Scaling perf

Worth an effort to understand if the different stochastic estimator is cleaner.

CLAUDE.md

@@ -0,0 +1,183 @@
+# CLAUDE.md
+
+This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository.
+
+## What This Is
+
+Grid is a data-parallel C++ library for lattice QCD. It provides SIMD-vectorised lattice containers, MPI-based domain decomposition, GPU acceleration (CUDA/HIP/SYCL), and a full suite of QCD algorithms including HMC.
+
+## Build
+
+Uses GNU Autotools. The bootstrap step only needs to run once (or after `configure.ac` changes).
+
+```bash
+./bootstrap.sh                    # downloads Eigen 3.4.0, generates configure
+mkdir build && cd build
+../configure [options]
+make -j$(nproc)
+make check                        # run root-level tests
+make install
+```
+
+Key configure options:
+
+| Option | Common values |
+|--------|---------------|
+| `--enable-simd=` | `AVX2`, `AVX512`, `KNL`, `A64FX`, `NEONv8`, `GPU` |
+| `--enable-comms=` | `mpi-auto`, `mpi3-auto`, `none` |
+| `--enable-accelerator=` | `cuda`, `hip`, `sycl` |
+| `--enable-shm=` | `shmopen`, `hugetlbfs`, `nvlink` |
+| `--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 |
+
+GPU builds additionally need `--enable-gen-simd-width=64` (sets 512-bit SIMD width for GPU warp/wavefront sizing) and `--enable-unified=no --enable-shm=nvlink` for multi-GPU runs.
+
+To speed up compilation, `--disable-fermion-reps --disable-gparity` skips instantiating G-parity and higher-representation fermion operators.
+
+Platform recipes from `README.md`:
+- **KNL**: `--enable-simd=KNL --enable-comms=mpi3-auto --enable-mkl`
+- **Skylake/Haswell**: `--enable-simd=AVX512` or `AVX2` + `--enable-comms=mpi3-auto`
+- **AMD EPYC**: `--enable-simd=AVX2 --enable-comms=mpi3`
+- **A64FX (Fugaku)**: `--enable-simd=A64FX --enable-comms=mpi3 --enable-shm=shmget` (see `SVE_README.txt`)
+
+Complete, working `configure` invocations for specific HPC systems (Frontier/ROCm, Perlmutter/CUDA, Summit, SDCC-A100, etc.) live in `systems/<platform>/config-command`. These are the canonical references for production builds.
+
+Required external libs: GMP, MPFR, OpenSSL, zlib.
+
+### Use `systems/` for real machines
+
+`systems/<machine>/` holds the known-good build for each production platform (`Frontier`, `Aurora`, `Perlmutter`, `Summit`, `Tursa`, `Lumi`, `Booster`, `Crusher`, `SDCC-*`, `mac-arm`, …). Each contains a `config-command` (the exact `../../configure` invocation) and a `sourceme.sh` (module loads and env). **Prefer copying/adapting these over hand-rolling configure flags** — they encode compiler workarounds, `LDFLAGS`, and shared-memory settings that are easy to get wrong. `systems/WorkArounds.txt` records known vendor bugs.
+
+Note the GPU builds use `--enable-simd=GPU --enable-gen-simd-width=64`, so `Nsimd` is *not* 1 on device (it is `64/sizeof(scalar)`).
+
+### Regenerating `Make.inc` — required after adding or deleting source files
+
+`Make.inc` files are generated, not tracked in git (`.gitignore`d). `scripts/filelist` walks `Grid/`, `tests/*`, `benchmarks/`, `examples/`, and `HMC/` and writes the file lists and per-test `bin_PROGRAMS` rules. Every new `.cc`/`.h` in `Grid/`, and every new `Test_*.cc` / `Benchmark_*.cc` / `Example_*.cc`, is invisible to the build until you run:
+
+```bash
+./scripts/filelist    # from the source root, then re-run configure/make
+```
+
+`bootstrap.sh` runs it for you on the first setup.
+
+## Running Tests and Benchmarks
+
+```bash
+# From build directory
+make check                          # root-level tests (Test_simd, Test_cshift, etc.)
+make -C tests/<subdir> tests        # build tests in a subdirectory
+make tests                          # build all tests across all subdirectories
+./tests/core/Test_simd              # run a single test binary directly
+mpirun -n 4 ./tests/core/Test_cshift --grid 16.16.16.16 --mpi 1.1.1.4
+```
+
+`make check` is a thin smoke test — building a subdirectory with `make -C tests/<subdir> tests` and running the relevant binaries directly is the normal development loop. Test binaries take Grid's standard command-line arguments (`--grid`, `--mpi`, `--accelerator-threads`, `--threads`, `--debug-signals`, `--log`); see `Grid/util/Init.cc`.
+
+Test subdirectories and their focus: `core` (SIMD, stencil, comms), `solver` (CG, GMRES, eigensolvers), `hmc` (MD integrators), `forces` (fermion forces), `lanczos`, `IO`, `smearing`, `sp2n`, `debug`.
+
+Tests and benchmarks that need optional fermion representations are guarded by `disable_tests_without_instantiations.h` / `disable_benchmarks_without_instantiations.h`, so a `--disable-fermion-reps --disable-gparity` build silently compiles them to no-ops.
+
+## Architecture
+
+### Layer stack (bottom to top)
+
+1. **SIMD layer** (`Grid/simd/`) — platform-specific intrinsics wrapped into `vRealF`, `vComplexD`, etc. The SIMD width and layout are compile-time constants controlled by `--enable-simd`.
+
+2. **Tensor layer** (`Grid/tensors/`) — Lorentz/colour/spin tensor algebra built on top of SIMD types. `iMatrix`, `iVector`, `iScalar` templates compose into QCD types like `ColourMatrix`, `SpinColourVector`.
+
+3. **Lattice layer** (`Grid/lattice/`) — `Lattice<T>` container: a site-local tensor replicated across a distributed Cartesian grid. All arithmetic is site-parallel and expression-template-fused.
+
+4. **Cartesian/comms layer** (`Grid/cartesian/`, `Grid/communicator/`) — `GridCartesian` holds the MPI topology and local/global geometry. `Grid/cshift/` implements nearest-neighbour halo exchange; `Grid/stencil/` is the optimised multi-hop stencil used by Dirac operators.
+
+5. **Algorithm layer** (`Grid/algorithms/`) — iterative solvers (CG, GMRES, BiCGSTAB, mixed-precision), eigensolvers (Lanczos, LAPACK), FFT, smearing, and multigrid.
+
+6. **QCD layer** (`Grid/qcd/`) — gauge and fermion actions, HMC integrators, observables.
+
+### QCD subsystem (`Grid/qcd/`)
+
+- `action/fermion/` — Wilson, Clover, DWF (Mobius), Staggered, twisted-mass, G-parity variants
+- `action/gauge/` — Wilson gauge, Symanzik, Iwasaki, DBW2, plaquette+rect
+- `representations/` — Fundamental, Adjoint, Two-index, Sp(2n)
+- `hmc/` — Leapfrog, OMF2/OMF4 integrators; pseudofermion refreshment; Metropolis accept/reject
+- `smearing/` — APE, Stout, HEX, gradient flow
+- `observables/` — Polyakov loop, plaquette, topological charge
+
+### GPU acceleration and the view/memory-manager discipline
+### Multigrid (`Grid/algorithms/multigrid/`)
+
+Aggregation-based algebraic multigrid for Wilson-type fermions. Key files: `CoarsenedMatrix.h` (coarse operator), `GeneralCoarsenedMatrix.h` and `GeneralCoarsenedMatrixMultiRHS.h` (general coarsening supporting multi-RHS solves), `Aggregates.h` (near-null vector construction), `Geometry.h` (coarse-grid geometry). `MultiGrid.h` is the top-level include.
+
+### GPU acceleration
+
+GPU support is injected via macros in `Grid/threads/Accelerator.h` — `accelerator_for(i, n, nsimd, {...})`, `accelerator_forNB` (non-blocking, must be followed by `accelerator_barrier()`), `accelerator_for2dNB`, and `accelerator_inline`. On a CPU build these degrade to `thread_for` (OpenMP). Unified virtual memory is on by default (`--enable-unified=yes`); device-aware MPI (`--enable-accelerator-aware-mpi`) avoids device→host copies on transfers.
+
+Lattice data is **not** directly addressable inside a kernel. You must open a view with the correct access mode so `Grid/allocator/MemoryManager.h` can move/mark the data:
+
+```cpp
+autoView(out_v, out, AcceleratorWriteDiscard);   // RAII; closes at end of scope
+autoView(in_v,  in,  AcceleratorRead);
+accelerator_for(ss, grid->oSites(), Nsimd, {
+    coalescedWrite(out_v[ss], coalescedRead(in_v[ss]));
+});
+```
+
+Modes are `AcceleratorRead/Write/WriteDiscard` and `CpuRead/Write/WriteDiscard`. Getting the mode wrong (e.g. `AcceleratorRead` on a field you write) produces stale-data bugs that only appear on GPU builds. Inside kernels use `coalescedRead`/`coalescedWrite` rather than raw `operator[]` — they map the SIMD lane onto `threadIdx.x` so accesses stay coalesced.
+
+### Repo-local debugging skills (`skills/`)
+
+`skills/` contains hard-won, Grid-specific playbooks written as invocable skill files. Consult them before debugging in these areas rather than reasoning from first principles:
+
+| File | Covers |
+|---|---|
+| `gpu-memory-performance.md` | `acceleratorThreads()`, LambdaApply thread mapping, `coalescedRead` idiom, fused vs staged HBM access |
+| `gpu-runtime-correctness.md` | GPU runtime returning early from sync, silent wrong answers |
+| `communication-overlap.md` | 7-phase halo pipeline, per-packet events, host-staging vs GPU-direct RDMA |
+| `mpi-heterogeneous.md` | `MPI_Sendrecv` device-buffer aliasing, deterministic reductions |
+| `compiler-validation.md` | Isolating GPU compiler codegen bugs, minimal reproducers |
+| `correctness-verification.md` | Double-run fingerprinting, per-packet checksums, flight recorder |
+| `hang-diagnosis.md` | Diagnosing MPI/accelerator hangs |
+
+The key loop macros (defined in `Grid/threads/Accelerator.h`) are:
+- `accelerator_for(iter, num, nsimd, {...})` — maps to CUDA/HIP kernel or OpenMP loop; `nsimd` is the innermost SIMD lane count
+- `accelerator_forNB(...)` — non-blocking variant (no implicit barrier)
+- `accelerator_for2dNB(iter1, num1, iter2, num2, nsimd, {...})` — 2D kernel launch
+- `thread_for(iter, num, {...})` — CPU OpenMP loop (never dispatches to GPU)
+
+On CPU builds, `accelerator_for` aliases to `thread_for`.
+
+### Solver patterns
+
+`SchurRedBlack` (`Grid/algorithms/iterative/SchurRedBlack.h`) implements red-black (even/odd) preconditioning for fermion operators. Most production fermion solves use `SchurRedBlackDiagMooeeSolve` or similar wrappers that internally call a `ConjugateGradient` on the Schur complement.
+
+Mixed-precision solvers (`ConjugateGradientMixedPrec`, `BiCGSTABMixedPrec`) drive a double-precision outer loop with single-precision inner solves.
+
+### Memory and I/O
+
+- `Grid/allocator/` — aligned/NUMA-aware allocators; caching allocator via `--enable-alloc-cache`
+- `Grid/parallelIO/` — distributed parallel reader/writer for ILDG (via LIME), SciDAC, and native binary formats
+- `Grid/serialisation/` — text, binary, HDF5, XML/JSON serialisation of arbitrary Grid objects
+
+### Executables
+
+- `HMC/` — production HMC driver programmes (e.g. `Mobius2p1f.cc`, `DWF_plus_DSDR_nf2plus1_Shamir_Gparity.cc`)
+- `benchmarks/` — `Benchmark_dwf`, `Benchmark_ITT`, `Benchmark_comms`, `Benchmark_memory_bandwidth`, … used to qualify a new machine
+- `examples/` — small, readable programmes (`Example_plaquette.cc`, `Example_Mobius_spectrum.cc`) that are the best starting point for learning the API
+
+Each of these directories auto-builds every top-level `.cc` as its own binary via `scripts/filelist`.
+
+Every programme is wrapped in `Grid_init(&argc, &argv)` / `Grid_finalize()` (`Grid/util/Init.h`).
+
+## Key Conventions
+
+- **C++17** is required throughout.
+- Template structure: most classes are templated on `<_FImpl>` (fermion impl) or `<Gimpl>` (gauge impl), which encode the representation and precision. Instantiation is controlled by `--enable-fermion-instantiations`.
+- **Tensor indices are positional, not labelled.** The `Grid/tensors/` arithmetic recurses structurally over the `iScalar`/`iVector`/`iMatrix` nest: each level defines only the {scalar,vector,matrix}² products at its own level, with element types resolved by automatic type deduction, so every colour/spin/lorentz combination composes from ~200 lines (versus the pre-C++11 QDP++/PETE approach of machine-generating every case). An index's meaning derives entirely from its nesting depth counted from the outside; `iScalar` is the identity/broadcast case at every level. Never insert or remove a nesting level casually — the multiplication tables contract by position.
+- **Multigrid coarsening deepens the tensor nest by one level.** A coarse site vector is `iVector<CComplex,nbasis>`, and `innerProduct` on it returns `iScalar<CComplex>` — one level deeper than the fine block scalar. So the block-inner-product scalar type gains one `iScalar` wrapper per MG level (fine: `vTComplex`; level 2: `iScalar<vTComplex>`; see `examples/Example_pvdagm_3level.cc`). When calling `blockInnerProduct`/`blockZAXPY`/`blockOrthogonalise` on coarse fields, the coarse scalar type must match `decltype(innerProduct(siteVector(),siteVector()))` exactly; a wrong depth fails to compile (no viable `operator=` deep in the instantiation chain) rather than mis-contracting.
+- The `RealD`/`RealF`/`ComplexD`/`ComplexF` typedefs are used everywhere; avoid raw `double`/`float`.
+- Use `GRID_ASSERT(cond)` (defined in `Grid/GridStd.h`), not bare `assert` — it prints a Grid-formatted message and aborts cleanly under MPI.
+- Logging is stream-based, not macro-based: `std::cout << GridLogMessage << ... << std::endl;`. Channels declared in `Grid/log/Log.h` include `GridLogError`, `GridLogWarning`, `GridLogDebug`, `GridLogPerformance`, `GridLogIterative`, `GridLogSolver`, `GridLogHMC`, `GridLogComms`, `GridLogMemory`, `GridLogDslash`, `GridLogIRL`, `GridLogMG`. A subset is switched on at runtime with e.g. `--log Error,Warning,Message,Performance,Iterative,Integrator,Debug,Colours` (names given without the `GridLog` prefix).
+- Performance-critical paths use `GRID_TRACE(name)` from `Grid/perfmon/Tracing.h` (compiled out unless `--enable-tracing` selects a backend) and the `GridStopWatch` timers in `Grid/perfmon/Timer.h`.
+- Reductions across MPI ranks go through `GridBase::GlobalSum` / `GlobalMax`; never reduce with bare MPI calls inside library code.
+- Everything lives in `NAMESPACE_BEGIN(Grid)` / `NAMESPACE_END(Grid)` macros; follow the surrounding file rather than writing `namespace Grid { }`.
+- British spelling is used in identifiers and comments (`colour`, `neighbour`, `serialisation`).

Grid/algorithms/FFT.h

@@ -1,6 +1,6 @@
 /*************************************************************************************
 
-    Grid physics library, www.github.com/paboyle/Grid 
+    Grid physics library, www.github.com/paboyle/Grid
 
     Source file: ./lib/Cshift.h
 
@@ -65,17 +65,16 @@ public:
   typedef hipfftDoubleComplex FFTW_scalar;
   typedef hipfftHandle        FFTW_plan;
   static FFTW_plan fftw_plan_many_dft(int rank, int *n,int howmany,
-				      FFTW_scalar *in, int *inembed,		
+				      FFTW_scalar *in, int *inembed,
-				      int istride, int idist,		
+				      int istride, int idist,
-				      FFTW_scalar *out, int *onembed,		
+				      FFTW_scalar *out, int *onembed,
-				      int ostride, int odist,		
+				      int ostride, int odist,
 				      int sign, unsigned flags) {
     FFTW_plan p;
     auto rv = hipfftPlanMany(&p,rank,n,n,istride,idist,n,ostride,odist,HIPFFT_Z2Z,howmany);
     GRID_ASSERT(rv==HIPFFT_SUCCESS);
     return p;
-  }	  
+  }
-    
   inline static void fftw_execute_dft(const FFTW_plan p,FFTW_scalar *in,FFTW_scalar *out, int sign) {
     hipfftResult rv;
     if ( sign == forward ) rv =hipfftExecZ2Z(p,in,out,HIPFFT_FORWARD);
@@ -83,29 +82,25 @@ public:
     accelerator_barrier();
     GRID_ASSERT(rv==HIPFFT_SUCCESS);
   }
-  inline static void fftw_destroy_plan(const FFTW_plan p) {
+  inline static void fftw_destroy_plan(const FFTW_plan p) { hipfftDestroy(p); }
-    hipfftDestroy(p);
-  }
 };
 template<> struct FFTW<ComplexF> {
 public:
   static const int forward=FFTW_FORWARD;
   static const int backward=FFTW_BACKWARD;
-  typedef hipfftComplex      FFTW_scalar;
+  typedef hipfftComplex FFTW_scalar;
-  typedef hipfftHandle        FFTW_plan;
+  typedef hipfftHandle  FFTW_plan;
-
   static FFTW_plan fftw_plan_many_dft(int rank, int *n,int howmany,
-				      FFTW_scalar *in, int *inembed,		
+				      FFTW_scalar *in, int *inembed,
-				      int istride, int idist,		
+				      int istride, int idist,
-				      FFTW_scalar *out, int *onembed,		
+				      FFTW_scalar *out, int *onembed,
-				      int ostride, int odist,		
+				      int ostride, int odist,
 				      int sign, unsigned flags) {
     FFTW_plan p;
     auto rv = hipfftPlanMany(&p,rank,n,n,istride,idist,n,ostride,odist,HIPFFT_C2C,howmany);
     GRID_ASSERT(rv==HIPFFT_SUCCESS);
     return p;
-  }	  
+  }
-    
   inline static void fftw_execute_dft(const FFTW_plan p,FFTW_scalar *in,FFTW_scalar *out, int sign) {
     hipfftResult rv;
     if ( sign == forward ) rv =hipfftExecC2C(p,in,out,HIPFFT_FORWARD);
@@ -113,9 +108,7 @@ public:
     accelerator_barrier();
     GRID_ASSERT(rv==HIPFFT_SUCCESS);
   }
-  inline static void fftw_destroy_plan(const FFTW_plan p) {
+  inline static void fftw_destroy_plan(const FFTW_plan p) { hipfftDestroy(p); }
-    hipfftDestroy(p);
-  }
 };
 #endif
 
@@ -126,53 +119,45 @@ public:
   static const int backward=FFTW_BACKWARD;
   typedef cufftDoubleComplex FFTW_scalar;
   typedef cufftHandle        FFTW_plan;
-
   static FFTW_plan fftw_plan_many_dft(int rank, int *n,int howmany,
-				      FFTW_scalar *in, int *inembed,		
+				      FFTW_scalar *in, int *inembed,
-				      int istride, int idist,		
+				      int istride, int idist,
-				      FFTW_scalar *out, int *onembed,		
+				      FFTW_scalar *out, int *onembed,
-				      int ostride, int odist,		
+				      int ostride, int odist,
 				      int sign, unsigned flags) {
     FFTW_plan p;
     cufftPlanMany(&p,rank,n,n,istride,idist,n,ostride,odist,CUFFT_Z2Z,howmany);
     return p;
-  }	  
+  }
-    
   inline static void fftw_execute_dft(const FFTW_plan p,FFTW_scalar *in,FFTW_scalar *out, int sign) {
     if ( sign == forward ) cufftExecZ2Z(p,in,out,CUFFT_FORWARD);
     else                   cufftExecZ2Z(p,in,out,CUFFT_INVERSE);
     accelerator_barrier();
   }
-  inline static void fftw_destroy_plan(const FFTW_plan p) {
+  inline static void fftw_destroy_plan(const FFTW_plan p) { cufftDestroy(p); }
-    cufftDestroy(p);
-  }
 };
 template<> struct FFTW<ComplexF> {
 public:
   static const int forward=FFTW_FORWARD;
   static const int backward=FFTW_BACKWARD;
   typedef cufftComplex FFTW_scalar;
-  typedef cufftHandle        FFTW_plan;
+  typedef cufftHandle  FFTW_plan;
-
   static FFTW_plan fftw_plan_many_dft(int rank, int *n,int howmany,
-				      FFTW_scalar *in, int *inembed,		
+				      FFTW_scalar *in, int *inembed,
-				      int istride, int idist,		
+				      int istride, int idist,
-				      FFTW_scalar *out, int *onembed,		
+				      FFTW_scalar *out, int *onembed,
-				      int ostride, int odist,		
+				      int ostride, int odist,
 				      int sign, unsigned flags) {
     FFTW_plan p;
     cufftPlanMany(&p,rank,n,n,istride,idist,n,ostride,odist,CUFFT_C2C,howmany);
     return p;
-  }	  
+  }
-    
   inline static void fftw_execute_dft(const FFTW_plan p,FFTW_scalar *in,FFTW_scalar *out, int sign) {
     if ( sign == forward ) cufftExecC2C(p,in,out,CUFFT_FORWARD);
     else                   cufftExecC2C(p,in,out,CUFFT_INVERSE);
     accelerator_barrier();
   }
-  inline static void fftw_destroy_plan(const FFTW_plan p) {
+  inline static void fftw_destroy_plan(const FFTW_plan p) { cufftDestroy(p); }
-    cufftDestroy(p);
-  }
 };
 #endif
 
@@ -183,313 +168,325 @@ public:
   typedef fftw_complex FFTW_scalar;
   typedef fftw_plan    FFTW_plan;
   static FFTW_plan fftw_plan_many_dft(int rank, int *n,int howmany,
-				      FFTW_scalar *in, int *inembed,		
+				      FFTW_scalar *in, int *inembed,
-				      int istride, int idist,		
+				      int istride, int idist,
-				      FFTW_scalar *out, int *onembed,		
+				      FFTW_scalar *out, int *onembed,
-				      int ostride, int odist,		
+				      int ostride, int odist,
 				      int sign, unsigned flags) {
     return ::fftw_plan_many_dft(rank,n,howmany,in,inembed,istride,idist,out,onembed,ostride,odist,sign,flags);
-  }	  
+  }
-    
   inline static void fftw_execute_dft(const FFTW_plan p,FFTW_scalar *in,FFTW_scalar *out, int sign) {
     ::fftw_execute_dft(p,in,out);
   }
-  inline static void fftw_destroy_plan(const FFTW_plan p) {
+  inline static void fftw_destroy_plan(const FFTW_plan p) { ::fftw_destroy_plan(p); }
-    ::fftw_destroy_plan(p);
-  }
 };
 template<> struct FFTW<ComplexF> {
 public:
   typedef fftwf_complex FFTW_scalar;
   typedef fftwf_plan    FFTW_plan;
   static FFTW_plan fftw_plan_many_dft(int rank, int *n,int howmany,
-				      FFTW_scalar *in, int *inembed,		
+				      FFTW_scalar *in, int *inembed,
-				      int istride, int idist,		
+				      int istride, int idist,
-				      FFTW_scalar *out, int *onembed,		
+				      FFTW_scalar *out, int *onembed,
-				      int ostride, int odist,		
+				      int ostride, int odist,
 				      int sign, unsigned flags) {
     return ::fftwf_plan_many_dft(rank,n,howmany,in,inembed,istride,idist,out,onembed,ostride,odist,sign,flags);
-  }	  
+  }
-    
   inline static void fftw_execute_dft(const FFTW_plan p,FFTW_scalar *in,FFTW_scalar *out, int sign) {
     ::fftwf_execute_dft(p,in,out);
   }
-  inline static void fftw_destroy_plan(const FFTW_plan p) {
+  inline static void fftw_destroy_plan(const FFTW_plan p) { ::fftwf_destroy_plan(p); }
-    ::fftwf_destroy_plan(p);
-  }
 };
 #endif
 #endif
 
-class FFT {
+struct FFTbase {
-private:
+  double        flops;
-    
+  double        flops_call;
-  double flops;
+  uint64_t      usec;
-  double flops_call;
+  GridCartesian *_grid;
-  uint64_t usec;
-    
-public:
-    
-  static const int forward=FFTW_FORWARD;
-  static const int backward=FFTW_BACKWARD;
-    
-  double Flops(void) {return flops;}
-  double MFlops(void) {return flops/usec;}
-  double USec(void)   {return (double)usec;}    
 
-  FFT ( GridCartesian * grid ) 
+  static const int forward  = FFTW_FORWARD;
-  {
+  static const int backward = FFTW_BACKWARD;
-    flops=0;
+
-    usec =0;
+  double Flops(void)  { return flops; }
-  };
+  double MFlops(void) { return flops / usec; }
-    
+  double USec(void)   { return (double)usec; }
-  ~FFT ( void)  {
+
-    //    delete sgrid;
+  FFTbase(GridCartesian *grid) : _grid(grid), flops(0), flops_call(0), usec(0) {}
+};
+
+// Barrel-shift gather, FFT execute, and insert. Called by both FFT and PlannedFFT.
+// The caller is responsible for plan acquisition and destruction.
+template<class vobj>
+static void FFT_dim_execute(
+    Lattice<vobj>       &result,
+    const Lattice<vobj> &source,
+    int dim, int sign,
+    typename FFTW<typename vobj::scalar_type>::FFTW_plan p,
+    GridCartesian *grid,
+    double &flops, double &flops_call, uint64_t &usec)
+{
+  typedef typename vobj::scalar_type   scalar;
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type   scalar_type;
+  typedef typename vobj::vector_type   vector_type;
+  typedef typename FFTW<scalar>::FFTW_scalar FFTW_scalar;
+
+  const int Ndim = grid->Nd();
+  int L = grid->_ldimensions[dim];
+  int G = grid->_fdimensions[dim];
+  int Ncomp = sizeof(sobj) / sizeof(scalar);
+  int64_t Nlow = 1, Nhigh = 1;
+  for (int d = 0; d < dim;      d++) Nlow  *= grid->_ldimensions[d];
+  for (int d = dim+1; d < Ndim; d++) Nhigh *= grid->_ldimensions[d];
+  int64_t Nperp = Nlow * Nhigh;
+
+  deviceVector<scalar> pgbuf(Nperp * Ncomp * G);
+  scalar *pgbuf_v = &pgbuf[0];
+  int howmany = Ncomp * Nperp;
+
+  scalar div;
+  if      (sign == FFTW_BACKWARD) div = 1.0 / G;
+  else if (sign == FFTW_FORWARD)  div = 1.0;
+  else GRID_ASSERT(0);
+
+  double t_pencil = 0, t_fft = 0, t_copy = 0, t_shift = 0;
+  double t_total  = -usecond();
+
+  result = source;
+  int pc = grid->_processor_coor[dim];
+
+  const Coordinate ldims      = grid->_ldimensions;
+  const Coordinate rdims      = grid->_rdimensions;
+  const Coordinate sdims      = grid->_simd_layout;
+  const Coordinate processors = grid->_processors;
+
+  Coordinate pgdims(Ndim);
+  pgdims[0] = G;
+  for (int d = 0, dd = 1; d < Ndim; d++)
+    if (d != dim) pgdims[dd++] = ldims[d];
+  int64_t pgvol = 1;
+  for (int d = 0; d < Ndim; d++) pgvol *= pgdims[d];
+
+  const int Nsimd = vobj::Nsimd();
+  t_pencil = -usecond();
+  for (int p_idx = 0; p_idx < processors[dim]; p_idx++) {
+    t_copy -= usecond();
+    autoView(r_v, result, AcceleratorRead);
+    accelerator_for(idx, grid->oSites(), vobj::Nsimd(), {
+#ifdef GRID_SIMT
+    {
+      int lane = acceleratorSIMTlane(Nsimd);
+#else
+    for (int lane = 0; lane < Nsimd; lane++) {
+#endif
+      Coordinate icoor, ocoor, pgcoor;
+      Lexicographic::CoorFromIndex(icoor, lane, sdims);
+      Lexicographic::CoorFromIndex(ocoor, idx,  rdims);
+      pgcoor[0] = ocoor[dim] + icoor[dim]*rdims[dim] + ((pc+p_idx)%processors[dim])*L;
+      for (int d = 0, dd = 1; d < Ndim; d++)
+        if (d != dim) { pgcoor[dd] = ocoor[d] + icoor[d]*rdims[d]; dd++; }
+      int64_t pgidx;
+      Lexicographic::IndexFromCoor(pgcoor, pgidx, pgdims);
+      vector_type *from = (vector_type *)&r_v[idx];
+      scalar_type  stmp;
+      for (int w = 0; w < Ncomp; w++) {
+        stmp = getlane(from[w], lane);
+        pgbuf_v[pgidx + w*pgvol] = stmp;
+      }
+#ifdef GRID_SIMT
+    }
+#else
+    }
+#endif
+    });
+    t_copy += usecond();
+    if (p_idx != processors[dim] - 1) {
+      Lattice<vobj> temp(grid);
+      t_shift -= usecond();
+      temp = Cshift(result, dim, L); result = temp;
+      t_shift += usecond();
+    }
   }
-    
+  t_pencil += usecond();
-  template<class vobj>
-  void FFT_dim_mask(Lattice<vobj> &result,const Lattice<vobj> &source,Coordinate mask,int sign){
 
-    //    vgrid=result.Grid();
+  FFTW_scalar *in  = (FFTW_scalar *)pgbuf_v;
-    //    conformable(result.Grid(),vgrid);
+  FFTW_scalar *out = (FFTW_scalar *)pgbuf_v;
-    //    conformable(source.Grid(),vgrid);
+  t_fft = -usecond();
-    const int Ndim = source.Grid()->Nd();
+  FFTW<scalar>::fftw_execute_dft(p, in, out, sign);
+  t_fft += usecond();
+
+  flops_call = 5.0 * howmany * G * log2(G);
+  usec  = t_fft;
+  flops = flops_call;
+
+  result = Zero();
+  double t_insert = -usecond();
+  {
+    autoView(r_v, result, AcceleratorWrite);
+    accelerator_for(idx, grid->oSites(), Nsimd, {
+#ifdef GRID_SIMT
+    {
+      int lane = acceleratorSIMTlane(Nsimd);
+#else
+    for (int lane = 0; lane < Nsimd; lane++) {
+#endif
+      Coordinate icoor(Ndim), ocoor(Ndim), pgcoor(Ndim);
+      Lexicographic::CoorFromIndex(icoor, lane, sdims);
+      Lexicographic::CoorFromIndex(ocoor, idx,  rdims);
+      pgcoor[0] = ocoor[dim] + icoor[dim]*rdims[dim] + pc*L;
+      for (int d = 0, dd = 1; d < Ndim; d++)
+        if (d != dim) { pgcoor[dd] = ocoor[d] + icoor[d]*rdims[d]; dd++; }
+      int64_t pgidx;
+      Lexicographic::IndexFromCoor(pgcoor, pgidx, pgdims);
+      vector_type *to  = (vector_type *)&r_v[idx];
+      scalar_type  stmp;
+      for (int w = 0; w < Ncomp; w++) {
+        stmp = pgbuf_v[pgidx + w*pgvol];
+        putlane(to[w], stmp, lane);
+      }
+#ifdef GRID_SIMT
+    }
+#else
+    }
+#endif
+    });
+  }
+  result = result * div;
+  t_insert += usecond();
+  t_total  += usecond();
+
+  std::cout << GridLogPerformance << " FFT took   " << t_total/1.0e6  << " s" << std::endl;
+  std::cout << GridLogPerformance << " FFT pencil " << t_pencil/1.0e6 << " s" << std::endl;
+  std::cout << GridLogPerformance << "  of which copy " << t_copy/1.0e6  << " s" << std::endl;
+  std::cout << GridLogPerformance << "  of which shift" << t_shift/1.0e6 << " s" << std::endl;
+  std::cout << GridLogPerformance << " FFT kernels " << t_fft/1.0e6    << " s" << std::endl;
+  std::cout << GridLogPerformance << " FFT insert  " << t_insert/1.0e6 << " s" << std::endl;
+}
+
+class FFT : public FFTbase {
+public:
+  FFT(GridCartesian *grid) : FFTbase(grid) {}
+  ~FFT() {}
+
+  template<class vobj>
+  void FFT_dim_mask(Lattice<vobj> &result, const Lattice<vobj> &source, Coordinate mask, int sign) {
+    const int Ndim = _grid->Nd();
     Lattice<vobj> tmp = source;
-    for(int d=0;d<Ndim;d++){
+    for (int d = 0; d < Ndim; d++) {
-      if( mask[d] ) {
+      if (mask[d]) {
-	FFT_dim(result,tmp,d,sign);
+        FFT_dim(result, tmp, d, sign);
-	tmp=result;
+        tmp = result;
       }
     }
   }
 
   template<class vobj>
-  void FFT_all_dim(Lattice<vobj> &result,const Lattice<vobj> &source,int sign){
+  void FFT_all_dim(Lattice<vobj> &result, const Lattice<vobj> &source, int sign) {
-    const int Ndim = source.Grid()->Nd();
+    Coordinate mask(_grid->Nd(), 1);
-    Coordinate mask(Ndim,1);
+    FFT_dim_mask(result, source, mask, sign);
-    FFT_dim_mask(result,source,mask,sign);
   }
 
-
   template<class vobj>
-  void FFT_dim(Lattice<vobj> &result,const Lattice<vobj> &source,int dim, int sign){
+  void FFT_dim(Lattice<vobj> &result, const Lattice<vobj> &source, int dim, int sign) {
-    const int Ndim = source.Grid()->Nd();
+    GRID_ASSERT(source.Grid() == _grid);
-    GridBase *grid = source.Grid();
+    GRID_ASSERT(result.Grid() == _grid);
-    conformable(result.Grid(),source.Grid());
+    conformable(result.Grid(), source.Grid());
 
-    int L = grid->_ldimensions[dim];
-    int G = grid->_fdimensions[dim];
-      
-    Coordinate layout(Ndim,1);
-    
-    // Construct pencils
-    typedef typename vobj::scalar_object sobj;
     typedef typename vobj::scalar_type   scalar;
-    typedef typename vobj::scalar_type   scalar_type;
+    typedef typename vobj::scalar_object sobj;
-    typedef typename vobj::vector_type   vector_type;
-      
-    //std::cout << "CPU view" << std::endl;
-    
     typedef typename FFTW<scalar>::FFTW_scalar FFTW_scalar;
     typedef typename FFTW<scalar>::FFTW_plan   FFTW_plan;
-      
-    int Ncomp = sizeof(sobj)/sizeof(scalar);
-    int64_t Nlow  = 1;
-    int64_t Nhigh = 1;
 
-    for(int d=0;d<dim;d++){
+    const int Ndim = _grid->Nd();
-      Nlow*=grid->_ldimensions[d];
+    int G     = _grid->_fdimensions[dim];
-    }
+    int Ncomp = sizeof(sobj) / sizeof(scalar);
-    for(int d=dim+1;d<Ndim;d++){
+    int64_t Nperp = 1;
-      Nhigh*=grid->_ldimensions[d];
+    for (int d = 0; d < Ndim; d++)
-    }
+      if (d != dim) Nperp *= _grid->_ldimensions[d];
-    int64_t Nperp=Nlow*Nhigh;
+    int n[]     = {G};
-    
-    deviceVector<scalar> pgbuf; // Layout is [perp][component][dim]
-    pgbuf.resize(Nperp*Ncomp*G);
-    scalar *pgbuf_v = &pgbuf[0];
-      
-    int rank = 1;  /* 1d transforms */
-    int n[] = {G}; /* 1d transforms of length G */
     int howmany = Ncomp * Nperp;
-    int odist,idist,istride,ostride;
-    idist   = odist   = G;            /* Distance between consecutive FT's */
-    istride = ostride = 1;            /* Distance between two elements in the same FT */
-    int *inembed = n, *onembed = n;
-      
-    scalar div;
-    if ( sign == backward ) div = 1.0/G;
-    else if ( sign == forward ) div = 1.0;
-    else GRID_ASSERT(0);
 
-    double t_pencil=0;
+    deviceVector<scalar> dummy(2);
-    double t_fft   =0;
+    FFTW_scalar *buf = (FFTW_scalar *)&dummy[0];
-    double t_total =-usecond();
+    FFTW_plan p = FFTW<scalar>::fftw_plan_many_dft(1, n, howmany,
-    //    std::cout << GridLogPerformance<<"Making FFTW plan" << std::endl;
+                                                    buf, n, 1, G,
-    /*
+                                                    buf, n, 1, G,
-     *
+                                                    sign, FFTW_ESTIMATE);
-     */
+    FFT_dim_execute(result, source, dim, sign, p, _grid, flops, flops_call, usec);
-    FFTW_plan p;
-    {
-      FFTW_scalar *in = (FFTW_scalar *)&pgbuf_v[0];
-      FFTW_scalar *out= (FFTW_scalar *)&pgbuf_v[0];
-      p = FFTW<scalar>::fftw_plan_many_dft(rank,n,howmany,
-					   in,inembed,
-					   istride,idist,
-					   out,onembed,
-					   ostride, odist,
-					   sign,FFTW_ESTIMATE);
-    }
-      
-    // Barrel shift and collect global pencil
-    //    std::cout << GridLogPerformance<<"Making pencil" << std::endl;
-    Coordinate lcoor(Ndim), gcoor(Ndim);
-    double t_copy=0;
-    double t_shift=0;
-    t_pencil = -usecond();
-    result = source;
-    int pc = grid->_processor_coor[dim];
-
-    const Coordinate ldims = grid->_ldimensions;
-    const Coordinate rdims = grid->_rdimensions;
-    const Coordinate sdims = grid->_simd_layout;
-
-    Coordinate processors = grid->_processors;
-    Coordinate pgdims(Ndim);
-    pgdims[0] = G;
-    for(int d=0, dd=1;d<Ndim;d++){
-      if ( d!=dim ) pgdims[dd++] = ldims[d];
-    }
-    int64_t pgvol=1;
-    for(int d=0;d<Ndim;d++) pgvol*=pgdims[d];
-    
-    const int Nsimd = vobj::Nsimd();
-    for(int p=0;p<processors[dim];p++) {
-      t_copy-=usecond();
-      autoView(r_v,result,AcceleratorRead);
-      accelerator_for(idx, grid->oSites(), vobj::Nsimd(), {
-#ifdef GRID_SIMT
-      {
-	int lane=acceleratorSIMTlane(Nsimd); // buffer lane
-#else
-      for(int lane=0;lane<Nsimd;lane++) {
-#endif
-	Coordinate icoor;
-	Coordinate ocoor;
-	Coordinate pgcoor;
-
-	Lexicographic::CoorFromIndex(icoor,lane,sdims);
-	Lexicographic::CoorFromIndex(ocoor,idx,rdims);
-
-	pgcoor[0] = ocoor[dim] + icoor[dim]*rdims[dim] + ((pc+p)%processors[dim])*L;
-	for(int d=0,dd=1;d<Ndim;d++){
-	  if ( d!=dim ) {
-	    pgcoor[dd] = ocoor[d] + icoor[d]*rdims[d];
-	    dd++;
-	  }
-	}
-
-	// Map coordinates in lattice layout to FFTW index
-	int64_t pgidx;
-	Lexicographic::IndexFromCoor(pgcoor,pgidx,pgdims);
-
-	vector_type *from = (vector_type *)&r_v[idx];
-	scalar_type stmp;
-	for(int w=0;w<Ncomp;w++){
-	  int64_t pg_idx = pgidx + w*pgvol;
-	  stmp = getlane(from[w], lane);
-	  pgbuf_v[pg_idx] = stmp;
-	}
-#ifdef GRID_SIMT
-      }
-#else
-      }
-#endif
-      });
-
-      t_copy+=usecond();
-      if (p != processors[dim] - 1) {
-	Lattice<vobj> temp(grid);
-	t_shift-=usecond();
-	temp = Cshift(result,dim,L); result = temp;
-	t_shift+=usecond();
-      }
-    }
-    t_pencil += usecond();
-      
-    FFTW_scalar *in = (FFTW_scalar *)pgbuf_v;
-    FFTW_scalar *out= (FFTW_scalar *)pgbuf_v;
-    t_fft = -usecond();
-    FFTW<scalar>::fftw_execute_dft(p,in,out,sign);
-    t_fft += usecond();
-    
-    // performance counting
-    flops_call = 5.0*howmany*G*log2(G);
-    usec = t_fft;
-    flops= flops_call;
-
-    result = Zero();
-    
-    double t_insert = -usecond();
-    {
-      autoView(r_v,result,AcceleratorWrite);
-      accelerator_for(idx,grid->oSites(),Nsimd,{
-#ifdef GRID_SIMT
-      {
-	int lane=acceleratorSIMTlane(Nsimd); // buffer lane
-#else
-      for(int lane=0;lane<Nsimd;lane++) {
-#endif
-	Coordinate icoor(Ndim);
-	Coordinate ocoor(Ndim);
-	Coordinate pgcoor(Ndim);
-
-	Lexicographic::CoorFromIndex(icoor,lane,sdims);
-	Lexicographic::CoorFromIndex(ocoor,idx,rdims);
-
-	pgcoor[0] = ocoor[dim] + icoor[dim]*rdims[dim] + pc*L;
-	for(int d=0,dd=1;d<Ndim;d++){
-	  if ( d!=dim ) {
-	    pgcoor[dd] = ocoor[d] + icoor[d]*rdims[d];
-	    dd++;
-	  }
-	}
-	// Map coordinates in lattice layout to FFTW index
-	int64_t pgidx;
-	Lexicographic::IndexFromCoor(pgcoor,pgidx,pgdims);
-
-	vector_type *to = (vector_type *)&r_v[idx];
-	scalar_type stmp;
-	for(int w=0;w<Ncomp;w++){
-	  int64_t pg_idx = pgidx + w*pgvol;
-	  stmp = pgbuf_v[pg_idx];
-	  putlane(to[w], stmp, lane);
-	}
-	
-#ifdef GRID_SIMT
-      }
-#else
-      }
-#endif
-      });
-    }
-
-    result = result*div;
-
-    t_insert +=usecond();
-    
-    // destroying plan
     FFTW<scalar>::fftw_destroy_plan(p);
+  }
+};
 
-    t_total +=usecond();
+template<class vobj>
+class PlannedFFT : public FFTbase {
+private:
+  typedef typename vobj::scalar_type   scalar;
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::vector_type   vector_type;
+  typedef typename FFTW<scalar>::FFTW_scalar FFTW_scalar;
+  typedef typename FFTW<scalar>::FFTW_plan   FFTW_plan;
 
-    std::cout <<GridLogPerformance<< " FFT took   "<<t_total/1.0e6 <<" s" << std::endl;
+  std::vector<FFTW_plan> forward_plans;
-    std::cout <<GridLogPerformance<< " FFT pencil "<<t_pencil/1.0e6 <<" s" << std::endl;
+  std::vector<FFTW_plan> backward_plans;
-    std::cout <<GridLogPerformance<< "  of which copy "<<t_copy/1.0e6 <<" s" << std::endl;
+
-    std::cout <<GridLogPerformance<< "  of which shift"<<t_shift/1.0e6 <<" s" << std::endl;
+  void PlanCreate() {
-    std::cout <<GridLogPerformance<< " FFT kernels "<<t_fft/1.0e6 <<" s" << std::endl;
+    const int Ndim = _grid->Nd();
-    std::cout <<GridLogPerformance<< " FFT insert  "<<t_insert/1.0e6 <<" s" << std::endl;
+    forward_plans.resize(Ndim);
-    
+    backward_plans.resize(Ndim);
+
+    for (int d = 0; d < Ndim; d++) {
+      int G       = _grid->_fdimensions[d];
+      int Ncomp   = sizeof(sobj) / sizeof(scalar);
+      int64_t Nperp = 1;
+      for (int dd = 0; dd < Ndim; dd++)
+        if (dd != d) Nperp *= _grid->_ldimensions[dd];
+      int howmany = Ncomp * (int)Nperp;
+      int n[]     = {G};
+
+      deviceVector<scalar> dummy(2);
+      FFTW_scalar *buf = (FFTW_scalar *)&dummy[0];
+
+      forward_plans[d]  = FFTW<scalar>::fftw_plan_many_dft(1, n, howmany, buf, n, 1, G, buf, n, 1, G, FFTW_FORWARD,  FFTW_ESTIMATE);
+      backward_plans[d] = FFTW<scalar>::fftw_plan_many_dft(1, n, howmany, buf, n, 1, G, buf, n, 1, G, FFTW_BACKWARD, FFTW_ESTIMATE);
+    }
+  }
+
+  void PlanDestroy() {
+    for (auto p : forward_plans)  FFTW<scalar>::fftw_destroy_plan(p);
+    for (auto p : backward_plans) FFTW<scalar>::fftw_destroy_plan(p);
+    forward_plans.clear();
+    backward_plans.clear();
+  }
+
+public:
+  PlannedFFT(GridCartesian *grid) : FFTbase(grid) { PlanCreate(); }
+  ~PlannedFFT() { PlanDestroy(); }
+
+  void FFT_dim_mask(Lattice<vobj> &result, const Lattice<vobj> &source, Coordinate mask, int sign) {
+    const int Ndim = _grid->Nd();
+    Lattice<vobj> tmp = source;
+    for (int d = 0; d < Ndim; d++) {
+      if (mask[d]) {
+        FFT_dim(result, tmp, d, sign);
+        tmp = result;
+      }
+    }
+  }
+
+  void FFT_all_dim(Lattice<vobj> &result, const Lattice<vobj> &source, int sign) {
+    Coordinate mask(_grid->Nd(), 1);
+    FFT_dim_mask(result, source, mask, sign);
+  }
+
+  void FFT_dim(Lattice<vobj> &result, const Lattice<vobj> &source, int dim, int sign) {
+    GRID_ASSERT(source.Grid() == _grid);
+    GRID_ASSERT(result.Grid() == _grid);
+    GRID_ASSERT((int)forward_plans.size() == _grid->Nd());
+    conformable(result.Grid(), source.Grid());
+    FFTW_plan p = (sign == forward ? forward_plans : backward_plans)[dim];
+    FFT_dim_execute(result, source, dim, sign, p, _grid, flops, flops_call, usec);
   }
 };
 

Grid/algorithms/blas/BatchedBlas.h

@@ -68,6 +68,59 @@ NAMESPACE_BEGIN(Grid);
 enum GridBLASOperation_t { GridBLAS_OP_N, GridBLAS_OP_T, GridBLAS_OP_C } ;
 enum GridBLASPrecision_t { GridBLAS_PRECISION_DEFAULT, GridBLAS_PRECISION_16F, GridBLAS_PRECISION_16BF, GridBLAS_PRECISION_TF32 };
 
+///////////////////////////////////////////////////////////////////////////
+// BLAS scalar constants: the put() wrapper OWNS the residency policy so
+// call sites just pass values (scalars-live-on-the-host rule).
+//
+// Policy per backend:
+//  - CUDA / HIP : handles are put in HOST pointer mode at Init (cuBLAS docs
+//    2.2.7: host mode is the documented default; 2.1.5: host-mode scalars
+//    are consumed AT CALL TIME, "can be freed just after the return of the
+//    call even though the kernel launch is asynchronous").  put() stores
+//    the value in persistent host memory and returns its address: ZERO
+//    host->device copies.
+//  - SYCL : the oneMKL group-API alpha/beta arrays are dereferenced
+//    USM-side (spec is silent for the group API; implementation observed
+//    to require USM-accessible storage -- host stack pointers fault).
+//    put() keeps a device-resident copy with VALUE CACHING: the copy is
+//    issued only when the value changes (accumulation pattern
+//    beta = (p==0 ? 0 : 1) costs two copies per Mult instead of npoint).
+//
+// Motivation (rocprof, Frontier, 2026-08-13): per-call alpha/beta device
+// staging generated ~92k tiny staged hipMemcpys in a 12s solve window
+// (~26% of host API time) at the latency-bound coarse level.
+// NB not thread safe -- matches the single-threaded host BLAS call
+// pattern of the per-call staging it replaces.
+///////////////////////////////////////////////////////////////////////////
+template<class T>
+class GridBLASDeviceConstant {
+#ifdef GRID_SYCL
+  deviceVector<T> dev;
+  T               host;
+  int             valid;
+public:
+  GridBLASDeviceConstant() : dev(1), valid(0) {};
+  T * put(T v) {
+    if ( (!valid) || (v != host) ) {
+      acceleratorCopyToDevice((void *)&v,(void *)&dev[0],sizeof(T));
+      host  = v;
+      valid = 1;
+    }
+    return &dev[0];
+  }
+#else
+  // CUDA / HIP in HOST pointer mode (and CPU/Eigen, where the pointer is
+  // unused): persistent host storage, no copies ever.
+  T host;
+public:
+  GridBLASDeviceConstant() {};
+  T * put(T v) {
+    host = v;
+    return &host;
+  }
+#endif
+};
+
 class GridBLAS {
 public:
 
@@ -81,11 +134,31 @@ public:
 #ifdef GRID_CUDA
       std::cout << "cublasCreate"<<std::endl;
       cublasCreate(&gridblasHandle);
-      cublasSetPointerMode(gridblasHandle, CUBLAS_POINTER_MODE_DEVICE);
+      // HOST pointer mode: scalars consumed at call time from host memory
+      // (cuBLAS docs 2.1.5/2.2.7) -- no device staging of alpha/beta.
+      // DEVICE mode would be a deliberate opt-in for device-produced
+      // scalars (e.g. a future graph-captured solver).
+      cublasSetPointerMode(gridblasHandle, CUBLAS_POINTER_MODE_HOST);
+      {
+        cublasPointerMode_t pm;
+        cublasGetPointerMode(gridblasHandle,&pm);
+        std::cout << "GridBLAS: cuBLAS pointer mode "
+                  << ((pm==CUBLAS_POINTER_MODE_DEVICE)?"DEVICE":"HOST") <<std::endl;
+      }
 #endif
 #ifdef GRID_HIP
       std::cout << "hipblasCreate"<<std::endl;
       hipblasCreate(&gridblasHandle);
+      // Explicit HOST mode: the hipBLAS default is UNDOCUMENTED in the
+      // headers (enum 0 == HOST by cuBLAS-mirroring convention only);
+      // set it and print it so every log carries the ground truth.
+      hipblasSetPointerMode(gridblasHandle, HIPBLAS_POINTER_MODE_HOST);
+      {
+        hipblasPointerMode_t pm;
+        hipblasGetPointerMode(gridblasHandle,&pm);
+        std::cout << "GridBLAS: hipBLAS pointer mode "
+                  << ((pm==HIPBLAS_POINTER_MODE_DEVICE)?"DEVICE":"HOST") <<std::endl;
+      }
 #endif
 #ifdef GRID_SYCL
       gridblasHandle = theGridAccelerator;
@@ -240,11 +313,11 @@ public:
     if(OpB!=GridBLAS_OP_N)
       ldb = n;
     
-    static deviceVector<ComplexD> alpha_p(1);
+    // Cached device constants: copy only on value change (see GridBLASDeviceConstant)
-    static deviceVector<ComplexD> beta_p(1);
+    static GridBLASDeviceConstant<ComplexD> alpha_c;
-    // can prestore the 1 and the zero on device
+    static GridBLASDeviceConstant<ComplexD> beta_c;
-    acceleratorCopyToDevice((void *)&alpha,(void *)&alpha_p[0],sizeof(ComplexD));
+    ComplexD *alpha_p = alpha_c.put(alpha);
-    acceleratorCopyToDevice((void *)&beta ,(void *)&beta_p[0],sizeof(ComplexD));
+    ComplexD *beta_p  = beta_c.put(beta);
     RealD t0=usecond();
     //    std::cout << "ZgemmBatched mnk  "<<m<<","<<n<<","<<k<<" count "<<batchCount<<std::endl;
 #ifdef GRID_HIP
@@ -279,7 +352,7 @@ public:
                                    (hipblasDoubleComplex **)&Cmn[0], ldc,
                                    batchCount);
 #endif
-    //	 std::cout << " hipblas return code " <<(int)err<<std::endl;
+    //    std::cout << " hipblas return code " <<(int)err<<" "<<__LINE__<<std::endl;
     GRID_ASSERT(err==HIPBLAS_STATUS_SUCCESS);
 #endif
 #ifdef GRID_CUDA
@@ -498,11 +571,11 @@ public:
       lda = k;
     if(OpB!=GridBLAS_OP_N)
       ldb = n;
-    static deviceVector<ComplexF> alpha_p(1);
+    // Cached device constants: copy only on value change (see GridBLASDeviceConstant)
-    static deviceVector<ComplexF> beta_p(1);
+    static GridBLASDeviceConstant<ComplexF> alpha_c;
-    // can prestore the 1 and the zero on device
+    static GridBLASDeviceConstant<ComplexF> beta_c;
-    acceleratorCopyToDevice((void *)&alpha,(void *)&alpha_p[0],sizeof(ComplexF));
+    ComplexF *alpha_p = alpha_c.put(alpha);
-    acceleratorCopyToDevice((void *)&beta ,(void *)&beta_p[0],sizeof(ComplexF));
+    ComplexF *beta_p  = beta_c.put(beta);
     RealD t0=usecond();
 
     GRID_ASSERT(Bkn.size()==batchCount);
@@ -541,6 +614,7 @@ public:
                                    batchCount);
 
 #endif
+    //    std::cout << " hipblas return code " <<(int)err<<" "<<__LINE__<<std::endl;
     GRID_ASSERT(err==HIPBLAS_STATUS_SUCCESS);
 #endif
 #ifdef GRID_CUDA
@@ -577,6 +651,7 @@ public:
 				(void **)&Cmn[0], CUDA_C_32F, ldc,
 				batchCount, compute_precision, CUBLAS_GEMM_DEFAULT);
     }
+    //    std::cout << " hipblas return code " <<(int)err<<" "<<__LINE__<<std::endl;
     GRID_ASSERT(err==CUBLAS_STATUS_SUCCESS);
 #endif
 #ifdef GRID_SYCL
@@ -693,6 +768,229 @@ public:
      RealD bytes = 1.0*sizeof(ComplexF)*(m*k+k*n+m*n)*batchCount;
   }
   
+  ///////////////////////////////////////////////////////////////////////////////////
+  // Explicit-leading-dimension complex single GEMM.
+  //
+  // A,B,C may be SLICES of larger parent allocations: lda/ldb/ldc are the
+  // PARENT strides (>= the compact values the ten-argument overload derives).
+  // Motivating use: software split-K for tiny-output/huge-K dense multiplies
+  // (arXiv:2409.03904 fig 11; cf MultiRHSBlockCGLinalg) -- batch over K-chunks
+  // of a dense slab by pointer offset j*Kchunk with lda = the full K extent,
+  // then reduce the partial C's.  Backends pass lda straight through; only
+  // the compact overload invented them.
+  ///////////////////////////////////////////////////////////////////////////////////
+  void gemmBatched(GridBLASOperation_t OpA,
+		   GridBLASOperation_t OpB,
+		   int m,int n, int k,
+		   ComplexF alpha,
+		   deviceVector<ComplexF*> &Amk, int lda,
+		   deviceVector<ComplexF*> &Bkn, int ldb,
+		   ComplexF beta,
+		   deviceVector<ComplexF*> &Cmn, int ldc,
+		   GridBLASPrecision_t precision = GridBLAS_PRECISION_DEFAULT)
+  {
+    RealD t2=usecond();
+    int32_t batchCount = Amk.size();
+
+    GRID_ASSERT( lda >= ((OpA==GridBLAS_OP_N) ? m : k) );
+    GRID_ASSERT( ldb >= ((OpB==GridBLAS_OP_N) ? k : n) );
+    GRID_ASSERT( ldc >= m );
+
+    // Cached device constants: copy only on value change (see GridBLASDeviceConstant)
+    static GridBLASDeviceConstant<ComplexF> alpha_c;
+    static GridBLASDeviceConstant<ComplexF> beta_c;
+    ComplexF *alpha_p = alpha_c.put(alpha);
+    ComplexF *beta_p  = beta_c.put(beta);
+    RealD t0=usecond();
+
+    GRID_ASSERT(Bkn.size()==batchCount);
+    GRID_ASSERT(Cmn.size()==batchCount);
+#ifdef GRID_HIP
+    GRID_ASSERT(precision == GridBLAS_PRECISION_DEFAULT);
+    hipblasOperation_t hOpA;
+    hipblasOperation_t hOpB;
+    if ( OpA == GridBLAS_OP_N ) hOpA = HIPBLAS_OP_N;
+    if ( OpA == GridBLAS_OP_T ) hOpA = HIPBLAS_OP_T;
+    if ( OpA == GridBLAS_OP_C ) hOpA = HIPBLAS_OP_C;
+    if ( OpB == GridBLAS_OP_N ) hOpB = HIPBLAS_OP_N;
+    if ( OpB == GridBLAS_OP_T ) hOpB = HIPBLAS_OP_T;
+    if ( OpB == GridBLAS_OP_C ) hOpB = HIPBLAS_OP_C;
+#if defined(HIP_VERSION_MAJOR) && (HIP_VERSION_MAJOR >=7)
+    auto err = hipblasCgemmBatched(gridblasHandle,
+				   hOpA,
+				   hOpB,
+				   m,n,k,
+				   (hipComplex *) &alpha_p[0],
+				   (hipComplex **)&Amk[0], lda,
+				   (hipComplex **)&Bkn[0], ldb,
+				   (hipComplex *) &beta_p[0],
+				   (hipComplex **)&Cmn[0], ldc,
+				   batchCount);
+#else
+    auto err = hipblasCgemmBatched(gridblasHandle,
+                                   hOpA,
+                                   hOpB,
+                                   m,n,k,
+                                   (hipblasComplex *) &alpha_p[0],
+                                   (hipblasComplex **)&Amk[0], lda,
+                                   (hipblasComplex **)&Bkn[0], ldb,
+                                   (hipblasComplex *) &beta_p[0],
+                                   (hipblasComplex **)&Cmn[0], ldc,
+                                   batchCount);
+#endif
+    GRID_ASSERT(err==HIPBLAS_STATUS_SUCCESS);
+#endif
+#ifdef GRID_CUDA
+    cublasOperation_t hOpA;
+    cublasOperation_t hOpB;
+    if ( OpA == GridBLAS_OP_N ) hOpA = CUBLAS_OP_N;
+    if ( OpA == GridBLAS_OP_T ) hOpA = CUBLAS_OP_T;
+    if ( OpA == GridBLAS_OP_C ) hOpA = CUBLAS_OP_C;
+    if ( OpB == GridBLAS_OP_N ) hOpB = CUBLAS_OP_N;
+    if ( OpB == GridBLAS_OP_T ) hOpB = CUBLAS_OP_T;
+    if ( OpB == GridBLAS_OP_C ) hOpB = CUBLAS_OP_C;
+    cublasStatus_t err;
+    if (precision == GridBLAS_PRECISION_DEFAULT) {
+      err = cublasCgemmBatched(gridblasHandle,
+			       hOpA,
+			       hOpB,
+			       m,n,k,
+			       (cuComplex *) &alpha_p[0],
+			       (cuComplex **)&Amk[0], lda,
+			       (cuComplex **)&Bkn[0], ldb,
+			       (cuComplex *) &beta_p[0],
+			       (cuComplex **)&Cmn[0], ldc,
+			       batchCount);
+    } else {
+      cublasComputeType_t compute_precision = toDataType(precision);
+      err = cublasGemmBatchedEx(gridblasHandle,
+				hOpA,
+				hOpB,
+				m,n,k,
+				(void *) &alpha_p[0],
+				(void **)&Amk[0], CUDA_C_32F, lda,
+				(void **)&Bkn[0], CUDA_C_32F, ldb,
+				(void *) &beta_p[0],
+				(void **)&Cmn[0], CUDA_C_32F, ldc,
+				batchCount, compute_precision, CUBLAS_GEMM_DEFAULT);
+    }
+    GRID_ASSERT(err==CUBLAS_STATUS_SUCCESS);
+#endif
+#ifdef GRID_SYCL
+    GRID_ASSERT(precision == GridBLAS_PRECISION_DEFAULT);
+    int64_t m64=m;
+    int64_t n64=n;
+    int64_t k64=k;
+    int64_t lda64=lda;
+    int64_t ldb64=ldb;
+    int64_t ldc64=ldc;
+    int64_t batchCount64=batchCount;
+
+    oneapi::mkl::transpose iOpA;
+    oneapi::mkl::transpose iOpB;
+
+    if ( OpA == GridBLAS_OP_N ) iOpA = oneapi::mkl::transpose::N;
+    if ( OpA == GridBLAS_OP_T ) iOpA = oneapi::mkl::transpose::T;
+    if ( OpA == GridBLAS_OP_C ) iOpA = oneapi::mkl::transpose::C;
+    if ( OpB == GridBLAS_OP_N ) iOpB = oneapi::mkl::transpose::N;
+    if ( OpB == GridBLAS_OP_T ) iOpB = oneapi::mkl::transpose::T;
+    if ( OpB == GridBLAS_OP_C ) iOpB = oneapi::mkl::transpose::C;
+
+    oneapi::mkl::blas::column_major::gemm_batch(*gridblasHandle,
+						&iOpA,
+						&iOpB,
+						&m64,&n64,&k64,
+						(ComplexF *) &alpha_p[0],
+						(const ComplexF **)&Amk[0], (const int64_t *)&lda64,
+						(const ComplexF **)&Bkn[0], (const int64_t *)&ldb64,
+						(ComplexF *) &beta_p[0],
+						(ComplexF **)&Cmn[0], (const int64_t *)&ldc64,
+						(int64_t)1,&batchCount64,std::vector<sycl::event>());
+    synchronise();
+#endif
+#if !defined(GRID_SYCL) && !defined(GRID_CUDA) && !defined(GRID_HIP)
+    GRID_ASSERT(precision == GridBLAS_PRECISION_DEFAULT);
+    // Reference implementation: Eigen with explicit outer stride
+    typedef Eigen::Map<Eigen::MatrixXcf,0,Eigen::OuterStride<> > eMat;
+    if ( (OpA == GridBLAS_OP_N ) && (OpB == GridBLAS_OP_N) ) {
+      thread_for (p, batchCount, {
+	eMat eAmk(Amk[p],m,k,Eigen::OuterStride<>(lda));
+	eMat eBkn(Bkn[p],k,n,Eigen::OuterStride<>(ldb));
+	eMat eCmn(Cmn[p],m,n,Eigen::OuterStride<>(ldc));
+	if (std::abs(beta) != 0.0)
+	  eCmn = beta * eCmn + alpha * eAmk * eBkn ;
+	else
+	  eCmn = alpha * eAmk * eBkn ;
+	});
+    } else if ( (OpA == GridBLAS_OP_C ) && (OpB == GridBLAS_OP_N) ) {
+      thread_for (p, batchCount, {
+	eMat eAmk(Amk[p],k,m,Eigen::OuterStride<>(lda));
+	eMat eBkn(Bkn[p],k,n,Eigen::OuterStride<>(ldb));
+	eMat eCmn(Cmn[p],m,n,Eigen::OuterStride<>(ldc));
+	if (std::abs(beta) != 0.0)
+	  eCmn = beta * eCmn + alpha * eAmk.adjoint() * eBkn ;
+	else
+	  eCmn = alpha * eAmk.adjoint() * eBkn ;
+	});
+    } else if ( (OpA == GridBLAS_OP_T ) && (OpB == GridBLAS_OP_N) ) {
+      thread_for (p, batchCount, {
+	eMat eAmk(Amk[p],k,m,Eigen::OuterStride<>(lda));
+	eMat eBkn(Bkn[p],k,n,Eigen::OuterStride<>(ldb));
+	eMat eCmn(Cmn[p],m,n,Eigen::OuterStride<>(ldc));
+	if (std::abs(beta) != 0.0)
+	  eCmn = beta * eCmn + alpha * eAmk.transpose() * eBkn ;
+	else
+	  eCmn = alpha * eAmk.transpose() * eBkn ;
+	});
+    } else if ( (OpA == GridBLAS_OP_N ) && (OpB == GridBLAS_OP_C) ) {
+      thread_for (p, batchCount, {
+	eMat eAmk(Amk[p],m,k,Eigen::OuterStride<>(lda));
+	eMat eBkn(Bkn[p],n,k,Eigen::OuterStride<>(ldb));
+	eMat eCmn(Cmn[p],m,n,Eigen::OuterStride<>(ldc));
+	if (std::abs(beta) != 0.0)
+	  eCmn = beta * eCmn + alpha * eAmk * eBkn.adjoint() ;
+	else
+	  eCmn = alpha * eAmk * eBkn.adjoint() ;
+	});
+    } else if ( (OpA == GridBLAS_OP_N ) && (OpB == GridBLAS_OP_T) ) {
+      thread_for (p, batchCount, {
+	eMat eAmk(Amk[p],m,k,Eigen::OuterStride<>(lda));
+	eMat eBkn(Bkn[p],n,k,Eigen::OuterStride<>(ldb));
+	eMat eCmn(Cmn[p],m,n,Eigen::OuterStride<>(ldc));
+	if (std::abs(beta) != 0.0)
+	  eCmn = beta * eCmn + alpha * eAmk * eBkn.transpose() ;
+	else
+	  eCmn = alpha * eAmk * eBkn.transpose() ;
+	});
+    } else if ( (OpA == GridBLAS_OP_C ) && (OpB == GridBLAS_OP_C) ) {
+      thread_for (p, batchCount, {
+	eMat eAmk(Amk[p],k,m,Eigen::OuterStride<>(lda));
+	eMat eBkn(Bkn[p],n,k,Eigen::OuterStride<>(ldb));
+	eMat eCmn(Cmn[p],m,n,Eigen::OuterStride<>(ldc));
+	if (std::abs(beta) != 0.0)
+	  eCmn = beta * eCmn + alpha * eAmk.adjoint() * eBkn.adjoint() ;
+	else
+	  eCmn = alpha * eAmk.adjoint() * eBkn.adjoint() ;
+	} );
+    } else if ( (OpA == GridBLAS_OP_T ) && (OpB == GridBLAS_OP_T) ) {
+      thread_for (p, batchCount, {
+	eMat eAmk(Amk[p],k,m,Eigen::OuterStride<>(lda));
+	eMat eBkn(Bkn[p],n,k,Eigen::OuterStride<>(ldb));
+	eMat eCmn(Cmn[p],m,n,Eigen::OuterStride<>(ldc));
+	if (std::abs(beta) != 0.0)
+	  eCmn = beta * eCmn + alpha * eAmk.transpose() * eBkn.transpose() ;
+	else
+	  eCmn = alpha * eAmk.transpose() * eBkn.transpose() ;
+	} );
+    } else {
+      assert(0);
+    }
+#endif
+    RealD t1=usecond();
+    RealD flops = 8.0*m*n*k*batchCount;
+    RealD bytes = 1.0*sizeof(ComplexF)*(m*k+k*n+m*n)*batchCount;
+  }
+
   ///////////////////////////////////////////////////////////////////////////
   // Single precision real GEMM
   ///////////////////////////////////////////////////////////////////////////
@@ -719,11 +1017,11 @@ public:
       lda = k;
     if(OpB!=GridBLAS_OP_N)
       ldb = n;
-    static deviceVector<RealF> alpha_p(1);
+    // Cached device constants: copy only on value change (see GridBLASDeviceConstant)
-    static deviceVector<RealF> beta_p(1);
+    static GridBLASDeviceConstant<RealF> alpha_c;
-    // can prestore the 1 and the zero on device
+    static GridBLASDeviceConstant<RealF> beta_c;
-    acceleratorCopyToDevice((void *)&alpha,(void *)&alpha_p[0],sizeof(RealF));
+    RealF *alpha_p = alpha_c.put(alpha);
-    acceleratorCopyToDevice((void *)&beta ,(void *)&beta_p[0],sizeof(RealF));
+    RealF *beta_p  = beta_c.put(beta);
     RealD t0=usecond();
 
     GRID_ASSERT(Bkn.size()==batchCount);
@@ -747,6 +1045,7 @@ public:
 				   (float *) &beta_p[0],
 				   (float **)&Cmn[0], ldc,
 				   batchCount);
+    //    std::cout << " hipblas return code " <<(int)err<<" "<<__LINE__<<std::endl;
     GRID_ASSERT(err==HIPBLAS_STATUS_SUCCESS);
 #endif
 #ifdef GRID_CUDA
@@ -879,11 +1178,11 @@ public:
     if(OpB!=GridBLAS_OP_N)
       ldb = n;
     
-    static deviceVector<RealD> alpha_p(1);
+    // Cached device constants: copy only on value change (see GridBLASDeviceConstant)
-    static deviceVector<RealD> beta_p(1);
+    static GridBLASDeviceConstant<RealD> alpha_c;
-    // can prestore the 1 and the zero on device
+    static GridBLASDeviceConstant<RealD> beta_c;
-    acceleratorCopyToDevice((void *)&alpha,(void *)&alpha_p[0],sizeof(RealD));
+    RealD *alpha_p = alpha_c.put(alpha);
-    acceleratorCopyToDevice((void *)&beta ,(void *)&beta_p[0],sizeof(RealD));
+    RealD *beta_p  = beta_c.put(beta);
     RealD t0=usecond();
 
     GRID_ASSERT(Bkn.size()==batchCount);
@@ -907,6 +1206,7 @@ public:
 				   (double *) &beta_p[0],
 				   (double **)&Cmn[0], ldc,
 				   batchCount);
+    //    std::cout << " hipblas return code " <<(int)err<<" "<<__LINE__<<std::endl;
     GRID_ASSERT(err==HIPBLAS_STATUS_SUCCESS);
 #endif
 #ifdef GRID_CUDA
@@ -1134,6 +1434,7 @@ public:
                                     (int*) &info[0],
                                     (int)batchCount);
 #endif
+    //    std::cout << " hipblas return code " <<(int)err<<" "<<__LINE__<<std::endl;
     GRID_ASSERT(err==HIPBLAS_STATUS_SUCCESS);
 #endif
 #ifdef GRID_CUDA
@@ -1173,6 +1474,7 @@ public:
                                     (int)batchCount);
 #endif
 
+    //    std::cout << " hipblas return code " <<(int)err<<" "<<__LINE__<<std::endl;
     GRID_ASSERT(err==HIPBLAS_STATUS_SUCCESS);
 #endif
 #ifdef GRID_CUDA
@@ -1261,6 +1563,7 @@ public:
                                     (int)batchCount);
 
 #endif
+    //    std::cout << " hipblas return code " <<(int)err<<" "<<__LINE__<<std::endl;
     GRID_ASSERT(err==HIPBLAS_STATUS_SUCCESS);
 #endif
 #ifdef GRID_CUDA
@@ -1304,6 +1607,7 @@ public:
                                     (int*) &info[0],
                                     (int)batchCount);
 #endif
+    //    std::cout << " hipblas return code " <<(int)err<<" "<<__LINE__<<std::endl;
     GRID_ASSERT(err==HIPBLAS_STATUS_SUCCESS);
 #endif
 #ifdef GRID_CUDA

Grid/algorithms/blas/BatchedInverse.h

@@ -0,0 +1,282 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: BatchedInverse.h
+
+    Copyright (C) 2026
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+#include <Grid/algorithms/blas/BatchedBlas.h>
+
+#ifdef GRID_HIP
+#include <rocsolver/rocsolver.h>
+#endif
+// GRID_CUDA: batched LU inversion lives in cuBLAS (getrfBatched/getriBatched);
+//            cublas_v2.h already included via BatchedBlas.h.
+// GRID_SYCL: oneapi/mkl.hpp already included via BatchedBlas.h (lapack::getrf/getri).
+
+NAMESPACE_BEGIN(Grid);
+
+///////////////////////////////////////////////////////////////////////////////
+// GridBLASInverse: cross-platform batched dense matrix inversion.
+//
+// HIGH LEVEL contract (deliberately NOT a getrf/getrs interface): invert a
+// batch of dense N x N matrices IN PLACE,
+//
+//     A[i] <- A[i]^{-1}       i = 0 .. batchCount-1
+//
+// Layout: column major, lda = N, contiguous per batch element; pointer list
+// exactly as GridBLAS::gemmBatched (deviceVector<T*> of device pointers).
+// Each backend chooses HOW:
+//   HIP  : rocSOLVER getrf_batched + getri_batched
+//   CUDA : cuBLAS getrfBatched + getriBatched (out-of-place getri; workspace
+//          hidden here, result copied back so the surface stays in-place)
+//   SYCL : oneMKL LAPACK getrf + getri per batch element (USM, in-order queue)
+//   CPU  : Eigen PartialPivLU (the correctness oracle for all of the above)
+//
+// The int32 vendor-batched entry points bound N < 2^31 (asserted); the huge
+// single-matrix ILP64 path (getrf_64 + blocked identity-getrs harvest, proven
+// in the dense coarse-coarse setup at N=69120) migrates here as a batch==1
+// large-N dispatch in a follow-up -- the recursive Schur leaves are the
+// batched consumers this surface is shaped for.
+//
+// NB GPU-backend call signatures are written to vendor documentation but the
+// air-gapped development loop compiles only the CPU/Eigen path; verify the
+// rocSOLVER/cuBLAS/oneMKL calls against headers on first device compile.
+// Semantics are locked by the CPU unit test (Test_batched_blas).
+///////////////////////////////////////////////////////////////////////////////
+class GridBLASInverse {
+public:
+
+#ifdef GRID_HIP
+  // rocSOLVER runs on a rocblas_handle (distinct type from hipblasHandle_t)
+  static rocblas_handle & Handle(void) {
+    static rocblas_handle h;
+    static int init = 0;
+    if ( !init ) {
+      auto st = rocblas_create_handle(&h);
+      GRID_ASSERT(st == rocblas_status_success);
+      init = 1;
+    }
+    return h;
+  }
+#endif
+#ifdef GRID_CUDA
+  // cuBLAS batched LU shares the GridBLAS handle
+  static cublasHandle_t & Handle(void) {
+    GridBLAS::Init();
+    return GridBLAS::gridblasHandle;
+  }
+#endif
+#ifdef GRID_SYCL
+  static sycl::queue * & Handle(void) {
+    GridBLAS::Init();
+    return GridBLAS::gridblasHandle;
+  }
+#endif
+
+  GridBLASInverse() {};
+  ~GridBLASInverse() {};
+
+  void inverseBatched(int64_t N, deviceVector<ComplexF*> &Amat)
+  {
+    int32_t batchCount = Amat.size();
+    GRID_ASSERT(batchCount > 0);
+
+#ifdef GRID_HIP
+    GRID_ASSERT( N < 2147483647L );
+    rocblas_int n   = (rocblas_int)N;
+    rocblas_int lda = (rocblas_int)N;
+
+    deviceVector<rocblas_int> ipiv((uint64_t)batchCount*N);
+    deviceVector<rocblas_int> info(batchCount);
+
+    auto st1 = rocsolver_cgetrf_batched(Handle(), n, n,
+					(rocblas_float_complex *const *)&Amat[0], lda,
+					&ipiv[0], (rocblas_stride)N,
+					&info[0], batchCount);
+    GRID_ASSERT(st1 == rocblas_status_success);
+    auto st2 = rocsolver_cgetri_batched(Handle(), n,
+					(rocblas_float_complex *const *)&Amat[0], lda,
+					&ipiv[0], (rocblas_stride)N,
+					&info[0], batchCount);
+    GRID_ASSERT(st2 == rocblas_status_success);
+    accelerator_barrier();
+    std::vector<rocblas_int> info_h(batchCount);
+    acceleratorCopyFromDevice(&info[0],&info_h[0],batchCount*sizeof(rocblas_int));
+    for(int i=0;i<batchCount;i++) GRID_ASSERT(info_h[i]==0); // singular pivot => abort loudly
+#endif
+#ifdef GRID_CUDA
+    GRID_ASSERT( N < 2147483647L );
+    int n = (int)N;
+
+    deviceVector<int> ipiv((uint64_t)batchCount*N);
+    deviceVector<int> info(batchCount);
+
+    auto st1 = cublasCgetrfBatched(Handle(), n,
+				   (cuComplex **)&Amat[0], n,
+				   &ipiv[0], &info[0], batchCount);
+    GRID_ASSERT(st1 == CUBLAS_STATUS_SUCCESS);
+
+    // getri is OUT of place: hidden workspace keeps the surface in-place
+    deviceVector<ComplexF>  work((uint64_t)batchCount*N*N);
+    deviceVector<ComplexF*> Cptr(batchCount);
+    std::vector<ComplexF*>  Cptr_h(batchCount);
+    std::vector<ComplexF*>  Aptr_h(batchCount);
+    for(int i=0;i<batchCount;i++) Cptr_h[i] = &work[(uint64_t)i*N*N];
+    acceleratorCopyToDevice(&Cptr_h[0],&Cptr[0],batchCount*sizeof(ComplexF*));
+    acceleratorCopyFromDevice(&Amat[0],&Aptr_h[0],batchCount*sizeof(ComplexF*));
+
+    auto st2 = cublasCgetriBatched(Handle(), n,
+				   (const cuComplex *const *)&Amat[0], n,
+				   &ipiv[0],
+				   (cuComplex **)&Cptr[0], n,
+				   &info[0], batchCount);
+    GRID_ASSERT(st2 == CUBLAS_STATUS_SUCCESS);
+    accelerator_barrier();
+    std::vector<int> info_h(batchCount);
+    acceleratorCopyFromDevice(&info[0],&info_h[0],batchCount*sizeof(int));
+    for(int i=0;i<batchCount;i++) GRID_ASSERT(info_h[i]==0);
+    for(int i=0;i<batchCount;i++)
+      acceleratorCopyDeviceToDevice(Cptr_h[i],Aptr_h[i],(uint64_t)N*N*sizeof(ComplexF));
+#endif
+#ifdef GRID_SYCL
+    // Per-element oneMKL LAPACK on the in-order queue; group API optimisation later.
+    sycl::queue *q = Handle();
+    std::vector<ComplexF*> Aptr_h(batchCount);
+    acceleratorCopyFromDevice(&Amat[0],&Aptr_h[0],batchCount*sizeof(ComplexF*));
+
+    int64_t lwf = oneapi::mkl::lapack::getrf_scratchpad_size<std::complex<float> >(*q,N,N,N);
+    int64_t lwi = oneapi::mkl::lapack::getri_scratchpad_size<std::complex<float> >(*q,N,N);
+    deviceVector<ComplexF> scratchf(lwf);
+    deviceVector<ComplexF> scratchi(lwi);
+    deviceVector<int64_t>  ipiv(N);
+    for(int i=0;i<batchCount;i++){
+      oneapi::mkl::lapack::getrf(*q,N,N,(std::complex<float>*)Aptr_h[i],N,&ipiv[0],
+				 (std::complex<float>*)&scratchf[0],lwf);
+      oneapi::mkl::lapack::getri(*q,N,  (std::complex<float>*)Aptr_h[i],N,&ipiv[0],
+				 (std::complex<float>*)&scratchi[0],lwi);
+    }
+    q->wait();
+#endif
+#if !defined(GRID_SYCL) && !defined(GRID_CUDA) && !defined(GRID_HIP)
+    // Reference implementation; the oracle the unit test locks semantics with.
+    thread_for (p, batchCount, {
+      Eigen::Map<Eigen::MatrixXcf> eA(Amat[p],N,N);
+      Eigen::PartialPivLU<Eigen::MatrixXcf> lu(eA);
+      eA = lu.inverse();
+      });
+#endif
+  }
+
+  void inverseBatched(int64_t N, deviceVector<ComplexD*> &Amat)
+  {
+    int32_t batchCount = Amat.size();
+    GRID_ASSERT(batchCount > 0);
+
+#ifdef GRID_HIP
+    GRID_ASSERT( N < 2147483647L );
+    rocblas_int n   = (rocblas_int)N;
+    rocblas_int lda = (rocblas_int)N;
+
+    deviceVector<rocblas_int> ipiv((uint64_t)batchCount*N);
+    deviceVector<rocblas_int> info(batchCount);
+
+    auto st1 = rocsolver_zgetrf_batched(Handle(), n, n,
+					(rocblas_double_complex *const *)&Amat[0], lda,
+					&ipiv[0], (rocblas_stride)N,
+					&info[0], batchCount);
+    GRID_ASSERT(st1 == rocblas_status_success);
+    auto st2 = rocsolver_zgetri_batched(Handle(), n,
+					(rocblas_double_complex *const *)&Amat[0], lda,
+					&ipiv[0], (rocblas_stride)N,
+					&info[0], batchCount);
+    GRID_ASSERT(st2 == rocblas_status_success);
+    accelerator_barrier();
+    std::vector<rocblas_int> info_h(batchCount);
+    acceleratorCopyFromDevice(&info[0],&info_h[0],batchCount*sizeof(rocblas_int));
+    for(int i=0;i<batchCount;i++) GRID_ASSERT(info_h[i]==0);
+#endif
+#ifdef GRID_CUDA
+    GRID_ASSERT( N < 2147483647L );
+    int n = (int)N;
+
+    deviceVector<int> ipiv((uint64_t)batchCount*N);
+    deviceVector<int> info(batchCount);
+
+    auto st1 = cublasZgetrfBatched(Handle(), n,
+				   (cuDoubleComplex **)&Amat[0], n,
+				   &ipiv[0], &info[0], batchCount);
+    GRID_ASSERT(st1 == CUBLAS_STATUS_SUCCESS);
+
+    deviceVector<ComplexD>  work((uint64_t)batchCount*N*N);
+    deviceVector<ComplexD*> Cptr(batchCount);
+    std::vector<ComplexD*>  Cptr_h(batchCount);
+    std::vector<ComplexD*>  Aptr_h(batchCount);
+    for(int i=0;i<batchCount;i++) Cptr_h[i] = &work[(uint64_t)i*N*N];
+    acceleratorCopyToDevice(&Cptr_h[0],&Cptr[0],batchCount*sizeof(ComplexD*));
+    acceleratorCopyFromDevice(&Amat[0],&Aptr_h[0],batchCount*sizeof(ComplexD*));
+
+    auto st2 = cublasZgetriBatched(Handle(), n,
+				   (const cuDoubleComplex *const *)&Amat[0], n,
+				   &ipiv[0],
+				   (cuDoubleComplex **)&Cptr[0], n,
+				   &info[0], batchCount);
+    GRID_ASSERT(st2 == CUBLAS_STATUS_SUCCESS);
+    accelerator_barrier();
+    std::vector<int> info_h(batchCount);
+    acceleratorCopyFromDevice(&info[0],&info_h[0],batchCount*sizeof(int));
+    for(int i=0;i<batchCount;i++) GRID_ASSERT(info_h[i]==0);
+    for(int i=0;i<batchCount;i++)
+      acceleratorCopyDeviceToDevice(Cptr_h[i],Aptr_h[i],(uint64_t)N*N*sizeof(ComplexD));
+#endif
+#ifdef GRID_SYCL
+    sycl::queue *q = Handle();
+    std::vector<ComplexD*> Aptr_h(batchCount);
+    acceleratorCopyFromDevice(&Amat[0],&Aptr_h[0],batchCount*sizeof(ComplexD*));
+
+    int64_t lwf = oneapi::mkl::lapack::getrf_scratchpad_size<std::complex<double> >(*q,N,N,N);
+    int64_t lwi = oneapi::mkl::lapack::getri_scratchpad_size<std::complex<double> >(*q,N,N);
+    deviceVector<ComplexD> scratchf(lwf);
+    deviceVector<ComplexD> scratchi(lwi);
+    deviceVector<int64_t>  ipiv(N);
+    for(int i=0;i<batchCount;i++){
+      oneapi::mkl::lapack::getrf(*q,N,N,(std::complex<double>*)Aptr_h[i],N,&ipiv[0],
+				 (std::complex<double>*)&scratchf[0],lwf);
+      oneapi::mkl::lapack::getri(*q,N,  (std::complex<double>*)Aptr_h[i],N,&ipiv[0],
+				 (std::complex<double>*)&scratchi[0],lwi);
+    }
+    q->wait();
+#endif
+#if !defined(GRID_SYCL) && !defined(GRID_CUDA) && !defined(GRID_HIP)
+    thread_for (p, batchCount, {
+      Eigen::Map<Eigen::MatrixXcd> eA(Amat[p],N,N);
+      Eigen::PartialPivLU<Eigen::MatrixXcd> lu(eA);
+      eA = lu.inverse();
+      });
+#endif
+  }
+};
+
+NAMESPACE_END(Grid);

Grid/algorithms/iterative/AdefGeneric.h

@@ -53,7 +53,22 @@ class TwoLevelCG : public LinearFunction<Field>
   // Fine operator, Smoother, CoarseSolver
   LinearOperatorBase<Field>   &_FineLinop;
   LinearFunction<Field>   &_Smoother;
-  
+
+  GridStopWatch ProjectTimer;
+  GridStopWatch PromoteTimer;
+  GridStopWatch CoarseTimer;
+  GridStopWatch SmoothTimer;
+  GridStopWatch MatrixTimer;
+  GridStopWatch M3Timer;
+  GridStopWatch LinalgTimer;
+
+  int64_t M3Calls;
+  int64_t SmoothCalls;
+  int64_t MatrixCalls;
+  int64_t ProjectCalls;
+  int64_t CoarseCalls;
+  int64_t PromoteCalls;
+
   // more most opertor functions
   TwoLevelCG(RealD tol,
 	     Integer maxit,
@@ -103,12 +118,20 @@ class TwoLevelCG : public LinearFunction<Field>
     RealD tn;
     
     GridStopWatch HDCGTimer;
+    ProjectTimer.Reset();
+    PromoteTimer.Reset();
+    CoarseTimer.Reset();
+    SmoothTimer.Reset();
+    MatrixTimer.Reset();
+    M3Timer.Reset();
+    LinalgTimer.Reset();
+    M3Calls = SmoothCalls = MatrixCalls = ProjectCalls = CoarseCalls = PromoteCalls = 0;
     HDCGTimer.Start();
     //////////////////////////
     // x0 = Vstart -- possibly modify guess
     //////////////////////////
     Vstart(x,src);
-    
+
     // r0 = b -A x0
     _FineLinop.HermOp(x,mmp[0]);
     axpy (r, -1.0,mmp[0], src);    // Recomputes r=src-Ax0
@@ -145,33 +168,40 @@ class TwoLevelCG : public LinearFunction<Field>
       int peri_kp = (k+1) % mmax;
 
       rtz=rtzp;
+      M3Timer.Start();
       d= PcgM3(p[peri_k],mmp[peri_k]);
+      M3Timer.Stop();
+      M3Calls++;
       a = rtz/d;
-    
+
       // Memorise this
       pAp[peri_k] = d;
-      
+
+      LinalgTimer.Start();
       axpy(x,a,p[peri_k],x);
       RealD rn = axpy_norm(r,-a,mmp[peri_k],r);
+      LinalgTimer.Stop();
 
       // Compute z = M x
       PcgM1(r,z);
-      
+
       {
 	RealD n1,n2;
 	n1=norm2(r);
 	n2=norm2(z);
 	std::cout << GridLogMessage<<"HDCG::fPcg iteration "<<k<<" : vector r,z "<<n1<<" "<<n2<<"\n";
       }
+      LinalgTimer.Start();
       rtzp =real(innerProduct(r,z));
+      LinalgTimer.Stop();
       std::cout << GridLogMessage<<"HDCG::fPcg iteration "<<k<<" : inner rtzp "<<rtzp<<"\n";
 
       //    PcgM2(z,p[0]);
       PcgM2(z,mu); // ADEF-2 this is identity. Axpy possible to eliminate
-      
+
       p[peri_kp]=mu;
 
-      // Standard search direction  p -> z + b p    
+      // Standard search direction  p -> z + b p
       b = (rtzp)/rtz;
       
       int northog;
@@ -202,8 +232,25 @@ class TwoLevelCG : public LinearFunction<Field>
       if ( rn <= rsq ) { 
 
 	HDCGTimer.Stop();
-	std::cout<<GridLogMessage<<"HDCG: fPcg converged in "<<k<<" iterations and "<<HDCGTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: fPcg converged in "<<k<<" iterations and "<<HDCGTimer.Elapsed()<<std::endl;
-	
+	std::cout<<GridLogMessage<<"HDCG: fPcg breakdown"<<std::endl;
+	auto mspc = [](GridStopWatch &sw, int64_t n) -> double {
+	  return (n > 0) ? sw.useconds() * 1e-3 / n : 0.0;
+	};
+	std::cout<<GridLogMessage<<"HDCG: fPcg M3 (fine MVM)  "<<M3Timer.Elapsed()
+		 <<"  "<<M3Calls<<" calls  "<<mspc(M3Timer,M3Calls)<<" ms/call"<<std::endl;
+	std::cout<<GridLogMessage<<"HDCG: fPcg linalg         "<<LinalgTimer.Elapsed()<<std::endl;
+	std::cout<<GridLogMessage<<"HDCG: fPcg smoother       "<<SmoothTimer.Elapsed()
+		 <<"  "<<SmoothCalls<<" calls  "<<mspc(SmoothTimer,SmoothCalls)<<" ms/call"<<std::endl;
+	std::cout<<GridLogMessage<<"HDCG: fPcg matrix (in M1) "<<MatrixTimer.Elapsed()
+		 <<"  "<<MatrixCalls<<" calls  "<<mspc(MatrixTimer,MatrixCalls)<<" ms/call"<<std::endl;
+	std::cout<<GridLogMessage<<"HDCG: fPcg project        "<<ProjectTimer.Elapsed()
+		 <<"  "<<ProjectCalls<<" calls  "<<mspc(ProjectTimer,ProjectCalls)<<" ms/call"<<std::endl;
+	std::cout<<GridLogMessage<<"HDCG: fPcg coarse         "<<CoarseTimer.Elapsed()
+		 <<"  "<<CoarseCalls<<" calls  "<<mspc(CoarseTimer,CoarseCalls)<<" ms/call"<<std::endl;
+	std::cout<<GridLogMessage<<"HDCG: fPcg promote        "<<PromoteTimer.Elapsed()
+		 <<"  "<<PromoteCalls<<" calls  "<<mspc(PromoteTimer,PromoteCalls)<<" ms/call"<<std::endl;
+
 	_FineLinop.HermOp(x,mmp[0]);			  
 	axpy(tmp,-1.0,src,mmp[0]);
 	
@@ -475,35 +522,29 @@ class TwoLevelADEF2 : public TwoLevelCG<Field>
     CoarseField PleftProj(this->coarsegrid);
     CoarseField PleftMss_proj(this->coarsegrid);
 
-    GridStopWatch SmootherTimer;
+    this->SmoothTimer.Start();
-    GridStopWatch MatrixTimer;
-    SmootherTimer.Start();
     this->_Smoother(in,Min);
-    SmootherTimer.Stop();
+    this->SmoothTimer.Stop();
+    this->SmoothCalls++;
 
-    MatrixTimer.Start();
+    this->MatrixTimer.Start();
     this->_FineLinop.HermOp(Min,out);
-    MatrixTimer.Stop();
+    this->MatrixTimer.Stop();
+    this->MatrixCalls++;
     axpy(tmp,-1.0,out,in);          // tmp  = in - A Min
 
-    GridStopWatch ProjTimer;
+    this->ProjectTimer.Start();
-    GridStopWatch CoarseTimer;
+    this->_Aggregates.ProjectToSubspace(PleftProj,tmp);
-    GridStopWatch PromTimer;
+    this->ProjectTimer.Stop();
-    ProjTimer.Start();
+    this->ProjectCalls++;
-    this->_Aggregates.ProjectToSubspace(PleftProj,tmp);     
+    this->CoarseTimer.Start();
-    ProjTimer.Stop();
-    CoarseTimer.Start();
     this->_CoarseSolver(PleftProj,PleftMss_proj); // Ass^{-1} [in - A Min]_s
-    CoarseTimer.Stop();
+    this->CoarseTimer.Stop();
-    PromTimer.Start();
+    this->CoarseCalls++;
-    this->_Aggregates.PromoteFromSubspace(PleftMss_proj,tmp);// tmp = Q[in - A Min]  
+    this->PromoteTimer.Start();
-    PromTimer.Stop();
+    this->_Aggregates.PromoteFromSubspace(PleftMss_proj,tmp);// tmp = Q[in - A Min]
-    std::cout << GridLogPerformance << "PcgM1 breakdown "<<std::endl;
+    this->PromoteTimer.Stop();
-    std::cout << GridLogPerformance << "\tSmoother   " << SmootherTimer.Elapsed() <<std::endl;
+    this->PromoteCalls++;
-    std::cout << GridLogPerformance << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
-    std::cout << GridLogPerformance << "\tProj       " << ProjTimer.Elapsed() <<std::endl;
-    std::cout << GridLogPerformance << "\tCoarse     " << CoarseTimer.Elapsed() <<std::endl;
-    std::cout << GridLogPerformance << "\tProm       " << PromTimer.Elapsed() <<std::endl;
 
     axpy(out,1.0,Min,tmp); // Min+tmp
   }

Grid/algorithms/iterative/ConjugateGradient.h

@@ -212,13 +212,17 @@ public:
 		  << "\tTarget " << Tolerance << std::endl;
 
 	//	std::cout << GridLogMessage << "\tPreamble   " << PreambleTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tSolver Elapsed    " << SolverTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tPreamble   " << PreambleTimer.Elapsed() <<std::endl;
-        std::cout << GridLogPerformance << "Time breakdown "<<std::endl;
+	std::cout << GridLogMessage << "\tConstruct  " << ConstructTimer.Elapsed() <<std::endl;
-	std::cout << GridLogPerformance << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tNorm       " << NormTimer.Elapsed() <<std::endl;
-	std::cout << GridLogPerformance << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tAssign     " << AssignTimer.Elapsed() <<std::endl;
-	std::cout << GridLogPerformance << "\t\tInner      " << InnerTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tSolver     " << SolverTimer.Elapsed() <<std::endl;
-	std::cout << GridLogPerformance << "\t\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "Solver breakdown "<<std::endl;
-	std::cout << GridLogPerformance << "\t\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\t\tInner      " << InnerTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\t\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\t\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
 
 	std::cout << GridLogDebug << "\tMobius flop rate " << DwfFlops/ usecs<< " Gflops " <<std::endl;
 

Grid/algorithms/iterative/PrecGeneralisedConjugateResidual.h

@@ -236,4 +236,5 @@ public:
   }
 };
 NAMESPACE_END(Grid);
+#undef GCRLogLevel
 #endif

Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.h

@@ -38,13 +38,14 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 ///////////////////////////////////////////////////////////////////////////////////////////////////////
 NAMESPACE_BEGIN(Grid);
 
-#define GCRLogLevel std::cout << GridLogMessage <<std::string(level,'\t')<< " Level "<<level<<" " 
+#define GCRLogLevel std::cout << GridLogMessage <<std::string(level,'\t')<< name<<" "
 
 template<class Field>
 class PrecGeneralisedConjugateResidualNonHermitian : public LinearFunction<Field> {
 public:                                                
   using LinearFunction<Field>::operator();
   RealD   Tolerance;
+  RealD   SSQ;
   Integer MaxIterations;
   int verbose;
   int mmax;
@@ -54,11 +55,18 @@ public:
   GridStopWatch PrecTimer;
   GridStopWatch MatTimer;
   GridStopWatch LinalgTimer;
+  std::string name;
+  int ZeroGuess  = 0;  // caller contract: guess is always zero => first-cycle r0 = src, skip the apply
+  int FirstCycle = 0;
 
   LinearFunction<Field>     &Preconditioner;
   LinearOperatorBase<Field> &Linop;
 
-  void Level(int lv) { level=lv; };
+  void Name(std::string _name) { name = _name; };
+
+  void Level(int n) { Name("Level " + std::to_string(n)); level = n; }
+
+  void SetZeroGuess(int z) { ZeroGuess = z; };
 
   PrecGeneralisedConjugateResidualNonHermitian(RealD tol,Integer maxit,LinearOperatorBase<Field> &_Linop,LinearFunction<Field> &Prec,int _mmax,int _nstep) : 
     Tolerance(tol), 
@@ -67,8 +75,8 @@ public:
     Preconditioner(Prec),
     mmax(_mmax),
     nstep(_nstep)
-  { 
+  {
-    level=1;
+    Level(1);
     verbose=1;
   };
 
@@ -77,6 +85,7 @@ public:
     //    psi=Zero();
     RealD cp, ssq,rsq;
     ssq=norm2(src);
+    SSQ=ssq;
     rsq=Tolerance*Tolerance*ssq;
       
