Merge branch 'develop' of https://github.com/paboyle/Grid into develop

Need to consolidate files.
Plan: Make this version able to go virtual base, then absorb chulwoos
version when it is proven

Grid/GridCore.h

@@ -59,6 +59,7 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
 #include <Grid/lattice/Lattice.h>      
 #include <Grid/cshift/Cshift.h>       
 #include <Grid/stencil/Stencil.h>      
+#include <Grid/stencil/GeneralLocalStencil.h>      
 #include <Grid/parallelIO/BinaryIO.h>
 #include <Grid/algorithms/Algorithms.h>   
 NAMESPACE_CHECK(GridCore)

Grid/algorithms/Algorithms.h

@@ -29,6 +29,9 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 #ifndef GRID_ALGORITHMS_H
 #define GRID_ALGORITHMS_H
 
+NAMESPACE_CHECK(blas);
+#include <Grid/algorithms/blas/BatchedBlas.h>
+
 NAMESPACE_CHECK(algorithms);
 #include <Grid/algorithms/SparseMatrix.h>
 #include <Grid/algorithms/LinearOperator.h>
@@ -44,7 +47,10 @@ NAMESPACE_CHECK(SparseMatrix);
 #include <Grid/algorithms/approx/RemezGeneral.h>
 #include <Grid/algorithms/approx/ZMobius.h>
 NAMESPACE_CHECK(approx);
-#include <Grid/algorithms/iterative/Deflation.h>
+#include <Grid/algorithms/deflation/Deflation.h>
+#include <Grid/algorithms/deflation/MultiRHSBlockProject.h>
+#include <Grid/algorithms/deflation/MultiRHSDeflation.h>
+NAMESPACE_CHECK(deflation);
 #include <Grid/algorithms/iterative/ConjugateGradient.h>
 NAMESPACE_CHECK(ConjGrad);
 #include <Grid/algorithms/iterative/BiCGSTAB.h>
@@ -67,10 +73,11 @@ NAMESPACE_CHECK(BiCGSTAB);
 #include <Grid/algorithms/iterative/MixedPrecisionFlexibleGeneralisedMinimalResidual.h>
 #include <Grid/algorithms/iterative/ImplicitlyRestartedLanczos.h>
 #include <Grid/algorithms/iterative/PowerMethod.h>
-
+#include <Grid/algorithms/iterative/AdefGeneric.h>
+#include <Grid/algorithms/iterative/AdefMrhs.h>
 NAMESPACE_CHECK(PowerMethod);
-#include <Grid/algorithms/CoarsenedMatrix.h>
+#include <Grid/algorithms/multigrid/MultiGrid.h>
-NAMESPACE_CHECK(CoarsendMatrix);
+NAMESPACE_CHECK(multigrid);
 #include <Grid/algorithms/FFT.h>
 
 #endif

Grid/algorithms/LinearOperator.h

@@ -145,6 +145,44 @@ public:
   }
 };
 
+////////////////////////////////////////////////////////////////////
+// Create a shifted HermOp
+////////////////////////////////////////////////////////////////////
+template<class Field>
+class ShiftedHermOpLinearOperator : public LinearOperatorBase<Field> {
+  LinearOperatorBase<Field> &_Mat;
+  RealD _shift;
+public:
+  ShiftedHermOpLinearOperator(LinearOperatorBase<Field> &Mat,RealD shift): _Mat(Mat), _shift(shift){};
+  // Support for coarsening to a multigrid
+  void OpDiag (const Field &in, Field &out) {
+    assert(0);
+  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {
+    assert(0);
+  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){
+    assert(0);
+  };
+  void Op     (const Field &in, Field &out){
+    HermOp(in,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    HermOp(in,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    _Mat.HermOp(in,out);
+    out = out + _shift*in;
+  }
+};
+
+
 ////////////////////////////////////////////////////////////////////
 // Wrap an already herm matrix
 ////////////////////////////////////////////////////////////////////

Grid/algorithms/approx/Chebyshev.h

@@ -90,9 +90,8 @@ public:
     order=_order;
       
     if(order < 2) exit(-1);
-    Coeffs.resize(order);
+    Coeffs.resize(order,0.0);
-    Coeffs.assign(0.,order);
+    Coeffs[order-1] = 1.0;
-    Coeffs[order-1] = 1.;
   };
   
   // PB - more efficient low pass drops high modes above the low as 1/x uses all Chebyshev's.

Grid/algorithms/approx/MultiShiftFunction.h

@@ -40,7 +40,7 @@ public:
   RealD norm;
   RealD lo,hi;
 
-  MultiShiftFunction(int n,RealD _lo,RealD _hi): poles(n), residues(n), lo(_lo), hi(_hi) {;};
+  MultiShiftFunction(int n,RealD _lo,RealD _hi): poles(n), residues(n), tolerances(n), lo(_lo), hi(_hi) {;};
   RealD approx(RealD x);
   void csv(std::ostream &out);
   void gnuplot(std::ostream &out);

Grid/algorithms/blas/BatchedBlas.h

@@ -42,6 +42,7 @@ Author: Peter Boyle <pboyle@bnl.gov>
 #ifdef GRID_ONE_MKL
 #include <oneapi/mkl.hpp>
 #endif
+
 ///////////////////////////////////////////////////////////////////////	  
 // Need to rearrange lattice data to be in the right format for a
 // batched multiply. Might as well make these static, dense packed
@@ -633,7 +634,6 @@ public:
     deviceVector<ComplexD> beta_p(1);
     acceleratorCopyToDevice((void *)&alpha,(void *)&alpha_p[0],sizeof(ComplexD));
     acceleratorCopyToDevice((void *)&beta ,(void *)&beta_p[0],sizeof(ComplexD));
-
     //    std::cout << "blasZgemmStridedBatched mnk  "<<m<<","<<n<<","<<k<<" count "<<batchCount<<std::endl;
     //    std::cout << "blasZgemmStridedBatched ld   "<<lda<<","<<ldb<<","<<ldc<<std::endl;
     //    std::cout << "blasZgemmStridedBatched sd   "<<sda<<","<<sdb<<","<<sdc<<std::endl;

Grid/algorithms/deflation/MultiRHSBlockProject.h

@@ -0,0 +1,513 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: MultiRHSDeflation.h
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    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 */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+
+/* 
+   MultiRHS block projection
+
+   Import basis -> nblock x nbasis x  (block x internal) 
+   Import vector of fine lattice objects -> nblock x nrhs x (block x internal) 
+
+   => coarse_(nrhs x nbasis )^block = via batched GEMM
+
+//template<class vobj,class CComplex,int nbasis,class VLattice>
+//inline void blockProject(Lattice<iVector<CComplex,nbasis > > &coarseData,
+//			   const VLattice &fineData,
+//			   const VLattice &Basis)
+*/
+
+template<class Field>
+class MultiRHSBlockProject
+{
+public:
+
+  typedef typename Field::scalar_type   scalar;
+  typedef typename Field::scalar_object scalar_object;
+  typedef Field Fermion;
+
+  int nbasis;
+  GridBase *coarse_grid;
+  GridBase *fine_grid;
+  uint64_t block_vol;
+  uint64_t fine_vol;
+  uint64_t coarse_vol;
+  uint64_t words;
+
+  // Row major layout "C" order:
+  // BLAS_V[coarse_vol][nbasis][block_vol][words]
+  // BLAS_F[coarse_vol][nrhs][block_vol][words]
+  // BLAS_C[coarse_vol][nrhs][nbasis]
+  /*
+   * in Fortran column major notation (cuBlas order)
+   *
+   * Vxb = [v1(x)][..][vn(x)] ... x coarse vol
+   *
+   * Fxr = [r1(x)][..][rm(x)] ... x coarse vol
+   *
+   * Block project:
+   * C_br = V^dag F x coarse vol
+   *
+   * Block promote:
+   * F_xr = Vxb Cbr x coarse_vol
+   */  
+  deviceVector<scalar> BLAS_V;      // words * block_vol * nbasis x coarse_vol 
+  deviceVector<scalar> BLAS_F;      // nrhs x fine_vol * words   -- the sources
+  deviceVector<scalar> BLAS_C;      // nrhs x coarse_vol * nbasis -- the coarse coeffs
+
+  RealD blasNorm2(deviceVector<scalar> &blas)
+  {
+    scalar ss(0.0);
+    std::vector<scalar> tmp(blas.size());
+    acceleratorCopyFromDevice(&blas[0],&tmp[0],blas.size()*sizeof(scalar));
+    for(int64_t s=0;s<blas.size();s++){
+      ss=ss+tmp[s]*adj(tmp[s]);
+    }
+    coarse_grid->GlobalSum(ss);
+    return real(ss);
+  }
+  
+  MultiRHSBlockProject(){};
+ ~MultiRHSBlockProject(){ Deallocate(); };
+  
+  void Deallocate(void)
+  {
+    nbasis=0;
+    coarse_grid=nullptr;
+    fine_grid=nullptr;
+    fine_vol=0;
+    block_vol=0;
+    coarse_vol=0;
+    words=0;
+    BLAS_V.resize(0);
+    BLAS_F.resize(0);
+    BLAS_C.resize(0);
+  }
+  void Allocate(int _nbasis,GridBase *_fgrid,GridBase *_cgrid)
+  {
+    nbasis=_nbasis;
+
+    fine_grid=_fgrid;
+    coarse_grid=_cgrid;
+
+    fine_vol   = fine_grid->lSites();
+    coarse_vol = coarse_grid->lSites();
+    block_vol = fine_vol/coarse_vol;
+    
+    words = sizeof(scalar_object)/sizeof(scalar);
+
+    BLAS_V.resize (fine_vol * words * nbasis );
+  }
+  void ImportFineGridVectors(std::vector <Field > &vecs, deviceVector<scalar> &blas)
+  {
+    int nvec = vecs.size();
+    typedef typename Field::vector_object vobj;
+    //    std::cout << GridLogMessage <<" BlockProjector importing "<<nvec<< " fine grid vectors" <<std::endl;
+
+    assert(vecs[0].Grid()==fine_grid);
+
+    subdivides(coarse_grid,fine_grid); // require they map
+
+    int _ndimension = coarse_grid->_ndimension;
+    assert(block_vol == fine_grid->oSites() / coarse_grid->oSites());
+    
+    Coordinate  block_r      (_ndimension);
+    for(int d=0 ; d<_ndimension;d++){
+      block_r[d] = fine_grid->_rdimensions[d] / coarse_grid->_rdimensions[d];
+    }
+
+    uint64_t sz = blas.size();
+
+    acceleratorMemSet(&blas[0],0,blas.size()*sizeof(scalar));
+
+    Coordinate fine_rdimensions = fine_grid->_rdimensions;
+    Coordinate coarse_rdimensions = coarse_grid->_rdimensions;
+    int64_t bv= block_vol;
+    for(int v=0;v<vecs.size();v++){
+
+      //      std::cout << " BlockProjector importing vector"<<v<<" "<<norm2(vecs[v])<<std::endl;
+      autoView( fineData   , vecs[v], AcceleratorRead);
+
+      auto blasData_p  = &blas[0];
+      auto fineData_p  = &fineData[0];
+
+      int64_t osites = fine_grid->oSites();
+
+      // loop over fine sites
+      const int Nsimd = vobj::Nsimd();
+      //      std::cout << "sz "<<sz<<std::endl;
+      //      std::cout << "prod "<<Nsimd * coarse_grid->oSites() * block_vol * nvec * words<<std::endl;
+      assert(sz == Nsimd * coarse_grid->oSites() * block_vol * nvec * words);
+      uint64_t lwords= words; // local variable for copy in to GPU
+      accelerator_for(sf,osites,Nsimd,{
+#ifdef GRID_SIMT
+        {
+	  int lane=acceleratorSIMTlane(Nsimd); // buffer lane
+#else
+	  for(int lane=0;lane<Nsimd;lane++) {
+#endif
+	  // One thread per fine site
+	  Coordinate coor_f(_ndimension);
+	  Coordinate coor_b(_ndimension);
+	  Coordinate coor_c(_ndimension);
+
+	  // Fine site to fine coor
+	  Lexicographic::CoorFromIndex(coor_f,sf,fine_rdimensions);
+
+	  for(int d=0;d<_ndimension;d++) coor_b[d] = coor_f[d]%block_r[d];
+	  for(int d=0;d<_ndimension;d++) coor_c[d] = coor_f[d]/block_r[d];
+	  
+	  int sc;// coarse site
+	  int sb;// block site
+	  Lexicographic::IndexFromCoor(coor_c,sc,coarse_rdimensions);
+	  Lexicographic::IndexFromCoor(coor_b,sb,block_r);
+
+          scalar_object data = extractLane(lane,fineData[sf]);
+
+	  // BLAS layout address calculation
+	  // words * block_vol * nbasis x coarse_vol
+	  // coarse oSite x block vole x lanes
+	  int64_t site = (lane*osites + sc*bv)*nvec
+   	               + v*bv
+	               + sb;
+
+	  //	  assert(site*lwords<sz);
+
+	  scalar_object * ptr = (scalar_object *)&blasData_p[site*lwords];
+
+	  *ptr = data;
+#ifdef GRID_SIMT
+	}
+#else
+	}
+#endif
+      });
+      //      std::cout << " import fine Blas norm "<<blasNorm2(blas)<<std::endl;
+      //      std::cout << " BlockProjector imported vector"<<v<<std::endl;
+    }
+  }
+  void ExportFineGridVectors(std::vector <Field> &vecs, deviceVector<scalar> &blas)
+  {
+    typedef typename Field::vector_object vobj;
+
+    int nvec = vecs.size();
+
+    assert(vecs[0].Grid()==fine_grid);
+
+    subdivides(coarse_grid,fine_grid); // require they map
+
+    int _ndimension = coarse_grid->_ndimension;
+    assert(block_vol == fine_grid->oSites() / coarse_grid->oSites());
+    
+    Coordinate  block_r      (_ndimension);
+    for(int d=0 ; d<_ndimension;d++){
+      block_r[d] = fine_grid->_rdimensions[d] / coarse_grid->_rdimensions[d];
+    }
+    Coordinate fine_rdimensions = fine_grid->_rdimensions;
+    Coordinate coarse_rdimensions = coarse_grid->_rdimensions;
+
+    //    std::cout << " export fine Blas norm "<<blasNorm2(blas)<<std::endl;
+
+    int64_t bv= block_vol;
+    for(int v=0;v<vecs.size();v++){
+
+      autoView( fineData   , vecs[v], AcceleratorWrite);
+
+      auto blasData_p  = &blas[0];
+      auto fineData_p    = &fineData[0];
+
+      int64_t osites = fine_grid->oSites();
+      uint64_t lwords = words;
+      //      std::cout << " Nsimd is "<<vobj::Nsimd() << std::endl;
+      //      std::cout << " lwords is "<<lwords << std::endl;
+      //      std::cout << " sizeof(scalar_object) is "<<sizeof(scalar_object) << std::endl;
+      // loop over fine sites
+      accelerator_for(sf,osites,vobj::Nsimd(),{
+      
+#ifdef GRID_SIMT
+        {
+	  int lane=acceleratorSIMTlane(vobj::Nsimd()); // buffer lane
+#else
+	  for(int lane=0;lane<vobj::Nsimd();lane++) {
+#endif
+	  // One thread per fine site
+	  Coordinate coor_f(_ndimension);
+	  Coordinate coor_b(_ndimension);
+	  Coordinate coor_c(_ndimension);
+
+	  Lexicographic::CoorFromIndex(coor_f,sf,fine_rdimensions);
+
+	  for(int d=0;d<_ndimension;d++) coor_b[d] = coor_f[d]%block_r[d];
+	  for(int d=0;d<_ndimension;d++) coor_c[d] = coor_f[d]/block_r[d];
+	  
+	  int sc;
+	  int sb;
+	  Lexicographic::IndexFromCoor(coor_c,sc,coarse_rdimensions);
+	  Lexicographic::IndexFromCoor(coor_b,sb,block_r);
+
+	  // BLAS layout address calculation
+	  // words * block_vol * nbasis x coarse_vol 	  
+	  int64_t site = (lane*osites + sc*bv)*nvec
+   	               + v*bv
+	               + sb;
+
+	  scalar_object * ptr = (scalar_object *)&blasData_p[site*lwords];
+
+	  scalar_object data = *ptr;
+
+	  insertLane(lane,fineData[sf],data);
+#ifdef GRID_SIMT
+	}
+#else
+	}
+#endif
+      });
+    }
+  }
+  template<class vobj>
+  void ImportCoarseGridVectors(std::vector <Lattice<vobj> > &vecs, deviceVector<scalar> &blas)
+  {
+    int nvec = vecs.size();
+    typedef typename vobj::scalar_object coarse_scalar_object;
+
+    //    std::cout << " BlockProjector importing "<<nvec<< " coarse grid vectors" <<std::endl;
+
+    assert(vecs[0].Grid()==coarse_grid);
+
+    int _ndimension = coarse_grid->_ndimension;
+
+    uint64_t sz = blas.size();
+
+    Coordinate coarse_rdimensions = coarse_grid->_rdimensions;
+    
+    for(int v=0;v<vecs.size();v++){
+
+      //      std::cout << " BlockProjector importing coarse vector"<<v<<" "<<norm2(vecs[v])<<std::endl;
+      autoView( coarseData   , vecs[v], AcceleratorRead);
+
+      auto blasData_p  = &blas[0];
+      auto coarseData_p  = &coarseData[0];
+
+      int64_t osites = coarse_grid->oSites();
+
+      // loop over fine sites
+      const int Nsimd = vobj::Nsimd();
+      uint64_t cwords=sizeof(typename vobj::scalar_object)/sizeof(scalar);
+      assert(cwords==nbasis);
+      
+      accelerator_for(sc,osites,Nsimd,{
+#ifdef GRID_SIMT
+        {
+	  int lane=acceleratorSIMTlane(Nsimd); // buffer lane
+#else
+	  for(int lane=0;lane<Nsimd;lane++) {
+#endif
+           // C_br per site
+	    int64_t blas_site = (lane*osites + sc)*nvec*cwords + v*cwords;
+	    
+	    coarse_scalar_object data = extractLane(lane,coarseData[sc]);
+
+	    coarse_scalar_object * ptr = (coarse_scalar_object *)&blasData_p[blas_site];
+
+	    *ptr = data;
+#ifdef GRID_SIMT
+	}
+#else
+	}
+#endif
+      });
+      //      std::cout << " import coarsee Blas norm "<<blasNorm2(blas)<<std::endl;
+    }
+  }
+  template<class vobj>
+  void ExportCoarseGridVectors(std::vector <Lattice<vobj> > &vecs, deviceVector<scalar> &blas)
+  {
+    int nvec = vecs.size();
+    typedef typename vobj::scalar_object coarse_scalar_object;
+    //    std::cout << GridLogMessage<<" BlockProjector exporting "<<nvec<< " coarse grid vectors" <<std::endl;
+
+    assert(vecs[0].Grid()==coarse_grid);
+
+    int _ndimension = coarse_grid->_ndimension;
+    
+    uint64_t sz = blas.size();
+
+    Coordinate coarse_rdimensions = coarse_grid->_rdimensions;
+    
+    //    std::cout << " export coarsee Blas norm "<<blasNorm2(blas)<<std::endl;
+    for(int v=0;v<vecs.size();v++){
+
+      //  std::cout << " BlockProjector exporting coarse vector"<<v<<std::endl;
+      autoView( coarseData   , vecs[v], AcceleratorWrite);
+
+      auto blasData_p  = &blas[0];
+      auto coarseData_p  = &coarseData[0];
+
+      int64_t osites = coarse_grid->oSites();
+
+      // loop over fine sites
+      const int Nsimd = vobj::Nsimd();
+      uint64_t cwords=sizeof(typename vobj::scalar_object)/sizeof(scalar);
+      assert(cwords==nbasis);
+      
+      accelerator_for(sc,osites,Nsimd,{
+	  // Wrap in a macro "FOR_ALL_LANES(lane,{ ... });
+#ifdef GRID_SIMT
+        {
+	  int lane=acceleratorSIMTlane(Nsimd); // buffer lane
+#else
+	  for(int lane=0;lane<Nsimd;lane++) {
+#endif
+	    int64_t blas_site = (lane*osites + sc)*nvec*cwords + v*cwords;
+	    coarse_scalar_object * ptr = (coarse_scalar_object *)&blasData_p[blas_site];
+	    coarse_scalar_object data = *ptr;
+	    insertLane(lane,coarseData[sc],data);
+#ifdef GRID_SIMT
+	}
+#else
+	}
+#endif
+      });
+    }
+  }
+  void ImportBasis(std::vector < Field > &vecs)
+  {
+    //    std::cout << " BlockProjector Import basis size "<<vecs.size()<<std::endl;
+    ImportFineGridVectors(vecs,BLAS_V);
+  }
+
+  template<class cobj>
+  void blockProject(std::vector<Field> &fine,std::vector< Lattice<cobj> > & coarse)
+  {
+    int nrhs=fine.size();
+    int _nbasis = sizeof(typename cobj::scalar_object)/sizeof(scalar);
+    //    std::cout << "blockProject nbasis " <<nbasis<<" " << _nbasis<<std::endl;
+    assert(nbasis==_nbasis);
+    
+    BLAS_F.resize (fine_vol * words * nrhs );
+    BLAS_C.resize (coarse_vol * nbasis * nrhs );
+
+    /////////////////////////////////////////////
+    // Copy in the multi-rhs sources to same data layout
+    /////////////////////////////////////////////
+    //    std::cout << "BlockProject import fine"<<std::endl;
+    ImportFineGridVectors(fine,BLAS_F);
+    
+    deviceVector<scalar *> Vd(coarse_vol);
+    deviceVector<scalar *> Fd(coarse_vol);
+    deviceVector<scalar *> Cd(coarse_vol);
+
+    //    std::cout << "BlockProject pointers"<<std::endl;
+    for(int c=0;c<coarse_vol;c++){
+      // BLAS_V[coarse_vol][nbasis][block_vol][words]
+      // BLAS_F[coarse_vol][nrhs][block_vol][words]
+      // BLAS_C[coarse_vol][nrhs][nbasis]
+      scalar * Vh = & BLAS_V[c*nbasis*block_vol*words];
+      scalar * Fh = & BLAS_F[c*nrhs*block_vol*words];
+      scalar * Ch = & BLAS_C[c*nrhs*nbasis];
+
+      acceleratorPut(Vd[c],Vh);
+      acceleratorPut(Fd[c],Fh);
+      acceleratorPut(Cd[c],Ch);
+    }
+
+    GridBLAS BLAS;
+
+    //    std::cout << "BlockProject BLAS"<<std::endl;
+    int64_t vw = block_vol * words;
+    /////////////////////////////////////////
+    // C_br = V^dag R
+    /////////////////////////////////////////
+    BLAS.gemmBatched(GridBLAS_OP_C,GridBLAS_OP_N, 
+    		     nbasis,nrhs,vw,
+		     ComplexD(1.0),
+		     Vd,
+		     Fd,
+		     ComplexD(0.0),  // wipe out C
+		     Cd);
+    BLAS.synchronise();
+    //    std::cout << "BlockProject done"<<std::endl;
+    ExportCoarseGridVectors(coarse, BLAS_C);
+    //    std::cout << "BlockProject done"<<std::endl;
+
+  }
+
+  template<class cobj>
+  void blockPromote(std::vector<Field> &fine,std::vector<Lattice<cobj> > & coarse)
+  {
+    int nrhs=fine.size();
+    int _nbasis = sizeof(typename cobj::scalar_object)/sizeof(scalar);
+    assert(nbasis==_nbasis);
+    
+    BLAS_F.resize (fine_vol * words * nrhs );
+    BLAS_C.resize (coarse_vol * nbasis * nrhs );
+
+    ImportCoarseGridVectors(coarse, BLAS_C);
+
+    GridBLAS BLAS;
+
+    deviceVector<scalar *> Vd(coarse_vol);
+    deviceVector<scalar *> Fd(coarse_vol);
+    deviceVector<scalar *> Cd(coarse_vol);
+
+    for(int c=0;c<coarse_vol;c++){
+      // BLAS_V[coarse_vol][nbasis][block_vol][words]
+      // BLAS_F[coarse_vol][nrhs][block_vol][words]
+      // BLAS_C[coarse_vol][nrhs][nbasis]
+      scalar * Vh = & BLAS_V[c*nbasis*block_vol*words];
+      scalar * Fh = & BLAS_F[c*nrhs*block_vol*words];
+      scalar * Ch = & BLAS_C[c*nrhs*nbasis];
+      acceleratorPut(Vd[c],Vh);
+      acceleratorPut(Fd[c],Fh);
+      acceleratorPut(Cd[c],Ch);
+    }
+
+    /////////////////////////////////////////
+    // Block promote:
+    // F_xr = Vxb Cbr (x coarse_vol)
+    /////////////////////////////////////////
+
+    int64_t vw = block_vol * words;
+    BLAS.gemmBatched(GridBLAS_OP_N,GridBLAS_OP_N, 
+    		     vw,nrhs,nbasis,
+		     ComplexD(1.0),
+		     Vd,
+		     Cd,
+		     ComplexD(0.0),  // wipe out C
+		     Fd);
+    BLAS.synchronise();
+    //    std::cout << " blas call done"<<std::endl;
+    
+    ExportFineGridVectors(fine, BLAS_F);
+    //    std::cout << " exported "<<std::endl;
+  }
+};
+
+NAMESPACE_END(Grid);

Grid/algorithms/deflation/MultiRHSDeflation.h

@@ -0,0 +1,233 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: MultiRHSDeflation.h
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    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 */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+
+/* Need helper object for BLAS accelerated mrhs projection
+
+   i) MultiRHS Deflation
+
+   Import Evecs -> nev x vol x internal 
+   Import vector of Lattice objects -> nrhs x vol x internal
+   => Cij (nrhs x Nev) via GEMM.
+   => Guess  (nrhs x vol x internal)  = C x evecs (via GEMM)
+   Export
+
+   
+   ii) MultiRHS block projection
+
+   Import basis -> nblock x nbasis x  (block x internal) 
+   Import vector of fine lattice objects -> nblock x nrhs x (block x internal) 
+
+   => coarse_(nrhs x nbasis )^block = via batched GEMM
+
+   iii)   Alternate interface: 
+   Import higher dim Lattice object-> vol x nrhs layout
+   
+*/
+template<class Field>
+class MultiRHSDeflation
+{
+public:
+
+  typedef typename Field::scalar_type   scalar;
+  typedef typename Field::scalar_object scalar_object;
+
+  int nev;
+  std::vector<RealD> eval;
+  GridBase *grid;
+  uint64_t vol;
+  uint64_t words;
+  
+  deviceVector<scalar> BLAS_E;      //  nev x vol -- the eigenbasis   (up to a 1/sqrt(lambda))
+  deviceVector<scalar> BLAS_R;      // nrhs x vol -- the sources
+  deviceVector<scalar> BLAS_G;      // nrhs x vol -- the guess
+  deviceVector<scalar> BLAS_C;      // nrhs x nev -- the coefficients 
+  
+  MultiRHSDeflation(){};
+  ~MultiRHSDeflation(){ Deallocate(); };
+  
+  void Deallocate(void)
+  {
+    nev=0;
+    grid=nullptr;
+    vol=0;
+    words=0;
+    BLAS_E.resize(0);
+    BLAS_R.resize(0);
+    BLAS_C.resize(0);
+    BLAS_G.resize(0);
+  }
+  void Allocate(int _nev,GridBase *_grid)
+  {
+    nev=_nev;
+    grid=_grid;
+    vol   = grid->lSites();
+    words = sizeof(scalar_object)/sizeof(scalar);
+    eval.resize(nev);
+    BLAS_E.resize (vol * words * nev );
+    std::cout << GridLogMessage << " Allocate for "<<nev<<" eigenvectors and volume "<<vol<<std::endl;
+  }
+  void ImportEigenVector(Field &evec,RealD &_eval, int ev)
+  {
+    //    std::cout << " ev " <<ev<<" eval "<<_eval<< std::endl;
+    assert(ev<eval.size());
+    eval[ev] = _eval;
+
+    int64_t offset = ev*vol*words;
+    autoView(v,evec,AcceleratorRead);
+    acceleratorCopyDeviceToDevice(&v[0],&BLAS_E[offset],sizeof(scalar_object)*vol);
+
+  }
+  void ImportEigenBasis(std::vector<Field> &evec,std::vector<RealD> &_eval)
+  {
+    ImportEigenBasis(evec,_eval,0,evec.size());
+  }
+  // Could use to import a batch of eigenvectors
+  void ImportEigenBasis(std::vector<Field> &evec,std::vector<RealD> &_eval, int _ev0, int _nev)
+  {
+    assert(_ev0+_nev<=evec.size());
+
+    Allocate(_nev,evec[0].Grid());
+    
+    // Imports a sub-batch of eigenvectors, _ev0, ..., _ev0+_nev-1
+    for(int e=0;e<nev;e++){
+      std::cout << "Importing eigenvector "<<e<<" evalue "<<_eval[_ev0+e]<<std::endl;
+      ImportEigenVector(evec[_ev0+e],_eval[_ev0+e],e);
+    }
+  }
+  void DeflateSources(std::vector<Field> &source,std::vector<Field> & guess)
+  {
+    int nrhs = source.size();
+    assert(source.size()==guess.size());
+    assert(grid == guess[0].Grid());
+    conformable(guess[0],source[0]);
+
+    int64_t vw = vol * words;
+
+    RealD t0 = usecond();
+    BLAS_R.resize(nrhs * vw); // cost free if size doesn't change
+    BLAS_G.resize(nrhs * vw); // cost free if size doesn't change
+    BLAS_C.resize(nev * nrhs);// cost free if size doesn't change
+
+    /////////////////////////////////////////////
+    // Copy in the multi-rhs sources
+    /////////////////////////////////////////////
+    //    for(int r=0;r<nrhs;r++){
+    //      std::cout << " source["<<r<<"] = "<<norm2(source[r])<<std::endl;
+    //    }
+    for(int r=0;r<nrhs;r++){
+      int64_t offset = r*vw;
+      autoView(v,source[r],AcceleratorRead);
+      acceleratorCopyDeviceToDevice(&v[0],&BLAS_R[offset],sizeof(scalar_object)*vol);
+    }
+
+  /*
+   * in Fortran column major notation (cuBlas order)
+   *
+   * Exe = [e1(x)][..][en(x)]
+   *
+   * Rxr = [r1(x)][..][rm(x)]
+   *
+   * C_er = E^dag R
+   * C_er = C_er / lambda_e 
+   * G_xr = Exe Cer
+   */
+    deviceVector<scalar *> Ed(1);
+    deviceVector<scalar *> Rd(1);
+    deviceVector<scalar *> Cd(1);
+    deviceVector<scalar *> Gd(1);
+
+    scalar * Eh = & BLAS_E[0];
+    scalar * Rh = & BLAS_R[0];
+    scalar * Ch = & BLAS_C[0];
+    scalar * Gh = & BLAS_G[0];
+
+    acceleratorPut(Ed[0],Eh);
+    acceleratorPut(Rd[0],Rh);
+    acceleratorPut(Cd[0],Ch);
+    acceleratorPut(Gd[0],Gh);
+
+    GridBLAS BLAS;
+
+    /////////////////////////////////////////
+    // C_er = E^dag R
+    /////////////////////////////////////////
+    BLAS.gemmBatched(GridBLAS_OP_C,GridBLAS_OP_N, 
+    		     nev,nrhs,vw,
+		     ComplexD(1.0),
+		     Ed,
+		     Rd,
+		     ComplexD(0.0),  // wipe out C
+		     Cd);
+    BLAS.synchronise();
+
+    assert(BLAS_C.size()==nev*nrhs);
+
+    std::vector<scalar> HOST_C(BLAS_C.size());      // nrhs . nev -- the coefficients 
+    acceleratorCopyFromDevice(&BLAS_C[0],&HOST_C[0],BLAS_C.size()*sizeof(scalar));
+    grid->GlobalSumVector(&HOST_C[0],nev*nrhs);
+    for(int e=0;e<nev;e++){
+      RealD lam(1.0/eval[e]);
+      for(int r=0;r<nrhs;r++){
+	int off = e+nev*r;
+	HOST_C[off]=HOST_C[off] * lam;
+	//	std::cout << "C["<<e<<"]["<<r<<"] ="<<HOST_C[off]<< " eval[e] "<<eval[e] <<std::endl;
+      }
+    }
+    acceleratorCopyToDevice(&HOST_C[0],&BLAS_C[0],BLAS_C.size()*sizeof(scalar));
+
+    
+    /////////////////////////////////////////
+    // Guess G_xr = Exe Cer
+    /////////////////////////////////////////
+    BLAS.gemmBatched(GridBLAS_OP_N,GridBLAS_OP_N, 
+		     vw,nrhs,nev,
+		     ComplexD(1.0),
+		     Ed, // x . nev
+		     Cd, // nev . nrhs
+		     ComplexD(0.0),
+		     Gd);
+    BLAS.synchronise();
+
+    ///////////////////////////////////////
+    // Copy out the multirhs
+    ///////////////////////////////////////
+    for(int r=0;r<nrhs;r++){
+      int64_t offset = r*vw;
+      autoView(v,guess[r],AcceleratorWrite);
+      acceleratorCopyDeviceToDevice(&BLAS_G[offset],&v[0],sizeof(scalar_object)*vol);
+    }
+    RealD t1 = usecond();
+    std::cout << GridLogMessage << "MultiRHSDeflation for "<<nrhs<<" sources with "<<nev<<" eigenvectors took " << (t1-t0)/1e3 <<" ms"<<std::endl;
+  }
+};
+
+NAMESPACE_END(Grid);

Grid/algorithms/iterative/AdefGeneric.h

@@ -33,109 +33,111 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
    * Script A = SolverMatrix 
    * Script P = Preconditioner
    *
-   * Deflation methods considered
-   *      -- Solve P A x = P b        [ like Luscher ]
-   * DEF-1        M P A x = M P b     [i.e. left precon]
-   * DEF-2        P^T M A x = P^T M b
-   * ADEF-1       Preconditioner = M P + Q      [ Q + M + M A Q]
-   * ADEF-2       Preconditioner = P^T M + Q
-   * BNN          Preconditioner = P^T M P + Q
-   * BNN2         Preconditioner = M P + P^TM +Q - M P A M 
-   * 
    * Implement ADEF-2
    *
    * Vstart = P^Tx + Qb
    * M1 = P^TM + Q
    * M2=M3=1
-   * Vout = x
    */
+NAMESPACE_BEGIN(Grid);
 
-// abstract base
+
-template<class Field, class CoarseField>
+template<class Field>
-class TwoLevelFlexiblePcg : public LinearFunction<Field>
+class TwoLevelCG : public LinearFunction<Field>
 {
  public:
-  int verbose;
   RealD   Tolerance;
   Integer MaxIterations;
-  const int mmax = 5;
   GridBase *grid;
-  GridBase *coarsegrid;
 
-  LinearOperatorBase<Field>   *_Linop
+  // Fine operator, Smoother, CoarseSolver
-  OperatorFunction<Field>     *_Smoother,
+  LinearOperatorBase<Field>   &_FineLinop;
-  LinearFunction<CoarseField> *_CoarseSolver;
+  LinearFunction<Field>   &_Smoother;
-
-  // Need somthing that knows how to get from Coarse to fine and back again
   
   // more most opertor functions
-  TwoLevelFlexiblePcg(RealD tol,
+  TwoLevelCG(RealD tol,
 	     Integer maxit,
-		     LinearOperatorBase<Field> *Linop,
+	     LinearOperatorBase<Field>   &FineLinop,
-		     LinearOperatorBase<Field> *SmootherLinop,
+	     LinearFunction<Field>       &Smoother,
-		     OperatorFunction<Field>   *Smoother,
+	     GridBase *fine) : 
-		     OperatorFunction<CoarseField>  CoarseLinop
-		     ) : 
       Tolerance(tol), 
       MaxIterations(maxit),
-      _Linop(Linop),
+      _FineLinop(FineLinop),
-      _PreconditionerLinop(PrecLinop),
+      _Smoother(Smoother)
-      _Preconditioner(Preconditioner)
   {
-    verbose=0;
+    grid       = fine;
   };
   
-  // The Pcg routine is common to all, but the various matrices differ from derived 
+  virtual void operator() (const Field &src, Field &x)
-  // implementation to derived implmentation
+  {
-  void operator() (const Field &src, Field &psi){
+    std::cout << GridLogMessage<<"HDCG: fPcg starting single RHS"<<std::endl;
-  void operator() (const Field &src, Field &psi){
-
-    psi.Checkerboard() = src.Checkerboard();
-    grid             = src.Grid();
-
     RealD f;
     RealD rtzp,rtz,a,d,b;
     RealD rptzp;
-    RealD tn;
-    RealD guess = norm2(psi);
-    RealD ssq   = norm2(src);
-    RealD rsq   = ssq*Tolerance*Tolerance;
 
     /////////////////////////////
     // Set up history vectors
     /////////////////////////////
+    int mmax = 5;
+    std::cout << GridLogMessage<<"HDCG: fPcg allocating"<<std::endl;
     std::vector<Field> p(mmax,grid);
     std::vector<Field> mmp(mmax,grid);
     std::vector<RealD> pAp(mmax);
-
-    Field x  (grid); x = psi;
     Field z(grid);
     Field tmp(grid);
+    Field  mp (grid);
     Field  r  (grid);
     Field  mu (grid);
     
+    std::cout << GridLogMessage<<"HDCG: fPcg allocated"<<std::endl;
+    //Initial residual computation & set up
+    RealD guess   = norm2(x);
+    std::cout << GridLogMessage<<"HDCG: fPcg guess nrm "<<guess<<std::endl;
+    RealD src_nrm = norm2(src);
+    std::cout << GridLogMessage<<"HDCG: fPcg src nrm "<<src_nrm<<std::endl;
+    
+    if ( src_nrm == 0.0 ) {
+      std::cout << GridLogMessage<<"HDCG: fPcg given trivial source norm "<<src_nrm<<std::endl;
+      x=Zero();
+    }
+    RealD tn;
+    
+    GridStopWatch HDCGTimer;
+    HDCGTimer.Start();
     //////////////////////////
     // x0 = Vstart -- possibly modify guess
     //////////////////////////
-    x=src;
     Vstart(x,src);
     
     // r0 = b -A x0
-    HermOp(x,mmp); // Shouldn't this be something else?
+    _FineLinop.HermOp(x,mmp[0]);
     axpy (r, -1.0,mmp[0], src);    // Recomputes r=src-Ax0
+    {
+      double n1 = norm2(x);
+      double n2 = norm2(mmp[0]);
+      double n3 = norm2(r);
+      std::cout<<GridLogMessage<<"x,vstart,r = "<<n1<<" "<<n2<<" "<<n3<<std::endl;
+    }
 
     //////////////////////////////////
     // Compute z = M1 x
     //////////////////////////////////
-    M1(r,z,tmp,mp,SmootherMirs);
+    PcgM1(r,z);
     rtzp =real(innerProduct(r,z));
     
     ///////////////////////////////////////
     // Solve for Mss mu = P A z and set p = z-mu
-    // Def2: p = 1 - Q Az = Pright z 
+    // Def2 p = 1 - Q Az = Pright z
     // Other algos M2 is trivial
     ///////////////////////////////////////
-    M2(z,p[0]);
+    PcgM2(z,p[0]);
+
+    RealD ssq =  norm2(src);
+    RealD rsq =  ssq*Tolerance*Tolerance;
+
+    std::cout << GridLogMessage<<"HDCG: k=0 residual "<<rtzp<<" rsq "<<rsq<<"\n";
+
+    Field pp(grid);
 
     for (int k=0;k<=MaxIterations;k++){
     
@@ -143,7 +145,7 @@ class TwoLevelFlexiblePcg : public LinearFunction<Field>
       int peri_kp = (k+1) % mmax;
 
       rtz=rtzp;
-      d= M3(p[peri_k],mp,mmp[peri_k],tmp);
+      d= PcgM3(p[peri_k],mmp[peri_k]);
       a = rtz/d;
     
       // Memorise this
@@ -153,21 +155,36 @@ class TwoLevelFlexiblePcg : public LinearFunction<Field>
       RealD rn = axpy_norm(r,-a,mmp[peri_k],r);
 
       // Compute z = M x
-      M1(r,z,tmp,mp);
+      PcgM1(r,z);
       
+      {
+	RealD n1,n2;
+	n1=norm2(r);
+	n2=norm2(z);
+	std::cout << GridLogMessage<<"HDCG::fPcg iteration "<<k<<" : vector r,z "<<n1<<" "<<n2<<"\n";
+      }
       rtzp =real(innerProduct(r,z));
+      std::cout << GridLogMessage<<"HDCG::fPcg iteration "<<k<<" : inner rtzp "<<rtzp<<"\n";
 
-      M2(z,mu); // ADEF-2 this is identity. Axpy possible to eliminate
+      //    PcgM2(z,p[0]);
+      PcgM2(z,mu); // ADEF-2 this is identity. Axpy possible to eliminate
       
-      p[peri_kp]=p[peri_k];
+      p[peri_kp]=mu;
 
-      // Standard search direction  p -> z + b p    ; b = 
+      // Standard search direction  p -> z + b p    
       b = (rtzp)/rtz;
       
       int northog;
+      // k=zero  <=> peri_kp=1;        northog = 1
+      // k=1     <=> peri_kp=2;        northog = 2
+      // ...               ...                  ...
+      // k=mmax-2<=> peri_kp=mmax-1;   northog = mmax-1
+      // k=mmax-1<=> peri_kp=0;        northog = 1
+
       //    northog     = (peri_kp==0)?1:peri_kp; // This is the fCG(mmax) algorithm
       northog     = (k>mmax-1)?(mmax-1):k;        // This is the fCG-Tr(mmax-1) algorithm
     
+      std::cout<<GridLogMessage<<"HDCG::fPcg iteration "<<k<<" : orthogonalising to last "<<northog<<" vectors\n";
       for(int back=0; back < northog; back++){
 	int peri_back = (k-back)%mmax;
 	RealD pbApk= real(innerProduct(mmp[peri_back],p[peri_kp]));
@@ -176,75 +193,324 @@ class TwoLevelFlexiblePcg : public LinearFunction<Field>
       }
 
       RealD rrn=sqrt(rn/ssq);
-      std::cout<<GridLogMessage<<"TwoLevelfPcg: k= "<<k<<" residual = "<<rrn<<std::endl;
+      RealD rtn=sqrt(rtz/ssq);
+      RealD rtnp=sqrt(rtzp/ssq);
+
+      std::cout<<GridLogMessage<<"HDCG: fPcg k= "<<k<<" residual = "<<rrn<<"\n";
 
       // Stopping condition
       if ( rn <= rsq ) { 
 
-	HermOp(x,mmp); // Shouldn't this be something else?
+	HDCGTimer.Stop();
+	std::cout<<GridLogMessage<<"HDCG: fPcg converged in "<<k<<" iterations and "<<HDCGTimer.Elapsed()<<std::endl;;
+	
+	_FineLinop.HermOp(x,mmp[0]);			  
 	axpy(tmp,-1.0,src,mmp[0]);
 	
