More info

Also add NaiveStaggeredFermionF to Benchmark_staggeredF, and fix bug where
NaiveStaggered timed loop was calling Ds.Dhop instead of Dn.Dhop.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

CLAUDE.md

@@ -30,6 +30,9 @@ Key configure options:
 | `--enable-Nc=` | `3` (default), `2`, `4`, `5` |
 | `--with-gmp=`, `--with-mpfr=`, `--with-fftw=`, `--with-lime=` | paths to libs |
 | `--enable-hdf5`, `--enable-mkl`, `--enable-lapack` | optional features |
+| `--enable-debug=yes` | adds `-g`, removes `-O3` |
+
+Use `make V=1` for verbose compiler output (shows full flags; required for bug reports).
 
 Platform recipes from `README.md`:
 - **KNL**: `--enable-simd=KNL --enable-comms=mpi3-auto --enable-mkl`
@@ -96,3 +99,17 @@ GPU support is injected via macros (`accelerator_for`, `accelerator_for2dNB`). T
 - The `RealD`/`RealF`/`ComplexD`/`ComplexF` typedefs are used everywhere; avoid raw `double`/`float`.
 - Logging uses `Grid_log`, `Grid_error` macros (from `Grid/log/`); performance-critical paths use the `GRID_TRACE` / timer macros from `Grid/perfmon/`.
 - Reductions across MPI ranks go through `GridBase::GlobalSum` / `GlobalMax`; never reduce with bare MPI calls inside library code.
+
+## Skills
+
+`skills/` contains seven user-invocable Claude Code skills encoding deep domain knowledge for HPC work in this repo. Invoke with `/skill-name` or ask Claude to use them by name:
+
+| Skill | When to use |
+|-------|-------------|
+| `gpu-memory-performance` | Bandwidth/occupancy problems — `acceleratorThreads()` pitfalls, `coalescedRead/Write`, fused vs staged HBM patterns |
+| `gpu-runtime-correctness` | Wrong answers, non-deterministic results, premature `q.wait()` returns |
+| `communication-overlap` | Designing GPU+MPI overlap pipelines; replacing broken accelerator-aware MPI paths with host-staged 7-phase pipeline |
+| `mpi-heterogeneous` | Collective hangs, buffer aliasing in `MPI_Sendrecv`, heterogeneous topology bugs |
+| `hang-diagnosis` | Distinguishing ioctl hangs, infinite poll loops, collective deadlocks, and silent wrong-answer races |
+| `correctness-verification` | Reproducibility checksums, double-wait testing, bisecting non-deterministic failures |
+| `compiler-validation` | Confirming compiler/optimisation flags are safe before production runs |

Grid/algorithms/Algorithms.h

@@ -53,7 +53,6 @@ NAMESPACE_CHECK(approx);
 #include <Grid/algorithms/deflation/MultiRHSBlockCGLinalg.h>
 // Not really deflation, but useful
 #include <Grid/algorithms/blas/MomentumProject.h>
-#include <Grid/algorithms/blas/A2ASpatialSum.h>
 NAMESPACE_CHECK(deflation);
 #include <Grid/algorithms/iterative/ConjugateGradient.h>
 NAMESPACE_CHECK(ConjGrad);

Grid/algorithms/blas/A2ASpatialSum.h

@@ -1,213 +0,0 @@
-/*************************************************************************************
-
-    Grid physics library, www.github.com/paboyle/Grid
-
-    Source file: Grid/algorithms/blas/A2ASpatialSum.h
-
-    Copyright (C) 2025
-
-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);
-
-/*
-  A2ASpatialSum
-
-  Replaces the scalar spatial accumulation loop in A2A extended meson field
-  contractions with a batched GEMM over local time slices, enabling GPU offload.
-
-  Given:
-    leftv[N_i][osite]    — conjugated left SpinColourVectors (SIMD-packed)
-    loopRight[N_j][osite]— type-contracted right SpinColourVectors (SIMD-packed)
-
-  Computes:
-    EMF[i,j,t] = sum_{x,s,c} leftv[i][x,t,s,c] * loopRight[j][x,t,s,c]
-
-  via batched GEMM over nt local time slices, then GlobalSumVector across MPI.
-
-  Memory layout (all C row-major):
-    W_buf  [nt][N_i][nxyz*Nsc]  — W[t][i][x*Nsc+sc]  = leftv[i] at (x,t)
-    LR_buf [nt][N_j][nxyz*Nsc]  — LR[t][j][x*Nsc+sc] = loopRight[j] at (x,t)
-    EMF_buf[nt][N_j][N_i]       — column-major result; EMF[i,j,t] = EMF_buf[t][j][i]
-
-  BLAS call (column-major, OP_T on A so A is read as W[i][k]):
-    C = A^T * B  where A=W[N_i×K C-row], B=LR[N_j×K C-row], C=[N_j×N_i C-row]
-    → C[i,j] = sum_k W[i][k] * LR[j][k] = EMF[i,j] ✓
-*/
-template<class vobj>
-class A2ASpatialSum
-{
-public:
-  typedef typename vobj::scalar_type   scalar;
-  typedef typename vobj::scalar_object sobj;
-
-  GridBase *grid;
-  int N_i, N_j;
-  int nt, nxyz, Nsc;
-
-  deviceVector<scalar>   W_buf;
-  deviceVector<scalar>   LR_buf;
-  deviceVector<scalar>   EMF_buf;
-  deviceVector<scalar *> W_ptrs;
-  deviceVector<scalar *> LR_ptrs;
-  deviceVector<scalar *> EMF_ptrs;
-
-  A2ASpatialSum() : grid(nullptr), N_i(0), N_j(0), nt(0), nxyz(0), Nsc(0) {}
-
-  void Allocate(int _N_i, int _N_j, GridBase *_grid)
-  {
-    grid = _grid;
-    N_i  = _N_i;
-    N_j  = _N_j;
-    Coordinate ldims = grid->LocalDimensions();
-    nt   = ldims[grid->Nd() - 1];
-    nxyz = grid->lSites() / nt;
-    Nsc  = sizeof(sobj) / sizeof(scalar);
-
-    W_buf.resize(nt * N_i * nxyz * Nsc);
-    LR_buf.resize(nt * N_j * nxyz * Nsc);
-    EMF_buf.resize(nt * N_j * N_i);
-
-    // Build persistent batch pointer arrays
-    W_ptrs.resize(nt);
-    LR_ptrs.resize(nt);
-    EMF_ptrs.resize(nt);
-    scalar *Wh   = &W_buf[0];
-    scalar *LRh  = &LR_buf[0];
-    scalar *EMFh = &EMF_buf[0];
-    int lN_i = N_i, lN_j = N_j, lnxyz = nxyz, lNsc = Nsc;
-    for (int t = 0; t < nt; t++) {
-      acceleratorPut(W_ptrs[t],   Wh   + t * lN_i * lnxyz * lNsc);
-      acceleratorPut(LR_ptrs[t],  LRh  + t * lN_j * lnxyz * lNsc);
-      acceleratorPut(EMF_ptrs[t], EMFh + t * lN_j * lN_i);
-    }
-  }
-
-  void PackLeft(const std::vector<Lattice<vobj>> &leftv)
-  {
-    GRID_ASSERT((int)leftv.size() == N_i);
-    PackVectors(leftv, &W_buf[0], N_i);
-  }
-
-  void PackRight(const std::vector<Lattice<vobj>> &loopRight)
-  {
-    GRID_ASSERT((int)loopRight.size() == N_j);
-    PackVectors(loopRight, &LR_buf[0], N_j);
-  }
-
-private:
-  // Pack vecs[N] lattice fields into buf[nt][N][nxyz*Nsc], extracting all SIMD lanes.
-  void PackVectors(const std::vector<Lattice<vobj>> &vecs, scalar *buf, int N)
-  {
-    int nd     = grid->_ndimension;
-    int osites = grid->oSites();
-    int Nsimd  = vobj::Nsimd();
-    int lN     = N;
-    int lNsc   = Nsc;
-    int lnxyz  = nxyz;
-    Coordinate rdimensions = grid->_rdimensions;
-    Coordinate ldims       = grid->LocalDimensions();
-    Coordinate simd        = grid->_simd_layout;
-
-    for (int n = 0; n < N; n++) {
-      autoView(src_v, vecs[n], AcceleratorRead);
-      accelerator_for(sf, osites, Nsimd, {
-#ifdef GRID_SIMT
-        {
-          int lane = acceleratorSIMTlane(Nsimd);
-#else
-          for (int lane = 0; lane < Nsimd; lane++) {
-#endif
-          Coordinate icoor(nd), ocoor(nd), lcoor(nd);
-          Lexicographic::CoorFromIndex(icoor, lane, simd);
-          Lexicographic::CoorFromIndex(ocoor, sf, rdimensions);
-          for (int d = 0; d < nd; d++)
-            lcoor[d] = rdimensions[d] * icoor[d] + ocoor[d];
-
-          int     l_t = lcoor[nd - 1];
-          Coordinate xyz_coor = lcoor;
-          xyz_coor[nd - 1] = 0;
-          int64_t l_xyz;
-          Lexicographic::IndexFromCoor(xyz_coor, l_xyz, ldims);
-
-          sobj    data   = extractLane(lane, src_v[sf]);
-          scalar *data_s = (scalar *)&data;
-
-          int64_t base = (int64_t)l_t * lN * lnxyz * lNsc
-                       + (int64_t)n   * lnxyz * lNsc
-                       + l_xyz * lNsc;
-          for (int sc = 0; sc < lNsc; sc++)
-            buf[base + sc] = data_s[sc];
-        }
-      });
-    }
-  }
-
-public:
-
-  // Batched GEMM + MPI reduction → result[nt_global][N_i][N_j]
-  //
-  // BLAS (column-major, OP_T on A):
-  //   C[N_j×N_i] = A^T[N_i×K] * B[N_j×K]    with K=nxyz*Nsc
-  //   reading A as C row-major [N_i][K] and B as C row-major [N_j][K]
-  //   → C[i,j] = sum_k W[i,k] * LR[j,k] = EMF[i,j] ✓
-  void Sum(Eigen::Tensor<ComplexD, 3> &result)
-  {
-    GridBLAS BLAS;
-
-    int K = nxyz * Nsc;
-    BLAS.gemmBatched(GridBLAS_OP_T, GridBLAS_OP_N,
-                     N_i, N_j, K,
-                     scalar(1.0),
-                     W_ptrs,
-                     LR_ptrs,
-                     scalar(0.0),
-                     EMF_ptrs);
-    BLAS.synchronise();
-
-    // Copy from device and distribute into global-t layout
-    int nt_global = result.dimension(0);
-    int nd        = grid->Nd();
-    int lt_start  = grid->LocalStarts()[nd - 1];
-
-    std::vector<scalar> host_emf(nt * N_j * N_i);
-    acceleratorCopyFromDevice(&EMF_buf[0], host_emf.data(),
-                              nt * N_j * N_i * sizeof(scalar));
-
-    // EMF_buf[t][j*N_i + i] = EMF[i,j] for local t
-    std::vector<scalar> global_emf(nt_global * N_i * N_j, scalar(0.0));
-    for (int lt = 0; lt < nt; lt++) {
-      int gt = lt + lt_start;
-      for (int i = 0; i < N_i; i++)
-      for (int j = 0; j < N_j; j++)
-        global_emf[gt * N_i * N_j + i * N_j + j] = host_emf[lt * N_j * N_i + j * N_i + i];
-    }
-    grid->GlobalSumVector(global_emf.data(), nt_global * N_i * N_j);
-
-    for (int gt = 0; gt < nt_global; gt++)
-    for (int i  = 0; i  < N_i;      i++)
-    for (int j  = 0; j  < N_j;      j++)
-      result(gt, i, j) = global_emf[gt * N_i * N_j + i * N_j + j];
-  }
-};
-
-NAMESPACE_END(Grid);

Grid/algorithms/iterative/ImplicitlyRestartedBlockLanczosCoarse.h

@@ -288,17 +288,21 @@ public:
       
       //----------------------------------------------------------------------
       if ( Nm>Nk ) {
-	//        Glog <<" #Apply shifted QR transformations "<<std::endl;
-        //int k2 = Nk+Nu;
+        Glog <<" #Ritz values of poly(A) before shift ["<<Nm<<" values]:"<<std::endl;
+        for(int i=0; i<Nm; ++i){
+          std::cout.precision(8);
+          std::cout << "[" << std::setw(4)<< std::setiosflags(std::ios_base::right) <<i<<"] ";
+          std::cout << "Rval = "<<std::setw(16)<< std::setiosflags(std::ios_base::left)<< eval2[i] << std::endl;
+        }
+
         int k2 = Nk;
-      
+
         Eigen::MatrixXcd BTDM = Eigen::MatrixXcd::Identity(Nm,Nm);
         Q = Eigen::MatrixXcd::Identity(Nm,Nm);
-        
+
         unpackHermitBlockTriDiagMatToEigen(lmd,lme,Nu,Nblock_m,Nm,Nm,BTDM);
 
         for(int ip=Nk; ip<Nm; ++ip){
-	  Glog << " ip "<<ip<<" / "<<Nm<<std::endl;
           shiftedQRDecompEigen(BTDM,Nu,Nm,eval2[ip],Q);
         }
         
@@ -326,11 +330,11 @@ public:
         Qt = Eigen::MatrixXcd::Identity(Nm,Nm);
         diagonalize(eval2,lmd2,lme2,Nu,Nk,Nm,Qt,grid);
         _sort.push(eval2,Nk);
-	//	Glog << "#Ritz value after shift: "<< std::endl;
+        Glog << "#Ritz values of poly(A) after shift ["<<Nk<<" values]:"<<std::endl;
         for(int i=0; i<Nk; ++i){
-	  //	  std::cout.precision(13);
-	  //	  std::cout << "[" << std::setw(4)<< std::setiosflags(std::ios_base::right) <<i<<"] ";
-	  //	  std::cout << "Rval = "<<std::setw(20)<< std::setiosflags(std::ios_base::left)<< eval2[i] << std::endl;
+          std::cout.precision(8);
+          std::cout << "[" << std::setw(4)<< std::setiosflags(std::ios_base::right) <<i<<"] ";
+          std::cout << "Rval = "<<std::setw(16)<< std::setiosflags(std::ios_base::left)<< eval2[i] << std::endl;
         }
       }
       //----------------------------------------------------------------------
@@ -710,11 +714,17 @@ private:
     //lme[0][L] = beta;
     
     for (int u=0; u<Nu; ++u) {
-      //      Glog << "norm2(w[" << u << "])= "<< norm2(w[u]) << std::endl;
       GRID_ASSERT (!isnan(norm2(w[u])));
-      for (int k=L+u; k<R; ++k) {
-	//        Glog <<" In block "<< b << "," <<" beta[" << u << "," << k-L << "] = " << lme[u][k] << std::endl;
-      }
+    }
+    // Diagnostic: print alpha (lmd) and beta (lme) block diagonals for this step
+    {
+      Glog << " blk b="<<std::setw(3)<<b<<"  alpha:";
+      for (int u=0; u<Nu; ++u)
+        std::cout << " " << std::setw(10) << std::setprecision(6) << real(lmd[u][L+u]);
+      std::cout << "   |beta|:";
+      for (int u=0; u<Nu; ++u)
+        std::cout << " " << std::setw(10) << std::setprecision(6) << abs(lme[u][L+u]);
+      std::cout << std::endl;
     }
     //    Glog << "LinAlg done "<< std::endl;
 

Grid/lattice/Lattice_slicesum_core.h

@@ -59,7 +59,7 @@ inline void sliceSumReduction_cub_small(const vobj *Data,
 #if defined(__CUDACC__) && (__CUDACC_VER_MAJOR__ >= 13)
   #define GRID_CUB_SUM_OP ::cuda::std::plus<>{}
 #else
-  #define GRID_CUB_SUM_OP ::cub::Sum()
+  #define GRID_CUB_SUM_OP ::gpucub::Sum()
 #endif
   
   gpuError_t gpuErr = gpucub::DeviceSegmentedReduce::Reduce(temp_storage_array, temp_storage_bytes, rb_p,d_out, rd, d_offsets, d_offsets+1, GRID_CUB_SUM_OP, zero_init, computeStream);

Grid/simd/Simd.h

@@ -113,6 +113,14 @@ accelerator_inline RealD    adj(const RealD  & r){ return r; }
 accelerator_inline ComplexD adj(const ComplexD& r){ return(conjugate(r)); }
 accelerator_inline ComplexF adj(const ComplexF& r ){ return(conjugate(r)); }
 
