no compile fix

Arm complex instructions on M3/M4 NEON v8.3 and simplify A64FX code paths/broaden.
Grid_vector_types and Simd.h mainly reorg and prep for sComplexD and sComplexF alternat Nsimd=1 types

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/Algorithms.h

@@ -75,7 +75,6 @@ NAMESPACE_CHECK(BiCGSTAB);
 #include <Grid/algorithms/iterative/FlexibleCommunicationAvoidingGeneralisedMinimalResidual.h>
 #include <Grid/algorithms/iterative/MixedPrecisionFlexibleGeneralisedMinimalResidual.h>
 #include <Grid/algorithms/iterative/ImplicitlyRestartedLanczos.h>
-#include <Grid/algorithms/iterative/SimpleLanczos.h>
 #include <Grid/algorithms/iterative/PowerMethod.h>
 #include <Grid/algorithms/iterative/AdefGeneric.h>
 #include <Grid/algorithms/iterative/AdefMrhs.h>
@@ -84,9 +83,4 @@ NAMESPACE_CHECK(PowerMethod);
 NAMESPACE_CHECK(multigrid);
 #include <Grid/algorithms/FFT.h>
 
-#include <Grid/algorithms/iterative/KrylovSchur.h>
-#include <Grid/algorithms/iterative/Arnoldi.h>
-#include <Grid/algorithms/iterative/LanczosBidiagonalization.h>
-#include <Grid/algorithms/iterative/RestartedLanczosBidiagonalization.h>
-
 #endif

Grid/algorithms/FFT.h

@@ -75,7 +75,6 @@ public:
     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);
@@ -83,9 +82,7 @@ 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);
-  }
 };
 template<> struct FFTW<ComplexF> {
 public:
@@ -93,7 +90,6 @@ public:
   static const int backward=FFTW_BACKWARD;
   typedef hipfftComplex FFTW_scalar;
   typedef hipfftHandle  FFTW_plan;
-
   static FFTW_plan fftw_plan_many_dft(int rank, int *n,int howmany,
 				      FFTW_scalar *in, int *inembed,
 				      int istride, int idist,
@@ -105,7 +101,6 @@ public:
     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
 
@@ -126,7 +119,6 @@ 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,
 				      int istride, int idist,
@@ -137,15 +129,12 @@ public:
     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:
@@ -153,7 +142,6 @@ public:
   static const int backward=FFTW_BACKWARD;
   typedef cufftComplex FFTW_scalar;
   typedef cufftHandle  FFTW_plan;
-
   static FFTW_plan fftw_plan_many_dft(int rank, int *n,int howmany,
 				      FFTW_scalar *in, int *inembed,
 				      int istride, int idist,
@@ -164,15 +152,12 @@ public:
     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
 
@@ -190,13 +175,10 @@ public:
 				      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:
@@ -210,25 +192,19 @@ public:
 				      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;
   uint64_t      usec;
-    
+  GridCartesian *_grid;
-public:
 
   static const int forward  = FFTW_FORWARD;
   static const int backward = FFTW_BACKWARD;
@@ -237,168 +213,87 @@ public:
   double MFlops(void) { return flops / usec; }
   double USec(void)   { return (double)usec; }
 
-  FFT ( GridCartesian * grid ) 
+  FFTbase(GridCartesian *grid) : _grid(grid), flops(0), flops_call(0), usec(0) {}
-  {
-    flops=0;
-    usec =0;
 };
 
-  ~FFT ( void)  {
+// Barrel-shift gather, FFT execute, and insert. Called by both FFT and PlannedFFT.
-    //    delete sgrid;
+// The caller is responsible for plan acquisition and destruction.
-  }
-    
 template<class vobj>
-  void FFT_dim_mask(Lattice<vobj> &result,const Lattice<vobj> &source,Coordinate mask,int sign){
+static void FFT_dim_execute(
-
+    Lattice<vobj>       &result,
-    //    vgrid=result.Grid();
+    const Lattice<vobj> &source,
-    //    conformable(result.Grid(),vgrid);
+    int dim, int sign,
-    //    conformable(source.Grid(),vgrid);
+    typename FFTW<typename vobj::scalar_type>::FFTW_plan p,
-    const int Ndim = source.Grid()->Nd();
+    GridCartesian *grid,
-    Lattice<vobj> tmp = source;
+    double &flops, double &flops_call, uint64_t &usec)
-    for(int d=0;d<Ndim;d++){
+{
-      if( mask[d] ) {
-	FFT_dim(result,tmp,d,sign);
-	tmp=result;
-      }
-    }
-  }
-
-  template<class vobj>
-  void FFT_all_dim(Lattice<vobj> &result,const Lattice<vobj> &source,int sign){
-    const int Ndim = source.Grid()->Nd();
-    Coordinate mask(Ndim,1);
-    FFT_dim_mask(result,source,mask,sign);
-  }
-
-
-  template<class vobj>
-  void FFT_dim(Lattice<vobj> &result,const Lattice<vobj> &source,int dim, int sign){
-    const int Ndim = source.Grid()->Nd();
-    GridBase *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_object sobj;
   typedef typename vobj::scalar_type   scalar_type;
   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;
 
+  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;
+  int64_t Nlow = 1, Nhigh = 1;
-    int64_t 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];
-    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; // Layout is [perp][component][dim]
+  deviceVector<scalar> pgbuf(Nperp * Ncomp * G);
-    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;
+  if      (sign == FFTW_BACKWARD) div = 1.0 / G;
-    else if ( sign == forward ) div = 1.0;
+  else if (sign == FFTW_FORWARD)  div = 1.0;
   else GRID_ASSERT(0);
 
-    double t_pencil=0;
+  double t_pencil = 0, t_fft = 0, t_copy = 0, t_shift = 0;
-    double t_fft   =0;
   double t_total  = -usecond();
-    //    std::cout << GridLogPerformance<<"Making FFTW plan" << std::endl;
-    /*
-     *
-     */
-    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;
+  const Coordinate processors = grid->_processors;
 