-	RealD psinorm = sqrt(norm2(x));
+	RealD  mmpnorm = sqrt(norm2(mmp[0]));
+	RealD  xnorm   = sqrt(norm2(x));
 	RealD  srcnorm = sqrt(norm2(src));
 	RealD  tmpnorm = sqrt(norm2(tmp));
 	RealD  true_residual = tmpnorm/srcnorm;
-	std::cout<<GridLogMessage<<"TwoLevelfPcg:   true residual is "<<true_residual<<std::endl;
+	std::cout<<GridLogMessage
-	std::cout<<GridLogMessage<<"TwoLevelfPcg: target residual was"<<Tolerance<<std::endl;
+	       <<"HDCG: true residual is "<<true_residual
-	return k;
+	       <<" solution "<<xnorm
+	       <<" source "<<srcnorm
+	       <<" mmp "<<mmpnorm	  
+	       <<std::endl;
+      
+	return;
+      }
+
+    }
+    HDCGTimer.Stop();
+    std::cout<<GridLogMessage<<"HDCG: not converged "<<HDCGTimer.Elapsed()<<std::endl;
+    RealD  xnorm   = sqrt(norm2(x));
+    RealD  srcnorm = sqrt(norm2(src));
+    std::cout<<GridLogMessage<<"HDCG: non-converged solution "<<xnorm<<" source "<<srcnorm<<std::endl;
+  }
+
+
+
+  virtual void operator() (std::vector<Field> &src, std::vector<Field> &x)
+  {
+    std::cout << GridLogMessage<<"HDCG: mrhs fPcg starting"<<std::endl;
+    src[0].Grid()->Barrier();
+    int nrhs = src.size();
+    std::vector<RealD> f(nrhs);
+    std::vector<RealD> rtzp(nrhs);
+    std::vector<RealD> rtz(nrhs);
+    std::vector<RealD> a(nrhs);
+    std::vector<RealD> d(nrhs);
+    std::vector<RealD> b(nrhs);
+    std::vector<RealD> rptzp(nrhs);
+    /////////////////////////////
+    // Set up history vectors
+    /////////////////////////////
+    int mmax = 3;
+    std::cout << GridLogMessage<<"HDCG: fPcg allocating"<<std::endl;
+    src[0].Grid()->Barrier();
+    std::vector<std::vector<Field> > p(nrhs);   for(int r=0;r<nrhs;r++)  p[r].resize(mmax,grid);
+    std::cout << GridLogMessage<<"HDCG: fPcg allocated p"<<std::endl;
+    src[0].Grid()->Barrier();
+    std::vector<std::vector<Field> > mmp(nrhs); for(int r=0;r<nrhs;r++) mmp[r].resize(mmax,grid);
+    std::cout << GridLogMessage<<"HDCG: fPcg allocated mmp"<<std::endl;
+    src[0].Grid()->Barrier();
+    std::vector<std::vector<RealD> > pAp(nrhs); for(int r=0;r<nrhs;r++) pAp[r].resize(mmax);
+    std::cout << GridLogMessage<<"HDCG: fPcg allocated pAp"<<std::endl;
+    src[0].Grid()->Barrier();
+    std::vector<Field> z(nrhs,grid);
+    std::vector<Field>  mp (nrhs,grid);
+    std::vector<Field>  r  (nrhs,grid);
+    std::vector<Field>  mu (nrhs,grid);
+    std::cout << GridLogMessage<<"HDCG: fPcg allocated z,mp,r,mu"<<std::endl;
+    src[0].Grid()->Barrier();
+
+    //Initial residual computation & set up
+    std::vector<RealD> src_nrm(nrhs);
+    for(int rhs=0;rhs<nrhs;rhs++) {
+      src_nrm[rhs]=norm2(src[rhs]);
+      assert(src_nrm[rhs]!=0.0);
+    }
+    std::vector<RealD> tn(nrhs);
+
+    GridStopWatch HDCGTimer;
+    HDCGTimer.Start();
+    //////////////////////////
+    // x0 = Vstart -- possibly modify guess
+    //////////////////////////
+    Vstart(x,src);
+
+    for(int rhs=0;rhs<nrhs;rhs++){
+      // r0 = b -A x0
+      _FineLinop.HermOp(x[rhs],mmp[rhs][0]);
+      axpy (r[rhs], -1.0,mmp[rhs][0], src[rhs]);    // Recomputes r=src-Ax0
+    }
+
+    //////////////////////////////////
+    // Compute z = M1 x
+    //////////////////////////////////
+    // This needs a multiRHS version for acceleration
+    PcgM1(r,z);
+
+    std::vector<RealD> ssq(nrhs);
+    std::vector<RealD> rsq(nrhs);
+    std::vector<Field> pp(nrhs,grid);
+
+    for(int rhs=0;rhs<nrhs;rhs++){
+      rtzp[rhs] =real(innerProduct(r[rhs],z[rhs]));
+      p[rhs][0]=z[rhs];
+      ssq[rhs]=norm2(src[rhs]);
+      rsq[rhs]=  ssq[rhs]*Tolerance*Tolerance;
+      std::cout << GridLogMessage<<"mrhs HDCG: "<<rhs<<" k=0 residual "<<rtzp[rhs]<<" rsq "<<rsq[rhs]<<"\n";
+    }
+
+    std::vector<RealD> rn(nrhs);
+    for (int k=0;k<=MaxIterations;k++){
+    
+      int peri_k  = k % mmax;
+      int peri_kp = (k+1) % mmax;
+
+      for(int rhs=0;rhs<nrhs;rhs++){
+	rtz[rhs]=rtzp[rhs];
+	d[rhs]= PcgM3(p[rhs][peri_k],mmp[rhs][peri_k]);
+	a[rhs] = rtz[rhs]/d[rhs];
+    
+	// Memorise this
+	pAp[rhs][peri_k] = d[rhs];
+
+	axpy(x[rhs],a[rhs],p[rhs][peri_k],x[rhs]);
+	rn[rhs] = axpy_norm(r[rhs],-a[rhs],mmp[rhs][peri_k],r[rhs]);
+      }
+
+      // Compute z = M x (for *all* RHS)
+      PcgM1(r,z);
+      std::cout << GridLogMessage<<"HDCG::fPcg M1 complete"<<std::endl;
+      grid->Barrier();
+      
+      RealD max_rn=0.0;
+      for(int rhs=0;rhs<nrhs;rhs++){
+
+	rtzp[rhs] =real(innerProduct(r[rhs],z[rhs]));
+
+	std::cout << GridLogMessage<<"HDCG::fPcg rhs"<<rhs<<" iteration "<<k<<" : inner rtzp "<<rtzp[rhs]<<"\n";
+	
+	mu[rhs]=z[rhs];
+
+	p[rhs][peri_kp]=mu[rhs];
+
+	// Standard search direction p == z + b p 
+	b[rhs] = (rtzp[rhs])/rtz[rhs];
+
+	int northog = (k>mmax-1)?(mmax-1):k;        // This is the fCG-Tr(mmax-1) algorithm
+	std::cout<<GridLogMessage<<"HDCG::fPcg iteration "<<k<<" : orthogonalising to last "<<northog<<" vectors\n";
+	for(int back=0; back < northog; back++){
+	  int peri_back = (k-back)%mmax;
+	  RealD pbApk= real(innerProduct(mmp[rhs][peri_back],p[rhs][peri_kp]));
+	  RealD beta = -pbApk/pAp[rhs][peri_back];
+	  axpy(p[rhs][peri_kp],beta,p[rhs][peri_back],p[rhs][peri_kp]);
+	}
+
+	RealD rrn=sqrt(rn[rhs]/ssq[rhs]);
+	RealD rtn=sqrt(rtz[rhs]/ssq[rhs]);
+	RealD rtnp=sqrt(rtzp[rhs]/ssq[rhs]);
+	
+	std::cout<<GridLogMessage<<"HDCG: rhs "<<rhs<<"fPcg k= "<<k<<" residual = "<<rrn<<"\n";
+	if ( rrn > max_rn ) max_rn = rrn;
+      }
+
+      // Stopping condition based on worst case
+      if ( max_rn <= Tolerance ) { 
+
+	HDCGTimer.Stop();
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg converged in "<<k<<" iterations and "<<HDCGTimer.Elapsed()<<std::endl;;
+
+	for(int rhs=0;rhs<nrhs;rhs++){
+	  _FineLinop.HermOp(x[rhs],mmp[rhs][0]);			  
+	  Field tmp(grid);
+	  axpy(tmp,-1.0,src[rhs],mmp[rhs][0]);
+      
+	  RealD  mmpnorm = sqrt(norm2(mmp[rhs][0]));
+	  RealD  xnorm   = sqrt(norm2(x[rhs]));
+	  RealD  srcnorm = sqrt(norm2(src[rhs]));
+	  RealD  tmpnorm = sqrt(norm2(tmp));
+	  RealD  true_residual = tmpnorm/srcnorm;
+	  std::cout<<GridLogMessage
+		   <<"HDCG: true residual ["<<rhs<<"] is "<<true_residual
+		   <<" solution "<<xnorm
+		   <<" source "<<srcnorm
+		   <<" mmp "<<mmpnorm	  
+		   <<std::endl;
+	}
+	return;
+      }
+      
+    }
+    HDCGTimer.Stop();
+    std::cout<<GridLogMessage<<"HDCG: not converged "<<HDCGTimer.Elapsed()<<std::endl;
+    for(int rhs=0;rhs<nrhs;rhs++){
+      RealD  xnorm   = sqrt(norm2(x[rhs]));
+      RealD  srcnorm = sqrt(norm2(src[rhs]));
+      std::cout<<GridLogMessage<<"HDCG: non-converged solution "<<xnorm<<" source "<<srcnorm<<std::endl;
     }
   }
-    // Non-convergence
+  
-    assert(0);
-  }
 
  public:
 
-  virtual void M(Field & in,Field & out,Field & tmp) {
+  virtual void PcgM1(std::vector<Field> & in,std::vector<Field> & out)
+  {
+    std::cout << "PcgM1 default (cheat) mrhs version"<<std::endl;
+    for(int rhs=0;rhs<in.size();rhs++){
+      this->PcgM1(in[rhs],out[rhs]);
+    }
+  }
+  virtual void PcgM1(Field & in, Field & out)     =0;
+  virtual void Vstart(std::vector<Field> & x,std::vector<Field> & src)
+  {
+    std::cout << "Vstart default (cheat) mrhs version"<<std::endl;
+    for(int rhs=0;rhs<x.size();rhs++){
+      this->Vstart(x[rhs],src[rhs]);
+    }
+  }
+  virtual void Vstart(Field & x,const Field & src)=0;
 
+  virtual void PcgM2(const Field & in, Field & out) {
+    out=in;
   }
 
-  virtual void M1(Field & in, Field & out) {// the smoother
+  virtual RealD PcgM3(const Field & p, Field & mmp){
+    RealD dd;
+    _FineLinop.HermOp(p,mmp);
+    ComplexD dot = innerProduct(p,mmp);
+    dd=real(dot);
+    return dd;
+  }
 
+  /////////////////////////////////////////////////////////////////////
+  // Only Def1 has non-trivial Vout.
+  /////////////////////////////////////////////////////////////////////
+
+};
+  
+template<class Field, class CoarseField, class Aggregation>
+class TwoLevelADEF2 : public TwoLevelCG<Field>
+{
+ public:
+  ///////////////////////////////////////////////////////////////////////////////////
+  // Need something that knows how to get from Coarse to fine and back again
+  //  void ProjectToSubspace(CoarseVector &CoarseVec,const FineField &FineVec){
+  //  void PromoteFromSubspace(const CoarseVector &CoarseVec,FineField &FineVec){
+  ///////////////////////////////////////////////////////////////////////////////////
+  GridBase *coarsegrid;
+  Aggregation &_Aggregates;                    
+  LinearFunction<CoarseField> &_CoarseSolver;
+  LinearFunction<CoarseField> &_CoarseSolverPrecise;
+  ///////////////////////////////////////////////////////////////////////////////////
+  
+  // more most opertor functions
+  TwoLevelADEF2(RealD tol,
+		Integer maxit,
+		LinearOperatorBase<Field>    &FineLinop,
+		LinearFunction<Field>        &Smoother,
+		LinearFunction<CoarseField>  &CoarseSolver,
+		LinearFunction<CoarseField>  &CoarseSolverPrecise,
+		Aggregation &Aggregates
+		) :
+      TwoLevelCG<Field>(tol,maxit,FineLinop,Smoother,Aggregates.FineGrid),
+      _CoarseSolver(CoarseSolver),
+      _CoarseSolverPrecise(CoarseSolverPrecise),
+      _Aggregates(Aggregates)
+  {
+    coarsegrid = Aggregates.CoarseGrid;
+  };
+
+  virtual void PcgM1(Field & in, Field & out)
+  {
+    GRID_TRACE("MultiGridPreconditioner ");
     // [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
-    Field tmp(grid);
-    Field Min(grid);
 
-    PcgM(in,Min); // Smoother call
+    Field tmp(this->grid);
+    Field Min(this->grid);
+    CoarseField PleftProj(this->coarsegrid);
+    CoarseField PleftMss_proj(this->coarsegrid);
 
-    HermOp(Min,out);
+    GridStopWatch SmootherTimer;
+    GridStopWatch MatrixTimer;
+    SmootherTimer.Start();
+    this->_Smoother(in,Min);
+    SmootherTimer.Stop();
+
+    MatrixTimer.Start();
+    this->_FineLinop.HermOp(Min,out);
+    MatrixTimer.Stop();
     axpy(tmp,-1.0,out,in);          // tmp  = in - A Min
 
-    ProjectToSubspace(tmp,PleftProj);     
+    GridStopWatch ProjTimer;
-    ApplyInverse(PleftProj,PleftMss_proj); // Ass^{-1} [in - A Min]_s
+    GridStopWatch CoarseTimer;
-    PromoteFromSubspace(PleftMss_proj,tmp);// tmp = Q[in - A Min]  
+    GridStopWatch PromTimer;
+    ProjTimer.Start();
+    this->_Aggregates.ProjectToSubspace(PleftProj,tmp);     
+    ProjTimer.Stop();
+    CoarseTimer.Start();
+    this->_CoarseSolver(PleftProj,PleftMss_proj); // Ass^{-1} [in - A Min]_s
+    CoarseTimer.Stop();
+    PromTimer.Start();
+    this->_Aggregates.PromoteFromSubspace(PleftMss_proj,tmp);// tmp = Q[in - A Min]  
+    PromTimer.Stop();
+    std::cout << GridLogPerformance << "PcgM1 breakdown "<<std::endl;
+    std::cout << GridLogPerformance << "\tSmoother   " << SmootherTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\tProj       " << ProjTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\tCoarse     " << CoarseTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\tProm       " << PromTimer.Elapsed() <<std::endl;
+
     axpy(out,1.0,Min,tmp); // Min+tmp
   }
 
-  virtual void M2(const Field & in, Field & out) {
+  virtual void Vstart(Field & x,const Field & src)
-    out=in;
+  {
-    // Must override for Def2 only
+    std::cout << GridLogMessage<<"HDCG: fPcg Vstart "<<std::endl;
-    //  case PcgDef2:
-    //    Pright(in,out);
-    //    break;
-  }
-
-  virtual RealD M3(const Field & p, Field & mmp){
-    double d,dd;
-    HermOpAndNorm(p,mmp,d,dd);
-    return dd;
-    // Must override for Def1 only
-    //  case PcgDef1:
-    //    d=linop_d->Mprec(p,mmp,tmp,0,1);// Dag no
-    //      linop_d->Mprec(mmp,mp,tmp,1);// Dag yes
-    //    Pleft(mp,mmp);
-    //    d=real(linop_d->inner(p,mmp));
-  }
-
-  virtual void VstartDef2(Field & xconst Field & src){
-    //case PcgDef2:
-    //case PcgAdef2: 
-    //case PcgAdef2f:
-    //case PcgV11f:
     ///////////////////////////////////
     // Choose x_0 such that 
     // x_0 = guess +  (A_ss^inv) r_s = guess + Ass_inv [src -Aguess]
@@ -256,142 +522,78 @@ class TwoLevelFlexiblePcg : public LinearFunction<Field>
     //                   = src_s - (A guess)_s - src_s  + (A guess)_s 
     //                   = 0 
     ///////////////////////////////////
-    Field r(grid);
+    Field r(this->grid);
-    Field mmp(grid);
+    Field mmp(this->grid);
+    CoarseField PleftProj(this->coarsegrid);
+    CoarseField PleftMss_proj(this->coarsegrid);
 
-    HermOp(x,mmp);
+    std::cout << GridLogMessage<<"HDCG: fPcg Vstart projecting "<<std::endl;
-    axpy (r, -1.0, mmp, src);        // r_{-1} = src - A x
+    this->_Aggregates.ProjectToSubspace(PleftProj,src);     
-    ProjectToSubspace(r,PleftProj);     
+    std::cout << GridLogMessage<<"HDCG: fPcg Vstart coarse solve "<<std::endl;
-    ApplyInverseCG(PleftProj,PleftMss_proj); // Ass^{-1} r_s
+    this->_CoarseSolverPrecise(PleftProj,PleftMss_proj); // Ass^{-1} r_s
-    PromoteFromSubspace(PleftMss_proj,mmp);  
+    std::cout << GridLogMessage<<"HDCG: fPcg Vstart promote "<<std::endl;
-    x=x+mmp;
+    this->_Aggregates.PromoteFromSubspace(PleftMss_proj,x);  
 
   }
 
+};
+
+  
+template<class Field>
+class TwoLevelADEF1defl : public TwoLevelCG<Field>
+{
+public:
+  const std::vector<Field> &evec;
+  const std::vector<RealD> &eval;
+  
+  TwoLevelADEF1defl(RealD tol,
+		   Integer maxit,
+		   LinearOperatorBase<Field>   &FineLinop,
+		   LinearFunction<Field>   &Smoother,
+		   std::vector<Field> &_evec,
+		   std::vector<RealD> &_eval) : 
+    TwoLevelCG<Field>(tol,maxit,FineLinop,Smoother,_evec[0].Grid()),
+    evec(_evec),
+    eval(_eval)
+  {};
+
+  // Can just inherit existing M2
+  // Can just inherit existing M3
+
+  // Simple vstart - do nothing
   virtual void Vstart(Field & x,const Field & src){
-    return;
+    x=src; // Could apply Q
+  };
+
+  // Override PcgM1
+  virtual void PcgM1(Field & in, Field & out)
+  {
+    GRID_TRACE("EvecPreconditioner ");
+    int N=evec.size();
+    Field Pin(this->grid);
+    Field Qin(this->grid);
+
+    //MP  + Q = M(1-AQ) + Q = M
+    // // If we are eigenvector deflating in coarse space
+    // // Q   = Sum_i |phi_i> 1/lambda_i <phi_i|
+    // // A Q = Sum_i |phi_i> <phi_i|
+    // // M(1-AQ) = M(1-proj) + Q
+    Qin.Checkerboard()=in.Checkerboard();
+    Qin = Zero();
+    Pin = in;
+    for (int i=0;i<N;i++) {
+      const Field& tmp = evec[i];
+      auto ip = TensorRemove(innerProduct(tmp,in));
+      axpy(Qin, ip / eval[i],tmp,Qin);
+      axpy(Pin, -ip ,tmp,Pin);
     }
 
-  /////////////////////////////////////////////////////////////////////
+    this->_Smoother(Pin,out);
-  // Only Def1 has non-trivial Vout. Override in Def1
+
-  /////////////////////////////////////////////////////////////////////
+    out = out + Qin;
-  virtual void   Vout  (Field & in, Field & out,Field & src){
-    out = in;
-    //case PcgDef1:
-    //    //Qb + PT x
-    //    ProjectToSubspace(src,PleftProj);     
-    //    ApplyInverse(PleftProj,PleftMss_proj); // Ass^{-1} r_s
-    //    PromoteFromSubspace(PleftMss_proj,tmp);  
-    //    
-    //    Pright(in,out);
-    //    
-    //    linop_d->axpy(out,tmp,out,1.0);
-    //    break;
   }
+};
 
-  ////////////////////////////////////////////////////////////////////////////////////////////////
+NAMESPACE_END(Grid);
-  // Pright and Pleft are common to all implementations
-  ////////////////////////////////////////////////////////////////////////////////////////////////
-  virtual void Pright(Field & in,Field & out){
-    // P_R  = [ 1              0 ] 
-    //        [ -Mss^-1 Msb    0 ] 
-    Field in_sbar(grid);
 
-    ProjectToSubspace(in,PleftProj);     
-    PromoteFromSubspace(PleftProj,out);  
-    axpy(in_sbar,-1.0,out,in);       // in_sbar = in - in_s 
-
-    HermOp(in_sbar,out);
-    ProjectToSubspace(out,PleftProj);           // Mssbar in_sbar  (project)
-
-    ApplyInverse     (PleftProj,PleftMss_proj); // Mss^{-1} Mssbar 
-    PromoteFromSubspace(PleftMss_proj,out);     // 
-
-    axpy(out,-1.0,out,in_sbar);     // in_sbar - Mss^{-1} Mssbar in_sbar
-  }
-  virtual void Pleft (Field & in,Field & out){
-    // P_L  = [ 1  -Mbs Mss^-1] 
-    //        [ 0   0         ] 
-    Field in_sbar(grid);
-    Field    tmp2(grid);
-    Field    Mtmp(grid);
-
-    ProjectToSubspace(in,PleftProj);     
-    PromoteFromSubspace(PleftProj,out);  
-    axpy(in_sbar,-1.0,out,in);      // in_sbar = in - in_s
-
-    ApplyInverse(PleftProj,PleftMss_proj); // Mss^{-1} in_s
-    PromoteFromSubspace(PleftMss_proj,out);
-
-    HermOp(out,Mtmp);
-
-    ProjectToSubspace(Mtmp,PleftProj);      // Msbar s Mss^{-1}
-    PromoteFromSubspace(PleftProj,tmp2);
-
-    axpy(out,-1.0,tmp2,Mtmp);
-    axpy(out,-1.0,out,in_sbar);     // in_sbar - Msbars Mss^{-1} in_s
-  }
-}
-
-template<class Field>
-class TwoLevelFlexiblePcgADef2 : public TwoLevelFlexiblePcg<Field> {
- public:
-  virtual void M(Field & in,Field & out,Field & tmp){
-
-  } 
-  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp){
-
-  }
-  virtual void M2(Field & in, Field & out){
-
-  }
-  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp){
-
-  }
-  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp){
-
-  }
-}
-/*
-template<class Field>
-class TwoLevelFlexiblePcgAD : public TwoLevelFlexiblePcg<Field> {
- public:
-  virtual void M(Field & in,Field & out,Field & tmp); 
-  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
-  virtual void M2(Field & in, Field & out);
-  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
-  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
-}
-
-template<class Field>
-class TwoLevelFlexiblePcgDef1 : public TwoLevelFlexiblePcg<Field> {
- public:
-  virtual void M(Field & in,Field & out,Field & tmp); 
-  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
-  virtual void M2(Field & in, Field & out);
-  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
-  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
-  virtual void   Vout  (Field & in, Field & out,Field & src,Field & tmp);
-}
-
-template<class Field>
-class TwoLevelFlexiblePcgDef2 : public TwoLevelFlexiblePcg<Field> {
- public:
-  virtual void M(Field & in,Field & out,Field & tmp); 
-  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
-  virtual void M2(Field & in, Field & out);
-  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
-  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
-}
-
-template<class Field>
-class TwoLevelFlexiblePcgV11: public TwoLevelFlexiblePcg<Field> {
- public:
-  virtual void M(Field & in,Field & out,Field & tmp); 
-  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
-  virtual void M2(Field & in, Field & out);
-  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
-  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
-}
-*/
 #endif

Grid/algorithms/iterative/AdefMrhs.h

@@ -0,0 +1,414 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/AdefGeneric.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.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 */
+#pragma once
+
+
+  /*
+   * Compared to Tang-2009:  P=Pleft. P^T = PRight Q=MssInv. 
+   * Script A = SolverMatrix 
+   * Script P = Preconditioner
+   *
+   * Implement ADEF-2
+   *
+   * Vstart = P^Tx + Qb
+   * M1 = P^TM + Q
+   * M2=M3=1
+   */
+NAMESPACE_BEGIN(Grid);
+
+
+template<class Field>
+class TwoLevelCGmrhs
+{
+ public:
+  RealD   Tolerance;
+  Integer MaxIterations;
+  GridBase *grid;
+
+  // Fine operator, Smoother, CoarseSolver
+  LinearOperatorBase<Field>   &_FineLinop;
+  LinearFunction<Field>   &_Smoother;
+
+  GridStopWatch ProjectTimer;
+  GridStopWatch PromoteTimer;
+  GridStopWatch DeflateTimer;
+  GridStopWatch CoarseTimer;
+  GridStopWatch FineTimer;
+  GridStopWatch SmoothTimer;
+  GridStopWatch InsertTimer;
+
+  
+  // more most opertor functions
+  TwoLevelCGmrhs(RealD tol,
+		 Integer maxit,
+		 LinearOperatorBase<Field>   &FineLinop,
+		 LinearFunction<Field>       &Smoother,
+		 GridBase *fine) : 
+    Tolerance(tol), 
+    MaxIterations(maxit),
+    _FineLinop(FineLinop),
+    _Smoother(Smoother)
+  {
+    grid       = fine;
+  };
+  
+  // Vector case
+  virtual void operator() (std::vector<Field> &src, std::vector<Field> &x)
+  {
+    std::cout << GridLogMessage<<"HDCG: mrhs fPcg starting"<<std::endl;
+    src[0].Grid()->Barrier();
+    int nrhs = src.size();
+    std::vector<RealD> f(nrhs);
+    std::vector<RealD> rtzp(nrhs);
+    std::vector<RealD> rtz(nrhs);
+    std::vector<RealD> a(nrhs);
+    std::vector<RealD> d(nrhs);
+    std::vector<RealD> b(nrhs);
+    std::vector<RealD> rptzp(nrhs);
+    /////////////////////////////
+    // Set up history vectors
+    /////////////////////////////
+    int mmax = 3;
+
+    std::vector<std::vector<Field> > p(nrhs);   for(int r=0;r<nrhs;r++)  p[r].resize(mmax,grid);
+    std::vector<std::vector<Field> > mmp(nrhs); for(int r=0;r<nrhs;r++) mmp[r].resize(mmax,grid);
+    std::vector<std::vector<RealD> > pAp(nrhs); for(int r=0;r<nrhs;r++) pAp[r].resize(mmax);
+
+    std::vector<Field> z(nrhs,grid);
+    std::vector<Field>  mp (nrhs,grid);
+    std::vector<Field>  r  (nrhs,grid);
+    std::vector<Field>  mu (nrhs,grid);
+
+    //Initial residual computation & set up
+    std::vector<RealD> src_nrm(nrhs);
+    for(int rhs=0;rhs<nrhs;rhs++) {
+      src_nrm[rhs]=norm2(src[rhs]);
+      assert(src_nrm[rhs]!=0.0);
+    }
+    std::vector<RealD> tn(nrhs);
+
+    GridStopWatch HDCGTimer;
+    //////////////////////////
+    // x0 = Vstart -- possibly modify guess
+    //////////////////////////
+    Vstart(x,src);
+
+    for(int rhs=0;rhs<nrhs;rhs++){
+      // r0 = b -A x0
+      _FineLinop.HermOp(x[rhs],mmp[rhs][0]);
+      axpy (r[rhs], -1.0,mmp[rhs][0], src[rhs]);    // Recomputes r=src-Ax0
+    }
+
+    //////////////////////////////////
+    // Compute z = M1 x
+    //////////////////////////////////
+    // This needs a multiRHS version for acceleration
+    PcgM1(r,z);
+
+    std::vector<RealD> ssq(nrhs);
+    std::vector<RealD> rsq(nrhs);
+    std::vector<Field> pp(nrhs,grid);
+
+    for(int rhs=0;rhs<nrhs;rhs++){
+      rtzp[rhs] =real(innerProduct(r[rhs],z[rhs]));
+      p[rhs][0]=z[rhs];
+      ssq[rhs]=norm2(src[rhs]);
+      rsq[rhs]=  ssq[rhs]*Tolerance*Tolerance;
+      //      std::cout << GridLogMessage<<"mrhs HDCG: "<<rhs<<" k=0 residual "<<rtzp[rhs]<<" rsq "<<rsq[rhs]<<"\n";
+    }
+
+    ProjectTimer.Reset();
+    PromoteTimer.Reset();
+    DeflateTimer.Reset();
+    CoarseTimer.Reset();
+    SmoothTimer.Reset();
+    FineTimer.Reset();
+    InsertTimer.Reset();
+
+    GridStopWatch M1Timer;
+    GridStopWatch M2Timer;
+    GridStopWatch M3Timer;
+    GridStopWatch LinalgTimer;
+
+    HDCGTimer.Start();
+
+    std::vector<RealD> rn(nrhs);
+    for (int k=0;k<=MaxIterations;k++){
+    
+      int peri_k  = k % mmax;
+      int peri_kp = (k+1) % mmax;
+
+      for(int rhs=0;rhs<nrhs;rhs++){
+	rtz[rhs]=rtzp[rhs];
+	M3Timer.Start();
+	d[rhs]= PcgM3(p[rhs][peri_k],mmp[rhs][peri_k]);
+	M3Timer.Stop();
+	a[rhs] = rtz[rhs]/d[rhs];
+
+	LinalgTimer.Start();
+	// Memorise this
+	pAp[rhs][peri_k] = d[rhs];
+
+	axpy(x[rhs],a[rhs],p[rhs][peri_k],x[rhs]);
+	rn[rhs] = axpy_norm(r[rhs],-a[rhs],mmp[rhs][peri_k],r[rhs]);
+	LinalgTimer.Stop();
+      }
+
+      // Compute z = M x (for *all* RHS)
+      M1Timer.Start();
+      PcgM1(r,z);
+      M1Timer.Stop();
+      
+      RealD max_rn=0.0;
+      LinalgTimer.Start();
+      for(int rhs=0;rhs<nrhs;rhs++){
+
+	rtzp[rhs] =real(innerProduct(r[rhs],z[rhs]));
+
+	//	std::cout << GridLogMessage<<"HDCG::fPcg rhs"<<rhs<<" iteration "<<k<<" : inner rtzp "<<rtzp[rhs]<<"\n";
+	mu[rhs]=z[rhs];
+
+	p[rhs][peri_kp]=mu[rhs];
+
+	// Standard search direction p == z + b p 
+	b[rhs] = (rtzp[rhs])/rtz[rhs];
+
+	int northog = (k>mmax-1)?(mmax-1):k;        // This is the fCG-Tr(mmax-1) algorithm
+	for(int back=0; back < northog; back++){
+	  int peri_back = (k-back)%mmax;
+	  RealD pbApk= real(innerProduct(mmp[rhs][peri_back],p[rhs][peri_kp]));
+	  RealD beta = -pbApk/pAp[rhs][peri_back];
+	  axpy(p[rhs][peri_kp],beta,p[rhs][peri_back],p[rhs][peri_kp]);
+	}
+
+	RealD rrn=sqrt(rn[rhs]/ssq[rhs]);
+	RealD rtn=sqrt(rtz[rhs]/ssq[rhs]);
+	RealD rtnp=sqrt(rtzp[rhs]/ssq[rhs]);
+	
+	std::cout<<GridLogMessage<<"HDCG:fPcg rhs "<<rhs<<" k= "<<k<<" residual = "<<rrn<<"\n";
+	if ( rrn > max_rn ) max_rn = rrn;
+      }
+      LinalgTimer.Stop();
+
+      // Stopping condition based on worst case
+      if ( max_rn <= Tolerance ) { 
+
+	HDCGTimer.Stop();
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg converged in "<<k<<" iterations and "<<HDCGTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Linalg  "<<LinalgTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : fine M3 "<<M3Timer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : prec M1 "<<M1Timer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"**** M1 breakdown:"<<std::endl;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Project "<<ProjectTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Promote "<<PromoteTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Deflate "<<DeflateTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Coarse  "<<CoarseTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Fine    "<<FineTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Smooth  "<<SmoothTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Insert  "<<InsertTimer.Elapsed()<<std::endl;;
+
+	for(int rhs=0;rhs<nrhs;rhs++){
+	  _FineLinop.HermOp(x[rhs],mmp[rhs][0]);			  
+	  Field tmp(grid);
+	  axpy(tmp,-1.0,src[rhs],mmp[rhs][0]);
+      
+	  RealD  mmpnorm = sqrt(norm2(mmp[rhs][0]));
+	  RealD  xnorm   = sqrt(norm2(x[rhs]));
+	  RealD  srcnorm = sqrt(norm2(src[rhs]));
+	  RealD  tmpnorm = sqrt(norm2(tmp));
+	  RealD  true_residual = tmpnorm/srcnorm;
+	  std::cout<<GridLogMessage
+		   <<"HDCG: true residual ["<<rhs<<"] is "<<true_residual
+		   <<" solution "<<xnorm
+		   <<" source "<<srcnorm
+		   <<" mmp "<<mmpnorm	  
+		   <<std::endl;
+	}
+	return;
+      }
+      
+    }
+    HDCGTimer.Stop();
+    std::cout<<GridLogMessage<<"HDCG: not converged "<<HDCGTimer.Elapsed()<<std::endl;
+    for(int rhs=0;rhs<nrhs;rhs++){
+      RealD  xnorm   = sqrt(norm2(x[rhs]));
+      RealD  srcnorm = sqrt(norm2(src[rhs]));
+      std::cout<<GridLogMessage<<"HDCG: non-converged solution "<<xnorm<<" source "<<srcnorm<<std::endl;
+    }
+  }
+  
+
+ public:
+
+  virtual void PcgM1(std::vector<Field> & in,std::vector<Field> & out) = 0;
+  virtual void Vstart(std::vector<Field> & x,std::vector<Field> & src) = 0;
+  virtual void PcgM2(const Field & in, Field & out) {
+    out=in;
+  }
+
+  virtual RealD PcgM3(const Field & p, Field & mmp){
+    RealD dd;
+    _FineLinop.HermOp(p,mmp);
+    ComplexD dot = innerProduct(p,mmp);
+    dd=real(dot);
+    return dd;
+  }
+
+};
+
+template<class Field, class CoarseField>
+class TwoLevelADEF2mrhs : public TwoLevelCGmrhs<Field>
+{
+public:
+  GridBase *coarsegrid;
+  GridBase *coarsegridmrhs;
+  LinearFunction<CoarseField> &_CoarseSolverMrhs;
+  LinearFunction<CoarseField> &_CoarseSolverPreciseMrhs;
+  MultiRHSBlockProject<Field>    &_Projector;
+  MultiRHSDeflation<CoarseField> &_Deflator;
+
+  
+  TwoLevelADEF2mrhs(RealD tol,
+		    Integer maxit,
+		    LinearOperatorBase<Field>    &FineLinop,
+		    LinearFunction<Field>        &Smoother,
+		    LinearFunction<CoarseField>  &CoarseSolverMrhs,
+		    LinearFunction<CoarseField>  &CoarseSolverPreciseMrhs,
+		    MultiRHSBlockProject<Field>    &Projector,
+		    MultiRHSDeflation<CoarseField> &Deflator,
+		    GridBase *_coarsemrhsgrid) :
+    TwoLevelCGmrhs<Field>(tol, maxit,FineLinop,Smoother,Projector.fine_grid),
+    _CoarseSolverMrhs(CoarseSolverMrhs),
+    _CoarseSolverPreciseMrhs(CoarseSolverPreciseMrhs),
+    _Projector(Projector),
+    _Deflator(Deflator)
+  {
+    coarsegrid = Projector.coarse_grid;
+    coarsegridmrhs = _coarsemrhsgrid;// Thi could be in projector
+  };
+
+  // Override Vstart
+  virtual void Vstart(std::vector<Field> & x,std::vector<Field> & src)
+  {
+    int nrhs=x.size();
+    ///////////////////////////////////
+    // Choose x_0 such that 
+    // x_0 = guess +  (A_ss^inv) r_s = guess + Ass_inv [src -Aguess]
+    //                               = [1 - Ass_inv A] Guess + Assinv src
+    //                               = P^T guess + Assinv src 
+    //                               = Vstart  [Tang notation]
+    // This gives:
+    // W^T (src - A x_0) = src_s - A guess_s - r_s
+    //                   = src_s - (A guess)_s - src_s  + (A guess)_s 
+    //                   = 0 
+    ///////////////////////////////////
+    std::vector<CoarseField> PleftProj(nrhs,this->coarsegrid);
+    std::vector<CoarseField> PleftMss_proj(nrhs,this->coarsegrid);
+    CoarseField PleftProjMrhs(this->coarsegridmrhs);
+    CoarseField PleftMss_projMrhs(this->coarsegridmrhs);
+
+    this->_Projector.blockProject(src,PleftProj);
+    this->_Deflator.DeflateSources(PleftProj,PleftMss_proj);
+    for(int rhs=0;rhs<nrhs;rhs++) {
+      InsertSliceFast(PleftProj[rhs],PleftProjMrhs,rhs,0);
+      InsertSliceFast(PleftMss_proj[rhs],PleftMss_projMrhs,rhs,0); // the guess
+    }
+    
+    this->_CoarseSolverPreciseMrhs(PleftProjMrhs,PleftMss_projMrhs); // Ass^{-1} r_s
+
+    for(int rhs=0;rhs<nrhs;rhs++) {
+      ExtractSliceFast(PleftMss_proj[rhs],PleftMss_projMrhs,rhs,0);
+    }
+    this->_Projector.blockPromote(x,PleftMss_proj);
+  }
+
+  virtual void PcgM1(std::vector<Field> & in,std::vector<Field> & out){
+
+    int nrhs=in.size();
+
+    // [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
+    std::vector<Field> tmp(nrhs,this->grid);
+    std::vector<Field> Min(nrhs,this->grid);
+
+    std::vector<CoarseField> PleftProj(nrhs,this->coarsegrid);
+    std::vector<CoarseField> PleftMss_proj(nrhs,this->coarsegrid);
+
+    CoarseField PleftProjMrhs(this->coarsegridmrhs);
+    CoarseField PleftMss_projMrhs(this->coarsegridmrhs);
+
+    for(int rhs=0;rhs<nrhs;rhs++) {
+
+      this->SmoothTimer.Start();
+      this->_Smoother(in[rhs],Min[rhs]);
+      this->SmoothTimer.Stop();
+
+      this->FineTimer.Start();
+      this->_FineLinop.HermOp(Min[rhs],out[rhs]);
+
+      axpy(tmp[rhs],-1.0,out[rhs],in[rhs]);          // resid  = in - A Min
+      this->FineTimer.Stop();
+
+    }
+
+    this->ProjectTimer.Start();
+    this->_Projector.blockProject(tmp,PleftProj);
+    this->ProjectTimer.Stop();
+    this->DeflateTimer.Start();
+    this->_Deflator.DeflateSources(PleftProj,PleftMss_proj);
+    this->DeflateTimer.Stop();
+    this->InsertTimer.Start();
+    for(int rhs=0;rhs<nrhs;rhs++) {
+      InsertSliceFast(PleftProj[rhs],PleftProjMrhs,rhs,0);
+      InsertSliceFast(PleftMss_proj[rhs],PleftMss_projMrhs,rhs,0); // the guess
+    }
+    this->InsertTimer.Stop();
+
+    this->CoarseTimer.Start();
+    this->_CoarseSolverMrhs(PleftProjMrhs,PleftMss_projMrhs); // Ass^{-1} [in - A Min]_s
+    this->CoarseTimer.Stop();
+
+    this->InsertTimer.Start();
+    for(int rhs=0;rhs<nrhs;rhs++) {
+      ExtractSliceFast(PleftMss_proj[rhs],PleftMss_projMrhs,rhs,0);
+    }
+    this->InsertTimer.Stop();
+    this->PromoteTimer.Start();
+    this->_Projector.blockPromote(tmp,PleftMss_proj);// tmp= Q[in - A Min]  
+    this->PromoteTimer.Stop();
+    this->FineTimer.Start();
+    for(int rhs=0;rhs<nrhs;rhs++) {
+      axpy(out[rhs],1.0,Min[rhs],tmp[rhs]); // Min+tmp
+    }
+    this->FineTimer.Stop();
+  }
+};
+  
+
+NAMESPACE_END(Grid);
+
+

Grid/algorithms/iterative/ConjugateGradient.h

@@ -54,11 +54,14 @@ public:
   ConjugateGradient(RealD tol, Integer maxit, bool err_on_no_conv = true)
     : Tolerance(tol),
       MaxIterations(maxit),
-      ErrorOnNoConverge(err_on_no_conv){};
+      ErrorOnNoConverge(err_on_no_conv)
+  {};
 
   void operator()(LinearOperatorBase<Field> &Linop, const Field &src, Field &psi) {
 
     GRID_TRACE("ConjugateGradient");
+    GridStopWatch PreambleTimer;
+    PreambleTimer.Start();
     psi.Checkerboard() = src.Checkerboard();
 
     conformable(psi, src);
@@ -66,22 +69,26 @@ public:
     RealD cp, c, a, d, b, ssq, qq;
     //RealD b_pred;
 
-    Field p(src);
+    // Was doing copies
-    Field mmp(src);
+    Field p(src.Grid());
-    Field r(src);
+    Field mmp(src.Grid());
+    Field r(src.Grid());
 
     // Initial residual computation & set up
+    ssq = norm2(src);
     RealD guess = norm2(psi);
     assert(std::isnan(guess) == 0);
-    
+    if ( guess == 0.0 ) {
+      r = src;
+      p = r;
+      a = ssq;
+    } else { 
       Linop.HermOpAndNorm(psi, mmp, d, b);
-    
       r = src - mmp;
       p = r;
-
       a = norm2(p);
+    }
     cp = a;
-    ssq = norm2(src);
 
     // Handle trivial case of zero src
     if (ssq == 0.){
@@ -111,6 +118,7 @@ public:
     std::cout << GridLogIterative << std::setprecision(8)
               << "ConjugateGradient: k=0 residual " << cp << " target " << rsq << std::endl;
 
+    PreambleTimer.Stop();
     GridStopWatch LinalgTimer;
     GridStopWatch InnerTimer;
     GridStopWatch AxpyNormTimer;
@@ -183,13 +191,14 @@ public:
 		  << "\tTrue residual " << true_residual
 		  << "\tTarget " << Tolerance << std::endl;
 
-        std::cout << GridLogMessage << "Time breakdown "<<std::endl;
+	//	std::cout << GridLogMessage << "\tPreamble   " << PreambleTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tSolver Elapsed    " << SolverTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+        std::cout << GridLogPerformance << "Time breakdown "<<std::endl;
-	std::cout << GridLogMessage << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
+	std::cout << GridLogPerformance << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tInner      " << InnerTimer.Elapsed() <<std::endl;
+	std::cout << GridLogPerformance << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
+	std::cout << GridLogPerformance << "\t\tInner      " << InnerTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
+	std::cout << GridLogPerformance << "\t\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
+	std::cout << GridLogPerformance << "\t\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
 
 	std::cout << GridLogDebug << "\tMobius flop rate " << DwfFlops/ usecs<< " Gflops " <<std::endl;
 
@@ -202,12 +211,22 @@ public:
       }
     }
     // Failed. Calculate true residual before giving up                                                         
-    Linop.HermOpAndNorm(psi, mmp, d, qq);
+    // Linop.HermOpAndNorm(psi, mmp, d, qq);
-    p = mmp - src;
+    //    p = mmp - src;
+    //TrueResidual = sqrt(norm2(p)/ssq);
+    //    TrueResidual = 1;
 
-    TrueResidual = sqrt(norm2(p)/ssq);
+    std::cout << GridLogMessage << "ConjugateGradient did NOT converge "<<k<<" / "<< MaxIterations
-
+    	      <<" residual "<< std::sqrt(cp / ssq)<< std::endl;
-    std::cout << GridLogMessage << "ConjugateGradient did NOT converge "<<k<<" / "<< MaxIterations<< std::endl;
+    SolverTimer.Stop();
+    std::cout << GridLogMessage << "\tPreamble   " << PreambleTimer.Elapsed() <<std::endl;
+    std::cout << GridLogMessage << "\tSolver     " << SolverTimer.Elapsed() <<std::endl;
+    std::cout << GridLogMessage << "Solver breakdown "<<std::endl;
+    std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+    std::cout << GridLogMessage<< "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\t\tInner      " << InnerTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\t\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\t\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
 
     if (ErrorOnNoConverge) assert(0);
     IterationsToComplete = k;

Grid/algorithms/iterative/ConjugateGradientMultiShift.h

@@ -144,7 +144,7 @@ public:
     for(int s=0;s<nshift;s++){
       rsq[s] = cp * mresidual[s] * mresidual[s];
       std::cout<<GridLogMessage<<"ConjugateGradientMultiShift: shift "<<s
-	       <<" target resid "<<rsq[s]<<std::endl;
+	       <<" target resid^2 "<<rsq[s]<<std::endl;
       ps[s] = src;
     }
     // r and p for primary

Grid/algorithms/iterative/ImplicitlyRestartedLanczos.h

@@ -79,14 +79,16 @@ template<class Field> class ImplicitlyRestartedLanczosHermOpTester  : public Imp
     RealD vv = norm2(v) / ::pow(evalMaxApprox,2.0);
 
     std::cout.precision(13);
-    std::cout<<GridLogIRL  << "[" << std::setw(3)<<j<<"] "
-	     <<"eval = "<<std::setw(25)<< eval << " (" << eval_poly << ")"
-	     <<" |H B[i] - eval[i]B[i]|^2 / evalMaxApprox^2 " << std::setw(25) << vv
-	     <<std::endl;
 
     int conv=0;
     if( (vv<eresid*eresid) ) conv = 1;
 
+    std::cout<<GridLogIRL  << "[" << std::setw(3)<<j<<"] "
+	     <<"eval = "<<std::setw(25)<< eval << " (" << eval_poly << ")"
+	     <<" |H B[i] - eval[i]B[i]|^2 / evalMaxApprox^2 " << std::setw(25) << vv
+	     <<" target " << eresid*eresid << " conv " <<conv
+	     <<std::endl;
+
     return conv;
   }
 };
@@ -457,7 +459,7 @@ until convergence
 	    std::vector<Field>& evec,
 	    Field& w,int Nm,int k)
   {
-    std::cout<<GridLogIRL << "Lanczos step " <<k<<std::endl;
+    std::cout<<GridLogDebug << "Lanczos step " <<k<<std::endl;
     const RealD tiny = 1.0e-20;
     assert( k< Nm );
 
@@ -465,7 +467,7 @@ until convergence
 
     Field& evec_k = evec[k];
 
-    _PolyOp(evec_k,w);    std::cout<<GridLogIRL << "PolyOp" <<std::endl;
+    _PolyOp(evec_k,w);    std::cout<<GridLogDebug << "PolyOp" <<std::endl;
 
     if(k>0) w -= lme[k-1] * evec[k-1];
 
@@ -480,18 +482,18 @@ until convergence
     lme[k] = beta;
 
     if ( (k>0) && ( (k % orth_period) == 0 )) {
-      std::cout<<GridLogIRL << "Orthogonalising " <<k<<std::endl;
+      std::cout<<GridLogDebug << "Orthogonalising " <<k<<std::endl;
       orthogonalize(w,evec,k); // orthonormalise
-      std::cout<<GridLogIRL << "Orthogonalised " <<k<<std::endl;
+      std::cout<<GridLogDebug << "Orthogonalised " <<k<<std::endl;
     }
 
     if(k < Nm-1) evec[k+1] = w;
 
-    std::cout<<GridLogIRL << "alpha[" << k << "] = " << zalph << " beta[" << k << "] = "<<beta<<std::endl;
+    std::cout<<GridLogIRL << "Lanczos step alpha[" << k << "] = " << zalph << " beta[" << k << "] = "<<beta<<std::endl;
     if ( beta < tiny ) 
       std::cout<<GridLogIRL << " beta is tiny "<<beta<<std::endl;
 
-    std::cout<<GridLogIRL << "Lanczos step complete " <<k<<std::endl;
+    std::cout<<GridLogDebug << "Lanczos step complete " <<k<<std::endl;
   }
 
   void diagonalize_Eigen(std::vector<RealD>& lmd, std::vector<RealD>& lme, 

Grid/algorithms/iterative/NormalEquations.h

@@ -33,7 +33,7 @@ NAMESPACE_BEGIN(Grid);
 ///////////////////////////////////////////////////////////////////////////////////////////////////////
 // Take a matrix and form an NE solver calling a Herm solver
 ///////////////////////////////////////////////////////////////////////////////////////////////////////
-template<class Field> class NormalEquations {
+template<class Field> class NormalEquations : public LinearFunction<Field>{
 private:
   SparseMatrixBase<Field> & _Matrix;
   OperatorFunction<Field> & _HermitianSolver;
@@ -60,7 +60,7 @@ public:
   }     
 };
 
-template<class Field> class HPDSolver {
+template<class Field> class HPDSolver : public LinearFunction<Field> {
 private:
   LinearOperatorBase<Field> & _Matrix;
   OperatorFunction<Field> & _HermitianSolver;
@@ -78,13 +78,13 @@ public:
   void operator() (const Field &in, Field &out){
  
     _Guess(in,out);
-    _HermitianSolver(_Matrix,in,out);  // Mdag M out = Mdag in
+    _HermitianSolver(_Matrix,in,out);  //M out = in
 
   }     
 };
 
 
-template<class Field> class MdagMSolver {
+template<class Field> class MdagMSolver : public LinearFunction<Field> {
 private:
   SparseMatrixBase<Field> & _Matrix;
   OperatorFunction<Field> & _HermitianSolver;