+#if defined(GRID_CUDA) || defined(GRID_HIP)
+//Provide for convenience
+accelerator_inline std::complex<double> conjugate(const std::complex<double>& r){ return(conj(r)); }
+accelerator_inline std::complex<float>  conjugate(const std::complex<float>& r) { return(conj(r)); }
+accelerator_inline std::complex<double> adj(const std::complex<double>& r)      { return(conj(r)); }
+accelerator_inline std::complex<float>  adj(const std::complex<float>& r)       { return(conj(r)); }
+#endif
+
 accelerator_inline RealF real(const RealF  & r){ return r; }
 accelerator_inline RealD real(const RealD  & r){ return r; }
 accelerator_inline RealF real(const ComplexF  & r){ return r.real(); }

benchmarks/Benchmark_staggered.cc

@@ -33,7 +33,6 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
 
 using namespace std;
 using namespace Grid;
- ;
 
 int main (int argc, char ** argv)
 {
@@ -97,19 +96,49 @@ int main (int argc, char ** argv)
   RealD c2=-1.0/24.0;
   RealD u0=1.0;
   ImprovedStaggeredFermionD Ds(Umu,Umu,Grid,RBGrid,mass,c1,c2,u0,params);
-  
-  std::cout<<GridLogMessage << "Calling Ds"<<std::endl;
+  NaiveStaggeredFermionD Dn(Umu,Grid,RBGrid,mass,c1,u0,params);
+
+  FermionField src_e(&RBGrid); pickCheckerboard(Even, src_e, src);
+  FermionField src_o(&RBGrid); pickCheckerboard(Odd,  src_o, src);
+  FermionField res_e(&RBGrid); res_e = Zero();
+
   int ncall=1000;
+
+  // ImprovedStaggered Dhop
+  for(int i=0;i<ncall;i++) Ds.Dhop(src,result,0);
   double t0=usecond();
-  for(int i=0;i<ncall;i++){
-    Ds.Dhop(src,result,0);
-  }
+  for(int i=0;i<ncall;i++) Ds.Dhop(src,result,0);
   double t1=usecond();
-  double flops=(16*(3*(6+8+8)) + 15*3*2)*volume*ncall; // == 66*16 +  == 1146
-  
-  std::cout<<GridLogMessage << "Called Ds"<<std::endl;
-  std::cout<<GridLogMessage << "norm result "<< norm2(result)<<std::endl;
-  std::cout<<GridLogMessage << "mflop/s =   "<< flops/(t1-t0)<<std::endl;
+  double flops=(16*(3*(6+8+8)) + 15*3*2)*volume*ncall; // 1146 flops/site
+  std::cout<<GridLogMessage << ncall << " ImprovedStaggered Dhop calls in "<< (t1-t0)<<" us"<<std::endl;
+  std::cout<<GridLogMessage << "ImprovedStaggered Dhop   mflop/s =   "<< flops/(t1-t0)<<std::endl;
+
+  // ImprovedStaggered DhopEO
+  for(int i=0;i<ncall;i++) Ds.DhopEO(src_o,res_e,0);
+  t0=usecond();
+  for(int i=0;i<ncall;i++) Ds.DhopEO(src_o,res_e,0);
+  t1=usecond();
+  flops=(16*(3*(6+8+8)) + 15*3*2)*(volume/2)*ncall;
+  std::cout<<GridLogMessage << ncall << " ImprovedStaggered DhopEO calls in "<< (t1-t0)<<" us"<<std::endl;
+  std::cout<<GridLogMessage << "ImprovedStaggered DhopEO mflop/s =   "<< flops/(t1-t0)<<std::endl;
+
+  // NaiveStaggered Dhop
+  for(int i=0;i<ncall;i++) Dn.Dhop(src,result,0);
+  t0=usecond();
+  for(int i=0;i<ncall;i++) Dn.Dhop(src,result,0);
+  t1=usecond();
+  flops=(8*(3*(6+8+8)) + 7*3*2)*volume*ncall;
+  std::cout<<GridLogMessage << ncall << " NaiveStaggered Dhop calls in "<< (t1-t0)<<" us"<<std::endl;
+  std::cout<<GridLogMessage << "NaiveStaggered    Dhop   mflop/s =   "<< flops/(t1-t0)<<std::endl;
+
+  // NaiveStaggered DhopEO
+  for(int i=0;i<ncall;i++) Dn.DhopEO(src_o,res_e,0);
+  t0=usecond();
+  for(int i=0;i<ncall;i++) Dn.DhopEO(src_o,res_e,0);
+  t1=usecond();
+  flops=(8*(3*(6+8+8)) + 7*3*2)*(volume/2)*ncall;
+  std::cout<<GridLogMessage << ncall << " NaiveStaggered DhopEO calls in "<< (t1-t0)<<" us"<<std::endl;
+  std::cout<<GridLogMessage << "NaiveStaggered    DhopEO mflop/s =   "<< flops/(t1-t0)<<std::endl;
 
   Grid_finalize();
 }

benchmarks/Benchmark_staggeredF.cc

@@ -96,22 +96,45 @@ int main (int argc, char ** argv)
   RealD c2=-1.0/24.0;
   RealD u0=1.0;
   ImprovedStaggeredFermionF Ds(Umu,Umu,Grid,RBGrid,mass,c1,c2,u0,params);
-  
-  std::cout<<GridLogMessage << "Calling Ds"<<std::endl;
-  int ncall=1000;
-  for(int i=0;i<ncall;i++){
-    Ds.Dhop(src,result,0);
-  }
+  NaiveStaggeredFermionF    Dn(Umu,Grid,RBGrid,mass,c1,u0,params);
+
+  FermionField src_e(&RBGrid); pickCheckerboard(Even, src_e, src);
+  FermionField src_o(&RBGrid); pickCheckerboard(Odd,  src_o, src);
+  FermionField res_e(&RBGrid); res_e = Zero();
+
+  int ncall=10000;
+
+  // ImprovedStaggered Dhop
+  for(int i=0;i<ncall;i++) Ds.Dhop(src,result,0);
   double t0=usecond();
-  for(int i=0;i<ncall;i++){
-    Ds.Dhop(src,result,0);
-  }
+  for(int i=0;i<ncall;i++) Ds.Dhop(src,result,0);
   double t1=usecond();
-  double flops=(16*(3*(6+8+8)) + 15*3*2)*volume*ncall; // == 66*16 +  == 1146
-  
-  std::cout<<GridLogMessage << "Called Ds"<<std::endl;
-  std::cout<<GridLogMessage << "norm result "<< norm2(result)<<std::endl;
-  std::cout<<GridLogMessage << "mflop/s =   "<< flops/(t1-t0)<<std::endl;
+  double flops=(16*(3*(6+8+8)) + 15*3*2)*volume*ncall; // 1146 flops/site
+  std::cout<<GridLogMessage << "ImprovedStaggered Dhop   mflop/s =   "<< flops/(t1-t0)<<std::endl;
+
+  // ImprovedStaggered DhopEO
+  for(int i=0;i<ncall;i++) Ds.DhopEO(src_o,res_e,0);
+  t0=usecond();
+  for(int i=0;i<ncall;i++) Ds.DhopEO(src_o,res_e,0);
+  t1=usecond();
+  flops=(16*(3*(6+8+8)) + 15*3*2)*(volume/2)*ncall;
+  std::cout<<GridLogMessage << "ImprovedStaggered DhopEO mflop/s =   "<< flops/(t1-t0)<<std::endl;
+
+  // NaiveStaggered Dhop
+  for(int i=0;i<ncall;i++) Dn.Dhop(src,result,0);
+  t0=usecond();
+  for(int i=0;i<ncall;i++) Dn.Dhop(src,result,0);
+  t1=usecond();
+  flops=(8*(3*(6+8+8)) + 7*3*2)*volume*ncall;
+  std::cout<<GridLogMessage << "NaiveStaggered    Dhop   mflop/s =   "<< flops/(t1-t0)<<std::endl;
+
+  // NaiveStaggered DhopEO
+  for(int i=0;i<ncall;i++) Dn.DhopEO(src_o,res_e,0);
+  t0=usecond();
+  for(int i=0;i<ncall;i++) Dn.DhopEO(src_o,res_e,0);
+  t1=usecond();
+  flops=(8*(3*(6+8+8)) + 7*3*2)*(volume/2)*ncall;
+  std::cout<<GridLogMessage << "NaiveStaggered    DhopEO mflop/s =   "<< flops/(t1-t0)<<std::endl;
 
   Grid_finalize();
 }

benchmarks/Benchmark_usqcd.cc

@@ -716,6 +716,161 @@ public:
     return mflops_best;
   }
 
+  static double NaiveStaggered(int L)
+  {
+    double mflops;
+    double mflops_best = 0;
+    double mflops_worst= 0;
+    std::vector<double> mflops_all;
+
+    ///////////////////////////////////////////////////////
+    // Set/Get the layout & grid size
+    ///////////////////////////////////////////////////////
+    int threads = GridThread::GetThreads();
+    Coordinate mpi = GridDefaultMpi(); GRID_ASSERT(mpi.size()==4);
+    Coordinate local({L,L,L,L});
+    Coordinate latt4({local[0]*mpi[0],local[1]*mpi[1],local[2]*mpi[2],local[3]*mpi[3]});
+    
+    GridCartesian         * TmpGrid   = SpaceTimeGrid::makeFourDimGrid(latt4,
+								       GridDefaultSimd(Nd,vComplex::Nsimd()),
+								       GridDefaultMpi());
+    uint64_t NP = TmpGrid->RankCount();
+    uint64_t NN = TmpGrid->NodeCount();
+    NN_global=NN;
+    uint64_t SHM=NP/NN;
+
+
+    ///////// Welcome message ////////////
+    std::cout<<GridLogMessage << "=================================================================================="<<std::endl;
+    std::cout<<GridLogMessage << "Benchmark NaiveStaggered on "<<L<<"^4 local volume "<<std::endl;
+    std::cout<<GridLogMessage << "* Global volume  : "<<GridCmdVectorIntToString(latt4)<<std::endl;
+    std::cout<<GridLogMessage << "* ranks          : "<<NP  <<std::endl;
+    std::cout<<GridLogMessage << "* nodes          : "<<NN  <<std::endl;
+    std::cout<<GridLogMessage << "* ranks/node     : "<<SHM <<std::endl;
+    std::cout<<GridLogMessage << "* ranks geom     : "<<GridCmdVectorIntToString(mpi)<<std::endl;
+    std::cout<<GridLogMessage << "* Using "<<threads<<" threads"<<std::endl;
+    std::cout<<GridLogMessage << "=================================================================================="<<std::endl;
+
+    ///////// Lattice Init ////////////
+    GridCartesian         * FGrid   = SpaceTimeGrid::makeFourDimGrid(latt4, GridDefaultSimd(Nd,vComplexF::Nsimd()),GridDefaultMpi());
+    GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(FGrid);
+    
+    ///////// RNG Init ////////////
+    std::vector<int> seeds4({1,2,3,4});
+    GridParallelRNG          RNG4(FGrid);  RNG4.SeedFixedIntegers(seeds4);
+    std::cout << GridLogMessage << "Initialised RNGs" << std::endl;
+
+    RealD mass=0.1;
+    RealD c1=9.0/8.0;
+    RealD c2=-1.0/24.0;
+    RealD u0=1.0;
+
+    typedef NaiveStaggeredFermionF Action;
+    typedef typename Action::FermionField Fermion; 
+    typedef LatticeGaugeFieldF Gauge;
+    
+    Gauge Umu(FGrid);  SU<Nc>::HotConfiguration(RNG4,Umu); 
+
+    typename Action::ImplParams params;
+    Action Ds(Umu,*FGrid,*FrbGrid,mass,c1,u0,params);
+
+    ///////// Source preparation ////////////
+    Fermion src   (FGrid); random(RNG4,src);
+    Fermion src_e (FrbGrid);
+    Fermion src_o (FrbGrid);
+    Fermion r_e   (FrbGrid);
+    Fermion r_o   (FrbGrid);
+    Fermion r_eo  (FGrid);
+  
+    {
+
+      pickCheckerboard(Even,src_e,src);
+      pickCheckerboard(Odd,src_o,src);
+    
+      const int num_cases = 2;
+      std::string fmt("G/S/C ; G/O/C ; G/S/S ; G/O/S ");
+      
+      controls Cases [] = {
+	{  StaggeredKernelsStatic::OptGeneric   ,  StaggeredKernelsStatic::CommsAndCompute  ,CartesianCommunicator::CommunicatorPolicyConcurrent  },
+	{  StaggeredKernelsStatic::OptHandUnroll,  StaggeredKernelsStatic::CommsAndCompute  ,CartesianCommunicator::CommunicatorPolicyConcurrent  },
+	{  StaggeredKernelsStatic::OptInlineAsm ,  StaggeredKernelsStatic::CommsAndCompute  ,CartesianCommunicator::CommunicatorPolicyConcurrent  }
+      }; 
+
+      for(int c=0;c<num_cases;c++) {
+	
+	StaggeredKernelsStatic::Comms = Cases[c].CommsOverlap;
+	StaggeredKernelsStatic::Opt   = Cases[c].Opt;
+	CartesianCommunicator::SetCommunicatorPolicy(Cases[c].CommsAsynch);
+      
+	std::cout<<GridLogMessage << "=================================================================================="<<std::endl;
+	if ( StaggeredKernelsStatic::Opt == StaggeredKernelsStatic::OptGeneric   ) std::cout << GridLogMessage<< "* Using GENERIC Nc StaggeredKernels" <<std::endl;
+	std::cout << GridLogMessage<< "* SINGLE precision "<<std::endl;
+	std::cout<<GridLogMessage << "=================================================================================="<<std::endl;
+	
+	int nwarm = 10;
+	double t0=usecond();
+	FGrid->Barrier();
+	for(int i=0;i<nwarm;i++){
+	  Ds.DhopEO(src_o,r_e,DaggerNo);
+	}
+	FGrid->Barrier();
+	double t1=usecond();
+
+	uint64_t no    = 50;
+	uint64_t ni    = 100;
+
+	//	std::cout << GridLogMessage << " Estimate " << ncall << " calls per second"<<std::endl;
+
+	time_statistics timestat;
+	std::vector<double> t_time(no);
+	for(uint64_t i=0;i<no;i++){
+	  t0=usecond();
+	  for(uint64_t j=0;j<ni;j++){
+	    Ds.DhopEO(src_o,r_e,DaggerNo);
+	  }
+	  t1=usecond();
+	  t_time[i] = t1-t0;
+	}
+	FGrid->Barrier();
+	
+	double volume=1;  for(int mu=0;mu<Nd;mu++) volume=volume*latt4[mu];
+	double flops=((8*(3*(6+8+8)) + 7*3*2)*1.0*volume)/2;
+	double mf_hi, mf_lo, mf_err;
+	
+	timestat.statistics(t_time);
+	mf_hi = flops/timestat.min*ni;
+	mf_lo = flops/timestat.max*ni;
+	mf_err= flops/timestat.min * timestat.err/timestat.mean;
+
+	mflops = flops/timestat.mean*ni;
+	mflops_all.push_back(mflops);
+	if ( mflops_best == 0   ) mflops_best = mflops;
+	if ( mflops_worst== 0   ) mflops_worst= mflops;
+	if ( mflops>mflops_best ) mflops_best = mflops;
+	if ( mflops<mflops_worst) mflops_worst= mflops;
+	
+	std::cout<<GridLogMessage << std::fixed << std::setprecision(1)<<"Deo mflop/s =   "<< mflops << " ("<<mf_err<<") " << mf_lo<<"-"<<mf_hi <<std::endl;
+	std::cout<<GridLogMessage << std::fixed << std::setprecision(1)<<"Deo mflop/s per rank   "<< mflops/NP<<std::endl;
+	std::cout<<GridLogMessage << std::fixed << std::setprecision(1)<<"Deo mflop/s per node   "<< mflops/NN<<std::endl;
+	std::cout<<GridLogMessage << std::fixed << std::setprecision(1)<<"Deo us per call   "<< timestat.mean/ni<<std::endl;
+      
+      }
+
+      std::cout<<GridLogMessage << "=================================================================================="<<std::endl;
+      std::cout<<GridLogMessage << L<<"^4  Deo Best  mflop/s        =   "<< mflops_best << " ; " << mflops_best/NN<<" per node " <<std::endl;
+      std::cout<<GridLogMessage << L<<"^4  Deo Worst mflop/s        =   "<< mflops_worst<< " ; " << mflops_worst/NN<<" per node " <<std::endl;
+      std::cout<<GridLogMessage <<fmt << std::endl;
+      std::cout<<GridLogMessage ;
+
+      for(int i=0;i<mflops_all.size();i++){
+	std::cout<<mflops_all[i]/NN<<" ; " ;
+      }
+      std::cout<<std::endl;
+    }
+    std::cout<<GridLogMessage << "=================================================================================="<<std::endl;
+    return mflops_best;
+  }
+  
   static double Clover(int L)
   {
     double mflops;
@@ -887,6 +1042,7 @@ int main (int argc, char ** argv)
   std::vector<double> clover;
   std::vector<double> dwf4;
   std::vector<double> staggered;
+  std::vector<double> naive_staggered;
 
   int Ls=1;
   if (do_dslash){
@@ -914,13 +1070,21 @@ int main (int argc, char ** argv)
     staggered.push_back(result);
   }
 
