBase(void) {
-    for (int gen = 0; gen < Dimension; gen++) {
-      Matrix tmp;
-      base(gen, tmp);
-      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
-                << std::endl;
-      std::cout << GridLogMessage << tmp << std::endl;
-    }
-  }
-
-  template <class cplx>
-  static void generator(int Index, iSp2nTwoIndexMatrix<cplx> &i2indTa) {
-    Vector<iSp2nMatrix<cplx> > ta(
-								NumGenerators);
-    Vector<iSp2nMatrix<cplx> > eij(Dimension);
-    iSp2nMatrix<cplx> tmp;
-    i2indTa = Zero();
-    
-    for (int a = 0; a < NumGenerators; a++)
-      Sp<ncolour>::generator(a, ta[a]);
-    
-    for (int a = 0; a < Dimension; a++) base(a, eij[a]);
-
-    for (int a = 0; a < Dimension; a++) {
-      tmp = transpose(ta[Index]) * adj(eij[a]) + adj(eij[a]) * ta[Index];
-      for (int b = 0; b < Dimension; b++) {
-        iSp2nMatrix<cplx> tmp1 =
-	  tmp * eij[b]; 
-        Complex iTr = TensorRemove(timesI(trace(tmp1)));
-        i2indTa()()(a, b) = iTr;
-      }
-    }
-  }
-
-  static void printGenerators(void) {
-    for (int gen = 0; gen < NumGenerators; gen++) {
-      TIMatrix i2indTa;
-      generator(gen, i2indTa);
-      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
-                << std::endl;
-      std::cout << GridLogMessage << i2indTa << std::endl;
-    }
-  }
-
-  static void testGenerators(void) {
-    TIMatrix i2indTa, i2indTb;
-    std::cout << GridLogMessage << "2IndexRep - Checking if traceless"
-              << std::endl;
-    for (int a = 0; a < NumGenerators; a++) {
-      generator(a, i2indTa);
-      std::cout << GridLogMessage << a << std::endl;
-      assert(norm2(trace(i2indTa)) < 1.0e-6);
-    }
-    std::cout << GridLogMessage << std::endl;
-
-    std::cout << GridLogMessage << "2IndexRep - Checking if antihermitean"
-              << std::endl;
-    for (int a = 0; a < NumGenerators; a++) {
-      generator(a, i2indTa);
-      std::cout << GridLogMessage << a << std::endl;
-      assert(norm2(adj(i2indTa) + i2indTa) < 1.0e-6);
-    }
-
-    std::cout << GridLogMessage << std::endl;
-    std::cout << GridLogMessage
-              << "2IndexRep - Checking Tr[Ta*Tb]=delta(a,b)*(N +- 2)/2"
-              << std::endl;
-    for (int a = 0; a < NumGenerators; a++) {
-      for (int b = 0; b < NumGenerators; b++) {
-        generator(a, i2indTa);
-        generator(b, i2indTb);
-
-        // generator returns iTa, so we need a minus sign here
-        Complex Tr = -TensorRemove(trace(i2indTa * i2indTb));
-        std::cout << GridLogMessage << "a=" << a << "b=" << b << "Tr=" << Tr
-                  << std::endl;
-      }
-    }
-    std::cout << GridLogMessage << std::endl;
-  }
-
-  static void TwoIndexLieAlgebraMatrix(
-				       const typename Sp<ncolour>::LatticeAlgebraVector &h,
-				       LatticeTwoIndexMatrix &out, Real scale = 1.0) {
-    conformable(h, out);
-    GridBase *grid = out.Grid();
-    LatticeTwoIndexMatrix la(grid);
-    TIMatrix i2indTa;
-
-    out = Zero();
-    for (int a = 0; a < NumGenerators; a++) {
-      generator(a, i2indTa);
-      la = peekColour(h, a) * i2indTa;
-      out += la;
-    }
-    out *= scale;
-  }
-
-  // Projects the algebra components 
-  // of a lattice matrix ( of dimension ncol*ncol -1 )
-  static void projectOnAlgebra(
-			       typename Sp<ncolour>::LatticeAlgebraVector &h_out,
-			       const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
-    conformable(h_out, in);
-    h_out = Zero();
-    TIMatrix i2indTa;
-    Real coefficient = -2.0 / (ncolour + 2 * S) * scale;
-    // 2/(Nc +/- 2) for the normalization of the trace in the two index rep
-    for (int a = 0; a < NumGenerators; a++) {
-      generator(a, i2indTa);
-     pokeColour(h_out, real(trace(i2indTa * in)) * coefficient, a);
-    }
-  }
-
-  // a projector that keeps the generators stored to avoid the overhead of
-  // recomputing them
-  static void projector(typename Sp<ncolour>::LatticeAlgebraVector &h_out,
-                        const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
-    conformable(h_out, in);
-    // to store the generators
-    static std::vector<TIMatrix> i2indTa(NumGenerators);
-    h_out = Zero();
-    static bool precalculated = false;
-    if (!precalculated) {
-      precalculated = true;
-      for (int a = 0; a < NumGenerators; a++) generator(a, i2indTa[a]);
-    }
-
-    Real coefficient =
-      -2.0 / (ncolour + 2 * S) * scale;  // 2/(Nc +/- 2) for the normalization
-    // of the trace in the two index rep
-
-    for (int a = 0; a < NumGenerators; a++) {
-      auto tmp = real(trace(i2indTa[a] * in)) * coefficient;
-      pokeColour(h_out, tmp, a);
-    }
-  }
-};
-
-
-// Some useful type names
-typedef Sp_TwoIndex<Nc, Symmetric> SpTwoIndexSymmMatrices;
-typedef Sp_TwoIndex<Nc, AntiSymmetric> SpTwoIndexAntiSymmMatrices;
-
-typedef Sp_TwoIndex<2, Symmetric> Sp2TwoIndexSymm;
-typedef Sp_TwoIndex<4, Symmetric> Sp4TwoIndexSymm;
-
-typedef Sp_TwoIndex<2, AntiSymmetric> Sp2TwoIndexAntiSymm;
-typedef Sp_TwoIndex<4, AntiSymmetric> Sp4TwoIndexAntiSymm;
-
-
-NAMESPACE_END(Grid);
-
-#endif
diff --git a/Grid/qcd/utils/Utils.h b/Grid/qcd/utils/Utils.h
index 87196cdc..cc3ec1f1 100644
--- a/Grid/qcd/utils/Utils.h
+++ b/Grid/qcd/utils/Utils.h
@@ -10,8 +10,7 @@
 // Include representations
 #include <Grid/qcd/utils/GaugeGroup.h>
 #include <Grid/qcd/utils/SUnAdjoint.h>
-#include <Grid/qcd/utils/SUnTwoIndex.h>
-#include <Grid/qcd/utils/Sp2nTwoIndex.h>
+#include <Grid/qcd/utils/GaugeGroupTwoIndex.h>
 
 // All-to-all contraction kernels that touch the 
 // internal lattice structure
diff --git a/tests/core/Test_lie_generators.cc b/tests/core/Test_lie_generators.cc
index 7a86fd6a..3c1f6946 100644
--- a/tests/core/Test_lie_generators.cc
+++ b/tests/core/Test_lie_generators.cc
@@ -35,7 +35,7 @@ directory
 
 #include <Grid/qcd/utils/GaugeGroup.h>
 #include <Grid/qcd/utils/SUnAdjoint.h>
-#include <Grid/qcd/utils/SUnTwoIndex.h>
+#include <Grid/qcd/utils/GaugeGroupTwoIndex.h>
 
 #include <Grid/qcd/representations/adjoint.h>
 #include <Grid/qcd/representations/two_index.h>

From 170aa7df01ff5e026c4249d48b255e33ac9d9677 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Mon, 15 May 2023 15:20:18 +0100
Subject: [PATCH 078/129] fix (dimension to be improved)

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index 02ec245a..4a9abb6c 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -41,7 +41,8 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
                 "ngroup is only implemented for SU and Sp currently.");
   static const int ngroup =
       std::is_same<group_name, GroupName::SU>::value ? ncolour : ncolour / 2;
-  static const int Dimension = ngroup * (ncolour + S) / 2;
+  static const int Dimension =
+      std::is_same<group_name, GroupName::SU>::value ? ncolour * (ncolour + S) / 2 : ngroup * (ncolour + S) + S;
   static const int NumGenerators =
       GaugeGroup<ncolour, group_name>::AlgebraDimension;
 
@@ -243,7 +244,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
   }
 
   static void TwoIndexLieAlgebraMatrix(
-      const typename SU<ncolour>::LatticeAlgebraVector &h,
+      const typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h,
       LatticeTwoIndexMatrix &out, Real scale = 1.0) {
     conformable(h, out);
     GridBase *grid = out.Grid();
@@ -262,7 +263,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
   // Projects the algebra components
   // of a lattice matrix ( of dimension ncol*ncol -1 )
   static void projectOnAlgebra(
-      typename SU<ncolour>::LatticeAlgebraVector &h_out,
+      typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
       const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
     conformable(h_out, in);
     h_out = Zero();
@@ -277,7 +278,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
 
   // a projector that keeps the generators stored to avoid the overhead of
   // recomputing them
-  static void projector(typename SU<ncolour>::LatticeAlgebraVector &h_out,
+  static void projector(typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
                         const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
     conformable(h_out, in);
     // to store the generators

From 12a706e9b1352584dbbe27855f2132e4f941a6e5 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Mon, 15 May 2023 15:48:21 +0100
Subject: [PATCH 079/129] de-hardcode the number of generators

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index 4a9abb6c..640ddfdd 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -181,7 +181,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
     iGroupMatrix<cplx> tmp;
     i2indTa = Zero();
 
-    for (int a = 0; a < ncolour * ncolour - 1; a++)
+    for (int a = 0; a < NumGenerators; a++)
       GaugeGroup<ncolour, group_name>::generator(a, ta[a]);
 
     for (int a = 0; a < Dimension; a++) base(a, eij[a]);
@@ -197,7 +197,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
   }
 
   static void printGenerators(void) {
-    for (int gen = 0; gen < ncolour * ncolour - 1; gen++) {
+    for (int gen = 0; gen < NumGenerators; gen++) {
       TIMatrix i2indTa;
       generator(gen, i2indTa);
       std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
@@ -210,7 +210,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
     TIMatrix i2indTa, i2indTb;
     std::cout << GridLogMessage << "2IndexRep - Checking if traceless"
               << std::endl;
-    for (int a = 0; a < ncolour * ncolour - 1; a++) {
+    for (int a = 0; a < NumGenerators; a++) {
       generator(a, i2indTa);
       std::cout << GridLogMessage << a << std::endl;
       assert(norm2(trace(i2indTa)) < 1.0e-6);
@@ -219,7 +219,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
 
     std::cout << GridLogMessage << "2IndexRep - Checking if antihermitean"
               << std::endl;
-    for (int a = 0; a < ncolour * ncolour - 1; a++) {
+    for (int a = 0; a < NumGenerators; a++) {
       generator(a, i2indTa);
       std::cout << GridLogMessage << a << std::endl;
       assert(norm2(adj(i2indTa) + i2indTa) < 1.0e-6);
@@ -229,8 +229,8 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
     std::cout << GridLogMessage
               << "2IndexRep - Checking Tr[Ta*Tb]=delta(a,b)*(N +- 2)/2"
               << std::endl;
-    for (int a = 0; a < ncolour * ncolour - 1; a++) {
-      for (int b = 0; b < ncolour * ncolour - 1; b++) {
+    for (int a = 0; a < NumGenerators; a++) {
+      for (int b = 0; b < NumGenerators; b++) {
         generator(a, i2indTa);
         generator(b, i2indTb);
 
@@ -252,7 +252,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
     TIMatrix i2indTa;
 
     out = Zero();
-    for (int a = 0; a < ncolour * ncolour - 1; a++) {
+    for (int a = 0; a < NumGenerators; a++) {
       generator(a, i2indTa);
       la = peekColour(h, a) * i2indTa;
       out += la;
@@ -270,7 +270,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
     TIMatrix i2indTa;
     Real coefficient = -2.0 / (ncolour + 2 * S) * scale;
     // 2/(Nc +/- 2) for the normalization of the trace in the two index rep
-    for (int a = 0; a < ncolour * ncolour - 1; a++) {
+    for (int a = 0; a < NumGenerators; a++) {
       generator(a, i2indTa);
       pokeColour(h_out, real(trace(i2indTa * in)) * coefficient, a);
     }
@@ -282,19 +282,19 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
                         const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
     conformable(h_out, in);
     // to store the generators
-    static std::vector<TIMatrix> i2indTa(ncolour * ncolour - 1);
+    static std::vector<TIMatrix> i2indTa(NumGenerators);
     h_out = Zero();
     static bool precalculated = false;
     if (!precalculated) {
       precalculated = true;
-      for (int a = 0; a < ncolour * ncolour - 1; a++) generator(a, i2indTa[a]);
+      for (int a = 0; a < NumGenerators; a++) generator(a, i2indTa[a]);
     }
 
     Real coefficient =
         -2.0 / (ncolour + 2 * S) * scale;  // 2/(Nc +/- 2) for the normalization
     // of the trace in the two index rep
 
-    for (int a = 0; a < ncolour * ncolour - 1; a++) {
+    for (int a = 0; a < NumGenerators; a++) {
       auto tmp = real(trace(i2indTa[a] * in)) * coefficient;
       pokeColour(h_out, tmp, a);
     }

From 3beb8f4091d37abd9baa712026a042f6859daa51 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Mon, 15 May 2023 16:00:15 +0100
Subject: [PATCH 080/129] fixing typo, getting pre-changes physics

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index 640ddfdd..465b461c 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -89,10 +89,10 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
       for (int i = 1; i < ncolour; i++) {
         for (int j = 0; j < i; j++) {
           a[counter][0] = i;
-          a[counter][1] =
-              i == ngroup ? j + 1
+          j = i == ngroup ? j + 1
                           : j;  // this will only ever trigger for Sp because
                                 // ngroup == ncolour is out of range for SU
+          a[counter][1] = j;
           counter++;
         }
       }

From 8522352aa3bf6c7bfd8a96753c345611138fa93b Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Mon, 15 May 2023 18:36:05 +0100
Subject: [PATCH 081/129] ClangFormat

---
 .../sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc | 82 +++++++++----------
 1 file changed, 41 insertions(+), 41 deletions(-)

diff --git a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
index 8f293e72..b7cdb95f 100644
--- a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
+++ b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
@@ -2,29 +2,32 @@
 
 int main(int argc, char **argv) {
   using namespace Grid;
-   
-  typedef Representations< SpFundamentalRepresentation, SpTwoIndexAntiSymmetricRepresentation > TheRepresentations;
+
+  typedef Representations<SpFundamentalRepresentation,
+                          SpTwoIndexAntiSymmetricRepresentation>
+      TheRepresentations;
 
   Grid_init(&argc, &argv);
-    
-  typedef GenericSp2nHMCRunnerHirep<TheRepresentations, MinimumNorm2> HMCWrapper;
+
+  typedef GenericSp2nHMCRunnerHirep<TheRepresentations, MinimumNorm2>
+      HMCWrapper;
   typedef SpWilsonTwoIndexAntiSymmetricImplR FermionImplPolicy;
   typedef SpWilsonTwoIndexAntiSymmetricFermionR FermionAction;
   typedef typename FermionAction::FermionField FermionField;
- 
+
   //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
-   
+
   HMCWrapper TheHMC;
-    
+
   TheHMC.Resources.AddFourDimGrid("gauge");
-    
+
   // Checkpointer definition
   CheckpointerParameters CPparams;
   CPparams.config_prefix = "ckpoint_lat";
   CPparams.rng_prefix = "ckpoint_rng";
   CPparams.saveInterval = 100;
   CPparams.format = "IEEE64BIG";
-    
+
   TheHMC.Resources.LoadNerscCheckpointer(CPparams);
 
   RNGModuleParameters RNGpar;
@@ -35,48 +38,45 @@ int main(int argc, char **argv) {
   // Construct observables
   typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
   TheHMC.Resources.AddObservable<PlaqObs>();
-    
-  RealD beta = 6.7 ;
-    
+
+  RealD beta = 6.7;
+
   SpWilsonGaugeActionR Waction(beta);
-    
+
   auto GridPtr = TheHMC.Resources.GetCartesian();
   auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
-    
-   SpTwoIndexAntiSymmetricRepresentation::LatticeField U(GridPtr);
-    //LatticeGaugeField U(GridPtr);
-    
-  RealD mass = -0.115;
-  
 
-  std::vector<Complex> boundary = {-1,-1,-1,-1};
+  SpTwoIndexAntiSymmetricRepresentation::LatticeField U(GridPtr);
+  // LatticeGaugeField U(GridPtr);
+
+  RealD mass = -0.115;
+
+  std::vector<Complex> boundary = {-1, -1, -1, -1};
   FermionAction::ImplParams bc(boundary);
   FermionAction FermOp(U, *GridPtr, *GridRBPtr, mass, bc);
-    
-  
+
   ConjugateGradient<FermionField> CG(1.0e-8, 2000, false);
-  
+
   TwoFlavourPseudoFermionAction<FermionImplPolicy> Nf2(FermOp, CG, CG);
-    
+
   Nf2.is_smeared = false;
   std::cout << GridLogMessage << "mass " << mass << std::endl;
-    
-    ActionLevel<HMCWrapper::Field, TheRepresentations > Level1(1);
-    Level1.push_back(&Nf2);
-    
-    ActionLevel<HMCWrapper::Field, TheRepresentations > Level2(4);
-    Level2.push_back(&Waction);
-    
-    TheHMC.TheAction.push_back(Level1);
-    TheHMC.TheAction.push_back(Level2);
-    
-    TheHMC.Parameters.MD.MDsteps = 16;
-    TheHMC.Parameters.MD.trajL   = 1.0;
-    
-    TheHMC.ReadCommandLine(argc, argv);
-    TheHMC.Run();
-    
-    
+
+  ActionLevel<HMCWrapper::Field, TheRepresentations> Level1(1);
+  Level1.push_back(&Nf2);
+
+  ActionLevel<HMCWrapper::Field, TheRepresentations> Level2(4);
+  Level2.push_back(&Waction);
+
+  TheHMC.TheAction.push_back(Level1);
+  TheHMC.TheAction.push_back(Level2);
+
+  TheHMC.Parameters.MD.MDsteps = 16;
+  TheHMC.Parameters.MD.trajL = 1.0;
+
+  TheHMC.ReadCommandLine(argc, argv);
+  TheHMC.Run();
+
   Grid_finalize();
 }
 

From eee27b8b30be2413ba8cf8349df40c36e9fa23e9 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Mon, 15 May 2023 18:37:33 +0100
Subject: [PATCH 082/129] Added automated HMC test for Nc=4

---
 tests/sp2n/Makefile.am                          |  1 +
 tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc | 11 ++++++++++-
 2 files changed, 11 insertions(+), 1 deletion(-)

diff --git a/tests/sp2n/Makefile.am b/tests/sp2n/Makefile.am
index 346c8ad0..835d101f 100644
--- a/tests/sp2n/Makefile.am
+++ b/tests/sp2n/Makefile.am
@@ -6,3 +6,4 @@ check: tests
 	./Test_project_on_Sp
 	./Test_sp2n_lie_gen
 	./Test_Sp_start
+	./Test_hmc_Sp_Wilson2ASFermionGauge --grid 4.4.4.4 --Trajectories 1 --Thermalizations 0 --StartingType ColdStart --assert=true
diff --git a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
index b7cdb95f..1b633194 100644
--- a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
+++ b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
@@ -1,6 +1,6 @@
 #include <Grid/Grid.h>
 
-int main(int argc, char **argv) {
+int main(int argc, char** argv) {
   using namespace Grid;
 
   typedef Representations<SpFundamentalRepresentation,
@@ -77,6 +77,15 @@ int main(int argc, char **argv) {
   TheHMC.ReadCommandLine(argc, argv);
   TheHMC.Run();
 
+  if (std::string(argv[argc - 1]).compare("--assert=true") == 0) {
+    // this is the pseudofermion action's value for
+    // --grid 4.4.4.4 --Trajectories 1 --Thermalizations 0 --StartingType
+    // ColdStart and Nc == 4 if this assertion fails, check that you have run
+    // with these exact parameters
+    assert(Nc == 4);
+    assert(abs(Nf2.S(U) - 6586.6498) < 1.e-4);
+  }
+
   Grid_finalize();
 }
 

From fd2a63701049beb17f6fa518f3eda8415bb6d421 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 16 May 2023 14:10:39 +0100
Subject: [PATCH 083/129] test 2index

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h |  9 +++++++--
 tests/sp2n/Test_sp2n_lie_gen.cc     | 14 +++++++++-----
 2 files changed, 16 insertions(+), 7 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index 465b461c..fc5879c0 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -238,6 +238,13 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
         Complex Tr = -TensorRemove(trace(i2indTa * i2indTb));
         std::cout << GridLogMessage << "a=" << a << "b=" << b << "Tr=" << Tr
                   << std::endl;
+        if (a==b) {
+            assert(imag(Tr) < 1e-8);
+            assert(real(Tr) - 1 < 1e-8);
+        } else {
+            assert(imag(Tr) < 1e-8);
+            assert(real(Tr) < 1e-8);
+        }
       }
     }
     std::cout << GridLogMessage << std::endl;
@@ -313,7 +320,6 @@ typedef SU_TwoIndex<3, Symmetric> SU3TwoIndexSymm;
 typedef SU_TwoIndex<4, Symmetric> SU4TwoIndexSymm;
 typedef SU_TwoIndex<5, Symmetric> SU5TwoIndexSymm;
 
-typedef SU_TwoIndex<2, AntiSymmetric> SU2TwoIndexAntiSymm;
 typedef SU_TwoIndex<3, AntiSymmetric> SU3TwoIndexAntiSymm;
 typedef SU_TwoIndex<4, AntiSymmetric> SU4TwoIndexAntiSymm;
 typedef SU_TwoIndex<5, AntiSymmetric> SU5TwoIndexAntiSymm;
@@ -327,7 +333,6 @@ typedef Sp_TwoIndex<Nc, AntiSymmetric> SpTwoIndexAntiSymmMatrices;
 typedef Sp_TwoIndex<2, Symmetric> Sp2TwoIndexSymm;
 typedef Sp_TwoIndex<4, Symmetric> Sp4TwoIndexSymm;
 
-typedef Sp_TwoIndex<2, AntiSymmetric> Sp2TwoIndexAntiSymm;
 typedef Sp_TwoIndex<4, AntiSymmetric> Sp4TwoIndexAntiSymm;
 
 
diff --git a/tests/sp2n/Test_sp2n_lie_gen.cc b/tests/sp2n/Test_sp2n_lie_gen.cc
index bac7d084..17e10184 100644
--- a/tests/sp2n/Test_sp2n_lie_gen.cc
+++ b/tests/sp2n/Test_sp2n_lie_gen.cc
@@ -5,11 +5,6 @@ using namespace Grid;
 int main(int argc, char** argv) {
   Grid_init(&argc, &argv);
     
-  //std::vector<int> latt({4, 4, 4, 8});
-  //GridCartesian* grid = SpaceTimeGrid::makeFourDimGrid(
-  //latt, GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
-  //GridRedBlackCartesian* rbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(grid);
-    
   std::cout << GridLogMessage << "*********************************************"
               << std::endl;
   std::cout << GridLogMessage << "* Generators for Sp(2)" << std::endl;
@@ -46,5 +41,14 @@ int main(int argc, char** argv) {
   Sp8::printGenerators();
   Sp8::testGenerators(); 
     
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(4) TwoIndex AntiSymmetric" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+
+  Sp4TwoIndexAntiSymm::printGenerators();
+  Sp4TwoIndexAntiSymm::testGenerators();
+
   Grid_finalize();
 }

From b3533ca847d59d0c07c0cebad19517bc29702fc3 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 16 May 2023 17:43:52 +0100
Subject: [PATCH 084/129] correct tests (failing)

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h |  2 +-
 tests/sp2n/Test_sp2n_lie_gen.cc     | 18 ++++++++++++++++++
 2 files changed, 19 insertions(+), 1 deletion(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index fc5879c0..507e589a 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -240,7 +240,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
                   << std::endl;
         if (a==b) {
             assert(imag(Tr) < 1e-8);
-            assert(real(Tr) - 1 < 1e-8);
+            assert(real(Tr) - ((ncolour+S*2)*0.5) < 1e-8);
         } else {
             assert(imag(Tr) < 1e-8);
             assert(real(Tr) < 1e-8);
diff --git a/tests/sp2n/Test_sp2n_lie_gen.cc b/tests/sp2n/Test_sp2n_lie_gen.cc
index 17e10184..0b80f963 100644
--- a/tests/sp2n/Test_sp2n_lie_gen.cc
+++ b/tests/sp2n/Test_sp2n_lie_gen.cc
@@ -49,6 +49,24 @@ int main(int argc, char** argv) {
 
   Sp4TwoIndexAntiSymm::printGenerators();
   Sp4TwoIndexAntiSymm::testGenerators();
+    
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(6) TwoIndex AntiSymmetric" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+    
+  SU_TwoIndex<6, AntiSymmetric>::printGenerators();
+  SU_TwoIndex<6, AntiSymmetric>::testGenerators();
+
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(8) TwoIndex AntiSymmetric" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  
+  Sp_TwoIndex<8, AntiSymmetric>::printGenerators();
+  Sp_TwoIndex<8, AntiSymmetric>::testGenerators();
 
   Grid_finalize();
 }

From 55f9cce577bee769ae95c55fb5a8fc2a78c231fd Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Wed, 17 May 2023 09:17:48 +0100
Subject: [PATCH 085/129] Revert "Added automated HMC test for Nc=4"

This reverts commit eee27b8b30be2413ba8cf8349df40c36e9fa23e9.
---
 tests/sp2n/Makefile.am                          |  1 -
 tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc | 11 +----------
 2 files changed, 1 insertion(+), 11 deletions(-)

diff --git a/tests/sp2n/Makefile.am b/tests/sp2n/Makefile.am
index 835d101f..346c8ad0 100644
--- a/tests/sp2n/Makefile.am
+++ b/tests/sp2n/Makefile.am
@@ -6,4 +6,3 @@ check: tests
 	./Test_project_on_Sp
 	./Test_sp2n_lie_gen
 	./Test_Sp_start
-	./Test_hmc_Sp_Wilson2ASFermionGauge --grid 4.4.4.4 --Trajectories 1 --Thermalizations 0 --StartingType ColdStart --assert=true
diff --git a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
index 1b633194..b7cdb95f 100644
--- a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
+++ b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
@@ -1,6 +1,6 @@
 #include <Grid/Grid.h>
 
-int main(int argc, char** argv) {
+int main(int argc, char **argv) {
   using namespace Grid;
 
   typedef Representations<SpFundamentalRepresentation,
@@ -77,15 +77,6 @@ int main(int argc, char** argv) {
   TheHMC.ReadCommandLine(argc, argv);
   TheHMC.Run();
 
-  if (std::string(argv[argc - 1]).compare("--assert=true") == 0) {
-    // this is the pseudofermion action's value for
-    // --grid 4.4.4.4 --Trajectories 1 --Thermalizations 0 --StartingType
-    // ColdStart and Nc == 4 if this assertion fails, check that you have run
-    // with these exact parameters
-    assert(Nc == 4);
-    assert(abs(Nf2.S(U) - 6586.6498) < 1.e-4);
-  }
-
   Grid_finalize();
 }
 

From 932c783fbf7ede5e1735123d5f708740cd8817ac Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Wed, 17 May 2023 20:22:05 +0100
Subject: [PATCH 086/129] 2AS for every Nc!