     Field r(src.Grid());
@@ -89,11 +98,12 @@ public:
     SolverTimer.Start();
 
     steps=0;
+    FirstCycle=1;
     for(int k=0;k<MaxIterations;k++){
 
       cp=GCRnStep(src,psi,rsq);
 
-      GCRLogLevel <<"PGCR("<<mmax<<","<<nstep<<") "<< steps <<" steps cp = "<<cp<<" target "<<rsq <<std::endl;
+      GCRLogLevel <<"PGCR("<<mmax<<","<<nstep<<") "<< steps <<" steps cp = "<<sqrt(cp/ssq)<<" target "<<sqrt(rsq/ssq) <<std::endl;
 
       if(cp<rsq) {
 
@@ -142,21 +152,25 @@ public:
     GCRLogLevel<< "PGCR nStep("<<nstep<<")"<<std::endl;
 
     //////////////////////////////////
-    // initial guess x0 is taken as nonzero.
+    // r0 = src - A x0.  ZeroGuess: on the first cycle x0==0 by caller
-    // r0=src-A x0 = src
+    // contract (enforced here), so r0 = src exactly; skip the apply.
+    // Restart cycles (psi!=0) always do the full computation.
     //////////////////////////////////
-    MatTimer.Start();
+    if (ZeroGuess && FirstCycle) {
-    Linop.Op(psi,Az);
+      psi = Zero();
-    //    zAz = innerProduct(Az,psi);
+      LinalgTimer.Start();
-    zAAz= norm2(Az);
+      r = src;
-    MatTimer.Stop();
+      LinalgTimer.Stop();
-    
+    } else {
+      MatTimer.Start();
+      Linop.Op(psi,Az);
+      MatTimer.Stop();
+      LinalgTimer.Start();
+      r=src-Az;
+      LinalgTimer.Stop();
+    }
+    FirstCycle=0;
 
-    LinalgTimer.Start();
-    r=src-Az;
-    LinalgTimer.Stop();
-    GCRLogLevel<< "PGCR true residual r = src - A psi   "<<norm2(r) <<std::endl;
-    
     /////////////////////
     // p = Prec(r)
     /////////////////////
@@ -181,6 +195,7 @@ public:
     
     cp =norm2(r);
     LinalgTimer.Stop();
+    GCRLogLevel<< "PGCR true residual "<< sqrt(cp/SSQ)     <<std::endl;
 
     for(int k=0;k<nstep;k++){
 
@@ -199,13 +214,12 @@ public:
       cp = axpy_norm(r,-a,q[peri_k],r);
       LinalgTimer.Stop();
 
-      GCRLogLevel<< "PGCR step["<<steps<<"]  resid " << cp << " target " <<rsq<<std::endl; 
+      GCRLogLevel<< "PGCR step["<<steps<<"]  resid " << sqrt(cp/SSQ)<<std::endl;
 
       if((k==nstep-1)||(cp<rsq)){
 	return cp;
       }
 
-
       PrecTimer.Start();
       Preconditioner(r,z);// solve Az = r
       PrecTimer.Stop();
@@ -239,4 +253,6 @@ public:
   }
 };
 NAMESPACE_END(Grid);
+
+#undef GCRLogLevel
 #endif

Grid/algorithms/multigrid/Aggregates.h

@@ -66,7 +66,21 @@ public:
   {
   };
   
-  
+  void GlobalOrthonormalise(void)
+  {
+    // Normalise all vectors
+    for(int i=0;i<nbasis; i++){
+      RealD scale = std::pow(norm2(subspace[i]),-0.5); 
+      subspace[i] = subspace[i]*scale;
+    }
+    for(int i=0;i<nbasis; i++){
+      for(int j=0;j<i; j++){
+	basisOrthogonalize(subspace,subspace[i],j);
+      }
+      RealD scale = std::pow(norm2(subspace[i]),-0.5); 
+      subspace[i] = subspace[i]*scale;
+    }
+  }  
   void Orthogonalise(void){
     CoarseScalar InnerProd(CoarseGrid); 
     //    std::cout << GridLogMessage <<" Block Gramm-Schmidt pass 1"<<std::endl;
@@ -110,14 +124,16 @@ public:
       
       hermop.Op(noise,Mn); std::cout<<GridLogMessage << "noise   ["<<b<<"] <n|MdagM|n> "<<norm2(Mn)<<std::endl;
 
-      for(int i=0;i<4;i++){
+      for(int i=0;i<2;i++){
 
 	CG(hermop,noise,subspace[b]);
 
 	noise = subspace[b];
 	scale = std::pow(norm2(noise),-0.5); 
 	noise=noise*scale;
-
+	
+	hermop.Op(noise,Mn); std::cout<<GridLogMessage << "intermediate["<<i<<"] <i|MdagM|i> "<<norm2(Mn)<<std::endl;
+	
       }
 
       hermop.Op(noise,Mn); std::cout<<GridLogMessage << "filtered["<<b<<"] <f|MdagM|f> "<<norm2(Mn)<<std::endl;
@@ -134,7 +150,8 @@ public:
     //    PrecGeneralisedConjugateResidualNonHermitian<FineField> GCR(0.001,10,DiracOp,simple_fine,30,30);
     //    PrecGeneralisedConjugateResidualNonHermitian<FineField> GCR(0.001,10,DiracOp,simple_fine,12,12);
     //    PrecGeneralisedConjugateResidualNonHermitian<FineField> GCR(0.001,30,DiracOp,simple_fine,12,12);
-    PrecGeneralisedConjugateResidualNonHermitian<FineField> GCR(0.001,30,DiracOp,simple_fine,10,10);
+    //    PrecGeneralisedConjugateResidualNonHermitian<FineField> GCR(0.0005,30,DiracOp,simple_fine,20,20);
+    PrecGeneralisedConjugateResidualNonHermitian<FineField> GCR(0.0005,30,DiracOp,simple_fine,10,10);
     FineField noise(FineGrid);
     FineField src(FineGrid);
     FineField guess(FineGrid);
@@ -167,6 +184,8 @@ public:
 	noise = subspace[b];
 	scale = std::pow(norm2(noise),-0.5); 
 	noise=noise*scale;
+	
+	DiracOp.Op(noise,Mn); std::cout<<GridLogMessage << "intermediate["<<i<<"] <f|Op|f> "<<innerProduct(noise,Mn)<<" <f|OpDagOp|f>"<<norm2(Mn)<<std::endl;
 
       }
 
@@ -174,6 +193,7 @@ public:
       subspace[b]   = noise;
 
     }
+    GlobalOrthonormalise();
   }
 
   ////////////////////////////////////////////////////////////////////////////////////////////////

Grid/algorithms/multigrid/DenseCoarseMatrix.h

@@ -0,0 +1,706 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./lib/algorithms/multigrid/DenseCoarseMatrix.h
+
+    Copyright (C) 2026
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+#include <Grid/algorithms/blas/BatchedBlas.h>
+#include <Grid/algorithms/blas/BatchedInverse.h>
+
+#include <unordered_map>
+
+NAMESPACE_BEGIN(Grid);
+
+//////////////////////////////////////////////////////////////////////////////////////
+// DenseCoarseMatrix: a coarsened operator treated as a DENSE matrix -- explicit,
+// row-distributed A^{-1} of a GeneralCoarsenedMatrix.  Library-grade successor of
+// the example-local DistributedDenseInverse (Example_pvdagm_mrhs_3level_dense.cc,
+// FROZEN as the regression baseline).
+//
+// What is new versus the example class:
+//  - Stencil -> dense DIRECT IMPORT.  The coarse operator IS the dense matrix
+//    unrolled: Dense[(s,a),(s+shift_p,b)] += A[p][s]_{a,b}.  Rows of my sites are
+//    assembled from purely LOCAL _A[p] data: no operator applies, no comms -- the
+//    O(N) probe assembly (93 s at N=69120) is retired.  ACCUMULATE (+=) because on
+//    short axes distinct shifts wrap to the same neighbour.  An IMPORT CERTIFICATE
+//    compares the dense apply against Op.M on a NON-CONSTANT vector (a constant one
+//    cannot see a shift-sign error); DENSE_IMPORT_SIGN=-1 flips the convention
+//    without recompiling.
+//  - Split-K apply through GridBLAS.gemmBatched with EXPLICIT leading dimensions
+//    (arXiv:2409.03904 fig 11): the tiny-output/huge-K GEMM Y = slab^T X becomes
+//    DENSE_SPLITK chunk-GEMMs by pointer offset into the resident slab (lda = N),
+//    partials reduced in one accelerator_for.  Platform-agnostic: deviceVector +
+//    GridBLAS run the SAME code on HIP/CUDA/SYCL and CPU(Eigen).
+//  - deviceVector everywhere in the apply path; the ONE surviving naked-HIP block
+//    is the boss inversion buffer (quarantined below, documented).
+//
+// Setup: SLAB_FILE=<stem> loads per-rank <stem>.<rank> (header-guarded N/nrows/
+// nbasis -- the interchange format shared with the frozen example; the STEM must
+// encode cfg/mass/blocking/nbasis, only the header is guarded).  Absent: direct
+// import -> import certificate -> chunked zero-fill+GlobalSum gather streamed to
+// the boss GCD -> cgetrf_64 (ILP64) -> rows of A^{-1} via blocked identity
+// cgetrs_64 + broadcast, each rank keeping the rows of its own sites -> save.
+// VERIFY ||A Ainv x - x||/||x|| runs in BOTH paths (and now certifies the DEVICE
+// slab + split-K path, since the single-RHS apply routes through the same core).
+//
+// Env: SLAB_FILE  DENSE_SPLITK (default 32, snapped to a divisor of N)
+//      DENSE_DEVICE_SUM  DENSE_IMPORT_SIGN  DENSE_APPLY_PROFILE  DENSE_CC_CHECK
+//
+// Eventual internal upgrade (unchanged surface): RecursiveSchur distributed
+// factorisation replacing the single-GCD gather/invert, lifting BOTH the fp32
+// N ~ 90k boss-HBM ceiling AND the CC-grid 256-rank SIMD cap; leaves land on
+// GridBLASInverse::inverseBatched.
+//
+// Tensor-depth agnostic: site scalar objects treated as contiguous ComplexD
+// (iScalar wrappers add no data), so any MG level's coarse operator imports.
+//////////////////////////////////////////////////////////////////////////////////////
+template<class Fobj,class CComplex,int nbasis>
+class DenseCoarseMatrix : public LinearFunction<typename GeneralCoarsenedMatrix<Fobj,CComplex,nbasis>::CoarseVector> {
+public:
+  typedef GeneralCoarsenedMatrix<Fobj,CComplex,nbasis> GeneralCoarseOp;
+  typedef typename GeneralCoarseOp::CoarseVector       Field;
+  typedef typename GeneralCoarseOp::CoarseMatrix       CoarseMatrix;
+  using LinearFunction<Field>::operator();
+  typedef typename Field::vector_object vobj;
+  typedef typename vobj::scalar_object  sobj;
+  typedef typename CoarseMatrix::vector_object Mvobj;
+  typedef typename Mvobj::scalar_object        Msobj;
+
+  GeneralCoarseOp &_Op;             // the coarse operator: stencil source + certificate oracle
+  GridBase *grid;
+  int      nd;
+  int64_t  N;                       // dense rank = gSites * nbasis
+  int      lsites;                  // my local sites
+  int64_t  nrows;                   // my rows = lsites * nbasis
+  std::vector<Coordinate> myLcoor;  // local coordinate of my site ss
+  std::vector<int64_t>    myGsite;  // global lex site index of my site ss
+  std::vector<ComplexF>   slab;     // nrows x N row-major: A during setup, rows of A^{-1} after
+
+  static const int64_t CHUNKROWS = 1024;  // getrs harvest block (trsm efficiency + fewer broadcasts)
+  static const int MRHS_MAX = 32;
+
+  // Apply machinery: resident slab + persistent buffers + AOT split-K pointers.
+  GridBLAS BLAS;
+  deviceVector<ComplexF>  dSlab;
+  deviceVector<ComplexF>  dX;       // N x MRHS_MAX
+  deviceVector<ComplexF>  dY;       // nrows x MRHS_MAX
+  deviceVector<ComplexF>  dPartial; // NK x (nrows x MRHS_MAX)
+  deviceVector<ComplexF*> aptrs;    // slab K-chunk pointers   (lda = N)
+  deviceVector<ComplexF*> xptrs;    // X    K-chunk pointers   (ldb = N)
+  deviceVector<ComplexF*> cptrs;    // partial buffers         (ldc = nrows)
+  std::vector<ComplexF>   hX;
+  std::vector<ComplexF>   hY;
+  int NK;                           // split-K chunk count (divides N)
+  int devSum;
+
+  DenseCoarseMatrix(GeneralCoarseOp &Op, GridBase *g)
+    : _Op(Op), grid(g)
+  {
+    GRID_ASSERT( sizeof(sobj)  == nbasis*sizeof(ComplexD) );
+    GRID_ASSERT( sizeof(Msobj) == nbasis*nbasis*sizeof(ComplexD) );
+    GRID_ASSERT( grid == Op.Grid() );
+    nd     = grid->_ndimension;
+    N      = grid->gSites() * nbasis;
+    lsites = grid->lSites();
+    nrows  = (int64_t)lsites * nbasis;
+
+    std::cout << GridLogMessage << "DenseCoarseMatrix: N = " << N
+              << " (" << grid->gSites() << " sites x " << nbasis << ")"
+              << "  rows/rank = " << nrows
+              << "  slab = " << (double)nrows*N*sizeof(ComplexF)/1024./1024. << " MB/rank"
+              << std::endl;
+
+    ////////////////////////////////////////////////////////////////////
+    // Enumerate my sites: local coords and global lexicographic indices
+    ////////////////////////////////////////////////////////////////////
+    Coordinate ldims = grid->LocalDimensions();
+    Coordinate gdims = grid->GlobalDimensions();
+    myLcoor.resize(lsites);
+    myGsite.resize(lsites);
+    for(int ss=0; ss<lsites; ss++){
+      Coordinate lcoor(nd);
+      Lexicographic::CoorFromIndex(lcoor, ss, ldims);
+      Coordinate gcoor(nd);
+      for(int d=0; d<nd; d++) gcoor[d] = grid->_lstart[d] + lcoor[d];
+      int64_t gsite;
+      Lexicographic::IndexFromCoor(gcoor, gsite, gdims);
+      myLcoor[ss] = lcoor;
+      myGsite[ss] = gsite;
+    }
+
+    slab.resize((uint64_t)nrows * N);
+
+    double t0 = usecond();
+    ////////////////////////////////////////////////////////////////////
+    // 0. Slab cache: SLAB_FILE=<stem> -> per-rank raw file <stem>.<rank>.
+    //    SAME format as the frozen example (interchange compatible).
+    ////////////////////////////////////////////////////////////////////
+    bool loaded = false;
+    char *sfile = getenv("SLAB_FILE");
+    std::string slabfile;
+    if (sfile) {
+      slabfile = std::string(sfile) + "." + std::to_string(grid->ThisRank());
+      FILE *f = fopen(slabfile.c_str(),"rb");
+      if (f) {
+        int64_t hdr[4] = {0,0,0,0};
+        GRID_ASSERT( fread(hdr,sizeof(int64_t),4,f) == 4 );
+        GRID_ASSERT( hdr[0] == (int64_t)0x44454E5345 );  // magic "DENSE"
+        GRID_ASSERT( hdr[1] == N && hdr[2] == (int64_t)nrows && hdr[3] == (int64_t)nbasis );
+        uint64_t nelem = (uint64_t)nrows * N;
+        GRID_ASSERT( fread(&slab[0], sizeof(ComplexF), nelem, f) == nelem );
+        fclose(f);
+        loaded = true;
+        std::cout << GridLogMessage << "DenseCoarseMatrix: slab loaded from "
+                  << slabfile << " -- skipping import/factor/solve" << std::endl;
+      } else {
+        std::cout << GridLogMessage << "DenseCoarseMatrix: slab cache " << slabfile
+                  << " absent -- full setup, will write it" << std::endl;
+      }
+    }
+    if (!loaded) {
+      ImportDense();          // slab <- my rows of A   (LOCAL, no comms)
+      ImportCertificate();    // dense apply == Op.M on a non-constant vector
+      InvertDense();          // slab <- my rows of A^{-1}
+      double t1 = usecond();
+      if (sfile) {
+        FILE *f = fopen(slabfile.c_str(),"wb");
+        GRID_ASSERT(f != nullptr);
+        int64_t hdr[4] = { (int64_t)0x44454E5345, N, (int64_t)nrows, (int64_t)nbasis };
+        GRID_ASSERT( fwrite(hdr,sizeof(int64_t),4,f) == 4 );
+        uint64_t nelem = (uint64_t)nrows * N;
+        GRID_ASSERT( fwrite(&slab[0], sizeof(ComplexF), nelem, f) == nelem );
+        fclose(f);
+        std::cout << GridLogMessage << "DenseCoarseMatrix: slab written to " << slabfile << std::endl;
+      }
+      std::cout << GridLogMessage << "DenseCoarseMatrix: import+invert took "
+                << (t1-t0)/1.0e6 << " s" << std::endl;
+    }
+
+    ////////////////////////////////////////////////////////////////////
+    // Device residency + persistent apply buffers + AOT split-K pointers
+    ////////////////////////////////////////////////////////////////////
+    {
+      uint64_t sbytes = (uint64_t)nrows * N * sizeof(ComplexF);
+      dSlab.resize((uint64_t)nrows*N);
+      acceleratorCopyToDevice(&slab[0],&dSlab[0],sbytes);
+
+      // DENSE_SPLITK: requested chunk count, snapped DOWN to a divisor of N.
+      int req = getenv("DENSE_SPLITK") ? atoi(getenv("DENSE_SPLITK")) : 32;
+      if (req < 1) req = 1;
+      NK = 1;
+      for(int j=1;j<=req;j++) if ( (N % j) == 0 ) NK = j;
+      int64_t Kc = N / NK;
+
+      dX.resize((uint64_t)N*MRHS_MAX);
+      dY.resize((uint64_t)nrows*MRHS_MAX);
+      dPartial.resize((uint64_t)NK*nrows*MRHS_MAX);
+      hX.resize((uint64_t)N*MRHS_MAX);
+      hY.resize((uint64_t)nrows*MRHS_MAX);
+
+      aptrs.resize(NK); xptrs.resize(NK); cptrs.resize(NK);
+      std::vector<ComplexF*> h(NK);
+      for(int j=0;j<NK;j++) h[j] = &dSlab[0]    + (uint64_t)j*Kc;              // K-offset, lda=N
+      acceleratorCopyToDevice(&h[0],&aptrs[0],NK*sizeof(ComplexF*));
+      for(int j=0;j<NK;j++) h[j] = &dX[0]       + (uint64_t)j*Kc;              // K-offset, ldb=N
+      acceleratorCopyToDevice(&h[0],&xptrs[0],NK*sizeof(ComplexF*));
+      for(int j=0;j<NK;j++) h[j] = &dPartial[0] + (uint64_t)j*nrows*MRHS_MAX;  // compact, ldc=nrows
+      acceleratorCopyToDevice(&h[0],&cptrs[0],NK*sizeof(ComplexF*));
+
+      devSum = getenv("DENSE_DEVICE_SUM") ? 1 : 0;
+      std::cout << GridLogMessage << "DenseCoarseMatrix: slab resident on device ("
+                << sbytes/1024./1024. << " MB/rank), split-K NK=" << NK << " (Kc=" << Kc << "); "
+                << (devSum ? "DEVICE-buffer allreduce (GPU-aware MPI)" : "host allreduce")
+                << std::endl;
+    }
+
+    ////////////////////////////////////////////////////////////////////
+    // VERIFY: || A (Ainv x) - x || / ||x|| through the DEVICE split-K core.
+    ////////////////////////////////////////////////////////////////////
+    {
+      Field x(grid); Field y(grid); Field z(grid);
+      x = ComplexD(1.0,0.0);
+      double ta = usecond();
+      (*this)(x, y);
+      double tb = usecond();
+      _Op.M(y, z);
+      z = z - x;
+      RealD rel = std::sqrt(norm2(z)/norm2(x));
+      std::cout << GridLogMessage << "DenseCoarseMatrix: VERIFY ||A Ainv x - x||/||x|| = "
+                << rel << "   (one apply took " << (tb-ta)/1000.0 << " ms)" << std::endl;
+      GRID_ASSERT(rel < 1.0e-2);
+    }
+    std::cout << GridLogMessage << "DenseCoarseMatrix: setup complete, total "
+              << (usecond()-t0)/1.0e6 << " s" << std::endl;
+  }
+
+  ////////////////////////////////////////////////////////////////////
+  // 1. Direct stencil -> dense import of MY ROWS of A (no comms):
+  //      Dense[(s,a),(wrap(s+shift_p),b)] += A[p][s]_{a,b}
+  ////////////////////////////////////////////////////////////////////
+  void ImportDense(void)
+  {
+    double t = -usecond();
+    Coordinate gdims = grid->GlobalDimensions();
+    int sign = getenv("DENSE_IMPORT_SIGN") ? atoi(getenv("DENSE_IMPORT_SIGN")) : 1;
+    GRID_ASSERT( sign==1 || sign==-1 );
+
+    uint64_t nelem = (uint64_t)nrows * N;
+    thread_for(i, nelem, { slab[i] = ComplexF(0.0,0.0); });
+
+    for(int p=0; p<_Op.geom.npoint; p++){
+      Coordinate shift = _Op.geom.shifts[p];
+      // _A[p] is PADDED after ExchangeCoarseLinks (end of CoarsenOperator):
+      // extract the unpadded field before peeking with unpadded coordinates
+      // (exactly as MultiGeneralCoarsenedMatrix::CopyMatrix does).
+      CoarseMatrix Aun = _Op.Cell.Extract(_Op._A[p]);
+      autoView(Av, Aun, CpuRead);
+      thread_for(ss, lsites, {
+        Coordinate ncoor(nd);
+        for(int d=0; d<nd; d++){
+          int64_t g = grid->_lstart[d] + myLcoor[ss][d] + sign*shift[d];
+          ncoor[d] = (int)((g % gdims[d] + gdims[d]) % gdims[d]);
+        }
+        int64_t nsite;
+        Lexicographic::IndexFromCoor(ncoor, nsite, gdims);
+        Msobj m;
+        peekLocalSite(m, Av, myLcoor[ss]);
+        ComplexD *md = (ComplexD *)&m;
+        for(int a=0; a<nbasis; a++){
+          ComplexF *row = &slab[(uint64_t)(ss*nbasis+a)*N + nsite*nbasis];
+          for(int b=0; b<nbasis; b++)
+            row[b] += ComplexF(md[a*nbasis+b]);   // += : wrapped shifts may collide
+        }
+      });
+    }
+    t += usecond();
+    std::cout << GridLogMessage << "DenseCoarseMatrix: stencil->dense import took "
+              << t/1.0e6 << " s  (" << _Op.geom.npoint << " points, local, no comms)" << std::endl;
+  }
+
+  ////////////////////////////////////////////////////////////////////
+  // 2. IMPORT CERTIFICATE: dense rows vs Op.M on a NON-CONSTANT vector.
+  //    (Constant x has x[s+d]==x[s-d]: blind to a shift-sign error.)
+  ////////////////////////////////////////////////////////////////////
+  void ImportCertificate(void)
+  {
+    Field x(grid); Field Ax(grid); Field Dx(grid);
+    for(int ss=0; ss<lsites; ss++){
+      sobj s;
+      for(int b=0; b<nbasis; b++){
+        double ph = 0.37*(double)(myGsite[ss]*nbasis+b);
+        ((ComplexD *)&s)[b] = ComplexD(std::cos(ph),std::sin(0.61*ph));
+      }
+      pokeLocalSite(s, x, myLcoor[ss]);
+    }
+    // gather full x (zero-fill + exact GlobalSum), dense rows on host
+    std::vector<ComplexD> xh((uint64_t)N, ComplexD(0.0,0.0));
+    for(int ss=0; ss<lsites; ss++){
+      sobj s;
+      peekLocalSite(s, x, myLcoor[ss]);
+      for(int b=0; b<nbasis; b++) xh[ myGsite[ss]*nbasis + b ] = ((ComplexD *)&s)[b];
+    }
+    grid->GlobalSumVector(&xh[0], (int)N);
+    std::vector<ComplexD> yh(nrows);
+    thread_for(r, nrows, {
+      ComplexD acc(0.0,0.0);
+      const ComplexF *row = &slab[(uint64_t)r * N];
+      for(int64_t j=0; j<N; j++) acc += ComplexD(row[j]) * xh[j];
+      yh[r] = acc;
+    });
+    for(int ss=0; ss<lsites; ss++){
+      sobj s;
+      for(int b=0; b<nbasis; b++) ((ComplexD *)&s)[b] = yh[ss*nbasis+b];
+      pokeLocalSite(s, Dx, myLcoor[ss]);
+    }
+    _Op.M(x, Ax);
+    Field d(grid); d = Dx - Ax;
+    RealD rel = std::sqrt(norm2(d)/norm2(Ax));
+    std::cout << GridLogMessage << "DenseCoarseMatrix: IMPORT CERTIFICATE ||Dense x - A x||/||A x|| = "
+              << rel << std::endl;
+    if ( rel >= 1.0e-3 ) {
+      std::cout << GridLogMessage << "DenseCoarseMatrix: IMPORT CERTIFICATE FAILED. If O(1), the "
+                << "stencil shift-sign convention is opposite: rerun with DENSE_IMPORT_SIGN=-1"
+                << std::endl;
+    }
+    GRID_ASSERT(rel < 1.0e-3);
+  }
+
+  ////////////////////////////////////////////////////////////////////
+  // 3. Invert: chunked zero-fill+GlobalSum gather of A streamed to the
+  //    boss GCD, cgetrf_64 (ILP64), rows of A^{-1} by blocked identity
+  //    cgetrs_64 + broadcast; each rank keeps its own rows (in `slab`,
+  //    overwriting A).  Ported proven path from the frozen example.
+  ////////////////////////////////////////////////////////////////////
+  void InvertDense(void)
+  {
+    double t1 = usecond();
+    int boss = grid->IsBoss();
+    std::vector<ComplexF> Afull;
+#ifdef GRID_HIP
+    // QUARANTINED naked HIP: the boss-only N^2 inversion buffer (34GB at
+    // N=65536) must come from raw HBM; EvictAll flushes the device-copy
+    // layer to make the window.  (FreePool of the allocator free-list
+    // awaits the type-dispatched fix.)  Confined to setup; the apply path
+    // is pure Grid primitives.
+    rocblas_float_complex *dA = nullptr;
+    rocblas_float_complex *dB = nullptr;
+    int64_t *dIpiv = nullptr;
+    uint64_t Abytes = (uint64_t)N * N * sizeof(ComplexF);
+    MemoryManager::EvictAll();
+    if (boss) {
+      auto aerr = hipMalloc((void **)&dA, Abytes);
+      if (aerr != hipSuccess) {
+        std::cout << GridLogMessage << "DenseCoarseMatrix: hipMalloc of "
+                  << Abytes/1024./1024./1024. << " GB FAILED -- reduce --device-mem" << std::endl;
+        GRID_ASSERT(aerr == hipSuccess);
+      }
+      std::cout << GridLogMessage << "DenseCoarseMatrix: device inversion buffer allocated ("
+                << Abytes/1024./1024./1024. << " GB)" << std::endl;
+    }
+#else
+    if (boss) Afull.resize((uint64_t)N * N);
+#endif
+    {
+      std::unordered_map<int64_t,int> rowmap;   // global row -> my slab row
+      for(int ss=0; ss<lsites; ss++)
+        for(int a=0; a<nbasis; a++)
+          rowmap[ myGsite[ss]*nbasis + a ] = ss*nbasis + a;
+
+      std::vector<ComplexF> chunk((uint64_t)CHUNKROWS * N);
+      for(int64_t row0=0; row0<N; row0+=CHUNKROWS){
+        int64_t nrow = std::min(CHUNKROWS, N-row0);
+        uint64_t nelem = (uint64_t)nrow * N;
+        for(uint64_t i=0;i<nelem;i++) chunk[i]=ComplexF(0.0,0.0);
+        for(int64_t r=row0; r<row0+nrow; r++){
+          auto it = rowmap.find(r);
+          if (it != rowmap.end()) {
+            uint64_t src = (uint64_t)(it->second) * N;
+            uint64_t dst = (uint64_t)(r-row0) * N;
+            for(int64_t j=0;j<N;j++) chunk[dst+j] = slab[src+j];
+          }
+        }
+        grid->GlobalSumVector(&chunk[0], (int)nelem);
+        if (boss) {
+#ifdef GRID_HIP
+          GRID_ASSERT( hipMemcpy((char *)dA + (uint64_t)row0*N*sizeof(ComplexF),
+                                 &chunk[0], nelem*sizeof(ComplexF),
+                                 hipMemcpyHostToDevice) == hipSuccess );
+#else
+          uint64_t dst = (uint64_t)row0 * N;
+          for(uint64_t i=0;i<nelem;i++) Afull[dst+i] = chunk[i];
+#endif
+        }
+      }
+    }
+    double t2 = usecond();
+    std::cout << GridLogMessage << "DenseCoarseMatrix: gather to boss took "
+              << (t2-t1)/1.0e6 << " s" << std::endl;
+
+    ////////////////////////////////////////////////////////////////////
+    // Factor in place on the boss (fp32, ILP64).  Row-major buffer handed
+    // to column-major LAPACK => LU of A^T.
+    ////////////////////////////////////////////////////////////////////
+    if (boss) {
+#ifdef GRID_HIP
+      std::cout << GridLogMessage << "DenseCoarseMatrix: rocSOLVER cgetrf_64 (ILP64 LU) N=" << N
+                << " in place on resident device buffer" << std::endl;
+      rocblas_handle handle = GridBLASInverse::Handle();
+      int64_t *dInfo;
+      GRID_ASSERT( hipMalloc((void **)&dIpiv, N*sizeof(int64_t)) == hipSuccess );
+      GRID_ASSERT( hipMalloc((void **)&dInfo, sizeof(int64_t))   == hipSuccess );
+      auto st1 = rocsolver_cgetrf_64(handle, (int64_t)N, (int64_t)N, dA, (int64_t)N, dIpiv, dInfo);
+      hipDeviceSynchronize();
+      int64_t info_h = -1;
+      hipMemcpy(&info_h, dInfo, sizeof(int64_t), hipMemcpyDeviceToHost);
+      std::cout << GridLogMessage << "DenseCoarseMatrix: cgetrf_64 status " << (int)st1
+                << " info = " << (int)info_h << std::endl;
+      GRID_ASSERT(st1 == rocblas_status_success);
+      GRID_ASSERT(info_h == 0);
+      hipFree(dInfo);
+      GRID_ASSERT( hipMalloc((void **)&dB, (uint64_t)CHUNKROWS*N*sizeof(ComplexF)) == hipSuccess );
+      // dA holds the LU of A^T; rows of A^{-1} are produced blockwise below via
+      // cgetrs_64 on identity-column blocks: A^T X = E => X columns = rows of
+      // A^{-1}, in exactly the linear layout the harvest expects.
+#else
+      // Eigen fallback: small local CPU tests only.
+      std::cout << GridLogMessage << "DenseCoarseMatrix: Eigen fallback inversion N=" << N
+                << (N > 10000 ? "  (WARNING: SLOW; use the HIP/rocSOLVER path)" : "")
+                << std::endl;
+      typedef Eigen::Matrix<std::complex<float>,Eigen::Dynamic,Eigen::Dynamic,Eigen::RowMajor> MatF;
+      Eigen::Map<MatF> A(reinterpret_cast<std::complex<float>*>(&Afull[0]), N, N);
+      MatF Ainv = A.inverse();
+      A = Ainv;
+#endif
+    }
+    double t3 = usecond();
+    std::cout << GridLogMessage << "DenseCoarseMatrix: factorisation took "
+              << (t3-t2)/1.0e6 << " s" << std::endl;
+
+    ////////////////////////////////////////////////////////////////////
+    // Blocked solve + broadcast: rows of A^{-1} chunk by chunk; each
+    // rank keeps the rows of its own sites (ownership-aligned).
+    ////////////////////////////////////////////////////////////////////
+    {
+      std::unordered_map<int64_t,int> rowmap;
+      for(int ss=0; ss<lsites; ss++)
+        for(int a=0; a<nbasis; a++)
+          rowmap[ myGsite[ss]*nbasis + a ] = ss*nbasis + a;
+
+      std::vector<ComplexF> chunk((uint64_t)CHUNKROWS * N);
+      for(int64_t row0=0; row0<N; row0+=CHUNKROWS){
+        int64_t nrow = std::min(CHUNKROWS, N-row0);
+        uint64_t nelem = (uint64_t)nrow * N;
+        if (boss) {
+#ifdef GRID_HIP
+          // Identity block E: column j = e_{row0+j}; solve A^T X = E so X's
+          // columns are rows [row0,row0+nrow) of A^{-1}.
+          for(uint64_t i=0;i<nelem;i++) chunk[i] = ComplexF(0.0,0.0);
+          for(int64_t j=0;j<nrow;j++) chunk[(uint64_t)j*N + (uint64_t)(row0+j)] = ComplexF(1.0,0.0);
+          GRID_ASSERT( hipMemcpy(dB, &chunk[0], nelem*sizeof(ComplexF), hipMemcpyHostToDevice) == hipSuccess );
+          auto strs = rocsolver_cgetrs_64(GridBLASInverse::Handle(), rocblas_operation_none,
+                                          (int64_t)N, (int64_t)nrow,
+                                          dA, (int64_t)N, dIpiv, dB, (int64_t)N);
+          GRID_ASSERT(strs == rocblas_status_success);
+          hipDeviceSynchronize();
+          GRID_ASSERT( hipMemcpy(&chunk[0], dB, nelem*sizeof(ComplexF), hipMemcpyDeviceToHost) == hipSuccess );
+#else
+          uint64_t src = (uint64_t)row0 * N;
+          for(uint64_t i=0;i<nelem;i++) chunk[i] = Afull[src+i];
+#endif
+        }
+        grid->Broadcast(0, &chunk[0], nelem*sizeof(ComplexF));
+        for(int64_t r=row0; r<row0+nrow; r++){
+          auto it = rowmap.find(r);
+          if (it != rowmap.end()) {
+            uint64_t dst = (uint64_t)(it->second) * N;
+            uint64_t src = (uint64_t)(r-row0) * N;
+            for(int64_t j=0;j<N;j++) slab[dst+j] = chunk[src+j];
+          }
+        }
+      }
+    }
+#ifdef GRID_HIP
+    if (boss) {
+      if (dA)    hipFree(dA);
+      if (dB)    hipFree(dB);
+      if (dIpiv) hipFree(dIpiv);
+    }
+#endif
+    double t4 = usecond();
+    std::cout << GridLogMessage << "DenseCoarseMatrix: blocked getrs solve+scatter took "
+              << (t4-t3)/1.0e6 << " s" << std::endl;
+  }
+
+  ////////////////////////////////////////////////////////////////////
+  // CORE apply on packed data: hX[N x nr] (zero-filled, my sites only)
+  // -> allreduce -> split-K GEMM against the resident slab -> reduce
+  // partials -> hY[nrows x nr] (column major).  Platform-agnostic:
+  // deviceVector + GridBLAS (Eigen fallback on CPU builds).
+  // fp32 allreduce is EXACT: zero-fill assembly gives every element
+  // exactly one contributing rank.
+  ////////////////////////////////////////////////////////////////////
+  void SlabApplyPacked(int nr, double *tprof)
+  {
+    GRID_ASSERT(nr <= MRHS_MAX);
+    uint64_t nX = (uint64_t)N * nr;
+    uint64_t nY = (uint64_t)nrows * nr;
+    int64_t  Kc = N / NK;
+    double t1 = usecond();
+    double t2, t3;
+    if (devSum) {
+      acceleratorCopyToDevice(&hX[0],&dX[0],nX*sizeof(ComplexF));
+      t2 = usecond();
+      grid->GlobalSumVector((ComplexF *)&dX[0], (int)nX);
+      t3 = usecond();
+    } else {
+      grid->GlobalSumVector(&hX[0], (int)nX);
+      t2 = usecond();
+      acceleratorCopyToDevice(&hX[0],&dX[0],nX*sizeof(ComplexF));
+      t3 = usecond();
+    }
+    // Y = op(slab,T) . X : row-major slab (nrows x N) == col-major A^T
+    // (N x nrows, lda=N) => transpose gives the nrows x N operator.
+    // Split-K: NK chunk-GEMMs by pointer offset (AOT lists), then reduce.
+    ComplexF one (1.0,0.0);
+    ComplexF zero(0.0,0.0);
+    BLAS.gemmBatched(GridBLAS_OP_T, GridBLAS_OP_N,
+                     (int)nrows, nr, (int)Kc,
+                     one,  aptrs, (int)N,
+                           xptrs, (int)N,
+                     zero, cptrs, (int)nrows);
+    BLAS.synchronise();
+    {
+      ComplexF *pp = &dPartial[0];
+      ComplexF *py = &dY[0];
+      uint64_t stride = (uint64_t)nrows*MRHS_MAX;
+      int nk = NK;
+      accelerator_for(i, nY, 1, {
+        ComplexF acc(0.0,0.0);
+        for(int j=0;j<nk;j++) acc += pp[(uint64_t)j*stride + i];
+        py[i] = acc;
+      });
+    }
+    double t4 = usecond();
+    acceleratorCopyFromDevice(&dY[0],&hY[0],nY*sizeof(ComplexF));
+    double t5 = usecond();
+    if (tprof) {
+      tprof[0] = devSum ? (t3-t2) : (t2-t1);   // allreduce
+      tprof[1] = devSum ? (t2-t1) : (t3-t2);   // H2D
+      tprof[2] = t4-t3;                        // gemm+reduce
+      tprof[3] = t5-t4;                        // D2H
+    }
+  }
+
+  ////////////////////////////////////////////////////////////////////
+  // Single-RHS apply (also the VERIFY path => certifies device slab).
+  ////////////////////////////////////////////////////////////////////
+  virtual void operator()(const Field &src, Field &psi)
+  {
+    uint64_t nX = (uint64_t)N;
+    thread_for(i, nX, { hX[i]=ComplexF(0.0,0.0); });
+    for(int ss=0; ss<lsites; ss++){
+      sobj s;
+      peekLocalSite(s, src, myLcoor[ss]);
+      for(int b=0; b<nbasis; b++)
+        hX[ myGsite[ss]*nbasis + b ] = ComplexF(((ComplexD *)&s)[b]);
+    }
+    SlabApplyPacked(1, nullptr);
+    for(int ss=0; ss<lsites; ss++){
+      sobj s;
+      for(int b=0; b<nbasis; b++)
+        ((ComplexD *)&s)[b] = ComplexD(hY[ss*nbasis + b]);
+      pokeLocalSite(s, psi, myLcoor[ss]);
+    }
+    if ( getenv("DENSE_CC_CHECK") ) {
+      Field tmp(grid);
+      _Op.M(psi, tmp);
+      tmp = tmp - src;
+      std::cout << GridLogMessage << "DenseCoarseMatrix: apply defect ||A x - b||/||b|| = "
+                << std::sqrt(norm2(tmp)/norm2(src)) << std::endl;
+    }
+  }
+
+  ////////////////////////////////////////////////////////////////////
+  // Batched (vector-of-fields) apply.
+  ////////////////////////////////////////////////////////////////////
+  void ApplyBatch(std::vector<Field> &src, std::vector<Field> &psi)
+  {
+    int nr = src.size();
+    GRID_ASSERT(nr <= MRHS_MAX);
+    double t0 = usecond();
+    uint64_t nX = (uint64_t)N*nr;
+    thread_for(i, nX, { hX[i]=ComplexF(0.0,0.0); });
+    for(int rr=0; rr<nr; rr++){
+      for(int ss=0; ss<lsites; ss++){
+        sobj s;
+        peekLocalSite(s, src[rr], myLcoor[ss]);
+        for(int b=0; b<nbasis; b++)
+          hX[ (uint64_t)rr*N + myGsite[ss]*nbasis + b ] = ComplexF(((ComplexD *)&s)[b]);
+      }
+    }
+    SlabApplyPacked(nr, nullptr);
+    for(int rr=0; rr<nr; rr++){
+      for(int ss=0; ss<lsites; ss++){
+        sobj s;
+        for(int b=0; b<nbasis; b++)
+          ((ComplexD *)&s)[b] = ComplexD(hY[(uint64_t)rr*nrows + (ss*nbasis+b)]);
+        pokeLocalSite(s, psi[rr], myLcoor[ss]);
+      }
+    }
+    double t1 = usecond();
+    std::cout << GridLogMessage << "DenseCoarseMatrix: batched apply " << nr << " rhs took "
+              << (t1-t0)/1000.0 << " ms  (" << (t1-t0)/1000.0/nr << " ms/rhs)" << std::endl;
+    if ( getenv("DENSE_CC_CHECK") ) {
+      Field tmp(grid);
+      for(int rr=0; rr<nr; rr++){
+        _Op.M(psi[rr], tmp);
+        tmp = tmp - src[rr];
+        std::cout << GridLogMessage << "DenseCoarseMatrix: batch defect["<<rr<<"] = "
+                  << std::sqrt(norm2(tmp)/norm2(src[rr])) << std::endl;
+      }
+    }
+  }
+
+  ////////////////////////////////////////////////////////////////////
+  // 6D mrhs apply: operates DIRECTLY on the packed 6D field (rhs = dim 0).
+  ////////////////////////////////////////////////////////////////////
+  void ApplyBatch6D(const Field &in6, Field &out6, int nr)
+  {
+    GRID_ASSERT(nr <= MRHS_MAX);
+    GRID_ASSERT(in6.Grid()->_ndimension == nd+1);   // {rhs, s, x,y,z,t}
+    double t0 = usecond();
+    Field &in = const_cast<Field &>(in6);
+    uint64_t nX = (uint64_t)N * nr;
+    thread_for(i, nX, { hX[i]=ComplexF(0.0,0.0); });
+    {
+      autoView(iv, in, CpuRead);
+      Coordinate c6(nd+1);
+      for(int ss=0; ss<lsites; ss++){
+        for(int d=0; d<nd; d++) c6[d+1] = myLcoor[ss][d];
+        for(int rr=0; rr<nr; rr++){
+          c6[0] = rr;
+          sobj s;
+          peekLocalSite(s, iv, c6);
+          for(int b=0; b<nbasis; b++)
+            hX[(uint64_t)rr*N + myGsite[ss]*nbasis + b] = ComplexF(((ComplexD *)&s)[b]);
+        }
+      }
+    }
+    double t1 = usecond();
+    double tprof[4];
+    SlabApplyPacked(nr, tprof);
+    double t5 = usecond();
+    {
+      autoView(ov, out6, CpuWrite);
+      Coordinate c6(nd+1);
+      for(int ss=0; ss<lsites; ss++){
+        for(int d=0; d<nd; d++) c6[d+1] = myLcoor[ss][d];
+        for(int rr=0; rr<nr; rr++){
+          c6[0] = rr;
+          sobj s;
+          for(int b=0; b<nbasis; b++)
+            ((ComplexD *)&s)[b] = ComplexD(hY[(uint64_t)rr*nrows + (ss*nbasis+b)]);  // Y col-major
+          pokeLocalSite(s, ov, c6);
+        }
+      }
+    }
+    double t6 = usecond();
+    std::cout << GridLogMessage << "DenseCoarseMatrix: apply6D " << nr << " rhs took "
+              << (t6-t0)/1000.0 << " ms" << std::endl;
+    if ( getenv("DENSE_APPLY_PROFILE") ) {
+      std::cout << GridLogMessage << "DenseCoarseMatrix: apply6D profile:"
+                << " pack "        << (t1-t0)/1000.0
+                << "  allreduce "  << tprof[0]/1000.0
+                << "  H2D "        << tprof[1]/1000.0
+                << "  gemm+reduce "<< tprof[2]/1000.0
+                << "  D2H "        << tprof[3]/1000.0
+                << "  unpack "     << (t6-t5)/1000.0
+                << "  ms" << std::endl;
+    }
+  }
+};
+
+NAMESPACE_END(Grid);

Grid/algorithms/multigrid/GeneralCoarsenedMatrix.h

@@ -31,6 +31,7 @@ Author: Peter Boyle <pboyle@bnl.gov>
 
 #include <Grid/lattice/PaddedCell.h>
 #include <Grid/stencil/GeneralLocalStencil.h>
+#include <Grid/algorithms/deflation/MultiRHSBlockProject.h>
 
 NAMESPACE_BEGIN(Grid);
 
@@ -66,6 +67,10 @@ public:
   std::vector<CoarseMatrix> _Adag;
   std::vector<CoarseVector> MultTemporaries;
 
+  int64_t MultCalls;
+  double  MultFlopsAccum;
+  double  MultUsecAccum;
+
   ///////////////////////
   // Interface
   ///////////////////////
@@ -104,19 +109,20 @@ public:
   }
   */
   
-  GeneralCoarsenedMatrix(NonLocalStencilGeometry &_geom,GridBase *FineGrid, GridCartesian * CoarseGrid)
+  GeneralCoarsenedMatrix(NonLocalStencilGeometry &_geom,GridBase *FineGrid, GridCartesian * CoarseGrid,int _herm=1)
     : geom(_geom),
       _FineGrid(FineGrid),
       _CoarseGrid(CoarseGrid),
-      hermitian(1),
+      hermitian(_herm),
       Cell(_geom.Depth(),_CoarseGrid),
-      Stencil(Cell.grids.back(),geom.shifts)
+      Stencil(Cell.grids.back(),geom.shifts),
+      MultCalls(0), MultFlopsAccum(0.0), MultUsecAccum(0.0)
   {
     {
       int npoint = _geom.npoint;
     }
     _A.resize(geom.npoint,CoarseGrid);
-    //    _Adag.resize(geom.npoint,CoarseGrid);
+    if ( !hermitian ) _Adag.resize(geom.npoint,CoarseGrid);
   }
   void M (const CoarseVector &in, CoarseVector &out)
   {
@@ -124,10 +130,10 @@ public:
   }
   void Mdag (const CoarseVector &in, CoarseVector &out)
   {
-    GRID_ASSERT(hermitian);
+    if(hermitian)
-    Mult(_A,in,out);
+      Mult(_A,in,out);
-    //    if ( hermitian ) M(in,out);
+    else
-    //    else Mult(_Adag,in,out);
+      Mult(_Adag,in,out);
   }
   void Mult (std::vector<CoarseMatrix> &A,const CoarseVector &in, CoarseVector &out)
   {
@@ -227,29 +233,28 @@ public:
     text+=usecond();
     ttot+=usecond();
     
-    std::cout << GridLogPerformance<<"Coarse 1rhs Mult Aviews "<<tviews<<" us"<<std::endl;
+    MultCalls++;
-    std::cout << GridLogPerformance<<"Coarse Mult exch "<<texch<<" us"<<std::endl;
+    MultFlopsAccum += flops;
-    std::cout << GridLogPerformance<<"Coarse Mult mult "<<tmult<<" us"<<std::endl;
+    MultUsecAccum  += ttot;
-    std::cout << GridLogPerformance<<" of which mult2  "<<tmult2<<" us"<<std::endl;
+    std::cout << GridLogPerformance
-    std::cout << GridLogPerformance<<"Coarse Mult ext  "<<text<<" us"<<std::endl;
+	      << "Coarse Mult call " << MultCalls
-    std::cout << GridLogPerformance<<"Coarse Mult temps "<<ttemps<<" us"<<std::endl;
+	      << "  tot " << ttot << " us"
-    std::cout << GridLogPerformance<<"Coarse Mult copy  "<<tcopy<<" us"<<std::endl;
+	      << "  kernel " << tmult << " us"
-    std::cout << GridLogPerformance<<"Coarse Mult tot  "<<ttot<<" us"<<std::endl;
+	      << "  kernel " << flops/tmult*1e-3 << " GFlop/s"
-    //    std::cout << GridLogPerformance<<std::endl;
+	      << "  overall " << MultFlopsAccum/MultUsecAccum*1e-3 << " GFlop/s (cumul)"
-    std::cout << GridLogPerformance<<"Coarse Kernel flops "<< flops<<std::endl;
+	      << "  bw " << bytes/tmult*1e-3 << " GB/s"
-    std::cout << GridLogPerformance<<"Coarse Kernel flop/s "<< flops/tmult<<" mflop/s"<<std::endl;
+	      << std::endl;
-    std::cout << GridLogPerformance<<"Coarse Kernel bytes/s "<< bytes/tmult<<" MB/s"<<std::endl;
-    std::cout << GridLogPerformance<<"Coarse overall flops/s "<< flops/ttot<<" mflop/s"<<std::endl;
-    std::cout << GridLogPerformance<<"Coarse total bytes   "<< bytes/1e6<<" MB"<<std::endl;
 
   };
   
   void PopulateAdag(void)
   {
+#if 0
+    // Serial global peek/poke reference implementation
     for(int64_t bidx=0;bidx<CoarseGrid()->gSites() ;bidx++){
       Coordinate bcoor;
       CoarseGrid()->GlobalIndexToGlobalCoor(bidx,bcoor);
-      
+
       for(int p=0;p<geom.npoint;p++){
 	Coordinate scoor = bcoor;
 	for(int mu=0;mu<bcoor.size();mu++){
@@ -262,6 +267,36 @@ public:
 	pokeSite(adj(link),_Adag[pp],bcoor);
       }
     }
+#else
+    // Parallel: _Adag[pp](x) = adj( _A[p](x + s_pp) ),  pp = Reverse(p), s_pp = -s_p.
+    // The neighbour fetch reuses the same padded-cell + stencil machinery as Mult,
+    // reading one matrix element per coalesced access so no whole site matrix
+    // (230KB at nbasis=60) ever lands on a GPU thread stack (HIP limit 128KB).
+    // Halo sites compute garbage neighbours; Cell.Extract discards them.
+    // Must run on the unpadded _A, i.e. before ExchangeCoarseLinks.
+    const int Nsimd = CComplex::Nsimd();
+    for(int p=0;p<geom.npoint;p++){
+      int pp = geom.Reverse(p);
+      CoarseMatrix Apad = Cell.ExchangePeriodic(_A[p]);
+      CoarseMatrix Dpad(Apad.Grid());
+      int64_t osites = Apad.Grid()->oSites();
+      {
+	autoView( Apad_v   , Apad, AcceleratorRead);
+	autoView( Dpad_v   , Dpad, AcceleratorWriteDiscard);
+	autoView( Stencil_v, Stencil, AcceleratorRead);
+	accelerator_for(sj, osites*nbasis, Nsimd, {
+	    int32_t ss = sj/nbasis;
+	    int32_t j  = sj%nbasis;
+	    auto SE = Stencil_v.GetEntry(pp,ss);
+	    for(int i=0;i<nbasis;i++){
+	      auto z = coalescedReadGeneralPermute(Apad_v[SE->_offset](i,j),SE->_permute,Nd);
+	      coalescedWrite(Dpad_v[ss](j,i),conjugate(z));
+	    }
+	});
+      }
+      _Adag[pp] = Cell.Extract(Dpad);
+    }
+#endif
   }
   /////////////////////////////////////////////////////////////
   // 
@@ -417,10 +452,9 @@ public:
 	int osites=CoarseGrid()->oSites();
 	autoView( A_v  , _A[k], AcceleratorWrite);
 	autoView( FT_v  , FT[k], AcceleratorRead);
-	accelerator_for(sss, osites, 1, {
+	accelerator_for(sss, osites, nbasis, {
-	    for(int j=0;j<nbasis;j++){
+	    int j = acceleratorSIMTlane(nbasis);
-	      A_v[sss](i,j) = FT_v[sss](j);
+	    A_v[sss](i,j) = FT_v[sss](j);
-	    }
         });
       }
       tinv+=usecond();
@@ -428,8 +462,8 @@ public:
 
     // Only needed if nonhermitian
     if ( ! hermitian ) {
-      //      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
+      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
-      //      PopulateAdag();
+      PopulateAdag();
     }
 
     // Need to write something to populate Adag from A
@@ -517,13 +551,9 @@ public:
     // Now compute the matrix elements of linop between the orthonormal
     // set of vectors.
     ///////////////////////////////////////////////////////////////////////
-    FineField phaV(grid); // Phased block basis vector
-    FineField MphaV(grid);// Matrix applied
     std::vector<FineComplexField> phaF(npoint,grid);
     std::vector<CoarseComplexField> pha(npoint,CoarseGrid());
-    
+
-    CoarseVector coarseInner(CoarseGrid());
-    
     typedef typename CComplex::scalar_type SComplex;
     FineComplexField one(grid); one=SComplex(1.0);
     FineComplexField zz(grid); zz = Zero();
@@ -542,37 +572,52 @@ public:
       pha[p]  =exp(pha[p]*ci);
 
       blockZAXPY(phaF[p],pha[p],one,zz);
-      
+
     }
     tphase+=usecond();
-    
+
-    std::vector<CoarseVector> ComputeProj(npoint,CoarseGrid());
+    // Import basis into BLAS layout once; blockProject then reads it once per
-    std::vector<CoarseVector>          FT(npoint,CoarseGrid());
+    // basis vector rather than once per (i,p) as in scalar blockProject.
+    // Process all npoint in a single batch.
+    MultiRHSBlockProject<FineField> Projector;
+    Projector.Allocate(nbasis, grid, CoarseGrid());
+    Projector.ImportBasis(U.subspace);
+
+    std::vector<FineField>    phaV_batch(npoint, grid);
+    std::vector<FineField>    MphaV_batch(npoint, grid);
+    std::vector<CoarseVector> proj_batch(npoint, CoarseGrid());
+    std::vector<CoarseVector> ComputeProj(npoint, CoarseGrid());
+    std::vector<CoarseVector>          FT(npoint, CoarseGrid());
+
+    // Pre-allocate BLAS_F and BLAS_C to avoid repeated hipMalloc/hipFree of
+    // ~5.6 GB per blockProject call, which hangs on ROCm for large allocations.
+    Projector.BLAS_F.resize(Projector.fine_vol * Projector.words * npoint);
+    Projector.BLAS_C.resize(Projector.coarse_vol * nbasis * npoint);
+
     for(int i=0;i<nbasis;i++){// Loop over basis vectors
+      accelerator_barrier(); // ensure prior iteration's async writes are retired
       std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<"/"<<nbasis<< std::endl;
-      for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
-	tphaseBZ-=usecond();
-	phaV = phaF[p]*V.subspace[i];
-	tphaseBZ+=usecond();
 
-	/////////////////////////////////////////////////////////////////////
+      tphaseBZ-=usecond();
-	// Multiple phased subspace vector by matrix and project to subspace
+      for(int p=0;p<npoint;p++)
-	// Remove local bulk phase to leave relative phases
+	phaV_batch[p] = phaF[p] * V.subspace[i];
-	/////////////////////////////////////////////////////////////////////
+      tphaseBZ+=usecond();
-	tmat-=usecond();
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<" phaseBZ done"<< std::endl;
-	linop.Op(phaV,MphaV);
-	tmat+=usecond();
-	//	std::cout << i << " " <<p << " MphaV "<<norm2(MphaV)<<" "<<norm2(phaV)<<std::endl;
 
-	tproj-=usecond();
+      tmat-=usecond();
-	blockProject(coarseInner,MphaV,U.subspace);
+      for(int p=0;p<npoint;p++)
-	coarseInner = conjugate(pha[p]) * coarseInner;
+	linop.Op(phaV_batch[p], MphaV_batch[p]);
+      tmat+=usecond();
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<" mat done"<< std::endl;
 
-	ComputeProj[p] = coarseInner;
+      // One batched GEMM reads BLAS_V once for all npoint vectors.
-	tproj+=usecond();
+      tproj-=usecond();
-	//	std::cout << i << " " <<p << " ComputeProj "<<norm2(ComputeProj[p])<<std::endl;
+      Projector.blockProject(MphaV_batch, proj_batch);
-
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<" blockProject done"<< std::endl;
-      }
+      for(int p=0;p<npoint;p++)
+	ComputeProj[p] = conjugate(pha[p]) * proj_batch[p];
+      tproj+=usecond();
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<" proj done"<< std::endl;
 
       tinv-=usecond();
       for(int k=0;k<npoint;k++){
@@ -580,14 +625,13 @@ public:
 	for(int l=0;l<npoint;l++){
 	  FT[k]= FT[k]+ invMkl(l,k)*ComputeProj[l];
 	}
-      
+
 	int osites=CoarseGrid()->oSites();
 	autoView( A_v  , _A[k], AcceleratorWrite);
 	autoView( FT_v  , FT[k], AcceleratorRead);
-	accelerator_for(sss, osites, 1, {
+	accelerator_for(sss, osites, nbasis, {
-	    for(int j=0;j<nbasis;j++){
+	    int j = acceleratorSIMTlane(nbasis);
-	      A_v[sss](i,j) = FT_v[sss](j);
+	    A_v[sss](i,j) = FT_v[sss](j);
-	    }
         });
       }
       tinv+=usecond();
@@ -595,13 +639,13 @@ public:
 
     // Only needed if nonhermitian
     if ( ! hermitian ) {
-      //      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
+      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
-      //      PopulateAdag();
+      PopulateAdag();
     }
 
-    for(int p=0;p<geom.npoint;p++){
+    //    for(int p=0;p<geom.npoint;p++){
-      std::cout << " _A["<<p<<"] "<<norm2(_A[p])<<std::endl;
+    //      std::cout << " _A["<<p<<"] "<<norm2(_A[p])<<std::endl;
-    }
+    //    }
 
     // Need to write something to populate Adag from A
     ExchangeCoarseLinks();
@@ -616,7 +660,7 @@ public:
   void ExchangeCoarseLinks(void){
     for(int p=0;p<geom.npoint;p++){
       _A[p] = Cell.ExchangePeriodic(_A[p]);
-      //      _Adag[p]= Cell.ExchangePeriodic(_Adag[p]);
+      if ( !hermitian ) _Adag[p]= Cell.ExchangePeriodic(_Adag[p]);
     }
   }
   virtual  void Mdiag    (const Field &in, Field &out){ GRID_ASSERT(0);};

Grid/allocator/MemoryManager.cc

@@ -63,12 +63,10 @@ void MemoryManager::PrintBytes(void)
   std::cout << " MemoryManager : "<<(total_device>>20)<<" accelerator Mbytes "<<std::endl;
   std::cout << " MemoryManager : "<<(total_host>>20)  <<" cpu         Mbytes "<<std::endl;
   uint64_t cacheBytes;
-  cacheBytes = CacheBytes[Cpu];
+  cacheBytes = HostCacheBytes();
-  std::cout << " MemoryManager : "<<(cacheBytes>>20) <<" cpu cache Mbytes "<<std::endl;
+  std::cout << " MemoryManager : "<<(cacheBytes>>20) <<" cpu alloc cache Mbytes "<<std::endl;
-  cacheBytes = CacheBytes[Acc];
+  cacheBytes = DeviceCacheBytes();
-  std::cout << " MemoryManager : "<<(cacheBytes>>20) <<" acc cache Mbytes "<<std::endl;
+  std::cout << " MemoryManager : "<<(cacheBytes>>20) <<" acc alloc cache Mbytes "<<std::endl;
-  cacheBytes = CacheBytes[Shared];
-  std::cout << " MemoryManager : "<<(cacheBytes>>20) <<" shared cache Mbytes "<<std::endl;
   
 #ifdef GRID_CUDA
   cuda_mem();

Grid/allocator/MemoryManager.h

@@ -113,7 +113,7 @@ private:
   static void *Insert(void *ptr,size_t bytes,AllocationCacheEntry *entries,int ncache,int &victim,uint64_t &cbytes) ;
   static void *Lookup(size_t bytes,AllocationCacheEntry *entries,int ncache,uint64_t &cbytes) ;
 
- public:
+public:  
   static void PrintBytes(void);
   static void Audit(std::string s);
   static void Init(void);
@@ -215,6 +215,7 @@ private:
   static void NotifyDeletion(void * CpuPtr);
   static void Print(void);
   static void PrintAll(void);
+  static void EvictAll(void);
   static void PrintState( void* CpuPtr);
   static int   isOpen   (void* CpuPtr);
   static void  ViewClose(void* CpuPtr,ViewMode mode);

Grid/allocator/MemoryManagerCache.cc

@@ -79,6 +79,25 @@ void MemoryManager::EntryErase(uint64_t CpuPtr)
   auto AccCache = EntryLookup(CpuPtr);
   AccViewTable.erase(CpuPtr);
 }
+/////////////////////////////////////////////////////////////////////////////////
+// LRU membership invariant:
+//
+//    LRU_valid == 1   <=>   AccPtr != NULL  &&  accLock == 0  &&  cpuLock == 0
+//
+// i.e. the LRU queue contains exactly the device-resident, completely unlocked
+// entries -- the evictable set.  Membership is maintained EAGERLY at the lock
+// 0<->1 edges, O(1) via the stored LRU_entry iterator:
+//
+//    AcceleratorViewOpen   lock 0->1 : LRUremove   (gated on LRU_valid)
+//    AcceleratorViewClose  accLock->0: LRUinsert   (AccPtr necessarily exists)
+//    CpuViewOpen           lock 0->1 : LRUremove   (gated on LRU_valid)
+//    CpuViewClose          cpuLock->0: LRUinsert   (iff AccPtr exists)
+//    Evict/AccDiscard                : LRUremove   (frees the device copy)
+//
+// Consequences: victims taken from LRU.back() are evictable by construction;
+// Evict() on a locked entry is an invariant violation (asserted), and the
+// eviction loops (EvictVictims/EvictAll) cannot spin.
+/////////////////////////////////////////////////////////////////////////////////
 void  MemoryManager::LRUinsert(AcceleratorViewEntry &AccCache)
 {
   GRID_ASSERT(AccCache.LRU_valid==0);
@@ -130,21 +149,21 @@ void MemoryManager::Evict(AcceleratorViewEntry &AccCache)
 {
   ///////////////////////////////////////////////////////////////////////////
   // Make CPU consistent, remove from Accelerator, remove from LRU, LEAVE CPU only entry
-  // Cannot be acclocked. If allocated must be in LRU pool.
+  // Cannot be locked. If allocated must be in LRU pool.
   //
-  // Nov 2022... Felix issue: Allocating two CpuPtrs, can have an entry in LRU-q with CPUlock.
+  // (Historical: a Nov 2022 incident (two CpuPtrs; eviction called from
-  //                          and require to evict the AccPtr copy. Eviction was a mistake in CpuViewOpen
+  //  CpuViewOpen -- since excised) could present a cpuLocked entry here, and
-  //                          but there is a weakness where CpuLock entries are attempted for erase
+  //  silent-return guards were added.  The LRU membership invariant (see
-  //                          Take these OUT LRU queue when CPU locked?
+  //  LRUinsert) now excludes ALL locked entries from the queue eagerly at the
-  //                          Cannot take out the table as cpuLock data is important.
+  //  lock edges, so a locked victim is an invariant violation: asserted.)
   ///////////////////////////////////////////////////////////////////////////
   GRID_ASSERT(AccCache.state!=Empty);
   
   mprintf("MemoryManager: Evict CpuPtr %lx AccPtr %lx cpuLock %ld accLock %ld",
 	  (uint64_t)AccCache.CpuPtr,(uint64_t)AccCache.AccPtr,
 	  (uint64_t)AccCache.cpuLock,(uint64_t)AccCache.accLock); 
-  if (AccCache.accLock!=0) return;
+  GRID_ASSERT(AccCache.accLock==0);
-  if (AccCache.cpuLock!=0) return;
+  GRID_ASSERT(AccCache.cpuLock==0);
   if(AccCache.state==AccDirty) {
     Flush(AccCache);
   }
@@ -250,6 +269,19 @@ void  MemoryManager::EvictVictims(uint64_t bytes)
     }
   }
 }
+void  MemoryManager::EvictAll(void)
+{
+  while(LRU.size()>0){
+    if ( DeviceLRUBytes > 0){
+      uint64_t victim = LRU.back(); // From the LRU
+      auto AccCacheIterator = EntryLookup(victim);
+      auto & AccCache = AccCacheIterator->second;
+      Evict(AccCache);
+    } else {
+      return;
+    }
+  }
+}
 uint64_t MemoryManager::AcceleratorViewOpen(uint64_t CpuPtr,size_t bytes,ViewMode mode,ViewAdvise hint)
 {
   ////////////////////////////////////////////////////////////////////////////
@@ -383,6 +415,13 @@ void MemoryManager::CpuViewClose(uint64_t CpuPtr)
   GRID_ASSERT(AccCache.accLock==0);
 
   AccCache.cpuLock--;
+  // Return to LRU queue when fully unlocked -- mirrors AcceleratorViewClose.
+  // Asymmetry vs the Acc side: a device copy need not exist for a host view;
+  // only device-resident entries belong in the (evictable) LRU queue.
+  if( (AccCache.cpuLock==0) && (AccCache.AccPtr!=(uint64_t)NULL) ) {
+    dprintf("CpuViewClose %lx cpuLock decremented to zero, move to LRU queue",(uint64_t)CpuPtr);
+    LRUinsert(AccCache);
+  }
 }
 /*
  *  Action  State   StateNext         Flush    Clone
@@ -449,6 +488,14 @@ uint64_t MemoryManager::CpuViewOpen(uint64_t CpuPtr,size_t bytes,ViewMode mode,V
     GRID_ASSERT(0); // should be unreachable
   }
 
+  GRID_ASSERT(AccCache.cpuLock>0);
+  // If view is opened on host must remove from LRU -- mirrors AcceleratorViewOpen.
+  // LRU_valid==1 here implies this is the 0->1 lock edge of a device-resident entry.
+  if(AccCache.LRU_valid==1){
+    dprintf("CpuViewOpen: entry removed from LRU ");
+    LRUremove(AccCache);
+  }
+
   AccCache.transient= transient? EvictNext : 0;
 
   return AccCache.CpuPtr;

Grid/communicator/Communicator_base.h

@@ -238,6 +238,16 @@ public:
   }
   void AllToAll(int dim  ,void *in,void *out,uint64_t words,uint64_t bytes);
   void AllToAll(void  *in,void *out,uint64_t words         ,uint64_t bytes);
+
+  ////////////////////////////////////////////////////////////////////////////
+  // Variable count all to all. Counts and displacements are in units of
+  // "bytes" sized words and are indexed by rank within this communicator.
+  // For exchanges that are a permutation but do not divide evenly between
+  // ranks; AllToAll above is the uniform count special case.
+  ////////////////////////////////////////////////////////////////////////////
+  void AllToAllV(void *in ,const std::vector<int> &sendcounts,const std::vector<int> &senddispls,
+                 void *out,const std::vector<int> &recvcounts,const std::vector<int> &recvdispls,
+                 uint64_t bytes);
   
   template<class obj> void Broadcast(int root,obj &data)
   {

Grid/communicator/Communicator_mpi3.cc

@@ -945,5 +945,25 @@ void CartesianCommunicator::AllToAll(void  *in,void *out,uint64_t words,uint64_t
   MPI_Alltoall(in,iwords,object,out,iwords,object,communicator);
   MPI_Type_free(&object);
 }
+void CartesianCommunicator::AllToAllV(void *in ,const std::vector<int> &sendcounts,const std::vector<int> &senddispls,
+                                      void *out,const std::vector<int> &recvcounts,const std::vector<int> &recvdispls,
+                                      uint64_t bytes)
+{
+  FlightRecorder::StepLog("AllToAllV");
+  GRID_ASSERT(sendcounts.size()==(size_t)_Nprocessors);
+  GRID_ASSERT(senddispls.size()==(size_t)_Nprocessors);
+  GRID_ASSERT(recvcounts.size()==(size_t)_Nprocessors);
+  GRID_ASSERT(recvdispls.size()==(size_t)_Nprocessors);
+  // MPI counts are "int"; the caller sizes the word to keep them in range
+  int ibytes = bytes;
+  GRID_ASSERT(bytes == (uint64_t)ibytes);
+  MPI_Datatype object;
+  MPI_Type_contiguous(ibytes,MPI_BYTE,&object);
+  MPI_Type_commit(&object);
+  int ierr = MPI_Alltoallv(in ,(int *)&sendcounts[0],(int *)&senddispls[0],object,
+                           out,(int *)&recvcounts[0],(int *)&recvdispls[0],object,communicator);
+  GRID_ASSERT(ierr==0);
+  MPI_Type_free(&object);
+}
 
 NAMESPACE_END(Grid);

Grid/communicator/Communicator_none.cc

@@ -113,6 +113,17 @@ void CartesianCommunicator::AllToAll(void  *in,void *out,uint64_t words,uint64_t
 {
   bcopy(in,out,bytes*words);
 }
+void CartesianCommunicator::AllToAllV(void *in ,const std::vector<int> &sendcounts,const std::vector<int> &senddispls,
+                                      void *out,const std::vector<int> &recvcounts,const std::vector<int> &recvdispls,
+                                      uint64_t bytes)
+{
+  // Single rank: the exchange degenerates to a copy of our own segment
+  GRID_ASSERT(sendcounts.size()==1);
+  GRID_ASSERT(recvcounts.size()==1);
+  GRID_ASSERT(sendcounts[0]==recvcounts[0]);
+  bcopy((char *)in +(uint64_t)senddispls[0]*bytes,
+        (char *)out+(uint64_t)recvdispls[0]*bytes,bytes*(uint64_t)sendcounts[0]);
+}
 
 int  CartesianCommunicator::RankWorld(void){return 0;}
 void CartesianCommunicator::Barrier(void){}

Grid/lattice/Lattice_base.h

@@ -289,7 +289,7 @@ public:
   ///////////////////////////////////////////
   // move constructor
   ///////////////////////////////////////////
-  Lattice(Lattice && r){ 
+  Lattice(Lattice && r) noexcept { 
     this->_grid = r.Grid();
     this->_odata      = r._odata;
     this->_odata_size = r._odata_size;
@@ -330,7 +330,7 @@ public:
   ///////////////////////////////////////////
   // Move assignment possible if same type
   ///////////////////////////////////////////
-  inline Lattice<vobj> & operator = (Lattice<vobj> && r){
+  inline Lattice<vobj> & operator = (Lattice<vobj> && r) noexcept {
 
     resize(0); // deletes if appropriate
     this->_grid       = r.Grid();

Grid/lattice/Lattice_reduction_gpu.h

@@ -197,12 +197,15 @@ __global__ void reduceKernel(const vobj *lat, sobj *buffer, Iterator n) {
 /////////////////////////////////////////////////////////////////////////////////////////////////////////
 // Possibly promote to double and sum
 /////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+#undef GRID_REDUCTION_TIMING
+
 template <class vobj>
-inline typename vobj::scalar_objectD sumD_gpu_small(const vobj *lat, Integer osites) 
+inline typename vobj::scalar_objectD sumD_gpu_small(const vobj *lat, Integer osites)
 {
   typedef typename vobj::scalar_objectD sobj;
   typedef decltype(lat) Iterator;
-  
+
   Integer nsimd= vobj::Nsimd();
   Integer size = osites*nsimd;
 
@@ -211,41 +214,188 @@ inline typename vobj::scalar_objectD sumD_gpu_small(const vobj *lat, Integer osi
   GRID_ASSERT(ok);
 
   Integer smemSize = numThreads * sizeof(sobj);
-  // Move out of UVM
-  // Turns out I had messed up the synchronise after move to compute stream
-  // as running this on the default stream fools the synchronise
   deviceVector<sobj> buffer(numBlocks);
   sobj *buffer_v = &buffer[0];
   sobj result;
+
+#ifdef GRID_REDUCTION_TIMING
+  RealD t_kernel = -usecond();
+#endif
   reduceKernel<<< numBlocks, numThreads, smemSize, computeStream >>>(lat, buffer_v, size);
   accelerator_barrier();
+#ifdef GRID_REDUCTION_TIMING
+  t_kernel += usecond();
+  RealD t_d2h = -usecond();
+#endif
   acceleratorCopyFromDevice(buffer_v,&result,sizeof(result));
+#ifdef GRID_REDUCTION_TIMING
+  t_d2h += usecond();
+  std::cout << GridLogDebug << "  sumD_gpu_small"
+            << " sizeof(sobj)=" << sizeof(sobj)
+            << " blocks=" << numBlocks << " threads=" << numThreads
+            << " kernel+barrier=" << t_kernel << " us"
+            << " D2H=" << t_d2h << " us" << std::endl;
+#endif
   return result;
 }
 
+// Fused pack+reduce: reads R words of each vobj at word offset 'base',
+// accumulates directly into iVector<iScalar<scalarD>,R> without staging
+// through an intermediate bundle buffer.  One HBM pass instead of three.
+template <int R, class vobj, class sobj, class Iterator>
+__device__ void packReduceBlocks(
+    const iScalar<typename vobj::vector_type> *idat,
+    sobj *g_odata, Iterator osites, int base, int words)
+{
+  constexpr Iterator nsimd = vobj::Nsimd();
+  Iterator blockSize = blockDim.x;
+
+  extern __shared__ __align__(COALESCE_GRANULARITY) unsigned char shmem_pointer[];
+  sobj *sdata = (sobj *)shmem_pointer;
+
+  Iterator tid      = threadIdx.x;
+  Iterator i        = blockIdx.x * (blockSize * 2) + threadIdx.x;
+  Iterator gridSize = blockSize * 2 * gridDim.x;
+  sobj mySum = Zero();
+
+  while (i < osites * nsimd) {
+    Iterator lane = i % nsimd;
+    Iterator ss   = i / nsimd;
+    sobj tmpD; zeroit(tmpD);
+    for (int k = 0; k < R; k++) {
+      auto w = extractLane(lane, idat[ss * words + base + k]);
+      iScalar<typename vobj::scalar_typeD> wd; wd = w;
+      tmpD._internal[k] = wd;
+    }
+    mySum += tmpD;
+
+    if (i + blockSize < osites * nsimd) {
+      lane = (i + blockSize) % nsimd;
+      ss   = (i + blockSize) / nsimd;
+      sobj tmpD2; zeroit(tmpD2);
+      for (int k = 0; k < R; k++) {
+        auto w = extractLane(lane, idat[ss * words + base + k]);
+        iScalar<typename vobj::scalar_typeD> wd; wd = w;
+        tmpD2._internal[k] = wd;
+      }
+      mySum += tmpD2;
+    }
+    i += gridSize;
+  }
+
+  reduceBlock(sdata, mySum, tid);
+  if (tid == 0) g_odata[blockIdx.x] = sdata[0];
+}
+
+template <int R, class vobj, class sobj, class Iterator>
+__global__ void packReduceKernel(
+    const iScalar<typename vobj::vector_type> *idat,
+    sobj *buffer, Iterator osites, int base, int words)
+{
+  Iterator blockSize = blockDim.x;
+
+  packReduceBlocks<R, vobj, sobj>(idat, buffer, osites, base, words);
+
+  if (gridDim.x > 1) {
+    const Iterator tid = threadIdx.x;
+    __shared__ bool amLast;
+    extern __shared__ __align__(COALESCE_GRANULARITY) unsigned char shmem_pointer[];
+    sobj *smem = (sobj *)shmem_pointer;
+
+    acceleratorFence();
+
+    if (tid == 0) {
+      unsigned int ticket = atomicInc(&retirementCount, gridDim.x);
+      amLast = (ticket == gridDim.x - 1);
+    }
+    acceleratorSynchroniseAll();
+
+    if (amLast) {
+      Iterator i = tid;
+      sobj mySum = Zero();
+      while (i < (Iterator)gridDim.x) {
+        mySum += buffer[i];
+        i += blockSize;
+      }
+      reduceBlock(smem, mySum, tid);
+      if (tid == 0) {
+        buffer[0] = smem[0];
+        retirementCount = 0;
+      }
+    }
+  }
+}
+
+template<int R, class vobj>
+inline void sumD_gpu_reduce_words(const vobj *lat, Integer osites,
+                                   typename vobj::scalar_typeD *ret_p, int base)
+{
+  typedef typename vobj::vector_type  vector;
+  typedef typename vobj::scalar_typeD scalarD;
+  using BundleScalarD = iVector<iScalar<scalarD>, R>;
+
+  constexpr int Nsimd = vobj::Nsimd();
+  const int words = sizeof(vobj) / sizeof(vector);
+  const iScalar<vector> *idat = (const iScalar<vector> *)lat;
+
+  Integer size = (Integer)osites * Nsimd;
+  Integer numThreads, numBlocks;
+  int ok = getNumBlocksAndThreads(size, sizeof(BundleScalarD), numThreads, numBlocks);
+  GRID_ASSERT(ok);
+
+  Integer smemSize = numThreads * sizeof(BundleScalarD);
+  deviceVector<BundleScalarD> buffer(numBlocks);
+  BundleScalarD *buffer_v = &buffer[0];
+  BundleScalarD result;
+
+#ifdef GRID_REDUCTION_TIMING
+  RealD t_kernel = -usecond();
+#endif
+  packReduceKernel<R, vobj, BundleScalarD, Integer>
+    <<<numBlocks, numThreads, smemSize, computeStream>>>
+    (idat, buffer_v, osites, base, words);
+  accelerator_barrier();
+#ifdef GRID_REDUCTION_TIMING
+  t_kernel += usecond();
+  RealD t_d2h = -usecond();
+#endif
+  acceleratorCopyFromDevice(buffer_v, &result, sizeof(result));
+#ifdef GRID_REDUCTION_TIMING
+  t_d2h += usecond();
+  std::cout << GridLogDebug << " sumD_gpu_reduce_words R=" << R
+            << " base=" << base
+            << " kernel=" << t_kernel << " D2H=" << t_d2h << " us" << std::endl;
+#endif
+
+  for (int k = 0; k < R; k++)
+    ret_p[base + k] = TensorRemove(result._internal[k]);
+}
+
 template <class vobj>
 inline typename vobj::scalar_objectD sumD_gpu_large(const vobj *lat, Integer osites)
 {
-  typedef typename vobj::vector_type  vector;
+  typedef typename vobj::vector_type    vector;
-  typedef typename vobj::scalar_typeD scalarD;
+  typedef typename vobj::scalar_typeD   scalarD;
-  typedef typename vobj::scalar_objectD sobj;
+  typedef typename vobj::scalar_objectD sobjD;
-  sobj ret;
+
+  const int words = sizeof(vobj) / sizeof(vector);
+  sobjD ret; zeroit(ret);
   scalarD *ret_p = (scalarD *)&ret;
-  
-  const int words = sizeof(vobj)/sizeof(vector);
 
-  deviceVector<vector> buffer(osites);
+#ifdef GRID_REDUCTION_TIMING
-  vector *dat = (vector *)lat;
+  RealD t_large = -usecond();
-  vector *buf = &buffer[0];
+#endif
-  iScalar<vector> *tbuf =(iScalar<vector> *)  &buffer[0];
+  int w = 0;
-  for(int w=0;w<words;w++) {
+  while (w + 12 <= words) { sumD_gpu_reduce_words<12>(lat, osites, ret_p, w); w += 12; }
+  while (w +  4 <= words) { sumD_gpu_reduce_words< 4>(lat, osites, ret_p, w); w +=  4; }
+  while (w      <  words) { sumD_gpu_reduce_words< 1>(lat, osites, ret_p, w); w +=  1; }
+#ifdef GRID_REDUCTION_TIMING
+  t_large += usecond();
+  std::cout << GridLogDebug << "sumD_gpu_large"
+            << " sizeof(sobjD)=" << sizeof(sobjD)
+            << " words=" << words << " total=" << t_large << " us" << std::endl;
+#endif
 
-    accelerator_for(ss,osites,1,{
-	buf[ss] = dat[ss*words+w];
-      });
-      
-    ret_p[w] = sumD_gpu_small(tbuf,osites);
-  }
   return ret;
 }
 
@@ -288,5 +438,11 @@ inline typename vobj::scalar_object sum_gpu_large(const vobj *lat, Integer osite
   result = sumD_gpu_large(lat,osites);
   return result;
 }
+template<class Word> Word checksum_gpu(Word *vec,uint64_t L)
+{
+  Word w;
+  bzero(&w,sizeof(w));
+  return w;
+}
 
 NAMESPACE_END(Grid);

Grid/lattice/Lattice_reduction_sycl.h

@@ -6,28 +6,27 @@ NAMESPACE_BEGIN(Grid);
 
 
 template <class vobj>
-inline typename vobj::scalar_objectD sumD_gpu_tensor(const vobj *lat, Integer osites) 
+inline typename vobj::scalar_objectD sumD_gpu_tensor(const vobj *lat, Integer osites)
 {
-  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_object  sobj;
   typedef typename vobj::scalar_objectD sobjD;
 
-  sobj identity; zeroit(identity);
+  sobjD identity; zeroit(identity);
-  sobj ret; zeroit(ret);
+  sobjD ret;      zeroit(ret);
-  Integer nsimd= vobj::Nsimd();
+  {
-  { 
+    sycl::buffer<sobjD, 1> abuff(&ret, {1});
-    sycl::buffer<sobj, 1> abuff(&ret, {1});
     theGridAccelerator->submit([&](sycl::handler &cgh) {
-      auto Reduction = sycl::reduction(abuff,cgh,identity,std::plus<>());
+      auto Reduction = sycl::reduction(abuff, cgh, identity, std::plus<>());
-      cgh.parallel_for(sycl::range<1>{osites},
+      cgh.parallel_for(sycl::range<1>{(size_t)osites},
-                      Reduction,
+                       Reduction,
-                      [=] (sycl::id<1> item, auto &sum) {
+                       [=](sycl::id<1> item, auto &sum) {
-                        auto osite   = item[0];
+                         sobj s = Reduce(lat[item[0]]);
-                        sum +=Reduce(lat[osite]);
+                         sobjD sd; sd = s;
-                      });
+                         sum += sd;
+                       });
     });
   }
-  sobjD dret; convertType(dret,ret);
+  return ret;
-  return dret;
 }
 
 template <class vobj>

Grid/lattice/Lattice_slicesum_core.h

@@ -1,7 +1,6 @@
 #pragma once
 
 #if defined(GRID_CUDA)
-
 #include <cub/cub.cuh>
 #define gpucub cub
 #define gpuError_t cudaError_t
@@ -57,8 +56,13 @@ inline void sliceSumReduction_cub_small(const vobj *Data,
   //copy offsets to device
   acceleratorCopyToDeviceAsynch(&offsets[0],d_offsets,sizeof(int)*(rd+1),computeStream);
   
+#if defined(__CUDACC__) && (__CUDACC_VER_MAJOR__ >= 13)
+  #define GRID_CUB_SUM_OP ::cuda::std::plus<>{}
+#else
+  #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, ::gpucub::Sum(), zero_init, computeStream);
+  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);
   if (gpuErr!=gpuSuccess) {
     std::cout << GridLogError << "Lattice_slicesum_gpu.h: Encountered error during gpucub::DeviceSegmentedReduce::Reduce (setup)! Error: " << gpuErr <<std::endl;
     exit(EXIT_FAILURE);
@@ -82,11 +86,13 @@ inline void sliceSumReduction_cub_small(const vobj *Data,
   });
   
   //issue segmented reductions in computeStream
-  gpuErr = gpucub::DeviceSegmentedReduce::Reduce(temp_storage_array, temp_storage_bytes, rb_p, d_out, rd, d_offsets, d_offsets+1,::gpucub::Sum(), zero_init, computeStream);
+  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);
   if (gpuErr!=gpuSuccess) {
     std::cout << GridLogError << "Lattice_slicesum_gpu.h: Encountered error during gpucub::DeviceSegmentedReduce::Reduce! Error: " << gpuErr <<std::endl;
     exit(EXIT_FAILURE);
   }
+
+#undef GRID_CUB_SUM_OP
   
   acceleratorCopyFromDeviceAsynch(d_out,&lvSum[0],rd*sizeof(vobj),computeStream);
   

Grid/lattice/Lattice_trace.h

@@ -124,6 +124,68 @@ Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > Inverse(const Lattice<iScala
   return ret;
 }
 
+template<int N>
+Lattice<iMatrix<iScalar<iScalar<iScalar<vComplexD> > > , N> > Inverse(const Lattice<iMatrix<iScalar<iScalar<iScalar<vComplexD> > >, N> > &Umu)
+{
+  GridBase *grid=Umu.Grid();
+  auto lvol = grid->lSites();
+  Lattice<iMatrix<iScalar<iScalar<iScalar<vComplexD> > >, N > > ret(grid);
+  
+  autoView(Umu_v,Umu,CpuRead);
+  autoView(ret_v,ret,CpuWrite);
+  thread_for(site,lvol,{
+    Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N,N);
+    Coordinate lcoor;
+    grid->LocalIndexToLocalCoor(site, lcoor);
+    iMatrix<iScalar<iScalar<iScalar<ComplexD> > >, N > Us;
+    iMatrix<iScalar<iScalar<iScalar<ComplexD> > >, N > Ui;
+    peekLocalSite(Us, Umu_v, lcoor);
+    for(int i=0;i<N;i++){
+      for(int j=0;j<N;j++){
+	EigenU(i,j) = Us(i,j)()()();
+      }}
+    Eigen::MatrixXcd EigenUinv = EigenU.inverse();
+    for(int i=0;i<N;i++){
+      for(int j=0;j<N;j++){
+	Ui(i,j)()()() = EigenUinv(i,j);
+      }}
+    pokeLocalSite(Ui,ret_v,lcoor);
+  });
+  return ret;
+}
+
+template<int N>
+Lattice<iMatrix<iScalar<iScalar<iScalar<iScalar<vComplexD> > > > , N> > Inverse(const Lattice<iMatrix<iScalar<iScalar<iScalar<iScalar<vComplexD> > > >, N> > &Umu)
+{
+  GridBase *grid=Umu.Grid();
+  auto lvol = grid->lSites();
+  Lattice<iMatrix<iScalar<iScalar<iScalar<iScalar<vComplexD> > > >, N > > ret(grid);
+  
+  autoView(Umu_v,Umu,CpuRead);
+  autoView(ret_v,ret,CpuWrite);
+  thread_for(site,lvol,{
+    Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N,N);
+    Coordinate lcoor;
+    grid->LocalIndexToLocalCoor(site, lcoor);
+    iMatrix<iScalar<iScalar<iScalar<iScalar<ComplexD> > > >, N > Us;
+    iMatrix<iScalar<iScalar<iScalar<iScalar<ComplexD> > > >, N > Ui;
+    peekLocalSite(Us, Umu_v, lcoor);
+    for(int i=0;i<N;i++){
+      for(int j=0;j<N;j++){
+	EigenU(i,j) = Us(i,j)()()()();
+      }}
+    Eigen::MatrixXcd EigenUinv = EigenU.inverse();
+    for(int i=0;i<N;i++){
+      for(int j=0;j<N;j++){
+	Ui(i,j)()()()() = EigenUinv(i,j);
+      }}
+    pokeLocalSite(Ui,ret_v,lcoor);
+  });
+  return ret;
+}
+
+
+
 
 NAMESPACE_END(Grid);
 #endif

Grid/parallelIO/BinaryIO.cc

@@ -2,3 +2,7 @@
 
 int                    Grid::BinaryIO::latticeWriteMaxRetry = -1;
 Grid::BinaryIO::IoPerf Grid::BinaryIO::lastPerf;
+
+// Target size of a single contiguous file extent under BINARYIO_AGGREGATE.
+// 4MB is around the knee for Lustre; exposed so it can be swept at runtime.
+uint64_t               Grid::BinaryIO::aggregateTargetBytes = 4*1024*1024;

Grid/parallelIO/BinaryIO.h

@@ -39,6 +39,7 @@
 #endif
 
 #include <arpa/inet.h>
+#include <sys/stat.h>
 #include <algorithm>
 
 NAMESPACE_BEGIN(Grid);
@@ -87,6 +88,7 @@ class BinaryIO {
 
   static IoPerf lastPerf;
   static int latticeWriteMaxRetry;
+  static uint64_t aggregateTargetBytes;
 
   /////////////////////////////////////////////////////////////////////////////
   // more byte manipulation helpers
@@ -253,12 +255,392 @@ class BinaryIO {
   // Read or Write distributed lexico array of ANY object to a specific location in file 
   //////////////////////////////////////////////////////////////////////////////////////
 
+  static const int BINARYIO_AGGREGATE     = 0x20;
   static const int BINARYIO_MASTER_APPEND = 0x10;
   static const int BINARYIO_UNORDERED     = 0x08;
   static const int BINARYIO_LEXICOGRAPHIC = 0x04;
   static const int BINARYIO_READ          = 0x02;
   static const int BINARYIO_WRITE         = 0x01;
 