+  std::cout<<GridLogMessage << "=================================================================================="<<std::endl;
+  std::cout<<GridLogMessage << " Naive Staggered dslash 4D vectorised" <<std::endl;
+  std::cout<<GridLogMessage << "=================================================================================="<<std::endl;
+  for(int l=0;l<L_list.size();l++){
+    double result = Benchmark::NaiveStaggered(L_list[l]) ;
+    naive_staggered.push_back(result);
+  }
+
 
   std::cout<<GridLogMessage << "=================================================================================="<<std::endl;
   std::cout<<GridLogMessage << " Summary table Ls="<<Ls <<std::endl;
   std::cout<<GridLogMessage << "=================================================================================="<<std::endl;
-  std::cout<<GridLogMessage << "L \t\t Clover \t\t DWF4 \t\t Staggered" <<std::endl;
+  std::cout<<GridLogMessage << "L \t\t Clover \t\t DWF4 \t\t Staggered \t\t Naive Staggered" <<std::endl;
   for(int l=0;l<L_list.size();l++){
-    std::cout<<GridLogMessage << L_list[l] <<" \t\t "<< clover[l]<<" \t\t "<<dwf4[l] << " \t\t "<< staggered[l]<<std::endl;
+    std::cout<<GridLogMessage << L_list[l] <<" \t\t "<< clover[l]<<" \t\t "<<dwf4[l] << " \t\t "<< staggered[l]<<" \t\t "<<naive_staggered[l]<<std::endl;
   }
   std::cout<<GridLogMessage << "=================================================================================="<<std::endl;
   }
@@ -930,14 +1094,14 @@ int main (int argc, char ** argv)
     std::cout<<GridLogMessage << "=================================================================================="<<std::endl;
     std::cout<<GridLogMessage << " Per Node Summary table Ls="<<Ls <<std::endl;
     std::cout<<GridLogMessage << "=================================================================================="<<std::endl;
-    std::cout<<GridLogMessage << " L \t\t Clover\t\t DWF4\t\t Staggered (GF/s per node)" <<std::endl;
+    std::cout<<GridLogMessage << " L \t\t Clover\t\t DWF4\t\t Staggered \t\t NaiveStag \t|\t (GF/s per node)" <<std::endl;
     fprintf(FP,"Per node summary table\n");
     fprintf(FP,"\n");
-    fprintf(FP,"L , Wilson, DWF4, Staggered, GF/s per node\n");
+    fprintf(FP,"L , Wilson, DWF4, Staggered, NaiveStag\n");
     fprintf(FP,"\n");
     for(int l=0;l<L_list.size();l++){
-      std::cout<<GridLogMessage << L_list[l] <<" \t\t "<< clover[l]/NN<<" \t "<<dwf4[l]/NN<< " \t "<<staggered[l]/NN<<std::endl;
-      fprintf(FP,"%d , %.0f, %.0f, %.0f\n",L_list[l],clover[l]/NN/1000.,dwf4[l]/NN/1000.,staggered[l]/NN/1000.);
+      std::cout<<GridLogMessage << L_list[l] <<" \t\t "<< clover[l]/NN<<" \t "<<dwf4[l]/NN<< " \t "<<staggered[l]/NN<<" \t " <<naive_staggered[l]/NN<<std::endl;
+      fprintf(FP,"%d , %.0f, %.0f, %.0f, %.0f\n",L_list[l],clover[l]/NN/1000.,dwf4[l]/NN/1000.,staggered[l]/NN/1000.,naive_staggered[l]/NN/1000.);
     }
     fprintf(FP,"\n");
     std::cout<<GridLogMessage << "=================================================================================="<<std::endl;

skills/ref_a2a_emf_work.md

@@ -1,61 +0,0 @@
----
-name: ref_a2a_emf_work
-description: "A2A Extended Meson Field GPU offload work — status, file locations, pending task"
-metadata: 
-  node_type: memory
-  type: project
-  originSessionId: 956e80aa-401d-481a-80bb-17f8abe1c131
----
-
-## What was built
-
-`Grid/algorithms/blas/A2ASpatialSum.h` — batched GEMM spatial sum replacing scalar SIMD accumulation. Included via `Grid/algorithms/Algorithms.h`.
-
-`tests/Test_extended_meson_field.cc` — test with class `A2AExtendedMesonFieldRef` containing:
-- CPU reference path (`use_blas=false`)
-- BLAS path (`use_blas=true`) using `A2ASpatialSum`
-- Per-phase timing with `[ref type=N]` / `[blas type=N]` labels
-- 4 contraction types (0-3), all verified at machine precision (~4e-16 rel_err)
-
-## Pending task: GPU offload class
-
-**Goal**: Write `A2AExtendedMesonFieldGPU` in the same test file, replacing all `thread_for` loops with `accelerator_for`-based free function kernels.
-
-The `thread_for` blocks to replace all have the form:
-```cpp
-thread_for(r, rd, {
-  int so = r * grid->_ostride[orthogdim];
-  for (int n = 0; n < e1; n++)
-  for (int b = 0; b < e2; b++) {
-    int ss = so + n * stride + b;
-    // work
-  }
-});
-```
-Replace with `accelerator_for(ss, grid->oSites(), Nsimd, { ... })`.
-
-**Free functions to write** (each takes `Lattice<T>` args, opens views internally):
-- `A2ALoopPropagator` — outerProduct sum (loop build)
-- `A2APackLeftConjugated` — conjugate left fermion fields into `Lattice<SpinColourVector_v>`
-- `A2ALoopLeftContractionType0/1/2/3` — per-site loop × loop propagator → `tloop`
-- `A2ALoopRightContractionType0/1/2/3` — per-site tloop × right → `loopRight[j]`
-
-**Data structure changes required**:
-- `tloopv`: `std::vector<SpinColourMatrix_v>` → `Lattice<SpinColourMatrix_v>` (PropagatorField)
-- `leftv[i]`: `std::vector<SpinColourVector_v>` → `Lattice<SpinColourVector_v>`
-- `loopRight[j]`: `std::vector<SpinColourVector_v>` → `Lattice<SpinColourVector_v>`
-
-**Why**: `std::vector<vobj>` is host memory, not GPU accessible. See [[ref_lattice_vs_vector]].
-
-**`A2ASpatialSum` impact**: `PackLeft`/`PackRight` currently take `std::vector<std::vector<vobj>>`. Once leftv/loopRight become `std::vector<Lattice<vobj>>`, those signatures must change to match.
-
-## Timing on 8.8.8.16 (N_i=N_j=8, Nloop=4, 1 MPI rank)
-
-Dominant costs:
-- `loop_build`: 4-6 ms (outerProduct over 4 propagators)
-- `pack_loopright`: 0.9-2.2 ms (type-dependent)
-- `spatial_sum` (ref): ~1.5 ms
-- `A2ASpatialSum TOTAL`: 2.5-4.3 ms (PackLeft+PackRight dominate GEMM on small volume)
-
-## Related
-[[ref_accelerator_for]] [[ref_coalesced_views]] [[ref_lattice_vs_vector]] [[ref_grid_simt_pattern]]

skills/ref_accelerator_for.md

@@ -1,43 +0,0 @@
----
-name: ref_accelerator_for
-description: Grid accelerator_for usage — converting block-strided thread_for to GPU-portable oSites loops
-metadata: 
-  node_type: memory
-  type: reference
-  originSessionId: 956e80aa-401d-481a-80bb-17f8abe1c131
----
-
-## Pattern: block-strided thread_for → accelerator_for over oSites
-
-Old CPU-only pattern (block-strided over orthog dimension):
-```cpp
-thread_for(r, rd, {
-  int so = r * grid->_ostride[orthogdim];
-  for (int n = 0; n < e1; n++)
-  for (int b = 0; b < e2; b++) {
-    int ss = so + n * stride + b;
-    // work on site ss
-  }
-});
-```
-
-GPU-portable replacement:
-```cpp
-accelerator_for(ss, grid->oSites(), Nsimd, {
-  // work on site ss — one SIMT thread per (osite, lane) on GPU
-  // one thread per osite (lane loop implicit via GRID_SIMT) on CPU
-});
-```
-
-Key rules:
-- `accelerator_for(iter, count, Nsimd, body)` — Nsimd is `vobj::Nsimd()` or `grid->Nsimd()`
-- On CPU: expands to `thread_for` over count, `acceleratorSIMTlane` always returns 0 — must use `#ifdef GRID_SIMT` pattern if iterating lanes explicitly (see [[ref_grid_simt_pattern]])
-- On GPU: one SIMT thread per (iter × lane), `acceleratorSIMTlane(Nsimd)` returns actual lane
-- Loop body must capture only scalar/POD by value or via device-accessible pointers; no `std::vector` or host containers inside the body
-- `Coordinate` inside `accelerator_for` must be `AcceleratorVector<int, MaxDims>` (stack-allocated, device-safe) — Grid's `Coordinate` typedef already satisfies this
-
-## Where defined
-`Grid/threads/Accelerator.h` — CPU path ~line 607; GPU paths in conditional blocks above.
-
-## Model file
-`Grid/algorithms/blas/MomentumProject.h` — `ImportVector` is the canonical example of correct `accelerator_for` + SIMD lane extraction.

skills/ref_coalesced_views.md

@@ -1,70 +0,0 @@
----
-name: ref_coalesced_views
-description: Grid coalescedRead/coalescedWrite and autoView — GPU-portable field access inside accelerator_for
-metadata: 
-  node_type: memory
-  type: reference
-  originSessionId: 956e80aa-401d-481a-80bb-17f8abe1c131
----
-
-## View access modes
-
-```cpp
-autoView(v, field, AcceleratorRead);   // read-only, device-accessible
-autoView(v, field, AcceleratorWrite);  // write-only, device-accessible
-autoView(v, field, AcceleratorReadWrite); // read-write, device-accessible
-autoView(v, field, CpuRead);           // CPU only (avoids GPU migration)
-autoView(v, field, CpuWrite);          // CPU only
-```
-
-Views must be opened **before** `accelerator_for` and closed (go out of scope) **after**. Never open a view inside the accelerator_for body.
-
-## coalescedRead / coalescedWrite
-
-Inside `accelerator_for(ss, oSites, Nsimd, { ... })`:
-
-```cpp
-auto site = coalescedRead(v[ss]);          // reads SIMT lane; returns scalar_object on GPU, vobj on CPU
-coalescedWrite(v[ss], site);               // writes SIMT lane
-```
-
-- `coalescedRead(v[ss])` calls `v.operator()(ss)` which on GPU returns `extractLane(lane, v[ss])` — one lane per SIMT thread, contiguous across threads → coalesced
-- On CPU returns the full vobj (no lane extraction needed; handled transparently)
-- The returned type is `decltype(coalescedRead(v[ss]))` — use `auto` or match with scalar_object
-
-## Typical kernel pattern
-
-```cpp
-autoView(out_v, out, AcceleratorWrite);
-autoView(in_v,  in,  AcceleratorRead);
-accelerator_for(ss, grid->oSites(), vobj::Nsimd(), {
-  auto x = coalescedRead(in_v[ss]);
-  // modify x ...
-  coalescedWrite(out_v[ss], x);
-});
-```
-
-## Free function kernel signature
-
-```cpp
-template<class vobj>
-void MyKernel(Lattice<vobj> &out, const Lattice<vobj> &in)
-{
-  GridBase *grid = in.Grid();
-  autoView(out_v, out, AcceleratorWrite);
-  autoView(in_v,  in,  AcceleratorRead);
-  accelerator_for(ss, grid->oSites(), vobj::Nsimd(), {
-    auto x = coalescedRead(in_v[ss]);
-    coalescedWrite(out_v[ss], x);
-  });
-}
-```
-
-## What NOT to do
-- Do not access `std::vector` elements inside `accelerator_for` — not device-accessible
-- Do not use `CpuRead`/`CpuWrite` views inside `accelerator_for` — GPU will fault
-- Do not assign to `v[ss]` directly inside `accelerator_for` — use `coalescedWrite`
-- Do not open multiple write views on the same field simultaneously
-
-## Related
-[[ref_accelerator_for]] [[ref_lattice_vs_vector]]

skills/ref_grid_simt_pattern.md

@@ -1,47 +0,0 @@
----
-name: ref_grid_simt_pattern
-description: Grid GRID_SIMT
-metadata: 
-  node_type: memory
-  type: reference
-  originSessionId: 956e80aa-401d-481a-80bb-17f8abe1c131
----
-
-## The problem
-
-On CPU, `accelerator_for(sf, oSites, Nsimd, {...})` expands to `thread_for(sf, oSites, {...})` — one thread per osite. `acceleratorSIMTlane(Nsimd)` always returns **0** on CPU. If you need to iterate all Nsimd lanes (e.g. to extract SIMD-packed data), you must loop explicitly on CPU.
-
-On GPU, `accelerator_for` launches one SIMT thread per (osite × lane). `acceleratorSIMTlane(Nsimd)` returns the actual lane index [0, Nsimd).
-
-## Correct pattern (from MomentumProject::ImportVector)
-
-```cpp
-accelerator_for(sf, osites, Nsimd, {
-#ifdef GRID_SIMT
-  {
-    int lane = acceleratorSIMTlane(Nsimd);
-#else
-    for (int lane = 0; lane < Nsimd; lane++) {
-#endif
-      // body using lane
-    }
-  });
-```
-
-- On GPU: `GRID_SIMT` is defined → single-lane body, lane from hardware
-- On CPU: `GRID_SIMT` is not defined → explicit lane loop inside the osite thread
-
-## When is this needed?
-
-Only when you explicitly need the lane index, e.g.:
-- Extracting scalar data from SIMD-packed `vobj` via `extractLane(lane, src[sf])`
-- Computing full local coordinates from (osite, lane) → `Lexicographic::CoorFromIndex(icoor, lane, simd_layout)`
-
-When using `coalescedRead`/`coalescedWrite`, this pattern is **not needed** — those handle lane selection transparently.
-
-## Pitfall that caused a bug
-
-`A2ASpatialSum::PackVectors` originally used `accelerator_for` without the `#ifdef GRID_SIMT` lane loop. On CPU, only lane=0 was extracted, giving wrong norms (~8× too small for `GEN_SIMD_WIDTH=64`, `Nsimd=4`). Fix: add the `#ifdef GRID_SIMT` pattern. See [[ref_accelerator_for]].
-
-## Model file
-`Grid/algorithms/blas/MomentumProject.h`, function `ImportVector`, lines ~166-207.

skills/ref_lattice_vs_vector.md

@@ -1,48 +0,0 @@
----
-name: ref_lattice_vs_vector
-description: When to use Lattice<T> vs std::vector<T> for GPU-portable field storage in Grid
-metadata: 
-  node_type: memory
-  type: reference
-  originSessionId: 956e80aa-401d-481a-80bb-17f8abe1c131
----
-
-## Rule
-
-Use `Lattice<vobj>` (or `std::vector<Lattice<vobj>>`) for any field that will be read or written inside `accelerator_for`. `std::vector<vobj>` is host memory and is NOT device-accessible.
-
-## Before vs after GPU offload
-
-```cpp
-// CPU-only (host memory, not GPU accessible)
-std::vector<SpinColourVector_v> tloopv(oSites, Zero());
-// accessed directly: tloopv[ss]
-
-// GPU-portable
-Lattice<SpinColourVector_v> tloop(grid);
-// accessed via view: autoView(tloop_v, tloop, AcceleratorWrite);
-//                    coalescedWrite(tloop_v[ss], val);
-```
-
-## Corollary: function signatures
-
-CPU-only version:
-```cpp
-void PackLeft(const std::vector<std::vector<vobj>> &leftv);
-```
-
-GPU-portable version:
-```cpp
-void PackLeft(const std::vector<Lattice<vobj>> &leftv);
-```
-
-## deviceVector for raw device buffers
-
-`deviceVector<T>` (defined in Grid) is like `std::vector<T>` but in device-accessible memory. Use for raw scalar scratch/pack buffers (e.g. GEMM input/output staging). Not for structured lattice data.
-
-## Pointer arrays for batched BLAS
-
-`deviceVector<scalar *>` holds batch pointer arrays. Populate with `acceleratorPut(ptrs[t], base + offset)` — sets device-side pointer from host. See `A2ASpatialSum::Allocate`.
-
-## Related
-[[ref_coalesced_views]] [[ref_accelerator_for]]

systems/Frontier/benchmarks/Benchmark_usqcd.csv

@@ -1,76 +1,91 @@
+Per node summary table
+
+L , Wilson, DWF4, Staggered, NaiveStag
+
+8 , 90, 933, 38, 23
+12 , 403, 1688, 178, 113
+16 , 188, 1647, 449, 295
+24 , 947, 1574, 674, 553
+32 , 931, 1371, 718, 643
+
 Memory Bandwidth
 
 Bytes, GB/s per node
-6291456, 379.297050
-100663296, 3754.674992
-509607936, 6521.472413
-1610612736, 8513.456479
-3932160000, 9018.901766
-
-
-GEMM
-
- M, N, K, BATCH, GF/s per rank
-16, 8, 16, 256, 0.564958
-16, 16, 16, 256, 243.148058
-16, 32, 16, 256, 440.346877
-32, 8, 32, 256, 439.194136
-32, 16, 32, 256, 847.334141
-32, 32, 32, 256, 1430.892623
-64, 8, 64, 256, 1242.756741
-64, 16, 64, 256, 2196.689493
-64, 32, 64, 256, 3697.458072
-16, 8, 256, 256, 899.582627
-16, 16, 256, 256, 1673.537756
-16, 32, 256, 256, 2959.597089
-32, 8, 256, 256, 1558.858630
-32, 16, 256, 256, 2864.839445
-32, 32, 256, 256, 4810.671254
-64, 8, 256, 256, 2386.092942
-64, 16, 256, 256, 4451.665937
-64, 32, 256, 256, 5942.124095
-8, 256, 16, 256, 799.867271
-16, 256, 16, 256, 1584.624888
-32, 256, 16, 256, 1949.422338
-8, 256, 32, 256, 1389.417474
-16, 256, 32, 256, 2668.344493
-32, 256, 32, 256, 3234.162120
-8, 256, 64, 256, 2150.925128
-16, 256, 64, 256, 4012.488132
-32, 256, 64, 256, 5154.785521
-
+786432, 40.271620
+12582912, 433.611792
+63700992, 905.374321
+201326592, 1114.979152
+491520000, 1180.241898
 
 
 Communications
 
 Packet bytes, direction, GB/s per node
-4718592, 1, 245.026198
-4718592, 2, 251.180996
-4718592, 3, 361.110977
-4718592, 5, 247.898447
-4718592, 6, 249.867523
-4718592, 7, 359.033061
-15925248, 1, 255.030946
-15925248, 2, 264.453890
-15925248, 3, 392.949183
-15925248, 5, 256.040644
-15925248, 6, 264.681896
-15925248, 7, 392.102622
-37748736, 1, 258.823333
-37748736, 2, 268.181577
-37748736, 3, 401.478191
-37748736, 5, 258.995363
-37748736, 6, 268.206586
-37748736, 7, 400.397611
 