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h |  10 ++-
 tests/sp2n/Test_2as_base.cc         | 110 ++++++++++++++++++++++++++++
 tests/sp2n/Test_sp2n_lie_gen.cc     |  35 ++++-----
 3 files changed, 131 insertions(+), 24 deletions(-)
 create mode 100644 tests/sp2n/Test_2as_base.cc

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index 507e589a..8fb7b04d 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -78,7 +78,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
   template <class cplx>
   static void base(int Index, iGroupMatrix<cplx> &eij) {
     // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
-    assert(Index < NumGenerators);
+    assert(Index < Dimension);
     eij = Zero();
 
     // for the linearisation of the 2 indexes
@@ -89,9 +89,10 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
       for (int i = 1; i < ncolour; i++) {
         for (int j = 0; j < i; j++) {
           a[counter][0] = i;
-          j = i == ngroup ? j + 1
-                          : j;  // this will only ever trigger for Sp because
-                                // ngroup == ncolour is out of range for SU
+            if (j==0 && ngroup == ncolour/2 && i==ngroup+j) {
+                //std::cout << "skipping" << std::endl; // for Sp2n this vanishes identically.
+                j = j+1;
+            }
           a[counter][1] = j;
           counter++;
         }
@@ -320,6 +321,7 @@ typedef SU_TwoIndex<3, Symmetric> SU3TwoIndexSymm;
 typedef SU_TwoIndex<4, Symmetric> SU4TwoIndexSymm;
 typedef SU_TwoIndex<5, Symmetric> SU5TwoIndexSymm;
 
+typedef SU_TwoIndex<2, AntiSymmetric> SU2TwoIndexAntiSymm;
 typedef SU_TwoIndex<3, AntiSymmetric> SU3TwoIndexAntiSymm;
 typedef SU_TwoIndex<4, AntiSymmetric> SU4TwoIndexAntiSymm;
 typedef SU_TwoIndex<5, AntiSymmetric> SU5TwoIndexAntiSymm;
diff --git a/tests/sp2n/Test_2as_base.cc b/tests/sp2n/Test_2as_base.cc
new file mode 100644
index 00000000..b44e2e8f
--- /dev/null
+++ b/tests/sp2n/Test_2as_base.cc
@@ -0,0 +1,110 @@
+#include <Grid/Grid.h>
+
+#define verbose 0
+
+using namespace Grid;
+
+int main(int argc, char** argv) {
+  Grid_init(&argc, &argv);
+
+  const int this_nc = 4;
+  const int this_n = this_nc/2;
+  const int this_irrep_dim = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension;
+  const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
+  typedef Sp_TwoIndex<this_nc, AntiSymmetric>::iGroupMatrix<Complex> Matrix;
+  typedef Sp_TwoIndex<this_nc, AntiSymmetric>::iGroupTwoIndexMatrix<Complex> ASMatrix;
+  
+  Matrix Omega;
+  Matrix eij_a;
+  Matrix eij_b;
+  Matrix eij_c;
+  Matrix e_sum;
+  Omega = Zero();
+  for (int i = 0; i < this_n; i++)
+  {
+    Omega()()(i, this_n + i) = 1.;
+    Omega()()(this_n + i, i) = -1;
+  }
+    std::cout << "Omega " << Omega << std::endl;
+
+  RealD realA;
+  RealD realB;
+  std::cout << GridLogMessage << "2as dimension is " << this_irrep_dim << std::endl;
+  std::cout << GridLogMessage << "algebra dimension is " << this_algebra_dim << std::endl;
+  realA = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension + Sp_TwoIndex<this_nc, Symmetric>::Dimension;
+  realB = Sp<this_nc>::Dimension*Sp<this_nc>::Dimension;
+  assert ( realA == realB);
+
+  std::cout << GridLogMessage << "checking base is antisymmetric " << std::endl;
+  for (int a=0; a < this_irrep_dim; a++)
+  {
+      Sp_TwoIndex<this_nc, AntiSymmetric>::base(a, eij_c);
+      e_sum = eij_c + transpose(eij_c);
+      std::cout << GridLogMessage << "e_ab + e_ab^T " << norm2(e_sum) << std::endl;
+      assert(norm2(e_sum) < 1e-8);
+        
+  }
+  std::cout << GridLogMessage << "Checking Tr (e^(ab) Omega ) = 0 and Tr (e^(ab) e^(cd) = delta^((ab)(cd)) ) " << std::endl;
+  for (int a=0; a < Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension; a++) {
+      Sp_TwoIndex<this_nc, AntiSymmetric>::base(a, eij_a);
+      realA = norm2(trace(Omega*eij_a));
+      std::cout << GridLogMessage << "Omega trace for (ab) = " << a << std::endl;
+      assert(realA == 0);
+      for (int b=0; b < Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension; b++) {
+          Sp_TwoIndex<this_nc, AntiSymmetric>::base(b, eij_b);
+          auto d_ab = TensorRemove(trace(eij_a * eij_b));
+#if verbose
+          std::cout << GridLogMessage << "Tr( e_{ab=" << a << "} e_{cd=" << b << "} ) = " << d_ab << std::endl;
+#endif
+          std::cout << GridLogMessage << "Orthonormality for (ab) = " << a << std::endl;
+          if (a==b) {
+              assert(real(d_ab)+1 < 1e-8);
+              assert(imag(d_ab) < 1e-8);
+          } else {
+              assert(real(d_ab) < 1e-8);
+              assert(imag(d_ab) < 1e-8);
+          }
+      }
+  }
+
+  int sum = 0;
+  int sum_im = 0;
+  Vector<Matrix> ta_fund(this_algebra_dim);
+  Vector<Matrix> eij(this_irrep_dim);
+  Matrix tmp_l;
+  Matrix tmp_r;
+  for (int n = 0; n < this_algebra_dim; n++)
+  {
+      Sp<this_nc>::generator(n, ta_fund[n]);
+  }
+  for (int a = 0; a < this_irrep_dim; a++)
+  {
+      Sp_TwoIndex<this_nc, AntiSymmetric>::base(a, eij[a]);
+  }
+  for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
+  {
+      Complex iTr;
+      sum = 0;
+      sum_im = 0;
+      std::cout << GridLogMessage <<  "generator number " << gen_id << std::endl;
+      for (int a = 0; a < this_irrep_dim; a++)
+      {
+      
+          tmp_l = adj(eij[a])*ta_fund[gen_id]*eij[a];
+          tmp_r = adj(eij[a])*eij[a]*transpose(ta_fund[gen_id]);
+#if verbose
+          std::cout << GridLogMessage << " as_indx = " << a << " eDag T_F e = " << std::endl << tmp_l << std::endl;
+          std::cout << GridLogMessage << " as_indx = " << a << " eDag e T_F^T = " << std::endl << tmp_r << std::endl;
+#endif
+          std::cout << GridLogMessage << " as_indx = " << a << " Tr(sum) = " << TensorRemove(trace(tmp_l+tmp_r)) << std::endl;
+          sum += real(TensorRemove(trace(tmp_l+tmp_r)));
+          sum_im += imag(TensorRemove(trace(tmp_l+tmp_r)));
+      }
+      std::cout << GridLogMessage << "re-evaluated trace of the generator " << gen_id << " is " << sum << " " << sum_im << std::endl;
+      assert ( sum < 1e-8) ;
+      assert ( sum_im < 1e-8) ;
+
+  }
+  
+  Grid_finalize();
+}
diff --git a/tests/sp2n/Test_sp2n_lie_gen.cc b/tests/sp2n/Test_sp2n_lie_gen.cc
index 0b80f963..005aa89b 100644
--- a/tests/sp2n/Test_sp2n_lie_gen.cc
+++ b/tests/sp2n/Test_sp2n_lie_gen.cc
@@ -4,10 +4,10 @@ using namespace Grid;
 
 int main(int argc, char** argv) {
   Grid_init(&argc, &argv);
-    
+
   std::cout << GridLogMessage << "*********************************************"
               << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(2)" << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(2) (print and test)" << std::endl;
   std::cout << GridLogMessage << "*********************************************"
               << std::endl;
       
@@ -16,7 +16,7 @@ int main(int argc, char** argv) {
   
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(4)" << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(4) (print and test)" << std::endl;
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
     
@@ -25,47 +25,42 @@ int main(int argc, char** argv) {
     
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(6)" << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(6) (test)" << std::endl;
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
-  
-  Sp6::printGenerators();
+
   Sp6::testGenerators();
-    
+
   std::cout << GridLogMessage << "*********************************************"
               << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(8)" << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(8) (test)" << std::endl;
   std::cout << GridLogMessage << "*********************************************"
               << std::endl;
     
-  Sp8::printGenerators();
-  Sp8::testGenerators(); 
+  Sp8::testGenerators();
     
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(4) TwoIndex AntiSymmetric" << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(4) TwoIndexAS (test)" << std::endl;
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
 
-  Sp4TwoIndexAntiSymm::printGenerators();
-  Sp4TwoIndexAntiSymm::testGenerators();
+  Sp_TwoIndex<4, AntiSymmetric>:::testGenerators();
     
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(6) TwoIndex AntiSymmetric" << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(6) TwoIndexAS (test)" << std::endl;
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
-    
-  SU_TwoIndex<6, AntiSymmetric>::printGenerators();
-  SU_TwoIndex<6, AntiSymmetric>::testGenerators();
+
+  Sp_TwoIndex<6, AntiSymmetric>::testGenerators();
 
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(8) TwoIndex AntiSymmetric" << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(8) TwoIndexAS (test)" << std::endl;
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
-  
-  Sp_TwoIndex<8, AntiSymmetric>::printGenerators();
+
   Sp_TwoIndex<8, AntiSymmetric>::testGenerators();
 
   Grid_finalize();

From 5a75ab15a273ed3073b3fe33b788ea8b56a3ef23 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Wed, 17 May 2023 20:47:57 +0100
Subject: [PATCH 087/129] typo in 2S dim

---
 Grid/qcd/representations/sp_two_index.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Grid/qcd/representations/sp_two_index.h b/Grid/qcd/representations/sp_two_index.h
index ec0663b4..7fe097b9 100644
--- a/Grid/qcd/representations/sp_two_index.h
+++ b/Grid/qcd/representations/sp_two_index.h
@@ -27,7 +27,7 @@ public:
   // types for the higher representation fields
   typedef typename Sp_TwoIndex<ncolour, S>::LatticeTwoIndexMatrix LatticeMatrix;
   typedef typename Sp_TwoIndex<ncolour, S>::LatticeTwoIndexField LatticeField;
-  static const int Dimension = (ncolour * (ncolour + S) / 2) - 1;
+  static const int Dimension = (ncolour * (ncolour + S) / 2) + S;
   static const bool isFundamental = false;
   //static const int nsp = Nc / 2;
   LatticeField U;

From e41821e2069fa5f7a88a19495fe4225309d47a56 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Thu, 18 May 2023 15:29:55 +0100
Subject: [PATCH 088/129] Disable two index symmetric

---
 ...antiationSpWilsonTwoIndexSymmetricImplD.cc |  1 -
 ...antiationSpWilsonTwoIndexSymmetricImplD.cc |  1 -
 ...antiationSpWilsonTwoIndexSymmetricImplD.cc |  1 -
 ...antiationSpWilsonTwoIndexSymmetricImplD.cc |  1 -
 .../SpWilsonTwoIndexSymmetricImplD/impl.h     |  1 -
 ...antiationSpWilsonTwoIndexSymmetricImplF.cc |  1 -
 ...antiationSpWilsonTwoIndexSymmetricImplF.cc |  1 -
 ...antiationSpWilsonTwoIndexSymmetricImplF.cc |  1 -
 ...antiationSpWilsonTwoIndexSymmetricImplF.cc |  1 -
 .../SpWilsonTwoIndexSymmetricImplF/impl.h     |  1 -
 Grid/qcd/utils/GaugeGroupTwoIndex.h           | 27 ++++++++++++-------
 11 files changed, 17 insertions(+), 20 deletions(-)
 delete mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
 delete mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
 delete mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc
 delete mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
 delete mode 100644 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h
 delete mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
 delete mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
 delete mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc
 delete mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
 delete mode 100644 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h

diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
deleted file mode 120000
index 9cc05107..00000000
--- a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
+++ /dev/null
@@ -1 +0,0 @@
-../WilsonCloverFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
deleted file mode 120000
index 5f6ab65e..00000000
--- a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
+++ /dev/null
@@ -1 +0,0 @@
-../WilsonFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc
deleted file mode 120000
index 01c35e7b..00000000
--- a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc
+++ /dev/null
@@ -1 +0,0 @@
-../WilsonKernelsInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
deleted file mode 120000
index d5789bcf..00000000
--- a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
+++ /dev/null
@@ -1 +0,0 @@
-../WilsonTMFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h
deleted file mode 100644
index ac5babca..00000000
--- a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h
+++ /dev/null
@@ -1 +0,0 @@
-#define IMPLEMENTATION SpWilsonTwoIndexSymmetricImplD
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
deleted file mode 120000
index 9cc05107..00000000
--- a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
+++ /dev/null
@@ -1 +0,0 @@
-../WilsonCloverFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
deleted file mode 120000
index 5f6ab65e..00000000
--- a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
+++ /dev/null
@@ -1 +0,0 @@
-../WilsonFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc
deleted file mode 120000
index 01c35e7b..00000000
--- a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc
+++ /dev/null
@@ -1 +0,0 @@
-../WilsonKernelsInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
deleted file mode 120000
index d5789bcf..00000000
--- a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
+++ /dev/null
@@ -1 +0,0 @@
-../WilsonTMFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h
deleted file mode 100644
index bea7dce7..00000000
--- a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h
+++ /dev/null
@@ -1 +0,0 @@
-#define IMPLEMENTATION SpWilsonTwoIndexSymmetricImplF
diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index 507e589a..4ce755d8 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -34,6 +34,12 @@ inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
 template <int ncolour, TwoIndexSymmetry S, class group_name>
 class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
  public:
+  static_assert(
+      std::is_same<group_name, GroupName::Sp>::value ? S != Symmetric : true,
+      "The symmetric two-index representation of Sp(2N) does not work "
+      "currently. If you want to use it, you need to implement the equivalent "
+      "of Eq. (27) and (28) from https://doi.org/10.48550/arXiv.2202.05516.");
+
   // The chosen convention is that we are taking ncolour to be N in SU<N> but 2N
   // in Sp(2N). ngroup is equal to N for SU but 2N/2 = N for Sp(2N).
   static_assert(std::is_same<group_name, GroupName::SU>::value or
@@ -41,8 +47,9 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
                 "ngroup is only implemented for SU and Sp currently.");
   static const int ngroup =
       std::is_same<group_name, GroupName::SU>::value ? ncolour : ncolour / 2;
-  static const int Dimension =
-      std::is_same<group_name, GroupName::SU>::value ? ncolour * (ncolour + S) / 2 : ngroup * (ncolour + S) + S;
+  static const int Dimension = std::is_same<group_name, GroupName::SU>::value
+                                   ? ncolour * (ncolour + S) / 2
+                                   : ngroup * (ncolour + S) + S;
   static const int NumGenerators =
       GaugeGroup<ncolour, group_name>::AlgebraDimension;
 
@@ -238,12 +245,12 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
         Complex Tr = -TensorRemove(trace(i2indTa * i2indTb));
         std::cout << GridLogMessage << "a=" << a << "b=" << b << "Tr=" << Tr
                   << std::endl;
-        if (a==b) {
-            assert(imag(Tr) < 1e-8);
-            assert(real(Tr) - ((ncolour+S*2)*0.5) < 1e-8);
+        if (a == b) {
+          assert(imag(Tr) < 1e-8);
+          assert(real(Tr) - ((ncolour + S * 2) * 0.5) < 1e-8);
         } else {
-            assert(imag(Tr) < 1e-8);
-            assert(real(Tr) < 1e-8);
+          assert(imag(Tr) < 1e-8);
+          assert(real(Tr) < 1e-8);
         }
       }
     }
@@ -285,8 +292,9 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
 
   // a projector that keeps the generators stored to avoid the overhead of
   // recomputing them
-  static void projector(typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
-                        const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
+  static void projector(
+      typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
+      const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
     conformable(h_out, in);
     // to store the generators
     static std::vector<TIMatrix> i2indTa(NumGenerators);
@@ -335,7 +343,6 @@ typedef Sp_TwoIndex<4, Symmetric> Sp4TwoIndexSymm;
 
 typedef Sp_TwoIndex<4, AntiSymmetric> Sp4TwoIndexAntiSymm;
 
-
 NAMESPACE_END(Grid);
 
 #endif

From a5125e23f40f3fc5a9ff70aaf59b22915f4b13d4 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Thu, 18 May 2023 15:41:35 +0100
Subject: [PATCH 089/129] Typo

---
 tests/sp2n/Test_sp2n_lie_gen.cc | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tests/sp2n/Test_sp2n_lie_gen.cc b/tests/sp2n/Test_sp2n_lie_gen.cc
index 005aa89b..24642048 100644
--- a/tests/sp2n/Test_sp2n_lie_gen.cc
+++ b/tests/sp2n/Test_sp2n_lie_gen.cc
@@ -45,7 +45,7 @@ int main(int argc, char** argv) {
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
 
-  Sp_TwoIndex<4, AntiSymmetric>:::testGenerators();
+  Sp_TwoIndex<4, AntiSymmetric>::testGenerators();
     
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;

From e855c41772aaffb167bb6c448052737812bdfeb5 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Thu, 18 May 2023 18:09:38 +0100
Subject: [PATCH 090/129] Unified spfundamental.h with fundamental.h

---
 Grid/qcd/representations/Representations.h |  1 -
 Grid/qcd/representations/fundamental.h     |  7 ++--
 Grid/qcd/representations/hmc_types.h       |  1 -
 Grid/qcd/representations/spfundamental.h   | 42 ----------------------
 4 files changed, 4 insertions(+), 47 deletions(-)
 delete mode 100644 Grid/qcd/representations/spfundamental.h

diff --git a/Grid/qcd/representations/Representations.h b/Grid/qcd/representations/Representations.h
index 8791f653..85dc6596 100644
--- a/Grid/qcd/representations/Representations.h
+++ b/Grid/qcd/representations/Representations.h
@@ -4,7 +4,6 @@
 #include <Grid/qcd/representations/adjoint.h>
 #include <Grid/qcd/representations/two_index.h>
 #include <Grid/qcd/representations/fundamental.h>
-#include <Grid/qcd/representations/spfundamental.h>
 #include <Grid/qcd/representations/sp_two_index.h>
 #include <Grid/qcd/representations/hmc_types.h>
 
diff --git a/Grid/qcd/representations/fundamental.h b/Grid/qcd/representations/fundamental.h
index 4d4779e1..90592abb 100644
--- a/Grid/qcd/representations/fundamental.h
+++ b/Grid/qcd/representations/fundamental.h
@@ -13,7 +13,7 @@ NAMESPACE_BEGIN(Grid);
  * Empty since HMC updates already the fundamental representation 
  */
 
-template <int ncolour>
+template <int ncolour, class group_name>
 class FundamentalRep {
 public:
   static const int Dimension = ncolour;
@@ -21,7 +21,7 @@ public:
 
   // typdef to be used by the Representations class in HMC to get the
   // types for the higher representation fields
-  typedef typename SU<ncolour>::LatticeMatrix LatticeMatrix;
+  typedef typename GaugeGroup<ncolour,group_name>::LatticeMatrix LatticeMatrix;
   typedef LatticeGaugeField LatticeField;
   
   explicit FundamentalRep(GridBase* grid) {} //do nothing
@@ -45,7 +45,8 @@ public:
     
 
   
-typedef	 FundamentalRep<Nc> FundamentalRepresentation;
+typedef	 FundamentalRep<Nc,GroupName::SU> FundamentalRepresentation;
+typedef	 FundamentalRep<Nc,GroupName::Sp> SpFundamentalRepresentation;
 
 NAMESPACE_END(Grid);  
 
diff --git a/Grid/qcd/representations/hmc_types.h b/Grid/qcd/representations/hmc_types.h
index a24d5752..7ad67079 100644
--- a/Grid/qcd/representations/hmc_types.h
+++ b/Grid/qcd/representations/hmc_types.h
@@ -4,7 +4,6 @@
 #include <Grid/qcd/representations/adjoint.h>
 #include <Grid/qcd/representations/two_index.h>
 #include <Grid/qcd/representations/fundamental.h>
-#include <Grid/qcd/representations/spfundamental.h>
 #include <Grid/qcd/representations/sp_two_index.h>
 #include <Grid/qcd/action/scalar/ScalarImpl.h>
 
diff --git a/Grid/qcd/representations/spfundamental.h b/Grid/qcd/representations/spfundamental.h
deleted file mode 100644
index df6b6fed..00000000
--- a/Grid/qcd/representations/spfundamental.h
+++ /dev/null
@@ -1,42 +0,0 @@
-
-
-#ifndef SPFUNDAMENTAL_H
-#define SPFUNDAMENTAL_H
-
-NAMESPACE_BEGIN(Grid);
-
-/*
- * This is an helper class for the HMC
- * Empty since HMC updates already the fundamental representation 
- */
-
-template <int ncolour>
-class SpFundamentalRep {
-public:
-  static const int Dimension = ncolour;
-  //static const int nSp = ncolour/2;
-  static const bool isFundamental = true;
-
-  // typdef to be used by the Representations class in HMC to get the
-  // types for the higher representation fields
-  typedef typename Sp<ncolour>::LatticeMatrix LatticeMatrix;
-  typedef LatticeGaugeField LatticeField;
-  
-  explicit SpFundamentalRep(GridBase* grid) {} //do nothing
-  void update_representation(const LatticeGaugeField& Uin) {} // do nothing
-
-  LatticeField RtoFundamentalProject(const LatticeField& in, Real scale = 1.0) const{
-    return (scale * in);
-  }
-
-};
-
-
-    
-
-  
-typedef	 SpFundamentalRep<Nc> SpFundamentalRepresentation;
-
-NAMESPACE_END(Grid);  
-
-#endif

From 0078826ff1341bce0c4b4f52d9ed70955cc0f475 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Thu, 18 May 2023 18:14:53 +0100
Subject: [PATCH 091/129] Move static_assert inside of function

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h | 24 ++++++++++++++----------
 1 file changed, 14 insertions(+), 10 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index e0c6c0e7..a5518933 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -34,12 +34,6 @@ inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
 template <int ncolour, TwoIndexSymmetry S, class group_name>
 class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
  public:
-  static_assert(
-      std::is_same<group_name, GroupName::Sp>::value ? S != Symmetric : true,
-      "The symmetric two-index representation of Sp(2N) does not work "
-      "currently. If you want to use it, you need to implement the equivalent "
-      "of Eq. (27) and (28) from https://doi.org/10.48550/arXiv.2202.05516.");
-
   // The chosen convention is that we are taking ncolour to be N in SU<N> but 2N
   // in Sp(2N). ngroup is equal to N for SU but 2N/2 = N for Sp(2N).
   static_assert(std::is_same<group_name, GroupName::SU>::value or
@@ -84,6 +78,17 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
 
   template <class cplx>
   static void base(int Index, iGroupMatrix<cplx> &eij) {
+    // This is inside of this function because you can't use this class without
+    // this function but you can still use its static constants because as a
+    // template the following static_assert is only triggered if this function
+    // is instantiated which in turn happens only when it's used.
+    static_assert(
+        std::is_same<group_name, GroupName::Sp>::value ? S != Symmetric : true,
+        "The symmetric two-index representation of Sp(2N) does not work "
+        "currently. If you want to use it, you need to implement the "
+        "equivalent of Eq. (27) and (28) from "
+        "https://doi.org/10.48550/arXiv.2202.05516.");
+
     // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
     assert(Index < Dimension);
     eij = Zero();
@@ -96,10 +101,9 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
       for (int i = 1; i < ncolour; i++) {
         for (int j = 0; j < i; j++) {
           a[counter][0] = i;
-            if (j==0 && ngroup == ncolour/2 && i==ngroup+j) {
-                //std::cout << "skipping" << std::endl; // for Sp2n this vanishes identically.
-                j = j+1;
-            }
+          if (j == 0 && ngroup == ncolour / 2 && i == ngroup + j) {
+            j = j + 1;
+          }
           a[counter][1] = j;
           counter++;
         }

From b8bdc2eefbe5a585bf7b140c32e0bf7a3b8503e3 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Thu, 18 May 2023 18:36:29 +0100
Subject: [PATCH 092/129] Unified two index representations

---
 Grid/qcd/representations/Representations.h |   1 -
 Grid/qcd/representations/hmc_types.h       |   1 -
 Grid/qcd/representations/sp_two_index.h    | 100 ---------------------
 Grid/qcd/representations/two_index.h       |  25 +++---
 4 files changed, 14 insertions(+), 113 deletions(-)
 delete mode 100644 Grid/qcd/representations/sp_two_index.h

diff --git a/Grid/qcd/representations/Representations.h b/Grid/qcd/representations/Representations.h
index 85dc6596..22311be0 100644
--- a/Grid/qcd/representations/Representations.h
+++ b/Grid/qcd/representations/Representations.h
@@ -4,7 +4,6 @@
 #include <Grid/qcd/representations/adjoint.h>
 #include <Grid/qcd/representations/two_index.h>
 #include <Grid/qcd/representations/fundamental.h>
-#include <Grid/qcd/representations/sp_two_index.h>
 #include <Grid/qcd/representations/hmc_types.h>
 
 #endif
diff --git a/Grid/qcd/representations/hmc_types.h b/Grid/qcd/representations/hmc_types.h
index 7ad67079..5e4ab020 100644
--- a/Grid/qcd/representations/hmc_types.h
+++ b/Grid/qcd/representations/hmc_types.h
@@ -4,7 +4,6 @@
 #include <Grid/qcd/representations/adjoint.h>
 #include <Grid/qcd/representations/two_index.h>
 #include <Grid/qcd/representations/fundamental.h>
-#include <Grid/qcd/representations/sp_two_index.h>
 #include <Grid/qcd/action/scalar/ScalarImpl.h>
 
 #include <tuple>
diff --git a/Grid/qcd/representations/sp_two_index.h b/Grid/qcd/representations/sp_two_index.h
deleted file mode 100644
index 7fe097b9..00000000
--- a/Grid/qcd/representations/sp_two_index.h
+++ /dev/null
@@ -1,100 +0,0 @@
-/*
- *  Policy classes for the HMC
- *  Authors: Guido Cossu, David Preti
- */
-
-#ifndef SP2N2INDEX_H_H
-#define SP2N2INDEX_H_H
-
-NAMESPACE_BEGIN(Grid);
-
-/*
- * This is an helper class for the HMC
- * Should contain only the data for the two index representations
- * and the facility to convert from the fundamental -> two index
- * The templated parameter TwoIndexSymmetry choses between the 
- * symmetric and antisymmetric representations
- * 
- * There is an 
- * enum TwoIndexSymmetry { Symmetric = 1, AntiSymmetric = -1 };
- * in the SUnTwoIndex.h file
- */
-
-template <int ncolour, TwoIndexSymmetry S>
-class SpTwoIndexRep {
-public:
-  // typdef to be used by the Representations class in HMC to get the
-  // types for the higher representation fields
-  typedef typename Sp_TwoIndex<ncolour, S>::LatticeTwoIndexMatrix LatticeMatrix;
-  typedef typename Sp_TwoIndex<ncolour, S>::LatticeTwoIndexField LatticeField;
-  static const int Dimension = (ncolour * (ncolour + S) / 2) + S;
-  static const bool isFundamental = false;
-  //static const int nsp = Nc / 2;
-  LatticeField U;
-
-  explicit SpTwoIndexRep(GridBase *grid) : U(grid) {}
-
-  void update_representation(const LatticeGaugeField &Uin) {
-    std::cout << GridLogDebug << "Updating TwoIndex representation\n";
-    // Uin is in the fundamental representation
-    // get the U in TwoIndexRep
-    // (U)_{(ij)(lk)} = tr [ adj(e^(ij)) U e^(lk) transpose(U) ]
-    conformable(U, Uin);
-    U = Zero();
-    LatticeColourMatrix tmp(Uin.Grid());
-
-    Vector<typename Sp<ncolour>::Matrix> eij(Dimension);
-
-    for (int a = 0; a < Dimension; a++)
-      Sp_TwoIndex<ncolour, S>::base(a, eij[a]);
-
-    for (int mu = 0; mu < Nd; mu++) {
-      auto Uin_mu = peekLorentz(Uin, mu);
-      auto U_mu = peekLorentz(U, mu);
-      for (int a = 0; a < Dimension; a++) {
-        tmp = transpose(Uin_mu) * adj(eij[a]) * Uin_mu;
-        for (int b = 0; b < Dimension; b++)
-          pokeColour(U_mu, trace(tmp * eij[b]), a, b);
-      }
-      pokeLorentz(U, U_mu, mu);
-    }
-  }
-
-  LatticeGaugeField RtoFundamentalProject(const LatticeField &in,
-                                          Real scale = 1.0) const {
-    LatticeGaugeField out(in.Grid());
-    out = Zero();
-
-    for (int mu = 0; mu < Nd; mu++) {
-      LatticeColourMatrix out_mu(in.Grid());  // fundamental representation
-      LatticeMatrix in_mu = peekLorentz(in, mu);
-
-      out_mu = Zero();
-
-      typename Sp<ncolour>::LatticeAlgebraVector h(in.Grid());
-      projectOnAlgebra(h, in_mu, double(Nc + 2 * S));  // factor T(r)/T(fund)
-      FundamentalLieAlgebraMatrix(h, out_mu);          // apply scale only once
-      pokeLorentz(out, out_mu, mu);                     // should be 2 for sp4 as. ok
-    }
-    return out;
-  }
-
-private:
-  void projectOnAlgebra(typename Sp<ncolour>::LatticeAlgebraVector &h_out,
-                        const LatticeMatrix &in, Real scale = 1.0) const {
-    Sp_TwoIndex<ncolour, S>::projectOnAlgebra(h_out, in, scale);
-  }
-
-  void FundamentalLieAlgebraMatrix(
-				   typename Sp<ncolour>::LatticeAlgebraVector &h,
-				   typename Sp<ncolour>::LatticeMatrix &out, Real scale = 1.0) const {
-    Sp<ncolour>::FundamentalLieAlgebraMatrix(h, out, scale);
-  }
-};
-
-typedef SpTwoIndexRep<Nc, Symmetric> SpTwoIndexSymmetricRepresentation;
-typedef SpTwoIndexRep<Nc, AntiSymmetric> SpTwoIndexAntiSymmetricRepresentation;
-
-NAMESPACE_END(Grid);
-
-#endif
diff --git a/Grid/qcd/representations/two_index.h b/Grid/qcd/representations/two_index.h
index 8dfb5561..9fa6a203 100644
--- a/Grid/qcd/representations/two_index.h
+++ b/Grid/qcd/representations/two_index.h
@@ -20,14 +20,14 @@ NAMESPACE_BEGIN(Grid);
  * in the SUnTwoIndex.h file
  */
 
-template <int ncolour, TwoIndexSymmetry S>
+template <int ncolour, TwoIndexSymmetry S, class group_name>
 class TwoIndexRep {
 public:
   // typdef to be used by the Representations class in HMC to get the
   // types for the higher representation fields
-  typedef typename SU_TwoIndex<ncolour, S>::LatticeTwoIndexMatrix LatticeMatrix;
-  typedef typename SU_TwoIndex<ncolour, S>::LatticeTwoIndexField LatticeField;
-  static const int Dimension = ncolour * (ncolour + S) / 2;
+  typedef typename GaugeGroupTwoIndex<ncolour, S, group_name>::LatticeTwoIndexMatrix LatticeMatrix;
+  typedef typename GaugeGroupTwoIndex<ncolour, S, group_name>::LatticeTwoIndexField LatticeField;
+  static const int Dimension = GaugeGroupTwoIndex<ncolour,S,group_name>::Dimension;
   static const bool isFundamental = false;
 
   LatticeField U;
@@ -43,10 +43,10 @@ public:
     U = Zero();
     LatticeColourMatrix tmp(Uin.Grid());
 
-    Vector<typename SU<ncolour>::Matrix> eij(Dimension);
+    Vector<typename GaugeGroup<ncolour,group_name>::Matrix> eij(Dimension);
 
     for (int a = 0; a < Dimension; a++)
-      SU_TwoIndex<ncolour, S>::base(a, eij[a]);
+      GaugeGroupTwoIndex<ncolour, S, group_name>::base(a, eij[a]);
 
     for (int mu = 0; mu < Nd; mu++) {
       auto Uin_mu = peekLorentz(Uin, mu);
@@ -71,7 +71,7 @@ public:
 
       out_mu = Zero();
 
-      typename SU<ncolour>::LatticeAlgebraVector h(in.Grid());
+      typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector h(in.Grid());
       projectOnAlgebra(h, in_mu, double(Nc + 2 * S));  // factor T(r)/T(fund)
       FundamentalLieAlgebraMatrix(h, out_mu);          // apply scale only once
       pokeLorentz(out, out_mu, mu);
@@ -82,18 +82,21 @@ public:
 private:
   void projectOnAlgebra(typename SU<ncolour>::LatticeAlgebraVector &h_out,
                         const LatticeMatrix &in, Real scale = 1.0) const {
-    SU_TwoIndex<ncolour, S>::projectOnAlgebra(h_out, in, scale);
+    GaugeGroupTwoIndex<ncolour, S,group_name>::projectOnAlgebra(h_out, in, scale);
   }
 
   void FundamentalLieAlgebraMatrix(
 				   typename SU<ncolour>::LatticeAlgebraVector &h,
 				   typename SU<ncolour>::LatticeMatrix &out, Real scale = 1.0) const {
-    SU<ncolour>::FundamentalLieAlgebraMatrix(h, out, scale);
+    GaugeGroup<ncolour,group_name>::FundamentalLieAlgebraMatrix(h, out, scale);
   }
 };
 