Grid/algorithms/iterative/PowerMethod.h

@@ -20,7 +20,7 @@ template<class Field> class PowerMethod
     RealD evalMaxApprox = 0.0; 
     auto src_n = src; 
     auto tmp = src; 
-    const int _MAX_ITER_EST_ = 50; 
+    const int _MAX_ITER_EST_ = 100; 
 
     for (int i=0;i<_MAX_ITER_EST_;i++) { 
       

Grid/algorithms/multigrid/Aggregates.h

@@ -0,0 +1,478 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/Aggregates.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
+Author: paboyle <paboyle@ph.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 */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+inline RealD AggregatePowerLaw(RealD x)
+{
+  //  return std::pow(x,-4);
+  //  return std::pow(x,-3);
+  return std::pow(x,-5);
+}
+
+template<class Fobj,class CComplex,int nbasis>
+class Aggregation {
+public:
+  constexpr int Nbasis(void) { return nbasis; };
+  
+  typedef iVector<CComplex,nbasis >             siteVector;
+  typedef Lattice<siteVector>                 CoarseVector;
+  typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
+
+  typedef Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj >        FineField;
+
+  GridBase *CoarseGrid;
+  GridBase *FineGrid;
+  std::vector<Lattice<Fobj> > subspace;
+  int checkerboard;
+  int Checkerboard(void){return checkerboard;}
+  Aggregation(GridBase *_CoarseGrid,GridBase *_FineGrid,int _checkerboard) : 
+    CoarseGrid(_CoarseGrid),
+    FineGrid(_FineGrid),
+    subspace(nbasis,_FineGrid),
+    checkerboard(_checkerboard)
+  {
+  };
+  
+  
+  void Orthogonalise(void){
+    CoarseScalar InnerProd(CoarseGrid); 
+    //    std::cout << GridLogMessage <<" Block Gramm-Schmidt pass 1"<<std::endl;
+    blockOrthogonalise(InnerProd,subspace);
+  } 
+  void ProjectToSubspace(CoarseVector &CoarseVec,const FineField &FineVec){
+    blockProject(CoarseVec,FineVec,subspace);
+  }
+  void PromoteFromSubspace(const CoarseVector &CoarseVec,FineField &FineVec){
+    FineVec.Checkerboard() = subspace[0].Checkerboard();
+    blockPromote(CoarseVec,FineVec,subspace);
+  }
+
+  virtual void CreateSubspaceRandom(GridParallelRNG  &RNG) {
+    int nn=nbasis;
+    RealD scale;
+    FineField noise(FineGrid);
+    for(int b=0;b<nn;b++){
+      subspace[b] = Zero();
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+      subspace[b] = noise;
+    }
+  }
+  virtual void CreateSubspace(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,int nn=nbasis)
+  {
+
+    RealD scale;
+
+    ConjugateGradient<FineField> CG(1.0e-2,100,false);
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+
+    for(int b=0;b<nn;b++){
+      
+      subspace[b] = Zero();
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+      
+      hermop.Op(noise,Mn); std::cout<<GridLogMessage << "noise   ["<<b<<"] <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+
+      for(int i=0;i<1;i++){
+
+	CG(hermop,noise,subspace[b]);
+
+	noise = subspace[b];
+	scale = std::pow(norm2(noise),-0.5); 
+	noise=noise*scale;
+
+      }
+
+      hermop.Op(noise,Mn); std::cout<<GridLogMessage << "filtered["<<b<<"] <f|MdagM|f> "<<norm2(Mn)<<std::endl;
+      subspace[b]   = noise;
+
+    }
+  }
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  // World of possibilities here. But have tried quite a lot of experiments (250+ jobs run on Summit)
+  // and this is the best I found
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+
+  virtual void CreateSubspaceChebyshev(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,
+				       int nn,
+				       double hi,
+				       double lo,
+				       int orderfilter,
+				       int ordermin,
+				       int orderstep,
+				       double filterlo
+				       ) {
+
+    RealD scale;
+
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+    FineField tmp(FineGrid);
+
+    // New normalised noise
+    gaussian(RNG,noise);
+    scale = std::pow(norm2(noise),-0.5); 
+    noise=noise*scale;
+
+    std::cout << GridLogMessage<<" Chebyshev subspace pass-1 : ord "<<orderfilter<<" ["<<lo<<","<<hi<<"]"<<std::endl;
+    std::cout << GridLogMessage<<" Chebyshev subspace pass-2 : nbasis"<<nn<<" min "
+	      <<ordermin<<" step "<<orderstep
+	      <<" lo"<<filterlo<<std::endl;
+
+    // Initial matrix element
+    hermop.Op(noise,Mn); std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+
+    int b =0;
+    {
+      // Filter
+      Chebyshev<FineField> Cheb(lo,hi,orderfilter);
+      Cheb(hermop,noise,Mn);
+      // normalise
+      scale = std::pow(norm2(Mn),-0.5); 	Mn=Mn*scale;
+      subspace[b]   = Mn;
+      hermop.Op(Mn,tmp); 
+      std::cout<<GridLogMessage << "filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+      b++;
+    }
+
+    // Generate a full sequence of Chebyshevs
+    {
+      lo=filterlo;
+      noise=Mn;
+
+      FineField T0(FineGrid); T0 = noise;  
+      FineField T1(FineGrid); 
+      FineField T2(FineGrid);
+      FineField y(FineGrid);
+      
+      FineField *Tnm = &T0;
+      FineField *Tn  = &T1;
+      FineField *Tnp = &T2;
+
+      // Tn=T1 = (xscale M + mscale)in
+      RealD xscale = 2.0/(hi-lo);
+      RealD mscale = -(hi+lo)/(hi-lo);
+      hermop.HermOp(T0,y);
+      T1=y*xscale+noise*mscale;
+
+      for(int n=2;n<=ordermin+orderstep*(nn-2);n++){
+	
+	hermop.HermOp(*Tn,y);
+
+	autoView( y_v , y, AcceleratorWrite);
+	autoView( Tn_v , (*Tn), AcceleratorWrite);
+	autoView( Tnp_v , (*Tnp), AcceleratorWrite);
+	autoView( Tnm_v , (*Tnm), AcceleratorWrite);
+	const int Nsimd = CComplex::Nsimd();
+	accelerator_for(ss, FineGrid->oSites(), Nsimd, {
+	  coalescedWrite(y_v[ss],xscale*y_v(ss)+mscale*Tn_v(ss));
+	  coalescedWrite(Tnp_v[ss],2.0*y_v(ss)-Tnm_v(ss));
+        });
+
+	// Possible more fine grained control is needed than a linear sweep,
+	// but huge productivity gain if this is simple algorithm and not a tunable
+	int m =1;
+	if ( n>=ordermin ) m=n-ordermin;
+	if ( (m%orderstep)==0 ) { 
+	  Mn=*Tnp;
+	  scale = std::pow(norm2(Mn),-0.5);         Mn=Mn*scale;
+	  subspace[b] = Mn;
+	  hermop.Op(Mn,tmp); 
+	  std::cout<<GridLogMessage << n<<" filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+	  b++;
+	}
+
+	// Cycle pointers to avoid copies
+	FineField *swizzle = Tnm;
+	Tnm    =Tn;
+	Tn     =Tnp;
+	Tnp    =swizzle;
+	  
+      }
+    }
+    assert(b==nn);
+  }
+  virtual void CreateSubspaceChebyshev(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,
+				       int nn,
+				       double hi,
+				       double lo,
+				       int orderfilter
+				       ) {
+
+    RealD scale;
+
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+    FineField tmp(FineGrid);
+
+    // New normalised noise
+    std::cout << GridLogMessage<<" Chebyshev subspace pure noise : ord "<<orderfilter<<" ["<<lo<<","<<hi<<"]"<<std::endl;
+    std::cout << GridLogMessage<<" Chebyshev subspace pure noise  : nbasis "<<nn<<std::endl;
+
+
+    for(int b =0;b<nbasis;b++)
+    {
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+
+      // Initial matrix element
+      hermop.Op(noise,Mn);
+      if(b==0) std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+
+      // Filter
+      Chebyshev<FineField> Cheb(lo,hi,orderfilter);
+      Cheb(hermop,noise,Mn);
+      scale = std::pow(norm2(Mn),-0.5); 	Mn=Mn*scale;
+
+      // Refine
+      Chebyshev<FineField> PowerLaw(lo,hi,1000,AggregatePowerLaw);
+      noise = Mn;
+      PowerLaw(hermop,noise,Mn);
+      scale = std::pow(norm2(Mn),-0.5); 	Mn=Mn*scale;
+
+      // normalise
+      subspace[b]   = Mn;
+      hermop.Op(Mn,tmp); 
+      std::cout<<GridLogMessage << "filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+    }
+
+  }
+
+  virtual void CreateSubspaceChebyshevPowerLaw(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,
+					       int nn,
+					       double hi,
+					       int orderfilter
+					       ) {
+
+    RealD scale;
+
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+    FineField tmp(FineGrid);
+
+    // New normalised noise
+    std::cout << GridLogMessage<<" Chebyshev subspace pure noise : ord "<<orderfilter<<" [0,"<<hi<<"]"<<std::endl;
+    std::cout << GridLogMessage<<" Chebyshev subspace pure noise  : nbasis "<<nn<<std::endl;
+
+    for(int b =0;b<nbasis;b++)
+    {
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+
+      // Initial matrix element
+      hermop.Op(noise,Mn);
+      if(b==0) std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+      // Filter
+      Chebyshev<FineField> Cheb(0.0,hi,orderfilter,AggregatePowerLaw);
+      Cheb(hermop,noise,Mn);
+      // normalise
+      scale = std::pow(norm2(Mn),-0.5); 	Mn=Mn*scale;
+      subspace[b]   = Mn;
+      hermop.Op(Mn,tmp); 
+      std::cout<<GridLogMessage << "filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+    }
+
+  }
+  virtual void CreateSubspaceChebyshevNew(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,
+					  double hi
+					  ) {
+
+    RealD scale;
+
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+    FineField tmp(FineGrid);
+
+    // New normalised noise
+    for(int b =0;b<nbasis;b++)
+    {
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+
+      // Initial matrix element
+      hermop.Op(noise,Mn);
+      if(b==0) std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+      // Filter
+      //#opt2(x) =  acheb(x,3,90,300)* acheb(x,1,90,50) * acheb(x,0.5,90,200) * acheb(x,0.05,90,400) * acheb(x,0.01,90,1500)
+      /*266
+      Chebyshev<FineField> Cheb1(3.0,hi,300);
+      Chebyshev<FineField> Cheb2(1.0,hi,50);
+      Chebyshev<FineField> Cheb3(0.5,hi,300);
+      Chebyshev<FineField> Cheb4(0.05,hi,500);
+      Chebyshev<FineField> Cheb5(0.01,hi,2000);
+      */
+      /* 242 */
+      /*
+      Chebyshev<FineField> Cheb3(0.1,hi,300);
+      Chebyshev<FineField> Cheb2(0.02,hi,1000);
+      Chebyshev<FineField> Cheb1(0.003,hi,2000);
+      8?
+      */
+      /* How many??
+      */
+      Chebyshev<FineField> Cheb2(0.001,hi,2500); // 169 iters on HDCG after refine
+      Chebyshev<FineField> Cheb1(0.02,hi,600);
+
+      //      Chebyshev<FineField> Cheb2(0.001,hi,1500);
+      //      Chebyshev<FineField> Cheb1(0.02,hi,600);
+      Cheb1(hermop,noise,Mn); scale = std::pow(norm2(Mn),-0.5); 	noise=Mn*scale;
+      hermop.Op(noise,tmp); std::cout<<GridLogMessage << "Cheb1 <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+      Cheb2(hermop,noise,Mn); scale = std::pow(norm2(Mn),-0.5); 	noise=Mn*scale;
+      hermop.Op(noise,tmp); std::cout<<GridLogMessage << "Cheb2 <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+      //      Cheb3(hermop,noise,Mn); scale = std::pow(norm2(Mn),-0.5); 	noise=Mn*scale;
+      //      hermop.Op(noise,tmp); std::cout<<GridLogMessage << "Cheb3 <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+      //      Cheb4(hermop,noise,Mn); scale = std::pow(norm2(Mn),-0.5); 	noise=Mn*scale;
+      //      hermop.Op(noise,tmp); std::cout<<GridLogMessage << "Cheb4 <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+      //      Cheb5(hermop,noise,Mn); scale = std::pow(norm2(Mn),-0.5); 	noise=Mn*scale;
+      //      hermop.Op(noise,tmp); std::cout<<GridLogMessage << "Cheb5 <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+      subspace[b]   = noise;
+      hermop.Op(subspace[b],tmp); 
+      std::cout<<GridLogMessage << "filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<< " norm " << norm2(noise)<<std::endl;
+    }
+
+  }
+
+  virtual void CreateSubspaceMultishift(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,
+					double Lo,double tol,int maxit)
+  {
+
+    RealD scale;
+
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+    FineField tmp(FineGrid);
+
+    // New normalised noise
+    std::cout << GridLogMessage<<" Multishift subspace : Lo "<<Lo<<std::endl;
+
+    // Filter
+    // [ 1/6(x+Lo)  - 1/2(x+2Lo) + 1/2(x+3Lo)  -1/6(x+4Lo) = Lo^3 /[ (x+1Lo)(x+2Lo)(x+3Lo)(x+4Lo) ]
+    //
+    // 1/(x+Lo)  - 1/(x+2 Lo)
+    double epsilon      = Lo/3;
+    std::vector<RealD> alpha({1.0/6.0,-1.0/2.0,1.0/2.0,-1.0/6.0});
+    std::vector<RealD> shifts({Lo,Lo+epsilon,Lo+2*epsilon,Lo+3*epsilon});
+    std::vector<RealD> tols({tol,tol,tol,tol});
+    std::cout << "sizes "<<alpha.size()<<" "<<shifts.size()<<" "<<tols.size()<<std::endl;
+
+    MultiShiftFunction msf(4,0.0,95.0);
+    std::cout << "msf constructed "<<std::endl;
+    msf.poles=shifts;
+    msf.residues=alpha;
+    msf.tolerances=tols;
+    msf.norm=0.0;
+    msf.order=alpha.size();
+    ConjugateGradientMultiShift<FineField> MSCG(maxit,msf);
+    
+    for(int b =0;b<nbasis;b++)
+    {
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+
+      // Initial matrix element
+      hermop.Op(noise,Mn);
+      if(b==0) std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+
+      MSCG(hermop,noise,Mn);
+      scale = std::pow(norm2(Mn),-0.5); 	Mn=Mn*scale;
+      subspace[b]   = Mn;
+      hermop.Op(Mn,tmp); 
+      std::cout<<GridLogMessage << "filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+
+    }
+
+  }
+  virtual void RefineSubspace(LinearOperatorBase<FineField> &hermop,
+			      double Lo,double tol,int maxit)
+  {
+    FineField tmp(FineGrid);
+    for(int b =0;b<nbasis;b++)
+    {
+      ConjugateGradient<FineField>  CGsloppy(tol,maxit,false);
+      ShiftedHermOpLinearOperator<FineField> ShiftedFineHermOp(hermop,Lo);
+      tmp=Zero();
+      CGsloppy(hermop,subspace[b],tmp);
+      RealD scale = std::pow(norm2(tmp),-0.5); 	tmp=tmp*scale;
+      subspace[b]=tmp;
+      hermop.Op(subspace[b],tmp);
+      std::cout<<GridLogMessage << "filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+    }
+  }
+  virtual void RefineSubspaceHDCG(LinearOperatorBase<FineField> &hermop,
+				  TwoLevelADEF2mrhs<FineField,CoarseVector> & theHDCG,
+				  int nrhs)
+  {
+    std::vector<FineField> src_mrhs(nrhs,FineGrid);
+    std::vector<FineField> res_mrhs(nrhs,FineGrid);
+    FineField tmp(FineGrid);
+    for(int b =0;b<nbasis;b+=nrhs)
+    {
+      tmp = subspace[b];
+      RealD scale = std::pow(norm2(tmp),-0.5); 	tmp=tmp*scale;
+      subspace[b] =tmp;
+      hermop.Op(subspace[b],tmp);
+      std::cout<<GridLogMessage << "before filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+
+      for(int r=0;r<MIN(nbasis-b,nrhs);r++){
+	src_mrhs[r] = subspace[b+r];
+      }
+      for(int r=0;r<nrhs;r++){
+	res_mrhs[r] = Zero();
+      }
+      theHDCG(src_mrhs,res_mrhs);
+
+      for(int r=0;r<MIN(nbasis-b,nrhs);r++){
+	tmp = res_mrhs[r];
+	RealD scale = std::pow(norm2(tmp),-0.5); tmp=tmp*scale;
+	subspace[b+r]=tmp;
+      }
+      hermop.Op(subspace[b],tmp);
+      std::cout<<GridLogMessage << "after filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+    }
+  }
+
+  
+  
+};
+NAMESPACE_END(Grid);
+

Grid/algorithms/multigrid/CoarsenedMatrix.h

@@ -56,243 +56,6 @@ inline void blockMaskedInnerProduct(Lattice<CComplex> &CoarseInner,
   blockSum(CoarseInner,fine_inner_msk);
 }
 
-
-class Geometry {
-public:
-  int npoint;
-  int base;
-  std::vector<int> directions   ;
-  std::vector<int> displacements;
-  std::vector<int> points_dagger;
-
-  Geometry(int _d)  {
-    
-    base = (_d==5) ? 1:0;
-
-    // make coarse grid stencil for 4d , not 5d
-    if ( _d==5 ) _d=4;
-
-    npoint = 2*_d+1;
-    directions.resize(npoint);
-    displacements.resize(npoint);
-    points_dagger.resize(npoint);
-    for(int d=0;d<_d;d++){
-      directions[d   ] = d+base;
-      directions[d+_d] = d+base;
-      displacements[d  ] = +1;
-      displacements[d+_d]= -1;
-      points_dagger[d   ] = d+_d;
-      points_dagger[d+_d] = d;
-    }
-    directions   [2*_d]=0;
-    displacements[2*_d]=0;
-    points_dagger[2*_d]=2*_d;
-  }
-
-  int point(int dir, int disp) {
-    assert(disp == -1 || disp == 0 || disp == 1);
-    assert(base+0 <= dir && dir < base+4);
-
-    // directions faster index = new indexing
-    // 4d (base = 0):
-    // point 0  1  2  3  4  5  6  7  8
-    // dir   0  1  2  3  0  1  2  3  0
-    // disp +1 +1 +1 +1 -1 -1 -1 -1  0
-    // 5d (base = 1):
-    // point 0  1  2  3  4  5  6  7  8
-    // dir   1  2  3  4  1  2  3  4  0
-    // disp +1 +1 +1 +1 -1 -1 -1 -1  0
-
-    // displacements faster index = old indexing
-    // 4d (base = 0):
-    // point 0  1  2  3  4  5  6  7  8
-    // dir   0  0  1  1  2  2  3  3  0
-    // disp +1 -1 +1 -1 +1 -1 +1 -1  0
-    // 5d (base = 1):
-    // point 0  1  2  3  4  5  6  7  8
-    // dir   1  1  2  2  3  3  4  4  0
-    // disp +1 -1 +1 -1 +1 -1 +1 -1  0
-
-    if(dir == 0 and disp == 0)
-      return 8;
-    else // New indexing
-      return (1 - disp) / 2 * 4 + dir - base;
-    // else // Old indexing
-    //   return (4 * (dir - base) + 1 - disp) / 2;
-  }
-};
-  
-template<class Fobj,class CComplex,int nbasis>
-class Aggregation   {
-public:
-  typedef iVector<CComplex,nbasis >             siteVector;
-  typedef Lattice<siteVector>                 CoarseVector;
-  typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
-
-  typedef Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
-  typedef Lattice<Fobj >        FineField;
-
-  GridBase *CoarseGrid;
-  GridBase *FineGrid;
-  std::vector<Lattice<Fobj> > subspace;
-  int checkerboard;
-  int Checkerboard(void){return checkerboard;}
-  Aggregation(GridBase *_CoarseGrid,GridBase *_FineGrid,int _checkerboard) : 
-    CoarseGrid(_CoarseGrid),
-    FineGrid(_FineGrid),
-    subspace(nbasis,_FineGrid),
-    checkerboard(_checkerboard)
-  {
-  };
-  
-  void Orthogonalise(void){
-    CoarseScalar InnerProd(CoarseGrid); 
-    std::cout << GridLogMessage <<" Block Gramm-Schmidt pass 1"<<std::endl;
-    blockOrthogonalise(InnerProd,subspace);
-  } 
-  void ProjectToSubspace(CoarseVector &CoarseVec,const FineField &FineVec){
-    blockProject(CoarseVec,FineVec,subspace);
-  }
-  void PromoteFromSubspace(const CoarseVector &CoarseVec,FineField &FineVec){
-    FineVec.Checkerboard() = subspace[0].Checkerboard();
-    blockPromote(CoarseVec,FineVec,subspace);
-  }
-
-  virtual void CreateSubspace(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,int nn=nbasis) {
-
-    RealD scale;
-
-    ConjugateGradient<FineField> CG(1.0e-2,100,false);
-    FineField noise(FineGrid);
-    FineField Mn(FineGrid);
-
-    for(int b=0;b<nn;b++){
-      
-      subspace[b] = Zero();
-      gaussian(RNG,noise);
-      scale = std::pow(norm2(noise),-0.5); 
-      noise=noise*scale;
-      
-      hermop.Op(noise,Mn); std::cout<<GridLogMessage << "noise   ["<<b<<"] <n|MdagM|n> "<<norm2(Mn)<<std::endl;
-
-      for(int i=0;i<1;i++){
-
-	CG(hermop,noise,subspace[b]);
-
-	noise = subspace[b];
-	scale = std::pow(norm2(noise),-0.5); 
-	noise=noise*scale;
-
-      }
-
-      hermop.Op(noise,Mn); std::cout<<GridLogMessage << "filtered["<<b<<"] <f|MdagM|f> "<<norm2(Mn)<<std::endl;
-      subspace[b]   = noise;
-
-    }
-  }
-
-  ////////////////////////////////////////////////////////////////////////////////////////////////
-  // World of possibilities here. But have tried quite a lot of experiments (250+ jobs run on Summit)
-  // and this is the best I found
-  ////////////////////////////////////////////////////////////////////////////////////////////////
-
-  virtual void CreateSubspaceChebyshev(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,
-				       int nn,
-				       double hi,
-				       double lo,
-				       int orderfilter,
-				       int ordermin,
-				       int orderstep,
-				       double filterlo
-				       ) {
-
-    RealD scale;
-
-    FineField noise(FineGrid);
-    FineField Mn(FineGrid);
-    FineField tmp(FineGrid);
-
-    // New normalised noise
-    gaussian(RNG,noise);
-    scale = std::pow(norm2(noise),-0.5); 
-    noise=noise*scale;
-
-    // Initial matrix element
-    hermop.Op(noise,Mn); std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
-
-    int b =0;
-    {
-      // Filter
-      Chebyshev<FineField> Cheb(lo,hi,orderfilter);
-      Cheb(hermop,noise,Mn);
-      // normalise
-      scale = std::pow(norm2(Mn),-0.5); 	Mn=Mn*scale;
-      subspace[b]   = Mn;
-      hermop.Op(Mn,tmp); 
-      std::cout<<GridLogMessage << "filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
-      b++;
-    }
-
-    // Generate a full sequence of Chebyshevs
-    {
-      lo=filterlo;
-      noise=Mn;
-
-      FineField T0(FineGrid); T0 = noise;  
-      FineField T1(FineGrid); 
-      FineField T2(FineGrid);
-      FineField y(FineGrid);
-      
-      FineField *Tnm = &T0;
-      FineField *Tn  = &T1;
-      FineField *Tnp = &T2;
-
-      // Tn=T1 = (xscale M + mscale)in
-      RealD xscale = 2.0/(hi-lo);
-      RealD mscale = -(hi+lo)/(hi-lo);
-      hermop.HermOp(T0,y);
-      T1=y*xscale+noise*mscale;
-
-      for(int n=2;n<=ordermin+orderstep*(nn-2);n++){
-	
-	hermop.HermOp(*Tn,y);
-
-	autoView( y_v , y, AcceleratorWrite);
-	autoView( Tn_v , (*Tn), AcceleratorWrite);
-	autoView( Tnp_v , (*Tnp), AcceleratorWrite);
-	autoView( Tnm_v , (*Tnm), AcceleratorWrite);
-	const int Nsimd = CComplex::Nsimd();
-	accelerator_for(ss, FineGrid->oSites(), Nsimd, {
-	  coalescedWrite(y_v[ss],xscale*y_v(ss)+mscale*Tn_v(ss));
-	  coalescedWrite(Tnp_v[ss],2.0*y_v(ss)-Tnm_v(ss));
-        });
-
-	// Possible more fine grained control is needed than a linear sweep,
-	// but huge productivity gain if this is simple algorithm and not a tunable
-	int m =1;
-	if ( n>=ordermin ) m=n-ordermin;
-	if ( (m%orderstep)==0 ) { 
-	  Mn=*Tnp;
-	  scale = std::pow(norm2(Mn),-0.5);         Mn=Mn*scale;
-	  subspace[b] = Mn;
-	  hermop.Op(Mn,tmp); 
-	  std::cout<<GridLogMessage << n<<" filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
-	  b++;
-	}
-
-	// Cycle pointers to avoid copies
-	FineField *swizzle = Tnm;
-	Tnm    =Tn;
-	Tn     =Tnp;
-	Tnp    =swizzle;
-	  
-      }
-    }
-    assert(b==nn);
-  }
-
-};
-
 // Fine Object == (per site) type of fine field
 // nbasis      == number of deflation vectors
 template<class Fobj,class CComplex,int nbasis>

Grid/algorithms/multigrid/GeneralCoarsenedMatrix.h

@@ -0,0 +1,619 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/GeneralCoarsenedMatrix.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    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 */
+#pragma once
+
+#include <Grid/qcd/QCD.h> // needed for Dagger(Yes|No), Inverse(Yes|No)
+
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+NAMESPACE_BEGIN(Grid);
+
+// Fine Object == (per site) type of fine field
+// nbasis      == number of deflation vectors
+template<class Fobj,class CComplex,int nbasis>
+class GeneralCoarsenedMatrix : public SparseMatrixBase<Lattice<iVector<CComplex,nbasis > > >  {
+public:
+
+  typedef GeneralCoarsenedMatrix<Fobj,CComplex,nbasis> GeneralCoarseOp;
+  typedef iVector<CComplex,nbasis >           siteVector;
+  typedef iMatrix<CComplex,nbasis >           siteMatrix;
+  typedef Lattice<iScalar<CComplex> >         CoarseComplexField;
+  typedef Lattice<siteVector>                 CoarseVector;
+  typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
+  typedef iMatrix<CComplex,nbasis >  Cobj;
+  typedef iVector<CComplex,nbasis >  Cvec;
+  typedef Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj >        FineField;
+  typedef Lattice<CComplex >    FineComplexField;
+  typedef CoarseVector Field;
+  ////////////////////
+  // Data members
+  ////////////////////
+  int hermitian;
+  GridBase      *       _FineGrid; 
+  GridCartesian *       _CoarseGrid; 
+  NonLocalStencilGeometry &geom;
+  PaddedCell Cell;
+  GeneralLocalStencil Stencil;
+  
+  std::vector<CoarseMatrix> _A;
+  std::vector<CoarseMatrix> _Adag;
+  std::vector<CoarseVector> MultTemporaries;
+
+  ///////////////////////
+  // Interface
+  ///////////////////////
+  GridBase      * Grid(void)           { return _CoarseGrid; };   // this is all the linalg routines need to know
+  GridBase      * FineGrid(void)       { return _FineGrid; };   // this is all the linalg routines need to know
+  GridCartesian * CoarseGrid(void)     { return _CoarseGrid; };   // this is all the linalg routines need to know
+
+  /*  void ShiftMatrix(RealD shift)
+  {
+    int Nd=_FineGrid->Nd(); 
+    Coordinate zero_shift(Nd,0);
+    for(int p=0;p<geom.npoint;p++){
+      if ( zero_shift==geom.shifts[p] ) {
+	_A[p] = _A[p]+shift;
+	//	_Adag[p] = _Adag[p]+shift;
+      }
+    }    
+  }
+  void ProjectNearestNeighbour(RealD shift, GeneralCoarseOp &CopyMe)
+  {
+    int nfound=0;
+    std::cout << GridLogMessage <<"GeneralCoarsenedMatrix::ProjectNearestNeighbour "<< CopyMe._A[0].Grid()<<std::endl;
+    for(int p=0;p<geom.npoint;p++){
+      for(int pp=0;pp<CopyMe.geom.npoint;pp++){
+ 	// Search for the same relative shift
+	// Avoids brutal handling of Grid pointers
+	if ( CopyMe.geom.shifts[pp]==geom.shifts[p] ) {
+	  _A[p] = CopyMe.Cell.Extract(CopyMe._A[pp]);
+	  //	  _Adag[p] = CopyMe.Cell.Extract(CopyMe._Adag[pp]);
+	  nfound++;
+	}
+      }
+    }
+    assert(nfound==geom.npoint);
+    ExchangeCoarseLinks();
+  }
+  */
+  
+  GeneralCoarsenedMatrix(NonLocalStencilGeometry &_geom,GridBase *FineGrid, GridCartesian * CoarseGrid)
+    : geom(_geom),
+      _FineGrid(FineGrid),
+      _CoarseGrid(CoarseGrid),
+      hermitian(1),
+      Cell(_geom.Depth(),_CoarseGrid),
+      Stencil(Cell.grids.back(),geom.shifts)
+  {
+    {
+      int npoint = _geom.npoint;
+    }
+    _A.resize(geom.npoint,CoarseGrid);
+    //    _Adag.resize(geom.npoint,CoarseGrid);
+  }
+  void M (const CoarseVector &in, CoarseVector &out)
+  {
+    Mult(_A,in,out);
+  }
+  void Mdag (const CoarseVector &in, CoarseVector &out)
+  {
+    assert(hermitian);
+    Mult(_A,in,out);
+    //    if ( hermitian ) M(in,out);
+    //    else Mult(_Adag,in,out);
+  }
+  void Mult (std::vector<CoarseMatrix> &A,const CoarseVector &in, CoarseVector &out)
+  {
+    RealD tviews=0;    RealD ttot=0;    RealD tmult=0;   RealD texch=0;    RealD text=0; RealD ttemps=0; RealD tcopy=0;
+    RealD tmult2=0;
+
+    ttot=-usecond();
+    conformable(CoarseGrid(),in.Grid());
+    conformable(in.Grid(),out.Grid());
+    out.Checkerboard() = in.Checkerboard();
+    CoarseVector tin=in;
+
+    texch-=usecond();
+    CoarseVector pin = Cell.ExchangePeriodic(tin);
+    texch+=usecond();
+
+    CoarseVector pout(pin.Grid());
+
+    int npoint = geom.npoint;
+    typedef LatticeView<Cobj> Aview;
+    typedef LatticeView<Cvec> Vview;
+      
+    const int Nsimd = CComplex::Nsimd();
+    
+    int64_t osites=pin.Grid()->oSites();
+
+    RealD flops = 1.0* npoint * nbasis * nbasis * 8.0 * osites * CComplex::Nsimd();
+    RealD bytes = 1.0*osites*sizeof(siteMatrix)*npoint
+                + 2.0*osites*sizeof(siteVector)*npoint;
+      
+    {
+      tviews-=usecond();
+      autoView( in_v , pin, AcceleratorRead);
+      autoView( out_v , pout, AcceleratorWriteDiscard);
+      autoView( Stencil_v  , Stencil, AcceleratorRead);
+      tviews+=usecond();
+
+      // Static and prereserve to keep UVM region live and not resized across multiple calls
+      ttemps-=usecond();
+      MultTemporaries.resize(npoint,pin.Grid());       
+      ttemps+=usecond();
+      std::vector<Aview> AcceleratorViewContainer_h;
+      std::vector<Vview> AcceleratorVecViewContainer_h; 
+
+      tviews-=usecond();
+      for(int p=0;p<npoint;p++) {
+	AcceleratorViewContainer_h.push_back(      A[p].View(AcceleratorRead));
+	AcceleratorVecViewContainer_h.push_back(MultTemporaries[p].View(AcceleratorWrite));
+      }
+      tviews+=usecond();
+
+      static deviceVector<Aview> AcceleratorViewContainer; AcceleratorViewContainer.resize(npoint);
+      static deviceVector<Vview> AcceleratorVecViewContainer; AcceleratorVecViewContainer.resize(npoint); 
+      
+      auto Aview_p = &AcceleratorViewContainer[0];
+      auto Vview_p = &AcceleratorVecViewContainer[0];
+      tcopy-=usecond();
+      acceleratorCopyToDevice(&AcceleratorViewContainer_h[0],&AcceleratorViewContainer[0],npoint *sizeof(Aview));
+      acceleratorCopyToDevice(&AcceleratorVecViewContainer_h[0],&AcceleratorVecViewContainer[0],npoint *sizeof(Vview));
+      tcopy+=usecond();
+
+      tmult-=usecond();
+      accelerator_for(spb, osites*nbasis*npoint, Nsimd, {
+	  typedef decltype(coalescedRead(in_v[0](0))) calcComplex;
+	  int32_t ss   = spb/(nbasis*npoint);
+	  int32_t bp   = spb%(nbasis*npoint);
+	  int32_t point= bp/nbasis;
+	  int32_t b    = bp%nbasis;
+	  auto SE  = Stencil_v.GetEntry(point,ss);
+	  auto nbr = coalescedReadGeneralPermute(in_v[SE->_offset],SE->_permute,Nd);
+	  auto res = coalescedRead(Aview_p[point][ss](0,b))*nbr(0);
+	  for(int bb=1;bb<nbasis;bb++) {
+	    res = res + coalescedRead(Aview_p[point][ss](bb,b))*nbr(bb);
+	  }
+	  coalescedWrite(Vview_p[point][ss](b),res);
+      });
+      tmult2-=usecond();
+      accelerator_for(sb, osites*nbasis, Nsimd, {
+	  int ss = sb/nbasis;
+	  int b  = sb%nbasis;
+	  auto res = coalescedRead(Vview_p[0][ss](b));
+	  for(int point=1;point<npoint;point++){
+	    res = res + coalescedRead(Vview_p[point][ss](b));
+	  }
+	  coalescedWrite(out_v[ss](b),res);
+      });
+      tmult2+=usecond();
+      tmult+=usecond();
+      for(int p=0;p<npoint;p++) {
+	AcceleratorViewContainer_h[p].ViewClose();
+	AcceleratorVecViewContainer_h[p].ViewClose();
+      }
+    }
+
+    text-=usecond();
+    out = Cell.Extract(pout);
+    text+=usecond();
+    ttot+=usecond();
+    
+    std::cout << GridLogPerformance<<"Coarse 1rhs Mult Aviews "<<tviews<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Mult exch "<<texch<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Mult mult "<<tmult<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<" of which mult2  "<<tmult2<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Mult ext  "<<text<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Mult temps "<<ttemps<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Mult copy  "<<tcopy<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Mult tot  "<<ttot<<" us"<<std::endl;
+    //    std::cout << GridLogPerformance<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Kernel flops "<< flops<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Kernel flop/s "<< flops/tmult<<" mflop/s"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Kernel bytes/s "<< bytes/tmult<<" MB/s"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse overall flops/s "<< flops/ttot<<" mflop/s"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse total bytes   "<< bytes/1e6<<" MB"<<std::endl;
+
+  };
+  
+  void PopulateAdag(void)
+  {
+    for(int64_t bidx=0;bidx<CoarseGrid()->gSites() ;bidx++){
+      Coordinate bcoor;
+      CoarseGrid()->GlobalIndexToGlobalCoor(bidx,bcoor);
+      
+      for(int p=0;p<geom.npoint;p++){
+	Coordinate scoor = bcoor;
+	for(int mu=0;mu<bcoor.size();mu++){
+	  int L = CoarseGrid()->GlobalDimensions()[mu];
+	  scoor[mu] = (bcoor[mu] - geom.shifts[p][mu] + L) % L; // Modulo arithmetic
+	}
+	// Flip to poke/peekLocalSite and not too bad
+	auto link = peekSite(_A[p],scoor);
+	int pp = geom.Reverse(p);
+	pokeSite(adj(link),_Adag[pp],bcoor);
+      }
+    }
+  }
+  /////////////////////////////////////////////////////////////
+  // 
+  // A) Only reduced flops option is to use a padded cell of depth 4
+  // and apply MpcDagMpc in the padded cell.
+  //
+  // Makes for ONE application of MpcDagMpc per vector instead of 30 or 80.
+  // With the effective cell size around (B+8)^4 perhaps 12^4/4^4 ratio
+  // Cost is 81x more, same as stencil size.
+  //
+  // But: can eliminate comms and do as local dirichlet.
+  //
+  // Local exchange gauge field once.
+  // Apply to all vectors, local only computation.
+  // Must exchange ghost subcells in reverse process of PaddedCell to take inner products
+  //
+  // B) Can reduce cost: pad by 1, apply Deo      (4^4+6^4+8^4+8^4 )/ (4x 4^4)
+  //                     pad by 2, apply Doe
+  //                     pad by 3, apply Deo
+  //                     then break out 8x directions; cost is ~10x MpcDagMpc per vector
+  //
+  // => almost factor of 10 in setup cost, excluding data rearrangement
+  //
+  // Intermediates -- ignore the corner terms, leave approximate and force Hermitian
+  // Intermediates -- pad by 2 and apply 1+8+24 = 33 times.
+  /////////////////////////////////////////////////////////////
+
+    //////////////////////////////////////////////////////////
+    // BFM HDCG style approach: Solve a system of equations to get Aij
+    //////////////////////////////////////////////////////////
+    /*
+     *     Here, k,l index which possible shift within the 3^Nd "ball" connected by MdagM.
+     *
+     *     conj(phases[block]) proj[k][ block*Nvec+j ] =  \sum_ball  e^{i q_k . delta} < phi_{block,j} | MdagM | phi_{(block+delta),i} > 
+     *                                                 =  \sum_ball e^{iqk.delta} A_ji
+     *
+     *     Must invert matrix M_k,l = e^[i q_k . delta_l]
+     *
+     *     Where q_k = delta_k . (2*M_PI/global_nb[mu])
+     */
+#if 0
+  void CoarsenOperator(LinearOperatorBase<Lattice<Fobj> > &linop,
+		       Aggregation<Fobj,CComplex,nbasis> & Subspace)
+  {
+    std::cout << GridLogMessage<< "GeneralCoarsenMatrix "<< std::endl;
+    GridBase *grid = FineGrid();
+
+    RealD tproj=0.0;
+    RealD teigen=0.0;
+    RealD tmat=0.0;
+    RealD tphase=0.0;
+    RealD tinv=0.0;
+
+    /////////////////////////////////////////////////////////////
+    // Orthogonalise the subblocks over the basis
+    /////////////////////////////////////////////////////////////
+    CoarseScalar InnerProd(CoarseGrid()); 
+    blockOrthogonalise(InnerProd,Subspace.subspace);
+
+    const int npoint = geom.npoint;
+      
+    Coordinate clatt = CoarseGrid()->GlobalDimensions();
+    int Nd = CoarseGrid()->Nd();
+
+      /*
+       *     Here, k,l index which possible momentum/shift within the N-points connected by MdagM.
+       *     Matrix index i is mapped to this shift via 
+       *               geom.shifts[i]
+       *
+       *     conj(pha[block]) proj[k (which mom)][j (basis vec cpt)][block] 
+       *       =  \sum_{l in ball}  e^{i q_k . delta_l} < phi_{block,j} | MdagM | phi_{(block+delta_l),i} > 
+       *       =  \sum_{l in ball} e^{iqk.delta_l} A_ji^{b.b+l}
+       *       = M_{kl} A_ji^{b.b+l}
+       *
+       *     Must assemble and invert matrix M_k,l = e^[i q_k . delta_l]
+       *  
+       *     Where q_k = delta_k . (2*M_PI/global_nb[mu])
+       *
+       *     Then A{ji}^{b,b+l} = M^{-1}_{lm} ComputeProj_{m,b,i,j}
+       */
+    teigen-=usecond();
+    Eigen::MatrixXcd Mkl    = Eigen::MatrixXcd::Zero(npoint,npoint);
+    Eigen::MatrixXcd invMkl = Eigen::MatrixXcd::Zero(npoint,npoint);
+    ComplexD ci(0.0,1.0);
+    for(int k=0;k<npoint;k++){ // Loop over momenta
+
+      for(int l=0;l<npoint;l++){ // Loop over nbr relative
+	ComplexD phase(0.0,0.0);
+	for(int mu=0;mu<Nd;mu++){
+	  RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	  phase=phase+TwoPiL*geom.shifts[k][mu]*geom.shifts[l][mu];
+	}
+	phase=exp(phase*ci);
+	Mkl(k,l) = phase;
+      }
+    }
+    invMkl = Mkl.inverse();
+    teigen+=usecond();
+
+    ///////////////////////////////////////////////////////////////////////
+    // Now compute the matrix elements of linop between the orthonormal
+    // set of vectors.
+    ///////////////////////////////////////////////////////////////////////
+    FineField phaV(grid); // Phased block basis vector
+    FineField MphaV(grid);// Matrix applied
+    CoarseVector coarseInner(CoarseGrid());
+
+    std::vector<CoarseVector> ComputeProj(npoint,CoarseGrid());
+    std::vector<CoarseVector>          FT(npoint,CoarseGrid());
+    for(int i=0;i<nbasis;i++){// Loop over basis vectors
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<"/"<<nbasis<< std::endl;
+      for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
+	/////////////////////////////////////////////////////
+	// Stick a phase on every block
+	/////////////////////////////////////////////////////
+	tphase-=usecond();
+	CoarseComplexField coor(CoarseGrid());
+	CoarseComplexField pha(CoarseGrid());	pha=Zero();
+	for(int mu=0;mu<Nd;mu++){
+	  LatticeCoordinate(coor,mu);
+	  RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	  pha = pha + (TwoPiL * geom.shifts[p][mu]) * coor;
+	}
+	pha  =exp(pha*ci);
+	phaV=Zero();
+	blockZAXPY(phaV,pha,Subspace.subspace[i],phaV);
+	tphase+=usecond();
+
+	/////////////////////////////////////////////////////////////////////
+	// Multiple phased subspace vector by matrix and project to subspace
+	// Remove local bulk phase to leave relative phases
+	/////////////////////////////////////////////////////////////////////
+	tmat-=usecond();
+	linop.Op(phaV,MphaV);
+	tmat+=usecond();
+
+	tproj-=usecond();
+	blockProject(coarseInner,MphaV,Subspace.subspace);
+	coarseInner = conjugate(pha) * coarseInner;
+
+	ComputeProj[p] = coarseInner;
+	tproj+=usecond();
+
+      }
+
+      tinv-=usecond();
+      for(int k=0;k<npoint;k++){
+	FT[k] = Zero();
+	for(int l=0;l<npoint;l++){
+	  FT[k]= FT[k]+ invMkl(l,k)*ComputeProj[l];
+	}
+      
+	int osites=CoarseGrid()->oSites();
+	autoView( A_v  , _A[k], AcceleratorWrite);
+	autoView( FT_v  , FT[k], AcceleratorRead);
+	accelerator_for(sss, osites, 1, {
+	    for(int j=0;j<nbasis;j++){
+	      A_v[sss](i,j) = FT_v[sss](j);
+	    }
+        });
+      }
+      tinv+=usecond();
+    }
+
+    // Only needed if nonhermitian
+    if ( ! hermitian ) {
+      //      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
+      //      PopulateAdag();
+    }
+
+    // Need to write something to populate Adag from A
+    ExchangeCoarseLinks();
+    std::cout << GridLogMessage<<"CoarsenOperator eigen  "<<teigen<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator phase  "<<tphase<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator mat    "<<tmat <<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator proj   "<<tproj<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator inv    "<<tinv<<" us"<<std::endl;
+  }
+#else
+  void CoarsenOperator(LinearOperatorBase<Lattice<Fobj> > &linop,
+		       Aggregation<Fobj,CComplex,nbasis> & Subspace)
+  {
+    std::cout << GridLogMessage<< "GeneralCoarsenMatrix "<< std::endl;
+    GridBase *grid = FineGrid();
+
+    RealD tproj=0.0;
+    RealD teigen=0.0;
+    RealD tmat=0.0;
+    RealD tphase=0.0;
+    RealD tphaseBZ=0.0;
+    RealD tinv=0.0;
+
+    /////////////////////////////////////////////////////////////
+    // Orthogonalise the subblocks over the basis
+    /////////////////////////////////////////////////////////////
+    CoarseScalar InnerProd(CoarseGrid()); 
+    blockOrthogonalise(InnerProd,Subspace.subspace);
+
+    //    for(int s=0;s<Subspace.subspace.size();s++){
+      //      std::cout << " subspace norm "<<norm2(Subspace.subspace[s])<<std::endl;
+    //    }
+    const int npoint = geom.npoint;
+      
+    Coordinate clatt = CoarseGrid()->GlobalDimensions();
+    int Nd = CoarseGrid()->Nd();
+
+      /*
+       *     Here, k,l index which possible momentum/shift within the N-points connected by MdagM.
+       *     Matrix index i is mapped to this shift via 
+       *               geom.shifts[i]
+       *
+       *     conj(pha[block]) proj[k (which mom)][j (basis vec cpt)][block] 
+       *       =  \sum_{l in ball}  e^{i q_k . delta_l} < phi_{block,j} | MdagM | phi_{(block+delta_l),i} > 
+       *       =  \sum_{l in ball} e^{iqk.delta_l} A_ji^{b.b+l}
+       *       = M_{kl} A_ji^{b.b+l}
+       *
+       *     Must assemble and invert matrix M_k,l = e^[i q_k . delta_l]
+       *  
+       *     Where q_k = delta_k . (2*M_PI/global_nb[mu])
+       *
+       *     Then A{ji}^{b,b+l} = M^{-1}_{lm} ComputeProj_{m,b,i,j}
+       */
+    teigen-=usecond();
+    Eigen::MatrixXcd Mkl    = Eigen::MatrixXcd::Zero(npoint,npoint);
+    Eigen::MatrixXcd invMkl = Eigen::MatrixXcd::Zero(npoint,npoint);
+    ComplexD ci(0.0,1.0);
+    for(int k=0;k<npoint;k++){ // Loop over momenta
+
+      for(int l=0;l<npoint;l++){ // Loop over nbr relative
+	ComplexD phase(0.0,0.0);
+	for(int mu=0;mu<Nd;mu++){
+	  RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	  phase=phase+TwoPiL*geom.shifts[k][mu]*geom.shifts[l][mu];
+	}
+	phase=exp(phase*ci);
+	Mkl(k,l) = phase;
+      }
+    }
+    invMkl = Mkl.inverse();
+    teigen+=usecond();
+
+    ///////////////////////////////////////////////////////////////////////
+    // Now compute the matrix elements of linop between the orthonormal
+    // set of vectors.
+    ///////////////////////////////////////////////////////////////////////
+    FineField phaV(grid); // Phased block basis vector
+    FineField MphaV(grid);// Matrix applied
+    std::vector<FineComplexField> phaF(npoint,grid);
+    std::vector<CoarseComplexField> pha(npoint,CoarseGrid());
+    
+    CoarseVector coarseInner(CoarseGrid());
+    
+    typedef typename CComplex::scalar_type SComplex;
+    FineComplexField one(grid); one=SComplex(1.0);
+    FineComplexField zz(grid); zz = Zero();
+    tphase=-usecond();
+    for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
+      /////////////////////////////////////////////////////
+      // Stick a phase on every block
+      /////////////////////////////////////////////////////
+      CoarseComplexField coor(CoarseGrid());
+      pha[p]=Zero();
+      for(int mu=0;mu<Nd;mu++){
+	LatticeCoordinate(coor,mu);
+	RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	pha[p] = pha[p] + (TwoPiL * geom.shifts[p][mu]) * coor;
+      }
+      pha[p]  =exp(pha[p]*ci);
+
+      blockZAXPY(phaF[p],pha[p],one,zz);
+      
+    }
+    tphase+=usecond();
+    
+    std::vector<CoarseVector> ComputeProj(npoint,CoarseGrid());
+    std::vector<CoarseVector>          FT(npoint,CoarseGrid());
+    for(int i=0;i<nbasis;i++){// Loop over basis vectors
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<"/"<<nbasis<< std::endl;
+      for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
+	tphaseBZ-=usecond();
+	phaV = phaF[p]*Subspace.subspace[i];
+	tphaseBZ+=usecond();
+
+	/////////////////////////////////////////////////////////////////////
+	// Multiple phased subspace vector by matrix and project to subspace
+	// Remove local bulk phase to leave relative phases
+	/////////////////////////////////////////////////////////////////////
+	tmat-=usecond();
+	linop.Op(phaV,MphaV);
+	tmat+=usecond();
+	//	std::cout << i << " " <<p << " MphaV "<<norm2(MphaV)<<" "<<norm2(phaV)<<std::endl;
+
+	tproj-=usecond();
+	blockProject(coarseInner,MphaV,Subspace.subspace);
+	coarseInner = conjugate(pha[p]) * coarseInner;
+
+	ComputeProj[p] = coarseInner;
+	tproj+=usecond();
+	//	std::cout << i << " " <<p << " ComputeProj "<<norm2(ComputeProj[p])<<std::endl;
+
+      }
+
+      tinv-=usecond();
+      for(int k=0;k<npoint;k++){
+	FT[k] = Zero();
+	for(int l=0;l<npoint;l++){
+	  FT[k]= FT[k]+ invMkl(l,k)*ComputeProj[l];
+	}
+      
+	int osites=CoarseGrid()->oSites();
+	autoView( A_v  , _A[k], AcceleratorWrite);
+	autoView( FT_v  , FT[k], AcceleratorRead);
+	accelerator_for(sss, osites, 1, {
+	    for(int j=0;j<nbasis;j++){
+	      A_v[sss](i,j) = FT_v[sss](j);
+	    }
+        });
+      }
+      tinv+=usecond();
+    }
+
+    // Only needed if nonhermitian
+    if ( ! hermitian ) {
+      //      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
+      //      PopulateAdag();
+    }
+
+    for(int p=0;p<geom.npoint;p++){
+      std::cout << " _A["<<p<<"] "<<norm2(_A[p])<<std::endl;
+    }
+
+    // Need to write something to populate Adag from A
+    ExchangeCoarseLinks();
+    std::cout << GridLogMessage<<"CoarsenOperator eigen  "<<teigen<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator phase  "<<tphase<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator phaseBZ "<<tphaseBZ<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator mat    "<<tmat <<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator proj   "<<tproj<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator inv    "<<tinv<<" us"<<std::endl;
+  }
+#endif  
+  void ExchangeCoarseLinks(void){
+    for(int p=0;p<geom.npoint;p++){
+      _A[p] = Cell.ExchangePeriodic(_A[p]);
+      //      _Adag[p]= Cell.ExchangePeriodic(_Adag[p]);
+    }
+  }
+  virtual  void Mdiag    (const Field &in, Field &out){ assert(0);};
+  virtual  void Mdir     (const Field &in, Field &out,int dir, int disp){assert(0);};
+  virtual  void MdirAll  (const Field &in, std::vector<Field> &out){assert(0);};
+};
+
+
+  
+NAMESPACE_END(Grid);