-    Coordinate processors = grid->_processors;
   Coordinate pgdims(Ndim);
   pgdims[0] = G;
-    for(int d=0, dd=1;d<Ndim;d++){
+  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_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); // buffer lane
+      int lane = acceleratorSIMTlane(Nsimd);
 #else
     for (int lane = 0; lane < Nsimd; lane++) {
 #endif
-	Coordinate icoor;
+      Coordinate icoor, ocoor, pgcoor;
-	Coordinate ocoor;
-	Coordinate 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;
-	pgcoor[0] = ocoor[dim] + icoor[dim]*rdims[dim] + ((pc+p)%processors[dim])*L;
+      for (int d = 0, dd = 1; d < Ndim; d++)
-	for(int d=0,dd=1;d<Ndim;d++){
+        if (d != dim) { pgcoor[dd] = ocoor[d] + icoor[d]*rdims[d]; dd++; }
-	  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;
+        pgbuf_v[pgidx + w*pgvol] = stmp;
       }
 #ifdef GRID_SIMT
     }
@@ -406,9 +301,8 @@ public:
     }
 #endif
     });
-
     t_copy += usecond();
-      if (p != processors[dim] - 1) {
+    if (p_idx != processors[dim] - 1) {
       Lattice<vobj> temp(grid);
       t_shift -= usecond();
       temp = Cshift(result, dim, L); result = temp;
@@ -423,49 +317,35 @@ public:
   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
+      int lane = acceleratorSIMTlane(Nsimd);
 #else
     for (int lane = 0; lane < Nsimd; lane++) {
 #endif
-	Coordinate icoor(Ndim);
+      Coordinate icoor(Ndim), ocoor(Ndim), pgcoor(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++){
+      for (int d = 0, dd = 1; d < Ndim; d++)
-	  if ( d!=dim ) {
+        if (d != dim) { pgcoor[dd] = ocoor[d] + icoor[d]*rdims[d]; dd++; }
-	    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[pgidx + w*pgvol];
-	  stmp = pgbuf_v[pg_idx];
         putlane(to[w], stmp, lane);
       }
-	
 #ifdef GRID_SIMT
     }
 #else
@@ -473,14 +353,8 @@ public:
 #endif
     });
   }
-
   result = result * div;
-
   t_insert += usecond();
-    
-    // destroying plan
-    FFTW<scalar>::fftw_destroy_plan(p);
-
   t_total  += usecond();
 
   std::cout << GridLogPerformance << " FFT took   " << t_total/1.0e6  << " s" << std::endl;
@@ -489,7 +363,130 @@ public:
   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++) {
+      if (mask[d]) {
+        FFT_dim(result, tmp, d, sign);
+        tmp = result;
+      }
+    }
+  }
+
+  template<class vobj>
+  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);
+  }
+
+  template<class vobj>
+  void FFT_dim(Lattice<vobj> &result, const Lattice<vobj> &source, int dim, int sign) {
+    GRID_ASSERT(source.Grid() == _grid);
+    GRID_ASSERT(result.Grid() == _grid);
+    conformable(result.Grid(), source.Grid());
+
+    typedef typename vobj::scalar_type   scalar;
+    typedef typename vobj::scalar_object sobj;
+    typedef typename FFTW<scalar>::FFTW_scalar FFTW_scalar;
+    typedef typename FFTW<scalar>::FFTW_plan   FFTW_plan;
+
+    const int Ndim = _grid->Nd();
+    int G     = _grid->_fdimensions[dim];
+    int Ncomp = sizeof(sobj) / sizeof(scalar);
+    int64_t Nperp = 1;
+    for (int d = 0; d < Ndim; d++)
+      if (d != dim) Nperp *= _grid->_ldimensions[d];
+    int n[]     = {G};
+    int howmany = Ncomp * Nperp;
+
+    deviceVector<scalar> dummy(2);
+    FFTW_scalar *buf = (FFTW_scalar *)&dummy[0];
+    FFTW_plan p = FFTW<scalar>::fftw_plan_many_dft(1, n, howmany,
+                                                    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<scalar>::fftw_destroy_plan(p);
+  }
+};
+
+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::vector<FFTW_plan> forward_plans;
+  std::vector<FFTW_plan> backward_plans;
+
+  void PlanCreate() {
+    const int Ndim = _grid->Nd();
+    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 +768,456 @@ 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;
+  }
+
+  ///////////////////////////////////////////////////////////////////////////////////
+  // Explicit-leading-dimension complex double GEMM.  Mirror of the ComplexF
+  // overload above; motivating use is the fp64 distributed recursive Schur
+  // inversion (RecursiveSchurInverse), whose operands are column windows of
+  // larger row-slab allocations.
+  ///////////////////////////////////////////////////////////////////////////////////
+  void gemmBatched(GridBLASOperation_t OpA,
+                   GridBLASOperation_t OpB,
+                   int m,int n, int k,
+                   ComplexD alpha,
+                   deviceVector<ComplexD*> &Amk, int lda,
+                   deviceVector<ComplexD*> &Bkn, int ldb,
+                   ComplexD beta,
+                   deviceVector<ComplexD*> &Cmn, int ldc)
+  {
+    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<ComplexD> alpha_c;
+    static GridBLASDeviceConstant<ComplexD> beta_c;
+    ComplexD *alpha_p = alpha_c.put(alpha);
+    ComplexD *beta_p  = beta_c.put(beta);
+    RealD t0=usecond();
+
+    GRID_ASSERT(Bkn.size()==batchCount);
+    GRID_ASSERT(Cmn.size()==batchCount);
+#ifdef GRID_HIP
+    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 = hipblasZgemmBatched(gridblasHandle,
+                                   hOpA,
+                                   hOpB,
+                                   m,n,k,
+                                   (hipDoubleComplex *) &alpha_p[0],
+                                   (hipDoubleComplex **)&Amk[0], lda,
+                                   (hipDoubleComplex **)&Bkn[0], ldb,
+                                   (hipDoubleComplex *) &beta_p[0],
+                                   (hipDoubleComplex **)&Cmn[0], ldc,
+                                   batchCount);
+#else
+    auto err = hipblasZgemmBatched(gridblasHandle,
+                                   hOpA,
+                                   hOpB,
+                                   m,n,k,
+                                   (hipblasDoubleComplex *) &alpha_p[0],
+                                   (hipblasDoubleComplex **)&Amk[0], lda,
+                                   (hipblasDoubleComplex **)&Bkn[0], ldb,
+                                   (hipblasDoubleComplex *) &beta_p[0],
+                                   (hipblasDoubleComplex **)&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;
+    auto err = cublasZgemmBatched(gridblasHandle,
+                                  hOpA,
+                                  hOpB,
+                                  m,n,k,
+                                  (cuDoubleComplex *) &alpha_p[0],
+                                  (cuDoubleComplex **)&Amk[0], lda,
+                                  (cuDoubleComplex **)&Bkn[0], ldb,
+                                  (cuDoubleComplex *) &beta_p[0],
+                                  (cuDoubleComplex **)&Cmn[0], ldc,
+                                  batchCount);
+    GRID_ASSERT(err==CUBLAS_STATUS_SUCCESS);
+#endif
+#ifdef GRID_SYCL
+    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,
+                                                (ComplexD *) &alpha_p[0],
+                                                (const ComplexD **)&Amk[0], (const int64_t *)&lda64,
+                                                (const ComplexD **)&Bkn[0], (const int64_t *)&ldb64,
+                                                (ComplexD *) &beta_p[0],
+                                                (ComplexD **)&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)
+    // Reference implementation: Eigen with explicit outer stride
+    typedef Eigen::Map<Eigen::MatrixXcd,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(ComplexD)*(m*k+k*n+m*n)*batchCount;
+  }
+
   ///////////////////////////////////////////////////////////////////////////
   // Single precision real GEMM
   ///////////////////////////////////////////////////////////////////////////
@@ -719,11 +1244,11 @@ 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 +1272,7 @@ 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 +1405,11 @@ 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 +1433,7 @@ 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 +1661,7 @@ 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 +1701,7 @@ 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 +1790,7 @@ 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 +1834,7 @@ 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/deflation/MultiRHSBlockProject.h