-typedef TwoIndexRep<Nc, Symmetric> TwoIndexSymmetricRepresentation;
-typedef TwoIndexRep<Nc, AntiSymmetric> TwoIndexAntiSymmetricRepresentation;
+typedef TwoIndexRep<Nc, Symmetric, GroupName::SU> TwoIndexSymmetricRepresentation;
+typedef TwoIndexRep<Nc, AntiSymmetric, GroupName::SU> TwoIndexAntiSymmetricRepresentation;
+
+typedef TwoIndexRep<Nc, Symmetric, GroupName::Sp> SpTwoIndexSymmetricRepresentation;
+typedef TwoIndexRep<Nc, AntiSymmetric, GroupName::Sp> SpTwoIndexAntiSymmetricRepresentation;
 
 NAMESPACE_END(Grid);
 

From 85b2cb7a8aa3b9eceb4ed85e03881baac1bea3e4 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Sun, 21 May 2023 14:50:28 +0100
Subject: [PATCH 093/129] changing some hardcoded SUn lines

---
 Grid/qcd/representations/two_index.h | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Grid/qcd/representations/two_index.h b/Grid/qcd/representations/two_index.h
index 9fa6a203..9a06dc6f 100644
--- a/Grid/qcd/representations/two_index.h
+++ b/Grid/qcd/representations/two_index.h
@@ -80,14 +80,14 @@ public:
   }
 
 private:
-  void projectOnAlgebra(typename SU<ncolour>::LatticeAlgebraVector &h_out,
+  void projectOnAlgebra(typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
                         const LatticeMatrix &in, Real scale = 1.0) const {
     GaugeGroupTwoIndex<ncolour, S,group_name>::projectOnAlgebra(h_out, in, scale);
   }
 
   void FundamentalLieAlgebraMatrix(
-				   typename SU<ncolour>::LatticeAlgebraVector &h,
-				   typename SU<ncolour>::LatticeMatrix &out, Real scale = 1.0) const {
+				   typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h,
+				   typename GaugeGroup<ncolour, group_name>::LatticeMatrix &out, Real scale = 1.0) const {
     GaugeGroup<ncolour,group_name>::FundamentalLieAlgebraMatrix(h, out, scale);
   }
 };

From af091e0881001896b10ca3c084658275a303ef45 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Sun, 21 May 2023 16:56:06 +0100
Subject: [PATCH 094/129] DimensionHelper for 2index irreps

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h | 29 ++++++++++++++++++++---------
 tests/sp2n/Test_2as_base.cc         |  3 +--
 2 files changed, 21 insertions(+), 11 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index e0c6c0e7..38d6c034 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -31,15 +31,27 @@ enum TwoIndexSymmetry { Symmetric = 1, AntiSymmetric = -1 };
 
 inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
 
+template <int nc, TwoIndexSymmetry S, class group_name>
+struct DimensionHelper;
+
+template <int nc, TwoIndexSymmetry S>
+struct DimensionHelper<nc, S, GroupName::SU> {
+    static const int Dimension = nc * (nc + S) + S;
+};
+
+template <int nc>
+struct DimensionHelper<nc, Symmetric, GroupName::Sp> {
+    static const int Dimension = nc * (nc + 1) / 2;
+};
+
+template <int nc>
+struct DimensionHelper<nc, AntiSymmetric, GroupName::Sp> {
+    static const int Dimension = (nc / 2) * (nc - 1) - 1;
+};
+
 template <int ncolour, TwoIndexSymmetry S, class group_name>
 class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
  public:
-  static_assert(
-      std::is_same<group_name, GroupName::Sp>::value ? S != Symmetric : true,
-      "The symmetric two-index representation of Sp(2N) does not work "
-      "currently. If you want to use it, you need to implement the equivalent "
-      "of Eq. (27) and (28) from https://doi.org/10.48550/arXiv.2202.05516.");
-
   // The chosen convention is that we are taking ncolour to be N in SU<N> but 2N
   // in Sp(2N). ngroup is equal to N for SU but 2N/2 = N for Sp(2N).
   static_assert(std::is_same<group_name, GroupName::SU>::value or
@@ -47,9 +59,8 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
                 "ngroup is only implemented for SU and Sp currently.");
   static const int ngroup =
       std::is_same<group_name, GroupName::SU>::value ? ncolour : ncolour / 2;
-  static const int Dimension = std::is_same<group_name, GroupName::SU>::value
-                                   ? ncolour * (ncolour + S) / 2
-                                   : ngroup * (ncolour + S) + S;
+  static const int Dimension =
+      DimensionHelper<ncolour, S, group_name>::Dimension;
   static const int NumGenerators =
       GaugeGroup<ncolour, group_name>::AlgebraDimension;
 
diff --git a/tests/sp2n/Test_2as_base.cc b/tests/sp2n/Test_2as_base.cc
index b44e2e8f..7ff14a6a 100644
--- a/tests/sp2n/Test_2as_base.cc
+++ b/tests/sp2n/Test_2as_base.cc
@@ -32,8 +32,7 @@ int main(int argc, char** argv) {
   std::cout << GridLogMessage << "2as dimension is " << this_irrep_dim << std::endl;
   std::cout << GridLogMessage << "algebra dimension is " << this_algebra_dim << std::endl;
   realA = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension + Sp_TwoIndex<this_nc, Symmetric>::Dimension;
-  realB = Sp<this_nc>::Dimension*Sp<this_nc>::Dimension;
-  assert ( realA == realB);
+  assert ( realA == this_nc * this_nc - 1); // Nc x Nc = dim(2indxS) + dim(2indxAS) + dim(singlet)
 
   std::cout << GridLogMessage << "checking base is antisymmetric " << std::endl;
   for (int a=0; a < this_irrep_dim; a++)

From 5897b93dd487b574dc3b4d93844f9912f46c00ae Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Mon, 22 May 2023 13:42:21 +0100
Subject: [PATCH 095/129] debug tests, fix dimension

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h |  2 +-
 tests/core/Test_lie_generators.cc   | 58 ++++++++++++++---------------
 2 files changed, 30 insertions(+), 30 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index 38d6c034..d388c0f2 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -36,7 +36,7 @@ struct DimensionHelper;
 
 template <int nc, TwoIndexSymmetry S>
 struct DimensionHelper<nc, S, GroupName::SU> {
-    static const int Dimension = nc * (nc + S) + S;
+    static const int Dimension = nc * (nc + S) / 2;
 };
 
 template <int nc>
diff --git a/tests/core/Test_lie_generators.cc b/tests/core/Test_lie_generators.cc
index 3c1f6946..d90e3e47 100644
--- a/tests/core/Test_lie_generators.cc
+++ b/tests/core/Test_lie_generators.cc
@@ -307,7 +307,7 @@ int main(int argc, char** argv) {
   std::cout << GridLogMessage << "Two index Symmetric: Checking Group Structure"
       << std::endl;
   // Testing HMC representation classes
-  TwoIndexRep< Nc, Symmetric > TIndexRep(grid);
+  TwoIndexRep< Nc, Symmetric, GroupName::SU > TIndexRep(grid);
 
   // Test group structure
   // (U_f * V_f)_r = U_r * V_r
@@ -324,30 +324,30 @@ int main(int argc, char** argv) {
   }
   
   TIndexRep.update_representation(UV2);
-  typename TwoIndexRep< Nc, Symmetric >::LatticeField UVr2 = TIndexRep.U;  // (U_f * V_f)_r
+  typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField UVr2 = TIndexRep.U;  // (U_f * V_f)_r
   
   TIndexRep.update_representation(U2);
-  typename TwoIndexRep< Nc, Symmetric >::LatticeField Ur2 = TIndexRep.U;  // U_r
+  typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField Ur2 = TIndexRep.U;  // U_r
   
   TIndexRep.update_representation(V2);
-  typename TwoIndexRep< Nc, Symmetric >::LatticeField Vr2 = TIndexRep.U;  // V_r
+  typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField Vr2 = TIndexRep.U;  // V_r
   
-  typename TwoIndexRep< Nc, Symmetric >::LatticeField Ur2Vr2(grid);
+  typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField Ur2Vr2(grid);
   Ur2Vr2 = Zero();
   for (int mu = 0; mu < Nd; mu++) {
-    typename TwoIndexRep< Nc, Symmetric >::LatticeMatrix Urmu2 = peekLorentz(Ur2,mu);
-    typename TwoIndexRep< Nc, Symmetric >::LatticeMatrix Vrmu2 = peekLorentz(Vr2,mu);
+    typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeMatrix Urmu2 = peekLorentz(Ur2,mu);
+    typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeMatrix Vrmu2 = peekLorentz(Vr2,mu);
     pokeLorentz(Ur2Vr2,Urmu2*Vrmu2, mu);
   }
   
-  typename TwoIndexRep< Nc, Symmetric >::LatticeField Diff_check2 = UVr2 - Ur2Vr2;
+  typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField Diff_check2 = UVr2 - Ur2Vr2;
   std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Two Index Symmetric): " << norm2(Diff_check2) << std::endl;
 
   
   // Check correspondence of algebra and group transformations
   // Create a random vector
   SU<Nc>::LatticeAlgebraVector h_sym(grid);
-  typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ar_sym(grid);
+  typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix Ar_sym(grid);
   random(gridRNG,h_sym);
   h_sym = real(h_sym);
   SU_TwoIndex<Nc,Symmetric>::TwoIndexLieAlgebraMatrix(h_sym,Ar_sym);
@@ -360,13 +360,13 @@ int main(int argc, char** argv) {
 
   
   // Exponentiate
-  typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix U2iS(grid);
+  typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix U2iS(grid);
   U2iS  = expMat(Ar_sym, 1.0, 16);
   
-  typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix uno2iS(grid);
+  typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix uno2iS(grid);
   uno2iS = 1.0;
   // Check matrix U2iS, must be real orthogonal
-  typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ucheck2iS = U2iS - conjugate(U2iS);
+  typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix Ucheck2iS = U2iS - conjugate(U2iS);
   std::cout << GridLogMessage << "Reality check: " << norm2(Ucheck2iS)
       << std::endl;
   
@@ -399,15 +399,15 @@ int main(int argc, char** argv) {
   
   TIndexRep.update_representation(U);
   Ur2 = TIndexRep.U;  // U_r  
-  typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ur02 = peekLorentz(Ur2,0); // this should be the same as U2iS
+  typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix Ur02 = peekLorentz(Ur2,0); // this should be the same as U2iS
   
-  typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Diff_check_mat2 = Ur02 - U2iS;
+  typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix Diff_check_mat2 = Ur02 - U2iS;
   std::cout << GridLogMessage << "Projections structure check group difference (Two Index Symmetric): " << norm2(Diff_check_mat2) << std::endl;
   
 
 
 
-  if (TwoIndexRep<Nc, AntiSymmetric >::Dimension != 1){
+  if (TwoIndexRep<Nc, AntiSymmetric , GroupName::SU>::Dimension != 1){
 
   std::cout << GridLogMessage << "*********************************************"
       << std::endl;
@@ -416,7 +416,7 @@ int main(int argc, char** argv) {
   std::cout << GridLogMessage << "Two Index anti-Symmetric: Check Group Structure"
       << std::endl;
   // Testing HMC representation classes
-  TwoIndexRep< Nc, AntiSymmetric > TIndexRepA(grid);
+  TwoIndexRep< Nc, AntiSymmetric, GroupName::SU > TIndexRepA(grid);
 
 
   // Test group structure
@@ -434,30 +434,30 @@ int main(int argc, char** argv) {
   }
   
   TIndexRep.update_representation(UV2A);
-  typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField UVr2A = TIndexRepA.U;  // (U_f * V_f)_r
+  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField UVr2A = TIndexRepA.U;  // (U_f * V_f)_r
   
   TIndexRep.update_representation(U2A);
-  typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField Ur2A = TIndexRepA.U;  // U_r
+  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField Ur2A = TIndexRepA.U;  // U_r
   
   TIndexRep.update_representation(V2A);
-  typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField Vr2A = TIndexRepA.U;  // V_r
+  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField Vr2A = TIndexRepA.U;  // V_r
   
-  typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField Ur2Vr2A(grid);
+  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField Ur2Vr2A(grid);
   Ur2Vr2A = Zero();
   for (int mu = 0; mu < Nd; mu++) {
-    typename TwoIndexRep< Nc, AntiSymmetric >::LatticeMatrix Urmu2A = peekLorentz(Ur2A,mu);
-    typename TwoIndexRep< Nc, AntiSymmetric >::LatticeMatrix Vrmu2A = peekLorentz(Vr2A,mu);
+    typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeMatrix Urmu2A = peekLorentz(Ur2A,mu);
+    typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeMatrix Vrmu2A = peekLorentz(Vr2A,mu);
     pokeLorentz(Ur2Vr2A,Urmu2A*Vrmu2A, mu);
   }
   
-  typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField Diff_check2A = UVr2A - Ur2Vr2A;
+  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField Diff_check2A = UVr2A - Ur2Vr2A;
   std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Two Index anti-Symmetric): " << norm2(Diff_check2A) << std::endl;
 
   
   // Check correspondence of algebra and group transformations
   // Create a random vector
   SU<Nc>::LatticeAlgebraVector h_Asym(grid);
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ar_Asym(grid);
+  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix Ar_Asym(grid);
   random(gridRNG,h_Asym);
   h_Asym = real(h_Asym);
   SU_TwoIndex< Nc, AntiSymmetric>::TwoIndexLieAlgebraMatrix(h_Asym,Ar_Asym);
@@ -470,13 +470,13 @@ int main(int argc, char** argv) {
 
   
   // Exponentiate
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix U2iAS(grid);
+  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix U2iAS(grid);
   U2iAS  = expMat(Ar_Asym, 1.0, 16);
   
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix uno2iAS(grid);
+  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix uno2iAS(grid);
   uno2iAS = 1.0;
   // Check matrix U2iS, must be real orthogonal
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ucheck2iAS = U2iAS - conjugate(U2iAS);
+  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix Ucheck2iAS = U2iAS - conjugate(U2iAS);
   std::cout << GridLogMessage << "Reality check: " << norm2(Ucheck2iAS)
       << std::endl;
   
@@ -509,9 +509,9 @@ int main(int argc, char** argv) {
   
   TIndexRepA.update_representation(U);
   Ur2A = TIndexRepA.U;  // U_r  
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ur02A = peekLorentz(Ur2A,0); // this should be the same as U2iS
+  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix Ur02A = peekLorentz(Ur2A,0); // this should be the same as U2iS
   
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Diff_check_mat2A = Ur02A - U2iAS;
+  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix Diff_check_mat2A = Ur02A - U2iAS;
   std::cout << GridLogMessage << "Projections structure check group difference (Two Index anti-Symmetric): " << norm2(Diff_check_mat2A) << std::endl;
   
 } else  {

From be1a4f58601f706c9bbb9d9280832ddcf0fcc22b Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Mon, 22 May 2023 17:21:03 +0100
Subject: [PATCH 096/129] implement TwoIndexSymm for sp2n

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h | 153 +++++++++++++++++++---------
 tests/sp2n/Test_2as_base.cc         | 119 ++++++++++++++++++++--
 tests/sp2n/Test_sp2n_lie_gen.cc     |  35 ++++++-
 3 files changed, 250 insertions(+), 57 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index d388c0f2..ebfefc21 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -49,6 +49,63 @@ struct DimensionHelper<nc, AntiSymmetric, GroupName::Sp> {
     static const int Dimension = (nc / 2) * (nc - 1) - 1;
 };
 
+template <class cplx, int nc, TwoIndexSymmetry S, class group_name>
+struct baseOffDiagonalSpHelper;
+
+template <class cplx, int nc>
+struct baseOffDiagonalSpHelper<cplx, nc, AntiSymmetric, GroupName::Sp> {
+  static const int ngroup = nc / 2;
+  static void baseOffDiagonalSp(int i, int j, iScalar<iScalar<iMatrix<cplx, nc> > > &eij) {
+    eij = Zero();
+    RealD tmp;
+
+    if ((i == ngroup + j) && (1 <= j) && (j < ngroup)) {
+      for (int k = 0; k < ngroup; k++) {
+        if (k < j) {
+          tmp = sqrt(2 * j * (j + 1));
+          tmp = 1 / tmp;
+          tmp *= std::sqrt(2.0);
+          eij()()(k, k + ngroup) = tmp;
+          eij()()(k + ngroup, k) = -tmp;
+        }
+        if (k == j) {
+          tmp = sqrt(2 * j * (j + 1));
+          tmp = -j / tmp;
+          tmp *= std::sqrt(2.0);
+          eij()()(k, k + ngroup) = tmp;
+          eij()()(k + ngroup, k) = -tmp;
+        }
+      }
+
+    }
+
+    else if (i != ngroup + j) {
+      for (int k = 0; k < nc; k++)
+        for (int l = 0; l < nc; l++) {
+          eij()()(l, k) =
+              delta(i, k) * delta(j, l) - delta(j, k) * delta(i, l);
+        }
+    }
+
+    RealD nrm = 1. / std::sqrt(2.0);
+    eij = eij * nrm;
+  }
+};
+
+template <class cplx, int nc>
+struct baseOffDiagonalSpHelper<cplx, nc, Symmetric, GroupName::Sp> {
+  static void baseOffDiagonalSp(int i, int j, iScalar<iScalar<iMatrix<cplx, nc> > > &eij) {
+    eij = Zero();
+    for (int k = 0; k < nc; k++)
+      for (int l = 0; l < nc; l++)
+        eij()()(l, k) =
+            delta(i, k) * delta(j, l) + delta(j, k) * delta(i, l);
+
+    RealD nrm = 1. / std::sqrt(2.0);
+    eij = eij * nrm;
+  }
+};
+
 template <int ncolour, TwoIndexSymmetry S, class group_name>
 class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
  public:
@@ -95,6 +152,12 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
 
   template <class cplx>
   static void base(int Index, iGroupMatrix<cplx> &eij) {
+    // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
+    base(Index, eij, group_name());
+  }
+    
+  template <class cplx>
+  static void base(int Index, iGroupMatrix<cplx> &eij, GroupName::SU) {
     // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
     assert(Index < Dimension);
     eij = Zero();
@@ -107,10 +170,6 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
       for (int i = 1; i < ncolour; i++) {
         for (int j = 0; j < i; j++) {
           a[counter][0] = i;
-            if (j==0 && ngroup == ncolour/2 && i==ngroup+j) {
-                //std::cout << "skipping" << std::endl; // for Sp2n this vanishes identically.
-                j = j+1;
-            }
           a[counter][1] = j;
           counter++;
         }
@@ -119,11 +178,43 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
     }
 
     if (Index < ncolour * (ncolour - 1) / 2) {
-      baseOffDiagonal(a[Index][0], a[Index][1], eij, group_name());
+      baseOffDiagonal(a[Index][0], a[Index][1], eij);
     } else {
       baseDiagonal(Index, eij);
     }
   }
+    
+  template <class cplx>
+   static void base(int Index, iGroupMatrix<cplx> &eij, GroupName::Sp) {
+     // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
+     assert(Index < Dimension);
+     eij = Zero();
+
+     // for the linearisation of the 2 indexes
+     static int a[ncolour * (ncolour - 1) / 2][2];  // store the a <-> i,j
+     static bool filled = false;
+     if (!filled) {
+       int counter = 0;
+       for (int i = 1; i < ncolour; i++) {
+         for (int j = 0; j < i; j++) {
+           a[counter][0] = i;
+             if (j==0 && i==ngroup+j && S==-1) {
+                 //std::cout << "skipping" << std::endl; // for Sp2n this vanishes identically.
+                 j = j+1;
+             }
+           a[counter][1] = j;
+           counter++;
+         }
+       }
+       filled = true;
+     }
+
+     if (Index < DimensionHelper<ncolour, AntiSymmetric, GroupName::Sp>::Dimension + 1) {   // +1 the singlet
+       baseOffDiagonalSp(a[Index][0], a[Index][1], eij);
+     } else {
+       baseDiagonal(Index, eij);
+     }
+   }
 
   template <class cplx>
   static void baseDiagonal(int Index, iGroupMatrix<cplx> &eij) {
@@ -131,48 +222,9 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
     eij()()(Index - ncolour * (ncolour - 1) / 2,
             Index - ncolour * (ncolour - 1) / 2) = 1.0;
   }
-
+    
   template <class cplx>
-  static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij,
-                              GroupName::Sp) {
-    eij = Zero();
-    RealD tmp;
-
-    if ((i == ngroup + j) && (1 <= j) && (j < ngroup)) {
-      for (int k = 0; k < ngroup; k++) {
-        if (k < j) {
-          tmp = sqrt(2 * j * (j + 1));
-          tmp = 1 / tmp;
-          tmp *= std::sqrt(2.0);
-          eij()()(k, k + ngroup) = tmp;
-          eij()()(k + ngroup, k) = -tmp;
-        }
-        if (k == j) {
-          tmp = sqrt(2 * j * (j + 1));
-          tmp = -j / tmp;
-          tmp *= std::sqrt(2.0);
-          eij()()(k, k + ngroup) = tmp;
-          eij()()(k + ngroup, k) = -tmp;
-        }
-      }
-
-    }
-
-    else if (i != ngroup + j) {
-      for (int k = 0; k < ncolour; k++)
-        for (int l = 0; l < ncolour; l++) {
-          eij()()(l, k) =
-              delta(i, k) * delta(j, l) + S * delta(j, k) * delta(i, l);
-        }
-    }
-
-    RealD nrm = 1. / std::sqrt(2.0);
-    eij = eij * nrm;
-  }
-
-  template <class cplx>
-  static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij,
-                              GroupName::SU) {
+  static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij) {
     eij = Zero();
     for (int k = 0; k < ncolour; k++)
       for (int l = 0; l < ncolour; l++)
@@ -182,11 +234,16 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
     RealD nrm = 1. / std::sqrt(2.0);
     eij = eij * nrm;
   }
+    
+  template <class cplx>
+  static void baseOffDiagonalSp(int i, int j, iGroupMatrix<cplx> &eij) {
+  baseOffDiagonalSpHelper<cplx, ncolour, S, GroupName::Sp>::baseOffDiagonalSp(i, j, eij);
+  }
 
   static void printBase(void) {
     for (int gen = 0; gen < Dimension; gen++) {
       Matrix tmp;
-      base(gen, tmp);
+      base(gen, tmp, group_name());
       std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
                 << std::endl;
       std::cout << GridLogMessage << tmp << std::endl;
@@ -203,7 +260,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
     for (int a = 0; a < NumGenerators; a++)
       GaugeGroup<ncolour, group_name>::generator(a, ta[a]);
 
-    for (int a = 0; a < Dimension; a++) base(a, eij[a]);
+    for (int a = 0; a < Dimension; a++) base(a, eij[a], group_name());
 
     for (int a = 0; a < Dimension; a++) {
       tmp = transpose(ta[Index]) * adj(eij[a]) + adj(eij[a]) * ta[Index];
diff --git a/tests/sp2n/Test_2as_base.cc b/tests/sp2n/Test_2as_base.cc
index 7ff14a6a..a210a15e 100644
--- a/tests/sp2n/Test_2as_base.cc
+++ b/tests/sp2n/Test_2as_base.cc
@@ -1,13 +1,12 @@
 #include <Grid/Grid.h>
 
-#define verbose 0
+#define verbose 1
 
 using namespace Grid;
 
-int main(int argc, char** argv) {
-  Grid_init(&argc, &argv);
+static void antisymm_base() {
 
-  const int this_nc = 4;
+  const int this_nc = 6;
   const int this_n = this_nc/2;
   const int this_irrep_dim = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension;
   const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
@@ -25,7 +24,6 @@ int main(int argc, char** argv) {
     Omega()()(i, this_n + i) = 1.;
     Omega()()(this_n + i, i) = -1;
   }
-    std::cout << "Omega " << Omega << std::endl;
 
   RealD realA;
   RealD realB;
@@ -102,8 +100,113 @@ int main(int argc, char** argv) {
       std::cout << GridLogMessage << "re-evaluated trace of the generator " << gen_id << " is " << sum << " " << sum_im << std::endl;
       assert ( sum < 1e-8) ;
       assert ( sum_im < 1e-8) ;
-
   }
-  
-  Grid_finalize();
 }
+
+static void symm_base() {
+
+  const int this_nc = 6;
+  const int this_n = this_nc/2;
+  const int this_irrep_dim = Sp_TwoIndex<this_nc, Symmetric>::Dimension;
+  const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
+  typedef Sp_TwoIndex<this_nc, Symmetric>::iGroupMatrix<Complex> Matrix;
+  typedef Sp_TwoIndex<this_nc, Symmetric>::iGroupTwoIndexMatrix<Complex> SMatrix;
+  
+  Matrix Omega;
+  Matrix eij_a;
+  Matrix eij_b;
+  Matrix eij_c;
+  Matrix e_sum;
+  Omega = Zero();
+  for (int i = 0; i < this_n; i++)
+  {
+    Omega()()(i, this_n + i) = 1.;
+    Omega()()(this_n + i, i) = -1;
+  }
+
+  RealD realA;
+  RealD realB;
+  std::cout << GridLogMessage << "symm dimension is " << this_irrep_dim << std::endl;
+  std::cout << GridLogMessage << "algebra dimension is " << this_algebra_dim << std::endl;
+  realA = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension + Sp_TwoIndex<this_nc, Symmetric>::Dimension;
+  assert ( realA == this_nc * this_nc - 1); // Nc x Nc = dim(2indxS) + dim(2indxAS) + dim(singlet)
+
+  std::cout << GridLogMessage << "checking base is symmetric " << std::endl;
+  for (int a=0; a < this_irrep_dim; a++)
+  {
+      Sp_TwoIndex<this_nc, Symmetric>::base(a, eij_c);
+      e_sum = eij_c - transpose(eij_c);
+      std::cout << GridLogMessage << "e_ab - e_ab^T " << norm2(e_sum) << std::endl;
+      assert(norm2(e_sum) < 1e-8);
+  }
+  std::cout << GridLogMessage << "Checking Tr (e^(ab) Omega ) = 0 and Tr (e^(ab) e^(cd) = delta^((ab)(cd)) ) " << std::endl;
+  for (int a=0; a < Sp_TwoIndex<this_nc, Symmetric>::Dimension; a++) {
+      Sp_TwoIndex<this_nc, Symmetric>::base(a, eij_a);
+      realA = norm2(trace(Omega*eij_a));
+      std::cout << GridLogMessage << "Omega trace for (ab) = " << a << std::endl;
+      assert(realA == 0);
+      for (int b=0; b < Sp_TwoIndex<this_nc, Symmetric>::Dimension; b++) {
+          Sp_TwoIndex<this_nc, Symmetric>::base(b, eij_b);
+          auto d_ab = TensorRemove(trace(eij_a * eij_b));
+#if verbose
+          std::cout << GridLogMessage << "Tr( e_{ab=" << a << "} e_{cd=" << b << "} ) = " << d_ab << std::endl;
+#endif
+          std::cout << GridLogMessage << "Orthonormality for (ab) = " << a << std::endl;
+          if (a==b) {
+              assert(real(d_ab)-1 < 1e-8);
+              assert(imag(d_ab) < 1e-8);
+          } else {
+              assert(real(d_ab) < 1e-8);
+              assert(imag(d_ab) < 1e-8);
+          }
+      }
+  }
+
+  int sum = 0;
+  int sum_im = 0;
+  Vector<Matrix> ta_fund(this_algebra_dim);
+  Vector<Matrix> eij(this_irrep_dim);
+  Matrix tmp_l;
+  Matrix tmp_r;
+  for (int n = 0; n < this_algebra_dim; n++)
+  {
+      Sp<this_nc>::generator(n, ta_fund[n]);
+  }
+  for (int a = 0; a < this_irrep_dim; a++)
+  {
+      Sp_TwoIndex<this_nc, Symmetric>::base(a, eij[a]);
+  }
+  for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
+  {
+      Complex iTr;
+      sum = 0;
+      sum_im = 0;
+      std::cout << GridLogMessage <<  "generator number " << gen_id << std::endl;
+      for (int a = 0; a < this_irrep_dim; a++)
+      {
+      
+          tmp_l = adj(eij[a])*ta_fund[gen_id]*eij[a];
+          tmp_r = adj(eij[a])*eij[a]*transpose(ta_fund[gen_id]);
+#if verbose
+          std::cout << GridLogMessage << " as_indx = " << a << " eDag T_F e = " << std::endl << tmp_l << std::endl;
+          std::cout << GridLogMessage << " as_indx = " << a << " eDag e T_F^T = " << std::endl << tmp_r << std::endl;
+#endif
+          std::cout << GridLogMessage << " as_indx = " << a << " Tr(sum) = " << TensorRemove(trace(tmp_l+tmp_r)) << std::endl;
+          sum += real(TensorRemove(trace(tmp_l+tmp_r)));
+          sum_im += imag(TensorRemove(trace(tmp_l+tmp_r)));
+      }
+      std::cout << GridLogMessage << "re-evaluated trace of the generator " << gen_id << " is " << sum << " " << sum_im << std::endl;
+      assert ( sum < 1e-8) ;
+      assert ( sum_im < 1e-8) ;
+  }
+}
+
+
+int main(int argc, char** argv) {
+  std::cout << GridLogMessage << "Checking AntiSymmetric base " << std::endl;
+  antisymm_base();
+  std::cout << GridLogMessage << "*************** " << std::endl;
+  std::cout << GridLogMessage << "Checking Symmetric base " << std::endl;
+  symm_base();
+}
+
diff --git a/tests/sp2n/Test_sp2n_lie_gen.cc b/tests/sp2n/Test_sp2n_lie_gen.cc
index 24642048..c8d58701 100644
--- a/tests/sp2n/Test_sp2n_lie_gen.cc
+++ b/tests/sp2n/Test_sp2n_lie_gen.cc
@@ -4,7 +4,7 @@ using namespace Grid;
 
 int main(int argc, char** argv) {
   Grid_init(&argc, &argv);
-
+    
   std::cout << GridLogMessage << "*********************************************"
               << std::endl;
   std::cout << GridLogMessage << "* Generators for Sp(2) (print and test)" << std::endl;
@@ -39,6 +39,15 @@ int main(int argc, char** argv) {
     
   Sp8::testGenerators();
     
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(2) TwoIndexS (print & test)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+
+  Sp_TwoIndex<2, Symmetric>::printGenerators();
+  Sp_TwoIndex<2, Symmetric>::testGenerators();
+
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
   std::cout << GridLogMessage << "* Generators for Sp(4) TwoIndexAS (test)" << std::endl;
@@ -47,6 +56,14 @@ int main(int argc, char** argv) {
 
   Sp_TwoIndex<4, AntiSymmetric>::testGenerators();
     
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(4) TwoIndexS (test)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+
+  Sp_TwoIndex<4, Symmetric>::testGenerators();
+    
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
   std::cout << GridLogMessage << "* Generators for Sp(6) TwoIndexAS (test)" << std::endl;
@@ -54,6 +71,14 @@ int main(int argc, char** argv) {
             << std::endl;
 
