diff --git a/tests/Test_cayley_ldop_cg.cc b/tests/Test_cayley_ldop_cg.cc
new file mode 100644
index 00000000..b146002d
--- /dev/null
+++ b/tests/Test_cayley_ldop_cg.cc
@@ -0,0 +1,136 @@
+#include <Grid.h>
+
+using namespace std;
+using namespace Grid;
+using namespace Grid::QCD;
+
+
+template<class d>
+struct scal {
+  d internal;
+};
+
+  Gamma::GammaMatrix Gmu [] = {
+    Gamma::GammaX,
+    Gamma::GammaY,
+    Gamma::GammaZ,
+    Gamma::GammaT
+  };
+
+double lowpass(double x)
+{
+  return pow(x*x+1.0,-2);
+}
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  Chebyshev<LatticeFermion> filter(-150.0, 150.0,16, lowpass);
+  ofstream csv(std::string("filter.dat"),std::ios::out|std::ios::trunc);
+  filter.csv(csv);
+  csv.close();
+
+  const int Ls=8;
+
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(), GridDefaultSimd(Nd,vComplexF::Nsimd()),GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Construct a coarsened grid
+  std::vector<int> clatt = GridDefaultLatt();
+  for(int d=0;d<clatt.size();d++){
+    clatt[d] = clatt[d]/2;
+  }
+  GridCartesian *Coarse4d =  SpaceTimeGrid::makeFourDimGrid(clatt, GridDefaultSimd(Nd,vComplexF::Nsimd()),GridDefaultMpi());;
+  GridCartesian *Coarse5d =  SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+
+  std::vector<int> seeds4({1,2,3,4});
+  std::vector<int> seeds5({5,6,7,8});
+  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); gaussian(RNG5,src);
+  LatticeFermion result(FGrid); result=zero;
+  LatticeFermion    ref(FGrid); ref=zero;
+  LatticeFermion    tmp(FGrid);
+  LatticeFermion    err(FGrid);
+  LatticeGaugeField Umu(UGrid); gaussian(RNG4,Umu);
+
+
+  //random(RNG4,Umu);
+  NerscField header;
+  std::string file("./ckpoint_lat.400");
+  readNerscConfiguration(Umu,header,file);
+
+#if 0
+  LatticeColourMatrix U(UGrid);
+  U=zero;
+  for(int nn=0;nn<Nd;nn++){
+    if (nn>2) {
+      pokeIndex<LorentzIndex>(Umu,U,nn);
+    }
+  }
+#endif  
+  RealD mass=0.1;
+  RealD M5=1.0;
+
+  DomainWallFermion Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5);
+  Gamma5R5HermitianLinearOperator<DomainWallFermion,LatticeFermion> HermIndefOp(Ddwf);
+
+  const int nbasis = 8;
+  std::vector<LatticeFermion> subspace(nbasis,FGrid);
+  LatticeFermion noise(FGrid);
+  LatticeFermion ms(FGrid);
+  for(int b=0;b<nbasis;b++){
+    Gamma g5(Gamma::Gamma5);
+    gaussian(RNG5,noise);
+    RealD scale = pow(norm2(noise),-0.5); 
+    noise=noise*scale;
+
+    HermIndefOp.HermOp(noise,ms); std::cout << "Noise    "<<b<<" Ms "<<norm2(ms)<< " "<< norm2(noise)<<std::endl;
+
+
+    //    filter(HermIndefOp,noise,subspace[b]);
+    // inverse iteration
+    MdagMLinearOperator<DomainWallFermion,LatticeFermion> HermDefOp(Ddwf);
+    ConjugateGradient<LatticeFermion> CG(1.0e-5,10000);
+
+    for(int i=0;i<4;i++){
+
+      CG(HermDefOp,noise,subspace[b]);
+      noise = subspace[b];
+
+      scale = pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+      HermDefOp.HermOp(noise,ms); std::cout << "filt    "<<b<<" <u|H|u> "<<norm2(ms)<< " "<< norm2(noise)<<std::endl;
+    }
+
+    subspace[b] = noise;
+    HermIndefOp.HermOp(subspace[b],ms); std::cout << "Filtered "<<b<<" Ms "<<norm2(ms)<< " "<<norm2(subspace[b]) <<std::endl;
+  }
+  std::cout << "Computed randoms"<< std::endl;
+
+  typedef CoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector CoarseVector;
+
+  LittleDiracOperator LittleDiracOp(*Coarse5d);
+  LittleDiracOp.CoarsenOperator(FGrid,HermIndefOp,subspace);
+  
+  CoarseVector c_src (Coarse5d);
+  CoarseVector c_res (Coarse5d);
+  gaussian(CRNG,c_src);
+  c_res=zero;
+
+  std::cout << "Solving CG on coarse space "<< std::endl;
+  MdagMLinearOperator<LittleDiracOperator,CoarseVector> PosdefLdop(LittleDiracOp);
+  ConjugateGradient<CoarseVector> CG(1.0e-8,10000);
+  CG(PosdefLdop,c_src,c_res);
+
+  std::cout << "Done "<< std::endl;
+  Grid_finalize();
+}