+#ifdef USE_MPI_IO
+  /////////////////////////////////////////////////////////////////////////////
+  // Aggregation: self controlled transposition onto an I/O friendly layout.
+  //
+  // Under BINARYIO_LEXICOGRAPHIC the subarray file view handed to MPI-IO has
+  // contiguous runs of only lLattice[0]*sizeof(fobj) bytes -- a few KB for
+  // typical local volumes. Rather than rely on collective buffering to repair
+  // that, redistribute the payload ourselves so every rank owns a contiguous
+  // range of the global lexicographic site ordering, then issue large plain
+  // contiguous writes.
+  //
+  // "Un-splitting" the nunsplit fastest dimensions means the row of ranks
+  // sharing the remaining process coordinates collectively owns whole global
+  // hyperplanes. All data movement is then confined to that row communicator.
+  // Every rank still owns exactly lSites() sites afterwards, so the exchange is
+  // a pure permutation and needs no divisibility condition on the process grid.
+  /////////////////////////////////////////////////////////////////////////////
+  struct AggregationPlan {
+    int      nunsplit{0};  // number of fastest dimensions un-split
+    int      rowsize{0};   // ranks in the aggregation (row) communicator
+    int      rowrank{0};   // our logical (lexicographic) index within the row
+    uint64_t lsites{0};    // sites per rank -- invariant under the permutation
+    uint64_t chunk{0};     // sites in one globally contiguous run owned by the row
+    std::unique_ptr<CartesianCommunicator> rowcomm;
+    // counts and displacements are indexed by rank within rowcomm
+    std::vector<int>      sendcounts, senddispls, recvcounts, recvdispls;
+    std::vector<uint64_t> scatter;     // recv slot -> slot in the aggregated buffer
+    std::vector<uint64_t> extentGsite; // global lex site index of extent start
+    std::vector<uint64_t> extentLocal; // offset of extent within aggregated buffer
+    std::vector<uint64_t> extentSites; // sites in this extent
+  };
+
+  static inline void BuildAggregationPlan(GridBase *grid,uint64_t fobjSize,AggregationPlan &p)
+  {
+    int ndim           = grid->Dimensions();
+    Coordinate psizes  = grid->ProcessorGrid();
+    Coordinate pcoor   = grid->ThisProcessorCoor();
+    Coordinate gLattice= grid->GlobalDimensions();
+    Coordinate lLattice= grid->LocalDimensions();
+    Coordinate lstart  = grid->LocalStarts();
+
+    uint64_t lsites = grid->lSites();
+    p.lsites = lsites;
+
+    //////////////////////////////////////////////////////////////////////////
+    // Un-splitting dims 0..k-1 gives the row a contiguous run of
+    //     chunk(k) = prod_{d<k} gLattice[d] * lLattice[k]
+    // sites, and each rank writes extents of min(chunk,lsites). Take the
+    // smallest k that reaches the target so we disturb as few dimensions --
+    // and move as little data -- as possible.
+    //////////////////////////////////////////////////////////////////////////
+    int k = ndim-1;
+    for(int trial=1; trial<ndim; trial++){
+      uint64_t chunk = lLattice[trial];
+      for(int d=0; d<trial; d++) chunk *= gLattice[d];
+      if ( std::min(chunk,lsites)*fobjSize >= aggregateTargetBytes ) { k = trial; break; }
+    }
+    p.nunsplit = k;
+
+    //////////////////////////////////////////////////////////////////////////
+    // The box the row collectively owns, expressed in global coordinates.
+    // Restricting the global lexicographic order to this box preserves the
+    // ordering, so the row index below is monotone in the global index.
+    //////////////////////////////////////////////////////////////////////////
+    Coordinate B(ndim), S(ndim);
+    for(int d=0; d<ndim; d++){
+      if ( d<k ) { B[d] = gLattice[d]; S[d] = 0;         }
+      else       { B[d] = lLattice[d]; S[d] = lstart[d]; }
+    }
+
+    uint64_t chunk = lLattice[k];
+    for(int d=0; d<k; d++) chunk *= gLattice[d];
+    p.chunk = chunk;
+
+    //////////////////////////////////////////////////////////////////////////
+    // Row communicator: the ranks sharing the process coordinates of the slow
+    // (still split) dimensions. This is the sub-division the Cartesian
+    // communicator already performs for AllToAll(dim,...), widened from one
+    // dimension to the k fastest.
+    //////////////////////////////////////////////////////////////////////////
+    Coordinate row(ndim,1);
+    for(int d=0; d<k; d++) row[d] = psizes[d];
+    int srank;
+    p.rowcomm.reset(new CartesianCommunicator(row,*grid,srank));
+    p.rowsize = p.rowcomm->ProcessorCount();
+
+    //////////////////////////////////////////////////////////////////////////
+    // Our logical index in the row is the forward lexicographic index of the
+    // un-split process coordinates, so that increasing logical index means
+    // increasing global lexicographic position in the file. The communicator
+    // numbers its own ranks by the reversed (MPI) convention, so build the map
+    // between the two rather than assuming either.
+    //////////////////////////////////////////////////////////////////////////
+    int64_t logical=0, lstride=1;
+    for(int d=0; d<k; d++){ logical += pcoor[d]*lstride; lstride *= psizes[d]; }
+    GRID_ASSERT(lstride == (int64_t)p.rowsize);
+    p.rowrank = (int)logical;
+
+    std::vector<uint64_t> commOf(p.rowsize,0);
+    commOf[p.rowrank] = (uint64_t)p.rowcomm->ThisRank();
+    p.rowcomm->GlobalSumVector(&commOf[0],p.rowsize);
+
+    uint64_t mystart = (uint64_t)p.rowrank * lsites;
+    uint64_t myend   = mystart + lsites;
+
+    Coordinate lcoor(ndim), bcoor(ndim), gcoor(ndim);
+
+    //////////////////////////////////////////////////////////////////////////
+    // Send side. Walking our local sites in local lexicographic order walks
+    // the row index monotonically, so the send buffer is iodata untouched and
+    // we need only the per destination counts.
+    //////////////////////////////////////////////////////////////////////////
+    std::vector<int> sendLogical(p.rowsize,0);
+    for(uint64_t L=0; L<lsites; L++){
+      Lexicographic::CoorFromIndex(lcoor,L,lLattice);
+      for(int d=0; d<ndim; d++) bcoor[d] = (d<k) ? (lstart[d]+lcoor[d]) : lcoor[d];
+      int64_t ri; Lexicographic::IndexFromCoor(bcoor,ri,B);
+      sendLogical[ ri/(int64_t)lsites ]++;
+    }
+    p.sendcounts.assign(p.rowsize,0);
+    p.senddispls.assign(p.rowsize,0);
+    { int64_t disp=0;
+      for(int d=0; d<p.rowsize; d++){          // send buffer is in logical order
+        int c = (int)commOf[d];
+        p.sendcounts[c] = sendLogical[d];
+        p.senddispls[c] = (int)disp;
+        disp += sendLogical[d];
+      }
+    }
+
+    //////////////////////////////////////////////////////////////////////////
+    // Receive side. For each slot of our aggregated range work out which rank
+    // of the row owns it. Within one source the slots arrive in increasing row
+    // index order, which is the order the source sends them in.
+    //////////////////////////////////////////////////////////////////////////
+    std::vector<int> recvLogical(p.rowsize,0), recvDisplLogical(p.rowsize,0);
+    std::vector<int> source(lsites);
+    for(uint64_t pos=0; pos<lsites; pos++){
+      Lexicographic::CoorFromIndex(bcoor,(int64_t)(mystart+pos),B);
+      int64_t j=0, jstride=1;
+      for(int d=0; d<k; d++){ j += (bcoor[d]/lLattice[d])*jstride; jstride *= psizes[d]; }
+      source[pos] = (int)j;
+      recvLogical[j]++;
+    }
+    p.recvcounts.assign(p.rowsize,0);
+    p.recvdispls.assign(p.rowsize,0);
+    { int64_t disp=0;
+      for(int s=0; s<p.rowsize; s++){         // recv buffer is in logical order
+        int c = (int)commOf[s];
+        recvDisplLogical[s] = (int)disp;
+        p.recvcounts[c] = recvLogical[s];
+        p.recvdispls[c] = (int)disp;
+        disp += recvLogical[s];
+      }
+    }
+    p.scatter.resize(lsites);
+    {
+      std::vector<int> fill(p.rowsize,0);
+      for(uint64_t pos=0; pos<lsites; pos++){
+        int j = source[pos];
+        p.scatter[ recvDisplLogical[j] + fill[j]++ ] = pos;
+      }
+    }
+
+    //////////////////////////////////////////////////////////////////////////
+    // The two sides are derived independently; make them check each other.
+    //////////////////////////////////////////////////////////////////////////
+    {
+      std::vector<uint64_t> sendc(p.rowsize),recvc(p.rowsize);
+      for(int c=0;c<p.rowsize;c++) sendc[c]=(uint64_t)p.sendcounts[c];
+      p.rowcomm->AllToAll(&sendc[0],&recvc[0],1,sizeof(uint64_t));
+      for(int c=0;c<p.rowsize;c++) GRID_ASSERT((int)recvc[c]==p.recvcounts[c]);
+    }
+
+    //////////////////////////////////////////////////////////////////////////
+    // Decompose our range into globally contiguous file extents.
+    //////////////////////////////////////////////////////////////////////////
+    for(uint64_t c = mystart/chunk; c <= (myend-1)/chunk; c++){
+      uint64_t lo = std::max(mystart, c*chunk);
+      uint64_t hi = std::min(myend, (c+1)*chunk);
+      Lexicographic::CoorFromIndex(bcoor,(int64_t)(c*chunk),B);
+      for(int d=0;d<ndim;d++) gcoor[d] = (d<k) ? bcoor[d] : bcoor[d]+S[d];
+      int64_t gbase; Lexicographic::IndexFromCoor(gcoor,gbase,gLattice);
+      p.extentGsite.push_back( (uint64_t)gbase + (lo - c*chunk) );
+      p.extentLocal.push_back( lo - mystart );
+      p.extentSites.push_back( hi - lo );
+    }
+  }
+
+  static inline void ReportAggregationPlan(GridBase *grid,const AggregationPlan &p,uint64_t fobjSize,const char *what)
+  {
+    if ( !grid->IsBoss() ) return;
+    std::cout << GridLogMessage << "IOobject: aggregate " << what
+              << " un-splitting " << p.nunsplit << " fastest dimensions, row of "
+              << p.rowsize << " ranks" << std::endl;
+    std::cout << GridLogMessage << "IOobject: aggregate " << p.extentSites.size()
+              << " extent(s)/rank, first " << p.extentSites[0]*fobjSize/1024./1024. << " MB"
+              << " (target " << aggregateTargetBytes/1024./1024. << " MB)" << std::endl;
+    std::cout << GridLogMessage << "IOobject: aggregate buffer overhead "
+              << p.lsites*fobjSize/1024./1024. << " MB/rank" << std::endl;
+  }
+
+  ////////////////////////////////////////////////////////////////////////////
+  // Stage timings.  The interesting quantity is the slowest rank, since every
+  // stage is followed sooner or later by a synchronisation, so reduce with
+  // GlobalMax rather than reporting whatever the boss happened to see.
+  ////////////////////////////////////////////////////////////////////////////
+  static inline void ReportStages(GridBase *grid,const char *what,
+                                  const std::vector<const char *> &names,
+                                  std::vector<RealD> &useconds)
+  {
+    GRID_ASSERT(names.size()==useconds.size());
+    for(uint64_t i=0;i<useconds.size();i++) grid->GlobalMax(useconds[i]);
+    if ( grid->IsBoss() ) {
+      std::cout << GridLogMessage << "IOobject: aggregate " << what << " stages (max over ranks, s):";
+      for(uint64_t i=0;i<names.size();i++)
+        std::cout << " " << names[i] << " " << useconds[i]/1.0e6;
+      std::cout << std::endl;
+    }
+  }
+
+  template<class fobj>
+  static inline void AggregateExchange(GridBase *grid,AggregationPlan &p,std::vector<fobj> &iodata,
+                                       std::vector<fobj> &aggregated,int forward)
+  {
+    uint64_t lsites = p.lsites;
+    GridStopWatch talloc,tperm,tcomm;
+
+    talloc.Start();
+    std::vector<fobj> tmp(lsites);
+    talloc.Stop();
+
+    if ( forward ) { // iodata (local order) -> aggregated (lexicographic order)
+      tcomm.Start();
+      p.rowcomm->AllToAllV(&iodata[0],p.sendcounts,p.senddispls,
+                           &tmp[0],   p.recvcounts,p.recvdispls,sizeof(fobj));
+      tcomm.Stop();
+      tperm.Start();
+      thread_for(s,lsites,{ aggregated[p.scatter[s]] = tmp[s]; });
+      tperm.Stop();
+    } else {         // aggregated -> iodata, the exact mirror
+      tperm.Start();
+      thread_for(s,lsites,{ tmp[s] = aggregated[p.scatter[s]]; });
+      tperm.Stop();
+      tcomm.Start();
+      p.rowcomm->AllToAllV(&tmp[0],   p.recvcounts,p.recvdispls,
+                           &iodata[0],p.sendcounts,p.senddispls,sizeof(fobj));
+      tcomm.Stop();
+    }
+
+    std::vector<RealD> us = { (RealD)talloc.useconds(), (RealD)tperm.useconds(), (RealD)tcomm.useconds() };
+    ReportStages(grid,forward?"exchange (write)":"exchange (read)",
+                 {"alloc","permute","alltoallv"},us);
+  }
+
+  template<class fobj>
+  static inline void AggregateWrite(GridBase *grid,AggregationPlan &p,std::vector<fobj> &aggregated,
+                                    std::string file,uint64_t offset)
+  {
+    //////////////////////////////////////////////////////////////////////////
+    // All ranks write concurrently into a shared file, so the file must exist
+    // before any of them open it for update, but it does NOT have to be the
+    // right length first: the extents tile the record exactly, so writing them
+    // extends a short file to precisely offset+payload.
+    //
+    // Records are created in sequence, so this payload ends the file: the
+    // length must end up precisely offset+payload. Anything beyond is left
+    // over from whatever the file previously held and must not survive -- a
+    // shorter new record written over a longer old one would otherwise leave
+    // a trailing fragment of the previous contents masquerading as data.
+    // That is the only case needing a truncate, so stat first and truncate
+    // afterwards only when the size actually came out wrong. Measured on
+    // Frontier, an unconditional truncate up front cost 0.22 to 5.4 s per
+    // record -- 15 to 25% of a 19 GB write and 100% of a small one -- while
+    // create, open and close together cost a few milliseconds. It is per
+    // record, so multi record files do not amortise it away.
+    //
+    // ::truncate is used because the C++ standard library cannot express this.
+    // std::filebuf has no length operation at all; ios::trunc only truncates to
+    // zero; seeking past the end and writing a byte can grow a file but never
+    // shrink one; and there is no portable way to recover a descriptor from a
+    // stream in order to call ftruncate. C++17 does finally offer
+    // std::filesystem::resize_file, but that would be Grid's first <filesystem>
+    // dependency and needs -lstdc++fs on the older toolchains still in use.
+    //////////////////////////////////////////////////////////////////////////
+    GridStopWatch tcreate,ttrunc,tbar,topen,twrite,tclose,tskew;
+    uint64_t need = offset + (uint64_t)grid->_gsites*sizeof(fobj);
+
+    tcreate.Start();
+    if ( grid->IsBoss() ) {
+      // opening for update needs the file to exist; create one only if not
+      std::fstream probe(file,std::ios::binary|std::ios::out|std::ios::in);
+      if ( !probe.is_open() ) {
+        std::ofstream create(file,std::ios::binary|std::ios::out);
+        create.close();
+      }
+    }
+    tcreate.Stop();
+
+    tbar.Start();
+    grid->Barrier();
+    tbar.Stop();
+
+    std::ofstream fout;
+    fout.exceptions( std::fstream::failbit | std::fstream::badbit );
+    try {
+      topen.Start();
+      fout.open(file,std::ios::binary|std::ios::out|std::ios::in);
+      topen.Stop();
+      twrite.Start();
+      for(uint64_t e=0;e<p.extentSites.size();e++){
+        fout.seekp(offset + p.extentGsite[e]*sizeof(fobj));
+        fout.write((char *)&aggregated[p.extentLocal[e]],p.extentSites[e]*sizeof(fobj));
+      }
+      twrite.Stop();
+      tclose.Start();
+      fout.close();   // flushes the stream buffer; does not force writeback
+      tclose.Stop();
+    } catch (const std::fstream::failure& exc) {
+      std::cout << GridLogError << "Error in aggregate write to " << file << std::endl;
+      std::cout << GridLogError << "Exception description: " << exc.what() << std::endl;
+      GridAbort();
+    }
+
+    ////////////////////////////////////////////////////////////////////////
+    // Timed apart from the truncate that follows it.  seek+write above is the
+    // slowest rank; this barrier is what the fastest rank then waits, so the
+    // pair separates the write cost from the spread across ranks. Folding it
+    // into the truncate makes a millisecond stat look like a second.
+    ////////////////////////////////////////////////////////////////////////
+    tskew.Start();
+    grid->Barrier();                 // every extent must be on its way first
+    tskew.Stop();
+
+    ttrunc.Start();
+    if ( grid->IsBoss() ) {
+      struct stat sb;
+      int ierr = ::stat(file.c_str(),&sb);
+      GRID_ASSERT(ierr==0);
+      if ( (uint64_t)sb.st_size != need ) {   // only when a longer record preceded us
+        ierr = ::truncate(file.c_str(),(off_t)need);
+        GRID_ASSERT(ierr==0);
+      }
+    }
+    grid->Barrier();
+    ttrunc.Stop();
+
+    std::vector<RealD> us = { (RealD)tcreate.useconds(), (RealD)tbar.useconds(),
+                              (RealD)topen.useconds(),   (RealD)twrite.useconds(),
+                              (RealD)tclose.useconds(),  (RealD)tskew.useconds(),
+                              (RealD)ttrunc.useconds() };
+    ReportStages(grid,"write",{"create","barrier","open","seek+write","close","skew","stat+truncate"},us);
+  }
+
+  template<class fobj>
+  static inline void AggregateRead(GridBase *grid,AggregationPlan &p,std::vector<fobj> &aggregated,
+                                   std::string file,uint64_t offset)
+  {
+    GridStopWatch topen,tread,tclose;
+    std::ifstream fin;
+    topen.Start();
+    fin.open(file,std::ios::binary|std::ios::in);
+    topen.Stop();
+    tread.Start();
+    for(uint64_t e=0;e<p.extentSites.size();e++){
+      fin.seekg(offset + p.extentGsite[e]*sizeof(fobj));
+      fin.read((char *)&aggregated[p.extentLocal[e]],p.extentSites[e]*sizeof(fobj));
+      GRID_ASSERT(fin.fail()==0);
+    }
+    tread.Stop();
+    tclose.Start();
+    fin.close();
+    tclose.Stop();
+
+    std::vector<RealD> us = { (RealD)topen.useconds(), (RealD)tread.useconds(), (RealD)tclose.useconds() };
+    ReportStages(grid,"read",{"open","seek+read","close"},us);
+  }
+#endif
+
   template<class word,class fobj>
   static inline void IOobject(word w,
 			      GridBase *grid,
@@ -302,6 +684,18 @@ class BinaryIO {
       lStart[d] = 0;
     }
 
+    //////////////////////////////////////////////////////////////////////////////
+    // Aggregate the lexicographic layout onto contiguous per rank extents
+    // ourselves rather than leaving it to MPI-IO collective buffering
+    //////////////////////////////////////////////////////////////////////////////
+    int aggregate = (control & BINARYIO_AGGREGATE)
+                 && (control & BINARYIO_LEXICOGRAPHIC)
+                 && !(control & BINARYIO_MASTER_APPEND)
+                 && (nrank > 1);
+#ifndef USE_MPI_IO
+    GRID_ASSERT(aggregate==0); // BINARYIO_AGGREGATE requires MPI
+#endif
+
 #ifdef USE_MPI_IO
     std::vector<int> distribs(ndim,MPI_DISTRIBUTE_BLOCK);
     std::vector<int> dargs   (ndim,MPI_DISTRIBUTE_DFLT_DARG);
@@ -329,6 +723,8 @@ class BinaryIO {
     ierr = MPI_Type_contiguous(numword,mpiword,&mpiObject);    GRID_ASSERT(ierr==0);
     ierr = MPI_Type_commit(&mpiObject);
 
+    // The subarray view is what aggregation exists to avoid; do not build it
+    if ( !aggregate ) {
     //////////////////////////////////////////////////////////////////////////////
     // File global array data type
     //////////////////////////////////////////////////////////////////////////////
@@ -340,6 +736,7 @@ class BinaryIO {
     //////////////////////////////////////////////////////////////////////////////
     ierr=MPI_Type_create_subarray(ndim,&lLattice[0],&lLattice[0],&lStart[0],MPI_ORDER_FORTRAN, mpiObject,&localArray);    GRID_ASSERT(ierr==0);
     ierr=MPI_Type_commit(&localArray);    GRID_ASSERT(ierr==0);
+    }
 #endif
 
     //////////////////////////////////////////////////////////////////////////////
@@ -358,7 +755,19 @@ class BinaryIO {
 
       timer.Start();
 
-      if ( (control & BINARYIO_LEXICOGRAPHIC) && (nrank > 1) ) {
+      if ( aggregate ) {
+#ifdef USE_MPI_IO
+        std::cout<< GridLogMessage<<"IOobject: aggregate read I/O "<< file<< std::endl;
+        AggregationPlan plan;
+        BuildAggregationPlan(grid,sizeof(fobj),plan);
+        ReportAggregationPlan(grid,plan,sizeof(fobj),"read");
+        std::vector<fobj> aggregated(lsites);
+        AggregateRead(grid,plan,aggregated,file,offset);
+        AggregateExchange(grid,plan,iodata,aggregated,0);
+#else
+        GRID_ASSERT(0);
+#endif
+      } else if ( (control & BINARYIO_LEXICOGRAPHIC) && (nrank > 1) ) {
 #ifdef USE_MPI_IO
 	std::cout<< GridLogMessage<<"IOobject: MPI read I/O "<< file<< std::endl;
 	ierr=MPI_File_open(grid->communicator,(char *) file.c_str(), MPI_MODE_RDONLY, MPI_INFO_NULL, &fh);    GRID_ASSERT(ierr==0);
@@ -416,7 +825,25 @@ class BinaryIO {
       grid->Barrier();
 
       timer.Start();
-      if ( (control & BINARYIO_LEXICOGRAPHIC) && (nrank > 1) ) {
+      if ( aggregate ) {
+#ifdef USE_MPI_IO
+        std::cout << GridLogMessage <<"IOobject: aggregate write I/O " << file << std::endl;
+        AggregationPlan plan;
+        BuildAggregationPlan(grid,sizeof(fobj),plan);
+        ReportAggregationPlan(grid,plan,sizeof(fobj),"write");
+        std::vector<fobj> aggregated(lsites);
+        AggregateExchange(grid,plan,iodata,aggregated,1);
+        AggregateWrite(grid,plan,aggregated,file,offset);
+        ////////////////////////////////////////////////////////////////////////
+        // Not every rank ends at the end of the payload, so the position can
+        // not be recovered from a file handle. Callers (Lime record chaining)
+        // rely on this being the first byte past the record.
+        ////////////////////////////////////////////////////////////////////////
+        offset = offset + (uint64_t)grid->_gsites*sizeof(fobj);
+#else
+        GRID_ASSERT(0);
+#endif
+      } else if ( (control & BINARYIO_LEXICOGRAPHIC) && (nrank > 1) ) {
 #ifdef USE_MPI_IO
         std::cout << GridLogMessage <<"IOobject: MPI write I/O " << file << std::endl;
         ierr = MPI_File_open(grid->communicator, (char *)file.c_str(), MPI_MODE_RDWR | MPI_MODE_CREATE, MPI_INFO_NULL, &fh);
@@ -461,12 +888,26 @@ class BinaryIO {
         
 	std::ofstream fout; 
 	fout.exceptions ( std::fstream::failbit | std::fstream::badbit );
+
+        ////////////////////////////////////////////////////////////////////
+        // Grid's model is that the boss rank performs the metadata
+        // operations and every other rank only seeks and writes into a file
+        // that already exists. Opening with ios::out on all ranks broke that:
+        // it is O_TRUNC, so a rank opening late truncated the file back to
+        // zero after an earlier rank had written its segment, leaving a hole
+        // in its place. The barriers around this block are outside it and do
+        // not order the opens against the writes. Let the boss create and
+        // empty the file, then everyone opens for update only. Same resulting
+        // length, one metadata operation instead of one per rank, no race.
+        ////////////////////////////////////////////////////////////////////
+        if ( !offset && grid->IsBoss() ) { // offset zero: this record starts the file
+          std::ofstream create(file,std::ios::binary|std::ios::out);
+          create.close();
+        }
+        grid->Barrier();
+
 	try {
-	  if (offset) { // Must already exist and contain data
+	  fout.open(file,std::ios::binary|std::ios::out|std::ios::in);
-	    fout.open(file,std::ios::binary|std::ios::out|std::ios::in);
-	  } else {     // Allow create
-	    fout.open(file,std::ios::binary|std::ios::out);
-	  }
 	} catch (const std::fstream::failure& exc) {
 	  std::cout << GridLogError << "Error in opening the file " << file << " for output" <<std::endl;
 	  std::cout << GridLogError << "Exception description: " << exc.what() << std::endl;
@@ -477,7 +918,7 @@ class BinaryIO {
 	  exit(1);
 #endif
 	}
-	
+
 	if ( control & BINARYIO_MASTER_APPEND )  {
 	  try {
 	    fout.seekp(0,fout.end);
@@ -548,7 +989,7 @@ class BinaryIO {
 				       uint32_t &nersc_csum,
 				       uint32_t &scidac_csuma,
 				       uint32_t &scidac_csumb,
-				       int control=BINARYIO_LEXICOGRAPHIC
+				       int control=BINARYIO_LEXICOGRAPHIC|BINARYIO_AGGREGATE
 				       )
   {
     typedef typename vobj::scalar_object sobj;
@@ -587,7 +1028,7 @@ class BinaryIO {
 					  uint32_t &nersc_csum,
 					  uint32_t &scidac_csuma,
 					  uint32_t &scidac_csumb,
-					  int control=BINARYIO_LEXICOGRAPHIC)
+					  int control=BINARYIO_LEXICOGRAPHIC|BINARYIO_AGGREGATE)
   {
     typedef typename vobj::scalar_object sobj;
     typedef typename vobj::Realified::scalar_type word;    word w=0;
@@ -674,7 +1115,7 @@ class BinaryIO {
     std::cout << GridLogMessage << "RNG read I/O on file " << file << std::endl;
 
     std::vector<RNGstate> iodata(lsites);
-    IOobject(w,grid,iodata,file,offset,format,BINARYIO_READ|BINARYIO_LEXICOGRAPHIC,
+    IOobject(w,grid,iodata,file,offset,format,BINARYIO_READ|BINARYIO_LEXICOGRAPHIC|BINARYIO_AGGREGATE,
 	     nersc_csum,scidac_csuma,scidac_csumb);
 
     timer.Start();
@@ -753,7 +1194,7 @@ class BinaryIO {
     });
     timer.Stop();
 
-    IOobject(w,grid,iodata,file,offset,format,BINARYIO_WRITE|BINARYIO_LEXICOGRAPHIC,
+    IOobject(w,grid,iodata,file,offset,format,BINARYIO_WRITE|BINARYIO_LEXICOGRAPHIC|BINARYIO_AGGREGATE,
 	     nersc_csum,scidac_csuma,scidac_csumb);
     iodata.resize(1);
     {

Grid/parallelIO/IldgIO.h

@@ -212,7 +212,7 @@ class GridLimeReader : public BinaryIO {
   // Read a generic lattice field and verify checksum
   ////////////////////////////////////////////
   template<class vobj>
-  void readLimeLatticeBinaryObject(Lattice<vobj> &field,std::string record_name,int control=BINARYIO_LEXICOGRAPHIC)
+  void readLimeLatticeBinaryObject(Lattice<vobj> &field,std::string record_name,int control=BINARYIO_LEXICOGRAPHIC|BINARYIO_AGGREGATE)
   {
     typedef typename vobj::scalar_object sobj;
     scidacChecksum scidacChecksum_;
@@ -414,7 +414,7 @@ class GridLimeWriter : public BinaryIO
   // in communicator used by the field.Grid()
   ////////////////////////////////////////////////////
   template<class vobj>
-  void writeLimeLatticeBinaryObject(Lattice<vobj> &field,std::string record_name,int control=BINARYIO_LEXICOGRAPHIC)
+  void writeLimeLatticeBinaryObject(Lattice<vobj> &field,std::string record_name,int control=BINARYIO_LEXICOGRAPHIC|BINARYIO_AGGREGATE)
   {
     ////////////////////////////////////////////////////////////////////
     // NB: FILE and iostream are jointly writing disjoint sequences in the
@@ -519,7 +519,7 @@ class ScidacWriter : public GridLimeWriter {
   template <class vobj, class userRecord>
   void writeScidacFieldRecord(Lattice<vobj> &field,userRecord _userRecord,
                               const unsigned int recordScientificPrec = 0,
-			      int control=BINARYIO_LEXICOGRAPHIC)
+			      int control=BINARYIO_LEXICOGRAPHIC|BINARYIO_AGGREGATE)
   {
     GridBase * grid = field.Grid();
 
@@ -561,7 +561,7 @@ class ScidacReader : public GridLimeReader {
   ////////////////////////////////////////////////
   template <class vobj, class userRecord>
   void readScidacFieldRecord(Lattice<vobj> &field,userRecord &_userRecord,
-			     int control=BINARYIO_LEXICOGRAPHIC) 
+			     int control=BINARYIO_LEXICOGRAPHIC|BINARYIO_AGGREGATE) 
   {
     typedef typename vobj::scalar_object sobj;
     GridBase * grid = field.Grid();

Grid/perfmon/PerfCount.h

@@ -51,8 +51,8 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
 #endif
 #ifdef __x86_64__
 #ifdef GRID_CUDA
-//accelerator_inline uint64_t __rdtsc(void) {  return 0; }
+accelerator_inline uint64_t __rdtsc(void) {  return 0; }
-//accelerator_inline uint64_t __rdpmc(int ) {  return 0; }
+accelerator_inline uint64_t __rdpmc(int ) {  return 0; }
 #else
 #include <x86intrin.h>
 #endif
@@ -93,8 +93,7 @@ inline uint64_t cyclecount(void){
 }
 #elif defined __x86_64__
 inline uint64_t cyclecount(void){ 
-  uint64_t ret = __rdtsc();
+  return (uint64_t)0;
-  return (uint64_t)ret;
 }
 #else
 

Grid/qcd/action/pseudofermion/TwoFlavourBosonPseudoFermion.h

@@ -0,0 +1,133 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./lib/qcd/action/pseudofermion/TwoFlavourBosonPseudoFermion.h
+
+    Copyright (C) 2026
+
+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);
+
+///////////////////////////////////////////////////////////////////////////////
+// Two flavour BOSON (wrong-sign) pseudofermion for any FermionOperator B:
+//
+//    S2 = chi^dag Bdag B chi = |B chi|^2
+//
+//    integral  ==>  det( Bdag B )^-1 = |det B|^-2
+//
+// A compensator monomial: supplies an INVERSE determinant with NO solve in
+// the force or the action -- both are matrix multiplies.  The only solve is
+// the heatbath  chi = B^-1 eta,  once per trajectory (for B = the
+// Pauli-Villars operator this is a mass-one solve, trivially cheap).
+//
+// Primary use: two instances with B = PV cancel the |det PV|^2 excess of
+// TwoFlavourPVdagMPseudoFermionAction down to the DWF quotient
+// |det M|^2/|det PV|^2 (two unsquared instances rather than one squared
+// kernel: first powers of PV in the force, milder).  Being generic in B it
+// also serves Hasenbusch-chain compensation at intermediate masses, or any
+// future inverse-det bookkeeping.  (Sibling of the domain-decomposed boson
+// in DomainDecomposedBoundaryTwoFlavourBosonPseudoFermion.h, without the
+// boundary machinery.)
+//
+// Heatbath exact by construction: S2 after refresh = |B B^-1 eta|^2 = |eta|^2.
+///////////////////////////////////////////////////////////////////////////////
+template<class Impl>
+class TwoFlavourBosonPseudoFermionAction : public Action<typename Impl::GaugeField> {
+public:
+  INHERIT_IMPL_TYPES(Impl);
+
+private:
+  FermionOperator<Impl> & BOp;  // the operator whose |det|^-2 is supplied
+
+  LinearFunction<FermionField> &HeatbathSolver; // b -> B^-1 b (heatbath only)
+
+  FermionField Chi; // the pseudo fermion field for this trajectory
+
+public:
+  TwoFlavourBosonPseudoFermionAction(FermionOperator<Impl>  &_BOp,
+				     LinearFunction<FermionField> & HS
+				     ) : BOp(_BOp),
+					 HeatbathSolver(HS),
+					 Chi(_BOp.FermionGrid())
+  {};
+
+  virtual std::string action_name(){return "TwoFlavourBosonPseudoFermionAction";}
+
+  virtual std::string LogParameters(){
+    std::stringstream sstream;
+    sstream << GridLogMessage << "["<<action_name()<<"] has no parameters" << std::endl;
+    return sstream.str();
+  }
+
+  virtual void refresh(const GaugeField &U, GridSerialRNG &sRNG, GridParallelRNG& pRNG) {
+    // P(chi) = e^{- chi^dag BdagB chi} ; chi = B^-1 eta ; P(eta) = e^{-eta^dag eta}
+    // e^{-x^2/2 sig^2} => sig^2 = 0.5 ; eta enters with width 1/sqrt(2).
+    RealD scale = std::sqrt(0.5);
+    FermionField eta(BOp.FermionGrid());
+    gaussian(pRNG,eta);
+    eta = eta * scale;
+    refresh(U,eta);
+  }
+
+  // Deterministic-noise variant (test hook):
+  // after this,  S(U) == norm2(eta)  exactly (to solver tolerance).
+  void refresh(const GaugeField &U, const FermionField &eta) {
+    BOp.ImportGauge(U);
+    Chi = Zero();
+    HeatbathSolver(eta,Chi);       // Chi = B^-1 eta : the ONLY solve
+    std::cout << GridLogMessage << action_name() << " refresh |Chi|^2 = "<< norm2(Chi)<<std::endl;
+  }
+
+  //////////////////////////////////////////////////////
+  // S2 = |B chi|^2  -- matrix multiply only
+  //////////////////////////////////////////////////////
+  virtual RealD S(const GaugeField &U) {
+    BOp.ImportGauge(U);
+
+    FermionField w(BOp.FermionGrid());
+    BOp.M(Chi,w);                  // w = B chi
+    RealD action = norm2(w);
+    return action;
+  }
+
+  //////////////////////////////////////////////////////
+  // dS2 = chi^dag dBdag w + w^dag dB chi ,   w = B chi
+  // NO solves.
+  //////////////////////////////////////////////////////
+  virtual void deriv(const GaugeField &U,GaugeField & dSdU) {
+    BOp.ImportGauge(U);
+
+    FermionField w(BOp.FermionGrid());
+    GaugeField force(BOp.GaugeGrid());
+
+    BOp.M(Chi,w);                  // w = B chi
+
+    BOp.MDeriv(force, Chi, w, DaggerYes); dSdU =      force;
+    BOp.MDeriv(force, w, Chi, DaggerNo ); dSdU = dSdU+force;
+
+    dSdU *= -1.0;  // Grid action sign convention (cf TwoFlavourRatio.h)
+  };
+};
+
+NAMESPACE_END(Grid);

Grid/qcd/action/pseudofermion/TwoFlavourRatio4DPseudoFermion.h

@@ -0,0 +1,264 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./lib/qcd/action/pseudofermion/TwoFlavourRatio4DPseudoFermion.h
+
+    Copyright (C) 2026
+
+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);
+
+///////////////////////////////////////////////////////////////////////////////
+// Two flavour ratio with FOUR dimensional pseudofermion, UNpreconditioned
+// (full grid) solves.
+//
+// Companion to TwoFlavourRatioEO4DPseudoFermion.h but with the solver
+// plumbing exposed as LinearFunction<FermionField> objects that already
+// know their operator -- the natural interface for the non-Hermitian
+// multigrid GCR stack (PVdagM), which solves M and Mdag DIRECTLY rather
+// than through SchurRedBlack normal equations.
+//
+// Why: with 5D pseudofermions the squared-operator formulation hands
+// normal-equation solvers (MdagM)^-1 phi AND Mdag^-1 phi from ONE Krylov
+// space; a direct solver must solve twice, halving its per-solve gain.
+// The 4D pseudofermion action needs one M^-1 and one M^-dag solve per
+// force evaluation FOR BOTH solver families, so the direct-solver gain
+// carries through undiluted.  In addition phi4 is Ls-agnostic, so the
+// force can be evaluated with a reduced-Ls operator pair while the
+// accept/reject uses full Ls (inexact force, exact action).
+//
+// Solver slots (all full-grid 5D LinearFunctions, solution overwritten,
+// zero guess imposed internally):
+//   DerivMinvSolver     : x = M^-1 b        (DenOp)
+//   DerivMdagInvSolver  : x = M^-dag b      (DenOp).  For G5R5-hermitian
+//                         actions this may be implemented by the caller as
+//                         G5R5 . DerivMinvSolver . G5R5 -- no adjoint
+//                         multigrid needed.
+//   ActionMinvSolver    : x = M^-1 b        (DenOp, accept/reject tolerance)
+//   HeatbathVinvSolver  : x = V^-1 b        (NumOp)
+//
+// 4D <-> 5D wall maps: the action is S = | P (M^-1 V) Pdag phi4 |^2 where
+// (P,Pdag) MUST be a mutually adjoint pair for S and deriv to be
+// consistent.  Two candidate conventions, selected by solution_walls:
+//   true  : P = P_- psi(0) + P_+ psi(Ls-1)   (solution walls, matches
+//           ExportPhysicalFermionSolution) and Pdag its literal adjoint.
+//   false : P = P_+ psi(0) + P_- psi(Ls-1)   (source walls, Pdag matches
+//           ImportUnphysicalFermion).
+// The heatbath is exact iff [P M^-1 V Pdag][P V^-1 M Pdag] = 1 (the 4D
+// effective-operator composition identity); which convention satisfies it
+// is settled numerically by the refresh test  S == 0.5*|eta4|^2  exactly.
+///////////////////////////////////////////////////////////////////////////////
+template<class Impl>
+class TwoFlavourRatio4DPseudoFermionAction : public Action<typename Impl::GaugeField> {
+public:
+  INHERIT_IMPL_TYPES(Impl);
+
+private:
+  typedef FermionOperator<Impl> FermOp;
+  FermionOperator<Impl> & NumOp;// the basic operator (V)
+  FermionOperator<Impl> & DenOp;// the basic operator (M)
+
+  LinearFunction<FermionField> &DerivMinvSolver;
+  LinearFunction<FermionField> &DerivMdagInvSolver;
+  LinearFunction<FermionField> &ActionMinvSolver;
+  LinearFunction<FermionField> &HeatbathVinvSolver;
+
+  FermionField phi4; // the pseudo fermion field for this trajectory
+
+  int solution_walls; // wall convention for the (P,Pdag) pair; see header
+
+  ////////////////////////////////////////////////////////////////////
+  // The mutually adjoint 4D <-> 5D pair.
+  //   Wall4D    : q4  = P psi5      (extract)
+  //   Wall4DAdj : psi5 = Pdag q4    (insert; literal adjoint of Wall4D)
+  ////////////////////////////////////////////////////////////////////
+  void Wall4D(const FermionField &psi5, FermionField &q4)
+  {
+    int Ls = NumOp.FermionGrid()->_fdimensions[0];
+    FermionField tmp(NumOp.FermionGrid());
+    if ( solution_walls ) {
+      // q4 = P_- psi(0) + P_+ psi(Ls-1)
+      axpby_ssp_pminus(tmp, 0., psi5, 1., psi5, 0, 0);
+      axpby_ssp_pplus (tmp, 1., tmp , 1., psi5, 0, Ls-1);
+    } else {
+      // q4 = P_+ psi(0) + P_- psi(Ls-1)
+      axpby_ssp_pplus (tmp, 0., psi5, 1., psi5, 0, 0);
+      axpby_ssp_pminus(tmp, 1., tmp , 1., psi5, 0, Ls-1);
+    }
+    ExtractSlice(q4, tmp, 0, 0);
+  }
+  void Wall4DAdj(const FermionField &q4, FermionField &psi5)
+  {
+    int Ls = NumOp.FermionGrid()->_fdimensions[0];
+    FermionField tmp(NumOp.FermionGrid());
+    tmp = Zero();
+    InsertSlice(q4, tmp, 0   , 0);
+    InsertSlice(q4, tmp, Ls-1, 0);
+    if ( solution_walls ) {
+      // psi(0) = P_- q4 ; psi(Ls-1) = P_+ q4
+      axpby_ssp_pminus(tmp, 0., tmp, 1., tmp, 0   , 0);
+      axpby_ssp_pplus (tmp, 0., tmp, 1., tmp, Ls-1, Ls-1);
+    } else {
+      // psi(0) = P_+ q4 ; psi(Ls-1) = P_- q4
+      axpby_ssp_pplus (tmp, 0., tmp, 1., tmp, 0   , 0);
+      axpby_ssp_pminus(tmp, 0., tmp, 1., tmp, Ls-1, Ls-1);
+    }
+    psi5 = tmp;
+  }
+
+public:
+  TwoFlavourRatio4DPseudoFermionAction(FermionOperator<Impl>  &_NumOp,
+				       FermionOperator<Impl>  &_DenOp,
+				       LinearFunction<FermionField> & DMS,
+				       LinearFunction<FermionField> & DMDS,
+				       LinearFunction<FermionField> & AMS,
+				       LinearFunction<FermionField> & HVS,
+				       int _solution_walls = 1
+				       ) : NumOp(_NumOp),
+					   DenOp(_DenOp),
+					   DerivMinvSolver(DMS),
+					   DerivMdagInvSolver(DMDS),
+					   ActionMinvSolver(AMS),
+					   HeatbathVinvSolver(HVS),
+					   phi4(_NumOp.GaugeGrid()),
+					   solution_walls(_solution_walls)
+  {};
+
+  virtual std::string action_name(){return "TwoFlavourRatio4DPseudoFermionAction";}
+
+  virtual std::string LogParameters(){
+    std::stringstream sstream;
+    sstream << GridLogMessage << "["<<action_name()<<"] solution_walls " << solution_walls << std::endl;
+    return sstream.str();
+  }
+
+  virtual void refresh(const GaugeField &U, GridSerialRNG &sRNG, GridParallelRNG& pRNG) {
+
+    // P(phi4) = e^{- phi4^dag Beff^dag Beff phi4}   ;  Beff = P M^-1 V Pdag
+    //
+    // NumOp == V
+    // DenOp == M
+    //
+    // Take phi4 = P V^-1 M Pdag eta4   ( = Beff^-1 eta4 by the composition
+    // identity; verified numerically by S == 0.5 |eta4|^2 after refresh )
+    //
+    // P(eta) = e^{- eta^dag eta} ;  e^{-x^2/2 sig^2} => sig^2 = 0.5
+    // so eta enters with width 1/sqrt(2).
+    //
+    RealD scale = std::sqrt(0.5);
+
+    FermionField eta4(NumOp.GaugeGrid());
+    FermionField eta5(NumOp.FermionGrid());
+    FermionField tmp (NumOp.FermionGrid());
+    FermionField phi5(NumOp.FermionGrid());
+
+    gaussian(pRNG,eta4);
+
+    NumOp.ImportGauge(U);
+    DenOp.ImportGauge(U);
+
+    Wall4DAdj(eta4,eta5);            // eta5 = Pdag eta4
+    DenOp.M(eta5,tmp);               // tmp  = M eta5
+    phi5 = Zero();
+    HeatbathVinvSolver(tmp,phi5);    // phi5 = V^-1 M eta5
+    Wall4D(phi5,phi4);               // phi4 = P phi5
+    phi4 = phi4*scale;
+
+    std::cout << GridLogMessage << "4d pf (non-EO) refresh "<< norm2(phi4)<<"\n";
+  };
+
+  //////////////////////////////////////////////////////
+  // S = phi4^dag (Pdag^dag V^dag M^-dag P^dag) (P M^-1 V Pdag) phi4
+  //   = | P M^-1 V Pdag phi4 |^2
+  //////////////////////////////////////////////////////
+  virtual RealD S(const GaugeField &U) {
+
+    NumOp.ImportGauge(U);
+    DenOp.ImportGauge(U);
+
+    FermionField Y4  (NumOp.GaugeGrid());
+    FermionField phi5(NumOp.FermionGrid());
+    FermionField X   (NumOp.FermionGrid());
+    FermionField Y   (NumOp.FermionGrid());
+
+    Wall4DAdj(phi4,phi5);            // phi5 = Pdag phi4
+    NumOp.M(phi5,X);                 // X    = V phi5
+    Y = Zero();
+    ActionMinvSolver(X,Y);           // Y    = M^-1 V phi5
+    Wall4D(Y,Y4);                    // Y4   = P Y
+
+    RealD action = norm2(Y4);
+
+    return action;
+  };
+
+  //////////////////////////////////////////////////////
+  // dS/du = 2 Re [ (M^-dag Pdag w4)^dag dV Pdag phi4 ]
+  //       - 2 Re [ (M^-dag Pdag w4)^dag dM (M^-1 V Pdag phi4) ]
+  // with w4 = P M^-1 V Pdag phi4.
+  // Two first-power solves: one M^-1, one M^-dag.
+  //////////////////////////////////////////////////////
+  virtual void deriv(const GaugeField &U,GaugeField & dSdU) {
+
+    NumOp.ImportGauge(U);
+    DenOp.ImportGauge(U);
+
+    FermionField  phi5           (NumOp.FermionGrid());
+    FermionField  Vphi           (NumOp.FermionGrid());
+    FermionField  MinvVphi       (NumOp.FermionGrid());
+    FermionField  w4             (NumOp.GaugeGrid());
+    FermionField  Y              (NumOp.FermionGrid());
+    FermionField  MdagInvPdagW   (NumOp.FermionGrid());
+
+    GaugeField   force(NumOp.GaugeGrid());
+
+    Wall4DAdj(phi4,phi5);              // phi5     = Pdag phi4
+    NumOp.M(phi5,Vphi);                // Vphi     = V phi5
+    MinvVphi = Zero();
+    DerivMinvSolver(Vphi,MinvVphi);    // MinvVphi = M^-1 V phi5
+    std::cout << GridLogMessage << "4d pf (non-EO) deriv solve "<< norm2(MinvVphi)<<"\n";
+
+    // Project onto the physical 4D subspace and back: Y = Pdag P MinvVphi.
+    // Pdag here MUST be the literal adjoint of the P used in S, else the
+    // force is inconsistent with the action.
+    Wall4D(MinvVphi,w4);               // w4 = P MinvVphi
+    Wall4DAdj(w4,Y);                   // Y  = Pdag w4
+
+    MdagInvPdagW = Zero();
+    DerivMdagInvSolver(Y,MdagInvPdagW);   // = M^-dag Pdag w4  (adjoint solve)
+    std::cout << GridLogMessage << "4d pf (non-EO) deriv solve dag "<< norm2(MdagInvPdagW)<<"\n";
+
+    // phi^dag (Pdag' Vdag Mdag^-1 P') (dV) Pdag phi   + h.c.
+    NumOp.MDeriv(force, MdagInvPdagW, phi5, DaggerNo );  dSdU=force;
+    NumOp.MDeriv(force, phi5, MdagInvPdagW, DaggerYes);  dSdU=dSdU+force;
+
+    // - phi^dag ( ... Mdag^-1 ) dM ( M^-1 V ... ) phi  + h.c.
+    DenOp.MDeriv(force, MdagInvPdagW, MinvVphi, DaggerNo );  dSdU=dSdU-force;
+    DenOp.MDeriv(force, MinvVphi, MdagInvPdagW, DaggerYes);  dSdU=dSdU-force;
+
+    dSdU *= -1.0;
+  };
+};
+
+NAMESPACE_END(Grid);

Grid/qcd/action/pseudofermion/TwoFlavourRatioLeftPrec.h

@@ -0,0 +1,206 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./lib/qcd/action/pseudofermion/TwoFlavourRatioLeftPrec.h
+
+    Copyright (C) 2026
+
+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);
+
+///////////////////////////////////////////////////////////////////////////////
+// Two flavour ratio with LEFT-PRECONDITIONED solves.
+//
+// Same action content as TwoFlavourRatio.h:
+//
+//    S = phi^dag V (Mdag M)^-1 Vdag phi     ==>   det[ Mdag M / Vdag V ]
+//
+// (V = NumOp the heavier / Pauli-Villars operator, M = DenOp the lighter),
+// but organised around the composite
+//
+//    F = Vdag M
+//
+// which is the 2-hop-coarsenable operator the non-Hermitian multigrid
+// serves.  Solving M X = b as F X = Vdag b is LEFT PRECONDITIONING by
+// Vdag; the determinant/action layer is the standard quotient, and all
+// novelty is confined to the solver contract.
+//
+// TwoFlavourRatio.h is tied to a normal-equations solver: one (MdagM)^-1
+// solve, then Y = M X gives Mdag^-1 Vdag phi almost free.  The left-
+// preconditioned idiom is DIFFERENT: the chain
+//
+//    b = Vdag phi
+//    z : Fdag z = b          (adjoint  F solve)
+//    Y = V z                 (= Mdag^-1 Vdag phi -- harvested from solve 1)
+//    s = Vdag Y              (= Vdag V z)
+//    X : F X = s             (forward F solve;  X = (MdagM)^-1 Vdag phi)
+//
+// yields Y BEFORE X (so S(U) needs only the adjoint solve), with Y's
+// accuracy independent of the second solve.  Force terms are then the
+// standard four MDeriv insertions of TwoFlavourRatio.
+//
+// Solver slots are LinearFunctions with the F-SOLVE contract (solution
+// overwritten, zero guess imposed internally):
+//    ForwardSolver(b,x)  :  F x    = b
+//    AdjointSolver(b,z)  :  Fdag z = b
+// implemented in production by the multigrid-GCR stack (forward cycle and
+// adjoint cycle); in tests by CG on the composite normal equations.
+// HeatbathSolver(b,x) : x = (Vdag V)^-1 b -- heavy operator, plain CG.
+//
+// Heatbath is exact by operator algebra:  phi = V (VdagV)^-1 Mdag eta
+// ==>  S = | Mdag^-1 Vdag phi |^2 = |eta|^2  (to solver tolerance); the
+// deterministic refresh(U,eta) hook below is the test point.
+//
+// Hasenbusch: nothing requires V to have mass one; any (heavier,lighter)
+// pair works, F(V,M) = Vdag M coarsenable by the same machinery, rungs'
+// solves are F-family (mrhs-batchable, mass-shared coarse space).
+///////////////////////////////////////////////////////////////////////////////
+template<class Impl>
+class TwoFlavourRatioLeftPrecPseudoFermionAction : public Action<typename Impl::GaugeField> {
+public:
+  INHERIT_IMPL_TYPES(Impl);
+
+private:
+  FermionOperator<Impl> & NumOp;// V
+  FermionOperator<Impl> & DenOp;// M
+
+  LinearFunction<FermionField> &DerivForwardSolver;  // F x = b, MD tolerance
+  LinearFunction<FermionField> &DerivAdjointSolver;  // Fdag z = b, MD tolerance
+  LinearFunction<FermionField> &ActionAdjointSolver; // Fdag z = b, accept/reject tolerance
+  LinearFunction<FermionField> &HeatbathSolver;      // (VdagV)^-1 b, heavy op
+
+  FermionField Phi; // the pseudo fermion field for this trajectory
+
+public:
+  TwoFlavourRatioLeftPrecPseudoFermionAction(FermionOperator<Impl>  &_NumOp,
+					     FermionOperator<Impl>  &_DenOp,
+					     LinearFunction<FermionField> & DFS,
+					     LinearFunction<FermionField> & DAS,
+					     LinearFunction<FermionField> & AAS,
+					     LinearFunction<FermionField> & HS
+					     ) : NumOp(_NumOp),
+						 DenOp(_DenOp),
+						 DerivForwardSolver(DFS),
+						 DerivAdjointSolver(DAS),
+						 ActionAdjointSolver(AAS),
+						 HeatbathSolver(HS),
+						 Phi(_NumOp.FermionGrid())
+  {};
+
+  virtual std::string action_name(){return "TwoFlavourRatioLeftPrecPseudoFermionAction";}
+
+  virtual std::string LogParameters(){
+    std::stringstream sstream;
+    sstream << GridLogMessage << "["<<action_name()<<"] has no parameters" << std::endl;
+    return sstream.str();
+  }
+
+  virtual void refresh(const GaugeField &U, GridSerialRNG &sRNG, GridParallelRNG& pRNG) {
+    // P(phi) = e^{- phi^dag V (MdagM)^-1 Vdag phi} ; phi = Vdag^-1 Mdag eta
+    // e^{-x^2/2 sig^2} => sig^2 = 0.5 ; eta enters with width 1/sqrt(2).
+    RealD scale = std::sqrt(0.5);
+    FermionField eta(NumOp.FermionGrid());
+    gaussian(pRNG,eta);
+    eta = eta * scale;
+    refresh(U,eta);
+  }
+
+  // Deterministic-noise variant (test hook):
+  // after this,  S(U) == norm2(eta)  exactly (to solver tolerance).
+  void refresh(const GaugeField &U, const FermionField &eta) {
+    NumOp.ImportGauge(U);
+    DenOp.ImportGauge(U);
+
+    FermionField tmp(NumOp.FermionGrid());
+    FermionField w  (NumOp.FermionGrid());
+
+    DenOp.Mdag(eta,tmp);           // tmp = Mdag eta
+    w = Zero();
+    HeatbathSolver(tmp,w);         // w   = (VdagV)^-1 Mdag eta
+    NumOp.M(w,Phi);                // Phi = V (VdagV)^-1 Mdag eta = Vdag^-1 Mdag eta
+    std::cout << GridLogMessage << action_name() << " refresh |Phi|^2 = "<< norm2(Phi)<<std::endl;
+  }
+
+  //////////////////////////////////////////////////////
+  // S = phi^dag V (MdagM)^-1 Vdag phi = | Mdag^-1 Vdag phi |^2
+  // ONE adjoint F solve:  Y = V Fdag^-1 Vdag phi = Mdag^-1 Vdag phi
+  //////////////////////////////////////////////////////
+  virtual RealD S(const GaugeField &U) {
+    NumOp.ImportGauge(U);
+    DenOp.ImportGauge(U);
+
+    FermionField b(NumOp.FermionGrid());
+    FermionField z(NumOp.FermionGrid());
+    FermionField Y(NumOp.FermionGrid());
+
+    NumOp.Mdag(Phi,b);             // b = Vdag phi
+    z = Zero();
+    ActionAdjointSolver(b,z);      // Fdag z = b
+    NumOp.M(z,Y);                  // Y = V z = Mdag^-1 Vdag phi
+
+    RealD action = norm2(Y);
+    return action;
+  }
+
+  //////////////////////////////////////////////////////
+  // dS/du = phi^dag dV (MdagM)^-1 Vdag phi
+  //       - phi^dag V (MdagM)^-1 [ Mdag dM + dMdag M ] (MdagM)^-1 Vdag phi
+  //       + phi^dag V (MdagM)^-1 dVdag phi
+  // Identical force insertions to TwoFlavourRatio.h; X and Y from the
+  // left-preconditioned chain (Y harvested from the adjoint solve).
+  //////////////////////////////////////////////////////
+  virtual void deriv(const GaugeField &U,GaugeField & dSdU) {
+    NumOp.ImportGauge(U);
+    DenOp.ImportGauge(U);
+
+    FermionField b(NumOp.FermionGrid());
+    FermionField z(NumOp.FermionGrid());
+    FermionField Y(NumOp.FermionGrid());
+    FermionField s(NumOp.FermionGrid());
+    FermionField X(NumOp.FermionGrid());
+
+    GaugeField force(NumOp.GaugeGrid());
+
+    NumOp.Mdag(Phi,b);             // b = Vdag phi
+    z = Zero();
+    DerivAdjointSolver(b,z);       // Fdag z = b
+    NumOp.M(z,Y);                  // Y = V z = Mdag^-1 Vdag phi   (solve-1 harvest)
+    NumOp.Mdag(Y,s);               // s = Vdag V z
+    X = Zero();
+    DerivForwardSolver(s,X);       // F X = s  ==>  X = (MdagM)^-1 Vdag phi
+
+    // phi^dag V (MdagM)^-1 dVdag phi
+    NumOp.MDeriv(force , X, Phi, DaggerYes);  dSdU  =      force;
+    // phi^dag dV (MdagM)^-1 Vdag phi
+    NumOp.MDeriv(force , Phi, X, DaggerNo );  dSdU  = dSdU+force;
+    //  - phi^dag V (MdagM)^-1 Mdag dM (MdagM)^-1 Vdag phi
+    //  - phi^dag V (MdagM)^-1 dMdag M (MdagM)^-1 Vdag phi
+    DenOp.MDeriv(force, Y, X, DaggerNo );     dSdU  = dSdU-force;
+    DenOp.MDeriv(force, X, Y, DaggerYes);     dSdU  = dSdU-force;
+
+    dSdU *= -1.0;
+  };
+};
+
+NAMESPACE_END(Grid);

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
+inline std::complex<double> conjugate(const std::complex<double>& r){ return(conj(r)); }
+inline std::complex<float>  conjugate(const std::complex<float>& r) { return(conj(r)); }
+inline std::complex<double> adj(const std::complex<double>& r)      { return(conj(r)); }
+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(); }

Grid/threads/Accelerator.cc

@@ -3,7 +3,7 @@
 NAMESPACE_BEGIN(Grid);
 int      world_rank; // Use to control world rank for print guarding
 int      acceleratorAbortOnGpuError=1;
-uint32_t accelerator_threads=2;
+uint32_t accelerator_threads=8;
 uint32_t acceleratorThreads(void)       {return accelerator_threads;};
 void     acceleratorThreads(uint32_t t) {accelerator_threads = t;};
 

Grid/threads/Accelerator.h

@@ -96,7 +96,9 @@ void     acceleratorInit(void);
 
 #ifdef GRID_CUDA
 
+NAMESPACE_END(Grid);
 #include <cuda.h>
+NAMESPACE_BEGIN(Grid);
 
 #ifdef __CUDA_ARCH__
 #define GRID_SIMT

MPI_benchmark/compile-command

@@ -1 +1,2 @@
-mpicxx  -fsycl halo_mpi.cc -o halo_mpi
+mpicxx  -fsycl halo_mpi.cc -o halo_mpi
+mpicxx -O2 -std=c++11 io_mpi.cc -o io_mpi

MPI_benchmark/io_aurora.pbs

@@ -0,0 +1,137 @@
+#!/bin/bash
+
+# Standalone MPI-only I/O reproducer on Aurora.  Host only -- no SYCL, no
+# gpu_tile_compact.sh -- so unlike halo_mpi this needs nothing but MPI:
+#
+#   mpicxx -O2 -std=c++11 io_mpi.cc -o io_mpi
+#
+# 12 ranks per node, one per tile, which is what the machine is.  That is a
+# deliberate difference from io_frontier.slurm (8 per node, one per GCD), so
+# read the comparison carefully -- see WHAT IS AND IS NOT COMPARABLE below.
+
+# Run io_aurora_debug.pbs first.  If the cross validation fails there, this
+# scan is 2 hours of 128 nodes producing numbers for a broken file.
+
+#PBS -q prod
+#PBS -l filesystems=flare
+#PBS -l filesystems=home
+#PBS -l select=128
+#PBS -l walltime=02:00:00
+#PBS -A 15479
+
+cd $PBS_O_WORKDIR
+cp $PBS_NODEFILE nodefile
+
+# Only if mpiexec is not already in the environment.  io_mpi is host only
+# and needs no part of the Grid build environment.
+#source ../../sourceme.sh
+
+##########################################################################
+# Environment.  io_mpi has no OpenMP and never touches a GPU, so one thread
+# per rank and a NUMA NIC policy rather than a GPU one.
+#
+# The MPICH_DBG_* variables are deliberately absent: at 1536 ranks they
+# produce gigabytes of log and perturb the timings they would explain.
+# MPICH_MPIIO_STATS/TIMERS are also off here -- they are per collective and
+# 1536 ranks x 6 rungs x 3 reps is unreadable.  Get them from the debug run.
+##########################################################################
+export OMP_NUM_THREADS=1
+export MPICH_CH4_SHM=XPMEM
+export MPICH_OFI_NIC_POLICY=NUMA
+
+##########################################################################
+# WHAT IS AND IS NOT COMPARABLE WITH THE FRONTIER SCAN
+#
+# Held identical at every rung of both scans:
+#   local volume  8.8.32.128 = 262144 sites x 576 B = 151 MB/rank
+#   file view     32768 contiguous runs of 4608 B per rank
+#   aggregation   k=2, row of 16, 8 extents of 18 MB
+# (verified: 4.4.3.1 at 48 ranks and 4.4.3.2 at 96 ranks give exactly the
+# same plan as Frontier's 4.4.2.1 at 32 ranks.)
+#
+# NOT identical, because 12 ranks/node is 1.5x the clients per node:
+#   record size at a given NODE count is 1.5x Frontier's
+#   client count at a given NODE count is 1.5x Frontier's
+#
+# So compare the two machines at equal RANK count (Aurora 4 nodes vs
+# Frontier 6, and so on) if what you want is equal client count and equal
+# record size; compare at equal NODE count if what you want is each machine
+# used as it is meant to be used.  Both are legitimate, they answer
+# different questions, and a table that does not say which one it is
+# reporting is worthless.  The quantity that carries the MPI-IO pathology --
+# per rank local volume and the resulting file view -- is invariant either
+# way, which is the point.
+##########################################################################
+
+##########################################################################
+# WHICH FILESYSTEM.  Point this at Lustre for the like-for-like comparison
+# with Frontier's Orion.  DAOS is a different architecture -- its numbers
+# are interesting but they are NOT a reproduction of the Frontier result,
+# and mixing them into one table would misrepresent both.  Label every set
+# of numbers with the filesystem it came from.
+##########################################################################
+# PROJECT is the flare project DIRECTORY name, which is not the -A account
+# number.  Set it once; the mkdir below fails loudly rather than writing
+# somewhere unintended.
+PROJECT=LatticeQCD_aesp_CNDA
+WORK=/lus/flare/projects/$PROJECT/$USER/iompi.$PBS_JOBID
+mkdir -p $WORK || { echo "cannot create $WORK -- set PROJECT correctly"; exit 1; }
+cd       $WORK
+
+# Match Frontier's default: no explicit striping.  Record what was inherited.
+lfs getstripe -d $WORK 2>/dev/null || echo "(no lfs getstripe -- not Lustre?)"
+
+# The largest rung writes three files of 232 GB, so budget ~700 GB and check
+# the quota before submitting.  Each run unlinks the three files first, so
+# that is peak usage, not cumulative.
+
+NRANKS=12          # one per tile
+
+BIN=$PBS_O_WORKDIR/io_mpi
+ARGS="--target 4194304 --reps 3"
+
+run () {   # run <nodes> <grid> <mpi> <comment> [extra args...]
+  local nodes=$1 gr=$2 mp=$3 note=$4
+  local ntot=$(( nodes * NRANKS ))
+  shift 4
+  echo
+  echo "==================================================================="
+  echo "=== nodes=$nodes ranks=$ntot grid=$gr mpi=$mp   $note"
+  echo "=== extra: $@"
+  echo "==================================================================="
+  mpiexec -np $ntot -ppn $NRANKS -envall $BIN --grid $gr --mpi $mp $ARGS "$@"
+  echo "=== exit $?"
+}
+
+#####################################################################
+# Phase 0.  Correctness.  Both count branches of MPI_Alltoallv are
+# covered; the labels below were checked, not assumed.  The whole-file
+# crc32 is serial, so keep these small.
+#####################################################################
+run 1 16.16.16.24  2.2.1.3  "correctness, UNIFORM counts, row of 4"      --reps 0 --serial-crc
+run 2 24.12.8.8    3.2.2.2  "correctness, NON-UNIFORM counts, row of 12" --reps 0 --serial-crc
+run 4 16.16.32.24  2.2.4.3  "correctness, NON-UNIFORM, non-zero offset"  --reps 0 --serial-crc --offset 1024
+
+#####################################################################
+# Phase 1.  Weak scan at 151 MB/rank.  Identical plan at every rung:
+# k=2, row of 16, 8 extents of 18 MB, 32768 runs of 4608 B in the view.
+#####################################################################
+#          nodes  global lattice    mpi        record
+run    4     32.32.96.128    4.4.3.1   "7.2 GB"    --no-validate
+run    8     32.32.96.256    4.4.3.2   "14.5 GB"   --no-validate
+run   16     32.32.96.512    4.4.3.4   "29.0 GB"   --no-validate
+run   32     32.32.192.512   4.4.6.4   "58.0 GB"   --no-validate
+run   64     32.32.192.1024  4.4.6.8   "116.0 GB"  --no-validate
+run  128     32.32.384.1024  4.4.12.8  "231.9 GB"  --no-validate
+
+#####################################################################
+# Phase 2.  The three questions a reviewer asks immediately.
+#####################################################################
+run  128     32.32.384.1024  4.4.12.8  "231.9 GB, durable"  --no-validate --fsync --drop-cache
+run  128     32.32.384.1024  4.4.12.8  "231.9 GB, cb hints" --no-validate \
+     --hints romio_cb_write=enable,romio_cb_read=enable,cb_nodes=128,cb_buffer_size=16777216
+run  128     32.32.384.1024  4.4.12.8  "231.9 GB, mem subarray" --no-validate --mem-subarray
+
+echo
+echo "=== done.  Files left in $WORK"
+ls -l $WORK

MPI_benchmark/io_frontier.slurm

@@ -0,0 +1,109 @@
+#!/bin/bash -l
+
+# Standalone MPI-only I/O reproducer on Frontier.  No Grid, no accelerator,
+# so no GCD/NUMA wrapper is needed -- the point of the exercise is that this
+# depends on nothing but an MPI installation and a filesystem.
+#
+#   mpicxx -O2 -std=c++11 io_mpi.cc -o io_mpi
+#
+# Weak scan: the local volume, and therefore the file view structure, is held
+# identical at every rung and only the number of Lustre clients changes:
+#
+#   local volume  8.8.32.128 = 262144 sites x 576 B = 151 MB/rank
+#   file view     32768 contiguous runs of 4608 B per rank, at every rung
+#   aggregate     k=2, row of 16, 8 extents of 18 MB, at every rung
+#
+# so any change in the relative bandwidth of the two lexicographic paths is a
+# property of the client count alone.
+#
+# The PERF lines are MiB/s (bytes/1024/1024/s), which is what BinaryIO.h
+# computes for lastPerf.mbytesPerSecond and prints as "MB/s", so the two
+# tools can be compared directly.  Grid's timed region is used here too:
+# barrier, start, [plan build + exchange + I/O], barrier, stop, quoting the
+# boss rank's stopwatch.  --reuse-plan hoists the plan build out, which is
+# how to show it is not where the time goes; do not use it when comparing
+# against Grid's own numbers.
+#
+# io_aurora.pbs runs 12 ranks per node, one per tile, because that is what
+# that machine is.  The per rank local volume and the file view are the same
+# there as here, but the record size and client count at a given NODE count
+# are 1.5x.  See the header of that script before tabulating the two
+# together.
+
+#SBATCH --job-name=ioMPI
+#SBATCH --nodes=128
+#SBATCH --ntasks-per-node=8
+#SBATCH --cpus-per-task=7
+#SBATCH --time=02:00:00
+#SBATCH --account=phy157_dwf
+#SBATCH --exclusive
+#SBATCH --mem=0
+
+module load cce/21.0.0
+module load cpe/26.03
+
+WORK=/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/iompi.$SLURM_JOB_ID
+mkdir -p $WORK
+cd       $WORK
+
+# Do NOT stripe by default.  Wide striping is what rescues the collective at
+# scale and costs every other path a factor of 1.2-2.2; the default layout is
+# what a user gets without knowing to ask.  Uncomment to reproduce that
+# interaction, and record which one you ran.
+#lfs setstripe -c -1 -S 8M $WORK
+lfs getstripe -d $WORK
+
+BIN=$SLURM_SUBMIT_DIR/io_mpi
+ARGS="--target 4194304 --reps 3"
+
+# ROMIO's own view of what it did.  Verbose, but the first thing anyone
+# reading the report will ask for.
+# export MPICH_MPIIO_STATS=1
+# export MPICH_MPIIO_TIMERS=1
+
+run () {   # run <nodes> <grid> <mpi> <comment> [extra args...]
+  local nodes=$1 gr=$2 mp=$3 note=$4
+  local nranks=$(( nodes * 8 ))
+  shift 4
+  echo
+  echo "==================================================================="
+  echo "=== nodes=$nodes ranks=$nranks grid=$gr mpi=$mp   $note"
+  echo "=== extra: $@"
+  echo "==================================================================="
+  srun -N$nodes -n$nranks --ntasks-per-node=8 $BIN --grid $gr --mpi $mp $ARGS "$@"
+  echo "=== exit $?"
+}
+
+#####################################################################
+# Phase 0.  Correctness, including the non-uniform Alltoallv branch
+# (odd process factor in an un-split dimension).  Small, and the
+# whole-file crc32 is serial, so keep the volume down here.
+#####################################################################
+run 1 12.12.8.8   2.2.2.1  "correctness, uniform counts"     --reps 0 --serial-crc
+run 3 24.12.8.8   3.2.2.2  "correctness, NON-uniform counts" --reps 0 --serial-crc
+run 4 16.16.16.32 2.2.2.4  "correctness, non-zero offset"    --reps 0 --serial-crc --offset 1024
+
+#####################################################################
+# Phase 1.  Weak scan, 151 MB/rank.  Timing only.
+#####################################################################
+run    4     32.32.64.128    4.4.2.1   "4.8 GB"    --no-validate
+run    8     32.32.64.256    4.4.2.2   "9.7 GB"    --no-validate
+run   16     32.32.64.512    4.4.2.4   "19.3 GB"   --no-validate
+run   32     32.32.128.512   4.4.4.4   "38.6 GB"   --no-validate
+run   64     32.32.128.1024  4.4.4.8   "77.3 GB"   --no-validate
+run  128     32.32.256.1024  4.4.8.8   "154.6 GB"  --no-validate
+
+#####################################################################
+# Phase 2.  Answer the two questions a reviewer will ask immediately.
+#####################################################################
+# Is the gap an artefact of measuring cache rather than the filesystem?
+run  128     32.32.256.1024  4.4.8.8   "154.6 GB, durable"  --no-validate --fsync --drop-cache
+# Does the collective recover if it is given the hints it wants?
+run  128     32.32.256.1024  4.4.8.8   "154.6 GB, cb hints" --no-validate \
+     --hints romio_cb_write=enable,romio_cb_read=enable,cb_nodes=128,cb_buffer_size=16777216
+# Does the degenerate memory subarray matter?
+run  128     32.32.256.1024  4.4.8.8   "154.6 GB, mem subarray" --no-validate --mem-subarray
+
+echo
+echo "=== done.  Files left in $WORK"
+ls -l $WORK

examples/Example_pvdagm.cc

@@ -0,0 +1,803 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./tests/Test_padded_cell.cc
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#include <Grid/Grid.h>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidual.h>
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.h>
+#include <Grid/algorithms/iterative/BiCGSTAB.h>
+
+using namespace std;
+using namespace Grid;
+RealD FineSmootherShift = 0.1;
+int   FineSmootherOrder = 8;
+int   FineSmootherTol   = 0;
+//RealD CoarseSmootherShift = 0.1;
+//int   CoarseSmootherOrder = 8;
+//int   CoarseSmootherTol   = 0;
+RealD CoarseSolverShift   = 0.002;
+RealD CoarseSolverTol     = 0.03;
+int   CoarseSolverOrder   = 200;
+int   CoarseMmax          = 20;   // coarse GCR restart length (was hardcoded 20)
+RealD mass=0.00078;
+void ParseEnvironment(void)
+{
+    
+  if(getenv("MASS") ) mass = atof(getenv("MASS"));
+  if(getenv("FineSmootherShift"))   FineSmootherShift   = atof(getenv("FineSmootherShift"));
+  if(getenv("FineSmootherOrder"))   FineSmootherOrder   = atoi(getenv("FineSmootherOrder"));
+  if(getenv("CoarseSolverShift"))   CoarseSolverShift   = atof(getenv("CoarseSolverShift"));
+  if(getenv("CoarseSolverTol"))     CoarseSolverTol     = atof(getenv("CoarseSolverTol"));
+  if(getenv("CoarseSolverOrder"))   CoarseSolverOrder   = atoi(getenv("CoarseSolverOrder"));
+  if(getenv("CoarseMmax"))          CoarseMmax          = atoi(getenv("CoarseMmax"));
+  if(getenv("DiagInvPrec"))
+  {
+    std::cout << GridLogMessage << "WARNING: DiagInvPrec option REMOVED (diagonal-inverse preconditioning wrecks fine->coarse null-vector inheritance); IGNORED" << std::endl;
+  }
+
+  //  if(getenv("CoarseSmootherShift")) CoarseSmootherShift = atof(getenv("CoarseSmootherShift"));
+  //  if(getenv("CoarseSmootherOrder")) CoarseSmootherOrder = atoi(getenv("CoarseSmootherOrder"));
+  
+  std::cout << GridLogMessage << "PARAM: FineSmootherShift   "<<FineSmootherShift<<std::endl;
+  std::cout << GridLogMessage << "PARAM: FineSmootherOrder   "<<FineSmootherOrder<<std::endl;
+  //  std::cout << GridLogMessage << "PARAM: CoarseSmootherShift "<<CoarseSmootherShift<<std::endl;
+  //  std::cout << GridLogMessage << "PARAM: CoarseSmootherOrder "<<CoarseSmootherOrder<<std::endl;
+  std::cout << GridLogMessage << "PARAM: CoarseSolverShift   "<<CoarseSolverShift<<std::endl;
+  std::cout << GridLogMessage << "PARAM: CoarseSolverTol     "<<CoarseSolverTol<<std::endl;
+  std::cout << GridLogMessage << "PARAM: CoarseSolverOrder   "<<CoarseSolverOrder<<std::endl;
+  std::cout << GridLogMessage << "PARAM: CoarseMmax          "<<CoarseMmax<<std::endl;
+
+  std::cout << GridLogMessage << "PARAM: MASS "<<mass<<std::endl;
+}
+
+template <class T> void readFile(T& out, std::string const fname){  
+  #ifdef HAVE_LIME
+    // Ref: https://github.com/paboyle/Grid/blob/feature/scidac-wp1/tests/debug/Test_general_coarse_hdcg_phys48.cc#L111
+    std::cout << Grid::GridLogMessage << "Reads at: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    // Grid::ScidacReader SR(out.Grid()->IsBoss());
+    Grid::ScidacReader SR;
+    SR.open(fname);
+    SR.readScidacFieldRecord(out, record);
+    SR.close();
+  #endif
+}
+template <class Field>
+void saveSubspace(std::vector<Field> &subspace, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Saving subspace (" << subspace.size() << " vectors) to: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacWriter SW(subspace[0].Grid()->IsBoss());
+    SW.open(fname);
+    for (int k = 0; k < (int)subspace.size(); k++)
+      SW.writeScidacFieldRecord(subspace[k], record);
+    SW.close();
+  #endif
+}
+
+template <class Field>
+void loadSubspace(std::vector<Field> &subspace, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Loading subspace (" << subspace.size() << " vectors) from: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacReader SR;
+    SR.open(fname);
+    for (int k = 0; k < (int)subspace.size(); k++)
+      SR.readScidacFieldRecord(subspace[k], record);
+    SR.close();
+  #endif
+}
+
+template<class Matrix,class Field>
+class PVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+  int nApp;
+  int nAppDag;
+public:
+  PVdagMLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV), nApp(0), nAppDag(0) {};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    //    std::cout << GridLogMessage<< "Op: PVdag M "<<std::endl;
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+    nApp++;
+  }
+  void AdjOp     (const Field &in, Field &out){
+    //    std::cout << GridLogMessage<<"AdjOp: Mdag PV "<<std::endl;
+    Field tmp(in.Grid());
+    _PV.M(in,tmp);
+    _Mat.Mdag(tmp,out);
+    nAppDag++;
+  }
+
+  void clear() {
+    nApp = 0;
+    nAppDag = 0;
+  }
+
+  void getApplications() {
+    std::cout << GridLogMessage << "# applications of PVdagM: " << nApp << std::endl;
+    std::cout << GridLogMessage << "# applications of PVdagM^dag: " << nAppDag << std::endl;
+    std::cout << GridLogMessage << "# applications total: " << nApp + nAppDag << std::endl;
+  }
+
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    //    std::cout <<GridLogMessage<< "HermOp: Mdag PV PVdag M"<<std::endl;
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+    //    std::cout << "HermOp done "<<norm2(out)<<std::endl;
+  }
+};
+template<class Matrix,class Field>
+class MdagPVLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+public:
+  MdagPVLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV){};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    //    std::cout <<GridLogMessage<< "Op: PVdag M "<<std::endl;
+    _PV.M(in,tmp);
+    _Mat.Mdag(tmp,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    //    std::cout <<GridLogMessage<< "AdjOp: Mdag PV "<<std::endl;
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    //    std::cout << GridLogMessage<<"HermOp: PVdag M Mdag PV "<<std::endl;
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+    //    std::cout << "HermOp done "<<norm2(out)<<std::endl;
+  }
+};
+template<class Matrix,class Field>
+class ShiftedPVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+  int nApp;
+  int nAppDag;
+public:
+  RealD shift;
+  ShiftedPVdagMLinearOperator(RealD _shift,Matrix &Mat,Matrix &PV): shift(_shift),_Mat(Mat),_PV(PV) , nApp(0), nAppDag(0){};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    //    std::cout << "Op: PVdag M "<<std::endl;
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+    nApp++;
+    out = out + shift * in;
+  }
+  void AdjOp     (const Field &in, Field &out){
+    //    std::cout << "AdjOp: Mdag PV "<<std::endl;
+    Field tmp(in.Grid());
+    _PV.M(tmp,out);
+    _Mat.Mdag(in,tmp);
+    nAppDag++;
+    out = out + shift * in;
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){    assert(0);  }
+  void HermOp(const Field &in, Field &out){
+    //    std::cout << "HermOp: Mdag PV PVdag M"<<std::endl;
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+  void clear() {
+    nApp = 0;
+    nAppDag = 0;
+  }
+  void getApplications() {
+    std::cout << GridLogMessage << "# applications of ShiftedPVdagM: " << nApp << std::endl;
+    std::cout << GridLogMessage << "# applications of ShiftedPVdagM^dag: " << nAppDag << std::endl;
+    std::cout << GridLogMessage << "# applications total: " << nApp + nAppDag << std::endl;
+  }
+};
+template<class Fobj,class CComplex,int nbasis>
+class MGPreconditioner : public LinearFunction< Lattice<Fobj> > {
+public:
+
+  using LinearFunction<Lattice<Fobj> >::operator();
+
+  typedef Aggregation<Fobj,CComplex,nbasis> Aggregates;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::FineField    FineField;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseVector CoarseVector;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseMatrix CoarseMatrix;
+  typedef LinearOperatorBase<FineField>                            FineOperator;
+  typedef LinearFunction    <FineField>                            FineSmoother;
+  typedef LinearOperatorBase<CoarseVector>                         CoarseOperator;
+  typedef LinearFunction    <CoarseVector>                         CoarseSolver;
+  Aggregates     & _Aggregates;
+  FineOperator   & _FineOperator;
+  FineSmoother   & _PreSmoother;
+  FineSmoother   & _PostSmoother;
+  CoarseOperator & _CoarseOperator;
+  CoarseSolver   & _CoarseSolve;
+  std::string name;
+
+  int    level;  void Level(int lv) {level = lv; };
+
+  MGPreconditioner(Aggregates &Agg,
+		   FineOperator &Fine,
+		   FineSmoother &PreSmoother,
+		   FineSmoother &PostSmoother,
+		   CoarseOperator &CoarseOperator_,
+		   CoarseSolver &CoarseSolve_,
+		   std::string _name = std::string("unnamed"))
+    : _Aggregates(Agg),
+      _FineOperator(Fine),
+      _PreSmoother(PreSmoother),
+      _PostSmoother(PostSmoother),
+      _CoarseOperator(CoarseOperator_),
+      _CoarseSolve(CoarseSolve_),
+      name(_name),
+      level(1)  {  }
+
+  virtual void operator()(const FineField &in, FineField & out) 
+  {
+    GridBase *CoarseGrid = _Aggregates.CoarseGrid;
+    //    auto CoarseGrid = _CoarseOperator.Grid();
+    CoarseVector Csrc(CoarseGrid);
+    CoarseVector Csol(CoarseGrid);
+    FineField vec1(in.Grid());
+    FineField vec2(in.Grid());
+
+    std::cout<<GridLogMessage << "Calling PreSmoother " <<std::endl;
+
+    //    std::cout<<GridLogMessage << "Calling PreSmoother input residual "<<norm2(in) <<std::endl;
+    double t;
+    // Fine Smoother
+    //    out = in;
+    out = Zero();
+    t=-usecond();
+    _PreSmoother(in,out);
+    t+=usecond();
+
+    std::cout<<GridLogMessage << "PreSmoother took "<< t/1000.0<< "ms" <<std::endl;
+
+    // Update the residual
+    _FineOperator.Op(out,vec1);  sub(vec1, in ,vec1);   
+    //    std::cout<<GridLogMessage <<"Residual-1 now " <<norm2(vec1)<<std::endl;
+
+    // Fine to Coarse 
+    t=-usecond();
+    _Aggregates.ProjectToSubspace  (Csrc,vec1);
+    t+=usecond();
+    std::cout<<GridLogMessage << "Project to coarse took "<< t/1000.0<< "ms" <<std::endl;
+
+    // Coarse correction
+    t=-usecond();
+    Csol = Zero();
+    _CoarseSolve(Csrc,Csol);
+    //Csol=Zero();
+    t+=usecond();
+    std::cout<<GridLogMessage << "Coarse solve took "<< t/1000.0<< "ms" <<std::endl;
+
+    // Coarse to Fine
+    t=-usecond();  
+    //    _CoarseOperator.PromoteFromSubspace(_Aggregates,Csol,vec1);
+    _Aggregates.PromoteFromSubspace(Csol,vec1); 
+    add(out,out,vec1);
+    t+=usecond();
+    std::cout<<GridLogMessage << "Promote to this level took "<< t/1000.0<< "ms" <<std::endl;
+
+    // Residual
+    _FineOperator.Op(out,vec1);  sub(vec1 ,in , vec1);  
+    //    std::cout<<GridLogMessage <<"Residual-2 now " <<norm2(vec1)<<std::endl;
+
+    // Fine Smoother
+    t=-usecond();
+    //    vec2=vec1;
+    vec2=Zero();
+    _PostSmoother(vec1,vec2);
+    t+=usecond();
+    std::cout<<GridLogMessage << "PostSmoother took "<< t/1000.0<< "ms" <<std::endl;
+
+    add( out,out,vec2);
+    std::cout<<GridLogMessage << "Done " <<std::endl;
+  }
+};
+
+template<class PVdagM_t, class ShiftedPVdagM_t, class Subspace, class LittleDiracOperator, class CoarseVector, class TwoLevelMG>
+void runMG(
+  GridCartesian *FGrid,
+  GridCartesian *Coarse5d, 
+  NextToNearestStencilGeometry5D geom,
+  PVdagM_t PVdagM,
+  ShiftedPVdagM_t ShiftedPVdagM,
+  // std::vector<LatticeFermion> subspace
+  Subspace AggregatesPD
+) {
+
+  // typedef Aggregation<vSpinColourVector,vTComplex,nbasis> Subspace;
+  // typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LittleDiracOperator;
+  // typedef LittleDiracOperator::CoarseVector CoarseVector;
+  ParseEnvironment();
+
+  std::vector<LatticeFermion> subspace = AggregatesPD.subspace;
+  int nbasis = subspace.size();
+  const int cb = 0 ;
+
+  LatticeFermion err(FGrid);
+  LatticeFermion prom(FGrid);
+  LatticeFermion tmp(FGrid);
+
+  CoarseVector c_src (Coarse5d);
+  CoarseVector c_res (Coarse5d);
+  CoarseVector c_proj(Coarse5d);
+  Complex one(1.0);
+
+  LatticeFermionD f_src(FGrid);
+  LatticeFermionD f_res(FGrid);
+  // typedef MGPreconditioner<vSpinColourVector,  vTComplex,nbasis> TwoLevelMG;
+  TrivialPrecon<CoarseVector> simple;
+  TrivialPrecon<LatticeFermionD> simple_fine;
+
+  // Subspace AggregatesPD(Coarse5d,FGrid,cb);
+
+  // Orthonormalize subspace and compute nulliness
+
+  ShiftedPVdagM.shift = CoarseSolverShift;
+  int nonherm = 0;
+  LittleDiracOperator LittleDiracOpPV(geom,FGrid,Coarse5d,nonherm);
+  LittleDiracOpPV.CoarsenOperator(ShiftedPVdagM, AggregatesPD);
+  ShiftedPVdagM.shift = FineSmootherShift;
+
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<"Testing coarsened operator "<<std::endl;
+
+  c_src = one;  // 1 in every element for vector 1.
+  blockPromote(c_src,err,subspace);
+
+  prom=Zero();
+  for(int b=0;b<nbasis;b++){
+    prom=prom+subspace[b];
+  }
+  err=err-prom; 
+  std::cout<<GridLogMessage<<"Promoted back from subspace: err "<<norm2(err)<<std::endl;
+  std::cout<<GridLogMessage<<"c_src "<<norm2(c_src)<<std::endl;
+  std::cout<<GridLogMessage<<"prom  "<<norm2(prom)<<std::endl;
+
+  // PVdagM.Op(prom,tmp);
+  // blockProject(c_proj,tmp,subspace);
+  // std::cout<<GridLogMessage<<" Called Big Dirac Op "<<norm2(tmp)<<std::endl;
+
+  // LittleDiracOpPV.M(c_src,c_res);
+  // std::cout<<GridLogMessage<<" Called Little Dirac Op c_src "<< norm2(c_src) << "  c_res "<< norm2(c_res) <<std::endl;
+
+  // std::cout<<GridLogMessage<<"Little dop : "<<norm2(c_res)<<std::endl;
+  // //  std::cout<<GridLogMessage<<" Little "<< c_res<<std::endl;
+  // std::cout<<GridLogMessage<<"Big dop in subspace : "<<norm2(c_proj)<<std::endl;
+  // //  std::cout<<GridLogMessage<<" Big "<< c_proj<<std::endl;
+  // c_proj = c_proj - c_res;
+  // std::cout<<GridLogMessage<<" ldop error: "<<norm2(c_proj)<<std::endl;
+  // //  std::cout<<GridLogMessage<<" error "<< c_proj<<std::endl;
+
+  ///////////////////////////////////////
+  // Coarse grid solver test
+  ///////////////////////////////////////
+
+  std::cout<<GridLogMessage<<"******************* "<<std::endl;
+  std::cout<<GridLogMessage<<" Coarse Grid Solve -- Level 2 "<<std::endl;
+  std::cout<<GridLogMessage<<"******************* "<<std::endl;
+  NonHermitianLinearOperator<LittleDiracOperator,CoarseVector> LinOpCoarse(LittleDiracOpPV);
+  // DiagonalInverse preconditioning REMOVED (library support withdrawn: it
+  // wrecks the collinearity that makes fine->coarse null-vector inheritance
+  // free).  TrivialPrecon reproduces the former DiagInvPrec=0 path exactly.
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector>  L2PGCR(CoarseSolverTol, (CoarseSolverOrder+CoarseMmax-1)/CoarseMmax, LinOpCoarse,simple,CoarseMmax,CoarseMmax);
+  L2PGCR.SetZeroGuess(1);              // callers zero Csol / c_res
+  L2PGCR.Level(2);
+  L2PGCR.Name("Couter");
+  c_res=Zero();
+  L2PGCR(c_src,c_res);
+
+
+  ////////////////////////////////////////
+  // Fine grid smoother
+  ////////////////////////////////////////
+  //  NonHermitianLinearOperator<PVdagM_t,LatticeFermionD> LinOpSmooth(PVdagM);
+  
+  //  PrecGeneralisedConjugateResidualNonHermitian<LatticeFermionD> SmootherGCR(0.05,1,ShiftedPVdagM,simple_fine,8,8);
+  // Force 10 iters exactly, no early termination
+  PrecGeneralisedConjugateResidualNonHermitian<LatticeFermionD> SmootherGCR(FineSmootherTol,1,
+									    ShiftedPVdagM,simple_fine,
+									    FineSmootherOrder,FineSmootherOrder);
+  SmootherGCR.Level(1);
+  SmootherGCR.Name("Fsmoother");
+  SmootherGCR.SetZeroGuess(1);         // pre/post slots + direct call all zero their guess
+
+  f_src = one;  // 1 in every element for vector 1.
+  f_res=Zero();
+  SmootherGCR(f_src,f_res);
+
+  TwoLevelMG TwoLevelPrecon(AggregatesPD,
+			    PVdagM,
+			    simple_fine,
+			    SmootherGCR,
+			    LinOpCoarse,
+			    L2PGCR,
+			    "PVdagM");
+  
+  PrecGeneralisedConjugateResidualNonHermitian<LatticeFermion> L1PGCR(1.0e-8,1000,PVdagM,TwoLevelPrecon,32,32);
+  L1PGCR.SetZeroGuess(1);              // f_res=Zero() before the solve
+  L1PGCR.Level(1);
+  L1PGCR.Name("Fouter");
+
+  std::cout<<GridLogMessage<<"******************* "<<std::endl;
+  std::cout<<GridLogMessage<<" Running Multi Grid Solver "<<std::endl;
+  std::cout<<GridLogMessage<<"******************* "<<std::endl;
+  f_res=Zero();
+  L1PGCR(f_src,f_res);
+
+  std::cout << GridLogMessage << "Fine Grid Smoother -- Level 2 operator uses: " << std::endl;
+  PVdagM.getApplications();
+  PVdagM.clear();
+  ShiftedPVdagM.getApplications();
+  ShiftedPVdagM.clear();
+
+}
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  // TODO read in more parameters: nbasis, GCR iters, smoother order, m
+  // Might be impossible because nbasis needs to be a constant to be a template parameter
+  // Usage : $ ./Example_pvdagm <nbasis> <smooth> <outerIters> <m>
+  // std::string nbasisStr  = argv[1];
+  // std::string smoothStr  = argv[2];
+  // std::string outerStr   = argv[3];
+  // std::string mStr       = argv[4];
+  // int nbasis = std::stoi(nbasisStr);
+  // int smooth = std::stoi(smoothStr);
+
+  const int Ls=24;
+  RealD M5=1.8;
+
+  
+  //  const int nbasis = 40;
+  const int nbasis = 60;
+  
+  std::cout << GridLogMessage << "Mass: " << mass << ", Ls: " << Ls << ", running Mobius kernel with b=1.5, c=0.5" << std::endl;
+  std::cout << GridLogMessage << "nbasis: " << nbasis << std::endl;
+
+  std::vector<int> lat_size {48, 48, 48, 96};
+
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(lat_size, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Construct a coarsened grid
+  // Coordinate clatt = GridDefaultLatt();
+  Coordinate clatt = lat_size;
+  Coordinate Block({4,4,4,4});
+  std::cout << GridLogMessage << "Lattice size: " << lat_size << std::endl;
+  for(int d=0;d<clatt.size();d++){
+    clatt[d] = lat_size[d]/Block[d];
+  }
+
+  std::cout << GridLogMessage << "constructing coarse grid" << std::endl;
+  GridCartesian *Coarse4d =  SpaceTimeGrid::makeFourDimGrid(clatt, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *Coarse5d =  SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+
+  std::vector<int> seeds4({1,2,3,4});
+  std::vector<int> seeds5({5,6,7,8});
+  std::vector<int> cseeds({5,6,7,8});
+  GridParallelRNG          RNG5(FGrid);   RNG5.SeedFixedIntegers(seeds5);
+  GridParallelRNG          RNG4(UGrid);   RNG4.SeedFixedIntegers(seeds4);
+  GridParallelRNG          CRNG(Coarse5d);CRNG.SeedFixedIntegers(cseeds);
+
+  LatticeFermion    src(FGrid); random(RNG5,src);
+  LatticeFermion result(FGrid); result=Zero();
+  LatticeFermion    ref(FGrid); ref=Zero();
+  LatticeFermion    tmp(FGrid);
+  LatticeFermion    err(FGrid);
+  LatticeGaugeField Umu(UGrid);
+
+
+  std::cout << GridLogMessage << "Reading in gauge field" << std::endl;
+  FieldMetaData header;
+  // std::string file("/sdcc/u/poare/PETSc-Grid/ckpoint_lat.4000");
+  std::string file("/ccs/home/poare/ckpoint_lat.1000");
+  NerscIO::readConfiguration(Umu,header,file);
+
+  /*
+
+  // DWF, m=0.01
+  // std::string eigenPath = "/hpcgpfs01/work/lqcd/staging/RBC/ckpoint_lat.4000/ks_evecs/PVdagM_Nm80_Nk40_Niter5000_337342/";
+
+  // DWF, m=0.001
+  // std::string eigenPath = "/hpcgpfs01/work/lqcd/staging/RBC/ckpoint_lat.4000/ks_evecs/PVdagM_Nm80_Nk40_Niter5000_m0p001_339143/";
+
+  // Mobius, m=0.001
+  // std::string eigenPath = "/hpcgpfs01/work/lqcd/staging/RBC/ckpoint_lat.4000/ks_evecs/PVdagM_Nm80_Nk40_Niter5000_346851/";
+
+  // Frontier path
+  std::string eigenPath = "/ccs/home/poare/lqcd/multigrid/spectra/ckpoint_lat.1000/...";
+  
+
+  std::cout << GridLogMessage << "Loading eigenvalues" << std::endl;
+  std::ifstream evalFile(eigenPath + "evals.txt");
+  std::string str;
+  std::vector<ComplexD> evals;
+  while (std::getline(evalFile, str)) {
+      std::cout << GridLogMessage << "Reading line: " << str << std::endl;
+      int i1 = str.find("(") + 1;
+      int i2 = str.find(",") + 1;
+      int i3 = str.find(")");
+      std::cout << "i1,i2,i3 = " << i1 << "," << i2 << "," << i3 << std::endl;
+      std::string reStr = str.substr(i1, i2 - i1);
+      std::string imStr = str.substr(i2, i3 - i2);
+      std::cout << GridLogMessage << "Parsed re = " << reStr << " and im = " << imStr << std::endl;
+      // ComplexD z (std::stof(reStr), std::stof(imStr));
+      ComplexD z (std::stod(reStr), std::stod(imStr));
+      evals.push_back(z);
+  }
+  std::cout << GridLogMessage << "Eigenvalues: " << evals << std::endl;
+
+  int Nevecs = 20;
+  std::vector<LatticeFermion> evecs;
+  LatticeFermion evec (FGrid);
+  for (int i = 0; i < Nevecs; i++) {
+    std::string evecPath = eigenPath + "evec" + std::to_string(i);
+    readFile(evec, evecPath);
+    evecs.push_back(evec);
+  }
+  std::cout << GridLogMessage << "Evecs loaded" << std::endl;
+
+  */
+  // TODO uncomment when evecs are computed!
+
+  // DomainWallFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5);
+  // DomainWallFermionD Dpv(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,1.0,M5);
+
+  // Mobius
+  RealD b=1.5;// Scale factor b+c=2, b-c=1
+  RealD c=0.5;
+  MobiusFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5,b,c);
+  MobiusFermionD Dpv(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,1.0,M5,b,c);
+
+  const int cb = 0 ;
+  LatticeFermion prom(FGrid);
+
+  // assert(nbasis <= Nevecs);     // need to have enough evecs
+
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector CoarseVector;
+
+  NextToNearestStencilGeometry5D geom(Coarse5d);
+
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<std::endl;
+
+  // typedef PVdagMLinearOperator<DomainWallFermionD,LatticeFermionD> PVdagM_t;
+  // typedef MdagPVLinearOperator<DomainWallFermionD,LatticeFermionD> MdagPV_t;
+  // typedef ShiftedPVdagMLinearOperator<DomainWallFermionD,LatticeFermionD> ShiftedPVdagM_t;
+  typedef PVdagMLinearOperator<MobiusFermionD,LatticeFermionD> PVdagM_t;
+  typedef MdagPVLinearOperator<MobiusFermionD,LatticeFermionD> MdagPV_t;
+  typedef ShiftedPVdagMLinearOperator<MobiusFermionD,LatticeFermionD> ShiftedPVdagM_t;
+
+  PVdagM_t PVdagM(Ddwf,Dpv);
+  MdagPV_t MdagPV(Ddwf,Dpv);
+  //  ShiftedPVdagM_t ShiftedPVdagM(2.0,Ddwf,Dpv); // 355
+  //  ShiftedPVdagM_t ShiftedPVdagM(1.0,Ddwf,Dpv); // 246
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.5,Ddwf,Dpv); // 183
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.25,Ddwf,Dpv); // 145
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.1,Ddwf,Dpv); // 134
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.1,Ddwf,Dpv); // 127 -- NULL space via inverse iteration
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.1,Ddwf,Dpv); // 57 -- NULL space via inverse iteration; 3 iterations
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.25,Ddwf,Dpv); // 57 , tighter inversion
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.25,Ddwf,Dpv); // nbasis 20 -- 49 iters
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.25,Ddwf,Dpv); // nbasis 20 -- 70 iters; asymmetric 
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.25,Ddwf,Dpv); // 58; Loosen coarse, tighten fine
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.1,Ddwf,Dpv); // 56 ... 
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.1,Ddwf,Dpv); // 51 ...  with 24 vecs
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.1,Ddwf,Dpv); // 31 ...  with 24 vecs and 2^4 blocking
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.1,Ddwf,Dpv); // 43 ...  with 16 vecs and 2^4 blocking, sloppier
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.1,Ddwf,Dpv); // 35  ...  with 20 vecs and 2^4 blocking
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.1,Ddwf,Dpv); // 35  ...  with 20 vecs and 2^4 blocking, looser coarse
+  //  ShiftedPVdagM_t ShiftedPVdagM(0.1,Ddwf,Dpv); // 64  ...  with 20 vecs, Christoph setup, and 2^4 blocking, looser coarse
+
+  ShiftedPVdagM_t ShiftedPVdagM(FineSmootherShift,Ddwf,Dpv); // 
+
+  // Run power method on HOA??
+  PowerMethod<LatticeFermion>       PM;
+
+  CoarseVector c_src (Coarse5d);
+  CoarseVector c_res (Coarse5d);
+  CoarseVector c_proj(Coarse5d);
+  Complex one(1.0);
+
+  std::vector<LatticeFermion> subspace(nbasis,FGrid);
+
+  LatticeFermionD f_src(FGrid);
+  LatticeFermionD f_res(FGrid);
+  typedef MGPreconditioner<vSpinColourVector,  vTComplex,nbasis> TwoLevelMG;
+  TrivialPrecon<CoarseVector> simple;
+  TrivialPrecon<LatticeFermionD> simple_fine;
+
+  // Warning: This routine calls PVdagM.Op, not PVdagM.HermOp
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis> Subspace;
+
+  // Breeds right singular vectors with call to HermOp (V)
+  // int chebyOrd = 500;
+  // V.CreateSubspaceChebyshev(RNG5,PVdagM,
+	// 		    nbasis,
+	// 		    4000.0,0.003,
+	// 		    chebyOrd);
+  // AggregatesPD.CreateSubspaceChebyshev(RNG5,
+	// 			       PVdagM,
+	// 			       nbasis,
+	// 			       4000.0,
+	// 			       0.003,
+	// 			       chebyOrd);
+  
+  // Subspace testing (uncomment blocks when needed)
+
+  // - nbasis = 20, m=0.01, 35 outer iterations
+  // - nbasis = 40, m=0.01, 23 outer iterations
+  std::cout << GridLogMessage << "*** GCR setup ***" << std::endl;
+
+  // Subspace cache: save after generation, reload on subsequent runs to skip expensive setup.
+  // Set SUBSPACE_FILE to override the default path.
+  std::string subspace_file = "/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/subspace_nb"
+                              + std::to_string(nbasis) + ".scidac";
+  if ( getenv("SUBSPACE_FILE") ) subspace_file = std::string(getenv("SUBSPACE_FILE"));
+
+  // Check if subspace file exists (boss rank checks, result broadcast via GlobalSum).
+  uint64_t file_exists = 0;
+  if ( UGrid->IsBoss() ) {
+    std::ifstream f(subspace_file);
+    file_exists = f.good() ? 1 : 0;
+  }
+  UGrid->GlobalSum(file_exists);
+
+  Subspace AggregatesGCR(Coarse5d,FGrid,cb);
+
+  if ( file_exists ) {
+    std::cout << GridLogMessage << "*** Loading subspace from disk ***" << std::endl;
+    loadSubspace(AggregatesGCR.subspace, subspace_file);
+    // Insurance: GLOBAL (whole-lattice) orthonormalise, matching what
+    // CreateSubspaceGCR applies to generated subspaces (Aggregates.h:196), so a
+    // reloaded file ends in the same state.  This replaces the block
+    // Orthogonalise() previously called here -- that is redundant (CoarsenOperator
+    // block-GS's the subspace internally) and would leave a loaded file block-
+    // orthonormal while a generated one is globally orthonormal.  Global GS is
+    // span-preserving, so the coarse operator is unchanged.
+    AggregatesGCR.GlobalOrthonormalise();
+    std::cout << GridLogMessage << "Subspace loaded and globally orthonormalised." << std::endl;
+  } else {
+    std::cout << GridLogMessage << "*** GCR subspace generation ***" << std::endl;
+    AggregatesGCR.CreateSubspaceGCR(RNG5,PVdagM,nbasis);
+    std::cout << GridLogMessage << "Subspace generation: PVdagM operator uses:" << std::endl;
+    PVdagM.getApplications();
+    PVdagM.clear();
+    saveSubspace(AggregatesGCR.subspace, subspace_file);
+    std::cout << GridLogMessage << "Subspace saved to: " << subspace_file << std::endl;
+  }
+  
+  std::cout << GridLogMessage << "Basis construction operator uses: " << std::endl;
+  PVdagM.getApplications();
+  PVdagM.clear();
+
+  std::cout << GridLogMessage << "Calling runMG " << std::endl;
+  runMG<PVdagM_t, ShiftedPVdagM_t, Subspace, LittleDiracOperator, CoarseVector, TwoLevelMG>(
+    FGrid, 
+    Coarse5d, 
+    geom, 
+    PVdagM, 
+    ShiftedPVdagM, 
+    AggregatesGCR
+  );
+
+  //////////////////////////////////
+  // Standard CG
+  //////////////////////////////////
+#if 0
+  {
+  std::cout << "**************************************"<<std::endl;
+  std::cout << "Calling red black CG"<<std::endl;
+  std::cout << "**************************************"<<std::endl;
+    ConjugateGradient<LatticeFermionD>  CGfine(1.0e-8,30000,false);
+    SchurDiagMooeeOperator<MobiusFermionD, LatticeFermion> HermOpEO(Ddwf);
+      
+    LatticeFermion result(FrbGrid); result=Zero();
+    LatticeFermion    src(FrbGrid); random(RNG5,src);
+    result=Zero();
+
+    CGfine(HermOpEO, src, result);
+  }
+  {
+    std::cout << "**************************************"<<std::endl;
+    std::cout << "Calling MdagM CG"<<std::endl;
+    std::cout << "**************************************"<<std::endl;
+      
+    LatticeFermion result(FGrid); result=Zero();
+    LatticeFermion    src(FGrid); random(RNG5,src);
+    result=Zero();
+
+    MdagMLinearOperator<MobiusFermionD, LatticeFermionD> HermOp(Ddwf);
+    ConjugateGradient<LatticeFermionD>  CGfine(1.0e-8,100000,false);
+    CGfine(HermOp, src, result);
+  }
+  {
+    std::cout << "**************************************"<<std::endl;
+    std::cout << "Calling PVdagM GCR"<<std::endl;
+    std::cout << "**************************************"<<std::endl;
+
+    LatticeFermion result(FGrid); result=Zero();
+    LatticeFermion    src(FGrid); random(RNG5,src);
+    result=Zero();
+    PrecGeneralisedConjugateResidualNonHermitian<LatticeFermionD> GCR(1.0e-8,3000,PVdagM,simple_fine,50,50);
+    GCR.Name("Fbaseline");
+    GCR.SetZeroGuess(1);               // result=Zero() above
+    GCR(src,result);
+  }
+#endif  
+
+  
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage << "Done "<< std::endl;
+
+  Grid_finalize();
+  return 0;
+}