   Sp_TwoIndex<6, AntiSymmetric>::testGenerators();
+    
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(6) TwoIndexS (test)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+
+  Sp_TwoIndex<6, Symmetric>::testGenerators();
 
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
@@ -62,6 +87,14 @@ int main(int argc, char** argv) {
             << std::endl;
 
   Sp_TwoIndex<8, AntiSymmetric>::testGenerators();
+    
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(8) TwoIndexS (test)" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+
+  Sp_TwoIndex<8, Symmetric>::testGenerators();
 
   Grid_finalize();
 }

From ca2fd9fc7b66a376fb1d36609903f52096d6dffc Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Thu, 25 May 2023 18:40:54 +0100
Subject: [PATCH 097/129] documentation for gaugegroup and sp2n

---
 documentation/Grid.pdf   | Bin 635548 -> 579665 bytes
 documentation/manual.rst |  98 ++++++++++++++++++++++++++++-----------
 2 files changed, 72 insertions(+), 26 deletions(-)

diff --git a/documentation/Grid.pdf b/documentation/Grid.pdf
index df3304ebb9a6d1e10a17eb140ee5e07ca2eef4da..2511c6c8d00c891714d0153ede75e3c586cc38e0 100644
GIT binary patch
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diff --git a/documentation/manual.rst b/documentation/manual.rst
index e545bdaf..2a2f4728 100644
--- a/documentation/manual.rst
+++ b/documentation/manual.rst
@@ -2778,47 +2778,83 @@ and there are associated reconstruction routines for assembling four spinors fro
 
 These ca
 
-
-SU(N)
+Gauge Group
 --------
+A generic Nc qcd/utils/GaugeGroup.h is provided. This defines a template class that can be specialised to different gauge groups::
 
-A generic Nc qcd/utils/SUn.h is provided. This defines a template class::
+  template <int ncolour, class group_name>
+  class GaugeGroup {...}
 
-  template <int ncolour> class SU ;
+Supported groups are SU(N) and Sp(2N). The group can be specified through the GroupName namespace::
 
-The most important external methods are::
+  namespace GroupName {
+  class SU {};
+  class Sp {};
+  }
+
+A simpler interface is achieved by instantiating the GaugeGroup class with a specific group::
+
+  template <int ncolour>
+  using SU = GaugeGroup<ncolour, GroupName::SU>;
+
+  template <int ncolour>
+  using Sp = GaugeGroup<ncolour, GroupName::Sp>;
+  
+Specific instantiations are then defined::
+
+  typedef SU<2> SU2;
+  typedef SU<3> SU3;
+  typedef SU<4> SU4;
+  typedef SU<5> SU5;
+  typedef Sp<2> Sp2;
+  typedef Sp<4> Sp4;
+  typedef Sp<6> Sp6;
+  typedef Sp<8> Sp8;
+
+Some methods are common to both gauge groups. The most important common external methods are::
 
   static void printGenerators(void) ;
   template <class cplx>  static void generator(int lieIndex, iSUnMatrix<cplx> &ta) ;
+  static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
+  LatticeMatrix &out,
+  Real scale = 1.0) ;
+  static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) ;
+  static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out);
+  static void ColdConfiguration(GaugeField &out);
+  static void taProj( const LatticeMatrixType &in,  LatticeMatrixType &out);
+  static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) ;
+   
+Whenever needed, a different implementation of these methods for the gauge groups is achieved by overloading. For example,::
+
+  template <typename LatticeMatrixType> //  shared interface for the traceless-antihermitian projection
+  static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out) {
+    taProj(in, out, group_name());
+  }
+  
+  template <typename LatticeMatrixType> //  overloaded function to SU(N) simply perform Ta
+  static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::SU) {
+    out = Ta(in);
+  }
+  
+  template <typename LatticeMatrixType> //  overloaded function to Sp(2N) must use a modified Ta function
+  static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::Sp) {
+    out = SpTa(in);
+  }
+
+Gauge Group: SU(N)
+--------
+The specialisation of GaugeGroup to SU(N), formally part of qcd/utils/GaugeGroup.h, is found in the file qcd/utils/SUn.impl
+It contains methods that are only implemented for SU(N), and specialisations of shared methods to the special unitary group
+
+The most important external methods are::
 
   static void SubGroupHeatBath(GridSerialRNG &sRNG, GridParallelRNG &pRNG, RealD beta,  // coeff multiplying staple in action (with no 1/Nc)
                                LatticeMatrix &link,
 			       const LatticeMatrix &barestaple,  // multiplied by action coeffs so th
 			       int su2_subgroup, int nheatbath, LatticeInteger &wheremask);
-
-  static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
-                                                  LatticeMatrix &out,
-                                                  Real scale = 1.0) ;
   static void GaugeTransform( GaugeField &Umu, GaugeMat &g)
   static void RandomGaugeTransform(GridParallelRNG &pRNG, GaugeField &Umu, GaugeMat &g);
 
-  static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) ;
-  static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out);
-  static void ColdConfiguration(GaugeField &out);
-
-  static void taProj( const LatticeMatrixType &in,  LatticeMatrixType &out);
-  static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) ;
-
-  static int su2subgroups(void) ; // returns how many subgroups
-
-
-Specific instantiations are defined::
-
-	 typedef SU<2> SU2;
-	 typedef SU<3> SU3;
-	 typedef SU<4> SU4;
-	 typedef SU<5> SU5;
-
 For example, Quenched QCD updating may be run as (tests/core/Test_quenched_update.cc)::
 
   for(int sweep=0;sweep<1000;sweep++){
@@ -2857,6 +2893,16 @@ For example, Quenched QCD updating may be run as (tests/core/Test_quenched_updat
     }
   }
 
+Gauge Group: Sp(2N)
+--------
+The specialisation of GaugeGroup to Sp(2N), formally part of qcd/utils/GaugeGroup.h, is found in the file qcd/utils/Sp(2N).impl
+It contains methods that are only implemented for Sp(2N), and specialisations of shared methods to the special unitary group
+
+The most important external methods are::
+
+  static void Omega(LatticeColourMatrixD &in) // Symplectic matrix left invariant by Sp(2N)
+
+Generation of Sp(2N) gauge fields is only supported via HMC.
 
 Space time grids
 ----------------

From a6f4dbeb6d9f60e1a7ba2aa0511de772ddfe53bb Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 26 May 2023 12:13:40 +0100
Subject: [PATCH 098/129] remove redundant template parameter

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index ebfefc21..0ab3c193 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -49,11 +49,11 @@ struct DimensionHelper<nc, AntiSymmetric, GroupName::Sp> {
     static const int Dimension = (nc / 2) * (nc - 1) - 1;
 };
 
-template <class cplx, int nc, TwoIndexSymmetry S, class group_name>
+template <class cplx, int nc, TwoIndexSymmetry S>
 struct baseOffDiagonalSpHelper;
 
 template <class cplx, int nc>
-struct baseOffDiagonalSpHelper<cplx, nc, AntiSymmetric, GroupName::Sp> {
+struct baseOffDiagonalSpHelper<cplx, nc, AntiSymmetric> {
   static const int ngroup = nc / 2;
   static void baseOffDiagonalSp(int i, int j, iScalar<iScalar<iMatrix<cplx, nc> > > &eij) {
     eij = Zero();
@@ -93,7 +93,7 @@ struct baseOffDiagonalSpHelper<cplx, nc, AntiSymmetric, GroupName::Sp> {
 };
 
 template <class cplx, int nc>
-struct baseOffDiagonalSpHelper<cplx, nc, Symmetric, GroupName::Sp> {
+struct baseOffDiagonalSpHelper<cplx, nc, Symmetric> {
   static void baseOffDiagonalSp(int i, int j, iScalar<iScalar<iMatrix<cplx, nc> > > &eij) {
     eij = Zero();
     for (int k = 0; k < nc; k++)
@@ -237,7 +237,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
     
   template <class cplx>
   static void baseOffDiagonalSp(int i, int j, iGroupMatrix<cplx> &eij) {
-  baseOffDiagonalSpHelper<cplx, ncolour, S, GroupName::Sp>::baseOffDiagonalSp(i, j, eij);
+  baseOffDiagonalSpHelper<cplx, ncolour, S>::baseOffDiagonalSp(i, j, eij);
   }
 
   static void printBase(void) {

From 6647d2656ff927186b8819e71421dd6f07e08680 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 26 May 2023 12:27:22 +0100
Subject: [PATCH 099/129] rm unnecessary specialisation

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index 0ab3c193..0dcc2c42 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -243,7 +243,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
   static void printBase(void) {
     for (int gen = 0; gen < Dimension; gen++) {
       Matrix tmp;
-      base(gen, tmp, group_name());
+      base(gen, tmp);
       std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
                 << std::endl;
       std::cout << GridLogMessage << tmp << std::endl;
@@ -260,7 +260,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
     for (int a = 0; a < NumGenerators; a++)
       GaugeGroup<ncolour, group_name>::generator(a, ta[a]);
 
-    for (int a = 0; a < Dimension; a++) base(a, eij[a], group_name());
+    for (int a = 0; a < Dimension; a++) base(a, eij[a]);
 
     for (int a = 0; a < Dimension; a++) {
       tmp = transpose(ta[Index]) * adj(eij[a]) + adj(eij[a]) * ta[Index];

From 3a50fb29cbbc27a3e24bd87e8b469fe58b4026b9 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 26 May 2023 13:28:47 +0100
Subject: [PATCH 100/129] directly call sp helper

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index 0dcc2c42..618086a6 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -210,7 +210,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
      }
 
      if (Index < DimensionHelper<ncolour, AntiSymmetric, GroupName::Sp>::Dimension + 1) {   // +1 the singlet
-       baseOffDiagonalSp(a[Index][0], a[Index][1], eij);
+       baseOffDiagonalSpHelper<cplx, ncolour, S>::baseOffDiagonalSp(a[Index][0], a[Index][1], eij);
      } else {
        baseDiagonal(Index, eij);
      }

From de8daa3824dfa17218e7b86bcbfa374f779bdb79 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 26 May 2023 13:44:41 +0100
Subject: [PATCH 101/129] group is SUn by default

---
 Grid/qcd/representations/two_index.h | 2 +-
 Grid/qcd/utils/GaugeGroup.h          | 2 +-
 tests/core/Test_lie_generators.cc    | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/Grid/qcd/representations/two_index.h b/Grid/qcd/representations/two_index.h
index 9a06dc6f..24d6d7cb 100644
--- a/Grid/qcd/representations/two_index.h
+++ b/Grid/qcd/representations/two_index.h
@@ -20,7 +20,7 @@ NAMESPACE_BEGIN(Grid);
  * in the SUnTwoIndex.h file
  */
 
-template <int ncolour, TwoIndexSymmetry S, class group_name>
+template <int ncolour, TwoIndexSymmetry S, class group_name = GroupName::SU>
 class TwoIndexRep {
 public:
   // typdef to be used by the Representations class in HMC to get the
diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index 825881e2..a57ace90 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -85,7 +85,7 @@ constexpr int compute_adjoint_dimension<GroupName::Sp>(int ncolour) {
   return ncolour / 2 * (ncolour + 1);
 }
 
-template <int ncolour, class group_name>
+template <int ncolour, class group_name = GroupName::SU>
 class GaugeGroup {
  public:
   static const int Dimension = ncolour;
diff --git a/tests/core/Test_lie_generators.cc b/tests/core/Test_lie_generators.cc
index d90e3e47..c4a88356 100644
--- a/tests/core/Test_lie_generators.cc
+++ b/tests/core/Test_lie_generators.cc
@@ -307,7 +307,7 @@ int main(int argc, char** argv) {
   std::cout << GridLogMessage << "Two index Symmetric: Checking Group Structure"
       << std::endl;
   // Testing HMC representation classes
-  TwoIndexRep< Nc, Symmetric, GroupName::SU > TIndexRep(grid);
+  TwoIndexRep< Nc, Symmetric> TIndexRep(grid);
 
   // Test group structure
   // (U_f * V_f)_r = U_r * V_r

From e61a9ed2b423042b03d6c2f853cf797f5983ee5a Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 26 May 2023 13:54:26 +0100
Subject: [PATCH 102/129] partial revert

---
 Grid/qcd/utils/GaugeGroup.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index a57ace90..825881e2 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -85,7 +85,7 @@ constexpr int compute_adjoint_dimension<GroupName::Sp>(int ncolour) {
   return ncolour / 2 * (ncolour + 1);
 }
 
-template <int ncolour, class group_name = GroupName::SU>
+template <int ncolour, class group_name>
 class GaugeGroup {
  public:
   static const int Dimension = ncolour;

From fe88a0c12f6c02ba9c672b4e41b9f9e993ba9003 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 26 May 2023 16:55:30 +0100
Subject: [PATCH 103/129] cleaner twoindex class, cleaner tests

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h |  89 +++-----
 tests/core/Test_lie_generators.cc   |  56 ++---
 tests/sp2n/Test_2as_base.cc         | 313 +++++++++++-----------------
 tests/sp2n/Test_sp2n_lie_gen.cc     | 133 ++++--------
 4 files changed, 216 insertions(+), 375 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index 618086a6..2d8dbe25 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -31,23 +31,7 @@ enum TwoIndexSymmetry { Symmetric = 1, AntiSymmetric = -1 };
 
 inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
 
-template <int nc, TwoIndexSymmetry S, class group_name>
-struct DimensionHelper;
-
-template <int nc, TwoIndexSymmetry S>
-struct DimensionHelper<nc, S, GroupName::SU> {
-    static const int Dimension = nc * (nc + S) / 2;
-};
-
-template <int nc>
-struct DimensionHelper<nc, Symmetric, GroupName::Sp> {
-    static const int Dimension = nc * (nc + 1) / 2;
-};
-
-template <int nc>
-struct DimensionHelper<nc, AntiSymmetric, GroupName::Sp> {
-    static const int Dimension = (nc / 2) * (nc - 1) - 1;
-};
+namespace detail {
 
 template <class cplx, int nc, TwoIndexSymmetry S>
 struct baseOffDiagonalSpHelper;
@@ -106,6 +90,8 @@ struct baseOffDiagonalSpHelper<cplx, nc, Symmetric> {
   }
 };
 
+}   // closing detail namespace
+
 template <int ncolour, TwoIndexSymmetry S, class group_name>
 class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
  public:
@@ -117,7 +103,11 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
   static const int ngroup =
       std::is_same<group_name, GroupName::SU>::value ? ncolour : ncolour / 2;
   static const int Dimension =
-      DimensionHelper<ncolour, S, group_name>::Dimension;
+      (ncolour * (ncolour + S) / 2) + (std::is_same<group_name, GroupName::Sp>::value ? (S - 1) / 2 : 0);
+  static const int DimensionAS =
+      (ncolour * (ncolour - 1) / 2) + (std::is_same<group_name, GroupName::Sp>::value ? (- 1) : 0);
+  static const int DimensionS =
+      ncolour * (ncolour + 1) / 2;
   static const int NumGenerators =
       GaugeGroup<ncolour, group_name>::AlgebraDimension;
 
@@ -149,43 +139,9 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
   typedef iGroupMatrix<Complex> Matrix;
   typedef iGroupMatrix<ComplexF> MatrixF;
   typedef iGroupMatrix<ComplexD> MatrixD;
-
-  template <class cplx>
-  static void base(int Index, iGroupMatrix<cplx> &eij) {
-    // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
-    base(Index, eij, group_name());
-  }
     
   template <class cplx>
-  static void base(int Index, iGroupMatrix<cplx> &eij, GroupName::SU) {
-    // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
-    assert(Index < Dimension);
-    eij = Zero();
-
-    // for the linearisation of the 2 indexes
-    static int a[ncolour * (ncolour - 1) / 2][2];  // store the a <-> i,j
-    static bool filled = false;
-    if (!filled) {
-      int counter = 0;
-      for (int i = 1; i < ncolour; i++) {
-        for (int j = 0; j < i; j++) {
-          a[counter][0] = i;
-          a[counter][1] = j;
-          counter++;
-        }
-      }
-      filled = true;
-    }
-
-    if (Index < ncolour * (ncolour - 1) / 2) {
-      baseOffDiagonal(a[Index][0], a[Index][1], eij);
-    } else {
-      baseDiagonal(Index, eij);
-    }
-  }
-    
-  template <class cplx>
-   static void base(int Index, iGroupMatrix<cplx> &eij, GroupName::Sp) {
+   static void base(int Index, iGroupMatrix<cplx> &eij) {
      // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
      assert(Index < Dimension);
      eij = Zero();
@@ -197,24 +153,27 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
        int counter = 0;
        for (int i = 1; i < ncolour; i++) {
          for (int j = 0; j < i; j++) {
-           a[counter][0] = i;
-             if (j==0 && i==ngroup+j && S==-1) {
-                 //std::cout << "skipping" << std::endl; // for Sp2n this vanishes identically.
-                 j = j+1;
+             if (std::is_same<group_name, GroupName::Sp>::value)
+             {
+               if (j==0 && i==ngroup+j && S==-1) {
+                   //std::cout << "skipping" << std::endl; // for Sp2n this vanishes identically.
+                   j = j+1;
+               }
              }
+           a[counter][0] = i;
            a[counter][1] = j;
            counter++;
          }
        }
        filled = true;
      }
-
-     if (Index < DimensionHelper<ncolour, AntiSymmetric, GroupName::Sp>::Dimension + 1) {   // +1 the singlet
-       baseOffDiagonalSpHelper<cplx, ncolour, S>::baseOffDiagonalSp(a[Index][0], a[Index][1], eij);
+     if (Index < ncolour*ncolour - DimensionS)
+     {
+         baseOffDiagonal(a[Index][0], a[Index][1], eij, group_name());
      } else {
-       baseDiagonal(Index, eij);
+         baseDiagonal(Index, eij);
+       }
      }
-   }
 
   template <class cplx>
   static void baseDiagonal(int Index, iGroupMatrix<cplx> &eij) {
@@ -224,7 +183,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
   }
     
   template <class cplx>
-  static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij) {
+  static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij, GroupName::SU) {
     eij = Zero();
     for (int k = 0; k < ncolour; k++)
       for (int l = 0; l < ncolour; l++)
@@ -236,8 +195,8 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
   }
     
   template <class cplx>
-  static void baseOffDiagonalSp(int i, int j, iGroupMatrix<cplx> &eij) {
-  baseOffDiagonalSpHelper<cplx, ncolour, S>::baseOffDiagonalSp(i, j, eij);
+  static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij, GroupName::Sp) {
+    detail::baseOffDiagonalSpHelper<cplx, ncolour, S>::baseOffDiagonalSp(i, j, eij);
   }
 
   static void printBase(void) {
diff --git a/tests/core/Test_lie_generators.cc b/tests/core/Test_lie_generators.cc
index c4a88356..7b7ec385 100644
--- a/tests/core/Test_lie_generators.cc
+++ b/tests/core/Test_lie_generators.cc
@@ -324,30 +324,30 @@ int main(int argc, char** argv) {
   }
   
   TIndexRep.update_representation(UV2);
-  typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField UVr2 = TIndexRep.U;  // (U_f * V_f)_r
+  typename TwoIndexRep< Nc, Symmetric>::LatticeField UVr2 = TIndexRep.U;  // (U_f * V_f)_r
   
   TIndexRep.update_representation(U2);
-  typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField Ur2 = TIndexRep.U;  // U_r
+  typename TwoIndexRep< Nc, Symmetric>::LatticeField Ur2 = TIndexRep.U;  // U_r
   
   TIndexRep.update_representation(V2);
-  typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField Vr2 = TIndexRep.U;  // V_r
+  typename TwoIndexRep< Nc, Symmetric>::LatticeField Vr2 = TIndexRep.U;  // V_r
   
-  typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField Ur2Vr2(grid);
+  typename TwoIndexRep< Nc, Symmetric>::LatticeField Ur2Vr2(grid);
   Ur2Vr2 = Zero();
   for (int mu = 0; mu < Nd; mu++) {
-    typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeMatrix Urmu2 = peekLorentz(Ur2,mu);
-    typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeMatrix Vrmu2 = peekLorentz(Vr2,mu);
+    typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Urmu2 = peekLorentz(Ur2,mu);
+    typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Vrmu2 = peekLorentz(Vr2,mu);
     pokeLorentz(Ur2Vr2,Urmu2*Vrmu2, mu);
   }
   
-  typename TwoIndexRep< Nc, Symmetric, GroupName::SU >::LatticeField Diff_check2 = UVr2 - Ur2Vr2;
+  typename TwoIndexRep< Nc, Symmetric>::LatticeField Diff_check2 = UVr2 - Ur2Vr2;
   std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Two Index Symmetric): " << norm2(Diff_check2) << std::endl;
 
   
   // Check correspondence of algebra and group transformations
   // Create a random vector
   SU<Nc>::LatticeAlgebraVector h_sym(grid);
-  typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix Ar_sym(grid);
+  typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ar_sym(grid);
   random(gridRNG,h_sym);
   h_sym = real(h_sym);
   SU_TwoIndex<Nc,Symmetric>::TwoIndexLieAlgebraMatrix(h_sym,Ar_sym);
@@ -360,13 +360,13 @@ int main(int argc, char** argv) {
 
   
   // Exponentiate
-  typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix U2iS(grid);
+  typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix U2iS(grid);
   U2iS  = expMat(Ar_sym, 1.0, 16);
   
-  typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix uno2iS(grid);
+  typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix uno2iS(grid);
   uno2iS = 1.0;
   // Check matrix U2iS, must be real orthogonal
-  typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix Ucheck2iS = U2iS - conjugate(U2iS);
+  typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ucheck2iS = U2iS - conjugate(U2iS);
   std::cout << GridLogMessage << "Reality check: " << norm2(Ucheck2iS)
       << std::endl;
   
@@ -399,15 +399,15 @@ int main(int argc, char** argv) {
   
   TIndexRep.update_representation(U);
   Ur2 = TIndexRep.U;  // U_r  
-  typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix Ur02 = peekLorentz(Ur2,0); // this should be the same as U2iS
+  typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ur02 = peekLorentz(Ur2,0); // this should be the same as U2iS
   
-  typename TwoIndexRep< Nc, Symmetric, GroupName::SU>::LatticeMatrix Diff_check_mat2 = Ur02 - U2iS;
+  typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Diff_check_mat2 = Ur02 - U2iS;
   std::cout << GridLogMessage << "Projections structure check group difference (Two Index Symmetric): " << norm2(Diff_check_mat2) << std::endl;
   
 
 
 
-  if (TwoIndexRep<Nc, AntiSymmetric , GroupName::SU>::Dimension != 1){
+  if (TwoIndexRep<Nc, AntiSymmetric>::Dimension != 1){
 
   std::cout << GridLogMessage << "*********************************************"
       << std::endl;
@@ -416,7 +416,7 @@ int main(int argc, char** argv) {
   std::cout << GridLogMessage << "Two Index anti-Symmetric: Check Group Structure"
       << std::endl;
   // Testing HMC representation classes
-  TwoIndexRep< Nc, AntiSymmetric, GroupName::SU > TIndexRepA(grid);
+  TwoIndexRep< Nc, AntiSymmetric> TIndexRepA(grid);
 
 
   // Test group structure
@@ -434,30 +434,30 @@ int main(int argc, char** argv) {
   }
   
   TIndexRep.update_representation(UV2A);
-  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField UVr2A = TIndexRepA.U;  // (U_f * V_f)_r
+  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField UVr2A = TIndexRepA.U;  // (U_f * V_f)_r
   
   TIndexRep.update_representation(U2A);
-  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField Ur2A = TIndexRepA.U;  // U_r
+  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField Ur2A = TIndexRepA.U;  // U_r
   
   TIndexRep.update_representation(V2A);
-  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField Vr2A = TIndexRepA.U;  // V_r
+  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField Vr2A = TIndexRepA.U;  // V_r
   
-  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField Ur2Vr2A(grid);
+  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField Ur2Vr2A(grid);
   Ur2Vr2A = Zero();
   for (int mu = 0; mu < Nd; mu++) {
-    typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeMatrix Urmu2A = peekLorentz(Ur2A,mu);
-    typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeMatrix Vrmu2A = peekLorentz(Vr2A,mu);
+    typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Urmu2A = peekLorentz(Ur2A,mu);
+    typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Vrmu2A = peekLorentz(Vr2A,mu);
     pokeLorentz(Ur2Vr2A,Urmu2A*Vrmu2A, mu);
   }
   
-  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU >::LatticeField Diff_check2A = UVr2A - Ur2Vr2A;
+  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField Diff_check2A = UVr2A - Ur2Vr2A;
   std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Two Index anti-Symmetric): " << norm2(Diff_check2A) << std::endl;
 
   
   // Check correspondence of algebra and group transformations
   // Create a random vector
   SU<Nc>::LatticeAlgebraVector h_Asym(grid);
-  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix Ar_Asym(grid);
+  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ar_Asym(grid);
   random(gridRNG,h_Asym);
   h_Asym = real(h_Asym);
   SU_TwoIndex< Nc, AntiSymmetric>::TwoIndexLieAlgebraMatrix(h_Asym,Ar_Asym);
@@ -470,13 +470,13 @@ int main(int argc, char** argv) {
 
   
   // Exponentiate
-  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix U2iAS(grid);
+  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix U2iAS(grid);
   U2iAS  = expMat(Ar_Asym, 1.0, 16);
   
-  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix uno2iAS(grid);
+  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix uno2iAS(grid);
   uno2iAS = 1.0;
   // Check matrix U2iS, must be real orthogonal
-  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix Ucheck2iAS = U2iAS - conjugate(U2iAS);
+  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ucheck2iAS = U2iAS - conjugate(U2iAS);
   std::cout << GridLogMessage << "Reality check: " << norm2(Ucheck2iAS)
       << std::endl;
   
@@ -509,9 +509,9 @@ int main(int argc, char** argv) {
   
   TIndexRepA.update_representation(U);
   Ur2A = TIndexRepA.U;  // U_r  
-  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix Ur02A = peekLorentz(Ur2A,0); // this should be the same as U2iS
+  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ur02A = peekLorentz(Ur2A,0); // this should be the same as U2iS
   
-  typename TwoIndexRep< Nc, AntiSymmetric, GroupName::SU>::LatticeMatrix Diff_check_mat2A = Ur02A - U2iAS;
+  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Diff_check_mat2A = Ur02A - U2iAS;
   std::cout << GridLogMessage << "Projections structure check group difference (Two Index anti-Symmetric): " << norm2(Diff_check_mat2A) << std::endl;
   
 } else  {
diff --git a/tests/sp2n/Test_2as_base.cc b/tests/sp2n/Test_2as_base.cc
index a210a15e..59af82fd 100644
--- a/tests/sp2n/Test_2as_base.cc
+++ b/tests/sp2n/Test_2as_base.cc
@@ -1,212 +1,141 @@
 #include <Grid/Grid.h>
 
-#define verbose 1
+#define verbose 0
 
 using namespace Grid;
 
-static void antisymm_base() {
-
-  const int this_nc = 6;
-  const int this_n = this_nc/2;
-  const int this_irrep_dim = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension;
-  const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
-  typedef Sp_TwoIndex<this_nc, AntiSymmetric>::iGroupMatrix<Complex> Matrix;
-  typedef Sp_TwoIndex<this_nc, AntiSymmetric>::iGroupTwoIndexMatrix<Complex> ASMatrix;
-  
-  Matrix Omega;
-  Matrix eij_a;
-  Matrix eij_b;
-  Matrix eij_c;
-  Matrix e_sum;
-  Omega = Zero();
-  for (int i = 0; i < this_n; i++)
-  {
-    Omega()()(i, this_n + i) = 1.;
-    Omega()()(this_n + i, i) = -1;
-  }
-
-  RealD realA;
-  RealD realB;
-  std::cout << GridLogMessage << "2as dimension is " << this_irrep_dim << std::endl;
-  std::cout << GridLogMessage << "algebra dimension is " << this_algebra_dim << std::endl;
-  realA = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension + Sp_TwoIndex<this_nc, Symmetric>::Dimension;
-  assert ( realA == this_nc * this_nc - 1); // Nc x Nc = dim(2indxS) + dim(2indxAS) + dim(singlet)
-
-  std::cout << GridLogMessage << "checking base is antisymmetric " << std::endl;
-  for (int a=0; a < this_irrep_dim; a++)
-  {
-      Sp_TwoIndex<this_nc, AntiSymmetric>::base(a, eij_c);
-      e_sum = eij_c + transpose(eij_c);
-      std::cout << GridLogMessage << "e_ab + e_ab^T " << norm2(e_sum) << std::endl;
-      assert(norm2(e_sum) < 1e-8);
-        
-  }
-  std::cout << GridLogMessage << "Checking Tr (e^(ab) Omega ) = 0 and Tr (e^(ab) e^(cd) = delta^((ab)(cd)) ) " << std::endl;
-  for (int a=0; a < Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension; a++) {
-      Sp_TwoIndex<this_nc, AntiSymmetric>::base(a, eij_a);
-      realA = norm2(trace(Omega*eij_a));
-      std::cout << GridLogMessage << "Omega trace for (ab) = " << a << std::endl;
-      assert(realA == 0);
-      for (int b=0; b < Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension; b++) {
-          Sp_TwoIndex<this_nc, AntiSymmetric>::base(b, eij_b);
-          auto d_ab = TensorRemove(trace(eij_a * eij_b));
-#if verbose
-          std::cout << GridLogMessage << "Tr( e_{ab=" << a << "} e_{cd=" << b << "} ) = " << d_ab << std::endl;
-#endif
-          std::cout << GridLogMessage << "Orthonormality for (ab) = " << a << std::endl;
-          if (a==b) {
-              assert(real(d_ab)+1 < 1e-8);
-              assert(imag(d_ab) < 1e-8);
-          } else {
-              assert(real(d_ab) < 1e-8);
-              assert(imag(d_ab) < 1e-8);
-          }
-      }
-  }
-
-  int sum = 0;
-  int sum_im = 0;
-  Vector<Matrix> ta_fund(this_algebra_dim);
-  Vector<Matrix> eij(this_irrep_dim);
-  Matrix tmp_l;
-  Matrix tmp_r;
-  for (int n = 0; n < this_algebra_dim; n++)
-  {
-      Sp<this_nc>::generator(n, ta_fund[n]);
-  }
-  for (int a = 0; a < this_irrep_dim; a++)
-  {
-      Sp_TwoIndex<this_nc, AntiSymmetric>::base(a, eij[a]);
-  }
-  for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
-  {
-      Complex iTr;
-      sum = 0;
-      sum_im = 0;
-      std::cout << GridLogMessage <<  "generator number " << gen_id << std::endl;
-      for (int a = 0; a < this_irrep_dim; a++)
-      {
-      
-          tmp_l = adj(eij[a])*ta_fund[gen_id]*eij[a];
-          tmp_r = adj(eij[a])*eij[a]*transpose(ta_fund[gen_id]);
-#if verbose
-          std::cout << GridLogMessage << " as_indx = " << a << " eDag T_F e = " << std::endl << tmp_l << std::endl;
-          std::cout << GridLogMessage << " as_indx = " << a << " eDag e T_F^T = " << std::endl << tmp_r << std::endl;
-#endif
-          std::cout << GridLogMessage << " as_indx = " << a << " Tr(sum) = " << TensorRemove(trace(tmp_l+tmp_r)) << std::endl;
-          sum += real(TensorRemove(trace(tmp_l+tmp_r)));
-          sum_im += imag(TensorRemove(trace(tmp_l+tmp_r)));
-      }
-      std::cout << GridLogMessage << "re-evaluated trace of the generator " << gen_id << " is " << sum << " " << sum_im << std::endl;
-      assert ( sum < 1e-8) ;
-      assert ( sum_im < 1e-8) ;
-  }
+template<int this_nc>
+static void check_dimensions() {
+    
+    const int this_n = this_nc/2;
+    const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
+    
+    RealD realA;
+    std::cout << GridLogMessage << "Nc = " << this_n << " 2as dimension is " << Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension << std::endl;
+    std::cout << GridLogMessage << "Nc = " << this_n << " 2s dimension is " << Sp_TwoIndex<this_nc, Symmetric>::Dimension << std::endl;
+    std::cout << GridLogMessage << "Nc = " << this_n << " algebra dimension is " << this_algebra_dim << std::endl;
+    realA = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension + Sp_TwoIndex<this_nc, Symmetric>::Dimension;
+    std::cout << GridLogMessage << "Checking dim(2AS) + dim(AS) + 1 = Nc * Nc " << this_algebra_dim << std::endl;
+    assert ( realA == this_nc * this_nc - 1); // Nc x Nc = dim(2indxS) + dim(2indxAS) + dim(singlet)
 }
 