 
-Per node summary table
+GEMM
+
+ M, N, K, BATCH, GF/s per rank fp64
+16, 8, 16, 4096, 693.316363
+16, 12, 16, 4096, 657.277058
+16, 16, 16, 4096, 711.992616
+32, 8, 32, 4096, 821.084324
+32, 12, 32, 4096, 1279.852719
+32, 16, 32, 4096, 2647.096674
+64, 8, 64, 4096, 2630.192325
+64, 12, 64, 4096, 3338.071321
+64, 16, 64, 4096, 3950.899281
+16, 8, 256, 4096, 1638.362501
+16, 12, 256, 4096, 2377.502234
+16, 16, 256, 4096, 3048.328833
+32, 8, 256, 4096, 2917.384276
+32, 12, 256, 4096, 4103.085151
+32, 16, 256, 4096, 5102.971860
+64, 8, 256, 4096, 3222.258206
+64, 12, 256, 4096, 4619.456391
+64, 16, 256, 4096, 5847.916650
+8, 256, 16, 4096, 1728.073337
+12, 256, 16, 4096, 2356.653970
+16, 256, 16, 4096, 2676.876038
+8, 256, 32, 4096, 2611.531990
+12, 256, 32, 4096, 3451.573106
+16, 256, 32, 4096, 3966.915301
+8, 256, 64, 4096, 3436.248737
+12, 256, 64, 4096, 4539.497945
+16, 256, 64, 4096, 5307.992323
+
+
+
+GEMM
+
+ M, N, K, BATCH, GF/s per rank fp32
+16, 8, 16, 4096, 499.017445
+16, 12, 16, 4096, 731.543385
+16, 16, 16, 4096, 958.800786
+32, 8, 32, 4096, 1549.813550
+32, 12, 32, 4096, 2147.907502
+32, 16, 32, 4096, 2601.698596
+64, 8, 64, 4096, 3785.446233
+64, 12, 64, 4096, 5116.694843
+64, 16, 64, 4096, 6109.345016
+16, 8, 256, 4096, 1206.627737
+16, 12, 256, 4096, 1809.699599
+16, 16, 256, 4096, 2412.014053
+32, 8, 256, 4096, 2406.114488
+32, 12, 256, 4096, 3605.531907
+32, 16, 256, 4096, 4798.444037
+64, 8, 256, 4096, 4688.711196
+64, 12, 256, 4096, 6990.696301
+64, 16, 256, 4096, 9214.749925
+8, 256, 16, 4096, 2596.307289
+12, 256, 16, 4096, 3439.892562
+16, 256, 16, 4096, 3907.201036
+8, 256, 32, 4096, 3012.752067
+12, 256, 32, 4096, 3904.217583
+16, 256, 32, 4096, 4599.047092
+8, 256, 64, 4096, 3721.999042
+12, 256, 64, 4096, 5098.573927
+16, 256, 64, 4096, 6159.080872
 
-L , Wilson, DWF4, Staggered, GF/s per node
 
-8 , 155, 1386, 50
-12 , 694, 4208, 230
-16 , 1841, 6675, 609
-24 , 3934, 8573, 1641
-32 , 5083, 9771, 3086
 

systems/Frontier/config-command

@@ -1,4 +1,3 @@
-CLIME=`spack find --paths c-lime@2-3-9 | grep c-lime| cut -c 15-`
 ../../configure --enable-comms=mpi-auto \
 --with-lime=$CLIME \
 --enable-unified=no \
@@ -9,12 +8,13 @@ CLIME=`spack find --paths c-lime@2-3-9 | grep c-lime| cut -c 15-`
 --disable-gparity \
 --disable-fermion-reps \
 --enable-simd=GPU \
---with-gmp=$OLCF_GMP_ROOT \
---with-mpfr=/opt/cray/pe/gcc/mpfr/3.1.4/ \
+--with-gmp=$GMP \
+--with-mpfr=$MPFR \
+--with-openssl=$OPENSSL \
 --disable-fermion-reps \
 CXX=hipcc MPICXX=mpicxx \
-CXXFLAGS="-fPIC -I${ROCM_PATH}/include/ -I${MPICH_DIR}/include -L/lib64 " \
- LDFLAGS="-L/lib64 -L${ROCM_PATH}/lib -L${MPICH_DIR}/lib -lmpi -L${CRAY_MPICH_ROOTDIR}/gtl/lib -lmpi_gtl_hsa -lhipblas -lrocblas -lhipfft"
+CXXFLAGS="-fPIC -I${ROCM_PATH}/include/ -I${MPICH_DIR}/include " \
+ LDFLAGS="-L${ROCM_PATH}/lib -L${MPICH_DIR}/lib -lmpi -lmpi_gtl_hsa -lhipblas -lrocblas -lhipfft -lamdhip64"
 
 
 

systems/Frontier/sourceme.sh

@@ -1,16 +1,14 @@
 
 echo spack
-. /autofs/nccs-svm1_home1/paboyle/Crusher/Grid/spack/share/spack/setup-env.sh
+. /autofs/nccs-svm1_home1/paboyle/spack/share/spack/setup-env.sh
 
-module load amd/7.0.2
-module load cray-fftw
-module load craype-accel-amd-gfx90a
-mkdir $HOME/LD_PATH
-ln -s /opt/rocm-6.4.2/lib/libamdhip* $HOME/LD_PATH
+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 OPENSSL=`spack find --paths openssl | grep openssl | awk  '{print $2}' `
+export GMP=`spack find --paths gmp      | grep ^gmp | awk '{print $2}' `
 
-#Ugly hacks to get down level software working on current system
-export LD_LIBRARY_PATH=/opt/cray/libfabric/1.20.1/lib64/:$LD_LIBRARY_PATH
-export LD_LIBRARY_PATH=/opt/gcc/mpfr/3.1.4/lib:$LD_LIBRARY_PATH
-#export LD_LIBRARY_PATH=`pwd`/:$LD_LIBRARY_PATH
-export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$HOME/LD_PATH/
-export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/opt/rocm-7.0.2/lib
+module load cce/21.0.0
+module load cpe/26.03
+module load rocm/7.0.2
+export LD_LIBRARY_PATH=$CRAY_LD_LIBRARY_PATH:$LD_LIBRARY_PATH
+export LD_LIBRARY_PATH=/opt/rocm-7.0.2/lib/llvm/lib/:$LD_LIBRARY_PATH

systems/Perlmutter/config-command

@@ -1,12 +1,12 @@
 DIR=`pwd`
-PREFIX=$HOME/DDHMC/Grid/systems/Prerequisites/install/
+
 ../../configure \
     --enable-comms=mpi \
     --enable-simd=GPU \
     --enable-shm=nvlink \
     --enable-gen-simd-width=64 \
-    --with-gmp=$PREFIX \
-    --with-mpfr=$PREFIX \
+    --with-gmp=$GMP \
+    --with-mpfr=$MPFR \
     --enable-accelerator=cuda \
     --disable-fermion-reps \
     --disable-unified \

systems/Perlmutter/sourceme.sh

@@ -1,4 +1,6 @@
-
 export CRAY_ACCEL_TARGET=nvidia80
+source /global/homes/p/pboyle/spack/share/spack/setup-env.sh
+export MPFR=`spack find --paths mpfr | grep mpfr | cut -c 13-`
+export GMP=`spack find --paths gmp   | grep gmp  | cut -c 12-`
 
-module load PrgEnv-gnu cpe-cuda cudatoolkit/11.4
+module load PrgEnv-gnu cpe-cuda cudatoolkit/12.0

systems/mac-arm/config-command-homebrew

@@ -0,0 +1,20 @@
+#!/usr/bin/env bash
+# Configure Grid from a build directory two levels below the source root,
+# e.g.: mkdir -p systems/mac-arm/build && cd systems/mac-arm/build && bash ../config-command-homebrew
+#
+# Prerequisites: source sourceme-homebrew.sh first.
+
+CXX=mpicxx ../../configure \
+    --enable-simd=GEN \
+    --enable-comms=mpi-auto \
+    --enable-unified=yes \
+    --prefix="${HOME}/Grid-install" \
+    --with-lime="${CLIME}" \
+    --with-openssl="${OPENSSL}" \
+    --with-gmp="${GMP}" \
+    --with-mpfr="${MPFR}" \
+    --with-fftw="${FFTW}" \
+    --enable-Sp=no \
+    --disable-fermion-reps \
+    --disable-gparity \
+    --disable-debug

systems/mac-arm/config-command-mpi

@@ -3,14 +3,15 @@
 CXX=mpicxx ../../configure \
 	   --enable-simd=GEN \
 	   --enable-comms=mpi-auto \
-	   --enable-unified=yes \
+	   --enable-Sp=no \
 	   --disable-fermion-reps \
 	   --disable-gparity \
-	   --prefix /Users/peterboyle/QCD/Grid-install \
+	   --with-fftw=$FFTW \
+	   --enable-unified=yes \
+	   --prefix /Users/peterboyle/QCD/vtk/Grid/install \
 	   --with-lime=$CLIME \
 	   --with-openssl=$OPENSSL \
 	   --with-gmp=$GMP \
 	   --with-mpfr=$MPFR \
-	   --with-fftw=$FFTW \
-	   --disable-debug
+	   --disable-debug 
 

systems/mac-arm/sourceme-homebrew.sh

@@ -0,0 +1,15 @@
+#!/usr/bin/env bash
+# Environment for building Grid on Apple Silicon Mac with Homebrew dependencies.
+# Usage: source systems/mac-arm/sourceme-homebrew.sh
+
+HOMEBREW=/opt/homebrew
+
+export GMP=${HOMEBREW}/opt/gmp
+export MPFR=${HOMEBREW}/opt/mpfr
+export FFTW=${HOMEBREW}/opt/fftw
+export OPENSSL=${HOMEBREW}/opt/openssl@3
+export CLIME=/usr/local
+
+export PATH="${HOMEBREW}/opt/open-mpi/bin:${HOMEBREW}/bin:${PATH}"
+export LDFLAGS="-L${OPENSSL}/lib"
+export CPPFLAGS="-I${OPENSSL}/include"

systems/mac-arm/sourceme.sh

@@ -1,4 +1,5 @@
 source /Users/peterboyle/QCD//Spack/spack//share/spack/setup-env.sh
+
 export FFTW=`spack find --paths fftw    | grep ^fftw   | awk '{print $2}' `
 #export HDF5=`spack find --paths hdf5+cxx   | grep ^hdf5   | awk '{print $2}' `
 export CLIME=`spack find --paths c-lime | grep ^c-lime | awk '{print $2}' `
@@ -8,4 +9,3 @@ export GMP=`spack find --paths gmp      | grep ^gmp | awk '{print $2}' `
 
 export LD_LIBRARY_PATH=$MPFR/lib:$LD_LIBRARY_PATH
 export LD_LIBRARY_PATH=$GMP/lib:$LD_LIBRARY_PATH
-