examples/Example_pvdagm_3level.cc

@@ -0,0 +1,699 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./examples/Example_pvdagm_3level.cc
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#include <Grid/Grid.h>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidual.h>
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.h>
+#include <Grid/algorithms/iterative/BiCGSTAB.h>
+
+using namespace std;
+using namespace Grid;
+
+template <class T> void readFile(T& out, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Reading: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacReader SR;
+    SR.open(fname);
+    SR.readScidacFieldRecord(out, record);
+    SR.close();
+  #endif
+}
+
+template <class T> void writeFile(T& in, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Writing: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacWriter SW(in.Grid()->IsBoss());
+    SW.open(fname);
+    SW.writeScidacFieldRecord(in, record);
+    SW.close();
+  #endif
+}
+
+template <class Field>
+void saveSubspace(std::vector<Field> &subspace, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Saving subspace (" << subspace.size() << " vectors) to: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacWriter SW(subspace[0].Grid()->IsBoss());
+    SW.open(fname);
+    for (int k = 0; k < (int)subspace.size(); k++)
+      SW.writeScidacFieldRecord(subspace[k], record);
+    SW.close();
+  #endif
+}
+
+template <class Field>
+void loadSubspace(std::vector<Field> &subspace, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Loading subspace (" << subspace.size() << " vectors) from: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacReader SR;
+    SR.open(fname);
+    for (int k = 0; k < (int)subspace.size(); k++)
+      SR.readScidacFieldRecord(subspace[k], record);
+    SR.close();
+  #endif
+}
+
+template<class Matrix,class Field>
+class PVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+  int nApp;
+  int nAppDag;
+public:
+  PVdagMLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV), nApp(0), nAppDag(0) {};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+    nApp++;
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(in,tmp);
+    _Mat.Mdag(tmp,out);
+    nAppDag++;
+  }
+  void clear() { nApp = 0; nAppDag = 0; }
+  void getApplications() {
+    std::cout << GridLogMessage << "# applications of PVdagM: " << nApp << std::endl;
+    std::cout << GridLogMessage << "# applications of PVdagM^dag: " << nAppDag << std::endl;
+    std::cout << GridLogMessage << "# applications total: " << nApp + nAppDag << std::endl;
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+template<class Matrix,class Field>
+class MdagPVLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+public:
+  MdagPVLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV){};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(in,tmp);
+    _Mat.Mdag(tmp,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+template<class Matrix,class Field>
+class ShiftedPVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+  RealD shift;
+public:
+  ShiftedPVdagMLinearOperator(RealD _shift,Matrix &Mat,Matrix &PV): shift(_shift),_Mat(Mat),_PV(PV){};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+    out = out + shift * in;
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(tmp,out);
+    _Mat.Mdag(in,tmp);
+    out = out + shift * in;
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){ assert(0); }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+// Lüscher deflated guesser (arXiv:0706.2298 Sec A.3) for a non-Hermitian solve.
+// C_{st} = <psi[s] | LinOp | psi[t]>;  guess = sum_s c_s psi[s]  where c = C^{-1} psi† src.
+template<class Field>
+class LuscherGuesser : public LinearFunction<Field> {
+  const std::vector<Field> &psi;
+  Eigen::MatrixXcd          C_inv;
+public:
+  using LinearFunction<Field>::operator();
+  LuscherGuesser(const std::vector<Field> &psi_, const Eigen::MatrixXcd &Cinv_)
+    : psi(psi_), C_inv(Cinv_) {}
+  virtual void operator()(const Field &src, Field &guess) {
+    int N = psi.size();
+    Eigen::VectorXcd b(N);
+    for (int t = 0; t < N; t++)
+      b(t) = TensorRemove(innerProduct(psi[t], src));
+    Eigen::VectorXcd c = C_inv * b;
+    guess = Zero();
+    for (int s = 0; s < N; s++)
+      guess += ComplexD(c(s)) * psi[s];
+  }
+};
+
+template<class Fobj,class CComplex,int nbasis>
+class MGPreconditioner : public LinearFunction< Lattice<Fobj> > {
+public:
+  using LinearFunction<Lattice<Fobj> >::operator();
+
+  typedef Aggregation<Fobj,CComplex,nbasis> Aggregates;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::FineField    FineField;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseVector CoarseVector;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseMatrix CoarseMatrix;
+  typedef LinearOperatorBase<FineField>                            FineOperator;
+  typedef LinearFunction    <FineField>                            FineSmoother;
+  typedef LinearOperatorBase<CoarseVector>                         CoarseOperator;
+  typedef LinearFunction    <CoarseVector>                         CoarseSolver;
+
+  Aggregates     & _Aggregates;
+  FineOperator   & _FineOperator;
+  FineSmoother   & _PreSmoother;
+  FineSmoother   & _PostSmoother;
+  CoarseOperator & _CoarseOperator;
+  CoarseSolver   & _CoarseSolve;
+  CoarseSolver   & _CoarseGuesser;
+
+  int    level;  void Level(int lv) {level = lv; };
+
+  MGPreconditioner(Aggregates &Agg,
+		   FineOperator &Fine,
+		   FineSmoother &PreSmoother,
+		   FineSmoother &PostSmoother,
+		   CoarseOperator &CoarseOperator_,
+		   CoarseSolver &CoarseSolve_,
+		   CoarseSolver &CoarseGuesser_)
+    : _Aggregates(Agg),
+      _FineOperator(Fine),
+      _PreSmoother(PreSmoother),
+      _PostSmoother(PostSmoother),
+      _CoarseOperator(CoarseOperator_),
+      _CoarseSolve(CoarseSolve_),
+      _CoarseGuesser(CoarseGuesser_),
+      level(1)  {  }
+
+  virtual void operator()(const FineField &in, FineField & out)
+  {
+    GridBase *CoarseGrid = _Aggregates.CoarseGrid;
+    CoarseVector Csrc(CoarseGrid);
+    CoarseVector Csol(CoarseGrid);
+    FineField vec1(in.Grid());
+    FineField vec2(in.Grid());
+
+    double t;
+    out = Zero();
+    t=-usecond();
+    _PreSmoother(in,out);
+    t+=usecond();
+    std::cout<<GridLogMessage << "PreSmoother took "<< t/1000.0<< "ms" <<std::endl;
+
+    _FineOperator.Op(out,vec1);  sub(vec1, in ,vec1);
+
+    t=-usecond();
+    _Aggregates.ProjectToSubspace(Csrc,vec1);
+    t+=usecond();
+    std::cout<<GridLogMessage << "Project to coarse took "<< t/1000.0<< "ms" <<std::endl;
+
+    t=-usecond();
+    _CoarseGuesser(Csrc,Csol);
+    _CoarseSolve(Csrc,Csol);
+    t+=usecond();
+    std::cout<<GridLogMessage << "Coarse solve took "<< t/1000.0<< "ms" <<std::endl;
+
+    t=-usecond();
+    _Aggregates.PromoteFromSubspace(Csol,vec1);
+    add(out,out,vec1);
+    t+=usecond();
+    std::cout<<GridLogMessage << "Promote to this level took "<< t/1000.0<< "ms" <<std::endl;
+
+    _FineOperator.Op(out,vec1);  sub(vec1 ,in , vec1);
+
+    t=-usecond();
+    vec2=Zero();
+    _PostSmoother(vec1,vec2);
+    t+=usecond();
+    std::cout<<GridLogMessage << "PostSmoother took "<< t/1000.0<< "ms" <<std::endl;
+
+    add(out,out,vec2);
+  }
+};
+
+// Generic shifted linear operator: wraps any LinearOperatorBase and adds shift*I.
+// Used to condition the coarse-level GCR smoother, analogous to ShiftedPVdagMLinearOperator
+// at the fine level.
+template<class Field>
+class ShiftedLinearOperator : public LinearOperatorBase<Field> {
+  LinearOperatorBase<Field> &_Op;
+  RealD shift;
+public:
+  ShiftedLinearOperator(RealD _shift, LinearOperatorBase<Field> &Op) : shift(_shift), _Op(Op) {}
+  void OpDiag   (const Field &in, Field &out)                         { assert(0); }
+  void OpDir    (const Field &in, Field &out, int dir, int disp)      { assert(0); }
+  void OpDirAll (const Field &in, std::vector<Field> &out)            { assert(0); }
+  void Op       (const Field &in, Field &out) { _Op.Op(in, out);    out = out + shift * in; }
+  void AdjOp    (const Field &in, Field &out) { _Op.AdjOp(in, out); out = out + shift * in; }
+  void HermOpAndNorm(const Field &in, Field &out, RealD &n1, RealD &n2) { assert(0); }
+  void HermOp   (const Field &in, Field &out) { Field tmp(in.Grid()); Op(in,tmp); AdjOp(tmp,out); }
+};
+
+template<int NB, class PVdagM_t, class ShiftedPVdagM_t, class Subspace, class LittleDiracOperator, class CoarseVector, class TwoLevelMG>
+void runMG(
+  GridCartesian *FGrid,
+  GridCartesian *Coarse5d,
+  GridCartesian *CoarseCoarse5d,
+  NextToNearestStencilGeometry5D geom,
+  PVdagM_t &PVdagM,
+  ShiftedPVdagM_t &ShiftedPVdagM,
+  Subspace &AggregatesPD
+) {
+  std::vector<LatticeFermion> subspace = AggregatesPD.subspace;
+  assert((int)subspace.size() == NB);
+  const int nbasis = NB;
+  const int cb = 0;
+
+  CoarseVector c_src(Coarse5d);
+  CoarseVector c_res(Coarse5d);
+  Complex one(1.0);
+
+  LatticeFermionD f_src(FGrid);
+  LatticeFermionD f_res(FGrid);
+
+  TrivialPrecon<CoarseVector>      simpleC;
+  TrivialPrecon<LatticeFermionD>   simple_fine;
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 0→1: coarsen PVdagM, build LinOpCoarse
+  //////////////////////////////////////////////////////////////////////
+  LittleDiracOperator LittleDiracOpPV(geom, FGrid, Coarse5d);
+  LittleDiracOpPV.CoarsenOperator(PVdagM, AggregatesPD);
+
+  NonHermitianLinearOperator<LittleDiracOperator,CoarseVector> LinOpCoarse(LittleDiracOpPV);
+
+  //////////////////////////////////////////////////////////////////////
+  // Baseline: plain PGCR on LinOpCoarse (reference for comparison)
+  //////////////////////////////////////////////////////////////////////
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<" Level 1 solve: plain PGCR baseline"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector> L2PGCR_baseline(3.0e-2,1100,LinOpCoarse,simpleC,10,10);
+  L2PGCR_baseline.Level(2);
+  L2PGCR_baseline.Name("Cbaseline");
+  c_src = one;
+  c_res = Zero();
+  L2PGCR_baseline(c_src,c_res);
+
+  //////////////////////////////////////////////////////////////////////
+  // psi_coarse: coarse projections of pre-GS fine null vectors.
+  // These are the Level 1 near-null vectors, promoted from Level 0.
+  // Used as the aggregation basis for Level 1→2 coarsening.
+  //////////////////////////////////////////////////////////////////////
+  std::vector<CoarseVector> psi_coarse(nbasis, Coarse5d);
+  for (int k = 0; k < nbasis; k++)
+    AggregatesPD.ProjectToSubspace(psi_coarse[k], subspace[k]);
+
+  //////////////////////////////////////////////////////////////////////
+  // Diagnostics: W (fine projected matrix) and C (Galerkin check)
+  //////////////////////////////////////////////////////////////////////
+  {
+    Eigen::MatrixXcd W = Eigen::MatrixXcd::Zero(nbasis, nbasis);
+    LatticeFermion ftmp(FGrid);
+    for (int j = 0; j < nbasis; j++) {
+      PVdagM.Op(subspace[j], ftmp);
+      for (int i = 0; i < nbasis; i++)
+        W(i,j) = TensorRemove(innerProduct(subspace[i], ftmp));
+    }
+    RealD normW = W.norm();
+    std::cout << GridLogMessage << "Fine projected matrix ||W|| = " << normW << std::endl;
+
+    Eigen::MatrixXcd C = Eigen::MatrixXcd::Zero(nbasis, nbasis);
+    CoarseVector Ac(Coarse5d);
+    for (int l = 0; l < nbasis; l++) {
+      LinOpCoarse.Op(psi_coarse[l], Ac);
+      for (int k = 0; k < nbasis; k++)
+        C(k,l) = TensorRemove(innerProduct(psi_coarse[k], Ac));
+    }
+    RealD normC      = C.norm();
+    RealD normCmCdag = (C - C.adjoint()).norm();
+    std::cout << GridLogMessage << "Coarse null matrix ||C||            = " << normC << std::endl;
+    std::cout << GridLogMessage << "Coarse null matrix ||C - C†||/||C|| = " << normCmCdag/normC << std::endl;
+    std::cout << GridLogMessage << "Galerkin check ||C||/||W||          = " << normC/normW << std::endl;
+  }
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 1→2: set up aggregation using psi_coarse as subspace.
+  // Block factor 2,2,3,2 (removes odd local sublattice in z given MPI
+  // geometry 3×6×4×4 where z-local at Level 1 is 6).
+  // psi_coarse are assigned directly; CoarsenOperator performs
+  // block-GS orthogonalisation before building LinOpCoarseCoarse.
+  //////////////////////////////////////////////////////////////////////
+  // innerProduct(CoarseSiteObj, CoarseSiteObj) returns iScalar<vTComplex>, so CComplex
+  // for the L1→L2 level must be iScalar<vTComplex>, not vTComplex.
+  typedef typename CoarseVector::vector_object                            CoarseSiteObj;
+  typedef iScalar<vTComplex>                                              vTTComplex;
+  typedef GeneralCoarsenedMatrix<CoarseSiteObj,vTTComplex,NB>            LittleDiracOperatorL2;
+  typedef typename LittleDiracOperatorL2::CoarseVector                   CoarseCoarseVector;
+  typedef Aggregation<CoarseSiteObj,vTTComplex,NB>                       SubspaceL2;
+  typedef MGPreconditioner<CoarseSiteObj,vTTComplex,NB>                  L1to2MG;
+
+  SubspaceL2 AggregatesL2(CoarseCoarse5d, Coarse5d, cb);
+  for (int k = 0; k < nbasis; k++)
+    AggregatesL2.subspace[k] = psi_coarse[k];
+
+  NextToNearestStencilGeometry5D geom2(CoarseCoarse5d);
+  LittleDiracOperatorL2 LittleDiracOpL2(geom2, Coarse5d, CoarseCoarse5d);
+  LittleDiracOpL2.CoarsenOperator(LinOpCoarse, AggregatesL2);
+
+  NonHermitianLinearOperator<LittleDiracOperatorL2,CoarseCoarseVector> LinOpCC(LittleDiracOpL2);
+
+  TrivialPrecon<CoarseCoarseVector> simpleCC;
+
+  //////////////////////////////////////////////////////////////////////
+  // Lüscher deflation guesser for L3PGCR.
+  // Step 1: project psi_coarse[k] (promoted fine null vectors) to
+  //         CoarseCoarseVector space — these cover the zero-momentum
+  //         component of the near-null space of LinOpCC.
+  // Step 2: breed Nextra additional null vectors directly on LinOpCC
+  //         using GCR with random sources — these pick up near-null
+  //         modes at all spatial frequencies not spanned by step 1.
+  // Step 3: build C_{st} = <psi_cc[s]|LinOpCC|psi_cc[t]> over the
+  //         full augmented basis and invert directly via Eigen LU.
+  //////////////////////////////////////////////////////////////////////
+  std::vector<CoarseCoarseVector> psi_cc(nbasis, CoarseCoarse5d);
+  for (int k = 0; k < nbasis; k++)
+    AggregatesL2.ProjectToSubspace(psi_cc[k], psi_coarse[k]);
+
+  {
+    int Nextra = nbasis;  // breed as many extra as we have promoted ones
+    if ( getenv("CC_NEXTRA") ) Nextra = atoi(getenv("CC_NEXTRA"));
+    GridParallelRNG RNG_CC(CoarseCoarse5d);
+    RNG_CC.SeedFixedIntegers({11,13,17,19});
+    PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseVector>
+      nullGCR(1e-2, 200, LinOpCC, simpleCC, 32, 32);
+    CoarseCoarseVector tmp(CoarseCoarse5d);
+    for (int k = 0; k < Nextra; k++) {
+      CoarseCoarseVector src(CoarseCoarse5d);
+      gaussian(RNG_CC, src);
+      tmp = Zero();
+      nullGCR(src, tmp);
+      psi_cc.push_back(tmp);
+    }
+    std::cout << GridLogMessage << "LinOpCC deflation basis: " << nbasis
+              << " promoted + " << Nextra << " bred = " << psi_cc.size() << " total" << std::endl;
+  }
+
+  const int Naug = psi_cc.size();
+  Eigen::MatrixXcd Ccc = Eigen::MatrixXcd::Zero(Naug, Naug);
+  {
+    CoarseCoarseVector Acc(CoarseCoarse5d);
+    for (int l = 0; l < Naug; l++) {
+      LinOpCC.Op(psi_cc[l], Acc);
+      for (int k = 0; k < Naug; k++)
+        Ccc(k,l) = TensorRemove(innerProduct(psi_cc[k], Acc));
+    }
+  }
+  {
+    RealD normCcc      = Ccc.norm();
+    RealD normCccmCdag = (Ccc - Ccc.adjoint()).norm();
+    std::cout << GridLogMessage << "Coarse-coarse deflation matrix ||Ccc||              = " << normCcc << std::endl;
+    std::cout << GridLogMessage << "Coarse-coarse deflation matrix ||Ccc-Ccc†||/||Ccc|| = " << normCccmCdag/normCcc << std::endl;
+  }
+  Eigen::MatrixXcd Ccc_inv = Ccc.inverse();
+  LuscherGuesser<CoarseCoarseVector> CCDeflGuesser(psi_cc, Ccc_inv);
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 2 solver: plain GCR, no further coarsening
+  //////////////////////////////////////////////////////////////////////
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseVector> L3PGCR(1.0e-1,200,LinOpCC,simpleCC,16,16);
+  L3PGCR.Level(3);
+  L3PGCR.Name("CCouter");
+
+  //////////////////////////////////////////////////////////////////////
+  // Coarse-level GCR smoother for Level 1→2 V-cycle.
+  // Mirrors fine-grid SmootherGCR: shifted operator + fixed step count.
+  // coarse_smoother_shift and coarse_smoother_nstep are the tuning knobs.
+  //////////////////////////////////////////////////////////////////////
+  RealD coarse_smoother_shift = 0.01;
+  int   coarse_smoother_nstep = 12;
+  if(getenv("coarse_smoother_shift")) coarse_smoother_shift = atof(getenv("coarse_smoother_shift"));
+  if(getenv("coarse_smoother_nstep")) coarse_smoother_nstep = atoi(getenv("coarse_smoother_nstep"));
+     
+  ShiftedLinearOperator<CoarseVector> ShiftedLinOpCoarse(coarse_smoother_shift, LinOpCoarse);
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector> CoarseSmootherGCR(0.01,1,ShiftedLinOpCoarse,simpleC,coarse_smoother_nstep,coarse_smoother_nstep);
+  CoarseSmootherGCR.SetZeroGuess(1);   // smoother slot: caller zeroes guess
+  CoarseSmootherGCR.Level(2);
+  CoarseSmootherGCR.Name("Csmoother");
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 1→2 V-cycle preconditioner.
+  //////////////////////////////////////////////////////////////////////
+  L1to2MG L1to2Precon(AggregatesL2,
+                       LinOpCoarse,
+                       simpleC,            // no pre-smoother (matches fine-grid setup)
+                       CoarseSmootherGCR,  // post-smoother: 12 GCR steps
+                       LinOpCC,
+                       L3PGCR,
+                       CCDeflGuesser);     // Lüscher guesser: psi_cc C^{-1} psi_cc†
+
+  //////////////////////////////////////////////////////////////////////
+  // Standalone Level 1 two-level solve test.
+  // Compare against plain PGCR baseline above.
+  //////////////////////////////////////////////////////////////////////
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<" Level 1 solve: two-level MG preconditioned PGCR"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector> L2MGsolver(3.0e-2,200,LinOpCoarse,L1to2Precon,16,16);
+  L2MGsolver.Level(2);
+  L2MGsolver.Name("Couter");
+  c_res = Zero();
+  L2MGsolver(c_src,c_res);
+
+  std::cout << GridLogMessage << "Level 1 two-level test: PVdagM operator uses:" << std::endl;
+  PVdagM.getApplications();
+  PVdagM.clear();
+
+  //////////////////////////////////////////////////////////////////////
+  // Full three-level outer solve
+  //////////////////////////////////////////////////////////////////////
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<" Three-level outer solve"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+
+  PrecGeneralisedConjugateResidualNonHermitian<LatticeFermionD> SmootherGCR(0.01,1,ShiftedPVdagM,simple_fine,16,16);
+  SmootherGCR.SetZeroGuess(1);         // pre/post smoother slots zero their guess
+  SmootherGCR.Level(1);
+  SmootherGCR.Name("Fsmoother");
+
+  f_src = one;
+
+  // Pre-smoother: none (TrivialPrecon); post-smoother: shifted PGCR.
+  // Coarse solver: L2MGsolver (PGCR preconditioned by Level 1→2 V-cycle).
+  TwoLevelMG ThreeLevelPrecon(AggregatesPD,
+                               PVdagM,
+                               simple_fine,
+                               SmootherGCR,
+                               LinOpCoarse,
+                               L2MGsolver,
+                               simpleC);
+
+  PrecGeneralisedConjugateResidualNonHermitian<LatticeFermion> L1PGCR(1.0e-8,1000,PVdagM,ThreeLevelPrecon,16,16);
+  L1PGCR.Level(1);
+  L1PGCR.Name("Fouter");
+
+  f_res = Zero();
+  L1PGCR(f_src,f_res);
+
+  std::cout << GridLogMessage << "Three-level outer solve: PVdagM operator uses:" << std::endl;
+  PVdagM.getApplications();
+  PVdagM.clear();
+}
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  const int Ls   = 24;
+  RealD     M5   = 1.8;
+  RealD     b    = 1.5;
+  RealD     c    = 0.5;
+  RealD     mass = 0.00078;
+  if ( getenv("MASS") ) mass = atof(getenv("MASS"));
+
+  const int nbasis = 60;
+
+  std::cout << GridLogMessage << "Mass: " << mass << ", Ls: " << Ls << ", b=" << b << ", c=" << c << std::endl;
+  std::cout << GridLogMessage << "nbasis: " << nbasis << std::endl;
+
+  std::vector<int> lat_size {48, 48, 48, 96};
+
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(lat_size, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Level 1 coarse grid: block 2^4 from fine (48×48×48×96 → 24×24×24×48, Ls=1)
+  Coordinate clatt = lat_size;
+  for (int d = 0; d < 4; d++) clatt[d] /= 2;
+  std::cout << GridLogMessage << "Level 1 coarse lattice: " << clatt << std::endl;
+
+  GridCartesian *Coarse4d  = SpaceTimeGrid::makeFourDimGrid(clatt, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *Coarse5d  = SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+
+  // Level 2 coarse-coarse grid: block 2,2,3,3 from Level 1 (24×24×24×48 → 12×12×8×16, Ls=1).
+  // MPI geometry 3.6.4.4 (288 ranks): fine local {16,8,12,24}.
+  // Level 1 local {8,4,6,12}; Level 2 local {4,2,2,4}.
+  // z blocked by 3: z-Level1-local=6; 6/3=2 (even), 6/2=3 (odd) → must use 3.
+  // t blocked by 3: t-Level1-local=12; 12/3=4 divisible by Nsimd=4 (gen-simd-width=64).
+  //   t-block=2 gives t2-local=6, 6 mod 4 ≠ 0, fails Grid SIMD assertion. ✓
+  // With {4,2,2,4}: Nsimd=4 goes into x or t (both =4). ✓
+  Coordinate clatt2 = clatt;
+  clatt2[0] /= 2;
+  clatt2[1] /= 2;
+  clatt2[2] /= 3;
+  clatt2[3] /= 3;
+  std::cout << GridLogMessage << "Level 2 coarse-coarse lattice: " << clatt2 << std::endl;
+
+  GridCartesian *CoarseCoarse4d = SpaceTimeGrid::makeFourDimGrid(clatt2, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *CoarseCoarse5d = SpaceTimeGrid::makeFiveDimGrid(1,CoarseCoarse4d);
+
+  std::vector<int> seeds4({1,2,3,4});
+  std::vector<int> seeds5({5,6,7,8});
+  GridParallelRNG  RNG5(FGrid);  RNG5.SeedFixedIntegers(seeds5);
+  GridParallelRNG  RNG4(UGrid);  RNG4.SeedFixedIntegers(seeds4);
+
+  LatticeGaugeField Umu(UGrid);
+  std::cout << GridLogMessage << "Reading gauge field" << std::endl;
+  FieldMetaData header;
+  std::string file("/ccs/home/poare/ckpoint_lat.1000");
+  NerscIO::readConfiguration(Umu,header,file);
+
+  RealD b_ = 1.5;
+  RealD c_ = 0.5;
+  MobiusFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5,b_,c_);
+  MobiusFermionD Dpv (Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,1.0, M5,b_,c_);
+
+  typedef PVdagMLinearOperator<MobiusFermionD,LatticeFermionD>        PVdagM_t;
+  typedef ShiftedPVdagMLinearOperator<MobiusFermionD,LatticeFermionD> ShiftedPVdagM_t;
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis>  LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector                           CoarseVector;
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis>             Subspace;
+  typedef MGPreconditioner<vSpinColourVector,vTComplex,nbasis>        TwoLevelMG;
+
+  PVdagM_t        PVdagM(Ddwf,Dpv);
+  ShiftedPVdagM_t ShiftedPVdagM(0.01,Ddwf,Dpv);
+
+  NextToNearestStencilGeometry5D geom(Coarse5d);
+
+  // Subspace cache: save after generation, reload on subsequent runs to skip expensive setup.
+  // Set SUBSPACE_FILE to override the default path.
+  std::string subspace_file = "/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/subspace_nb"
+                              + std::to_string(nbasis) + ".scidac";
+  if ( getenv("SUBSPACE_FILE") ) subspace_file = std::string(getenv("SUBSPACE_FILE"));
+
+  // Check if subspace file exists (boss rank checks, result broadcast via GlobalSum).
+  uint64_t file_exists = 0;
+  if ( UGrid->IsBoss() ) {
+    std::ifstream f(subspace_file);
+    file_exists = f.good() ? 1 : 0;
+  }
+  UGrid->GlobalSum(file_exists);
+
+  const int cb = 0;
+  Subspace AggregatesGCR(Coarse5d,FGrid,cb);
+
+  if ( file_exists ) {
+    std::cout << GridLogMessage << "*** Loading subspace from disk ***" << std::endl;
+    loadSubspace(AggregatesGCR.subspace, subspace_file);
+    // Insurance: GLOBAL (whole-lattice) orthonormalise, matching CreateSubspaceGCR
+    // (Aggregates.h:196), in case the cached file predates it.  Span-preserving
+    // and globally orthonormal -- NOT the block Orthogonalise() below, which would
+    // defeat the raw-null discipline (runMG promotes the RAW subspace to build L2;
+    // block-GS here -> psi_coarse = e_k).  The raw copy in runMG happens AFTER this.
+    AggregatesGCR.GlobalOrthonormalise();
+    //    AggregatesGCR.Orthogonalise();
+    std::cout << GridLogMessage << "Subspace loaded, globally orthonormalised (raw block basis preserved)." << std::endl;
+  } else {
+    std::cout << GridLogMessage << "*** GCR subspace generation ***" << std::endl;
+    AggregatesGCR.CreateSubspaceGCR(RNG5,PVdagM,nbasis);
+    std::cout << GridLogMessage << "Subspace generation: PVdagM operator uses:" << std::endl;
+    PVdagM.getApplications();
+    PVdagM.clear();
+    saveSubspace(AggregatesGCR.subspace, subspace_file);
+    std::cout << GridLogMessage << "Subspace saved to: " << subspace_file << std::endl;
+  }
+
+  runMG<nbasis,PVdagM_t,ShiftedPVdagM_t,Subspace,LittleDiracOperator,CoarseVector,TwoLevelMG>(
+    FGrid,
+    Coarse5d,
+    CoarseCoarse5d,
+    geom,
+    PVdagM,
+    ShiftedPVdagM,
+    AggregatesGCR
+  );
+
+  std::cout << GridLogMessage << "Done" << std::endl;
+  Grid_finalize();
+  return 0;
+}

examples/Example_pvdagm_3level_madj.cc

@@ -0,0 +1,625 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./examples/Example_pvdagm_3level.cc
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#include <Grid/Grid.h>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidual.h>
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.h>
+#include <Grid/algorithms/iterative/BiCGSTAB.h>
+
+using namespace std;
+using namespace Grid;
+
+template <class T> void readFile(T& out, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Reading: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacReader SR;
+    SR.open(fname);
+    SR.readScidacFieldRecord(out, record);
+    SR.close();
+  #endif
+}
+
+template <class T> void writeFile(T& in, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Writing: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacWriter SW(in.Grid()->IsBoss());
+    SW.open(fname);
+    SW.writeScidacFieldRecord(in, record);
+    SW.close();
+  #endif
+}
+
+template <class Field>
+void saveSubspace(std::vector<Field> &subspace, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Saving subspace (" << subspace.size() << " vectors) to: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacWriter SW(subspace[0].Grid()->IsBoss());
+    SW.open(fname);
+    for (int k = 0; k < (int)subspace.size(); k++)
+      SW.writeScidacFieldRecord(subspace[k], record);
+    SW.close();
+  #endif
+}
+
+template <class Field>
+void loadSubspace(std::vector<Field> &subspace, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Loading subspace (" << subspace.size() << " vectors) from: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacReader SR;
+    SR.open(fname);
+    for (int k = 0; k < (int)subspace.size(); k++)
+      SR.readScidacFieldRecord(subspace[k], record);
+    SR.close();
+  #endif
+}
+
+template<class Matrix,class Field>
+class PVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+  int nApp;
+  int nAppDag;
+public:
+  PVdagMLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV), nApp(0), nAppDag(0) {};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+    nApp++;
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(in,tmp);
+    _Mat.Mdag(tmp,out);
+    nAppDag++;
+  }
+  void clear() { nApp = 0; nAppDag = 0; }
+  void getApplications() {
+    std::cout << GridLogMessage << "# applications of PVdagM: " << nApp << std::endl;
+    std::cout << GridLogMessage << "# applications of PVdagM^dag: " << nAppDag << std::endl;
+    std::cout << GridLogMessage << "# applications total: " << nApp + nAppDag << std::endl;
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+template<class Matrix,class Field>
+class MdagPVLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+public:
+  MdagPVLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV){};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(in,tmp);
+    _Mat.Mdag(tmp,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+template<class Matrix,class Field>
+class ShiftedPVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+  RealD shift;
+public:
+  ShiftedPVdagMLinearOperator(RealD _shift,Matrix &Mat,Matrix &PV): shift(_shift),_Mat(Mat),_PV(PV){};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+    out = out + shift * in;
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(tmp,out);
+    _Mat.Mdag(in,tmp);
+    out = out + shift * in;
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){ assert(0); }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+template<class Fobj,class CComplex,int nbasis>
+class MGPreconditioner : public LinearFunction< Lattice<Fobj> > {
+public:
+  using LinearFunction<Lattice<Fobj> >::operator();
+
+  typedef Aggregation<Fobj,CComplex,nbasis> Aggregates;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::FineField    FineField;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseVector CoarseVector;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseMatrix CoarseMatrix;
+  typedef LinearOperatorBase<FineField>                            FineOperator;
+  typedef LinearFunction    <FineField>                            FineSmoother;
+  typedef LinearOperatorBase<CoarseVector>                         CoarseOperator;
+  typedef LinearFunction    <CoarseVector>                         CoarseSolver;
+
+  Aggregates     & _Aggregates;
+  FineOperator   & _FineOperator;
+  FineSmoother   & _PreSmoother;
+  FineSmoother   & _PostSmoother;
+  CoarseOperator & _CoarseOperator;
+  CoarseSolver   & _CoarseSolve;
+  CoarseSolver   & _CoarseGuesser;
+  std::string      _name;
+  
+  int    level;  void Level(int lv) {level = lv; };
+
+  MGPreconditioner(Aggregates &Agg,
+		   FineOperator &Fine,
+		   FineSmoother &PreSmoother,
+		   FineSmoother &PostSmoother,
+		   CoarseOperator &CoarseOperator_,
+		   CoarseSolver &CoarseSolve_,
+		   CoarseSolver &CoarseGuesser_,
+		   std::string name = std::string("unnamed"))
+    : _Aggregates(Agg),
+      _FineOperator(Fine),
+      _PreSmoother(PreSmoother),
+      _PostSmoother(PostSmoother),
+      _CoarseOperator(CoarseOperator_),
+      _CoarseSolve(CoarseSolve_),
+      _CoarseGuesser(CoarseGuesser_),
+      _name(name),
+      level(1)  {  }
+
+  virtual void operator()(const FineField &in, FineField & out)
+  {
+    GridBase *CoarseGrid = _Aggregates.CoarseGrid;
+    CoarseVector Csrc(CoarseGrid);
+    CoarseVector Csol(CoarseGrid);
+    FineField vec1(in.Grid());
+    FineField vec2(in.Grid());
+
+    double t;
+    out = Zero();
+    t=-usecond();
+    _PreSmoother(in,out);
+    t+=usecond();
+    std::cout<<GridLogMessage << _name << "PreSmoother took "<< t/1000.0<< "ms" <<std::endl;
+
+    _FineOperator.Op(out,vec1);  sub(vec1, in ,vec1);
+
+    t=-usecond();
+    _Aggregates.ProjectToSubspace(Csrc,vec1);
+    t+=usecond();
+    std::cout<<GridLogMessage << "Project to coarse took "<< t/1000.0<< "ms" <<std::endl;
+
+    t=-usecond();
+    _CoarseGuesser(Csrc,Csol);
+    _CoarseSolve(Csrc,Csol);
+    t+=usecond();
+    std::cout<<GridLogMessage << "Coarse solve took "<< t/1000.0<< "ms" <<std::endl;
+
+    t=-usecond();
+    _Aggregates.PromoteFromSubspace(Csol,vec1);
+    add(out,out,vec1);
+    t+=usecond();
+    std::cout<<GridLogMessage << _name << "Promote to this level took "<< t/1000.0<< "ms" <<std::endl;
+
+    _FineOperator.Op(out,vec1);  sub(vec1 ,in , vec1);
+
+    t=-usecond();
+    vec2=Zero();
+    _PostSmoother(vec1,vec2);
+    t+=usecond();
+    std::cout<<GridLogMessage << _name <<"PostSmoother took "<< t/1000.0<< "ms" <<std::endl;
+
+    add(out,out,vec2);
+  }
+};
+
+// Generic shifted linear operator: wraps any LinearOperatorBase and adds shift*I.
+// Used to condition the coarse-level GCR smoother, analogous to ShiftedPVdagMLinearOperator
+// at the fine level.
+template<class Field>
+class ShiftedLinearOperator : public LinearOperatorBase<Field> {
+  LinearOperatorBase<Field> &_Op;
+  RealD shift;
+public:
+  ShiftedLinearOperator(RealD _shift, LinearOperatorBase<Field> &Op) : shift(_shift), _Op(Op) {}
+  void OpDiag   (const Field &in, Field &out)                         { assert(0); }
+  void OpDir    (const Field &in, Field &out, int dir, int disp)      { assert(0); }
+  void OpDirAll (const Field &in, std::vector<Field> &out)            { assert(0); }
+  void Op       (const Field &in, Field &out) { _Op.Op(in, out);    out = out + shift * in; }
+  void AdjOp    (const Field &in, Field &out) { _Op.AdjOp(in, out); out = out + shift * in; }
+  void HermOpAndNorm(const Field &in, Field &out, RealD &n1, RealD &n2) { assert(0); }
+  void HermOp   (const Field &in, Field &out) { Field tmp(in.Grid()); Op(in,tmp); AdjOp(tmp,out); }
+};
+
+template<int NB, class PVdagM_t, class ShiftedPVdagM_t, class Subspace, class LittleDiracOperator, class CoarseVector, class TwoLevelMG>
+void runMG(
+  GridCartesian *FGrid,
+  GridCartesian *Coarse5d,
+  GridCartesian *CoarseCoarse5d,
+  NextToNearestStencilGeometry5D geom,
+  PVdagM_t &PVdagM,
+  ShiftedPVdagM_t &ShiftedPVdagM,
+  Subspace &AggregatesPD
+) {
+  std::vector<LatticeFermion> subspace = AggregatesPD.subspace;
+  assert((int)subspace.size() == NB);
+  const int nbasis = NB;
+  const int cb = 0;
+
+  CoarseVector c_src(Coarse5d);
+  CoarseVector c_res(Coarse5d);
+  Complex one(1.0);
+
+  LatticeFermionD f_src(FGrid);
+  LatticeFermionD f_res(FGrid);
+
+  TrivialPrecon<CoarseVector>      simpleC;
+  TrivialPrecon<LatticeFermionD>   simple_fine;
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 0→1: coarsen PVdagM, build LinOpCoarse
+  //////////////////////////////////////////////////////////////////////
+  LittleDiracOperator LittleDiracOpPV(geom, FGrid, Coarse5d);
+  LittleDiracOpPV.CoarsenOperator(PVdagM, AggregatesPD);
+
+  NonHermitianLinearOperator<LittleDiracOperator,CoarseVector> LinOpCoarse(LittleDiracOpPV);
+
+  //////////////////////////////////////////////////////////////////////
+  // Baseline: plain PGCR on LinOpCoarse (reference for comparison)
+  //////////////////////////////////////////////////////////////////////
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<" Level 1 solve: plain PGCR baseline"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector> L2PGCR_baseline(3.0e-2,1100,LinOpCoarse,simpleC,10,10);
+  L2PGCR_baseline.Level(2);
+  c_src = one;
+  c_res = Zero();
+  L2PGCR_baseline(c_src,c_res);
+  PVdagM.getApplications();
+  PVdagM.clear();
+
+  //////////////////////////////////////////////////////////////////////
+  // psi_coarse: coarse projections of pre-GS fine null vectors.
+  // These are the Level 1 near-null vectors, promoted from Level 0.
+  // Used as the aggregation basis for Level 1→2 coarsening.
+  //////////////////////////////////////////////////////////////////////
+  std::vector<CoarseVector> psi_coarse(nbasis, Coarse5d);
+  for (int k = 0; k < nbasis; k++)
+    AggregatesPD.ProjectToSubspace(psi_coarse[k], subspace[k]);
+
+  //////////////////////////////////////////////////////////////////////
+  // Diagnostics: W (fine projected matrix) and C (Galerkin check)
+  //////////////////////////////////////////////////////////////////////
+  {
+    Eigen::MatrixXcd W = Eigen::MatrixXcd::Zero(nbasis, nbasis);
+    LatticeFermion ftmp(FGrid);
+    for (int j = 0; j < nbasis; j++) {
+      PVdagM.Op(subspace[j], ftmp);
+      for (int i = 0; i < nbasis; i++)
+        W(i,j) = TensorRemove(innerProduct(subspace[i], ftmp));
+    }
+    RealD normW = W.norm();
+    std::cout << GridLogMessage << "Fine projected matrix ||W|| = " << normW << std::endl;
+
+    Eigen::MatrixXcd C = Eigen::MatrixXcd::Zero(nbasis, nbasis);
+    CoarseVector Ac(Coarse5d);
+    for (int l = 0; l < nbasis; l++) {
+      LinOpCoarse.Op(psi_coarse[l], Ac);
+      for (int k = 0; k < nbasis; k++)
+        C(k,l) = TensorRemove(innerProduct(psi_coarse[k], Ac));
+    }
+    RealD normC      = C.norm();
+    RealD normCmCdag = (C - C.adjoint()).norm();
+    std::cout << GridLogMessage << "Coarse null matrix ||C||            = " << normC << std::endl;
+    std::cout << GridLogMessage << "Coarse null matrix ||C - C†||/||C|| = " << normCmCdag/normC << std::endl;
+    std::cout << GridLogMessage << "Galerkin check ||C||/||W||          = " << normC/normW << std::endl;
+  }
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 1→2: set up aggregation using psi_coarse as subspace.
+  // Block factor 2,2,3,2 (removes odd local sublattice in z given MPI
+  // geometry 3×6×4×4 where z-local at Level 1 is 6).
+  // psi_coarse are assigned directly; CoarsenOperator performs
+  // block-GS orthogonalisation before building LinOpCoarseCoarse.
+  //////////////////////////////////////////////////////////////////////
+  // innerProduct(CoarseSiteObj, CoarseSiteObj) returns iScalar<vTComplex>, so CComplex
+  // for the L1→L2 level must be iScalar<vTComplex>, not vTComplex.
+  typedef typename CoarseVector::vector_object                            CoarseSiteObj;
+  typedef iScalar<vTComplex>                                              vTTComplex;
+  typedef GeneralCoarsenedMatrix<CoarseSiteObj,vTTComplex,NB>            LittleDiracOperatorL2;
+  typedef typename LittleDiracOperatorL2::CoarseVector                   CoarseCoarseVector;
+  typedef Aggregation<CoarseSiteObj,vTTComplex,NB>                       SubspaceL2;
+  typedef MGPreconditioner<CoarseSiteObj,vTTComplex,NB>                  L1to2MG;
+
+  SubspaceL2 AggregatesL2(CoarseCoarse5d, Coarse5d, cb);
+  for (int k = 0; k < nbasis; k++)
+    AggregatesL2.subspace[k] = psi_coarse[k];
+
+  NextToNearestStencilGeometry5D geom2(CoarseCoarse5d);
+  LittleDiracOperatorL2 LittleDiracOpL2(geom2, Coarse5d, CoarseCoarse5d);
+  LittleDiracOpL2.CoarsenOperator(LinOpCoarse, AggregatesL2);
+
+  NonHermitianLinearOperator<LittleDiracOperatorL2,CoarseCoarseVector> LinOpCC(LittleDiracOpL2);
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 2 solver: plain GCR, no further coarsening
+  //////////////////////////////////////////////////////////////////////
+  TrivialPrecon<CoarseCoarseVector> simpleCC;
+  // L3PGCR is an inner solver inside the L1→2 V-cycle; does not need to converge
+  // to fine-grid precision. Loose tolerance (3e-2) and large restart (64) to allow
+  // the Krylov space to span enough of the near-null spectrum of LinOpCC per cycle.
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseVector> L3PGCR(1.0e-4,5,LinOpCC,simpleCC,64,64);
+  L3PGCR.Level(3);
+
+  //////////////////////////////////////////////////////////////////////
+  // Coarse-level GCR smoother for Level 1→2 V-cycle.
+  // Mirrors fine-grid SmootherGCR: shifted operator + fixed step count.
+  // coarse_smoother_shift and coarse_smoother_nstep are the tuning knobs.
+  //////////////////////////////////////////////////////////////////////
+  RealD coarse_smoother_shift = 0.0;
+  int   coarse_smoother_nstep = 8;
+  if(getenv("coarse_smoother_shift")) coarse_smoother_shift = atof(getenv("coarse_smoother_shift"));
+  if(getenv("coarse_smoother_nstep")) coarse_smoother_nstep = atoi(getenv("coarse_smoother_nstep"));
+     
+  ShiftedLinearOperator<CoarseVector> ShiftedLinOpCoarse(coarse_smoother_shift, LinOpCoarse);
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector> CoarseSmootherGCR(0.0,1,ShiftedLinOpCoarse,simpleC,coarse_smoother_nstep,coarse_smoother_nstep);
+  CoarseSmootherGCR.Level(2);
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 1→2 V-cycle preconditioner.
+  //////////////////////////////////////////////////////////////////////
+  L1to2MG L1to2Precon(AggregatesL2,
+		      LinOpCoarse,
+		      simpleC,            // no pre-smoother (matches fine-grid setup)
+		      CoarseSmootherGCR,  // post-smoother: 12 GCR steps
+		      LinOpCC,
+		      L3PGCR,
+		      simpleCC,
+		      std::string("LinOpC"));
+
+  //////////////////////////////////////////////////////////////////////
+  // Standalone Level 1 two-level solve test.
+  // Compare against plain PGCR baseline above.
+  //////////////////////////////////////////////////////////////////////
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<" Level 1 solve: two-level MG preconditioned PGCR"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector> L2MGsolver(3.0e-2,200,LinOpCoarse,L1to2Precon,16,16);
+  L2MGsolver.Level(2);
+  c_res = Zero();
+  L2MGsolver(c_src,c_res);
+
+  std::cout << GridLogMessage << "Level 1 two-level test: PVdagM operator uses:" << std::endl;
+  PVdagM.getApplications();
+  PVdagM.clear();
+
+  //////////////////////////////////////////////////////////////////////
+  // Full three-level outer solve
+  //////////////////////////////////////////////////////////////////////
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<" Three-level outer solve"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+
+  PrecGeneralisedConjugateResidualNonHermitian<LatticeFermionD> SmootherGCR(0.00,1,ShiftedPVdagM,simple_fine,16,16);
+  SmootherGCR.Level(1);
+
+  f_src = one;
+
+  // Pre-smoother: none (TrivialPrecon); post-smoother: shifted PGCR.
+  // Coarse solver: L2MGsolver (PGCR preconditioned by Level 1→2 V-cycle).
+  TwoLevelMG ThreeLevelPrecon(AggregatesPD,
+			      PVdagM,
+			      simple_fine,
+			      SmootherGCR,
+			      LinOpCoarse,
+			      L2MGsolver,
+			      simpleC,
+			      std::string("PVdagM"));
+
+  PrecGeneralisedConjugateResidualNonHermitian<LatticeFermion> L1PGCR(1.0e-8,1000,PVdagM,ThreeLevelPrecon,16,16);
+  L1PGCR.Level(1);
+
+  f_res = Zero();
+  L1PGCR(f_src,f_res);
+
+  std::cout << GridLogMessage << "Three-level outer solve: PVdagM operator uses:" << std::endl;
+  PVdagM.getApplications();
+  PVdagM.clear();
+}
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  const int Ls   = 24;
+  RealD     M5   = 1.8;
+  RealD     b    = 1.5;
+  RealD     c    = 0.5;
+  RealD     mass = 0.00078;
+  if ( getenv("MASS") ) mass = atof(getenv("MASS"));
+
+  const int nbasis = 60;
+
+  std::cout << GridLogMessage << "Mass: " << mass << ", Ls: " << Ls << ", b=" << b << ", c=" << c << std::endl;
+  std::cout << GridLogMessage << "nbasis: " << nbasis << std::endl;
+
+  std::vector<int> lat_size {48, 48, 48, 96};
+
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(lat_size, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Level 1 coarse grid: block 2^4 from fine (48×48×48×96 → 24×24×24×48, Ls=1)
+  Coordinate clatt = lat_size;
+  for (int d = 0; d < 4; d++) clatt[d] /= 2;
+  std::cout << GridLogMessage << "Level 1 coarse lattice: " << clatt << std::endl;
+
+  GridCartesian *Coarse4d  = SpaceTimeGrid::makeFourDimGrid(clatt, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *Coarse5d  = SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+
+  // Level 2 coarse-coarse grid: block 2,2,3,3 from Level 1 (24×24×24×48 → 12×12×8×16, Ls=1).
+  // MPI geometry 3.6.4.4 (288 ranks): fine local {16,8,12,24}.
+  // Level 1 local {8,4,6,12}; Level 2 local {4,2,2,4}.
+  // z blocked by 3: z-Level1-local=6; 6/3=2 (even), 6/2=3 (odd) → must use 3.
+  // t blocked by 3: t-Level1-local=12; 12/3=4 divisible by Nsimd=4 (gen-simd-width=64).
+  //   t-block=2 gives t2-local=6, 6 mod 4 ≠ 0, fails Grid SIMD assertion. ✓
+  // With {4,2,2,4}: Nsimd=4 goes into x or t (both =4). ✓
+  Coordinate clatt2 = clatt;
+  clatt2[0] /= 2;
+  clatt2[1] /= 2;
+  clatt2[2] /= 3;
+  clatt2[3] /= 3;
+  std::cout << GridLogMessage << "Level 2 coarse-coarse lattice: " << clatt2 << std::endl;
+
+  GridCartesian *CoarseCoarse4d = SpaceTimeGrid::makeFourDimGrid(clatt2, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *CoarseCoarse5d = SpaceTimeGrid::makeFiveDimGrid(1,CoarseCoarse4d);
+
+  std::vector<int> seeds4({1,2,3,4});
+  std::vector<int> seeds5({5,6,7,8});
+  GridParallelRNG  RNG5(FGrid);  RNG5.SeedFixedIntegers(seeds5);
+  GridParallelRNG  RNG4(UGrid);  RNG4.SeedFixedIntegers(seeds4);
+
+  LatticeGaugeField Umu(UGrid);
+  std::cout << GridLogMessage << "Reading gauge field" << std::endl;
+  FieldMetaData header;
+  std::string file("/ccs/home/poare/ckpoint_lat.1000");
+  NerscIO::readConfiguration(Umu,header,file);
+
+  RealD b_ = 1.5;
+  RealD c_ = 0.5;
+
+  RealD madj = 1.0;
+  if ( getenv("MADJ") ) madj=atof(getenv("MADJ"));
+  std::cout << "PV mass set to "<<madj<<std::endl;
+
+  MobiusFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5,b_,c_);
+  MobiusFermionD Dpv (Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,madj, M5,b_,c_);
+
+  typedef PVdagMLinearOperator<MobiusFermionD,LatticeFermionD>        PVdagM_t;
+  typedef ShiftedPVdagMLinearOperator<MobiusFermionD,LatticeFermionD> ShiftedPVdagM_t;
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis>  LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector                           CoarseVector;
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis>             Subspace;
+  typedef MGPreconditioner<vSpinColourVector,vTComplex,nbasis>        TwoLevelMG;
+
+  PVdagM_t        PVdagM(Ddwf,Dpv);
+  ShiftedPVdagM_t ShiftedPVdagM(0.00,Ddwf,Dpv);
+
+  NextToNearestStencilGeometry5D geom(Coarse5d);
+
+  // Subspace cache: save after generation, reload on subsequent runs to skip expensive setup.
+  // Set SUBSPACE_FILE to override the default path.
+  std::string subspace_file = "/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/subspace_nb"
+                              + std::to_string(nbasis) + ".scidac";
+  if ( getenv("SUBSPACE_FILE") ) subspace_file = std::string(getenv("SUBSPACE_FILE"));
+
+  // Check if subspace file exists (boss rank checks, result broadcast via GlobalSum).
+  uint64_t file_exists = 0;
+  if ( UGrid->IsBoss() ) {
+    std::ifstream f(subspace_file);
+    file_exists = f.good() ? 1 : 0;
+  }
+  UGrid->GlobalSum(file_exists);
+
+  const int cb = 0;
+  Subspace AggregatesGCR(Coarse5d,FGrid,cb);
+
+  if ( file_exists ) {
+    std::cout << GridLogMessage << "*** Loading subspace from disk ***" << std::endl;
+    loadSubspace(AggregatesGCR.subspace, subspace_file);
+    // Re-orthogonalise after loading to ensure block-GS condition holds.
+    //    AggregatesGCR.Orthogonalise();
+    std::cout << GridLogMessage << "Subspace loaded and re-orthogonalised." << std::endl;
+  } else {
+    std::cout << GridLogMessage << "*** GCR subspace generation ***" << std::endl;
+    AggregatesGCR.CreateSubspaceGCR(RNG5,PVdagM,nbasis);
+    std::cout << GridLogMessage << "Subspace generation: PVdagM operator uses:" << std::endl;
+    PVdagM.getApplications();
+    PVdagM.clear();
+    saveSubspace(AggregatesGCR.subspace, subspace_file);
+    std::cout << GridLogMessage << "Subspace saved to: " << subspace_file << std::endl;
+  }
+
+  runMG<nbasis,PVdagM_t,ShiftedPVdagM_t,Subspace,LittleDiracOperator,CoarseVector,TwoLevelMG>(
+    FGrid,
+    Coarse5d,
+    CoarseCoarse5d,
+    geom,
+    PVdagM,
+    ShiftedPVdagM,
+    AggregatesGCR
+  );
+
+  std::cout << GridLogMessage << "Done" << std::endl;
+  Grid_finalize();
+  return 0;
+}

examples/Example_pvdagm_4level.cc

@@ -0,0 +1,798 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./examples/Example_pvdagm_3level.cc
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#include <Grid/Grid.h>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidual.h>
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.h>
+#include <Grid/algorithms/iterative/BiCGSTAB.h>
+
+using namespace std;
+using namespace Grid;
+
+template <class T> void readFile(T& out, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Reading: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacReader SR;
+    SR.open(fname);
+    SR.readScidacFieldRecord(out, record);
+    SR.close();
+  #endif
+}
+
+template <class T> void writeFile(T& in, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Writing: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacWriter SW(in.Grid()->IsBoss());
+    SW.open(fname);
+    SW.writeScidacFieldRecord(in, record);
+    SW.close();
+  #endif
+}
+
+template <class Field>
+void saveSubspace(std::vector<Field> &subspace, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Saving subspace (" << subspace.size() << " vectors) to: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacWriter SW(subspace[0].Grid()->IsBoss());
+    SW.open(fname);
+    for (int k = 0; k < (int)subspace.size(); k++)
+      SW.writeScidacFieldRecord(subspace[k], record);
+    SW.close();
+  #endif
+}
+
+template <class Field>
+void loadSubspace(std::vector<Field> &subspace, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Loading subspace (" << subspace.size() << " vectors) from: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacReader SR;
+    SR.open(fname);
+    for (int k = 0; k < (int)subspace.size(); k++)
+      SR.readScidacFieldRecord(subspace[k], record);
+    SR.close();
+  #endif
+}
+
+template<class Matrix,class Field>
+class PVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+  int nApp;
+  int nAppDag;
+public:
+  PVdagMLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV), nApp(0), nAppDag(0) {};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+    nApp++;
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(in,tmp);
+    _Mat.Mdag(tmp,out);
+    nAppDag++;
+  }
+  void clear() { nApp = 0; nAppDag = 0; }
+  void getApplications() {
+    std::cout << GridLogMessage << "# applications of PVdagM: " << nApp << std::endl;
+    std::cout << GridLogMessage << "# applications of PVdagM^dag: " << nAppDag << std::endl;
+    std::cout << GridLogMessage << "# applications total: " << nApp + nAppDag << std::endl;
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+template<class Matrix,class Field>
+class MdagPVLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+public:
+  MdagPVLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV){};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(in,tmp);
+    _Mat.Mdag(tmp,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+template<class Matrix,class Field>
+class ShiftedPVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+  RealD shift;
+public:
+  ShiftedPVdagMLinearOperator(RealD _shift,Matrix &Mat,Matrix &PV): shift(_shift),_Mat(Mat),_PV(PV){};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+    out = out + shift * in;
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(tmp,out);
+    _Mat.Mdag(in,tmp);
+    out = out + shift * in;
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){ assert(0); }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+// Lüscher deflated guesser (arXiv:0706.2298 Sec A.3) for a non-Hermitian solve.
+// C_{st} = <psi[s] | LinOp | psi[t]>;  guess = sum_s c_s psi[s]  where c = C^{-1} psi† src.
+template<class Field>
+class LuscherGuesser : public LinearFunction<Field> {
+  const std::vector<Field> &psi;
+  Eigen::MatrixXcd          C_inv;
+public:
+  using LinearFunction<Field>::operator();
+  LuscherGuesser(const std::vector<Field> &psi_, const Eigen::MatrixXcd &Cinv_)
+    : psi(psi_), C_inv(Cinv_) {}
+  virtual void operator()(const Field &src, Field &guess) {
+    int N = psi.size();
+    Eigen::VectorXcd b(N);
+    for (int t = 0; t < N; t++)
+      b(t) = TensorRemove(innerProduct(psi[t], src));
+    Eigen::VectorXcd c = C_inv * b;
+    guess = Zero();
+    for (int s = 0; s < N; s++)
+      guess += ComplexD(c(s)) * psi[s];
+  }
+};
+
+template<class Fobj,class CComplex,int nbasis>
+class MGPreconditioner : public LinearFunction< Lattice<Fobj> > {
+public:
+  using LinearFunction<Lattice<Fobj> >::operator();
+
+  typedef Aggregation<Fobj,CComplex,nbasis> Aggregates;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::FineField    FineField;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseVector CoarseVector;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseMatrix CoarseMatrix;
+  typedef LinearOperatorBase<FineField>                            FineOperator;
+  typedef LinearFunction    <FineField>                            FineSmoother;
+  typedef LinearOperatorBase<CoarseVector>                         CoarseOperator;
+  typedef LinearFunction    <CoarseVector>                         CoarseSolver;
+
+  Aggregates     & _Aggregates;
+  FineOperator   & _FineOperator;
+  FineSmoother   & _PreSmoother;
+  FineSmoother   & _PostSmoother;
+  CoarseOperator & _CoarseOperator;
+  CoarseSolver   & _CoarseSolve;
+  CoarseSolver   & _CoarseGuesser;
+
+  int    level;  void Level(int lv) {level = lv; };
+
+  MGPreconditioner(Aggregates &Agg,
+		   FineOperator &Fine,
+		   FineSmoother &PreSmoother,
+		   FineSmoother &PostSmoother,
+		   CoarseOperator &CoarseOperator_,
+		   CoarseSolver &CoarseSolve_,
+		   CoarseSolver &CoarseGuesser_)
+    : _Aggregates(Agg),
+      _FineOperator(Fine),
+      _PreSmoother(PreSmoother),
+      _PostSmoother(PostSmoother),
+      _CoarseOperator(CoarseOperator_),
+      _CoarseSolve(CoarseSolve_),
+      _CoarseGuesser(CoarseGuesser_),
+      level(1)  {  }
+
+  virtual void operator()(const FineField &in, FineField & out)
+  {
+    GridBase *CoarseGrid = _Aggregates.CoarseGrid;
+    CoarseVector Csrc(CoarseGrid);
+    CoarseVector Csol(CoarseGrid);
+    FineField vec1(in.Grid());
+    FineField vec2(in.Grid());
+
+    double t;
+    out = Zero();
+    t=-usecond();
+    _PreSmoother(in,out);
+    t+=usecond();
+    std::cout<<GridLogMessage << "PreSmoother took "<< t/1000.0<< "ms" <<std::endl;
+
+    _FineOperator.Op(out,vec1);  sub(vec1, in ,vec1);
+
+    t=-usecond();
+    _Aggregates.ProjectToSubspace(Csrc,vec1);
+    t+=usecond();
+    std::cout<<GridLogMessage << "Project to coarse took "<< t/1000.0<< "ms" <<std::endl;
+
+    t=-usecond();
+    _CoarseGuesser(Csrc,Csol);
+    _CoarseSolve(Csrc,Csol);
+    t+=usecond();
+    std::cout<<GridLogMessage << "Coarse solve took "<< t/1000.0<< "ms" <<std::endl;
+
+    t=-usecond();
+    _Aggregates.PromoteFromSubspace(Csol,vec1);
+    add(out,out,vec1);
+    t+=usecond();
+    std::cout<<GridLogMessage << "Promote to this level took "<< t/1000.0<< "ms" <<std::endl;
+
+    _FineOperator.Op(out,vec1);  sub(vec1 ,in , vec1);
+
+    t=-usecond();
+    vec2=Zero();
+    _PostSmoother(vec1,vec2);
+    t+=usecond();
+    std::cout<<GridLogMessage << "PostSmoother took "<< t/1000.0<< "ms" <<std::endl;
+
+    add(out,out,vec2);
+  }
+};
+
+// Generic shifted linear operator: wraps any LinearOperatorBase and adds shift*I.
+// Used to condition the coarse-level GCR smoother, analogous to ShiftedPVdagMLinearOperator
+// at the fine level.
+template<class Field>
+class ShiftedLinearOperator : public LinearOperatorBase<Field> {
+  LinearOperatorBase<Field> &_Op;
+  RealD shift;
+public:
+  ShiftedLinearOperator(RealD _shift, LinearOperatorBase<Field> &Op) : shift(_shift), _Op(Op) {}
+  void OpDiag   (const Field &in, Field &out)                         { assert(0); }
+  void OpDir    (const Field &in, Field &out, int dir, int disp)      { assert(0); }
+  void OpDirAll (const Field &in, std::vector<Field> &out)            { assert(0); }
+  void Op       (const Field &in, Field &out) { _Op.Op(in, out);    out = out + shift * in; }
+  void AdjOp    (const Field &in, Field &out) { _Op.AdjOp(in, out); out = out + shift * in; }
+  void HermOpAndNorm(const Field &in, Field &out, RealD &n1, RealD &n2) { assert(0); }
+  void HermOp   (const Field &in, Field &out) { Field tmp(in.Grid()); Op(in,tmp); AdjOp(tmp,out); }
+};
+
+template<int NB, class PVdagM_t, class ShiftedPVdagM_t, class Subspace, class LittleDiracOperator, class CoarseVector, class TwoLevelMG>
+void runMG(
+  GridCartesian *FGrid,
+  GridCartesian *Coarse5d,
+  GridCartesian *CoarseCoarse5d,
+  GridCartesian *CoarseCoarseCoarse5d,
+  NextToNearestStencilGeometry5D geom,
+  PVdagM_t &PVdagM,
+  ShiftedPVdagM_t &ShiftedPVdagM,
+  Subspace &AggregatesPD
+) {
+  std::vector<LatticeFermion> subspace = AggregatesPD.subspace;
+  assert((int)subspace.size() == NB);
+  const int nbasis = NB;
+  const int cb = 0;
+
+  CoarseVector c_src(Coarse5d);
+  CoarseVector c_res(Coarse5d);
+  Complex one(1.0);
+
+  LatticeFermionD f_src(FGrid);
+  LatticeFermionD f_res(FGrid);
+
+  TrivialPrecon<CoarseVector>      simpleC;
+  TrivialPrecon<LatticeFermionD>   simple_fine;
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 0→1: coarsen PVdagM, build LinOpCoarse
+  //////////////////////////////////////////////////////////////////////
+  LittleDiracOperator LittleDiracOpPV(geom, FGrid, Coarse5d);
+  LittleDiracOpPV.CoarsenOperator(PVdagM, AggregatesPD);
+
+  NonHermitianLinearOperator<LittleDiracOperator,CoarseVector> LinOpCoarse(LittleDiracOpPV);
+
+  //////////////////////////////////////////////////////////////////////
+  // Baseline: plain PGCR on LinOpCoarse (reference for comparison)
+  //////////////////////////////////////////////////////////////////////
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<" Level 1 solve: plain PGCR baseline"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector> L2PGCR_baseline(3.0e-2,1100,LinOpCoarse,simpleC,10,10);
+  L2PGCR_baseline.Level(2);
+  L2PGCR_baseline.Name("Cbaseline");
+  c_src = one;
+  c_res = Zero();
+  L2PGCR_baseline(c_src,c_res);
+
+  //////////////////////////////////////////////////////////////////////
+  // psi_coarse: coarse projections of pre-GS fine null vectors.
+  // These are the Level 1 near-null vectors, promoted from Level 0.
+  // Used as the aggregation basis for Level 1→2 coarsening.
+  //////////////////////////////////////////////////////////////////////
+  std::vector<CoarseVector> psi_coarse(nbasis, Coarse5d);
+  for (int k = 0; k < nbasis; k++)
+    AggregatesPD.ProjectToSubspace(psi_coarse[k], subspace[k]);
+
+  //////////////////////////////////////////////////////////////////////
+  // Diagnostics: W (fine projected matrix) and C (Galerkin check)
+  //////////////////////////////////////////////////////////////////////
+  {
+    Eigen::MatrixXcd W = Eigen::MatrixXcd::Zero(nbasis, nbasis);
+    LatticeFermion ftmp(FGrid);
+    for (int j = 0; j < nbasis; j++) {
+      PVdagM.Op(subspace[j], ftmp);
+      for (int i = 0; i < nbasis; i++)
+        W(i,j) = TensorRemove(innerProduct(subspace[i], ftmp));
+    }
+    RealD normW = W.norm();
+    std::cout << GridLogMessage << "Fine projected matrix ||W|| = " << normW << std::endl;
+
+    Eigen::MatrixXcd C = Eigen::MatrixXcd::Zero(nbasis, nbasis);
+    CoarseVector Ac(Coarse5d);
+    for (int l = 0; l < nbasis; l++) {
+      LinOpCoarse.Op(psi_coarse[l], Ac);
+      for (int k = 0; k < nbasis; k++)
+        C(k,l) = TensorRemove(innerProduct(psi_coarse[k], Ac));
+    }
+    RealD normC      = C.norm();
+    RealD normCmCdag = (C - C.adjoint()).norm();
+    std::cout << GridLogMessage << "Coarse null matrix ||C||            = " << normC << std::endl;
+    std::cout << GridLogMessage << "Coarse null matrix ||C - C†||/||C|| = " << normCmCdag/normC << std::endl;
+    std::cout << GridLogMessage << "Galerkin check ||C||/||W||          = " << normC/normW << std::endl;
+  }
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 1→2: set up aggregation using psi_coarse as subspace.
+  // Block factor 2,2,3,2 (removes odd local sublattice in z given MPI
+  // geometry 3×6×4×4 where z-local at Level 1 is 6).
+  // psi_coarse are assigned directly; CoarsenOperator performs
+  // block-GS orthogonalisation before building LinOpCoarseCoarse.
+  //////////////////////////////////////////////////////////////////////
+  // innerProduct(CoarseSiteObj, CoarseSiteObj) returns iScalar<vTComplex>, so CComplex
+  // for the L1→L2 level must be iScalar<vTComplex>, not vTComplex.
+  typedef typename CoarseVector::vector_object                            CoarseSiteObj;
+  typedef iScalar<vTComplex>                                              vTTComplex;
+  typedef GeneralCoarsenedMatrix<CoarseSiteObj,vTTComplex,NB>            LittleDiracOperatorL2;
+  typedef typename LittleDiracOperatorL2::CoarseVector                   CoarseCoarseVector;
+  typedef Aggregation<CoarseSiteObj,vTTComplex,NB>                       SubspaceL2;
+  typedef MGPreconditioner<CoarseSiteObj,vTTComplex,NB>                  L1to2MG;
+
+  SubspaceL2 AggregatesL2(CoarseCoarse5d, Coarse5d, cb);
+  for (int k = 0; k < nbasis; k++)
+    AggregatesL2.subspace[k] = psi_coarse[k];
+
+  NextToNearestStencilGeometry5D geom2(CoarseCoarse5d);
+  LittleDiracOperatorL2 LittleDiracOpL2(geom2, Coarse5d, CoarseCoarse5d);
+  LittleDiracOpL2.CoarsenOperator(LinOpCoarse, AggregatesL2);
+
+  NonHermitianLinearOperator<LittleDiracOperatorL2,CoarseCoarseVector> LinOpCC(LittleDiracOpL2);
+
+  TrivialPrecon<CoarseCoarseVector> simpleCC;
+
+  //////////////////////////////////////////////////////////////////////
+  // Lüscher deflation guesser for L3PGCR.
+  // Step 1: project psi_coarse[k] (promoted fine null vectors) to
+  //         CoarseCoarseVector space — these cover the zero-momentum
+  //         component of the near-null space of LinOpCC.
+  // Step 2: breed Nextra additional null vectors directly on LinOpCC
+  //         using GCR with random sources — these pick up near-null
+  //         modes at all spatial frequencies not spanned by step 1.
+  // Step 3: build C_{st} = <psi_cc[s]|LinOpCC|psi_cc[t]> over the
+  //         full augmented basis and invert directly via Eigen LU.
+  //////////////////////////////////////////////////////////////////////
+  std::vector<CoarseCoarseVector> psi_cc(nbasis, CoarseCoarse5d);
+  for (int k = 0; k < nbasis; k++)
+    AggregatesL2.ProjectToSubspace(psi_cc[k], psi_coarse[k]);
+
+  {
+    int Nextra = nbasis;  // breed as many extra as we have promoted ones
+    if ( getenv("CC_NEXTRA") ) Nextra = atoi(getenv("CC_NEXTRA"));
+    GridParallelRNG RNG_CC(CoarseCoarse5d);
+    RNG_CC.SeedFixedIntegers({11,13,17,19});
+    PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseVector>
+      nullGCR(1e-2, 200, LinOpCC, simpleCC, 32, 32);
+    CoarseCoarseVector tmp(CoarseCoarse5d);
+    for (int k = 0; k < Nextra; k++) {
+      CoarseCoarseVector src(CoarseCoarse5d);
+      gaussian(RNG_CC, src);
+      tmp = Zero();
+      nullGCR(src, tmp);
+      psi_cc.push_back(tmp);
+    }
+    std::cout << GridLogMessage << "LinOpCC deflation basis: " << nbasis
+              << " promoted + " << Nextra << " bred = " << psi_cc.size() << " total" << std::endl;
+  }
+
+  const int Naug = psi_cc.size();
+  Eigen::MatrixXcd Ccc = Eigen::MatrixXcd::Zero(Naug, Naug);
+  {
+    CoarseCoarseVector Acc(CoarseCoarse5d);
+    for (int l = 0; l < Naug; l++) {
+      LinOpCC.Op(psi_cc[l], Acc);
+      for (int k = 0; k < Naug; k++)
+        Ccc(k,l) = TensorRemove(innerProduct(psi_cc[k], Acc));
+    }
+  }
+  {
+    RealD normCcc      = Ccc.norm();
+    RealD normCccmCdag = (Ccc - Ccc.adjoint()).norm();
+    std::cout << GridLogMessage << "Coarse-coarse deflation matrix ||Ccc||              = " << normCcc << std::endl;
+    std::cout << GridLogMessage << "Coarse-coarse deflation matrix ||Ccc-Ccc†||/||Ccc|| = " << normCccmCdag/normCcc << std::endl;
+  }
+  Eigen::MatrixXcd Ccc_inv = Ccc.inverse();
+  LuscherGuesser<CoarseCoarseVector> CCDeflGuesser(psi_cc, Ccc_inv);
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 2→3: coarsen LinOpCC using the RAW promoted psi_cc as aggregation
+  // to build the Level 4 (coarse-coarse-coarse) operator.
+  //   psi_cc[0..nbasis-1] are the coarse-coarse near-null vectors, projected
+  //   from the RAW psi_coarse (themselves projected from the RAW fine null
+  //   vectors) -- the pre-block-GS chain the whole construction depends on.
+  //   CoarsenOperator block-GS orthogonalises AggregatesL3.subspace IN PLACE,
+  //   so assign COPIES of psi_cc and keep psi_cc itself raw.
+  //
+  // Tensor depth deepens once more: innerProduct(CoarseCoarseSiteObj,...) returns
+  // iScalar<vTTComplex>, so CComplex for the L2→L3 level is iScalar<iScalar<vTComplex>>.
+  //////////////////////////////////////////////////////////////////////
+  typedef typename CoarseCoarseVector::vector_object                     CoarseCoarseSiteObj;
+  typedef iScalar<vTTComplex>                                            vTTTComplex;
+  typedef GeneralCoarsenedMatrix<CoarseCoarseSiteObj,vTTTComplex,NB>     LittleDiracOperatorL3;
+  typedef typename LittleDiracOperatorL3::CoarseVector                   CoarseCoarseCoarseVector;
+  typedef Aggregation<CoarseCoarseSiteObj,vTTTComplex,NB>               SubspaceL3;
+  typedef MGPreconditioner<CoarseCoarseSiteObj,vTTTComplex,NB>          L2to3MG;
+
+  SubspaceL3 AggregatesL3(CoarseCoarseCoarse5d, CoarseCoarse5d, cb);
+  for (int k = 0; k < nbasis; k++)
+    AggregatesL3.subspace[k] = psi_cc[k];          // raw promoted; COPY, keeps psi_cc raw
+
+  NextToNearestStencilGeometry5D geom3(CoarseCoarseCoarse5d);
+  LittleDiracOperatorL3 LittleDiracOpL3(geom3, CoarseCoarse5d, CoarseCoarseCoarse5d);
+  LittleDiracOpL3.CoarsenOperator(LinOpCC, AggregatesL3);   // block-GS's AggregatesL3.subspace in place
+
+  NonHermitianLinearOperator<LittleDiracOperatorL3,CoarseCoarseCoarseVector> LinOpCCC(LittleDiracOpL3);
+  TrivialPrecon<CoarseCoarseCoarseVector> simpleCCC;
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 4 bottom solve: GCR on a SHIFTED LinOpCCC.  This is the one level
+  // with no IRS shift, and it is the most non-normal (coarsest) operator, so
+  // the bare bottom GCR wanders in a field of values that wraps the origin and
+  // its iteration count blows out (observed 5..54 iters to hit 0.2).  Solving
+  // (A_ccc + l4_shift) instead slides the FoV off the origin; the correction is
+  // only ever a loose 0.2 approximation anyway, so the detuning is free.
+  // l4_shift defaults to 0.0 => bare LinOpCCC, baseline unchanged until opted in.
+  //////////////////////////////////////////////////////////////////////
+  RealD l4_shift = 0.0;
+  if(getenv("l4_shift")) l4_shift = atof(getenv("l4_shift"));
+  std::cout << GridLogMessage << "PARAM l4_shift = " << l4_shift << std::endl;
+
+  ShiftedLinearOperator<CoarseCoarseCoarseVector> ShiftedLinOpCCC(l4_shift, LinOpCCC);
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseCoarseVector> L4PGCR(1.0e-1,200,ShiftedLinOpCCC,simpleCCC,16,16);
+  L4PGCR.Level(4);
+  L4PGCR.Name("CCCouter");
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 2→3 V-cycle: depth-2 SHIFTED smoother on LinOpCC + L4 bottom.
+  // The shift slides the coarse-coarse field of values off the origin so a
+  // 2-step smoother has something to bite on a non-normal operator (IRS idea).
+  //////////////////////////////////////////////////////////////////////
+  RealD cc_smoother_shift = 0.01;
+  int   cc_smoother_nstep = 2;
+  if(getenv("cc_smoother_shift")) cc_smoother_shift = atof(getenv("cc_smoother_shift"));
+  if(getenv("cc_smoother_nstep")) cc_smoother_nstep = atoi(getenv("cc_smoother_nstep"));
+
+  ShiftedLinearOperator<CoarseCoarseVector> ShiftedLinOpCC(cc_smoother_shift, LinOpCC);
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseVector>
+    CoarseCoarseSmootherGCR(0.01,1,ShiftedLinOpCC,simpleCC,cc_smoother_nstep,cc_smoother_nstep);
+  CoarseCoarseSmootherGCR.SetZeroGuess(1);  // smoother slot: caller zeroes guess
+  CoarseCoarseSmootherGCR.Level(3);
+  CoarseCoarseSmootherGCR.Name("CCsmoother");
+
+  L2to3MG L2to3Precon(AggregatesL3,
+                      LinOpCC,
+                      simpleCC,                  // no pre-smoother
+                      CoarseCoarseSmootherGCR,   // post-smoother: depth-2 shifted GCR
+                      LinOpCCC,
+                      L4PGCR,
+                      simpleCCC);                // trivial guesser at the bottom
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 3 (coarse-coarse) solve: GCR preconditioned by the L2→L3 V-cycle.
+  // Replaces the plain L3PGCR of the 3-level build -- the coarse-coarse level
+  // is now smoothed shallowly and recursed rather than solved deeply.
+  //////////////////////////////////////////////////////////////////////
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseVector> L3MGsolver(1.0e-1,200,LinOpCC,L2to3Precon,16,16);
+  L3MGsolver.Level(3);
+  L3MGsolver.Name("CCouter");
+
+  //////////////////////////////////////////////////////////////////////
+  // Coarse-level GCR smoother for Level 1→2 V-cycle.
+  // Mirrors fine-grid SmootherGCR: shifted operator + fixed step count.
+  // coarse_smoother_shift and coarse_smoother_nstep are the tuning knobs.
+  //////////////////////////////////////////////////////////////////////
+  RealD coarse_smoother_shift = 0.01;
+  int   coarse_smoother_nstep = 2;   // depth-2 smoother on the coarse level
+  if(getenv("coarse_smoother_shift")) coarse_smoother_shift = atof(getenv("coarse_smoother_shift"));
+  if(getenv("coarse_smoother_nstep")) coarse_smoother_nstep = atoi(getenv("coarse_smoother_nstep"));
+     
+  ShiftedLinearOperator<CoarseVector> ShiftedLinOpCoarse(coarse_smoother_shift, LinOpCoarse);
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector> CoarseSmootherGCR(0.01,1,ShiftedLinOpCoarse,simpleC,coarse_smoother_nstep,coarse_smoother_nstep);
+  CoarseSmootherGCR.SetZeroGuess(1);   // smoother slot: caller zeroes guess
+  CoarseSmootherGCR.Level(2);
+  CoarseSmootherGCR.Name("Csmoother");
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 1→2 V-cycle preconditioner.
+  //////////////////////////////////////////////////////////////////////
+  L1to2MG L1to2Precon(AggregatesL2,
+                       LinOpCoarse,
+                       simpleC,            // no pre-smoother (matches fine-grid setup)
+                       CoarseSmootherGCR,  // post-smoother: depth-2 shifted GCR
+                       LinOpCC,
+                       L3MGsolver,         // coarse-coarse solve is now the L2→L3 V-cycle
+                       CCDeflGuesser);     // Lüscher guesser: psi_cc C^{-1} psi_cc†
+
+  //////////////////////////////////////////////////////////////////////
+  // Standalone Level 1 two-level solve test.
+  // Compare against plain PGCR baseline above.
+  //////////////////////////////////////////////////////////////////////
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<" Level 1 solve: two-level MG preconditioned PGCR"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector> L2MGsolver(3.0e-2,200,LinOpCoarse,L1to2Precon,16,16);
+  L2MGsolver.Level(2);
+  L2MGsolver.Name("Couter");
+  c_res = Zero();
+  L2MGsolver(c_src,c_res);
+
+  std::cout << GridLogMessage << "Level 1 two-level test: PVdagM operator uses:" << std::endl;
+  PVdagM.getApplications();
+  PVdagM.clear();
+
+  //////////////////////////////////////////////////////////////////////
+  // Full three-level outer solve
+  //////////////////////////////////////////////////////////////////////
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<" Three-level outer solve"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+
+  PrecGeneralisedConjugateResidualNonHermitian<LatticeFermionD> SmootherGCR(0.01,1,ShiftedPVdagM,simple_fine,16,16);
+  SmootherGCR.SetZeroGuess(1);         // pre/post smoother slots zero their guess
+  SmootherGCR.Level(1);
+  SmootherGCR.Name("Fsmoother");
+
+  f_src = one;
+
+  // Pre-smoother: none (TrivialPrecon); post-smoother: shifted PGCR.
+  // Coarse solver: L2MGsolver (PGCR preconditioned by Level 1→2 V-cycle).
+  TwoLevelMG ThreeLevelPrecon(AggregatesPD,
+                               PVdagM,
+                               simple_fine,
+                               SmootherGCR,
+                               LinOpCoarse,
+                               L2MGsolver,
+                               simpleC);
+
+  PrecGeneralisedConjugateResidualNonHermitian<LatticeFermion> L1PGCR(1.0e-8,1000,PVdagM,ThreeLevelPrecon,16,16);
+  L1PGCR.Level(1);
+  L1PGCR.Name("Fouter");
+
+  f_res = Zero();
+  L1PGCR(f_src,f_res);
+
+  std::cout << GridLogMessage << "Three-level outer solve: PVdagM operator uses:" << std::endl;
+  PVdagM.getApplications();
+  PVdagM.clear();
+}
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  const int Ls   = 24;
+  RealD     M5   = 1.8;
+  RealD     b    = 1.5;
+  RealD     c    = 0.5;
+  RealD     mass = 0.00078;
+  if ( getenv("MASS") ) mass = atof(getenv("MASS"));
+
+  const int nbasis = 60;
+
+  std::cout << GridLogMessage << "Mass: " << mass << ", Ls: " << Ls << ", b=" << b << ", c=" << c << std::endl;
+  std::cout << GridLogMessage << "nbasis: " << nbasis << std::endl;
+
+  std::vector<int> lat_size {48, 48, 48, 96};
+
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(lat_size, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Level 1 coarse grid: block 2^4 from fine (48×48×48×96 → 24×24×24×48, Ls=1)
+  Coordinate clatt = lat_size;
+  for (int d = 0; d < 4; d++) clatt[d] /= 2;
+  std::cout << GridLogMessage << "Level 1 coarse lattice: " << clatt << std::endl;
+
+  GridCartesian *Coarse4d  = SpaceTimeGrid::makeFourDimGrid(clatt, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *Coarse5d  = SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+
+  // Level 2 coarse-coarse grid: block 2,2,3,3 from Level 1 (24×24×24×48 → 12×12×8×16, Ls=1).
+  // MPI geometry 3.6.4.4 (288 ranks): fine local {16,8,12,24}.
+  // Level 1 local {8,4,6,12}; Level 2 local {4,2,2,4}.
+  // z blocked by 3: z-Level1-local=6; 6/3=2 (even), 6/2=3 (odd) → must use 3.
+  // t blocked by 3: t-Level1-local=12; 12/3=4 divisible by Nsimd=4 (gen-simd-width=64).
+  //   t-block=2 gives t2-local=6, 6 mod 4 ≠ 0, fails Grid SIMD assertion. ✓
+  // With {4,2,2,4}: Nsimd=4 goes into x or t (both =4). ✓
+  Coordinate clatt2 = clatt;
+  clatt2[0] /= 2;
+  clatt2[1] /= 2;
+  clatt2[2] /= 3;
+  clatt2[3] /= 3;
+  std::cout << GridLogMessage << "Level 2 coarse-coarse lattice: " << clatt2 << std::endl;
+
+  GridCartesian *CoarseCoarse4d = SpaceTimeGrid::makeFourDimGrid(clatt2, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *CoarseCoarse5d = SpaceTimeGrid::makeFiveDimGrid(1,CoarseCoarse4d);
+
+  // Level 3 coarse-coarse-coarse grid: block clatt2 = {12,12,8,16} -> {6,12,8,8}.
+  // GEOMETRY (mpi 3.6.4.4, Nsimd=4 => SIMD layout {1,1,2,2}, factor 2 on z and t):
+  //   every grid needs z-local and t-local EVEN.  clatt2-local is {4,2,2,4}, so
+  //   z-local=2 is already at its minimum even value and CANNOT be blocked (2->1
+  //   is odd and trips the SIMD assertion); y-local=2 would go to 1 (degenerate).
+  //   Only x and t have room, so block {2,1,1,2}: clatt3 {6,12,8,8}, L4-local
+  //   {2,2,2,2} -- all dims even and >=2.  z stays unblocked by construction.
+  Coordinate clatt3 = clatt2;
+  clatt3[0] /= 2;   // x: 12 -> 6   (x-local 4 -> 2)
+  // clatt3[1] (y) unblocked: y-local 2 -> blocking gives 1 (degenerate)
+  // clatt3[2] (z) unblocked: z-local 2 is SIMD-pinned even, cannot halve
+  clatt3[3] /= 2;   // t: 16 -> 8   (t-local 4 -> 2)
+  std::cout << GridLogMessage << "Level 3 coarse-coarse-coarse lattice: " << clatt3 << std::endl;
+
+  GridCartesian *CoarseCoarseCoarse4d = SpaceTimeGrid::makeFourDimGrid(clatt3, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *CoarseCoarseCoarse5d = SpaceTimeGrid::makeFiveDimGrid(1,CoarseCoarseCoarse4d);
+
+  std::vector<int> seeds4({1,2,3,4});
+  std::vector<int> seeds5({5,6,7,8});
+  GridParallelRNG  RNG5(FGrid);  RNG5.SeedFixedIntegers(seeds5);
+  GridParallelRNG  RNG4(UGrid);  RNG4.SeedFixedIntegers(seeds4);
+
+  LatticeGaugeField Umu(UGrid);
+  std::cout << GridLogMessage << "Reading gauge field" << std::endl;
+  FieldMetaData header;
+  std::string file("/ccs/home/poare/ckpoint_lat.1000");
+  NerscIO::readConfiguration(Umu,header,file);
+
+  RealD b_ = 1.5;
+  RealD c_ = 0.5;
+  MobiusFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5,b_,c_);
+  MobiusFermionD Dpv (Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,1.0, M5,b_,c_);
+
+  typedef PVdagMLinearOperator<MobiusFermionD,LatticeFermionD>        PVdagM_t;
+  typedef ShiftedPVdagMLinearOperator<MobiusFermionD,LatticeFermionD> ShiftedPVdagM_t;
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis>  LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector                           CoarseVector;
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis>             Subspace;
+  typedef MGPreconditioner<vSpinColourVector,vTComplex,nbasis>        TwoLevelMG;
+
+  PVdagM_t        PVdagM(Ddwf,Dpv);
+  ShiftedPVdagM_t ShiftedPVdagM(0.01,Ddwf,Dpv);
+
+  NextToNearestStencilGeometry5D geom(Coarse5d);
+
+  // Subspace cache: save after generation, reload on subsequent runs to skip expensive setup.
+  // Set SUBSPACE_FILE to override the default path.
+  std::string subspace_file = "/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/subspace_nb"
+                              + std::to_string(nbasis) + ".scidac";
+  if ( getenv("SUBSPACE_FILE") ) subspace_file = std::string(getenv("SUBSPACE_FILE"));
+
+  // Check if subspace file exists (boss rank checks, result broadcast via GlobalSum).
+  uint64_t file_exists = 0;
+  if ( UGrid->IsBoss() ) {
+    std::ifstream f(subspace_file);
+    file_exists = f.good() ? 1 : 0;
+  }
+  UGrid->GlobalSum(file_exists);
+
+  const int cb = 0;
+  Subspace AggregatesGCR(Coarse5d,FGrid,cb);
+
+  if ( file_exists ) {
+    std::cout << GridLogMessage << "*** Loading subspace from disk ***" << std::endl;
+    loadSubspace(AggregatesGCR.subspace, subspace_file);
+    // Insurance: GLOBAL (whole-lattice) orthonormalise, in case the cached file
+    // predates the GlobalOrthonormalise() that CreateSubspaceGCR now applies
+    // (Aggregates.h:196).  It is span-preserving and makes the vectors globally
+    // orthonormal -- it is NOT the block Orthogonalise() below, so it does NOT
+    // cause the psi_coarse->e_k trap.  The RAW subspace copy in runMG happens
+    // AFTER this call, so the raw-null (pre-block-GS) discipline is preserved.
+    AggregatesGCR.GlobalOrthonormalise();
+    // DO NOT block-orthogonalise here: runMG copies subspace[] as the RAW
+    // (pre-block-GS) basis and CoarsenOperator block-GS's it in place later.
+    // Orthogonalising now defeats the raw-null discipline (psi_coarse -> e_k)
+    // and poisons L2/L3/L4.  See project_block_orthogonalise_leak.
+    // AggregatesGCR.Orthogonalise();
+    std::cout << GridLogMessage << "Subspace loaded, globally orthonormalised (raw block basis preserved)." << std::endl;
+  } else {
+    std::cout << GridLogMessage << "*** GCR subspace generation ***" << std::endl;
+    AggregatesGCR.CreateSubspaceGCR(RNG5,PVdagM,nbasis);
+    std::cout << GridLogMessage << "Subspace generation: PVdagM operator uses:" << std::endl;
+    PVdagM.getApplications();
+    PVdagM.clear();
+    saveSubspace(AggregatesGCR.subspace, subspace_file);
+    std::cout << GridLogMessage << "Subspace saved to: " << subspace_file << std::endl;
+  }
+
+  runMG<nbasis,PVdagM_t,ShiftedPVdagM_t,Subspace,LittleDiracOperator,CoarseVector,TwoLevelMG>(
+    FGrid,
+    Coarse5d,
+    CoarseCoarse5d,
+    CoarseCoarseCoarse5d,
+    geom,
+    PVdagM,
+    ShiftedPVdagM,
+    AggregatesGCR
+  );
+
+  std::cout << GridLogMessage << "Done" << std::endl;
+  Grid_finalize();
+  return 0;
+}