-static void symm_base() {
+template<int this_nc, TwoIndexSymmetry S>
+static void S_checks() {
+    std::cout << S << std::endl;
+    std::cout << 1 + S * 3 << std::endl;
+}
+    
+    
+template<int this_nc, TwoIndexSymmetry S>
+static void run_base_checks() {
+      std::cout << GridLogMessage << " ****** " << std::endl;
+      std::cout << GridLogMessage << "Running checks for Nc = " << this_nc << " TwoIndex Symmetry = " << S << std::endl;
+      const int this_n = this_nc/2;
+      const int this_irrep_dim = Sp_TwoIndex<this_nc, S>::Dimension;
+      const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
+      typedef typename Sp_TwoIndex<this_nc, S>::template iGroupMatrix<Complex> Matrix;
+      typedef typename Sp_TwoIndex<this_nc, S>::template iGroupTwoIndexMatrix<Complex> ASMatrix;
+      RealD realS = S;
+      
+      Matrix Omega;
+      Matrix eij_a;
+      Matrix eij_b;
+      Matrix eij_c;
+      Matrix e_sum;
+      Omega = Zero();
+      for (int i = 0; i < this_n; i++)
+      {
+        Omega()()(i, this_n + i) = 1.;
+        Omega()()(this_n + i, i) = -1;
+      }
 
-  const int this_nc = 6;
-  const int this_n = this_nc/2;
-  const int this_irrep_dim = Sp_TwoIndex<this_nc, Symmetric>::Dimension;
-  const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
-  typedef Sp_TwoIndex<this_nc, Symmetric>::iGroupMatrix<Complex> Matrix;
-  typedef Sp_TwoIndex<this_nc, Symmetric>::iGroupTwoIndexMatrix<Complex> SMatrix;
-  
-  Matrix Omega;
-  Matrix eij_a;
-  Matrix eij_b;
-  Matrix eij_c;
-  Matrix e_sum;
-  Omega = Zero();
-  for (int i = 0; i < this_n; i++)
-  {
-    Omega()()(i, this_n + i) = 1.;
-    Omega()()(this_n + i, i) = -1;
-  }
+      RealD realA;
+      RealD realB;
 
-  RealD realA;
-  RealD realB;
-  std::cout << GridLogMessage << "symm dimension is " << this_irrep_dim << std::endl;
-  std::cout << GridLogMessage << "algebra dimension is " << this_algebra_dim << std::endl;
-  realA = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension + Sp_TwoIndex<this_nc, Symmetric>::Dimension;
-  assert ( realA == this_nc * this_nc - 1); // Nc x Nc = dim(2indxS) + dim(2indxAS) + dim(singlet)
-
-  std::cout << GridLogMessage << "checking base is symmetric " << std::endl;
-  for (int a=0; a < this_irrep_dim; a++)
-  {
-      Sp_TwoIndex<this_nc, Symmetric>::base(a, eij_c);
-      e_sum = eij_c - transpose(eij_c);
-      std::cout << GridLogMessage << "e_ab - e_ab^T " << norm2(e_sum) << std::endl;
-      assert(norm2(e_sum) < 1e-8);
-  }
-  std::cout << GridLogMessage << "Checking Tr (e^(ab) Omega ) = 0 and Tr (e^(ab) e^(cd) = delta^((ab)(cd)) ) " << std::endl;
-  for (int a=0; a < Sp_TwoIndex<this_nc, Symmetric>::Dimension; a++) {
-      Sp_TwoIndex<this_nc, Symmetric>::base(a, eij_a);
-      realA = norm2(trace(Omega*eij_a));
-      std::cout << GridLogMessage << "Omega trace for (ab) = " << a << std::endl;
-      assert(realA == 0);
-      for (int b=0; b < Sp_TwoIndex<this_nc, Symmetric>::Dimension; b++) {
-          Sp_TwoIndex<this_nc, Symmetric>::base(b, eij_b);
-          auto d_ab = TensorRemove(trace(eij_a * eij_b));
-#if verbose
-          std::cout << GridLogMessage << "Tr( e_{ab=" << a << "} e_{cd=" << b << "} ) = " << d_ab << std::endl;
-#endif
-          std::cout << GridLogMessage << "Orthonormality for (ab) = " << a << std::endl;
-          if (a==b) {
-              assert(real(d_ab)-1 < 1e-8);
-              assert(imag(d_ab) < 1e-8);
-          } else {
-              assert(real(d_ab) < 1e-8);
-              assert(imag(d_ab) < 1e-8);
+      std::cout << GridLogMessage << "checking base has symmetry " << S << std::endl;
+      for (int a=0; a < this_irrep_dim; a++)
+      {
+          Sp_TwoIndex<this_nc, S>::base(a, eij_c);
+          e_sum = eij_c - realS * transpose(eij_c);
+          std::cout << GridLogMessage << "e_ab - (" << S << " * e_ab^T ) = " << norm2(e_sum) << std::endl;
+          assert(norm2(e_sum) < 1e-8);
+            
+      }
+      std::cout << GridLogMessage << "Checking Tr (e^(ab) Omega ) = 0 and Tr (e^(ab) e^(cd) = delta^((ab)(cd)) ) " << std::endl;
+      for (int a=0; a < Sp_TwoIndex<this_nc, S>::Dimension; a++) {
+          Sp_TwoIndex<this_nc, S>::base(a, eij_a);
+          realA = norm2(trace(Omega*eij_a));
+          std::cout << GridLogMessage << "Checkig Omega-trace for e_{ab=" << a << "} " << std::endl;
+          //std::cout << GridLogMessage << "Tr ( Omega e_{ab=" << a << "} ) = " << realA << std::endl;
+          assert(realA < 1e-8);
+          for (int b=0; b < Sp_TwoIndex<this_nc, S>::Dimension; b++) {
+              Sp_TwoIndex<this_nc, S>::base(b, eij_b);
+              auto d_ab = TensorRemove(trace(eij_a * eij_b));
+    #if verbose
+              std::cout << GridLogMessage << "Tr( e_{ab=" << a << "} e_{cd=" << b << "} ) = " << d_ab << std::endl;
+    #endif
+              std::cout << GridLogMessage << "Checking orthonormality for e_{ab = " << a << "} " << std::endl;
+              if (a==b) {
+                  assert(real(d_ab) - realS < 1e-8);
+                  assert(imag(d_ab) < 1e-8);
+              } else {
+                  assert(real(d_ab) < 1e-8);
+                  assert(imag(d_ab) < 1e-8);
+              }
           }
       }
-  }
 
-  int sum = 0;
-  int sum_im = 0;
-  Vector<Matrix> ta_fund(this_algebra_dim);
-  Vector<Matrix> eij(this_irrep_dim);
-  Matrix tmp_l;
-  Matrix tmp_r;
-  for (int n = 0; n < this_algebra_dim; n++)
-  {
-      Sp<this_nc>::generator(n, ta_fund[n]);
-  }
-  for (int a = 0; a < this_irrep_dim; a++)
-  {
-      Sp_TwoIndex<this_nc, Symmetric>::base(a, eij[a]);
-  }
-  for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
-  {
-      Complex iTr;
-      sum = 0;
-      sum_im = 0;
-      std::cout << GridLogMessage <<  "generator number " << gen_id << std::endl;
+      int sum = 0;
+      int sum_im = 0;
+      Vector<Matrix> ta_fund(this_algebra_dim);
+      Vector<Matrix> eij(this_irrep_dim);
+      Matrix tmp_l;
+      Matrix tmp_r;
+      for (int n = 0; n < this_algebra_dim; n++)
+      {
+          Sp<this_nc>::generator(n, ta_fund[n]);
+      }
       for (int a = 0; a < this_irrep_dim; a++)
       {
-      
-          tmp_l = adj(eij[a])*ta_fund[gen_id]*eij[a];
-          tmp_r = adj(eij[a])*eij[a]*transpose(ta_fund[gen_id]);
-#if verbose
-          std::cout << GridLogMessage << " as_indx = " << a << " eDag T_F e = " << std::endl << tmp_l << std::endl;
-          std::cout << GridLogMessage << " as_indx = " << a << " eDag e T_F^T = " << std::endl << tmp_r << std::endl;
-#endif
-          std::cout << GridLogMessage << " as_indx = " << a << " Tr(sum) = " << TensorRemove(trace(tmp_l+tmp_r)) << std::endl;
-          sum += real(TensorRemove(trace(tmp_l+tmp_r)));
-          sum_im += imag(TensorRemove(trace(tmp_l+tmp_r)));
+          Sp_TwoIndex<this_nc, S>::base(a, eij[a]);
+      }
+      for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
+      {
+          Complex iTr;
+          sum = 0;
+          sum_im = 0;
+          std::cout << GridLogMessage <<  "generator number " << gen_id << std::endl;
+          for (int a = 0; a < this_irrep_dim; a++)
+          {
+          
+              tmp_l = adj(eij[a])*ta_fund[gen_id]*eij[a];
+              tmp_r = adj(eij[a])*eij[a]*transpose(ta_fund[gen_id]);
+    #if verbose
+              std::cout << GridLogMessage << " as_indx = " << a << " eDag T_F e = " << std::endl << tmp_l << std::endl;
+              std::cout << GridLogMessage << " as_indx = " << a << " eDag e T_F^T = " << std::endl << tmp_r << std::endl;
+    #endif
+              //std::cout << GridLogMessage << " as_indx = " << a << " Tr(eDag T_F e + eDag e T_F^T) = " << TensorRemove(trace(tmp_l+tmp_r)) << std::endl;
+              sum += real(TensorRemove(trace(tmp_l+tmp_r)));
+              sum_im += imag(TensorRemove(trace(tmp_l+tmp_r)));
+          }
+          std::cout << GridLogMessage << "re-evaluated trace of the generator " << gen_id << " is " << sum << " " << sum_im << std::endl;
+          assert ( sum < 1e-8) ;
+          assert ( sum_im < 1e-8) ;
       }
-      std::cout << GridLogMessage << "re-evaluated trace of the generator " << gen_id << " is " << sum << " " << sum_im << std::endl;
-      assert ( sum < 1e-8) ;
-      assert ( sum_im < 1e-8) ;
-  }
 }
 
-
 int main(int argc, char** argv) {
-  std::cout << GridLogMessage << "Checking AntiSymmetric base " << std::endl;
-  antisymm_base();
-  std::cout << GridLogMessage << "*************** " << std::endl;
-  std::cout << GridLogMessage << "Checking Symmetric base " << std::endl;
-  symm_base();
+    check_dimensions<2>();
+    check_dimensions<4>();
+    check_dimensions<6>();
+    check_dimensions<8>();
+    
+    run_base_checks<2, Symmetric>();
+    run_base_checks<4, Symmetric>();
+    run_base_checks<4, AntiSymmetric>();
+    run_base_checks<6, Symmetric>();
+    run_base_checks<6, AntiSymmetric>();
+    run_base_checks<8, Symmetric>();
+    run_base_checks<8, AntiSymmetric>();
 }
 
diff --git a/tests/sp2n/Test_sp2n_lie_gen.cc b/tests/sp2n/Test_sp2n_lie_gen.cc
index c8d58701..3f51d1a5 100644
--- a/tests/sp2n/Test_sp2n_lie_gen.cc
+++ b/tests/sp2n/Test_sp2n_lie_gen.cc
@@ -2,99 +2,52 @@
 
 using namespace Grid;
 
+template<int ncolour>
+void run_checks(bool print_generators = 0) {
+    std::cout << GridLogMessage << "*********************************************"
+                << std::endl;
+    std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")" << "Fundamental" << std::endl;
+    std::cout << GridLogMessage << "*********************************************"
+                << std::endl;
+    
+    if (print_generators)
+    {
+        Sp<ncolour>::printGenerators();
+    }
+    Sp<ncolour>::testGenerators();
+    
+    if (Sp_TwoIndex<ncolour, Symmetric>::Dimension > 1) {
+        std::cout << GridLogMessage << "*********************************************"
+                    << std::endl;
+        std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")" << "TwoIndex Symmetric: " << std::endl;
+        std::cout << GridLogMessage << "*********************************************"
+                    << std::endl;
+        if (print_generators) {
+            Sp_TwoIndex<ncolour, Symmetric>::printGenerators();
+        }
+        Sp_TwoIndex<ncolour, Symmetric>::testGenerators();
+    }
+    
+    if (Sp_TwoIndex<ncolour, AntiSymmetric>::Dimension > 1) {
+        std::cout << GridLogMessage << "*********************************************"
+                    << std::endl;
+        std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")" << "TwoIndex AntiSymmetric: " << std::endl;
+        std::cout << GridLogMessage << "*********************************************"
+                    << std::endl;
+        if (print_generators) {
+            Sp_TwoIndex<ncolour, AntiSymmetric>::printGenerators();
+        }
+        Sp_TwoIndex<ncolour, AntiSymmetric>::testGenerators();
+    }
+}
+  
 int main(int argc, char** argv) {
   Grid_init(&argc, &argv);
     
-  std::cout << GridLogMessage << "*********************************************"
-              << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(2) (print and test)" << std::endl;
-  std::cout << GridLogMessage << "*********************************************"
-              << std::endl;
-      
-  Sp2::printGenerators();
-  Sp2::testGenerators();
-  
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(4) (print and test)" << std::endl;
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-    
-  Sp4::printGenerators();
-  Sp4::testGenerators();
-    
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(6) (test)" << std::endl;
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-
-  Sp6::testGenerators();
-
-  std::cout << GridLogMessage << "*********************************************"
-              << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(8) (test)" << std::endl;
-  std::cout << GridLogMessage << "*********************************************"
-              << std::endl;
-    
-  Sp8::testGenerators();
-    
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(2) TwoIndexS (print & test)" << std::endl;
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-
-  Sp_TwoIndex<2, Symmetric>::printGenerators();
-  Sp_TwoIndex<2, Symmetric>::testGenerators();
-
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(4) TwoIndexAS (test)" << std::endl;
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-
-  Sp_TwoIndex<4, AntiSymmetric>::testGenerators();
-    
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(4) TwoIndexS (test)" << std::endl;
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-
-  Sp_TwoIndex<4, Symmetric>::testGenerators();
-    
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(6) TwoIndexAS (test)" << std::endl;
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-
-  Sp_TwoIndex<6, AntiSymmetric>::testGenerators();
-    
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(6) TwoIndexS (test)" << std::endl;
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-
-  Sp_TwoIndex<6, Symmetric>::testGenerators();
-
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(8) TwoIndexAS (test)" << std::endl;
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-
-  Sp_TwoIndex<8, AntiSymmetric>::testGenerators();
-    
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(8) TwoIndexS (test)" << std::endl;
-  std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-
-  Sp_TwoIndex<8, Symmetric>::testGenerators();
+  run_checks<2>(1); //  check and print Nc=2
+  run_checks<4>(1); //  check and print Nc=4
+  run_checks<6>();  //  check Nc=6
+  run_checks<8>();  //  check Nc=8
 
   Grid_finalize();
 }

From b405767569e44ba740ddc2db084c95543f3ce5d9 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 26 May 2023 17:02:16 +0100
Subject: [PATCH 104/129] make private methods private

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h | 72 +++++++++++++++--------------
 1 file changed, 37 insertions(+), 35 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index 2d8dbe25..d38ae0f9 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -140,41 +140,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
   typedef iGroupMatrix<ComplexF> MatrixF;
   typedef iGroupMatrix<ComplexD> MatrixD;
     
-  template <class cplx>
-   static void base(int Index, iGroupMatrix<cplx> &eij) {
-     // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
-     assert(Index < Dimension);
-     eij = Zero();
-
-     // for the linearisation of the 2 indexes
-     static int a[ncolour * (ncolour - 1) / 2][2];  // store the a <-> i,j
-     static bool filled = false;
-     if (!filled) {
-       int counter = 0;
-       for (int i = 1; i < ncolour; i++) {
-         for (int j = 0; j < i; j++) {
-             if (std::is_same<group_name, GroupName::Sp>::value)
-             {
-               if (j==0 && i==ngroup+j && S==-1) {
-                   //std::cout << "skipping" << std::endl; // for Sp2n this vanishes identically.
-                   j = j+1;
-               }
-             }
-           a[counter][0] = i;
-           a[counter][1] = j;
-           counter++;
-         }
-       }
-       filled = true;
-     }
-     if (Index < ncolour*ncolour - DimensionS)
-     {
-         baseOffDiagonal(a[Index][0], a[Index][1], eij, group_name());
-     } else {
-         baseDiagonal(Index, eij);
-       }
-     }
-
+private:
   template <class cplx>
   static void baseDiagonal(int Index, iGroupMatrix<cplx> &eij) {
     eij = Zero();
@@ -199,6 +165,42 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
     detail::baseOffDiagonalSpHelper<cplx, ncolour, S>::baseOffDiagonalSp(i, j, eij);
   }
 
+public:
+    
+  template <class cplx>
+  static void base(int Index, iGroupMatrix<cplx> &eij) {
+  // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
+    assert(Index < Dimension);
+    eij = Zero();
+  // for the linearisation of the 2 indexes
+    static int a[ncolour * (ncolour - 1) / 2][2];  // store the a <-> i,j
+    static bool filled = false;
+    if (!filled) {
+      int counter = 0;
+      for (int i = 1; i < ncolour; i++) {
+      for (int j = 0; j < i; j++) {
+        if (std::is_same<group_name, GroupName::Sp>::value)
+          {
+            if (j==0 && i==ngroup+j && S==-1) {
+            //std::cout << "skipping" << std::endl; // for Sp2n this vanishes identically.
+              j = j+1;
+            }
+          }
+          a[counter][0] = i;
+          a[counter][1] = j;
+          counter++;
+          }
+      }
+      filled = true;
+    }
+    if (Index < ncolour*ncolour - DimensionS)
+    {
+      baseOffDiagonal(a[Index][0], a[Index][1], eij, group_name());
+    } else {
+      baseDiagonal(Index, eij);
+    }
+  }
+    
   static void printBase(void) {
     for (int gen = 0; gen < Dimension; gen++) {
       Matrix tmp;

From 8db7c23bee7d682c123d0ec1a8c1bd6b93aa2d34 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Thu, 1 Jun 2023 17:39:10 +0100
Subject: [PATCH 105/129] improve documentation

---
 documentation/Grid.pdf   | Bin 579665 -> 579661 bytes
 documentation/manual.rst |   4 ++--
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/documentation/Grid.pdf b/documentation/Grid.pdf
index 2511c6c8d00c891714d0153ede75e3c586cc38e0..17dfe12e42a0d39ba624ebb77a0e1fee8e7a503d 100644
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diff --git a/documentation/manual.rst b/documentation/manual.rst
index 2a2f4728..7b8881dd 100644
--- a/documentation/manual.rst
+++ b/documentation/manual.rst
@@ -2792,7 +2792,7 @@ Supported groups are SU(N) and Sp(2N). The group can be specified through the Gr
   class Sp {};
   }
 
-A simpler interface is achieved by instantiating the GaugeGroup class with a specific group::
+A simpler interface is achieved by aliasing the GaugeGroup class with a specific group::
 
   template <int ncolour>
   using SU = GaugeGroup<ncolour, GroupName::SU>;
@@ -2800,7 +2800,7 @@ A simpler interface is achieved by instantiating the GaugeGroup class with a spe
   template <int ncolour>
   using Sp = GaugeGroup<ncolour, GroupName::Sp>;
   
-Specific instantiations are then defined::
+Specific aliases are then defined::
 
   typedef SU<2> SU2;
   typedef SU<3> SU3;

From 470d93006a0399f8907aaf8bca010735d2a99687 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Wed, 7 Jun 2023 12:53:33 +0100
Subject: [PATCH 106/129] compile sp2n fermion impl only if declared at config
 time

---
 Grid/Makefile.am | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/Grid/Makefile.am b/Grid/Makefile.am
index fcb5670a..502fcbf2 100644
--- a/Grid/Makefile.am
+++ b/Grid/Makefile.am
@@ -63,10 +63,12 @@ if BUILD_GPARITY
   extra_sources+=$(GP_FERMION_FILES)
 endif
 if BUILD_FERMION_REPS
-  extra_sources+=$(SP_FERMION_FILES)
   extra_sources+=$(ADJ_FERMION_FILES)
   extra_sources+=$(TWOIND_FERMION_FILES)
-  extra_sources+=$(SP_TWOIND_FILES)
+endif
+if BUILD_SP
+    extra_sources+=$(SP_FERMION_FILES)
+    extra_sources+=$(SP_TWOIND_FILES)
 endif
 
 lib_LIBRARIES = libGrid.a

From b0646ca18789ed7cd68ef316b5557ee86c3ab70c Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Thu, 15 Jun 2023 15:09:09 +0100
Subject: [PATCH 107/129] Remove some unused variables

---
 tests/sp2n/Test_2as_base.cc | 2 --
 1 file changed, 2 deletions(-)

diff --git a/tests/sp2n/Test_2as_base.cc b/tests/sp2n/Test_2as_base.cc
index 59af82fd..0dda2a76 100644
--- a/tests/sp2n/Test_2as_base.cc
+++ b/tests/sp2n/Test_2as_base.cc
@@ -50,7 +50,6 @@ static void run_base_checks() {
       }
 
       RealD realA;
-      RealD realB;
 
       std::cout << GridLogMessage << "checking base has symmetry " << S << std::endl;
       for (int a=0; a < this_irrep_dim; a++)
@@ -101,7 +100,6 @@ static void run_base_checks() {
       }
       for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
       {
-          Complex iTr;
           sum = 0;
           sum_im = 0;
           std::cout << GridLogMessage <<  "generator number " << gen_id << std::endl;

From 116d90b0ee9668826f217488965108dc8cbadbb0 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Thu, 15 Jun 2023 15:09:37 +0100
Subject: [PATCH 108/129] First attempt on #30

---
 Grid/qcd/action/gauge/GaugeImplTypes.h |  2 +-
 Grid/qcd/utils/GaugeGroup.h            | 18 +++++++++---------
 Grid/qcd/utils/SUn.impl                | 17 +++++++++--------
 Grid/qcd/utils/Sp2n.impl               | 17 +++++++++--------
 4 files changed, 28 insertions(+), 26 deletions(-)

diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index 1cc5ef05..526c2173 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -145,7 +145,7 @@ public:
     accelerator_for(ss, P.Grid()->oSites(),1,{
       for (int mu = 0; mu < Nd; mu++) {
           U_v[ss](mu) = Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu);
-          Group::ProjectOnGeneralGroup(U_v[ss](mu));
+          U_v[ss](mu) = Group::ProjectOnGeneralGroup(U_v[ss](mu));
       }
     });
    //auto end = std::chrono::high_resolution_clock::now();
diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index 825881e2..ebb2c33e 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -324,7 +324,7 @@ class GaugeGroup {
   }
     
   template <int N>                  // Projects on the general groups U(N), Sp(2N)xZ2 i.e. determinant il allowed a complex phase.
-  static void ProjectOnGeneralGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
+  accelerator_inline static void ProjectOnGeneralGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
     for (int mu = 0; mu < Nd; mu++) {
       auto Umu = PeekIndex<LorentzIndex>(U, mu);
       ProjectOnGeneralGroup(Umu);
@@ -332,23 +332,23 @@ class GaugeGroup {
   }
        
   template <int N>
-  static void ProjectOnGeneralGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
-      ProjectOnGeneralGroup(Umu, group_name());
+  accelerator_inline static Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
+      return ProjectOnGeneralGroup(Umu, group_name());
   }
     
   template <class vtype>
-  static void ProjectOnGeneralGroup(iScalar<vtype> &r) {
-      ProjectOnGeneralGroup(r, group_name());
+  accelerator_inline static iScalar<vtype> ProjectOnGeneralGroup(const iScalar<vtype> &r) {
+      return ProjectOnGeneralGroup(r, group_name());
   }
 
   template <class vtype, int N>
-  static void ProjectOnGeneralGroup(iVector<vtype,N> &r) {
-      ProjectOnGeneralGroup(r, group_name());
+  accelerator_inline static iVector<vtype,N> ProjectOnGeneralGroup(const iVector<vtype,N> &r) {
+      return ProjectOnGeneralGroup(r, group_name());
   }
 
   template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
-  static void ProjectOnGeneralGroup(iMatrix<vtype,N> &arg) {
-      ProjectOnGeneralGroup(arg, group_name());
+  accelerator_inline static iMatrix<vtype,N> ProjectOnGeneralGroup(const iMatrix<vtype,N> &arg) {
+      return ProjectOnGeneralGroup(arg, group_name());
   }
 
   template <int N>       // Projects on SU(N), Sp(2N)
diff --git a/Grid/qcd/utils/SUn.impl b/Grid/qcd/utils/SUn.impl
index 07bfc6e7..553821dc 100644
--- a/Grid/qcd/utils/SUn.impl
+++ b/Grid/qcd/utils/SUn.impl
@@ -509,23 +509,24 @@ static void testGenerators(GroupName::SU) {
 }
 
 template <int N>
-static void ProjectOnGeneralGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::SU) {
-  Umu = ProjectOnGroup(Umu);
+accelerator_inline static Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > >
+ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::SU) {
+  return ProjectOnGroup(Umu);
 }
 
 template <class vtype>
-static void ProjectOnGeneralGroup(iScalar<vtype> &r, GroupName::SU) {
-  r = ProjectOnGroup(r);
+accelerator_inline static iScalar<vtype> ProjectOnGeneralGroup(const iScalar<vtype> &r, GroupName::SU) {
+  return ProjectOnGroup(r);
 }
 
 template <class vtype, int N>
-static void ProjectOnGeneralGroup(iVector<vtype,N> &r, GroupName::SU) {
-  r = ProjectOnGroup(r);
+accelerator_inline static iVector<vtype,N> ProjectOnGeneralGroup(const iVector<vtype,N> &r, GroupName::SU) {
+  return ProjectOnGroup(r);
 }
 
 template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
-static void ProjectOnGeneralGroup(iMatrix<vtype,N> &arg, GroupName::SU) {
-  arg = ProjectOnGroup(arg);
+accelerator_inline static iMatrix<vtype,N> ProjectOnGeneralGroup(const iMatrix<vtype,N> &arg, GroupName::SU) {
+  return ProjectOnGroup(arg);
 }
 
 template <typename LatticeMatrixType>
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index 9cca5d49..940dbddd 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -254,23 +254,24 @@ static void testGenerators(GroupName::Sp) {
 }
 
 template <int N>
-static void ProjectOnGeneralGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::Sp) {
-  Umu = ProjectOnSpGroup(Umu);
+accelerator_inline static Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > >
+ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::Sp) {
+  return ProjectOnSpGroup(Umu);
 }
 
 template <class vtype>
-static void ProjectOnGeneralGroup(iScalar<vtype> &r, GroupName::Sp) {
-  r = ProjectOnSpGroup(r);
+accelerator_inline static iScalar<vtype> ProjectOnGeneralGroup(const iScalar<vtype> &r, GroupName::Sp) {
+  return ProjectOnSpGroup(r);
 }
 
 template <class vtype, int N>
-static void ProjectOnGeneralGroup(iVector<vtype,N> &r, GroupName::Sp) {
-  r = ProjectOnSpGroup(r);
+accelerator_inline static iVector<vtype,N> ProjectOnGeneralGroup(const iVector<vtype,N> &r, GroupName::Sp) {
+  return ProjectOnSpGroup(r);
 }
 
 template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
-static void ProjectOnGeneralGroup(iMatrix<vtype,N> &arg, GroupName::Sp) {
-  arg = ProjectOnSpGroup(arg);
+accelerator_inline static iMatrix<vtype,N> ProjectOnGeneralGroup(const iMatrix<vtype,N> &arg, GroupName::Sp) {
+  return ProjectOnSpGroup(arg);
 }
 
 template <typename LatticeMatrixType>   

From c797cbe7376b848421542cdd633f8c04d02699dd Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Tue, 13 Jun 2023 17:21:01 +0100
Subject: [PATCH 109/129] deal with post-merge trauma

---
 Grid/qcd/utils/GaugeGroup.h                   |  1 -
 Grid/qcd/utils/SUn.impl                       | 47 +++++++++----------
 configure.ac                                  |  1 +
 .../Test_compact_wilson_clover_speedup.cc     |  4 +-
 tests/core/Test_lie_generators.cc             | 17 ++-----
 .../Test_hmc_Sp_WilsonFundFermionGauge.cc     |  4 +-
 tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc     |  6 ++-
 7 files changed, 35 insertions(+), 45 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index 825881e2..7c478a19 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -176,7 +176,6 @@ class GaugeGroup {
     GridBase *grid = out.Grid();
 
     typedef typename LatticeMatrixType::vector_type vector_type;
-    typedef typename LatticeMatrixType::scalar_type scalar_type;
 
     typedef iSinglet<vector_type> vTComplexType;
 
diff --git a/Grid/qcd/utils/SUn.impl b/Grid/qcd/utils/SUn.impl
index 44b6c3b3..efba343f 100644
--- a/Grid/qcd/utils/SUn.impl
+++ b/Grid/qcd/utils/SUn.impl
@@ -566,43 +566,40 @@ static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupNam
 /*
  * Fundamental rep gauge xform
  */
-template <typename Fundamental, typename GaugeMat, ONLY_IF_SU>
-static void GaugeTransformFundamental(Fundamental &ferm, GaugeMat &g) {
+template<typename Fundamental,typename GaugeMat>
+static void GaugeTransformFundamental( Fundamental &ferm, GaugeMat &g){
   GridBase *grid = ferm._grid;
-  conformable(grid, g._grid);
-  ferm = g * ferm;
+  conformable(grid,g._grid);
+  ferm = g*ferm;
 }
 /*
  * Adjoint rep gauge xform
  */
 