tests/Test_extended_meson_field.cc

@@ -1,790 +0,0 @@
-/*************************************************************************************
-
-Grid physics library, www.github.com/paboyle/Grid
-
-Source file: tests/Test_extended_meson_field.cc
-
-Copyright (C) 2015-2025
-
-Author: Peter Boyle <pboyle@bnl.gov>
-Author: Masaaki Tomii <masaaki.tomii@uconn.edu> (original Hadrons kernels)
-
-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
-*************************************************************************************/
-#include "disable_tests_without_instantiations.h"
-#ifdef ENABLE_FERMION_INSTANTIATIONS
-
-#include <Grid/Grid.h>
-#include <Grid/qcd/utils/A2Autils.h>
-
-using namespace Grid;
-
-typedef WilsonImplD FImpl;
-typedef typename FImpl::FermionField FermionField;
-typedef typename FImpl::SiteSpinor   vobj;
-typedef typename vobj::scalar_type   scalar_type;
-typedef typename vobj::vector_type   vector_type;
-typedef iSpinColourMatrix<vector_type> SpinColourMatrix_v;
-typedef iSpinColourVector<vector_type> SpinColourVector_v;
-typedef iSpinMatrix<vector_type>       SpinMatrix_v;
-typedef iSinglet<vector_type>          Scalar_v;
-typedef iSinglet<scalar_type>          Scalar_s;
-typedef Lattice<SpinColourMatrix_v>    PropagatorField;
-
-// CPU reference + optionally batched GEMM spatial sum, ported from
-// Hadrons/Modules/MContraction/A2AExtendedMesonField.hpp
-// (M. Tomii, mtomii/Hadrons:local-2025-edits). Hadrons infrastructure removed.
-// thread_for / CpuRead / orthogdim=3 preserved.
-class A2AExtendedMesonFieldRef
-{
-public:
-  // result is indexed [nt][N_i][N_j].
-  // use_blas=true replaces the scalar spatial accumulation with A2ASpatialSum.
-  static void compute(
-      Eigen::Tensor<ComplexD, 3> &result,
-      const std::vector<FermionField> &left,
-      const std::vector<FermionField> &right,
-      const std::vector<FermionField> &loop1,
-      const std::vector<FermionField> &loop2,
-      const std::vector<Gamma::Algebra> &gamma1,
-      const std::vector<Gamma::Algebra> &gamma2,
-      int type,
-      bool use_blas = false)
-  {
-    GridBase *grid = left[0].Grid();
-
-    const int orthogdim = 3;
-    int rd     = grid->_rdimensions[orthogdim];
-    int ld     = grid->_ldimensions[orthogdim];
-    int Nd     = grid->_ndimension;
-    int Nsimd  = grid->Nsimd();
-
-    int nt  = result.dimension(0);
-    int N_i = (int)left.size();
-    int N_j = (int)right.size();
-
-    std::string tag = std::string(use_blas ? "[blas" : "[ref ") + " type=" + std::to_string(type) + "]";
-    auto Tms = [](double us) { return us * 1e-3; };
-    double t0;
-
-    // ------------------------------------------------------------------
-    // Loop propagator: sum_k outerProduct(loop1[k], loop2[k])
-    // ------------------------------------------------------------------
-    t0 = usecond();
-    PropagatorField loop(grid);
-    loop = Zero();
-    for (unsigned int k = 0; k < loop1.size(); ++k)
-      loop += outerProduct(loop1[k], loop2[k]);
-    std::cout << GridLogMessage << tag << " loop_build:      " << Tms(usecond()-t0) << " ms\n";
-
-    // ------------------------------------------------------------------
-    // Pack conjugated left vectors
-    // ------------------------------------------------------------------
-    t0 = usecond();
-    std::vector<FermionField> leftv(N_i, grid);
-    for (int i = 0; i < N_i; i++)
-      leftv[i] = conjugate(left[i]);
-    std::cout << GridLogMessage << tag << " pack_left:       " << Tms(usecond()-t0) << " ms\n";
-
-    // ------------------------------------------------------------------
-    // Per-site loop contraction into PropagatorField tloop (type-dependent)
-    // ------------------------------------------------------------------
-    t0 = usecond();
-    PropagatorField tloop(grid);
-    tloop = Zero();
-    {
-      autoView(tloopv, tloop, CpuWrite);
-      autoView(loopv,  loop,  CpuRead);
-      if (type == 0) {
-        thread_for(ss, grid->oSites(), {
-          for (int s1 = 0; s1 < Ns; ++s1)
-          for (int s2 = 0; s2 < Ns; ++s2)
-            tloopv[ss]()(s1,s2)(0,0) = loopv[ss]()(s1,s2)(0,0)
-                                     + loopv[ss]()(s1,s2)(1,1)
-                                     + loopv[ss]()(s1,s2)(2,2);
-        });
-      }
-      if (type == 1) {
-        thread_for(ss, grid->oSites(), {
-          tloopv[ss] = Zero();
-          for (int mu = 0; mu < (int)gamma1.size(); ++mu)
-            tloopv[ss] = tloopv[ss] + Gamma(gamma1[mu]) * loopv[ss] * Gamma(gamma2[mu]);
-        });
-      }
-      if (type == 2) {
-        thread_for(ss, grid->oSites(), {
-          tloopv[ss] = Zero();
-          for (int mu = 0; mu < (int)gamma2.size(); ++mu) {
-            SpinColourMatrix_v tmp = Gamma(gamma2[mu]) * loopv[ss];
-            int s1 = mu / Ns;
-            int s2 = mu % Ns;
-            for (int c1 = 0; c1 < Nc; ++c1)
-            for (int c2 = 0; c2 < Nc; ++c2)
-              tloopv[ss]()(s1,s2)(c1,c2) = tmp()(0,0)(c1,c2) + tmp()(1,1)(c1,c2)
-                                          + tmp()(2,2)(c1,c2) + tmp()(3,3)(c1,c2);
-          }
-        });
-      }
-      if (type == 3) {
-        thread_for(ss, grid->oSites(), {
-          SpinMatrix_v spinLoop = Zero();
-          for (int s1 = 0; s1 < Ns; ++s1)
-          for (int s2 = 0; s2 < Ns; ++s2)
-            spinLoop()(s1,s2)() = loopv[ss]()(s1,s2)(0,0)
-                                + loopv[ss]()(s1,s2)(1,1)
-                                + loopv[ss]()(s1,s2)(2,2);
-          tloopv[ss] = Zero();
-          for (int mu = 0; mu < (int)gamma1.size(); ++mu) {
-            SpinMatrix_v tmp2 = Gamma(gamma1[mu]) * spinLoop * Gamma(gamma2[mu]);
-            for (int s1 = 0; s1 < Ns; ++s1)
-            for (int s2 = 0; s2 < Ns; ++s2)
-              tloopv[ss]()(s1,s2)(0,0) = tloopv[ss]()(s1,s2)(0,0) + tmp2()(s1,s2)();
-          }
-        });
-      }
-    }
-    std::cout << GridLogMessage << tag << " tloop:           " << Tms(usecond()-t0) << " ms\n";
-
-    // Select addLoopRight kernel for this type
-    std::function<void(SpinColourVector_v &,
-                       const SpinColourMatrix_v &,
-                       const SpinColourVector_v &,
-                       const std::vector<Gamma::Algebra> &,
-                       const std::vector<Gamma::Algebra> &)> addLoopRight;
-
-    if (type == 0) {
-      addLoopRight = [](SpinColourVector_v &lR,
-                        const SpinColourMatrix_v &loopm,
-                        const SpinColourVector_v &rightv,
-                        const std::vector<Gamma::Algebra> &g1,
-                        const std::vector<Gamma::Algebra> &g2) {
-        SpinMatrix_v spinLoop = Zero();
-        for (int s1 = 0; s1 < Ns; ++s1)
-        for (int s2 = 0; s2 < Ns; ++s2)
-          spinLoop()(s1,s2)() = loopm()(s1,s2)(0,0);
-        for (int mu = 0; mu < (int)g1.size(); ++mu) {
-          SpinMatrix_v GLoop = Gamma(g2[mu]) * spinLoop;
-          auto trGLoop = GLoop()(0,0)() + GLoop()(1,1)() + GLoop()(2,2)() + GLoop()(3,3)();
-          SpinColourVector_v Grightv = Gamma(g1[mu]) * rightv;
-          for (int s = 0; s < Ns; ++s)
-          for (int c = 0; c < Nc; ++c)
-            lR()(s)(c) += Grightv()(s)(c) * trGLoop;
-        }
-      };
-    }
-    if (type == 1) {
-      addLoopRight = [](SpinColourVector_v &lR,
-                        const SpinColourMatrix_v &loopm,
-                        const SpinColourVector_v &rightv,
-                        const std::vector<Gamma::Algebra> &g1,
-                        const std::vector<Gamma::Algebra> &g2) {
-        for (int s = 0; s < Ns; ++s)
-        for (int c = 0; c < Nc; ++c) {
-          lR()(s)(c)
-            += loopm()(s,0)(c,0) * rightv()(0)(0)
-            +  loopm()(s,0)(c,1) * rightv()(0)(1)
-            +  loopm()(s,0)(c,2) * rightv()(0)(2)
-            +  loopm()(s,1)(c,0) * rightv()(1)(0)
-            +  loopm()(s,1)(c,1) * rightv()(1)(1)
-            +  loopm()(s,1)(c,2) * rightv()(1)(2)
-            +  loopm()(s,2)(c,0) * rightv()(2)(0)
-            +  loopm()(s,2)(c,1) * rightv()(2)(1)
-            +  loopm()(s,2)(c,2) * rightv()(2)(2)
-            +  loopm()(s,3)(c,0) * rightv()(3)(0)
-            +  loopm()(s,3)(c,1) * rightv()(3)(1)
-            +  loopm()(s,3)(c,2) * rightv()(3)(2);
-        }
-      };
-    }
-    if (type == 2) {
-      addLoopRight = [](SpinColourVector_v &lR,
-                        const SpinColourMatrix_v &loopm,
-                        const SpinColourVector_v &rightv,
-                        const std::vector<Gamma::Algebra> &g1,
-                        const std::vector<Gamma::Algebra> &g2) {
-        for (int mu = 0; mu < (int)g1.size(); ++mu) {
-          int s1 = mu / Ns;
-          int s2 = mu % Ns;
-          SpinColourVector_v Grightv = Gamma(g1[mu]) * rightv;
-          for (int s = 0; s < Ns; ++s)
-          for (int c = 0; c < Nc; ++c)
-            lR()(s)(c) += loopm()(s1,s2)(c,0) * Grightv()(s)(0)
-                       +  loopm()(s1,s2)(c,1) * Grightv()(s)(1)
-                       +  loopm()(s1,s2)(c,2) * Grightv()(s)(2);
-        }
-      };
-    }
-    if (type == 3) {
-      addLoopRight = [](SpinColourVector_v &lR,
-                        const SpinColourMatrix_v &loopm,
-                        const SpinColourVector_v &rightv,
-                        const std::vector<Gamma::Algebra> &g1,
-                        const std::vector<Gamma::Algebra> &g2) {
-        for (int s = 0; s < Ns; ++s)
-        for (int c = 0; c < Nc; ++c)
-          lR()(s)(c) += loopm()(s,0)(0,0) * rightv()(0)(c)
-                     +  loopm()(s,1)(0,0) * rightv()(1)(c)
-                     +  loopm()(s,2)(0,0) * rightv()(2)(c)
-                     +  loopm()(s,3)(0,0) * rightv()(3)(c);
-      };
-    }
-
-    // ------------------------------------------------------------------
-    // Pack loopRight[j] = type-kernel(tloop, right[j]) per site
-    // ------------------------------------------------------------------
-    t0 = usecond();
-    std::vector<FermionField> loopRight(N_j, grid);
-    {
-      autoView(tlv, tloop, CpuRead);
-      for (int j = 0; j < N_j; j++) {
-        loopRight[j] = Zero();
-        autoView(lRv, loopRight[j], CpuWrite);
-        autoView(rv,  right[j],     CpuRead);
-        thread_for(ss, grid->oSites(), {
-          addLoopRight(lRv[ss], tlv[ss], rv[ss], gamma1, gamma2);
-        });
-      }
-    }
-    std::cout << GridLogMessage << tag << " pack_loopright:  " << Tms(usecond()-t0) << " ms\n";
-
-    if (use_blas) {
-      // ------------------------------------------------------------------
-      // BLAS path: A2ASpatialSum (Allocate + PackLeft + PackRight + Sum)
-      // ------------------------------------------------------------------
-      A2ASpatialSum<SpinColourVector_v> spatial_sum;
-      double t_blas_start = usecond();
-
-      t0 = usecond();
-      spatial_sum.Allocate(N_i, N_j, grid);
-      std::cout << GridLogMessage << tag << " Allocate:        " << Tms(usecond()-t0) << " ms\n";
-
-      t0 = usecond();
-      spatial_sum.PackLeft(leftv);
-      std::cout << GridLogMessage << tag << " PackLeft:        " << Tms(usecond()-t0) << " ms\n";
-
-      t0 = usecond();
-      spatial_sum.PackRight(loopRight);
-      std::cout << GridLogMessage << tag << " PackRight:       " << Tms(usecond()-t0) << " ms\n";
-
-      t0 = usecond();
-      spatial_sum.Sum(result);
-      std::cout << GridLogMessage << tag << " Sum (GEMM+MPI):  " << Tms(usecond()-t0) << " ms\n";
-
-      std::cout << GridLogMessage << tag << " A2ASpatialSum:   " << Tms(usecond()-t_blas_start) << " ms  [TOTAL]\n";
-
-    } else {
-      // ------------------------------------------------------------------
-      // Reference path: SIMD spatial sum + scalar extraction
-      // ------------------------------------------------------------------
-      int MFrvol = rd * N_i * N_j;
-      int MFlvol = ld * N_i * N_j;
-
-      Vector<Scalar_v> lvSum(MFrvol);
-      thread_for(r, MFrvol, { lvSum[r] = Zero(); });
-
-      t0 = usecond();
-      {
-        int e1     = grid->_slice_nblock[orthogdim];
-        int e2     = grid->_slice_block [orthogdim];
-        int stride = grid->_slice_stride[orthogdim];
-        using LView = decltype(leftv[0].View(CpuRead));
-        using RView = decltype(loopRight[0].View(CpuRead));
-        std::vector<LView> lv_views;
-        std::vector<RView> lr_views;
-        lv_views.reserve(N_i);
-        lr_views.reserve(N_j);
-        for (int i = 0; i < N_i; i++) lv_views.push_back(leftv[i].View(CpuRead));
-        for (int j = 0; j < N_j; j++) lr_views.push_back(loopRight[j].View(CpuRead));
-        thread_for(r, rd, {
-          int so   = r * grid->_ostride[orthogdim];
-          int base = N_i * N_j * r;
-          for (int n = 0; n < e1; n++)
-          for (int b = 0; b < e2; b++) {
-            int ss = so + n * stride + b;
-            for (int ii = 0; ii < N_i; ii++)
-            for (int jj = 0; jj < N_j; jj++) {
-              int idx = jj + N_j * ii + base;
-              for (int s = 0; s < Ns; ++s)
-              for (int c = 0; c < Nc; ++c)
-                lvSum[idx]()()() += lv_views[ii][ss]()(s)(c) * lr_views[jj][ss]()(s)(c);
-            }
-          }
-        });
-        for (auto &v : lv_views) v.ViewClose();
-        for (auto &v : lr_views) v.ViewClose();
-      }
-      std::cout << GridLogMessage << tag << " spatial_sum:     " << Tms(usecond()-t0) << " ms\n";
-
-      Vector<Scalar_s> lsSum(MFlvol);
-      thread_for(r, MFlvol, { lsSum[r] = scalar_type(0.0); });
-
-      t0 = usecond();
-      thread_for(rt, rd, {
-        Coordinate icoor(Nd);
-        ExtractBuffer<Scalar_s> extracted(Nsimd);
-        for (int ii = 0; ii < N_i; ii++)
-        for (int jj = 0; jj < N_j; jj++) {
-          int ij_rdx = jj + N_j * (ii + N_i * rt);
-          extract(lvSum[ij_rdx], extracted);
-          for (int idx = 0; idx < Nsimd; idx++) {
-            grid->iCoorFromIindex(icoor, idx);
-            int ldx    = rt + icoor[orthogdim] * rd;
-            int ij_ldx = jj + N_j * (ii + N_i * ldx);
-            lsSum[ij_ldx] = lsSum[ij_ldx] + extracted[idx];
-          }
-        }
-      });
-      std::cout << GridLogMessage << tag << " simd_extract:    " << Tms(usecond()-t0) << " ms\n";
-
-      int pd = grid->_processors[orthogdim];
-      int pc = grid->_processor_coor[orthogdim];
-
-      t0 = usecond();
-      Vector<ComplexD> cache(nt * N_i * N_j, ComplexD(0.0));
-      for (int lt = 0; lt < ld; lt++)
-      for (int pt = 0; pt < pd; pt++) {
-        int t = lt + pt * ld;
-        for (int ii = 0; ii < N_i; ii++)
-        for (int jj = 0; jj < N_j; jj++) {
-          if (pt == pc) {
-            int ij_ldx = jj + N_j * (ii + N_i * lt);
-            cache[jj + N_j * (ii + N_i * t)] = lsSum[ij_ldx]()()();
-          }
-        }
-      }
-      grid->GlobalSumVector(cache.data(), nt * N_i * N_j);
-      std::cout << GridLogMessage << tag << " globalsum:       " << Tms(usecond()-t0) << " ms\n";
-
-      for (int t  = 0; t  < nt;  t++)
-      for (int ii = 0; ii < N_i; ii++)
-      for (int jj = 0; jj < N_j; jj++)
-        result(t, ii, jj) = cache[jj + N_j * (ii + N_i * t)];
-    }
-  }
-};
-
-// ================================================================
-// Free-function GPU kernels — accelerator_for, v(ss) reads,
-// coalescedWrite writes, vobj-level arithmetic throughout.
-// Gamma arrays passed as Vector<Gamma::Algebra> (UVM).
-// ================================================================
-
-void A2ALoopPropagator(PropagatorField &loop,
-                       const std::vector<FermionField> &loop1,