examples/Example_pvdagm_5level.cc

@@ -0,0 +1,954 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./examples/Example_pvdagm_5level.cc
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#include <Grid/Grid.h>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidual.h>
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.h>
+#include <Grid/algorithms/iterative/BiCGSTAB.h>
+
+using namespace std;
+using namespace Grid;
+
+template <class T> void readFile(T& out, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Reading: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacReader SR;
+    SR.open(fname);
+    SR.readScidacFieldRecord(out, record);
+    SR.close();
+  #endif
+}
+
+template <class T> void writeFile(T& in, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Writing: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacWriter SW(in.Grid()->IsBoss());
+    SW.open(fname);
+    SW.writeScidacFieldRecord(in, record);
+    SW.close();
+  #endif
+}
+
+template <class Field>
+void saveSubspace(std::vector<Field> &subspace, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Saving subspace (" << subspace.size() << " vectors) to: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacWriter SW(subspace[0].Grid()->IsBoss());
+    SW.open(fname);
+    for (int k = 0; k < (int)subspace.size(); k++)
+      SW.writeScidacFieldRecord(subspace[k], record);
+    SW.close();
+  #endif
+}
+
+template <class Field>
+void loadSubspace(std::vector<Field> &subspace, std::string const fname){
+  #ifdef HAVE_LIME
+    std::cout << Grid::GridLogMessage << "Loading subspace (" << subspace.size() << " vectors) from: " << fname << std::endl;
+    Grid::emptyUserRecord record;
+    Grid::ScidacReader SR;
+    SR.open(fname);
+    for (int k = 0; k < (int)subspace.size(); k++)
+      SR.readScidacFieldRecord(subspace[k], record);
+    SR.close();
+  #endif
+}
+
+template<class Matrix,class Field>
+class PVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+  int nApp;
+  int nAppDag;
+public:
+  PVdagMLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV), nApp(0), nAppDag(0) {};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+    nApp++;
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(in,tmp);
+    _Mat.Mdag(tmp,out);
+    nAppDag++;
+  }
+  void clear() { nApp = 0; nAppDag = 0; }
+  void getApplications() {
+    std::cout << GridLogMessage << "# applications of PVdagM: " << nApp << std::endl;
+    std::cout << GridLogMessage << "# applications of PVdagM^dag: " << nAppDag << std::endl;
+    std::cout << GridLogMessage << "# applications total: " << nApp + nAppDag << std::endl;
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+template<class Matrix,class Field>
+class MdagPVLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+public:
+  MdagPVLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV){};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(in,tmp);
+    _Mat.Mdag(tmp,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+template<class Matrix,class Field>
+class ShiftedPVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+  RealD shift;
+public:
+  ShiftedPVdagMLinearOperator(RealD _shift,Matrix &Mat,Matrix &PV): shift(_shift),_Mat(Mat),_PV(PV){};
+
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+    out = out + shift * in;
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(tmp,out);
+    _Mat.Mdag(in,tmp);
+    out = out + shift * in;
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){ assert(0); }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+// Lüscher deflated guesser (arXiv:0706.2298 Sec A.3) for a non-Hermitian solve.
+// C_{st} = <psi[s] | LinOp | psi[t]>;  guess = sum_s c_s psi[s]  where c = C^{-1} psi† src.
+template<class Field>
+class LuscherGuesser : public LinearFunction<Field> {
+  const std::vector<Field> &psi;
+  Eigen::MatrixXcd          C_inv;
+public:
+  using LinearFunction<Field>::operator();
+  LuscherGuesser(const std::vector<Field> &psi_, const Eigen::MatrixXcd &Cinv_)
+    : psi(psi_), C_inv(Cinv_) {}
+  virtual void operator()(const Field &src, Field &guess) {
+    int N = psi.size();
+    Eigen::VectorXcd b(N);
+    for (int t = 0; t < N; t++)
+      b(t) = TensorRemove(innerProduct(psi[t], src));
+    Eigen::VectorXcd c = C_inv * b;
+    guess = Zero();
+    for (int s = 0; s < N; s++)
+      guess += ComplexD(c(s)) * psi[s];
+  }
+};
+
+template<class Fobj,class CComplex,int nbasis>
+class MGPreconditioner : public LinearFunction< Lattice<Fobj> > {
+public:
+  using LinearFunction<Lattice<Fobj> >::operator();
+
+  typedef Aggregation<Fobj,CComplex,nbasis> Aggregates;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::FineField    FineField;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseVector CoarseVector;
+  typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseMatrix CoarseMatrix;
+  typedef LinearOperatorBase<FineField>                            FineOperator;
+  typedef LinearFunction    <FineField>                            FineSmoother;
+  typedef LinearOperatorBase<CoarseVector>                         CoarseOperator;
+  typedef LinearFunction    <CoarseVector>                         CoarseSolver;
+
+  Aggregates     & _Aggregates;
+  FineOperator   & _FineOperator;
+  FineSmoother   & _PreSmoother;
+  FineSmoother   & _PostSmoother;
+  CoarseOperator & _CoarseOperator;
+  CoarseSolver   & _CoarseSolve;
+  CoarseSolver   & _CoarseGuesser;
+
+  int    level;  void Level(int lv) {level = lv; };
+
+  MGPreconditioner(Aggregates &Agg,
+		   FineOperator &Fine,
+		   FineSmoother &PreSmoother,
+		   FineSmoother &PostSmoother,
+		   CoarseOperator &CoarseOperator_,
+		   CoarseSolver &CoarseSolve_,
+		   CoarseSolver &CoarseGuesser_)
+    : _Aggregates(Agg),
+      _FineOperator(Fine),
+      _PreSmoother(PreSmoother),
+      _PostSmoother(PostSmoother),
+      _CoarseOperator(CoarseOperator_),
+      _CoarseSolve(CoarseSolve_),
+      _CoarseGuesser(CoarseGuesser_),
+      level(1)  {  }
+
+  virtual void operator()(const FineField &in, FineField & out)
+  {
+    GridBase *CoarseGrid = _Aggregates.CoarseGrid;
+    CoarseVector Csrc(CoarseGrid);
+    CoarseVector Csol(CoarseGrid);
+    FineField vec1(in.Grid());
+    FineField vec2(in.Grid());
+
+    double t;
+    out = Zero();
+    t=-usecond();
+    _PreSmoother(in,out);
+    t+=usecond();
+    std::cout<<GridLogMessage << "PreSmoother took "<< t/1000.0<< "ms" <<std::endl;
+
+    _FineOperator.Op(out,vec1);  sub(vec1, in ,vec1);
+
+    t=-usecond();
+    _Aggregates.ProjectToSubspace(Csrc,vec1);
+    t+=usecond();
+    std::cout<<GridLogMessage << "Project to coarse took "<< t/1000.0<< "ms" <<std::endl;
+
+    t=-usecond();
+    _CoarseGuesser(Csrc,Csol);
+    _CoarseSolve(Csrc,Csol);
+    t+=usecond();
+    std::cout<<GridLogMessage << "Coarse solve took "<< t/1000.0<< "ms" <<std::endl;
+
+    t=-usecond();
+    _Aggregates.PromoteFromSubspace(Csol,vec1);
+    add(out,out,vec1);
+    t+=usecond();
+    std::cout<<GridLogMessage << "Promote to this level took "<< t/1000.0<< "ms" <<std::endl;
+
+    _FineOperator.Op(out,vec1);  sub(vec1 ,in , vec1);
+
+    t=-usecond();
+    vec2=Zero();
+    _PostSmoother(vec1,vec2);
+    t+=usecond();
+    std::cout<<GridLogMessage << "PostSmoother took "<< t/1000.0<< "ms" <<std::endl;
+
+    add(out,out,vec2);
+  }
+};
+
+// Generic shifted linear operator: wraps any LinearOperatorBase and adds shift*I.
+// Used to condition the coarse-level GCR smoother, analogous to ShiftedPVdagMLinearOperator
+// at the fine level.
+template<class Field>
+class ShiftedLinearOperator : public LinearOperatorBase<Field> {
+  LinearOperatorBase<Field> &_Op;
+  RealD shift;
+public:
+  ShiftedLinearOperator(RealD _shift, LinearOperatorBase<Field> &Op) : shift(_shift), _Op(Op) {}
+  void OpDiag   (const Field &in, Field &out)                         { assert(0); }
+  void OpDir    (const Field &in, Field &out, int dir, int disp)      { assert(0); }
+  void OpDirAll (const Field &in, std::vector<Field> &out)            { assert(0); }
+  void Op       (const Field &in, Field &out) { _Op.Op(in, out);    out = out + shift * in; }
+  void AdjOp    (const Field &in, Field &out) { _Op.AdjOp(in, out); out = out + shift * in; }
+  void HermOpAndNorm(const Field &in, Field &out, RealD &n1, RealD &n2) { assert(0); }
+  void HermOp   (const Field &in, Field &out) { Field tmp(in.Grid()); Op(in,tmp); AdjOp(tmp,out); }
+};
+
+template<int NB, class PVdagM_t, class ShiftedPVdagM_t, class Subspace, class LittleDiracOperator, class CoarseVector, class TwoLevelMG>
+void runMG(
+  GridCartesian *FGrid,
+  GridCartesian *Coarse5d,
+  GridCartesian *CoarseCoarse5d,
+  GridCartesian *CoarseCoarseCoarse5d,
+  GridCartesian *CoarseCoarseCoarseCoarse5d,
+  NextToNearestStencilGeometry5D geom,
+  PVdagM_t &PVdagM,
+  ShiftedPVdagM_t &ShiftedPVdagM,
+  Subspace &AggregatesPD
+) {
+  std::vector<LatticeFermion> subspace = AggregatesPD.subspace;
+  assert((int)subspace.size() == NB);
+  const int nbasis = NB;
+  const int cb = 0;
+
+  CoarseVector c_src(Coarse5d);
+  CoarseVector c_res(Coarse5d);
+  Complex one(1.0);
+
+  LatticeFermionD f_src(FGrid);
+  LatticeFermionD f_res(FGrid);
+
+  TrivialPrecon<CoarseVector>      simpleC;
+  TrivialPrecon<LatticeFermionD>   simple_fine;
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 0→1: coarsen PVdagM, build LinOpCoarse
+  //////////////////////////////////////////////////////////////////////
+  LittleDiracOperator LittleDiracOpPV(geom, FGrid, Coarse5d);
+  LittleDiracOpPV.CoarsenOperator(PVdagM, AggregatesPD);
+
+  NonHermitianLinearOperator<LittleDiracOperator,CoarseVector> LinOpCoarse(LittleDiracOpPV);
+
+  //////////////////////////////////////////////////////////////////////
+  // Baseline: plain PGCR on LinOpCoarse (reference for comparison)
+  //////////////////////////////////////////////////////////////////////
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<" Level 1 solve: plain PGCR baseline"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector> L2PGCR_baseline(3.0e-2,1100,LinOpCoarse,simpleC,10,10);
+  L2PGCR_baseline.Level(2);
+  L2PGCR_baseline.Name("Cbaseline");
+  c_src = one;
+  c_res = Zero();
+  L2PGCR_baseline(c_src,c_res);
+
+  //////////////////////////////////////////////////////////////////////
+  // psi_coarse: coarse projections of pre-GS fine null vectors.
+  // These are the Level 1 near-null vectors, promoted from Level 0.
+  // Used as the aggregation basis for Level 1→2 coarsening.
+  //////////////////////////////////////////////////////////////////////
+  std::vector<CoarseVector> psi_coarse(nbasis, Coarse5d);
+  for (int k = 0; k < nbasis; k++)
+    AggregatesPD.ProjectToSubspace(psi_coarse[k], subspace[k]);
+
+  //////////////////////////////////////////////////////////////////////
+  // Diagnostics: W (fine projected matrix) and C (Galerkin check)
+  //////////////////////////////////////////////////////////////////////
+  {
+    Eigen::MatrixXcd W = Eigen::MatrixXcd::Zero(nbasis, nbasis);
+    LatticeFermion ftmp(FGrid);
+    for (int j = 0; j < nbasis; j++) {
+      PVdagM.Op(subspace[j], ftmp);
+      for (int i = 0; i < nbasis; i++)
+        W(i,j) = TensorRemove(innerProduct(subspace[i], ftmp));
+    }
+    RealD normW = W.norm();
+    std::cout << GridLogMessage << "Fine projected matrix ||W|| = " << normW << std::endl;
+
+    Eigen::MatrixXcd C = Eigen::MatrixXcd::Zero(nbasis, nbasis);
+    CoarseVector Ac(Coarse5d);
+    for (int l = 0; l < nbasis; l++) {
+      LinOpCoarse.Op(psi_coarse[l], Ac);
+      for (int k = 0; k < nbasis; k++)
+        C(k,l) = TensorRemove(innerProduct(psi_coarse[k], Ac));
+    }
+    RealD normC      = C.norm();
+    RealD normCmCdag = (C - C.adjoint()).norm();
+    std::cout << GridLogMessage << "Coarse null matrix ||C||            = " << normC << std::endl;
+    std::cout << GridLogMessage << "Coarse null matrix ||C - C†||/||C|| = " << normCmCdag/normC << std::endl;
+    std::cout << GridLogMessage << "Galerkin check ||C||/||W||          = " << normC/normW << std::endl;
+  }
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 1→2: set up aggregation using psi_coarse as subspace.
+  // Block factor 2,2,3,2 (removes odd local sublattice in z given MPI
+  // geometry 3×6×4×4 where z-local at Level 1 is 6).
+  // psi_coarse are assigned directly; CoarsenOperator performs
+  // block-GS orthogonalisation before building LinOpCoarseCoarse.
+  //////////////////////////////////////////////////////////////////////
+  // innerProduct(CoarseSiteObj, CoarseSiteObj) returns iScalar<vTComplex>, so CComplex
+  // for the L1→L2 level must be iScalar<vTComplex>, not vTComplex.
+  typedef typename CoarseVector::vector_object                            CoarseSiteObj;
+  typedef iScalar<vTComplex>                                              vTTComplex;
+  typedef GeneralCoarsenedMatrix<CoarseSiteObj,vTTComplex,NB>            LittleDiracOperatorL2;
+  typedef typename LittleDiracOperatorL2::CoarseVector                   CoarseCoarseVector;
+  typedef Aggregation<CoarseSiteObj,vTTComplex,NB>                       SubspaceL2;
+  typedef MGPreconditioner<CoarseSiteObj,vTTComplex,NB>                  L1to2MG;
+
+  SubspaceL2 AggregatesL2(CoarseCoarse5d, Coarse5d, cb);
+  for (int k = 0; k < nbasis; k++)
+    AggregatesL2.subspace[k] = psi_coarse[k];
+
+  NextToNearestStencilGeometry5D geom2(CoarseCoarse5d);
+  LittleDiracOperatorL2 LittleDiracOpL2(geom2, Coarse5d, CoarseCoarse5d);
+  LittleDiracOpL2.CoarsenOperator(LinOpCoarse, AggregatesL2);
+
+  NonHermitianLinearOperator<LittleDiracOperatorL2,CoarseCoarseVector> LinOpCC(LittleDiracOpL2);
+
+  TrivialPrecon<CoarseCoarseVector> simpleCC;
+
+  //////////////////////////////////////////////////////////////////////
+  // Lüscher deflation guesser for L3PGCR.
+  // Step 1: project psi_coarse[k] (promoted fine null vectors) to
+  //         CoarseCoarseVector space — these cover the zero-momentum
+  //         component of the near-null space of LinOpCC.
+  // Step 2: breed Nextra additional null vectors directly on LinOpCC
+  //         using GCR with random sources — these pick up near-null
+  //         modes at all spatial frequencies not spanned by step 1.
+  // Step 3: build C_{st} = <psi_cc[s]|LinOpCC|psi_cc[t]> over the
+  //         full augmented basis and invert directly via Eigen LU.
+  //////////////////////////////////////////////////////////////////////
+  std::vector<CoarseCoarseVector> psi_cc(nbasis, CoarseCoarse5d);
+  for (int k = 0; k < nbasis; k++)
+    AggregatesL2.ProjectToSubspace(psi_cc[k], psi_coarse[k]);
+
+  {
+    int Nextra = nbasis;  // breed as many extra as we have promoted ones
+    if ( getenv("CC_NEXTRA") ) Nextra = atoi(getenv("CC_NEXTRA"));
+    GridParallelRNG RNG_CC(CoarseCoarse5d);
+    RNG_CC.SeedFixedIntegers({11,13,17,19});
+    PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseVector>
+      nullGCR(1e-2, 200, LinOpCC, simpleCC, 32, 32);
+    CoarseCoarseVector tmp(CoarseCoarse5d);
+    for (int k = 0; k < Nextra; k++) {
+      CoarseCoarseVector src(CoarseCoarse5d);
+      gaussian(RNG_CC, src);
+      tmp = Zero();
+      nullGCR(src, tmp);
+      psi_cc.push_back(tmp);
+    }
+    std::cout << GridLogMessage << "LinOpCC deflation basis: " << nbasis
+              << " promoted + " << Nextra << " bred = " << psi_cc.size() << " total" << std::endl;
+  }
+
+  const int Naug = psi_cc.size();
+  Eigen::MatrixXcd Ccc = Eigen::MatrixXcd::Zero(Naug, Naug);
+  {
+    CoarseCoarseVector Acc(CoarseCoarse5d);
+    for (int l = 0; l < Naug; l++) {
+      LinOpCC.Op(psi_cc[l], Acc);
+      for (int k = 0; k < Naug; k++)
+        Ccc(k,l) = TensorRemove(innerProduct(psi_cc[k], Acc));
+    }
+  }
+  {
+    RealD normCcc      = Ccc.norm();
+    RealD normCccmCdag = (Ccc - Ccc.adjoint()).norm();
+    std::cout << GridLogMessage << "Coarse-coarse deflation matrix ||Ccc||              = " << normCcc << std::endl;
+    std::cout << GridLogMessage << "Coarse-coarse deflation matrix ||Ccc-Ccc†||/||Ccc|| = " << normCccmCdag/normCcc << std::endl;
+  }
+  Eigen::MatrixXcd Ccc_inv = Ccc.inverse();
+  LuscherGuesser<CoarseCoarseVector> CCDeflGuesser(psi_cc, Ccc_inv);
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 2→3: coarsen LinOpCC using the RAW promoted psi_cc as aggregation
+  // to build the Level 4 (coarse-coarse-coarse) operator.
+  //   psi_cc[0..nbasis-1] are the coarse-coarse near-null vectors, projected
+  //   from the RAW psi_coarse (themselves projected from the RAW fine null
+  //   vectors) -- the pre-block-GS chain the whole construction depends on.
+  //   CoarsenOperator block-GS orthogonalises AggregatesL3.subspace IN PLACE,
+  //   so assign COPIES of psi_cc and keep psi_cc itself raw.
+  //
+  // Tensor depth deepens once more: innerProduct(CoarseCoarseSiteObj,...) returns
+  // iScalar<vTTComplex>, so CComplex for the L2→L3 level is iScalar<iScalar<vTComplex>>.
+  //////////////////////////////////////////////////////////////////////
+  typedef typename CoarseCoarseVector::vector_object                     CoarseCoarseSiteObj;
+  typedef iScalar<vTTComplex>                                            vTTTComplex;
+  typedef GeneralCoarsenedMatrix<CoarseCoarseSiteObj,vTTTComplex,NB>     LittleDiracOperatorL3;
+  typedef typename LittleDiracOperatorL3::CoarseVector                   CoarseCoarseCoarseVector;
+  typedef Aggregation<CoarseCoarseSiteObj,vTTTComplex,NB>               SubspaceL3;
+  typedef MGPreconditioner<CoarseCoarseSiteObj,vTTTComplex,NB>          L2to3MG;
+
+  SubspaceL3 AggregatesL3(CoarseCoarseCoarse5d, CoarseCoarse5d, cb);
+  for (int k = 0; k < nbasis; k++)
+    AggregatesL3.subspace[k] = psi_cc[k];          // raw promoted; COPY, keeps psi_cc raw
+
+  NextToNearestStencilGeometry5D geom3(CoarseCoarseCoarse5d);
+  LittleDiracOperatorL3 LittleDiracOpL3(geom3, CoarseCoarse5d, CoarseCoarseCoarse5d);
+  LittleDiracOpL3.CoarsenOperator(LinOpCC, AggregatesL3);   // block-GS's AggregatesL3.subspace in place
+
+  NonHermitianLinearOperator<LittleDiracOperatorL3,CoarseCoarseCoarseVector> LinOpCCC(LittleDiracOpL3);
+  TrivialPrecon<CoarseCoarseCoarseVector> simpleCCC;
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 3→4: coarsen LinOpCCC to build the Level 5 operator, using a
+  // TRUNCATED basis of only the first NB5 (< nbasis) raw promoted null vectors.
+  //   psi_ccc[k] = raw psi_cc projected through the (block-GS'd) L3 aggregation
+  //   -- the pre-block-GS chain continued one level deeper.  We keep only the
+  //   leading NB5: after the global orthogonalisation of the original fine null
+  //   vectors the early indices retain the most-null content (shared low-mode
+  //   components are peeled in first), so the leading NB5 are the crudely-most-
+  //   null slice.  This is the cheap "first 30" truncation test; a principled
+  //   sigma-ordered rotation of psi_ccc would replace the slice, not the idea.
+  //   NB: a positive result is conservative (sigma-ordering can only help); a
+  //   negative one is inconclusive until the sigma-ordered NB5 is tried.
+  //
+  // Tensor depth deepens once more: CComplex for the L3→L4 level is
+  // iScalar<vTTTComplex>.  NB5 (the coarse dimension) is independent of the
+  // depth -- it just makes the coarsest site vector NB5-dimensional.
+  //////////////////////////////////////////////////////////////////////
+  const int NB5 = 30;   // compile-time: changing it re-instantiates the L4/L5 tensors
+  std::cout << GridLogMessage << "PARAM NB5 (truncated coarsest basis) = " << NB5 << std::endl;
+  assert(NB5 <= nbasis);
+
+  std::vector<CoarseCoarseCoarseVector> psi_ccc(nbasis, CoarseCoarseCoarse5d);
+  for (int k = 0; k < nbasis; k++)
+    AggregatesL3.ProjectToSubspace(psi_ccc[k], psi_cc[k]);   // raw psi_cc -> L4 null vectors
+
+  //////////////////////////////////////////////////////////////////////
+  // Optional sigma-ordering of psi_ccc (SVD_REORDER set): replace the crude
+  // first-NB5 slice with the NB5 genuinely-most-null directions of span(psi_ccc)
+  // under LinOpCCC.  For a NON-NORMAL operator the nullness measure is the
+  // singular value of A restricted to the span -- eig of Q†A†AQ -- NOT the
+  // numerical range Q†AQ (which non-normality contaminates).  Robust route:
+  // whiten by the Gram (drop near-dependent directions), Hermitian-eig the
+  // whitened A†A, rotate.  The printed singular spectrum IS the SVD study: where
+  // it falls off tells you the natural NB5, and the same numbers illuminate why
+  // the earlier singular-subspace deflation re-entered.  Safe here because we
+  // ORDER vectors that then feed a Galerkin projection, not REMOVE a subspace.
+  // Default (unset) leaves psi_ccc in raw order == the "first 30" test.
+  //////////////////////////////////////////////////////////////////////
+  if ( getenv("SVD_REORDER") ) {
+    std::cout << GridLogMessage << "SVD_REORDER: sigma-ordering psi_ccc under LinOpCCC" << std::endl;
+
+    Eigen::MatrixXcd G(nbasis,nbasis);                    // Gram  = Psi^dag Psi
+    for (int i=0;i<nbasis;i++)
+    for (int j=0;j<nbasis;j++)
+      G(i,j) = TensorRemove(innerProduct(psi_ccc[i],psi_ccc[j]));
+
+    std::vector<CoarseCoarseCoarseVector> Apsi(nbasis, CoarseCoarseCoarse5d);
+    for (int j=0;j<nbasis;j++) LinOpCCC.Op(psi_ccc[j], Apsi[j]);
+
+    Eigen::MatrixXcd M(nbasis,nbasis);                    // A^dagA = Psi^dag A^dag A Psi
+    for (int i=0;i<nbasis;i++)
+    for (int j=0;j<nbasis;j++)
+      M(i,j) = TensorRemove(innerProduct(Apsi[i],Apsi[j]));
+
+    // Whiten by the Gram: G = Ug diag(g) Ug^dag; keep g > tol*max; T = Ug diag(1/sqrt g).
+    // Q = Psi T is then orthonormal (Q^dag Q = T^dag G T = I).
+    Eigen::SelfAdjointEigenSolver<Eigen::MatrixXcd> esG(G);
+    Eigen::VectorXd g = esG.eigenvalues();               // ascending, real
+    RealD gmax = g(nbasis-1);
+    RealD gtol = 1.0e-9 * gmax;
+    int keep = 0; for (int i=0;i<nbasis;i++) if (g(i) > gtol) keep++;
+    std::cout << GridLogMessage << "  Gram spectrum: min=" << g(0) << " max=" << gmax
+              << " cond=" << gmax/std::max(g(0),1.0e-300) << " keep=" << keep << "/" << nbasis << std::endl;
+    assert(keep >= NB5);
+
+    Eigen::MatrixXcd T(nbasis, keep);                    // whitening (largest-g first)
+    { int c=0;
+      for (int i=nbasis-1;i>=0;i--) if (g(i) > gtol) { T.col(c) = esG.eigenvectors().col(i)/std::sqrt(g(i)); c++; }
+    }
+
+    Eigen::MatrixXcd Mw = T.adjoint() * M * T;           // whitened A^dagA (keep x keep, Hermitian)
+    Eigen::SelfAdjointEigenSolver<Eigen::MatrixXcd> esM(Mw);
+    Eigen::VectorXd s2 = esM.eigenvalues();              // ascending sigma^2 (most-null first)
+    std::cout << GridLogMessage << "  Singular spectrum sigma_k (most-null first):" << std::endl;
+    for (int k=0;k<keep;k++)
+      std::cout << GridLogMessage << "    sigma[" << k << "] = " << std::sqrt(std::max(s2(k),0.0)) << std::endl;
+
+    Eigen::MatrixXcd R = T * esM.eigenvectors();         // coeffs over Psi, sigma-ordered orthonormal dirs
+    std::vector<CoarseCoarseCoarseVector> phi(keep, CoarseCoarseCoarse5d);
+    for (int k=0;k<keep;k++) {
+      phi[k] = Zero();
+      for (int j=0;j<nbasis;j++)
+        phi[k] = phi[k] + ComplexD(R(j,k)) * psi_ccc[j];
+    }
+    for (int k=0;k<keep;k++) psi_ccc[k] = phi[k];        // psi_ccc[0..NB5-1] now = most-null dirs
+    std::cout << GridLogMessage << "SVD_REORDER: psi_ccc replaced by sigma-ordered directions" << std::endl;
+  }
+
+  typedef typename CoarseCoarseCoarseVector::vector_object              CoarseCoarseCoarseSiteObj;
+  typedef iScalar<vTTTComplex>                                          vTTTTComplex;
+  typedef GeneralCoarsenedMatrix<CoarseCoarseCoarseSiteObj,vTTTTComplex,NB5> LittleDiracOperatorL4;
+  typedef typename LittleDiracOperatorL4::CoarseVector                  CoarseCoarseCoarseCoarseVector;
+  typedef Aggregation<CoarseCoarseCoarseSiteObj,vTTTTComplex,NB5>       SubspaceL4;
+  typedef MGPreconditioner<CoarseCoarseCoarseSiteObj,vTTTTComplex,NB5>  L3to4MG;
+
+  SubspaceL4 AggregatesL4(CoarseCoarseCoarseCoarse5d, CoarseCoarseCoarse5d, cb);
+  for (int k = 0; k < NB5; k++)
+    AggregatesL4.subspace[k] = psi_ccc[k];         // FIRST NB5 raw promoted vectors (truncation)
+
+  NextToNearestStencilGeometry5D geom4(CoarseCoarseCoarseCoarse5d);
+  LittleDiracOperatorL4 LittleDiracOpL4(geom4, CoarseCoarseCoarse5d, CoarseCoarseCoarseCoarse5d);
+  LittleDiracOpL4.CoarsenOperator(LinOpCCC, AggregatesL4);   // block-GS's AggregatesL4.subspace in place
+
+  NonHermitianLinearOperator<LittleDiracOperatorL4,CoarseCoarseCoarseCoarseVector> LinOpCCCC(LittleDiracOpL4);
+  TrivialPrecon<CoarseCoarseCoarseCoarseVector> simpleCCCC;
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 5 bottom solve: GCR on a SHIFTED LinOpCCCC (the coarsest, most
+  // non-normal operator).  l5_shift slides its field of values off the origin;
+  // defaults to 0.0 (bare LinOpCCCC) until opted in.  This is the level a dense
+  // direct inverse would eventually replace: rank = NB5 * sites(clatt4).
+  //////////////////////////////////////////////////////////////////////
+  RealD l5_shift = 0.0;
+  if(getenv("l5_shift")) l5_shift = atof(getenv("l5_shift"));
+  std::cout << GridLogMessage << "PARAM l5_shift = " << l5_shift << std::endl;
+
+  ShiftedLinearOperator<CoarseCoarseCoarseCoarseVector> ShiftedLinOpCCCC(l5_shift, LinOpCCCC);
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseCoarseCoarseVector> L5PGCR(1.0e-1,200,ShiftedLinOpCCCC,simpleCCCC,16,16);
+  L5PGCR.Level(5);
+  L5PGCR.Name("CCCCouter");
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 3→4 V-cycle: depth-2 SHIFTED smoother on LinOpCCC + Level 5 bottom.
+  // Level 4 is no longer the bottom -- it is smoothed shallowly and recursed to
+  // Level 5, mirroring how Level 3 recurses to Level 4.
+  //////////////////////////////////////////////////////////////////////
+  RealD ccc_smoother_shift = 0.05;
+  int   ccc_smoother_nstep = 2;
+  if(getenv("ccc_smoother_shift")) ccc_smoother_shift = atof(getenv("ccc_smoother_shift"));
+  if(getenv("ccc_smoother_nstep")) ccc_smoother_nstep = atoi(getenv("ccc_smoother_nstep"));
+
+  ShiftedLinearOperator<CoarseCoarseCoarseVector> ShiftedLinOpCCC(ccc_smoother_shift, LinOpCCC);
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseCoarseVector>
+    CoarseCoarseCoarseSmootherGCR(0.01,1,ShiftedLinOpCCC,simpleCCC,ccc_smoother_nstep,ccc_smoother_nstep);
+  CoarseCoarseCoarseSmootherGCR.SetZeroGuess(1);  // smoother slot: caller zeroes guess
+  CoarseCoarseCoarseSmootherGCR.Level(4);
+  CoarseCoarseCoarseSmootherGCR.Name("CCCsmoother");
+
+  L3to4MG L3to4Precon(AggregatesL4,
+                      LinOpCCC,
+                      simpleCCC,                     // no pre-smoother
+                      CoarseCoarseCoarseSmootherGCR, // post-smoother: depth-2 shifted GCR
+                      LinOpCCCC,
+                      L5PGCR,
+                      simpleCCCC);                   // trivial guesser at the bottom
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 4 (coarse-coarse-coarse) solve: GCR preconditioned by the L3→L4 V-cycle.
+  //////////////////////////////////////////////////////////////////////
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseCoarseVector> L4MGsolver(1.0e-1,200,LinOpCCC,L3to4Precon,16,16);
+  L4MGsolver.Level(4);
+  L4MGsolver.Name("CCCouter");
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 2→3 V-cycle: depth-2 SHIFTED smoother on LinOpCC + Level 4 solve.
+  // The shift slides the coarse-coarse field of values off the origin so a
+  // 2-step smoother has something to bite on a non-normal operator (IRS idea).
+  //////////////////////////////////////////////////////////////////////
+  RealD cc_smoother_shift = 0.01;
+  int   cc_smoother_nstep = 2;
+  if(getenv("cc_smoother_shift")) cc_smoother_shift = atof(getenv("cc_smoother_shift"));
+  if(getenv("cc_smoother_nstep")) cc_smoother_nstep = atoi(getenv("cc_smoother_nstep"));
+
+  ShiftedLinearOperator<CoarseCoarseVector> ShiftedLinOpCC(cc_smoother_shift, LinOpCC);
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseVector>
+    CoarseCoarseSmootherGCR(0.01,1,ShiftedLinOpCC,simpleCC,cc_smoother_nstep,cc_smoother_nstep);
+  CoarseCoarseSmootherGCR.SetZeroGuess(1);  // smoother slot: caller zeroes guess
+  CoarseCoarseSmootherGCR.Level(3);
+  CoarseCoarseSmootherGCR.Name("CCsmoother");
+
+  L2to3MG L2to3Precon(AggregatesL3,
+                      LinOpCC,
+                      simpleCC,                  // no pre-smoother
+                      CoarseCoarseSmootherGCR,   // post-smoother: depth-2 shifted GCR
+                      LinOpCCC,
+                      L4MGsolver,                // coarse solve is now the L3→L4 V-cycle
+                      simpleCCC);                // trivial guesser
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 3 (coarse-coarse) solve: GCR preconditioned by the L2→L3 V-cycle.
+  // Replaces the plain L3PGCR of the 3-level build -- the coarse-coarse level
+  // is now smoothed shallowly and recursed rather than solved deeply.
+  //////////////////////////////////////////////////////////////////////
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseVector> L3MGsolver(1.0e-1,200,LinOpCC,L2to3Precon,16,16);
+  L3MGsolver.Level(3);
+  L3MGsolver.Name("CCouter");
+
+  //////////////////////////////////////////////////////////////////////
+  // Coarse-level GCR smoother for Level 1→2 V-cycle.
+  // Mirrors fine-grid SmootherGCR: shifted operator + fixed step count.
+  // coarse_smoother_shift and coarse_smoother_nstep are the tuning knobs.
+  //////////////////////////////////////////////////////////////////////
+  RealD coarse_smoother_shift = 0.01;
+  int   coarse_smoother_nstep = 2;   // depth-2 smoother on the coarse level
+  if(getenv("coarse_smoother_shift")) coarse_smoother_shift = atof(getenv("coarse_smoother_shift"));
+  if(getenv("coarse_smoother_nstep")) coarse_smoother_nstep = atoi(getenv("coarse_smoother_nstep"));
+     
+  ShiftedLinearOperator<CoarseVector> ShiftedLinOpCoarse(coarse_smoother_shift, LinOpCoarse);
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector> CoarseSmootherGCR(0.01,1,ShiftedLinOpCoarse,simpleC,coarse_smoother_nstep,coarse_smoother_nstep);
+  CoarseSmootherGCR.SetZeroGuess(1);   // smoother slot: caller zeroes guess
+  CoarseSmootherGCR.Level(2);
+  CoarseSmootherGCR.Name("Csmoother");
+
+  //////////////////////////////////////////////////////////////////////
+  // Level 1→2 V-cycle preconditioner.
+  //////////////////////////////////////////////////////////////////////
+  L1to2MG L1to2Precon(AggregatesL2,
+                       LinOpCoarse,
+                       simpleC,            // no pre-smoother (matches fine-grid setup)
+                       CoarseSmootherGCR,  // post-smoother: depth-2 shifted GCR
+                       LinOpCC,
+                       L3MGsolver,         // coarse-coarse solve is now the L2→L3 V-cycle
+                       CCDeflGuesser);     // Lüscher guesser: psi_cc C^{-1} psi_cc†
+
+  //////////////////////////////////////////////////////////////////////
+  // Standalone Level 1 two-level solve test.
+  // Compare against plain PGCR baseline above.
+  //////////////////////////////////////////////////////////////////////
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<" Level 1 solve: two-level MG preconditioned PGCR"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector> L2MGsolver(3.0e-2,200,LinOpCoarse,L1to2Precon,16,16);
+  L2MGsolver.Level(2);
+  L2MGsolver.Name("Couter");
+  c_res = Zero();
+  L2MGsolver(c_src,c_res);
+
+  std::cout << GridLogMessage << "Level 1 two-level test: PVdagM operator uses:" << std::endl;
+  PVdagM.getApplications();
+  PVdagM.clear();
+
+  //////////////////////////////////////////////////////////////////////
+  // Full five-level outer solve
+  //////////////////////////////////////////////////////////////////////
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<" Five-level outer solve"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+
+  PrecGeneralisedConjugateResidualNonHermitian<LatticeFermionD> SmootherGCR(0.01,1,ShiftedPVdagM,simple_fine,16,16);
+  SmootherGCR.SetZeroGuess(1);         // pre/post smoother slots zero their guess
+  SmootherGCR.Level(1);
+  SmootherGCR.Name("Fsmoother");
+
+  f_src = one;
+
+  // Pre-smoother: none (TrivialPrecon); post-smoother: shifted PGCR.
+  // Coarse solver: L2MGsolver (PGCR preconditioned by Level 1→2 V-cycle).
+  TwoLevelMG ThreeLevelPrecon(AggregatesPD,
+                               PVdagM,
+                               simple_fine,
+                               SmootherGCR,
+                               LinOpCoarse,
+                               L2MGsolver,
+                               simpleC);
+
+  PrecGeneralisedConjugateResidualNonHermitian<LatticeFermion> L1PGCR(1.0e-8,1000,PVdagM,ThreeLevelPrecon,16,16);
+  L1PGCR.Level(1);
+  L1PGCR.Name("Fouter");
+
+  f_res = Zero();
+  L1PGCR(f_src,f_res);
+
+  std::cout << GridLogMessage << "Five-level outer solve: PVdagM operator uses:" << std::endl;
+  PVdagM.getApplications();
+  PVdagM.clear();
+}
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  const int Ls   = 24;
+  RealD     M5   = 1.8;
+  RealD     b    = 1.5;
+  RealD     c    = 0.5;
+  RealD     mass = 0.00078;
+  if ( getenv("MASS") ) mass = atof(getenv("MASS"));
+
+  const int nbasis = 60;
+
+  std::cout << GridLogMessage << "Mass: " << mass << ", Ls: " << Ls << ", b=" << b << ", c=" << c << std::endl;
+  std::cout << GridLogMessage << "nbasis: " << nbasis << std::endl;
+
+  std::vector<int> lat_size {48, 48, 48, 96};
+
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(lat_size, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Level 1 coarse grid: block 2^4 from fine (48×48×48×96 → 24×24×24×48, Ls=1)
+  Coordinate clatt = lat_size;
+  for (int d = 0; d < 4; d++) clatt[d] /= 2;
+  std::cout << GridLogMessage << "Level 1 coarse lattice: " << clatt << std::endl;
+
+  GridCartesian *Coarse4d  = SpaceTimeGrid::makeFourDimGrid(clatt, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *Coarse5d  = SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+
+  // Level 2 coarse-coarse grid: block 2,2,3,3 from Level 1 (24×24×24×48 → 12×12×8×16, Ls=1).
+  // MPI geometry 3.6.4.4 (288 ranks): fine local {16,8,12,24}.
+  // Level 1 local {8,4,6,12}; Level 2 local {4,2,2,4}.
+  // z blocked by 3: z-Level1-local=6; 6/3=2 (even), 6/2=3 (odd) → must use 3.
+  // t blocked by 3: t-Level1-local=12; 12/3=4 divisible by Nsimd=4 (gen-simd-width=64).
+  //   t-block=2 gives t2-local=6, 6 mod 4 ≠ 0, fails Grid SIMD assertion. ✓
+  // With {4,2,2,4}: Nsimd=4 goes into x or t (both =4). ✓
+  Coordinate clatt2 = clatt;
+  clatt2[0] /= 2;
+  clatt2[1] /= 2;
+  clatt2[2] /= 3;
+  clatt2[3] /= 3;
+  std::cout << GridLogMessage << "Level 2 coarse-coarse lattice: " << clatt2 << std::endl;
+
+  GridCartesian *CoarseCoarse4d = SpaceTimeGrid::makeFourDimGrid(clatt2, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *CoarseCoarse5d = SpaceTimeGrid::makeFiveDimGrid(1,CoarseCoarse4d);
+
+  // Level 3 coarse-coarse-coarse grid: block clatt2 = {12,12,8,16} -> {6,12,8,8}.
+  // GEOMETRY (mpi 3.6.4.4, Nsimd=4 => SIMD layout {1,1,2,2}, factor 2 on z and t):
+  //   every grid needs z-local and t-local EVEN.  clatt2-local is {4,2,2,4}, so
+  //   z-local=2 is already at its minimum even value and CANNOT be blocked (2->1
+  //   is odd and trips the SIMD assertion); y-local=2 would go to 1 (degenerate).
+  //   Only x and t have room, so block {2,1,1,2}: clatt3 {6,12,8,8}, L4-local
+  //   {2,2,2,2} -- all dims even and >=2.  z stays unblocked by construction.
+  Coordinate clatt3 = clatt2;
+  clatt3[0] /= 2;   // x: 12 -> 6   (x-local 4 -> 2)
+  // clatt3[1] (y) unblocked: y-local 2 -> blocking gives 1 (degenerate)
+  // clatt3[2] (z) unblocked: z-local 2 is SIMD-pinned even, cannot halve
+  clatt3[3] /= 2;   // t: 16 -> 8   (t-local 4 -> 2)
+  std::cout << GridLogMessage << "Level 3 coarse-coarse-coarse lattice: " << clatt3 << std::endl;
+
+  GridCartesian *CoarseCoarseCoarse4d = SpaceTimeGrid::makeFourDimGrid(clatt3, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *CoarseCoarseCoarse5d = SpaceTimeGrid::makeFiveDimGrid(1,CoarseCoarseCoarse4d);
+
+  // Level 4 coarse^4 grid: block clatt3 = {6,12,8,8} -> {3,6,8,8} via {2,2,1,1}.
+  //   mpi 3.6.4.4 => clatt4-local {1,1,2,2}: z-local=2, t-local=2 stay EVEN (SIMD
+  //   factor 2 pins them), so z,t are unblocked; x,y (SIMD factor 1) halve to
+  //   local 1 -- fully distributed but legal for the halo-depth-1 NextToNearest
+  //   stencil.  1152 sites; with NB5=30 that is the 34,560-rank coarsest operator
+  //   a dense direct inverse would target.
+  Coordinate clatt4 = clatt3;
+  clatt4[0] /= 2;   // x: 6  -> 3   (x-local 2 -> 1)
+  clatt4[1] /= 2;   // y: 12 -> 6   (y-local 2 -> 1)
+  // clatt4[2] (z) unblocked: z-local 2 is SIMD-pinned even
+  // clatt4[3] (t) unblocked: t-local 2 is SIMD-pinned even
+  std::cout << GridLogMessage << "Level 4 coarse^4 lattice: " << clatt4 << std::endl;
+
+  GridCartesian *CoarseCoarseCoarseCoarse4d = SpaceTimeGrid::makeFourDimGrid(clatt4, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *CoarseCoarseCoarseCoarse5d = SpaceTimeGrid::makeFiveDimGrid(1,CoarseCoarseCoarseCoarse4d);
+
+  std::vector<int> seeds4({1,2,3,4});
+  std::vector<int> seeds5({5,6,7,8});
+  GridParallelRNG  RNG5(FGrid);  RNG5.SeedFixedIntegers(seeds5);
+  GridParallelRNG  RNG4(UGrid);  RNG4.SeedFixedIntegers(seeds4);
+
+  LatticeGaugeField Umu(UGrid);
+  std::cout << GridLogMessage << "Reading gauge field" << std::endl;
+  FieldMetaData header;
+  std::string file("/ccs/home/poare/ckpoint_lat.1000");
+  NerscIO::readConfiguration(Umu,header,file);
+
+  RealD b_ = 1.5;
+  RealD c_ = 0.5;
+  MobiusFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5,b_,c_);
+  MobiusFermionD Dpv (Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,1.0, M5,b_,c_);
+
+  typedef PVdagMLinearOperator<MobiusFermionD,LatticeFermionD>        PVdagM_t;
+  typedef ShiftedPVdagMLinearOperator<MobiusFermionD,LatticeFermionD> ShiftedPVdagM_t;
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis>  LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector                           CoarseVector;
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis>             Subspace;
+  typedef MGPreconditioner<vSpinColourVector,vTComplex,nbasis>        TwoLevelMG;
+
+  PVdagM_t        PVdagM(Ddwf,Dpv);
+  ShiftedPVdagM_t ShiftedPVdagM(0.01,Ddwf,Dpv);
+
+  NextToNearestStencilGeometry5D geom(Coarse5d);
+
+  // Subspace cache: save after generation, reload on subsequent runs to skip expensive setup.
+  // Set SUBSPACE_FILE to override the default path.
+  std::string subspace_file = "/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/subspace_nb"
+                              + std::to_string(nbasis) + ".scidac";
+  if ( getenv("SUBSPACE_FILE") ) subspace_file = std::string(getenv("SUBSPACE_FILE"));
+
+  // Check if subspace file exists (boss rank checks, result broadcast via GlobalSum).
+  uint64_t file_exists = 0;
+  if ( UGrid->IsBoss() ) {
+    std::ifstream f(subspace_file);
+    file_exists = f.good() ? 1 : 0;
+  }
+  UGrid->GlobalSum(file_exists);
+
+  const int cb = 0;
+  Subspace AggregatesGCR(Coarse5d,FGrid,cb);
+
+  if ( file_exists ) {
+    std::cout << GridLogMessage << "*** Loading subspace from disk ***" << std::endl;
+    loadSubspace(AggregatesGCR.subspace, subspace_file);
+    // Insurance: GLOBAL (whole-lattice) orthonormalise, in case the cached file
+    // predates the GlobalOrthonormalise() that CreateSubspaceGCR now applies
+    // (Aggregates.h:196).  It is span-preserving and makes the vectors globally
+    // orthonormal -- it is NOT the block Orthogonalise() below, so it does NOT
+    // cause the psi_coarse->e_k trap.  It also (re)establishes the weak nullness
+    // gradient (shared most-null components peeled into the early indices) that
+    // the "first NB5" truncation relies on.  Idempotent if the file was already
+    // globally orthonormal.  The RAW subspace copy in runMG happens AFTER this
+    // call, so the raw-null (pre-block-GS) discipline is preserved.
+    AggregatesGCR.GlobalOrthonormalise();
+    // DO NOT block-orthogonalise here: runMG copies subspace[] as the RAW
+    // (pre-block-GS) basis and CoarsenOperator block-GS's it in place later.
+    // Orthogonalising now defeats the raw-null discipline (psi_coarse -> e_k)
+    // and poisons L2/L3/L4.  See project_block_orthogonalise_leak.
+    // AggregatesGCR.Orthogonalise();
+    std::cout << GridLogMessage << "Subspace loaded, globally orthonormalised (raw block basis preserved)." << std::endl;
+  } else {
+    std::cout << GridLogMessage << "*** GCR subspace generation ***" << std::endl;
+    AggregatesGCR.CreateSubspaceGCR(RNG5,PVdagM,nbasis);
+    std::cout << GridLogMessage << "Subspace generation: PVdagM operator uses:" << std::endl;
+    PVdagM.getApplications();
+    PVdagM.clear();
+    saveSubspace(AggregatesGCR.subspace, subspace_file);
+    std::cout << GridLogMessage << "Subspace saved to: " << subspace_file << std::endl;
+  }
+
+  runMG<nbasis,PVdagM_t,ShiftedPVdagM_t,Subspace,LittleDiracOperator,CoarseVector,TwoLevelMG>(
+    FGrid,
+    Coarse5d,
+    CoarseCoarse5d,
+    CoarseCoarseCoarse5d,
+    CoarseCoarseCoarseCoarse5d,
+    geom,
+    PVdagM,
+    ShiftedPVdagM,
+    AggregatesGCR
+  );
+
+  std::cout << GridLogMessage << "Done" << std::endl;
+  Grid_finalize();
+  return 0;
+}

examples/Example_pvdagm_census.cc

@@ -0,0 +1,717 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./examples/Example_pvdagm_census.cc
+
+    Copyright (C) 2026
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+
+// Spectral census of the coarsened PVdagM operator A_c.
+//
+// Measures the three sets that discriminate between the candidate explanations
+// for slow coarse-grid Krylov convergence:
+//
+//   0. Fine Ritz diagonal of RAW subspace vectors (pre-block-orthog).
+//      NB CoarsenOperator block-orthogonalises subspace[] IN PLACE; all
+//      nulliness/deflation bases must be built from a raw copy.
+//   1. Adjoint correctness check    <y|A x> == <A^dag y|x>      (fail-fast)
+//   2. Raw-vector coarse images vs A_c: RQ (must equal CENSUS 0 by Galerkin),
+//      ||A_c psi_c||/||psi_c||, and representability error
+//   3. sigma_max^2 = lambda_max(A_c^dag A_c)  via power method
+//   4. Low singular values          Chebyshev-filtered IRL on A_c^dag A_c
+//      -> sigma_min census = pseudospectrum of A_c evaluated at the origin
+//   5. Half-plane margin            lambda_min/max of H = (A_c + A_c^dag)/2
+//      -> min Re W(A_c);  positive-real check (Eisenstat-Elman-Schultz bound)
+//
+// Interpretation:
+//   sigma_min ~ min|lambda|, ~nbasis tiny then gap : effectively normal, bipartite
+//   sigma_min ~ min|lambda|, dense low tail        : normal but rank-starved
+//   sigma_min << min|lambda|                       : non-normal near origin
+//   lambda_min(H) < 0                              : half-plane condition violated
+//
+// Requires the dagger code path in GeneralCoarsenedMatrix:
+//   _Adag allocated, PopulateAdag active, _Adag exchanged, hermitian=0.
+//
+// Env vars:
+//   MASS               fermion mass                     (default 0.00078)
+//   SUBSPACE_FILE      subspace cache path
+//   CoarseSolverShift  shift baked into coarsening      (default 0.0: pure Galerkin)
+//   CENSUS_NSTOP       converged low modes wanted       (default 60)
+//   CENSUS_NK          Lanczos Nk                       (default 96)
+//   CENSUS_NM          Lanczos Nm                       (default 192)
+//   CENSUS_TOL         Lanczos residual                 (default 1e-5)
+//   CENSUS_MAXIT       Lanczos max restarts             (default 50)
+//   CHEBY_LO           filter low edge in sigma^2       (default 4.0)
+//   CHEBY_HI           filter high edge; 0 = auto from power method x1.1
+//   CHEBY_ORDER        filter order                     (default 401)
+//                      filter gain at 0 ~ cosh(order*2*sqrt(lo/hi)); with
+//                      hi~2200, lo=4, order=401 => gain ~ 1e14. lo=0.01 at
+//                      order 201 gives gain ~1.4 (stagnation).
+
+#include <Grid/Grid.h>
+#include <Grid/Grid_Eigen_Dense.h>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+using namespace std;
+using namespace Grid;
+
+RealD mass              = 0.00078;
+RealD CoarseSolverShift = 0.0;
+int   CensusNstop       = 60;
+int   CensusNk          = 96;
+int   CensusNm          = 192;
+RealD CensusTol         = 1.0e-5;
+int   CensusMaxIt       = 50;
+RealD ChebyLo           = 4.0;   // sigma^2 cutoff: amplifies sigma < 2. Filter gain ~ cosh(order*2*sqrt(lo/hi))
+RealD ChebyHi           = 0.0;   // 0 => auto: 1.1 * power-method sigma_max^2
+int   ChebyOrder        = 401;
+RealD CGdeflTol         = 1.0e-8; // CENSUS 6 deflated-CG tolerance
+int   CGdeflMaxIt       = 4000;   // CENSUS 6 deflated-CG max iterations
+int   DeflRank          = 0;      // CENSUS 6 deflation rank; 0 => all available per basis
+
+void ParseEnvironment(void)
+{
+  if(getenv("MASS"))              mass              = atof(getenv("MASS"));
+  if(getenv("CoarseSolverShift")) CoarseSolverShift = atof(getenv("CoarseSolverShift"));
+  if(getenv("CENSUS_NSTOP"))      CensusNstop       = atoi(getenv("CENSUS_NSTOP"));
+  if(getenv("CENSUS_NK"))         CensusNk          = atoi(getenv("CENSUS_NK"));
+  if(getenv("CENSUS_NM"))         CensusNm          = atoi(getenv("CENSUS_NM"));
+  if(getenv("CENSUS_TOL"))        CensusTol         = atof(getenv("CENSUS_TOL"));
+  if(getenv("CENSUS_MAXIT"))      CensusMaxIt       = atoi(getenv("CENSUS_MAXIT"));
+  if(getenv("CHEBY_LO"))          ChebyLo           = atof(getenv("CHEBY_LO"));
+  if(getenv("CHEBY_HI"))          ChebyHi           = atof(getenv("CHEBY_HI"));
+  if(getenv("CHEBY_ORDER"))       ChebyOrder        = atoi(getenv("CHEBY_ORDER"));
+  if(getenv("CGDEFL_TOL"))        CGdeflTol         = atof(getenv("CGDEFL_TOL"));
+  if(getenv("CGDEFL_MAXIT"))      CGdeflMaxIt       = atoi(getenv("CGDEFL_MAXIT"));
+  if(getenv("DEFL_RANK"))         DeflRank          = atoi(getenv("DEFL_RANK"));
+
+  std::cout << GridLogMessage << "PARAM: MASS              " << mass              << std::endl;
+  std::cout << GridLogMessage << "PARAM: CoarseSolverShift " << CoarseSolverShift << std::endl;
+  std::cout << GridLogMessage << "PARAM: CENSUS_NSTOP      " << CensusNstop       << std::endl;
+  std::cout << GridLogMessage << "PARAM: CENSUS_NK         " << CensusNk          << std::endl;
+  std::cout << GridLogMessage << "PARAM: CENSUS_NM         " << CensusNm          << std::endl;
+  std::cout << GridLogMessage << "PARAM: CENSUS_TOL        " << CensusTol         << std::endl;
+  std::cout << GridLogMessage << "PARAM: CENSUS_MAXIT      " << CensusMaxIt       << std::endl;
+  std::cout << GridLogMessage << "PARAM: CHEBY_LO          " << ChebyLo           << std::endl;
+  std::cout << GridLogMessage << "PARAM: CHEBY_HI          " << ChebyHi           << std::endl;
+  std::cout << GridLogMessage << "PARAM: CHEBY_ORDER       " << ChebyOrder        << std::endl;
+}
+
+template <class Field>
+void saveSubspace(std::vector<Field> &subspace, std::string const fname){
+#ifdef HAVE_LIME
+  std::cout << Grid::GridLogMessage << "Saving subspace (" << subspace.size() << " vectors) to: " << fname << std::endl;
+  Grid::emptyUserRecord record;
+  Grid::ScidacWriter SW(subspace[0].Grid()->IsBoss());
+  SW.open(fname);
+  for (int k = 0; k < (int)subspace.size(); k++)
+    SW.writeScidacFieldRecord(subspace[k], record);
+  SW.close();
+#endif
+}
+
+template <class Field>
+void loadSubspace(std::vector<Field> &subspace, std::string const fname){
+#ifdef HAVE_LIME
+  std::cout << Grid::GridLogMessage << "Loading subspace (" << subspace.size() << " vectors) from: " << fname << std::endl;
+  Grid::emptyUserRecord record;
+  Grid::ScidacReader SR;
+  SR.open(fname);
+  for (int k = 0; k < (int)subspace.size(); k++)
+    SR.readScidacFieldRecord(subspace[k], record);
+  SR.close();
+#endif
+}
+
+template<class Matrix,class Field>
+class PVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+public:
+  PVdagMLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV) {};
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(in,tmp);
+    _Mat.Mdag(tmp,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+template<class Matrix,class Field>
+class ShiftedPVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+public:
+  RealD shift;
+  ShiftedPVdagMLinearOperator(RealD _shift,Matrix &Mat,Matrix &PV): shift(_shift),_Mat(Mat),_PV(PV){};
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+    out = out + shift * in;
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(tmp,out);
+    _Mat.Mdag(in,tmp);
+    out = out + shift * in;
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){    assert(0);  }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+// H = (A + A^dag)/2 : Hermitian part of the coarse operator.
+// lambda_min(H) = min Re W(A) is the half-plane margin; the EES GCR
+// convergence theorem requires it positive.
+template<class Matrix,class Field>
+class HermitianPartOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+public:
+  HermitianPartOperator(Matrix &Mat): _Mat(Mat) {};
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){ HermOp(in,out); }
+  void AdjOp  (const Field &in, Field &out){ HermOp(in,out); }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,out);
+    _Mat.Mdag(in,tmp);
+    out = 0.5*(out + tmp);
+  }
+};
+
+// s*I - Op : power method on this gives s - lambda_min(Op) for Hermitian Op.
+template<class Field>
+class ShiftedNegatedOperator : public LinearOperatorBase<Field> {
+  LinearOperatorBase<Field> &_Op;
+  RealD s;
+public:
+  ShiftedNegatedOperator(RealD _s, LinearOperatorBase<Field> &Op): _Op(Op), s(_s) {};
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){ HermOp(in,out); }
+  void AdjOp  (const Field &in, Field &out){ HermOp(in,out); }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    _Op.HermOp(in,out);
+    out = s*in - out;
+  }
+};
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+  ParseEnvironment();
+
+  const int Ls=24;
+  RealD M5=1.8;
+  RealD b=1.5;
+  RealD c=0.5;
+  const int nbasis = 60;
+
+  std::cout << GridLogMessage << "Census of coarse PVdagM: mass=" << mass << " Ls=" << Ls << " nbasis=" << nbasis << std::endl;
+
+  std::vector<int> lat_size {48, 48, 48, 96};
+
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(lat_size, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Blocking: default matches Example_pvdagm.cc; override with e.g. BLOCK=2.2.2.2
+  Coordinate clatt = lat_size;
+  Coordinate Block({4,4,6,4});
+  if ( getenv("BLOCK") ) {
+    GridCmdOptionIntVector(std::string(getenv("BLOCK")),Block);
+    GRID_ASSERT(Block.size()==4);
+  }
+  for(int d=0;d<clatt.size();d++){
+    GRID_ASSERT(lat_size[d] % Block[d] == 0);
+    clatt[d] = lat_size[d]/Block[d];
+  }
+  std::cout << GridLogMessage << "Block " << Block << "  coarse lattice " << clatt << std::endl;
+
+  GridCartesian *Coarse4d =  SpaceTimeGrid::makeFourDimGrid(clatt, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *Coarse5d =  SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+
+  GridParallelRNG RNG5(FGrid);    RNG5.SeedFixedIntegers({5,6,7,8});
+  GridParallelRNG RNG4(UGrid);    RNG4.SeedFixedIntegers({1,2,3,4});
+  GridParallelRNG CRNG(Coarse5d); CRNG.SeedFixedIntegers({5,6,7,8});
+
+  LatticeGaugeField Umu(UGrid);
+  std::cout << GridLogMessage << "Reading gauge field" << std::endl;
+  FieldMetaData header;
+  std::string file("/ccs/home/poare/ckpoint_lat.1000");
+  NerscIO::readConfiguration(Umu,header,file);
+
+  MobiusFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5,b,c);
+  MobiusFermionD Dpv (Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,1.0, M5,b,c);
+
+  typedef PVdagMLinearOperator<MobiusFermionD,LatticeFermionD>        PVdagM_t;
+  typedef ShiftedPVdagMLinearOperator<MobiusFermionD,LatticeFermionD> ShiftedPVdagM_t;
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis>  LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector                           CoarseVector;
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis>             Subspace;
+
+  PVdagM_t        PVdagM(Ddwf,Dpv);
+  ShiftedPVdagM_t ShiftedPVdagM(CoarseSolverShift,Ddwf,Dpv);
+
+  NextToNearestStencilGeometry5D geom(Coarse5d);
+
+  //////////////////////////////////////////////////////////////////////
+  // Subspace: load from cache or generate
+  //////////////////////////////////////////////////////////////////////
+  std::string subspace_file = "/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/subspace_nb"
+                              + std::to_string(nbasis) + ".scidac";
+  if ( getenv("SUBSPACE_FILE") ) subspace_file = std::string(getenv("SUBSPACE_FILE"));
+
+  uint64_t file_exists = 0;
+  if ( UGrid->IsBoss() ) {
+    std::ifstream f(subspace_file);
+    file_exists = f.good() ? 1 : 0;
+  }
+  UGrid->GlobalSum(file_exists);
+
+  const int cb = 0;
+  Subspace AggregatesGCR(Coarse5d,FGrid,cb);
+
+  if ( file_exists ) {
+    std::cout << GridLogMessage << "*** Loading subspace from disk ***" << std::endl;
+    loadSubspace(AggregatesGCR.subspace, subspace_file);
+  } else {
+    std::cout << GridLogMessage << "*** GCR subspace generation ***" << std::endl;
+    AggregatesGCR.CreateSubspaceGCR(RNG5,PVdagM,nbasis);
+    saveSubspace(AggregatesGCR.subspace, subspace_file);
+  }
+
+  //////////////////////////////////////////////////////////////////////
+  // Keep the RAW (pre-block-orthogonalisation) near-null vectors.
+  // CoarsenOperator block-orthogonalises subspace[] IN PLACE, after which
+  // subspace[k] is the orthonormal basis phi_k and Project(phi_k) = e_k,
+  // the block-constant unit vector -- NOT a near-null direction.
+  // All nulliness measurements and any deflation basis must use raw[].
+  //////////////////////////////////////////////////////////////////////
+  std::vector<LatticeFermionD> raw(nbasis,FGrid);
+  for(int k=0;k<nbasis;k++) raw[k] = AggregatesGCR.subspace[k];
+
+  //////////////////////////////////////////////////////////////////////
+  // CENSUS 0: fine-grid Ritz diagonal on the loaded/generated raw vectors.
+  // Expect Re <psi|A|psi>/<psi|psi> ~ the nulliness achieved at generation
+  // (~2e-3). O(0.1-10) values mean the cache holds orthogonalised vectors
+  // and must be regenerated.
+  //////////////////////////////////////////////////////////////////////
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  std::cout << GridLogMessage << "CENSUS 0: fine Ritz diagonal of raw subspace vectors" << std::endl;
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  {
+    LatticeFermionD Ap(FGrid);
+    for(int k=0;k<nbasis;k++){
+      PVdagM.Op(raw[k],Ap);
+      RealD    n2psi = norm2(raw[k]);
+      ComplexD rq    = innerProduct(raw[k],Ap)/n2psi;
+      std::cout << GridLogMessage << "CENSUS: raw[" << k << "]  <psi|A|psi>/<psi|psi> = " << rq
+                << "   ||A psi||/||psi|| = " << std::sqrt(norm2(Ap)/n2psi) << std::endl;
+    }
+  }
+
+  //////////////////////////////////////////////////////////////////////
+  // Coarsen. hermitian=0 is REQUIRED: enables PopulateAdag so that
+  // Mdag applies A^dag rather than silently aliasing to A.
+  //////////////////////////////////////////////////////////////////////
+  LittleDiracOperator LittleDiracOpPV(geom,FGrid,Coarse5d,0);
+  if ( CoarseSolverShift != 0.0 ) {
+    std::cout << GridLogMessage << "Coarsening SHIFTED operator, shift=" << CoarseSolverShift << std::endl;
+    LittleDiracOpPV.CoarsenOperator(ShiftedPVdagM, AggregatesGCR);
+  } else {
+    std::cout << GridLogMessage << "Coarsening pure Galerkin operator (no shift)" << std::endl;
+    LittleDiracOpPV.CoarsenOperator(PVdagM, AggregatesGCR);
+  }
+
+  CoarseVector c_x(Coarse5d);
+  CoarseVector c_y(Coarse5d);
+  CoarseVector c_t1(Coarse5d);
+  CoarseVector c_t2(Coarse5d);
+
+  //////////////////////////////////////////////////////////////////////
+  // CENSUS 1: adjoint correctness (fail fast)
+  //   <y|A x> == <A^dag y|x>  for random x,y
+  //////////////////////////////////////////////////////////////////////
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  std::cout << GridLogMessage << "CENSUS 1: adjoint correctness of dagger code path" << std::endl;
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  random(CRNG,c_x);
+  random(CRNG,c_y);
+  LittleDiracOpPV.M   (c_x,c_t1);       // A x
+  LittleDiracOpPV.Mdag(c_y,c_t2);       // A^dag y
+  ComplexD ip1 = innerProduct(c_y,c_t1);   // <y|A x>
+  ComplexD ip2 = innerProduct(c_t2,c_x);   // <A^dag y|x>
+  RealD reldiff = abs(ip1-ip2)/abs(ip1);
+  std::cout << GridLogMessage << "CENSUS: <y|Ax>       = " << ip1 << std::endl;
+  std::cout << GridLogMessage << "CENSUS: <Adag y|x>   = " << ip2 << std::endl;
+  std::cout << GridLogMessage << "CENSUS: rel diff     = " << reldiff << "  (expect ~1e-14; FAIL if O(1))" << std::endl;
+  GRID_ASSERT(reldiff < 1.0e-8);
+
+  // Coarse near-null ("global") vectors psi_c[k] = P^dag raw[k], stored for the
+  // Ritz-matrix + deflation study in CENSUS 6 (filled in CENSUS 2's projection
+  // loop below, before raw[]/subspace[] are freed).
+  std::vector<CoarseVector> psi_c(nbasis,Coarse5d);
+
+  //////////////////////////////////////////////////////////////////////
+  // CENSUS 2: nulliness of the RAW vectors' coarse images against A_c.
+  //   psi_c[k] = P^dag raw[k].  Galerkin guarantees the Rayleigh quotient
+  //   equals CENSUS 0's fine value exactly (raw[k] is in span of its own
+  //   chopped pieces) -- agreement is a machine-precision validation of
+  //   the coarsening.  ||A_c psi_c||/||psi_c|| is the sigma-relevant norm.
+  //   The representability column ||raw - P psi_c||/||raw|| must be ~eps.
+  //////////////////////////////////////////////////////////////////////
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  std::cout << GridLogMessage << "CENSUS 2: raw-vector coarse images against coarse operator" << std::endl;
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  {
+    LatticeFermionD back(FGrid);
+    for(int k=0;k<nbasis;k++){
+      AggregatesGCR.ProjectToSubspace(c_x, raw[k]);
+      psi_c[k] = c_x;                       // store coarse near-null vector for CENSUS 6
+      AggregatesGCR.PromoteFromSubspace(c_x, back);
+      back = back - raw[k];
+      RealD represent = std::sqrt(norm2(back)/norm2(raw[k]));
+      LittleDiracOpPV.M(c_x, c_t1);
+      RealD    n2psi = norm2(c_x);
+      RealD    n2Apsi= norm2(c_t1);
+      ComplexD rq    = innerProduct(c_x,c_t1) / n2psi;
+      std::cout << GridLogMessage << "CENSUS: psi_c[" << k << "]  <psi|A|psi>/<psi|psi> = " << rq
+                << "   ||A psi||/||psi|| = " << std::sqrt(n2Apsi/n2psi)
+                << "   represent_err = " << represent << std::endl;
+    }
+  }
+
+  // Fine subspace + raw copy are needed only through CENSUS 2; CENSUS 3-5 are
+  // entirely coarse (LittleDiracOpPV only), and the CENSUS 4 evec save writes the
+  // coarse vectors directly.  Release the ~2*nbasis fine 5D fields (~14 GB/GCD at
+  // 2^4) HERE, before the order-ChebyOrder Lanczos whose padded coarse temporaries
+  // otherwise push host memory over the top on top of _A + _Adag (the AccCache
+  // CpuPtr!=NULL abort seen mid-iteration).
+  // Direct orthonormality check of the fine near-null vectors (GlobalOrthonormalise
+  // in CreateSubspaceGCR).  raw is freed just below, so this runs here, not CENSUS 6.
+  // If this is ~0 but the coarse Gram S (CENSUS 6) is not, the gap is representability,
+  // not orthonormality.
+  {
+    Eigen::MatrixXcd Gfine(nbasis,nbasis);
+    for(int i=0;i<nbasis;i++){
+      for(int j=i;j<nbasis;j++){
+        ComplexD g = innerProduct(raw[i],raw[j]);
+        Gfine(i,j) = std::complex<double>(g.real(),g.imag());
+        Gfine(j,i) = std::conj(Gfine(i,j));
+      }
+    }
+    double GmI = (Gfine - Eigen::MatrixXcd::Identity(nbasis,nbasis)).norm();
+    std::cout << GridLogMessage << "CENSUS 2b: fine Gram ||<raw_i|raw_j> - I||_F = " << GmI
+              << "   (expect ~0 if fine vectors orthonormal)" << std::endl;
+  }
+
+  raw.clear();                    raw.shrink_to_fit();
+  AggregatesGCR.subspace.clear(); AggregatesGCR.subspace.shrink_to_fit();
+
+  //////////////////////////////////////////////////////////////////////
+  // CENSUS 3: sigma_max^2 = lambda_max( A_c^dag A_c ) by power method
+  //////////////////////////////////////////////////////////////////////
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  std::cout << GridLogMessage << "CENSUS 3: power method for sigma_max" << std::endl;
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  MdagMLinearOperator<LittleDiracOperator,CoarseVector> HermOpAdagA(LittleDiracOpPV);
+  random(CRNG,c_x);
+  PowerMethod<CoarseVector> PM;
+  RealD sigmax2 = PM(HermOpAdagA,c_x);
+  std::cout << GridLogMessage << "CENSUS: lambda_max(AdagA) = " << sigmax2
+            << "   sigma_max = " << std::sqrt(sigmax2) << std::endl;
+
+  //////////////////////////////////////////////////////////////////////
+  // CENSUS 4: low singular values via Chebyshev-filtered IRL on A^dag A
+  //   The low end of sigma(A_c) is the pseudospectrum of A_c at z=0.
+  //////////////////////////////////////////////////////////////////////
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  std::cout << GridLogMessage << "CENSUS 4: Chebyshev-filtered Lanczos, low sigma^2" << std::endl;
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  RealD cheby_hi = (ChebyHi > 0.0) ? ChebyHi : 1.1*sigmax2;
+  std::cout << GridLogMessage << "Chebyshev filter [" << ChebyLo << "," << cheby_hi << "] order " << ChebyOrder << std::endl;
+
+  // eval/evec/Nconv hoisted out of the block so CENSUS 6 can deflate with them.
+  std::vector<RealD>        eval(CensusNm);
+  std::vector<CoarseVector> evec(CensusNm,Coarse5d);
+  int Nconv=0;
+  {
+    Chebyshev<CoarseVector>      Cheby(ChebyLo,cheby_hi,ChebyOrder);
+    FunctionHermOp<CoarseVector> OpCheby(Cheby,HermOpAdagA);
+    PlainHermOp<CoarseVector>    Op     (HermOpAdagA);
+
+    ImplicitlyRestartedLanczos<CoarseVector> IRL(OpCheby,Op,CensusNstop,CensusNk,CensusNm,CensusTol,CensusMaxIt);
+
+    random(CRNG,c_x);
+    IRL.calc(eval,evec,c_x,Nconv);
+
+    std::cout << GridLogMessage << "CENSUS: converged " << Nconv << " modes of AdagA" << std::endl;
+    for(int i=0;i<Nconv;i++){
+      std::cout << GridLogMessage << "CENSUS: sigma[" << i << "]^2 = " << eval[i]
+                << "   sigma = " << std::sqrt(std::max(eval[i],0.0)) << std::endl;
+    }
+
+    // Optionally persist the low right-singular-vector basis: this IS the
+    // deflation basis for the coarse solve (ADEF1 / MultiRHSDeflation).
+    // Set CENSUS_EVEC_FILE to enable.
+    if ( getenv("CENSUS_EVEC_FILE") && Nconv>0 ) {
+#ifdef HAVE_LIME
+      std::string evec_file(getenv("CENSUS_EVEC_FILE"));
+      std::string eval_file = evec_file + ".evals.xml";
+      std::cout << GridLogMessage << "CENSUS: saving " << Nconv << " singular vectors to " << evec_file << std::endl;
+      emptyUserRecord record;
+      ScidacWriter WR(evec[0].Grid()->IsBoss());
+      WR.open(evec_file);
+      for(int i=0;i<Nconv;i++) WR.writeScidacFieldRecord(evec[i],record);
+      WR.close();
+      XmlWriter WRx(eval_file);
+      std::vector<RealD> eval_out(eval.begin(),eval.begin()+Nconv); // don't shrink shared eval
+      write(WRx,"evals",eval_out);
+#endif
+    }
+  }
+
+  // NB: evec/eval stay sized CensusNm (Lattice has no default ctor, so
+  // std::vector<CoarseVector>::resize won't instantiate).  They match in size,
+  // which is all DeflatedGuesser asserts; CENSUS 6 only ever indexes [0,Nconv).
+
+  //////////////////////////////////////////////////////////////////////
+  // CENSUS 5: half-plane margin from the Hermitian part
+  //   lambda_min(H) = min Re W(A_c) > 0 <=> positive-real (EES applies)
+  //////////////////////////////////////////////////////////////////////
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  std::cout << GridLogMessage << "CENSUS 5: Hermitian part H=(A+Adag)/2, half-plane margin" << std::endl;
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  HermitianPartOperator<LittleDiracOperator,CoarseVector> HermPart(LittleDiracOpPV);
+
+  random(CRNG,c_x);
+  RealD lamHmax = PM(HermPart,c_x);
+  std::cout << GridLogMessage << "CENSUS: lambda_max(H) = " << lamHmax << std::endl;
+
+  // lambda_min(H): most-negative eigenvalue via Chebyshev-filtered IRL on H.
+  // A shifted power method cannot separate it from the dense low tail (which is
+  // why the earlier -0.006 is suspect); Cheby(lo, hi>=lambda_max) amplifies the
+  // most-negative mode hardest so IRL isolates the true bottom of the spectrum.
+  RealD hpLo    = getenv("HPLANE_CHEBY_LO")    ? atof(getenv("HPLANE_CHEBY_LO"))    : 0.1;
+  RealD hpHi    = getenv("HPLANE_CHEBY_HI")    ? atof(getenv("HPLANE_CHEBY_HI"))    : 1.1*lamHmax;
+  int   hpOrder = getenv("HPLANE_CHEBY_ORDER") ? atoi(getenv("HPLANE_CHEBY_ORDER")) : 61;
+  // Grid's Chebyshev filter MUST be odd order (positive for x < -1, where the low/
+  // negative modes map); an even order flips the sign there and the IRL blows up.
+  if(hpOrder%2==0){ hpOrder++;
+    std::cout<<GridLogMessage<<"HPLANE_CHEBY_ORDER forced odd -> "<<hpOrder<<std::endl; }
+  int   hpNstop = getenv("HPLANE_NSTOP")       ? atoi(getenv("HPLANE_NSTOP"))       : 8;
+  int   hpNk    = getenv("HPLANE_NK")          ? atoi(getenv("HPLANE_NK"))          : 24;
+  int   hpNm    = getenv("HPLANE_NM")          ? atoi(getenv("HPLANE_NM"))          : 48;
+  RealD hpTol   = getenv("HPLANE_TOL")         ? atof(getenv("HPLANE_TOL"))         : 1.0e-4;
+  int   hpMaxIt = getenv("HPLANE_MAXIT")       ? atoi(getenv("HPLANE_MAXIT"))       : 20;
+
+  Chebyshev<CoarseVector>      HCheby(hpLo,hpHi,hpOrder);
+  FunctionHermOp<CoarseVector> HOpCheby(HCheby,HermPart);
+  PlainHermOp<CoarseVector>    HOpPlain(HermPart);
+  ImplicitlyRestartedLanczos<CoarseVector> HIRL(HOpCheby,HOpPlain,hpNstop,hpNk,hpNm,hpTol,hpMaxIt);
+  std::vector<RealD>        heval(hpNm);
+  std::vector<CoarseVector> hevec(hpNm,Coarse5d);
+  int hNconv=0;
+  random(CRNG,c_x);
+  HIRL.calc(heval,hevec,c_x,hNconv);
+  RealD lamHmin = (hNconv>0) ? heval[0] : 9.99e99;
+  for(int kk=0;kk<hNconv;kk++) lamHmin = std::min(lamHmin, heval[kk]);
+  std::cout << GridLogMessage << "CENSUS: IRL H-bottom converged " << hNconv
+            << " eigenvalues; most-negative = " << lamHmin << std::endl;
+  std::cout << GridLogMessage << "CENSUS: lambda_min(H) = " << lamHmin
+            << "  (positive-real / half-plane margin; NEGATIVE => GCR unguaranteed)" << std::endl;
+
+  //////////////////////////////////////////////////////////////////////
+  // CENSUS 6: Ritz matrix of the coarse near-null basis + deflated-CG study
+  //
+  //   C_ij = <psi_c^i | A^dag A | psi_c^j>,   S_ij = <psi_c^i | psi_c^j>.
+  //   psi_c are NOT orthonormal (raw near-null projected to coarse), so the
+  //   Rayleigh-Ritz problem is the GENERALISED Hermitian one  C v = theta S v.
+  //   Its eigenpairs (theta_i, g_i = sum_j V(j,i) psi_c^j) are the best approximate
+  //   eigenpairs of A^dag A available from span{psi_c}; Eigen normalises so that
+  //   V^dag S V = I, hence <g_i|g_j> = delta_ij and the g_i are an orthonormal
+  //   DeflatedGuesser basis.  Compare theta_i to the Lanczos sigma_i^2, then run
+  //   three CG solves on A^dag A: [1] no deflation, [2] Lanczos-eigenvector
+  //   deflated guess, [3] Ritz global-vector deflated guess (g_i treated as pure
+  //   eigenvectors with eigenvalue theta_i).
+  //////////////////////////////////////////////////////////////////////
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  std::cout << GridLogMessage << "CENSUS 6: Ritz matrix C_ij = <psi_c^i|AdagA|psi_c^j> + deflated CG" << std::endl;
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+
+  std::vector<CoarseVector> Apsi(nbasis,Coarse5d);
+  for(int j=0;j<nbasis;j++) HermOpAdagA.HermOp(psi_c[j],Apsi[j]);   // A^dag A psi_c^j
+
+  Eigen::MatrixXcd Cmat(nbasis,nbasis);
+  Eigen::MatrixXcd Smat(nbasis,nbasis);
+  for(int i=0;i<nbasis;i++){
+    for(int j=0;j<nbasis;j++){
+      ComplexD cij = innerProduct(psi_c[i],Apsi[j]);
+      ComplexD sij = innerProduct(psi_c[i],psi_c[j]);
+      Cmat(i,j) = std::complex<double>(cij.real(),cij.imag());
+      Smat(i,j) = std::complex<double>(sij.real(),sij.imag());
+    }
+  }
+
+  {
+    Eigen::SelfAdjointEigenSolver<Eigen::MatrixXcd> ses(Smat);
+    Eigen::MatrixXcd Id = Eigen::MatrixXcd::Identity(nbasis,nbasis);
+    double SmI = (Smat - Id).norm();   // ||S - I||_F : ~0 iff psi_c orthonormal
+    std::cout << GridLogMessage << "CENSUS 6: Gram S eig range [" << ses.eigenvalues()(0)
+              << ", " << ses.eigenvalues()(nbasis-1)
+              << "]   ||S - I||_F = " << SmI
+              << "   (expect ~0: fine vectors are GlobalOrthonormalise'd => psi_c orthonormal)" << std::endl;
+  }
+  Eigen::GeneralizedSelfAdjointEigenSolver<Eigen::MatrixXcd> ges(Cmat,Smat);
+  Eigen::VectorXd  theta = ges.eigenvalues();    // ascending, real
+  Eigen::MatrixXcd Vr    = ges.eigenvectors();   // columns; V^dag S V = I
+
+  int ncmp = std::min((int)nbasis,Nconv);
+  std::cout << GridLogMessage << "CENSUS 6: Ritz theta vs Lanczos sigma^2 (both ascending):" << std::endl;
+  for(int i=0;i<nbasis;i++){
+    if(i<ncmp)
+      std::cout << GridLogMessage << "CENSUS: theta["<<i<<"] = "<<theta(i)
+                <<"   sqrt = "<<std::sqrt(std::max(theta(i),0.0))
+                <<"   | sigma^2 = "<<eval[i]<<"   theta/sigma^2 = "<<theta(i)/eval[i] << std::endl;
+    else
+      std::cout << GridLogMessage << "CENSUS: theta["<<i<<"] = "<<theta(i)
+                <<"   sqrt = "<<std::sqrt(std::max(theta(i),0.0)) << std::endl;
+  }
+
+  // Ritz global vectors g_i = sum_j V(j,i) psi_c^j  (S-orthonormal), eigenvalue theta_i
+  std::vector<CoarseVector> gvec(nbasis,Coarse5d);
+  std::vector<RealD>        gval(nbasis);
+  for(int i=0;i<nbasis;i++){
+    gvec[i] = Zero();
+    for(int j=0;j<nbasis;j++){
+      ComplexD coeff(Vr(j,i).real(),Vr(j,i).imag());
+      axpy(gvec[i],coeff,psi_c[j],gvec[i]);
+    }
+    gval[i] = theta(i);
+  }
+
+  // How good are the diagonalised global vectors as actual eigenvectors of A^dag A?
+  {
+    CoarseVector Ag(Coarse5d), rr(Coarse5d);
+    int nchk = std::min((int)nbasis,16);
+    for(int i=0;i<nchk;i++){
+      HermOpAdagA.HermOp(gvec[i],Ag);
+      axpy(rr,-gval[i],gvec[i],Ag);          // rr = A^dag A g - theta g
+      RealD rn = std::sqrt(norm2(rr));
+      std::cout << GridLogMessage << "CENSUS 6: Ritz resid ["<<i<<"] ||AdagA g - theta g||/theta = "
+                << rn/std::max(gval[i],1.0e-30) << "   (theta="<<gval[i]<<")" << std::endl;
+    }
+  }
+
+  // --- Three CG solves on A^dag A, common random source ---
+  int rankLanc = (DeflRank>0) ? std::min(DeflRank,Nconv)       : Nconv;
+  int rankRitz = (DeflRank>0) ? std::min(DeflRank,(int)nbasis) : (int)nbasis;
+  std::cout << GridLogMessage << "CENSUS 6: CG tol "<<CGdeflTol<<" maxit "<<CGdeflMaxIt
+            << " ; deflation ranks -- Lanczos "<<rankLanc<<", Ritz "<<rankRitz << std::endl;
+
+  CoarseVector cg_src(Coarse5d);  random(CRNG,cg_src);
+  CoarseVector cg_x  (Coarse5d);
+  ConjugateGradient<CoarseVector> CGdefl(CGdeflTol,CGdeflMaxIt,false);
+
+  cg_x = Zero();
+  CGdefl(HermOpAdagA,cg_src,cg_x);
+  std::cout << GridLogMessage << "CENSUS 6: [1] no deflation          : iters = "
+            << CGdefl.IterationsToComplete << "   true_resid = " << CGdefl.TrueResidual << std::endl;
+
+  if(rankLanc>0){
+    DeflatedGuesser<CoarseVector> guessL(evec,eval,rankLanc);
+    guessL(cg_src,cg_x);
+    CGdefl(HermOpAdagA,cg_src,cg_x);
+    std::cout << GridLogMessage << "CENSUS 6: [2] Lanczos-evec deflation : iters = "
+              << CGdefl.IterationsToComplete << "   true_resid = " << CGdefl.TrueResidual << std::endl;
+  }
+
+  {
+    DeflatedGuesser<CoarseVector> guessR(gvec,gval,rankRitz);
+    guessR(cg_src,cg_x);
+    CGdefl(HermOpAdagA,cg_src,cg_x);
+    std::cout << GridLogMessage << "CENSUS 6: [3] Ritz-vector deflation  : iters = "
+              << CGdefl.IterationsToComplete << "   true_resid = " << CGdefl.TrueResidual << std::endl;
+  }
+
+  //////////////////////////////////////////////////////////////////////
+  // Summary
+  //////////////////////////////////////////////////////////////////////
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  std::cout << GridLogMessage << "CENSUS SUMMARY" << std::endl;
+  std::cout << GridLogMessage << "  sigma_max        = " << std::sqrt(sigmax2) << std::endl;
+  std::cout << GridLogMessage << "  lambda_max(H)    = " << lamHmax  << std::endl;
+  std::cout << GridLogMessage << "  lambda_min(H)    = " << lamHmin  << std::endl;
+  std::cout << GridLogMessage << "  low sigma census : see CENSUS 4 table above" << std::endl;
+  std::cout << GridLogMessage << "  Compare min sigma with |lambda| from Krylov-Schur (Patrick):" << std::endl;
+  std::cout << GridLogMessage << "    sigma_min ~ min|lambda| : effectively normal; deflation rank is the issue" << std::endl;
+  std::cout << GridLogMessage << "    sigma_min << min|lambda|: non-normal; need two-sided/singular-vector deflation" << std::endl;
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+
+  std::cout << GridLogMessage << "Done" << std::endl;
+  Grid_finalize();
+  return 0;
+}

examples/Example_pvdagm_halfplane.cc

@@ -0,0 +1,278 @@
+/*
+ * Example_pvdagm_halfplane.cc
+ *
+ * Standalone fine-operator diagnostic: the EES half-plane margin of the
+ * (non-Hermitian) PV-preconditioned Mobius DWF operator
+ *
+ *     A(m_adj) = D_adj^dag D_light      (D_adj plays the Pauli-Villars role)
+ *
+ * as a function of the adjoint mass m_adj, dialled from the light quark mass
+ * up to the Pauli-Villars mass (=1).  No coarse grid, no subspace, no Lanczos
+ * -- pure power-method spectral tests on the fine grid.
+ *
+ * Purpose: A is the LEFT preconditioner for inverting the light operator.
+ * To solve  D_light X = B  we iterate the preconditioned system
+ *     (D_adj^dag D_light) X = D_adj^dag B ,
+ * whose solution X is independent of m_adj -- only the conditioning and the
+ * iterative convergence change.  m_adj = m_light is the usual CGNR (symmetric
+ * normal equations); m_adj = 1 is the Pauli-Villars preconditioned system.
+ * The sweep asks which m_adj keeps the preconditioned operator well-behaved
+ * (positive-real / EES-guaranteed) while buying the wider spectral range.
+ *
+ * For the Hermitian part  H(A) = (A + A^dag)/2  we measure, per m_adj:
+ *
+ *   lambda_max(H)   -- power method on H
+ *   lambda_min(H)   -- power method on (sI - H) => min Re W(A), the half-plane
+ *                      margin.  EES (Eisenstat-Elman-Schultz 1983, Thm 3.3)
+ *                      GUARANTEES GCR convergence with rate
+ *                          [ 1 - lambda_min(H)^2 / sigma_max^2 ]^{1/2}
+ *                      ONLY when lambda_min(H) > 0 (positive-real / A's field
+ *                      of values in the open right half-plane).  A negative
+ *                      value means the guarantee is lost (not that GCR
+ *                      diverges); the magnitude is then the distance-to-
+ *                      positive-realness, i.e. the shift/deflation needed to
+ *                      recover it.
+ *   sigma_max       -- power method on A^dag A (= A.HermOp)
+ *
+ * Endpoints:
+ *   m_adj = m_light  =>  A = M^dag M, Hermitian PD, positive-real by
+ *                        construction, lambda_min(H) = sigma_min^2 > 0 (the
+ *                        squared / CGNR operator).
+ *   m_adj = 1        =>  A = PV^dag M, the standard PVdagM operator.
+ *
+ * Env: MASS, M5, MOBIUS_B, MOBIUS_C, LS, CONFIG,
+ *      MADJ_LIST (comma separated) OR MADJ_MIN / MADJ_MAX / MADJ_N (geometric).
+ *
+ * Caveat: lambda_min(H) via a shifted power method can be soft when it sits
+ * near zero over a dense low spectrum.  The SIGN and the TREND across m_adj
+ * are the robust signal; confirm an individual near-zero value with a proper
+ * shifted Lanczos if it is load-bearing.
+ */
+
+#include <Grid/Grid.h>
+
+using namespace std;
+using namespace Grid;
+
+//////////////////////////////////////////////////////////////////////
+// A = PV^dag M : Op = _PV.Mdag . _Mat.M ,  AdjOp = _Mat.Mdag . _PV.M
+//////////////////////////////////////////////////////////////////////
+template<class Matrix,class Field>
+class PVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  Matrix &_PV;
+public:
+  PVdagMLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV) {};
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _PV.M(in,tmp);
+    _Mat.Mdag(tmp,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){ // A^dag A
+    Field tmp(in.Grid());
+    Op(in,tmp);
+    AdjOp(tmp,out);
+  }
+};
+
+//////////////////////////////////////////////////////////////////////
+// H = (A + A^dag)/2 for a general non-Hermitian LinearOperator A.
+//////////////////////////////////////////////////////////////////////
+template<class Field>
+class HermitianPartLinOp : public LinearOperatorBase<Field> {
+  LinearOperatorBase<Field> &_A;
+public:
+  HermitianPartLinOp(LinearOperatorBase<Field> &A): _A(A) {};
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){ HermOp(in,out); }
+  void AdjOp  (const Field &in, Field &out){ HermOp(in,out); }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    Field tmp(in.Grid());
+    _A.Op(in,out);      // A in
+    _A.AdjOp(in,tmp);   // A^dag in
+    out = 0.5*(out + tmp);
+  }
+};
+
+//////////////////////////////////////////////////////////////////////
+// s*I - Op : power method on this gives s - lambda_min(Op) for Hermitian Op.
+//////////////////////////////////////////////////////////////////////
+template<class Field>
+class ShiftedNegatedOperator : public LinearOperatorBase<Field> {
+  LinearOperatorBase<Field> &_Op;
+  RealD s;
+public:
+  ShiftedNegatedOperator(RealD _s, LinearOperatorBase<Field> &Op): _Op(Op), s(_s) {};
+  void OpDiag (const Field &in, Field &out) {    assert(0);  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {    assert(0);  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){    assert(0);  };
+  void Op     (const Field &in, Field &out){ HermOp(in,out); }
+  void AdjOp  (const Field &in, Field &out){ HermOp(in,out); }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    _Op.HermOp(in,out);
+    out = s*in - out;
+  }
+};
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  RealD mass = 0.00078;
+  RealD M5   = 1.8;
+  RealD b    = 1.5;
+  RealD c    = 0.5;
+  int   Ls   = 24;
+  std::string config("ckpoint_lat.1000");
+
+  if(getenv("MASS"))     mass = atof(getenv("MASS"));
+  if(getenv("M5"))       M5   = atof(getenv("M5"));
+  if(getenv("MOBIUS_B")) b    = atof(getenv("MOBIUS_B"));
+  if(getenv("MOBIUS_C")) c    = atof(getenv("MOBIUS_C"));
+  if(getenv("LS"))       Ls   = atoi(getenv("LS"));
+  if(getenv("CONFIG"))   config = std::string(getenv("CONFIG"));
+
+  // Adjoint-mass sweep: explicit list, or geometric MADJ_MIN..MADJ_MAX in MADJ_N steps.
+  std::vector<RealD> madj_list;
+  if(getenv("MADJ_LIST")){
+    std::stringstream ss(getenv("MADJ_LIST"));
+    std::string tok;
+    while(std::getline(ss,tok,',')) if(tok.size()) madj_list.push_back(std::stod(tok));
+  } else {
+    int   N  = getenv("MADJ_N")   ? atoi(getenv("MADJ_N"))   : 6;
+    RealD lo = getenv("MADJ_MIN") ? atof(getenv("MADJ_MIN")) : mass;
+    RealD hi = getenv("MADJ_MAX") ? atof(getenv("MADJ_MAX")) : 1.0;
+    GRID_ASSERT(N>=1);
+    for(int i=0;i<N;i++)
+      madj_list.push_back( (N==1) ? lo : lo*std::pow(hi/lo, double(i)/double(N-1)) );
+  }
+
+  // lambda_min(H) is the most-negative eigenvalue; resolved by Chebyshev-filtered
+  // Lanczos on H (a shifted power method cannot separate it from the dense low tail).
+  RealD HalfChebyLo    = getenv("HALF_CHEBY_LO")    ? atof(getenv("HALF_CHEBY_LO"))    : 0.1;
+  RealD HalfChebyHi    = getenv("HALF_CHEBY_HI")    ? atof(getenv("HALF_CHEBY_HI"))    : 0.0; // 0 => auto
+  int   HalfChebyOrder = getenv("HALF_CHEBY_ORDER") ? atoi(getenv("HALF_CHEBY_ORDER")) : 61;
+  // Grid's Chebyshev filter MUST be odd order: only then is the polynomial positive
+  // for x < -1, the region the low/negative modes map to.  An even order flips the
+  // sign there, the filtered operator explodes negative, and the IRL never converges.
+  if(HalfChebyOrder%2==0){ HalfChebyOrder++;
+    std::cout<<GridLogMessage<<"HALF_CHEBY_ORDER forced odd -> "<<HalfChebyOrder<<std::endl; }
+  int   HalfNstop      = getenv("HALF_NSTOP")       ? atoi(getenv("HALF_NSTOP"))       : 8;
+  int   HalfNk         = getenv("HALF_NK")          ? atoi(getenv("HALF_NK"))          : 24;
+  int   HalfNm         = getenv("HALF_NM")          ? atoi(getenv("HALF_NM"))          : 48;
+  RealD HalfTol        = getenv("HALF_TOL")         ? atof(getenv("HALF_TOL"))         : 1.0e-4;
+  int   HalfMaxIt      = getenv("HALF_MAXIT")       ? atoi(getenv("HALF_MAXIT"))       : 20;
+
+  std::vector<int> lat = {48,48,48,96};
+
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(lat, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  GridParallelRNG RNG5(FGrid); RNG5.SeedFixedIntegers({5,6,7,8});
+
+  std::cout << GridLogMessage << "PARAM: MASS(light) " << mass << "  M5 " << M5
+            << "  b " << b << "  c " << c << "  Ls " << Ls << std::endl;
+  std::cout << GridLogMessage << "PARAM: CONFIG " << config << std::endl;
+
+  LatticeGaugeField Umu(UGrid);
+  FieldMetaData header;
+  std::cout << GridLogMessage << "Reading gauge field " << config << std::endl;
+  NerscIO::readConfiguration(Umu,header,config);
+
+  // Fixed light operator (never changes across the sweep).
+  MobiusFermionD Dlight(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid, mass, M5, b, c);
+
+  LatticeFermionD x(FGrid);
+
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  std::cout << GridLogMessage << "FINE HALF-PLANE SWEEP  A(m_adj) = D_adj^dag D_light" << std::endl;
+  std::cout << GridLogMessage << "  m_adj = " << mass << " => M^dag M (positive-real); m_adj = 1 => PVdagM" << std::endl;
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+
+  for(auto madj : madj_list){
+
+    MobiusFermionD Dadj(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid, madj, M5, b, c);
+
+    PVdagMLinearOperator<MobiusFermionD,LatticeFermionD> A(Dlight,Dadj); // A = Dadj^dag Dlight
+    HermitianPartLinOp<LatticeFermionD>                  H(A);
+
+    PowerMethod<LatticeFermionD> PM;
+
+    random(RNG5,x); RealD lamHmax = PM(H,x);
+
+    // lambda_min(H): most-negative eigenvalue via Chebyshev-filtered IRL on H.
+    // Cheby(lo,hi) amplifies eigenvalues below lo; with hi>=lambda_max(H) the most
+    // negative mode is amplified hardest, so IRL isolates the true bottom of the
+    // (possibly indefinite) spectrum where the shifted power method could not.
+    RealD fhi = (HalfChebyHi>0.0)? HalfChebyHi : 1.1*lamHmax;
+    Chebyshev<LatticeFermionD>      Cheby(HalfChebyLo,fhi,HalfChebyOrder);
+    FunctionHermOp<LatticeFermionD> OpCheby(Cheby,H);
+    PlainHermOp<LatticeFermionD>    OpPlain(H);
+    ImplicitlyRestartedLanczos<LatticeFermionD> IRL(OpCheby,OpPlain,HalfNstop,HalfNk,HalfNm,HalfTol,HalfMaxIt);
+    std::vector<RealD>           heval(HalfNm);
+    std::vector<LatticeFermionD> hevec(HalfNm,FGrid);
+    int hNconv=0;
+    random(RNG5,x);
+    IRL.calc(heval,hevec,x,hNconv);
+    RealD lamHmin = (hNconv>0) ? heval[0] : 9.99e99;
+    for(int kk=0;kk<hNconv;kk++) lamHmin = std::min(lamHmin, heval[kk]);
+    std::cout << GridLogMessage << "  (IRL H-bottom: " << hNconv
+              << " converged, most-negative eval " << lamHmin << ")" << std::endl;
+
+    random(RNG5,x); RealD sigmax2 = PM(A,x);   // A.HermOp = A^dag A
+    RealD sigmax  = std::sqrt(sigmax2);
+
+    bool  posreal = (lamHmin > 0.0);
+    RealD ratefac = posreal ? std::sqrt(1.0 - lamHmin*lamHmin/sigmax2) : 0.0; // EES per-iter
+    RealD iters8  = (posreal && ratefac < 1.0) ? std::log(1.0e-8)/std::log(ratefac) : 0.0;
+
+    std::cout << GridLogMessage << "HALFPLANE: m_adj " << madj
+              << "  lambda_min(H) " << lamHmin
+              << "  lambda_max(H) " << lamHmax
+              << "  sigma_max " << sigmax
+              << "  positive_real " << (posreal ? "YES" : "NO ")
+              << (posreal
+                    ? ("  EES_rate " + std::to_string(ratefac) + "  EES_iters(1e-8) " + std::to_string(iters8))
+                    : ("  margin_below_zero " + std::to_string(-lamHmin) + " (EES guarantee lost)"))
+              << std::endl;
+  }
+
+  std::cout << GridLogMessage << "=================================================" << std::endl;
+  std::cout << GridLogMessage << "Reading: lambda_min(H) > 0 => EES guarantees GCR at the quoted rate." << std::endl;
+  std::cout << GridLogMessage << "         crossing to < 0 as m_adj -> 1 marks loss of positive-realness." << std::endl;
+  std::cout << GridLogMessage << "         (non-normality: eigenvalues may still be right-half-plane.)" << std::endl;
+  std::cout << GridLogMessage << "Done" << std::endl;
+
+  Grid_finalize();
+  return 0;
+}