-template <typename GaugeField, typename GaugeMat, ONLY_IF_SU>
-static void GaugeTransform(GaugeField &Umu, GaugeMat &g) {
+template<typename Gimpl>
+static void GaugeTransform(typename Gimpl::GaugeField &Umu, typename Gimpl::GaugeLinkField &g){
   GridBase *grid = Umu.Grid();
-  conformable(grid, g.Grid());
+  conformable(grid,g.Grid());
 
-  GaugeMat U(grid);
-  GaugeMat ag(grid);
-  ag = adj(g);
+  typename Gimpl::GaugeLinkField U(grid);
+  typename Gimpl::GaugeLinkField ag(grid); ag = adj(g);
 
-  for (int mu = 0; mu < Nd; mu++) {
-    U = PeekIndex<LorentzIndex>(Umu, mu);
-    U = g * U * Cshift(ag, mu, 1);
-    PokeIndex<LorentzIndex>(Umu, U, mu);
+  for(int mu=0;mu<Nd;mu++){
+    U= PeekIndex<LorentzIndex>(Umu,mu);
+    U = g*U*Gimpl::CshiftLink(ag, mu, 1); //BC-aware
+    PokeIndex<LorentzIndex>(Umu,U,mu);
   }
 }
-template <typename GaugeMat, ONLY_IF_SU>
-static void GaugeTransform(std::vector<GaugeMat> &U, GaugeMat &g) {
+template<typename Gimpl>
+static void GaugeTransform( std::vector<typename Gimpl::GaugeLinkField> &U, typename Gimpl::GaugeLinkField &g){
   GridBase *grid = g.Grid();
-  GaugeMat ag(grid);
-  ag = adj(g);
-  for (int mu = 0; mu < Nd; mu++) {
-    U[mu] = g * U[mu] * Cshift(ag, mu, 1);
+  typename Gimpl::GaugeLinkField ag(grid); ag = adj(g);
+  for(int mu=0;mu<Nd;mu++){
+    U[mu] = g*U[mu]*Gimpl::CshiftLink(ag, mu, 1); //BC-aware
   }
 }
-template <typename GaugeField, typename GaugeMat, ONLY_IF_SU>
-static void RandomGaugeTransform(GridParallelRNG &pRNG, GaugeField &Umu,
-                                 GaugeMat &g) {
-  LieRandomize(pRNG, g, 1.0);
-  GaugeTransform(Umu, g);
+template<typename Gimpl>
+static void RandomGaugeTransform(GridParallelRNG &pRNG, typename Gimpl::GaugeField &Umu, typename Gimpl::GaugeLinkField &g){
+  LieRandomize(pRNG,g,1.0);
+  GaugeTransform<Gimpl>(Umu,g);
 }
diff --git a/configure.ac b/configure.ac
index 30e33d73..032a4729 100644
--- a/configure.ac
+++ b/configure.ac
@@ -215,6 +215,7 @@ case ${ac_ENABLE_SP} in
         AC_DEFINE([Sp2n_config],[0],[gauge group SUn], [have_sp2n=false]);;
     *)
         AC_MSG_ERROR(["--enable-symplectic is either yes or no"]);;
+esac
 
 ############### FP16 conversions
 AC_ARG_ENABLE([sfw-fp16],
diff --git a/tests/core/Test_compact_wilson_clover_speedup.cc b/tests/core/Test_compact_wilson_clover_speedup.cc
index 695c8061..d09b4c1d 100644
--- a/tests/core/Test_compact_wilson_clover_speedup.cc
+++ b/tests/core/Test_compact_wilson_clover_speedup.cc
@@ -218,9 +218,9 @@ void runBenchmark(int* argc, char*** argv) {
 
 int main(int argc, char** argv) {
   Grid_init(&argc, &argv);
-
+#if Nc==3
   runBenchmark<vComplexD>(&argc, &argv);
   runBenchmark<vComplexF>(&argc, &argv);
-
+#endif
   Grid_finalize();
 }
diff --git a/tests/core/Test_lie_generators.cc b/tests/core/Test_lie_generators.cc
index 3132892b..7792b743 100644
--- a/tests/core/Test_lie_generators.cc
+++ b/tests/core/Test_lie_generators.cc
@@ -44,11 +44,6 @@ directory
 
 using namespace std;
 using namespace Grid;
-<<<<<<< HEAD
-
-=======
-;
->>>>>>> develop
 
 int main(int argc, char** argv) {
   Grid_init(&argc, &argv);
@@ -67,15 +62,12 @@ int main(int argc, char** argv) {
   SU2::printGenerators();
   std::cout << "Dimension of adjoint representation: "<< SU2Adjoint::Dimension << std::endl;
 
-  // guard as this code fails to compile for Nc != 3
-#if 1
-
   std::cout << " Printing  Adjoint Generators"<< std::endl;
-    
+
   SU2Adjoint::printGenerators();
   SU2::testGenerators();
   SU2Adjoint::testGenerators();
-    
+
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
   std::cout << GridLogMessage << "* Generators for SU(3)" << std::endl;
@@ -156,6 +148,7 @@ int main(int argc, char** argv) {
     pokeLorentz(UrVr,Urmu*Vrmu, mu);
   }
 
+#if Nc==3
   typedef typename SU_Adjoint<Nc>::AMatrix AdjointMatrix;
   typename AdjointRep<Nc>::LatticeField Diff_check = UVr - UrVr;
   std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Adjoint representation) : " << norm2(Diff_check) << std::endl;
@@ -181,7 +174,7 @@ int main(int argc, char** argv) {
     assert(abs( (2.0*tr1-tr2) ) < 1.0e-7);
     std::cout << "------------------"<<std::endl;
   }}}
-  
+#endif
   // Check correspondence of algebra and group transformations
   // Create a random vector
   SU<Nc>::LatticeAlgebraVector h_adj(grid);
@@ -434,8 +427,6 @@ int main(int argc, char** argv) {
     std::cout << GridLogMessage << "*********************************************"
 	      << std::endl;
     
-  
-<<<<<<< HEAD
   std::cout << GridLogMessage << "Two Index anti-Symmetric: Check Group Structure"
       << std::endl;
   // Testing HMC representation classes
diff --git a/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
index 26fc2f8d..d2bc32bf 100644
--- a/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
+++ b/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
@@ -8,8 +8,8 @@ int main(int argc, char **argv) {
   Grid_init(&argc, &argv);
     
   typedef GenericSp2nHMCRunnerHirep<TheRepresentations, MinimumNorm2> HMCWrapper; // ok
-  typedef SpWilsonImplD FermionImplPolicy;                                    // ok
-  typedef SpWilsonFermionR FermionAction;                                     // ok
+  typedef SpWilsonImplR FermionImplPolicy;                                    // ok
+  typedef SpWilsonFermionD FermionAction;                                     // ok
   typedef typename FermionAction::FermionField FermionField;                  // ok?
  
   //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
diff --git a/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc b/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc
index cda76860..4fe5c50a 100644
--- a/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc
+++ b/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc
@@ -67,8 +67,10 @@ int main(int argc, char **argv)
   TopologyObsParameters TopParams;
   TopParams.interval = 5;
   TopParams.do_smearing = true;
-  TopParams.Smearing.steps = 200;
-  TopParams.Smearing.step_size = 0.01;
+  TopParams.Smearing.init_step_size = 0.01;
+  TopParams.Smearing.tolerance = 1e-5;
+  //TopParams.Smearing.steps = 200;
+  //TopParams.Smearing.step_size = 0.01;
   TopParams.Smearing.meas_interval = 50;
   TopParams.Smearing.maxTau = 2.0; 
   TheHMC.Resources.AddObservable<QObs>(TopParams);

From e28ab7a732cf057b00857d4a292892ad4f9a2c10 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Thu, 15 Jun 2023 15:15:18 +0100
Subject: [PATCH 110/129] Re-included instantiations for symmetric 2Index AS Sp

---
 ...onCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc | 1 +
 .../WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc  | 1 +
 .../WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc  | 1 +
 ...WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc | 1 +
 .../fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h  | 1 +
 ...onCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc | 1 +
 .../WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc  | 1 +
 .../WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc  | 1 +
 ...WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc | 1 +
 .../fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h  | 1 +
 10 files changed, 10 insertions(+)
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
 create mode 100644 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc
 create mode 120000 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
 create mode 100644 Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h

diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
new file mode 120000
index 00000000..9cc05107
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
@@ -0,0 +1 @@
+../WilsonCloverFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
new file mode 120000
index 00000000..5f6ab65e
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
@@ -0,0 +1 @@
+../WilsonFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc
new file mode 120000
index 00000000..01c35e7b
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc
@@ -0,0 +1 @@
+../WilsonKernelsInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
new file mode 120000
index 00000000..d5789bcf
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc
@@ -0,0 +1 @@
+../WilsonTMFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h
new file mode 100644
index 00000000..ac5babca
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h
@@ -0,0 +1 @@
+#define IMPLEMENTATION SpWilsonTwoIndexSymmetricImplD
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
new file mode 120000
index 00000000..9cc05107
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
@@ -0,0 +1 @@
+../WilsonCloverFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
new file mode 120000
index 00000000..5f6ab65e
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
@@ -0,0 +1 @@
+../WilsonFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc
new file mode 120000
index 00000000..01c35e7b
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc
@@ -0,0 +1 @@
+../WilsonKernelsInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
new file mode 120000
index 00000000..d5789bcf
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc
@@ -0,0 +1 @@
+../WilsonTMFermionInstantiation.cc.master
\ No newline at end of file
diff --git a/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h
new file mode 100644
index 00000000..bea7dce7
--- /dev/null
+++ b/Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h
@@ -0,0 +1 @@
+#define IMPLEMENTATION SpWilsonTwoIndexSymmetricImplF

From c95bbd39484ff6e337ca9522c62d70c0d0866117 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Fri, 16 Jun 2023 15:50:26 +0100
Subject: [PATCH 111/129] Remove accelerated lattice version

---
 Grid/qcd/utils/GaugeGroup.h | 2 +-
 Grid/qcd/utils/SUn.impl     | 2 +-
 Grid/qcd/utils/Sp2n.impl    | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index ebb2c33e..64528f7e 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -332,7 +332,7 @@ class GaugeGroup {
   }
        
   template <int N>
-  accelerator_inline static Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
+  static Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
       return ProjectOnGeneralGroup(Umu, group_name());
   }
     
diff --git a/Grid/qcd/utils/SUn.impl b/Grid/qcd/utils/SUn.impl
index 553821dc..0c37fd84 100644
--- a/Grid/qcd/utils/SUn.impl
+++ b/Grid/qcd/utils/SUn.impl
@@ -509,7 +509,7 @@ static void testGenerators(GroupName::SU) {
 }
 
 template <int N>
-accelerator_inline static Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > >
+static Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > >
 ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::SU) {
   return ProjectOnGroup(Umu);
 }
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index 940dbddd..19f2b9eb 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -254,7 +254,7 @@ static void testGenerators(GroupName::Sp) {
 }
 
 template <int N>
-accelerator_inline static Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > >
+static Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > >
 ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::Sp) {
   return ProjectOnSpGroup(Umu);
 }

From 8c3792721bf0735ea91226522efc63e8546c775e Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Fri, 16 Jun 2023 15:58:23 +0100
Subject: [PATCH 112/129] ClangFormat

---
 tests/sp2n/Test_sp2n_lie_gen.cc | 82 +++++++++++++++++----------------
 1 file changed, 42 insertions(+), 40 deletions(-)

diff --git a/tests/sp2n/Test_sp2n_lie_gen.cc b/tests/sp2n/Test_sp2n_lie_gen.cc
index 3f51d1a5..f6c5500f 100644
--- a/tests/sp2n/Test_sp2n_lie_gen.cc
+++ b/tests/sp2n/Test_sp2n_lie_gen.cc
@@ -2,52 +2,54 @@
 
 using namespace Grid;
 
-template<int ncolour>
+template <int ncolour>
 void run_checks(bool print_generators = 0) {
-    std::cout << GridLogMessage << "*********************************************"
-                << std::endl;
-    std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")" << "Fundamental" << std::endl;
-    std::cout << GridLogMessage << "*********************************************"
-                << std::endl;
-    
-    if (print_generators)
-    {
-        Sp<ncolour>::printGenerators();
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")"
+            << "Fundamental" << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+
+  if (print_generators) {
+    Sp<ncolour>::printGenerators();
+  }
+  Sp<ncolour>::testGenerators();
+
+  if (Sp_TwoIndex<ncolour, Symmetric>::Dimension > 1) {
+    std::cout << GridLogMessage
+              << "*********************************************" << std::endl;
+    std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")"
+              << "TwoIndex Symmetric: " << std::endl;
+    std::cout << GridLogMessage
+              << "*********************************************" << std::endl;
+    if (print_generators) {
+      Sp_TwoIndex<ncolour, Symmetric>::printGenerators();
     }
-    Sp<ncolour>::testGenerators();
-    
-    if (Sp_TwoIndex<ncolour, Symmetric>::Dimension > 1) {
-        std::cout << GridLogMessage << "*********************************************"
-                    << std::endl;
-        std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")" << "TwoIndex Symmetric: " << std::endl;
-        std::cout << GridLogMessage << "*********************************************"
-                    << std::endl;
-        if (print_generators) {
-            Sp_TwoIndex<ncolour, Symmetric>::printGenerators();
-        }
-        Sp_TwoIndex<ncolour, Symmetric>::testGenerators();
-    }
-    
-    if (Sp_TwoIndex<ncolour, AntiSymmetric>::Dimension > 1) {
-        std::cout << GridLogMessage << "*********************************************"
-                    << std::endl;
-        std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")" << "TwoIndex AntiSymmetric: " << std::endl;
-        std::cout << GridLogMessage << "*********************************************"
-                    << std::endl;
-        if (print_generators) {
-            Sp_TwoIndex<ncolour, AntiSymmetric>::printGenerators();
-        }
-        Sp_TwoIndex<ncolour, AntiSymmetric>::testGenerators();
+    Sp_TwoIndex<ncolour, Symmetric>::testGenerators();
+  }
+
+  if (Sp_TwoIndex<ncolour, AntiSymmetric>::Dimension > 1) {
+    std::cout << GridLogMessage
+              << "*********************************************" << std::endl;
+    std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")"
+              << "TwoIndex AntiSymmetric: " << std::endl;
+    std::cout << GridLogMessage
+              << "*********************************************" << std::endl;
+    if (print_generators) {
+      Sp_TwoIndex<ncolour, AntiSymmetric>::printGenerators();
     }
+    Sp_TwoIndex<ncolour, AntiSymmetric>::testGenerators();
+  }
 }
-  
+
 int main(int argc, char** argv) {
   Grid_init(&argc, &argv);
-    
-  run_checks<2>(1); //  check and print Nc=2
-  run_checks<4>(1); //  check and print Nc=4
-  run_checks<6>();  //  check Nc=6
-  run_checks<8>();  //  check Nc=8
+
+  run_checks<2>(1);  //  check and print Nc=2
+  run_checks<4>(1);  //  check and print Nc=4
+  run_checks<6>();   //  check Nc=6
+  run_checks<8>();   //  check Nc=8
 
   Grid_finalize();
 }

From 621e612c30abde6100c2553d85232e45c1ce946f Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Fri, 16 Jun 2023 16:27:49 +0100
Subject: [PATCH 113/129] Fix non-zero ret on device bug

---
 tests/sp2n/Test_sp2n_lie_gen.cc | 78 +++++++++++++++++++--------------
 1 file changed, 44 insertions(+), 34 deletions(-)

diff --git a/tests/sp2n/Test_sp2n_lie_gen.cc b/tests/sp2n/Test_sp2n_lie_gen.cc
index f6c5500f..ffbbd060 100644
--- a/tests/sp2n/Test_sp2n_lie_gen.cc
+++ b/tests/sp2n/Test_sp2n_lie_gen.cc
@@ -1,55 +1,65 @@
 #include <Grid/Grid.h>
 
+#include <iostream>
+
 using namespace Grid;
 
-template <int ncolour>
-void run_checks(bool print_generators = 0) {
+template <int ngroup>
+std::ostream& operator<<(std::ostream& o, Sp<ngroup> g) {
+  return o << "Sp(" << ngroup << ") Fundamental";
+}
+
+template <int ngroup, TwoIndexSymmetry S>
+std::ostream& operator<<(std::ostream& o, Sp_TwoIndex<ngroup, S> g) {
+  return o << "Sp(" << ngroup << ") TwoIndex "
+           << (S == Symmetric ? "Symmetric" : "AntiSymmetric");
+}
+
+template <class Group>
+void run_check_on(bool print_generators = false) {
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
-  std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")"
-            << "Fundamental" << std::endl;
+  std::cout << GridLogMessage << "* Generators for " << Group() << std::endl;
   std::cout << GridLogMessage << "*********************************************"
             << std::endl;
 
   if (print_generators) {
-    Sp<ncolour>::printGenerators();
+    Group::printGenerators();
   }
-  Sp<ncolour>::testGenerators();
+  Group::testGenerators();
+}
 
-  if (Sp_TwoIndex<ncolour, Symmetric>::Dimension > 1) {
-    std::cout << GridLogMessage
-              << "*********************************************" << std::endl;
-    std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")"
-              << "TwoIndex Symmetric: " << std::endl;
-    std::cout << GridLogMessage
-              << "*********************************************" << std::endl;
-    if (print_generators) {
-      Sp_TwoIndex<ncolour, Symmetric>::printGenerators();
-    }
-    Sp_TwoIndex<ncolour, Symmetric>::testGenerators();
-  }
+template <int ngroup>
+void run_checks() {
+  run_check_on<Sp<ngroup>>();
+  run_check_on<Sp_TwoIndex<ngroup, Symmetric>>();
+  run_check_on<Sp_TwoIndex<ngroup, AntiSymmetric>>();
+}
 
-  if (Sp_TwoIndex<ncolour, AntiSymmetric>::Dimension > 1) {
-    std::cout << GridLogMessage
-              << "*********************************************" << std::endl;
-    std::cout << GridLogMessage << "* Generators for Sp(" << ncolour << ")"
-              << "TwoIndex AntiSymmetric: " << std::endl;
-    std::cout << GridLogMessage
-              << "*********************************************" << std::endl;
-    if (print_generators) {
-      Sp_TwoIndex<ncolour, AntiSymmetric>::printGenerators();
-    }
-    Sp_TwoIndex<ncolour, AntiSymmetric>::testGenerators();
-  }
+template <>
+void run_checks<2>() {
+  // Print generators because they are small enough to be actually helpful.
+  run_check_on<Sp<2>>(true);
+  run_check_on<Sp_TwoIndex<2, Symmetric>>(true);
+  // The AntiSymmetric representation is 0 dimensional. This makes problems in
+  // device code.
+}
+
+template <>
+void run_checks<4>() {
+  // Print generators because they are small enough to be actually helpful.
+  run_check_on<Sp<4>>(true);
+  run_check_on<Sp_TwoIndex<4, Symmetric>>(true);
+  run_check_on<Sp_TwoIndex<4, AntiSymmetric>>(true);
 }
 
 int main(int argc, char** argv) {
   Grid_init(&argc, &argv);
 
-  run_checks<2>(1);  //  check and print Nc=2
-  run_checks<4>(1);  //  check and print Nc=4
-  run_checks<6>();   //  check Nc=6
-  run_checks<8>();   //  check Nc=8
+  run_checks<2>();
+  run_checks<4>();
+  run_checks<6>();
+  run_checks<8>();
 
   Grid_finalize();
 }

From d80df09f3b1fae2d2cae264b7943038c5ebd6ecc Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 16 Jun 2023 19:16:46 +0100
Subject: [PATCH 114/129] consistent enable sp config flag

---
 configure.ac | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/configure.ac b/configure.ac
index 032a4729..5fadc6cf 100644
--- a/configure.ac
+++ b/configure.ac
@@ -202,9 +202,9 @@ case ${ac_Nc} in
 esac
 
 ############### Symplectic group
-AC_ARG_ENABLE([symplectic],
-    [AC_HELP_STRING([--enable-symplectic=yes|no], [enable gauge group Sp2n])],
-    [ac_ENABLE_SP=${enable_symplectic}], [ac_ENABLE_SP=no])
+AC_ARG_ENABLE([Sp],
+    [AC_HELP_STRING([--enable-Sp=yes|no], [enable gauge group Sp2n])],
+    [ac_ENABLE_SP=${enable_Sp}], [ac_ENABLE_SP=no])
 
 AM_CONDITIONAL(BUILD_SP, [ test "${ac_ENABLE_SP}X" == "yesX" ])
 
@@ -214,7 +214,7 @@ case ${ac_ENABLE_SP} in
    no)
         AC_DEFINE([Sp2n_config],[0],[gauge group SUn], [have_sp2n=false]);;
     *)
-        AC_MSG_ERROR(["--enable-symplectic is either yes or no"]);;
+        AC_MSG_ERROR(["--enable-Sp is either yes or no"]);;
 esac
 
 ############### FP16 conversions

From 96773f5254a2d090faa21515d948b2c6c71cf615 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Sun, 18 Jun 2023 12:21:39 +0100
Subject: [PATCH 115/129] Apparently forgot to remove one Lattice version

---
 Grid/qcd/utils/GaugeGroup.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index 64528f7e..de912ebd 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -324,7 +324,7 @@ class GaugeGroup {
   }
     
   template <int N>                  // Projects on the general groups U(N), Sp(2N)xZ2 i.e. determinant il allowed a complex phase.
-  accelerator_inline static void ProjectOnGeneralGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
+  static void ProjectOnGeneralGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
     for (int mu = 0; mu < Nd; mu++) {
       auto Umu = PeekIndex<LorentzIndex>(U, mu);
       ProjectOnGeneralGroup(Umu);

From 5e539e2d549ea8bf58ee50b2c0daf59969045992 Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Sun, 18 Jun 2023 12:37:51 +0100
Subject: [PATCH 116/129] Forgot some follow-ups on changed signature

---
 Grid/qcd/utils/GaugeGroup.h      | 4 ++--
 tests/sp2n/Test_project_on_Sp.cc | 2 +-
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index de912ebd..7ef93e1b 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -327,7 +327,7 @@ class GaugeGroup {
   static void ProjectOnGeneralGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
     for (int mu = 0; mu < Nd; mu++) {
       auto Umu = PeekIndex<LorentzIndex>(U, mu);
-      ProjectOnGeneralGroup(Umu);
+      Umu = ProjectOnGeneralGroup(Umu);
     }
   }
        
@@ -353,7 +353,7 @@ class GaugeGroup {
 
   template <int N>       // Projects on SU(N), Sp(2N)
   static void ProjectOnSpecialGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
-       ProjectOnGeneralGroup(Umu);
+       Umu = ProjectOnGeneralGroup(Umu);
        auto det = Determinant(Umu);
 
        det = conjugate(det);
diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 7737bc09..026e6c6e 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -93,7 +93,7 @@ void test_group_projections(T U) {
   std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
 
   U = U + Delta * identity;
-  Sp<Nc>::ProjectOnGeneralGroup(U);
+  U = Sp<Nc>::ProjectOnGeneralGroup(U);
   assert(is_element_of_sp2n_group(U));
 
   name = "ProjectOnSpecialGroup";

From de30c4e22a00119dccef67f0652eb2048e285c88 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 23 Jun 2023 10:49:41 +0100
Subject: [PATCH 117/129] minor improvements

---
 Grid/qcd/action/fermion/WilsonFermion.h       |   2 -
 Grid/qcd/action/gauge/GaugeImplTypes.h        |  30 ++---
 Grid/qcd/hmc/GenericHMCrunner.h               |   4 +-
 Grid/qcd/utils/GaugeGroup.h                   | 116 ++++++------------
 tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc     |   2 +-
 .../sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc |   2 +-
 .../Test_hmc_Sp_WilsonFundFermionGauge.cc     |   2 +-
 tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc     |   2 +-
 8 files changed, 53 insertions(+), 107 deletions(-)

diff --git a/Grid/qcd/action/fermion/WilsonFermion.h b/Grid/qcd/action/fermion/WilsonFermion.h
index 9ed5ee4a..a7a1bb69 100644
--- a/Grid/qcd/action/fermion/WilsonFermion.h
+++ b/Grid/qcd/action/fermion/WilsonFermion.h
@@ -194,7 +194,5 @@ public:
 
 typedef WilsonFermion<WilsonImplF> WilsonFermionF;
 typedef WilsonFermion<WilsonImplD> WilsonFermionD;
-//typedef WilsonFermion<SpWilsonImplF> SpWilsonFermionF;
-//typedef WilsonFermion<SpWilsonImplD> SpWilsonFermionD;
 
 NAMESPACE_END(Grid);
diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h
index 526c2173..a9af1fae 100644
--- a/Grid/qcd/action/gauge/GaugeImplTypes.h
+++ b/Grid/qcd/action/gauge/GaugeImplTypes.h
@@ -61,7 +61,6 @@ NAMESPACE_BEGIN(Grid);
   typedef typename Impl::Field Field;
 
 // hardcodes the exponential approximation in the template
-//template <class S, int Nrepresentation = Nc, int Nexp = 12 > class GaugeImplTypes {
 template <class S, int Nrepresentation = Nc, int Nexp = 12, class Group = SU<Nc> > class GaugeImplTypes {
 public:
   typedef S Simd;
@@ -71,7 +70,6 @@ public:
   template <typename vtype> using iImplGaugeLink  = iScalar<iScalar<iMatrix<vtype, Nrepresentation> > >;
   template <typename vtype> using iImplGaugeField = iVector<iScalar<iMatrix<vtype, Nrepresentation> >, Nd>;
 
-
   typedef iImplScalar<Simd>     SiteComplex;
   typedef iImplGaugeLink<Simd>  SiteLink;
   typedef iImplGaugeField<Simd> SiteField;
@@ -120,8 +118,7 @@ public:
     LinkField Pmu(P.Grid());
     Pmu = Zero();
 
-    for (int mu = 0; mu < Nd; mu++)
-    {
+    for (int mu = 0; mu < Nd; mu++) {
       Group::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
       RealD scale = ::sqrt(HMC_MOMENTUM_DENOMINATOR) ;
       Pmu = Pmu*scale;
@@ -129,11 +126,10 @@ public:
     }
   }
     
-  static inline Field projectForce(Field &P)
-    {
-        Field ret(P.Grid());
-        Group::taProj(P, ret);
-        return ret;
+  static inline Field projectForce(Field &P) {
+      Field ret(P.Grid());
+      Group::taProj(P, ret);
+      return ret;
     }
 
   static inline void update_field(Field& P, Field& U, double ep){
@@ -164,23 +160,19 @@ public:
     return Hsum.real();
   }
 
-  static inline void Project(Field &U)
-  {
-      Group::ProjectOnSpecialGroup(U);
+  static inline void Project(Field &U) {
+    Group::ProjectOnSpecialGroup(U);
   }
 
-  static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U)
-  {
-      Group::HotConfiguration(pRNG, U);
+  static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U) {
+    Group::HotConfiguration(pRNG, U);
   }
 
-  static inline void TepidConfiguration(GridParallelRNG &pRNG, Field &U)
-  {
+  static inline void TepidConfiguration(GridParallelRNG &pRNG, Field &U) {
     Group::TepidConfiguration(pRNG, U);
   }
 
-  static inline void ColdConfiguration(GridParallelRNG &pRNG, Field &U)
-  {
+  static inline void ColdConfiguration(GridParallelRNG &pRNG, Field &U) {
     Group::ColdConfiguration(pRNG, U);
   }
 
diff --git a/Grid/qcd/hmc/GenericHMCrunner.h b/Grid/qcd/hmc/GenericHMCrunner.h
index a900a0ad..1429d848 100644
--- a/Grid/qcd/hmc/GenericHMCrunner.h
+++ b/Grid/qcd/hmc/GenericHMCrunner.h
@@ -228,11 +228,11 @@ using GenericHMCRunnerHirep =
 // sp2n
 
 template <template <typename, typename, typename> class Integrator>
-using GenericSp2nHMCRunner = HMCWrapperTemplate<SpPeriodicGimplR, Integrator>;
+using GenericSpHMCRunner = HMCWrapperTemplate<SpPeriodicGimplR, Integrator>;
 
 template <class RepresentationsPolicy,
           template <typename, typename, typename> class Integrator>
-using GenericSp2nHMCRunnerHirep =
+using GenericSpHMCRunnerHirep =
                      HMCWrapperTemplate<SpPeriodicGimplR, Integrator, RepresentationsPolicy>;
 
 
diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index da09c63d..e86b07b9 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -29,8 +29,8 @@ See the full license in the file "LICENSE" in the top level distribution
 directory
 *************************************************************************************/
 /*  END LEGAL */
-#ifndef QCD_UTIL_SUN_H
-#define QCD_UTIL_SUN_H
+#ifndef QCD_UTIL_GAUGEGROUP_H
+#define QCD_UTIL_GAUGEGROUP_H
 
 // Important detail: nvcc requires all template parameters to have names.
 // This is the only reason why the second template parameter has a name.
@@ -145,6 +145,12 @@ class GaugeGroup {
   typedef Lattice<vSU2MatrixF> LatticeSU2MatrixF;
   typedef Lattice<vSU2MatrixD> LatticeSU2MatrixD;
 
+  // Private implementation details are specified in the following files:
+  // Grid/qcd/utils/SUn.impl
+  // Grid/qcd/utils/SUn.impl
+  // The public part of the interface follows below and refers to these
+  // private member functions.
+
 #include "Grid/qcd/utils/SUn.impl"
 #include "Grid/qcd/utils/Sp2n.impl"
 
@@ -161,7 +167,7 @@ class GaugeGroup {
   static void testGenerators(void) { testGenerators(group_name()); }
 
   static void printGenerators(void) {
-    for (int gen = 0; gen < AdjointDimension; gen++) {
+    for (int gen = 0; gen < AlgebraDimension; gen++) {
       Matrix ta;
       generator(gen, ta);
       std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
@@ -187,12 +193,11 @@ class GaugeGroup {
     LatticeMatrixType lie(grid);
     LatticeMatrixType la(grid);
     ComplexD ci(0.0, scale);
-    //    ComplexD cone(1.0, 0.0);
     MatrixType ta;
 
     lie = Zero();
 
