diff --git a/tests/Test_cayley_coarsen_support.cc b/tests/Test_cayley_coarsen_support.cc
index 064f5f13..b68a5cc3 100644
--- a/tests/Test_cayley_coarsen_support.cc
+++ b/tests/Test_cayley_coarsen_support.cc
@@ -21,9 +21,7 @@ int main (int argc, char ** argv)
 {
   Grid_init(&argc,&argv);
 
-
-
-  const int Ls=4;
+  const int Ls=8;
 
   GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(), GridDefaultSimd(Nd,vComplexF::Nsimd()),GridDefaultMpi());
   GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
@@ -41,8 +39,10 @@ int main (int argc, char ** argv)
 
   std::vector<int> seeds4({1,2,3,4});
   std::vector<int> seeds5({5,6,7,8});
-  GridParallelRNG          RNG5(FGrid);  RNG5.SeedFixedIntegers(seeds5);
-  GridParallelRNG          RNG4(UGrid);  RNG4.SeedFixedIntegers(seeds4);
+  std::vector<int> cseeds({5,6,7,8});
+  GridParallelRNG          RNG5(FGrid);   RNG5.SeedFixedIntegers(seeds5);
+  GridParallelRNG          RNG4(UGrid);   RNG4.SeedFixedIntegers(seeds4);
+  GridParallelRNG          CRNG(Coarse5d);CRNG.SeedFixedIntegers(cseeds);
 
   LatticeFermion    src(FGrid); random(RNG5,src);
   LatticeFermion result(FGrid); result=zero;
@@ -50,31 +50,33 @@ int main (int argc, char ** argv)
   LatticeFermion    tmp(FGrid);
   LatticeFermion    err(FGrid);
   LatticeGaugeField Umu(UGrid); random(RNG4,Umu);
+
 #if 0
   std::vector<LatticeColourMatrix> U(4,UGrid);
   Umu=zero;
   Complex cone(1.0,0.0);
   for(int nn=0;nn<Nd;nn++){
     if(1) {
-      if (nn!=0) { U[nn]=zero; std::cout << "zeroing gauge field in dir "<<nn<<std::endl; }
-      else       { U[nn] = cone;std::cout << "unit gauge field in dir "<<nn<<std::endl; }
+      if (nn>2) { U[nn]=zero; std::cout << "zeroing gauge field in dir "<<nn<<std::endl; }
+      else      { U[nn]=cone; std::cout << "unit gauge field in dir "<<nn<<std::endl; }
     }
     pokeIndex<LorentzIndex>(Umu,U[nn],nn);
   }
 #endif  
+
   RealD mass=0.5;
   RealD M5=1.8;
 
   DomainWallFermion Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5);
-  Gamma5HermitianLinearOperator<DomainWallFermion,LatticeFermion> HermIndefOp(Ddwf);
+  Gamma5R5HermitianLinearOperator<DomainWallFermion,LatticeFermion> HermIndefOp(Ddwf);
 
   HermIndefOp.Op(src,ref);
   HermIndefOp.OpDiag(src,result);
   
   for(int d=0;d<4;d++){
-    HermIndefOp.OpDir(src,tmp,d,+1); result=result+tmp; 
+    HermIndefOp.OpDir(src,tmp,d+1,+1); result=result+tmp; 
     std::cout<<"dir "<<d<<" tmp "<<norm2(tmp)<<std::endl;
-    HermIndefOp.OpDir(src,tmp,d,-1); result=result+tmp;
+    HermIndefOp.OpDir(src,tmp,d+1,-1); result=result+tmp;
     std::cout<<"dir "<<d<<" tmp "<<norm2(tmp)<<std::endl;
   }
   err = result-ref;
@@ -82,32 +84,91 @@ int main (int argc, char ** argv)
 
   const int nbasis = 2;
   std::vector<LatticeFermion> subspace(nbasis,FGrid);
-  
+  LatticeFermion prom(FGrid);
+
   for(int b=0;b<nbasis;b++){
     random(RNG5,subspace[b]);
   }
   std::cout << "Computed randoms"<< std::endl;
 
-  CoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LittleDiracOp(*Coarse5d);
+  typedef CoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector CoarseVector;
+
+  LittleDiracOperator LittleDiracOp(*Coarse5d);
 
   LittleDiracOp.CoarsenOperator(FGrid,HermIndefOp,subspace);
-
-  typedef   Lattice<iVector<vComplex,nbasis > > coarse_vec;
   
-  coarse_vec c_src (Coarse5d);  c_src= zero;
-  coarse_vec c_res (Coarse5d);
+  CoarseVector c_src (Coarse5d);
+  CoarseVector c_res (Coarse5d);
+  CoarseVector c_proj(Coarse5d);
   
-  Complex one(1.0);
-  c_src = one;  // 1 in every element for vector 1.
-
   //  TODO
   // -- promote from subspace, check we get the vector we wanted
   // -- apply ldop; check we get the same as inner product of M times big vec
   // -- pick blocks one by one. Evaluate matrix elements.
+  Complex one(1.0);
+  c_src = one;  // 1 in every element for vector 1.
+  
+  blockPromote(c_src,err,subspace);
+
+
+  prom=zero;
+  for(int b=0;b<nbasis;b++){
+    prom=prom+subspace[b];
+  }
+  err=err-prom; 
+  std::cout<<"Promoted back from subspace err "<<norm2(err)<<std::endl;
+
+  HermIndefOp.HermOp(prom,tmp);
+  blockProject(c_proj,tmp,subspace);
+
+  LittleDiracOp.M(c_src,c_res);
+
+  c_proj = c_proj - c_res;
+  std::cout<<"Representation of ldop within subspace "<<norm2(c_proj)<<std::endl;
 
   std::cout << "Multiplying by LittleDiracOp "<< std::endl;
   LittleDiracOp.M(c_src,c_res);
 
+  std::cout<<"Testing hermiticity explicitly by inspecting matrix elements"<<std::endl;
+  LittleDiracOp.AssertHermitian();
+
+  std::cout << "Testing Hermiticity stochastically "<< std::endl;
+  CoarseVector phi(Coarse5d);
+  CoarseVector chi(Coarse5d);
+  CoarseVector Aphi(Coarse5d);
+  CoarseVector Achi(Coarse5d);
+
+  random(CRNG,phi);
+  random(CRNG,chi);
+
+
+  std::cout<<"Made randoms"<<std::endl;
+
+  LittleDiracOp.M(phi,Aphi);
+  LittleDiracOp.Mdag(chi,Achi);
+
+  ComplexD pAc = innerProduct(chi,Aphi);
+  ComplexD cAp = innerProduct(phi,Achi);
+  ComplexD cAc = innerProduct(chi,Achi);
+  ComplexD pAp = innerProduct(phi,Aphi);
+
+  std::cout<< "pAc "<<pAc<<" cAp "<< cAp<< " diff "<<pAc-adj(cAp)<<std::endl;
+
+  std::cout<< "pAp "<<pAp<<" cAc "<< cAc<<"Should be real"<< std::endl;
+
+  std::cout<<"Testing linearity"<<std::endl;
+  CoarseVector PhiPlusChi(Coarse5d);
+  CoarseVector APhiPlusChi(Coarse5d);
+  CoarseVector linerr(Coarse5d);
+  PhiPlusChi = phi+chi;
+  LittleDiracOp.M(PhiPlusChi,APhiPlusChi);
+
+  linerr= APhiPlusChi-Aphi;
+  linerr= linerr-Achi;
+  std::cout<<"**Diff "<<norm2(linerr)<<std::endl;
+
+
   std::cout << "Done "<< std::endl;
   Grid_finalize();
 }