Grid/algorithms/multigrid/GeneralCoarsenedMatrixMultiRHS.h

@@ -0,0 +1,729 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/GeneralCoarsenedMatrixMultiRHS.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    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 */
+#pragma once
+
+
+NAMESPACE_BEGIN(Grid);
+
+
+// Fine Object == (per site) type of fine field
+// nbasis      == number of deflation vectors
+template<class Fobj,class CComplex,int nbasis>
+class MultiGeneralCoarsenedMatrix : public SparseMatrixBase<Lattice<iVector<CComplex,nbasis > > >  {
+public:
+  typedef typename CComplex::scalar_object SComplex;
+  typedef GeneralCoarsenedMatrix<Fobj,CComplex,nbasis> GeneralCoarseOp;
+  typedef MultiGeneralCoarsenedMatrix<Fobj,CComplex,nbasis> MultiGeneralCoarseOp;
+
+  typedef iVector<CComplex,nbasis >           siteVector;
+  typedef iMatrix<CComplex,nbasis >           siteMatrix;
+  typedef iVector<SComplex,nbasis >           calcVector;
+  typedef iMatrix<SComplex,nbasis >           calcMatrix;
+  typedef Lattice<iScalar<CComplex> >         CoarseComplexField;
+  typedef Lattice<siteVector>                 CoarseVector;
+  typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
+  typedef iMatrix<CComplex,nbasis >  Cobj;
+  typedef iVector<CComplex,nbasis >  Cvec;
+  typedef Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj >        FineField;
+  typedef Lattice<CComplex >    FineComplexField;
+  typedef CoarseVector Field;
+
+  ////////////////////
+  // Data members
+  ////////////////////
+  GridCartesian *       _CoarseGridMulti; 
+  NonLocalStencilGeometry geom;
+  NonLocalStencilGeometry geom_srhs;
+  PaddedCell Cell;
+  GeneralLocalStencil Stencil;
+
+  deviceVector<calcVector> BLAS_B;
+  deviceVector<calcVector> BLAS_C;
+  std::vector<deviceVector<calcMatrix> > BLAS_A;
+
+  std::vector<deviceVector<ComplexD *> > BLAS_AP;
+  std::vector<deviceVector<ComplexD *> > BLAS_BP;
+  deviceVector<ComplexD *>               BLAS_CP;
+
+  ///////////////////////
+  // Interface
+  ///////////////////////
+  GridBase      * Grid(void)           { return _CoarseGridMulti; };   // this is all the linalg routines need to know
+  GridCartesian * CoarseGrid(void)     { return _CoarseGridMulti; };   // this is all the linalg routines need to know
+
+  // Can be used to do I/O on the operator matrices externally
+  void SetMatrix (int p,CoarseMatrix & A)
+  {
+    assert(A.size()==geom_srhs.npoint);
+    GridtoBLAS(A[p],BLAS_A[p]);
+  }
+  void GetMatrix (int p,CoarseMatrix & A)
+  {
+    assert(A.size()==geom_srhs.npoint);
+    BLAStoGrid(A[p],BLAS_A[p]);
+  }
+  void CopyMatrix (GeneralCoarseOp &_Op)
+  {
+    for(int p=0;p<geom.npoint;p++){
+      auto Aup = _Op.Cell.Extract(_Op._A[p]);
+      //Unpadded
+      GridtoBLAS(Aup,BLAS_A[p]);
+    }
+  }
+  /*
+  void CheckMatrix (GeneralCoarseOp &_Op)
+  {
+    std::cout <<"************* Checking the little direc operator mRHS"<<std::endl;
+    for(int p=0;p<geom.npoint;p++){
+      //Unpadded
+      auto Aup = _Op.Cell.Extract(_Op._A[p]);
+      auto Ack = Aup;
+      BLAStoGrid(Ack,BLAS_A[p]);
+      std::cout << p<<" Ack "<<norm2(Ack)<<std::endl;
+      std::cout << p<<" Aup "<<norm2(Aup)<<std::endl;
+    }
+    std::cout <<"************* "<<std::endl;
+  }
+  */
+  
+  MultiGeneralCoarsenedMatrix(NonLocalStencilGeometry &_geom,GridCartesian *CoarseGridMulti) :
+    _CoarseGridMulti(CoarseGridMulti),
+    geom_srhs(_geom),
+    geom(_CoarseGridMulti,_geom.hops,_geom.skip+1),
+    Cell(geom.Depth(),_CoarseGridMulti),
+    Stencil(Cell.grids.back(),geom.shifts) // padded cell stencil
+  {
+    int32_t padded_sites   = Cell.grids.back()->lSites();
+    int32_t unpadded_sites = CoarseGridMulti->lSites();
+    
+    int32_t nrhs  = CoarseGridMulti->FullDimensions()[0];  // # RHS
+    int32_t orhs  = nrhs/CComplex::Nsimd();
+
+    padded_sites   = padded_sites/nrhs;
+    unpadded_sites = unpadded_sites/nrhs;
+    
+    /////////////////////////////////////////////////
+    // Device data vector storage
+    /////////////////////////////////////////////////
+    BLAS_A.resize(geom.npoint);
+    for(int p=0;p<geom.npoint;p++){
+      BLAS_A[p].resize (unpadded_sites); // no ghost zone, npoint elements
+    }
+    
+    BLAS_B.resize(nrhs *padded_sites);   // includes ghost zone
+    BLAS_C.resize(nrhs *unpadded_sites); // no ghost zone
+    BLAS_AP.resize(geom.npoint);
+    BLAS_BP.resize(geom.npoint);
+    for(int p=0;p<geom.npoint;p++){
+      BLAS_AP[p].resize(unpadded_sites);
+      BLAS_BP[p].resize(unpadded_sites);
+    }
+    BLAS_CP.resize(unpadded_sites);
+
+    /////////////////////////////////////////////////
+    // Pointers to data
+    /////////////////////////////////////////////////
+
+    // Site identity mapping for A
+    for(int p=0;p<geom.npoint;p++){
+      for(int ss=0;ss<unpadded_sites;ss++){
+	ComplexD *ptr = (ComplexD *)&BLAS_A[p][ss];
+	acceleratorPut(BLAS_AP[p][ss],ptr);
+      }
+    }
+    // Site identity mapping for C
+    for(int ss=0;ss<unpadded_sites;ss++){
+      ComplexD *ptr = (ComplexD *)&BLAS_C[ss*nrhs];
+      acceleratorPut(BLAS_CP[ss],ptr);
+    }
+
+    // Neighbour table is more complicated
+    int32_t j=0; // Interior point counter (unpadded)
+    for(int32_t s=0;s<padded_sites;s++){ // 4 volume, padded
+      int ghost_zone=0;
+      for(int32_t point = 0 ; point < geom.npoint; point++){
+	int i=s*orhs*geom.npoint+point;
+	if( Stencil._entries[i]._wrap ) { // stencil is indexed by the oSite of the CoarseGridMulti, hence orhs factor
+	  ghost_zone=1; // If general stencil wrapped in any direction, wrap=1
+	}
+      }
+
+      if( ghost_zone==0) {
+	for(int32_t point = 0 ; point < geom.npoint; point++){
+	  int i=s*orhs*geom.npoint+point;
+ 	  int32_t nbr = Stencil._entries[i]._offset*CComplex::Nsimd(); // oSite -> lSite
+	  assert(nbr<BLAS_B.size());
+	  ComplexD * ptr = (ComplexD *)&BLAS_B[nbr];
+	  acceleratorPut(BLAS_BP[point][j],ptr); // neighbour indexing in ghost zone volume
+	}
+	j++;
+      }
+    }
+    assert(j==unpadded_sites);
+  }
+  template<class vobj> void GridtoBLAS(const Lattice<vobj> &from,deviceVector<typename vobj::scalar_object> &to)
+  {
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  GridBase *Fg = from.Grid();
+  assert(!Fg->_isCheckerBoarded);
+  int nd = Fg->_ndimension;
+
+  to.resize(Fg->lSites());
+
+  Coordinate LocalLatt = Fg->LocalDimensions();
+  size_t nsite = 1;
+  for(int i=0;i<nd;i++) nsite *= LocalLatt[i];
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  // do the index calc on the GPU
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  Coordinate f_ostride = Fg->_ostride;
+  Coordinate f_istride = Fg->_istride;
+  Coordinate f_rdimensions = Fg->_rdimensions;
+
+  autoView(from_v,from,AcceleratorRead);
+  auto to_v = &to[0];
+
+  const int words=sizeof(vobj)/sizeof(vector_type);
+  accelerator_for(idx,nsite,1,{
+      
+      Coordinate from_coor, base;
+      Lexicographic::CoorFromIndex(base,idx,LocalLatt);
+      for(int i=0;i<nd;i++){
+	from_coor[i] = base[i];
+      }
+      int from_oidx = 0; for(int d=0;d<nd;d++) from_oidx+=f_ostride[d]*(from_coor[d]%f_rdimensions[d]);
+      int from_lane = 0; for(int d=0;d<nd;d++) from_lane+=f_istride[d]*(from_coor[d]/f_rdimensions[d]);
+
+      const vector_type* from = (const vector_type *)&from_v[from_oidx];
+      scalar_type* to = (scalar_type *)&to_v[idx];
+      
+      scalar_type stmp;
+      for(int w=0;w<words;w++){
+	stmp = getlane(from[w], from_lane);
+	to[w] = stmp;
+      }
+    });
+  }    
+  template<class vobj> void BLAStoGrid(Lattice<vobj> &grid,deviceVector<typename vobj::scalar_object> &in)
+  {
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  GridBase *Tg = grid.Grid();
+  assert(!Tg->_isCheckerBoarded);
+  int nd = Tg->_ndimension;
+  
+  assert(in.size()==Tg->lSites());
+
+  Coordinate LocalLatt = Tg->LocalDimensions();
+  size_t nsite = 1;
+  for(int i=0;i<nd;i++) nsite *= LocalLatt[i];
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  // do the index calc on the GPU
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  Coordinate t_ostride = Tg->_ostride;
+  Coordinate t_istride = Tg->_istride;
+  Coordinate t_rdimensions = Tg->_rdimensions;
+
+  autoView(to_v,grid,AcceleratorWrite);
+  auto from_v = &in[0];
+
+  const int words=sizeof(vobj)/sizeof(vector_type);
+  accelerator_for(idx,nsite,1,{
+      
+      Coordinate to_coor, base;
+      Lexicographic::CoorFromIndex(base,idx,LocalLatt);
+      for(int i=0;i<nd;i++){
+	to_coor[i] = base[i];
+      }
+      int to_oidx = 0; for(int d=0;d<nd;d++) to_oidx+=t_ostride[d]*(to_coor[d]%t_rdimensions[d]);
+      int to_lane = 0; for(int d=0;d<nd;d++) to_lane+=t_istride[d]*(to_coor[d]/t_rdimensions[d]);
+
+      vector_type* to = (vector_type *)&to_v[to_oidx];
+      scalar_type* from = (scalar_type *)&from_v[idx];
+      
+      scalar_type stmp;
+      for(int w=0;w<words;w++){
+	stmp=from[w];
+	putlane(to[w], stmp, to_lane);
+      }
+    });
+  }
+  void CoarsenOperator(LinearOperatorBase<Lattice<Fobj> > &linop,
+		       Aggregation<Fobj,CComplex,nbasis> & Subspace,
+		       GridBase *CoarseGrid)
+  {
+#if 0
+    std::cout << GridLogMessage<< "GeneralCoarsenMatrixMrhs "<< std::endl;
+
+    GridBase *grid = Subspace.FineGrid;
+
+    /////////////////////////////////////////////////////////////
+    // Orthogonalise the subblocks over the basis
+    /////////////////////////////////////////////////////////////
+    CoarseScalar InnerProd(CoarseGrid); 
+    blockOrthogonalise(InnerProd,Subspace.subspace);
+
+    const int npoint = geom_srhs.npoint;
+
+    Coordinate clatt = CoarseGrid->GlobalDimensions();
+    int Nd = CoarseGrid->Nd();
+      /*
+       *     Here, k,l index which possible momentum/shift within the N-points connected by MdagM.
+       *     Matrix index i is mapped to this shift via 
+       *               geom.shifts[i]
+       *
+       *     conj(pha[block]) proj[k (which mom)][j (basis vec cpt)][block] 
+       *       =  \sum_{l in ball}  e^{i q_k . delta_l} < phi_{block,j} | MdagM | phi_{(block+delta_l),i} > 
+       *       =  \sum_{l in ball} e^{iqk.delta_l} A_ji^{b.b+l}
+       *       = M_{kl} A_ji^{b.b+l}
+       *
+       *     Must assemble and invert matrix M_k,l = e^[i q_k . delta_l]
+       *  
+       *     Where q_k = delta_k . (2*M_PI/global_nb[mu])
+       *
+       *     Then A{ji}^{b,b+l} = M^{-1}_{lm} ComputeProj_{m,b,i,j}
+       */
+    Eigen::MatrixXcd Mkl    = Eigen::MatrixXcd::Zero(npoint,npoint);
+    Eigen::MatrixXcd invMkl = Eigen::MatrixXcd::Zero(npoint,npoint);
+    ComplexD ci(0.0,1.0);
+    for(int k=0;k<npoint;k++){ // Loop over momenta
+
+      for(int l=0;l<npoint;l++){ // Loop over nbr relative
+	ComplexD phase(0.0,0.0);
+	for(int mu=0;mu<Nd;mu++){
+	  RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	  phase=phase+TwoPiL*geom_srhs.shifts[k][mu]*geom_srhs.shifts[l][mu];
+	}
+	phase=exp(phase*ci);
+	Mkl(k,l) = phase;
+      }
+    }
+    invMkl = Mkl.inverse();
+
+    ///////////////////////////////////////////////////////////////////////
+    // Now compute the matrix elements of linop between the orthonormal
+    // set of vectors.
+    ///////////////////////////////////////////////////////////////////////
+    FineField phaV(grid); // Phased block basis vector
+    FineField MphaV(grid);// Matrix applied
+    std::vector<FineComplexField> phaF(npoint,grid);
+    std::vector<CoarseComplexField> pha(npoint,CoarseGrid);
+    
+    CoarseVector coarseInner(CoarseGrid);
+    
+    typedef typename CComplex::scalar_type SComplex;
+    FineComplexField one(grid); one=SComplex(1.0);
+    FineComplexField zz(grid); zz = Zero();
+    for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
+      /////////////////////////////////////////////////////
+      // Stick a phase on every block
+      /////////////////////////////////////////////////////
+      CoarseComplexField coor(CoarseGrid);
+      pha[p]=Zero();
+      for(int mu=0;mu<Nd;mu++){
+	LatticeCoordinate(coor,mu);
+	RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	pha[p] = pha[p] + (TwoPiL * geom_srhs.shifts[p][mu]) * coor;
+      }
+      pha[p]  =exp(pha[p]*ci);	
+
+      blockZAXPY(phaF[p],pha[p],one,zz);
+    }
+
+    // Could save on temporary storage here
+    std::vector<CoarseMatrix> _A;
+    _A.resize(geom_srhs.npoint,CoarseGrid);
+
+    std::vector<CoarseVector> ComputeProj(npoint,CoarseGrid);
+    CoarseVector          FT(CoarseGrid);
+    for(int i=0;i<nbasis;i++){// Loop over basis vectors
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<"/"<<nbasis<< std::endl;
+      for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
+
+	phaV = phaF[p]*Subspace.subspace[i];
+
+	/////////////////////////////////////////////////////////////////////
+	// Multiple phased subspace vector by matrix and project to subspace
+	// Remove local bulk phase to leave relative phases
+	/////////////////////////////////////////////////////////////////////
+	linop.Op(phaV,MphaV);
+
+	// Fixme, could use batched block projector here
+	blockProject(coarseInner,MphaV,Subspace.subspace);
+
+	coarseInner = conjugate(pha[p]) * coarseInner;
+
+	ComputeProj[p] = coarseInner;
+      }
+
+      // Could do this with a block promote or similar BLAS call via the MultiRHSBlockProjector with a const matrix.
+      for(int k=0;k<npoint;k++){
+
+	FT = Zero();
+	for(int l=0;l<npoint;l++){
+	  FT= FT+ invMkl(l,k)*ComputeProj[l];
+	}
+      
+	int osites=CoarseGrid->oSites();
+	autoView( A_v  , _A[k], AcceleratorWrite);
+	autoView( FT_v  , FT, AcceleratorRead);
+	accelerator_for(sss, osites, 1, {
+	    for(int j=0;j<nbasis;j++){
+	      A_v[sss](i,j) = FT_v[sss](j);
+	    }
+        });
+      }
+    }
+
+    // Only needed if nonhermitian
+    //    if ( ! hermitian ) {
+    //      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
+    //      PopulateAdag();
+    //    }
+    // Need to write something to populate Adag from A
+
+    for(int p=0;p<geom_srhs.npoint;p++){
+      GridtoBLAS(_A[p],BLAS_A[p]);
+    }
+    /*
+Grid : Message : 11698.730546 s : CoarsenOperator eigen  1334 us
+Grid : Message : 11698.730563 s : CoarsenOperator phase  34729 us
+Grid : Message : 11698.730565 s : CoarsenOperator phaseBZ 2423814 us
+Grid : Message : 11698.730566 s : CoarsenOperator mat    127890998 us
+Grid : Message : 11698.730567 s : CoarsenOperator proj   515840840 us
+Grid : Message : 11698.730568 s : CoarsenOperator inv    103948313 us
+Takes 600s to compute matrix elements, DOMINATED by the block project.
+Easy to speed up with the batched block project.
+Store npoint vectors, get npoint x Nbasis block projection, and 81 fold faster.
+
+// Block project below taks to 240s
+Grid : Message : 328.193418 s : CoarsenOperator phase      38338 us
+Grid : Message : 328.193434 s : CoarsenOperator phaseBZ  1711226 us
+Grid : Message : 328.193436 s : CoarsenOperator mat    122213270 us
+//Grid : Message : 328.193438 s : CoarsenOperator proj   1181154 us <-- this is mistimed
+//Grid : Message : 11698.730568 s : CoarsenOperator inv  103948313 us <-- Cut this ~10x if lucky by loop fusion
+     */
+#else
+    RealD tproj=0.0;
+    RealD tmat=0.0;
+    RealD tphase=0.0;
+    RealD tphaseBZ=0.0;
+    RealD tinv=0.0;
+
+    std::cout << GridLogMessage<< "GeneralCoarsenMatrixMrhs "<< std::endl;
+
+    GridBase *grid = Subspace.FineGrid;
+
+    /////////////////////////////////////////////////////////////
+    // Orthogonalise the subblocks over the basis
+    /////////////////////////////////////////////////////////////
+    CoarseScalar InnerProd(CoarseGrid); 
+    blockOrthogonalise(InnerProd,Subspace.subspace);
+
+
+    MultiRHSBlockProject<Lattice<Fobj> >    Projector;
+    Projector.Allocate(nbasis,grid,CoarseGrid);
+    Projector.ImportBasis(Subspace.subspace);
+    
+    const int npoint = geom_srhs.npoint;
+
+    Coordinate clatt = CoarseGrid->GlobalDimensions();
+    int Nd = CoarseGrid->Nd();
+      /*
+       *     Here, k,l index which possible momentum/shift within the N-points connected by MdagM.
+       *     Matrix index i is mapped to this shift via 
+       *               geom.shifts[i]
+       *
+       *     conj(pha[block]) proj[k (which mom)][j (basis vec cpt)][block] 
+       *       =  \sum_{l in ball}  e^{i q_k . delta_l} < phi_{block,j} | MdagM | phi_{(block+delta_l),i} > 
+       *       =  \sum_{l in ball} e^{iqk.delta_l} A_ji^{b.b+l}
+       *       = M_{kl} A_ji^{b.b+l}
+       *
+       *     Must assemble and invert matrix M_k,l = e^[i q_k . delta_l]
+       *  
+       *     Where q_k = delta_k . (2*M_PI/global_nb[mu])
+       *
+       *     Then A{ji}^{b,b+l} = M^{-1}_{lm} ComputeProj_{m,b,i,j}
+       */
+    Eigen::MatrixXcd Mkl    = Eigen::MatrixXcd::Zero(npoint,npoint);
+    Eigen::MatrixXcd invMkl = Eigen::MatrixXcd::Zero(npoint,npoint);
+    ComplexD ci(0.0,1.0);
+    for(int k=0;k<npoint;k++){ // Loop over momenta
+
+      for(int l=0;l<npoint;l++){ // Loop over nbr relative
+	ComplexD phase(0.0,0.0);
+	for(int mu=0;mu<Nd;mu++){
+	  RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	  phase=phase+TwoPiL*geom_srhs.shifts[k][mu]*geom_srhs.shifts[l][mu];
+	}
+	phase=exp(phase*ci);
+	Mkl(k,l) = phase;
+      }
+    }
+    invMkl = Mkl.inverse();
+
+    ///////////////////////////////////////////////////////////////////////
+    // Now compute the matrix elements of linop between the orthonormal
+    // set of vectors.
+    ///////////////////////////////////////////////////////////////////////
+    FineField phaV(grid); // Phased block basis vector
+    FineField MphaV(grid);// Matrix applied
+    std::vector<FineComplexField> phaF(npoint,grid);
+    std::vector<CoarseComplexField> pha(npoint,CoarseGrid);
+    
+    CoarseVector coarseInner(CoarseGrid);
+    
+    tphase=-usecond();
+    typedef typename CComplex::scalar_type SComplex;
+    FineComplexField one(grid); one=SComplex(1.0);
+    FineComplexField zz(grid); zz = Zero();
+    for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
+      /////////////////////////////////////////////////////
+      // Stick a phase on every block
+      /////////////////////////////////////////////////////
+      CoarseComplexField coor(CoarseGrid);
+      pha[p]=Zero();
+      for(int mu=0;mu<Nd;mu++){
+	LatticeCoordinate(coor,mu);
+	RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	pha[p] = pha[p] + (TwoPiL * geom_srhs.shifts[p][mu]) * coor;
+      }
+      pha[p]  =exp(pha[p]*ci);	
+
+      blockZAXPY(phaF[p],pha[p],one,zz);
+    }
+    tphase+=usecond();
+
+    // Could save on temporary storage here
+    std::vector<CoarseMatrix> _A;
+    _A.resize(geom_srhs.npoint,CoarseGrid);
+
+    // Count use small chunks than npoint == 81 and save memory
+    int batch = 9;
+    std::vector<FineField>    _MphaV(batch,grid);
+    std::vector<CoarseVector> TmpProj(batch,CoarseGrid);
+
+    std::vector<CoarseVector> ComputeProj(npoint,CoarseGrid);
+    CoarseVector          FT(CoarseGrid);
+    for(int i=0;i<nbasis;i++){// Loop over basis vectors
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<"/"<<nbasis<< std::endl;
+
+      //      std::cout << GridLogMessage << " phasing the fine vector "<<std::endl;
+      // Fixme : do this in batches
+      for(int p=0;p<npoint;p+=batch){ // Loop over momenta in npoint
+
+	for(int b=0;b<MIN(batch,npoint-p);b++){
+	  tphaseBZ-=usecond();
+	  phaV = phaF[p+b]*Subspace.subspace[i];
+	  tphaseBZ+=usecond();
+
+	  /////////////////////////////////////////////////////////////////////
+	  // Multiple phased subspace vector by matrix and project to subspace
+	  // Remove local bulk phase to leave relative phases
+	  /////////////////////////////////////////////////////////////////////
+	  // Memory footprint was an issue
+	  tmat-=usecond();
+	  linop.Op(phaV,MphaV);
+	  _MphaV[b] = MphaV;
+	  tmat+=usecond();
+	}      
+
+	//	std::cout << GridLogMessage << " Calling block project "<<std::endl;
+	tproj-=usecond();
+	Projector.blockProject(_MphaV,TmpProj);
+	tproj+=usecond();
+	
+	//	std::cout << GridLogMessage << " conj phasing the coarse vectors "<<std::endl;
+	for(int b=0;b<MIN(batch,npoint-p);b++){
+	  ComputeProj[p+b] = conjugate(pha[p+b])*TmpProj[b];
+	}
+      }
+
+      // Could do this with a block promote or similar BLAS call via the MultiRHSBlockProjector with a const matrix.
+      
+      // std::cout << GridLogMessage << " Starting FT inv "<<std::endl;
+      tinv-=usecond();
+      for(int k=0;k<npoint;k++){
+	FT = Zero();
+	// 81 kernel calls as many ComputeProj vectors
+	// Could fuse with a vector of views, but ugly
+	// Could unroll the expression and run fewer kernels -- much more attractive
+	// Could also do non blocking.
+#if 0	
+	for(int l=0;l<npoint;l++){
+	  FT= FT+ invMkl(l,k)*ComputeProj[l];
+	}
+#else
+	const int radix = 9;
+	int ll;
+	for(ll=0;ll+radix-1<npoint;ll+=radix){
+	  // When ll = npoint-radix, ll+radix-1 = npoint-1, and we do it all.
+	  FT = FT 
+	    + invMkl(ll+0,k)*ComputeProj[ll+0]
+	    + invMkl(ll+1,k)*ComputeProj[ll+1]
+	    + invMkl(ll+2,k)*ComputeProj[ll+2]
+	    + invMkl(ll+3,k)*ComputeProj[ll+3]
+	    + invMkl(ll+4,k)*ComputeProj[ll+4]
+	    + invMkl(ll+5,k)*ComputeProj[ll+5]
+	    + invMkl(ll+6,k)*ComputeProj[ll+6]
+	    + invMkl(ll+7,k)*ComputeProj[ll+7]
+	    + invMkl(ll+8,k)*ComputeProj[ll+8];
+	}
+	for(int l=ll;l<npoint;l++){
+	  FT= FT+ invMkl(l,k)*ComputeProj[l];
+	}
+#endif
+      
+	// 1 kernel call -- must be cheaper
+	int osites=CoarseGrid->oSites();
+	autoView( A_v  , _A[k], AcceleratorWrite);
+	autoView( FT_v  , FT, AcceleratorRead);
+	accelerator_for(sss, osites, 1, {
+	    for(int j=0;j<nbasis;j++){
+	      A_v[sss](i,j) = FT_v[sss](j);
+	    }
+        });
+      }
+      tinv+=usecond();
+    }
+
+    // Only needed if nonhermitian
+    //    if ( ! hermitian ) {
+    //      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
+    //      PopulateAdag();
+    //    }
+    // Need to write something to populate Adag from A
+    //    std::cout << GridLogMessage << " Calling GridtoBLAS "<<std::endl;
+    for(int p=0;p<geom_srhs.npoint;p++){
+      GridtoBLAS(_A[p],BLAS_A[p]);
+    }
+    std::cout << GridLogMessage<<"CoarsenOperator phase  "<<tphase<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator phaseBZ "<<tphaseBZ<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator mat    "<<tmat <<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator proj   "<<tproj<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator inv    "<<tinv<<" us"<<std::endl;
+#endif
+  }
+  void Mdag(const CoarseVector &in, CoarseVector &out)
+  {
+    this->M(in,out);
+  }
+  void M (const CoarseVector &in, CoarseVector &out)
+  {
+    //    std::cout << GridLogMessage << "New Mrhs coarse"<<std::endl;
+    conformable(CoarseGrid(),in.Grid());
+    conformable(in.Grid(),out.Grid());
+    out.Checkerboard() = in.Checkerboard();
+
+    RealD t_tot;
+    RealD t_exch;
+    RealD t_GtoB;
+    RealD t_BtoG;
+    RealD t_mult;
+
+    t_tot=-usecond();
+    CoarseVector tin=in;
+    t_exch=-usecond();
+    CoarseVector pin = Cell.ExchangePeriodic(tin); //padded input
+    t_exch+=usecond();
+
+    CoarseVector pout(pin.Grid());
+
+    int npoint = geom.npoint;
+    typedef calcMatrix* Aview;
+    typedef LatticeView<Cvec> Vview;
+      
+    const int Nsimd = CComplex::Nsimd();
+
+    int64_t nrhs  =pin.Grid()->GlobalDimensions()[0];
+    assert(nrhs>=1);
+
+    RealD flops,bytes;
+    int64_t osites=in.Grid()->oSites(); // unpadded
+    int64_t unpadded_vol = CoarseGrid()->lSites()/nrhs;
+    
+    flops = 1.0* npoint * nbasis * nbasis * 8.0 * osites * CComplex::Nsimd();
+    bytes = 1.0*osites*sizeof(siteMatrix)*npoint/pin.Grid()->GlobalDimensions()[0]
+          + 2.0*osites*sizeof(siteVector)*npoint;
+    
+
+    t_GtoB=-usecond();
+    GridtoBLAS(pin,BLAS_B);
+    t_GtoB+=usecond();
+
+    GridBLAS BLAS;
+
+    t_mult=-usecond();
+    for(int p=0;p<geom.npoint;p++){
+      RealD c = 1.0;
+      if (p==0) c = 0.0;
+      ComplexD beta(c);
+
+      BLAS.gemmBatched(nbasis,nrhs,nbasis,
+		       ComplexD(1.0),
+		       BLAS_AP[p], 
+		       BLAS_BP[p], 
+		       ComplexD(c), 
+		       BLAS_CP);
+    }
+    BLAS.synchronise();
+    t_mult+=usecond();
+
+    t_BtoG=-usecond();
+    BLAStoGrid(out,BLAS_C);
+    t_BtoG+=usecond();
+    t_tot+=usecond();
+    /*
+    std::cout << GridLogMessage << "New Mrhs coarse DONE "<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult exch "<<t_exch<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult mult "<<t_mult<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult GtoB  "<<t_GtoB<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult BtoG  "<<t_BtoG<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult tot  "<<t_tot<<" us"<<std::endl;
+    */
+    //    std::cout << GridLogMessage<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse Kernel flops "<< flops<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse Kernel flop/s "<< flops/t_mult<<" mflop/s"<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse Kernel bytes/s "<< bytes/t_mult/1000<<" GB/s"<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse overall flops/s "<< flops/t_tot<<" mflop/s"<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse total bytes   "<< bytes/1e6<<" MB"<<std::endl;
+  };
+  virtual  void Mdiag    (const Field &in, Field &out){ assert(0);};
+  virtual  void Mdir     (const Field &in, Field &out,int dir, int disp){assert(0);};
+  virtual  void MdirAll  (const Field &in, std::vector<Field> &out){assert(0);};
+};
+  
+NAMESPACE_END(Grid);

Grid/algorithms/multigrid/Geometry.h

@@ -0,0 +1,238 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/GeneralCoarsenedMatrix.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    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 */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+
+/////////////////////////////////////////////////////////////////
+// Geometry class in cartesian case
+/////////////////////////////////////////////////////////////////
+
+class Geometry {
+public:
+  int npoint;
+  int base;
+  std::vector<int> directions   ;
+  std::vector<int> displacements;
+  std::vector<int> points_dagger;
+
+  Geometry(int _d)  {
+    
+    base = (_d==5) ? 1:0;
+
+    // make coarse grid stencil for 4d , not 5d
+    if ( _d==5 ) _d=4;
+
+    npoint = 2*_d+1;
+    directions.resize(npoint);
+    displacements.resize(npoint);
+    points_dagger.resize(npoint);
+    for(int d=0;d<_d;d++){
+      directions[d   ] = d+base;
+      directions[d+_d] = d+base;
+      displacements[d  ] = +1;
+      displacements[d+_d]= -1;
+      points_dagger[d   ] = d+_d;
+      points_dagger[d+_d] = d;
+    }
+    directions   [2*_d]=0;
+    displacements[2*_d]=0;
+    points_dagger[2*_d]=2*_d;
+  }
+
+  int point(int dir, int disp) {
+    assert(disp == -1 || disp == 0 || disp == 1);
+    assert(base+0 <= dir && dir < base+4);
+
+    // directions faster index = new indexing
+    // 4d (base = 0):
+    // point 0  1  2  3  4  5  6  7  8
+    // dir   0  1  2  3  0  1  2  3  0
+    // disp +1 +1 +1 +1 -1 -1 -1 -1  0
+    // 5d (base = 1):
+    // point 0  1  2  3  4  5  6  7  8
+    // dir   1  2  3  4  1  2  3  4  0
+    // disp +1 +1 +1 +1 -1 -1 -1 -1  0
+
+    // displacements faster index = old indexing
+    // 4d (base = 0):
+    // point 0  1  2  3  4  5  6  7  8
+    // dir   0  0  1  1  2  2  3  3  0
+    // disp +1 -1 +1 -1 +1 -1 +1 -1  0
+    // 5d (base = 1):
+    // point 0  1  2  3  4  5  6  7  8
+    // dir   1  1  2  2  3  3  4  4  0
+    // disp +1 -1 +1 -1 +1 -1 +1 -1  0
+
+    if(dir == 0 and disp == 0)
+      return 8;
+    else // New indexing
+      return (1 - disp) / 2 * 4 + dir - base;
+    // else // Old indexing
+    //   return (4 * (dir - base) + 1 - disp) / 2;
+  }
+};
+
+/////////////////////////////////////////////////////////////////
+// Less local equivalent of Geometry class in cartesian case
+/////////////////////////////////////////////////////////////////
+class NonLocalStencilGeometry {
+public:
+  //  int depth;
+  int skip;
+  int hops;
+  int npoint;
+  std::vector<Coordinate> shifts;
+  Coordinate stencil_size;
+  Coordinate stencil_lo;
+  Coordinate stencil_hi;
+  GridCartesian *grid;
+  GridCartesian *Grid() {return grid;};
+  int Depth(void){return 1;};   // Ghost zone depth
+  int Hops(void){return hops;}; // # of hops=> level of corner fill in in stencil
+  int DimSkip(void){return skip;};
+
+  virtual ~NonLocalStencilGeometry() {};
+
+  int  Reverse(int point)
+  {
+    int Nd = Grid()->Nd();
+    Coordinate shft = shifts[point];
+    Coordinate rev(Nd);
+    for(int mu=0;mu<Nd;mu++) rev[mu]= -shft[mu];
+    for(int p=0;p<npoint;p++){
+      if(rev==shifts[p]){
+	return p;
+      }
+    }
+    assert(0);
+    return -1;
+  }
+  void BuildShifts(void)
+  {
+    this->shifts.resize(0);
+    int Nd = this->grid->Nd();
+
+    int dd = this->DimSkip();
+    for(int s0=this->stencil_lo[dd+0];s0<=this->stencil_hi[dd+0];s0++){
+    for(int s1=this->stencil_lo[dd+1];s1<=this->stencil_hi[dd+1];s1++){
+    for(int s2=this->stencil_lo[dd+2];s2<=this->stencil_hi[dd+2];s2++){
+    for(int s3=this->stencil_lo[dd+3];s3<=this->stencil_hi[dd+3];s3++){
+      Coordinate sft(Nd,0);
+      sft[dd+0] = s0;
+      sft[dd+1] = s1;
+      sft[dd+2] = s2;
+      sft[dd+3] = s3;
+      int nhops = abs(s0)+abs(s1)+abs(s2)+abs(s3);
+      if(nhops<=this->hops) this->shifts.push_back(sft);
+    }}}}
+    this->npoint = this->shifts.size();
+    std::cout << GridLogMessage << "NonLocalStencilGeometry has "<< this->npoint << " terms in stencil "<<std::endl;
+  }
+  
+  NonLocalStencilGeometry(GridCartesian *_coarse_grid,int _hops,int _skip) : grid(_coarse_grid), hops(_hops), skip(_skip)
+  {
+    Coordinate latt = grid->GlobalDimensions();
+    stencil_size.resize(grid->Nd());
+    stencil_lo.resize(grid->Nd());
+    stencil_hi.resize(grid->Nd());
+    for(int d=0;d<grid->Nd();d++){
+     if ( latt[d] == 1 ) {
+      stencil_lo[d] = 0;
+      stencil_hi[d] = 0;
+      stencil_size[d]= 1;
+     } else if ( latt[d] == 2 ) {
+      stencil_lo[d] = -1;
+      stencil_hi[d] = 0;
+      stencil_size[d]= 2;
+     } else if ( latt[d] > 2 ) {
+       stencil_lo[d] = -1;
+       stencil_hi[d] =  1;
+       stencil_size[d]= 3;
+     }
+    }
+    this->BuildShifts();
+  };
+
+};
+
+// Need to worry about red-black now
+class NonLocalStencilGeometry4D : public NonLocalStencilGeometry {
+public:
+  virtual int DerivedDimSkip(void) { return 0;};
+  NonLocalStencilGeometry4D(GridCartesian *Coarse,int _hops) : NonLocalStencilGeometry(Coarse,_hops,0) { };
+  virtual ~NonLocalStencilGeometry4D() {};
+};
+class NonLocalStencilGeometry5D : public NonLocalStencilGeometry {
+public:
+  virtual int DerivedDimSkip(void) { return 1; }; 
+  NonLocalStencilGeometry5D(GridCartesian *Coarse,int _hops) : NonLocalStencilGeometry(Coarse,_hops,1)  { };
+  virtual ~NonLocalStencilGeometry5D() {};
+};
+/*
+ * Bunch of different options classes
+ */
+class NextToNextToNextToNearestStencilGeometry4D : public NonLocalStencilGeometry4D {
+public:
+  NextToNextToNextToNearestStencilGeometry4D(GridCartesian *Coarse) :  NonLocalStencilGeometry4D(Coarse,4)
+  {
+  };
+};
+class NextToNextToNextToNearestStencilGeometry5D : public  NonLocalStencilGeometry5D {
+public:
+  NextToNextToNextToNearestStencilGeometry5D(GridCartesian *Coarse) :  NonLocalStencilGeometry5D(Coarse,4)
+  {
+  };
+};
+class NextToNearestStencilGeometry4D : public  NonLocalStencilGeometry4D {
+public:
+  NextToNearestStencilGeometry4D(GridCartesian *Coarse) :  NonLocalStencilGeometry4D(Coarse,2)
+  {
+  };
+};
+class NextToNearestStencilGeometry5D : public  NonLocalStencilGeometry5D {
+public:
+  NextToNearestStencilGeometry5D(GridCartesian *Coarse) :  NonLocalStencilGeometry5D(Coarse,2)
+  {
+  };
+};
+class NearestStencilGeometry4D : public  NonLocalStencilGeometry4D {
+public:
+  NearestStencilGeometry4D(GridCartesian *Coarse) :  NonLocalStencilGeometry4D(Coarse,1)
+  {
+  };
+};
+class NearestStencilGeometry5D : public  NonLocalStencilGeometry5D {
+public:
+  NearestStencilGeometry5D(GridCartesian *Coarse) :  NonLocalStencilGeometry5D(Coarse,1)
+  {
+  };
+};
+
+NAMESPACE_END(Grid);

Grid/algorithms/multigrid/MultiGrid.h

@@ -0,0 +1,34 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: Grid/algorithms/multigrid/MultiGrid.h
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    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 */
+#pragma once
+
+#include <Grid/algorithms/multigrid/Aggregates.h>
+#include <Grid/algorithms/multigrid/Geometry.h>
+#include <Grid/algorithms/multigrid/CoarsenedMatrix.h>
+#include <Grid/algorithms/multigrid/GeneralCoarsenedMatrix.h>
+#include <Grid/algorithms/multigrid/GeneralCoarsenedMatrixMultiRHS.h>

Grid/allocator/AlignedAllocator.h

@@ -179,6 +179,53 @@ template<class T> using commVector = std::vector<T,devAllocator<T> >;
 template<class T> using deviceVector  = std::vector<T,devAllocator<T> >;
 template<class T> using cshiftVector  = std::vector<T,cshiftAllocator<T> >;
 
+/*
+template<class T> class vecView
+{
+ protected:
+  T * data;
+  uint64_t size;
+  ViewMode mode;
+  void * cpu_ptr;
+ public:
+  accelerator_inline T & operator[](size_t i) const { return this->data[i]; };
+  vecView(std::vector<T> &refer_to_me,ViewMode _mode)
+  {
+    cpu_ptr = &refer_to_me[0];
+    size = refer_to_me.size();
+    mode = _mode;
+    data =(T *) MemoryManager::ViewOpen(cpu_ptr,
+					size*sizeof(T),
+					mode,
+					AdviseDefault);
+  }
+  void ViewClose(void)
+  { // Inform the manager
+    MemoryManager::ViewClose(this->cpu_ptr,this->mode);    
+  }
+};
+
+template<class T> vecView<T> VectorView(std::vector<T> &vec,ViewMode _mode)
+{
+  vecView<T> ret(vec,_mode); // does the open
+  return ret;                // must be closed
+}
+
+// Little autoscope assister
+template<class View> 
+class VectorViewCloser
+{
+  View v;  // Take a copy of view and call view close when I go out of scope automatically
+ public:
+  VectorViewCloser(View &_v) : v(_v) {};
+  ~VectorViewCloser() { auto ptr = v.cpu_ptr; v.ViewClose();  MemoryManager::NotifyDeletion(ptr);}
+};
+
+#define autoVecView(v_v,v,mode)					\
+  auto v_v = VectorView(v,mode);				\
+  ViewCloser<decltype(v_v)> _autoView##v_v(v_v);
+*/
+
 NAMESPACE_END(Grid);
 
 

Grid/allocator/MemoryManager.h

@@ -209,9 +209,9 @@ private:
   static void     CpuViewClose(uint64_t Ptr);
   static uint64_t CpuViewOpen(uint64_t  CpuPtr,size_t bytes,ViewMode mode,ViewAdvise hint);
 #endif
-  static void NotifyDeletion(void * CpuPtr);
 
  public:
+  static void NotifyDeletion(void * CpuPtr);
   static void Print(void);
   static void PrintAll(void);
   static void PrintState( void* CpuPtr);

Grid/allocator/MemoryManagerCache.cc

@@ -8,7 +8,7 @@ NAMESPACE_BEGIN(Grid);
 static char print_buffer [ MAXLINE ];
 
 #define mprintf(...) snprintf (print_buffer,MAXLINE, __VA_ARGS__ ); std::cout << GridLogMemory << print_buffer;
-#define dprintf(...) snprintf (print_buffer,MAXLINE, __VA_ARGS__ ); std::cout << GridLogMemory << print_buffer;
+#define dprintf(...) snprintf (print_buffer,MAXLINE, __VA_ARGS__ ); std::cout << GridLogDebug << print_buffer;
 //#define dprintf(...) 
 