@@ -61,6 +61,17 @@ public:
   uint64_t coarse_vol;
   uint64_t words;
 
+  ////////////////////////////////////////////////////////////////////////////
+  // Blocking geometry in full local coordinates. Addressing in lSites rather
+  // than (lane,oSite) lets the fine and coarse spaces carry different SIMD
+  // layouts, so an unvectorised coarse space may block a vectorised fine one.
+  ////////////////////////////////////////////////////////////////////////////
+  Coordinate fine_ldimensions;
+  Coordinate coarse_ldimensions;
+  Coordinate block_ldimensions;
+  Coordinate fine_simd;
+  Coordinate coarse_simd;
+
   // Row major layout "C" order:
   // BLAS_V[coarse_vol][nbasis][block_vol][words]
   // BLAS_F[coarse_vol][nrhs][block_vol][words]
@@ -123,6 +134,23 @@ public:
 
     words = sizeof(scalar_object)/sizeof(scalar);
 
+    int nd = coarse_grid->_ndimension;
+    GRID_ASSERT(fine_grid->_ndimension == nd);
+
+    fine_ldimensions.resize(nd);
+    coarse_ldimensions.resize(nd);
+    block_ldimensions.resize(nd);
+    fine_simd   = fine_grid->_simd_layout;
+    coarse_simd = coarse_grid->_simd_layout;
+    for(int d=0;d<nd;d++){
+      GRID_ASSERT(fine_grid->_processors[d] == coarse_grid->_processors[d]);
+      fine_ldimensions  [d] = fine_grid->_rdimensions  [d]*fine_grid->_simd_layout  [d];
+      coarse_ldimensions[d] = coarse_grid->_rdimensions[d]*coarse_grid->_simd_layout[d];
+      block_ldimensions [d] = fine_ldimensions[d]/coarse_ldimensions[d];
+      GRID_ASSERT(block_ldimensions[d]*coarse_ldimensions[d] == fine_ldimensions[d]);
+    }
+    GRID_ASSERT(block_vol == fine_vol/coarse_vol);
+
     BLAS_V.resize (fine_vol * words * nbasis );
   }
   void ImportFineGridVectors(std::vector <Field > &vecs, deviceVector<scalar> &blas)
@@ -133,22 +161,16 @@ public:
 
     GRID_ASSERT(vecs[0].Grid()==fine_grid);
 
-    subdivides(coarse_grid,fine_grid); // require they map
-
     int _ndimension = coarse_grid->_ndimension;
-    GRID_ASSERT(block_vol == fine_grid->oSites() / coarse_grid->oSites());
-    
-    Coordinate  block_r      (_ndimension);
-    for(int d=0 ; d<_ndimension;d++){
-      block_r[d] = fine_grid->_rdimensions[d] / coarse_grid->_rdimensions[d];
-    }
 
     uint64_t sz = blas.size();
 
     acceleratorMemSet(&blas[0],0,blas.size()*sizeof(scalar));
 
     Coordinate fine_rdimensions = fine_grid->_rdimensions;
-    Coordinate coarse_rdimensions = coarse_grid->_rdimensions;
+    Coordinate coarse_l = coarse_ldimensions;
+    Coordinate block_l  = block_ldimensions;
+    Coordinate fsimd    = fine_simd;
     int64_t bv= block_vol;
     for(int v=0;v<vecs.size();v++){
 
@@ -162,9 +184,7 @@ public:
 
       // loop over fine sites
       const int Nsimd = vobj::Nsimd();
-      //      std::cout << "sz "<<sz<<std::endl;
+      GRID_ASSERT(sz == coarse_vol * block_vol * nvec * words);
-      //      std::cout << "prod "<<Nsimd * coarse_grid->oSites() * block_vol * nvec * words<<std::endl;
-      GRID_ASSERT(sz == Nsimd * coarse_grid->oSites() * block_vol * nvec * words);
       uint64_t lwords= words; // local variable for copy in to GPU
       accelerator_for(sf,osites,Nsimd,{
 #ifdef GRID_SIMT
@@ -175,27 +195,27 @@ public:
 #endif
 	  // One thread per fine site
 	  Coordinate coor_f(_ndimension);
+	  Coordinate coor_l(_ndimension);
 	  Coordinate coor_b(_ndimension);
 	  Coordinate coor_c(_ndimension);
 
-	  // Fine site to fine coor
+	  // Fine (oSite,lane) to full local coor
 	  Lexicographic::CoorFromIndex(coor_f,sf,fine_rdimensions);
+	  Lexicographic::CoorFromIndex(coor_l,lane,fsimd);
+	  for(int d=0;d<_ndimension;d++) coor_f[d] += fine_rdimensions[d]*coor_l[d];
 
-	  for(int d=0;d<_ndimension;d++) coor_b[d] = coor_f[d]%block_r[d];
+	  for(int d=0;d<_ndimension;d++) coor_b[d] = coor_f[d]%block_l[d];
-	  for(int d=0;d<_ndimension;d++) coor_c[d] = coor_f[d]/block_r[d];
+	  for(int d=0;d<_ndimension;d++) coor_c[d] = coor_f[d]/block_l[d];
 
 	  int sc;// coarse site
 	  int sb;// block site
-	  Lexicographic::IndexFromCoor(coor_c,sc,coarse_rdimensions);
+	  Lexicographic::IndexFromCoor(coor_c,sc,coarse_l);
-	  Lexicographic::IndexFromCoor(coor_b,sb,block_r);
+	  Lexicographic::IndexFromCoor(coor_b,sb,block_l);
 
           scalar_object data = extractLane(lane,fineData[sf]);
 