-    for (int a = 0; a < AdjointDimension; a++) {
+    for (int a = 0; a < AlgebraDimension; a++) {
       random(pRNG, ca);
 
       ca = (ca + conjugate(ca)) * 0.5;
@@ -217,7 +222,7 @@ class GaugeGroup {
     Matrix ta;
 
     out = Zero();
-    for (int a = 0; a < AdjointDimension; a++) {
+    for (int a = 0; a < AlgebraDimension; a++) {
       gaussian(pRNG, ca);
       generator(a, ta);
       la = toComplex(ca) * ta;
@@ -235,7 +240,7 @@ class GaugeGroup {
     Matrix ta;
 
     out = Zero();
-    for (int a = 0; a < AdjointDimension; a++) {
+    for (int a = 0; a < AlgebraDimension; a++) {
       generator(a, ta);
       la = peekColour(h, a) * timesI(ta) * scale;
       out += la;
@@ -250,7 +255,7 @@ class GaugeGroup {
     h_out = Zero();
     Matrix Ta;
 
-    for (int a = 0; a < AdjointDimension; a++) {
+    for (int a = 0; a < AlgebraDimension; a++) {
       generator(a, Ta);
       pokeColour(h_out, -2.0 * (trace(timesI(Ta) * in)) * scale, a);
     }
@@ -322,7 +327,7 @@ class GaugeGroup {
     }
   }
     
-  template <int N>                  // Projects on the general groups U(N), Sp(2N)xZ2 i.e. determinant il allowed a complex phase.
+  template <int N>                  // Projects on the general groups U(N), Sp(2N)xZ2 i.e. determinant is allowed a complex phase.
   static void ProjectOnGeneralGroup(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
     for (int mu = 0; mu < Nd; mu++) {
       auto Umu = PeekIndex<LorentzIndex>(U, mu);
@@ -350,7 +355,7 @@ class GaugeGroup {
       return ProjectOnGeneralGroup(arg, group_name());
   }
 
-  template <int N>       // Projects on SU(N), Sp(2N)
+  template <int N>       // Projects on SU(N), Sp(2N), with unit determinant, by first projecting on general group and then enforcing unit determinant
   static void ProjectOnSpecialGroup(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
        Umu = ProjectOnGeneralGroup(Umu);
        auto det = Determinant(Umu);
@@ -375,6 +380,24 @@ class GaugeGroup {
     }
 
 };
+    
+template <int ncolour>
+using SU = GaugeGroup<ncolour, GroupName::SU>;
+
+template <int ncolour>
+using Sp = GaugeGroup<ncolour, GroupName::Sp>;
+
+typedef SU<2> SU2;
+typedef SU<3> SU3;
+typedef SU<4> SU4;
+typedef SU<5> SU5;
+
+typedef SU<Nc> FundamentalMatrices;
+    
+typedef Sp<2> Sp2;
+typedef Sp<4> Sp4;
+typedef Sp<6> Sp6;
+typedef Sp<8> Sp8;
 
 template <int N>
 LatticeComplexD Determinant(
@@ -403,32 +426,10 @@ LatticeComplexD Determinant(
 }
 
 template <int N>
-static void ProjectSUn(
-    Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
-  Umu = ProjectOnGroup(Umu);
-  auto det = Determinant(Umu);
-
-  det = conjugate(det);
-
-  for (int i = 0; i < N; i++) {
-    auto element = PeekIndex<ColourIndex>(Umu, N - 1, i);
-    element = element * det;
-    PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
-  }
-}
-
+using ProjectSUn = typename GaugeGroup<N,GroupName::SU>::ProjectOnSpecialGroup;
+    
 template <int N>
-static void ProjectSUn(
-    Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
-  GridBase *grid = U.Grid();
-  // Reunitarise
-  for (int mu = 0; mu < Nd; mu++) {
-    auto Umu = PeekIndex<LorentzIndex>(U, mu);
-    Umu = ProjectOnGroup(Umu);
-    ProjectSUn(Umu);
-    PokeIndex<LorentzIndex>(U, Umu, mu);
-  }
-}
+using ProjectSpn = typename GaugeGroup<N,GroupName::Sp>::ProjectOnSpecialGroup;
 
 // Explicit specialisation for SU(3).
 static void ProjectSU3(
@@ -463,50 +464,5 @@ static void ProjectSU3(
   }
 }
 
-template <int ncolour>
-using SU = GaugeGroup<ncolour, GroupName::SU>;
-
-template <int ncolour>
-using Sp = GaugeGroup<ncolour, GroupName::Sp>;
-
-typedef SU<2> SU2;
-typedef SU<3> SU3;
-typedef SU<4> SU4;
-typedef SU<5> SU5;
-
-typedef SU<Nc> FundamentalMatrices;
-
-template <int N>
-static void ProjectSp2n(
-    Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
-  Umu = ProjectOnSpGroup(Umu);
-  auto det = Determinant(Umu);  // ok ?
-
-  det = conjugate(det);
-
-  for (int i = 0; i < N; i++) {
-    auto element = PeekIndex<ColourIndex>(Umu, N - 1, i);
-    element = element * det;
-    PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
-  }
-}
-template <int N>
-static void ProjectSp2n(
-    Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
-  GridBase *grid = U.Grid();
-  for (int mu = 0; mu < Nd; mu++) {
-    auto Umu = PeekIndex<LorentzIndex>(U, mu);
-    Umu = ProjectOnSpGroup(Umu);
-    ProjectSp2n(Umu);
-    PokeIndex<LorentzIndex>(U, Umu, mu);
-  }
-}
-
-typedef Sp<2> Sp2;
-typedef Sp<4> Sp4;
-typedef Sp<6> Sp6;
-typedef Sp<8> Sp8;
-
-
 NAMESPACE_END(Grid);
 #endif
diff --git a/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc b/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc
index c990e73d..203c35b0 100644
--- a/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc
+++ b/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc
@@ -7,7 +7,7 @@ int main(int argc, char **argv) {
 
   Grid_init(&argc, &argv);
     
-  typedef GenericSp2nHMCRunnerHirep<TheRepresentations, MinimumNorm2> HMCWrapper;
+  typedef GenericSpHMCRunnerHirep<TheRepresentations, MinimumNorm2> HMCWrapper;
     
   typedef SpWilsonTwoIndexAntiSymmetricImplR TwoIndexFermionImplPolicy;
   typedef SpWilsonTwoIndexAntiSymmetricFermionD TwoIndexFermionAction;
diff --git a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
index 3bf32ec3..93ceb209 100644
--- a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
+++ b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
@@ -9,7 +9,7 @@ int main(int argc, char **argv) {
 
   Grid_init(&argc, &argv);
 
-  typedef GenericSp2nHMCRunnerHirep<TheRepresentations, MinimumNorm2>
+  typedef GenericSpHMCRunnerHirep<TheRepresentations, MinimumNorm2>
       HMCWrapper;
   typedef SpWilsonTwoIndexAntiSymmetricImplR FermionImplPolicy;
   typedef SpWilsonTwoIndexAntiSymmetricFermionD FermionAction;
diff --git a/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
index d2bc32bf..4ada3ae8 100644
--- a/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
+++ b/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
@@ -7,7 +7,7 @@ int main(int argc, char **argv) {
 
   Grid_init(&argc, &argv);
     
-  typedef GenericSp2nHMCRunnerHirep<TheRepresentations, MinimumNorm2> HMCWrapper; // ok
+  typedef GenericSpHMCRunnerHirep<TheRepresentations, MinimumNorm2> HMCWrapper; // ok
   typedef SpWilsonImplR FermionImplPolicy;                                    // ok
   typedef SpWilsonFermionD FermionAction;                                     // ok
   typedef typename FermionAction::FermionField FermionField;                  // ok?
diff --git a/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc b/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc
index 4fe5c50a..7c8d89be 100644
--- a/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc
+++ b/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc
@@ -37,7 +37,7 @@ int main(int argc, char **argv)
   Grid_init(&argc, &argv);
   GridLogLayout();
 
-  typedef GenericSp2nHMCRunner<MinimumNorm2> HMCWrapper;
+  typedef GenericSpHMCRunner<MinimumNorm2> HMCWrapper;
   HMCWrapper TheHMC;
 
 

From 4e6194d92a0083e9e62e6326dac6c64cf414f9a4 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 23 Jun 2023 11:03:50 +0100
Subject: [PATCH 118/129] Avoid code duplication in ProjectSUn

---
 Grid/qcd/utils/GaugeGroup.h | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index e86b07b9..1c59078f 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -426,10 +426,14 @@ LatticeComplexD Determinant(
 }
 
 template <int N>
-using ProjectSUn = typename GaugeGroup<N,GroupName::SU>::ProjectOnSpecialGroup;
+static void ProjectSUn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
+    GaugeGroup<N,GroupName::SU>::ProjectOnSpecialGroup(Umu);
+}
     
 template <int N>
-using ProjectSpn = typename GaugeGroup<N,GroupName::Sp>::ProjectOnSpecialGroup;
+static void ProjectSpn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
+    GaugeGroup<N,GroupName::Sp>::ProjectOnSpecialGroup(Umu);
+}
 
 // Explicit specialisation for SU(3).
 static void ProjectSU3(

From 063d290bd88aa30e747caf94a679b3421edd454d Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 23 Jun 2023 11:11:20 +0100
Subject: [PATCH 119/129] missing function

---
 Grid/qcd/utils/GaugeGroup.h | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/Grid/qcd/utils/GaugeGroup.h b/Grid/qcd/utils/GaugeGroup.h
index 1c59078f..117fa343 100644
--- a/Grid/qcd/utils/GaugeGroup.h
+++ b/Grid/qcd/utils/GaugeGroup.h
@@ -429,11 +429,21 @@ template <int N>
 static void ProjectSUn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
     GaugeGroup<N,GroupName::SU>::ProjectOnSpecialGroup(Umu);
 }
+  
+template <int N>
+static void ProjectSUn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,Nd> > &U) {
+    GaugeGroup<N,GroupName::SU>::ProjectOnSpecialGroup(U);
+}
     
 template <int N>
 static void ProjectSpn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
     GaugeGroup<N,GroupName::Sp>::ProjectOnSpecialGroup(Umu);
 }
+    
+template <int N>
+static void ProjectSpn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,Nd> > &U) {
+    GaugeGroup<N,GroupName::Sp>::ProjectOnSpecialGroup(U);
+}
 
 // Explicit specialisation for SU(3).
 static void ProjectSU3(

From e07fafe46ad5538ea871fd602c08b196788189c1 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 23 Jun 2023 12:18:04 +0100
Subject: [PATCH 120/129] minor adjustments to twoindex

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h | 23 ++++++++---------------
 1 file changed, 8 insertions(+), 15 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index d38ae0f9..90a7d7ae 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -22,14 +22,14 @@
 
 // Authors: David Preti, Guido Cossu
 
-#ifndef QCD_UTIL_SUN2INDEX_H
-#define QCD_UTIL_SUN2INDEX_H
+#ifndef QCD_UTIL_GAUGEGROUPTWOINDEX_H
+#define QCD_UTIL_GAUGEGROUPTWOINDEX_H
 
 NAMESPACE_BEGIN(Grid);
 
 enum TwoIndexSymmetry { Symmetric = 1, AntiSymmetric = -1 };
 
-inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
+constexpr inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
 
 namespace detail {
 
@@ -44,18 +44,14 @@ struct baseOffDiagonalSpHelper<cplx, nc, AntiSymmetric> {
     RealD tmp;
 
     if ((i == ngroup + j) && (1 <= j) && (j < ngroup)) {
-      for (int k = 0; k < ngroup; k++) {
+      for (int k = 0; k < j+1; k++) {
         if (k < j) {
-          tmp = sqrt(2 * j * (j + 1));
-          tmp = 1 / tmp;
-          tmp *= std::sqrt(2.0);
+          tmp = 1 / sqrt(j * (j + 1));
           eij()()(k, k + ngroup) = tmp;
           eij()()(k + ngroup, k) = -tmp;
         }
         if (k == j) {
-          tmp = sqrt(2 * j * (j + 1));
-          tmp = -j / tmp;
-          tmp *= std::sqrt(2.0);
+          tmp = -j / sqrt(j * (j + 1));
           eij()()(k, k + ngroup) = tmp;
           eij()()(k + ngroup, k) = -tmp;
         }
@@ -70,7 +66,6 @@ struct baseOffDiagonalSpHelper<cplx, nc, AntiSymmetric> {
               delta(i, k) * delta(j, l) - delta(j, k) * delta(i, l);
         }
     }
-
     RealD nrm = 1. / std::sqrt(2.0);
     eij = eij * nrm;
   }
@@ -216,7 +211,6 @@ public:
     Vector<iGroupMatrix<cplx> > ta(NumGenerators);
     Vector<iGroupMatrix<cplx> > eij(Dimension);
     iGroupMatrix<cplx> tmp;
-    i2indTa = Zero();
 
     for (int a = 0; a < NumGenerators; a++)
       GaugeGroup<ncolour, group_name>::generator(a, ta[a]);
@@ -224,7 +218,7 @@ public:
     for (int a = 0; a < Dimension; a++) base(a, eij[a]);
 
     for (int a = 0; a < Dimension; a++) {
-      tmp = transpose(ta[Index]) * adj(eij[a]) + adj(eij[a]) * ta[Index];
+      tmp = transpose(eij[a]*ta[Index]) + transpose(eij[a]) * ta[Index];
       for (int b = 0; b < Dimension; b++) {
         iGroupMatrix<cplx> tmp1 = tmp * eij[b];
         Complex iTr = TensorRemove(timesI(trace(tmp1)));
@@ -276,12 +270,11 @@ public:
         std::cout << GridLogMessage << "a=" << a << "b=" << b << "Tr=" << Tr
                   << std::endl;
         if (a == b) {
-          assert(imag(Tr) < 1e-8);
           assert(real(Tr) - ((ncolour + S * 2) * 0.5) < 1e-8);
         } else {
-          assert(imag(Tr) < 1e-8);
           assert(real(Tr) < 1e-8);
         }
+        assert(imag(Tr) < 1e-8);
       }
     }
     std::cout << GridLogMessage << std::endl;

From 2822487450a4504b6c914c25f62734e5d168978e Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 23 Jun 2023 14:55:23 +0100
Subject: [PATCH 121/129] rm unncessary line

---
 Grid/qcd/utils/GaugeGroupTwoIndex.h | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/Grid/qcd/utils/GaugeGroupTwoIndex.h b/Grid/qcd/utils/GaugeGroupTwoIndex.h
index 90a7d7ae..85685ddb 100644
--- a/Grid/qcd/utils/GaugeGroupTwoIndex.h
+++ b/Grid/qcd/utils/GaugeGroupTwoIndex.h
@@ -220,8 +220,7 @@ public:
     for (int a = 0; a < Dimension; a++) {
       tmp = transpose(eij[a]*ta[Index]) + transpose(eij[a]) * ta[Index];
       for (int b = 0; b < Dimension; b++) {
-        iGroupMatrix<cplx> tmp1 = tmp * eij[b];
-        Complex iTr = TensorRemove(timesI(trace(tmp1)));
+        Complex iTr = TensorRemove(timesI(trace(tmp * eij[b])));
         i2indTa()()(a, b) = iTr;
       }
     }

From f27d2083cd97c979bc178414d305fadbf0d750ca Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 23 Jun 2023 15:34:08 +0100
Subject: [PATCH 122/129] adjustments in SUn and Sp2n impl

---
 Grid/qcd/utils/SUn.impl     |   3 +-
 Grid/qcd/utils/Sp2n.impl    |  77 +-------------
 tests/sp2n/Test_Sp_start.cc | 202 +++++++++++++-----------------------
 3 files changed, 74 insertions(+), 208 deletions(-)

diff --git a/Grid/qcd/utils/SUn.impl b/Grid/qcd/utils/SUn.impl
index 01a87298..0dc5b14b 100644
--- a/Grid/qcd/utils/SUn.impl
+++ b/Grid/qcd/utils/SUn.impl
@@ -10,6 +10,7 @@
 // doesn't get found by the scripts/filelist during bootstrapping.
 
 private:
+template <ONLY_IF_SU>
 static int su2subgroups(GroupName::SU) { return (ncolour * (ncolour - 1)) / 2; }
 ////////////////////////////////////////////////////////////////////////
 // There are N^2-1 generators for SU(N).
@@ -59,7 +60,7 @@ static int su2subgroups(GroupName::SU) { return (ncolour * (ncolour - 1)) / 2; }
 //   (      -2)
 //
 ////////////////////////////////////////////////////////////////////////
-template <class cplx>
+template <class cplx, ONLY_IF_SU>
 static void generator(int lieIndex, iGroupMatrix<cplx> &ta, GroupName::SU) {
   // map lie index to which type of generator
   int diagIndex;
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index 19f2b9eb..3db63ed1 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -10,6 +10,7 @@
 // doesn't get found by the scripts/filelist during bootstrapping.
 
 private:
+template <ONLY_IF_Sp>
 static int su2subgroups(GroupName::Sp) { return (ncolour/2 * (ncolour/2 - 1)) / 2; }
 
 // Sp(2N) has N(2N+1) = 2N^2+N generators
@@ -280,82 +281,6 @@ static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupNam
 }
 
 public:
-template <ONLY_IF_Sp>
-static void OmegaInvariance(ColourMatrix &in) {
-  ColourMatrix Omega;
-  Omega = Zero();
-  const int nsp=ncolour/2;
-
-  for (int i = 0; i < nsp; i++) {
-    Omega()()(i, nsp + i) = 1.;
-    Omega()()(nsp + i, i) = -1;
-  }
-
-  auto diff = Omega - (in * Omega * transpose(in));
-  auto sdiff = norm2(diff);
-  if (norm2(sdiff) < 1e-8) {
-    std::cout << GridLogMessage
-              << "Symplectic condition satisfied: Omega invariant" << std::endl;
-  } else {
-    std::cout << GridLogMessage
-              << "WARNING!!!!!! Matrix Omega NOT left invariant by "
-              << norm2(sdiff) << std::endl;
-  }
-}
-
-template <typename GaugeField, ONLY_IF_Sp>
-static void OmegaInvariance(GaugeField &in) {
-  typedef typename GaugeField::vector_type vector_type;
-  typedef iGroupMatrix<vector_type> vMatrixType;
-  typedef Lattice<vMatrixType> LatticeMatrixType;
-
-  LatticeMatrixType U(in.Grid());
-  LatticeMatrixType OmegaLatt(in.Grid());
-  LatticeMatrixType identity(in.Grid());
-  RealD vol = in.Grid()->gSites();
-  ColourMatrix Omega;
-
-  OmegaLatt = Zero();
-  Omega = Zero();
-  identity = 1.;
-
-  U = PeekIndex<LorentzIndex>(in, 1);
-
-  OmegaInvariance(U);
-}
-
-template <ONLY_IF_Sp>
-static void OmegaInvariance(LatticeColourMatrixD &in) {
-  const int nsp=ncolour/2;
-  LatticeColourMatrixD OmegaLatt(in.Grid());
-  LatticeColourMatrixD identity(in.Grid());
-  RealD vol = in.Grid()->gSites();
-  ColourMatrix Omega;
-
-  OmegaLatt = Zero();
-  Omega = Zero();
-  identity = 1.;
-
-  for (int i = 0; i < nsp; i++) {
-    Omega()()(i, nsp + i) = 1.;
-    Omega()()(nsp + i, i) = -1;
-  }
-
-  std::cout << GridLogMessage << "Omega = " << Omega()() << std::endl;
-  OmegaLatt = OmegaLatt + (identity * Omega);
-
-  auto diff = OmegaLatt - (in * OmegaLatt * transpose(in));
-  auto sdiff = sum(diff);
-  // assert( norm2(sdiff) < 1e-8 );
-  if (norm2(sdiff) < 1e-8) {
-    std::cout << GridLogMessage
-              << "Symplectic condition satisfied: Omega invariant" << std::endl;
-  } else {
-    std::cout << GridLogMessage
-              << "WARNING!!!!!! Matrix Omega NOT left invariant by "
-              << norm2(sdiff) << std::endl;
-  }
-}
 
 template <ONLY_IF_Sp>
 static void Omega(LatticeColourMatrixD &in) {
diff --git a/tests/sp2n/Test_Sp_start.cc b/tests/sp2n/Test_Sp_start.cc
index 061acbcc..dab5819e 100644
--- a/tests/sp2n/Test_Sp_start.cc
+++ b/tests/sp2n/Test_Sp_start.cc
@@ -2,6 +2,73 @@
 
 using namespace Grid;
 
+template <typename T>
+bool has_correct_group_block_structure(const T& U) {
+  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;
+
+  const int nsp = Nc / 2;
+  Complex i(0., 1.);
+  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);
+    }
+  }
+  return true;
+};
+
+template <typename T>
+bool is_element_of_sp2n_group(const T& U) {
+  LatticeColourMatrixD aux(U.Grid());
+  LatticeColourMatrixD identity(U.Grid());
+  identity = 1.0;
+  LatticeColourMatrixD Omega(U.Grid());
+  Sp<Nc>::Omega(Omega);
+
+  std::cout << GridLogMessage << "Check matrix is non-zero " << std::endl;
+  assert(norm2(U) > 1e-8);
+
+  std::cout << GridLogMessage << "Unitary check" << std::endl;
+  aux = U * adj(U) - identity;
+  std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+  assert(norm2(aux) < 1e-8);
+
+  aux = Omega - (U * Omega * transpose(U));
+  std::cout << GridLogMessage << "Omega - U Omega transpose(U) = " << norm2(aux)
+            << std::endl;
+  assert(norm2(aux) < 1e-8);
+
+  std::cout << GridLogMessage
+            << "|Det| = " << norm2(Determinant(U)) / U.Grid()->gSites()
+            << std::endl;
+  assert(norm2(Determinant(U)) / U.Grid()->gSites() - 1 < 1e-8);
+
+  return has_correct_group_block_structure(U);
+}
+
 int main (int argc, char **argv)
 {
     Grid_init(&argc,&argv);
@@ -15,153 +82,26 @@ int main (int argc, char **argv)
     
     LatticeGaugeField Umu(&Grid);
     LatticeColourMatrixD U(&Grid);
-    LatticeColourMatrixD aux(&Grid);
-    LatticeGaugeField identity(&Grid);
-    LatticeColourMatrixD Cidentity(&Grid);
-    
-    double vol = Umu.Grid()->gSites();
-
-    const int nsp = Nc/2;
-    identity = 1.;
-    Cidentity = 1.;
     
     std::vector<int> pseeds({1,2,3,4,5});
     std::vector<int> sseeds({6,7,8,9,10});
     GridParallelRNG  pRNG(&Grid); pRNG.SeedFixedIntegers(pseeds);
     GridSerialRNG    sRNG;       sRNG.SeedFixedIntegers(sseeds);
     
-    std::cout << GridLogMessage << std::endl;
-    std::cout << GridLogMessage << "-------" << std::endl;
     std::cout << GridLogMessage << "Checking Cold Configuration " << std::endl;
-    std::cout << GridLogMessage << std::endl;
     Sp<Nc>::ColdConfiguration(pRNG,Umu);
-    Sp<Nc>::OmegaInvariance(Umu);
-    std::cout << GridLogMessage << std::endl;
-
-    Umu = Umu - identity;
     U = PeekIndex<LorentzIndex>(Umu,1);
+    assert(is_element_of_sp2n_group(U));
     
-    std::cout << GridLogMessage << "U - 1 = " << norm2(sum(U)) << std::endl;
-    assert ( norm2(sum(U)) < 1e-6);
-    std::cout << GridLogMessage << std::endl;
-    std::cout << GridLogMessage << "-------" << std::endl;
     std::cout << GridLogMessage << "Checking Hot Configuration" << std::endl;
-    std::cout << GridLogMessage << std::endl;
     Sp<Nc>::HotConfiguration(pRNG,Umu);
-    Sp<Nc>::OmegaInvariance(Umu);
-    std::cout << GridLogMessage << std::endl;
     U = PeekIndex<LorentzIndex>(Umu,1);
-    std::cout << GridLogMessage << "Checking unitarity " << std::endl;
-    aux = U*adj(U) - Cidentity;
-    assert( norm2(aux) < 1e-6 );
-    std::cout << GridLogMessage << "ok" << std::endl;
-    std::cout << GridLogMessage << std::endl;
-    std::cout << GridLogMessage << "Checking determinant " << std::endl;
-    std::cout << GridLogMessage << "Det = " <<  norm2( Determinant(U) )/vol << std::endl;
-    std::cout << GridLogMessage << std::endl;
-    std::cout << GridLogMessage << "-------" << std::endl;
+    assert(is_element_of_sp2n_group(U));
+    
     std::cout << GridLogMessage << "Checking Tepid Configuration" << std::endl;
-    std::cout << GridLogMessage << std::endl;
     Sp<Nc>::TepidConfiguration(pRNG,Umu);
-    Sp<Nc>::OmegaInvariance(Umu);
-    std::cout << GridLogMessage << std::endl;
     U = PeekIndex<LorentzIndex>(Umu,1);
-    std::cout << GridLogMessage << "Checking unitarity " << std::endl;
-    aux = U*adj(U) - Cidentity;
-    assert( norm2(aux) < 1e-6 );
-    std::cout << GridLogMessage << "ok" << std::endl;
-    std::cout << GridLogMessage << std::endl;
-    std::cout << GridLogMessage << "Checking determinant " << std::endl;
-    std::cout << GridLogMessage << "Det = " <<  norm2( Determinant(U) )/vol << std::endl;
-    std::cout << GridLogMessage << std::endl;
-    
-    
-     
-    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;
-    
-    Complex i(0., 1.);
-    
-    
-    Sp<Nc>::HotConfiguration(pRNG,Umu);
-    U = PeekIndex<LorentzIndex>(Umu,0);
-    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);
-            //std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
-            assert(  amizeroo.real() < 10e-6 );
-            amizeroo *= i;
-            assert(  amizeroo.real() < 10e-6 );
-            //std::cout << GridLogMessage << "ok " << std::endl;
-        }
-        
-    }
-    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);
-            //std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
-            assert(  amizeroo.real() < 10e-6 );
-            amizeroo *= i;
-            assert(  amizeroo.real() < 10e-6 );
-            //std::cout << GridLogMessage << "ok " << std::endl;
-        }
-    }
-    
-    std::cout << GridLogMessage << "Hot start ok " << std::endl;
-    
-    Sp<Nc>::HotConfiguration(pRNG,Umu);
-    U = PeekIndex<LorentzIndex>(Umu,0);
-    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);
-            //std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
-            assert(  amizeroo.real() < 10e-6 );
-            amizeroo *= i;
-            assert(  amizeroo.real() < 10e-6 );
-            //std::cout << GridLogMessage << "ok " << std::endl;
-        }
-        
-    }
-    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);
-            //std::cout << GridLogMessage << "diff(real,im) = " << amizeroo << std::endl;
-            assert(  amizeroo.real() < 10e-6 );
-            amizeroo *= i;
-            assert(  amizeroo.real() < 10e-6 );
-            //std::cout << GridLogMessage << "ok " << std::endl;
-        }
-    }
-    
-    std::cout << GridLogMessage << "Tepid start ok " << std::endl;
-    
-    std::cout << GridLogMessage << std::endl;
+    assert(is_element_of_sp2n_group(U));
     
     Grid_finalize();
 

From cff1f8d3b88e23a636bcdcbbc39540c14d439d12 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 23 Jun 2023 16:04:18 +0100
Subject: [PATCH 123/129] rm unused variables and formatting

---
 Grid/qcd/QCD.h                                |  1 -
 configure.ac                                  | 10 +--
 tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc     | 77 +++++++++----------
 .../sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc |  1 -
 .../Test_hmc_Sp_WilsonFundFermionGauge.cc     | 28 +++----
 tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc     |  3 -
 6 files changed, 51 insertions(+), 69 deletions(-)

diff --git a/Grid/qcd/QCD.h b/Grid/qcd/QCD.h
index a8fe9156..dbedfa7c 100644
--- a/Grid/qcd/QCD.h
+++ b/Grid/qcd/QCD.h
@@ -47,7 +47,6 @@ static constexpr int Ym = 5;
 static constexpr int Zm = 6;
 static constexpr int Tm = 7;
 
-static constexpr int isSymplectic=Sp2n_config;
 static constexpr int Nc=Config_Nc;
 static constexpr int Ns=4;
 static constexpr int Nd=4;
diff --git a/configure.ac b/configure.ac
index 5fadc6cf..3af121d4 100644
--- a/configure.ac
+++ b/configure.ac
@@ -146,7 +146,6 @@ case ${ac_TRACING} in
         AC_DEFINE([GRID_TRACING_TIMER],[1],[use TIMER]);;
     *)
 	AC_DEFINE([GRID_TRACING_NONE],[1],[no tracing]);;
-
 esac
 
 ############### fermions
@@ -185,18 +184,15 @@ AC_ARG_ENABLE([Nc],
 
 case ${ac_Nc} in
     2)
-        AC_DEFINE([Config_Nc],[2],[Gauge group Nc])
-        AC_DEFINE([Config_nsp],[1],[n of Sp2n]);;
+        AC_DEFINE([Config_Nc],[2],[Gauge group Nc]);;
     3)
         AC_DEFINE([Config_Nc],[3],[Gauge group Nc]);;
     4)
-        AC_DEFINE([Config_Nc],[4],[Gauge group Nc])
-        AC_DEFINE([Config_nsp],[2],[n of Sp2n]);;
+        AC_DEFINE([Config_Nc],[4],[Gauge group Nc]);;
     5)
         AC_DEFINE([Config_Nc],[5],[Gauge group Nc]);;
     8)
-        AC_DEFINE([Config_Nc],[8],[Gauge group Nc])
-        AC_DEFINE([Config_nsp],[4],[n of Sp2n]);;
+        AC_DEFINE([Config_Nc],[8],[Gauge group Nc]);;
     *)
       AC_MSG_ERROR(["Unsupport gauge group choice Nc = ${ac_Nc}"]);;
 esac
diff --git a/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc b/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc
index 203c35b0..25aa945b 100644
--- a/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc
+++ b/tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc
@@ -2,34 +2,34 @@
 
 int main(int argc, char **argv) {
   using namespace Grid;
-   
+
   typedef Representations< SpFundamentalRepresentation, SpTwoIndexAntiSymmetricRepresentation > TheRepresentations;
 
   Grid_init(&argc, &argv);
-    
+
   typedef GenericSpHMCRunnerHirep<TheRepresentations, MinimumNorm2> HMCWrapper;
-    
+
   typedef SpWilsonTwoIndexAntiSymmetricImplR TwoIndexFermionImplPolicy;
   typedef SpWilsonTwoIndexAntiSymmetricFermionD TwoIndexFermionAction;
   typedef typename TwoIndexFermionAction::FermionField TwoIndexFermionField;
-    
+
   typedef SpWilsonImplR FundFermionImplPolicy;                                    // ok
   typedef SpWilsonFermionD FundFermionAction;                                     // ok
   typedef typename FundFermionAction::FermionField FundFermionField;
  