 
@@ -111,7 +111,7 @@ void MemoryManager::AccDiscard(AcceleratorViewEntry &AccCache)
   ///////////////////////////////////////////////////////////
   assert(AccCache.state!=Empty);
   
-  mprintf("MemoryManager: Discard(%lx) %lx\n",(uint64_t)AccCache.CpuPtr,(uint64_t)AccCache.AccPtr); 
+  dprintf("MemoryManager: Discard(%lx) %lx\n",(uint64_t)AccCache.CpuPtr,(uint64_t)AccCache.AccPtr); 
   assert(AccCache.accLock==0);
   assert(AccCache.cpuLock==0);
   assert(AccCache.CpuPtr!=(uint64_t)NULL);
@@ -141,7 +141,7 @@ void MemoryManager::Evict(AcceleratorViewEntry &AccCache)
   ///////////////////////////////////////////////////////////////////////////
   assert(AccCache.state!=Empty);
   
-  mprintf("MemoryManager: Evict cpu %lx acc %lx cpuLock %ld accLock %ld\n",
+  mprintf("MemoryManager: Evict CpuPtr %lx AccPtr %lx cpuLock %ld accLock %ld\n",
 	  (uint64_t)AccCache.CpuPtr,(uint64_t)AccCache.AccPtr,
 	  (uint64_t)AccCache.cpuLock,(uint64_t)AccCache.accLock); 
   if (AccCache.accLock!=0) return;
@@ -155,7 +155,7 @@ void MemoryManager::Evict(AcceleratorViewEntry &AccCache)
     AccCache.AccPtr=(uint64_t)NULL;
     AccCache.state=CpuDirty; // CPU primary now
     DeviceBytes   -=AccCache.bytes;
-    dprintf("MemoryManager: Free(%lx) footprint now %ld \n",(uint64_t)AccCache.AccPtr,DeviceBytes);  
+    dprintf("MemoryManager: Free(AccPtr %lx) footprint now %ld \n",(uint64_t)AccCache.AccPtr,DeviceBytes);  
   }
   //  uint64_t CpuPtr = AccCache.CpuPtr;
   DeviceEvictions++;
@@ -169,7 +169,7 @@ void MemoryManager::Flush(AcceleratorViewEntry &AccCache)
   assert(AccCache.AccPtr!=(uint64_t)NULL);
   assert(AccCache.CpuPtr!=(uint64_t)NULL);
   acceleratorCopyFromDevice((void *)AccCache.AccPtr,(void *)AccCache.CpuPtr,AccCache.bytes);
-  mprintf("MemoryManager: Flush  %lx -> %lx\n",(uint64_t)AccCache.AccPtr,(uint64_t)AccCache.CpuPtr); fflush(stdout);
+  mprintf("MemoryManager: acceleratorCopyFromDevice Flush AccPtr %lx -> CpuPtr %lx\n",(uint64_t)AccCache.AccPtr,(uint64_t)AccCache.CpuPtr); fflush(stdout);
   DeviceToHostBytes+=AccCache.bytes;
   DeviceToHostXfer++;
   AccCache.state=Consistent;
@@ -184,7 +184,7 @@ void MemoryManager::Clone(AcceleratorViewEntry &AccCache)
     AccCache.AccPtr=(uint64_t)AcceleratorAllocate(AccCache.bytes);
     DeviceBytes+=AccCache.bytes;
   }
-  mprintf("MemoryManager: Clone %lx <- %lx\n",(uint64_t)AccCache.AccPtr,(uint64_t)AccCache.CpuPtr); fflush(stdout);
+  mprintf("MemoryManager: acceleratorCopyToDevice   Clone AccPtr %lx <- CpuPtr %lx\n",(uint64_t)AccCache.AccPtr,(uint64_t)AccCache.CpuPtr); fflush(stdout);
   acceleratorCopyToDevice((void *)AccCache.CpuPtr,(void *)AccCache.AccPtr,AccCache.bytes);
   HostToDeviceBytes+=AccCache.bytes;
   HostToDeviceXfer++;
@@ -474,6 +474,7 @@ void  MemoryManager::Print(void)
   std::cout << GridLogMessage << DeviceEvictions  << " Evictions from device " << std::endl;
   std::cout << GridLogMessage << DeviceDestroy    << " Destroyed vectors on device " << std::endl;
   std::cout << GridLogMessage << AccViewTable.size()<< " vectors " << LRU.size()<<" evictable"<< std::endl;
+  acceleratorMem();
   std::cout << GridLogMessage << "--------------------------------------------" << std::endl;
 }
 void  MemoryManager::PrintAll(void)

Grid/cartesian/Cartesian_base.h

@@ -70,8 +70,8 @@ public:
   Coordinate _istride;    // Inner stride i.e. within simd lane
   int _osites;                  // _isites*_osites = product(dimensions).
   int _isites;
-  int _fsites;                  // _isites*_osites = product(dimensions).
+  int64_t _fsites;                  // _isites*_osites = product(dimensions).
-  int _gsites;
+  int64_t _gsites;
   Coordinate _slice_block;// subslice information
   Coordinate _slice_stride;
   Coordinate _slice_nblock;
@@ -183,7 +183,7 @@ public:
   inline int Nsimd(void)  const { return _isites; };// Synonymous with iSites
   inline int oSites(void) const { return _osites; };
   inline int lSites(void) const { return _isites*_osites; }; 
-  inline int gSites(void) const { return _isites*_osites*_Nprocessors; }; 
+  inline int64_t gSites(void) const { return (int64_t)_isites*(int64_t)_osites*(int64_t)_Nprocessors; }; 
   inline int Nd    (void) const { return _ndimension;};
 
   inline const Coordinate LocalStarts(void)             { return _lstart;    };
@@ -214,7 +214,7 @@ public:
   ////////////////////////////////////////////////////////////////
   // Global addressing
   ////////////////////////////////////////////////////////////////
-  void GlobalIndexToGlobalCoor(int gidx,Coordinate &gcoor){
+  void GlobalIndexToGlobalCoor(int64_t gidx,Coordinate &gcoor){
     assert(gidx< gSites());
     Lexicographic::CoorFromIndex(gcoor,gidx,_gdimensions);
   }
@@ -222,7 +222,7 @@ public:
     assert(lidx<lSites());
     Lexicographic::CoorFromIndex(lcoor,lidx,_ldimensions);
   }
-  void GlobalCoorToGlobalIndex(const Coordinate & gcoor,int & gidx){
+  void GlobalCoorToGlobalIndex(const Coordinate & gcoor,int64_t & gidx){
     gidx=0;
     int mult=1;
     for(int mu=0;mu<_ndimension;mu++) {

Grid/communicator/Communicator_base.h

@@ -138,6 +138,14 @@ public:
   ////////////////////////////////////////////////////////////
   // Face exchange, buffer swap in translational invariant way
   ////////////////////////////////////////////////////////////
+  void CommsComplete(std::vector<CommsRequest_t> &list);
+  void SendToRecvFromBegin(std::vector<CommsRequest_t> &list,
+			   void *xmit,
+			   int dest,
+			   void *recv,
+			   int from,
+			   int bytes,int dir);
+  
   void SendToRecvFrom(void *xmit,
 		      int xmit_to_rank,
 		      void *recv,

Grid/communicator/Communicator_mpi3.cc

@@ -306,6 +306,44 @@ void CartesianCommunicator::GlobalSumVector(double *d,int N)
   int ierr = MPI_Allreduce(MPI_IN_PLACE,d,N,MPI_DOUBLE,MPI_SUM,communicator);
   assert(ierr==0);
 }
+
+void CartesianCommunicator::SendToRecvFromBegin(std::vector<CommsRequest_t> &list,
+						void *xmit,
+						int dest,
+						void *recv,
+						int from,
+						int bytes,int dir)
+{
+  MPI_Request xrq;
+  MPI_Request rrq;
+
+  assert(dest != _processor);
+  assert(from != _processor);
+
+  int tag;
+
+  tag= dir+from*32;
+  int ierr=MPI_Irecv(recv, bytes, MPI_CHAR,from,tag,communicator,&rrq);
+  assert(ierr==0);
+  list.push_back(rrq);
+  
+  tag= dir+_processor*32;
+  ierr =MPI_Isend(xmit, bytes, MPI_CHAR,dest,tag,communicator,&xrq);
+  assert(ierr==0);
+  list.push_back(xrq);
+}
+void CartesianCommunicator::CommsComplete(std::vector<CommsRequest_t> &list)
+{
+  int nreq=list.size();
+
+  if (nreq==0) return;
+
+  std::vector<MPI_Status> status(nreq);
+  int ierr = MPI_Waitall(nreq,&list[0],&status[0]);
+  assert(ierr==0);
+  list.resize(0);
+}
+
 // Basic Halo comms primitive
 void CartesianCommunicator::SendToRecvFrom(void *xmit,
 					   int dest,

Grid/communicator/Communicator_none.cc

@@ -91,6 +91,17 @@ void CartesianCommunicator::SendToRecvFrom(void *xmit,
 {
   assert(0);
 }
+void CartesianCommunicator::CommsComplete(std::vector<CommsRequest_t> &list){ assert(0);}
+void CartesianCommunicator::SendToRecvFromBegin(std::vector<CommsRequest_t> &list,
+						void *xmit,
+						int dest,
+						void *recv,
+						int from,
+						int bytes,int dir)
+{
+  assert(0);
+}
+
 void CartesianCommunicator::AllToAll(int dim,void  *in,void *out,uint64_t words,uint64_t bytes)
 {
   bcopy(in,out,bytes*words);

Grid/lattice/Lattice_base.h

@@ -234,9 +234,12 @@ public:
   }
 
   template<class sobj> inline Lattice<vobj> & operator = (const sobj & r){
-    auto me  = View(CpuWrite);
+    vobj vtmp;
-    thread_for(ss,me.size(),{
+    vtmp = r;
-	me[ss]= r;
+    auto me  = View(AcceleratorWrite);
+    accelerator_for(ss,me.size(),vobj::Nsimd(),{
+	auto stmp=coalescedRead(vtmp);
+	coalescedWrite(me[ss],stmp);
     });
     me.ViewClose();
     return *this;
@@ -360,7 +363,7 @@ public:
 
 template<class vobj> std::ostream& operator<< (std::ostream& stream, const Lattice<vobj> &o){
   typedef typename vobj::scalar_object sobj;
-  for(int g=0;g<o.Grid()->_gsites;g++){
+  for(int64_t g=0;g<o.Grid()->_gsites;g++){
 
     Coordinate gcoor;
     o.Grid()->GlobalIndexToGlobalCoor(g,gcoor);

Grid/lattice/Lattice_crc.h

@@ -29,7 +29,7 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 
 NAMESPACE_BEGIN(Grid);
 
-template<class vobj> void DumpSliceNorm(std::string s,Lattice<vobj> &f,int mu=-1)
+template<class vobj> void DumpSliceNorm(std::string s,const Lattice<vobj> &f,int mu=-1)
 {
   auto ff = localNorm2(f);
   if ( mu==-1 ) mu = f.Grid()->Nd()-1;

Grid/lattice/Lattice_reduction.h

@@ -204,6 +204,27 @@ template<class vobj> inline RealD norm2(const Lattice<vobj> &arg){
   return real(nrm); 
 }
 
+
+template<class Op,class T1>
+inline auto norm2(const LatticeUnaryExpression<Op,T1> & expr)  ->RealD
+{
+  return norm2(closure(expr));
+}
+
+template<class Op,class T1,class T2>
+inline auto norm2(const LatticeBinaryExpression<Op,T1,T2> & expr)      ->RealD
+{
+  return norm2(closure(expr));
+}
+
+
+template<class Op,class T1,class T2,class T3>
+inline auto norm2(const LatticeTrinaryExpression<Op,T1,T2,T3> & expr)      ->RealD
+{
+  return norm2(closure(expr));
+}
+
+
 //The global maximum of the site norm2
 template<class vobj> inline RealD maxLocalNorm2(const Lattice<vobj> &arg)
 {

Grid/lattice/Lattice_rng.h

@@ -365,9 +365,14 @@ public:
     _bernoulli.resize(_vol,std::discrete_distribution<int32_t>{1,1});
     _uid.resize(_vol,std::uniform_int_distribution<uint32_t>() );
   }
-
+  template <class vobj,class distribution> inline void fill(Lattice<vobj> &l,std::vector<distribution> &dist)
-  template <class vobj,class distribution> inline void fill(Lattice<vobj> &l,std::vector<distribution> &dist){
+  {
-
+    if ( l.Grid()->_isCheckerBoarded ) {
+      Lattice<vobj> tmp(_grid);
+      fill(tmp,dist);
+      pickCheckerboard(l.Checkerboard(),l,tmp);
+      return;
+    }
     typedef typename vobj::scalar_object scalar_object;
     typedef typename vobj::scalar_type scalar_type;
     typedef typename vobj::vector_type vector_type;
@@ -430,7 +435,7 @@ public:
     ////////////////////////////////////////////////
     thread_for( lidx, _grid->lSites(), {
 
-	int gidx;
+	int64_t gidx;
 	int o_idx;
 	int i_idx;
 	int rank;

Grid/lattice/Lattice_transfer.h

@@ -276,18 +276,33 @@ inline void blockProject(Lattice<iVector<CComplex,nbasis > > &coarseData,
 
   autoView( coarseData_ , coarseData, AcceleratorWrite);
   autoView( ip_         , ip,         AcceleratorWrite);
+  RealD t_IP=0;
+  RealD t_co=0;
+  RealD t_za=0;
   for(int v=0;v<nbasis;v++) {
+    t_IP-=usecond();
     blockInnerProductD(ip,Basis[v],fineDataRed); // ip = <basis|fine>
+    t_IP+=usecond();
+    t_co-=usecond();
     accelerator_for( sc, coarse->oSites(), vobj::Nsimd(), {
 	convertType(coarseData_[sc](v),ip_[sc]);
     });
+    t_co+=usecond();
 
     // improve numerical stability of projection
     // |fine> = |fine> - <basis|fine> |basis>
     ip=-ip;
+    t_za-=usecond();
     blockZAXPY(fineDataRed,ip,Basis[v],fineDataRed); 
+    t_za+=usecond();
   }
+  //  std::cout << GridLogPerformance << " blockProject : blockInnerProduct :  "<<t_IP<<" us"<<std::endl;
+  //  std::cout << GridLogPerformance << " blockProject : conv              :  "<<t_co<<" us"<<std::endl;
+  //  std::cout << GridLogPerformance << " blockProject : blockZaxpy        :  "<<t_za<<" us"<<std::endl;
 }
+// This only minimises data motion from CPU to GPU
+// there is chance of better implementation that does a vxk loop of inner products to data share
+// at the GPU thread level
 template<class vobj,class CComplex,int nbasis,class VLattice>
 inline void batchBlockProject(std::vector<Lattice<iVector<CComplex,nbasis>>> &coarseData,
                                const std::vector<Lattice<vobj>> &fineData,
@@ -393,8 +408,15 @@ template<class vobj,class CComplex>
   Lattice<dotp> coarse_inner(coarse);
 
   // Precision promotion
+  RealD t;
+  t=-usecond();
   fine_inner = localInnerProductD<vobj>(fineX,fineY);
+  //  t+=usecond(); std::cout << GridLogPerformance << " blockInnerProduct : localInnerProductD "<<t<<" us"<<std::endl;
+  
+  t=-usecond();
   blockSum(coarse_inner,fine_inner);
+  //  t+=usecond(); std::cout << GridLogPerformance << " blockInnerProduct : blockSum "<<t<<" us"<<std::endl;
+  t=-usecond();
   {
     autoView( CoarseInner_  , CoarseInner,AcceleratorWrite);
     autoView( coarse_inner_ , coarse_inner,AcceleratorRead);
@@ -402,6 +424,7 @@ template<class vobj,class CComplex>
       convertType(CoarseInner_[ss], TensorRemove(coarse_inner_[ss]));
     });
   }
+  //  t+=usecond(); std::cout << GridLogPerformance << " blockInnerProduct : convertType "<<t<<" us"<<std::endl;
  
 }
 
@@ -444,6 +467,9 @@ inline void blockNormalise(Lattice<CComplex> &ip,Lattice<vobj> &fineX)
 template<class vobj>
 inline void blockSum(Lattice<vobj> &coarseData,const Lattice<vobj> &fineData) 
 {
+  const int maxsubsec=256;
+  typedef iVector<vobj,maxsubsec> vSubsec;
+
   GridBase * fine  = fineData.Grid();
   GridBase * coarse= coarseData.Grid();
 
@@ -469,16 +495,34 @@ inline void blockSum(Lattice<vobj> &coarseData,const Lattice<vobj> &fineData)
   Coordinate fine_rdimensions = fine->_rdimensions;
   Coordinate coarse_rdimensions = coarse->_rdimensions;
 
-  accelerator_for(sc,coarse->oSites(),1,{
+  vobj zz = Zero();
+
+  // Somewhat lazy calculation
+  // Find the biggest power of two subsection divisor less than or equal to maxsubsec
+  int subsec=maxsubsec;
+  int subvol;
+  subvol=blockVol/subsec;
+  while(subvol*subsec!=blockVol){
+    subsec = subsec/2;
+    subvol=blockVol/subsec;
+  };
+
+  Lattice<vSubsec> coarseTmp(coarse);
+  autoView( coarseTmp_, coarseTmp, AcceleratorWriteDiscard);
+  auto coarseTmp_p= &coarseTmp_[0];
+  
+  // Sum within subsecs in a first kernel
+  accelerator_for(sce,subsec*coarse->oSites(),vobj::Nsimd(),{
+
+      int sc=sce/subsec;
+      int e=sce%subsec;
       
       // One thread per sub block
       Coordinate coor_c(_ndimension);
       Lexicographic::CoorFromIndex(coor_c,sc,coarse_rdimensions);  // Block coordinate
 
-      vobj cd = Zero();
+      auto cd = coalescedRead(zz);
-      
+      for(int sb=e*subvol;sb<MIN((e+1)*subvol,blockVol);sb++){
-      for(int sb=0;sb<blockVol;sb++){
-
 	int sf;
 	Coordinate coor_b(_ndimension);
 	Coordinate coor_f(_ndimension);
@@ -486,12 +530,21 @@ inline void blockSum(Lattice<vobj> &coarseData,const Lattice<vobj> &fineData)
 	for(int d=0;d<_ndimension;d++) coor_f[d]=coor_c[d]*block_r[d] + coor_b[d];
 	Lexicographic::IndexFromCoor(coor_f,sf,fine_rdimensions);
 	
-	cd=cd+fineData_p[sf];
+	cd=cd+coalescedRead(fineData_p[sf]);
       }
 
-      coarseData_p[sc] = cd;
+      coalescedWrite(coarseTmp_[sc](e),cd);
 
     });
+   // Sum across subsecs in a second kernel
+   accelerator_for(sc,coarse->oSites(),vobj::Nsimd(),{
+      auto cd = coalescedRead(coarseTmp_p[sc](0));
+      for(int e=1;e<subsec;e++){
+	cd=cd+coalescedRead(coarseTmp_p[sc](e));
+      }
+      coalescedWrite(coarseData_p[sc],cd);
+   });
+
   return;
 }
 
@@ -548,7 +601,7 @@ inline void blockOrthogonalise(Lattice<CComplex> &ip,std::vector<Lattice<vobj> >
   blockOrthonormalize(ip,Basis);
 }
 
-#if 0
+#ifdef GRID_ACCELERATED
 // TODO: CPU optimized version here
 template<class vobj,class CComplex,int nbasis>
 inline void blockPromote(const Lattice<iVector<CComplex,nbasis > > &coarseData,
@@ -574,26 +627,37 @@ inline void blockPromote(const Lattice<iVector<CComplex,nbasis > > &coarseData,
   autoView( fineData_   , fineData, AcceleratorWrite);
   autoView( coarseData_ , coarseData, AcceleratorRead);
 
+  typedef LatticeView<vobj> Vview;
+  std::vector<Vview> AcceleratorVecViewContainer_h; 
+  for(int v=0;v<nbasis;v++) {
+    AcceleratorVecViewContainer_h.push_back(Basis[v].View(AcceleratorRead));
+  }
+  static deviceVector<Vview> AcceleratorVecViewContainer; AcceleratorVecViewContainer.resize(nbasis); 
+  acceleratorCopyToDevice(&AcceleratorVecViewContainer_h[0],&AcceleratorVecViewContainer[0],nbasis *sizeof(Vview));
+  auto Basis_p = &AcceleratorVecViewContainer[0];
   // Loop with a cache friendly loop ordering
-  accelerator_for(sf,fine->oSites(),1,{
+  Coordinate frdimensions=fine->_rdimensions;
+  Coordinate crdimensions=coarse->_rdimensions;
+  accelerator_for(sf,fine->oSites(),vobj::Nsimd(),{
     int sc;
     Coordinate coor_c(_ndimension);
     Coordinate coor_f(_ndimension);
 
-    Lexicographic::CoorFromIndex(coor_f,sf,fine->_rdimensions);
+    Lexicographic::CoorFromIndex(coor_f,sf,frdimensions);
     for(int d=0;d<_ndimension;d++) coor_c[d]=coor_f[d]/block_r[d];
-    Lexicographic::IndexFromCoor(coor_c,sc,coarse->_rdimensions);
+    Lexicographic::IndexFromCoor(coor_c,sc,crdimensions);
 
-    for(int i=0;i<nbasis;i++) {
+    auto sum= coarseData_(sc)(0) *Basis_p[0](sf);
-      /*      auto basis_ = Basis[i],  );*/
+    for(int i=1;i<nbasis;i++) sum = sum + coarseData_(sc)(i)*Basis_p[i](sf);
-      if(i==0) fineData_[sf]=coarseData_[sc](i) *basis_[sf]);
+    coalescedWrite(fineData_[sf],sum);
-      else     fineData_[sf]=fineData_[sf]+coarseData_[sc](i)*basis_[sf]);
-    }
   });
+  for(int v=0;v<nbasis;v++) {
+    AcceleratorVecViewContainer_h[v].ViewClose();
+  }
   return;
-  
 }
 #else
+// CPU version
 template<class vobj,class CComplex,int nbasis,class VLattice>
 inline void blockPromote(const Lattice<iVector<CComplex,nbasis > > &coarseData,
 			 Lattice<vobj>   &fineData,
@@ -680,7 +744,11 @@ void localCopyRegion(const Lattice<vobj> &From,Lattice<vobj> & To,Coordinate Fro
   typedef typename vobj::scalar_type scalar_type;
   typedef typename vobj::vector_type vector_type;
 
-  static const int words=sizeof(vobj)/sizeof(vector_type);
+  const int words=sizeof(vobj)/sizeof(vector_type);
+
+  //////////////////////////////////////////////////////////////////////////////////////////
+  // checks should guarantee that the operations are local
+  //////////////////////////////////////////////////////////////////////////////////////////
 
   GridBase *Fg = From.Grid();
   GridBase *Tg = To.Grid();
@@ -695,39 +763,20 @@ void localCopyRegion(const Lattice<vobj> &From,Lattice<vobj> & To,Coordinate Fro
   for(int d=0;d<nd;d++){
     assert(Fg->_processors[d]  == Tg->_processors[d]);
   }
-  // the above should guarantee that the operations are local
 
-#if 1
+  ///////////////////////////////////////////////////////////
+  // do the index calc on the GPU
+  ///////////////////////////////////////////////////////////
+  Coordinate f_ostride = Fg->_ostride;
+  Coordinate f_istride = Fg->_istride;
+  Coordinate f_rdimensions = Fg->_rdimensions;
+  Coordinate t_ostride = Tg->_ostride;
+  Coordinate t_istride = Tg->_istride;
+  Coordinate t_rdimensions = Tg->_rdimensions;
 
   size_t nsite = 1;
   for(int i=0;i<nd;i++) nsite *= RegionSize[i];
 
-  size_t tbytes = 4*nsite*sizeof(int);
-  int *table = (int*)malloc(tbytes);
- 
-  thread_for(idx, nsite, {
-      Coordinate from_coor, to_coor;
-      size_t rem = idx;
-      for(int i=0;i<nd;i++){
-	size_t base_i  = rem % RegionSize[i]; rem /= RegionSize[i];
-	from_coor[i] = base_i + FromLowerLeft[i];
-	to_coor[i] = base_i + ToLowerLeft[i];
-      }
-      
-      int foidx = Fg->oIndex(from_coor);
-      int fiidx = Fg->iIndex(from_coor);
-      int toidx = Tg->oIndex(to_coor);
-      int tiidx = Tg->iIndex(to_coor);
-      int* tt = table + 4*idx;
-      tt[0] = foidx;
-      tt[1] = fiidx;
-      tt[2] = toidx;
-      tt[3] = tiidx;
-    });
-  
-  int* table_d = (int*)acceleratorAllocDevice(tbytes);
-  acceleratorCopyToDevice(table,table_d,tbytes);
-
   typedef typename vobj::vector_type vector_type;
   typedef typename vobj::scalar_type scalar_type;
 
@@ -735,12 +784,17 @@ void localCopyRegion(const Lattice<vobj> &From,Lattice<vobj> & To,Coordinate Fro
   autoView(to_v,To,AcceleratorWrite);
 
   accelerator_for(idx,nsite,1,{
-      static const int words=sizeof(vobj)/sizeof(vector_type);
+
-      int* tt = table_d + 4*idx;
+      Coordinate from_coor, to_coor, base;
-      int from_oidx = *tt++;
+      Lexicographic::CoorFromIndex(base,idx,RegionSize);
-      int from_lane = *tt++;
+      for(int i=0;i<nd;i++){
-      int to_oidx = *tt++;
+	from_coor[i] = base[i] + FromLowerLeft[i];
-      int to_lane = *tt;
+	to_coor[i] = base[i] + ToLowerLeft[i];
+      }
+      int from_oidx = 0; for(int d=0;d<nd;d++) from_oidx+=f_ostride[d]*(from_coor[d]%f_rdimensions[d]);
+      int from_lane = 0; for(int d=0;d<nd;d++) from_lane+=f_istride[d]*(from_coor[d]/f_rdimensions[d]);
+      int to_oidx   = 0; for(int d=0;d<nd;d++) to_oidx+=t_ostride[d]*(to_coor[d]%t_rdimensions[d]);
+      int to_lane   = 0; for(int d=0;d<nd;d++) to_lane+=t_istride[d]*(to_coor[d]/t_rdimensions[d]);
 
       const vector_type* from = (const vector_type *)&from_v[from_oidx];
       vector_type* to = (vector_type *)&to_v[to_oidx];
@@ -751,55 +805,145 @@ void localCopyRegion(const Lattice<vobj> &From,Lattice<vobj> & To,Coordinate Fro
 	putlane(to[w], stmp, to_lane);
       }
   });
-  
-  acceleratorFreeDevice(table_d);    
-  free(table);
-  
-
-#else  
-  Coordinate ldf = Fg->_ldimensions;
-  Coordinate rdf = Fg->_rdimensions;
-  Coordinate isf = Fg->_istride;
-  Coordinate osf = Fg->_ostride;
-  Coordinate rdt = Tg->_rdimensions;
-  Coordinate ist = Tg->_istride;
-  Coordinate ost = Tg->_ostride;
-
-  autoView( t_v , To, CpuWrite);
-  autoView( f_v , From, CpuRead);
-  thread_for(idx,Fg->lSites(),{
-    sobj s;
-    Coordinate Fcoor(nd);
-    Coordinate Tcoor(nd);
-    Lexicographic::CoorFromIndex(Fcoor,idx,ldf);
-    int in_region=1;
-    for(int d=0;d<nd;d++){
-      if ( (Fcoor[d] < FromLowerLeft[d]) || (Fcoor[d]>=FromLowerLeft[d]+RegionSize[d]) ){ 
-	in_region=0;
 }
-      Tcoor[d] = ToLowerLeft[d]+ Fcoor[d]-FromLowerLeft[d];
+
+template<class vobj>
+void InsertSliceFast(const Lattice<vobj> &From,Lattice<vobj> & To,int slice, int orthog)
+{
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  const int words=sizeof(vobj)/sizeof(vector_type);
+
+  //////////////////////////////////////////////////////////////////////////////////////////
+  // checks should guarantee that the operations are local
+  //////////////////////////////////////////////////////////////////////////////////////////
+  GridBase *Fg = From.Grid();
+  GridBase *Tg = To.Grid();
+  assert(!Fg->_isCheckerBoarded);
+  assert(!Tg->_isCheckerBoarded);
+  int Nsimd = Fg->Nsimd();
+  int nF = Fg->_ndimension;
+  int nT = Tg->_ndimension;
+  assert(nF+1 == nT);
+
+  ///////////////////////////////////////////////////////////
+  // do the index calc on the GPU
+  ///////////////////////////////////////////////////////////
+  Coordinate f_ostride = Fg->_ostride;
+  Coordinate f_istride = Fg->_istride;
+  Coordinate f_rdimensions = Fg->_rdimensions;
+  Coordinate t_ostride = Tg->_ostride;
+  Coordinate t_istride = Tg->_istride;
+  Coordinate t_rdimensions = Tg->_rdimensions;
+  Coordinate RegionSize = Fg->_ldimensions;
+  size_t nsite = 1;
+  for(int i=0;i<nF;i++) nsite *= RegionSize[i]; // whole volume of lower dim grid
+
+  typedef typename vobj::vector_type vector_type;
+  typedef typename vobj::scalar_type scalar_type;
+
+  autoView(from_v,From,AcceleratorRead);
+  autoView(to_v,To,AcceleratorWrite);
+
+  accelerator_for(idx,nsite,1,{
+
+      Coordinate from_coor(nF), to_coor(nT);
+      Lexicographic::CoorFromIndex(from_coor,idx,RegionSize);
+      int j=0;
+      for(int i=0;i<nT;i++){
+	if ( i!=orthog ) { 
+	  to_coor[i] = from_coor[j];
+	  j++;
+	} else {
+	  to_coor[i] = slice;
 	}
-    if (in_region) {
+      }
-#if 0      
+      int from_oidx = 0; for(int d=0;d<nF;d++) from_oidx+=f_ostride[d]*(from_coor[d]%f_rdimensions[d]);
-      Integer idx_f = 0; for(int d=0;d<nd;d++) idx_f+=isf[d]*(Fcoor[d]/rdf[d]); // inner index from
+      int from_lane = 0; for(int d=0;d<nF;d++) from_lane+=f_istride[d]*(from_coor[d]/f_rdimensions[d]);
-      Integer idx_t = 0; for(int d=0;d<nd;d++) idx_t+=ist[d]*(Tcoor[d]/rdt[d]); // inner index to
+      int to_oidx   = 0; for(int d=0;d<nT;d++) to_oidx+=t_ostride[d]*(to_coor[d]%t_rdimensions[d]);
-      Integer odx_f = 0; for(int d=0;d<nd;d++) odx_f+=osf[d]*(Fcoor[d]%rdf[d]); // outer index from
+      int to_lane   = 0; for(int d=0;d<nT;d++) to_lane+=t_istride[d]*(to_coor[d]/t_rdimensions[d]);
-      Integer odx_t = 0; for(int d=0;d<nd;d++) odx_t+=ost[d]*(Tcoor[d]%rdt[d]); // outer index to
+
-      scalar_type * fp = (scalar_type *)&f_v[odx_f];
+      const vector_type* from = (const vector_type *)&from_v[from_oidx];
-      scalar_type * tp = (scalar_type *)&t_v[odx_t];
+      vector_type* to = (vector_type *)&to_v[to_oidx];
+      
+      scalar_type stmp;
       for(int w=0;w<words;w++){
-	tp[w].putlane(fp[w].getlane(idx_f),idx_t);
+	stmp = getlane(from[w], from_lane);
-      }
+	putlane(to[w], stmp, to_lane);
-#else
-    peekLocalSite(s,f_v,Fcoor);
-    pokeLocalSite(s,t_v,Tcoor);
-#endif
       }
   });
-
-#endif
 }
 
+template<class vobj>
+void ExtractSliceFast(Lattice<vobj> &To,const Lattice<vobj> & From,int slice, int orthog)
+{
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  const int words=sizeof(vobj)/sizeof(vector_type);
+
+  //////////////////////////////////////////////////////////////////////////////////////////
+  // checks should guarantee that the operations are local
+  //////////////////////////////////////////////////////////////////////////////////////////
+  GridBase *Fg = From.Grid();
+  GridBase *Tg = To.Grid();
+  assert(!Fg->_isCheckerBoarded);
+  assert(!Tg->_isCheckerBoarded);
+  int Nsimd = Fg->Nsimd();
+  int nF = Fg->_ndimension;
+  int nT = Tg->_ndimension;
+  assert(nT+1 == nF);
+
+  ///////////////////////////////////////////////////////////
+  // do the index calc on the GPU
+  ///////////////////////////////////////////////////////////
+  Coordinate f_ostride = Fg->_ostride;
+  Coordinate f_istride = Fg->_istride;
+  Coordinate f_rdimensions = Fg->_rdimensions;
+  Coordinate t_ostride = Tg->_ostride;
+  Coordinate t_istride = Tg->_istride;
+  Coordinate t_rdimensions = Tg->_rdimensions;
+  Coordinate RegionSize = Tg->_ldimensions;
+  size_t nsite = 1;
+  for(int i=0;i<nT;i++) nsite *= RegionSize[i]; // whole volume of lower dim grid
+
+  typedef typename vobj::vector_type vector_type;
+  typedef typename vobj::scalar_type scalar_type;
+
+  autoView(from_v,From,AcceleratorRead);
+  autoView(to_v,To,AcceleratorWrite);
+
+  accelerator_for(idx,nsite,1,{
+
+      Coordinate from_coor(nF), to_coor(nT);
+      Lexicographic::CoorFromIndex(to_coor,idx,RegionSize);
+      int j=0;
+      for(int i=0;i<nF;i++){
+	if ( i!=orthog ) { 
+	  from_coor[i] = to_coor[j];
+	  j++;
+	} else {
+	  from_coor[i] = slice;
+	}
+      }
+      int from_oidx = 0; for(int d=0;d<nF;d++) from_oidx+=f_ostride[d]*(from_coor[d]%f_rdimensions[d]);
+      int from_lane = 0; for(int d=0;d<nF;d++) from_lane+=f_istride[d]*(from_coor[d]/f_rdimensions[d]);
+      int to_oidx   = 0; for(int d=0;d<nT;d++) to_oidx+=t_ostride[d]*(to_coor[d]%t_rdimensions[d]);
+      int to_lane   = 0; for(int d=0;d<nT;d++) to_lane+=t_istride[d]*(to_coor[d]/t_rdimensions[d]);
+
+      const vector_type* from = (const vector_type *)&from_v[from_oidx];
+      vector_type* to = (vector_type *)&to_v[to_oidx];
+      
+      scalar_type stmp;
+      for(int w=0;w<words;w++){
+	stmp = getlane(from[w], from_lane);
+	putlane(to[w], stmp, to_lane);
+      }
+  });
+}
 
 template<class vobj>
 void InsertSlice(const Lattice<vobj> &lowDim,Lattice<vobj> & higherDim,int slice, int orthog)
@@ -889,9 +1033,7 @@ void ExtractSlice(Lattice<vobj> &lowDim,const Lattice<vobj> & higherDim,int slic
 
 }
 
-
+//Can I implement with local copyregion??
-//Insert subvolume orthogonal to direction 'orthog' with slice index 'slice_lo' from 'lowDim' onto slice index 'slice_hi' of higherDim
-//The local dimensions of both 'lowDim' and 'higherDim' orthogonal to 'orthog' should be the same
 template<class vobj>
 void InsertSliceLocal(const Lattice<vobj> &lowDim, Lattice<vobj> & higherDim,int slice_lo,int slice_hi, int orthog)
 {
@@ -912,121 +1054,18 @@ void InsertSliceLocal(const Lattice<vobj> &lowDim, Lattice<vobj> & higherDim,int
       assert(lg->_ldimensions[d] == hg->_ldimensions[d]);
     }
   }
-
+  Coordinate sz = lg->_ldimensions;
-#if 1
+  sz[orthog]=1;
-  size_t nsite = lg->lSites()/lg->LocalDimensions()[orthog];
+  Coordinate f_ll(nl,0); f_ll[orthog]=slice_lo;
-  size_t tbytes = 4*nsite*sizeof(int);
+  Coordinate t_ll(nh,0); t_ll[orthog]=slice_hi;
-  int *table = (int*)malloc(tbytes);
+  localCopyRegion(lowDim,higherDim,f_ll,t_ll,sz);
-  
-  thread_for(idx,nsite,{
-    Coordinate lcoor(nl);
-    Coordinate hcoor(nh);
-    lcoor[orthog] = slice_lo;
-    hcoor[orthog] = slice_hi;
-    size_t rem = idx;
-    for(int mu=0;mu<nl;mu++){
-      if(mu != orthog){
-	int xmu = rem % lg->LocalDimensions()[mu];  rem /= lg->LocalDimensions()[mu];
-	lcoor[mu] = hcoor[mu] = xmu;
-      }
-    }
-    int loidx = lg->oIndex(lcoor);
-    int liidx = lg->iIndex(lcoor);
-    int hoidx = hg->oIndex(hcoor);
-    int hiidx = hg->iIndex(hcoor);
-    int* tt = table + 4*idx;
-    tt[0] = loidx;
-    tt[1] = liidx;
-    tt[2] = hoidx;
-    tt[3] = hiidx;
-    });
-   
-  int* table_d = (int*)acceleratorAllocDevice(tbytes);
-  acceleratorCopyToDevice(table,table_d,tbytes);
-
-  typedef typename vobj::vector_type vector_type;
-  typedef typename vobj::scalar_type scalar_type;
-
-  autoView(lowDim_v,lowDim,AcceleratorRead);
-  autoView(higherDim_v,higherDim,AcceleratorWrite);
-  
-  accelerator_for(idx,nsite,1,{
-      static const int words=sizeof(vobj)/sizeof(vector_type);
-      int* tt = table_d + 4*idx;
-      int from_oidx = *tt++;
-      int from_lane = *tt++;
-      int to_oidx = *tt++;
-      int to_lane = *tt;
-
-      const vector_type* from = (const vector_type *)&lowDim_v[from_oidx];
-      vector_type* to = (vector_type *)&higherDim_v[to_oidx];
-      
-      scalar_type stmp;
-      for(int w=0;w<words;w++){
-	stmp = getlane(from[w], from_lane);
-	putlane(to[w], stmp, to_lane);
-      }
-    });
-  
-  acceleratorFreeDevice(table_d);    
-  free(table);
-  
-#else
-  // the above should guarantee that the operations are local
-  autoView(lowDimv,lowDim,CpuRead);
-  autoView(higherDimv,higherDim,CpuWrite);
-  thread_for(idx,lg->lSites(),{
-    sobj s;
-    Coordinate lcoor(nl);
-    Coordinate hcoor(nh);
-    lg->LocalIndexToLocalCoor(idx,lcoor);
-    if( lcoor[orthog] == slice_lo ) { 
-      hcoor=lcoor;
-      hcoor[orthog] = slice_hi;
-      peekLocalSite(s,lowDimv,lcoor);
-      pokeLocalSite(s,higherDimv,hcoor);
-    }
-  });
-#endif
 }
 
 
 template<class vobj>
 void ExtractSliceLocal(Lattice<vobj> &lowDim,const Lattice<vobj> & higherDim,int slice_lo,int slice_hi, int orthog)
 {
-  typedef typename vobj::scalar_object sobj;
+  InsertSliceLocal(higherDim,lowDim,slice_hi,slice_lo,orthog);
-
-  GridBase *lg = lowDim.Grid();
-  GridBase *hg = higherDim.Grid();
-  int nl = lg->_ndimension;
-  int nh = hg->_ndimension;
-
-  assert(nl == nh);
-  assert(orthog<nh);
-  assert(orthog>=0);
-
-  for(int d=0;d<nh;d++){
-    if ( d!=orthog ) {
-    assert(lg->_processors[d]  == hg->_processors[d]);
-    assert(lg->_ldimensions[d] == hg->_ldimensions[d]);
-  }
-  }
-
-  // the above should guarantee that the operations are local
-  autoView(lowDimv,lowDim,CpuWrite);
-  autoView(higherDimv,higherDim,CpuRead);
-  thread_for(idx,lg->lSites(),{
-    sobj s;
-    Coordinate lcoor(nl);
-    Coordinate hcoor(nh);
-    lg->LocalIndexToLocalCoor(idx,lcoor);
-    if( lcoor[orthog] == slice_lo ) { 
-      hcoor=lcoor;
-      hcoor[orthog] = slice_hi;
-      peekLocalSite(s,higherDimv,hcoor);
-      pokeLocalSite(s,lowDimv,lcoor);
-    }
-  });
 }
 
 
@@ -1052,7 +1091,7 @@ void Replicate(const Lattice<vobj> &coarse,Lattice<vobj> & fine)
 
   Coordinate fcoor(nd);
   Coordinate ccoor(nd);
-  for(int g=0;g<fg->gSites();g++){
+  for(int64_t g=0;g<fg->gSites();g++){
 
     fg->GlobalIndexToGlobalCoor(g,fcoor);
     for(int d=0;d<nd;d++){
@@ -1738,5 +1777,35 @@ void Grid_unsplit(std::vector<Lattice<Vobj> > & full,Lattice<Vobj>   & split)
   }
 }
 
+//////////////////////////////////////////////////////
+// Faster but less accurate blockProject
+//////////////////////////////////////////////////////
+template<class vobj,class CComplex,int nbasis,class VLattice>
+inline void blockProjectFast(Lattice<iVector<CComplex,nbasis > > &coarseData,
+			     const             Lattice<vobj>   &fineData,
+			     const VLattice &Basis)
+{
+  GridBase * fine  = fineData.Grid();
+  GridBase * coarse= coarseData.Grid();
+
+  Lattice<iScalar<CComplex> > ip(coarse);
+
+  autoView( coarseData_ , coarseData, AcceleratorWrite);
+  autoView( ip_         , ip,         AcceleratorWrite);
+  RealD t_IP=0;
+  RealD t_co=0;
+  for(int v=0;v<nbasis;v++) {
+    t_IP-=usecond();
+    blockInnerProductD(ip,Basis[v],fineData); 
+    t_IP+=usecond();
+    t_co-=usecond();
+    accelerator_for( sc, coarse->oSites(), vobj::Nsimd(), {
+	convertType(coarseData_[sc](v),ip_[sc]);
+      });
+    t_co+=usecond();
+  }
+}
+
+
 NAMESPACE_END(Grid);
 

Grid/lattice/PaddedCell.h

@@ -45,6 +45,188 @@ struct CshiftImplGauge: public CshiftImplBase<typename Gimpl::GaugeLinkField::ve
   typename Gimpl::GaugeLinkField Cshift(const typename Gimpl::GaugeLinkField &in, int dir, int shift) const override{ return Gimpl::CshiftLink(in,dir,shift); }
 };  
 
+
+/*
+ *
+ * TODO: 
+ *  -- address elementsof vobj via thread block in Scatter/Gather
+ *  -- overlap comms with motion in Face_exchange
+ *
+ */
+
+template<class vobj> inline void ScatterSlice(const cshiftVector<vobj> &buf,
+					      Lattice<vobj> &lat,
+					      int x,
+					      int dim,
+					      int offset=0)
+{
+  const int Nsimd=vobj::Nsimd();
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  GridBase *grid = lat.Grid();
+  Coordinate simd = grid->_simd_layout;
+  int Nd          = grid->Nd();
+  int block       = grid->_slice_block[dim];
+  int stride      = grid->_slice_stride[dim];
+  int nblock      = grid->_slice_nblock[dim];
+  int rd          = grid->_rdimensions[dim];
+
+  int ox = x%rd;
+  int ix = x/rd;
+
+  int isites = 1; for(int d=0;d<Nd;d++) if( d!=dim) isites*=simd[d];
+
+  Coordinate rsimd= simd;  rsimd[dim]=1; // maybe reduce Nsimd
+
+  int rNsimd = 1; for(int d=0;d<Nd;d++) rNsimd*=rsimd[d];
+  int rNsimda= Nsimd/simd[dim]; // should be equal
+  assert(rNsimda==rNsimd);
+  int face_ovol=block*nblock;
+
+  //  assert(buf.size()==face_ovol*rNsimd);
+
+  /*This will work GPU ONLY unless rNsimd is put in the lexico index*/
+  //Let's make it work on GPU and then make a special accelerator_for that
+  //doesn't hide the SIMD direction and keeps explicit in the threadIdx
+  //for cross platform
+  // FIXME -- can put internal indices into thread loop
+  auto buf_p = & buf[0];
+  autoView(lat_v, lat, AcceleratorWrite);
+  accelerator_for(ss, face_ovol/simd[dim],Nsimd,{
+
+    // scalar layout won't coalesce
+#ifdef GRID_SIMT
+      {
+	int blane=acceleratorSIMTlane(Nsimd); // buffer lane
+#else
+      for(int blane=0;blane<Nsimd;blane++) {
+#endif
+	int olane=blane%rNsimd;               // reduced lattice lane
+	int obit =blane/rNsimd;
+
+	///////////////////////////////////////////////////////////////
+	// osite -- potentially one bit from simd in the buffer: (ss<<1)|obit
+	///////////////////////////////////////////////////////////////
+	int ssp = ss*simd[dim]+obit;
+	int b    = ssp%block;
+	int n    = ssp/block;
+	int osite= b+n*stride + ox*block;
+	
+	////////////////////////////////////////////
+	// isite -- map lane within buffer to lane within lattice
+	////////////////////////////////////////////
+	Coordinate icoor;
+	int lane;
+	Lexicographic::CoorFromIndex(icoor,olane,rsimd);
+	icoor[dim]=ix;
+	Lexicographic::IndexFromCoor(icoor,lane,simd);
+	
+	///////////////////////////////////////////
+	// Transfer into lattice - will coalesce
+	///////////////////////////////////////////
+	//	sobj obj = extractLane(blane,buf_p[ss+offset]);
+	//	insertLane(lane,lat_v[osite],obj);
+	const int words=sizeof(vobj)/sizeof(vector_type);
+	vector_type * from = (vector_type *)&buf_p[ss+offset];
+	vector_type * to   = (vector_type *)&lat_v[osite];
+	scalar_type stmp;
+	for(int w=0;w<words;w++){
+	  stmp = getlane(from[w], blane);
+	  putlane(to[w], stmp, lane);
+	}
+      }
+  });
+}
+
+template<class vobj> inline void GatherSlice(cshiftVector<vobj> &buf,
+					     const Lattice<vobj> &lat,
+					     int x,
+					     int dim,
+					     int offset=0)
+{
+  const int Nsimd=vobj::Nsimd();
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  autoView(lat_v, lat, AcceleratorRead);
+
+  GridBase *grid = lat.Grid();
+  Coordinate simd = grid->_simd_layout;
+  int Nd          = grid->Nd();
+  int block       = grid->_slice_block[dim];
+  int stride      = grid->_slice_stride[dim];
+  int nblock      = grid->_slice_nblock[dim];
+  int rd          = grid->_rdimensions[dim];
+
+  int ox = x%rd;
+  int ix = x/rd;
+
+  int isites = 1; for(int d=0;d<Nd;d++) if( d!=dim) isites*=simd[d];
+
+  Coordinate rsimd= simd;  rsimd[dim]=1; // maybe reduce Nsimd
+
+  int rNsimd = 1; for(int d=0;d<Nd;d++) rNsimd*=rsimd[d];
+  
+  int face_ovol=block*nblock;
+
+  //  assert(buf.size()==face_ovol*rNsimd);
+
+  /*This will work GPU ONLY unless rNsimd is put in the lexico index*/
+  //Let's make it work on GPU and then make a special accelerator_for that
+  //doesn't hide the SIMD direction and keeps explicit in the threadIdx
+  //for cross platform
+  //For CPU perhaps just run a loop over Nsimd
+  auto buf_p = & buf[0];
+  accelerator_for(ss, face_ovol/simd[dim],Nsimd,{
+
+    // scalar layout won't coalesce
+#ifdef GRID_SIMT
+      {
+	int blane=acceleratorSIMTlane(Nsimd); // buffer lane
+#else
+      for(int blane=0;blane<Nsimd;blane++) {
+#endif
+	int olane=blane%rNsimd;               // reduced lattice lane
+	int obit =blane/rNsimd;
+	
+	////////////////////////////////////////////
+	// osite
+	////////////////////////////////////////////
+	int ssp = ss*simd[dim]+obit;
+	int b    = ssp%block;
+	int n    = ssp/block;
+	int osite= b+n*stride + ox*block;
+
+	////////////////////////////////////////////
+	// isite -- map lane within buffer to lane within lattice
+	////////////////////////////////////////////
+	Coordinate icoor;
+	int lane;
+	Lexicographic::CoorFromIndex(icoor,olane,rsimd);
+	icoor[dim]=ix;
+	Lexicographic::IndexFromCoor(icoor,lane,simd);
+	
+	///////////////////////////////////////////
+	// Take out of lattice
+	///////////////////////////////////////////
+	//	sobj obj = extractLane(lane,lat_v[osite]);
+	//	insertLane(blane,buf_p[ss+offset],obj);
+	const int words=sizeof(vobj)/sizeof(vector_type);
+	vector_type * to    = (vector_type *)&buf_p[ss+offset];
+	vector_type * from  = (vector_type *)&lat_v[osite];
+	scalar_type stmp;
+	for(int w=0;w<words;w++){
+	  stmp = getlane(from[w], lane);
+	  putlane(to[w], stmp, blane);
+	}
+      }
+  });
+}
+
+
 class PaddedCell {
 public:
   GridCartesian * unpadded_grid;
@@ -63,15 +245,19 @@ public:
     dims=_grid->Nd();
     AllocateGrids();
     Coordinate local     =unpadded_grid->LocalDimensions();
+    Coordinate procs     =unpadded_grid->ProcessorGrid();
     for(int d=0;d<dims;d++){
-      assert(local[d]>=depth);
+      if ( procs[d] > 1 ) assert(local[d]>=depth);
     }
   }
   void DeleteGrids(void)
   {
+    Coordinate processors=unpadded_grid->_processors;
     for(int d=0;d<grids.size();d++){
+      if ( processors[d] > 1 ) { 
 	delete grids[d];
       }
+    }
     grids.resize(0);
   };
   void AllocateGrids(void)
@@ -81,27 +267,36 @@ public:
     Coordinate processors=unpadded_grid->_processors;
     Coordinate plocal    =unpadded_grid->LocalDimensions();
     Coordinate global(dims);
-
+    GridCartesian *old_grid = unpadded_grid;
     // expand up one dim at a time
     for(int d=0;d<dims;d++){
 