-	  // BLAS layout address calculation
+	  // BLAS_F[coarse_vol][nvec][block_vol][words]
-	  // words * block_vol * nbasis x coarse_vol
+	  int64_t site = (sc*nvec + v)*bv
-	  // coarse oSite x block vole x lanes
-	  int64_t site = (lane*osites + sc*bv)*nvec
-   	               + v*bv
 	               + sb;
 
 	  //	  GRID_ASSERT(site*lwords<sz);
@@ -213,6 +233,318 @@ public:
       //      std::cout << " BlockProjector imported vector"<<v<<std::endl;
     }
   }
+  ////////////////////////////////////////////////////////////////////////////
+  // Import direct from multiRHS fine order, avoiding the unpack to a vector
+  // of single RHS fields.
+  //
+  //   fine mrhs grid  : rhs is dimension 0, undistributed, unvectorised
+  //   Grid  order     : F[fine_vol][nrhs][words]
+  //   BLAS  order     : BLAS_F[lane][coarse_vol][nrhs][block_vol][words]
+  //
+  // The gather of block_vol from fine_vol, and the transpose of nrhs against
+  // block_vol, are the irreducible part: this is not the identity.
+  ////////////////////////////////////////////////////////////////////////////
+  void ImportFineGridMrhsVectors(Field &vec_mrhs, deviceVector<scalar> &blas)
+  {
+    typedef typename Field::vector_object vobj;
+
+    GridBase *fine_mrhs_grid = vec_mrhs.Grid();
+    int _ndimension = coarse_grid->_ndimension;
+
+    GRID_ASSERT(fine_mrhs_grid->_ndimension == _ndimension+1);
+    GRID_ASSERT(fine_mrhs_grid->_simd_layout[0] == 1);
+    GRID_ASSERT(fine_mrhs_grid->_processors[0] == 1);
+    for(int d=0;d<_ndimension;d++){
+      GRID_ASSERT(fine_mrhs_grid->_rdimensions[d+1] == fine_grid->_rdimensions[d]);
+      GRID_ASSERT(fine_mrhs_grid->_simd_layout[d+1] == fine_grid->_simd_layout[d]);
+    }
+    int nvec = fine_mrhs_grid->_rdimensions[0];   // nrhs
+
+    uint64_t sz = blas.size();
+    acceleratorMemSet(&blas[0],0,blas.size()*sizeof(scalar));
+
+    Coordinate fine_mrhs_rdimensions = fine_mrhs_grid->_rdimensions;
+    Coordinate fine_rdimensions      = fine_grid->_rdimensions;
+    Coordinate coarse_l = coarse_ldimensions;
+    Coordinate block_l  = block_ldimensions;
+    Coordinate fsimd    = fine_simd;
+    int64_t bv= block_vol;
+
+    autoView( fineData   , vec_mrhs, AcceleratorRead);
+    auto blasData_p  = &blas[0];
+    auto fineData_p  = &fineData[0];
+
+    int64_t osites     = fine_grid->oSites();       // D dimensional
+    int64_t osites_hi  = fine_mrhs_grid->oSites();  // nvec * osites
+
+    const int Nsimd = vobj::Nsimd();
+    GRID_ASSERT(sz == coarse_vol * block_vol * nvec * words);
+    uint64_t lwords= words;
+    int64_t lnvec = nvec;
+
+    accelerator_for(sfr,osites_hi,Nsimd,{
+#ifdef GRID_SIMT
+      {
+	int lane=acceleratorSIMTlane(Nsimd); // buffer lane
+#else
+	for(int lane=0;lane<Nsimd;lane++) {
+#endif
+	  Coordinate coor_hi(_ndimension+1);
+	  Coordinate coor_f(_ndimension);
+	  Coordinate coor_l(_ndimension);
+	  Coordinate coor_b(_ndimension);
+	  Coordinate coor_c(_ndimension);
+
+	  // rhs is dimension 0 of the D+1 grid
+	  Lexicographic::CoorFromIndex(coor_hi,sfr,fine_mrhs_rdimensions);
+	  int v = coor_hi[0];
+	  for(int d=0;d<_ndimension;d++) coor_f[d] = coor_hi[d+1];
+
+	  Lexicographic::CoorFromIndex(coor_l,lane,fsimd);
+	  for(int d=0;d<_ndimension;d++) coor_f[d] += fine_rdimensions[d]*coor_l[d];
+
+	  for(int d=0;d<_ndimension;d++) coor_b[d] = coor_f[d]%block_l[d];
+	  for(int d=0;d<_ndimension;d++) coor_c[d] = coor_f[d]/block_l[d];
+
+	  int sc;// coarse site
+	  int sb;// block site
+	  Lexicographic::IndexFromCoor(coor_c,sc,coarse_l);
+	  Lexicographic::IndexFromCoor(coor_b,sb,block_l);
+
+	  scalar_object data = extractLane(lane,fineData[sfr]);
+
+	  int64_t site = (sc*lnvec + v)*bv
+	               + sb;
+
+	  scalar_object * ptr = (scalar_object *)&blasData_p[site*lwords];
+	  *ptr = data;
+#ifdef GRID_SIMT
+      }
+#else
+      }
+#endif
+    });
+  }
+
+  ////////////////////////////////////////////////////////////////////////////
+  // Export direct to multiRHS coarse order.
+  //
+  //   Grid  order : C[coarse_vol][nrhs][nbasis]
+  //   BLAS  order : BLAS_C[lane][coarse_vol][nrhs][nbasis]
+  //
+  // At Nsimd()==1 these are the same sequence of addresses.
+  ////////////////////////////////////////////////////////////////////////////
+  template<class vobj>
+  void ExportCoarseGridMrhsVectors(Lattice<vobj> &vec_mrhs, deviceVector<scalar> &blas)
+  {
+    typedef typename vobj::scalar_object coarse_scalar_object;
+
+    GridBase *coarse_mrhs_grid = vec_mrhs.Grid();
+    int _ndimension = coarse_grid->_ndimension;
+
+    GRID_ASSERT(coarse_mrhs_grid->_ndimension == _ndimension+1);
+    GRID_ASSERT(coarse_mrhs_grid->_simd_layout[0] == 1);
+    GRID_ASSERT(coarse_mrhs_grid->_processors[0] == 1);
+    for(int d=0;d<_ndimension;d++){
+      GRID_ASSERT(coarse_mrhs_grid->_rdimensions[d+1] == coarse_grid->_rdimensions[d]);
+      GRID_ASSERT(coarse_mrhs_grid->_simd_layout[d+1] == coarse_grid->_simd_layout[d]);
+    }
+    int nvec = coarse_mrhs_grid->_rdimensions[0];   // nrhs
+
+    Coordinate coarse_mrhs_rdimensions = coarse_mrhs_grid->_rdimensions;
+    Coordinate coarse_rdimensions      = coarse_grid->_rdimensions;
+    Coordinate coarse_l = coarse_ldimensions;
+    Coordinate csimd    = coarse_simd;
+
+    autoView( coarseData   , vec_mrhs, AcceleratorWrite);
+    auto blasData_p    = &blas[0];
+    auto coarseData_p  = &coarseData[0];
+
+    int64_t osites    = coarse_grid->oSites();       // D dimensional
+    int64_t osites_hi = coarse_mrhs_grid->oSites();  // nvec * osites
+
+    const int Nsimd = vobj::Nsimd();
+    uint64_t cwords=sizeof(typename vobj::scalar_object)/sizeof(scalar);
+    GRID_ASSERT(cwords==nbasis);
+    int64_t lnvec = nvec;
+
+    accelerator_for(scr,osites_hi,Nsimd,{
+#ifdef GRID_SIMT
+      {
+	int lane=acceleratorSIMTlane(Nsimd); // buffer lane
+#else
+	for(int lane=0;lane<Nsimd;lane++) {