-                       const std::vector<FermionField> &loop2)
-{
-  loop = Zero();
-  for (unsigned int k = 0; k < loop1.size(); ++k)
-    loop += outerProduct(loop1[k], loop2[k]);
-}
-
-void A2APackLeftConjugated(FermionField &out, const FermionField &in)
-{
-  autoView(outv, out, AcceleratorWrite);
-  autoView(inv,  in,  AcceleratorRead);
-  uint64_t Osites = in.Grid()->oSites();
-  int Nsimd = SpinColourVector_v::Nsimd();
-  accelerator_for(ss, Osites, Nsimd, {
-    coalescedWrite(outv[ss], conjugate(inv(ss)));
-  });
-}
-
-// Type 0: colour-trace stored in (s1,s2)(0,0)
-void A2ALoopLeftContractionType0(PropagatorField &tloop, const PropagatorField &loop)
-{
-  autoView(tloopv, tloop, AcceleratorWrite);
-  autoView(loopv,  loop,  AcceleratorRead);
-  uint64_t Osites = loop.Grid()->oSites();
-  int Nsimd = SpinColourMatrix_v::Nsimd();
-  accelerator_for(ss, Osites, Nsimd, {
-    auto l = loopv(ss);
-    auto tmp = l; tmp = Zero();
-    for (int s1 = 0; s1 < Ns; ++s1)
-    for (int s2 = 0; s2 < Ns; ++s2)
-      tmp()(s1,s2)(0,0) = l()(s1,s2)(0,0) + l()(s1,s2)(1,1) + l()(s1,s2)(2,2);
-    coalescedWrite(tloopv[ss], tmp);
-  });
-}
-
-// Type 1: tloop = sum_mu Gamma(g1[mu]) * loop * Gamma(g2[mu])
-void A2ALoopLeftContractionType1(PropagatorField &tloop, const PropagatorField &loop,
-                                  const Vector<Gamma::Algebra> &gamma1,
-                                  const Vector<Gamma::Algebra> &gamma2)
-{
-  int ng = (int)gamma1.size();
-  const Gamma::Algebra *g1 = gamma1.data();
-  const Gamma::Algebra *g2 = gamma2.data();
-  autoView(tloopv, tloop, AcceleratorWrite);
-  autoView(loopv,  loop,  AcceleratorRead);
-  uint64_t Osites = loop.Grid()->oSites();
-  int Nsimd = SpinColourMatrix_v::Nsimd();
-  accelerator_for(ss, Osites, Nsimd, {
-    auto l = loopv(ss);
-    auto tmp = l; tmp = Zero();
-    for (int mu = 0; mu < ng; ++mu)
-      tmp = tmp + Gamma(g1[mu]) * l * Gamma(g2[mu]);
-    coalescedWrite(tloopv[ss], tmp);
-  });
-}
-
-// Type 2: for mu=[0..ng), s1=mu/Ns, s2=mu%Ns;
-//         tloop(s1,s2)(c1,c2) = Tr_spin( Gamma(g2[mu]) * loop )(c1,c2)
-void A2ALoopLeftContractionType2(PropagatorField &tloop, const PropagatorField &loop,
-                                  const Vector<Gamma::Algebra> &gamma2)
-{
-  int ng = (int)gamma2.size();
-  const Gamma::Algebra *g2 = gamma2.data();
-  autoView(tloopv, tloop, AcceleratorWrite);
-  autoView(loopv,  loop,  AcceleratorRead);
-  uint64_t Osites = loop.Grid()->oSites();
-  int Nsimd = SpinColourMatrix_v::Nsimd();
-  accelerator_for(ss, Osites, Nsimd, {
-    auto l = loopv(ss);
-    auto tmp = l; tmp = Zero();
-    for (int mu = 0; mu < ng; ++mu) {
-      auto gtmp = Gamma(g2[mu]) * l;
-      int s1 = mu / Ns;
-      int s2 = mu % Ns;
-      for (int c1 = 0; c1 < Nc; ++c1)
-      for (int c2 = 0; c2 < Nc; ++c2)
-        tmp()(s1,s2)(c1,c2) = gtmp()(0,0)(c1,c2) + gtmp()(1,1)(c1,c2)
-                            + gtmp()(2,2)(c1,c2) + gtmp()(3,3)(c1,c2);
-    }
-    coalescedWrite(tloopv[ss], tmp);
-  });
-}
-
-// Type 3: colour-trace → spin matrix → sum_mu G1*spinLoop*G2 stored in (s1,s2)(0,0)
-void A2ALoopLeftContractionType3(PropagatorField &tloop, const PropagatorField &loop,
-                                  const Vector<Gamma::Algebra> &gamma1,
-                                  const Vector<Gamma::Algebra> &gamma2)
-{
-  int ng = (int)gamma1.size();
-  const Gamma::Algebra *g1 = gamma1.data();
-  const Gamma::Algebra *g2 = gamma2.data();
-  autoView(tloopv, tloop, AcceleratorWrite);
-  autoView(loopv,  loop,  AcceleratorRead);
-  uint64_t Osites = loop.Grid()->oSites();
-  int Nsimd = SpinColourMatrix_v::Nsimd();
-  accelerator_for(ss, Osites, Nsimd, {
-    auto l = loopv(ss);
-    SpinMatrix_v spinLoop; spinLoop = Zero();
-    for (int s1 = 0; s1 < Ns; ++s1)
-    for (int s2 = 0; s2 < Ns; ++s2)
-      spinLoop()(s1,s2)() = l()(s1,s2)(0,0) + l()(s1,s2)(1,1) + l()(s1,s2)(2,2);
-    auto tmp = l; tmp = Zero();
-    for (int mu = 0; mu < ng; ++mu) {
-      SpinMatrix_v tmp2 = Gamma(g1[mu]) * spinLoop * Gamma(g2[mu]);
-      for (int s1 = 0; s1 < Ns; ++s1)
-      for (int s2 = 0; s2 < Ns; ++s2)
-        tmp()(s1,s2)(0,0) = tmp()(s1,s2)(0,0) + tmp2()(s1,s2)();
-    }
-    coalescedWrite(tloopv[ss], tmp);
-  });
-}
-
-// Type 0: loopRight = sum_mu Tr(G2*spinLoop) * G1*right
-//   where spinLoop(s1,s2) = tloop(s1,s2)(0,0)
-void A2ALoopRightContractionType0(FermionField &loopRight,
-                                   const PropagatorField &tloop,
-                                   const FermionField &right,
-                                   const Vector<Gamma::Algebra> &gamma1,
-                                   const Vector<Gamma::Algebra> &gamma2)
-{
-  int ng = (int)gamma1.size();
-  const Gamma::Algebra *g1 = gamma1.data();
-  const Gamma::Algebra *g2 = gamma2.data();
-  autoView(lRv, loopRight, AcceleratorWrite);
-  autoView(tlv, tloop,     AcceleratorRead);
-  autoView(rv,  right,     AcceleratorRead);
-  uint64_t Osites = right.Grid()->oSites();
-  int Nsimd = SpinColourVector_v::Nsimd();
-  accelerator_for(ss, Osites, Nsimd, {
-    auto loopm  = tlv(ss);
-    auto rightv = rv(ss);
-    SpinMatrix_v spinLoop; spinLoop = Zero();
-    for (int s1 = 0; s1 < Ns; ++s1)
-    for (int s2 = 0; s2 < Ns; ++s2)
-      spinLoop()(s1,s2)() = loopm()(s1,s2)(0,0);
-    SpinColourVector_v lR; lR = Zero();
-    for (int mu = 0; mu < ng; ++mu) {
-      auto GLoop   = Gamma(g2[mu]) * spinLoop;
-      auto trGLoop = GLoop()(0,0)() + GLoop()(1,1)() + GLoop()(2,2)() + GLoop()(3,3)();
-      auto Grightv = Gamma(g1[mu]) * rightv;
-      for (int s = 0; s < Ns; ++s)
-      for (int c = 0; c < Nc; ++c)
-        lR()(s)(c) = lR()(s)(c) + Grightv()(s)(c) * trGLoop;
-    }
-    coalescedWrite(lRv[ss], lR);
-  });
-}
-
-// Type 1: loopRight = tloop * right  (SpinColourMatrix * SpinColourVector)
-void A2ALoopRightContractionType1(FermionField &loopRight,
-                                   const PropagatorField &tloop,
-                                   const FermionField &right)
-{
-  autoView(lRv, loopRight, AcceleratorWrite);
-  autoView(tlv, tloop,     AcceleratorRead);
-  autoView(rv,  right,     AcceleratorRead);
-  uint64_t Osites = right.Grid()->oSites();
-  int Nsimd = SpinColourVector_v::Nsimd();
-  accelerator_for(ss, Osites, Nsimd, {
-    coalescedWrite(lRv[ss], tlv(ss) * rv(ss));
-  });
-}
-
-// Type 2: loopRight(s)(c) = sum_{mu,c'} tloop(s1,s2)(c,c') * (G(g1[mu])*right)(s)(c')
-void A2ALoopRightContractionType2(FermionField &loopRight,
-                                   const PropagatorField &tloop,
-                                   const FermionField &right,
-                                   const Vector<Gamma::Algebra> &gamma1)
-{
-  int ng = (int)gamma1.size();
-  const Gamma::Algebra *g1 = gamma1.data();
-  autoView(lRv, loopRight, AcceleratorWrite);
-  autoView(tlv, tloop,     AcceleratorRead);
-  autoView(rv,  right,     AcceleratorRead);
-  uint64_t Osites = right.Grid()->oSites();
-  int Nsimd = SpinColourVector_v::Nsimd();
-  accelerator_for(ss, Osites, Nsimd, {
-    auto loopm  = tlv(ss);
-    auto rightv = rv(ss);
-    SpinColourVector_v lR; lR = Zero();
-    for (int mu = 0; mu < ng; ++mu) {
-      int s1 = mu / Ns;
-      int s2 = mu % Ns;
-      auto Grightv = Gamma(g1[mu]) * rightv;
-      for (int s = 0; s < Ns; ++s)
-      for (int c = 0; c < Nc; ++c)
-        lR()(s)(c) = lR()(s)(c)
-                   + loopm()(s1,s2)(c,0) * Grightv()(s)(0)
-                   + loopm()(s1,s2)(c,1) * Grightv()(s)(1)
-                   + loopm()(s1,s2)(c,2) * Grightv()(s)(2);
-    }
-    coalescedWrite(lRv[ss], lR);
-  });
-}
-
-// Type 3: loopRight(s)(c) = sum_{s'} tloop(s,s')(0,0) * right(s')(c)
-void A2ALoopRightContractionType3(FermionField &loopRight,
-                                   const PropagatorField &tloop,
-                                   const FermionField &right)
-{
-  autoView(lRv, loopRight, AcceleratorWrite);
-  autoView(tlv, tloop,     AcceleratorRead);
-  autoView(rv,  right,     AcceleratorRead);
-  uint64_t Osites = right.Grid()->oSites();
-  int Nsimd = SpinColourVector_v::Nsimd();
-  accelerator_for(ss, Osites, Nsimd, {
-    auto loopm  = tlv(ss);
-    auto rightv = rv(ss);
-    SpinColourVector_v lR; lR = Zero();
-    for (int s = 0; s < Ns; ++s)
-    for (int c = 0; c < Nc; ++c)
-      lR()(s)(c) = loopm()(s,0)(0,0) * rightv()(0)(c)
-                 + loopm()(s,1)(0,0) * rightv()(1)(c)
-                 + loopm()(s,2)(0,0) * rightv()(2)(c)
-                 + loopm()(s,3)(0,0) * rightv()(3)(c);
-    coalescedWrite(lRv[ss], lR);
-  });
-}
-
-// ================================================================
-// GPU-offloaded extended meson field: accelerator_for contractions
-// + A2ASpatialSum GEMM spatial reduction.
-// ================================================================
-class A2AExtendedMesonFieldGPU
-{
-public:
-  static void compute(
-      Eigen::Tensor<ComplexD, 3> &result,
-      const std::vector<FermionField> &left,
-      const std::vector<FermionField> &right,
-      const std::vector<FermionField> &loop1,
-      const std::vector<FermionField> &loop2,
-      const std::vector<Gamma::Algebra> &gamma1_in,
-      const std::vector<Gamma::Algebra> &gamma2_in,
-      int type)
-  {
-    GridBase *grid = left[0].Grid();
-    int N_i = (int)left.size();
-    int N_j = (int)right.size();
-
-    std::string tag = std::string("[gpu  type=") + std::to_string(type) + "]";
-    auto Tms = [](double us) { return us * 1e-3; };
-    double t0;
-
-    Vector<Gamma::Algebra> gamma1(gamma1_in.begin(), gamma1_in.end());
-    Vector<Gamma::Algebra> gamma2(gamma2_in.begin(), gamma2_in.end());
-
-    t0 = usecond();
-    PropagatorField loop(grid);
-    A2ALoopPropagator(loop, loop1, loop2);
-    std::cout << GridLogMessage << tag << " loop_build:      " << Tms(usecond()-t0) << " ms\n";
-
-    t0 = usecond();
-    std::vector<FermionField> leftv(N_i, grid);
-    for (int i = 0; i < N_i; i++)
-      A2APackLeftConjugated(leftv[i], left[i]);
-    std::cout << GridLogMessage << tag << " pack_left:       " << Tms(usecond()-t0) << " ms\n";
-
-    t0 = usecond();
-    PropagatorField tloop(grid);
-    tloop = Zero();
-    switch (type) {
-    case 0: A2ALoopLeftContractionType0(tloop, loop);                break;
-    case 1: A2ALoopLeftContractionType1(tloop, loop, gamma1, gamma2); break;
-    case 2: A2ALoopLeftContractionType2(tloop, loop, gamma2);         break;
-    case 3: A2ALoopLeftContractionType3(tloop, loop, gamma1, gamma2); break;
-    }
-    std::cout << GridLogMessage << tag << " tloop:           " << Tms(usecond()-t0) << " ms\n";
-
-    t0 = usecond();
-    std::vector<FermionField> loopRight(N_j, grid);
-    for (int j = 0; j < N_j; j++) {
-      switch (type) {
-      case 0: A2ALoopRightContractionType0(loopRight[j], tloop, right[j], gamma1, gamma2); break;
-      case 1: A2ALoopRightContractionType1(loopRight[j], tloop, right[j]);                 break;
-      case 2: A2ALoopRightContractionType2(loopRight[j], tloop, right[j], gamma1);         break;
-      case 3: A2ALoopRightContractionType3(loopRight[j], tloop, right[j]);                 break;
-      }
-    }
-    std::cout << GridLogMessage << tag << " pack_loopright:  " << Tms(usecond()-t0) << " ms\n";
-
-    A2ASpatialSum<SpinColourVector_v> spatial_sum;
-    double t_blas = usecond();
-
-    t0 = usecond();
-    spatial_sum.Allocate(N_i, N_j, grid);
-    std::cout << GridLogMessage << tag << " Allocate:        " << Tms(usecond()-t0) << " ms\n";
-
-    t0 = usecond();
-    spatial_sum.PackLeft(leftv);
-    std::cout << GridLogMessage << tag << " PackLeft:        " << Tms(usecond()-t0) << " ms\n";
-
-    t0 = usecond();
-    spatial_sum.PackRight(loopRight);
-    std::cout << GridLogMessage << tag << " PackRight:       " << Tms(usecond()-t0) << " ms\n";
-
-    t0 = usecond();
-    spatial_sum.Sum(result);
-    std::cout << GridLogMessage << tag << " Sum (GEMM+MPI):  " << Tms(usecond()-t0) << " ms\n";
-
-    std::cout << GridLogMessage << tag << " A2ASpatialSum:   " << Tms(usecond()-t_blas) << " ms  [TOTAL]\n";
-  }
-};
-
-int main(int argc, char *argv[])
-{
-  Grid_init(&argc, &argv);
-
-  Coordinate latt_size   = GridDefaultLatt();
-  Coordinate simd_layout = GridDefaultSimd(4, vComplexD::Nsimd());
-  Coordinate mpi_layout  = GridDefaultMpi();
-  GridCartesian grid(latt_size, simd_layout, mpi_layout);
-
-  int Nt    = latt_size[Tp];
-  int N_i   = 8;
-  int N_j   = 8;
-  int Nloop = 4;
-
-  GridParallelRNG pRNG(&grid);
-  pRNG.SeedFixedIntegers({1, 2, 3, 4});
-
-  std::vector<FermionField> left(N_i,   &grid);
-  std::vector<FermionField> right(N_j,  &grid);
-  std::vector<FermionField> loop1(Nloop, &grid);
-  std::vector<FermionField> loop2(Nloop, &grid);
-
-  for (auto &f : left)  random(pRNG, f);
-  for (auto &f : right) random(pRNG, f);
-  for (auto &f : loop1) random(pRNG, f);
-  for (auto &f : loop2) random(pRNG, f);
-
-  std::vector<Gamma::Algebra> GammaMU = {
-    Gamma::Algebra::GammaX,
-    Gamma::Algebra::GammaY,
-    Gamma::Algebra::GammaZ,
-    Gamma::Algebra::GammaT
-  };
-
-  Eigen::Tensor<ComplexD, 3> result_ref(Nt, N_i, N_j);
-  Eigen::Tensor<ComplexD, 3> result_blas(Nt, N_i, N_j);
-  Eigen::Tensor<ComplexD, 3> result_gpu(Nt, N_i, N_j);
-  double t_ref = 0, t_blas = 0, t_gpu = 0, start, stop;
-
-  for (int type = 0; type < 4; type++) {
-
-    result_ref.setZero();
-    start = usecond();
-    A2AExtendedMesonFieldRef::compute(result_ref,  left, right, loop1, loop2,
-                                      GammaMU, GammaMU, type, false);
-    stop = usecond(); t_ref = stop - start;
-
-    result_blas.setZero();
-    start = usecond();
-    A2AExtendedMesonFieldRef::compute(result_blas, left, right, loop1, loop2,
-                                      GammaMU, GammaMU, type, true);
-    stop = usecond(); t_blas = stop - start;
-
-    result_gpu.setZero();
-    start = usecond();
-    A2AExtendedMesonFieldGPU::compute(result_gpu, left, right, loop1, loop2,
-                                      GammaMU, GammaMU, type);
-    stop = usecond(); t_gpu = stop - start;
-
-    double norm2_ref = 0.0, norm2_blas = 0.0, norm2_gpu = 0.0;
-    double norm2_diff_blas = 0.0, norm2_diff_gpu = 0.0;
-    for (int t  = 0; t  < Nt;  t++)
-    for (int ii = 0; ii < N_i; ii++)
-    for (int jj = 0; jj < N_j; jj++) {
-      norm2_ref  += std::norm(result_ref(t, ii, jj));
-      norm2_blas += std::norm(result_blas(t, ii, jj));
-      norm2_gpu  += std::norm(result_gpu(t, ii, jj));
-      ComplexD diff_blas = result_ref(t, ii, jj) - result_blas(t, ii, jj);
-      ComplexD diff_gpu  = result_ref(t, ii, jj) - result_gpu(t, ii, jj);
-      norm2_diff_blas += std::norm(diff_blas);
-      norm2_diff_gpu  += std::norm(diff_gpu);
-    }
-
-    double rel_blas = (norm2_ref > 0) ? std::sqrt(norm2_diff_blas / norm2_ref) : 0.0;
-    double rel_gpu  = (norm2_ref > 0) ? std::sqrt(norm2_diff_gpu  / norm2_ref) : 0.0;
-
-    std::cout << GridLogMessage
-              << "type=" << type
-              << "  norm2_ref="  << norm2_ref
-              << "  norm2_blas=" << norm2_blas
-              << "  norm2_gpu="  << norm2_gpu
-              << "  rel_blas="   << rel_blas
-              << "  rel_gpu="    << rel_gpu
-              << "  t_ref="  << t_ref  * 1e-6 << "s"
-              << "  t_blas=" << t_blas * 1e-6 << "s"
-              << "  t_gpu="  << t_gpu  * 1e-6 << "s"
-              << std::endl;
-
-    GRID_ASSERT(rel_blas < 1e-10);
-    GRID_ASSERT(rel_gpu  < 1e-10);
-  }
-
-  std::cout << GridLogMessage << "All types passed A2ASpatialSum and GPU regression." << std::endl;
-
-  Grid_finalize();
-  return EXIT_SUCCESS;
-}
-
-#endif