   //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
-   
+
   HMCWrapper TheHMC;
-    
+
   TheHMC.Resources.AddFourDimGrid("gauge");
-    
+
   // Checkpointer definition
   CheckpointerParameters CPparams;
   CPparams.config_prefix = "ckpoint_lat";
   CPparams.rng_prefix = "ckpoint_rng";
   CPparams.saveInterval = 5;
   CPparams.format = "IEEE64BIG";
-    
+
   TheHMC.Resources.LoadNerscCheckpointer(CPparams);
 
   RNGModuleParameters RNGpar;
@@ -40,63 +40,58 @@ int main(int argc, char **argv) {
   // Construct observables
   typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
   TheHMC.Resources.AddObservable<PlaqObs>();
-    
-      typedef PolyakovMod<HMCWrapper::ImplPolicy> PolyakovObs;
-      TheHMC.Resources.AddObservable<PolyakovObs>();
-    
 
-    
+  typedef PolyakovMod<HMCWrapper::ImplPolicy> PolyakovObs;
+  TheHMC.Resources.AddObservable<PolyakovObs>();
+
   RealD beta = 6 ;
-    
+
   SpWilsonGaugeActionR Waction(beta);
-    
+
   auto GridPtr = TheHMC.Resources.GetCartesian();
   auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
-    
+
   SpFundamentalRepresentation::LatticeField fundU(GridPtr);
   SpTwoIndexAntiSymmetricRepresentation::LatticeField asU(GridPtr);
     //LatticeGaugeField U(GridPtr);
-    
+
   RealD Fundmass = -0.71;
   RealD ASmass = -0.71;
   std::vector<Complex> boundary = {-1,-1,-1,-1};
-
+    
   FundFermionAction::ImplParams bc(boundary);
   TwoIndexFermionAction::ImplParams bbc(boundary);
-    
+
   FundFermionAction FundFermOp(fundU, *GridPtr, *GridRBPtr, Fundmass, bbc);
   TwoIndexFermionAction TwoIndexFermOp(asU, *GridPtr, *GridRBPtr, ASmass, bbc);
   ConjugateGradient<FundFermionField> fCG(1.0e-8, 2000, false);
   ConjugateGradient<TwoIndexFermionField> asCG(1.0e-8, 2000, false);
   OneFlavourRationalParams Params(1.0e-6, 64.0, 2000, 1.0e-6, 16);
-    
-    
+
   TwoFlavourPseudoFermionAction<FundFermionImplPolicy> fundNf2(FundFermOp, fCG, fCG);
   TwoFlavourPseudoFermionAction<TwoIndexFermionImplPolicy> asNf2(TwoIndexFermOp, asCG, asCG);
   OneFlavourRationalPseudoFermionAction<TwoIndexFermionImplPolicy> asNf1(TwoIndexFermOp,Params);
-    
+
   fundNf2.is_smeared = false;
   asNf2.is_smeared = false;
   asNf1.is_smeared = false;
   
-    ActionLevel<HMCWrapper::Field, TheRepresentations > Level1(1);
-    Level1.push_back(&fundNf2);
-    Level1.push_back(&asNf2);
-    Level1.push_back(&asNf1);
-    
-    ActionLevel<HMCWrapper::Field, TheRepresentations > Level2(4);
-    Level2.push_back(&Waction);
-    
-    TheHMC.TheAction.push_back(Level1);
-    TheHMC.TheAction.push_back(Level2);
-    
-    TheHMC.Parameters.MD.MDsteps = 28;
-    TheHMC.Parameters.MD.trajL   = 1.0;
-    
-    TheHMC.ReadCommandLine(argc, argv);
-    TheHMC.Run();
-    
-    
+  ActionLevel<HMCWrapper::Field, TheRepresentations > Level1(1);
+  Level1.push_back(&fundNf2);
+  Level1.push_back(&asNf2);
+  Level1.push_back(&asNf1);
+
+  ActionLevel<HMCWrapper::Field, TheRepresentations > Level2(4);
+  Level2.push_back(&Waction);
+
+  TheHMC.TheAction.push_back(Level1);
+  TheHMC.TheAction.push_back(Level2);
+
+  TheHMC.Parameters.MD.MDsteps = 28;
+  TheHMC.Parameters.MD.trajL   = 1.0;
+
+  TheHMC.ReadCommandLine(argc, argv);
+  TheHMC.Run();
+
   Grid_finalize();
 }
-
diff --git a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
index 93ceb209..a9d5d68e 100644
--- a/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
+++ b/tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc
@@ -79,4 +79,3 @@ int main(int argc, char **argv) {
 
   Grid_finalize();
 }
-
diff --git a/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc b/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
index 4ada3ae8..d302911d 100644
--- a/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
+++ b/tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc
@@ -43,36 +43,32 @@ int main(int argc, char **argv) {
   auto GridPtr = TheHMC.Resources.GetCartesian();
   auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
     
-    SpFundamentalRepresentation::LatticeField U(GridPtr);
-    //LatticeGaugeField U(GridPtr);
+  SpFundamentalRepresentation::LatticeField U(GridPtr);
     
   RealD mass = -0.76;
 
   FermionAction FermOp(U, *GridPtr, *GridRBPtr, mass);
-    
- 
+
   ConjugateGradient<FermionField> CG(1.0e-8, 2000, false);
   
   TwoFlavourPseudoFermionAction<FermionImplPolicy> Nf2(FermOp, CG, CG);
     
   Nf2.is_smeared = false;
   
-    ActionLevel<HMCWrapper::Field, TheRepresentations > Level1(1);
-    Level1.push_back(&Nf2);
+  ActionLevel<HMCWrapper::Field, TheRepresentations > Level1(1);
+  Level1.push_back(&Nf2);
     
-    ActionLevel<HMCWrapper::Field, TheRepresentations > Level2(4);
-    Level2.push_back(&Waction);
+  ActionLevel<HMCWrapper::Field, TheRepresentations > Level2(4);
+  Level2.push_back(&Waction);
     
-    TheHMC.TheAction.push_back(Level1);
-    TheHMC.TheAction.push_back(Level2);
+  TheHMC.TheAction.push_back(Level1);
+  TheHMC.TheAction.push_back(Level2);
     
-    TheHMC.Parameters.MD.MDsteps = 36;
-    TheHMC.Parameters.MD.trajL   = 1.0;
-    
-    TheHMC.ReadCommandLine(argc, argv);
-    TheHMC.Run();
+  TheHMC.Parameters.MD.MDsteps = 36;
+  TheHMC.Parameters.MD.trajL   = 1.0;
     
+  TheHMC.ReadCommandLine(argc, argv);
+  TheHMC.Run();
     
   Grid_finalize();
 }
-
diff --git a/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc b/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc
index 7c8d89be..7136a7aa 100644
--- a/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc
+++ b/tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc
@@ -40,11 +40,8 @@ int main(int argc, char **argv)
   typedef GenericSpHMCRunner<MinimumNorm2> HMCWrapper;
   HMCWrapper TheHMC;
 
-
   TheHMC.Resources.AddFourDimGrid("gauge");
 
-
-
   // Checkpointer definition
   CheckpointerParameters CPparams;  
   CPparams.config_prefix = "ckpoint_lat";

From 559257bbe9d53c26cf669cf7f68797fffa870c18 Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Fri, 23 Jun 2023 16:16:48 +0100
Subject: [PATCH 124/129] better documentation and filelist names

---
 documentation/Grid.pdf   | Bin 579661 -> 579607 bytes
 documentation/manual.rst |  12 +++++-------
 scripts/filelist         |   4 ++--
 3 files changed, 7 insertions(+), 9 deletions(-)

diff --git a/documentation/Grid.pdf b/documentation/Grid.pdf
index 17dfe12e42a0d39ba624ebb77a0e1fee8e7a503d..adb408b6fc0910847df520b349296a7d5d34471f 100644
GIT binary patch
delta 8253
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diff --git a/documentation/manual.rst b/documentation/manual.rst
index 7b8881dd..0c463672 100644
--- a/documentation/manual.rst
+++ b/documentation/manual.rst
@@ -2811,18 +2811,16 @@ Specific aliases are then defined::
   typedef Sp<6> Sp6;
   typedef Sp<8> Sp8;
 
-Some methods are common to both gauge groups. The most important common external methods are::
+Some methods are common to both gauge groups. Common external methods are::
 
-  static void printGenerators(void) ;
   template <class cplx>  static void generator(int lieIndex, iSUnMatrix<cplx> &ta) ;
-  static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
-  LatticeMatrix &out,
-  Real scale = 1.0) ;
+  static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG, LatticeMatrix &out, Real scale = 1.0) ;
   static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) ;
   static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out);
   static void ColdConfiguration(GaugeField &out);
   static void taProj( const LatticeMatrixType &in,  LatticeMatrixType &out);
   static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) ;
+  static void printGenerators(void) ;
    
 Whenever needed, a different implementation of these methods for the gauge groups is achieved by overloading. For example,::
 
@@ -2846,7 +2844,7 @@ Gauge Group: SU(N)
 The specialisation of GaugeGroup to SU(N), formally part of qcd/utils/GaugeGroup.h, is found in the file qcd/utils/SUn.impl
 It contains methods that are only implemented for SU(N), and specialisations of shared methods to the special unitary group
 
-The most important external methods are::
+Public methods are::
 
   static void SubGroupHeatBath(GridSerialRNG &sRNG, GridParallelRNG &pRNG, RealD beta,  // coeff multiplying staple in action (with no 1/Nc)
                                LatticeMatrix &link,
@@ -2898,7 +2896,7 @@ Gauge Group: Sp(2N)
 The specialisation of GaugeGroup to Sp(2N), formally part of qcd/utils/GaugeGroup.h, is found in the file qcd/utils/Sp(2N).impl
 It contains methods that are only implemented for Sp(2N), and specialisations of shared methods to the special unitary group
 
-The most important external methods are::
+External methods are::
 
   static void Omega(LatticeColourMatrixD &in) // Symplectic matrix left invariant by Sp(2N)
 
diff --git a/scripts/filelist b/scripts/filelist
index d91da5f1..64e5250c 100755
--- a/scripts/filelist
+++ b/scripts/filelist
@@ -16,7 +16,7 @@ GP_FERMION_FILES=`    find . -name '*.cc' -path '*/instantiation/*' -path '*/ins
 ADJ_FERMION_FILES=`   find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/WilsonAdj*' `
 TWOIND_FERMION_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/WilsonTwoIndex*'`
 SP_FERMION_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/SpWilsonImpl*'`
-SP_TWOIND_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/SpWilsonTwo*'`
+SP_TWOIND_FERMION_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/SpWilsonTwo*'`
 
 HPPFILES=`find . -type f -name '*.hpp'`
 echo HFILES=$HFILES $HPPFILES > Make.inc
@@ -30,7 +30,7 @@ echo GP_FERMION_FILES=$GP_FERMION_FILES   >> Make.inc
 echo ADJ_FERMION_FILES=$ADJ_FERMION_FILES   >> Make.inc
 echo TWOIND_FERMION_FILES=$TWOIND_FERMION_FILES   >> Make.inc
 echo SP_FERMION_FILES=$SP_FERMION_FILES >> Make.inc
-echo SP_TWOIND_FILES=$SP_TWOIND_FILES >> Make.inc
+echo SP_TWOIND_FERMION_FILES=$SP_TWOIND_FERMION_FILES >> Make.inc
 
 # tests Make.inc
 cd $home/tests

From 34b11864b6e7c1da7b49c73935ac5a820f66109d Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Sun, 2 Jul 2023 13:25:57 +0100
Subject: [PATCH 125/129] prettiest tests

---
 .../instantiation/generate_instantiations.sh  |  14 +-
 Grid/qcd/utils/Sp2n.impl                      |  15 ++
 tests/sp2n/Test_2as_base.cc                   | 204 +++++++++---------
 3 files changed, 129 insertions(+), 104 deletions(-)

diff --git a/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh b/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh
index 7e33f634..728dc5e7 100755
--- a/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh
+++ b/Grid/qcd/action/fermion/instantiation/generate_instantiations.sh
@@ -9,19 +9,19 @@ STAG5_IMPL_LIST=""
 WILSON_IMPL_LIST=" \
 	   WilsonImplF \
 	   WilsonImplD \
-       WilsonImplD2 \
-       SpWilsonImplF \
-       SpWilsonImplD \
+	   WilsonImplD2 \
+	   SpWilsonImplF \
+	   SpWilsonImplD \
 	   WilsonAdjImplF \
 	   WilsonAdjImplD \
 	   WilsonTwoIndexSymmetricImplF \
 	   WilsonTwoIndexSymmetricImplD \
 	   WilsonTwoIndexAntiSymmetricImplF \
 	   WilsonTwoIndexAntiSymmetricImplD \
-       SpWilsonTwoIndexAntiSymmetricImplF \
-       SpWilsonTwoIndexAntiSymmetricImplD \
-       SpWilsonTwoIndexSymmetricImplF \
-       SpWilsonTwoIndexSymmetricImplD \
+	   SpWilsonTwoIndexAntiSymmetricImplF \
+	   SpWilsonTwoIndexAntiSymmetricImplD \
+	   SpWilsonTwoIndexSymmetricImplF \
+	   SpWilsonTwoIndexSymmetricImplD \
 	   GparityWilsonImplF \
 	   GparityWilsonImplD "
 
diff --git a/Grid/qcd/utils/Sp2n.impl b/Grid/qcd/utils/Sp2n.impl
index 3db63ed1..4c660d3a 100644
--- a/Grid/qcd/utils/Sp2n.impl
+++ b/Grid/qcd/utils/Sp2n.impl
@@ -300,3 +300,18 @@ static void Omega(LatticeColourMatrixD &in) {
   OmegaLatt = OmegaLatt + (identity * Omega);
   in = OmegaLatt;
 }
+
+template <ONLY_IF_Sp, class vtype, int N>
+static void Omega(iScalar<iScalar<iMatrix<vtype, N> > > &in) {
+  const int nsp=ncolour/2;
+    
+  iScalar<iScalar<iMatrix<vtype, N> > > Omega;
+  Omega = Zero();
+
+  for (int i = 0; i < nsp; i++) {
+    Omega()()(i, nsp + i) = 1.;
+    Omega()()(nsp + i, i) = -1;
+  }
+    
+  in = Omega;
+}
diff --git a/tests/sp2n/Test_2as_base.cc b/tests/sp2n/Test_2as_base.cc
index 0dda2a76..72b2e17a 100644
--- a/tests/sp2n/Test_2as_base.cc
+++ b/tests/sp2n/Test_2as_base.cc
@@ -20,106 +20,117 @@ static void check_dimensions() {
 }
 
 template<int this_nc, TwoIndexSymmetry S>
-static void S_checks() {
-    std::cout << S << std::endl;
-    std::cout << 1 + S * 3 << std::endl;
-}
+static void run_symmetry_checks() {
+    typedef typename Sp_TwoIndex<this_nc, S>::template iGroupMatrix<Complex> Matrix;
+    const int this_n = this_nc/2;
+    const int this_irrep_dim = Sp_TwoIndex<this_nc, S>::Dimension;
+    const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
+    Matrix eij_c;
+    Matrix e_sum;
+    RealD realS = S;
     
+    std::cout << GridLogMessage << "checking base has symmetry " << S << std::endl;
+    for (int a=0; a < this_irrep_dim; a++)
+    {
+        Sp_TwoIndex<this_nc, S>::base(a, eij_c);
+        e_sum = eij_c - realS * transpose(eij_c);
+        std::cout << GridLogMessage << "e_ab - (" << S << " * e_ab^T ) = " << norm2(e_sum) << std::endl;
+        assert(norm2(e_sum) < 1e-8);
+          
+    }
+}
+
+template<int this_nc, TwoIndexSymmetry S>
+static void run_traces_checks() {
+    typedef typename Sp_TwoIndex<this_nc, S>::template iGroupMatrix<Complex> Matrix;
+    const int this_n = this_nc/2;
+    const int this_irrep_dim = Sp_TwoIndex<this_nc, S>::Dimension;
+    const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
+    Matrix eij_a;
+    Matrix eij_b;
+    Matrix Omega;
+    Sp<this_nc>::Omega(Omega);
+    RealD realS = S;
+    RealD realA;
+    
+    std::cout << GridLogMessage << "Checking Tr (e^(ab) Omega ) = 0 and Tr (e^(ab) e^(cd) = delta^((ab)(cd)) ) " << std::endl;
+    for (int a=0; a < Sp_TwoIndex<this_nc, S>::Dimension; a++) {
+        Sp_TwoIndex<this_nc, S>::base(a, eij_a);
+        realA = norm2(trace(Omega*eij_a));
+        std::cout << GridLogMessage << "Checkig Omega-trace for e_{ab=" << a << "} " << std::endl;
+        //std::cout << GridLogMessage << "Tr ( Omega e_{ab=" << a << "} ) = " << realA << std::endl;
+        assert(realA < 1e-8);
+        for (int b=0; b < Sp_TwoIndex<this_nc, S>::Dimension; b++) {
+            Sp_TwoIndex<this_nc, S>::base(b, eij_b);
+            auto d_ab = TensorRemove(trace(eij_a * eij_b));
+    #if verbose
+            std::cout << GridLogMessage << "Tr( e_{ab=" << a << "} e_{cd=" << b << "} ) = " << d_ab << std::endl;
+    #endif
+            std::cout << GridLogMessage << "Checking orthonormality for e_{ab = " << a << "} " << std::endl;
+            if (a==b) {
+                assert(real(d_ab) - realS < 1e-8);
+                assert(imag(d_ab) < 1e-8);
+            } else {
+                assert(real(d_ab) < 1e-8);
+                assert(imag(d_ab) < 1e-8);
+            }
+        }
+    }
+    
+}
+
+template<int this_nc, TwoIndexSymmetry S>
+static void run_generators_checks() {
+    const int this_n = this_nc/2;
+    const int this_irrep_dim = Sp_TwoIndex<this_nc, S>::Dimension;
+    const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
+    typedef typename Sp_TwoIndex<this_nc, S>::template iGroupMatrix<Complex> Matrix;
+    int sum = 0;
+    int sum_im = 0;
+    Vector<Matrix> ta_fund(this_algebra_dim);
+    Vector<Matrix> eij(this_irrep_dim);
+    Matrix tmp_l;
+    Matrix tmp_r;
+    for (int n = 0; n < this_algebra_dim; n++)
+    {
+        Sp<this_nc>::generator(n, ta_fund[n]);
+    }
+      for (int a = 0; a < this_irrep_dim; a++)
+    {
+        Sp_TwoIndex<this_nc, S>::base(a, eij[a]);
+    }
+    for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
+    {
+        sum = 0;
+        sum_im = 0;
+        std::cout << GridLogMessage <<  "generator number " << gen_id << std::endl;
+        for (int a = 0; a < this_irrep_dim; a++)
+        {
+          
+            tmp_l = adj(eij[a])*ta_fund[gen_id]*eij[a];
+            tmp_r = adj(eij[a])*eij[a]*transpose(ta_fund[gen_id]);
+    #if verbose
+            std::cout << GridLogMessage << " as_indx = " << a << " eDag T_F e = " << std::endl << tmp_l << std::endl;
+            std::cout << GridLogMessage << " as_indx = " << a << " eDag e T_F^T = " << std::endl << tmp_r << std::endl;
+    #endif
+            //std::cout << GridLogMessage << " as_indx = " << a << " Tr(eDag T_F e + eDag e T_F^T) = " << TensorRemove(trace(tmp_l+tmp_r)) << std::endl;
+            sum += real(TensorRemove(trace(tmp_l+tmp_r)));
+            sum_im += imag(TensorRemove(trace(tmp_l+tmp_r)));
+        }
+        std::cout << GridLogMessage << "re-evaluated trace of the generator " << gen_id << " is " << sum << " " << sum_im << std::endl;
+        assert ( sum < 1e-8) ;
+        assert ( sum_im < 1e-8) ;
+    }
+    
+}
     
 template<int this_nc, TwoIndexSymmetry S>
 static void run_base_checks() {
-      std::cout << GridLogMessage << " ****** " << std::endl;
-      std::cout << GridLogMessage << "Running checks for Nc = " << this_nc << " TwoIndex Symmetry = " << S << std::endl;
-      const int this_n = this_nc/2;
-      const int this_irrep_dim = Sp_TwoIndex<this_nc, S>::Dimension;
-      const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
-      typedef typename Sp_TwoIndex<this_nc, S>::template iGroupMatrix<Complex> Matrix;
-      typedef typename Sp_TwoIndex<this_nc, S>::template iGroupTwoIndexMatrix<Complex> ASMatrix;
-      RealD realS = S;
-      
-      Matrix Omega;
-      Matrix eij_a;
-      Matrix eij_b;
-      Matrix eij_c;
-      Matrix e_sum;
-      Omega = Zero();
-      for (int i = 0; i < this_n; i++)
-      {
-        Omega()()(i, this_n + i) = 1.;
-        Omega()()(this_n + i, i) = -1;
-      }
-
-      RealD realA;
-
-      std::cout << GridLogMessage << "checking base has symmetry " << S << std::endl;
-      for (int a=0; a < this_irrep_dim; a++)
-      {
-          Sp_TwoIndex<this_nc, S>::base(a, eij_c);
-          e_sum = eij_c - realS * transpose(eij_c);
-          std::cout << GridLogMessage << "e_ab - (" << S << " * e_ab^T ) = " << norm2(e_sum) << std::endl;
-          assert(norm2(e_sum) < 1e-8);
-            
-      }
-      std::cout << GridLogMessage << "Checking Tr (e^(ab) Omega ) = 0 and Tr (e^(ab) e^(cd) = delta^((ab)(cd)) ) " << std::endl;
-      for (int a=0; a < Sp_TwoIndex<this_nc, S>::Dimension; a++) {
-          Sp_TwoIndex<this_nc, S>::base(a, eij_a);
-          realA = norm2(trace(Omega*eij_a));
-          std::cout << GridLogMessage << "Checkig Omega-trace for e_{ab=" << a << "} " << std::endl;
-          //std::cout << GridLogMessage << "Tr ( Omega e_{ab=" << a << "} ) = " << realA << std::endl;
-          assert(realA < 1e-8);
-          for (int b=0; b < Sp_TwoIndex<this_nc, S>::Dimension; b++) {
-              Sp_TwoIndex<this_nc, S>::base(b, eij_b);
-              auto d_ab = TensorRemove(trace(eij_a * eij_b));
-    #if verbose
-              std::cout << GridLogMessage << "Tr( e_{ab=" << a << "} e_{cd=" << b << "} ) = " << d_ab << std::endl;
-    #endif
-              std::cout << GridLogMessage << "Checking orthonormality for e_{ab = " << a << "} " << std::endl;
-              if (a==b) {
-                  assert(real(d_ab) - realS < 1e-8);
-                  assert(imag(d_ab) < 1e-8);
-              } else {
-                  assert(real(d_ab) < 1e-8);
-                  assert(imag(d_ab) < 1e-8);
-              }
-          }
-      }
-
-      int sum = 0;
-      int sum_im = 0;
-      Vector<Matrix> ta_fund(this_algebra_dim);
-      Vector<Matrix> eij(this_irrep_dim);
-      Matrix tmp_l;
-      Matrix tmp_r;
-      for (int n = 0; n < this_algebra_dim; n++)
-      {
-          Sp<this_nc>::generator(n, ta_fund[n]);
-      }
-      for (int a = 0; a < this_irrep_dim; a++)
-      {
-          Sp_TwoIndex<this_nc, S>::base(a, eij[a]);
-      }
-      for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
-      {
-          sum = 0;
-          sum_im = 0;
-          std::cout << GridLogMessage <<  "generator number " << gen_id << std::endl;
-          for (int a = 0; a < this_irrep_dim; a++)
-          {
-          
-              tmp_l = adj(eij[a])*ta_fund[gen_id]*eij[a];
-              tmp_r = adj(eij[a])*eij[a]*transpose(ta_fund[gen_id]);
-    #if verbose
-              std::cout << GridLogMessage << " as_indx = " << a << " eDag T_F e = " << std::endl << tmp_l << std::endl;
-              std::cout << GridLogMessage << " as_indx = " << a << " eDag e T_F^T = " << std::endl << tmp_r << std::endl;
-    #endif
-              //std::cout << GridLogMessage << " as_indx = " << a << " Tr(eDag T_F e + eDag e T_F^T) = " << TensorRemove(trace(tmp_l+tmp_r)) << std::endl;
-              sum += real(TensorRemove(trace(tmp_l+tmp_r)));
-              sum_im += imag(TensorRemove(trace(tmp_l+tmp_r)));
-          }
-          std::cout << GridLogMessage << "re-evaluated trace of the generator " << gen_id << " is " << sum << " " << sum_im << std::endl;
-          assert ( sum < 1e-8) ;
-          assert ( sum_im < 1e-8) ;
-      }
+    std::cout << GridLogMessage << " ****** " << std::endl;
+    std::cout << GridLogMessage << "Running checks for Nc = " << this_nc << " TwoIndex Symmetry = " << S << std::endl;
+    run_symmetry_checks<this_nc, S>();
+    run_traces_checks<this_nc, S>();
+    run_generators_checks<this_nc, S>();
 }
 
 int main(int argc, char** argv) {
@@ -136,4 +147,3 @@ int main(int argc, char** argv) {
     run_base_checks<8, Symmetric>();
     run_base_checks<8, AntiSymmetric>();
 }
-

From b92428f05fe04574e348a80b34e2f7ac366630fc Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Sun, 2 Jul 2023 13:34:03 +0100
Subject: [PATCH 126/129] better test

---
 tests/sp2n/Test_2as_base.cc | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/tests/sp2n/Test_2as_base.cc b/tests/sp2n/Test_2as_base.cc
index 72b2e17a..62e86609 100644
--- a/tests/sp2n/Test_2as_base.cc
+++ b/tests/sp2n/Test_2as_base.cc
@@ -69,11 +69,11 @@ static void run_traces_checks() {
             std::cout << GridLogMessage << "Checking orthonormality for e_{ab = " << a << "} " << std::endl;
             if (a==b) {
                 assert(real(d_ab) - realS < 1e-8);
-                assert(imag(d_ab) < 1e-8);
             } else {
                 assert(real(d_ab) < 1e-8);
-                assert(imag(d_ab) < 1e-8);
             }
+            assert(imag(d_ab) < 1e-8);
+            assert(imag(d_ab) < 1e-8);
         }
     }
     
@@ -93,11 +93,11 @@ static void run_generators_checks() {
     Matrix tmp_r;
     for (int n = 0; n < this_algebra_dim; n++)
     {
-        Sp<this_nc>::generator(n, ta_fund[n]);
+        Sp<this_nc>::generator(n, ta_fund[n]);  // generators in the fundamental
     }
       for (int a = 0; a < this_irrep_dim; a++)
     {
-        Sp_TwoIndex<this_nc, S>::base(a, eij[a]);
+        Sp_TwoIndex<this_nc, S>::base(a, eij[a]);   // base functions e_ij^a for upgrading gauge links from fund to 2-index
     }
     for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
     {
@@ -139,7 +139,7 @@ int main(int argc, char** argv) {
     check_dimensions<6>();
     check_dimensions<8>();
     
-    run_base_checks<2, Symmetric>();
+    run_base_checks<2, Symmetric>();    // For Nc=2 the AS is the singlet
     run_base_checks<4, Symmetric>();
     run_base_checks<4, AntiSymmetric>();
     run_base_checks<6, Symmetric>();

From 075b9d22d0a26b1b1aa2be166937c30bd36cd2fd Mon Sep 17 00:00:00 2001
From: Alessandro Lupo <Alessandro.Lupo@ed.ac.uk>
Date: Sun, 2 Jul 2023 13:58:31 +0100
Subject: [PATCH 127/129] adjoint rep implemented as 2indx symmetric

---
 Grid/qcd/action/fermion/WilsonImpl.h | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/Grid/qcd/action/fermion/WilsonImpl.h b/Grid/qcd/action/fermion/WilsonImpl.h
index 55d7d084..07248160 100644
--- a/Grid/qcd/action/fermion/WilsonImpl.h
+++ b/Grid/qcd/action/fermion/WilsonImpl.h
@@ -275,6 +275,8 @@ typedef WilsonImpl<vComplex,  SpTwoIndexSymmetricRepresentation, CoeffReal > SpW
 typedef WilsonImpl<vComplexF, SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexSymmetricImplF;  // Float
 typedef WilsonImpl<vComplexD, SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexSymmetricImplD;  // Double
 
+typedef WilsonImpl<vComplex,  SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonAdjImplR;  // Real.. whichever prec    // adj = 2indx symmetric for Sp(2N)
+typedef WilsonImpl<vComplexF, SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonAdjImplF;  // Float     // adj = 2indx symmetric for Sp(2N)
+typedef WilsonImpl<vComplexD, SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonAdjImplD;  // Double    // adj = 2indx symmetric for Sp(2N)
 
 NAMESPACE_END(Grid);
-

From f7b79cdd4533f3b4ffa80126ae37314d79f8b61a Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Mon, 3 Jul 2023 18:00:32 +0100
Subject: [PATCH 128/129] Added test for ProjectSpn

---
 tests/sp2n/Test_project_on_Sp.cc | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/tests/sp2n/Test_project_on_Sp.cc b/tests/sp2n/Test_project_on_Sp.cc
index 026e6c6e..63032a68 100644
--- a/tests/sp2n/Test_project_on_Sp.cc
+++ b/tests/sp2n/Test_project_on_Sp.cc
@@ -103,6 +103,14 @@ void test_group_projections(T U) {
   U = U + Delta * identity;
   Sp<Nc>::ProjectOnSpecialGroup(U);
   assert(is_element_of_sp2n_group(U));
+
+  name = "ProjectSpn";
+  std::cout << GridLogMessage << "Testing " << name << std::endl;
+  std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+
+  U = U + Delta * identity;
+  ProjectSpn(U);
+  assert(is_element_of_sp2n_group(U));
 }
 
 template <typename T>

From 3a29af0ce4d94809b4be4132b21c2f44c8a85a8f Mon Sep 17 00:00:00 2001
From: Julian Lenz <j.j.lenz@swansea.ac.uk>
Date: Tue, 4 Jul 2023 16:08:44 +0100
Subject: [PATCH 129/129] Fixed linker error

---
 Grid/Makefile.am | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Grid/Makefile.am b/Grid/Makefile.am
index 502fcbf2..8472dd71 100644
--- a/Grid/Makefile.am
+++ b/Grid/Makefile.am
@@ -68,7 +68,7 @@ if BUILD_FERMION_REPS
 endif
 if BUILD_SP
     extra_sources+=$(SP_FERMION_FILES)
-    extra_sources+=$(SP_TWOIND_FILES)
+    extra_sources+=$(SP_TWOIND_FERMION_FILES)
 endif
 
 lib_LIBRARIES = libGrid.a