+#endif
+	  Coordinate coor_hi(_ndimension+1);
+	  Coordinate coor_l(_ndimension);
+	  Coordinate coor_c(_ndimension);
+
+	  Lexicographic::CoorFromIndex(coor_hi,scr,coarse_mrhs_rdimensions);
+	  int v = coor_hi[0];
+	  for(int d=0;d<_ndimension;d++) coor_c[d] = coor_hi[d+1];
+
+	  Lexicographic::CoorFromIndex(coor_l,lane,csimd);
+	  for(int d=0;d<_ndimension;d++) coor_c[d] += coarse_rdimensions[d]*coor_l[d];
+
+	  int sc;
+	  Lexicographic::IndexFromCoor(coor_c,sc,coarse_l);
+
+	  int64_t blas_site = (sc*lnvec + v)*cwords;
+	  coarse_scalar_object * ptr = (coarse_scalar_object *)&blasData_p[blas_site];
+	  coarse_scalar_object data = *ptr;
+	  insertLane(lane,coarseData[scr],data);
+#ifdef GRID_SIMT
+      }
+#else
+      }
+#endif
+    });
+  }
+
+  ////////////////////////////////////////////////////////////////////////////
+  // Reverse directions: BLAS_F -> fine mrhs field, coarse mrhs field -> BLAS_C
+  ////////////////////////////////////////////////////////////////////////////
+  void ExportFineGridMrhsVectors(Field &vec_mrhs, deviceVector<scalar> &blas)
+  {
+    typedef typename Field::vector_object vobj;
+
+    GridBase *fine_mrhs_grid = vec_mrhs.Grid();
+    int _ndimension = coarse_grid->_ndimension;
+
+    GRID_ASSERT(fine_mrhs_grid->_ndimension == _ndimension+1);
+    GRID_ASSERT(fine_mrhs_grid->_simd_layout[0] == 1);
+    for(int d=0;d<_ndimension;d++){
+      GRID_ASSERT(fine_mrhs_grid->_rdimensions[d+1] == fine_grid->_rdimensions[d]);
+      GRID_ASSERT(fine_mrhs_grid->_simd_layout[d+1] == fine_grid->_simd_layout[d]);
+    }
+    int nvec = fine_mrhs_grid->_rdimensions[0];
+
+    Coordinate fine_mrhs_rdimensions = fine_mrhs_grid->_rdimensions;
+    Coordinate fine_rdimensions      = fine_grid->_rdimensions;
+    Coordinate coarse_l = coarse_ldimensions;
+    Coordinate block_l  = block_ldimensions;
+    Coordinate fsimd    = fine_simd;
+    int64_t bv= block_vol;
+
+    autoView( fineData   , vec_mrhs, AcceleratorWrite);
+    auto blasData_p  = &blas[0];
+    auto fineData_p  = &fineData[0];
+
+    int64_t osites     = fine_grid->oSites();
+    int64_t osites_hi  = fine_mrhs_grid->oSites();
+
+    const int Nsimd = vobj::Nsimd();
+    uint64_t lwords= words;
+    int64_t lnvec = nvec;
+
+    accelerator_for(sfr,osites_hi,Nsimd,{
+#ifdef GRID_SIMT
+      {
+	int lane=acceleratorSIMTlane(Nsimd);
+#else
+	for(int lane=0;lane<Nsimd;lane++) {
+#endif
+	  Coordinate coor_hi(_ndimension+1);
+	  Coordinate coor_f(_ndimension);
+	  Coordinate coor_l(_ndimension);
+	  Coordinate coor_b(_ndimension);
+	  Coordinate coor_c(_ndimension);
+
+	  Lexicographic::CoorFromIndex(coor_hi,sfr,fine_mrhs_rdimensions);
+	  int v = coor_hi[0];
+	  for(int d=0;d<_ndimension;d++) coor_f[d] = coor_hi[d+1];
+
+	  Lexicographic::CoorFromIndex(coor_l,lane,fsimd);
+	  for(int d=0;d<_ndimension;d++) coor_f[d] += fine_rdimensions[d]*coor_l[d];
+
+	  for(int d=0;d<_ndimension;d++) coor_b[d] = coor_f[d]%block_l[d];
+	  for(int d=0;d<_ndimension;d++) coor_c[d] = coor_f[d]/block_l[d];
+
+	  int sc,sb;
+	  Lexicographic::IndexFromCoor(coor_c,sc,coarse_l);
+	  Lexicographic::IndexFromCoor(coor_b,sb,block_l);
+
+	  int64_t site = (sc*lnvec + v)*bv
+	               + sb;
+
+	  scalar_object * ptr = (scalar_object *)&blasData_p[site*lwords];
+	  scalar_object data = *ptr;
+	  insertLane(lane,fineData[sfr],data);
+#ifdef GRID_SIMT
+      }
+#else
+      }
+#endif
+    });
+  }
+
+  template<class vobj>
+  void ImportCoarseGridMrhsVectors(Lattice<vobj> &vec_mrhs, deviceVector<scalar> &blas)
+  {
+    typedef typename vobj::scalar_object coarse_scalar_object;
+
+    GridBase *coarse_mrhs_grid = vec_mrhs.Grid();
+    int _ndimension = coarse_grid->_ndimension;
+
+    GRID_ASSERT(coarse_mrhs_grid->_ndimension == _ndimension+1);
+    GRID_ASSERT(coarse_mrhs_grid->_simd_layout[0] == 1);
+    for(int d=0;d<_ndimension;d++){
+      GRID_ASSERT(coarse_mrhs_grid->_rdimensions[d+1] == coarse_grid->_rdimensions[d]);
+      GRID_ASSERT(coarse_mrhs_grid->_simd_layout[d+1] == coarse_grid->_simd_layout[d]);
+    }
+    int nvec = coarse_mrhs_grid->_rdimensions[0];
+
+    Coordinate coarse_mrhs_rdimensions = coarse_mrhs_grid->_rdimensions;
+    Coordinate coarse_rdimensions      = coarse_grid->_rdimensions;
+    Coordinate coarse_l = coarse_ldimensions;
+    Coordinate csimd    = coarse_simd;
+
+    autoView( coarseData   , vec_mrhs, AcceleratorRead);
+    auto blasData_p    = &blas[0];
+    auto coarseData_p  = &coarseData[0];
+
+    int64_t osites    = coarse_grid->oSites();
+    int64_t osites_hi = coarse_mrhs_grid->oSites();
+
+    const int Nsimd = vobj::Nsimd();
+    uint64_t cwords=sizeof(typename vobj::scalar_object)/sizeof(scalar);
+    GRID_ASSERT(cwords==nbasis);
+    int64_t lnvec = nvec;
+
+    accelerator_for(scr,osites_hi,Nsimd,{
+#ifdef GRID_SIMT
+      {
+	int lane=acceleratorSIMTlane(Nsimd);
+#else
+	for(int lane=0;lane<Nsimd;lane++) {
+#endif
+	  Coordinate coor_hi(_ndimension+1);
+	  Coordinate coor_l(_ndimension);
+	  Coordinate coor_c(_ndimension);
+
+	  Lexicographic::CoorFromIndex(coor_hi,scr,coarse_mrhs_rdimensions);
+	  int v = coor_hi[0];
+	  for(int d=0;d<_ndimension;d++) coor_c[d] = coor_hi[d+1];
+
+	  Lexicographic::CoorFromIndex(coor_l,lane,csimd);
+	  for(int d=0;d<_ndimension;d++) coor_c[d] += coarse_rdimensions[d]*coor_l[d];
+
+	  int sc;
+	  Lexicographic::IndexFromCoor(coor_c,sc,coarse_l);
+
+	  coarse_scalar_object data = extractLane(lane,coarseData[scr]);
+
+	  int64_t blas_site = (sc*lnvec + v)*cwords;
+	  coarse_scalar_object * ptr = (coarse_scalar_object *)&blasData_p[blas_site];
+	  *ptr = data;
+#ifdef GRID_SIMT
+      }
+#else
+      }
+#endif
+    });
+  }
+
   void ExportFineGridVectors(std::vector <Field> &vecs, deviceVector<scalar> &blas)
   {
     typedef typename Field::vector_object vobj;
@@ -221,17 +553,12 @@ public:
 