tests/debug/Test_general_coarse.cc

@@ -36,8 +36,8 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 using namespace std;
 using namespace Grid;
 
-gridblasHandle_t GridBLAS::gridblasHandle;
-int            GridBLAS::gridblasInit;
+//gridblasHandle_t GridBLAS::gridblasHandle;
+//int            GridBLAS::gridblasInit;
 
 ///////////////////////
 // Tells little dirac op to use MdagM as the .Op()

tests/debug/Test_staggered_hdcg.cc

@@ -0,0 +1,362 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: tests/debug/Test_staggered_hdcg.cc
+
+    Authors: Thomas Blum, Peter Boyle
+
+    HDCG (Hierarchical Deflation Conjugate Gradient) multigrid solver
+    for naive staggered fermions, based on arXiv:2409.03904.
+
+    Adapts the DWF HDCG infrastructure (Test_general_coarse_hdcg_phys48.cc) to:
+      - NaiveStaggeredFermion (nearest-neighbour only, no Naik 3-hop term)
+      - 4D SchurStaggeredOperator:  Mpc = m^2 - D_oe * D_eo  (hermitian, positive-definite)
+      - vColourVector fine field type (staggered has colour but no spin)
+      - NextToNearestStencilGeometry4D: 33-point coarse stencil
+
+    Stencil count: D_oe*D_eo has 2-hop fine range.  With blocking B >= 2 the coarse
+    shifts have L1-distance <= 2, giving 33 stencil points in 4D:
+      1 (identity) + 8 (+-e_mu) + 24 (+-e_mu +- e_nu).
+    NaiveStaggeredFermion has no Naik term, so any B >= 2 suffices.
+    To extend to ImprovedStaggeredFermion later, use B >= 6.
+
+    Reference: arXiv:2409.03904 (mrhs hermitian multigrid for DWF).
+
+    Usage (after build):
+      ./Test_staggered_hdcg --grid 16.16.16.16 --mpi 1.1.1.1
+
+*************************************************************************************/
+#include <Grid/Grid.h>
+#include <Grid/algorithms/iterative/AdefMrhs.h>
+#include <Grid/algorithms/iterative/ImplicitlyRestartedBlockLanczos.h>
+#include <Grid/algorithms/iterative/ImplicitlyRestartedBlockLanczosCoarse.h>
+
+using namespace Grid;
+
+// Non-converging CG used as a smoother (fixed number of iterations)
+template<class Field>
+class CGSmoother : public LinearFunction<Field>
+{
+public:
+  typedef LinearOperatorBase<Field> FineOperator;
+  FineOperator &_Op;
+  int iters;
+  CGSmoother(int _iters, FineOperator &Op) : _Op(Op), iters(_iters) {}
+  void operator()(const Field &in, Field &out)
+  {
+    ConjugateGradient<Field> CG(0.0, iters, false);
+    out = Zero();
+    CG(_Op, in, out);
+  }
+};
+
+int main(int argc, char **argv)
+{
+  fprintf(stderr, "TRACE: entering main\n"); fflush(stderr);
+  Grid_init(&argc, &argv);
+  fprintf(stderr, "TRACE: Grid_init done\n"); fflush(stderr);
+
+  //--------------------------------------------------------------------
+  // Parameters — tune for production
+  //--------------------------------------------------------------------
+  const int nbasis = 24;   // near-null space dimension
+  const int cb     = 0;    // even checkerboard
+
+  RealD mass = 0.05;
+
+  // NaiveStaggeredFermion: nearest-neighbour hop only (no Naik term).
+  // c1 = coefficient of the hopping term (1.0 = standard normalisation).
+  // u0 = tadpole factor (1.0 = no tadpole improvement).
+  RealD c1 = 1.0;
+  RealD u0 = 1.0;
+
+  //--------------------------------------------------------------------
+  // Grids
+  // Fine:   UGrid (4D full), UrbGrid (4D red-black)
+  // Coarse: Coarse4d  with dimensions = GridDefaultLatt() / Block
+  //
+  // Recommended: GridDefaultLatt() >= 16^4, Block = {4,4,4,4}
+  // NaiveStaggeredFermion works with any Block >= {2,2,2,2}
+  //--------------------------------------------------------------------
+  fprintf(stderr, "TRACE: making UGrid\n"); fflush(stderr);
+  GridCartesian *UGrid = SpaceTimeGrid::makeFourDimGrid(
+      GridDefaultLatt(), GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
+  fprintf(stderr, "TRACE: making UrbGrid\n"); fflush(stderr);
+  GridRedBlackCartesian *UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+
+  Coordinate Block({4, 4, 4, 4});
+  Coordinate clatt = GridDefaultLatt();
+  for (int d = 0; d < clatt.size(); d++) clatt[d] /= Block[d];
+  Coordinate csimd = GridDefaultSimd(Nd, vComplex::Nsimd());
+  Coordinate cmpi  = GridDefaultMpi();
+  fprintf(stderr, "TRACE: making Coarse4d clatt=%d %d %d %d simd=%d %d %d %d mpi=%d %d %d %d Nsimd=%d\n",
+          clatt[0],clatt[1],clatt[2],clatt[3],
+          csimd[0],csimd[1],csimd[2],csimd[3],
+          cmpi[0],cmpi[1],cmpi[2],cmpi[3],
+          (int)vComplex::Nsimd()); fflush(stderr);
+
+  GridCartesian *Coarse4d = SpaceTimeGrid::makeFourDimGrid(clatt, csimd, cmpi);
+  fprintf(stderr, "TRACE: Coarse4d made\n"); fflush(stderr);
+
+  //--------------------------------------------------------------------
+  // RNG + gauge field
+  //--------------------------------------------------------------------
+  fprintf(stderr, "TRACE: RNG4\n"); fflush(stderr);
+  GridParallelRNG RNG4(UGrid);    RNG4.SeedFixedIntegers({1,2,3,4});
+  fprintf(stderr, "TRACE: RNGrb\n"); fflush(stderr);
+  GridParallelRNG RNGrb(UGrid); RNGrb.SeedFixedIntegers({5,6,7,8}); // must use full grid, not UrbGrid
+  fprintf(stderr, "TRACE: Umu\n"); fflush(stderr);
+  LatticeGaugeField Umu(UGrid);
+  fprintf(stderr, "TRACE: HotConfig\n"); fflush(stderr);
+  SU<Nc>::HotConfiguration(RNG4, Umu);
+  fprintf(stderr, "TRACE: NaiveStaggeredFermionD\n"); fflush(stderr);
+  NaiveStaggeredFermionD Ds(Umu, *UGrid, *UrbGrid, mass, c1, u0);
+  fprintf(stderr, "TRACE: SchurStaggeredOperator\n"); fflush(stderr);
+  SchurStaggeredOperator<NaiveStaggeredFermionD, LatticeStaggeredFermionD> HermOp(Ds);
+  fprintf(stderr, "TRACE: HermOp done\n"); fflush(stderr);
+
+  //--------------------------------------------------------------------
+  // Subspace: inverse-iteration near-null vectors
+  //
+  // CreateSubspace applies CG (4 solves, tol=1e-4) to random noise vectors,
+  // converging naturally to the low modes of HermOp without needing spectral
+  // bound tuning.  Switch to CreateSubspaceChebyshevNew once the spectrum is
+  // well characterised (hi ~ 5.0 for naive staggered SchurStaggeredOperator).
+  //--------------------------------------------------------------------
+  typedef Aggregation<vColourVector, vTComplex, nbasis> Subspace;
+  Subspace Aggregates(Coarse4d, UrbGrid, cb);
+
+  Aggregates.CreateSubspace(RNGrb, HermOp);
+  Aggregates.Orthogonalise();
+
+  //--------------------------------------------------------------------
+  // Coarse geometry: NextToNearestStencilGeometry4D
+  //   hops=2  ->  33 stencil points in 4D
+  //--------------------------------------------------------------------
+  NextToNearestStencilGeometry4D geom(Coarse4d);
+
+  std::cout << GridLogMessage << "Coarse stencil: " << geom.npoint << " points" << std::endl;
+
+  //--------------------------------------------------------------------
+  // Single-RHS coarse operator (used for correctness check below)
+  //--------------------------------------------------------------------
+  typedef GeneralCoarsenedMatrix<vColourVector, vTComplex, nbasis> LittleDiracOp;
+  typedef LittleDiracOp::CoarseVector CoarseVector;
+
+  LittleDiracOp LDO(geom, UrbGrid, Coarse4d);
+  LDO.CoarsenOperator(HermOp, Aggregates);
+
+  //--------------------------------------------------------------------
+  // Correctness check: P M_fine P^T c  ≈  M_coarse c
+  //
+  // Promote a random coarse vector into the fine subspace, apply the
+  // fine operator, project back, and compare with the coarse operator
+  // applied directly.  Error should be at the level of subspace
+  // approximation quality (smaller = better basis vectors).
+  //--------------------------------------------------------------------
+  {
+    GridParallelRNG RNGc(Coarse4d); RNGc.SeedFixedIntegers({9,10,11,12});
+    CoarseVector c_src(Coarse4d), c_ldop(Coarse4d), c_proj(Coarse4d);
+    random(RNGc, c_src);
+
+    LatticeStaggeredFermionD f_v(UrbGrid), f_Mv(UrbGrid);
+    Aggregates.PromoteFromSubspace(c_src, f_v);
+    HermOp.Op(f_v, f_Mv);
+    Aggregates.ProjectToSubspace(c_proj, f_Mv);
+
+    LDO.M(c_src, c_ldop);
+
+    c_proj -= c_ldop;
+    RealD err = norm2(c_proj) / norm2(c_ldop);
+    std::cout << GridLogMessage
+              << "Coarsen check |P*M_fine - M_coarse| / |M_coarse| = " << err << std::endl;
+  }
+
+  //--------------------------------------------------------------------
+  // Multi-RHS coarse grid
+  //
+  // The extra leading dimension holds nrhs right-hand sides packed into
+  // SIMD lanes, matching the pattern of Test_general_coarse_hdcg_phys48.
+  //--------------------------------------------------------------------
+  const int nrhs = vComplex::Nsimd() * 2;
+
+  Coordinate mpi   = GridDefaultMpi();
+  Coordinate rhMpi ({1,    mpi[0],  mpi[1],  mpi[2],  mpi[3]});
+  Coordinate rhLatt({nrhs, clatt[0], clatt[1], clatt[2], clatt[3]});
+  Coordinate rhSimd({vComplex::Nsimd(), 1, 1, 1, 1});
+
+  GridCartesian *CoarseMrhs = new GridCartesian(rhLatt, rhSimd, rhMpi);
+
+  typedef MultiGeneralCoarsenedMatrix<vColourVector, vTComplex, nbasis> MultiCoarseOp;
+  MultiCoarseOp mrhs(geom, CoarseMrhs);
+  mrhs.CoarsenOperator(HermOp, Aggregates, Coarse4d);
+
+  //--------------------------------------------------------------------
+  // Coarse-grid Lanczos for deflation
+  //--------------------------------------------------------------------
+  typedef HermitianLinearOperator<MultiCoarseOp, CoarseVector> MrhsHermOp;
+  MrhsHermOp MrhsCoarseOp(mrhs);
+
+  // Estimate spectral bounds for Lanczos Chebyshev filter
+  CoarseVector pm_src(CoarseMrhs); pm_src = ComplexD(1.0);
+  PowerMethod<CoarseVector> cPM;
+  RealD lambda_max = cPM(MrhsCoarseOp, pm_src);
+  // Chebyshev filter window [lo, hi]:
+  //   lo must sit in the spectral gap between the Nstop-th and (Nstop+1)-th
+  //   coarse eigenvalues so that only the target modes receive cosh amplification.
+  //
+  // From a pilot run (16^4 fine, 4^4 coarse, mass=0.05, hot config):
+  //   Group 1 (near-null, 24 modes): lambda in [0.002647, 0.002746]  ~= mass^2
+  //   Spectral gap: factor 60 (lambda_24/lambda_23 = 0.165/0.00275)
+  //   Group 2 (second group): lambda in [0.165, 0.179]
+  //
+  // lo = 0.02 sits in the spectral gap (factor 7x above lambda_23=0.00275,
+  // factor 8x below lambda_24=0.165).
+  //   hi = lambda_max_coarse * 1.1 ~= 2.121
+  //   y(lambda_0=0.002647)  ~ -1.016 -> T_70 ~ 1.7e5  (cosh(70*0.182))
+  //   y(lambda_23=0.002746) ~ -1.015 -> T_70 ~ 1.6e5
+  //   Relative spread across near-null cluster: ~4.3%
+  //   y(lambda_24=0.165)    ~ -0.862 -> inside [lo,hi] -> |T_70| <= 1
+  //
+  // order=71 (degree 70) is needed to give ~4% relative spread across the
+  // near-null cluster of 24 nearly-degenerate eigenvalues; order=31 (tried)
+  // gave only ~1.7% spread, insufficient for Nk=24/Nm=48 to converge.
+  // Absolute amplification ~1e5; what matters for IRL convergence is the
+  // relative spread, not the absolute value.
+  // lo=0.005 failed (T_70~53, 0/24 modes in 10 restarts).
+  // lo=0.01 worked but needed 2 restarts (13/24 then 24/24); lo=0.02 converges in 1.
+  RealD lambda_lo  = 0.02;
+
+  std::cout << GridLogMessage << "Chebyshev filter: lo=" << lambda_lo
+            << " hi=" << lambda_max*1.1 << " order=71" << std::endl;
+
+  Chebyshev<CoarseVector> IRLCheby(lambda_lo, lambda_max * 1.1, 71);
+
+  // 24 near-null modes (eigenvalues ~mass^2) converge to resid^2~1e-28
+  // in the first Lanczos restart.  The remaining modes (~0.165) are a
+  // second spectral group that needs more Krylov vectors; handle them
+  // separately once the basic HDCG solve is validated.
+  int Nk    = 24;
+  int Nm    = 48;
+  int Nstop = Nk;
+
+  GridParallelRNG CRNG(Coarse4d); CRNG.SeedFixedIntegers({13,14,15,16});
+
+  ImplicitlyRestartedBlockLanczosCoarse<CoarseVector>
+    IRL(MrhsCoarseOp, Coarse4d, CoarseMrhs, nrhs, IRLCheby,
+        Nstop, /*conv_test_interval*/1, nrhs, Nk, Nm, 1.0e-5, 10);
+
+  int Nconv;
+  std::vector<RealD>        eval(Nm);
+  std::vector<CoarseVector> evec(Nm,   Coarse4d);  // evec on f_grid (single-RHS coarse)
+  std::vector<CoarseVector> c_srcs(nrhs, Coarse4d); // src on same grid as evec
+  for (int r = 0; r < nrhs; r++) random(CRNG, c_srcs[r]);
+  IRL.calc(eval, evec, c_srcs, Nconv, LanczosType::irbl);
+
+  //--------------------------------------------------------------------
+  // HDCG solver assembly
+  //--------------------------------------------------------------------
+  MultiRHSDeflation<CoarseVector> MrhsGuesser;
+  MrhsGuesser.ImportEigenBasis(evec, eval);
+
+  // MrhsProjector maps between fine (UrbGrid) and coarse (Coarse4d) spaces
+  MultiRHSBlockProject<LatticeStaggeredFermionD> MrhsProjector;
+  MrhsProjector.Allocate(nbasis, UrbGrid, Coarse4d);
+  MrhsProjector.ImportBasis(Aggregates.subspace);
+
+  ConjugateGradient<CoarseVector> CoarseCG(5.0e-2, 5000, false);
+  DoNothingGuesser<CoarseVector>  DoNothing;
+  HPDSolver<CoarseVector> HPDSolve(MrhsCoarseOp, CoarseCG, DoNothing);
+
+  // Spectral radius of the fine operator, needed for the smoother shift.
+  // Use a random checkerboard vector (UrbGrid) as starting guess for PowerMethod.
+  LatticeStaggeredFermionD fine_pm_src(UrbGrid);
+  random(RNGrb, fine_pm_src);
+  PowerMethod<LatticeStaggeredFermionD> finePM;
+  RealD fine_lambda_max = finePM(HermOp, fine_pm_src);
+
+  // Shifted smoother: CG on (HermOp + shift*I) with shift = lambda_max / 100.
+  //
+  // The O(8) CG polynomial has 8 roots. With this shift all 8 roots lie in the
+  // interval [shift, lambda_max + shift] ~ [0.046, 4.65], so the polynomial
+  // focuses entirely on the HIGH-frequency part of the spectrum and leaves
+  // near-null modes (lambda << shift) essentially untouched (polynomial ~ 1 there).
+  //
+  // This is the right target because the coarse-grid correction always introduces
+  // high-frequency spectral leakage: the blocked coarse-grid degrees of freedom
+  // are piecewise constant across coarse cells and therefore have sharp edges at
+  // cell boundaries (like lego-block edges). Smoothness is measured by the
+  // covariant Dirac derivative, so promoting the coarse solution back to the
+  // fine grid inevitably excites high-frequency components — just as a step
+  // function always carries high-frequency Fourier content.  The smoother must
+  // repair exactly these high modes.
+  //
+  // The smoother and the coarse-grid correction are applied alternately: together
+  // they both lift the low eigenvalues and pull down the upper eigenvalues of the
+  // composite preconditioned operator, reducing the condition number seen by the
+  // outer HDCG iterations.
+  //
+  // DWF HDCG convention; using mass^2 = 0.0025 was far too small: it scattered
+  // the 8 roots over [0.005, 4.6] and diluted their effect on the high modes.
+  RealD smootherShift = fine_lambda_max / 200.0;
+  std::cout << GridLogMessage << "Smoother shift: lambda_max_fine/200 = "
+            << fine_lambda_max << "/200 = " << smootherShift << std::endl;
+  ShiftedHermOpLinearOperator<LatticeStaggeredFermionD> ShiftedOp(HermOp, smootherShift);
+  CGSmoother<LatticeStaggeredFermionD> smoother(8, ShiftedOp);
+
+  TwoLevelADEF2mrhs<LatticeStaggeredFermionD, CoarseVector>
+    HDCG(1.0e-8, 500,
+         HermOp,
+         smoother,
+         HPDSolve,   // M1 (coarse correction)
+         HPDSolve,   // Vstart (initial guess projection)
+         MrhsProjector,
+         MrhsGuesser,
+         CoarseMrhs);
+
+  //--------------------------------------------------------------------
+  // Solve: nrhs right-hand sides simultaneously
+  //--------------------------------------------------------------------
+  std::vector<LatticeStaggeredFermionD> src(nrhs, UrbGrid);
+  std::vector<LatticeStaggeredFermionD> sol(nrhs, UrbGrid);
+
+  GridParallelRNG RNGrb2(UGrid); RNGrb2.SeedFixedIntegers({17,18,19,20}); // must use full grid, not UrbGrid
+  for (int r = 0; r < nrhs; r++) {
+    random(RNGrb2, src[r]);
+    sol[r] = Zero();
+  }
+
+  //--------------------------------------------------------------------
+  // Baseline: standard single-RHS CG on HermOp (no preconditioning)
+  // Run before HDCG to establish the unpreconditioned iteration count
+  // and wall-clock time for direct comparison.
+  //--------------------------------------------------------------------
+  {
+    ConjugateGradient<LatticeStaggeredFermionD> CG(1.0e-8, 50000, false);
+    std::vector<LatticeStaggeredFermionD> cg_sol(nrhs, UrbGrid);
+    for (int r = 0; r < nrhs; r++) cg_sol[r] = Zero();
+
+    RealD t0 = usecond();
+    int total_iters = 0;
+    for (int r = 0; r < nrhs; r++) {
+      std::cout << GridLogMessage << "====== CG baseline RHS " << r
+                << " ======" << std::endl;
+      CG(HermOp, src[r], cg_sol[r]);
+      total_iters += CG.IterationsToComplete;
+    }
+    RealD t1 = usecond();
+    std::cout << GridLogMessage << "CG baseline: " << nrhs << " RHS, "
+              << total_iters << " total iterations, "
+              << (t1 - t0) / 1.0e6 << " s total, "
+              << (t1 - t0) / 1.0e6 / nrhs << " s/RHS" << std::endl;
+  }
+
+  //--------------------------------------------------------------------
+  // HDCG solve
+  //--------------------------------------------------------------------
+  HDCG(src, sol);
+
+  Grid_finalize();
+  return 0;
+}