examples/Example_pvdagm_mrhs_3level.cc

@@ -0,0 +1,613 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./examples/Example_pvdagm_mrhs_3level.cc
+
+    Copyright (C) 2026
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+
+// MultiRHS (valence) THREE-level multigrid for PVdagM.
+//
+// This is exactly the plain three-level algorithm of Example_pvdagm_3level_SVDdefl.cc
+// with L3_DEFL=0 (NO deflation), applied to the enlarged block-diagonal mRHS system:
+// the coarse and coarse-coarse levels run a SINGLE Krylov (one GCR polynomial, inner
+// products summed over rhs) on the packed 6D mrhs fields, so both coarse levels batch
+// through GEMM (MultiGeneralCoarsenedMatrix) -- the valence throughput win at BOTH levels.
+//
+// Level structure (each coarse level is a single-field PGCR on a packed 6D mrhs field):
+//   L1 (fine)         : std::vector<LatticeFermionD>, MrhsPGCRNonHermitian on PVdagM,
+//                       preconditioned by the L1->L2 mrhs V-cycle (MrhsTwoLevelMG).
+//   L2 (coarse)       : 6D mrhs coarse field, PGCR, preconditioned by the L2->L3 mrhs
+//                       V-cycle (MrhsCoarseThreeLevelPrec) -- coarse-coarse correction + coarse smoother.
+//   L3 (coarse-coarse): 6D mrhs coarse-coarse field, PGCR (the innermost solve).
+//
+// RAW-NULL DISCIPLINE (critical -- see project_block_orthogonalise_leak): the L2->L3
+// aggregation MUST be built from RAW fine near-null vectors (pre block-GS).  We take a
+// raw copy of the loaded subspace BEFORE the L1->L2 CoarsenOperator (which block-
+// orthonormalises in place) and project THAT.  Guards print ||<psi|psi> - I||: ~0.23 =
+// content preserved, ~N_coarse = the e_k leak is back.
+//
+// Env: MASS SUBSPACE_FILE NRHS
+//      BLOCK  (dotted, default 2.2.2.2)  BLOCK2 (dotted, default 2.2.3.3)
+//      FineSmootherShift FineSmootherOrder
+//      CoarseSmootherShift CoarseSmootherNstep
+//      CoarseSolverTol CoarseSolverOrder
+//      L3_TOL L3_MAXIT L3_NSTEP
+//      OuterMmax OuterNstep OuterTol
+
+#include <Grid/Grid.h>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.h>
+
+using namespace std;
+using namespace Grid;
+
+RealD FineSmootherShift    = 0.1;
+int   FineSmootherOrder    = 16;
+RealD CoarseSmootherShift  = 0.1;
+int   CoarseSmootherNstep  = 4;
+RealD CoarseSolverTol      = 0.03;
+int   CoarseSolverOrder    = 200;
+RealD L3Tol                = 2.5e-1;
+int   L3MaxIt              = 50;
+int   L3Nstep              = 50;
+RealD OuterTol             = 1.0e-8;
+int   OuterMmax            = 8;
+int   OuterNstep           = 8;
+int   Nrhs                 = 12;
+RealD mass                 = 0.00078;
+
+void ParseEnvironment(void)
+{
+  if(getenv("MASS"))               mass               = atof(getenv("MASS"));
+  if(getenv("FineSmootherShift"))  FineSmootherShift  = atof(getenv("FineSmootherShift"));
+  if(getenv("FineSmootherOrder"))  FineSmootherOrder  = atoi(getenv("FineSmootherOrder"));
+  if(getenv("CoarseSmootherShift"))CoarseSmootherShift= atof(getenv("CoarseSmootherShift"));
+  if(getenv("CoarseSmootherNstep"))CoarseSmootherNstep= atoi(getenv("CoarseSmootherNstep"));
+  if(getenv("CoarseSolverTol"))    CoarseSolverTol    = atof(getenv("CoarseSolverTol"));
+  if(getenv("CoarseSolverOrder"))  CoarseSolverOrder  = atoi(getenv("CoarseSolverOrder"));
+  if(getenv("L3_TOL"))             L3Tol              = atof(getenv("L3_TOL"));
+  if(getenv("L3_MAXIT"))           L3MaxIt            = atoi(getenv("L3_MAXIT"));
+  if(getenv("L3_NSTEP"))           L3Nstep            = atoi(getenv("L3_NSTEP"));
+  if(getenv("OuterTol"))           OuterTol           = atof(getenv("OuterTol"));
+  if(getenv("OuterMmax"))          OuterMmax          = atoi(getenv("OuterMmax"));
+  if(getenv("OuterNstep"))         OuterNstep         = atoi(getenv("OuterNstep"));
+  if(getenv("NRHS"))               Nrhs               = atoi(getenv("NRHS"));
+
+  std::cout << GridLogMessage << "PARAM: MASS               " << mass               << std::endl;
+  std::cout << GridLogMessage << "PARAM: NRHS               " << Nrhs               << std::endl;
+  std::cout << GridLogMessage << "PARAM: FineSmootherShift  " << FineSmootherShift  << std::endl;
+  std::cout << GridLogMessage << "PARAM: FineSmootherOrder  " << FineSmootherOrder  << std::endl;
+  std::cout << GridLogMessage << "PARAM: CoarseSmootherShift" << CoarseSmootherShift<< std::endl;
+  std::cout << GridLogMessage << "PARAM: CoarseSmootherNstep" << CoarseSmootherNstep<< std::endl;
+  std::cout << GridLogMessage << "PARAM: CoarseSolverTol    " << CoarseSolverTol    << std::endl;
+  std::cout << GridLogMessage << "PARAM: CoarseSolverOrder  " << CoarseSolverOrder  << std::endl;
+  std::cout << GridLogMessage << "PARAM: L3_TOL             " << L3Tol              << std::endl;
+  std::cout << GridLogMessage << "PARAM: OuterMmax          " << OuterMmax          << std::endl;
+  std::cout << GridLogMessage << "PARAM: OuterNstep         " << OuterNstep         << std::endl;
+}
+
+template <class Field>
+void saveSubspace(std::vector<Field> &subspace, std::string const fname){
+#ifdef HAVE_LIME
+  Grid::emptyUserRecord record;
+  Grid::ScidacWriter SW(subspace[0].Grid()->IsBoss());
+  SW.open(fname);
+  for (int k = 0; k < (int)subspace.size(); k++) SW.writeScidacFieldRecord(subspace[k], record);
+  SW.close();
+#endif
+}
+template <class Field>
+void loadSubspace(std::vector<Field> &subspace, std::string const fname){
+#ifdef HAVE_LIME
+  Grid::emptyUserRecord record;
+  Grid::ScidacReader SR;
+  SR.open(fname);
+  for (int k = 0; k < (int)subspace.size(); k++) SR.readScidacFieldRecord(subspace[k], record);
+  SR.close();
+#endif
+}
+
+//////////////////////////////////////////////////////////////////////
+// A = PV^dag M (non-Hermitian), and shifted variant for smoothers.
+//////////////////////////////////////////////////////////////////////
+template<class Matrix,class Field>
+class PVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat; Matrix &_PV;
+public:
+  PVdagMLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV) {};
+  void OpDiag (const Field &in, Field &out) { assert(0); }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) { assert(0); }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){ assert(0); };
+  void Op     (const Field &in, Field &out){ Field tmp(in.Grid()); _Mat.M(in,tmp); _PV.Mdag(tmp,out); }
+  void AdjOp  (const Field &in, Field &out){ Field tmp(in.Grid()); _PV.M(in,tmp); _Mat.Mdag(tmp,out); }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){ HermOp(in,out); ComplexD d=innerProduct(in,out); n1=real(d); n2=norm2(out); }
+  void HermOp(const Field &in, Field &out){ Field tmp(in.Grid()); Op(in,tmp); AdjOp(tmp,out); }
+};
+
+template<class Matrix,class Field>
+class ShiftedPVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat; Matrix &_PV;
+public:
+  RealD shift;
+  ShiftedPVdagMLinearOperator(RealD _shift,Matrix &Mat,Matrix &PV): shift(_shift),_Mat(Mat),_PV(PV){};
+  void OpDiag (const Field &in, Field &out) { assert(0); }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) { assert(0); }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){ assert(0); };
+  void Op     (const Field &in, Field &out){ Field tmp(in.Grid()); _Mat.M(in,tmp); _PV.Mdag(tmp,out); out = out + shift*in; }
+  void AdjOp  (const Field &in, Field &out){ Field tmp(in.Grid()); _PV.M(tmp,out); _Mat.Mdag(in,tmp); out = out + shift*in; }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){ assert(0); }
+  void HermOp(const Field &in, Field &out){ Field tmp(in.Grid()); Op(in,tmp); AdjOp(tmp,out); }
+};
+
+// Generic shift wrapper (for the coarse-level smoother on the 6D mrhs coarse operator).
+template<class Field>
+class ShiftedLinearOperator : public LinearOperatorBase<Field> {
+  LinearOperatorBase<Field> &_Op; RealD shift;
+public:
+  ShiftedLinearOperator(RealD _shift, LinearOperatorBase<Field> &Op) : _Op(Op), shift(_shift) {}
+  void OpDiag  (const Field &in, Field &out) { assert(0); }
+  void OpDir   (const Field &in, Field &out,int dir,int disp) { assert(0); }
+  void OpDirAll (const Field &in, std::vector<Field> &out) { assert(0); }
+  void Op      (const Field &in, Field &out) { _Op.Op(in,out);    out = out + shift*in; }
+  void AdjOp   (const Field &in, Field &out) { _Op.AdjOp(in,out); out = out + shift*in; }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){ assert(0); }
+  void HermOp  (const Field &in, Field &out) { Field tmp(in.Grid()); Op(in,tmp); AdjOp(tmp,out); }
+};
+
+//////////////////////////////////////////////////////////////////////
+// mrhs interfaces + single-polynomial mrhs PGCR (verbatim from Example_pvdagm_mrhs.cc):
+// reductions summed over rhs -> one alpha/beta per step for the enlarged system.
+//////////////////////////////////////////////////////////////////////
+template<class Field>
+class MrhsLinearFunction {
+public:
+  virtual void operator()(std::vector<Field> &in, std::vector<Field> &out) = 0;
+};
+
+template<class Field>
+class MrhsPGCRNonHermitian {
+public:
+  RealD Tolerance; Integer MaxIterations; int mmax,nstep,steps,level;
+  int ZeroGuess = 0; int FirstCycle = 0;   // caller contract: zero guess => first-cycle r0 = src
+  std::string name = "Level 1";
+  LinearOperatorBase<Field> &Linop;
+  MrhsLinearFunction<Field> &Preconditioner;
+  void Level(int lv){ name = "Level " + std::to_string(lv); level=lv; }
+  void Name(std::string n){ name = n; }
+  void SetZeroGuess(int z){ ZeroGuess=z; }
+  MrhsPGCRNonHermitian(RealD tol,Integer maxit,LinearOperatorBase<Field> &_Linop,MrhsLinearFunction<Field> &Prec,int _mmax,int _nstep)
+    : Tolerance(tol),MaxIterations(maxit),Linop(_Linop),Preconditioner(Prec),mmax(_mmax),nstep(_nstep){ level=1; }
+  static RealD vnorm2(std::vector<Field> &x){ RealD s=0; for(auto &f:x) s+=norm2(f); return s; }
+  static ComplexD vinnerProduct(std::vector<Field> &x,std::vector<Field> &y){ ComplexD s(0); for(int r=0;r<(int)x.size();r++) s+=innerProduct(x[r],y[r]); return s; }
+  static void vaxpy(std::vector<Field> &z,ComplexD a,std::vector<Field> &x,std::vector<Field> &y){ for(int r=0;r<(int)z.size();r++) axpy(z[r],a,x[r],y[r]); }
+  void vOp(std::vector<Field> &in,std::vector<Field> &out){ for(int r=0;r<(int)in.size();r++) Linop.Op(in[r],out[r]); }
+  void operator()(std::vector<Field> &src,std::vector<Field> &psi){
+    RealD cp,ssq,rsq; int nrhs=src.size(); GridBase *grid=src[0].Grid();
+    ssq=vnorm2(src); rsq=Tolerance*Tolerance*ssq;
+    std::vector<Field> r(nrhs,grid);
+    GridStopWatch T; T.Start(); steps=0; FirstCycle=1;
+    for(int k=0;k<MaxIterations;k++){
+      cp=GCRnStep(src,psi,rsq);
+      std::cout<<GridLogMessage<<std::string(level,'\t')<<" "<<name<<" MrhsPGCR("<<mmax<<","<<nstep<<") "<<steps<<" steps cp = "<<cp<<" target "<<rsq<<std::endl;
+      if(cp<rsq){
+        T.Stop(); vOp(psi,r); for(int rr=0;rr<nrhs;rr++) axpy(r[rr],-1.0,src[rr],r[rr]);
+        RealD tr=vnorm2(r);
+        std::cout<<GridLogMessage<<std::string(level,'\t')<<" "<<name<<" MrhsPGCR: Converged on iteration "<<steps
+                 <<" computed residual "<<std::sqrt(cp/ssq)<<" true residual "<<std::sqrt(tr/ssq)<<" target "<<Tolerance<<std::endl;
+        std::cout<<GridLogMessage<<std::string(level,'\t')<<" "<<name<<" MrhsPGCR Time elapsed: Total "<<T.Elapsed()<<std::endl;
+        for(int rr=0;rr<nrhs;rr++){ RealD rn=std::sqrt(norm2(r[rr])/norm2(src[rr])); std::cout<<GridLogMessage<<"MrhsPGCR per-rhs true residual["<<rr<<"] = "<<rn<<std::endl; }
+        return;
+      }
+    }
+    std::cout<<GridLogMessage<<"MrhsPGCR: did not converge"<<std::endl;
+  }
+  RealD GCRnStep(std::vector<Field> &src,std::vector<Field> &psi,RealD rsq){
+    RealD cp; ComplexD a,b,rq; RealD zAAz; int nrhs=src.size(); GridBase *grid=src[0].Grid();
+    std::vector<Field> r(nrhs,grid),z(nrhs,grid),Az(nrhs,grid);
+    std::vector< std::vector<Field> > q(mmax,std::vector<Field>(nrhs,grid));
+    std::vector< std::vector<Field> > p(mmax,std::vector<Field>(nrhs,grid));
+    std::vector<RealD> qq(mmax);
+    std::cout<<GridLogMessage<<std::string(level,'\t')<<" "<<name<<" MrhsPGCR nStep("<<nstep<<")"<<std::endl;
+    if (ZeroGuess && FirstCycle) { for(int rr=0;rr<nrhs;rr++){ psi[rr]=Zero(); r[rr]=src[rr]; } }
+    else                         { vOp(psi,Az); for(int rr=0;rr<nrhs;rr++) r[rr]=src[rr]-Az[rr]; }
+    FirstCycle=0;
+    Preconditioner(r,z); vOp(z,Az); zAAz=vnorm2(Az);
+    p[0]=z; q[0]=Az; qq[0]=zAAz; cp=vnorm2(r);
+    for(int k=0;k<nstep;k++){
+      steps++; int kp=k+1, peri_k=k%mmax, peri_kp=kp%mmax;
+      rq=vinnerProduct(q[peri_k],r); a=rq/qq[peri_k];
+      vaxpy(psi,a,p[peri_k],psi); vaxpy(r,-a,q[peri_k],r); cp=vnorm2(r);
+      std::cout<<GridLogMessage<<std::string(level,'\t')<<" "<<name<<" MrhsPGCR step["<<steps<<"]  resid "<<cp<<" target "<<rsq<<std::endl;
+      if((k==nstep-1)||(cp<rsq)) return cp;
+      Preconditioner(r,z); vOp(z,Az); zAAz=vnorm2(Az);
+      q[peri_kp]=Az; p[peri_kp]=z;
+      int northog=((kp)>(mmax-1))?(mmax-1):(kp);
+      for(int back=0;back<northog;back++){ int peri_back=(k-back)%mmax; GRID_ASSERT((k-back)>=0);
+        b=-real(vinnerProduct(q[peri_back],Az))/qq[peri_back];
+        vaxpy(p[peri_kp],b,p[peri_back],p[peri_kp]); vaxpy(q[peri_kp],b,q[peri_back],q[peri_kp]); }
+      qq[peri_kp]=vnorm2(q[peri_kp]);
+    }
+    GRID_ASSERT(0); return cp;
+  }
+};
+
+//////////////////////////////////////////////////////////////////////
+// L2->L3 mrhs V-cycle: a LinearFunction on the 6D mrhs COARSE field.
+// Mirrors Example_pvdagm_mrhs.cc's MrhsTwoLevelMG one level down, and the
+// single-RHS MGPreconditioner of Example_pvdagm_3level_SVDdefl.cc:
+//   out = in (trivial pre)
+//   r = in - A_coarse out
+//   restrict (unpack 6D coarse -> blockProject -> pack 6D coarse-coarse)
+//   ONE coarse-coarse solve (L3, GEMM)
+//   prolong (unpack -> blockPromote -> pack); out += correction
+//   r = in - A_coarse out
+//   coarse smoother (shifted 6D coarse op); out += smooth(r)
+//////////////////////////////////////////////////////////////////////
+template<class CoarseField, class CoarseCoarseField>
+class MrhsCoarseThreeLevelPrec : public LinearFunction<CoarseField> {
+public:
+  LinearOperatorBase<CoarseField>          &_CoarseOp;          // mrhs coarse op (6D)
+  LinearFunction<CoarseField>              &_CoarseSmoother;    // shifted 6D coarse smoother
+  MultiRHSBlockProject<CoarseField>        &_Projector;         // L2->L3 (vector-based)
+  LinearFunction<CoarseCoarseField>        &_CoarseCoarseSolve; // L3 solve (6D cc)
+  GridBase *_Coarse5d, *_CoarseCoarse5d, *_CoarseCoarseMrhs;
+  int _nrhs;
+
+  MrhsCoarseThreeLevelPrec(LinearOperatorBase<CoarseField> &CoarseOp,
+                           LinearFunction<CoarseField> &CoarseSmoother,
+                           MultiRHSBlockProject<CoarseField> &Projector,
+                           LinearFunction<CoarseCoarseField> &CoarseCoarseSolve,
+                           GridBase *Coarse5d, GridBase *CoarseCoarse5d, GridBase *CoarseCoarseMrhs, int nrhs)
+    : _CoarseOp(CoarseOp), _CoarseSmoother(CoarseSmoother), _Projector(Projector),
+      _CoarseCoarseSolve(CoarseCoarseSolve),
+      _Coarse5d(Coarse5d), _CoarseCoarse5d(CoarseCoarse5d), _CoarseCoarseMrhs(CoarseCoarseMrhs), _nrhs(nrhs) {}
+
+  using LinearFunction<CoarseField>::operator();
+  virtual void operator()(const CoarseField &in, CoarseField &out) {
+    int nrhs=_nrhs; double t;
+    CoarseField vec1(in.Grid());
+    CoarseField vec2(in.Grid());
+
+    // trivial pre-smoother
+    out = in;
+
+    // residual (6D coarse)
+    _CoarseOp.Op(out,vec1);  sub(vec1,in,vec1);
+
+    // restrict: unpack 6D coarse -> vector<Coarse> -> blockProject -> vector<CoarseCoarse> -> pack 6D cc
+    std::vector<CoarseField>       csplit(nrhs,_Coarse5d);
+    std::vector<CoarseCoarseField> ccsplit(nrhs,_CoarseCoarse5d);
+    CoarseCoarseField CCsrc(_CoarseCoarseMrhs);
+    CoarseCoarseField CCsol(_CoarseCoarseMrhs);
+
+    t=-usecond();
+    for(int r=0;r<nrhs;r++) ExtractSliceFast(csplit[r],vec1,r,0);
+    _Projector.blockProject(csplit,ccsplit);
+    for(int r=0;r<nrhs;r++) InsertSliceFast(ccsplit[r],CCsrc,r,0);
+    t+=usecond();
+    std::cout<<GridLogMessage<<"L2->L3 restrict took "<<t/1000.0<<"ms"<<std::endl;
+
+    // L3 solve (6D coarse-coarse, GEMM)
+    t=-usecond();
+    CCsol=Zero();
+    _CoarseCoarseSolve(CCsrc,CCsol);
+    t+=usecond();
+    std::cout<<GridLogMessage<<"L3 coarse-coarse solve took "<<t/1000.0<<"ms  ("<<t/1000.0/nrhs<<"ms/rhs)"<<std::endl;
+
+    // prolong: unpack 6D cc -> blockPromote -> pack 6D coarse; add correction
+    t=-usecond();
+    for(int r=0;r<nrhs;r++) ExtractSliceFast(ccsplit[r],CCsol,r,0);
+    _Projector.blockPromote(csplit,ccsplit);
+    for(int r=0;r<nrhs;r++) InsertSliceFast(csplit[r],vec1,r,0);
+    add(out,out,vec1);
+    t+=usecond();
+    std::cout<<GridLogMessage<<"L2->L3 prolong took "<<t/1000.0<<"ms"<<std::endl;
+
+    // residual + coarse smoother (6D coarse)
+    _CoarseOp.Op(out,vec1);  sub(vec1,in,vec1);
+    vec2=Zero();
+    _CoarseSmoother(vec1,vec2);
+    add(out,out,vec2);
+  }
+};
+
+//////////////////////////////////////////////////////////////////////
+// L1->L2 mrhs V-cycle (verbatim from Example_pvdagm_mrhs.cc):
+// per-rhs fine smoother + batched restriction + ONE coarse solve + batched prolong.
+// The coarse solve passed in is now itself three-level (preconditioned by L2->L3).
+//////////////////////////////////////////////////////////////////////
+template<class FineField, class MrhsCoarseVector, class FineSmoother>
+class MrhsTwoLevelMG : public MrhsLinearFunction<FineField> {
+public:
+  typedef MrhsCoarseVector CoarseVector;
+  LinearOperatorBase<FineField>   &_FineOperator;
+  FineSmoother                    &_PostSmoother;
+  MultiRHSBlockProject<FineField> &_Projector;
+  LinearFunction<CoarseVector>    &_CoarseSolve;
+  GridBase *_CoarseGrid, *_CoarseGridMrhs;
+  MrhsTwoLevelMG(LinearOperatorBase<FineField> &FineOp, FineSmoother &Post,
+                 MultiRHSBlockProject<FineField> &Projector, LinearFunction<CoarseVector> &CoarseSolve,
+                 GridBase *CoarseGrid, GridBase *CoarseGridMrhs)
+    : _FineOperator(FineOp),_PostSmoother(Post),_Projector(Projector),_CoarseSolve(CoarseSolve),
+      _CoarseGrid(CoarseGrid),_CoarseGridMrhs(CoarseGridMrhs){}
+  virtual void operator()(std::vector<FineField> &in, std::vector<FineField> &out){
+    int nrhs=in.size(); GridBase *fgrid=in[0].Grid(); double t;
+    std::vector<FineField> vec1(nrhs,fgrid),vec2(nrhs,fgrid);
+    for(int r=0;r<nrhs;r++) out[r]=in[r];
+    for(int r=0;r<nrhs;r++){ _FineOperator.Op(out[r],vec1[r]); sub(vec1[r],in[r],vec1[r]); }
+    std::vector<CoarseVector> Csrc_split(nrhs,_CoarseGrid), Csol_split(nrhs,_CoarseGrid);
+    CoarseVector CsrcMrhs(_CoarseGridMrhs), CsolMrhs(_CoarseGridMrhs);
+    t=-usecond();
+    _Projector.blockProject(vec1,Csrc_split);
+    for(int r=0;r<nrhs;r++) InsertSliceFast(Csrc_split[r],CsrcMrhs,r,0);
+    t+=usecond(); std::cout<<GridLogMessage<<"Mrhs project+pack took "<<t/1000.0<<"ms"<<std::endl;
+    t=-usecond(); CsolMrhs=Zero(); _CoarseSolve(CsrcMrhs,CsolMrhs); t+=usecond();
+    std::cout<<GridLogMessage<<"Mrhs coarse solve took "<<t/1000.0<<"ms  ("<<t/1000.0/nrhs<<"ms/rhs)"<<std::endl;
+    t=-usecond();
+    for(int r=0;r<nrhs;r++) ExtractSliceFast(Csol_split[r],CsolMrhs,r,0);
+    _Projector.blockPromote(vec1,Csol_split);
+    for(int r=0;r<nrhs;r++) add(out[r],out[r],vec1[r]);
+    t+=usecond(); std::cout<<GridLogMessage<<"Mrhs unpack+promote took "<<t/1000.0<<"ms"<<std::endl;
+    for(int r=0;r<nrhs;r++){ _FineOperator.Op(out[r],vec1[r]); sub(vec1[r],in[r],vec1[r]); }
+    t=-usecond();
+    for(int r=0;r<nrhs;r++){ vec2[r]=Zero(); _PostSmoother(vec1[r],vec2[r]); add(out[r],out[r],vec2[r]); }
+    t+=usecond(); std::cout<<GridLogMessage<<"Mrhs post-smooth took "<<t/1000.0<<"ms  ("<<t/1000.0/nrhs<<"ms/rhs)"<<std::endl;
+  }
+};
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+  ParseEnvironment();
+
+  const int Ls=24; RealD M5=1.8, b=1.5, c=0.5;
+  const int nbasis=60; const int nrhs=Nrhs;
+  GRID_ASSERT(nrhs % vComplex::Nsimd() == 0);
+
+  std::vector<int> lat_size {48,48,48,96};
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(lat_size, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Level 1 blocking (default 2^4)
+  Coordinate clatt = lat_size;
+  Coordinate Block({2,2,2,2});
+  if ( getenv("BLOCK") ){ GridCmdOptionIntVector(std::string(getenv("BLOCK")),Block); GRID_ASSERT(Block.size()==4); }
+  for(int d=0;d<4;d++){ GRID_ASSERT(lat_size[d]%Block[d]==0); clatt[d]=lat_size[d]/Block[d]; }
+  std::cout << GridLogMessage << "Block  " << Block  << "  coarse lattice       " << clatt << std::endl;
+
+  // Level 2 blocking (default 2,2,3,3)  -- matches Example_pvdagm_3level_SVDdefl
+  Coordinate cclatt = clatt;
+  Coordinate Block2({2,2,3,3});
+  if ( getenv("BLOCK2") ){ GridCmdOptionIntVector(std::string(getenv("BLOCK2")),Block2); GRID_ASSERT(Block2.size()==4); }
+  for(int d=0;d<4;d++){ GRID_ASSERT(clatt[d]%Block2[d]==0); cclatt[d]=clatt[d]/Block2[d]; }
+  std::cout << GridLogMessage << "Block2 " << Block2 << "  coarse-coarse lattice " << cclatt << std::endl;
+
+  GridCartesian *Coarse4d = SpaceTimeGrid::makeFourDimGrid(clatt, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *Coarse5d = SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+  GridCartesian *CoarseCoarse4d = SpaceTimeGrid::makeFourDimGrid(cclatt, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *CoarseCoarse5d = SpaceTimeGrid::makeFiveDimGrid(1,CoarseCoarse4d);
+
+  // 6D mrhs grids: rhs is dim 0, SIMD across rhs (pattern: Test_general_coarse_hdcg_phys48.cc)
+  Coordinate mpi=GridDefaultMpi();
+  Coordinate rhMpi ({1,1,mpi[0],mpi[1],mpi[2],mpi[3]});
+  Coordinate rhSimd({vComplex::Nsimd(),1,1,1,1,1});
+  Coordinate rhLatt ({nrhs,1,clatt[0], clatt[1], clatt[2], clatt[3]});
+  Coordinate rhLatt2({nrhs,1,cclatt[0],cclatt[1],cclatt[2],cclatt[3]});
+  GridCartesian *CoarseMrhs       = new GridCartesian(rhLatt, rhSimd,rhMpi);
+  GridCartesian *CoarseCoarseMrhs = new GridCartesian(rhLatt2,rhSimd,rhMpi);
+
+  GridParallelRNG RNG5(FGrid); RNG5.SeedFixedIntegers({5,6,7,8});
+
+  LatticeGaugeField Umu(UGrid);
+  std::cout << GridLogMessage << "Reading gauge field" << std::endl;
+  FieldMetaData header;
+  std::string file("/ccs/home/poare/ckpoint_lat.1000");
+  NerscIO::readConfiguration(Umu,header,file);
+
+  MobiusFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5,b,c);
+  MobiusFermionD Dpv (Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,1.0, M5,b,c);
+
+  typedef PVdagMLinearOperator<MobiusFermionD,LatticeFermionD>        PVdagM_t;
+  typedef ShiftedPVdagMLinearOperator<MobiusFermionD,LatticeFermionD> ShiftedPVdagM_t;
+
+  // Level 1 tensor types
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis>       LittleDiracOperator;
+  typedef MultiGeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis>  MrhsLittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector                                CoarseVector;
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis>                  Subspace;
+
+  // Level 2 tensor types (coarsening deepens the nest by one iScalar -- see CLAUDE.md)
+  typedef CoarseVector::vector_object                                      CoarseSiteObj;
+  typedef iScalar<vTComplex>                                              vTTComplex;
+  typedef GeneralCoarsenedMatrix<CoarseSiteObj,vTTComplex,nbasis>          LittleDiracOperatorL2;
+  typedef MultiGeneralCoarsenedMatrix<CoarseSiteObj,vTTComplex,nbasis>     MrhsLittleDiracOperatorL2;
+  typedef LittleDiracOperatorL2::CoarseVector                              CoarseCoarseVector;
+  typedef Aggregation<CoarseSiteObj,vTTComplex,nbasis>                     SubspaceL2;
+
+  PVdagM_t        PVdagM(Ddwf,Dpv);
+  ShiftedPVdagM_t ShiftedPVdagM(FineSmootherShift,Ddwf,Dpv);
+
+  NextToNearestStencilGeometry5D geom (Coarse5d);
+  NextToNearestStencilGeometry5D geom2(CoarseCoarse5d);   // 33-point at L2->L3, matching SVDdefl
+
+  //////////////////////////////////////////////////////////////////////
+  // Subspace: load RAW (no Orthogonalise!), or generate.
+  //////////////////////////////////////////////////////////////////////
+  std::string subspace_file = "/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/subspace_nb"
+                            + std::to_string(nbasis) + ".scidac";
+  if ( getenv("SUBSPACE_FILE") ) subspace_file = std::string(getenv("SUBSPACE_FILE"));
+  uint64_t file_exists=0;
+  if ( UGrid->IsBoss() ){ std::ifstream f(subspace_file); file_exists=f.good()?1:0; }
+  UGrid->GlobalSum(file_exists);
+
+  const int cb=0;
+  Subspace AggregatesGCR(Coarse5d,FGrid,cb);
+  if ( file_exists ){
+    std::cout << GridLogMessage << "*** Loading subspace from disk (kept RAW) ***" << std::endl;
+    loadSubspace(AggregatesGCR.subspace, subspace_file);
+  } else {
+    std::cout << GridLogMessage << "*** GCR subspace generation ***" << std::endl;
+    AggregatesGCR.CreateSubspaceGCR(RNG5,PVdagM,nbasis);
+    saveSubspace(AggregatesGCR.subspace, subspace_file);
+  }
+
+  // RAW copy of the fine null vectors BEFORE CoarsenOperator block-orthonormalises in place.
+  std::vector<LatticeFermionD> rawNull(nbasis,FGrid);
+  for(int k=0;k<nbasis;k++) rawNull[k]=AggregatesGCR.subspace[k];
+
+  //////////////////////////////////////////////////////////////////////
+  // Coarsen L1->L2 and L2->L3 with SINGLE-RHS machinery, import into the mrhs
+  // operators via CopyMatrix.  The single-RHS L1->L2 coarse operator must stay
+  // alive to be the "fine" operator for the L2->L3 coarsening, so BOTH single-RHS
+  // ops (and their padded _A) live in one scope and free together.  [MEMORY: this
+  // is the setup peak -- L1->L2 padded _A (~large at 2^4) + L2->L3 padded _A.]
+  //////////////////////////////////////////////////////////////////////
+  MrhsLittleDiracOperator   mrhsLittleDiracOpPV(geom,  CoarseMrhs);
+  MrhsLittleDiracOperatorL2 mrhsLittleDiracOpL2(geom2, CoarseCoarseMrhs);
+  MultiRHSBlockProject<LatticeFermionD> MrhsProjector;
+  MultiRHSBlockProject<CoarseVector>    MrhsProjectorL2;
+  {
+    // --- L1->L2 single-RHS coarse operator (kept alive for the L2->L3 coarsening) ---
+    LittleDiracOperator LittleDiracOpPV(geom,FGrid,Coarse5d);
+    LittleDiracOpPV.CoarsenOperator(PVdagM, AggregatesGCR);   // orthonormalises AggregatesGCR.subspace in place
+    mrhsLittleDiracOpPV.CopyMatrix(LittleDiracOpPV);
+    MrhsProjector.Allocate(nbasis,FGrid,Coarse5d);
+    MrhsProjector.ImportBasis(AggregatesGCR.subspace);       // orthonormalised, matches the coarse op
+    NonHermitianLinearOperator<LittleDiracOperator,CoarseVector> LinOpCoarse(LittleDiracOpPV);
+
+    // --- psi_coarse = P^dag (RAW fine null) -> Galerkin images, NOT e_k ---
+    std::vector<CoarseVector> psi_coarse(nbasis,Coarse5d);
+    for(int k=0;k<nbasis;k++) AggregatesGCR.ProjectToSubspace(psi_coarse[k], rawNull[k]);
+    rawNull.clear(); rawNull.shrink_to_fit();
+    {
+      RealD s2=0.0;
+      for(int i=0;i<nbasis;i++) for(int j=0;j<nbasis;j++){
+        ComplexD sij=TensorRemove(innerProduct(psi_coarse[i],psi_coarse[j]));
+        ComplexD d=sij-(i==j?ComplexD(1.0):ComplexD(0.0)); s2+=real(d)*real(d)+imag(d)*imag(d);
+      }
+      std::cout<<GridLogMessage<<"GUARD: ||<psi_coarse|psi_coarse> - I||_F = "<<std::sqrt(s2)
+               <<"   (~0.23 good; ~sqrt(N_coarse)="<<std::sqrt((double)Coarse5d->gSites())<<" = e_k leak)"<<std::endl;
+    }
+
+    // --- L2->L3 single-RHS coarsening (coarsen the single-RHS LinOpCoarse) ---
+    SubspaceL2 AggregatesL2(CoarseCoarse5d,Coarse5d,cb);
+    for(int k=0;k<nbasis;k++) AggregatesL2.subspace[k]=psi_coarse[k];
+    LittleDiracOperatorL2 LittleDiracOpL2(geom2,Coarse5d,CoarseCoarse5d);
+    LittleDiracOpL2.CoarsenOperator(LinOpCoarse, AggregatesL2);
+    mrhsLittleDiracOpL2.CopyMatrix(LittleDiracOpL2);
+    MrhsProjectorL2.Allocate(nbasis,Coarse5d,CoarseCoarse5d);
+    MrhsProjectorL2.ImportBasis(AggregatesL2.subspace);      // orthonormalised by CoarsenOperator
+
+    // --- guard psi_cc (RAW psi_coarse; AggregatesL2 holds a separate orthonormalised copy) ---
+    {
+      std::vector<CoarseCoarseVector> psi_cc(nbasis,CoarseCoarse5d);
+      for(int k=0;k<nbasis;k++) AggregatesL2.ProjectToSubspace(psi_cc[k], psi_coarse[k]);
+      RealD s2=0.0;
+      for(int i=0;i<nbasis;i++) for(int j=0;j<nbasis;j++){
+        ComplexD sij=TensorRemove(innerProduct(psi_cc[i],psi_cc[j]));
+        ComplexD d=sij-(i==j?ComplexD(1.0):ComplexD(0.0)); s2+=real(d)*real(d)+imag(d)*imag(d);
+      }
+      std::cout<<GridLogMessage<<"GUARD: ||<psi_cc|psi_cc> - I||_F = "<<std::sqrt(s2)
+               <<"   (~0.23 good; ~sqrt(N_cc)="<<std::sqrt((double)CoarseCoarse5d->gSites())<<" = e_k leak)"<<std::endl;
+    }
+  } // both single-RHS ops + padded _A + AggregatesL2 + psi_coarse freed here
+
+  NonHermitianLinearOperator<MrhsLittleDiracOperator,CoarseVector>         mrhsLinOpCoarse(mrhsLittleDiracOpPV);
+  NonHermitianLinearOperator<MrhsLittleDiracOperatorL2,CoarseCoarseVector> mrhsLinOpCC(mrhsLittleDiracOpL2);
+
+  //////////////////////////////////////////////////////////////////////
+  // Solvers, innermost first.
+  //////////////////////////////////////////////////////////////////////
+  TrivialPrecon<CoarseVector>       simpleC;
+  TrivialPrecon<CoarseCoarseVector> simpleCC;
+  TrivialPrecon<LatticeFermionD>    simple_fine;
+
+  // L3 (coarse-coarse) solve: PGCR on the 6D cc operator
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseVector>
+    L3PGCR(L3Tol,L3MaxIt,mrhsLinOpCC,simpleCC,L3Nstep,L3Nstep);
+  L3PGCR.Level(3);
+  L3PGCR.Name("CCouter");
+  L3PGCR.SetZeroGuess(1);              // caller zeroes CCsol
+
+  // L2 coarse smoother: shifted 6D coarse op, fixed nstep
+  ShiftedLinearOperator<CoarseVector> ShiftedMrhsCoarse(CoarseSmootherShift, mrhsLinOpCoarse);
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector>
+    CoarseSmootherGCR(0.01,1,ShiftedMrhsCoarse,simpleC,CoarseSmootherNstep,CoarseSmootherNstep);
+  CoarseSmootherGCR.Level(2);
+  CoarseSmootherGCR.Name("Csmoother");
+  CoarseSmootherGCR.SetZeroGuess(1);   // caller zeroes vec2
+
+  // L2->L3 V-cycle preconditioner (operates on 6D coarse field)
+  MrhsCoarseThreeLevelPrec<CoarseVector,CoarseCoarseVector>
+    L2to3Precon(mrhsLinOpCoarse, CoarseSmootherGCR, MrhsProjectorL2, L3PGCR,
+                Coarse5d, CoarseCoarse5d, CoarseCoarseMrhs, nrhs);
+
+  // L2 coarse solve: PGCR on 6D coarse op, preconditioned by the L2->L3 V-cycle
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector>
+    L2PGCR(CoarseSolverTol, CoarseSolverOrder/16, mrhsLinOpCoarse, L2to3Precon, 16, 16);
+  L2PGCR.Level(2);
+  L2PGCR.Name("Couter");
+  L2PGCR.SetZeroGuess(1);              // caller zeroes CsolMrhs
+
+  // Fine smoother (per-rhs, looped in the L1->L2 V-cycle)
+  PrecGeneralisedConjugateResidualNonHermitian<LatticeFermionD>
+    SmootherGCR(0.0,1,ShiftedPVdagM,simple_fine,FineSmootherOrder,FineSmootherOrder);
+  SmootherGCR.Level(1);
+  SmootherGCR.Name("Fsmoother");
+  SmootherGCR.SetZeroGuess(1);         // caller zeroes vec2[r]
+
+  // L1->L2 V-cycle (fine); its coarse solve is the three-level L2PGCR
+  typedef PrecGeneralisedConjugateResidualNonHermitian<LatticeFermionD> FineSmoother_t;
+  MrhsTwoLevelMG<LatticeFermionD,CoarseVector,FineSmoother_t>
+    ThreeLevelPrecon(PVdagM, SmootherGCR, MrhsProjector, L2PGCR, Coarse5d, CoarseMrhs);
+
+  // Outer mrhs solve
+  MrhsPGCRNonHermitian<LatticeFermionD>
+    L1PGCR(OuterTol,1000,PVdagM,ThreeLevelPrecon,OuterMmax,OuterNstep);
+  L1PGCR.Level(1);
+  L1PGCR.Name("Fouter");
+  L1PGCR.SetZeroGuess(1);              // sol[r]=Zero() at source setup
+
+  //////////////////////////////////////////////////////////////////////
+  // Sources and solve
+  //////////////////////////////////////////////////////////////////////
+  std::vector<LatticeFermionD> src(nrhs,FGrid), sol(nrhs,FGrid);
+  for(int r=0;r<nrhs;r++){ gaussian(RNG5,src[r]); sol[r]=Zero(); }
+
+  std::cout << GridLogMessage << "**********************************************" << std::endl;
+  std::cout << GridLogMessage << " MultiRHS THREE-level solve: " << nrhs << " RHS " << std::endl;
+  std::cout << GridLogMessage << "**********************************************" << std::endl;
+
+  GridStopWatch w; w.Start();
+  L1PGCR(src,sol);
+  w.Stop();
+  std::cout << GridLogMessage << "MultiRHS 3-level solve total " << w.Elapsed()
+            << "  (per RHS: " << w.useconds()/1.0e6/nrhs << " s)" << std::endl;
+
+  { LatticeFermionD Ax(FGrid); RealD worst=0.0;
+    for(int r=0;r<nrhs;r++){ PVdagM.Op(sol[r],Ax); Ax=Ax-src[r];
+      RealD rn=std::sqrt(norm2(Ax)/norm2(src[r]));
+      std::cout << GridLogMessage << "FINAL: rhs["<<r<<"] true residual = " << rn << std::endl;
+      worst=std::max(worst,rn); }
+    std::cout << GridLogMessage << "FINAL: worst-case residual = " << worst << std::endl;
+  }
+
+  std::cout << GridLogMessage << "Done" << std::endl;
+  Grid_finalize();
+  return 0;
+}

examples/Example_pvdagm_mrhs_3level_DenseCoarseMatrix.cc

@@ -0,0 +1,663 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./examples/Example_pvdagm_mrhs_3level_DenseCoarseMatrix.cc
+
+    Copyright (C) 2026
+
+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.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+
+// MultiRHS (valence) THREE-level multigrid for PVdagM with a DENSE, EXACT,
+// non-iterative coarse-coarse bottom -- the LIBRARY-CLASS successor of
+// Example_pvdagm_mrhs_3level_dense.cc, which is FROZEN as the regression
+// baseline / champion-provenance artifact (21.7 s/RHS at BLOCK=2.2.3.3,
+// BLOCK2=8.4.2.4, nb60, CSO3/FSO6/CST0.04 on 36 Frontier nodes).
+//
+// The dense bottom is now Grid/algorithms/multigrid/DenseCoarseMatrix.h:
+//  - stencil -> dense DIRECT import (no probe assembly: rows are local data)
+//    + IMPORT CERTIFICATE  (DENSE_IMPORT_SIGN=-1 flips convention, no rebuild)
+//  - split-K apply via GridBLAS.gemmBatched with explicit leading dimensions
+//    (DENSE_SPLITK chunks, default 32) -- the fig-11 software split-K
+//  - deviceVector / GridBLAS throughout the apply: platform-agnostic
+//
+// INTERCHANGE: same SLAB_FILE per-rank format as the frozen example (stem MUST
+// encode cfg/mass/blocking/nbasis; the header guards only N/nrows/nbasis) and
+// the same env-var set, so existing sbatch scripts drive either binary.
+//
+// A/B acceptance (old binary = control):
+//   slab-cached  : outer counts match EXACTLY (identical apply data; split-K
+//                  changes only fp32 reduction order); wall delta = split-K gain.
+//   fresh setup  : outer equal-or-+-1 (import vs probe = rounding); VERIFY
+//                  ~7e-4 both; setup delta = import gain (~93 s probe retired).
+//
+// Level structure, solvers, and tuning knobs are UNCHANGED from the frozen
+// example.  Env: MASS SUBSPACE_FILE NRHS BLOCK BLOCK2 FineSmootherShift/Order
+// CoarseSmootherShift/Nstep CoarseSolverTol/Order DENSE_CC DENSE_CC_CHECK
+// DENSE_SPLITK DENSE_DEVICE_SUM DENSE_IMPORT_SIGN DENSE_APPLY_PROFILE
+// L3_TOL L3_MAXIT L3_NSTEP OuterMmax OuterNstep OuterTol
+
+#include <Grid/Grid.h>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.h>
+#include <Grid/algorithms/multigrid/DenseCoarseMatrix.h>
+
+#include <memory>
+
+using namespace std;
+using namespace Grid;
+
+RealD FineSmootherShift    = 0.1;
+int   FineSmootherOrder    = 16;
+RealD CoarseSmootherShift  = 0.1;
+int   CoarseSmootherNstep  = 4;
+RealD CoarseSolverTol      = 0.03;
+int   CoarseSolverOrder    = 200;
+RealD L3Tol                = 2.5e-1;
+int   L3MaxIt              = 50;
+int   L3Nstep              = 50;
+RealD OuterTol             = 1.0e-8;
+int   OuterMmax            = 8;
+int   OuterNstep           = 8;
+int   Nrhs                 = 12;
+int   UseDenseCC           = 1;
+RealD mass                 = 0.00078;
+
+void ParseEnvironment(void)
+{
+  if(getenv("MASS"))               mass               = atof(getenv("MASS"));
+  if(getenv("FineSmootherShift"))  FineSmootherShift  = atof(getenv("FineSmootherShift"));
+  if(getenv("FineSmootherOrder"))  FineSmootherOrder  = atoi(getenv("FineSmootherOrder"));
+  if(getenv("CoarseSmootherShift"))CoarseSmootherShift= atof(getenv("CoarseSmootherShift"));
+  if(getenv("CoarseSmootherNstep"))CoarseSmootherNstep= atoi(getenv("CoarseSmootherNstep"));
+  if(getenv("CoarseSolverTol"))    CoarseSolverTol    = atof(getenv("CoarseSolverTol"));
+  if(getenv("CoarseSolverOrder"))  CoarseSolverOrder  = atoi(getenv("CoarseSolverOrder"));
+  if(getenv("L3_TOL"))             L3Tol              = atof(getenv("L3_TOL"));
+  if(getenv("L3_MAXIT"))           L3MaxIt            = atoi(getenv("L3_MAXIT"));
+  if(getenv("L3_NSTEP"))           L3Nstep            = atoi(getenv("L3_NSTEP"));
+  if(getenv("OuterTol"))           OuterTol           = atof(getenv("OuterTol"));
+  if(getenv("OuterMmax"))          OuterMmax          = atoi(getenv("OuterMmax"));
+  if(getenv("OuterNstep"))         OuterNstep         = atoi(getenv("OuterNstep"));
+  if(getenv("NRHS"))               Nrhs               = atoi(getenv("NRHS"));
+  if(getenv("DENSE_CC"))           UseDenseCC         = atoi(getenv("DENSE_CC"));
+
+  std::cout << GridLogMessage << "PARAM: MASS               " << mass               << std::endl;
+  std::cout << GridLogMessage << "PARAM: NRHS               " << Nrhs               << std::endl;
+  std::cout << GridLogMessage << "PARAM: DENSE_CC           " << UseDenseCC         << std::endl;
+  std::cout << GridLogMessage << "PARAM: FineSmootherShift  " << FineSmootherShift  << std::endl;
+  std::cout << GridLogMessage << "PARAM: FineSmootherOrder  " << FineSmootherOrder  << std::endl;
+  std::cout << GridLogMessage << "PARAM: CoarseSmootherShift" << CoarseSmootherShift<< std::endl;
+  std::cout << GridLogMessage << "PARAM: CoarseSmootherNstep" << CoarseSmootherNstep<< std::endl;
+  std::cout << GridLogMessage << "PARAM: CoarseSolverTol    " << CoarseSolverTol    << std::endl;
+  std::cout << GridLogMessage << "PARAM: CoarseSolverOrder  " << CoarseSolverOrder  << std::endl;
+  std::cout << GridLogMessage << "PARAM: L3_TOL             " << L3Tol              << std::endl;
+  std::cout << GridLogMessage << "PARAM: OuterMmax          " << OuterMmax          << std::endl;
+  std::cout << GridLogMessage << "PARAM: OuterNstep         " << OuterNstep         << std::endl;
+}
+
+template <class Field>
+void saveSubspace(std::vector<Field> &subspace, std::string const fname){
+#ifdef HAVE_LIME
+  Grid::emptyUserRecord record;
+  Grid::ScidacWriter SW(subspace[0].Grid()->IsBoss());
+  SW.open(fname);
+  for (int k = 0; k < (int)subspace.size(); k++) SW.writeScidacFieldRecord(subspace[k], record);
+  SW.close();
+#endif
+}
+template <class Field>
+void loadSubspace(std::vector<Field> &subspace, std::string const fname){
+#ifdef HAVE_LIME
+  Grid::emptyUserRecord record;
+  Grid::ScidacReader SR;
+  SR.open(fname);
+  for (int k = 0; k < (int)subspace.size(); k++) SR.readScidacFieldRecord(subspace[k], record);
+  SR.close();
+#endif
+}
+
+//////////////////////////////////////////////////////////////////////
+// A = PV^dag M (non-Hermitian), and shifted variant for smoothers.
+//////////////////////////////////////////////////////////////////////
+template<class Matrix,class Field>
+class PVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat; Matrix &_PV;
+public:
+  PVdagMLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV) {};
+  void OpDiag (const Field &in, Field &out) { assert(0); }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) { assert(0); }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){ assert(0); };
+  void Op     (const Field &in, Field &out){ Field tmp(in.Grid()); _Mat.M(in,tmp); _PV.Mdag(tmp,out); }
+  void AdjOp  (const Field &in, Field &out){ Field tmp(in.Grid()); _PV.M(in,tmp); _Mat.Mdag(tmp,out); }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){ HermOp(in,out); ComplexD d=innerProduct(in,out); n1=real(d); n2=norm2(out); }
+  void HermOp(const Field &in, Field &out){ Field tmp(in.Grid()); Op(in,tmp); AdjOp(tmp,out); }
+};
+
+template<class Matrix,class Field>
+class ShiftedPVdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat; Matrix &_PV;
+public:
+  RealD shift;
+  ShiftedPVdagMLinearOperator(RealD _shift,Matrix &Mat,Matrix &PV): shift(_shift),_Mat(Mat),_PV(PV){};
+  void OpDiag (const Field &in, Field &out) { assert(0); }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) { assert(0); }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){ assert(0); };
+  void Op     (const Field &in, Field &out){ Field tmp(in.Grid()); _Mat.M(in,tmp); _PV.Mdag(tmp,out); out = out + shift*in; }
+  void AdjOp  (const Field &in, Field &out){ Field tmp(in.Grid()); _PV.M(tmp,out); _Mat.Mdag(in,tmp); out = out + shift*in; }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){ assert(0); }
+  void HermOp(const Field &in, Field &out){ Field tmp(in.Grid()); Op(in,tmp); AdjOp(tmp,out); }
+};
+
+// Generic shift wrapper (for the coarse-level smoother on the 6D mrhs coarse operator).
+template<class Field>
+class ShiftedLinearOperator : public LinearOperatorBase<Field> {
+  LinearOperatorBase<Field> &_Op; RealD shift;
+public:
+  ShiftedLinearOperator(RealD _shift, LinearOperatorBase<Field> &Op) : _Op(Op), shift(_shift) {}
+  void OpDiag  (const Field &in, Field &out) { assert(0); }
+  void OpDir   (const Field &in, Field &out,int dir,int disp) { assert(0); }
+  void OpDirAll (const Field &in, std::vector<Field> &out) { assert(0); }
+  void Op      (const Field &in, Field &out) { _Op.Op(in,out);    out = out + shift*in; }
+  void AdjOp   (const Field &in, Field &out) { _Op.AdjOp(in,out); out = out + shift*in; }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){ assert(0); }
+  void HermOp  (const Field &in, Field &out) { Field tmp(in.Grid()); Op(in,tmp); AdjOp(tmp,out); }
+};
+
+//////////////////////////////////////////////////////////////////////
+// Dense CC solve on the PACKED 6D mrhs coarse-coarse field: drop-in
+// for the L3 PGCR, delegating to the library DenseCoarseMatrix.
+//////////////////////////////////////////////////////////////////////
+template<class DenseType, class CoarseCoarseField>
+class MrhsDenseCCSolve : public LinearFunction<CoarseCoarseField> {
+public:
+  DenseType &_Dense;
+  GridBase *_CoarseCoarse5d;
+  int _nrhs;
+  MrhsDenseCCSolve(DenseType &D, GridBase *cc5d, int nrhs)
+    : _Dense(D), _CoarseCoarse5d(cc5d), _nrhs(nrhs) {}
+  using LinearFunction<CoarseCoarseField>::operator();
+  virtual void operator()(const CoarseCoarseField &in, CoarseCoarseField &out){
+    if ( getenv("DENSE_CC_CHECK") ) {
+      // Audit path: per-rhs 5D unpack so ApplyBatch can run the _Op defect
+      // check per rhs.  ~50ms/call of slice/split overhead -- audit only.
+      CoarseCoarseField tmp(in.Grid());
+      tmp = in;
+      std::vector<CoarseCoarseField> split_in (_nrhs,_CoarseCoarse5d);
+      std::vector<CoarseCoarseField> split_out(_nrhs,_CoarseCoarse5d);
+      for(int r=0;r<_nrhs;r++) ExtractSliceFast(split_in[r], tmp, r, 0);
+      _Dense.ApplyBatch(split_in, split_out);
+      for(int r=0;r<_nrhs;r++) InsertSliceFast(split_out[r], out, r, 0);
+    } else {
+      _Dense.ApplyBatch6D(in, out, _nrhs);
+    }
+  }
+};
+
+//////////////////////////////////////////////////////////////////////
+// mrhs interfaces + single-polynomial mrhs PGCR (verbatim from the
+// frozen Example_pvdagm_mrhs_3level_dense.cc)
+//////////////////////////////////////////////////////////////////////
+template<class Field>
+class MrhsLinearFunction {
+public:
+  virtual void operator()(std::vector<Field> &in, std::vector<Field> &out) = 0;
+};
+
+template<class Field>
+class MrhsPGCRNonHermitian {
+public:
+  RealD Tolerance; Integer MaxIterations; int mmax,nstep,steps,level;
+  int ZeroGuess = 0; int FirstCycle = 0;   // caller contract: zero guess => first-cycle r0 = src
+  std::string name = "Level 1";
+  LinearOperatorBase<Field> &Linop;
+  MrhsLinearFunction<Field> &Preconditioner;
+  void Level(int lv){ name = "Level " + std::to_string(lv); level=lv; }
+  void Name(std::string n){ name = n; }
+  void SetZeroGuess(int z){ ZeroGuess=z; }
+  MrhsPGCRNonHermitian(RealD tol,Integer maxit,LinearOperatorBase<Field> &_Linop,MrhsLinearFunction<Field> &Prec,int _mmax,int _nstep)
+    : Tolerance(tol),MaxIterations(maxit),Linop(_Linop),Preconditioner(Prec),mmax(_mmax),nstep(_nstep){ level=1; }
+  static RealD vnorm2(std::vector<Field> &x){ RealD s=0; for(auto &f:x) s+=norm2(f); return s; }
+  static ComplexD vinnerProduct(std::vector<Field> &x,std::vector<Field> &y){ ComplexD s(0); for(int r=0;r<(int)x.size();r++) s+=innerProduct(x[r],y[r]); return s; }
+  static void vaxpy(std::vector<Field> &z,ComplexD a,std::vector<Field> &x,std::vector<Field> &y){ for(int r=0;r<(int)z.size();r++) axpy(z[r],a,x[r],y[r]); }
+  void vOp(std::vector<Field> &in,std::vector<Field> &out){ for(int r=0;r<(int)in.size();r++) Linop.Op(in[r],out[r]); }
+  void operator()(std::vector<Field> &src,std::vector<Field> &psi){
+    RealD cp,ssq,rsq; int nrhs=src.size(); GridBase *grid=src[0].Grid();
+    ssq=vnorm2(src); rsq=Tolerance*Tolerance*ssq;
+    std::vector<Field> r(nrhs,grid);
+    GridStopWatch T; T.Start(); steps=0; FirstCycle=1;
+    for(int k=0;k<MaxIterations;k++){
+      cp=GCRnStep(src,psi,rsq);
+      std::cout<<GridLogMessage<<std::string(level,'\t')<<" "<<name<<" MrhsPGCR("<<mmax<<","<<nstep<<") "<<steps<<" steps cp = "<<cp<<" target "<<rsq<<std::endl;
+      if(cp<rsq){
+        T.Stop(); vOp(psi,r); for(int rr=0;rr<nrhs;rr++) axpy(r[rr],-1.0,src[rr],r[rr]);
+        RealD tr=vnorm2(r);
+        std::cout<<GridLogMessage<<std::string(level,'\t')<<" "<<name<<" MrhsPGCR: Converged on iteration "<<steps
+                 <<" computed residual "<<std::sqrt(cp/ssq)<<" true residual "<<std::sqrt(tr/ssq)<<" target "<<Tolerance<<std::endl;
+        std::cout<<GridLogMessage<<std::string(level,'\t')<<" "<<name<<" MrhsPGCR Time elapsed: Total "<<T.Elapsed()<<std::endl;
+        for(int rr=0;rr<nrhs;rr++){ RealD rn=std::sqrt(norm2(r[rr])/norm2(src[rr])); std::cout<<GridLogMessage<<"MrhsPGCR per-rhs true residual["<<rr<<"] = "<<rn<<std::endl; }
+        return;
+      }
+    }
+    std::cout<<GridLogMessage<<"MrhsPGCR: did not converge"<<std::endl;
+  }
+  RealD GCRnStep(std::vector<Field> &src,std::vector<Field> &psi,RealD rsq){
+    RealD cp; ComplexD a,b,rq; RealD zAAz; int nrhs=src.size(); GridBase *grid=src[0].Grid();
+    std::vector<Field> r(nrhs,grid),z(nrhs,grid),Az(nrhs,grid);
+    std::vector< std::vector<Field> > q(mmax,std::vector<Field>(nrhs,grid));
+    std::vector< std::vector<Field> > p(mmax,std::vector<Field>(nrhs,grid));
+    std::vector<RealD> qq(mmax);
+    std::cout<<GridLogMessage<<std::string(level,'\t')<<" "<<name<<" MrhsPGCR nStep("<<nstep<<")"<<std::endl;
+    if (ZeroGuess && FirstCycle) { for(int rr=0;rr<nrhs;rr++){ psi[rr]=Zero(); r[rr]=src[rr]; } }
+    else                         { vOp(psi,Az); for(int rr=0;rr<nrhs;rr++) r[rr]=src[rr]-Az[rr]; }
+    FirstCycle=0;
+    Preconditioner(r,z); vOp(z,Az); zAAz=vnorm2(Az);
+    p[0]=z; q[0]=Az; qq[0]=zAAz; cp=vnorm2(r);
+    for(int k=0;k<nstep;k++){
+      steps++; int kp=k+1, peri_k=k%mmax, peri_kp=kp%mmax;
+      rq=vinnerProduct(q[peri_k],r); a=rq/qq[peri_k];
+      vaxpy(psi,a,p[peri_k],psi); vaxpy(r,-a,q[peri_k],r); cp=vnorm2(r);
+      std::cout<<GridLogMessage<<std::string(level,'\t')<<" "<<name<<" MrhsPGCR step["<<steps<<"]  resid "<<cp<<" target "<<rsq<<std::endl;
+      if((k==nstep-1)||(cp<rsq)) return cp;
+      Preconditioner(r,z); vOp(z,Az); zAAz=vnorm2(Az);
+      q[peri_kp]=Az; p[peri_kp]=z;
+      int northog=((kp)>(mmax-1))?(mmax-1):(kp);
+      for(int back=0;back<northog;back++){ int peri_back=(k-back)%mmax; GRID_ASSERT((k-back)>=0);
+        b=-real(vinnerProduct(q[peri_back],Az))/qq[peri_back];
+        vaxpy(p[peri_kp],b,p[peri_back],p[peri_kp]); vaxpy(q[peri_kp],b,q[peri_back],q[peri_kp]); }
+      qq[peri_kp]=vnorm2(q[peri_kp]);
+    }
+    GRID_ASSERT(0); return cp;
+  }
+};
+
+//////////////////////////////////////////////////////////////////////
+// L2->L3 mrhs V-cycle: LinearFunction on the 6D mrhs COARSE field.
+// The coarse-coarse solve slot takes EITHER the dense mrhs solve
+// (DENSE_CC=1) or the L3 PGCR (DENSE_CC=0).
+//////////////////////////////////////////////////////////////////////
+template<class CoarseField, class CoarseCoarseField>
+class MrhsCoarseThreeLevelPrec : public LinearFunction<CoarseField> {
+public:
+  LinearOperatorBase<CoarseField>          &_CoarseOp;          // mrhs coarse op (6D)
+  LinearFunction<CoarseField>              &_CoarseSmoother;    // shifted 6D coarse smoother
+  MultiRHSBlockProject<CoarseField>        &_Projector;         // L2->L3 (vector-based)
+  LinearFunction<CoarseCoarseField>        &_CoarseCoarseSolve; // L3 solve (6D cc)
+  GridBase *_Coarse5d, *_CoarseCoarse5d, *_CoarseCoarseMrhs;
+  int _nrhs;
+
+  MrhsCoarseThreeLevelPrec(LinearOperatorBase<CoarseField> &CoarseOp,
+                           LinearFunction<CoarseField> &CoarseSmoother,
+                           MultiRHSBlockProject<CoarseField> &Projector,
+                           LinearFunction<CoarseCoarseField> &CoarseCoarseSolve,
+                           GridBase *Coarse5d, GridBase *CoarseCoarse5d, GridBase *CoarseCoarseMrhs, int nrhs)
+    : _CoarseOp(CoarseOp), _CoarseSmoother(CoarseSmoother), _Projector(Projector),
+      _CoarseCoarseSolve(CoarseCoarseSolve),
+      _Coarse5d(Coarse5d), _CoarseCoarse5d(CoarseCoarse5d), _CoarseCoarseMrhs(CoarseCoarseMrhs), _nrhs(nrhs) {}
+
+  using LinearFunction<CoarseField>::operator();
+  virtual void operator()(const CoarseField &in, CoarseField &out) {
+    int nrhs=_nrhs; double t;
+    CoarseField vec1(in.Grid());
+    CoarseField vec2(in.Grid());
+
+    // trivial pre-smoother
+    out = in;
+
+    // residual (6D coarse)
+    _CoarseOp.Op(out,vec1);  sub(vec1,in,vec1);
+
+    // restrict: unpack 6D coarse -> vector<Coarse> -> blockProject -> vector<CoarseCoarse> -> pack 6D cc
+    std::vector<CoarseField>       csplit(nrhs,_Coarse5d);
+    std::vector<CoarseCoarseField> ccsplit(nrhs,_CoarseCoarse5d);
+    CoarseCoarseField CCsrc(_CoarseCoarseMrhs);
+    CoarseCoarseField CCsol(_CoarseCoarseMrhs);
+
+    t=-usecond();
+    for(int r=0;r<nrhs;r++) ExtractSliceFast(csplit[r],vec1,r,0);
+    _Projector.blockProject(csplit,ccsplit);
+    for(int r=0;r<nrhs;r++) InsertSliceFast(ccsplit[r],CCsrc,r,0);
+    t+=usecond();
+    std::cout<<GridLogMessage<<"L2->L3 restrict took "<<t/1000.0<<"ms"<<std::endl;
+
+    // L3 solve (dense mrhs GEMM, or PGCR)
+    t=-usecond();
+    CCsol=Zero();
+    _CoarseCoarseSolve(CCsrc,CCsol);
+    t+=usecond();
+    std::cout<<GridLogMessage<<"L3 coarse-coarse solve took "<<t/1000.0<<"ms  ("<<t/1000.0/nrhs<<"ms/rhs)"<<std::endl;
+
+    // prolong: unpack 6D cc -> blockPromote -> pack 6D coarse; add correction
+    t=-usecond();
+    for(int r=0;r<nrhs;r++) ExtractSliceFast(ccsplit[r],CCsol,r,0);
+    _Projector.blockPromote(csplit,ccsplit);
+    for(int r=0;r<nrhs;r++) InsertSliceFast(csplit[r],vec1,r,0);
+    add(out,out,vec1);
+    t+=usecond();
+    std::cout<<GridLogMessage<<"L2->L3 prolong took "<<t/1000.0<<"ms"<<std::endl;
+
+    // residual + coarse smoother (6D coarse)
+    _CoarseOp.Op(out,vec1);  sub(vec1,in,vec1);
+    vec2=Zero();
+    _CoarseSmoother(vec1,vec2);
+    add(out,out,vec2);
+  }
+};
+
+//////////////////////////////////////////////////////////////////////
+// L1->L2 mrhs V-cycle (verbatim from the frozen example)
+//////////////////////////////////////////////////////////////////////
+template<class FineField, class MrhsCoarseVector, class FineSmoother>
+class MrhsTwoLevelMG : public MrhsLinearFunction<FineField> {
+public:
+  typedef MrhsCoarseVector CoarseVector;
+  LinearOperatorBase<FineField>   &_FineOperator;
+  FineSmoother                    &_PostSmoother;
+  MultiRHSBlockProject<FineField> &_Projector;
+  LinearFunction<CoarseVector>    &_CoarseSolve;
+  GridBase *_CoarseGrid, *_CoarseGridMrhs;
+  MrhsTwoLevelMG(LinearOperatorBase<FineField> &FineOp, FineSmoother &Post,
+                 MultiRHSBlockProject<FineField> &Projector, LinearFunction<CoarseVector> &CoarseSolve,
+                 GridBase *CoarseGrid, GridBase *CoarseGridMrhs)
+    : _FineOperator(FineOp),_PostSmoother(Post),_Projector(Projector),_CoarseSolve(CoarseSolve),
+      _CoarseGrid(CoarseGrid),_CoarseGridMrhs(CoarseGridMrhs){}
+  virtual void operator()(std::vector<FineField> &in, std::vector<FineField> &out){
+    int nrhs=in.size(); GridBase *fgrid=in[0].Grid(); double t;
+    std::vector<FineField> vec1(nrhs,fgrid),vec2(nrhs,fgrid);
+    for(int r=0;r<nrhs;r++) out[r]=in[r];
+    for(int r=0;r<nrhs;r++){ _FineOperator.Op(out[r],vec1[r]); sub(vec1[r],in[r],vec1[r]); }
+    std::vector<CoarseVector> Csrc_split(nrhs,_CoarseGrid), Csol_split(nrhs,_CoarseGrid);
+    CoarseVector CsrcMrhs(_CoarseGridMrhs), CsolMrhs(_CoarseGridMrhs);
+    t=-usecond();
+    _Projector.blockProject(vec1,Csrc_split);
+    for(int r=0;r<nrhs;r++) InsertSliceFast(Csrc_split[r],CsrcMrhs,r,0);
+    t+=usecond(); std::cout<<GridLogMessage<<"Mrhs project+pack took "<<t/1000.0<<"ms"<<std::endl;
+    t=-usecond(); CsolMrhs=Zero(); _CoarseSolve(CsrcMrhs,CsolMrhs); t+=usecond();
+    std::cout<<GridLogMessage<<"Mrhs coarse solve took "<<t/1000.0<<"ms  ("<<t/1000.0/nrhs<<"ms/rhs)"<<std::endl;
+    t=-usecond();
+    for(int r=0;r<nrhs;r++) ExtractSliceFast(Csol_split[r],CsolMrhs,r,0);
+    _Projector.blockPromote(vec1,Csol_split);
+    for(int r=0;r<nrhs;r++) add(out[r],out[r],vec1[r]);
+    t+=usecond(); std::cout<<GridLogMessage<<"Mrhs unpack+promote took "<<t/1000.0<<"ms"<<std::endl;
+    for(int r=0;r<nrhs;r++){ _FineOperator.Op(out[r],vec1[r]); sub(vec1[r],in[r],vec1[r]); }
+    t=-usecond();
+    for(int r=0;r<nrhs;r++){ vec2[r]=Zero(); _PostSmoother(vec1[r],vec2[r]); add(out[r],out[r],vec2[r]); }
+    t+=usecond(); std::cout<<GridLogMessage<<"Mrhs post-smooth took "<<t/1000.0<<"ms  ("<<t/1000.0/nrhs<<"ms/rhs)"<<std::endl;
+  }
+};
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+  ParseEnvironment();
+
+  const int Ls=24; RealD M5=1.8, b=1.5, c=0.5;
+  const int nbasis=60; const int nrhs=Nrhs;
+  GRID_ASSERT(nrhs % vComplex::Nsimd() == 0);
+
+  std::vector<int> lat_size {48,48,48,96};
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(lat_size, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  // Level 1 blocking (default 2^4)
+  Coordinate clatt = lat_size;
+  Coordinate Block({2,2,2,2});
+  if ( getenv("BLOCK") ){ GridCmdOptionIntVector(std::string(getenv("BLOCK")),Block); GRID_ASSERT(Block.size()==4); }
+  for(int d=0;d<4;d++){ GRID_ASSERT(lat_size[d]%Block[d]==0); clatt[d]=lat_size[d]/Block[d]; }
+  std::cout << GridLogMessage << "Block  " << Block  << "  coarse lattice       " << clatt << std::endl;
+
+  // Level 2 blocking: SUPERCOARSE default 8,4,3,6 -> CC [3,6,8,8], the dense floor.
+  Coordinate cclatt = clatt;
+  Coordinate Block2({8,4,3,6});
+  if ( getenv("BLOCK2") ){ GridCmdOptionIntVector(std::string(getenv("BLOCK2")),Block2); GRID_ASSERT(Block2.size()==4); }
+  for(int d=0;d<4;d++){ GRID_ASSERT(clatt[d]%Block2[d]==0); cclatt[d]=clatt[d]/Block2[d]; }
+  std::cout << GridLogMessage << "Block2 " << Block2 << "  coarse-coarse lattice " << cclatt << std::endl;
+
+  GridCartesian *Coarse4d = SpaceTimeGrid::makeFourDimGrid(clatt, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *Coarse5d = SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+  GridCartesian *CoarseCoarse4d = SpaceTimeGrid::makeFourDimGrid(cclatt, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridCartesian *CoarseCoarse5d = SpaceTimeGrid::makeFiveDimGrid(1,CoarseCoarse4d);
+
+  // 6D mrhs grids: rhs is dim 0, SIMD across rhs
+  Coordinate mpi=GridDefaultMpi();
+  Coordinate rhMpi ({1,1,mpi[0],mpi[1],mpi[2],mpi[3]});
+  Coordinate rhSimd({vComplex::Nsimd(),1,1,1,1,1});
+  Coordinate rhLatt ({nrhs,1,clatt[0], clatt[1], clatt[2], clatt[3]});
+  Coordinate rhLatt2({nrhs,1,cclatt[0],cclatt[1],cclatt[2],cclatt[3]});
+  GridCartesian *CoarseMrhs       = new GridCartesian(rhLatt, rhSimd,rhMpi);
+  GridCartesian *CoarseCoarseMrhs = new GridCartesian(rhLatt2,rhSimd,rhMpi);
+
+  GridParallelRNG RNG5(FGrid); RNG5.SeedFixedIntegers({5,6,7,8});
+
+  LatticeGaugeField Umu(UGrid);
+  std::cout << GridLogMessage << "Reading gauge field" << std::endl;
+  FieldMetaData header;
+  std::string file("/ccs/home/poare/ckpoint_lat.1000");
+  NerscIO::readConfiguration(Umu,header,file);
+
+  MobiusFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5,b,c);
+  MobiusFermionD Dpv (Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,1.0, M5,b,c);
+
+  typedef PVdagMLinearOperator<MobiusFermionD,LatticeFermionD>        PVdagM_t;
+  typedef ShiftedPVdagMLinearOperator<MobiusFermionD,LatticeFermionD> ShiftedPVdagM_t;
+
+  // Level 1 tensor types
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis>       LittleDiracOperator;
+  typedef MultiGeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis>  MrhsLittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector                                CoarseVector;
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis>                  Subspace;
+
+  // Level 2 tensor types (coarsening deepens the nest by one iScalar)
+  typedef CoarseVector::vector_object                                      CoarseSiteObj;
+  typedef iScalar<vTComplex>                                              vTTComplex;
+  typedef GeneralCoarsenedMatrix<CoarseSiteObj,vTTComplex,nbasis>          LittleDiracOperatorL2;
+  typedef MultiGeneralCoarsenedMatrix<CoarseSiteObj,vTTComplex,nbasis>     MrhsLittleDiracOperatorL2;
+  typedef LittleDiracOperatorL2::CoarseVector                              CoarseCoarseVector;
+  typedef Aggregation<CoarseSiteObj,vTTComplex,nbasis>                     SubspaceL2;
+
+  // The library dense bottom over the L2 coarse operator
+  typedef DenseCoarseMatrix<CoarseSiteObj,vTTComplex,nbasis>               DenseCC_t;
+
+  PVdagM_t        PVdagM(Ddwf,Dpv);
+  ShiftedPVdagM_t ShiftedPVdagM(FineSmootherShift,Ddwf,Dpv);
+
+  NextToNearestStencilGeometry5D geom (Coarse5d);
+  NextToNearestStencilGeometry5D geom2(CoarseCoarse5d);
+
+  //////////////////////////////////////////////////////////////////////
+  // Subspace: load RAW (no Orthogonalise!), or generate.
+  //////////////////////////////////////////////////////////////////////
+  std::string subspace_file = "/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/subspace_nb"
+                            + std::to_string(nbasis) + ".scidac";
+  if ( getenv("SUBSPACE_FILE") ) subspace_file = std::string(getenv("SUBSPACE_FILE"));
+  uint64_t file_exists=0;
+  if ( UGrid->IsBoss() ){ std::ifstream f(subspace_file); file_exists=f.good()?1:0; }
+  UGrid->GlobalSum(file_exists);
+
+  const int cb=0;
+  Subspace AggregatesGCR(Coarse5d,FGrid,cb);
+  if ( file_exists ){
+    std::cout << GridLogMessage << "*** Loading subspace from disk (kept RAW) ***" << std::endl;
+    loadSubspace(AggregatesGCR.subspace, subspace_file);
+  } else {
+    std::cout << GridLogMessage << "*** GCR subspace generation ***" << std::endl;
+    AggregatesGCR.CreateSubspaceGCR(RNG5,PVdagM,nbasis);
+    saveSubspace(AggregatesGCR.subspace, subspace_file);
+  }
+
+  // RAW copy of the fine null vectors BEFORE CoarsenOperator block-orthonormalises in place.
+  std::vector<LatticeFermionD> rawNull(nbasis,FGrid);
+  for(int k=0;k<nbasis;k++) rawNull[k]=AggregatesGCR.subspace[k];
+
+  //////////////////////////////////////////////////////////////////////
+  // Coarsen L1->L2 and L2->L3 with SINGLE-RHS machinery; import to mrhs via
+  // CopyMatrix.  The L2 (coarse-coarse) single-RHS operator is HOISTED to
+  // main scope: DenseCoarseMatrix imports its stencil and uses its M for
+  // certificates, so it must stay alive for the whole run.
+  //////////////////////////////////////////////////////////////////////
+  MrhsLittleDiracOperator   mrhsLittleDiracOpPV(geom,  CoarseMrhs);
+  MrhsLittleDiracOperatorL2 mrhsLittleDiracOpL2(geom2, CoarseCoarseMrhs);
+  MultiRHSBlockProject<LatticeFermionD> MrhsProjector;
+  MultiRHSBlockProject<CoarseVector>    MrhsProjectorL2;
+
+  LittleDiracOperatorL2 LittleDiracOpL2(geom2,Coarse5d,CoarseCoarse5d);
+  NonHermitianLinearOperator<LittleDiracOperatorL2,CoarseCoarseVector> LinOpCC5d(LittleDiracOpL2);
+
+  {
+    // --- L1->L2 single-RHS coarse operator (scoped: its padded _A is the memory peak) ---
+    LittleDiracOperator LittleDiracOpPV(geom,FGrid,Coarse5d);
+    LittleDiracOpPV.CoarsenOperator(PVdagM, AggregatesGCR);   // orthonormalises AggregatesGCR.subspace in place
+    mrhsLittleDiracOpPV.CopyMatrix(LittleDiracOpPV);
+    MrhsProjector.Allocate(nbasis,FGrid,Coarse5d);
+    MrhsProjector.ImportBasis(AggregatesGCR.subspace);
+    NonHermitianLinearOperator<LittleDiracOperator,CoarseVector> LinOpCoarse(LittleDiracOpPV);
+
+    // --- psi_coarse = P^dag (RAW fine null) -> Galerkin images, NOT e_k ---
+    std::vector<CoarseVector> psi_coarse(nbasis,Coarse5d);
+    for(int k=0;k<nbasis;k++) AggregatesGCR.ProjectToSubspace(psi_coarse[k], rawNull[k]);
+    rawNull.clear(); rawNull.shrink_to_fit();
+    {
+      RealD s2=0.0;
+      for(int i=0;i<nbasis;i++) for(int j=0;j<nbasis;j++){
+        ComplexD sij=TensorRemove(innerProduct(psi_coarse[i],psi_coarse[j]));
+        ComplexD d=sij-(i==j?ComplexD(1.0):ComplexD(0.0)); s2+=real(d)*real(d)+imag(d)*imag(d);
+      }
+      std::cout<<GridLogMessage<<"GUARD: ||<psi_coarse|psi_coarse> - I||_F = "<<std::sqrt(s2)
+               <<"   (~0.23 good; ~sqrt(N_coarse)="<<std::sqrt((double)Coarse5d->gSites())<<" = e_k leak)"<<std::endl;
+    }
+
+    // --- L2->L3 single-RHS coarsening ---
+    SubspaceL2 AggregatesL2(CoarseCoarse5d,Coarse5d,cb);
+    for(int k=0;k<nbasis;k++) AggregatesL2.subspace[k]=psi_coarse[k];
+    LittleDiracOpL2.CoarsenOperator(LinOpCoarse, AggregatesL2);
+    mrhsLittleDiracOpL2.CopyMatrix(LittleDiracOpL2);
+    MrhsProjectorL2.Allocate(nbasis,Coarse5d,CoarseCoarse5d);
+    MrhsProjectorL2.ImportBasis(AggregatesL2.subspace);
+
+    // --- guard psi_cc ---
+    {
+      std::vector<CoarseCoarseVector> psi_cc(nbasis,CoarseCoarse5d);
+      for(int k=0;k<nbasis;k++) AggregatesL2.ProjectToSubspace(psi_cc[k], psi_coarse[k]);
+      RealD s2=0.0;
+      for(int i=0;i<nbasis;i++) for(int j=0;j<nbasis;j++){
+        ComplexD sij=TensorRemove(innerProduct(psi_cc[i],psi_cc[j]));
+        ComplexD d=sij-(i==j?ComplexD(1.0):ComplexD(0.0)); s2+=real(d)*real(d)+imag(d)*imag(d);
+      }
+      std::cout<<GridLogMessage<<"GUARD: ||<psi_cc|psi_cc> - I||_F = "<<std::sqrt(s2)
+               <<"   (~0.23 good; ~sqrt(N_cc)="<<std::sqrt((double)CoarseCoarse5d->gSites())<<" = e_k leak)"<<std::endl;
+    }
+  } // single-RHS FINE op + padded _A + AggregatesL2 + psi_coarse freed here
+
+  NonHermitianLinearOperator<MrhsLittleDiracOperator,CoarseVector>         mrhsLinOpCoarse(mrhsLittleDiracOpPV);
+  NonHermitianLinearOperator<MrhsLittleDiracOperatorL2,CoarseCoarseVector> mrhsLinOpCC(mrhsLittleDiracOpL2);
+
+  //////////////////////////////////////////////////////////////////////
+  // DENSE coarse-coarse bottom: the LIBRARY class, constructed AFTER the
+  // fine coarsening frees its memory peak.  Imports the stencil of the
+  // hoisted single-RHS LittleDiracOpL2 directly (no probing).
+  //////////////////////////////////////////////////////////////////////
+  std::unique_ptr<DenseCC_t> DenseCC;
+  std::unique_ptr<MrhsDenseCCSolve<DenseCC_t,CoarseCoarseVector>> MrhsDenseCC;
+  if (UseDenseCC) {
+    std::cout << GridLogMessage << "**********************************************" << std::endl;
+    std::cout << GridLogMessage << " Dense CC inverse setup (library DenseCoarseMatrix)" << std::endl;
+    std::cout << GridLogMessage << "**********************************************" << std::endl;
+    DenseCC.reset(new DenseCC_t(LittleDiracOpL2, CoarseCoarse5d));
+    MrhsDenseCC.reset(new MrhsDenseCCSolve<DenseCC_t,CoarseCoarseVector>(*DenseCC, CoarseCoarse5d, nrhs));
+  }
+
+  //////////////////////////////////////////////////////////////////////
+  // Solvers, innermost first.
+  //////////////////////////////////////////////////////////////////////
+  TrivialPrecon<CoarseVector>       simpleC;
+  TrivialPrecon<CoarseCoarseVector> simpleCC;
+  TrivialPrecon<LatticeFermionD>    simple_fine;
+
+  // L3 (coarse-coarse) iterative solve: PGCR on the 6D cc operator (DENSE_CC=0 branch)
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseCoarseVector>
+    L3PGCR(L3Tol,L3MaxIt,mrhsLinOpCC,simpleCC,L3Nstep,L3Nstep);
+  L3PGCR.Level(3);
+  L3PGCR.Name("CCouter");
+
+  LinearFunction<CoarseCoarseVector> *ccSolve;
+  if (UseDenseCC) ccSolve = MrhsDenseCC.get();
+  else            ccSolve = &L3PGCR;
+
+  // L2 coarse smoother: shifted 6D coarse op, fixed nstep
+  ShiftedLinearOperator<CoarseVector> ShiftedMrhsCoarse(CoarseSmootherShift, mrhsLinOpCoarse);
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector>
+    CoarseSmootherGCR(0.01,1,ShiftedMrhsCoarse,simpleC,CoarseSmootherNstep,CoarseSmootherNstep);
+  CoarseSmootherGCR.Level(2);
+  CoarseSmootherGCR.Name("Csmoother");
+  CoarseSmootherGCR.SetZeroGuess(1);   // caller zeroes vec2: skip r0 apply every L2 iteration
+
+  // L2->L3 V-cycle preconditioner (operates on 6D coarse field)
+  MrhsCoarseThreeLevelPrec<CoarseVector,CoarseCoarseVector>
+    L2to3Precon(mrhsLinOpCoarse, CoarseSmootherGCR, MrhsProjectorL2, *ccSolve,
+                Coarse5d, CoarseCoarse5d, CoarseCoarseMrhs, nrhs);
+
+  // L2 coarse solve: PGCR on 6D coarse op, preconditioned by the L2->L3 V-cycle
+  PrecGeneralisedConjugateResidualNonHermitian<CoarseVector>
+    L2PGCR(CoarseSolverTol, CoarseSolverOrder/16, mrhsLinOpCoarse, L2to3Precon, 16, 16);
+  L2PGCR.Level(2);
+  L2PGCR.Name("Couter");
+  L2PGCR.SetZeroGuess(1);              // caller zeroes CsolMrhs; restarts still recompute r
+
+  // Fine smoother (per-rhs, looped in the L1->L2 V-cycle)
+  PrecGeneralisedConjugateResidualNonHermitian<LatticeFermionD>
+    SmootherGCR(0.0,1,ShiftedPVdagM,simple_fine,FineSmootherOrder,FineSmootherOrder);
+  SmootherGCR.Level(1);
+  SmootherGCR.Name("Fsmoother");
+  SmootherGCR.SetZeroGuess(1);         // caller zeroes vec2[r]: saves 12 fine mults/outer
+
+  // L1->L2 V-cycle (fine); its coarse solve is the three-level L2PGCR
+  typedef PrecGeneralisedConjugateResidualNonHermitian<LatticeFermionD> FineSmoother_t;
+  MrhsTwoLevelMG<LatticeFermionD,CoarseVector,FineSmoother_t>
+    ThreeLevelPrecon(PVdagM, SmootherGCR, MrhsProjector, L2PGCR, Coarse5d, CoarseMrhs);
+
+  // Outer mrhs solve
+  MrhsPGCRNonHermitian<LatticeFermionD>
+    L1PGCR(OuterTol,1000,PVdagM,ThreeLevelPrecon,OuterMmax,OuterNstep);
+  L1PGCR.Level(1);
+  L1PGCR.Name("Fouter");
+  L1PGCR.SetZeroGuess(1);              // sol[r]=Zero() below; restarts recompute r as always
+
+  //////////////////////////////////////////////////////////////////////
+  // Sources and solve
+  //////////////////////////////////////////////////////////////////////
+  std::vector<LatticeFermionD> src(nrhs,FGrid), sol(nrhs,FGrid);
+  for(int r=0;r<nrhs;r++){ gaussian(RNG5,src[r]); sol[r]=Zero(); }
+
+  std::cout << GridLogMessage << "**********************************************" << std::endl;
+  std::cout << GridLogMessage << " MultiRHS THREE-level solve (DenseCoarseMatrix bottom): " << nrhs << " RHS " << std::endl;
+  std::cout << GridLogMessage << "**********************************************" << std::endl;
+
+  GridStopWatch w; w.Start();
+  L1PGCR(src,sol);
+  w.Stop();
+  std::cout << GridLogMessage << "MultiRHS 3-level dense solve total " << w.Elapsed()
+            << "  (per RHS: " << w.useconds()/1.0e6/nrhs << " s)" << std::endl;
+
+  { LatticeFermionD Ax(FGrid); RealD worst=0.0;
+    for(int r=0;r<nrhs;r++){ PVdagM.Op(sol[r],Ax); Ax=Ax-src[r];
+      RealD rn=std::sqrt(norm2(Ax)/norm2(src[r]));
+      std::cout << GridLogMessage << "FINAL: rhs["<<r<<"] true residual = " << rn << std::endl;
+      worst=std::max(worst,rn); }
+    std::cout << GridLogMessage << "FINAL: worst-case residual = " << worst << std::endl;
+  }
+
+  std::cout << GridLogMessage << "Done" << std::endl;
+  Grid_finalize();
+  return 0;
+}

scripts/filelist

@@ -11,7 +11,7 @@ CCFILES=`find . -name '*.cc' -not -path '*/instantiation/*/*' -not -path '*/gamm
 
 ZWILS_FERMION_FILES=` find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/ZWilsonImpl*' `
 WILS_FERMION_FILES=`  find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/WilsonImpl*' `
-STAG_FERMION_FILES=`  find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/Staggered*' `
+STAG_FERMION_FILES=`  find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/StaggeredImpl*' `
 GP_FERMION_FILES=`    find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/Gparity*' `
 ADJ_FERMION_FILES=`   find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/WilsonAdj*' `
 TWOIND_FERMION_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/WilsonTwoIndex*'`

skills/communication-overlap.md

@@ -0,0 +1,196 @@
+---
+name: communication-overlap
+description: Design and implement communication/computation overlap pipelines for GPU+MPI codes — per-packet event tracking, host-staging through pinned memory, internode/intranode bandwidth separation, and the 7-phase pipeline pattern that replaces broken accelerator-aware MPI paths.
+user-invocable: true
+allowed-tools:
+  - Read
+  - Bash(grep -r)
+---
+
+# Communication/Computation Overlap Pipeline Design
+
+## Why GPU-Direct MPI Is Often Not the Right Default
+
+GPU-direct RDMA (passing GPU buffer pointers directly to MPI) is appealing because it eliminates explicit D2H/H2D copies. In practice on several leadership systems:
+
+- **Bandwidth**: RDMA at 30% of wirespeed has been observed on Pontevecchio/Aurora. The overhead of staging through pinned host memory can be *lower* total latency than slow RDMA.
+- **Correctness**: Device buffer aliasing in `MPI_Sendrecv` (see `mpi-heterogeneous.md`) makes direct GPU-to-GPU transfer unreliable.
+- **Overlap**: Host-staging enables fine-grained overlap — each packet's D2H can be issued as a separate asynchronous event, and the corresponding MPI send can fire as soon as *that packet* arrives in host memory, not after all packets are ready.
+
+The pipeline pattern below was developed to replace broken MPICH accelerator-aware paths. It achieves genuine computation/communication overlap by tracking per-packet GPU events.
+
+## The 7-Phase Pipeline
+
+Given a set of halo exchange operations (each identified by a `packet_index`):
+
+### Phase 0: Prepare data on device
+Pack halo data into contiguous GPU buffers. One buffer per direction/neighbour.
+
+### Phase 1: Post receives + start D2H
+Post all `MPI_Irecv` calls immediately (into pinned host buffers). Simultaneously, start asynchronous D2H copies for all send buffers:
+
+```cpp
+for (auto &pkt : send_packets) {
+    MPI_Irecv(pkt.host_recv_buf, pkt.bytes, MPI_BYTE,
+               pkt.src_rank, pkt.tag, comm, &pkt.recv_req);
+    
+    acceleratorCopyFromDeviceAsync(pkt.device_send_buf,
+                                   pkt.host_send_buf,
+                                   pkt.bytes, &pkt.d2h_event);
+}
+```
+
+The key: `pkt.d2h_event` is a per-packet GPU event (e.g. `cudaEvent_t`, `hipEvent_t`, or SYCL event). We can poll individual packet completion rather than waiting for all.
+
+### Phase 2: Fire sends as D2H completes (packet by packet)
+Poll packet D2H events. As each packet becomes ready in host memory, immediately fire the corresponding `MPI_Isend`. Also start intranode D2D copies at this point — these are deferred until now to avoid competing with the internode D2H on PCIe bandwidth:
+
+```cpp
+bool all_sent = false;
+while (!all_sent) {
+    all_sent = true;
+    for (auto &pkt : send_packets) {
+        if (!pkt.sent && acceleratorEventIsComplete(pkt.d2h_event)) {
+            MPI_Isend(pkt.host_send_buf, pkt.bytes, MPI_BYTE,
+                       pkt.dst_rank, pkt.tag, comm, &pkt.send_req);
+            pkt.sent = true;
+            start_intranode_copy(pkt);  // now safe, D2H is done
+        }
+        if (!pkt.sent) all_sent = false;
+    }
+}
+```
+
+### Phase 3: Poll receives + start H2D as each arrives
+`MPI_Test` individual receive requests. As each completes, immediately start the H2D copy into device-resident halo buffer:
+
+```cpp
+bool all_recvd = false;
+while (!all_recvd) {
+    all_recvd = true;
+    for (auto &pkt : recv_packets) {
+        if (!pkt.h2d_started) {
+            int flag = 0;
+            MPI_Test(&pkt.recv_req, &flag, MPI_STATUS_IGNORE);
+            if (flag) {
+                acceleratorCopyToDeviceAsync(pkt.host_recv_buf,
+                                              pkt.device_recv_buf,
+                                              pkt.bytes, &pkt.h2d_event);
+                pkt.h2d_started = true;
+            }
+        }
+        if (!pkt.h2d_started) all_recvd = false;
+    }
+}
+```
+
+### Phase 4: Wait for all sends
+```cpp
+std::vector<MPI_Request> send_reqs;
+for (auto &pkt : send_packets) send_reqs.push_back(pkt.send_req);
+MPI_Waitall(send_reqs.size(), send_reqs.data(), MPI_STATUSES_IGNORE);
+```
+
+### Phase 5: Wait for all H2D copies
+```cpp
+for (auto &pkt : recv_packets) acceleratorEventWait(pkt.h2d_event);
+```
+
+### Phase 6: Run interior computation
+The interior (non-halo) computation can run from Phase 1 onwards, overlapped with all of the above:
+
+```cpp
+// Launched in Phase 1, runs in parallel with the pipeline
+accelerator_for(ss, interior_sites, ...) { compute_interior(ss); }
+```
+
+Synchronise with interior before using the full field:
+```cpp
+accelerator_barrier();  // interior kernel done
+// Halo H2D is also complete (Phase 5 above)
+// Now safe to use full field
+```
+
+## Per-Packet Event Tracking Data Structure
+
+```cpp
+struct Packet {
+    // Buffers
+    void *device_send_buf;
+    void *host_send_buf;    // pinned
+    void *device_recv_buf;
+    void *host_recv_buf;    // pinned
+    size_t bytes;
+    
+    // MPI
+    int src_rank, dst_rank, tag;
+    MPI_Request send_req, recv_req;
+    
+    // GPU events (one per packet, not one global barrier)
+    AcceleratorEvent d2h_event;
+    AcceleratorEvent h2d_event;
+    
+    // State flags
+    bool sent = false;
+    bool h2d_started = false;
+};
+```
+
+The critical design point: `d2h_event` and `h2d_event` are **per-packet**, not global. This allows the MPI send for packet 0 to fire while packet 1's D2H is still in progress.
+
+## Internode vs Intranode Separation
+
+PCIe (GPU-to-CPU) and NVLink/xGMI (GPU-to-GPU within a node) are separate bandwidth resources. They do not compete with each other, but they *do* compete with each other for transactions if both are active simultaneously.
+
+Strategy: complete all internode D2H copies first (to maximise NIC injection bandwidth), then start intranode D2D copies (which use NVLink/xGMI and do not contend with PCIe for internode traffic):
+
+```cpp
+// In Phase 2: start intranode D2D only after D2H is confirmed complete
+if (pkt.is_intranode && pkt.d2h_done) {
+    // Use peer access (cudaMemcpyPeerAsync / hipMemcpyPeerAsync)
+    // rather than staging through host for intranode
+    cudaMemcpyPeerAsync(pkt.peer_recv_buf, pkt.dst_device,
+                         pkt.device_send_buf, pkt.src_device,
+                         pkt.bytes, computeStream);
+}
+```
+
+Grid reference: `Grid/communicator/Communicator_mpi3.cc` — search for `NVLINK_GET` and `ACCELERATOR_AWARE_MPI` conditional blocks.
+
+## Pinned Memory Allocation
+
+All host staging buffers must be pinned (page-locked) for async D2H/H2D:
+
+```cpp
+// CUDA
+cudaMallocHost(&host_buf, bytes);
+cudaFreeHost(host_buf);
+
+// HIP  
+hipHostMalloc(&host_buf, bytes, hipHostMallocDefault);
+hipHostFree(host_buf);
+
+// SYCL
+host_buf = sycl::malloc_host(bytes, *queue);
+sycl::free(host_buf, *queue);
+```
+
+Pre-allocate at startup. Repeated `cudaMallocHost` in the hot path adds latency from the OS memory manager.
+
+## Checksumming in the Pipeline
+
+Insert checksum computation before D2H (on the GPU-resident data) and verification after H2D (on the received GPU-resident data). See `correctness-verification.md` for the checksum pattern. The salting (`packet_index + 1000 * tag`) detects packet transposition — critical for diagnosing MPI buffer aliasing bugs where two packets' contents are swapped.
+
+## Smoke Test for a New System
+
+Before running physics, validate the pipeline on a synthetic benchmark:
+
+```cpp
+// Send a buffer of known values, receive and check
+// Run at multiple message sizes: 4KB, 64KB, 1MB, 16MB
+// Run at multiple process counts: 2, 8, 64, 512
+// Verify checksums on every packet
+// Measure bandwidth: should be ≥ 80% of FDR/HDR/NDR peak for host-staged
+```
+
+Any bandwidth below 50% of theoretical, or any checksum failure, indicates a problem in the communication stack that must be resolved before production runs.

skills/compiler-validation.md

@@ -0,0 +1,154 @@
+---
+name: compiler-validation
+description: Identify GPU compiler code generation bugs, distinguish them from hardware and runtime bugs, construct minimal reproducers, and validate correctness of generated assembly for performance-critical HPC kernels.
+user-invocable: true
+allowed-tools:
+  - Read
+  - Bash(grep -r)
+  - Bash(objdump)
+---
+
+# Compiler Validation for GPU HPC Codes
+
+## Why Compiler Bugs Are Distinct
+
+Compiler bugs have a unique diagnostic signature: they produce *deterministically wrong* results. The same input always produces the same wrong output. This distinguishes them from:
+
+- Hardware bugs: usually stochastic (wrong answer sometimes, correct answer other times)
+- Runtime bugs (premature barrier, buffer aliasing): often stochastic or history-dependent
+- Race conditions: non-deterministic
+
+**The determinism test**: run the same kernel 100 times with the same input. If the wrong answer is always the same wrong answer, suspect the compiler.
+
+## The Minimal Reproducer Protocol
+
+When a kernel produces wrong results, isolate the compiler as quickly as possible:
+
+**Step 1: Eliminate the physics**. Reduce the failing kernel to the smallest possible computation that still exhibits the bug. Replace QCD fields with `double` arrays. Replace lattice operations with scalar arithmetic. The goal is a 20-line CUDA/HIP/SYCL file that any compiler engineer can compile and run.
+
+**Step 2: Binary search over optimisation levels**. Compile at `-O0` (or equivalent). If the answer becomes correct, the bug is in an optimisation pass. Then test `-O1`, `-O2`, `-O3` individually to find which optimisation level introduces the bug.
+
+```bash
+# HIP example
+hipcc -O0 minimal_repro.cc -o test_O0 && ./test_O0   # should be correct
+hipcc -O1 minimal_repro.cc -o test_O1 && ./test_O1   # compare
+hipcc -O2 minimal_repro.cc -o test_O2 && ./test_O2   # compare
+```
+
+**Step 3: Identify the optimisation pass**. For LLVM-based compilers (clang, hipcc, dpcpp, nvcc via ptxas):
+```bash
+# Disable individual optimisation passes:
+hipcc -O2 -mllvm -disable-loop-unrolling minimal_repro.cc -o test
+hipcc -O2 -fno-vectorize minimal_repro.cc -o test
+hipcc -O2 -fno-slp-vectorize minimal_repro.cc -o test
+```
+
+**Step 4: Inspect the generated code**. For CUDA/HIP, use `--generate-line-info` and `cuobjdump` or `roc-obj-extract` to get annotated assembly:
+```bash
+# CUDA
+nvcc -O2 --generate-line-info --keep minimal_repro.cu
+cuobjdump --dump-ptx minimal_repro.o
+# HIP/ROCm
+hipcc -O2 --save-temps minimal_repro.cc
+llvm-objdump -d minimal_repro.o
+# SYCL/DPC++
+icpx -O2 -fsycl -Xclang -ast-dump minimal_repro.cc 2>&1 | grep -A5 "suspicious_expr"
+```
+
+Look for: incorrect register spill/fill sequences, loop trip count miscalculation, vectorisation across iteration boundaries, incorrect address arithmetic.
+
+## Known Compiler Bug Patterns in GPU Code
+
+### Register Pressure / Spill Bugs
+High register usage forces spills to local memory. Some compiler versions generate incorrect spill/fill code — the value is written to local memory but a stale register value is read back instead of the spilled value.
+
+**Signature**: Wrong answer with high-register-count kernels; becomes correct when `--maxrregcount=N` forces lower register count (more spilling) or higher (`--maxrregcount=256`, fewer spills).
+
+**Diagnostic**: Check register usage:
+```bash
+nvcc -O2 --ptxas-options=-v minimal_repro.cu 2>&1 | grep "registers"
+hipcc -O2 --offload-arch=gfx90a --save-temps minimal_repro.cc
+llvm-mc --arch=amdgcn minimal_repro.s 2>&1 | grep "VGPRs"
+```
+
+### Vectorisation Across Loop Boundaries
+The compiler vectorises two successive loop iterations as a SIMD unit when they have a data dependency that the compiler has incorrectly determined does not exist.
+
+**Signature**: Wrong answer that becomes correct when the loop body is extracted to a non-inlined function (disabling auto-vectorisation across iterations).
+
+### Incorrect Constant Propagation
+The compiler evaluates a compile-time expression incorrectly, substituting a wrong constant. Common in template-heavy code where `sizeof(T)` or `alignof(T)` is used in arithmetic that the compiler folds at compile time.
+
+**Signature**: Wrong array index or wrong stride. Inspecting the generated assembly shows a literal constant where you expect a computed value.
+
+## Stress Patterns for Compiler Validation
+
+These patterns exercise the compiler in ways that commonly expose bugs:
+
+```cpp
+// 1. Aliased pointer write followed by immediate read
+// (tests correct handling of write-after-write in register allocation)
+__global__ void alias_stress(double *a, double *b, int n) {
+    int i = blockIdx.x * blockDim.x + threadIdx.x;
+    if (i < n) {
+        a[i] = a[i] * 2.0;
+        b[i] = a[i] + 1.0;  // must read the updated value, not the original
+    }
+}
+
+// 2. Mixed-precision accumulation
+// (tests correct type promotion in FMA sequences)
+__global__ void precision_stress(float *in, double *out, int n) {
+    double acc = 0.0;
+    for (int i = 0; i < n; i++) acc += (double)in[i];
+    *out = acc;
+}
+
+// 3. Large struct in shared memory
+// (tests alignment and offset calculation for non-power-of-2-sized objects)
+struct S { double x[3]; };  // sizeof = 24 bytes, not a power of 2
+__global__ void struct_stress(S *in, S *out, int n) {
+    extern __shared__ S smem[];
+    int tid = threadIdx.x;
+    smem[tid] = in[tid];
+    __syncthreads();
+    out[tid] = smem[(tid + 1) % blockDim.x];
+}
+```
+
+## Separating Compiler from Runtime/Hardware
+
+When results are deterministically wrong:
+
+| Test | Compiler bug | Runtime/hardware bug |
+|---|---|---|
+| Recompile at -O0 | Fixes it | No effect |
+| Run on CPU (host code equivalent) | Fixes it | No effect |
+| Reorder loop iterations | Changes wrong answer | No effect or different pattern |
+| Different compiler version | Fixes or changes wrong answer | No effect |
+| Different GPU of same model | Same wrong answer | Different or no error |
+| Different GPU model | Fixes it (ISA-specific codegen bug) | May or may not fix |
+
+## Reporting to Compiler Teams
+
+A compiler bug report needs:
+1. Minimal reproducer (< 50 lines)
+2. Compiler version (`hipcc --version`, `nvcc --version`, `icpx --version`)
+3. GPU model and driver version
+4. Exact wrong and correct answers (hexfloat for reproducibility)
+5. Which compile flags change the behaviour
+6. Generated assembly for the correct and incorrect variants
+
+File with: LLVM Bugzilla (for hipcc/clang/dpcpp backends), NVIDIA bug portal (nvcc/ptxas), or vendor-specific developer forum. The minimal reproducer is the single most important element — without it, compiler teams cannot prioritise.
+
+## Pragmatic In-Production Workaround
+
+When a compiler bug is confirmed but the fix is not yet available, the lowest-risk workaround is to mark the affected function with reduced optimisation:
+
+```cpp
+#pragma clang optimize off  // clang/hipcc/dpcpp
+void __attribute__((optimize("O0"))) affected_kernel_host_wrapper() { ... }
+// For device code, use per-file compilation flags via CMake/Makefile
+```
+
+Document the workaround with a comment referencing the compiler bug report number so it can be removed when the compiler is updated.