     GRID_ASSERT(vecs[0].Grid()==fine_grid);
 
-    subdivides(coarse_grid,fine_grid); // require they map
-
     int _ndimension = coarse_grid->_ndimension;
-    GRID_ASSERT(block_vol == fine_grid->oSites() / coarse_grid->oSites());
 
-    Coordinate  block_r      (_ndimension);
-    for(int d=0 ; d<_ndimension;d++){
-      block_r[d] = fine_grid->_rdimensions[d] / coarse_grid->_rdimensions[d];
-    }
     Coordinate fine_rdimensions = fine_grid->_rdimensions;
-    Coordinate coarse_rdimensions = coarse_grid->_rdimensions;
+    Coordinate coarse_l = coarse_ldimensions;
+    Coordinate block_l  = block_ldimensions;
+    Coordinate fsimd    = fine_simd;
 
     //    std::cout << " export fine Blas norm "<<blasNorm2(blas)<<std::endl;
 
@@ -259,23 +586,24 @@ public:
 #endif
 	  // One thread per fine site
 	  Coordinate coor_f(_ndimension);
+	  Coordinate coor_l(_ndimension);
 	  Coordinate coor_b(_ndimension);
 	  Coordinate coor_c(_ndimension);
 
 	  Lexicographic::CoorFromIndex(coor_f,sf,fine_rdimensions);
+	  Lexicographic::CoorFromIndex(coor_l,lane,fsimd);
+	  for(int d=0;d<_ndimension;d++) coor_f[d] += fine_rdimensions[d]*coor_l[d];
 
-	  for(int d=0;d<_ndimension;d++) coor_b[d] = coor_f[d]%block_r[d];
+	  for(int d=0;d<_ndimension;d++) coor_b[d] = coor_f[d]%block_l[d];
-	  for(int d=0;d<_ndimension;d++) coor_c[d] = coor_f[d]/block_r[d];
+	  for(int d=0;d<_ndimension;d++) coor_c[d] = coor_f[d]/block_l[d];
 
 	  int sc;
 	  int sb;
-	  Lexicographic::IndexFromCoor(coor_c,sc,coarse_rdimensions);
+	  Lexicographic::IndexFromCoor(coor_c,sc,coarse_l);
-	  Lexicographic::IndexFromCoor(coor_b,sb,block_r);
+	  Lexicographic::IndexFromCoor(coor_b,sb,block_l);
 
-	  // BLAS layout address calculation
+	  // BLAS_F[coarse_vol][nvec][block_vol][words]
-	  // words * block_vol * nbasis x coarse_vol 	  
+	  int64_t site = (sc*nvec + v)*bv
-	  int64_t site = (lane*osites + sc*bv)*nvec
-   	               + v*bv
 	               + sb;
 
 	  scalar_object * ptr = (scalar_object *)&blasData_p[site*lwords];
@@ -306,6 +634,8 @@ public:
     uint64_t sz = blas.size();
 