+      if ( processors[d] > 1 ) { 
 	plocal[d] += 2*depth; 
       
 	for(int d=0;d<dims;d++){
 	  global[d] = plocal[d]*processors[d];
 	}
 
-      grids.push_back(new GridCartesian(global,simd,processors));
+	old_grid = new GridCartesian(global,simd,processors);
+      }
+      grids.push_back(old_grid);
     }
   };
   template<class vobj>
   inline Lattice<vobj> Extract(const Lattice<vobj> &in) const
   {
+    Coordinate processors=unpadded_grid->_processors;
+
     Lattice<vobj> out(unpadded_grid);
 
     Coordinate local     =unpadded_grid->LocalDimensions();
-    Coordinate fll(dims,depth); // depends on the MPI spread
+    // depends on the MPI spread      
+    Coordinate fll(dims,depth);
     Coordinate tll(dims,0); // depends on the MPI spread
+    for(int d=0;d<dims;d++){
+      if( processors[d]==1 ) fll[d]=0;
+    }
     localCopyRegion(in,out,fll,tll,local);
     return out;
   }
@@ -116,10 +311,22 @@ public:
     }
     return tmp;
   }
+  template<class vobj>
+  inline Lattice<vobj> ExchangePeriodic(const Lattice<vobj> &in) const
+  {
+    GridBase *old_grid = in.Grid();
+    int dims = old_grid->Nd();
+    Lattice<vobj> tmp = in;
+    for(int d=0;d<dims;d++){
+      tmp = ExpandPeriodic(d,tmp); // rvalue && assignment
+    }
+    return tmp;
+  }
   // expand up one dim at a time
   template<class vobj>
   inline Lattice<vobj> Expand(int dim, const Lattice<vobj> &in, const CshiftImplBase<vobj> &cshift = CshiftImplDefault<vobj>()) const
   {
+    Coordinate processors=unpadded_grid->_processors;
     GridBase *old_grid = in.Grid();
     GridCartesian *new_grid = grids[dim];//These are new grids
     Lattice<vobj>  padded(new_grid);
@@ -129,10 +336,30 @@ public:
     if(dim==0) conformable(old_grid,unpadded_grid);
     else       conformable(old_grid,grids[dim-1]);
 
-    std::cout << " dim "<<dim<<" local "<<local << " padding to "<<plocal<<std::endl;
-
     double tins=0, tshift=0;
 
+    int islocal = 0 ;
+    if ( processors[dim] == 1 ) islocal = 1;
+
+    if ( islocal ) {
+
+      // replace with a copy and maybe grid swizzle
+      // return in;??
+      double t = usecond();
+      padded = in;
+      tins += usecond() - t;
+      
+    } else {
+
+      //////////////////////////////////////////////
+      // Replace sequence with
+      // ---------------------
+      // (i) Gather high face(s); start comms
+      // (ii) Gather low  face(s); start comms
+      // (iii) Copy middle bit with localCopyRegion
+      // (iv) Complete high face(s), insert slice(s)
+      // (iv) Complete low  face(s), insert slice(s)
+      //////////////////////////////////////////////
       // Middle bit
       double t = usecond();
       for(int x=0;x<local[dim];x++){
@@ -162,13 +389,183 @@ public:
       }
       tins += usecond() - t;
 
+    }
     std::cout << GridLogPerformance << "PaddedCell::Expand timings: cshift:" << tshift/1000 << "ms, insert-slice:" << tins/1000 << "ms" << std::endl;
     
     return padded;
   }
 
+  template<class vobj>
+  inline Lattice<vobj> ExpandPeriodic(int dim, const Lattice<vobj> &in) const
+  {
+    Coordinate processors=unpadded_grid->_processors;
+    GridBase *old_grid = in.Grid();
+    GridCartesian *new_grid = grids[dim];//These are new grids
+    Lattice<vobj>  padded(new_grid);
+    //    Lattice<vobj> shifted(old_grid);    
+    Coordinate local     =old_grid->LocalDimensions();
+    Coordinate plocal    =new_grid->LocalDimensions();
+    if(dim==0) conformable(old_grid,unpadded_grid);
+    else       conformable(old_grid,grids[dim-1]);
+
+    //    std::cout << " dim "<<dim<<" local "<<local << " padding to "<<plocal<<std::endl;
+    double tins=0, tshift=0;
+
+    int islocal = 0 ;
+    if ( processors[dim] == 1 ) islocal = 1;
+
+    if ( islocal ) {
+      padded=in; // slightly different interface could avoid a copy operation
+    } else {
+      Face_exchange(in,padded,dim,depth);
+      return padded;
+    }
+    return padded;
+  }
+  template<class vobj>
+  void Face_exchange(const Lattice<vobj> &from,
+		     Lattice<vobj> &to,
+		     int dimension,int depth) const
+  {
+    typedef typename vobj::vector_type vector_type;
+    typedef typename vobj::scalar_type scalar_type;
+    typedef typename vobj::scalar_object sobj;
+
+    RealD t_gather=0.0;
+    RealD t_scatter=0.0;
+    RealD t_comms=0.0;
+    RealD t_copy=0.0;
+    
+    //    std::cout << GridLogMessage << "dimension " <<dimension<<std::endl;
+    //    DumpSliceNorm(std::string("Face_exchange from"),from,dimension);
+    GridBase *grid=from.Grid();
+    GridBase *new_grid=to.Grid();
+
+    Coordinate lds = from.Grid()->_ldimensions;
+    Coordinate nlds=   to.Grid()->_ldimensions;
+    Coordinate simd= from.Grid()->_simd_layout;
+    int ld    = lds[dimension];
+    int nld   = to.Grid()->_ldimensions[dimension];
+    const int Nsimd = vobj::Nsimd();
+
+    assert(depth<=lds[dimension]); // A must be on neighbouring node
+    assert(depth>0);   // A caller bug if zero
+    assert(ld+2*depth==nld);
+    ////////////////////////////////////////////////////////////////////////////
+    // Face size and byte calculations
+    ////////////////////////////////////////////////////////////////////////////
+    int buffer_size = 1;
+    for(int d=0;d<lds.size();d++){
+      if ( d!= dimension) buffer_size=buffer_size*lds[d];
+    }
+    buffer_size = buffer_size  / Nsimd;
+    int rNsimd = Nsimd / simd[dimension];
+    assert( buffer_size == from.Grid()->_slice_nblock[dimension]*from.Grid()->_slice_block[dimension] / simd[dimension]);
+
+    static cshiftVector<vobj> send_buf; 
+    static cshiftVector<vobj> recv_buf;
+    send_buf.resize(buffer_size*2*depth);    
+    recv_buf.resize(buffer_size*2*depth);
+
+    std::vector<CommsRequest_t> fwd_req;   
+    std::vector<CommsRequest_t> bwd_req;   
+
+    int words = buffer_size;
+    int bytes = words * sizeof(vobj);
+
+    ////////////////////////////////////////////////////////////////////////////
+    // Communication coords
+    ////////////////////////////////////////////////////////////////////////////
+    int comm_proc = 1;
+    int xmit_to_rank;
+    int recv_from_rank;
+    grid->ShiftedRanks(dimension,comm_proc,xmit_to_rank,recv_from_rank);
+
+    ////////////////////////////////////////////////////////////////////////////
+    // Gather all surface terms up to depth "d"
+    ////////////////////////////////////////////////////////////////////////////
+    RealD t;
+    RealD t_tot=-usecond();
+    int plane=0;
+    for ( int d=0;d < depth ; d ++ ) {
+      int tag = d*1024 + dimension*2+0;
+
+      t=usecond();
+      GatherSlice(send_buf,from,d,dimension,plane*buffer_size); plane++;
+      t_gather+=usecond()-t;
+
+      t=usecond();
+      grid->SendToRecvFromBegin(fwd_req,
+				(void *)&send_buf[d*buffer_size], xmit_to_rank,
+				(void *)&recv_buf[d*buffer_size], recv_from_rank, bytes, tag);
+      t_comms+=usecond()-t;
+     }
+    for ( int d=0;d < depth ; d ++ ) {
+      int tag = d*1024 + dimension*2+1;
+
+      t=usecond();
+      GatherSlice(send_buf,from,ld-depth+d,dimension,plane*buffer_size); plane++;
+      t_gather+= usecond() - t;
+
+      t=usecond();
+      grid->SendToRecvFromBegin(bwd_req,
+				(void *)&send_buf[(d+depth)*buffer_size], recv_from_rank,
+				(void *)&recv_buf[(d+depth)*buffer_size], xmit_to_rank, bytes,tag);
+      t_comms+=usecond()-t;
+    }
+
+    ////////////////////////////////////////////////////////////////////////////
+    // Copy interior -- overlap this with comms
+    ////////////////////////////////////////////////////////////////////////////
+    int Nd = new_grid->Nd();
+    Coordinate LL(Nd,0);
+    Coordinate sz = grid->_ldimensions;
+    Coordinate toLL(Nd,0);
+    toLL[dimension]=depth;
+    t=usecond();
+    localCopyRegion(from,to,LL,toLL,sz);
+    t_copy= usecond() - t;
+    
+    ////////////////////////////////////////////////////////////////////////////
+    // Scatter all faces
+    ////////////////////////////////////////////////////////////////////////////
+    plane=0;
+
+    t=usecond();
+    grid->CommsComplete(fwd_req);
+    t_comms+= usecond() - t;
+
+    t=usecond();
+    for ( int d=0;d < depth ; d ++ ) {
+      ScatterSlice(recv_buf,to,nld-depth+d,dimension,plane*buffer_size); plane++;
+    }
+    t_scatter= usecond() - t;
+
+    t=usecond();
+    grid->CommsComplete(bwd_req);
+    t_comms+= usecond() - t;
+    
+    t=usecond();
+    for ( int d=0;d < depth ; d ++ ) {
+      ScatterSlice(recv_buf,to,d,dimension,plane*buffer_size); plane++;
+    }
+    t_scatter+= usecond() - t;
+    t_tot+=usecond();
+
+    std::cout << GridLogPerformance << "PaddedCell::Expand new timings: gather :" << t_gather/1000  << "ms"<<std::endl;
+    std::cout << GridLogPerformance << "PaddedCell::Expand new timings: scatter:" << t_scatter/1000   << "ms"<<std::endl;
+    std::cout << GridLogPerformance << "PaddedCell::Expand new timings: copy   :" << t_copy/1000      << "ms"<<std::endl;
+    std::cout << GridLogPerformance << "PaddedCell::Expand new timings: comms  :" << t_comms/1000     << "ms"<<std::endl;
+    std::cout << GridLogPerformance << "PaddedCell::Expand new timings: total  :" << t_tot/1000     << "ms"<<std::endl;
+    std::cout << GridLogPerformance << "PaddedCell::Expand new timings: gather :" << depth*4.0*bytes/t_gather << "MB/s"<<std::endl;
+    std::cout << GridLogPerformance << "PaddedCell::Expand new timings: scatter:" << depth*4.0*bytes/t_scatter<< "MB/s"<<std::endl;
+    std::cout << GridLogPerformance << "PaddedCell::Expand new timings: comms  :" << (RealD)4.0*bytes/t_comms   << "MB/s"<<std::endl;
+    std::cout << GridLogPerformance << "PaddedCell::Expand new timings: face bytes  :" << depth*bytes/1e6 << "MB"<<std::endl;
+  }
+  
 };
  
 
 NAMESPACE_END(Grid);
 
+

Grid/parallelIO/BinaryIO.h

@@ -165,7 +165,7 @@ class BinaryIO {
 	 * FIXME -- 128^3 x 256 x 16 will overflow.
 	 */
 	
-	int global_site;
+	int64_t global_site;
 
 	Lexicographic::CoorFromIndex(coor,local_site,local_vol);
 
@@ -175,8 +175,8 @@ class BinaryIO {
 
 	Lexicographic::IndexFromCoor(coor,global_site,global_vol);
 
-	uint32_t gsite29   = global_site%29;
+	uint64_t gsite29   = global_site%29;
-	uint32_t gsite31   = global_site%31;
+	uint64_t gsite31   = global_site%31;
 	
 	site_crc = crc32(0,(unsigned char *)site_buf,sizeof(fobj));
 	//	std::cout << "Site "<<local_site << " crc "<<std::hex<<site_crc<<std::dec<<std::endl;
@@ -545,7 +545,9 @@ class BinaryIO {
 				       const std::string &format,
 				       uint32_t &nersc_csum,
 				       uint32_t &scidac_csuma,
-				       uint32_t &scidac_csumb)
+				       uint32_t &scidac_csumb,
+				       int control=BINARYIO_LEXICOGRAPHIC
+				       )
   {
     typedef typename vobj::scalar_object sobj;
     typedef typename vobj::Realified::scalar_type word;    word w=0;
@@ -556,7 +558,7 @@ class BinaryIO {
     std::vector<sobj> scalardata(lsites); 
     std::vector<fobj>     iodata(lsites); // Munge, checksum, byte order in here
     
-    IOobject(w,grid,iodata,file,offset,format,BINARYIO_READ|BINARYIO_LEXICOGRAPHIC,
+    IOobject(w,grid,iodata,file,offset,format,BINARYIO_READ|control,
 	     nersc_csum,scidac_csuma,scidac_csumb);
 
     GridStopWatch timer; 
@@ -582,7 +584,8 @@ class BinaryIO {
 					  const std::string &format,
 					  uint32_t &nersc_csum,
 					  uint32_t &scidac_csuma,
-					  uint32_t &scidac_csumb)
+					  uint32_t &scidac_csumb,
+					  int control=BINARYIO_LEXICOGRAPHIC)
   {
     typedef typename vobj::scalar_object sobj;
     typedef typename vobj::Realified::scalar_type word;    word w=0;
@@ -607,7 +610,7 @@ class BinaryIO {
     while (attemptsLeft >= 0)
     {
       grid->Barrier();
-      IOobject(w,grid,iodata,file,offset,format,BINARYIO_WRITE|BINARYIO_LEXICOGRAPHIC,
+      IOobject(w,grid,iodata,file,offset,format,BINARYIO_WRITE|control,
 	             nersc_csum,scidac_csuma,scidac_csumb);
       if (checkWrite)
       {
@@ -617,7 +620,7 @@ class BinaryIO {
 
         std::cout << GridLogMessage << "writeLatticeObject: read back object" << std::endl;
         grid->Barrier();
-        IOobject(w,grid,ckiodata,file,ckoffset,format,BINARYIO_READ|BINARYIO_LEXICOGRAPHIC,
+        IOobject(w,grid,ckiodata,file,ckoffset,format,BINARYIO_READ|control,
 	               cknersc_csum,ckscidac_csuma,ckscidac_csumb);
         if ((cknersc_csum != nersc_csum) or (ckscidac_csuma != scidac_csuma) or (ckscidac_csumb != scidac_csumb))
         {

Grid/parallelIO/IldgIO.h

@@ -162,8 +162,14 @@ template<class vobj> void ScidacMetaData(Lattice<vobj> & field,
  {
    uint32_t scidac_checksuma = stoull(scidacChecksum_.suma,0,16);
    uint32_t scidac_checksumb = stoull(scidacChecksum_.sumb,0,16);
-   if ( scidac_csuma !=scidac_checksuma) return 0;
+   std::cout << GridLogMessage << " scidacChecksumVerify computed "<<scidac_csuma<<" expected "<<scidac_checksuma <<std::endl;
-   if ( scidac_csumb !=scidac_checksumb) return 0;
+   std::cout << GridLogMessage << " scidacChecksumVerify computed "<<scidac_csumb<<" expected "<<scidac_checksumb <<std::endl;
+   if ( scidac_csuma !=scidac_checksuma) {
+     return 0;
+   };
+   if ( scidac_csumb !=scidac_checksumb) {
+     return 0;
+   };
    return 1;
  }
 
@@ -206,7 +212,7 @@ class GridLimeReader : public BinaryIO {
   // Read a generic lattice field and verify checksum
   ////////////////////////////////////////////
   template<class vobj>
-  void readLimeLatticeBinaryObject(Lattice<vobj> &field,std::string record_name)
+  void readLimeLatticeBinaryObject(Lattice<vobj> &field,std::string record_name,int control=BINARYIO_LEXICOGRAPHIC)
   {
     typedef typename vobj::scalar_object sobj;
     scidacChecksum scidacChecksum_;
@@ -238,7 +244,7 @@ class GridLimeReader : public BinaryIO {
 	uint64_t offset= ftello(File);
 	//	std::cout << " ReadLatticeObject from offset "<<offset << std::endl;
 	BinarySimpleMunger<sobj,sobj> munge;
-	BinaryIO::readLatticeObject< vobj, sobj >(field, filename, munge, offset, format,nersc_csum,scidac_csuma,scidac_csumb);
+	BinaryIO::readLatticeObject< vobj, sobj >(field, filename, munge, offset, format,nersc_csum,scidac_csuma,scidac_csumb,control);
 	std::cout << GridLogMessage << "SciDAC checksum A " << std::hex << scidac_csuma << std::dec << std::endl;
 	std::cout << GridLogMessage << "SciDAC checksum B " << std::hex << scidac_csumb << std::dec << std::endl;
 	/////////////////////////////////////////////
@@ -408,7 +414,7 @@ class GridLimeWriter : public BinaryIO
   // in communicator used by the field.Grid()
   ////////////////////////////////////////////////////
   template<class vobj>
-  void writeLimeLatticeBinaryObject(Lattice<vobj> &field,std::string record_name)
+  void writeLimeLatticeBinaryObject(Lattice<vobj> &field,std::string record_name,int control=BINARYIO_LEXICOGRAPHIC)
   {
     ////////////////////////////////////////////////////////////////////
     // NB: FILE and iostream are jointly writing disjoint sequences in the
@@ -459,7 +465,7 @@ class GridLimeWriter : public BinaryIO
     ///////////////////////////////////////////
     std::string format = getFormatString<vobj>();
     BinarySimpleMunger<sobj,sobj> munge;
-    BinaryIO::writeLatticeObject<vobj,sobj>(field, filename, munge, offset1, format,nersc_csum,scidac_csuma,scidac_csumb);
+    BinaryIO::writeLatticeObject<vobj,sobj>(field, filename, munge, offset1, format,nersc_csum,scidac_csuma,scidac_csumb,control);
 
     ///////////////////////////////////////////
     // Wind forward and close the record
@@ -512,7 +518,8 @@ class ScidacWriter : public GridLimeWriter {
   ////////////////////////////////////////////////
   template <class vobj, class userRecord>
   void writeScidacFieldRecord(Lattice<vobj> &field,userRecord _userRecord,
-                              const unsigned int recordScientificPrec = 0) 
+                              const unsigned int recordScientificPrec = 0,
+			      int control=BINARYIO_LEXICOGRAPHIC)
   {
     GridBase * grid = field.Grid();
 
@@ -534,7 +541,7 @@ class ScidacWriter : public GridLimeWriter {
       writeLimeObject(0,0,_scidacRecord,_scidacRecord.SerialisableClassName(),std::string(SCIDAC_PRIVATE_RECORD_XML));
     }
     // Collective call
-    writeLimeLatticeBinaryObject(field,std::string(ILDG_BINARY_DATA));      // Closes message with checksum
+    writeLimeLatticeBinaryObject(field,std::string(ILDG_BINARY_DATA),control);      // Closes message with checksum
   }
 };
 
@@ -553,7 +560,8 @@ class ScidacReader : public GridLimeReader {
   // Write generic lattice field in scidac format
   ////////////////////////////////////////////////
   template <class vobj, class userRecord>
-  void readScidacFieldRecord(Lattice<vobj> &field,userRecord &_userRecord) 
+  void readScidacFieldRecord(Lattice<vobj> &field,userRecord &_userRecord,
+			     int control=BINARYIO_LEXICOGRAPHIC) 
   {
     typedef typename vobj::scalar_object sobj;
     GridBase * grid = field.Grid();
@@ -571,7 +579,7 @@ class ScidacReader : public GridLimeReader {
     readLimeObject(header ,std::string("FieldMetaData"),std::string(GRID_FORMAT)); // Open message 
     readLimeObject(_userRecord,_userRecord.SerialisableClassName(),std::string(SCIDAC_RECORD_XML));
     readLimeObject(_scidacRecord,_scidacRecord.SerialisableClassName(),std::string(SCIDAC_PRIVATE_RECORD_XML));
-    readLimeLatticeBinaryObject(field,std::string(ILDG_BINARY_DATA));
+    readLimeLatticeBinaryObject(field,std::string(ILDG_BINARY_DATA),control);
   }
   void skipPastBinaryRecord(void) {
     std::string rec_name(ILDG_BINARY_DATA);

Grid/qcd/smearing/HISQSmearing.h

@@ -170,7 +170,7 @@ public:
             typedef decltype(coalescedReadGeneralPermute(U_v[0](0),gStencil.GetEntry(0,0)->_permute,Nd)) U3matrix;
 
             int Nsites = U_v.size();
-            auto gStencil_v = gStencil.View(); 
+            auto gStencil_v = gStencil.View(AcceleratorRead); 
 
             accelerator_for(site,Nsites,Simd::Nsimd(),{ // ----------- 3-link constructs
                 stencilElement SE0, SE1, SE2, SE3, SE4, SE5;

Grid/qcd/utils/WilsonLoops.h

@@ -488,7 +488,7 @@ public:
     for(int mu=0;mu<Nd;mu++){
       { //view scope
 	autoView( gStaple_v , gStaple, AcceleratorWrite);
-	auto gStencil_v = gStencil.View();
+	auto gStencil_v = gStencil.View(AcceleratorRead);
 	
 	accelerator_for(ss, ggrid->oSites(), (size_t)ggrid->Nsimd(), {
 	    decltype(coalescedRead(Ug_dirs_v[0][0])) stencil_ss;
@@ -1200,7 +1200,7 @@ public:
 
       { //view scope
 	autoView( gStaple_v , gStaple, AcceleratorWrite);
-	auto gStencil_v = gStencil.View();
+	auto gStencil_v = gStencil.View(AcceleratorRead);
 
 	accelerator_for(ss, ggrid->oSites(), (size_t)ggrid->Nsimd(), {
 	    decltype(coalescedRead(Ug_dirs_v[0][0])) stencil_ss;

Grid/simd/Grid_vector_types.h

@@ -1130,6 +1130,14 @@ static_assert(sizeof(SIMD_Ftype) == sizeof(SIMD_Itype), "SIMD vector lengths inc
 #endif
 #endif
 
+// Fixme need coalesced read gpermute
+template<class vobj> void gpermute(vobj & inout,int perm){
+  vobj tmp=inout;
+  if (perm & 0x1 ) { permute(inout,tmp,0); tmp=inout;}
+  if (perm & 0x2 ) { permute(inout,tmp,1); tmp=inout;}
+  if (perm & 0x4 ) { permute(inout,tmp,2); tmp=inout;}
+  if (perm & 0x8 ) { permute(inout,tmp,3); tmp=inout;}
+}
 
 NAMESPACE_END(Grid);
 

Grid/stencil/GeneralLocalStencil.h

@@ -32,7 +32,12 @@ NAMESPACE_BEGIN(Grid);
 struct GeneralStencilEntry { 
   uint64_t _offset;            // 4 bytes 
   uint8_t _permute;            // 1 bytes // Horrible alignment properties
+  uint8_t _wrap;               // 1 bytes // Horrible alignment properties
 };
+struct GeneralStencilEntryReordered : public GeneralStencilEntry {
+  uint64_t _input;
+};
+
 // Could pack to 8 + 4 + 4 = 128 bit and use 
 
 class GeneralLocalStencilView {
@@ -46,7 +51,7 @@ class GeneralLocalStencilView {
   accelerator_inline GeneralStencilEntry * GetEntry(int point,int osite) const { 
     return & this->_entries_p[point+this->_npoints*osite]; 
   }
-
+  void ViewClose(void){};
 };
 ////////////////////////////////////////
 // The Stencil Class itself
@@ -61,7 +66,7 @@ protected:
 public: 
   GridBase *Grid(void) const { return _grid; }
 
-  View_type View(void) const {
+  View_type View(int mode) const {
     View_type accessor(*( (View_type *) this));
     return accessor;
   }
@@ -101,17 +106,23 @@ public:
 	  // Simpler version using icoor calculation
 	  ////////////////////////////////////////////////
 	  SE._permute =0;
+	  SE._wrap=0;
 	  for(int d=0;d<Coor.size();d++){
 
 	    int fd = grid->_fdimensions[d];
 	    int rd = grid->_rdimensions[d];
+	    int ld = grid->_ldimensions[d];
 	    int ly = grid->_simd_layout[d];
 
-	    assert((ly==1)||(ly==2));
+	    assert((ly==1)||(ly==2)||(ly==grid->Nsimd()));
 
 	    int shift = (shifts[ii][d]+fd)%fd;  // make it strictly positive 0.. L-1
 	    int x = Coor[d];                // x in [0... rd-1] as an oSite 
 
+	    if ( (x + shift)%fd != (x+shift)%ld ){
+	      SE._wrap = 1;
+	    }
+	    
 	    int permute_dim  = grid->PermuteDim(d);
 	    int permute_slice=0;
 	    if(permute_dim){    

Grid/threads/Accelerator.cc

@@ -122,7 +122,7 @@ hipStream_t computeStream;
 void acceleratorInit(void)
 {
   int nDevices = 1;
-  hipGetDeviceCount(&nDevices);
+  auto discard = hipGetDeviceCount(&nDevices);
   gpu_props = new hipDeviceProp_t[nDevices];
 
   char * localRankStr = NULL;
@@ -149,7 +149,7 @@ void acceleratorInit(void)
 #define GPU_PROP_FMT(canMapHostMemory,FMT)     printf("AcceleratorHipInit:   " #canMapHostMemory ": " FMT" \n",prop.canMapHostMemory);
 #define GPU_PROP(canMapHostMemory)             GPU_PROP_FMT(canMapHostMemory,"%d");
     
-    auto r=hipGetDeviceProperties(&gpu_props[i], i);
+    discard = hipGetDeviceProperties(&gpu_props[i], i);
     hipDeviceProp_t prop; 
     prop = gpu_props[i];
     totalDeviceMem = prop.totalGlobalMem;
@@ -186,13 +186,13 @@ void acceleratorInit(void)
   }
   int device = rank;
 #endif
-  hipSetDevice(device);
+  discard = hipSetDevice(device);
-  hipStreamCreate(&copyStream);
+  discard = hipStreamCreate(&copyStream);
-  hipStreamCreate(&computeStream);
+  discard = hipStreamCreate(&computeStream);
   const int len=64;
   char busid[len];
   if( rank == world_rank ) { 
-    hipDeviceGetPCIBusId(busid, len, device);
+    discard = hipDeviceGetPCIBusId(busid, len, device);
     printf("local rank %d device %d bus id: %s\n", rank, device, busid);
   }
   if ( world_rank == 0 )  printf("AcceleratorHipInit: ================================================\n");

Grid/threads/Accelerator.h

@@ -117,7 +117,7 @@ accelerator_inline int acceleratorSIMTlane(int Nsimd) {
 #endif
 } // CUDA specific
 
-inline void cuda_mem(void)
+inline void acceleratorMem(void)
 {
   size_t free_t,total_t,used_t;
   cudaMemGetInfo(&free_t,&total_t);
@@ -125,6 +125,11 @@ inline void cuda_mem(void)
   std::cout << " MemoryManager : GPU used "<<used_t<<" free "<<free_t<< " total "<<total_t<<std::endl;
 }
 
+inline void cuda_mem(void)
+{
+  acceleratorMem();
+}
+
 #define accelerator_for2dNB( iter1, num1, iter2, num2, nsimd, ... )	\
   {									\
     int nt=acceleratorThreads();					\
@@ -137,6 +142,18 @@ inline void cuda_mem(void)
     dim3 cu_blocks ((num1+nt-1)/nt,num2,1);				\
     LambdaApply<<<cu_blocks,cu_threads,0,computeStream>>>(num1,num2,nsimd,lambda);	\
   }
+#define prof_accelerator_for2dNB( iter1, num1, iter2, num2, nsimd, ... )	\
+  {									\
+    int nt=acceleratorThreads();					\
+    typedef uint64_t Iterator;						\
+    auto lambda = [=] accelerator					\
+      (Iterator iter1,Iterator iter2,Iterator lane) mutable {		\
+      __VA_ARGS__;							\
+    };									\
+    dim3 cu_threads(nsimd,acceleratorThreads(),1);			\
+    dim3 cu_blocks ((num1+nt-1)/nt,num2,1);				\
+    ProfileLambdaApply<<<cu_blocks,cu_threads,0,computeStream>>>(num1,num2,nsimd,lambda); \
+  }
 
 #define accelerator_for6dNB(iter1, num1,				\
                             iter2, num2,				\
@@ -157,6 +174,20 @@ inline void cuda_mem(void)
     Lambda6Apply<<<cu_blocks,cu_threads,0,computeStream>>>(num1,num2,num3,num4,num5,num6,lambda); \
   }
 
+
+#define accelerator_for2dNB( iter1, num1, iter2, num2, nsimd, ... )	\
+  {									\
+    int nt=acceleratorThreads();					\
+    typedef uint64_t Iterator;						\
+    auto lambda = [=] accelerator					\
+      (Iterator iter1,Iterator iter2,Iterator lane) mutable {		\
+      __VA_ARGS__;							\
+    };									\
+    dim3 cu_threads(nsimd,acceleratorThreads(),1);			\
+    dim3 cu_blocks ((num1+nt-1)/nt,num2,1);				\
+    LambdaApply<<<cu_blocks,cu_threads,0,computeStream>>>(num1,num2,nsimd,lambda);	\
+  }
+
 template<typename lambda>  __global__
 void LambdaApply(uint64_t num1, uint64_t num2, uint64_t num3, lambda Lambda)
 {
@@ -168,6 +199,17 @@ void LambdaApply(uint64_t num1, uint64_t num2, uint64_t num3, lambda Lambda)
     Lambda(x,y,z);
   }
 }
+template<typename lambda>  __global__
+void ProfileLambdaApply(uint64_t num1, uint64_t num2, uint64_t num3, lambda Lambda)
+{
+  // Weird permute is to make lane coalesce for large blocks
+  uint64_t x = threadIdx.y + blockDim.y*blockIdx.x;
+  uint64_t y = threadIdx.z + blockDim.z*blockIdx.y;
+  uint64_t z = threadIdx.x;
+  if ( (x < num1) && (y<num2) && (z<num3) ) {
+    Lambda(x,y,z);
+  }
+}
 
 template<typename lambda>  __global__
 void Lambda6Apply(uint64_t num1, uint64_t num2, uint64_t num3,
@@ -208,6 +250,7 @@ inline void *acceleratorAllocShared(size_t bytes)
   if( err != cudaSuccess ) {
     ptr = (void *) NULL;
     printf(" cudaMallocManaged failed for %d %s \n",bytes,cudaGetErrorString(err));
+    assert(0);
   }
   return ptr;
 };
@@ -234,6 +277,7 @@ inline void acceleratorCopyDeviceToDeviceAsynch(void *from,void *to,size_t bytes
 }
 inline void acceleratorCopySynchronise(void) { cudaStreamSynchronize(copyStream); };
 
+
 inline int  acceleratorIsCommunicable(void *ptr)
 {
   //  int uvm=0;
@@ -265,6 +309,11 @@ NAMESPACE_END(Grid);
 
 NAMESPACE_BEGIN(Grid);
 
+inline void acceleratorMem(void)
+{
+  std::cout <<" SYCL acceleratorMem not implemented"<<std::endl;
+}
+
 extern cl::sycl::queue *theGridAccelerator;
 extern cl::sycl::queue *theCopyAccelerator;
 
@@ -344,6 +393,15 @@ NAMESPACE_BEGIN(Grid);
 #define accelerator        __host__ __device__
 #define accelerator_inline __host__ __device__ inline
 
+inline void acceleratorMem(void)
+{
+  size_t free_t,total_t,used_t;
+  auto discard = hipMemGetInfo(&free_t,&total_t);
+  used_t=total_t-free_t;
+  std::cout << " MemoryManager : GPU used "<<used_t<<" free "<<free_t<< " total "<<total_t<<std::endl;
+}
+
+
 extern hipStream_t copyStream;
 extern hipStream_t computeStream;
 /*These routines define mapping from thread grid to loop & vector lane indexing */
@@ -404,7 +462,7 @@ void LambdaApply(uint64_t numx, uint64_t numy, uint64_t numz, lambda Lambda)
 
 #define accelerator_barrier(dummy)				\
   {								\
-    auto r=hipStreamSynchronize(computeStream);			\
+    auto tmp=hipStreamSynchronize(computeStream);		\
     auto err = hipGetLastError();				\
     if ( err != hipSuccess ) {					\
       printf("After hipDeviceSynchronize() : HIP error %s \n", hipGetErrorString( err )); \
@@ -420,7 +478,7 @@ inline void *acceleratorAllocShared(size_t bytes)
   auto err = hipMallocManaged((void **)&ptr,bytes);
   if( err != hipSuccess ) {
     ptr = (void *) NULL;
-    printf(" hipMallocManaged failed for %ld %s \n",bytes,hipGetErrorString(err));
+    fprintf(stderr," hipMallocManaged failed for %ld %s \n",bytes,hipGetErrorString(err)); fflush(stderr);
   }
   return ptr;
 };
@@ -432,26 +490,30 @@ inline void *acceleratorAllocDevice(size_t bytes)
   auto err = hipMalloc((void **)&ptr,bytes);
   if( err != hipSuccess ) {
     ptr = (void *) NULL;
-    printf(" hipMalloc failed for %ld %s \n",bytes,hipGetErrorString(err));
+    fprintf(stderr," hipMalloc failed for %ld %s \n",bytes,hipGetErrorString(err)); fflush(stderr);
   }
   return ptr;
 };
 
-inline void acceleratorFreeShared(void *ptr){ auto r=hipFree(ptr);};
+inline void acceleratorFreeShared(void *ptr){ auto discard=hipFree(ptr);};
-inline void acceleratorFreeDevice(void *ptr){ auto r=hipFree(ptr);};
+inline void acceleratorFreeDevice(void *ptr){ auto discard=hipFree(ptr);};
-inline void acceleratorCopyToDevice(void *from,void *to,size_t bytes)  { auto r=hipMemcpy(to,from,bytes, hipMemcpyHostToDevice);}
+inline void acceleratorCopyToDevice(void *from,void *to,size_t bytes)  { auto discard=hipMemcpy(to,from,bytes, hipMemcpyHostToDevice);}
-inline void acceleratorCopyFromDevice(void *from,void *to,size_t bytes){ auto r=hipMemcpy(to,from,bytes, hipMemcpyDeviceToHost);}
+inline void acceleratorCopyFromDevice(void *from,void *to,size_t bytes){ auto discard=hipMemcpy(to,from,bytes, hipMemcpyDeviceToHost);}
-inline void acceleratorCopyToDeviceAsync(void *from, void *to, size_t bytes, hipStream_t stream = copyStream) { auto r = hipMemcpyAsync(to,from,bytes, hipMemcpyHostToDevice, stream);}
-inline void acceleratorCopyFromDeviceAsync(void *from, void *to, size_t bytes, hipStream_t stream = copyStream) { auto r = hipMemcpyAsync(to,from,bytes, hipMemcpyDeviceToHost, stream);}
 //inline void acceleratorCopyDeviceToDeviceAsynch(void *from,void *to,size_t bytes)  { hipMemcpy(to,from,bytes, hipMemcpyDeviceToDevice);}
 //inline void acceleratorCopySynchronise(void) {  }
-inline void acceleratorMemSet(void *base,int value,size_t bytes) { auto r=hipMemset(base,value,bytes);}
+inline void acceleratorMemSet(void *base,int value,size_t bytes) { auto discard=hipMemset(base,value,bytes);}
 
 inline void acceleratorCopyDeviceToDeviceAsynch(void *from,void *to,size_t bytes) // Asynch
 {
-  auto r=hipMemcpyDtoDAsync(to,from,bytes, copyStream);
+  auto discard=hipMemcpyDtoDAsync(to,from,bytes, copyStream);
 }
-inline void acceleratorCopySynchronise(void) { auto r=hipStreamSynchronize(copyStream); };
+inline void acceleratorCopyToDeviceAsync(void *from, void *to, size_t bytes, hipStream_t stream = copyStream) {
+  auto r = hipMemcpyAsync(to,from,bytes, hipMemcpyHostToDevice, stream);
+}
+inline void acceleratorCopyFromDeviceAsync(void *from, void *to, size_t bytes, hipStream_t stream = copyStream) {
+  auto r = hipMemcpyAsync(to,from,bytes, hipMemcpyDeviceToHost, stream);
+}
+inline void acceleratorCopySynchronise(void) { auto discard=hipStreamSynchronize(copyStream); };
 
 #endif
 
@@ -461,6 +523,9 @@ inline void acceleratorCopySynchronise(void) { auto r=hipStreamSynchronize(copyS
 #if defined(GRID_SYCL) || defined(GRID_CUDA) || defined(GRID_HIP)
 // FIXME -- the non-blocking nature got broken March 30 2023 by PAB
 #define accelerator_forNB( iter1, num1, nsimd, ... ) accelerator_for2dNB( iter1, num1, iter2, 1, nsimd, {__VA_ARGS__} );  
+#define prof_accelerator_for( iter1, num1, nsimd, ... ) \
+  prof_accelerator_for2dNB( iter1, num1, iter2, 1, nsimd, {__VA_ARGS__} );\
+  accelerator_barrier(dummy);
 
 #define accelerator_for( iter, num, nsimd, ... )		\
   accelerator_forNB(iter, num, nsimd, { __VA_ARGS__ } );	\
@@ -474,6 +539,12 @@ inline void acceleratorCopySynchronise(void) { auto r=hipStreamSynchronize(copyS
 
 #endif
 
+inline void acceleratorCopyDeviceToDevice(void *from,void *to,size_t bytes)
+{
+  acceleratorCopyDeviceToDeviceAsynch(from,to,bytes);
+  acceleratorCopySynchronise();
+}
+
 //////////////////////////////////////////////
 // CPU Target - No accelerator just thread instead
 //////////////////////////////////////////////
@@ -483,6 +554,15 @@ inline void acceleratorCopySynchronise(void) { auto r=hipStreamSynchronize(copyS
 #undef GRID_SIMT
 
 
+inline void acceleratorMem(void)
+{
+  /*
+    struct rusage rusage;
+    getrusage( RUSAGE_SELF, &rusage );
+    return (size_t)rusage.ru_maxrss;
+  */
+  std::cout <<" system acceleratorMem not implemented"<<std::endl;
+}
 
 #define accelerator 
 #define accelerator_inline strong_inline
@@ -576,11 +656,18 @@ accelerator_inline void acceleratorFence(void)
   return;
 }
 
-inline void acceleratorCopyDeviceToDevice(void *from,void *to,size_t bytes)
+template<class T> void acceleratorPut(T& dev,T&host)
 {
-  acceleratorCopyDeviceToDeviceAsynch(from,to,bytes);
+  acceleratorCopyToDevice(&host,&dev,sizeof(T));
-  acceleratorCopySynchronise();
+}
+template<class T> T acceleratorGet(T& dev)
+{
+  T host;
+  acceleratorCopyFromDevice(&dev,&host,sizeof(T));
+  return host;
 }
 
 
+
+
 NAMESPACE_END(Grid);

Grid/util/Coordinate.h

@@ -94,6 +94,13 @@ static constexpr int MaxDims = GRID_MAX_LATTICE_DIMENSION;
 
 typedef AcceleratorVector<int,MaxDims> Coordinate;
 
+template<class T,int _ndim>
+inline bool operator==(const AcceleratorVector<T,_ndim> &v,const AcceleratorVector<T,_ndim> &w)
+{
+  if (v.size()!=w.size()) return false;
+  for(int i=0;i<v.size();i++) if ( v[i]!=w[i] ) return false;
+  return true;
+}
 template<class T,int _ndim>
 inline std::ostream & operator<<(std::ostream &os, const AcceleratorVector<T,_ndim> &v)
 {

Grid/util/Init.cc

@@ -292,6 +292,7 @@ void GridBanner(void)
     std::cout << "Build " << GRID_BUILD_STR(GRID_BUILD_REF) << std::endl;
 #endif
     std::cout << std::endl;
+    std::cout << std::setprecision(9);
 }
 
 void Grid_init(int *argc,char ***argv)
@@ -424,7 +425,7 @@ void Grid_init(int *argc,char ***argv)
   // Logging
   ////////////////////////////////////
   std::vector<std::string> logstreams;
-  std::string defaultLog("Error,Warning,Message,Performance");
+  std::string defaultLog("Error,Warning,Message");
   GridCmdOptionCSL(defaultLog,logstreams);
   GridLogConfigure(logstreams);
 
@@ -548,6 +549,10 @@ void Grid_init(int *argc,char ***argv)
 
 void Grid_finalize(void)
 {
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<"******* Grid Finalize                ******"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+
 #if defined (GRID_COMMS_MPI) || defined (GRID_COMMS_MPI3) || defined (GRID_COMMS_MPIT)
   MPI_Barrier(MPI_COMM_WORLD);
   MPI_Finalize();

Grid/util/Lexicographic.h

@@ -8,7 +8,7 @@ namespace Grid{
   public:
 
     template<class coor_t>
-    static accelerator_inline void CoorFromIndex (coor_t& coor,int index,const coor_t &dims){
+    static accelerator_inline void CoorFromIndex (coor_t& coor,int64_t index,const coor_t &dims){
       int nd= dims.size();
       coor.resize(nd);
       for(int d=0;d<nd;d++){
@@ -18,28 +18,45 @@ namespace Grid{
     }
 
     template<class coor_t>
-    static accelerator_inline void IndexFromCoor (const coor_t& coor,int &index,const coor_t &dims){
+    static accelerator_inline void IndexFromCoor (const coor_t& coor,int64_t &index,const coor_t &dims){
       int nd=dims.size();
       int stride=1;
       index=0;
       for(int d=0;d<nd;d++){
-	index = index+stride*coor[d];
+	index = index+(int64_t)stride*coor[d];
 	stride=stride*dims[d];
       }
     }
+    template<class coor_t>
+    static accelerator_inline void IndexFromCoor (const coor_t& coor,int &index,const coor_t &dims){
+      int64_t index64;
+      IndexFromCoor(coor,index64,dims);
+      assert(index64<2*1024*1024*1024LL);
+      index = (int) index64;
+    }
 
     template<class coor_t>
-    static inline void IndexFromCoorReversed (const coor_t& coor,int &index,const coor_t &dims){
+    static inline void IndexFromCoorReversed (const coor_t& coor,int64_t &index,const coor_t &dims){
       int nd=dims.size();
       int stride=1;
       index=0;
       for(int d=nd-1;d>=0;d--){
-	index = index+stride*coor[d];
+	index = index+(int64_t)stride*coor[d];
 	stride=stride*dims[d];
       }
     }
     template<class coor_t>
-    static inline void CoorFromIndexReversed (coor_t& coor,int index,const coor_t &dims){
+    static inline void IndexFromCoorReversed (const coor_t& coor,int &index,const coor_t &dims){
+      int64_t index64;
+      IndexFromCoorReversed(coor,index64,dims);
+      if ( index64>=2*1024*1024*1024LL ){
+	std::cout << " IndexFromCoorReversed " << coor<<" index " << index64<< " dims "<<dims<<std::endl;
+      }
+      assert(index64<2*1024*1024*1024LL);
+      index = (int) index64;
+    }
+    template<class coor_t>
+    static inline void CoorFromIndexReversed (coor_t& coor,int64_t index,const coor_t &dims){
       int nd= dims.size();
       coor.resize(nd);
       for(int d=nd-1;d>=0;d--){

HMC/site_autocorrelation.cc

@@ -0,0 +1,90 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: 
+
+Copyright (C) 2017
+
+Author: Peter Boyle
+
+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>
+#include <string>
+
+template <class T> void readFile(T& out, std::string const fname){
+  Grid::emptyUserRecord record;
+  Grid::ScidacReader RD;
+  RD.open(fname);
+  RD.readScidacFieldRecord(out,record);
+  RD.close();
+}
+
+
+int main(int argc, char **argv) {
+  using namespace Grid;
+  
+  Grid_init(&argc, &argv);
+  GridLogLayout();
+
+  auto latt_size   = GridDefaultLatt();
+  auto simd_layout = GridDefaultSimd(Nd, vComplex::Nsimd());
+  auto mpi_layout  = GridDefaultMpi();
+  GridCartesian               Grid(latt_size, simd_layout, mpi_layout);
+
+  LatticeComplexD plaq1(&Grid), plaq2(&Grid);
+
+  FieldMetaData header;
+
+  double vol = plaq1.Grid()->gSites();
+  
+  std::string file1(argv[1]);
+  std::cout << "Reading "<<file1<<std::endl;
+  readFile(plaq1,file1);
+  std::string file2(argv[2]);
+  std::cout << "Reading "<<file2<<std::endl;
+  readFile(plaq2,file2);
+  
+  auto p1bar = TensorRemove(sum(plaq1));
+  auto p2bar = TensorRemove(sum(plaq2));
+
+  p1bar = p1bar / vol;
+  p2bar = p2bar / vol;
+
+  std::cout<< GridLogMessage << "p1bar = "<<p1bar<<std::endl;
+  std::cout<< GridLogMessage << "p2bar = "<<p2bar<<std::endl;
+
+  auto corr_site = plaq1 * plaq2 - p1bar * p2bar;
+  auto corr_bar  = TensorRemove(sum(corr_site))/vol;
+
+  auto cov1_site = plaq1 * plaq1 - p1bar * p1bar;
+  auto cov1_bar  = TensorRemove(sum(cov1_site))/vol;
+
+  auto cov2_site = plaq2 * plaq2 - p2bar * p2bar;
+  auto cov2_bar  = TensorRemove(sum(cov2_site))/vol;
+
+  std::cout<< GridLogMessage << "cov_bar = "<<corr_bar<<std::endl;
+
+  std::cout<< GridLogMessage << "corr_bar = "<<corr_bar/sqrt(cov1_bar*cov2_bar)<<std::endl;
+  
+  Grid_finalize();
+}  // main
+
+