skills/correctness-verification.md

@@ -0,0 +1,169 @@
+---
+name: correctness-verification
+description: Implement application-level correctness verification for HPC codes on unreliable hardware — double-run pattern, deterministic reductions, per-packet checksums, and flight recorder step logging.
+user-invocable: true
+allowed-tools:
+  - Read
+  - Bash(grep -r)
+---
+
+# Correctness Verification Infrastructure for HPC Codes
+
+## The Problem
+
+Leadership computing facilities sometimes have hardware or firmware bugs below the level visible to application code. The accelerator runtime can return from `q.wait()` or `cudaDeviceSynchronize()` before work is actually complete, or silently produce wrong answers in DMA transfers. Standard testing does not catch these because they are non-deterministic and often topology-dependent (fail only at specific process counts or on specific node configurations).
+
+The symptoms look like numerical instabilities, random MPI hangs, or wrong physics results — not like crashes. Without deliberate infrastructure, diagnosing root cause takes months.
+
+## The Double-Run Pattern
+
+The most reliable correctness check for non-deterministic hardware bugs is to run every computation twice and compare bit-identical fingerprints.
+
+**Key constraint**: the second run must use a *deterministic* code path. Non-deterministic floating-point ordering (e.g. from MPI_Allreduce with different reduction trees on retry) produces false mismatches. See `mpi-heterogeneous.md` for how to make reductions deterministic.
+
+```cpp
+// Pseudocode: double-run a step and compare CRC fingerprints
+void run_step_verified(State &state) {
+    state.save_checkpoint();
+    
+    uint64_t crc_a = run_step_and_fingerprint(state);
+    state.restore_checkpoint();
+    uint64_t crc_b = run_step_and_fingerprint(state);
+    
+    if (crc_a != crc_b) {
+        report_mismatch("step", crc_a, crc_b);
+        // Policy: abort, retry from checkpoint, or continue with alarm
+    }
+}
+```
+
+**Fingerprinting**: XOR-fold a CRC32 over all floating-point data after each step. XOR is order-independent, so it works across distributed nodes without communication. For field data:
+
+```cpp
+uint64_t fingerprint(const double *data, size_t n) {
+    uint64_t acc = 0;
+    for (size_t i = 0; i < n; i++) {
+        uint64_t bits;
+        memcpy(&bits, &data[i], sizeof(bits));
+        acc ^= crc32(bits);
+    }
+    return acc;
+}
+```
+
+On GPU, compute the XOR reduction on-device (avoids D2H transfer of the full field):
+
+```cpp
+// SYCL
+uint64_t svm_xor(uint64_t *vec, uint64_t L) {
+    uint64_t ret = 0;
+    { sycl::buffer<uint64_t,1> abuff(&ret, {1});
+      theGridAccelerator->submit([&](sycl::handler &cgh) {
+        auto R = sycl::reduction(abuff, cgh, uint64_t(0), std::bit_xor<>());
+        cgh.parallel_for(sycl::range<1>{L}, R,
+          [=](sycl::id<1> i, auto &sum) { sum ^= vec[i]; });
+      }); }
+    theGridAccelerator->wait();
+    return ret;
+}
+```
+
+## Per-Packet Communication Checksums
+
+Silent data corruption in MPI buffers (documented in MPICH with device-resident buffers; see `mpi-heterogeneous.md`) requires per-packet verification, not just end-to-end. The pattern:
+
+1. Before packing a send buffer, compute a GPU-side checksum of the payload.
+2. Append the checksum to the host staging buffer alongside the data.
+3. After receiving and copying to device, recompute the checksum on-device and compare.
+
+Salt each checksum with `packet_index + 1000 * mpi_tag` to detect transposition (packet A landing in packet B's slot):
+
+```cpp
+uint64_t salt = (uint64_t)packet_index + 1000ULL * mpi_tag;
+checksum_send = checksum_gpu(payload_gpu, payload_words) ^ salt;
+// ... transmit payload + checksum_send ...
+checksum_recv = checksum_gpu(payload_gpu_recv, payload_words) ^ salt;
+assert(checksum_recv == checksum_send);
+```
+
+Grid reference: `Grid/communicator/Communicator_mpi3.cc`, `#ifdef GRID_CHECKSUM_COMMS`.
+
+## Flight Recorder: Step-Level Logging
+
+Maintain a monotonic counter that names the current operation. On a hang, this is the only way to know *which* operation the process is stuck in without a debugger.
+
+```cpp
+struct FlightRecorder {
+    std::atomic<uint64_t> step_counter{0};
+    const char *step_name = "init";
+    
+    void step_log(const char *name) {
+        step_name = name;
+        step_counter.fetch_add(1, std::memory_order_relaxed);
+    }
+};
+extern FlightRecorder gRecorder;
+```
+
+In Record mode, also store floating-point norms and communication checksums to vectors. In Verify mode, compare against stored values:
+
+```cpp
+void norm_log(double val) {
+    if (mode == Record) norm_log_vec.push_back(val);
+    if (mode == Verify) {
+        double expected = norm_log_vec[norm_counter];
+        if (val != expected) {  // bit-exact for deterministic paths
+            std::cerr << "MISMATCH at step " << step_counter
+                      << " (" << step_name << "): "
+                      << std::hexfloat << val << " vs " << expected << "\n";
+            print_backtrace();
+        }
+        norm_counter++;
+    }
+}
+```
+
+Grid reference: `Grid/util/FlightRecorder.h`, `Grid/util/FlightRecorder.cc`.
+
+## Signal Handler for Hang Detection
+
+Install a SIGHUP handler that dumps the current flight recorder state. This is async-safe only if the handler writes to a pre-allocated buffer using `write()` (not `printf`):
+
+```cpp
+static char hang_buf[4096];
+
+static void sighup_handler(int) {
+    int n = snprintf(hang_buf, sizeof(hang_buf),
+        "rank=%d step=%llu name=%s\n",
+        mpi_rank,
+        (unsigned long long)gRecorder.step_counter.load(),
+        gRecorder.step_name);
+    write(STDERR_FILENO, hang_buf, n);
+    // Optional: call backtrace_symbols_fd (async-safe on Linux)
+    void *frames[64];
+    int depth = backtrace(frames, 64);
+    backtrace_symbols_fd(frames, depth, STDERR_FILENO);
+}
+
+// In main():
+signal(SIGHUP, sighup_handler);
+```
+
+To diagnose a hang across all ranks: `kill -HUP $(pgrep my_app)` or via job scheduler.
+
+## What to Verify at Each Step
+
+| Data type | Fingerprint method | Frequency |
+|---|---|---|
+| Lattice fields | XOR of CRC32 over float64 words | Every algorithmic step |
+| Communication buffers | GPU XOR reduction, salted | Every MPI operation |
+| Scalar reductions | Bit-exact match of double | Every GlobalSum |
+| Iteration counters | Exact integer match | Every solver iteration |
+
+## When to Abort vs Continue
+
+- **Abort immediately**: communication checksum mismatch (data is corrupt, continuing will silently propagate errors).
+- **Log and continue**: norm mismatch in Verify mode if you need to map out which operations are unreliable.
+- **Retry from checkpoint**: double-run mismatch when the underlying bug is non-deterministic (second retry will usually pass).
+
+Track the mismatch rate over a production run. A rate above ~1/1000 steps indicates a systemic hardware issue that should be escalated to the facility.

skills/gpu-memory-performance.md

@@ -0,0 +1,205 @@
+---
+name: gpu-memory-performance
+description: Diagnose and fix GPU memory bandwidth and occupancy problems in Grid HPC kernels — acceleratorThreads() pitfalls, LambdaApply thread mapping, coalescedRead/Write idiom, when to use accelerator_for vs a hand-rolled __global__ kernel, and fused vs staged HBM access patterns.
+user-invocable: true
+allowed-tools:
+  - Read
+  - Bash(grep -r)
+---
+
+# GPU Memory Performance in Grid
+
+## Nsimd on GPU builds
+
+With `GEN_SIMD_WIDTH=64B` (the typical production setting), `Nsimd` is **not 1**:
+
+| Scalar type | `sizeof` | `Nsimd = 64 / sizeof` |
+|---|---|---|
+| `ComplexD` | 16 B | **4** |
+| `ComplexF` | 8 B  | **8** |
+| `RealD`    | 8 B  | **8** |
+| `RealF`    | 4 B  | **16** |
+
+So for `LatticePropagatorD` (scalar type `ComplexD`), `Nsimd=4` and the SIMD lane runs `threadIdx.x ∈ {0,1,2,3}`.  True `Nsimd=1` scalar-GPU builds are the exception, not the rule.
+
+## The acceleratorThreads() Trap
+
+`acceleratorThreads()` is a runtime-settable global (default **8**) that controls the `blockDim.y` of every `accelerator_for` launch.  It is NOT the SIMD width — it is the number of sites processed per block in the y-dimension.
+
+```cpp
+// Grid/threads/Accelerator.cc
+uint32_t accelerator_threads = 8;
+```
+
+With `accelerator_for(ss, osites, nsimd, ...)`, the launch is:
+
+```
+dim3 threads(nsimd, acceleratorThreads(), 1)
+dim3 blocks ((osites + acceleratorThreads() - 1) / acceleratorThreads(), 1, 1)
+```
+
+Total threads per block = `Nsimd × acceleratorThreads()`.  With `GEN_SIMD_WIDTH=64B` and `Nsimd=8` (fp32 / ComplexF):
+
+| `acceleratorThreads()` | threads/block | AMD wavefront | note |
+|---|---|---|---|
+| 2 (original default) | 16 | 25% | sub-wavefront, poor |
+| 4 | 32 | 50% | half wavefront |
+| **8 (current default)** | **64** | **100%** | **one full wavefront — Dslash sweet spot** |
+| 16 | 128 | 200% | two wavefronts/block; register-pressure cliff for heavy kernels |
+| 32 | 256 | 400% | severe register spill for stencil kernels |
+
+**Why 8 and not higher?**  Compute-heavy kernels like the Domain Wall Dslash carry many live registers per thread (spinors + gauge links + projections).  Doubling `acceleratorThreads` from 8→16 doubles the register demand per block, which on AMD GFX90A triggers a hard occupancy cliff: `Benchmark_dwf_fp32` drops from 1.7 TF/s (nt=8) to ~300 GF/s (nt=16).  The sweet spot is one full wavefront per block, which with `Nsimd=8` (fp32) means `nt=8`.
+
+For fp64 work (`Nsimd=4`), `nt=8` gives 32 threads = half a wavefront (AMD pads to 64 with idle lanes).  Kernels that are not register-limited (e.g. simple lattice arithmetic) can benefit from `--accelerator-threads 16` at runtime.  Reduction kernels bypass `acceleratorThreads()` entirely via `getNumBlocksAndThreads`.
+
+**Why was the default ever 2?**  Before the `threadIdx.x`/`threadIdx.y` remap (see LambdaApply section below), the site index lived in `threadIdx.x` — the fast, coalescing dimension.  Increasing `acceleratorThreads` widened the block in the *site* direction, so adjacent threads in a warp hit adjacent sites, each stride `sizeof(vobj)` apart in AoS memory — breaking coalescing.  On early NVIDIA ports with `Nsimd≈8`, `nt=2` gave 16 threads = 50% of a 32-thread warp; NVIDIA recovers this via multiple concurrent blocks per SM, so occupancy was barely tolerable.  AMD has no such multiplier when blocks are already sub-wavefront.  After the remap put the site index in `threadIdx.y` and the SIMD lane in `threadIdx.x`, coalescing became independent of `acceleratorThreads`, removing the constraint.
+
+**Diagnostic**: observed bandwidth << peak, kernel time >> expected from data volume.  Check with `--accelerator-threads 32` at runtime.  A large speedup confirms occupancy starvation.
+
+**Fix options** (in order of preference):
+1. Kernel needs its own thread count — use `getNumBlocksAndThreads` and launch a `__global__` kernel directly (see below).
+2. Temporarily acceptable: set `--accelerator-threads 32` at the application level.  Note this affects every `accelerator_for` site in the binary.
+
+## LambdaApply Thread Mapping
+
+`accelerator_for` and `accelerator_for2d` go through `LambdaApply`:
+
+```cpp
+// HIP/CUDA LambdaApply kernel:
+uint64_t x = threadIdx.y + blockDim.y * blockIdx.x;  // iter1 (site index)
+uint64_t y = threadIdx.z + blockDim.z * blockIdx.y;  // iter2
+uint64_t z = threadIdx.x;                             // lane (SIMD lane)
+Lambda(x, y, z);
+```
+
+`threadIdx.x` is the **fast** (lane) dimension — consecutive thread IDs within a warp/wavefront correspond to consecutive lane values on the **same** site, not consecutive sites.
+
+With `GEN_SIMD_WIDTH=64B` and `Nsimd=4` (PropagatorD), a 64-thread AMD wavefront contains 64/4 = 16 sites, each processed by 4 lanes.  Adjacent threads within the wavefront read different lanes of the same site — this is a broadcast pattern (hardware handles this efficiently), not a stride.  The stride between consecutive *sites* (`sizeof(vobj)`) only appears between groups of `Nsimd` threads, spaced `Nsimd` apart in threadIdx.x — not between adjacent threads within a warp.
+
+## coalescedRead / coalescedWrite
+
+These are Grid's canonical way to read/write one SIMD lane from a vector type inside a `GRID_SIMT` kernel:
+
+```cpp
+// accelerator_for(ss, osites, Nsimd, {
+//   lane = acceleratorSIMTlane(Nsimd) = threadIdx.x  ∈ {0..Nsimd-1}
+auto scalar_val = coalescedRead(field[ss]);       // extractLane(lane, field[ss])
+coalescedWrite(field[ss], scalar_val);             // insertLane(lane, field[ss], scalar_val)
+```
+
+For `vobj` aggregate types, `coalescedRead` calls `extractLane(lane, vobj)` which recurses through the tensor hierarchy and returns `vobj::scalar_object`.
+
+For `vsimd` (raw SIMD vector) types, it casts to `scalar_type*` and indexes with `lane`.
+
+## Coalescing the Iteration Structure
+
+For an AoS input array where each site is `words` 16-byte elements, adjacent threads reading the same site's consecutive words achieve coalesced access:
+
+```cpp
+// Good: k varies across threads in a block → consecutive 16-byte reads
+accelerator_for2d(k, R, ss, osites, Nsimd, {
+    coalescedWrite(out[ss]._internal[k],
+                   coalescedRead(idat[ss * words + base + k]));
+});
+// dim3(Nsimd, nt, 1): threadIdx.y = k (consecutive words, coalesced)
+//                      threadIdx.x = lane (SIMD sub-lane, coalesced for Nsimd>1)
+```
+
+```cpp
+// Bad: each thread reads all R words of its site serially
+accelerator_for(ss, osites, 1, {
+    Bundle b;
+    for (int k = 0; k < R; k++)
+        b._internal[k] = idat[ss * words + base + k];  // serial, not coalesced across threads
+    out[ss] = b;                                         // bulk struct write
+});
+```
+
+The bad pattern also accumulates a large struct in registers (192 bytes for R=12), increasing register pressure and reducing occupancy further.
+
+## When to Use a __global__ Kernel Instead of accelerator_for
+
+`accelerator_for` is correct for site-parallel work where `acceleratorThreads()` is tuned appropriately.  Use a direct `__global__` kernel when:
+
+- The kernel requires a **specific thread count** for correctness or performance (reductions, shared-memory algorithms).
+- The optimal thread count depends on `sizeof(sobj)` and `sharedMemPerBlock`, not on a runtime global.
+- You need the retirement-count pattern for cross-block final reduction.
+
+Pattern: use `getNumBlocksAndThreads` to pick `numThreads` and `numBlocks`:
+
+```cpp
+Integer numThreads, numBlocks;
+int ok = getNumBlocksAndThreads(n, sizeof(sobj), numThreads, numBlocks);
+// starts at warpSize (32/64), doubles while 2*threads*sizeof(sobj) < sharedMemPerBlock
+// gives 64–256 threads/block → correct occupancy independent of acceleratorThreads()
+Integer smemSize = numThreads * sizeof(sobj);
+myKernel<<<numBlocks, numThreads, smemSize, computeStream>>>(args...);
+```
+
+Grid's `reduceKernel` uses this pattern and achieves ~400 GB/s on MI250X.
+
+## Fused vs Staged HBM Access
+
+A staged pack+reduce reads the data **three times**:
+
+```
+pack kernel:   reads vobj array (N bytes), writes bundle buffer (N bytes)
+reduce kernel: reads bundle buffer (N bytes), writes tiny result buffer
+```
+
+Total HBM: 3N bytes for N bytes of useful input.
+
+A fused kernel reads the data **once**:
+
+```
+packReduceKernel: reads R words of vobj array (N bytes), reduces in-place
+```
+
+Total HBM: N bytes.  Register pressure increases (R words held per thread) but the 3× HBM saving dominates for large objects.
+
+The fused pattern in Grid's `sumD_gpu_reduce_words<R>`:
+
+```cpp
+template <int R, class vobj, class sobj, class Iterator>
+__device__ void packReduceBlocks(
+    const iScalar<typename vobj::vector_type> *idat,
+    sobj *g_odata, Iterator osites, int base, int words)
+{
+  // sobj = iVector<iScalar<scalarD>, R>  (R double-precision scalars per site)
+  constexpr Iterator nsimd = vobj::Nsimd();
+  ...
+  while (i < osites * nsimd) {
+    Iterator lane = i % nsimd;
+    Iterator ss   = i / nsimd;
+    sobj tmpD; zeroit(tmpD);
+    for (int k = 0; k < R; k++) {
+      auto w = extractLane(lane, idat[ss * words + base + k]);
+      iScalar<typename vobj::scalar_typeD> wd; wd = w;   // float→double promotion
+      tmpD._internal[k] = wd;
+    }
+    mySum += tmpD;
+    ...
+  }
+  reduceBlock(sdata, mySum, tid);
+}
+```
+
+Launched with `getNumBlocksAndThreads` → 128 threads/block for R=12 (`BundleScalarD`=192 B, sharedMem=64 KB) → correct occupancy without depending on `acceleratorThreads()`.
+
+## Observed Numbers on MI250X (32^4 LatticePropagatorD, Nsimd=4, GEN_SIMD_WIDTH=64B)
+
+| Configuration | pack µs/group | reduce µs/group | total µs | GB/s |
+|---|---|---|---|---|
+| acceleratorThreads=2 (8 threads/block), staged | 10,080 | 470 | 126,909 | 50 |
+| acceleratorThreads=16 (64 threads/block), staged | 342 | 310 | 8,251 | 297 |
+| acceleratorThreads=16, fused (128 threads/block via getNumBlocksAndThreads) | — | 349 | 4,584 | 546 |
+
+The fused kernel at 349 µs/group reads 201 MB at 576 GB/s — 36% of MI250X HBM peak.  The remaining gap from peak is the in-kernel serial loop over R=12 words and the 12 serial kernel launches.
+
+## Quick Checklist When a Kernel Is Slow
+
+1. **Check Nsimd**: `GEN_SIMD_WIDTH=64B` → Nsimd=4 (ComplexD), 8 (ComplexF).  Total threads/block = `Nsimd × acceleratorThreads()`.  With old default nt=2 and Nsimd=4: 8 threads = 12.5% of AMD wavefront.
+2. Check threads per block: for `accelerator_for` kernels use `--accelerator-threads 32` and measure; a large speedup confirms occupancy starvation.
+3. Check for bulk struct accumulation in registers (`Bundle b; for(...) b._internal[k] = ...;`).  Replace with per-element writes via `coalescedWrite`.
+4. Check for staged HBM access (pack → buffer → reduce).  Count the passes; fuse if ≥ 2 passes over the same data.
+5. For reduction kernels, always use `getNumBlocksAndThreads` rather than `accelerator_for` so thread count is independent of `acceleratorThreads()`.

skills/gpu-runtime-correctness.md

@@ -0,0 +1,101 @@
+---
+name: gpu-runtime-correctness
+description: Detect and work around GPU runtime correctness failures — premature completion signalling, infinite poll hangs, stale completion flags, and the double-wait diagnostic pattern. Covers CUDA, HIP/ROCm, and SYCL/Level Zero runtimes.
+user-invocable: true
+allowed-tools:
+  - Read
+  - Bash(grep -r)
+---
+
+# GPU Runtime Correctness
+
+## The Completion Signalling Problem
+
+GPU runtimes expose a synchronisation primitive — `cudaDeviceSynchronize()`, `hipDeviceSynchronize()`, `q.wait()` — that is supposed to block until all previously submitted GPU work is complete. On several production systems, this guarantee has been violated in two distinct ways:
+
+### Failure Mode A: Premature Return
+The wait returns before the GPU work is done. The subsequent CPU code reads stale data from the output buffer. This is the most dangerous failure because it looks like a numerical instability, not a crash. Results are wrong but the program exits normally.
+
+**Identifying Premature Return**: Insert a second, independent wait immediately after the first. If a second `q.wait()` "fixes" incorrect results that appeared with a single `q.wait()`, the first wait was returning prematurely.
+
+```cpp
+// Diagnostic version — if this stabilises results, you have premature return
+accelerator_barrier();  // first wait
+accelerator_barrier();  // second wait (diagnostic)
+```
+
+Production fix: submit a trivially cheap no-op kernel after the real work and wait for it. The no-op kernel cannot complete until all previous commands in the queue are done (command queue ordering guarantee), so waiting for the no-op is a stronger barrier than waiting for the queue itself:
+
+```cpp
+// Lightweight fence kernel
+template<class T>
+__global__ void noop_kernel(T *p) { if (threadIdx.x == 0) (void)(*p); }
+
+void strong_barrier(T *device_ptr) {
+    noop_kernel<<<1, 1, 0, computeStream>>>(device_ptr);
+    cudaStreamSynchronize(computeStream);  // wait for the no-op
+}
+```
+
+### Failure Mode B: Infinite Poll
+The wait enters a polling loop that never terminates. The process consumes 100% CPU in a runtime library. The GPU has either stopped signalling progress entirely, or the completion flag is in a memory region that has become incoherent.
+
+This is distinct from Failure Mode A: with premature return the CPU proceeds; with infinite poll the CPU is stuck.
+
+**Identifying Infinite Poll**: `top` shows the MPI rank at 100% CPU. `perf top -p PID` or `strace -p PID` shows the process burning cycles inside the GPU runtime library (e.g. `libze_intel_gpu.so`, `libamdhip64.so`).
+
+**Documented instances**: 
+- Intel Level Zero on Pontevecchio (Aurora): both premature return *and* infinite poll have been observed as independent bugs on the same system.
+- The two failure modes can co-exist and have overlapping symptoms at the application level.
+
+## Completion Signalling Architecture
+
+Understanding why these bugs happen requires knowing how completion signalling works:
+
+```
+GPU command processor
+  → signals completion by writing to a host-visible memory address
+  → CPU runtime polls that address (or uses OS event notification via ioctl)
+```
+
+A premature return means the memory write happened before the actual work completed (e.g. the signal is on a different command stream that has not been serialised with the work stream). An infinite poll means the memory write never happens (hardware or driver bug preventing the signal from being written).
+
+**Implication**: `accelerator_barrier()` is not an unconditional correctness guarantee on all production systems. Application-level verification (double-run, checksums) is necessary as a second line of defence.
+
+## The Double-Wait Pattern in Practice
+
+The double-wait is a pragmatic workaround when premature return is suspected but not yet confirmed. It adds latency but does not change correctness if the barrier is working properly, so it is safe to enable in production:
+
+```cpp
+#ifdef WORKAROUND_PREMATURE_BARRIER
+#define accelerator_barrier() do { \
+    real_accelerator_barrier();    \
+    real_accelerator_barrier();    \
+} while(0)
+#endif
+```
+
+Monitor whether this changes observed behaviour. If double-wait eliminates wrong answers, you have confirmed premature return. If it does not help but inserting a no-op kernel does, the issue is with the wait primitive specifically, not with the underlying completion signal.
+
+## SYCL/Level Zero Specifics
+
+Level Zero (the backend for Intel GPU runtimes) separates command submission from synchronisation. A `q.wait()` should wait for all previously submitted command lists to retire. Documented bugs include:
+
+- `q.wait()` returning before the associated fence in Level Zero has been signalled.
+- `q.wait()` entering an `ioctl(i915, I915_GEM_WAIT)` call that never returns (kernel driver bug, not runtime bug).
+
+The latter requires a node reboot and cannot be worked around in application code. Detect it by checking process state (`D` in `ps aux`) and the kernel function via `/proc/PID/wchan`.
+
+## Stream Ordering and Compute Streams
+
+All GPU work must be submitted to the *same* stream/queue if you rely on in-order execution guarantees. Mixing default stream and non-default streams invalidates ordering assumptions on some backends.
+
+Grid uses `computeStream` (CUDA/HIP) or `theGridAccelerator` (SYCL) consistently throughout. If mixing Grid with third-party GPU code, ensure the third-party code is directed to the same stream, or insert explicit inter-stream barriers.
+
+## Checklist for New GPU Code
+
+1. Every kernel launch is followed by an `accelerator_barrier()` before reading device-side output on the host.
+2. All device-to-host copies use an explicit stream synchronisation after the copy, not before.
+3. If results are non-deterministic across runs, insert a second barrier and observe whether reproducibility improves.
+4. For correctness-critical operations (reductions that will be compared against reference values), add the double-run checksum test from `correctness-verification.md`.
+5. If the process hangs at 100% CPU in a runtime library function, this is a driver/runtime bug — there is no application-level fix beyond scheduling a node reboot.

skills/hang-diagnosis.md

@@ -0,0 +1,102 @@
+---
+name: hang-diagnosis
+description: Diagnose and isolate process hangs on HPC systems — distinguishing kernel-level ioctl hangs, infinite poll loops, collective deadlocks, and GPU completion signalling failures using async-safe signal handlers and flight recorder step counters.
+user-invocable: true
+allowed-tools:
+  - Read
+  - Bash(grep -r)
+  - Bash(strace)
+  - Bash(gdb)
+---
+
+# Hang Diagnosis on HPC Systems
+
+## Taxonomy of Hangs
+
+Not all hangs are the same. Misidentifying the type leads to wrong mitigation. The four distinct classes encountered on production leadership systems:
+
+### 1. Kernel-level ioctl hang (never returns)
+The process is in `D` (uninterruptible sleep) state. `strace` shows it blocked in an `ioctl` syscall. The GPU device driver has entered an unrecoverable state.
+
+**Diagnosis**: `ps aux | grep D` — the process shows `D` state. `cat /proc/PID/wchan` shows `i915_gem_wait_for_error` or similar.
+
+**Resolution**: Only a driver reload or node reboot recovers it. Log the node identifier and request replacement from the facility scheduler.
+
+### 2. Infinite poll loop (`q.wait()` or `cudaDeviceSynchronize()` never returns)
+The process is in `R` (running) state, consuming 100% CPU. A polling loop inside the runtime is checking a completion flag that never becomes true, either because the hardware never sets it or because the flag is in a memory region not visible to the polling thread.
+
+**Diagnosis**: `top` shows the rank at 100% CPU. `strace -p PID` shows repeated `futex` or `read` syscalls with zero-length results, or no syscalls at all (pure spinloop). `perf top -p PID` shows the process burning cycles in a single tight loop in a runtime library (e.g., `ze_intel_gpu.so`).
+
+**Resolution**: The double-wait workaround — submit a trivially cheap kernel after the operation under test to act as a fence, then wait for the trivial kernel. See `gpu-runtime-correctness.md`.
+
+### 3. Collective deadlock
+One or more ranks are blocked in an MPI call, usually `MPI_Allreduce` or `MPI_Barrier`, while others are not. Root cause: a topology-dependent bug in the MPI library's collective algorithm where some ranks' contributions never arrive.
+
+**Diagnosis**: Flight recorder step logs show some ranks at step N (inside the collective) while others are at step N+1 or stuck at step N with different `step_name` strings. The hung ranks will show `D` or `S` state in `ps`.
+
+**Resolution**: Replace `MPI_Allreduce` with a deterministic point-to-point tree reduction. See `mpi-heterogeneous.md`.
+
+### 4. Premature return from wait (silent wrong answer, not a hang)
+The runtime returns from `q.wait()` before the GPU work is complete. The next operation reads stale data. This is not a hang — it manifests as a wrong answer or non-deterministic floating-point results. It is listed here because it is the most confusing failure mode: the code appears to run correctly and completes normally.
+
+**Diagnosis**: Double-run with checksum (see `correctness-verification.md`). Insert a second `q.wait()` after the first and observe if results become reproducible. If inserting the second wait "fixes" wrong answers, the first wait was returning prematurely.
+
+## Flight Recorder for Hang Localization
+
+The most important diagnostic tool is knowing *which operation* a process is in when it hangs. Maintain a named step counter:
+
+```cpp
+// Call at the start of every major operation
+FlightRecorder::StepLog("MPI_Allreduce::norm");
+// ... do the operation ...
+FlightRecorder::StepLog("MPI_Allreduce::done");
+```
+
+On SIGHUP, dump rank, step counter value, and step name to stderr in an async-safe manner:
+
+```cpp
+static void sighup_handler(int) {
+    char buf[256];
+    int n = snprintf(buf, sizeof(buf), "rank %d: step %llu '%s'\n",
+        comm_rank,
+        (unsigned long long)step_counter,
+        step_name);
+    write(2, buf, n);
+    // backtrace_symbols_fd is async-safe on Linux glibc
+    void *frames[32];
+    backtrace_symbols_fd(frames, backtrace(frames, 32), 2);
+}
+signal(SIGHUP, sighup_handler);
+```
+
+Broadcast SIGHUP to all ranks from outside the job:
+```bash
+# In a separate shell while the job is hung
+squeue --job $JOBID -o "%i %N" | awk '{print $2}' | \
+  xargs -I{} ssh {} "pkill -SIGHUP -f my_application"
+```
+
+The step names from all ranks will reveal which collective operation has diverged.
+
+## Distinguishing Driver Hang from MPI Hang
+
+| Symptom | Driver hang | MPI hang |
+|---|---|---|
+| Process state | `D` (ioctl) or `R` (spinloop) | `S` (blocked in syscall) |
+| `strace` | blocked `ioctl` or tight loop | blocked `recvmsg` / `read` |
+| Scope | single rank / single node | subset of ranks, pattern-dependent |
+| Recovery | reboot node | cancel job |
+| Flight recorder | step name is a GPU operation | step name is a collective |
+
+## Reducing Diagnostic Time
+
+1. **Name every collective operation** in the flight recorder before calling it.
+2. **Separate GPU work from MPI work** in the code so the step name unambiguously identifies which subsystem is hung.
+3. **Log node identifiers** alongside step names so flaky nodes can be identified and blacklisted.
+4. **Request flight recorder dumps from all ranks simultaneously** (SIGHUP broadcast) rather than attaching a debugger — attaching `gdb` to one rank of a hung MPI job usually deadlocks the debugger too.
+
+## What Not to Do
+
+- Do not `kill -9` a hung rank immediately — get the flight recorder dump first, otherwise diagnostic information is lost.
+- Do not assume the first rank that prints an error is the faulty one — collective hangs are frequently caused by the *last* rank to arrive at the barrier.
+- Do not use `MPI_Abort` in the hang handler — it may itself hang on some implementations. Use `_exit(1)` to force termination.

skills/mpi-heterogeneous.md

@@ -0,0 +1,182 @@
+---
+name: mpi-heterogeneous
+description: Diagnose and work around MPI correctness bugs on heterogeneous (CPU+GPU) systems — device buffer aliasing in MPI_Sendrecv, AARCH64 PLT corruption from libfabric, topology-dependent allreduce hangs, mixed-ABI HIP runtime from wrong GTL library (Frontier/ROCm), and deterministic point-to-point reduction trees as a replacement for MPI_Allreduce.
+user-invocable: true
+allowed-tools:
+  - Read
+  - Bash(grep -r)
+---
+
+# MPI Correctness on Heterogeneous HPC Systems
+
+## The Core Problem
+
+MPI libraries were designed for CPU-resident buffers. When GPU-resident buffers are passed directly (GPU-aware MPI / GPU direct RDMA), several correctness assumptions break:
+
+- **Buffer aliasing**: The MPI library may internally alias send/receive buffer addresses for `MPI_Sendrecv` in ways that are safe for CPU memory but wrong for GPU memory with different cache coherency rules.
+- **RDMA bandwidth**: GPU direct RDMA on some fabrics operates at a fraction of peak wirespeed (documented at ~30% on Pontevecchio/Aurora), making host-staging mandatory for performance even when correctness is not an issue.
+- **Collective tree topology**: `MPI_Allreduce` implementations may select reduction trees based on process count or communicator topology that expose rank-ordering bugs, causing hangs on some configurations but not others.
+
+## Bug Class 1: Device Buffer Aliasing in MPI_Sendrecv
+
+**Symptom**: `MPI_Sendrecv` with GPU-resident send and receive buffers produces wrong results. The received data matches neither the expected payload nor a host-staged copy. The failure is *deterministic* for a given problem size and process count, but *history-dependent* — earlier sends affect which alias is selected.
+
+**Root cause**: The MPI library internally reuses GPU buffer addresses for temporary staging without proper device memory ordering. When the same physical GPU memory pages appear in both the send and receive paths, writes from one path corrupt the other.
+
+**Diagnosis**: 
+1. Enable per-packet checksumming (see `correctness-verification.md`). If the checksum on the received packet does not match the sent checksum, the data was corrupted in transit.
+2. Replace `MPI_Sendrecv` with separate `MPI_Isend` + `MPI_Irecv` + `MPI_Waitall`. If this fixes the problem, the bug is in the `MPI_Sendrecv` implementation's internal buffer handling.
+3. Stage through host memory (`cudaMemcpy`/`hipMemcpy` to a host buffer, then `MPI_Sendrecv` on host buffers, then copy back). If this fixes the problem, confirms GPU-specific aliasing.
+
+**Reported as**: MPICH issue #7302. Affects MPICH on Intel Pontevecchio (Aurora) with device-resident buffers.
+
+**Workaround**: Do not use `MPI_Sendrecv` with GPU buffers. Use asynchronous send/receive pairs or host-staging. See `communication-overlap.md` for the full pipeline pattern.
+
+## Bug Class 2: PLT Corruption on AARCH64 (libfabric)
+
+**Symptom**: Application crashes or hangs on first `MPI_Comm_dup` call on AARCH64 systems (e.g. NVIDIA Grace/H200). Backtrace shows a bad instruction in the PLT (Procedure Linkage Table) for `MPI_Comm_dup` — specifically a `br x15` instruction that should instead be a proper trampoline.
+
+**Root cause**: `libfabric`'s memory registration cache monitor patches PLT entries at runtime to intercept memory allocation calls. Its AARCH64 trampoline generation writes an incorrect instruction sequence, leaving `br x15` (branch to whatever happens to be in x15) in the PLT entry. The next call through that PLT entry executes garbage.
+
+**Diagnosis**:
+```bash
+# Check if the PLT entry is corrupted
+objdump -d /proc/PID/exe | grep -A5 "MPI_Comm_dup@plt"
+# Look for "br x15" — this should be a proper stub, not a register branch
+```
+
+Or check the disassembly of the live process:
+```bash
+gdb -p PID -batch -ex "disassemble 'MPI_Comm_dup@plt'"
+```
+
+**Workaround**:
+```bash
+export FI_MR_CACHE_MONITOR=disabled
+```
+This prevents libfabric from patching PLT entries. It may reduce MR cache performance but restores correctness.
+
+**Reported as**: libfabric issue #11451. Affects systems using AARCH64 + libfabric OFI provider (Cray Slingshot, AWS EFA) with memory registration cache enabled.
+
+## Bug Class 3: Topology-Dependent Allreduce Hangs
+
+**Symptom**: `MPI_Allreduce` hangs indefinitely on some node configurations but completes correctly on others. The failure correlates with process count (e.g. fails at 512 ranks, works at 256) or network topology (fails when crossing specific router boundaries).
+
+**Root cause**: The MPI library's collective selection algorithm picks a reduction tree implementation that assumes symmetric participation from all ranks. A bug in one rank's contribution path (e.g. a GPU-side buffer not yet flushed when MPI reads it, due to premature barrier — see `gpu-runtime-correctness.md`) causes that rank to send wrong or incomplete data, and the tree-reduction protocol deadlocks waiting for data that never arrives correctly.
+
+**Diagnosis**: Flight recorder step logging (see `hang-diagnosis.md`). SIGHUP broadcast to all ranks. Ranks that are hung will show step name `MPI_Allreduce::...`; ranks that completed will show the next step. The hung ranks are the *recipients* of the stale data, not necessarily the *cause*.
+
+**Workaround — deterministic P2P reduction tree**:
+
+Replace `MPI_Allreduce` with an explicit point-to-point binary tree reduction. This is slower for large communicators but:
+1. Is immune to topology-dependent collective bugs.
+2. Is deterministic in floating-point ordering (the tree is fixed, not chosen at runtime).
+3. Makes the hang location explicit — each P2P operation is a named step in the flight recorder.
+
+```cpp
+// Binary tree reduction: rank 0 collects, then broadcasts
+void GlobalSumP2P(double *data, int count, MPI_Comm comm) {
+    int rank, size;
+    MPI_Comm_rank(comm, &rank); MPI_Comm_size(comm, &size);
+    
+    // Reduce phase: even ranks receive from odd neighbours
+    for (int stride = 1; stride < size; stride *= 2) {
+        if (rank % (2*stride) == 0) {
+            int partner = rank + stride;
+            if (partner < size) {
+                std::vector<double> tmp(count);
+                MPI_Recv(tmp.data(), count, MPI_DOUBLE, partner, 0, comm, MPI_STATUS_IGNORE);
+                for (int i = 0; i < count; i++) data[i] += tmp[i];
+            }
+        } else if (rank % stride == 0) {
+            int partner = rank - stride;
+            MPI_Send(data, count, MPI_DOUBLE, partner, 0, comm);
+            break;
+        }
+    }
+    // Broadcast phase
+    for (int stride = /* highest power of 2 <= size */; stride >= 1; stride /= 2) {
+        if (rank % (2*stride) == 0) {
+            int partner = rank + stride;
+            if (partner < size)
+                MPI_Send(data, count, MPI_DOUBLE, partner, 0, comm);
+        } else if (rank % stride == 0) {
+            int partner = rank - stride;
+            MPI_Recv(data, count, MPI_DOUBLE, partner, 0, comm, MPI_STATUS_IGNORE);
+        }
+    }
+}
+```
+
+Grid reference: `USE_GRID_REDUCTION` macro in `Grid/communicator/Communicator_mpi3.cc`.
+
+## Bug Class 4: Mixed HIP ABI from Wrong GTL Library (Frontier / ROCm)
+
+**Symptom**: `HIPFFT_PARSE_ERROR` (error code 12) returned by `hipfftPlanMany` / `hipfftMakePlanMany` / `hipfftPlan1d` for FFT sizes G < 32, but G ≥ 32 succeeds. The failure only occurs with an empty rocFFT kernel cache (`~/.cache/rocfft`); a warm cache may mask it. Host-side operations and GPU kernels that do not invoke rocFFT JIT work correctly.
+
+**Root cause — mixed HIP ABI**: rocFFT uses JIT compilation (via `libamd_comgr`) for small transforms (G < 32); for G ≥ 32 it uses pre-compiled device code bundled in the library, so the JIT path is never exercised. When two HIP runtime versions are loaded in the same process — e.g. `libamdhip64.so.7` (ROCm 7) and `libamdhip64.so.6` (ROCm 6) — the rocFFT JIT cannot complete successfully.
+
+The hidden source of the old library is the Cray MPI GPU Transport Layer. On Frontier, `cray-mpich`'s `libmpi_gtl_hsa.so` may be compiled against `libamdhip64.so.6` (ROCm 6 ABI) even when the loaded ROCm module is 7.0.2. Because `LD_LIBRARY_PATH` picks up the GTL directory before the ROCm 7 library directory, `libamdhip64.so.6` is pulled in first, and both ABI versions end up resident in the process.
+
+**Diagnosis**:
+```bash
+# Check which libamdhip64 versions are actually linked into your binary at runtime
+ldd --verbose ./your_binary 2>&1 | grep amdhip
+# Bad output — two different .so versions:
+#   libamdhip64.so.6 => /opt/rocm-6.4.2/lib/libamdhip64.so.6
+#   libamdhip64.so.7 => /opt/rocm-7.0.2/lib/libamdhip64.so.7
+# Good output — only one:
+#   libamdhip64.so.7 => /opt/rocm-7.0.2/lib/libamdhip64.so.7
+```
+
+If two versions appear, the problem is the GTL/LD_LIBRARY_PATH ordering.
+
+**Fix — correct module stack and LD_LIBRARY_PATH ordering (Frontier)**:
+```bash
+module load cce/21.0.0
+module load cpe/26.03
+module load rocm/7.0.2
+# Prepend CRAY_LD_LIBRARY_PATH so the ROCm-7-aware GTL is found first
+export LD_LIBRARY_PATH=$CRAY_LD_LIBRARY_PATH:$LD_LIBRARY_PATH
+# Ensure ROCm 7 LLVM libs (needed by libamd_comgr JIT) are on the path
+export LD_LIBRARY_PATH=/opt/rocm-7.0.2/lib/llvm/lib/:$LD_LIBRARY_PATH
+```
+
+The critical step is prepending `CRAY_LD_LIBRARY_PATH`: this ensures the GTL library built against the ROCm 7 ABI is resolved before any older version that may appear further down `LD_LIBRARY_PATH`. Without this step, a stale symlink or directory ordering can silently load the wrong `libmpi_gtl_hsa.so`.
+
+**Reproducer**: `tests/debug/Test_hipfft_repro.cc` — standalone hipFFT test (no Grid headers) that sweeps G and howmany values matching realistic Grid lattice geometries. Compile with:
+```bash
+hipcc -o Test_hipfft_repro Test_hipfft_repro.cc -lhipfft
+rm -rf ~/.cache/rocfft   # empty cache required to trigger JIT path
+./Test_hipfft_repro
+```
+
+**Reference**: `systems/WorkArounds.txt`, Frontier section — GPU mapping, XPMEM, and `FI_MR_CACHE_MONITOR=disabled` settings for Frontier are documented there.
+
+**Systems affected**: Frontier (ORNL, MI250X). Likely applies to any Cray PE system where the loaded `cray-mpich` GTL was compiled against an older ROCm ABI than the runtime ROCm module. LumiG (CSC, MI250X) uses the same Cray PE and may exhibit the same issue.
+
+## Compile-Time Guard Structure
+
+Recommended macro structure to switch between the workaround paths:
+
+```cpp
+// In configure / CMake, expose as options:
+// ACCELERATOR_AWARE_MPI  — use GPU direct (fast, potentially broken)
+// GRID_CHECKSUM_COMMS    — per-packet checksums (overhead: ~5%)
+// USE_GRID_REDUCTION     — P2P tree instead of MPI_Allreduce (slower, deterministic)
+// FI_MR_CACHE_MONITOR    — libfabric PLT workaround (env var, not compile-time)
+```
+
+On a known-good system, enable `ACCELERATOR_AWARE_MPI` and disable the others. On a system with known bugs, disable `ACCELERATOR_AWARE_MPI` and enable `GRID_CHECKSUM_COMMS` + `USE_GRID_REDUCTION` as needed.
+
+## Escalation Checklist
+
+Before concluding a bug is in your code:
+
+1. [ ] Can you reproduce with a minimal reproducer (two MPI ranks, no physics code)?
+2. [ ] Does the failure rate correlate with buffer size, process count, or network route?
+3. [ ] Does staging through host memory eliminate the failure?
+4. [ ] Is the failure deterministic for a given input (same answer, always wrong) or stochastic?
+5. [ ] Does the failure appear on a different MPI implementation (e.g. OpenMPI vs MPICH)?
+
+Deterministic wrong answers that reproduce with minimal reproducers and disappear with host-staging are strong evidence of an MPI library bug. File with the MPI library issue tracker with the minimal reproducer.

systems/Aurora/aggregate_io.pbs

@@ -0,0 +1,144 @@
+#!/bin/bash
+
+# Grid's tests/IO/Test_aggregate_io on Aurora, 12 ranks per node (one per
+# tile).  This is the Grid-side counterpart of MPI_benchmark/io_aurora.pbs:
+# same three paths, same comparison, but exercising the real BinaryIO.h
+# code that production uses, with Grid's checksums and its munge/endian
+# conversion in the loop.  Run both -- if they disagree, the difference is
+# in Grid, not in MPI-IO.
+#
+# Submit from the BUILD directory: BIN below is $PBS_O_WORKDIR relative.
+
+#PBS -q debug-scaling
+#PBS -l filesystems=flare
+#PBS -l filesystems=home
+#PBS -l select=4
+#PBS -l walltime=01:00:00
+#PBS -A 15479
+##PBS -A LatticeQCD_aesp_CNDA
+
+cd $PBS_O_WORKDIR
+cp $PBS_NODEFILE nodefile
+
+##########################################################################
+# Grid source tree.  Unlike io_mpi this IS a Grid binary -- SYCL, c-lime,
+# the lot -- so sourceme.sh is required, and so is the tile wrapper.
+##########################################################################
+root=$HOME/Grid/systems/Aurora            # <-- adjust to your source tree
+source ${root}/sourceme.sh
+TILE=${root}/benchmarks/gpu_tile.sh
+
+BIN=$PBS_O_WORKDIR/tests/IO/Test_aggregate_io
+[ -x $BIN   ] || { echo "no $BIN -- submit from the build directory"; exit 1; }
+[ -x $TILE  ] || { echo "no $TILE -- check \$root"; exit 1; }
+
+export OMP_NUM_THREADS=4
+export MPICH_OFI_NIC_POLICY=GPU
+# The aggregate path's MPI_Alltoallv runs on HOST buffers, so NIC policy
+# NUMA is arguably the better match here even though GPU is the standard
+# for Grid on this machine.  Worth one comparison run; do not change it
+# silently, the rest of the Grid numbers on Aurora were taken with GPU.
+#export MPICH_OFI_NIC_POLICY=NUMA
+
+##########################################################################
+# Test_aggregate_io writes ref.bin / agg.bin / raw.bin / trunc.bin with
+# RELATIVE paths, so they land in the cwd.  Home is not the point of the
+# exercise.
+##########################################################################
+# PROJECT is the flare project DIRECTORY name, not the -A account number.
+PROJECT=LatticeQCD_aesp_CNDA
+WORK=/lus/flare/projects/$PROJECT/$USER/aggio.$PBS_JOBID
+mkdir -p $WORK || { echo "cannot create $WORK -- set PROJECT correctly"; exit 1; }
+cd       $WORK
+
+# Leave striping at the directory default, as the Frontier runs did.  At
+# 128 nodes there the aggregate path was 2.2x faster on the default layout
+# than on -c -1, while MPI-IO was 2.4x slower on it; the two paths want
+# opposite things.  Set it only to reproduce that interaction, and say so.
+#lfs setstripe -c -1 -S 8M $WORK
+lfs getstripe -d $WORK 2>/dev/null || echo "(no lfs getstripe -- not Lustre?)"
+
+# ROMIO's own account of what the reference path did.  Verbose; switch on
+# deliberately.
+#export MPICH_MPIIO_STATS=1
+#export MPICH_MPIIO_TIMERS=1
+
+AT=8        # accelerator threads; immaterial to an I/O test, kept canonical
+
+run () {   # run <nodes> <grid> <mpi> <comment> [extra args...]
+  local nodes=$1 gr=$2 mp=$3 note=$4
+  local ntot=$(( nodes * 12 ))
+  shift 4
+  echo
+  echo "==================================================================="
+  echo "=== nodes=$nodes ranks=$ntot grid=$gr mpi=$mp   $note"
+  echo "=== extra: $@"
+  echo "==================================================================="
+  # Deliberately NOT removing ref.bin/agg.bin/raw.bin here.  The test does
+  # it itself (Test_aggregate_io.cc:203 and :370) for exactly the stale-tail
+  # reason, and doing it in the script would destroy the files a later
+  # --io-read-only job needs.
+  mpiexec -np $ntot -ppn 12 -envall $TILE $BIN --mpi $mp --grid $gr \
+          --shm-mpi 0 --shm 2048 --device-mem 32000 --accelerator-threads $AT "$@"
+  echo "=== exit $?"
+}
+
+#####################################################################
+# Phase 0.  Logic corners, correctness only, no bandwidth claimed.
+#
+# These run the FULL default target sweep {1, 1024, 64K, 4M}, which walks
+# k from 1 to Nd-1 and so exercises every shape of aggregation plan on a
+# volume small enough that the serial byte-for-byte file comparison is
+# affordable.  1.3 MB/rank means nothing for bandwidth and is not meant to.
+#
+# Both branches of MPI_Alltoallv are covered; the labels were checked with
+# MPI_benchmark/io_mpi, not assumed.
+#####################################################################
+run 1 16.16.16.24 2.2.1.3 "UNIFORM counts, row of 4"      --io-reps 0
+run 1 12.12.24.8  2.2.3.1 "NON-UNIFORM counts, row of 12" --io-reps 0
+
+#####################################################################
+# Phase 1.  151 MB/rank, 3.6 GB record, 24 ranks.  Correctness AND
+# performance at the production 4 MB target only -- the byte-for-byte
+# comparison reads the whole file on one rank, so the four-target sweep
+# is not affordable here.
+#####################################################################
+run 2 16.16.96.256 2.2.3.2 "3.6 GB, row of 4, 32 extents, correctness + perf" \
+    --aggregate-target 4194304
+
+# Same volume per rank, but an odd process factor in an un-split dimension
+# puts the variable-count branch of Alltoallv where the bandwidth is real.
+run 2 24.16.64.256 3.2.2.2 "3.6 GB, NON-UNIFORM counts, row of 6, 22 extents" \
+    --aggregate-target 4194304
+
+#####################################################################
+# Phase 2.  604 MB/rank, 29.0 GB record, 48 ranks.  Correctness off.
+#
+# Per-rank volume is held at 16.16.32.128 in ALL FOUR, so the only thing
+# changing is how much work the aggregation has to do:
+#
+#   4.4.3.1   row 16    8 extents of 72 MB   <- old path: 9 KB runs
+#   4.2.3.2   row  8   16 extents of 36 MB
+#   2.2.12.1  row  4   32 extents of 18 MB
+#   1.1.3.16  row  1  128 extents of 4.5 MB  <- no exchange at all
+#
+# The last is the interesting control: with the fast dimensions unsplit
+# the aggregate path degenerates to plain large-extent POSIX and the
+# Alltoallv is trivial, so it separates "the transposition is cheap" from
+# "the writes are large".  Note the test's own header warns that 1.1.X.Y
+# makes the CORRECTNESS section vacuous -- rows of size one exchange
+# nothing.  That is fine here because correctness is off; it would not be
+# fine as a correctness run.
+#####################################################################
+run 4 64.64.96.128   4.4.3.1  "29.0 GB, row of 16"  --aggregate-target 4194304 --io-no-correctness
+run 4 64.32.96.256   4.2.3.2  "29.0 GB, row of 8"   --aggregate-target 4194304 --io-no-correctness
+run 4 32.32.384.128  2.2.12.1 "29.0 GB, row of 4"   --aggregate-target 4194304 --io-no-correctness
+run 4 16.16.96.2048  1.1.3.16 "29.0 GB, row of 1, no exchange" \
+    --aggregate-target 4194304 --io-no-correctness
+
+echo
+echo "=== done.  Output left in $WORK"
+echo "=== For COLD read numbers, submit a second job on a fresh allocation"
+echo "=== with WORK pointed at this directory and --io-read-only added."
+echo "=== Reading back what this job just wrote only measures page cache."
+ls -l $WORK

systems/Aurora/aggregate_io_scaling.pbs

@@ -0,0 +1,117 @@
+#!/bin/bash
+
+# Node count scan for Grid's tests/IO/Test_aggregate_io on Aurora, 12 ranks
+# per node.  The Aurora counterpart of systems/Frontier/aggregate_io_scaling.slurm.
+#
+# Everything that could confound the comparison is held fixed and only the
+# number of Lustre clients changes:
+#
+#   local volume   8.8.32.128        = 262144 sites x 576 B = 151 MB / rank
+#   aggregation    k=2, row of 16, 8 extents of 18 MB        (identical at
+#                                                             every node count)
+#   old path       contiguous run = lLattice[0]*576 = 4.6 KB (identical too)
+#
+# So the ratio of contiguous extent between the two layout preserving paths
+# is a constant 4000x across the whole scan, and any change in their relative
+# bandwidth is a property of the client count alone.
+#
+# The mpi decompositions differ from the Frontier scan because 12 ranks per
+# node is not 8, but they were chosen to give the SAME aggregation plan --
+# verified with MPI_benchmark/io_mpi, which uses the identical plan algorithm
+# and the same 576 B site object:
+#
+#   Frontier   4.4.2.1  at   32 ranks  ->  k=2, row 16, 8 extents
+#   Aurora     4.4.3.1  at   48 ranks  ->  k=2, row 16, 8 extents
+#   Aurora     4.4.12.8 at 1536 ranks  ->  k=2, row 16, 8 extents
+#
+# Consequence of 12 rather than 8: at a given NODE count the record and the
+# client count are 1.5x Frontier's.  Compare the machines at equal RANK count
+# for equal record size, or at equal NODE count for each machine used as it
+# is meant to be used.  Say which one any table is reporting.
+#
+# Trim the tail of the run list for a smaller allocation; the geometries are
+# independent.
+#
+# Submit from the BUILD directory.
+
+#PBS -q prod
+#PBS -l filesystems=flare
+#PBS -l filesystems=home
+#PBS -l select=128
+#PBS -l walltime=02:00:00
+#PBS -A 15479
+##PBS -A LatticeQCD_aesp_CNDA
+
+cd $PBS_O_WORKDIR
+cp $PBS_NODEFILE nodefile
+
+root=$HOME/Grid/systems/Aurora            # <-- adjust to your source tree
+source ${root}/sourceme.sh
+TILE=${root}/benchmarks/gpu_tile.sh
+
+BIN=$PBS_O_WORKDIR/tests/IO/Test_aggregate_io
+[ -x $BIN  ] || { echo "no $BIN -- submit from the build directory"; exit 1; }
+[ -x $TILE ] || { echo "no $TILE -- check \$root"; exit 1; }
+
+export OMP_NUM_THREADS=4
+export MPICH_OFI_NIC_POLICY=GPU
+
+# MPICH_DBG_* and MPICH_MPIIO_STATS are deliberately absent: at 1536 ranks
+# they produce gigabytes of log and perturb the timings they would explain.
+# Get those from systems/Aurora/aggregate_io.pbs on the debug queue.
+
+# PROJECT is the flare project DIRECTORY name, not the -A account number.
+PROJECT=LatticeQCD_aesp_CNDA
+WORK=/lus/flare/projects/$PROJECT/$USER/aggscale.$PBS_JOBID
+mkdir -p $WORK || { echo "cannot create $WORK -- set PROJECT correctly"; exit 1; }
+cd       $WORK
+
+# The largest rung writes three files of 232 GB, so budget ~700 GB for the
+# scan and check the quota before submitting.  The test unlinks its three
+# files at the start of each run, so that is peak, not cumulative.
+#
+# Do NOT stripe by default.  Measured on FRONTIER at 128 nodes / 1024 ranks,
+# 154.6 GB record, best of 3 (MB/s) -- these are Frontier numbers, quoted for
+# what to look for, not a prediction for Aurora:
+#
+#                     default layout    lfs setstripe -c -1 -S 8M
+#   raw                    97673                81728
+#   MPI-IO lexicographic   31675                77534
+#   aggregate             189535                86063
+#
+# The two layout preserving paths want opposite things.  Wide striping is
+# what rescues MPI-IO at scale, 32 -> 78 GB/s; it costs the aggregate path a
+# factor of 2.2 and costs raw as well.  With the default layout MPI-IO
+# plateaued at ~30 GB/s from 64 nodes upward while the aggregate path kept
+# scaling.  Uncomment only to reproduce that interaction, and record which.
+#lfs setstripe -c -1 -S 8M $WORK
+lfs getstripe -d $WORK 2>/dev/null || echo "(no lfs getstripe -- not Lustre?)"
+
+ARGS="--aggregate-target 4194304 --io-no-correctness --io-reps 3"
+AT=8
+
+run () {   # run <nodes> <grid> <mpi> <comment>
+  local nodes=$1 nranks=$(( $1 * 12 ))
+  echo
+  echo "==================================================================="
+  echo "=== SCAN nodes=$nodes ranks=$nranks  grid=$2  mpi=$3   $4"
+  echo "==================================================================="
+  mpiexec -np $nranks -ppn 12 -envall $TILE $BIN --grid $2 --mpi $3 \
+          --shm-mpi 0 --shm 2048 --device-mem 32000 --accelerator-threads $AT $ARGS
+  echo "=== exit $?"
+}
+
+#            nodes  global lattice      decomposition   record
+run    4     32.32.96.128    4.4.3.1   "7.2 GB"
+run    8     32.32.96.256    4.4.3.2   "14.5 GB"
+run   16     32.32.96.512    4.4.3.4   "29.0 GB"
+run   32     32.32.192.512   4.4.6.4   "58.0 GB"
+run   64     32.32.192.1024  4.4.6.8   "116.0 GB"
+run  128     32.32.384.1024  4.4.12.8  "231.9 GB"
+
+echo
+echo "=== done.  Files left in $WORK"
+echo "=== For cold read numbers, submit a SECOND job on a fresh allocation"
+echo "=== with WORK pointed at this directory and --io-read-only added to"
+echo "=== ARGS.  Reading back what this job wrote only measures page cache."
+ls -l $WORK

systems/Booster/config-command

@@ -8,7 +8,6 @@ LIME=/p/home/jusers/boyle2/juwels/gm2dwf/boyle/
     --disable-gparity \
     --disable-fermion-reps \
     --with-lime=$LIME \
-    --enable-accelerator-cshift \
     --disable-unified \
     CXX=nvcc \
     LDFLAGS="-cudart shared " \

systems/Frontier/aggregate_io.slurm

@@ -0,0 +1,152 @@
+#!/bin/bash -l
+
+#SBATCH --job-name=runIO
+#SBATCH --nodes=4
+#SBATCH --ntasks-per-node=8
+#SBATCH --cpus-per-task=7
+#SBATCH --gpus-per-node=8
+#SBATCH --time=02:00:00
+#SBATCH --account=phy157_dwf
+#SBATCH --gpu-bind=none
+#SBATCH --exclusive
+#SBATCH --mem=0
+#SBATCH -q debug
+
+cat << EOF > select_gpu
+#!/bin/bash
+export GPU_MAP=(0 1 2 3 7 6 5 4)
+export NUMA_MAP=(3 3 1 1 2 2 0 0)
+export GPU=\${GPU_MAP[\$SLURM_LOCALID]}
+export NUMA=\${NUMA_MAP[\$SLURM_LOCALID]}
+unset ROCR_VISIBLE_DEVICES
+export HIP_VISIBLE_DEVICES=\$GPU
+
+rank=\$SLURM_PROCID
+CMD="numactl -m \$NUMA -N \$NUMA  \$*"
+exec \$CMD
+EOF
+
+chmod +x ./select_gpu
+
+# GPU_MAP/NUMA_MAP above describe a full node.  At fewer than 8 ranks per node
+# Slurm hands each task cpus-per-task cores block-wise from core 0, so the NUMA
+# domain NUMA_MAP names is not in the task's allowed cpu mask and numactl fails
+# with EINVAL before Grid starts.  The GPU choice stays valid; only the memory
+# binding does not.  For the small correctness runs the binding is irrelevant,
+# so use a wrapper that picks the GCD and leaves placement to Slurm.
+cat << EOF > select_gcd
+#!/bin/bash
+export GPU_MAP=(0 1 2 3 7 6 5 4)
+export GPU=\${GPU_MAP[\$SLURM_LOCALID]}
+unset ROCR_VISIBLE_DEVICES
+export HIP_VISIBLE_DEVICES=\$GPU
+exec \$*
+EOF
+
+chmod +x ./select_gcd
+SELECT=$SLURM_SUBMIT_DIR/select_gpu
+SELECT_NONUMA=$SLURM_SUBMIT_DIR/select_gcd
+
+root=$HOME/ParallelIO/systems/Frontier/
+source ${root}/sourceme-rocm7.2.sh
+
+export OMP_NUM_THREADS=7
+export MPICH_GPU_SUPPORT_ENABLED=1
+
+# Test_aggregate_io writes ref.bin / agg.bin / trunc.bin with *relative* paths,
+# so they land in the cwd of each rank, which is the submission directory unless
+# we move.  Home is NFS; the whole point of the exercise is Lustre.
+WORK=/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/aggio.$SLURM_JOB_ID
+mkdir -p $WORK
+cd       $WORK
+
+# Striping has to be set on the directory before the files are created, and
+# all three paths inherit it, so the A/B comparison stays fair either way.
+# Left unset: at 128 nodes the aggregate path is 2.2x faster on the default
+# layout than on -c -1, while MPI-IO is 2.4x slower on it.  See the table in
+# aggregate_io_scaling.slurm.  Set it only to reproduce that interaction.
+#lfs setstripe -c 32 -S 8M $WORK
+lfs getstripe -d $WORK      # record the inherited layout; needed to read the numbers
+
+BIN=$SLURM_SUBMIT_DIR/tests/IO/Test_aggregate_io
+
+# ROMIO / Cray MPICH collective buffering report for the reference path.
+# Verbose; switch on when you want to see what the old path is doing.
+# export MPICH_MPIIO_STATS=1
+# export MPICH_MPIIO_TIMERS=1
+
+# Always state ntasks-per-node explicitly.  Letting srun derive it from -n
+# gives an uneven packing (3,2,2,2 for -n9 over 4 nodes) which no fixed
+# localid -> GCD map can describe.  Ranks per node must not exceed 8.
+run () {   # run <nodes> <ranks-per-node> <grid> <mpi> <comment> [extra args...]
+  local nodes=$1 rpn=$2 gr=$3 mp=$4 note=$5 wrap=$SELECT
+  local nranks=$(( $1 * $2 ))
+  shift 5
+  if [ $rpn -ne 8 ]; then wrap=$SELECT_NONUMA; fi   # NUMA_MAP only valid at 8
+  echo
+  echo "==================================================================="
+  echo "=== N=$nodes x $rpn = $nranks  grid=$gr  mpi=$mp   $note"
+  echo "=== extra: $@"
+  echo "==================================================================="
+  srun -N$nodes -n$nranks --ntasks-per-node=$rpn $wrap $BIN --grid $gr --mpi $mp \
+       --accelerator-threads 8 --shm 2048 --device-mem 32000 "$@"
+  echo "=== exit $?"
+}
+
+#####################################################################
+# Phase 0.  Non-uniform AllToAllV, correctness only.
+#
+# The variable-count branch of CartesianCommunicator::AllToAllV only runs
+# when the send counts differ between destinations, which needs an odd
+# process factor in an un-split (fast) dimension.  It does NOT need a toy
+# volume -- see phase 1b, which hits it at 226 MB/rank.  The one small run
+# kept here is the only way to reach the non-uniform case at k=1 with many
+# extents per rank; it is a logic corner, carries --io-reps 0, and reports
+# no bandwidth.  2.2.4.4 per rank is 9 KB and means nothing for I/O.
+#####################################################################
+run 3 3 6.6.4.4  3.3.1.1  "non-uniform at all four targets, k=1 and k=3" --io-reps 0
+
+#####################################################################
+# Phase 1.  Medium volume, 4.8 GB record, 151 MB/rank.
+# Correctness plus performance at the production 4MB target only; the
+# byte-for-byte comparison reads the whole file on one rank, so the
+# full four target sweep is not affordable above a few GB.
+#####################################################################
+run 4 8 32.32.64.128  4.4.2.1  "4.8 GB, correctness + perf" --aggregate-target 4194304
+
+#####################################################################
+# Phase 1b.  Non-uniform AllToAllV at a volume that means something.
+# 24 ranks = 3 nodes x 8, so the NUMA map stays valid.
+#   48.48.64.64 / 3.2.2.2  k=2 row=6  <=6 extents of 13.5 MB  NON-UNIFORM
+# 5.4 GB record, 226 MB/rank.  Correctness and performance together, so
+# the variable-count path is covered where the bandwidth is also real.
+#####################################################################
+run 3 8 48.48.64.64  3.2.2.2  "5.4 GB, NON-UNIFORM counts, correctness + perf" --aggregate-target 4194304
+
+#####################################################################
+# Phase 2.  Production volume, 19.3 GB record, 604 MB/rank.
+# Correctness off.  Modelled extents at the 4MB target (fobj = 576 B):
+#   1.1.4.8   k=2  row=1   16 extents of 36 MB   <- old path gives 36 KB runs
+#   4.4.2.1   k=2  row=16   8 extents of 72 MB   <- old path gives  9 KB runs
+#   2.2.2.4   k=2  row=4    8 extents
+#   8.4.1.1   k=2  row=32   4 extents
+#####################################################################
+run 4 8 64.64.64.128  1.1.4.8  "19.3 GB, baseline decomposition" --aggregate-target 4194304 --io-no-correctness
+run 4 8 64.64.64.128  4.4.2.1  "19.3 GB, row of 32"             --aggregate-target 4194304 --io-no-correctness
+run 4 8 64.64.64.128  2.2.2.4  "19.3 GB, row of 4"              --aggregate-target 4194304 --io-no-correctness
+run 4 8 64.64.64.128  8.4.1.1  "19.3 GB, row of 32, x heavy"    --aggregate-target 4194304 --io-no-correctness
+
+# 10.9 GB with non-uniform counts, 453 MB/rank, 27 MB extents, 24 ranks.
+run 3 8 48.96.64.64   3.4.2.1  "10.9 GB, NON-UNIFORM counts"    --aggregate-target 4194304 --io-no-correctness
+
+#####################################################################
+# Phase 3.  Large volume, 43.5 GB record, 1.36 GB/rank.
+# Host side buffering is 3 copies of the local slice, so ~4 GB/rank
+# and ~33 GB/node.  Two repetitions only.
+#####################################################################
+run 4 8 64.64.96.192  1.1.4.8  "43.5 GB, baseline"  --aggregate-target 4194304 --io-no-correctness --io-reps 2
+run 4 8 64.64.96.192  4.4.2.1  "43.5 GB, row of 32" --aggregate-target 4194304 --io-no-correctness --io-reps 2
+
+echo
+echo "=== done.  Output left in $WORK"
+ls -l $WORK

systems/Frontier/aggregate_io_scaling.slurm

@@ -0,0 +1,104 @@
+#!/bin/bash -l
+
+# Node count scan.  Everything that could confound the comparison is held
+# fixed and only the number of Lustre clients changes:
+#
+#   local volume   8.8.32.128        = 262144 sites x 576 B = 151 MB / rank
+#   aggregation    k=2, row of 16, 8 extents of 18 MB        (identical at
+#                                                             every node count)
+#   old path       contiguous run = lLattice[0]*576 = 4.6 KB (identical too)
+#
+# So the ratio of contiguous extent between the two layout preserving paths is
+# a constant 4000x across the whole scan, and any change in their relative
+# bandwidth is a property of the client count alone.  That is the variable the
+# 4 node runs could not move.
+#
+# Trim the tail of the run list if you want a smaller allocation; the
+# geometries are independent.
+
+#SBATCH --job-name=ioScale
+#SBATCH --nodes=128
+#SBATCH --ntasks-per-node=8
+#SBATCH --cpus-per-task=7
+#SBATCH --gpus-per-node=8
+#SBATCH --time=02:00:00
+#SBATCH --account=phy157_dwf
+#SBATCH --gpu-bind=none
+#SBATCH --exclusive
+#SBATCH --mem=0
+
+cat << EOF > select_gpu
+#!/bin/bash
+export GPU_MAP=(0 1 2 3 7 6 5 4)
+export NUMA_MAP=(3 3 1 1 2 2 0 0)
+export GPU=\${GPU_MAP[\$SLURM_LOCALID]}
+export NUMA=\${NUMA_MAP[\$SLURM_LOCALID]}
+unset ROCR_VISIBLE_DEVICES
+export HIP_VISIBLE_DEVICES=\$GPU
+
+rank=\$SLURM_PROCID
+CMD="numactl -m \$NUMA -N \$NUMA  \$*"
+exec \$CMD
+EOF
+
+chmod +x ./select_gpu
+SELECT=$SLURM_SUBMIT_DIR/select_gpu
+
+root=$HOME/ParallelIO/systems/Frontier/
+source ${root}/sourceme-rocm7.2.sh
+
+export OMP_NUM_THREADS=7
+export MPICH_GPU_SUPPORT_ENABLED=1
+
+WORK=/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/aggscale.$SLURM_JOB_ID
+mkdir -p $WORK
+cd       $WORK
+
+# The largest rung writes three files of 154 GB, so budget ~700 GB for the
+# whole scan and check the quota before submitting.
+#
+# Do NOT stripe by default.  Measured on Frontier at 128 nodes / 1024 ranks,
+# 154.6 GB record, best of 3 (MB/s):
+#
+#                     default layout    lfs setstripe -c -1 -S 8M
+#   raw                    97673                81728
+#   MPI-IO lexicographic   31675                77534
+#   aggregate             189535                86063
+#
+# The two layout preserving paths want opposite things.  Wide striping is what
+# rescues MPI-IO at scale, 32 -> 78 GB/s, which is presumably what careful
+# striping has been buying in production.  It costs the aggregate path a factor
+# of 2.2, and costs raw as well.  With the default layout MPI-IO plateaus at
+# ~30 GB/s from 64 nodes upward -- the 20-40 GB/s seen in production -- while
+# the aggregate path keeps scaling.  Uncomment only to reproduce that.
+#lfs setstripe -c -1 -S 8M $WORK
+lfs getstripe -d $WORK      # record the inherited layout; needed to read the numbers
+
+BIN=$SLURM_SUBMIT_DIR/tests/IO/Test_aggregate_io
+ARGS="--aggregate-target 4194304 --io-no-correctness --io-reps 3"
+
+run () {   # run <nodes> <grid> <mpi> <comment>
+  local nodes=$1 nranks=$(( $1 * 8 ))
+  echo
+  echo "==================================================================="
+  echo "=== SCAN nodes=$nodes ranks=$nranks  grid=$2  mpi=$3   $4"
+  echo "==================================================================="
+  srun -N$nodes -n$nranks --ntasks-per-node=8 $SELECT $BIN --grid $2 --mpi $3 \
+       --accelerator-threads 8 --shm 2048 --device-mem 32000 $ARGS
+  echo "=== exit $?"
+}
+
+#            nodes  global lattice      decomposition   record
+run    4     32.32.64.128    4.4.2.1   "4.8 GB"
+run    8     32.32.64.256    4.4.2.2   "9.7 GB"
+run   16     32.32.64.512    4.4.2.4   "19.3 GB"
+run   32     32.32.128.512   4.4.4.4   "38.6 GB"
+run   64     32.32.128.1024  4.4.4.8   "77.3 GB"
+run  128     32.32.256.1024  4.4.8.8   "154.6 GB"
+
+echo
+echo "=== done.  Files left in $WORK"
+echo "=== For cold read numbers, submit a SECOND job on a fresh allocation"
+echo "=== with WORK pointed at this directory and --io-read-only added to"
+echo "=== ARGS.  Reading back what this job wrote only measures page cache."
+ls -l $WORK

systems/Frontier/config-command

@@ -1,4 +1,5 @@
 CLIME=`spack find --paths c-lime@2-3-9 | grep c-lime| cut -c 15-`
+
 ../../configure --enable-comms=mpi-auto \
 --with-lime=$CLIME \
 --enable-unified=no \
@@ -9,12 +10,13 @@ CLIME=`spack find --paths c-lime@2-3-9 | grep c-lime| cut -c 15-`
 --disable-gparity \
 --disable-fermion-reps \
 --enable-simd=GPU \
---with-gmp=$OLCF_GMP_ROOT \
+--with-openssl=$OPENSSL \
---with-mpfr=/opt/cray/pe/gcc/mpfr/3.1.4/ \
+--with-gmp=$GMP \
+--with-mpfr=$MPFR \
 --disable-fermion-reps \
 CXX=hipcc MPICXX=mpicxx \
-CXXFLAGS="-fPIC -I${ROCM_PATH}/include/ -I${MPICH_DIR}/include -L/lib64 " \
+CXXFLAGS="-fPIC -I${ROCM_PATH}/include/ -I${MPICH_DIR}/include " \
- LDFLAGS="-L/lib64 -L${ROCM_PATH}/lib -L${MPICH_DIR}/lib -lmpi -L${CRAY_MPICH_ROOTDIR}/gtl/lib -lmpi_gtl_hsa -lhipblas -lrocblas -lhipfft"
+ LDFLAGS="-L${ROCM_PATH}/lib -L${MPICH_DIR}/lib -lmpi -lmpi_gtl_hsa -lhipblas -lrocsolver -lrocblas -lhipfft -lamdhip64"
 
 
 

systems/Frontier/sourceme-rocm6.4.sh

@@ -0,0 +1,15 @@
+
+echo spack
+. /autofs/nccs-svm1_home1/paboyle/spack/share/spack/setup-env.sh
+
+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 $2}' `
+
+module load cce/20.0.0
+module load cpe/25.09
+module load rocm/6.4.0
+export LD_LIBRARY_PATH=$CRAY_LD_LIBRARY_PATH:$LD_LIBRARY_PATH
+export LD_LIBRARY_PATH=/opt/rocm-6.4.0/lib/llvm/lib/:$LD_LIBRARY_PATH
+module load emacs

systems/Frontier/sourceme-rocm7.0.sh

@@ -0,0 +1,13 @@
+
+echo spack
+. /autofs/nccs-svm1_home1/paboyle/spack/share/spack/setup-env.sh
+
+
+module load cce/21.0.0
+module load cpe/26.03
+module load rocm/7.0.2
+
+export LD_LIBRARY_PATH=/opt/rocm-7.0.2/lib/llvm/lib/:$LD_LIBRARY_PATH
+export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$CRAY_LD_LIBRARY_PATH
+
+module load emacs

systems/Frontier/sourceme-rocm7.2.sh

@@ -0,0 +1,15 @@
+
+echo spack
+. /autofs/nccs-svm1_home1/paboyle/spack/share/spack/setup-env.sh
+
+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 $2}' `
+
+module load cce/21.0.0
+module load cpe/26.03
+module load rocm/7.2.0
+export LD_LIBRARY_PATH=/opt/rocm-7.2.0/lib/llvm/lib/:$LD_LIBRARY_PATH
+export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$CRAY_LD_LIBRARY_PATH
+module load emacs

systems/Frontier/sourceme.sh

@@ -1,25 +0,0 @@
-
-echo spack
-. /autofs/nccs-svm1_home1/paboyle/Crusher/Grid/spack/share/spack/setup-env.sh
-
-module load cce/15.0.1
-module load rocm/5.3.0
-module load cray-fftw
-module load craype-accel-amd-gfx90a
-
-#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`/:$LD_LIBRARY_PATH
-ln -s /opt/rocm-6.0.0/lib/libamdhip64.so.6 .
-
-#echo spack load c-lime
-#spack load c-lime
-#module load emacs 
-##module load PrgEnv-gnu
-##module load cray-mpich
-##module load cray-fftw
-##module load craype-accel-amd-gfx90a
-##export LD_LIBRARY_PATH=/opt/gcc/mpfr/3.1.4/lib:$LD_LIBRARY_PATH
-#Hack for lib
-##export LD_LIBRARY_PATH=`pwd`/:$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-gmp=$GMP \
-    --with-mpfr=$PREFIX \
+    --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-mpi

@@ -3,7 +3,10 @@
 CXX=mpicxx ../../configure \
 	   --enable-simd=GEN \
 	   --enable-comms=mpi-auto \
-	   --enable-Sp=yes \
+	   --enable-Sp=no \
+	   --disable-fermion-reps \
+	   --disable-gparity \
+	   --with-fftw=$FFTW \
 	   --enable-unified=yes \
 	   --prefix /Users/peterboyle/QCD/vtk/Grid/install \
 	   --with-lime=$CLIME \

systems/mac-arm/sourceme.sh

@@ -0,0 +1,11 @@
+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}' `
+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 $2}' `
+
+export LD_LIBRARY_PATH=$MPFR/lib:$LD_LIBRARY_PATH
+export LD_LIBRARY_PATH=$GMP/lib:$LD_LIBRARY_PATH

tests/IO/Test_aggregate_io.cc

@@ -0,0 +1,458 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./tests/IO/Test_aggregate_io.cc
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+
+// Correctness and performance test for BINARYIO_AGGREGATE.
+//
+// Correctness, per aggregateTargetBytes:
+//   1. write via the MPI-IO lexicographic path      -> ref.bin
+//   2. write via the aggregate path                 -> agg.bin
+//   3. the two files must be byte identical         <- proves the layout matches
+//   4. read agg.bin back through the aggregate path <- proves the mirror inverts
+//   5. write and read the non-lexicographic path    -> raw.bin.  Its layout is
+//      different by construction (each rank owns one contiguous segment in
+//      rank order) so it cannot be compared byte for byte, but the NERSC and
+//      SciDAC checksums are computed from the global site index and are
+//      therefore layout independent: they must match the other two paths.
+//   6. a record written over a longer pre-existing file must leave the file at
+//      exactly offset+payload, with no trailing fragment of the old contents
+//
+// Performance: three paths, both directions, timed with the client page cache
+// dropped before every read so that a read back reports filesystem bandwidth
+// rather than memory bandwidth.  The non-lexicographic path is the zero
+// overhead reference: no transposition, no layout independence, one disjoint
+// contiguous segment per rank, which is the arrangement that reaches full
+// filesystem bandwidth on a leadership machine.  It is the upper bound the
+// other two are trying to approach.
+//
+// Options:
+//   --aggregate-target <bytes>   sweep this one target only (default: sweep
+//                                1, 1024, 64K, 4M)
+//   --io-reps <n>                repetitions in the performance section
+//                                (default 3; 0 disables it)
+//   --io-no-correctness          skip the correctness section, which reads the
+//                                whole file on one rank and is not affordable
+//                                at very large volume
+//   --io-read-only               time reads only, of files left in place by an
+//                                earlier job.  Reading back what this job just
+//                                wrote measures the client page cache; a fresh
+//                                allocation pointed at the same directory is
+//                                the only way to get a cold read without root.
+//
+// The exchange is only meaningfully exercised when the fast dimensions are
+// split across ranks; --mpi 1.1.X.Y leaves the rows of size one and the test
+// then passes vacuously.  Non-uniform AllToAllV counts additionally need an
+// odd process factor in a fast dimension and a small local volume.
+
+#include <Grid/Grid.h>
+#include <fcntl.h>
+
+using namespace Grid;
+
+/////////////////////////////////////////////////////////////////////////////
+// Compare in chunks.  Slurping both files into memory is fine for a few MB
+// and fatal for the multi-GB records this test is meant to reach.
+/////////////////////////////////////////////////////////////////////////////
+static bool FilesIdentical(std::string a,std::string b)
+{
+  std::ifstream fa(a,std::ios::binary), fb(b,std::ios::binary);
+  if ( !fa.good() || !fb.good() ) {
+    std::cout<<GridLogMessage<<"  could not open "<<a<<" and/or "<<b<<std::endl;
+    return false;
+  }
+  fa.seekg(0,std::ios::end); fb.seekg(0,std::ios::end);
+  uint64_t sa = (uint64_t)fa.tellg(), sb = (uint64_t)fb.tellg();
+  if ( sa != sb ) {
+    std::cout<<GridLogMessage<<"  size mismatch "<<sa<<" vs "<<sb<<std::endl;
+    return false;
+  }
+  fa.seekg(0,std::ios::beg); fb.seekg(0,std::ios::beg);
+
+  const uint64_t chunk = 8*1024*1024;
+  std::vector<char> va(chunk), vb(chunk);
+  uint64_t done=0;
+  while ( done < sa ) {
+    uint64_t n = std::min(chunk,sa-done);
+    fa.read(&va[0],n);
+    fb.read(&vb[0],n);
+    for(uint64_t i=0;i<n;i++){
+      if ( va[i]!=vb[i] ) {
+        std::cout<<GridLogMessage<<"  first differing byte at "<<done+i<<" of "<<sa<<std::endl;
+        return false;
+      }
+    }
+    done += n;
+  }
+  return true;
+}
+
+/////////////////////////////////////////////////////////////////////////////
+// Reading back a file we have just written measures the client page cache,
+// not the filesystem: the earlier runs of this test reported 8 GB/s on reads
+// and ~1 GB/s on writes for the same data.  POSIX_FADV_DONTNEED asks the
+// kernel to drop the cached pages for the file.  It is advisory and every
+// rank must do it, since each client caches independently, so treat this as
+// best effort rather than a guarantee of a cold read.
+/////////////////////////////////////////////////////////////////////////////
+static void DropCache(GridBase *grid,std::string file)
+{
+  grid->Barrier();
+  int fd = ::open(file.c_str(),O_RDONLY);
+  if ( fd >= 0 ) {
+#ifdef POSIX_FADV_DONTNEED
+    ::posix_fadvise(fd,0,0,POSIX_FADV_DONTNEED);
+#endif
+    ::close(fd);
+  }
+  grid->Barrier();
+}
+
+static uint64_t OptionU64(int argc,char **argv,const char *opt,uint64_t def)
+{
+  if ( GridCmdOptionExists(argv,argv+argc,opt) ) {
+    std::string arg = GridCmdOptionPayload(argv,argv+argc,opt);
+    return (uint64_t)std::stoull(arg);
+  }
+  return def;
+}
+
+int main(int argc,char **argv)
+{
+  Grid_init(&argc,&argv);
+
+  Coordinate latt = GridDefaultLatt();
+  Coordinate simd = GridDefaultSimd(Nd,vComplexD::Nsimd());
+  Coordinate mpi  = GridDefaultMpi();
+  GridCartesian grid(latt,simd,mpi);
+
+  typedef vLorentzColourMatrixD vobj;
+  typedef LorentzColourMatrixD  sobj;
+
+  GridParallelRNG pRNG(&grid);
+  pRNG.SeedFixedIntegers(std::vector<int>({1,2,3,4}));
+  LatticeGaugeFieldD Umu(&grid);
+  random(pRNG,Umu);
+
+  BinarySimpleMunger<sobj,sobj> munge;
+  const std::string format("IEEE64BIG");
+
+  const int lex = BinaryIO::BINARYIO_LEXICOGRAPHIC;
+  const int agg = BinaryIO::BINARYIO_LEXICOGRAPHIC|BinaryIO::BINARYIO_AGGREGATE;
+  const int raw = 0;   // no BINARYIO_LEXICOGRAPHIC: contiguous segment per rank
+
+  uint64_t payload = (uint64_t)grid._gsites*sizeof(sobj);
+
+  std::vector<uint64_t> targets = {1, 1024, 64*1024, 4*1024*1024};
+  if ( GridCmdOptionExists(argv,argv+argc,"--aggregate-target") ) {
+    targets.clear();
+    targets.push_back(OptionU64(argc,argv,"--aggregate-target",4*1024*1024));
+  }
+  uint64_t reps        = OptionU64(argc,argv,"--io-reps",3);
+  bool     correctness = !GridCmdOptionExists(argv,argv+argc,"--io-no-correctness");
+  // Read only: time reads of files left by an earlier job.  The only way to
+  // get a cold client cache without root is to read on an allocation that did
+  // not write the data, so run one job to write and a second, pointed at the
+  // same directory, with this flag.
+  bool     readonly    = GridCmdOptionExists(argv,argv+argc,"--io-read-only");
+  if ( readonly ) correctness = false;
+
+  std::cout<<GridLogMessage<<"Record payload "<<payload<<" bytes = "
+           <<payload/1024./1024.<<" MB, "
+           <<payload/(RealD)grid.ProcessorCount()/1024./1024.<<" MB/rank"<<std::endl;
+
+  int failures=0;
+
+  //////////////////////////////////////////////////////////////////////////
+  // Correctness
+  //////////////////////////////////////////////////////////////////////////
+  if ( correctness ) for(auto target : targets){
+
+    std::cout<<GridLogMessage<<"=== correctness, aggregateTargetBytes = "<<target<<" ==="<<std::endl;
+
+    uint32_t n1,a1,b1, n2,a2,b2, n3,a3,b3;
+    uint64_t off;
+
+    // Start from a clean slate.  The aggregate path sets the file length to
+    // exactly offset+payload; the MPI-IO path (MPI_MODE_CREATE) leaves any
+    // pre-existing tail in place.  Comparing stale files would therefore
+    // report a size mismatch that says nothing about the payload.
+    if ( grid.IsBoss() ) { ::unlink("ref.bin"); ::unlink("agg.bin"); ::unlink("raw.bin"); }
+    grid.Barrier();
+
+    off=0;
+    BinaryIO::writeLatticeObject<vobj,sobj>(Umu,"ref.bin",munge,off,format,n1,a1,b1,lex);
+
+    BinaryIO::aggregateTargetBytes = target;
+    off=0;
+    BinaryIO::writeLatticeObject<vobj,sobj>(Umu,"agg.bin",munge,off,format,n2,a2,b2,agg);
+
+    grid.Barrier();
+
+    if ( grid.IsBoss() ) {
+      if ( !FilesIdentical("ref.bin","agg.bin") ) {
+        std::cout<<GridLogError<<"  FAIL: aggregate file differs from lexicographic file"<<std::endl;
+        failures++;
+      } else {
+        std::cout<<GridLogMessage<<"  files byte identical"<<std::endl;
+      }
+    }
+    if ( (n1!=n2)||(a1!=a2)||(b1!=b2) ) {
+      std::cout<<GridLogError<<"  FAIL: checksum mismatch between paths"<<std::endl;
+      failures++;
+    }
+    // writeLatticeObject takes offset by value, so the out-parameter that
+    // IOobject sets never reaches us here and cannot be checked directly.
+    // The observable equivalent is the file length: both paths must leave the
+    // record ending at exactly offset+payload.
+    if ( grid.IsBoss() ) {
+      for(auto f : {std::string("ref.bin"),std::string("agg.bin")}){
+        std::ifstream fs(f,std::ios::binary|std::ios::ate);
+        uint64_t sz = (uint64_t)fs.tellg();
+        if ( sz != payload ) {
+          std::cout<<GridLogError<<"  FAIL: "<<f<<" is "<<sz<<" bytes, expected "<<payload<<std::endl;
+          failures++;
+        }
+      }
+    }
+
+    LatticeGaugeFieldD Uchk(&grid);
+    DropCache(&grid,"agg.bin");
+    off=0;
+    BinaryIO::readLatticeObject<vobj,sobj>(Uchk,"agg.bin",munge,off,format,n3,a3,b3,agg);
+    if ( (n3!=n1)||(a3!=a1)||(b3!=b1) ) {
+      std::cout<<GridLogError<<"  FAIL: read back checksum mismatch"<<std::endl;
+      failures++;
+    }
+    Uchk = Uchk - Umu;
+    RealD residual = norm2(Uchk);
+    std::cout<<GridLogMessage<<"  read back residual "<<residual<<std::endl;
+    if ( residual != 0.0 ) {
+      std::cout<<GridLogError<<"  FAIL: read back does not reproduce the field"<<std::endl;
+      failures++;
+    }
+
+    ////////////////////////////////////////////////////////////////////////
+    // Non-lexicographic.  Different file layout by construction, so compare
+    // by checksum and by round trip rather than by bytes.
+    ////////////////////////////////////////////////////////////////////////
+    uint32_t n4,a4,b4, n5,a5,b5;
+    off=0;
+    BinaryIO::writeLatticeObject<vobj,sobj>(Umu,"raw.bin",munge,off,format,n4,a4,b4,raw);
+    grid.Barrier();
+    if ( (n4!=n1)||(a4!=a1)||(b4!=b1) ) {
+      std::cout<<GridLogError<<"  FAIL: raw path checksum differs; the NERSC and"
+               <<" SciDAC checksums are layout independent and must agree"<<std::endl;
+      failures++;
+    }
+    DropCache(&grid,"raw.bin");
+    off=0;
+    BinaryIO::readLatticeObject<vobj,sobj>(Uchk,"raw.bin",munge,off,format,n5,a5,b5,raw);
+    if ( (n5!=n1)||(a5!=a1)||(b5!=b1) ) {
+      std::cout<<GridLogError<<"  FAIL: raw read back checksum mismatch"<<std::endl;
+      failures++;
+    }
+    Uchk = Uchk - Umu;
+    RealD rawresidual = norm2(Uchk);
+    std::cout<<GridLogMessage<<"  raw read back residual "<<rawresidual<<std::endl;
+    if ( rawresidual != 0.0 ) {
+      std::cout<<GridLogError<<"  FAIL: raw read back does not reproduce the field"<<std::endl;
+      failures++;
+    }
+  }
+
+  //////////////////////////////////////////////////////////////////////////
+  // Truncation.  offset!=0 is the case that matters: it is what ILDG and
+  // NERSC use, and it is the branch that used to only ever grow the file.
+  // The oversized starting file is made by extending a sparse one rather
+  // than writing padding from a single rank, which does not scale.
+  //////////////////////////////////////////////////////////////////////////
+  if ( correctness ) {
+    BinaryIO::aggregateTargetBytes = 4*1024*1024;
+    for(uint64_t testOffset : {(uint64_t)0, (uint64_t)1024}){
+
+      uint64_t expect = testOffset + payload;
+
+      if ( grid.IsBoss() ) {
+        { std::ofstream create("trunc.bin",std::ios::binary|std::ios::out); create.close(); }
+        int ierr = ::truncate("trunc.bin",(off_t)(expect+65536));
+        GRID_ASSERT(ierr==0);
+      }
+      grid.Barrier();
+
+      uint32_t n,a,b;
+      uint64_t off = testOffset;
+      BinaryIO::writeLatticeObject<vobj,sobj>(Umu,"trunc.bin",munge,off,format,n,a,b,agg);
+      grid.Barrier();
+
+      if ( grid.IsBoss() ) {
+        std::ifstream f("trunc.bin",std::ios::binary|std::ios::ate);
+        uint64_t sz = (uint64_t)f.tellg();
+        f.close();
+        if ( sz != expect ) {
+          std::cout<<GridLogError<<"  FAIL: offset "<<testOffset<<" left file "<<sz
+                   <<" bytes, expected "<<expect<<std::endl;
+          failures++;
+        } else {
+          std::cout<<GridLogMessage<<"  truncation ok at offset "<<testOffset
+                   <<": file is exactly "<<sz<<" bytes"<<std::endl;
+        }
+      }
+    }
+  }
+
+  //////////////////////////////////////////////////////////////////////////
+  // Performance.  Four numbers per repetition: write and read, old path and
+  // new.  Reads are preceded by a cache drop; writes are not, so a write
+  // number is "time to hand the data to the client cache and close", the
+  // same convention for both paths.
+  //////////////////////////////////////////////////////////////////////////
+  if ( reps ) {
+
+    LatticeGaugeFieldD Uio(&grid);
+    uint32_t n,a,b;
+
+    // The NERSC and SciDAC checksums are computed from the global site index,
+    // so all three layouts must produce the same values.  This costs nothing
+    // and is the only correctness check available at a volume where the byte
+    // for byte comparison (single rank, whole file) is unaffordable.
+    uint32_t cn[6],ca[6],cb[6];
+    auto agreeing = [&](const char *what,int lo,int hi){
+      for(int i=lo+1;i<=hi;i++){
+        if ( (cn[i]!=cn[lo])||(ca[i]!=ca[lo])||(cb[i]!=cb[lo]) ) {
+          std::cout<<GridLogError<<"  FAIL: "<<what<<" checksums disagree between paths"<<std::endl;
+          return false;
+        }
+      }
+      return true;
+    };
+
+    for(auto target : targets){
+
+      BinaryIO::aggregateTargetBytes = target;
+      std::cout<<GridLogMessage<<"=== performance, aggregateTargetBytes = "<<target<<" ==="<<std::endl;
+
+      std::vector<RealD> wref,wagg,wraw,rref,ragg,rraw;
+
+      for(uint64_t rep=0;rep<reps;rep++){
+
+        uint64_t off;
+
+        // Unlink only before the first repetition.  Lustre metadata cost is
+        // per file, not per byte, so rep 0 reports "create the file and write
+        // it" and the later reps report the steady state of overwriting an
+        // existing file -- which is what a multi record file does for every
+        // record after the first, and what production actually looks like.
+        if ( (rep==0) && !readonly && grid.IsBoss() ) {
+          ::unlink("ref.bin"); ::unlink("agg.bin"); ::unlink("raw.bin");
+        }
+        grid.Barrier();
+
+        if ( !readonly ) {
+
+        off=0;
+        BinaryIO::writeLatticeObject<vobj,sobj>(Umu,"ref.bin",munge,off,format,n,a,b,lex);
+        wref.push_back(BinaryIO::lastPerf.mbytesPerSecond);
+        cn[0]=n; ca[0]=a; cb[0]=b;
+
+        off=0;
+        BinaryIO::writeLatticeObject<vobj,sobj>(Umu,"agg.bin",munge,off,format,n,a,b,agg);
+        wagg.push_back(BinaryIO::lastPerf.mbytesPerSecond);
+        cn[1]=n; ca[1]=a; cb[1]=b;
+
+        off=0;
+        BinaryIO::writeLatticeObject<vobj,sobj>(Umu,"raw.bin",munge,off,format,n,a,b,raw);
+        wraw.push_back(BinaryIO::lastPerf.mbytesPerSecond);
+        cn[2]=n; ca[2]=a; cb[2]=b;
+        if ( !agreeing("write",0,2) ) failures++;
+
+        }  // !readonly
+
+        DropCache(&grid,"ref.bin");
+        off=0;
+        BinaryIO::readLatticeObject<vobj,sobj>(Uio,"ref.bin",munge,off,format,n,a,b,lex);
+        rref.push_back(BinaryIO::lastPerf.mbytesPerSecond);
+        cn[3]=n; ca[3]=a; cb[3]=b;
+
+        DropCache(&grid,"agg.bin");
+        off=0;
+        BinaryIO::readLatticeObject<vobj,sobj>(Uio,"agg.bin",munge,off,format,n,a,b,agg);
+        ragg.push_back(BinaryIO::lastPerf.mbytesPerSecond);
+        cn[4]=n; ca[4]=a; cb[4]=b;
+
+        DropCache(&grid,"raw.bin");
+        off=0;
+        BinaryIO::readLatticeObject<vobj,sobj>(Uio,"raw.bin",munge,off,format,n,a,b,raw);
+        rraw.push_back(BinaryIO::lastPerf.mbytesPerSecond);
+        cn[5]=n; ca[5]=a; cb[5]=b;
+        if ( !agreeing("read back",readonly?3:0,5) ) failures++;
+      }
+
+      if ( grid.IsBoss() ) {
+        auto report = [&](const char *name,std::vector<RealD> &v){
+          if ( v.empty() ) return;
+          RealD best=0, sum=0;
+          for(auto x : v){ if(x>best) best=x; sum+=x; }
+          // First sample includes file creation, later ones do not; quote both
+          // rather than a mean that mixes the two.
+          std::cout<<GridLogMessage<<"  PERF target="<<target<<" "<<name
+                   <<" best "<<best<<" MB/s, mean "<<sum/v.size()
+                   <<" MB/s, first(cold create) "<<v[0]<<" MB/s, samples";
+          for(auto x : v) std::cout<<" "<<x;
+          std::cout<<std::endl;
+        };
+        report("write raw       ",wraw);   // zero overhead reference
+        report("write MPI-IO    ",wref);
+        report("write aggregate ",wagg);
+        report("read  raw       ",rraw);
+        report("read  MPI-IO    ",rref);
+        report("read  aggregate ",ragg);
+
+        // Fraction of the zero overhead reference that each layout preserving
+        // path achieves.  This is the number the whole exercise is about.
+        auto best = [](std::vector<RealD> &v){ RealD m=0; for(auto x:v) if(x>m) m=x; return m; };
+        if ( !wraw.empty() && best(wraw) > 0 ) {
+          std::cout<<GridLogMessage<<"  PERF target="<<target
+                   <<" write fraction of raw: MPI-IO "<<best(wref)/best(wraw)
+                   <<"  aggregate "<<best(wagg)/best(wraw)<<std::endl;
+        }
+        if ( !rraw.empty() && best(rraw) > 0 ) {
+          std::cout<<GridLogMessage<<"  PERF target="<<target
+                   <<" read  fraction of raw: MPI-IO "<<best(rref)/best(rraw)
+                   <<"  aggregate "<<best(ragg)/best(rraw)<<std::endl;
+        }
+      }
+    }
+  }
+
+  if ( grid.IsBoss() ) {
+    if ( failures ) std::cout<<GridLogError  <<failures<<" FAILURE(S)"<<std::endl;
+    else            std::cout<<GridLogMessage<<"ALL AGGREGATE IO TESTS PASSED"<<std::endl;
+  }
+
+  Grid_finalize();
+  return failures!=0;
+}