     Coordinate coarse_rdimensions = coarse_grid->_rdimensions;
+    Coordinate coarse_l = coarse_ldimensions;
+    Coordinate csimd    = coarse_simd;
 
     for(int v=0;v<vecs.size();v++){
 
@@ -330,7 +660,16 @@ public:
 	  for(int lane=0;lane<Nsimd;lane++) {
 #endif
            // C_br per site
-	    int64_t blas_site = (lane*osites + sc)*nvec*cwords + v*cwords;
+	    Coordinate coor_c(_ndimension);
+	    Coordinate coor_l(_ndimension);
+	    Lexicographic::CoorFromIndex(coor_c,sc,coarse_rdimensions);
+	    Lexicographic::CoorFromIndex(coor_l,lane,csimd);
+	    for(int d=0;d<_ndimension;d++) coor_c[d] += coarse_rdimensions[d]*coor_l[d];
+
+	    int scl;
+	    Lexicographic::IndexFromCoor(coor_c,scl,coarse_l);
+
+	    int64_t blas_site = (scl*nvec + v)*cwords;
 
 	    coarse_scalar_object data = extractLane(lane,coarseData[sc]);
 
@@ -360,6 +699,8 @@ public:
     uint64_t sz = blas.size();
 
     Coordinate coarse_rdimensions = coarse_grid->_rdimensions;
+    Coordinate coarse_l = coarse_ldimensions;
+    Coordinate csimd    = coarse_simd;
 
     //    std::cout << " export coarsee Blas norm "<<blasNorm2(blas)<<std::endl;
     for(int v=0;v<vecs.size();v++){
@@ -385,7 +726,16 @@ public:
 #else
 	  for(int lane=0;lane<Nsimd;lane++) {
 #endif
-	    int64_t blas_site = (lane*osites + sc)*nvec*cwords + v*cwords;
+	    Coordinate coor_c(_ndimension);
+	    Coordinate coor_l(_ndimension);
+	    Lexicographic::CoorFromIndex(coor_c,sc,coarse_rdimensions);
+	    Lexicographic::CoorFromIndex(coor_l,lane,csimd);
+	    for(int d=0;d<_ndimension;d++) coor_c[d] += coarse_rdimensions[d]*coor_l[d];
+
+	    int scl;
+	    Lexicographic::IndexFromCoor(coor_c,scl,coarse_l);
+
+	    int64_t blas_site = (scl*nvec + v)*cwords;
 	    coarse_scalar_object * ptr = (coarse_scalar_object *)&blasData_p[blas_site];
 	    coarse_scalar_object data = *ptr;
 	    insertLane(lane,coarseData[sc],data);
@@ -508,6 +858,168 @@ public:
     ExportFineGridVectors(fine, BLAS_F);
     //    std::cout << " exported "<<std::endl;
   }
+
+  ////////////////////////////////////////////////////////////////////////////
+  // multiRHS ordered interfaces.  The GEMM is identical; only the import and
+  // export differ, so those are the whole of the layout question.
+  ////////////////////////////////////////////////////////////////////////////
+  template<class cobj>
+  void blockProject(Field &fine_mrhs,Lattice<cobj> &coarse_mrhs)
+  {
+    int nrhs = fine_mrhs.Grid()->_rdimensions[0];
+    int _nbasis = sizeof(typename cobj::scalar_object)/sizeof(scalar);
+    GRID_ASSERT(nbasis==_nbasis);
+    GRID_ASSERT(coarse_mrhs.Grid()->_rdimensions[0]==nrhs);
+
+    BLAS_F.resize (fine_vol * words * nrhs );
+    BLAS_C.resize (coarse_vol * nbasis * nrhs );
+
+    ImportFineGridMrhsVectors(fine_mrhs,BLAS_F);
+    ProjectBLAS(nrhs);
+    ExportCoarseGridMrhsVectors(coarse_mrhs,BLAS_C);
+  }
+
+  template<class cobj>
+  void blockPromote(Field &fine_mrhs,Lattice<cobj> &coarse_mrhs)
+  {
+    int nrhs = fine_mrhs.Grid()->_rdimensions[0];
+    int _nbasis = sizeof(typename cobj::scalar_object)/sizeof(scalar);
+    GRID_ASSERT(nbasis==_nbasis);
+    GRID_ASSERT(coarse_mrhs.Grid()->_rdimensions[0]==nrhs);
+
+    BLAS_F.resize (fine_vol * words * nrhs );
+    BLAS_C.resize (coarse_vol * nbasis * nrhs );
+
+    ImportCoarseGridMrhsVectors(coarse_mrhs,BLAS_C);
+    PromoteBLAS(nrhs);
+    ExportFineGridMrhsVectors(fine_mrhs,BLAS_F);
+  }
+
+  ////////////////////////////////////////////////////////////////////////////
+  // Mixed orderings. A single RHS fine operator produces a vector of fine
+  // fields with no packing; the coarse side is still wanted in mrhs order.
+  ////////////////////////////////////////////////////////////////////////////
+  template<class cobj>
+  void blockProject(std::vector<Field> &fine,Lattice<cobj> &coarse_mrhs)
+  {
+    int nrhs = fine.size();
+    int _nbasis = sizeof(typename cobj::scalar_object)/sizeof(scalar);
+    GRID_ASSERT(nbasis==_nbasis);
+    GRID_ASSERT(coarse_mrhs.Grid()->_rdimensions[0]==nrhs);
+
+    BLAS_F.resize (fine_vol * words * nrhs );
+    BLAS_C.resize (coarse_vol * nbasis * nrhs );
+
+    ImportFineGridVectors(fine,BLAS_F);
+    ProjectBLAS(nrhs);
+    ExportCoarseGridMrhsVectors(coarse_mrhs,BLAS_C);
+  }
+
+  template<class cobj>
+  void blockProject(Field &fine_mrhs,std::vector< Lattice<cobj> > &coarse)
+  {
+    int nrhs = fine_mrhs.Grid()->_rdimensions[0];
+    int _nbasis = sizeof(typename cobj::scalar_object)/sizeof(scalar);
+    GRID_ASSERT(nbasis==_nbasis);
+    GRID_ASSERT(coarse.size()==nrhs);
+
+    BLAS_F.resize (fine_vol * words * nrhs );
+    BLAS_C.resize (coarse_vol * nbasis * nrhs );
+
+    ImportFineGridMrhsVectors(fine_mrhs,BLAS_F);
+    ProjectBLAS(nrhs);
+    ExportCoarseGridVectors(coarse,BLAS_C);
+  }
+
+  template<class cobj>
+  void blockPromote(std::vector<Field> &fine,Lattice<cobj> &coarse_mrhs)
+  {
+    int nrhs = fine.size();
+    int _nbasis = sizeof(typename cobj::scalar_object)/sizeof(scalar);
+    GRID_ASSERT(nbasis==_nbasis);
+    GRID_ASSERT(coarse_mrhs.Grid()->_rdimensions[0]==nrhs);
+
+    BLAS_F.resize (fine_vol * words * nrhs );
+    BLAS_C.resize (coarse_vol * nbasis * nrhs );
+
+    ImportCoarseGridMrhsVectors(coarse_mrhs,BLAS_C);
+    PromoteBLAS(nrhs);
+    ExportFineGridVectors(fine,BLAS_F);
+  }
+
+  template<class cobj>
+  void blockPromote(Field &fine_mrhs,std::vector< Lattice<cobj> > &coarse)
+  {
+    int nrhs = fine_mrhs.Grid()->_rdimensions[0];
+    int _nbasis = sizeof(typename cobj::scalar_object)/sizeof(scalar);
+    GRID_ASSERT(nbasis==_nbasis);
+    GRID_ASSERT(coarse.size()==nrhs);
+
+    BLAS_F.resize (fine_vol * words * nrhs );
+    BLAS_C.resize (coarse_vol * nbasis * nrhs );
+
+    ImportCoarseGridVectors(coarse,BLAS_C);
+    PromoteBLAS(nrhs);
+    ExportFineGridMrhsVectors(fine_mrhs,BLAS_F);
+  }
+
+  ////////////////////////////////////////////////////////////////////////////
+  // Pointer tables and the batched GEMM, shared by both orderings
+  ////////////////////////////////////////////////////////////////////////////
+  void BLASPointers(int nrhs,
+		    deviceVector<scalar *> &Vd,
+		    deviceVector<scalar *> &Fd,
+		    deviceVector<scalar *> &Cd)
+  {
+    for(int c=0;c<coarse_vol;c++){
+      scalar * Vh = & BLAS_V[c*nbasis*block_vol*words];
+      scalar * Fh = & BLAS_F[c*nrhs*block_vol*words];
+      scalar * Ch = & BLAS_C[c*nrhs*nbasis];
+      acceleratorPut(Vd[c],Vh);
+      acceleratorPut(Fd[c],Fh);
+      acceleratorPut(Cd[c],Ch);
+    }
+  }
+
+  // C_br = V^dag F
+  void ProjectBLAS(int nrhs)
+  {
+    deviceVector<scalar *> Vd(coarse_vol);
+    deviceVector<scalar *> Fd(coarse_vol);
+    deviceVector<scalar *> Cd(coarse_vol);
+    BLASPointers(nrhs,Vd,Fd,Cd);
+
+    GridBLAS BLAS;
+    int64_t vw = block_vol * words;
+    BLAS.gemmBatched(GridBLAS_OP_C,GridBLAS_OP_N,
+		     nbasis,nrhs,vw,
+		     scalar(1.0),
+		     Vd,
+		     Fd,
+		     scalar(0.0),  // wipe out C
+		     Cd);
+    BLAS.synchronise();
+  }
+
+  // F_xr = Vxb Cbr
+  void PromoteBLAS(int nrhs)
+  {
+    deviceVector<scalar *> Vd(coarse_vol);
+    deviceVector<scalar *> Fd(coarse_vol);
+    deviceVector<scalar *> Cd(coarse_vol);
+    BLASPointers(nrhs,Vd,Fd,Cd);
+
+    GridBLAS BLAS;
+    int64_t vw = block_vol * words;
+    BLAS.gemmBatched(GridBLAS_OP_N,GridBLAS_OP_N,
+		     vw,nrhs,nbasis,
+		     scalar(1.0),
+		     Vd,
+		     Cd,
+		     scalar(0.0),  // wipe out F
+		     Fd);
+    BLAS.synchronise();
+  }
 };
 