HMC/site_plaquette.cc

@@ -0,0 +1,79 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: 
+
+Copyright (C) 2017
+
+Author: Peter Boyle
+
+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>
+#include <string>
+
+NAMESPACE_BEGIN(Grid);
+template <class T> void writeFile(T& out, std::string const fname){
+  emptyUserRecord record;
+  ScidacWriter WR(out.Grid()->IsBoss());
+  WR.open(fname);
+  WR.writeScidacFieldRecord(out,record,0,Grid::BinaryIO::BINARYIO_LEXICOGRAPHIC);
+  WR.close();
+}
+NAMESPACE_END(Grid);
+int main(int argc, char **argv) {
+  using namespace Grid;
+  
+  Grid_init(&argc, &argv);
+  GridLogLayout();
+
+  auto latt_size   = GridDefaultLatt();
+  auto simd_layout = GridDefaultSimd(Nd, vComplex::Nsimd());
+  auto mpi_layout  = GridDefaultMpi();
+  GridCartesian               Grid(latt_size, simd_layout, mpi_layout);
+
+  LatticeGaugeField Umu(&Grid);
+  std::vector<LatticeColourMatrix> U(4,&Grid);
+  LatticeComplexD plaq(&Grid);
+
+  FieldMetaData header;
+
+  double vol = Umu.Grid()->gSites();
+  double faces = (1.0 * Nd * (Nd - 1)) / 2.0;
+  double Ncdiv = 1.0/Nc;
+  
+  std::string file1(argv[1]);
+  std::string file2(argv[2]);
+  std::cout << "Reading "<<file1<<std::endl;
+  NerscIO::readConfiguration(Umu,header,file1);
+  for(int mu=0;mu<Nd;mu++){
+    U[mu] = PeekIndex<LorentzIndex>(Umu,mu);
+  }
+  SU3WilsonLoops::sitePlaquette(plaq,U);
+
+  plaq = plaq *(Ncdiv/faces);
+  
+  std::cout << "Writing "<<file2<<std::endl;
+  writeFile(plaq,file2);
+  
+  Grid_finalize();
+}  // main
+
+

TODO

@@ -1,6 +1,50 @@
-- - Slice sum optimisation & A2A - atomic addition
+i)    Refine subspace with HDCG & recompute
+ii)   Block Lanczos in coarse space
+iii)  Batched block project in the operator computation
+
+-------
+
+i) Clean up CoarsenedMatrix, GeneralCoarsenedMatrix, GeneralCoarsenedMatrixMultiRHS
+
+ -- Ideally want a SINGLE implementation that does MultiRHS **AND** works with one RHS.
+
+ -- -- Getting there. One RHS is hard due to vectorisation & hardwired coarse5d layout
+ -- Compromise: Wrap it in a copy in/out for a slice.
+ 
+ -- Bad for Lanczos: need to do a BLOCK Lanczos instead. Longer term.
+
+ -- **** Make the test do ONLY the single RHS. ****
+ -- I/O for the matrix elements required.
+ -- Make the Adef2 build an eigenvector deflater and a block projector
+ -- 
+ 
+ -- Work with Regensburg on tests.
+ -- Plan interface preserving the coarsened matrix interface (??)
+
+-- Move functionality from GeneralCoarsenedMatrix INTO GeneralCoarsenedMatrixMultiRHS -- DONE
+   -- Don't immediately delete original
+   -- Instead make the new one self contained, then delete.
+   -- New DWF inverter test.
+
+  // void PopulateAdag(void)
+  void CoarsenOperator(LinearOperatorBase<Lattice<Fobj> > &linop, Aggregation<Fobj,CComplex,nbasis> & Subspace) -- DONE
+  ExchangeCoarseLinks();
+
+iii) Aurora -- christoph's problem -- DONE
+     Aurora -- Carleton's problem staggered.
+
+iv) Dennis merge and test Aurora -- DONE (save test)
+
+v) Merge Ed Bennet's request --DONE 
+
+vi) Repro CG  -- get down to the level of single node testing via split grid test 
+
+
+=========================
+
+===============
+- - Slice sum optimisation & A2A - atomic addition -- Dennis
 - - Also faster non-atomic reduction
-- - Remaining PRs
 - - DDHMC
   - - MixedPrec is the action eval, high precision
   - - MixedPrecCleanup is the force eval, low precision
@@ -17,7 +61,6 @@ DDHMC
 -- Multishift Mixed Precision - DONE
 -- Pole dependent residual  - DONE
 
-
 =======
 -- comms threads issue??
 -- Part done: Staggered kernel performance on GPU

scripts/prequisites.sh

@@ -0,0 +1,44 @@
+#!/bin/bash
+
+if [ $1 = "install" ]
+then
+    dir=`pwd`
+    cd $HOME
+    git clone -c feature.manyFiles=true https://github.com/spack/spack.git
+    source $HOME/spack/share/spack/setup-env.sh
+
+    spack install autoconf
+    spack install automake
+    spack install c-lime cppflags=-fPIE
+    spack install fftw
+    spack install llvm
+    spack install gmp
+    spack install mpfr
+    spack install cuda@11.8
+    spack install openmpi
+    spack install openssl
+    spack install hdf5
+else
+    source $HOME/spack/share/spack/setup-env.sh
+fi
+
+spack load autoconf
+spack load automake
+spack load c-lime
+spack load fftw
+spack load llvm
+spack load gmp
+spack load mpfr
+spack load cuda@11.8
+spack load openmpi
+spack load openssl
+spack load hdf5
+
+export FFTW=`spack find --paths fftw    | grep ^fftw   | awk '{print $2}' `
+export HDF5=`spack find --paths hdf5    | grep ^hdf5   | awk '{print $2}' `
+export CLIME=`spack find --paths c-lime | grep ^c-lime | awk '{print $2}' `
+export MPFR=`spack find --paths mpfr    | grep ^mpfr  | awk '{print $2}' `
+export GMP=`spack find --paths gmp      | grep ^gmp | awk '{print $2}' `
+export NVIDIA=$CUDA_HOME
+export NVIDIALIB=$NVIDIA/targets/x86_64-linux/lib/
+export LD_LIBRARY_PATH=$NVIDIALIB:$FFTW/lib/:$MPFR/lib:$LD_LIBRARY_PATH

systems/Frontier/benchmarks/bench2.slurm

@@ -0,0 +1,43 @@
+#!/bin/bash -l
+#SBATCH --job-name=bench
+##SBATCH --partition=small-g
+#SBATCH --nodes=2
+#SBATCH --ntasks-per-node=8
+#SBATCH --cpus-per-task=7
+#SBATCH --gpus-per-node=8
+#SBATCH --time=00:10:00
+#SBATCH --account=phy157_dwf
+#SBATCH --gpu-bind=none
+#SBATCH --exclusive
+#SBATCH --mem=0
+
+cat << EOF > select_gpu
+#!/bin/bash
+export GPU_MAP=(0 1 2 3 7 6 5 4)
+export NUMA_MAP=(3 3 1 1 2 2 0 0)
+export GPU=\${GPU_MAP[\$SLURM_LOCALID]}
+export NUMA=\${NUMA_MAP[\$SLURM_LOCALID]}
+export HIP_VISIBLE_DEVICES=\$GPU
+unset ROCR_VISIBLE_DEVICES
+echo RANK \$SLURM_LOCALID using GPU \$GPU    
+exec numactl -m \$NUMA -N \$NUMA \$*
+EOF
+
+chmod +x ./select_gpu
+
+root=$HOME/Frontier/Grid/systems/Frontier/
+source ${root}/sourceme.sh
+
+export OMP_NUM_THREADS=7
+export MPICH_GPU_SUPPORT_ENABLED=1
+export MPICH_SMP_SINGLE_COPY_MODE=XPMEM
+
+for vol in 32.32.32.64
+do
+srun ./select_gpu ./Benchmark_dwf_fp32 --mpi 2.2.2.2 --accelerator-threads 8 --comms-overlap --shm 2048 --shm-mpi 0 --grid $vol  > log.shm0.ov.$vol
+srun ./select_gpu ./Benchmark_dwf_fp32 --mpi 2.2.2.2 --accelerator-threads 8 --comms-overlap --shm 2048 --shm-mpi 1 --grid $vol  > log.shm1.ov.$vol
+
+srun ./select_gpu ./Benchmark_dwf_fp32 --mpi 2.2.2.2 --accelerator-threads 8 --comms-sequential --shm 2048 --shm-mpi 0 --grid $vol  > log.shm0.seq.$vol
+srun ./select_gpu ./Benchmark_dwf_fp32 --mpi 2.2.2.2 --accelerator-threads 8 --comms-sequential --shm 2048 --shm-mpi 1 --grid $vol > log.shm1.seq.$vol
+done
+

systems/Frontier/config-command

@@ -15,7 +15,7 @@ CLIME=`spack find --paths c-lime@2-3-9 | grep c-lime| cut -c 15-`
 --with-mpfr=/opt/cray/pe/gcc/mpfr/3.1.4/ \
 --disable-fermion-reps \
 CXX=hipcc MPICXX=mpicxx \
-CXXFLAGS="-fPIC -I{$ROCM_PATH}/include/ -I${MPICH_DIR}/include -L/lib64 -fgpu-sanitize" \
+CXXFLAGS="-fPIC -I{$ROCM_PATH}/include/ -I${MPICH_DIR}/include -L/lib64 " \
  LDFLAGS="-L/lib64 -L${MPICH_DIR}/lib -lmpi -L${CRAY_MPICH_ROOTDIR}/gtl/lib -lmpi_gtl_hsa -lamdhip64 -lhipblas -lrocblas"
 
 

systems/Frontier/mpiwrapper.sh

@@ -0,0 +1,13 @@
+#!/bin/bash
+
+lrank=$SLURM_LOCALID
+lgpu=(0 1 2 3 7 6 5 4)
+
+export ROCR_VISIBLE_DEVICES=${lgpu[$lrank]}
+
+echo "`hostname` - $lrank device=$ROCR_VISIBLE_DEVICES "
+
+$*
+
+
+

systems/Frontier/sourceme.sh

@@ -1,6 +1,5 @@
 . /autofs/nccs-svm1_home1/paboyle/Crusher/Grid/spack/share/spack/setup-env.sh
 spack load c-lime
-#export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/sw/crusher/spack-envs/base/opt/cray-sles15-zen3/gcc-11.2.0/gperftools-2.9.1-72ubwtuc5wcz2meqltbfdb76epufgzo2/lib
 module load emacs 
 module load PrgEnv-gnu
 module load rocm

systems/Frontier/wrap.sh

@@ -0,0 +1,9 @@
+#!/bin/sh
+
+export HIP_VISIBLE_DEVICES=$ROCR_VISIBLE_DEVICES
+unset ROCR_VISIBLE_DEVICES
+
+#rank=$SLURM_PROCID
+#rocprof -d rocprof.$rank -o rocprof.$rank/results.rank$SLURM_PROCID.csv --sys-trace $@
+
+$@

systems/mac-arm/config-command-mpi

@@ -1,3 +1,2 @@
 CXXFLAGS=-I/opt/local/include LDFLAGS=-L/opt/local/lib/ CXX=c++-13 MPICXX=mpicxx ../../configure --enable-simd=GEN --enable-comms=mpi-auto --enable-unified=yes --prefix $HOME/QCD/GridInstall --with-lime=/Users/peterboyle/QCD/SciDAC/install/ --with-openssl=$BREW --disable-fermion-reps --disable-gparity --disable-debug 
 
-

tests/debug/Test_general_coarse.cc

@@ -0,0 +1,319 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./tests/Test_padded_cell.cc
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <paboyle@ph.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>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidual.h>
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.h>
+#include <Grid/algorithms/iterative/BiCGSTAB.h>
+
+using namespace std;
+using namespace Grid;
+
+gridblasHandle_t GridBLAS::gridblasHandle;
+int            GridBLAS::gridblasInit;
+
+///////////////////////
+// Tells little dirac op to use MdagM as the .Op()
+///////////////////////
+template<class Field>
+class HermOpAdaptor : public LinearOperatorBase<Field>
+{
+  LinearOperatorBase<Field> & wrapped;
+public:
+  HermOpAdaptor(LinearOperatorBase<Field> &wrapme) : wrapped(wrapme)  {};
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    wrapped.HermOp(in,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    wrapped.HermOp(in,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){    assert(0);  }
+  void HermOp(const Field &in, Field &out){
+    wrapped.HermOp(in,out);
+  }
+};
+
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  const int Ls=4;
+
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(),
+								   GridDefaultSimd(Nd,vComplex::Nsimd()),
+								   GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Construct a coarsened grid
+  Coordinate clatt = GridDefaultLatt();
+  for(int d=0;d<clatt.size();d++){
+    clatt[d] = clatt[d]/4;
+  }
+
+  GridCartesian *Coarse4d =  SpaceTimeGrid::makeFourDimGrid(clatt,
+							    GridDefaultSimd(Nd,vComplex::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); random(RNG5,src);
+  LatticeFermion result(FGrid); result=Zero();
+  LatticeFermion    ref(FGrid); ref=Zero();
+  LatticeFermion    tmp(FGrid);
+  LatticeFermion    err(FGrid);
+  LatticeGaugeField Umu(UGrid);
+  SU<Nc>::HotConfiguration(RNG4,Umu);
+  //  Umu=Zero();
+  
+  RealD mass=0.1;
+  RealD M5=1.8;
+
+  DomainWallFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5);
+
+  const int nbasis = 62;
+  const int cb = 0 ;
+  LatticeFermion prom(FGrid);
+
+  std::vector<LatticeFermion> subspace(nbasis,FGrid);
+
+  std::cout<<GridLogMessage<<"Calling Aggregation class" <<std::endl;
+
+  ///////////////////////////////////////////////////////////
+  // Squared operator is in HermOp
+  ///////////////////////////////////////////////////////////
+  MdagMLinearOperator<DomainWallFermionD,LatticeFermion> HermDefOp(Ddwf);
+
+  ///////////////////////////////////////////////////
+  // Random aggregation space
+  ///////////////////////////////////////////////////
+  std::cout<<GridLogMessage << "Building random aggregation class"<< std::endl;
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis> Subspace;
+  Subspace Aggregates(Coarse5d,FGrid,cb);
+  Aggregates.CreateSubspaceRandom(RNG5);
+
+  ///////////////////////////////////////////////////
+  // Build little dirac op
+  ///////////////////////////////////////////////////
+  std::cout<<GridLogMessage << "Building little Dirac operator"<< std::endl;
+
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector CoarseVector;
+
+  NextToNextToNextToNearestStencilGeometry5D geom(Coarse5d);
+  LittleDiracOperator LittleDiracOp(geom,FGrid,Coarse5d);
+  LittleDiracOperator LittleDiracOpCol(geom,FGrid,Coarse5d);
+
+  HermOpAdaptor<LatticeFermionD> HOA(HermDefOp);
+
+  LittleDiracOp.CoarsenOperator(HOA,Aggregates);
+  
+  ///////////////////////////////////////////////////
+  // Test the operator
+  ///////////////////////////////////////////////////
+  CoarseVector c_src (Coarse5d);
+  CoarseVector c_res (Coarse5d);
+  CoarseVector c_res_dag(Coarse5d);
+  CoarseVector c_proj(Coarse5d);
+
+  subspace=Aggregates.subspace;
+
+  //  random(CRNG,c_src);
+  c_src = 1.0;
+
+  blockPromote(c_src,err,subspace);
+
+  prom=Zero();
+  for(int b=0;b<nbasis;b++){
+    prom=prom+subspace[b];
+  }
+  err=err-prom; 
+  std::cout<<GridLogMessage<<"Promoted back from subspace: err "<<norm2(err)<<std::endl;
+  std::cout<<GridLogMessage<<"c_src "<<norm2(c_src)<<std::endl;
+  std::cout<<GridLogMessage<<"prom  "<<norm2(prom)<<std::endl;
+
+  HermDefOp.HermOp(prom,tmp);
+
+  blockProject(c_proj,tmp,subspace);
+  std::cout<<GridLogMessage<<" Called Big Dirac Op "<<norm2(tmp)<<std::endl;
+
+  std::cout<<GridLogMessage<<" Calling little Dirac Op "<<std::endl;
+  LittleDiracOp.M(c_src,c_res);
+  LittleDiracOp.Mdag(c_src,c_res_dag);
+
+  std::cout<<GridLogMessage<<"Little dop : "<<norm2(c_res)<<std::endl;
+  std::cout<<GridLogMessage<<"Little dop dag : "<<norm2(c_res_dag)<<std::endl;
+  std::cout<<GridLogMessage<<"Big dop in subspace : "<<norm2(c_proj)<<std::endl;
+
+  c_proj = c_proj - c_res;
+  std::cout<<GridLogMessage<<" ldop error: "<<norm2(c_proj)<<std::endl;
+
+  c_res_dag = c_res_dag - c_res;
+  std::cout<<GridLogMessage<<"Little dopDag - dop: "<<norm2(c_res_dag)<<std::endl;
+
+  std::cout<<GridLogMessage << "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<<GridLogMessage<<"Made randoms "<<norm2(phi)<<" " << norm2(chi)<<std::endl;
+
+  LittleDiracOp.M(phi,Aphi);
+
+  LittleDiracOp.Mdag(chi,Achi);
+
+  std::cout<<GridLogMessage<<"Aphi "<<norm2(Aphi)<<" A chi" << norm2(Achi)<<std::endl;
+
+  ComplexD pAc = innerProduct(chi,Aphi);
+  ComplexD cAp = innerProduct(phi,Achi);
+  ComplexD cAc = innerProduct(chi,Achi);
+  ComplexD pAp = innerProduct(phi,Aphi);
+
+  std::cout<<GridLogMessage<< "pAc "<<pAc<<" cAp "<< cAp<< " diff "<<pAc-adj(cAp)<<std::endl;
+  std::cout<<GridLogMessage<< "pAp "<<pAp<<" cAc "<< cAc<<"Should be real"<< std::endl;
+
+  std::cout<<GridLogMessage<<"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<<GridLogMessage<<"**Diff "<<norm2(linerr)<<std::endl;
+
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  //////////////////////////////////////////////////////////////////////////////////////
+  //  Create a higher dim coarse grid
+  //////////////////////////////////////////////////////////////////////////////////////
+
+  const int nrhs=vComplex::Nsimd()*3;
+
+  Coordinate mpi=GridDefaultMpi();
+  Coordinate rhMpi ({1,1,mpi[0],mpi[1],mpi[2],mpi[3]});
+  Coordinate rhLatt({nrhs,1,clatt[0],clatt[1],clatt[2],clatt[3]});
+  Coordinate rhSimd({vComplex::Nsimd(),1, 1,1,1,1});
+
+  GridCartesian *CoarseMrhs = new GridCartesian(rhLatt,rhSimd,rhMpi); 
+
+  
+  MultiGeneralCoarsenedMatrix mrhs(LittleDiracOp,CoarseMrhs);
+  typedef decltype(mrhs) MultiGeneralCoarsenedMatrix_t;
+  
+  //////////////////////////////////////////
+  // Test against single RHS
+  //////////////////////////////////////////
+  {
+    GridParallelRNG          rh_CRNG(CoarseMrhs);rh_CRNG.SeedFixedIntegers(cseeds);
+    CoarseVector rh_phi(CoarseMrhs);
+    CoarseVector rh_res(CoarseMrhs);
+    random(rh_CRNG,rh_phi);
+
+    std::cout << "Warmup"<<std::endl;
+    mrhs.M(rh_phi,rh_res);
+    const int ncall=5;
+    RealD t0=-usecond();
+    for(int i=0;i<ncall;i++){
+      std::cout << "Call "<<i<<"/"<<ncall<<std::endl;
+      mrhs.M(rh_phi,rh_res);
+    }
+    t0+=usecond();
+    RealD t1=0;
+    for(int r=0;r<nrhs;r++){
+      std::cout << " compare to single RHS "<<r<<"/"<<nrhs<<std::endl;
+      ExtractSlice(phi,rh_phi,r,0);
+      ExtractSlice(chi,rh_res,r,0);
+      LittleDiracOp.M(phi,Aphi);
+      t1-=usecond();
+      for(int i=0;i<ncall;i++){
+	std::cout << "Call "<<i<<"/"<<ncall<<std::endl;
+	LittleDiracOp.M(phi,Aphi);
+      }
+      t1+=usecond();
+      Coordinate site({0,0,0,0,0});
+      auto  bad = peekSite(chi,site);
+      auto good = peekSite(Aphi,site);
+      std::cout << " mrhs [" <<r <<"] "<< norm2(chi)<<std::endl;
+      std::cout << " srhs [" <<r <<"] "<< norm2(Aphi)<<std::endl;
+      chi=chi-Aphi;
+      RealD diff =norm2(chi);
+      std::cout << r << " diff " << diff<<std::endl;
+      assert(diff < 1.0e-10);
+    }
+    std::cout << nrhs<< " mrhs " << t0/ncall/nrhs <<" us"<<std::endl;
+    std::cout << nrhs<< " srhs " << t1/ncall/nrhs <<" us"<<std::endl;
+  }
+
+  //////////////////////////////////////////
+  // Test against single RHS
+  //////////////////////////////////////////
+  {
+    typedef HermitianLinearOperator<MultiGeneralCoarsenedMatrix_t,CoarseVector> HermMatrix;
+    HermMatrix MrhsCoarseOp     (mrhs);
+
+    GridParallelRNG          rh_CRNG(CoarseMrhs);rh_CRNG.SeedFixedIntegers(cseeds);
+    ConjugateGradient<CoarseVector>  mrhsCG(1.0e-8,2000,true);
+    CoarseVector rh_res(CoarseMrhs);
+    CoarseVector rh_src(CoarseMrhs);
+    random(rh_CRNG,rh_src);
+    rh_res= Zero();
+    mrhsCG(MrhsCoarseOp,rh_src,rh_res);
+  }
+  
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+
+  Grid_finalize();
+  return 0;
+}

tests/debug/Test_general_coarse_hdcg.cc

@@ -0,0 +1,426 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./tests/Test_general_coarse_hdcg.cc
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    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>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+//#include <Grid/algorithms/GeneralCoarsenedMatrix.h>
+#include <Grid/algorithms/iterative/AdefGeneric.h>
+
+using namespace std;
+using namespace Grid;
+
+template<class Coarsened>
+void SaveOperator(Coarsened &Operator,std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  ScidacWriter WR(Operator.Grid()->IsBoss());
+  assert(Operator._A.size()==Operator.geom.npoint);
+  WR.open(file);
+  for(int p=0;p<Operator._A.size();p++){
+    auto tmp = Operator.Cell.Extract(Operator._A[p]);
+    WR.writeScidacFieldRecord(tmp,record);
+  }
+  WR.close();
+#endif
+}
+template<class Coarsened>
+void LoadOperator(Coarsened &Operator,std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  Grid::ScidacReader RD ;
+  RD.open(file);
+  assert(Operator._A.size()==Operator.geom.npoint);
+  for(int p=0;p<Operator.geom.npoint;p++){
+    conformable(Operator._A[p].Grid(),Operator.CoarseGrid());
+    RD.readScidacFieldRecord(Operator._A[p],record);
+  }    
+  RD.close();
+  Operator.ExchangeCoarseLinks();
+#endif
+}
+template<class aggregation>
+void SaveBasis(aggregation &Agg,std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  ScidacWriter WR(Agg.FineGrid->IsBoss());
+  WR.open(file);
+  for(int b=0;b<Agg.subspace.size();b++){
+    WR.writeScidacFieldRecord(Agg.subspace[b],record);
+  }
+  WR.close();
+#endif
+}
+template<class aggregation>
+void LoadBasis(aggregation &Agg, std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  ScidacReader RD ;
+  RD.open(file);
+  for(int b=0;b<Agg.subspace.size();b++){
+    RD.readScidacFieldRecord(Agg.subspace[b],record);
+  }    
+  RD.close();
+#endif
+}
+
+
+template<class Field> class TestSolver : public LinearFunction<Field> {
+public:
+  TestSolver() {};
+  void operator() (const Field &in, Field &out){    out = Zero();  }     
+};
+
+
+RealD InverseApproximation(RealD x){
+  return 1.0/x;
+}
+
+// Want Op in CoarsenOp to call MatPcDagMatPc
+template<class Field>
+class HermOpAdaptor : public LinearOperatorBase<Field>
+{
+  LinearOperatorBase<Field> & wrapped;
+public:
+  HermOpAdaptor(LinearOperatorBase<Field> &wrapme) : wrapped(wrapme)  {};
+  void Op     (const Field &in, Field &out)   { wrapped.HermOp(in,out);  }
+  void HermOp(const Field &in, Field &out)    { wrapped.HermOp(in,out); }
+  void AdjOp     (const Field &in, Field &out){ wrapped.HermOp(in,out);  }
+  void OpDiag (const Field &in, Field &out)                  {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out)  {    assert(0);  };
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){    assert(0);  }
+};
+template<class Field,class Matrix> class ChebyshevSmoother : public LinearFunction<Field>
+{
+public:
+  using LinearFunction<Field>::operator();
+  typedef LinearOperatorBase<Field> FineOperator;
+  FineOperator   & _SmootherOperator;
+  Chebyshev<Field> Cheby;
+  ChebyshevSmoother(RealD _lo,RealD _hi,int _ord, FineOperator &SmootherOperator) :
+    _SmootherOperator(SmootherOperator),
+    Cheby(_lo,_hi,_ord,InverseApproximation)
+  {
+    std::cout << GridLogMessage<<" Chebyshev smoother order "<<_ord<<" ["<<_lo<<","<<_hi<<"]"<<std::endl;
+  };
+  void operator() (const Field &in, Field &out) 
+  {
+    Field tmp(in.Grid());
+    tmp = in;
+    Cheby(_SmootherOperator,tmp,out);
+  }
+};
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  const int Ls=24;
+  const int nbasis = 40;
+  const int cb = 0 ;
+  RealD mass=0.00078;
+  RealD M5=1.8;
+  RealD b=1.5;
+  RealD c=0.5;
+
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(),
+								   GridDefaultSimd(Nd,vComplex::Nsimd()),
+								   GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Construct a coarsened grid with 4^4 cell
+  Coordinate clatt = GridDefaultLatt();
+  for(int d=0;d<clatt.size();d++){
+    clatt[d] = clatt[d]/4;
+  }
+  GridCartesian *Coarse4d =  SpaceTimeGrid::makeFourDimGrid(clatt,
+							    GridDefaultSimd(Nd,vComplex::Nsimd()),
+							    GridDefaultMpi());;
+  GridCartesian *Coarse5d =  SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+
+  ///////////////////////// RNGs /////////////////////////////////
+  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);
+
+  ///////////////////////// Configuration /////////////////////////////////
+  LatticeGaugeField Umu(UGrid);
+
+  FieldMetaData header;
+  std::string file("ckpoint_lat.4000");
+  NerscIO::readConfiguration(Umu,header,file);
+
+  //////////////////////// Fermion action //////////////////////////////////
+  MobiusFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5,b,c);
+
+  SchurDiagMooeeOperator<MobiusFermionD, LatticeFermion> HermOpEO(Ddwf);
+
+  typedef HermOpAdaptor<LatticeFermionD> HermFineMatrix;
+  HermFineMatrix FineHermOp(HermOpEO);
+  
+  LatticeFermion result(FrbGrid); result=Zero();
+
+  LatticeFermion    src(FrbGrid); random(RNG5,src);
+
+  // Run power method on FineHermOp
+  PowerMethod<LatticeFermion>       PM;   PM(HermOpEO,src);
+
+ 
+  ////////////////////////////////////////////////////////////
+  ///////////// Coarse basis and Little Dirac Operator ///////
+  ////////////////////////////////////////////////////////////
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector CoarseVector;
+
+  NextToNextToNextToNearestStencilGeometry5D geom(Coarse5d);
+  NearestStencilGeometry5D geom_nn(Coarse5d);
+  
+  // Warning: This routine calls PVdagM.Op, not PVdagM.HermOp
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis> Subspace;
+  Subspace Aggregates(Coarse5d,FrbGrid,cb);
+
+  ////////////////////////////////////////////////////////////
+  // Need to check about red-black grid coarsening
+  ////////////////////////////////////////////////////////////
+  LittleDiracOperator LittleDiracOp(geom,FrbGrid,Coarse5d);
+
+  bool load=false;
+  if ( load ) {
+    LoadBasis(Aggregates,"/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/Subspace.scidac");
+    LoadOperator(LittleDiracOp,"/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/LittleDiracOp.scidac");
+  } else {
+    Aggregates.CreateSubspaceChebyshev(RNG5,HermOpEO,nbasis,
+				       95.0,0.1,
+				       //				     400,200,200 -- 48 iters
+				       //				     600,200,200 -- 38 iters, 162s
+				       //				     600,200,100 -- 38 iters, 169s
+				       //				     600,200,50  -- 88 iters. 370s 
+				       800,
+				       200,
+				       100,
+				       0.0);
+    LittleDiracOp.CoarsenOperator(FineHermOp,Aggregates);
+    SaveBasis(Aggregates,"/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/Subspace.scidac");
+    SaveOperator(LittleDiracOp,"/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/LittleDiracOp.scidac");
+  }
+  
+  // Try projecting to one hop only
+  LittleDiracOperator LittleDiracOpProj(geom_nn,FrbGrid,Coarse5d);
+  LittleDiracOpProj.ProjectNearestNeighbour(0.01,LittleDiracOp); // smaller shift 0.02? n
+
+  typedef HermitianLinearOperator<LittleDiracOperator,CoarseVector> HermMatrix;
+  HermMatrix CoarseOp     (LittleDiracOp);
+  HermMatrix CoarseOpProj (LittleDiracOpProj);
+  
+  //////////////////////////////////////////
+  // Build a coarse lanczos
+  //////////////////////////////////////////
+  Chebyshev<CoarseVector>      IRLCheby(0.2,40.0,71);  // 1 iter
+  FunctionHermOp<CoarseVector> IRLOpCheby(IRLCheby,CoarseOp);
+  PlainHermOp<CoarseVector>    IRLOp    (CoarseOp);
+  int Nk=48;
+  int Nm=64;
+  int Nstop=Nk;
+  ImplicitlyRestartedLanczos<CoarseVector> IRL(IRLOpCheby,IRLOp,Nstop,Nk,Nm,1.0e-5,20);
+
+  int Nconv;
+  std::vector<RealD>            eval(Nm);
+  std::vector<CoarseVector>     evec(Nm,Coarse5d);
+  CoarseVector c_src(Coarse5d);
+  //c_src=1.0;
+  random(CRNG,c_src);
+
+  CoarseVector c_res(Coarse5d); 
+  CoarseVector c_ref(Coarse5d); 
+
+  PowerMethod<CoarseVector>       cPM;   cPM(CoarseOp,c_src);
+
+  IRL.calc(eval,evec,c_src,Nconv);
+  DeflatedGuesser<CoarseVector> DeflCoarseGuesser(evec,eval);
+
+  //////////////////////////////////////////
+  // Build a coarse space solver
+  //////////////////////////////////////////
+  int maxit=20000;
+  ConjugateGradient<CoarseVector>  CG(1.0e-8,maxit,false);
+  ConjugateGradient<LatticeFermionD>  CGfine(1.0e-8,10000,false);
+  ZeroGuesser<CoarseVector> CoarseZeroGuesser;
+
+  //  HPDSolver<CoarseVector> HPDSolve(CoarseOp,CG,CoarseZeroGuesser);
+  HPDSolver<CoarseVector> HPDSolve(CoarseOp,CG,DeflCoarseGuesser);
+  c_res=Zero();
+  HPDSolve(c_src,c_res); c_ref = c_res;
+  std::cout << GridLogMessage<<"src norm "<<norm2(c_src)<<std::endl;
+  std::cout << GridLogMessage<<"ref norm "<<norm2(c_ref)<<std::endl;
+  //////////////////////////////////////////////////////////////////////////
+  // Deflated (with real op EV's) solve for the projected coarse op
+  // Work towards ADEF1 in the coarse space
+  //////////////////////////////////////////////////////////////////////////
+  HPDSolver<CoarseVector> HPDSolveProj(CoarseOpProj,CG,DeflCoarseGuesser);
+  c_res=Zero();
+  HPDSolveProj(c_src,c_res);
+  std::cout << GridLogMessage<<"src norm "<<norm2(c_src)<<std::endl;
+  std::cout << GridLogMessage<<"res norm "<<norm2(c_res)<<std::endl;
+  c_res = c_res - c_ref;
+  std::cout << "Projected solver error "<<norm2(c_res)<<std::endl;
+
+  //////////////////////////////////////////////////////////////////////
+  // Coarse ADEF1 with deflation space
+  //////////////////////////////////////////////////////////////////////
+  ChebyshevSmoother<CoarseVector,HermMatrix >
+    CoarseSmoother(1.0,37.,8,CoarseOpProj);  // just go to sloppy 0.1 convergence
+    //  CoarseSmoother(0.1,37.,8,CoarseOpProj);  //
+  //  CoarseSmoother(0.5,37.,6,CoarseOpProj);  //  8 iter 0.36s
+  //    CoarseSmoother(0.5,37.,12,CoarseOpProj);  // 8 iter, 0.55s
+  //    CoarseSmoother(0.5,37.,8,CoarseOpProj);// 7-9 iter
+  //  CoarseSmoother(1.0,37.,8,CoarseOpProj); // 0.4 - 0.5s solve to 0.04, 7-9 iter
+  //  ChebyshevSmoother<CoarseVector,HermMatrix > CoarseSmoother(0.5,36.,10,CoarseOpProj);  // 311
+
+  ////////////////////////////////////////////////////////
+  // CG, Cheby mode spacing 200,200
+  // Unprojected Coarse CG solve to 1e-8 : 190 iters, 4.9s
+  // Unprojected Coarse CG solve to 4e-2 :  33 iters, 0.8s
+  // Projected Coarse CG solve to 1e-8 : 100 iters, 0.36s
+  ////////////////////////////////////////////////////////
+  // CoarseSmoother(1.0,48.,8,CoarseOpProj); 48 evecs 
+  ////////////////////////////////////////////////////////
+  // ADEF1 Coarse solve to 1e-8 : 44 iters, 2.34s  2.1x gain
+  // ADEF1 Coarse solve to 4e-2 : 7 iters, 0.4s
+  // HDCG 38 iters 162s
+  //
+  // CoarseSmoother(1.0,40.,8,CoarseOpProj); 48 evecs 
+  // ADEF1 Coarse solve to 1e-8 : 37 iters, 2.0s  2.1x gain
+  // ADEF1 Coarse solve to 4e-2 : 6 iters, 0.36s
+  // HDCG 38 iters 169s
+
+  TwoLevelADEF1defl<CoarseVector>
+    cADEF1(1.0e-8, 500,
+	   CoarseOp,
+	   CoarseSmoother,
+	   evec,eval);
+
+  c_res=Zero();
+  cADEF1(c_src,c_res);
+  std::cout << GridLogMessage<<"src norm "<<norm2(c_src)<<std::endl;
+  std::cout << GridLogMessage<<"cADEF1 res norm "<<norm2(c_res)<<std::endl;
+  c_res = c_res - c_ref;
+  std::cout << "cADEF1 solver error "<<norm2(c_res)<<std::endl;
+  
+  //  cADEF1.Tolerance = 4.0e-2;
+  //  cADEF1.Tolerance = 1.0e-1;
+  cADEF1.Tolerance = 5.0e-2;
+  c_res=Zero();
+  cADEF1(c_src,c_res);
+  std::cout << GridLogMessage<<"src norm "<<norm2(c_src)<<std::endl;
+  std::cout << GridLogMessage<<"cADEF1 res norm "<<norm2(c_res)<<std::endl;
+  c_res = c_res - c_ref;
+  std::cout << "cADEF1 solver error "<<norm2(c_res)<<std::endl;
+  
+  //////////////////////////////////////////
+  // Build a smoother
+  //////////////////////////////////////////
+  //  ChebyshevSmoother<LatticeFermionD,HermFineMatrix > Smoother(10.0,100.0,10,FineHermOp); //499
+  //  ChebyshevSmoother<LatticeFermionD,HermFineMatrix > Smoother(3.0,100.0,10,FineHermOp);  //383
+  //  ChebyshevSmoother<LatticeFermionD,HermFineMatrix > Smoother(1.0,100.0,10,FineHermOp);  //328
+  //  std::vector<RealD> los({0.5,1.0,3.0}); // 147/142/146 nbasis 1
+  //  std::vector<RealD> los({1.0,2.0}); // Nbasis 24: 88,86 iterations
+  //  std::vector<RealD> los({2.0,4.0}); // Nbasis 32 == 52, iters
+  //  std::vector<RealD> los({2.0,4.0}); // Nbasis 40 == 36,36 iters
+
+  //
+  // Turns approx 2700 iterations into 340 fine multiplies with Nbasis 40
+  // Need to measure cost of coarse space.
+  //
+  // -- i) Reduce coarse residual   -- 0.04
+  // -- ii) Lanczos on coarse space -- done
+  // -- iii) Possible 1 hop project and/or preconditioning it - easy - PrecCG it and
+  //         use a limited stencil. Reread BFM code to check on evecs / deflation strategy with prec
+  //
+  std::vector<RealD> los({3.0}); // Nbasis 40 == 36,36 iters
+
+  //  std::vector<int> ords({7,8,10}); // Nbasis 40 == 40,38,36 iters (320,342,396 mults)
+  std::vector<int> ords({7}); // Nbasis 40 == 40 iters (320 mults)  
+
+  for(int l=0;l<los.size();l++){
+
+    RealD lo = los[l];
+
+    for(int o=0;o<ords.size();o++){
+
+      ConjugateGradient<CoarseVector>  CGsloppy(4.0e-2,maxit,false);
+      HPDSolver<CoarseVector> HPDSolveSloppy(CoarseOp,CGsloppy,DeflCoarseGuesser);
+      
+      //    ChebyshevSmoother<LatticeFermionD,HermFineMatrix > Smoother(lo,92,10,FineHermOp); // 36 best case
+      ChebyshevSmoother<LatticeFermionD,HermFineMatrix > Smoother(lo,92,ords[o],FineHermOp);  // 311
+
+      //////////////////////////////////////////
+      // Build a HDCG solver
+      //////////////////////////////////////////
+      TwoLevelADEF2<LatticeFermion,CoarseVector,Subspace>
+	HDCG(1.0e-8, 100,
+	     FineHermOp,
+	     Smoother,
+	     HPDSolveSloppy,
+	     HPDSolve,
+	     Aggregates);
+
+      TwoLevelADEF2<LatticeFermion,CoarseVector,Subspace>
+	HDCGdefl(1.0e-8, 100,
+		 FineHermOp,
+		 Smoother,
+		 cADEF1,
+		 HPDSolve,
+		 Aggregates);
+      
+      result=Zero();
+      HDCGdefl(src,result);
+
+      result=Zero();
+      HDCG(src,result);
+
+      
+    }
+  }
+
+  // Standard CG
+  result=Zero();
+  CGfine(HermOpEO, src, result);
+  
+  Grid_finalize();
+  return 0;
+}