tests/debug/Test_staggered_hdcg_ildg.cc

@@ -0,0 +1,373 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: tests/debug/Test_staggered_hdcg.cc
+
+    Authors: Thomas Blum, Peter Boyle
+
+    HDCG (Hierarchical Deflation Conjugate Gradient) multigrid solver
+    for naive staggered fermions, based on arXiv:2409.03904.
+
+    Adapts the DWF HDCG infrastructure (Test_general_coarse_hdcg_phys48.cc) to:
+      - NaiveStaggeredFermion (nearest-neighbour only, no Naik 3-hop term)
+      - 4D SchurStaggeredOperator:  Mpc = m^2 - D_oe * D_eo  (hermitian, positive-definite)
+      - vColourVector fine field type (staggered has colour but no spin)
+      - NextToNearestStencilGeometry4D: 33-point coarse stencil
+
+    Stencil count: D_oe*D_eo has 2-hop fine range.  With blocking B >= 2 the coarse
+    shifts have L1-distance <= 2, giving 33 stencil points in 4D:
+      1 (identity) + 8 (+-e_mu) + 24 (+-e_mu +- e_nu).
+    NaiveStaggeredFermion has no Naik term, so any B >= 2 suffices.
+    To extend to ImprovedStaggeredFermion later, use B >= 6.
+
+    Reference: arXiv:2409.03904 (mrhs hermitian multigrid for DWF).
+
+    Usage (after build):
+      ./Test_staggered_hdcg --grid 16.16.16.16 --mpi 1.1.1.1
+
+*************************************************************************************/
+#include <Grid/Grid.h>
+#include <Grid/algorithms/iterative/AdefMrhs.h>
+#include <Grid/algorithms/iterative/ImplicitlyRestartedBlockLanczos.h>
+#include <Grid/algorithms/iterative/ImplicitlyRestartedBlockLanczosCoarse.h>
+
+using namespace Grid;
+
+// Non-converging CG used as a smoother (fixed number of iterations)
+template<class Field>
+class CGSmoother : public LinearFunction<Field>
+{
+public:
+  typedef LinearOperatorBase<Field> FineOperator;
+  FineOperator &_Op;
+  int iters;
+  CGSmoother(int _iters, FineOperator &Op) : _Op(Op), iters(_iters) {}
+  void operator()(const Field &in, Field &out)
+  {
+    ConjugateGradient<Field> CG(0.0, iters, false);
+    out = Zero();
+    CG(_Op, in, out);
+  }
+};
+
+int main(int argc, char **argv)
+{
+  fprintf(stderr, "TRACE: entering main\n"); fflush(stderr);
+  Grid_init(&argc, &argv);
+  fprintf(stderr, "TRACE: Grid_init done\n"); fflush(stderr);
+
+  //--------------------------------------------------------------------
+  // Parameters — tune for production
+  //--------------------------------------------------------------------
+  const int nbasis = 24;   // near-null space dimension
+  const int cb     = 0;    // even checkerboard
+
+  RealD mass = 0.00184;
+
+  // NaiveStaggeredFermion: nearest-neighbour hop only (no Naik term).
+  // c1 = coefficient of the hopping term (1.0 = standard normalisation).
+  // u0 = tadpole factor (1.0 = no tadpole improvement).
+  RealD c1 = 1.0;
+  RealD u0 = 1.0;
+
+  //--------------------------------------------------------------------
+  // Grids
+  // Fine:   UGrid (4D full), UrbGrid (4D red-black)
+  // Coarse: Coarse4d  with dimensions = GridDefaultLatt() / Block
+  //
+  // Recommended: GridDefaultLatt() >= 16^4, Block = {4,4,4,4}
+  // NaiveStaggeredFermion works with any Block >= {2,2,2,2}
+  //--------------------------------------------------------------------
+  fprintf(stderr, "TRACE: making UGrid\n"); fflush(stderr);
+  GridCartesian *UGrid = SpaceTimeGrid::makeFourDimGrid(
+      GridDefaultLatt(), GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
+  fprintf(stderr, "TRACE: making UrbGrid\n"); fflush(stderr);
+  GridRedBlackCartesian *UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+
+  Coordinate Block({4, 4, 4, 4});
+  Coordinate clatt = GridDefaultLatt();
+  for (int d = 0; d < clatt.size(); d++) clatt[d] /= Block[d];
+  Coordinate csimd = GridDefaultSimd(Nd, vComplex::Nsimd());
+  Coordinate cmpi  = GridDefaultMpi();
+  fprintf(stderr, "TRACE: making Coarse4d clatt=%d %d %d %d simd=%d %d %d %d mpi=%d %d %d %d Nsimd=%d\n",
+          clatt[0],clatt[1],clatt[2],clatt[3],
+          csimd[0],csimd[1],csimd[2],csimd[3],
+          cmpi[0],cmpi[1],cmpi[2],cmpi[3],
+          (int)vComplex::Nsimd()); fflush(stderr);
+
+  GridCartesian *Coarse4d = SpaceTimeGrid::makeFourDimGrid(clatt, csimd, cmpi);
+  fprintf(stderr, "TRACE: Coarse4d made\n"); fflush(stderr);
+
+  //--------------------------------------------------------------------
+  // RNG + gauge field
+  //--------------------------------------------------------------------
+  fprintf(stderr, "TRACE: RNG4\n"); fflush(stderr);
+  GridParallelRNG RNG4(UGrid);    RNG4.SeedFixedIntegers({1,2,3,4});
+  fprintf(stderr, "TRACE: RNGrb\n"); fflush(stderr);
+  GridParallelRNG RNGrb(UGrid); RNGrb.SeedFixedIntegers({5,6,7,8}); // must use full grid, not UrbGrid
+  fprintf(stderr, "TRACE: Umu\n"); fflush(stderr);
+  LatticeGaugeField Umu(UGrid);
+  int HotStart = 0;
+  if ( HotStart ) {
+    fprintf(stderr, "TRACE: HotConfig\n"); fflush(stderr);
+    SU<Nc>::HotConfiguration(RNG4, Umu);
+  } else { 
+    FieldMetaData header;
+    std::string file("./configuration.ildg");
+    IldgReader IR;
+    IR.open(file);
+    IR.readConfiguration(Umu,header);
+    IR.close();
+  }
+  
+  fprintf(stderr, "TRACE: NaiveStaggeredFermionD\n"); fflush(stderr);
+  NaiveStaggeredFermionD Ds(Umu, *UGrid, *UrbGrid, mass, c1, u0);
+  fprintf(stderr, "TRACE: SchurStaggeredOperator\n"); fflush(stderr);
+  SchurStaggeredOperator<NaiveStaggeredFermionD, LatticeStaggeredFermionD> HermOp(Ds);
+  fprintf(stderr, "TRACE: HermOp done\n"); fflush(stderr);
+
+  //--------------------------------------------------------------------
+  // Subspace: inverse-iteration near-null vectors
+  //
+  // CreateSubspace applies CG (4 solves, tol=1e-4) to random noise vectors,
+  // converging naturally to the low modes of HermOp without needing spectral
+  // bound tuning.  Switch to CreateSubspaceChebyshevNew once the spectrum is
+  // well characterised (hi ~ 5.0 for naive staggered SchurStaggeredOperator).
+  //--------------------------------------------------------------------
+  typedef Aggregation<vColourVector, vTComplex, nbasis> Subspace;
+  Subspace Aggregates(Coarse4d, UrbGrid, cb);
+
+  Aggregates.CreateSubspace(RNGrb, HermOp);
+  Aggregates.Orthogonalise();
+
+  //--------------------------------------------------------------------
+  // Coarse geometry: NextToNearestStencilGeometry4D
+  //   hops=2  ->  33 stencil points in 4D
+  //--------------------------------------------------------------------
+  NextToNearestStencilGeometry4D geom(Coarse4d);
+
+  std::cout << GridLogMessage << "Coarse stencil: " << geom.npoint << " points" << std::endl;
+
+  //--------------------------------------------------------------------
+  // Single-RHS coarse operator (used for correctness check below)
+  //--------------------------------------------------------------------
+  typedef GeneralCoarsenedMatrix<vColourVector, vTComplex, nbasis> LittleDiracOp;
+  typedef LittleDiracOp::CoarseVector CoarseVector;
+
+  LittleDiracOp LDO(geom, UrbGrid, Coarse4d);
+  LDO.CoarsenOperator(HermOp, Aggregates);
+
+  //--------------------------------------------------------------------
+  // Correctness check: P M_fine P^T c  ≈  M_coarse c
+  //
+  // Promote a random coarse vector into the fine subspace, apply the
+  // fine operator, project back, and compare with the coarse operator
+  // applied directly.  Error should be at the level of subspace
+  // approximation quality (smaller = better basis vectors).
+  //--------------------------------------------------------------------
+  {
+    GridParallelRNG RNGc(Coarse4d); RNGc.SeedFixedIntegers({9,10,11,12});
+    CoarseVector c_src(Coarse4d), c_ldop(Coarse4d), c_proj(Coarse4d);
+    random(RNGc, c_src);
+
+    LatticeStaggeredFermionD f_v(UrbGrid), f_Mv(UrbGrid);
+    Aggregates.PromoteFromSubspace(c_src, f_v);
+    HermOp.Op(f_v, f_Mv);
+    Aggregates.ProjectToSubspace(c_proj, f_Mv);
+
+    LDO.M(c_src, c_ldop);
+
+    c_proj -= c_ldop;
+    RealD err = norm2(c_proj) / norm2(c_ldop);
+    std::cout << GridLogMessage
+              << "Coarsen check |P*M_fine - M_coarse| / |M_coarse| = " << err << std::endl;
+  }
+
+  //--------------------------------------------------------------------
+  // Multi-RHS coarse grid
+  //
+  // The extra leading dimension holds nrhs right-hand sides packed into
+  // SIMD lanes, matching the pattern of Test_general_coarse_hdcg_phys48.
+  //--------------------------------------------------------------------
+  const int nrhs = vComplex::Nsimd() * 2;
+
+  Coordinate mpi   = GridDefaultMpi();
+  Coordinate rhMpi ({1,    mpi[0],  mpi[1],  mpi[2],  mpi[3]});
+  Coordinate rhLatt({nrhs, clatt[0], clatt[1], clatt[2], clatt[3]});
+  Coordinate rhSimd({vComplex::Nsimd(), 1, 1, 1, 1});
+
+  GridCartesian *CoarseMrhs = new GridCartesian(rhLatt, rhSimd, rhMpi);
+
+  typedef MultiGeneralCoarsenedMatrix<vColourVector, vTComplex, nbasis> MultiCoarseOp;
+  MultiCoarseOp mrhs(geom, CoarseMrhs);
+  mrhs.CoarsenOperator(HermOp, Aggregates, Coarse4d);
+
+  //--------------------------------------------------------------------
+  // Coarse-grid Lanczos for deflation
+  //--------------------------------------------------------------------
+  typedef HermitianLinearOperator<MultiCoarseOp, CoarseVector> MrhsHermOp;
+  MrhsHermOp MrhsCoarseOp(mrhs);
+
+  // Estimate spectral bounds for Lanczos Chebyshev filter
+  CoarseVector pm_src(CoarseMrhs); pm_src = ComplexD(1.0);
+  PowerMethod<CoarseVector> cPM;
+  RealD lambda_max = cPM(MrhsCoarseOp, pm_src);
+  // Chebyshev filter window [lo, hi]:
+  //   lo must sit in the spectral gap between the Nstop-th and (Nstop+1)-th
+  //   coarse eigenvalues so that only the target modes receive cosh amplification.
+  //
+  // From a pilot run (16^4 fine, 4^4 coarse, mass=0.05, hot config):
+  //   Group 1 (near-null, 24 modes): lambda in [0.002647, 0.002746]  ~= mass^2
+  //   Spectral gap: factor 60 (lambda_24/lambda_23 = 0.165/0.00275)
+  //   Group 2 (second group): lambda in [0.165, 0.179]
+  //
+  // lo = 0.02 sits in the spectral gap (factor 7x above lambda_23=0.00275,
+  // factor 8x below lambda_24=0.165).
+  //   hi = lambda_max_coarse * 1.1 ~= 2.121
+  //   y(lambda_0=0.002647)  ~ -1.016 -> T_70 ~ 1.7e5  (cosh(70*0.182))
+  //   y(lambda_23=0.002746) ~ -1.015 -> T_70 ~ 1.6e5
+  //   Relative spread across near-null cluster: ~4.3%
+  //   y(lambda_24=0.165)    ~ -0.862 -> inside [lo,hi] -> |T_70| <= 1
+  //
+  // order=71 (degree 70) is needed to give ~4% relative spread across the
+  // near-null cluster of 24 nearly-degenerate eigenvalues; order=31 (tried)
+  // gave only ~1.7% spread, insufficient for Nk=24/Nm=48 to converge.
+  // Absolute amplification ~1e5; what matters for IRL convergence is the
+  // relative spread, not the absolute value.
+  // lo=0.005 failed (T_70~53, 0/24 modes in 10 restarts).
+  // lo=0.01 worked but needed 2 restarts (13/24 then 24/24); lo=0.02 converges in 1.
+  RealD lambda_lo  = 0.02;
+
+  std::cout << GridLogMessage << "Chebyshev filter: lo=" << lambda_lo
+            << " hi=" << lambda_max*1.1 << " order=71" << std::endl;
+
+  Chebyshev<CoarseVector> IRLCheby(lambda_lo, lambda_max * 1.1, 71);
+
+  // 24 near-null modes (eigenvalues ~mass^2) converge to resid^2~1e-28
+  // in the first Lanczos restart.  The remaining modes (~0.165) are a
+  // second spectral group that needs more Krylov vectors; handle them
+  // separately once the basic HDCG solve is validated.
+  int Nk    = 24;
+  int Nm    = 48;
+  int Nstop = Nk;
+
+  GridParallelRNG CRNG(Coarse4d); CRNG.SeedFixedIntegers({13,14,15,16});
+
+  ImplicitlyRestartedBlockLanczosCoarse<CoarseVector>
+    IRL(MrhsCoarseOp, Coarse4d, CoarseMrhs, nrhs, IRLCheby,
+        Nstop, /*conv_test_interval*/1, nrhs, Nk, Nm, 1.0e-5, 10);
+
+  int Nconv;
+  std::vector<RealD>        eval(Nm);
+  std::vector<CoarseVector> evec(Nm,   Coarse4d);  // evec on f_grid (single-RHS coarse)
+  std::vector<CoarseVector> c_srcs(nrhs, Coarse4d); // src on same grid as evec
+  for (int r = 0; r < nrhs; r++) random(CRNG, c_srcs[r]);
+  IRL.calc(eval, evec, c_srcs, Nconv, LanczosType::irbl);
+
+  //--------------------------------------------------------------------
+  // HDCG solver assembly
+  //--------------------------------------------------------------------
+  MultiRHSDeflation<CoarseVector> MrhsGuesser;
+  MrhsGuesser.ImportEigenBasis(evec, eval);
+
+  // MrhsProjector maps between fine (UrbGrid) and coarse (Coarse4d) spaces
+  MultiRHSBlockProject<LatticeStaggeredFermionD> MrhsProjector;
+  MrhsProjector.Allocate(nbasis, UrbGrid, Coarse4d);
+  MrhsProjector.ImportBasis(Aggregates.subspace);
+
+  ConjugateGradient<CoarseVector> CoarseCG(5.0e-2, 5000, false);
+  DoNothingGuesser<CoarseVector>  DoNothing;
+  HPDSolver<CoarseVector> HPDSolve(MrhsCoarseOp, CoarseCG, DoNothing);
+
+  // Spectral radius of the fine operator, needed for the smoother shift.
+  // Use a random checkerboard vector (UrbGrid) as starting guess for PowerMethod.
+  LatticeStaggeredFermionD fine_pm_src(UrbGrid);
+  random(RNGrb, fine_pm_src);
+  PowerMethod<LatticeStaggeredFermionD> finePM;
+  RealD fine_lambda_max = finePM(HermOp, fine_pm_src);
+
+  // Shifted smoother: CG on (HermOp + shift*I) with shift = lambda_max / 100.
+  //
+  // The O(8) CG polynomial has 8 roots. With this shift all 8 roots lie in the
+  // interval [shift, lambda_max + shift] ~ [0.046, 4.65], so the polynomial
+  // focuses entirely on the HIGH-frequency part of the spectrum and leaves
+  // near-null modes (lambda << shift) essentially untouched (polynomial ~ 1 there).
+  //
+  // This is the right target because the coarse-grid correction always introduces
+  // high-frequency spectral leakage: the blocked coarse-grid degrees of freedom
+  // are piecewise constant across coarse cells and therefore have sharp edges at
+  // cell boundaries (like lego-block edges). Smoothness is measured by the
+  // covariant Dirac derivative, so promoting the coarse solution back to the
+  // fine grid inevitably excites high-frequency components — just as a step
+  // function always carries high-frequency Fourier content.  The smoother must
+  // repair exactly these high modes.
+  //
+  // The smoother and the coarse-grid correction are applied alternately: together
+  // they both lift the low eigenvalues and pull down the upper eigenvalues of the
+  // composite preconditioned operator, reducing the condition number seen by the
+  // outer HDCG iterations.
+  //
+  // DWF HDCG convention; using mass^2 = 0.0025 was far too small: it scattered
+  // the 8 roots over [0.005, 4.6] and diluted their effect on the high modes.
+  RealD smootherShift = fine_lambda_max / 200.0;
+  std::cout << GridLogMessage << "Smoother shift: lambda_max_fine/200 = "
+            << fine_lambda_max << "/200 = " << smootherShift << std::endl;
+  ShiftedHermOpLinearOperator<LatticeStaggeredFermionD> ShiftedOp(HermOp, smootherShift);
+  CGSmoother<LatticeStaggeredFermionD> smoother(8, ShiftedOp);
+
+  TwoLevelADEF2mrhs<LatticeStaggeredFermionD, CoarseVector>
+    HDCG(1.0e-8, 500,
+         HermOp,
+         smoother,
+         HPDSolve,   // M1 (coarse correction)
+         HPDSolve,   // Vstart (initial guess projection)
+         MrhsProjector,
+         MrhsGuesser,
+         CoarseMrhs);
+
+  //--------------------------------------------------------------------
+  // Solve: nrhs right-hand sides simultaneously
+  //--------------------------------------------------------------------
+  std::vector<LatticeStaggeredFermionD> src(nrhs, UrbGrid);
+  std::vector<LatticeStaggeredFermionD> sol(nrhs, UrbGrid);
+
+  GridParallelRNG RNGrb2(UGrid); RNGrb2.SeedFixedIntegers({17,18,19,20}); // must use full grid, not UrbGrid
+  for (int r = 0; r < nrhs; r++) {
+    random(RNGrb2, src[r]);
+    sol[r] = Zero();
+  }
+
+  //--------------------------------------------------------------------
+  // Baseline: standard single-RHS CG on HermOp (no preconditioning)
+  // Run before HDCG to establish the unpreconditioned iteration count
+  // and wall-clock time for direct comparison.
+  //--------------------------------------------------------------------
+  {
+    ConjugateGradient<LatticeStaggeredFermionD> CG(1.0e-8, 100000, false);
+    std::vector<LatticeStaggeredFermionD> cg_sol(nrhs, UrbGrid);
+    for (int r = 0; r < nrhs; r++) cg_sol[r] = Zero();
+
+    RealD t0 = usecond();
+    int total_iters = 0;
+    for (int r = 0; r < nrhs; r++) {
+      std::cout << GridLogMessage << "====== CG baseline RHS " << r
+                << " ======" << std::endl;
+      CG(HermOp, src[r], cg_sol[r]);
+      total_iters += CG.IterationsToComplete;
+    }
+    RealD t1 = usecond();
+    std::cout << GridLogMessage << "CG baseline: " << nrhs << " RHS, "
+              << total_iters << " total iterations, "
+              << (t1 - t0) / 1.0e6 << " s total, "
+              << (t1 - t0) / 1.0e6 / nrhs << " s/RHS" << std::endl;
+  }
+
+  //--------------------------------------------------------------------
+  // HDCG solve
+  //--------------------------------------------------------------------
+  HDCG(src, sol);
+
+  Grid_finalize();
+  return 0;
+}