tests/Test_fft_memory.cc

@@ -0,0 +1,261 @@
+/*************************************************************************************
+
+ Test_fft_memory.cc
+
+ Memory growth test for PlannedFFT on a spin-colour matrix (propagator) field.
+
+ The test creates a single PlannedFFT object (which allocates FFTW plans once),
+ then repeatedly applies FFT_all_dim to the same propagator 400 times.
+
+ If PlannedFFT is working correctly the RSS should remain flat after the first
+ iteration — no new plans, no new deviceVector allocations beyond the per-call
+ pencil buffer which is freed at the end of each FFT_dim_execute call.
+
+ Build exactly like any other Grid test, e.g.:
+   make Test_fft_memory
+ or compile manually:
+   $(CXX) $(CXXFLAGS) Test_fft_memory.cc -o Test_fft_memory $(LDFLAGS)
+
+*************************************************************************************/
+
+#include <Grid/Grid.h>
+using namespace Grid;
+
+// --------------------------------------------------------------------------
+// Helper: read RSS (resident set size) in kB from /proc/self/status.
+// Returns 0 on platforms where /proc is unavailable.
+// --------------------------------------------------------------------------
+static long getCPURSSKb()
+{
+  long rss = 0;
+  FILE *fp = fopen("/proc/self/status", "r");
+  if (!fp) return -1;
+  char line[256];
+  while (fgets(line, sizeof(line), fp)) {
+    if (strncmp(line, "VmRSS:", 6) == 0) {
+      sscanf(line + 6, "%ld", &rss);
+      break;
+    }
+  }
+  fclose(fp);
+  return rss;
+}
+
+static long getGPUUsedMb()
+{
+#if defined(GRID_CUDA)
+  size_t free_bytes  = 0;
+  size_t total_bytes = 0;
+  cudaError_t err = cudaMemGetInfo(&free_bytes, &total_bytes);
+  if (err != cudaSuccess) return -1;
+  return (long)((total_bytes - free_bytes) / (1024 * 1024));
+ 
+#elif defined(GRID_HIP)
+  size_t free_bytes  = 0;
+  size_t total_bytes = 0;
+  hipError_t err = hipMemGetInfo(&free_bytes, &total_bytes);
+  if (err != hipSuccess) return -1;
+  return (long)((total_bytes - free_bytes) / (1024 * 1024));
+ 
+#else
+  return -1;   // CPU-only build: no GPU to query
+#endif
+}
+
+// ============================================================
+//  Convenience struct — one snapshot of both sides
+// ============================================================
+struct MemSnapshot {
+  long cpu_rss_kb;   // host RSS in kB  (-1 if unavailable)
+  long gpu_used_mb;  // device used in MB (-1 if no GPU)
+};
+ 
+static MemSnapshot takeSnapshot()
+{
+  MemSnapshot s;
+  s.cpu_rss_kb  = getCPURSSKb();
+  s.gpu_used_mb = getGPUUsedMb();
+  return s;
+}
+ 
+// ============================================================
+//  Pretty-print one row of the monitoring table
+// ============================================================
+static void printRow(int iter,
+                     const MemSnapshot &now,
+                     const MemSnapshot &prev)
+{
+  long cpu_delta = (now.cpu_rss_kb  >= 0 && prev.cpu_rss_kb  >= 0)
+                 ? now.cpu_rss_kb  - prev.cpu_rss_kb  : 0;
+  long gpu_delta = (now.gpu_used_mb >= 0 && prev.gpu_used_mb >= 0)
+                 ? now.gpu_used_mb - prev.gpu_used_mb : 0;
+ 
+  // Sign prefix so deltas are unambiguous
+  auto sign = [](long v) -> const char* { return v >= 0 ? "+" : ""; };
+ 
+  std::cout << GridLogMessage
+            << std::setw(6)  << iter
+            << "  CPU: " << std::setw(10) << now.cpu_rss_kb  << " kB"
+            << "  (" << sign(cpu_delta) << std::setw(7) << cpu_delta << " kB)"
+            << "  GPU: " << std::setw(7)  << now.gpu_used_mb << " MB"
+            << "  (" << sign(gpu_delta) << std::setw(5) << gpu_delta << " MB)"
+            << "\n";
+}
+
+// ============================================================
+
+int main(int argc, char **argv)
+{
+  Grid_init(&argc, &argv);
+
+  int threads = GridThread::GetThreads();
+  std::cout << GridLogMessage
+            << "Grid is setup to use " << threads << " threads" << std::endl;
+
+  // ------------------------------------------------------------------
+  // Grid setup — use whatever lattice/mpi/simd was passed on the CLI,
+  // e.g.  --grid 8.8.8.8 --mpi 1.1.1.1
+  // ------------------------------------------------------------------
+  Coordinate latt_size   = GridDefaultLatt();
+  Coordinate simd_layout = GridDefaultSimd(Nd, vComplexD::Nsimd());
+  Coordinate mpi_layout  = GridDefaultMpi();
+
+  GridCartesian GRID(latt_size, simd_layout, mpi_layout);
+
+  int vol = 1;
+  for (int d = 0; d < (int)latt_size.size(); d++) vol *= latt_size[d];
+
+  std::cout << GridLogMessage << "Lattice : ";
+  for (int d = 0; d < Nd; d++) std::cout << latt_size[d] << " ";
+  std::cout << std::endl;
+
+  // ------------------------------------------------------------------
+  // Propagator field: SpinColourMatrix = 12x12 complex, i.e.
+  // LatticePropagatorD (= Lattice<iSpinColourMatrix<vComplexD>>).
+  // This is the standard QCD quark propagator type.
+  // ------------------------------------------------------------------
+  LatticePropagatorD prop(&GRID);
+  
+  // ------------------------------------------------------------------
+  // Fill the propagator with a momentum-space plane wave,
+  // following the pattern from Test_fft.cc.
+  // We set each spin-colour component (a,b) to exp(i * sum_mu p_mu x_mu)
+  // with a fixed momentum p = (1,2,1,2).
+  // ------------------------------------------------------------------
+  Coordinate pvec({1, 2, 1, 2});
+
+  LatticeComplexD phase(&GRID);
+  LatticeComplexD coor(&GRID);
+  ComplexD ci(0.0, 1.0);
+
+  phase = Zero();
+  for (int mu = 0; mu < Nd; mu++) {
+    RealD TwoPiL = M_PI * 2.0 / latt_size[mu];
+    LatticeCoordinate(coor, mu);
+    phase = phase + (TwoPiL * pvec[mu]) * coor;
+  }
+  phase = exp(phase * ci);   // e^{i p.x}
+
+  // Broadcast the phase into every spin-colour matrix entry
+  prop = Zero();
+  prop = prop + phase;
+
+  std::cout << GridLogMessage
+            << "Propagator norm2 = " << norm2(prop) << std::endl;
+
+  // ------------------------------------------------------------------
+  // Baseline snapshot BEFORE PlannedFFT construction
+  // ------------------------------------------------------------------
+  MemSnapshot snap_before_plan = takeSnapshot();
+  std::cout << GridLogMessage
+            << "[mem] Before PlannedFFT construction"
+            << "  CPU: " << snap_before_plan.cpu_rss_kb  << " kB"
+            << "  GPU: " << snap_before_plan.gpu_used_mb << " MB"
+            << std::endl;
+ 
+  // ------------------------------------------------------------------
+  // Create the PlannedFFT — plans are allocated here ONCE for all
+  // dimensions and stored inside the object.
+  // ------------------------------------------------------------------
+  PlannedFFT<iSpinColourMatrix<vComplexD>> plannedFFT(&GRID);
+
+  // ------------------------------------------------------------------
+  // Snapshot AFTER plan construction — this is the true baseline
+  // for the loop, because cufftPlanMany itself grabs device memory.
+  // ------------------------------------------------------------------
+  MemSnapshot snap_after_plan = takeSnapshot();
+  std::cout << GridLogMessage
+            << "[mem] After  PlannedFFT construction"
+            << "  CPU: " << snap_after_plan.cpu_rss_kb  << " kB"
+            << "  GPU: " << snap_after_plan.gpu_used_mb << " MB"
+            << "  (plan overhead:"
+            << "  CPU +" << snap_after_plan.cpu_rss_kb - snap_before_plan.cpu_rss_kb << " kB"
+            << "  GPU +" << snap_after_plan.gpu_used_mb - snap_before_plan.gpu_used_mb << " MB)"
+            << std::endl;
+
+  MemoryManager::Print();
+  // ------------------------------------------------------------------
+  // 400-iteration loop.
+  // Each iteration computes the full 4d forward FFT of `prop`.
+  // We deliberately do NOT cache the result — we always start from
+  // the same `prop` so the FFT is recomputed identically each time.
+  // The point is to watch memory, not correctness.
+  // ------------------------------------------------------------------
+  const int Niter = 40;
+  const int Niter2 = 32;
+
+  // Print header for the memory table
+  std::cout << GridLogMessage
+              << "\n"
+              << std::setw(6)  << "iter"
+              << "  CPU: " << std::setw(10) << "RSS[kB]"
+              << "  (  delta  )"
+              << "  GPU: " << std::setw(7)  << "used[MB]"
+              << "  (delta)"
+              << "\n";
+ 
+  MemSnapshot snap_prev = snap_after_plan;
+
+  for (int i = 0; i < Niter; i++) {
+    std::vector<LatticePropagatorD> G;
+
+    for (int j = 0; j < Niter2; j++) {
+      LatticePropagatorD prop_fft(&GRID);
+
+      // Full 4d forward FFT using the pre-built plans
+      plannedFFT.FFT_all_dim(prop_fft, prop, FFT::forward);
+
+      G.push_back(prop_fft);
+    }
+ 
+    // cudaMemGetInfo reflects the state *after* any pooled frees have
+    // been committed, so this is accurate without an explicit sync —
+    // FFT_dim_execute already calls accelerator_barrier() internally.
+    MemSnapshot snap_now = takeSnapshot();
+    printRow(i, snap_now, snap_prev);
+    MemoryManager::Print();
+    snap_prev = snap_now;
+  }
+
+  // ------------------------------------------------------------------
+  // Summary
+  // ------------------------------------------------------------------
+  MemSnapshot snap_final = takeSnapshot();
+ 
+  long cpu_growth = snap_final.cpu_rss_kb  - snap_after_plan.cpu_rss_kb;
+  long gpu_growth = snap_final.gpu_used_mb - snap_after_plan.gpu_used_mb;
+ 
+  std::cout << GridLogMessage
+            << "\n==== Memory summary (baseline = after plan construction) ====\n"
+            << "  CPU RSS growth over " << Niter << " FFTs : "
+            << cpu_growth << " kB"
+            << (cpu_growth == 0 ? "  OK" : "  *** GROWING ***") << "\n"
+            << "  GPU used growth over " << Niter << " FFTs : "
+            << gpu_growth << " MB"
+            << (gpu_growth == 0 ? "  OK" : "  *** GROWING ***") << "\n"
+            << "  Note: first-call watermark from pool fill is expected and benign.\n"
+            << "        A leak shows as continuous growth beyond iter ~2-3.\n";
+ 
+  Grid_finalize();
+  return 0;
+}

tests/core/Test_planned_fft.cc

@@ -0,0 +1,321 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./tests/core/Test_planned_fft.cc
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#include <Grid/Grid.h>
+
+using namespace Grid;
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  int threads = GridThread::GetThreads();
+  std::cout<<GridLogMessage << "Grid is setup to use "<<threads<<" threads"<<std::endl;
+
+  Coordinate latt_size   = GridDefaultLatt();
+  Coordinate simd_layout = GridDefaultSimd(Nd,vComplexD::Nsimd());
+  Coordinate mpi_layout  = GridDefaultMpi();
+
+  int vol = 1;
+  for(int d=0;d<latt_size.size();d++) vol *= latt_size[d];
+
+  GridCartesian         GRID(latt_size,simd_layout,mpi_layout);
+  GridRedBlackCartesian RBGRID(&GRID);
+
+  LatticeComplexD     one(&GRID);
+  LatticeComplexD      zz(&GRID);
+  LatticeComplexD       C(&GRID);
+  LatticeComplexD  Ctilde(&GRID);
+  LatticeComplexD  Cref  (&GRID);
+  LatticeComplexD  Csav  (&GRID);
+  LatticeComplexD    coor(&GRID);
+
+  LatticeSpinMatrixD    S(&GRID);
+  LatticeSpinMatrixD    Stilde(&GRID);
+
+  Coordinate p({1,3,2,3});
+
+  one = ComplexD(1.0,0.0);
+  zz  = ComplexD(0.0,0.0);
+  ComplexD ci(0.0,1.0);
+
+  std::cout<<"*************************************************"<<std::endl;
+  std::cout<<"Testing Fourier form of known plane wave         "<<std::endl;
+  std::cout<<"*************************************************"<<std::endl;
+  C=Zero();
+  for(int mu=0;mu<4;mu++){
+    RealD TwoPiL =  M_PI * 2.0/ latt_size[mu];
+    LatticeCoordinate(coor,mu);
+    C = C + (TwoPiL * p[mu]) * coor;
+  }
+  C = exp(C*ci);
+  Csav = C;
+  S=Zero();
+  S = S+C;
+
+  // PlannedFFT is templated on the lattice element type (vector_object), not the Lattice<> itself.
+  PlannedFFT<LatticeComplexD::vector_object>    theFFT(&GRID);
+  PlannedFFT<LatticeSpinMatrixD::vector_object> theFFT_spin(&GRID);
+
+  Ctilde=C;
+  std::cout<<" Benchmarking PlannedFFT of LatticeComplex  "<<std::endl;
+  theFFT.FFT_dim(Ctilde,Ctilde,0,FFTbase::forward); std::cout << theFFT.MFlops()<<" Mflops "<<std::endl;
+  theFFT.FFT_dim(Ctilde,Ctilde,1,FFTbase::forward); std::cout << theFFT.MFlops()<<" Mflops "<<std::endl;
+  theFFT.FFT_dim(Ctilde,Ctilde,2,FFTbase::forward); std::cout << theFFT.MFlops()<<" Mflops "<<std::endl;
+  theFFT.FFT_dim(Ctilde,Ctilde,3,FFTbase::forward); std::cout << theFFT.MFlops()<<" Mflops "<<std::endl;
+
+  TComplexD cVol;
+  cVol()()() = vol;
+
+  Cref=Zero();
+  pokeSite(cVol,Cref,p);
+
+  Cref=Cref-Ctilde;
+  std::cout << "diff scalar "<<norm2(Cref) << std::endl;
+
+  C=Csav;
+  theFFT.FFT_all_dim(Ctilde,C,FFTbase::forward);
+  theFFT.FFT_all_dim(Cref,Ctilde,FFTbase::backward);
+
+  std::cout << norm2(C) << " " << norm2(Ctilde) << " " << norm2(Cref)<< " vol " << vol<< std::endl;
+
+  Cref= Cref - C;
+  std::cout << " invertible check " << norm2(Cref)<<std::endl;
+
+  Stilde=S;
+  std::cout<<" Benchmarking PlannedFFT of LatticeSpinMatrix  "<<std::endl;
+  theFFT_spin.FFT_dim(Stilde,Stilde,0,FFTbase::forward); std::cout << theFFT_spin.MFlops()<<" mflops "<<std::endl;
+  theFFT_spin.FFT_dim(Stilde,Stilde,1,FFTbase::forward); std::cout << theFFT_spin.MFlops()<<" mflops "<<std::endl;
+  theFFT_spin.FFT_dim(Stilde,Stilde,2,FFTbase::forward); std::cout << theFFT_spin.MFlops()<<" mflops "<<std::endl;
+  theFFT_spin.FFT_dim(Stilde,Stilde,3,FFTbase::forward); std::cout << theFFT_spin.MFlops()<<" mflops "<<std::endl;
+
+  SpinMatrixD Sp;
+  Sp = Zero(); Sp = Sp+cVol;
+
+  S=Zero();
+  pokeSite(Sp,S,p);
+
+  S= S-Stilde;
+  std::cout << "diff FT[SpinMat] "<<norm2(S) << std::endl;
+
+  std::vector<int> seeds({1,2,3,4});
+  GridSerialRNG          sRNG;  sRNG.SeedFixedIntegers(seeds);
+  GridParallelRNG          pRNG(&GRID);
+  pRNG.SeedFixedIntegers(seeds);
+
+  LatticeGaugeFieldD Umu(&GRID);
+  SU<Nc>::ColdConfiguration(pRNG,Umu);
+
+  ////////////////////////////////////////////////////
+  // Wilson test
+  ////////////////////////////////////////////////////
+  {
+    LatticeFermionD    src(&GRID); gaussian(pRNG,src);
+    LatticeFermionD    tmp(&GRID);
+    LatticeFermionD    ref(&GRID);
+
+    RealD mass=0.01;
+    WilsonFermionD Dw(Umu,GRID,RBGRID,mass);
+
+    Dw.M(src,tmp);
+
+    std::cout << "Dw src = " <<norm2(src)<<std::endl;
+    std::cout << "Dw tmp = " <<norm2(tmp)<<std::endl;
+
+    Dw.FreePropagator(tmp,ref,mass);
+
+    std::cout << "Dw ref = " <<norm2(ref)<<std::endl;
+
+    ref = ref - src;
+    std::cout << "Dw ref-src = " <<norm2(ref)<<std::endl;
+  }
+
+  ////////////////////////////////////////////////////
+  // Dwf matrix — verify Fourier representation using PlannedFFT<LatticeFermionD>
+  ////////////////////////////////////////////////////
+  {
+    std::cout<<"****************************************"<<std::endl;
+    std::cout<<"Testing Fourier representation of Ddwf"<<std::endl;
+    std::cout<<"****************************************"<<std::endl;
+
+    const int Ls=16;
+    const int sdir=0;
+    RealD mass=0.01;
+    RealD M5  =1.0;
+    Gamma G5(Gamma::Algebra::Gamma5);
+
+    GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,&GRID);
+    GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,&GRID);
+
+    DomainWallFermionD Ddwf(Umu,*FGrid,*FrbGrid,GRID,RBGRID,mass,M5);
+
+    GridParallelRNG          RNG5(FGrid);      RNG5.SeedFixedIntegers(seeds);
+    LatticeFermionD    src5(FGrid); gaussian(RNG5,src5);
+    LatticeFermionD    src5_p(FGrid);
+    LatticeFermionD    result5(FGrid);
+    LatticeFermionD    ref5(FGrid);
+    LatticeFermionD    tmp5(FGrid);
+
+    Ddwf.M(src5,tmp5);
+    ref5 = tmp5;
+
+    PlannedFFT<LatticeFermionD::vector_object> theFFT5(FGrid);
+
+    theFFT5.FFT_dim(result5,tmp5,1,FFTbase::forward); tmp5 = result5;
+    std::cout<<"Fourier xformed Ddwf 1 "<<norm2(result5)<<std::endl;
+    theFFT5.FFT_dim(result5,tmp5,2,FFTbase::forward); tmp5 = result5;
+    std::cout<<"Fourier xformed Ddwf 2 "<<norm2(result5)<<std::endl;
+    theFFT5.FFT_dim(result5,tmp5,3,FFTbase::forward); tmp5 = result5;
+    std::cout<<"Fourier xformed Ddwf 3 "<<norm2(result5)<<std::endl;
+    theFFT5.FFT_dim(result5,tmp5,4,FFTbase::forward);
+    std::cout<<"Fourier xformed Ddwf 4 "<<norm2(result5)<<std::endl;
+    result5 = result5*ComplexD(::sqrt(1.0/vol),0.0);
+
+    std::cout<<"Fourier xformed Ddwf "<<norm2(result5)<<std::endl;
+
+    tmp5 = src5;
+    theFFT5.FFT_dim(src5_p,tmp5,1,FFTbase::forward); tmp5 = src5_p;
+    theFFT5.FFT_dim(src5_p,tmp5,2,FFTbase::forward); tmp5 = src5_p;
+    theFFT5.FFT_dim(src5_p,tmp5,3,FFTbase::forward); tmp5 = src5_p;
+    theFFT5.FFT_dim(src5_p,tmp5,4,FFTbase::forward); src5_p = src5_p*ComplexD(::sqrt(1.0/vol),0.0);
+
+    std::cout<<"Fourier xformed src5"<< norm2(src5)<<" -> "<<norm2(src5_p)<<std::endl;
+
+    Gamma::Algebra Gmu [] = {
+      Gamma::Algebra::GammaX,
+      Gamma::Algebra::GammaY,
+      Gamma::Algebra::GammaZ,
+      Gamma::Algebra::GammaT,
+      Gamma::Algebra::Gamma5
+    };
+    LatticeFermionD    Kinetic(FGrid); Kinetic = Zero();
+    LatticeComplexD    kmu(FGrid);
+    LatticeInteger     scoor(FGrid);
+    LatticeComplexD    sk (FGrid); sk = Zero();
+    LatticeComplexD    sk2(FGrid); sk2= Zero();
+    LatticeComplexD    W(FGrid); W= Zero();
+    LatticeComplexD    one5(FGrid); one5 =ComplexD(1.0,0.0);
+
+    for(int mu=0;mu<Nd;mu++) {
+      LatticeCoordinate(kmu,mu+1);
+      RealD TwoPiL =  M_PI * 2.0/ latt_size[mu];
+      kmu = TwoPiL * kmu;
+      sk2 = sk2 + 2.0*sin(kmu*0.5)*sin(kmu*0.5);
+      sk  = sk  +     sin(kmu)    *sin(kmu);
+      Kinetic = Kinetic + sin(kmu)*ci*(Gamma(Gmu[mu])*src5_p);
+    }
+    std::cout << " src5    "<<norm2(src5_p)<<std::endl;
+    std::cout << " Kinetic "<<norm2(Kinetic)<<std::endl;
+
+    W = one5 - M5 + sk2;
+    std::cout << " W "<<norm2(W)<<std::endl;
+    Kinetic = Kinetic + W * src5_p;
+    std::cout << " Kinetic "<<norm2(Kinetic)<<std::endl;
+
+    LatticeCoordinate(scoor,sdir);
+
+    tmp5 = Cshift(src5_p,sdir,+1);
+    tmp5 = (tmp5 - G5*tmp5)*0.5;
+    tmp5 = where(scoor==Integer(Ls-1),mass*tmp5,-tmp5);
+    Kinetic = Kinetic + tmp5;
+
+    tmp5 = Cshift(src5_p,sdir,-1);
+    tmp5 = (tmp5 + G5*tmp5)*0.5;
+    tmp5 = where(scoor==Integer(0),mass*tmp5,-tmp5);
+    Kinetic = Kinetic + tmp5;
+
+    std::cout<<"Momentum space Ddwf  "<< norm2(Kinetic)<<std::endl;
+    std::cout<<"Stencil Ddwf         "<< norm2(result5)<<std::endl;
+
+    result5 = result5 - Kinetic;
+    std::cout<<"diff "<< norm2(result5)<<std::endl;
+    GRID_ASSERT(norm2(result5)<1.0e-4);
+  }
+
+  ////////////////////////////////////////////////////
+  // Dwf prop
+  ////////////////////////////////////////////////////
+  {
+    std::cout<<"****************************************"<<std::endl;
+    std::cout << "Testing Ddwf Ht Mom space 4d propagator \n";
+    std::cout<<"****************************************"<<std::endl;
+
+    LatticeFermionD    src(&GRID); gaussian(pRNG,src);
+    LatticeFermionD    tmp(&GRID);
+    LatticeFermionD    ref(&GRID);
+    LatticeFermionD    diff(&GRID);
+
+    Coordinate point(4,0);
+    src=Zero();
+    SpinColourVectorD ferm; gaussian(sRNG,ferm);
+    pokeSite(ferm,src,point);
+
+    const int Ls=32;
+    GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,&GRID);
+    GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,&GRID);
+
+    RealD mass=0.01;
+    RealD M5  =0.8;
+    DomainWallFermionD Ddwf(Umu,*FGrid,*FrbGrid,GRID,RBGRID,mass,M5);
+
+    std::cout << " Solving by FFT and Feynman rules" <<std::endl;
+    bool fiveD = false;
+    Ddwf.FreePropagator(src,ref,mass,fiveD);
+
+    Gamma G5(Gamma::Algebra::Gamma5);
+
+    LatticeFermionD    src5(FGrid); src5=Zero();
+    LatticeFermionD    tmp5(FGrid);
+    LatticeFermionD    result5(FGrid); result5=Zero();
+    LatticeFermionD    result4(&GRID);
+    const int sdir=0;
+
+    tmp =   (src + G5*src)*0.5;      InsertSlice(tmp,src5,   0,sdir);
+    tmp =   (src - G5*src)*0.5;      InsertSlice(tmp,src5,Ls-1,sdir);
+
+    std::cout << " Solving by Conjugate Gradient (CGNE)" <<std::endl;
+    Ddwf.Mdag(src5,tmp5);
+    src5=tmp5;
+    MdagMLinearOperator<DomainWallFermionD,LatticeFermionD> HermOp(Ddwf);
+    ConjugateGradient<LatticeFermionD> CG(1.0e-8,10000);
+    CG(HermOp,src5,result5);
+
+    ExtractSlice(tmp,result5,0   ,sdir);   result4 =         (tmp-G5*tmp)*0.5;
+    ExtractSlice(tmp,result5,Ls-1,sdir);   result4 = result4+(tmp+G5*tmp)*0.5;
+
+    std::cout << " Taking difference" <<std::endl;
+    std::cout << "Ddwf result4 "<<norm2(result4)<<std::endl;
+    std::cout << "Ddwf ref     "<<norm2(ref)<<std::endl;
+
+    diff = ref - result4;
+    std::cout << "result - ref     "<<norm2(diff)<<std::endl;
+    GRID_ASSERT(norm2(diff)<1.0e-4);
+  }
+
+  Grid_finalize();
+}

tests/debug/Test_batched_blas.cc

@@ -0,0 +1,256 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./tests/debug/Test_batched_blas.cc
+
+    Copyright (C) 2026
+
+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 */
+
+//
+// Unit tests for the blas-layer dense primitives:
+//
+//  T1 : GridBLASInverse::inverseBatched (ComplexF and ComplexD) --
+//       || A A^{-1} - I ||_max over a random well-conditioned batch.
+//       On a CPU build this exercises the Eigen reference (the semantic
+//       oracle); the SAME binary exercises rocSOLVER/cuBLAS/oneMKL on a
+//       device build.
+//  T2 : explicit-leading-dimension gemmBatched == SOFTWARE SPLIT-K in
+//       miniature.  Y = op(A,T).X computed (a) in one compact batch=1 call
+//       and (b) as NK K-chunks by POINTER OFFSET with lda = full K, partials
+//       reduced on the host.  (a)==(b) validates the strided overload AND
+//       the production dense-slab apply pattern (arXiv:2409.03904 fig 11).
+//
+// Hard asserts throughout: regression gate for Grid/algorithms/blas.
+//
+#include <Grid/Grid.h>
+#include <Grid/algorithms/blas/BatchedInverse.h>
+
+#include <random>
+
+using namespace std;
+using namespace Grid;
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  GridBLAS        blas;
+  GridBLASInverse inverse;
+
+  std::mt19937 rng(12345);
+  std::uniform_real_distribution<double> dist(-1.0,1.0);
+
+  ////////////////////////////////////////////////////////////////
+  // T1a : batched inversion, ComplexF
+  ////////////////////////////////////////////////////////////////
+  {
+    const int64_t N = 64;
+    const int  batch = 4;
+    const uint64_t elems = (uint64_t)batch*N*N;
+
+    // Random diagonally-dominant batch: A = N*I + R, |R_ij| <= 1
+    std::vector<ComplexF> Ahost(elems);
+    for(uint64_t i=0;i<elems;i++) Ahost[i] = ComplexF(dist(rng),dist(rng));
+    for(int b=0;b<batch;b++)
+      for(int64_t d=0;d<N;d++)
+	Ahost[(uint64_t)b*N*N + d*N + d] += ComplexF((RealF)N,0.0);
+
+    deviceVector<ComplexF> Adev(elems);   // gets inverted in place
+    deviceVector<ComplexF> Aorig(elems);  // untouched copy for the residual
+    deviceVector<ComplexF> Cdev(elems);
+    acceleratorCopyToDevice(&Ahost[0],&Adev[0], elems*sizeof(ComplexF));
+    acceleratorCopyToDevice(&Ahost[0],&Aorig[0],elems*sizeof(ComplexF));
+
+    deviceVector<ComplexF*> Ap(batch);
+    deviceVector<ComplexF*> Op(batch);
+    deviceVector<ComplexF*> Cp(batch);
+    std::vector<ComplexF*> ptr_h(batch);
+    for(int b=0;b<batch;b++) ptr_h[b] = &Adev[(uint64_t)b*N*N];
+    acceleratorCopyToDevice(&ptr_h[0],&Ap[0],batch*sizeof(ComplexF*));
+    for(int b=0;b<batch;b++) ptr_h[b] = &Aorig[(uint64_t)b*N*N];
+    acceleratorCopyToDevice(&ptr_h[0],&Op[0],batch*sizeof(ComplexF*));
+    for(int b=0;b<batch;b++) ptr_h[b] = &Cdev[(uint64_t)b*N*N];
+    acceleratorCopyToDevice(&ptr_h[0],&Cp[0],batch*sizeof(ComplexF*));
+
+    inverse.inverseBatched(N,Ap);                      // A <- A^{-1}
+
+    ComplexF one (1.0,0.0);
+    ComplexF zero(0.0,0.0);
+    blas.gemmBatched(GridBLAS_OP_N,GridBLAS_OP_N,
+		     (int)N,(int)N,(int)N,
+		     one, Op, Ap, zero, Cp);           // C = A A^{-1}
+    blas.synchronise();
+
+    std::vector<ComplexF> Chost(elems);
+    acceleratorCopyFromDevice(&Cdev[0],&Chost[0],elems*sizeof(ComplexF));
+
+    double maxdev = 0.0;
+    for(int b=0;b<batch;b++)
+      for(int64_t j=0;j<N;j++)
+	for(int64_t i=0;i<N;i++){
+	  ComplexF expect = (i==j) ? ComplexF(1.0,0.0) : ComplexF(0.0,0.0);
+	  ComplexF got = Chost[(uint64_t)b*N*N + j*N + i];
+	  maxdev = std::max(maxdev,(double)abs(got-expect));
+	}
+    std::cout << GridLogMessage << "T1a inverseBatched ComplexF  ||A Ainv - I||_max = "
+	      << maxdev << ( maxdev < 1.0e-4 ? "   PASS" : "   FAIL" ) << std::endl;
+    GRID_ASSERT(maxdev < 1.0e-4);
+  }
+
+  ////////////////////////////////////////////////////////////////
+  // T1b : batched inversion, ComplexD
+  ////////////////////////////////////////////////////////////////
+  {
+    const int64_t N = 48;
+    const int  batch = 3;
+    const uint64_t elems = (uint64_t)batch*N*N;
+
+    std::vector<ComplexD> Ahost(elems);
+    for(uint64_t i=0;i<elems;i++) Ahost[i] = ComplexD(dist(rng),dist(rng));
+    for(int b=0;b<batch;b++)
+      for(int64_t d=0;d<N;d++)
+	Ahost[(uint64_t)b*N*N + d*N + d] += ComplexD((RealD)N,0.0);
+
+    deviceVector<ComplexD> Adev(elems);
+    deviceVector<ComplexD> Aorig(elems);
+    deviceVector<ComplexD> Cdev(elems);
+    acceleratorCopyToDevice(&Ahost[0],&Adev[0], elems*sizeof(ComplexD));
+    acceleratorCopyToDevice(&Ahost[0],&Aorig[0],elems*sizeof(ComplexD));
+
+    deviceVector<ComplexD*> Ap(batch);
+    deviceVector<ComplexD*> Op(batch);
+    deviceVector<ComplexD*> Cp(batch);
+    std::vector<ComplexD*> ptr_h(batch);
+    for(int b=0;b<batch;b++) ptr_h[b] = &Adev[(uint64_t)b*N*N];
+    acceleratorCopyToDevice(&ptr_h[0],&Ap[0],batch*sizeof(ComplexD*));
+    for(int b=0;b<batch;b++) ptr_h[b] = &Aorig[(uint64_t)b*N*N];
+    acceleratorCopyToDevice(&ptr_h[0],&Op[0],batch*sizeof(ComplexD*));
+    for(int b=0;b<batch;b++) ptr_h[b] = &Cdev[(uint64_t)b*N*N];
+    acceleratorCopyToDevice(&ptr_h[0],&Cp[0],batch*sizeof(ComplexD*));
+
+    inverse.inverseBatched(N,Ap);
+
+    ComplexD one (1.0,0.0);
+    ComplexD zero(0.0,0.0);
+    blas.gemmBatched(GridBLAS_OP_N,GridBLAS_OP_N,
+		     (int)N,(int)N,(int)N,
+		     one, Op, Ap, zero, Cp);
+    blas.synchronise();
+
+    std::vector<ComplexD> Chost(elems);
+    acceleratorCopyFromDevice(&Cdev[0],&Chost[0],elems*sizeof(ComplexD));
+
+    double maxdev = 0.0;
+    for(int b=0;b<batch;b++)
+      for(int64_t j=0;j<N;j++)
+	for(int64_t i=0;i<N;i++){
+	  ComplexD expect = (i==j) ? ComplexD(1.0,0.0) : ComplexD(0.0,0.0);
+	  ComplexD got = Chost[(uint64_t)b*N*N + j*N + i];
+	  maxdev = std::max(maxdev,(double)abs(got-expect));
+	}
+    std::cout << GridLogMessage << "T1b inverseBatched ComplexD  ||A Ainv - I||_max = "
+	      << maxdev << ( maxdev < 1.0e-10 ? "   PASS" : "   FAIL" ) << std::endl;
+    GRID_ASSERT(maxdev < 1.0e-10);
+  }
+
+  ////////////////////////////////////////////////////////////////
+  // T2 : explicit-ld gemmBatched == software split-K miniature.
+  // Slab layout as in the dense coarse-coarse apply: A is K x nrows
+  // column major (lda=K); Y = op(A,T).X with X K x nrhs (ldb=K).
+  ////////////////////////////////////////////////////////////////
+  {
+    const int nrows = 8;
+    const int nrhs  = 4;
+    const int K     = 256;
+    const int NK    = 8;        // split-K chunks
+    const int Kc    = K/NK;
+
+    std::vector<ComplexF> Ahost((uint64_t)K*nrows);
+    std::vector<ComplexF> Xhost((uint64_t)K*nrhs);
+    for(auto &z : Ahost) z = ComplexF(dist(rng),dist(rng));
+    for(auto &z : Xhost) z = ComplexF(dist(rng),dist(rng));
+
+    deviceVector<ComplexF> Adev(Ahost.size());
+    deviceVector<ComplexF> Xdev(Xhost.size());
+    deviceVector<ComplexF> Yref((uint64_t)nrows*nrhs);
+    deviceVector<ComplexF> Ypart((uint64_t)NK*nrows*nrhs);
+    acceleratorCopyToDevice(&Ahost[0],&Adev[0],Ahost.size()*sizeof(ComplexF));
+    acceleratorCopyToDevice(&Xhost[0],&Xdev[0],Xhost.size()*sizeof(ComplexF));
+
+    ComplexF one (1.0,0.0);
+    ComplexF zero(0.0,0.0);
+
+    // (a) reference: one compact batch=1 call (compact lda == K for OP_T)
+    {
+      deviceVector<ComplexF*> Ap(1), Xp(1), Yp(1);
+      std::vector<ComplexF*> h(1);
+      h[0]=&Adev[0]; acceleratorCopyToDevice(&h[0],&Ap[0],sizeof(ComplexF*));
+      h[0]=&Xdev[0]; acceleratorCopyToDevice(&h[0],&Xp[0],sizeof(ComplexF*));
+      h[0]=&Yref[0]; acceleratorCopyToDevice(&h[0],&Yp[0],sizeof(ComplexF*));
+      blas.gemmBatched(GridBLAS_OP_T,GridBLAS_OP_N,
+		       nrows,nrhs,K,
+		       one, Ap, Xp, zero, Yp);
+      blas.synchronise();
+    }
+
+    // (b) split-K: NK chunk-pointers into the SAME allocations, lda/ldb = K
+    {
+      deviceVector<ComplexF*> Ap(NK), Xp(NK), Yp(NK);
+      std::vector<ComplexF*> h(NK);
+      for(int j=0;j<NK;j++) h[j] = &Adev[(uint64_t)j*Kc];        // K-offset slice
+      acceleratorCopyToDevice(&h[0],&Ap[0],NK*sizeof(ComplexF*));
+      for(int j=0;j<NK;j++) h[j] = &Xdev[(uint64_t)j*Kc];
+      acceleratorCopyToDevice(&h[0],&Xp[0],NK*sizeof(ComplexF*));
+      for(int j=0;j<NK;j++) h[j] = &Ypart[(uint64_t)j*nrows*nrhs];
+      acceleratorCopyToDevice(&h[0],&Yp[0],NK*sizeof(ComplexF*));
+      blas.gemmBatched(GridBLAS_OP_T,GridBLAS_OP_N,
+		       nrows,nrhs,Kc,
+		       one, Ap, /*lda*/ K,
+		            Xp, /*ldb*/ K,
+		       zero,Yp, /*ldc*/ nrows);
+      blas.synchronise();
+    }
+
+    std::vector<ComplexF> Yref_h((uint64_t)nrows*nrhs);
+    std::vector<ComplexF> Ypart_h((uint64_t)NK*nrows*nrhs);
+    acceleratorCopyFromDevice(&Yref[0], &Yref_h[0], Yref_h.size()*sizeof(ComplexF));
+    acceleratorCopyFromDevice(&Ypart[0],&Ypart_h[0],Ypart_h.size()*sizeof(ComplexF));
+
+    double maxdev = 0.0;
+    double maxval = 0.0;
+    for(int i=0;i<nrows*nrhs;i++){
+      ComplexF sum(0.0,0.0);
+      for(int j=0;j<NK;j++) sum = sum + Ypart_h[(uint64_t)j*nrows*nrhs + i];
+      maxdev = std::max(maxdev,(double)abs(sum-Yref_h[i]));
+      maxval = std::max(maxval,(double)abs(Yref_h[i]));
+    }
+    double rel = maxdev/maxval;
+    std::cout << GridLogMessage << "T2  split-K strided gemmBatched  max rel dev vs compact = "
+	      << rel << ( rel < 1.0e-4 ? "   PASS" : "   FAIL" ) << std::endl;
+    GRID_ASSERT(rel < 1.0e-4);
+  }
+
+  std::cout << GridLogMessage << "All batched-blas tests PASSED" << std::endl;
+
+  Grid_finalize();
+}

tests/debug/Test_hipfft_bug_fail.cc

@@ -0,0 +1,76 @@
+/*
+ * Isolating the hipfft HIPFFT_PARSE_ERROR on ROCm 7 / hipFFT 1.0.20.
+ *
+ * Tests three orderings with an empty rocFFT cache to find which GPU
+ * operation before plan creation triggers the failure:
+ *   A) hipMalloc only            — hypothesis: passes (no async GPU work)
+ *   B) hipMalloc + hipMemset     — hypothesis: fails  (async GPU work in flight)
+ *   C) hipMalloc + hipMemset     — hypothesis: passes (work completed before plan)
+ *      + hipDeviceSynchronize
+ *
+ * Compile:
+ *   hipcc -o Test_hipfft_bug_fail Test_hipfft_bug_fail.cc -lhipfft
+ *
+ * Run with empty cache:
+ *   rm -rf ~/.cache/
+ *   ./Test_hipfft_bug_fail
+ */
+
+#include <cstdio>
+#include <hipfft/hipfft.h>
+#include <hip/hip_runtime.h>
+
+static const char *res(hipfftResult rv) {
+  return rv == HIPFFT_SUCCESS ? "SUCCESS" : "PARSE_ERROR";
+}
+
+static hipfftResult makePlan(int G, int howmany) {
+  int n[] = {G};
+  hipfftHandle p;
+  size_t workSize = 0;
+  hipfftCreate(&p);
+  hipfftResult rv = hipfftMakePlanMany(p, 1, n,
+                                       nullptr, 1, G, nullptr, 1, G,
+                                       HIPFFT_Z2Z, howmany, &workSize);
+  hipfftDestroy(p);
+  return rv;
+}
+
+int main(void) {
+  hipDeviceProp_t prop;
+  hipGetDeviceProperties(&prop, 0);
+  printf("Device: %s\n", prop.name);
+#ifdef hipfftVersionMinor
+  printf("hipFFT version: %d.%d.%d\n\n",
+         hipfftVersionMajor, hipfftVersionMinor, hipfftVersionPatch);
+#endif
+
+  for (int G : {4, 8, 16, 32}) {
+    int howmany = 512;
+    long nelems = (long)G * howmany;
+    hipfftDoubleComplex *buf = nullptr;
+    hipMalloc(&buf, nelems * sizeof(hipfftDoubleComplex));
+
+    // Tests ordered so each runs before a prior success can populate the cache.
+
+    // B first: hipMalloc + hipMemset (async GPU work in flight)
+    // If this fails, A (no hipMemset) will pass, confirming hipMemset is the trigger.
+    hipMemset(buf, 0, nelems * sizeof(hipfftDoubleComplex));
+    hipfftResult rvB = makePlan(G, howmany);
+    printf("G=%-4d  B) hipMalloc + hipMemset       : %s\n", G, res(rvB));
+
+    // C: hipMalloc + hipMemset + sync — does syncing before plan creation fix it?
+    hipMemset(buf, 0, nelems * sizeof(hipfftDoubleComplex));
+    hipDeviceSynchronize();
+    hipfftResult rvC = makePlan(G, howmany);
+    printf("G=%-4d  C) hipMalloc + hipMemset + sync: %s\n", G, res(rvC));
+
+    // A last: hipMalloc only, no async GPU work — should always pass
+    hipfftResult rvA = makePlan(G, howmany);
+    printf("G=%-4d  A) hipMalloc only             : %s\n\n", G, res(rvA));
+
+    hipFree(buf);
+  }
+
+  return 0;
+}

tests/debug/Test_hipfft_bug_pass.cc

@@ -0,0 +1,61 @@
+/*
+ * Minimal program demonstrating the workaround for the hipfft ROCm 7 bug.
+ *
+ * Workaround: create the hipfft plan BEFORE any hipMalloc.  Plan creation
+ * for G < 32 then succeeds even with an empty rocFFT cache.
+ *
+ * Compile:
+ *   hipcc -o Test_hipfft_bug_pass Test_hipfft_bug_pass.cc -lhipfft
+ *
+ * Run:
+ *   rm -rf ~/.cache/rocfft
+ *   ./Test_hipfft_bug_pass
+ *
+ * Expected: all G values succeed.
+ * Compare with Test_hipfft_bug_fail.cc which uses the opposite ordering.
+ */
+
+#include <cstdio>
+#include <hipfft/hipfft.h>
+#include <hip/hip_runtime.h>
+
+int main(void) {
+  hipDeviceProp_t prop;
+  hipGetDeviceProperties(&prop, 0);
+  printf("Device: %s\n", prop.name);
+#ifdef hipfftVersionMinor
+  printf("hipFFT version: %d.%d.%d\n\n",
+         hipfftVersionMajor, hipfftVersionMinor, hipfftVersionPatch);
+#endif
+
+  for (int G : {8, 16, 32}) {
+    int howmany = 512;
+    int n[] = {G};
+    long nelems = (long)G * howmany;
+
+    // Plan created BEFORE hipMalloc — succeeds for all G
+    hipfftHandle p;
+    size_t workSize = 0;
+    hipfftCreate(&p);
+    hipfftResult rv = hipfftMakePlanMany(p, 1, n,
+                                         nullptr, 1, G, nullptr, 1, G,
+                                         HIPFFT_Z2Z, howmany, &workSize);
+    printf("G=%-4d  plan-then-hipMalloc: %d (%s)\n",
+           G, (int)rv, rv == HIPFFT_SUCCESS ? "HIPFFT_SUCCESS" : "HIPFFT_PARSE_ERROR");
+
+    if (rv == HIPFFT_SUCCESS) {
+      hipfftDoubleComplex *buf = nullptr;
+      hipMalloc(&buf, nelems * sizeof(hipfftDoubleComplex));
+      hipMemset(buf, 0, nelems * sizeof(hipfftDoubleComplex));
+      rv = hipfftExecZ2Z(p, buf, buf, HIPFFT_FORWARD);
+      hipDeviceSynchronize();
+      printf("G=%-4d  execFwd:             %d (%s)\n",
+             G, (int)rv, rv == HIPFFT_SUCCESS ? "HIPFFT_SUCCESS" : "FAILED");
+      hipFree(buf);
+    }
+
+    hipfftDestroy(p);
+  }
+
+  return 0;
+}

tests/debug/Test_hipfft_minimal.cc

@@ -0,0 +1,142 @@
+/*
+ * Minimal reproducer for hipfftMakePlanMany / hipfftPlanMany failures.
+ *
+ * Compile on Frontier (no Grid headers needed):
+ *   hipcc -o Test_hipfft_minimal Test_hipfft_minimal.cc -lhipfft
+ *
+ * Run:
+ *   ./Test_hipfft_minimal
+ */
+
+#include <cstdio>
+#include <cstdlib>
+#include <hipfft/hipfft.h>
+#include <hip/hip_runtime.h>
+
+static const char *hipfftResultString(hipfftResult r) {
+  switch (r) {
+  case HIPFFT_SUCCESS:                  return "HIPFFT_SUCCESS";
+  case HIPFFT_INVALID_PLAN:             return "HIPFFT_INVALID_PLAN";
+  case HIPFFT_ALLOC_FAILED:             return "HIPFFT_ALLOC_FAILED";
+  case HIPFFT_INVALID_TYPE:             return "HIPFFT_INVALID_TYPE";
+  case HIPFFT_INVALID_VALUE:            return "HIPFFT_INVALID_VALUE";
+  case HIPFFT_INTERNAL_ERROR:           return "HIPFFT_INTERNAL_ERROR";
+  case HIPFFT_EXEC_FAILED:              return "HIPFFT_EXEC_FAILED";
+  case HIPFFT_SETUP_FAILED:             return "HIPFFT_SETUP_FAILED";
+  case HIPFFT_INVALID_SIZE:             return "HIPFFT_INVALID_SIZE";
+  case HIPFFT_UNALIGNED_DATA:           return "HIPFFT_UNALIGNED_DATA";
+  case HIPFFT_INCOMPLETE_PARAMETER_LIST:return "HIPFFT_INCOMPLETE_PARAMETER_LIST";
+  case HIPFFT_INVALID_DEVICE:           return "HIPFFT_INVALID_DEVICE";
+  case HIPFFT_PARSE_ERROR:              return "HIPFFT_PARSE_ERROR";
+  case HIPFFT_NO_WORKSPACE:             return "HIPFFT_NO_WORKSPACE";
+  case HIPFFT_NOT_IMPLEMENTED:          return "HIPFFT_NOT_IMPLEMENTED";
+  case HIPFFT_NOT_SUPPORTED:            return "HIPFFT_NOT_SUPPORTED";
+  default:                              return "UNKNOWN";
+  }
+}
+
+// Plan creation + execution for (G, howmany).
+// Tests two orderings to isolate whether a prior hipMalloc poisons hipfft
+// plan creation for small G on ROCm 7:
+//   A) plan BEFORE hipMalloc  — hypothesis: succeeds
+//   B) hipMalloc BEFORE plan  — hypothesis: fails for G < 32
+static void tryPlanAndExec(int G, long howmany) {
+  int n[] = {G};
+  long nelems = (long)G * howmany;
+
+  printf("--- G=%-4d  howmany=%-10ld  total_elems=%-12ld ---\n",
+         G, howmany, nelems);
+
+  // --- A: create plan first, allocate buffer afterwards ---
+  {
+    hipfftHandle p;
+    size_t workSize = 0;
+    hipfftCreate(&p);
+    hipfftResult rv = hipfftMakePlanMany(p, 1, n,
+                                         nullptr, 1, G, nullptr, 1, G,
+                                         HIPFFT_Z2Z, (int)howmany, &workSize);
+    printf("  plan-first  create : %d (%s)\n", (int)rv, hipfftResultString(rv));
+    if (rv == HIPFFT_SUCCESS) {
+      hipfftDoubleComplex *buf = nullptr;
+      hipMalloc(&buf, nelems * sizeof(hipfftDoubleComplex));
+      hipMemset(buf, 0, nelems * sizeof(hipfftDoubleComplex));
+      rv = hipfftExecZ2Z(p, buf, buf, HIPFFT_FORWARD);
+      hipDeviceSynchronize();
+      printf("  plan-first  execFwd: %d (%s)\n", (int)rv, hipfftResultString(rv));
+      hipFree(buf);
+    }
+    hipfftDestroy(p);
+  }
+
+  // --- B: hipMalloc first, create plan afterwards ---
+  {
+    hipfftDoubleComplex *buf = nullptr;
+    hipMalloc(&buf, nelems * sizeof(hipfftDoubleComplex));
+    hipMemset(buf, 0, nelems * sizeof(hipfftDoubleComplex));
+
+    hipfftHandle p;
+    size_t workSize = 0;
+    hipfftCreate(&p);
+    hipfftResult rv = hipfftMakePlanMany(p, 1, n,
+                                         nullptr, 1, G, nullptr, 1, G,
+                                         HIPFFT_Z2Z, (int)howmany, &workSize);
+    printf("  malloc-first create : %d (%s)\n", (int)rv, hipfftResultString(rv));
+    if (rv == HIPFFT_SUCCESS) {
+      rv = hipfftExecZ2Z(p, buf, buf, HIPFFT_FORWARD);
+      hipDeviceSynchronize();
+      printf("  malloc-first execFwd: %d (%s)\n", (int)rv, hipfftResultString(rv));
+    }
+    hipfftDestroy(p);
+    hipFree(buf);
+  }
+
+  printf("\n");
+}
+
+int main(void) {
+  // Print HIP device info
+  int device = 0;
+  hipGetDevice(&device);
+  hipDeviceProp_t prop;
+  hipGetDeviceProperties(&prop, device);
+  printf("Device %d: %s  warpSize=%d\n\n", device, prop.name, prop.warpSize);
+
+#ifdef hipfftVersionMinor
+  printf("hipFFT version: %d.%d.%d\n\n",
+         hipfftVersionMajor, hipfftVersionMinor, hipfftVersionPatch);
+#endif
+
+  // Original sweep with small howmany (these passed first time)
+  printf("=== Small howmany (original sweep) ===\n\n");
+  for (int G : {4, 8, 12, 16, 24, 32, 48, 64})
+    tryPlanAndExec(G, 512);
+
+  // Grid-realistic howmany values derived from actual lattice geometries.
+  // howmany = Ncomp * product(ldimensions[d] for d != dim)
+  // For LatticeComplexD: Ncomp=1.
+  printf("=== Grid-realistic parameters ===\n\n");
+
+  // --grid 16.16.16.16  4D FFT  (KNOWN TO FAIL in Grid)
+  // Each dim: G=16, Nperp=16^3=4096
+  tryPlanAndExec(16, 4096);
+
+  // --grid 32.32.32.32  4D FFT  (KNOWN TO SUCCEED in Grid)
+  // Each dim: G=32, Nperp=32^3=32768
+  tryPlanAndExec(32, 32768);
+
+  // --grid 32.32.32.32 Ls=8  5D DWF FFT  (KNOWN TO FAIL on dim 0 in Grid)
+  // dim 0: G=8,  Nperp=32^4=1048576
+  tryPlanAndExec(8, 1048576);
+  // dim 1-4: G=32, Nperp=8*32^3=262144
+  tryPlanAndExec(32, 262144);
+
+  // Extra intermediate cases to bracket the failure
+  tryPlanAndExec(16, 1024);
+  tryPlanAndExec(16, 2048);
+  tryPlanAndExec(16, 8192);
+  tryPlanAndExec(8,  4096);
+  tryPlanAndExec(8,  65536);
+  tryPlanAndExec(8,  262144);
+
+  return 0;
+}

tests/debug/Test_hipfft_repro.cc

@@ -0,0 +1,168 @@
+/*
+ * Reproducer for HIPFFT_PARSE_ERROR (error 12) from hipfftMakePlanMany on
+ * ROCm 7 / hipFFT 1.0.20 (Frontier, MI210 login and MI250X compute nodes).
+ *
+ * Observed failure: G < 32 returns HIPFFT_PARSE_ERROR from all three plan
+ * creation APIs (hipfftPlanMany, hipfftMakePlanMany, hipfftPlan1d) when a
+ * device buffer is allocated and zeroed with hipMalloc+hipMemset before the
+ * plan creation call.  G >= 32 succeeds.
+ *
+ * Contrast with Test_hipfft_minimal.cc (plan-first ordering) which passes
+ * for all G even with an empty rocFFT cache.
+ *
+ * Compile on Frontier (no Grid headers needed):
+ *   hipcc -o Test_hipfft_repro Test_hipfft_repro.cc -lhipfft
+ *
+ * Run with empty cache to reproduce the failure:
+ *   rm -rf ~/.cache/rocfft
+ *   ./Test_hipfft_repro
+ */
+
+#include <cstdio>
+#include <cstdlib>
+#include <hipfft/hipfft.h>
+#include <hip/hip_runtime.h>
+
+static const char *hipfftResultString(hipfftResult r) {
+  switch (r) {
+  case HIPFFT_SUCCESS:                  return "HIPFFT_SUCCESS";
+  case HIPFFT_INVALID_PLAN:             return "HIPFFT_INVALID_PLAN";
+  case HIPFFT_ALLOC_FAILED:             return "HIPFFT_ALLOC_FAILED";
+  case HIPFFT_INVALID_TYPE:             return "HIPFFT_INVALID_TYPE";
+  case HIPFFT_INVALID_VALUE:            return "HIPFFT_INVALID_VALUE";
+  case HIPFFT_INTERNAL_ERROR:           return "HIPFFT_INTERNAL_ERROR";
+  case HIPFFT_EXEC_FAILED:              return "HIPFFT_EXEC_FAILED";
+  case HIPFFT_SETUP_FAILED:             return "HIPFFT_SETUP_FAILED";
+  case HIPFFT_INVALID_SIZE:             return "HIPFFT_INVALID_SIZE";
+  case HIPFFT_UNALIGNED_DATA:           return "HIPFFT_UNALIGNED_DATA";
+  case HIPFFT_INCOMPLETE_PARAMETER_LIST:return "HIPFFT_INCOMPLETE_PARAMETER_LIST";
+  case HIPFFT_INVALID_DEVICE:           return "HIPFFT_INVALID_DEVICE";
+  case HIPFFT_PARSE_ERROR:              return "HIPFFT_PARSE_ERROR";
+  case HIPFFT_NO_WORKSPACE:             return "HIPFFT_NO_WORKSPACE";
+  case HIPFFT_NOT_IMPLEMENTED:          return "HIPFFT_NOT_IMPLEMENTED";
+  case HIPFFT_NOT_SUPPORTED:            return "HIPFFT_NOT_SUPPORTED";
+  default:                              return "UNKNOWN";
+  }
+}
+
+// Plan creation + execution for (G, howmany) using hipfftCreate+hipfftMakePlanMany.
+// This is the path Grid's FFT.h now uses.
+static void tryPlanAndExec(int G, long howmany) {
+  int n[] = {G};
+  long nelems = (long)G * howmany;
+
+  printf("--- G=%-4d  howmany=%-10ld  total_elems=%-12ld ---\n",
+         G, howmany, nelems);
+
+  // Allocate device buffer (hipfftDoubleComplex = 16 bytes each)
+  hipfftDoubleComplex *dbuf = nullptr;
+  hipError_t herr = hipMalloc(&dbuf, nelems * sizeof(hipfftDoubleComplex));
+  if (herr != hipSuccess) {
+    printf("  hipMalloc failed (%d) for %ld elems — skipping\n\n", (int)herr, nelems);
+    return;
+  }
+  hipMemset(dbuf, 0, nelems * sizeof(hipfftDoubleComplex));
+
+  // 1. hipfftPlanMany (one-step, nullptr embed) — current Grid path
+  {
+    hipfftHandle p;
+    hipfftResult rv = hipfftPlanMany(&p, 1, n,
+                                     nullptr, 1, G,
+                                     nullptr, 1, G,
+                                     HIPFFT_Z2Z, (int)howmany);
+    printf("  hipfftPlanMany   create : %d (%s)\n", (int)rv, hipfftResultString(rv));
+    if (rv == HIPFFT_SUCCESS) {
+      rv = hipfftExecZ2Z(p, dbuf, dbuf, HIPFFT_FORWARD);
+      hipDeviceSynchronize();
+      printf("  hipfftPlanMany   execFwd: %d (%s)\n", (int)rv, hipfftResultString(rv));
+      hipfftDestroy(p);
+    }
+  }
+
+  // 2. hipfftCreate + hipfftMakePlanMany (two-step) — also current Grid path
+  {
+    hipfftHandle p;
+    size_t workSize = 0;
+    hipfftResult rc = hipfftCreate(&p);
+    if (rc == HIPFFT_SUCCESS) {
+      hipfftResult rv = hipfftMakePlanMany(p, 1, n,
+                                           nullptr, 1, G,
+                                           nullptr, 1, G,
+                                           HIPFFT_Z2Z, (int)howmany, &workSize);
+      printf("  hipfftMakePlanMany      : %d (%s)  workSize=%zu\n",
+             (int)rv, hipfftResultString(rv), workSize);
+      if (rv == HIPFFT_SUCCESS) {
+        rv = hipfftExecZ2Z(p, dbuf, dbuf, HIPFFT_FORWARD);
+        hipDeviceSynchronize();
+        printf("  hipfftMakePlanMany exec : %d (%s)\n", (int)rv, hipfftResultString(rv));
+      }
+      hipfftDestroy(p);
+    } else {
+      printf("  hipfftCreate            : %d (%s)\n", (int)rc, hipfftResultString(rc));
+    }
+  }
+
+  // 3. hipfftPlan1d (simplest API, batch = howmany)
+  {
+    hipfftHandle p;
+    hipfftResult rv = hipfftPlan1d(&p, G, HIPFFT_Z2Z, (int)howmany);
+    printf("  hipfftPlan1d     create : %d (%s)\n", (int)rv, hipfftResultString(rv));
+    if (rv == HIPFFT_SUCCESS) {
+      rv = hipfftExecZ2Z(p, dbuf, dbuf, HIPFFT_FORWARD);
+      hipDeviceSynchronize();
+      printf("  hipfftPlan1d     execFwd: %d (%s)\n", (int)rv, hipfftResultString(rv));
+      hipfftDestroy(p);
+    }
+  }
+
+  hipFree(dbuf);
+  printf("\n");
+}
+
+int main(void) {
+  // Print HIP device info
+  int device = 0;
+  hipGetDevice(&device);
+  hipDeviceProp_t prop;
+  hipGetDeviceProperties(&prop, device);
+  printf("Device %d: %s  warpSize=%d\n\n", device, prop.name, prop.warpSize);
+
+#ifdef hipfftVersionMinor
+  printf("hipFFT version: %d.%d.%d\n\n",
+         hipfftVersionMajor, hipfftVersionMinor, hipfftVersionPatch);
+#endif
+
+  // Original sweep with small howmany (these passed first time)
+  printf("=== Small howmany (original sweep) ===\n\n");
+  for (int G : {4, 8, 12, 16, 24, 32, 48, 64})
+    tryPlanAndExec(G, 512);
+
+  // Grid-realistic howmany values derived from actual lattice geometries.
+  // howmany = Ncomp * product(ldimensions[d] for d != dim)
+  // For LatticeComplexD: Ncomp=1.
+  printf("=== Grid-realistic parameters ===\n\n");
+
+  // --grid 16.16.16.16  4D FFT  (KNOWN TO FAIL in Grid)
+  // Each dim: G=16, Nperp=16^3=4096
+  tryPlanAndExec(16, 4096);
+
+  // --grid 32.32.32.32  4D FFT  (KNOWN TO SUCCEED in Grid)
+  // Each dim: G=32, Nperp=32^3=32768
+  tryPlanAndExec(32, 32768);
+
+  // --grid 32.32.32.32 Ls=8  5D DWF FFT  (KNOWN TO FAIL on dim 0 in Grid)
+  // dim 0: G=8,  Nperp=32^4=1048576
+  tryPlanAndExec(8, 1048576);
+  // dim 1-4: G=32, Nperp=8*32^3=262144
+  tryPlanAndExec(32, 262144);
+
+  // Extra intermediate cases to bracket the failure
+  tryPlanAndExec(16, 1024);
+  tryPlanAndExec(16, 2048);
+  tryPlanAndExec(16, 8192);
+  tryPlanAndExec(8,  4096);
+  tryPlanAndExec(8,  65536);
+  tryPlanAndExec(8,  262144);
+
+  return 0;
+}

tests/debug/Test_reduction.cc

@@ -0,0 +1,167 @@
+/*************************************************************************************
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./tests/debug/Test_reduction.cc
+
+    Copyright (C) 2024
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#include <Grid/Grid.h>
+
+using namespace std;
+using namespace Grid;
+
+static int passed = 0;
+static int failed = 0;
+
+static void check(bool ok, const std::string &msg)
+{
+  if (ok) {
+    std::cout << GridLogMessage << "PASS  " << msg << std::endl;
+    passed++;
+  } else {
+    std::cout << GridLogMessage << "FAIL  " << msg << std::endl;
+    failed++;
+  }
+}
+
+// Squared magnitude of a Grid scalar tensor aggregate: innerProduct(a,a).
+// For iScalar:      real(conj(a)*a)
+// For iMatrix<T,N>: sum_{i,j} real(conj(a_ij)*a_ij)  (Frobenius)
+// Named squaredSum to make clear the squaring is applied to the aggregate
+// (the sum), not to individual site values before summing.
+template<class T>
+RealD squaredSum(const T &a)
+{
+  return (RealD)real(TensorRemove(innerProduct(a, a)));
+}
+
+template<class Field>
+void testReduction(GridCartesian *grid, GridParallelRNG &rng,
+                   const std::string &name, int Ncomp)
+{
+  typedef typename Field::vector_object vobj;
+  typedef typename vobj::scalar_object  sobj;
+  typedef typename vobj::scalar_type    scalar_type;
+
+  const Integer V      = grid->_gsites;
+  const Integer osites = grid->oSites();
+
+  // Detect single vs double precision by comparing fundamental scalar sizes.
+  const bool isFloat = (sizeof(scalar_type) < sizeof(ComplexD));
+
+  std::cout << GridLogMessage << "=== " << name << " ===" << std::endl;
+
+  Field field(grid);
+
+  //--------------------------------------------------------------------
+  // a) Timing: Niter timed calls reporting us/call and GB/s.
+  //--------------------------------------------------------------------
+#if defined(GRID_CUDA) || defined(GRID_HIP) || defined(GRID_SYCL)
+  {
+    const int Nwarm = 5;
+    const int Niter = 100;
+
+    gaussian(rng, field);
+
+    {
+      autoView(v, field, AcceleratorRead);
+      for (int i = 0; i < Nwarm; i++) sum_gpu(&v[0], osites);
+    }
+
+    RealD t_new;
+    {
+      autoView(v, field, AcceleratorRead);
+      t_new = -usecond();
+      for (int i = 0; i < Niter; i++) sum_gpu(&v[0], osites);
+      t_new += usecond();
+    }
+
+    RealD bytes = (RealD)osites * sizeof(vobj);
+    RealD GBs   = bytes / (t_new / Niter) * 1e-3;
+
+    std::cout << GridLogMessage << name << " timing (" << Niter << " calls):" << std::endl;
+    std::cout << GridLogMessage
+              << "  sum_gpu " << t_new/Niter << " us   " << GBs << " GB/s" << std::endl;
+  }
+#endif
+
+  //--------------------------------------------------------------------
+  // b) Constant field via field = 1.0.
+  //
+  //    Grid's iMatrix::operator=(scalar) sets only the diagonal, so:
+  //      LatticeComplex       -> scalar 1.0        (Ncomp = 1  nonzero per site)
+  //      LatticeColourMatrix  -> Nc x Nc identity  (Ncomp = Nc nonzero per site)
+  //      LatticePropagator    -> (Ns*Nc)^2 identity (Ncomp = Ns*Nc nonzero per site)
+  //
+  //    After GlobalSum: sum_result has Ncomp diagonal entries each equal to V,
+  //    all off-diagonal entries zero.  Grid's recursive innerProduct computes
+  //    the Frobenius inner product (sum of |element|^2 over all indices), giving
+  //
+  //        innerProduct(sum_result, sum_result) = Ncomp * V^2
+  //--------------------------------------------------------------------
+  {
+    field = 1.0;
+    sobj sum_result = sum(field);   // uses new GPU path + GlobalSum
+
+    RealD got      = squaredSum(sum_result);
+    RealD expected = (RealD)Ncomp * (RealD)V * (RealD)V;
+    RealD reldiff  = std::abs(got - expected) / expected;
+
+    std::cout << GridLogMessage
+              << name << " const: got " << got
+              << "  expected " << expected
+              << "  reldiff "  << reldiff << std::endl;
+    check(reldiff < 1e-8, name + " const: innerProduct(sum,sum) = Ncomp*V^2");
+  }
+}
+
+int main(int argc, char **argv)
+{
+  Grid_init(&argc, &argv);
+
+  Coordinate latt = GridDefaultLatt();
+  Coordinate mpi  = GridDefaultMpi();
+
+  GridCartesian *UGrid   = SpaceTimeGrid::makeFourDimGrid(latt, GridDefaultSimd(Nd, vComplexD::Nsimd()), mpi);
+  GridCartesian *UGrid_f = SpaceTimeGrid::makeFourDimGrid(latt, GridDefaultSimd(Nd, vComplexF::Nsimd()), mpi);
+
+  GridParallelRNG rng(UGrid);
+  rng.SeedFixedIntegers({1, 2, 3, 4});
+  GridParallelRNG rng_f(UGrid_f);
+  rng_f.SeedFixedIntegers({1, 2, 3, 4});
+
+  std::cout << GridLogMessage << "Lattice : " << latt << std::endl;
+  std::cout << GridLogMessage << "Volume  : " << UGrid->_gsites << std::endl;
+
+  testReduction<LatticeComplexF>      (UGrid_f, rng_f, "LatticeComplexF",      1      );
+  testReduction<LatticeComplexD>      (UGrid,   rng,   "LatticeComplexD",      1      );
+  testReduction<LatticeColourMatrixF> (UGrid_f, rng_f, "LatticeColourMatrixF", Nc     );
+  testReduction<LatticeColourMatrixD> (UGrid,   rng,   "LatticeColourMatrixD", Nc     );
+  testReduction<LatticePropagatorF>   (UGrid_f, rng_f, "LatticePropagatorF",   Ns*Nc  );
+  testReduction<LatticePropagatorD>   (UGrid,   rng,   "LatticePropagatorD",   Ns*Nc  );
+
+  std::cout << GridLogMessage << "==============================" << std::endl;
+  std::cout << GridLogMessage << passed << " PASSED   " << failed << " FAILED" << std::endl;
+
+  Grid_finalize();
+  return (failed > 0) ? EXIT_FAILURE : EXIT_SUCCESS;
+}

tests/forces/Test_dwf_ratio_4dpf_force.cc

@@ -0,0 +1,279 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./tests/forces/Test_dwf_ratio_4dpf_force.cc
+
+    Copyright (C) 2026
+
+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 */
+
+//
+// Validation of TwoFlavourRatio4DPseudoFermionAction (non-EO, LinearFunction
+// solver slots).  Three tests, run for BOTH wall conventions:
+//
+//  T1 HeatbathIdentityTest : refresh then S; PASS iff S == 0.5*|eta4|^2 to
+//     solver tolerance.  This adjudicates the 4D effective-operator
+//     composition identity [P M^-1 V Pdag][P V^-1 M Pdag] = 1 for the chosen
+//     (P,Pdag) wall pair.  NO PREDICTION is made about which convention
+//     passes -- that is what the test decides.
+//  T2 ForceTest (idiom from Test_double_ratio.cc) : midpoint-derivative
+//     check of deriv against S.  Should PASS for BOTH conventions (S and
+//     deriv use the same literal-adjoint pair by construction).
+//  T3 Trivial-ratio control (V == M) : T1 with NumOp = DenOp.  The solve
+//     cancels against the multiply, so S = 0.5|eta4|^2 requires only
+//     P Pdag = 1_4d.  Should PASS for BOTH conventions; isolates plumbing
+//     from the composition identity.
+//
+// Solvers here are plain CG on the normal equations (CGNR), tolerance 1e-12,
+// so every defect above ~1e-10 is structural, not solver noise.  Run small,
+// e.g.:  ./Test_dwf_ratio_4dpf_force --grid 8.8.8.8
+//
+#include <Grid/Grid.h>
+#include <Grid/qcd/action/pseudofermion/TwoFlavourRatio4DPseudoFermion.h>
+
+using namespace std;
+using namespace Grid;
+
+////////////////////////////////////////////////////////////////////
+// LinearFunction wrappers: direct M^-1 and M^-dag via CG on the
+// normal equations.  These stand in for the MG-GCR stack in this
+// test; the action class sees only LinearFunction.
+////////////////////////////////////////////////////////////////////
+template<class Matrix,class Field>
+class CGNRLinearFunction : public LinearFunction<Field> {   // out = M^-1 in
+public:
+  using LinearFunction<Field>::operator();
+  Matrix &_Mat; RealD tol; Integer maxit;
+  CGNRLinearFunction(Matrix &Mat,RealD _tol,Integer _maxit) : _Mat(Mat), tol(_tol), maxit(_maxit) {};
+  void operator()(const Field &in, Field &out) {
+    MdagMLinearOperator<Matrix,Field> MdagM(_Mat);
+    Field src(in.Grid());
+    _Mat.Mdag(in,src);                 // src = Mdag in
+    ConjugateGradient<Field> CG(tol,maxit);
+    out = Zero();
+    CG(MdagM,src,out);                 // out = (MdagM)^-1 Mdag in = M^-1 in
+  }
+};
+template<class Matrix,class Field>
+class CGNRDagLinearFunction : public LinearFunction<Field> { // out = M^-dag in
+public:
+  using LinearFunction<Field>::operator();
+  Matrix &_Mat; RealD tol; Integer maxit;
+  CGNRDagLinearFunction(Matrix &Mat,RealD _tol,Integer _maxit) : _Mat(Mat), tol(_tol), maxit(_maxit) {};
+  void operator()(const Field &in, Field &out) {
+    MdagMLinearOperator<Matrix,Field> MdagM(_Mat);
+    Field tmp(in.Grid());
+    tmp = Zero();
+    ConjugateGradient<Field> CG(tol,maxit);
+    CG(MdagM,in,tmp);                  // tmp = (MdagM)^-1 in
+    _Mat.M(tmp,out);                   // out = M (MdagM)^-1 in = M^-dag in
+  }
+};
+
+////////////////////////////////////////////////////////////////////
+// T1 / T3 : heatbath composition-identity test.
+// Twin-seeded RNG reproduces the eta4 drawn inside refresh.
+////////////////////////////////////////////////////////////////////
+template<class Impl>
+RealD HeatbathIdentityTest(TwoFlavourRatio4DPseudoFermionAction<Impl> &action,
+			   LatticeGaugeField &U,
+			   GridCartesian *UGrid,
+			   const std::string &tag)
+{
+  typedef typename Impl::FermionField FermionField;
+
+  std::vector<int> seeds({9,11,13,17});
+  GridSerialRNG   sRNG;                 sRNG.SeedFixedIntegers(seeds);
+  GridParallelRNG RNG4(UGrid);          RNG4.SeedFixedIntegers(seeds);
+  GridParallelRNG RNG4check(UGrid);     RNG4check.SeedFixedIntegers(seeds);
+
+  FermionField eta4check(UGrid);
+  gaussian(RNG4check,eta4check);        // identical to the draw inside refresh
+
+  action.refresh(U,sRNG,RNG4);
+  RealD S       = action.S(U);
+  RealD Sexpect = 0.5*norm2(eta4check);
+  RealD defect  = std::abs(S-Sexpect)/Sexpect;
+
+  std::cout << GridLogMessage << "=========================================================" << std::endl;
+  std::cout << GridLogMessage << " HeatbathIdentityTest ["<<tag<<"]" << std::endl;
+  std::cout << GridLogMessage << "   S              = " << S << std::endl;
+  std::cout << GridLogMessage << "   0.5|eta4|^2    = " << Sexpect << std::endl;
+  std::cout << GridLogMessage << "   relative defect = " << defect
+	    << ( defect < 1.0e-8 ? "   PASS" : "   FAIL" ) << std::endl;
+  std::cout << GridLogMessage << "=========================================================" << std::endl;
+  return defect;
+}
+
+////////////////////////////////////////////////////////////////////
+// T2 : ForceTest idiom from Test_double_ratio.cc (midpoint derivative)
+////////////////////////////////////////////////////////////////////
+template<class Gimpl>
+void ForceTest(Action<LatticeGaugeField> &action,LatticeGaugeField & U,MomentumFilterBase<LatticeGaugeField> &Filter)
+{
+  GridBase *UGrid = U.Grid();
+
+  std::vector<int> seeds({1,2,3,5});
+  GridSerialRNG            sRNG;         sRNG.SeedFixedIntegers(seeds);
+  GridParallelRNG          RNG4(UGrid);  RNG4.SeedFixedIntegers(seeds);
+
+  LatticeColourMatrix Pmu(UGrid);
+  LatticeGaugeField P(UGrid);
+  LatticeGaugeField UdSdU(UGrid);
+
+  std::cout << GridLogMessage << "*********************************************************"<<std::endl;
+  std::cout << GridLogMessage << " Force test for "<<action.action_name()<<std::endl;
+  std::cout << GridLogMessage << "*********************************************************"<<std::endl;
+
+  RealD eps=0.005;
+
+  Gimpl::generate_momenta(P,sRNG,RNG4);
+  Filter.applyFilter(P);
+
+  action.refresh(U,sRNG,RNG4);
+
+  RealD S1 = action.S(U);
+
+  Gimpl::update_field(P,U,eps);
+
+  action.deriv(U,UdSdU);
+  UdSdU = Ta(UdSdU);
+  Filter.applyFilter(UdSdU);
+
+  DumpSliceNorm("Force",UdSdU,Nd-1);
+
+  Gimpl::update_field(P,U,eps);
+
+  RealD S2 = action.S(U);
+
+  // Use the derivative
+  LatticeComplex dS(UGrid); dS = Zero();
+  for(int mu=0;mu<Nd;mu++){
+    auto UdSdUmu = PeekIndex<LorentzIndex>(UdSdU,mu);
+    Pmu= PeekIndex<LorentzIndex>(P,mu);
+    dS = dS - trace(Pmu*UdSdUmu)*eps*2.0*2.0;
+  }
+  ComplexD dSpred    = sum(dS);
+  RealD diff =  S2-S1-dSpred.real();
+
+  std::cout<< GridLogMessage << "+++++++++++++++++++++++++++++++++++++++++++++++++++++++++"<<std::endl;
+  std::cout<< GridLogMessage << "S1 : "<< S1    <<std::endl;
+  std::cout<< GridLogMessage << "S2 : "<< S2    <<std::endl;
+  std::cout<< GridLogMessage << "dS : "<< S2-S1 <<std::endl;
+  std::cout<< GridLogMessage << "dSpred : "<< dSpred.real() <<std::endl;
+  std::cout<< GridLogMessage << "diff : "<< diff<<std::endl;
+  std::cout<< GridLogMessage << "diff/dS : "<< diff/(S2-S1)<<std::endl;
+  std::cout<< GridLogMessage << "*********************************************************"<<std::endl;
+  //  GRID_ASSERT(diff<1.0);
+  std::cout<< GridLogMessage << "Done" <<std::endl;
+  std::cout << GridLogMessage << "*********************************************************"<<std::endl;
+}
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  std::cout << std::setprecision(14);
+
+  const int Ls=8;
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(), GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  std::vector<int> seeds4({1,2,3,4});
+  GridParallelRNG RNG4(UGrid);  RNG4.SeedFixedIntegers(seeds4);
+
+  LatticeGaugeField U(UGrid);
+  SU<Nc>::HotConfiguration(RNG4,U);
+
+  ////////////////////////////////////////////////////////////////
+  // Operators: Mobius, campaign-like b,c; heavyish masses so CGNR
+  // is fast and well-conditioned even on a hot configuration.
+  ////////////////////////////////////////////////////////////////
+  RealD mden = 0.2;
+  RealD mnum = 0.5;
+  RealD M5   = 1.8;
+  RealD b    = 1.5;
+  RealD c    = 0.5;
+
+  WilsonImplParams p;
+  p.boundary_phases[0] = 1.0;
+  p.boundary_phases[1] = 1.0;
+  p.boundary_phases[2] = 1.0;
+  p.boundary_phases[3] = -1.0;
+
+  MobiusFermionD DenOp(U,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mden,M5,b,c,p);
+  MobiusFermionD NumOp(U,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mnum,M5,b,c,p);
+
+  RealD tol   = 1.0e-12;
+  Integer maxit = 20000;
+
+  typedef WilsonImplD::FermionField FermionField;
+  CGNRLinearFunction<MobiusFermionD,FermionField>    MinvSolver   (DenOp,tol,maxit);
+  CGNRDagLinearFunction<MobiusFermionD,FermionField> MdagInvSolver(DenOp,tol,maxit);
+  CGNRLinearFunction<MobiusFermionD,FermionField>    VinvSolver   (NumOp,tol,maxit);
+
+  ////////////////////////////////////////////////////////////////
+  // Actions: both wall conventions, plus the V==M trivial control
+  ////////////////////////////////////////////////////////////////
+  TwoFlavourRatio4DPseudoFermionAction<WilsonImplD> ActSol(NumOp,DenOp,MinvSolver,MdagInvSolver,MinvSolver,VinvSolver,1);
+  TwoFlavourRatio4DPseudoFermionAction<WilsonImplD> ActSrc(NumOp,DenOp,MinvSolver,MdagInvSolver,MinvSolver,VinvSolver,0);
+  TwoFlavourRatio4DPseudoFermionAction<WilsonImplD> ActTrivSol(DenOp,DenOp,MinvSolver,MdagInvSolver,MinvSolver,MinvSolver,1);
+  TwoFlavourRatio4DPseudoFermionAction<WilsonImplD> ActTrivSrc(DenOp,DenOp,MinvSolver,MdagInvSolver,MinvSolver,MinvSolver,0);
+
+  ////////////////////////////////////////////////////////////////
+  // T3 controls first (must both pass; isolates plumbing)
+  ////////////////////////////////////////////////////////////////
+  RealD d3s = HeatbathIdentityTest(ActTrivSol,U,UGrid,"T3 trivial V==M, solution walls");
+  RealD d3q = HeatbathIdentityTest(ActTrivSrc,U,UGrid,"T3 trivial V==M, source walls");
+
+  ////////////////////////////////////////////////////////////////
+  // T1 : the composition-identity adjudication
+  ////////////////////////////////////////////////////////////////
+  RealD d1s = HeatbathIdentityTest(ActSol,U,UGrid,"T1 ratio, solution walls");
+  RealD d1q = HeatbathIdentityTest(ActSrc,U,UGrid,"T1 ratio, source walls");
+
+  ////////////////////////////////////////////////////////////////
+  // T2 : force consistency (expected PASS for both conventions)
+  ////////////////////////////////////////////////////////////////
+  MomentumFilterNone<LatticeGaugeField> FilterNone;
+  ForceTest<GimplTypesR>(ActSol,U,FilterNone);
+  ForceTest<GimplTypesR>(ActSrc,U,FilterNone);
+
+  ////////////////////////////////////////////////////////////////
+  // Summary
+  ////////////////////////////////////////////////////////////////
+  std::cout << GridLogMessage << "=========================================================" << std::endl;
+  std::cout << GridLogMessage << " SUMMARY (relative heatbath defects)" << std::endl;
+  std::cout << GridLogMessage << "   T3 trivial  solution walls : " << d3s << std::endl;
+  std::cout << GridLogMessage << "   T3 trivial  source   walls : " << d3q << std::endl;
+  std::cout << GridLogMessage << "   T1 ratio    solution walls : " << d1s << std::endl;
+  std::cout << GridLogMessage << "   T1 ratio    source   walls : " << d1q << std::endl;
+  std::cout << GridLogMessage << " T3 must pass for both; T1 selects the wall convention." << std::endl;
+  std::cout << GridLogMessage << "=========================================================" << std::endl;
+
+  GRID_ASSERT(d3s < 1.0e-8);
+  GRID_ASSERT(d3q < 1.0e-8);
+
+  Grid_finalize();
+}

tests/forces/Test_dwf_ratio_leftprec.cc

@@ -0,0 +1,341 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./tests/forces/Test_dwf_ratio_leftprec.cc
+
+    Copyright (C) 2026
+
+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 */
+
+//
+// Correctness of TwoFlavourRatioLeftPrecPseudoFermionAction against the
+// decades-proven TwoFlavourRatioPseudoFermionAction.  Both classes compute
+// the SAME action S = phi^dag V (MdagM)^-1 Vdag phi through different solve
+// chains (normal-equations vs left-preconditioned F = Vdag M), so with
+// twin-seeded refreshes and 1e-12 solvers they must agree to solver
+// tolerance.  Tests:
+//
+//   E0a/E0b : heatbath identity, S == 0.5|eta|^2 after RNG refresh, for
+//             BOTH classes (E0a also validates the twin-eta capture).
+//   E1      : S_classic == S_leftprec       (relative, ~1e-8)
+//   E2      : deriv_classic == deriv_leftprec (pointwise field norm, ~1e-8)
+//   F1      : ForceTest (Test_double_ratio.cc idiom) on the LeftPrec class.
+//
+// All asserts are hard: this is the regression gate for the new class.
+// Run small, e.g.:  ./Test_dwf_ratio_leftprec --grid 8.8.8.8
+//
+#include <Grid/Grid.h>
+#include <Grid/qcd/action/pseudofermion/TwoFlavourRatioLeftPrec.h>
+
+using namespace std;
+using namespace Grid;
+
+////////////////////////////////////////////////////////////////////
+// Minimal LinearOperator for the composite F = Vdag M, exposing the
+// Hermitian normal operator FdagF for CG.  Stencil entries assert.
+////////////////////////////////////////////////////////////////////
+template<class Impl>
+class VdagMNormalOperator : public LinearOperatorBase<typename Impl::FermionField> {
+public:
+  typedef typename Impl::FermionField Field;
+  FermionOperator<Impl> &VOp;
+  FermionOperator<Impl> &MOp;
+  VdagMNormalOperator(FermionOperator<Impl> &V,FermionOperator<Impl> &M) : VOp(V), MOp(M) {};
+
+  void Fapply(const Field &in, Field &out) {          // out = Vdag M in
+    Field tmp(in.Grid());
+    MOp.M(in,tmp);
+    VOp.Mdag(tmp,out);
+  }
+  void FdagApply(const Field &in, Field &out) {       // out = Mdag V in
+    Field tmp(in.Grid());
+    VOp.M(in,tmp);
+    MOp.Mdag(tmp,out);
+  }
+  virtual void Op     (const Field &in, Field &out) { Fapply(in,out); }
+  virtual void AdjOp  (const Field &in, Field &out) { FdagApply(in,out); }
+  virtual void HermOp (const Field &in, Field &out) {
+    Field tmp(in.Grid());
+    Fapply(in,tmp);
+    FdagApply(tmp,out);
+  }
+  virtual void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2) {
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1 = real(dot);
+    n2 = norm2(out);
+  }
+  virtual void OpDiag (const Field &in, Field &out)                  { GRID_ASSERT(0); }
+  virtual void OpDir  (const Field &in, Field &out,int dir,int disp) { GRID_ASSERT(0); }
+  virtual void OpDirAll(const Field &in, std::vector<Field> &out)    { GRID_ASSERT(0); }
+};
+
+////////////////////////////////////////////////////////////////////
+// F-contract LinearFunctions for the test, both via CG on FdagF:
+//   forward :  F x = b     ==>  x = (FdagF)^-1 Fdag b
+//   adjoint :  Fdag z = b  ==>  z = F (FdagF)^-1 b
+////////////////////////////////////////////////////////////////////
+template<class Impl>
+class ForwardFSolve : public LinearFunction<typename Impl::FermionField> {
+public:
+  typedef typename Impl::FermionField Field;
+  using LinearFunction<Field>::operator();
+  VdagMNormalOperator<Impl> &FdagF; RealD tol; Integer maxit;
+  ForwardFSolve(VdagMNormalOperator<Impl> &Op,RealD _tol,Integer _maxit) : FdagF(Op), tol(_tol), maxit(_maxit) {};
+  void operator()(const Field &in, Field &out) {
+    Field src(in.Grid());
+    FdagF.FdagApply(in,src);
+    ConjugateGradient<Field> CG(tol,maxit);
+    out = Zero();
+    CG(FdagF,src,out);
+  }
+};
+template<class Impl>
+class AdjointFSolve : public LinearFunction<typename Impl::FermionField> {
+public:
+  typedef typename Impl::FermionField Field;
+  using LinearFunction<Field>::operator();
+  VdagMNormalOperator<Impl> &FdagF; RealD tol; Integer maxit;
+  AdjointFSolve(VdagMNormalOperator<Impl> &Op,RealD _tol,Integer _maxit) : FdagF(Op), tol(_tol), maxit(_maxit) {};
+  void operator()(const Field &in, Field &out) {
+    Field y(in.Grid());
+    y = Zero();
+    ConjugateGradient<Field> CG(tol,maxit);
+    CG(FdagF,in,y);
+    FdagF.Fapply(y,out);
+  }
+};
+template<class Matrix,class Field>
+class NormalEqSolve : public LinearFunction<Field> {   // out = (MdagM)^-1 in
+public:
+  using LinearFunction<Field>::operator();
+  Matrix &_Mat; RealD tol; Integer maxit;
+  NormalEqSolve(Matrix &Mat,RealD _tol,Integer _maxit) : _Mat(Mat), tol(_tol), maxit(_maxit) {};
+  void operator()(const Field &in, Field &out) {
+    MdagMLinearOperator<Matrix,Field> MdagM(_Mat);
+    ConjugateGradient<Field> CG(tol,maxit);
+    out = Zero();
+    CG(MdagM,in,out);
+  }
+};
+
+////////////////////////////////////////////////////////////////////
+// ForceTest idiom from Test_double_ratio.cc (midpoint derivative)
+////////////////////////////////////////////////////////////////////
+template<class Gimpl>
+void ForceTest(Action<LatticeGaugeField> &action,LatticeGaugeField & U,MomentumFilterBase<LatticeGaugeField> &Filter)
+{
+  GridBase *UGrid = U.Grid();
+
+  std::vector<int> seeds({1,2,3,5});
+  GridSerialRNG            sRNG;         sRNG.SeedFixedIntegers(seeds);
+  GridParallelRNG          RNG4(UGrid);  RNG4.SeedFixedIntegers(seeds);
+
+  LatticeColourMatrix Pmu(UGrid);
+  LatticeGaugeField P(UGrid);
+  LatticeGaugeField UdSdU(UGrid);
+
+  std::cout << GridLogMessage << "*********************************************************"<<std::endl;
+  std::cout << GridLogMessage << " Force test for "<<action.action_name()<<std::endl;
+  std::cout << GridLogMessage << "*********************************************************"<<std::endl;
+
+  RealD eps=0.005;
+
+  Gimpl::generate_momenta(P,sRNG,RNG4);
+  Filter.applyFilter(P);
+
+  action.refresh(U,sRNG,RNG4);
+
+  RealD S1 = action.S(U);
+
+  Gimpl::update_field(P,U,eps);
+
+  action.deriv(U,UdSdU);
+  UdSdU = Ta(UdSdU);
+  Filter.applyFilter(UdSdU);
+
+  DumpSliceNorm("Force",UdSdU,Nd-1);
+
+  Gimpl::update_field(P,U,eps);
+
+  RealD S2 = action.S(U);
+
+  LatticeComplex dS(UGrid); dS = Zero();
+  for(int mu=0;mu<Nd;mu++){
+    auto UdSdUmu = PeekIndex<LorentzIndex>(UdSdU,mu);
+    Pmu= PeekIndex<LorentzIndex>(P,mu);
+    dS = dS - trace(Pmu*UdSdUmu)*eps*2.0*2.0;
+  }
+  ComplexD dSpred    = sum(dS);
+  RealD diff =  S2-S1-dSpred.real();
+
+  std::cout<< GridLogMessage << "+++++++++++++++++++++++++++++++++++++++++++++++++++++++++"<<std::endl;
+  std::cout<< GridLogMessage << "S1 : "<< S1    <<std::endl;
+  std::cout<< GridLogMessage << "S2 : "<< S2    <<std::endl;
+  std::cout<< GridLogMessage << "dS : "<< S2-S1 <<std::endl;
+  std::cout<< GridLogMessage << "dSpred : "<< dSpred.real() <<std::endl;
+  std::cout<< GridLogMessage << "diff : "<< diff<<std::endl;
+  std::cout<< GridLogMessage << "diff/dS : "<< diff/(S2-S1)<<std::endl;
+  std::cout<< GridLogMessage << "*********************************************************"<<std::endl;
+  std::cout<< GridLogMessage << "Done" <<std::endl;
+  std::cout << GridLogMessage << "*********************************************************"<<std::endl;
+}
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  std::cout << std::setprecision(14);
+
+  const int Ls=8;
+  GridCartesian         * UGrid   = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(), GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
+  GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
+  GridCartesian         * FGrid   = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
+  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
+
+  std::vector<int> seeds4({1,2,3,4});
+  GridParallelRNG RNG4(UGrid);  RNG4.SeedFixedIntegers(seeds4);
+
+  LatticeGaugeField U(UGrid);
+  SU<Nc>::HotConfiguration(RNG4,U);
+
+  ////////////////////////////////////////////////////////////////
+  // Operators: quotient pair (V = PV mass 1, M light-ish), Mobius,
+  // campaign b,c.  Heavyish M so CG is quick on a hot configuration.
+  ////////////////////////////////////////////////////////////////
+  RealD mden = 0.2;
+  RealD mnum = 1.0;
+  RealD M5   = 1.8;
+  RealD b    = 1.5;
+  RealD c    = 0.5;
+
+  WilsonImplParams p;
+  p.boundary_phases[0] = 1.0;
+  p.boundary_phases[1] = 1.0;
+  p.boundary_phases[2] = 1.0;
+  p.boundary_phases[3] = -1.0;
+
+  MobiusFermionD DenOp(U,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mden,M5,b,c,p);
+  MobiusFermionD NumOp(U,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mnum,M5,b,c,p);
+
+  RealD tol     = 1.0e-12;
+  Integer maxit = 30000;
+
+  typedef WilsonImplD::FermionField FermionField;
+
+  ////////////////////////////////////////////////////////////////
+  // Solvers.  Classic: CG as OperatorFunction on the MdagM linop the
+  // action supplies.  LeftPrec: F-contract solves via CG on FdagF.
+  ////////////////////////////////////////////////////////////////
+  ConjugateGradient<FermionField> CG(tol,maxit);
+
+  VdagMNormalOperator<WilsonImplD> FdagF(NumOp,DenOp);
+  ForwardFSolve<WilsonImplD>       Ffwd (FdagF,tol,maxit);
+  AdjointFSolve<WilsonImplD>       Fadj (FdagF,tol,maxit);
+  NormalEqSolve<MobiusFermionD,FermionField> VdagVinv(NumOp,tol,maxit);
+
+  TwoFlavourRatioPseudoFermionAction<WilsonImplD>         Classic (NumOp,DenOp,CG,CG);
+  TwoFlavourRatioLeftPrecPseudoFermionAction<WilsonImplD> LeftPrec(NumOp,DenOp,Ffwd,Fadj,Fadj,VdagVinv);
+
+  ////////////////////////////////////////////////////////////////
+  // Twin-seeded refreshes: identical eta into both classes.
+  ////////////////////////////////////////////////////////////////
+  std::vector<int> seedsR({9,11,13,17});
+  GridSerialRNG   sRNGa;         sRNGa.SeedFixedIntegers(seedsR);
+  GridSerialRNG   sRNGb;         sRNGb.SeedFixedIntegers(seedsR);
+  GridParallelRNG RNG5a(FGrid);  RNG5a.SeedFixedIntegers(seedsR);
+  GridParallelRNG RNG5b(FGrid);  RNG5b.SeedFixedIntegers(seedsR);
+  GridParallelRNG RNG5c(FGrid);  RNG5c.SeedFixedIntegers(seedsR);
+
+  FermionField etaTwin(FGrid);
+  gaussian(RNG5c,etaTwin);                    // identical to both refresh draws
+
+  Classic.refresh (U,sRNGa,RNG5a);
+  LeftPrec.refresh(U,sRNGb,RNG5b);
+
+  ////////////////////////////////////////////////////////////////
+  // E0 : heatbath identity for both classes
+  ////////////////////////////////////////////////////////////////
+  RealD Sexpect = 0.5*norm2(etaTwin);
+  RealD Sc = Classic.S(U);
+  RealD Sl = LeftPrec.S(U);
+
+  RealD e0a = std::abs(Sc-Sexpect)/Sexpect;
+  RealD e0b = std::abs(Sl-Sexpect)/Sexpect;
+  std::cout << GridLogMessage << "=========================================================" << std::endl;
+  std::cout << GridLogMessage << " E0 heatbath identity: 0.5|eta|^2 = " << Sexpect << std::endl;
+  std::cout << GridLogMessage << "   classic  S = " << Sc << "  rel defect " << e0a
+	    << ( e0a < 1.0e-8 ? "   PASS" : "   FAIL" ) << std::endl;
+  std::cout << GridLogMessage << "   leftprec S = " << Sl << "  rel defect " << e0b
+	    << ( e0b < 1.0e-8 ? "   PASS" : "   FAIL" ) << std::endl;
+
+  ////////////////////////////////////////////////////////////////
+  // E1 : action equivalence
+  ////////////////////////////////////////////////////////////////
+  RealD e1 = std::abs(Sc-Sl)/std::abs(Sc);
+  std::cout << GridLogMessage << " E1 action equivalence: rel diff = " << e1
+	    << ( e1 < 1.0e-8 ? "   PASS" : "   FAIL" ) << std::endl;
+
+  ////////////////////////////////////////////////////////////////
+  // E2 : derivative equivalence (pointwise field comparison)
+  ////////////////////////////////////////////////////////////////
+  LatticeGaugeField dSdUc(UGrid);
+  LatticeGaugeField dSdUl(UGrid);
+  LatticeGaugeField dDiff(UGrid);
+
+  Classic.deriv (U,dSdUc);
+  LeftPrec.deriv(U,dSdUl);
+  dDiff = dSdUc - dSdUl;
+
+  RealD e2 = std::sqrt( norm2(dDiff) / norm2(dSdUc) );
+  std::cout << GridLogMessage << " E2 deriv equivalence: |diff|/|classic| = " << e2
+	    << ( e2 < 1.0e-8 ? "   PASS" : "   FAIL" ) << std::endl;
+  std::cout << GridLogMessage << "   |dSdU classic |^2 = " << norm2(dSdUc) << std::endl;
+  std::cout << GridLogMessage << "   |dSdU leftprec|^2 = " << norm2(dSdUl) << std::endl;
+  std::cout << GridLogMessage << "=========================================================" << std::endl;
+
+  ////////////////////////////////////////////////////////////////
+  // F1 : standalone force test on the LeftPrec class
+  ////////////////////////////////////////////////////////////////
+  MomentumFilterNone<LatticeGaugeField> FilterNone;
+  ForceTest<GimplTypesR>(LeftPrec,U,FilterNone);
+
+  ////////////////////////////////////////////////////////////////
+  // Summary + hard asserts (this is the regression gate)
+  ////////////////////////////////////////////////////////////////
+  std::cout << GridLogMessage << "=========================================================" << std::endl;
+  std::cout << GridLogMessage << " SUMMARY" << std::endl;
+  std::cout << GridLogMessage << "   E0a classic  heatbath defect : " << e0a << std::endl;
+  std::cout << GridLogMessage << "   E0b leftprec heatbath defect : " << e0b << std::endl;
+  std::cout << GridLogMessage << "   E1  action   equivalence     : " << e1  << std::endl;
+  std::cout << GridLogMessage << "   E2  deriv    equivalence     : " << e2  << std::endl;
+  std::cout << GridLogMessage << "=========================================================" << std::endl;
+
+  GRID_ASSERT(e0a < 1.0e-8);
+  GRID_ASSERT(e0b < 1.0e-8);
+  GRID_ASSERT(e1  < 1.0e-8);
+  GRID_ASSERT(e2  < 1.0e-8);
+
+  std::cout << GridLogMessage << "All equivalence tests PASSED" << std::endl;
+
+  Grid_finalize();
+}