tests/debug/Test_general_coarse_hdcg_phys.cc

@@ -0,0 +1,444 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./tests/Test_general_coarse_hdcg.cc
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    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>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+//#include <Grid/algorithms/GeneralCoarsenedMatrix.h>
+#include <Grid/algorithms/iterative/AdefGeneric.h>
+
+using namespace std;
+using namespace Grid;
+
+template<class Coarsened>
+void SaveOperator(Coarsened &Operator,std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  ScidacWriter WR(Operator.Grid()->IsBoss());
+  assert(Operator._A.size()==Operator.geom.npoint);
+  WR.open(file);
+  for(int p=0;p<Operator._A.size();p++){
+    auto tmp = Operator.Cell.Extract(Operator._A[p]);
+    WR.writeScidacFieldRecord(tmp,record,0,0);
+    //    WR.writeScidacFieldRecord(tmp,record,0,BINARYIO_LEXICOGRAPHIC);
+  }
+  WR.close();
+#endif
+}
+template<class Coarsened>
+void LoadOperator(Coarsened &Operator,std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  Grid::ScidacReader RD ;
+  RD.open(file);
+  assert(Operator._A.size()==Operator.geom.npoint);
+  for(int p=0;p<Operator.geom.npoint;p++){
+    conformable(Operator._A[p].Grid(),Operator.CoarseGrid());
+    //    RD.readScidacFieldRecord(Operator._A[p],record,BINARYIO_LEXICOGRAPHIC);
+    RD.readScidacFieldRecord(Operator._A[p],record,0);
+  }    
+  RD.close();
+  Operator.ExchangeCoarseLinks();
+#endif
+}
+template<class Coarsened>
+void ReLoadOperator(Coarsened &Operator,std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  Grid::ScidacReader RD ;
+  RD.open(file);
+  assert(Operator._A.size()==Operator.geom.npoint);
+  for(int p=0;p<Operator.geom.npoint;p++){
+    auto tmp=Operator.Cell.Extract(Operator._A[p]);
+    RD.readScidacFieldRecord(tmp,record,0);
+    Operator._A[p] = Operator.Cell.ExchangePeriodic(tmp);
+  }    
+  RD.close();
+#endif
+}
+template<class aggregation>
+void SaveBasis(aggregation &Agg,std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  ScidacWriter WR(Agg.FineGrid->IsBoss());
+  WR.open(file);
+  for(int b=0;b<Agg.subspace.size();b++){
+    //WR.writeScidacFieldRecord(Agg.subspace[b],record,0,BINARYIO_LEXICOGRAPHIC);
+    WR.writeScidacFieldRecord(Agg.subspace[b],record,0,0);
+  }
+  WR.close();
+#endif
+}
+template<class aggregation>
+void LoadBasis(aggregation &Agg, std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  ScidacReader RD ;
+  RD.open(file);
+  for(int b=0;b<Agg.subspace.size();b++){
+    //    RD.readScidacFieldRecord(Agg.subspace[b],record,BINARYIO_LEXICOGRAPHIC);
+    RD.readScidacFieldRecord(Agg.subspace[b],record,0);
+  }    
+  RD.close();
+#endif
+}
+
+RealD InverseApproximation(RealD x){
+  return 1.0/x;
+}
+
+// Want Op in CoarsenOp to call MatPcDagMatPc
+template<class Field>
+class HermOpAdaptor : public LinearOperatorBase<Field>
+{
+  LinearOperatorBase<Field> & wrapped;
+public:
+  HermOpAdaptor(LinearOperatorBase<Field> &wrapme) : wrapped(wrapme)  {};
+  void Op     (const Field &in, Field &out)   { wrapped.HermOp(in,out);  }
+  void HermOp(const Field &in, Field &out)    { wrapped.HermOp(in,out); }
+  void AdjOp     (const Field &in, Field &out){ wrapped.HermOp(in,out);  }
+  void OpDiag (const Field &in, Field &out)                  {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out)  {    assert(0);  };
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){    assert(0);  }
+};
+/*
+template<class Field> class ChebyshevSmoother : public LinearFunction<Field>
+{
+public:
+  using LinearFunction<Field>::operator();
+  typedef LinearOperatorBase<Field> FineOperator;
+  FineOperator   & _SmootherOperator;
+  Chebyshev<Field> Cheby;
+  ChebyshevSmoother(RealD _lo,RealD _hi,int _ord, FineOperator &SmootherOperator) :
+    _SmootherOperator(SmootherOperator),
+    Cheby(_lo,_hi,_ord,InverseApproximation)
+  {
+    std::cout << GridLogMessage<<" Chebyshev smoother order "<<_ord<<" ["<<_lo<<","<<_hi<<"]"<<std::endl;
+  };
+  void operator() (const Field &in, Field &out) 
+  {
+    Field tmp(in.Grid());
+    tmp = in;
+    Cheby(_SmootherOperator,tmp,out);
+  }
+};
+*/
+template<class Field> class CGSmoother : public LinearFunction<Field>
+{
+public:
+  using LinearFunction<Field>::operator();
+  typedef LinearOperatorBase<Field> FineOperator;
+  FineOperator   & _SmootherOperator;
+  int iters;
+  CGSmoother(int _iters, FineOperator &SmootherOperator) :
+    _SmootherOperator(SmootherOperator),
+    iters(_iters)
+  {
+    std::cout << GridLogMessage<<" Mirs smoother order "<<iters<<std::endl;
+  };
+  void operator() (const Field &in, Field &out) 
+  {
+    ConjugateGradient<Field>  CG(0.0,iters,false); // non-converge is just fine in a smoother
+    CG(_SmootherOperator,in,out);
+  }
+};
+
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  const int Ls=24;
+  const int nbasis = 62;
+  const int cb = 0 ;
+  RealD mass=0.00078;
+  RealD M5=1.8;
+  RealD b=1.5;
+  RealD c=0.5;
+
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(),
+								   GridDefaultSimd(Nd,vComplex::Nsimd()),
+								   GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Construct a coarsened grid with 4^4 cell
+  Coordinate Block({4,4,6,4});
+  Coordinate clatt = GridDefaultLatt();
+  for(int d=0;d<clatt.size();d++){
+    clatt[d] = clatt[d]/Block[d];
+  }
+
+  GridCartesian *Coarse4d =  SpaceTimeGrid::makeFourDimGrid(clatt,
+							    GridDefaultSimd(Nd,vComplex::Nsimd()),
+							    GridDefaultMpi());;
+  GridCartesian *Coarse5d =  SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+
+  ///////////////////////// RNGs /////////////////////////////////
+  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);
+
+  ///////////////////////// Configuration /////////////////////////////////
+  LatticeGaugeField Umu(UGrid);
+
+  FieldMetaData header;
+  std::string file("ckpoint_lat.1000");
+  NerscIO::readConfiguration(Umu,header,file);
+
+  //////////////////////// Fermion action //////////////////////////////////
+  MobiusFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5,b,c);
+
+  SchurDiagMooeeOperator<MobiusFermionD, LatticeFermion> HermOpEO(Ddwf);
+
+  typedef HermOpAdaptor<LatticeFermionD> HermFineMatrix;
+  HermFineMatrix FineHermOp(HermOpEO);
+
+  LatticeFermion result(FrbGrid); result=Zero();
+
+  LatticeFermion    src(FrbGrid); random(RNG5,src);
+
+  // Run power method on FineHermOp
+  PowerMethod<LatticeFermion>       PM;   PM(HermOpEO,src);
+ 
+  ////////////////////////////////////////////////////////////
+  ///////////// Coarse basis and Little Dirac Operator ///////
+  ////////////////////////////////////////////////////////////
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector CoarseVector;
+
+  NextToNextToNextToNearestStencilGeometry5D geom(Coarse5d);
+  NearestStencilGeometry5D geom_nn(Coarse5d);
+  
+  // Warning: This routine calls PVdagM.Op, not PVdagM.HermOp
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis> Subspace;
+  Subspace Aggregates(Coarse5d,FrbGrid,cb);
+
+  ////////////////////////////////////////////////////////////
+  // Need to check about red-black grid coarsening
+  ////////////////////////////////////////////////////////////
+  LittleDiracOperator LittleDiracOp(geom,FrbGrid,Coarse5d);
+
+  std::string subspace_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/Subspace.phys48.rat.scidac.62");
+  std::string refine_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/Refine.phys48.rat.scidac.62");
+  std::string ldop_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/LittleDiracOp.phys48.rat.scidac.62");
+  bool load_agg=true;
+  bool load_refine=true;
+  bool load_mat=true;
+  if ( load_agg ) {
+    LoadBasis(Aggregates,subspace_file);
+  } else {
+
+    // NBASIS=40
+    // Best so far: ord 2000 [0.01,95], 500,500  -- 466 iters
+    // slurm-398626.out:Grid : Message : 141.295253 s : 500 filt [1] <n|MdagM|n> 0.000103622063
+
+
+    //Grid : Message : 33.870465 s :  Chebyshev subspace pass-1 : ord 2000 [0.001,95]
+    //Grid : Message : 33.870485 s :  Chebyshev subspace pass-2 : nbasis40 min 1000 step 1000 lo0
+    //slurm-1482200.out : filt ~ 0.004 -- not as low mode projecting -- took 626 iters
+
+    // To try: 2000 [0.1,95]  ,2000,500,500 -- slurm-1482213.out 586 iterations
+
+    // To try: 2000 [0.01,95] ,2000,500,500 -- 469 (think I bumped 92 to 95) (??)
+    // To try: 2000 [0.025,95],2000,500,500
+    // To try: 2000 [0.005,95],2000,500,500
+
+    // NBASIS=44 -- HDCG paper was 64 vectors; AMD compiler craps out at 48
+    // To try: 2000 [0.01,95] ,2000,500,500 -- 419 lowest slurm-1482355.out
+    // To try: 2000 [0.025,95] ,2000,500,500 -- 487 
+    // To try: 2000 [0.005,95] ,2000,500,500
+    /*
+      Smoother [3,92] order 16
+slurm-1482355.out:Grid : Message : 35.239686 s :  Chebyshev subspace pass-1 : ord 2000 [0.01,95]
+slurm-1482355.out:Grid : Message : 35.239714 s :  Chebyshev subspace pass-2 : nbasis44 min 500 step 500 lo0
+slurm-1482355.out:Grid : Message : 5561.305552 s : HDCG: Pcg converged in 419 iterations and 2616.202598 s
+
+slurm-1482367.out:Grid : Message : 43.157235 s :  Chebyshev subspace pass-1 : ord 2000 [0.025,95]
+slurm-1482367.out:Grid : Message : 43.157257 s :  Chebyshev subspace pass-2 : nbasis44 min 500 step 500 lo0
+slurm-1482367.out:Grid : Message : 6169.469330 s : HDCG: Pcg converged in 487 iterations and 3131.185821 s
+    */
+		 /*
+		   Aggregates.CreateSubspaceChebyshev(RNG5,HermOpEO,nbasis,
+				       95.0,0.0075,
+				       2500,
+				       500,
+				       500,
+				       0.0);
+		 */
+
+		 /*
+		   Aggregates.CreateSubspaceChebyshevPowerLaw(RNG5,HermOpEO,nbasis,
+							      95.0,
+							      2000);
+		 */
+
+    Aggregates.CreateSubspaceMultishift(RNG5,HermOpEO,
+					0.0003,1.0e-5,2000); // Lo, tol, maxit
+  /*
+    Aggregates.CreateSubspaceChebyshev(RNG5,HermOpEO,nbasis,
+				       95.0,0.05,
+				       2000,
+				       500,
+				       500,
+				       0.0);
+ */
+    /*
+      Aggregates.CreateSubspaceChebyshev(RNG5,HermOpEO,nbasis,
+				       95.0,0.01,
+				       2000,
+				       500,
+				       500,
+				       0.0);
+    */
+    //    Aggregates.CreateSubspaceChebyshev(RNG5,HermOpEO,nbasis,95.,0.01,1500); -- running slurm-1484934.out nbasis 56
+
+    //    Aggregates.CreateSubspaceChebyshev(RNG5,HermOpEO,nbasis,95.,0.01,1500); <== last run
+    SaveBasis(Aggregates,subspace_file);
+  }
+
+  int refine=1;
+  if(refine){
+    if ( load_refine ) {
+      LoadBasis(Aggregates,refine_file);
+    } else {
+      // HDCG used Pcg to refine
+      Aggregates.RefineSubspace(HermOpEO,0.001,1.0e-3,3000);
+      SaveBasis(Aggregates,refine_file);
+    }
+  }
+
+  Aggregates.Orthogonalise();
+  if ( load_mat ) {
+    LoadOperator(LittleDiracOp,ldop_file);
+  } else {
+    LittleDiracOp.CoarsenOperator(FineHermOp,Aggregates);
+    SaveOperator(LittleDiracOp,ldop_file);
+  }
+
+  // I/O test:
+  CoarseVector c_src(Coarse5d);   random(CRNG,c_src);
+  CoarseVector c_res(Coarse5d); 
+  CoarseVector c_ref(Coarse5d);
+
+  //////////////////////////////////////////
+  // Build a coarse lanczos
+  //////////////////////////////////////////
+  typedef HermitianLinearOperator<LittleDiracOperator,CoarseVector> HermMatrix;
+  HermMatrix CoarseOp     (LittleDiracOp);
+  
+  int Nk=192;
+  int Nm=256;
+  int Nstop=Nk;
+  
+  Chebyshev<CoarseVector>      IRLCheby(0.005,40.0,201);
+  //  Chebyshev<CoarseVector>      IRLCheby(0.010,45.0,201);  // 1 iter
+  FunctionHermOp<CoarseVector> IRLOpCheby(IRLCheby,CoarseOp);
+  PlainHermOp<CoarseVector>    IRLOp    (CoarseOp);
+  
+  ImplicitlyRestartedLanczos<CoarseVector> IRL(IRLOpCheby,IRLOp,Nstop,Nk,Nm,1e-5,10);
+
+  int Nconv;
+  std::vector<RealD>            eval(Nm);
+  std::vector<CoarseVector>     evec(Nm,Coarse5d);
+
+  PowerMethod<CoarseVector>       cPM;   cPM(CoarseOp,c_src);
+
+  IRL.calc(eval,evec,c_src,Nconv);
+
+  //////////////////////////////////////////
+  // Deflated guesser
+  //////////////////////////////////////////
+  DeflatedGuesser<CoarseVector> DeflCoarseGuesser(evec,eval);
+
+  int maxit=30000;
+  ConjugateGradient<CoarseVector>  CG(1.0e-10,maxit,false);
+  ConjugateGradient<LatticeFermionD>  CGfine(1.0e-8,30000,false);
+
+  //////////////////////////////////////////
+  // HDCG
+  //////////////////////////////////////////
+  
+  std::vector<RealD> los({2.0,2.5}); // Nbasis 40 == 36,36 iters
+  std::vector<int> ords({9}); // Nbasis 40 == 40 iters (320 mults)  
+
+  for(int l=0;l<los.size();l++){
+
+    RealD lo = los[l];
+
+    for(int o=0;o<ords.size();o++){
+
+      //////////////////////////////////////////
+      // Sloppy coarse solve
+      //////////////////////////////////////////
+      
+      ConjugateGradient<CoarseVector>  CGsloppy(4.0e-2,maxit,false);
+      HPDSolver<CoarseVector> HPDSolveSloppy(CoarseOp,CGsloppy,DeflCoarseGuesser);
+      HPDSolver<CoarseVector> HPDSolve(CoarseOp,CG,DeflCoarseGuesser);
+
+      //////////////////////////////////////////
+      // IRS shifted smoother based on CG
+      //////////////////////////////////////////
+      RealD MirsShift = lo;
+      ShiftedHermOpLinearOperator<LatticeFermionD> ShiftedFineHermOp(HermOpEO,MirsShift);
+      CGSmoother<LatticeFermionD> CGsmooth(ords[o],ShiftedFineHermOp) ;
+  
+      //////////////////////////////////////////
+      // Build a HDCG solver
+      //////////////////////////////////////////
+      TwoLevelADEF2<LatticeFermion,CoarseVector,Subspace>
+	HDCG(1.0e-8, 700,
+	     FineHermOp,
+	     CGsmooth,
+	     HPDSolveSloppy,
+	     HPDSolve,
+	     Aggregates);
+
+      result=Zero();
+      HDCG(src,result);
+      
+    }
+  }
+
+  // Standard CG
+  result=Zero();
+  CGfine(HermOpEO, src, result);
+  
+  Grid_finalize();
+  return 0;
+}

tests/debug/Test_general_coarse_hdcg_phys48.cc

@@ -0,0 +1,513 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./tests/Test_general_coarse_hdcg.cc
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    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>
+#include <Grid/algorithms/iterative/ImplicitlyRestartedBlockLanczos.h>
+#include <Grid/algorithms/iterative/ImplicitlyRestartedBlockLanczosCoarse.h>
+#include <Grid/algorithms/iterative/AdefMrhs.h>
+
+using namespace std;
+using namespace Grid;
+
+class HDCGwrapper {
+
+};
+
+/*
+template<class Coarsened>
+void SaveOperator(Coarsened &Operator,std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  ScidacWriter WR(Operator.Grid()->IsBoss());
+  assert(Operator._A.size()==Operator.geom.npoint);
+  WR.open(file);
+  for(int p=0;p<Operator._A.size();p++){
+    auto tmp = Operator.Cell.Extract(Operator._A[p]);
+    WR.writeScidacFieldRecord(tmp,record,0,0);
+    //    WR.writeScidacFieldRecord(tmp,record,0,BINARYIO_LEXICOGRAPHIC);
+  }
+  WR.close();
+#endif
+}
+template<class Coarsened>
+void LoadOperator(Coarsened &Operator,std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  Grid::ScidacReader RD ;
+  RD.open(file);
+  assert(Operator._A.size()==Operator.geom.npoint);
+  for(int p=0;p<Operator.geom.npoint;p++){
+    conformable(Operator._A[p].Grid(),Operator.CoarseGrid());
+    //    RD.readScidacFieldRecord(Operator._A[p],record,BINARYIO_LEXICOGRAPHIC);
+    RD.readScidacFieldRecord(Operator._A[p],record,0);
+  }    
+  RD.close();
+  Operator.ExchangeCoarseLinks();
+#endif
+}
+template<class Coarsened>
+void ReLoadOperator(Coarsened &Operator,std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  Grid::ScidacReader RD ;
+  RD.open(file);
+  assert(Operator._A.size()==Operator.geom.npoint);
+  for(int p=0;p<Operator.geom.npoint;p++){
+    auto tmp=Operator.Cell.Extract(Operator._A[p]);
+    RD.readScidacFieldRecord(tmp,record,0);
+    Operator._A[p] = Operator.Cell.ExchangePeriodic(tmp);
+  }    
+  RD.close();
+#endif
+}
+*/
+template<class aggregation>
+void SaveBasis(aggregation &Agg,std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  ScidacWriter WR(Agg.FineGrid->IsBoss());
+  WR.open(file);
+  for(int b=0;b<Agg.subspace.size();b++){
+    //WR.writeScidacFieldRecord(Agg.subspace[b],record,0,BINARYIO_LEXICOGRAPHIC);
+    WR.writeScidacFieldRecord(Agg.subspace[b],record,0,0);
+  }
+  WR.close();
+#endif
+}
+template<class aggregation>
+void LoadBasis(aggregation &Agg, std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  ScidacReader RD ;
+  RD.open(file);
+  for(int b=0;b<Agg.subspace.size();b++){
+    //    RD.readScidacFieldRecord(Agg.subspace[b],record,BINARYIO_LEXICOGRAPHIC);
+    RD.readScidacFieldRecord(Agg.subspace[b],record,0);
+  }    
+  RD.close();
+#endif
+}
+template<class CoarseVector>
+void SaveEigenvectors(std::vector<RealD>            &eval,
+		      std::vector<CoarseVector>     &evec,
+		      std::string evec_file,
+		      std::string eval_file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  ScidacWriter WR(evec[0].Grid()->IsBoss());
+  WR.open(evec_file);
+  for(int b=0;b<evec.size();b++){
+    WR.writeScidacFieldRecord(evec[b],record,0,0);
+  }
+  WR.close();
+  XmlWriter WRx(eval_file);
+  write(WRx,"evals",eval);
+#endif
+}
+template<class CoarseVector>
+void LoadEigenvectors(std::vector<RealD>            &eval,
+		      std::vector<CoarseVector>     &evec,
+		      std::string evec_file,
+		      std::string eval_file)
+{
+#ifdef HAVE_LIME
+    XmlReader RDx(eval_file);
+    read(RDx,"evals",eval);
+    emptyUserRecord record;
+
+    Grid::ScidacReader RD ;
+    RD.open(evec_file);
+    assert(evec.size()==eval.size());
+    for(int k=0;k<eval.size();k++) {
+      RD.readScidacFieldRecord(evec[k],record);
+    }
+    RD.close();
+#endif
+}
+
+// Want Op in CoarsenOp to call MatPcDagMatPc
+template<class Field>
+class HermOpAdaptor : public LinearOperatorBase<Field>
+{
+  LinearOperatorBase<Field> & wrapped;
+public:
+  HermOpAdaptor(LinearOperatorBase<Field> &wrapme) : wrapped(wrapme)  {};
+  void Op     (const Field &in, Field &out)   { wrapped.HermOp(in,out);  }
+  void HermOp(const Field &in, Field &out)    { wrapped.HermOp(in,out); }
+  void AdjOp     (const Field &in, Field &out){ wrapped.HermOp(in,out);  }
+  void OpDiag (const Field &in, Field &out)                  {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out)  {    assert(0);  };
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){    assert(0);  }
+};
+
+template<class Field> class CGSmoother : public LinearFunction<Field>
+{
+public:
+  using LinearFunction<Field>::operator();
+  typedef LinearOperatorBase<Field> FineOperator;
+  FineOperator   & _SmootherOperator;
+  int iters;
+  CGSmoother(int _iters, FineOperator &SmootherOperator) :
+    _SmootherOperator(SmootherOperator),
+    iters(_iters)
+  {
+    std::cout << GridLogMessage<<" Mirs smoother order "<<iters<<std::endl;
+  };
+  void operator() (const Field &in, Field &out) 
+  {
+    ConjugateGradient<Field>  CG(0.0,iters,false); // non-converge is just fine in a smoother
+
+    out=Zero();
+
+    CG(_SmootherOperator,in,out);
+  }
+};
+
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  const int Ls=24;
+  const int nbasis = 62;
+  const int cb = 0 ;
+  RealD mass=0.00078;
+  RealD M5=1.8;
+  RealD b=1.5;
+  RealD c=0.5;
+
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(),
+								   GridDefaultSimd(Nd,vComplex::Nsimd()),
+								   GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Construct a coarsened grid with 4^4 cell
+  Coordinate Block({4,4,6,4});
+  Coordinate clatt = GridDefaultLatt();
+  for(int d=0;d<clatt.size();d++){
+    clatt[d] = clatt[d]/Block[d];
+  }
+
+  GridCartesian *Coarse4d =  SpaceTimeGrid::makeFourDimGrid(clatt,
+							    GridDefaultSimd(Nd,vComplex::Nsimd()),
+							    GridDefaultMpi());;
+  GridCartesian *Coarse5d =  SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+
+  ///////////////////////// RNGs /////////////////////////////////
+  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);
+
+  ///////////////////////// Configuration /////////////////////////////////
+  LatticeGaugeField Umu(UGrid);
+
+  FieldMetaData header;
+  std::string file("ckpoint_lat.1000");
+  NerscIO::readConfiguration(Umu,header,file);
+
+  //////////////////////// Fermion action //////////////////////////////////
+  MobiusFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5,b,c);
+
+  SchurDiagMooeeOperator<MobiusFermionD, LatticeFermion> HermOpEO(Ddwf);
+
+  typedef HermOpAdaptor<LatticeFermionD> HermFineMatrix;
+  HermFineMatrix FineHermOp(HermOpEO);
+
+  // Run power method on FineHermOp
+  // PowerMethod<LatticeFermion>       PM;   PM(HermOpEO,src);
+  ////////////////////////////////////////////////////////////
+  ///////////// Coarse basis and Little Dirac Operator ///////
+  ////////////////////////////////////////////////////////////
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector CoarseVector;
+
+  NextToNextToNextToNearestStencilGeometry5D geom(Coarse5d);
+  
+  // Warning: This routine calls PVdagM.Op, not PVdagM.HermOp
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis> Subspace;
+  Subspace Aggregates(Coarse5d,FrbGrid,cb);
+
+  ////////////////////////////////////////////////////////////
+  // Need to check about red-black grid coarsening
+  ////////////////////////////////////////////////////////////
+  //  LittleDiracOperator LittleDiracOp(geom,FrbGrid,Coarse5d);
+
+  std::string subspace_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/Subspace.phys48.new.62");
+  std::string refine_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/Refine.phys48.hdcg.62");
+  std::string ldop_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/LittleDiracOp.phys48.new.62");
+  std::string evec_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/evecs.scidac");
+  std::string eval_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/eval.xml");
+  bool load_agg=false;
+  bool load_refine=false;
+  bool load_mat=false;
+  bool load_evec=false;
+  std::cout << GridLogMessage <<" Restoring from checkpoint "<<std::endl;
+  int refine=1;
+  if ( load_agg ) {
+    if ( !(refine) || (!load_refine) ) { 
+      LoadBasis(Aggregates,subspace_file);
+    }
+  } else {
+    //    Aggregates.CreateSubspaceMultishift(RNG5,HermOpEO,
+    //					0.0003,1.0e-5,2000); // Lo, tol, maxit
+    Aggregates.CreateSubspaceChebyshev(RNG5,HermOpEO,nbasis,95.,0.01,1500); <== last run
+    //    Aggregates.CreateSubspaceChebyshevNew(RNG5,HermOpEO,95.); // 176 with refinement
+    //    Aggregates.CreateSubspaceChebyshev(RNG5,HermOpEO,nbasis,95.,0.001,3000,1500,200,0.0); // Attempt to resurrect
+    SaveBasis(Aggregates,subspace_file);
+  }
+
+  std::cout << "**************************************"<<std::endl;
+  std::cout << "Building MultiRHS Coarse operator"<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+  ConjugateGradient<CoarseVector>  coarseCG(4.0e-2,20000,true);
+    
+  const int nrhs=vComplex::Nsimd()*3; // 12
+    
+  Coordinate mpi=GridDefaultMpi();
+  Coordinate rhMpi ({1,1,mpi[0],mpi[1],mpi[2],mpi[3]});
+  Coordinate rhLatt({nrhs,1,clatt[0],clatt[1],clatt[2],clatt[3]});
+  Coordinate rhSimd({vComplex::Nsimd(),1, 1,1,1,1});
+    
+  GridCartesian *CoarseMrhs = new GridCartesian(rhLatt,rhSimd,rhMpi); 
+  typedef MultiGeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> MultiGeneralCoarsenedMatrix_t;
+  MultiGeneralCoarsenedMatrix_t mrhs(geom,CoarseMrhs);
+
+  std::cout << "**************************************"<<std::endl;
+  std::cout << "         Coarse Lanczos               "<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+
+  typedef HermitianLinearOperator<MultiGeneralCoarsenedMatrix_t,CoarseVector> MrhsHermMatrix;
+  //  FunctionHermOp<CoarseVector> IRLOpCheby(IRLCheby,CoarseOp);
+  //  PlainHermOp<CoarseVector>    IRLOp    (CoarseOp);
+  Chebyshev<CoarseVector>      IRLCheby(0.006,42.0,301);  // 1 iter
+  MrhsHermMatrix MrhsCoarseOp     (mrhs);
+
+  CoarseVector pm_src(CoarseMrhs);
+  pm_src = ComplexD(1.0);
+  PowerMethod<CoarseVector>       cPM;   cPM(MrhsCoarseOp,pm_src);
+
+  int Nk=192;
+  int Nm=384;
+  int Nstop=Nk;
+  int Nconv_test_interval=1;
+  
+  ImplicitlyRestartedBlockLanczosCoarse<CoarseVector> IRL(MrhsCoarseOp,
+							  Coarse5d,
+							  CoarseMrhs,
+							  nrhs,
+							  IRLCheby,
+							  Nstop,
+							  Nconv_test_interval,
+							  nrhs,
+							  Nk,
+							  Nm,
+							  1e-5,10);
+
+  int Nconv;
+  std::vector<RealD>            eval(Nm);
+  std::vector<CoarseVector>     evec(Nm,Coarse5d);
+  std::vector<CoarseVector>     c_src(nrhs,Coarse5d);
+
+  ///////////////////////
+  // Deflation guesser object
+  ///////////////////////
+  MultiRHSDeflation<CoarseVector> MrhsGuesser;
+
+  //////////////////////////////////////////
+  // Block projector for coarse/fine
+  //////////////////////////////////////////
+  MultiRHSBlockProject<LatticeFermionD> MrhsProjector;
+
+  //////////////////////////
+  // Extra HDCG parameters
+  //////////////////////////
+  int maxit=3000;
+  ConjugateGradient<CoarseVector>  CG(5.0e-2,maxit,false);
+  RealD lo=2.0;
+  int ord = 7;
+
+  DoNothingGuesser<CoarseVector> DoNothing;
+  HPDSolver<CoarseVector> HPDSolveMrhs(MrhsCoarseOp,CG,DoNothing);
+  HPDSolver<CoarseVector> HPDSolveMrhsRefine(MrhsCoarseOp,CG,DoNothing);
+
+  /////////////////////////////////////////////////
+  // Mirs smoother
+  /////////////////////////////////////////////////
+  RealD MirsShift = lo;
+  ShiftedHermOpLinearOperator<LatticeFermionD> ShiftedFineHermOp(HermOpEO,MirsShift);
+  CGSmoother<LatticeFermionD> CGsmooth(ord,ShiftedFineHermOp) ;
+
+  
+  if ( load_refine ) {
+    LoadBasis(Aggregates,refine_file);
+  } else {
+#if 1
+    // Make a copy as subspace gets block orthogonalised
+    // HDCG used Pcg to refine
+    int Refineord = 11;
+    // Not as good as refining with shifted CG (169 iters), but 10%
+    // Datapoints
+    //- refining to 0.001 and shift 0.0 is expensive, but gets to 180 outer iterations
+    //- refining to 0.001 and shift 0.001 is cheap, but gets to 240 outer iterations  
+    //- refining to 0.0005 and shift 0.0005 is cheap, but gets to 230 outer iterations  
+    //- refining to 0.001 and shift 0.0001 220 iterations
+    //- refining to 0.001 and shift 0.00003 
+    RealD RefineShift = 0.00003;
+    RealD RefineTol   = 0.001;
+    ShiftedHermOpLinearOperator<LatticeFermionD> RefineFineHermOp(HermOpEO,RefineShift);
+    
+    mrhs.CoarsenOperator(RefineFineHermOp,Aggregates,Coarse5d);
+
+    MrhsProjector.Allocate(nbasis,FrbGrid,Coarse5d);
+
+    MrhsProjector.ImportBasis(Aggregates.subspace);
+
+    // Lanczos with random start
+    for(int r=0;r<nrhs;r++){
+      random(CRNG,c_src[r]);
+    }
+    IRL.calc(eval,evec,c_src,Nconv,LanczosType::irbl);
+
+    MrhsGuesser.ImportEigenBasis(evec,eval);
+
+    CGSmoother<LatticeFermionD> CGsmooth(Refineord,ShiftedFineHermOp) ;
+    TwoLevelADEF2mrhs<LatticeFermion,CoarseVector>
+      HDCGmrhsRefine(RefineTol, 500,
+		     RefineFineHermOp,
+		     CGsmooth,
+		     HPDSolveMrhs,    // Used in M1
+		     HPDSolveMrhs,    // Used in Vstart
+		     MrhsProjector,
+		     MrhsGuesser,
+		     CoarseMrhs);
+
+    // Reload the first pass aggregates, because we orthogonalised them
+    LoadBasis(Aggregates,subspace_file);
+
+    Aggregates.RefineSubspaceHDCG(HermOpEO,
+				  HDCGmrhsRefine,
+				  nrhs);
+
+#else     
+    Aggregates.RefineSubspace(HermOpEO,0.001,1.0e-3,3000); // 172 iters
+#endif
+
+    SaveBasis(Aggregates,refine_file);
+  }
+  Aggregates.Orthogonalise();
+
+  /*
+  if ( load_mat ) {
+    LoadOperator(LittleDiracOp,ldop_file);
+  } else {
+    LittleDiracOp.CoarsenOperator(FineHermOp,Aggregates);
+    SaveOperator(LittleDiracOp,ldop_file);
+  }
+  */
+
+  std::cout << "**************************************"<<std::endl;
+  std::cout << "Coarsen after refine"<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+
+  mrhs.CoarsenOperator(FineHermOp,Aggregates,Coarse5d);
+
+  std::cout << "**************************************"<<std::endl;
+  std::cout << " Recompute coarse evecs ; use old evecs as source  "<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+  evec.resize(Nm,Coarse5d);
+  eval.resize(Nm);
+  for(int r=0;r<nrhs;r++){
+    //    c_src[r]=Zero();
+    random(CRNG,c_src[r]);
+  }
+  for(int e=0;e<evec.size();e++){
+    //    int r = e%nrhs;
+    //    c_src[r] = c_src[r]+evec[r];
+  }
+ IRL.calc(eval,evec,c_src,Nconv,LanczosType::irbl);
+
+  std::cout << "**************************************"<<std::endl;
+  std::cout << " Reimport coarse evecs  "<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+  MrhsGuesser.ImportEigenBasis(evec,eval);
+
+  std::cout << "**************************************"<<std::endl;
+  std::cout << "Calling mRHS HDCG"<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+  MrhsProjector.Allocate(nbasis,FrbGrid,Coarse5d);
+  MrhsProjector.ImportBasis(Aggregates.subspace);
+      
+  TwoLevelADEF2mrhs<LatticeFermion,CoarseVector>
+    HDCGmrhs(1.0e-8, 500,
+	     FineHermOp,
+	     CGsmooth,
+	     HPDSolveMrhs,    // Used in M1
+	     HPDSolveMrhs,          // Used in Vstart
+	     MrhsProjector,
+	     MrhsGuesser,
+	     CoarseMrhs);
+    
+  std::vector<LatticeFermionD> src_mrhs(nrhs,FrbGrid);
+  std::vector<LatticeFermionD> res_mrhs(nrhs,FrbGrid);
+  
+  for(int r=0;r<nrhs;r++){
+    random(RNG5,src_mrhs[r]);
+    res_mrhs[r]=Zero();
+  }
+  
+  HDCGmrhs(src_mrhs,res_mrhs);
+
+  // Standard CG
+#if 0
+  {
+  std::cout << "**************************************"<<std::endl;
+  std::cout << "Calling red black CG"<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+      
+    LatticeFermion result(FrbGrid); result=Zero();
+    LatticeFermion    src(FrbGrid); random(RNG5,src);
+    result=Zero();
+
+    CGfine(HermOpEO, src, result);
+  }
+#endif  
+  Grid_finalize();
+  return 0;
+}

tests/debug/Test_general_coarse_hdcg_phys48_mixed.cc

@@ -0,0 +1,388 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./tests/Test_general_coarse_hdcg.cc
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    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>
+#include <Grid/algorithms/iterative/ImplicitlyRestartedBlockLanczos.h>
+#include <Grid/algorithms/iterative/ImplicitlyRestartedBlockLanczosCoarse.h>
+#include <Grid/algorithms/iterative/AdefMrhs.h>
+
+using namespace std;
+using namespace Grid;
+
+template<class aggregation>
+void SaveBasis(aggregation &Agg,std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  ScidacWriter WR(Agg.FineGrid->IsBoss());
+  WR.open(file);
+  for(int b=0;b<Agg.subspace.size();b++){
+    WR.writeScidacFieldRecord(Agg.subspace[b],record,0,Grid::BinaryIO::BINARYIO_LEXICOGRAPHIC);
+    //    WR.writeScidacFieldRecord(Agg.subspace[b],record);
+  }
+  WR.close();
+#endif
+}
+template<class aggregation>
+void LoadBasis(aggregation &Agg, std::string file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  ScidacReader RD ;
+  RD.open(file);
+  for(int b=0;b<Agg.subspace.size();b++){
+    RD.readScidacFieldRecord(Agg.subspace[b],record,Grid::BinaryIO::BINARYIO_LEXICOGRAPHIC);
+    //    RD.readScidacFieldRecord(Agg.subspace[b],record,0);
+  }    
+  RD.close();
+#endif
+}
+template<class CoarseVector>
+void SaveEigenvectors(std::vector<RealD>            &eval,
+		      std::vector<CoarseVector>     &evec,
+		      std::string evec_file,
+		      std::string eval_file)
+{
+#ifdef HAVE_LIME
+  emptyUserRecord record;
+  ScidacWriter WR(evec[0].Grid()->IsBoss());
+  WR.open(evec_file);
+  for(int b=0;b<evec.size();b++){
+    WR.writeScidacFieldRecord(evec[b],record,0,0);
+  }
+  WR.close();
+  XmlWriter WRx(eval_file);
+  write(WRx,"evals",eval);
+#endif
+}
+template<class CoarseVector>
+void LoadEigenvectors(std::vector<RealD>            &eval,
+		      std::vector<CoarseVector>     &evec,
+		      std::string evec_file,
+		      std::string eval_file)
+{
+#ifdef HAVE_LIME
+    XmlReader RDx(eval_file);
+    read(RDx,"evals",eval);
+    emptyUserRecord record;
+
+    Grid::ScidacReader RD ;
+    RD.open(evec_file);
+    assert(evec.size()==eval.size());
+    for(int k=0;k<eval.size();k++) {
+      RD.readScidacFieldRecord(evec[k],record);
+    }
+    RD.close();
+#endif
+}
+
+// Want Op in CoarsenOp to call MatPcDagMatPc
+template<class Field>
+class HermOpAdaptor : public LinearOperatorBase<Field>
+{
+  LinearOperatorBase<Field> & wrapped;
+public:
+  HermOpAdaptor(LinearOperatorBase<Field> &wrapme) : wrapped(wrapme)  {};
+  void Op     (const Field &in, Field &out)   { wrapped.HermOp(in,out);  }
+  void HermOp(const Field &in, Field &out)    { wrapped.HermOp(in,out); }
+  void AdjOp     (const Field &in, Field &out){ wrapped.HermOp(in,out);  }
+  void OpDiag (const Field &in, Field &out)                  {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out)  {    assert(0);  };
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){    assert(0);  }
+};
+
+template<class Field> class CGSmoother : public LinearFunction<Field>
+{
+public:
+  using LinearFunction<Field>::operator();
+  typedef LinearOperatorBase<Field> FineOperator;
+  FineOperator   & _SmootherOperator;
+  int iters;
+  CGSmoother(int _iters, FineOperator &SmootherOperator) :
+    _SmootherOperator(SmootherOperator),
+    iters(_iters)
+  {
+    std::cout << GridLogMessage<<" Mirs smoother order "<<iters<<std::endl;
+  };
+  void operator() (const Field &in, Field &out) 
+  {
+    ConjugateGradient<Field>  CG(0.0,iters,false); // non-converge is just fine in a smoother
+
+    out=Zero();
+
+    CG(_SmootherOperator,in,out);
+  }
+};
+
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  const int Ls=24;
+  const int nbasis = 60;
+  const int cb = 0 ;
+  RealD mass=0.00078;
+  RealD M5=1.8;
+  RealD b=1.5;
+  RealD c=0.5;
+
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(),
+								   GridDefaultSimd(Nd,vComplex::Nsimd()),
+								   GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Construct a coarsened grid with 4^4 cell
+  Coordinate Block({4,4,4,4});
+  Coordinate clatt = GridDefaultLatt();
+  for(int d=0;d<clatt.size();d++){
+    clatt[d] = clatt[d]/Block[d];
+  }
+
+  GridCartesian *Coarse4d =  SpaceTimeGrid::makeFourDimGrid(clatt,
+							    GridDefaultSimd(Nd,vComplex::Nsimd()),
+							    GridDefaultMpi());;
+  GridCartesian *Coarse5d =  SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+
+  ///////////////////////// RNGs /////////////////////////////////
+  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);
+
+  ///////////////////////// Configuration /////////////////////////////////
+  LatticeGaugeField Umu(UGrid);
+
+  FieldMetaData header;
+  std::string file("ckpoint_lat.1000");
+  NerscIO::readConfiguration(Umu,header,file);
+
+  //////////////////////// Fermion action //////////////////////////////////
+  MobiusFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5,b,c);
+
+  SchurDiagMooeeOperator<MobiusFermionD, LatticeFermion> HermOpEO(Ddwf);
+
+  typedef HermOpAdaptor<LatticeFermionD> HermFineMatrix;
+  HermFineMatrix FineHermOp(HermOpEO);
+
+  ////////////////////////////////////////////////////////////
+  ///////////// Coarse basis and Little Dirac Operator ///////
+  ////////////////////////////////////////////////////////////
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector CoarseVector;
+
+  NextToNextToNextToNearestStencilGeometry5D geom(Coarse5d);
+
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis> Subspace;
+  Subspace Aggregates(Coarse5d,FrbGrid,cb);
+
+  ////////////////////////////////////////////////////////////
+  // Need to check about red-black grid coarsening
+  ////////////////////////////////////////////////////////////
+
+  std::string subspace_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/Subspace.phys48.mixed.2500.60");
+  //  std::string subspace_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/Subspace.phys48.new.62");
+  std::string refine_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/Refine.phys48.mixed.2500.60");
+  std::string ldop_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/LittleDiracOp.phys48.mixed.60");
+  std::string evec_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/evecs.scidac");
+  std::string eval_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/eval.xml");
+  bool load_agg=true;
+  bool load_refine=true;
+  bool load_mat=false;
+  bool load_evec=false;
+
+  int refine=1;
+  if ( load_agg ) {
+    if ( !(refine) || (!load_refine) ) { 
+      LoadBasis(Aggregates,subspace_file);
+    }
+  } else {
+    //    Aggregates.CreateSubspaceMultishift(RNG5,HermOpEO,
+    //    					0.0003,1.0e-5,2000); // Lo, tol, maxit
+    //    Aggregates.CreateSubspaceChebyshev(RNG5,HermOpEO,nbasis,95.,0.01,1500);// <== last run
+    Aggregates.CreateSubspaceChebyshevNew(RNG5,HermOpEO,95.); 
+    SaveBasis(Aggregates,subspace_file);
+  }
+
+  std::cout << "**************************************"<<std::endl;
+  std::cout << "Building MultiRHS Coarse operator"<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+  ConjugateGradient<CoarseVector>  coarseCG(4.0e-2,20000,true);
+    
+  const int nrhs=12;
+    
+  Coordinate mpi=GridDefaultMpi();
+  Coordinate rhMpi ({1,1,mpi[0],mpi[1],mpi[2],mpi[3]});
+  Coordinate rhLatt({nrhs,1,clatt[0],clatt[1],clatt[2],clatt[3]});
+  Coordinate rhSimd({vComplex::Nsimd(),1, 1,1,1,1});
+    
+  GridCartesian *CoarseMrhs = new GridCartesian(rhLatt,rhSimd,rhMpi); 
+  typedef MultiGeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> MultiGeneralCoarsenedMatrix_t;
+  MultiGeneralCoarsenedMatrix_t mrhs(geom,CoarseMrhs);
+
+  std::cout << "**************************************"<<std::endl;
+  std::cout << "         Coarse Lanczos               "<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+
+  typedef HermitianLinearOperator<MultiGeneralCoarsenedMatrix_t,CoarseVector> MrhsHermMatrix;
+  Chebyshev<CoarseVector>      IRLCheby(0.005,42.0,301);  // 1 iter
+  MrhsHermMatrix MrhsCoarseOp     (mrhs);
+
+  CoarseVector pm_src(CoarseMrhs);
+  pm_src = ComplexD(1.0);
+  PowerMethod<CoarseVector>       cPM;   cPM(MrhsCoarseOp,pm_src);
+
+  int Nk=192;
+  int Nm=384;
+  int Nstop=Nk;
+  int Nconv_test_interval=1;
+  
+  ImplicitlyRestartedBlockLanczosCoarse<CoarseVector> IRL(MrhsCoarseOp,
+							  Coarse5d,
+							  CoarseMrhs,
+							  nrhs,
+							  IRLCheby,
+							  Nstop,
+							  Nconv_test_interval,
+							  nrhs,
+							  Nk,
+							  Nm,
+							  1e-5,10);
+
+  int Nconv;
+  std::vector<RealD>            eval(Nm);
+  std::vector<CoarseVector>     evec(Nm,Coarse5d);
+  std::vector<CoarseVector>     c_src(nrhs,Coarse5d);
+
+  ///////////////////////
+  // Deflation guesser object
+  ///////////////////////
+  MultiRHSDeflation<CoarseVector> MrhsGuesser;
+
+  //////////////////////////////////////////
+  // Block projector for coarse/fine
+  //////////////////////////////////////////
+  MultiRHSBlockProject<LatticeFermionD> MrhsProjector;
+
+  //////////////////////////
+  // Extra HDCG parameters
+  //////////////////////////
+  int maxit=3000;
+  ConjugateGradient<CoarseVector>  CG(5.0e-2,maxit,false);
+  RealD lo=2.0;
+  int ord = 7;
+
+  DoNothingGuesser<CoarseVector> DoNothing;
+  HPDSolver<CoarseVector> HPDSolveMrhs(MrhsCoarseOp,CG,DoNothing);
+  HPDSolver<CoarseVector> HPDSolveMrhsRefine(MrhsCoarseOp,CG,DoNothing);
+
+  /////////////////////////////////////////////////
+  // Mirs smoother
+  /////////////////////////////////////////////////
+  RealD MirsShift = lo;
+  ShiftedHermOpLinearOperator<LatticeFermionD> ShiftedFineHermOp(HermOpEO,MirsShift);
+  CGSmoother<LatticeFermionD> CGsmooth(ord,ShiftedFineHermOp) ;
+
+  
+  if ( load_refine ) {
+    LoadBasis(Aggregates,refine_file);
+  } else {
+    Aggregates.RefineSubspace(HermOpEO,0.001,1.0e-3,3000); // 172 iters
+    SaveBasis(Aggregates,refine_file);
+  }
+  Aggregates.Orthogonalise();
+
+  std::cout << "**************************************"<<std::endl;
+  std::cout << "Coarsen after refine"<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+  mrhs.CoarsenOperator(FineHermOp,Aggregates,Coarse5d);
+
+  std::cout << "**************************************"<<std::endl;
+  std::cout << " Recompute coarse evecs  "<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+  evec.resize(Nm,Coarse5d);
+  eval.resize(Nm);
+  for(int r=0;r<nrhs;r++){
+    random(CRNG,c_src[r]);
+  }
+ IRL.calc(eval,evec,c_src,Nconv,LanczosType::irbl);
+
+  std::cout << "**************************************"<<std::endl;
+  std::cout << " Reimport coarse evecs  "<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+  MrhsGuesser.ImportEigenBasis(evec,eval);
+
+  std::cout << "**************************************"<<std::endl;
+  std::cout << "Calling mRHS HDCG"<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+  MrhsProjector.Allocate(nbasis,FrbGrid,Coarse5d);
+  MrhsProjector.ImportBasis(Aggregates.subspace);
+      
+  TwoLevelADEF2mrhs<LatticeFermion,CoarseVector>
+    HDCGmrhs(1.0e-8, 500,
+	     FineHermOp,
+	     CGsmooth,
+	     HPDSolveMrhs,    // Used in M1
+	     HPDSolveMrhs,          // Used in Vstart
+	     MrhsProjector,
+	     MrhsGuesser,
+	     CoarseMrhs);
+    
+  std::vector<LatticeFermionD> src_mrhs(nrhs,FrbGrid);
+  std::vector<LatticeFermionD> res_mrhs(nrhs,FrbGrid);
+  
+  for(int r=0;r<nrhs;r++){
+    random(RNG5,src_mrhs[r]);
+    res_mrhs[r]=Zero();
+  }
+  
+  HDCGmrhs(src_mrhs,res_mrhs);
+
+  // Standard CG
+#if 1
+  {
+  std::cout << "**************************************"<<std::endl;
+  std::cout << "Calling red black CG"<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+      
+    LatticeFermion result(FrbGrid); result=Zero();
+    LatticeFermion    src(FrbGrid); random(RNG5,src);
+    result=Zero();
+
+    ConjugateGradient<LatticeFermionD>  CGfine(1.0e-8,30000,false);
+    CGfine(HermOpEO, src, result);
+  }
+#endif  
+  Grid_finalize();
+  return 0;
+}

tests/debug/Test_general_coarse_pvdagm.cc

@@ -0,0 +1,267 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./tests/Test_padded_cell.cc
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <paboyle@ph.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>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidual.h>
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.h>
+#include <Grid/algorithms/iterative/BiCGSTAB.h>
+
+using namespace std;
+using namespace Grid;
+
+template<class Field>
+class HermOpAdaptor : public LinearOperatorBase<Field>
+{
+  LinearOperatorBase<Field> & wrapped;
+public:
+  HermOpAdaptor(LinearOperatorBase<Field> &wrapme) : wrapped(wrapme)  {};
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    wrapped.HermOp(in,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    wrapped.HermOp(in,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){    assert(0);  }
+  void HermOp(const Field &in, Field &out){
+    wrapped.HermOp(in,out);
+  }
+  
+};
+
+template<class Matrix,class Field>
+class PVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+public:
+  PVdagMLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV){};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(tmp,out);
+    _Mat.Mdag(in,tmp);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){    assert(0);  }
+  void HermOp(const Field &in, Field &out){
+    std::cout << "HermOp"<<std::endl;
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+    _PV.M(out,tmp);
+    _Mat.Mdag(tmp,out);
+    std::cout << "HermOp done "<<norm2(out)<<std::endl;
+    
+  }
+};
+
+template<class Field> class DumbOperator  : public LinearOperatorBase<Field> {
+public:
+  LatticeComplex scale;
+  DumbOperator(GridBase *grid) : scale(grid)
+  {
+    scale = 0.0;
+    LatticeComplex scalesft(grid);
+    LatticeComplex scaletmp(grid);
+    for(int d=0;d<4;d++){
+      Lattice<iScalar<vInteger> > x(grid); LatticeCoordinate(x,d+1);
+      LatticeCoordinate(scaletmp,d+1);
+      scalesft = Cshift(scaletmp,d+1,1);
+      scale = 100.0*scale + where( mod(x    ,2)==(Integer)0, scalesft,scaletmp);
+    }
+    std::cout << " scale\n" << scale << std::endl;
+  }
+  // Support for coarsening to a multigrid
+  void OpDiag (const Field &in, Field &out) {};
+  void OpDir  (const Field &in, Field &out,int dir,int disp){};
+  void OpDirAll  (const Field &in, std::vector<Field> &out) {};
+
+  void Op     (const Field &in, Field &out){
+    out = scale * in;
+  }
+  void AdjOp  (const Field &in, Field &out){
+    out = scale * in;
+  }
+  void HermOp(const Field &in, Field &out){
+    double n1, n2;
+    HermOpAndNorm(in,out,n1,n2);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,double &n1,double &n2){
+    ComplexD dot;
+
+    out = scale * in;
+
+    dot= innerProduct(in,out);
+    n1=real(dot);
+
+    dot = innerProduct(out,out);
+    n2=real(dot);
+  }
+};
+
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  const int Ls=2;
+
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(), GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Construct a coarsened grid
+  Coordinate clatt = GridDefaultLatt();
+  for(int d=0;d<clatt.size();d++){
+    clatt[d] = clatt[d]/4;
+  }
+  GridCartesian *Coarse4d =  SpaceTimeGrid::makeFourDimGrid(clatt, GridDefaultSimd(Nd,vComplex::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); random(RNG5,src);
+  LatticeFermion result(FGrid); result=Zero();
+  LatticeFermion    ref(FGrid); ref=Zero();
+  LatticeFermion    tmp(FGrid);
+  LatticeFermion    err(FGrid);
+  LatticeGaugeField Umu(UGrid);
+
+  FieldMetaData header;
+  std::string file("ckpoint_lat.4000");
+  NerscIO::readConfiguration(Umu,header,file);
+  //Umu = 1.0;
+  
+  RealD mass=0.5;
+  RealD M5=1.8;
+
+  DomainWallFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5);
+  DomainWallFermionD Dpv(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,1.0,M5);
+
+  const int nbasis = 1;
+  const int cb = 0 ;
+  LatticeFermion prom(FGrid);
+
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector CoarseVector;
+
+  NextToNearestStencilGeometry5D geom(Coarse5d);
+
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<std::endl;
+  
+  PVdagMLinearOperator<DomainWallFermionD,LatticeFermionD> PVdagM(Ddwf,Dpv);
+  HermOpAdaptor<LatticeFermionD> HOA(PVdagM);
+
+  // Run power method on HOA??
+  PowerMethod<LatticeFermion>       PM;   PM(HOA,src);
+ 
+  // Warning: This routine calls PVdagM.Op, not PVdagM.HermOp
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis> Subspace;
+  Subspace AggregatesPD(Coarse5d,FGrid,cb);
+  AggregatesPD.CreateSubspaceChebyshev(RNG5,
+				       HOA,
+				       nbasis,
+				       5000.0,
+				       0.02,
+				       100,
+				       50,
+				       50,
+				       0.0);
+  
+  LittleDiracOperator LittleDiracOpPV(geom,FGrid,Coarse5d);
+  LittleDiracOpPV.CoarsenOperator(PVdagM,AggregatesPD);
+
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<"Testing coarsened operator "<<std::endl;
+  
+  CoarseVector c_src (Coarse5d);
+  CoarseVector c_res (Coarse5d);
+  CoarseVector c_proj(Coarse5d);
+
+  std::vector<LatticeFermion> subspace(nbasis,FGrid);
+  subspace=AggregatesPD.subspace;
+
+  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<<GridLogMessage<<"Promoted back from subspace: err "<<norm2(err)<<std::endl;
+  std::cout<<GridLogMessage<<"c_src "<<norm2(c_src)<<std::endl;
+  std::cout<<GridLogMessage<<"prom  "<<norm2(prom)<<std::endl;
+
+  PVdagM.Op(prom,tmp);
+  blockProject(c_proj,tmp,subspace);
+  std::cout<<GridLogMessage<<" Called Big Dirac Op "<<norm2(tmp)<<std::endl;
+
+  LittleDiracOpPV.M(c_src,c_res);
+  std::cout<<GridLogMessage<<" Called Little Dirac Op c_src "<< norm2(c_src) << "  c_res "<< norm2(c_res) <<std::endl;
+
+  std::cout<<GridLogMessage<<"Little dop : "<<norm2(c_res)<<std::endl;
+  //  std::cout<<GridLogMessage<<" Little "<< c_res<<std::endl;
+
+  std::cout<<GridLogMessage<<"Big dop in subspace : "<<norm2(c_proj)<<std::endl;
+  //  std::cout<<GridLogMessage<<" Big "<< c_proj<<std::endl;
+  c_proj = c_proj - c_res;
+  std::cout<<GridLogMessage<<" ldop error: "<<norm2(c_proj)<<std::endl;
+  //  std::cout<<GridLogMessage<<" error "<< c_proj<<std::endl;
+
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage << "Done "<< std::endl;
+
+  Grid_finalize();
+  return 0;
+}