 NAMESPACE_END(Grid);

Grid/algorithms/iterative/AdefGeneric.h

@@ -54,6 +54,21 @@ class TwoLevelCG : public LinearFunction<Field>
   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,
@@ -103,6 +118,14 @@ 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
@@ -145,14 +168,19 @@ 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);
@@ -163,7 +191,9 @@ class TwoLevelCG : public LinearFunction<Field>
 	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]);
@@ -202,7 +232,24 @@ 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;
-    GridStopWatch PromTimer;
-    ProjTimer.Start();
     this->_Aggregates.ProjectToSubspace(PleftProj,tmp);
-    ProjTimer.Stop();
+    this->ProjectTimer.Stop();
-    CoarseTimer.Start();
+    this->ProjectCalls++;
+    this->CoarseTimer.Start();
     this->_CoarseSolver(PleftProj,PleftMss_proj); // Ass^{-1} [in - A Min]_s
-    CoarseTimer.Stop();
+    this->CoarseTimer.Stop();
-    PromTimer.Start();
+    this->CoarseCalls++;
+    this->PromoteTimer.Start();
     this->_Aggregates.PromoteFromSubspace(PleftMss_proj,tmp);// tmp = Q[in - A Min]
-    PromTimer.Stop();
+    this->PromoteTimer.Stop();
-    std::cout << GridLogPerformance << "PcgM1 breakdown "<<std::endl;
+    this->PromoteCalls++;
-    std::cout << GridLogPerformance << "\tSmoother   " << SmootherTimer.Elapsed() <<std::endl;
-    std::cout << GridLogPerformance << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
-    std::cout << GridLogPerformance << "\tProj       " << ProjTimer.Elapsed() <<std::endl;
-    std::cout << GridLogPerformance << "\tCoarse     " << CoarseTimer.Elapsed() <<std::endl;
-    std::cout << GridLogPerformance << "\tProm       " << PromTimer.Elapsed() <<std::endl;
 
     axpy(out,1.0,Min,tmp); // Min+tmp
   }

Grid/algorithms/iterative/Arnoldi.h

@@ -1,433 +0,0 @@
-/*************************************************************************************
-
-Grid physics library, www.github.com/paboyle/Grid 
-
-Source file: ./lib/algorithms/iterative/Arnoldi.h
-
-Copyright (C) 2015
-
-Author: Peter Boyle <paboyle@ph.ed.ac.uk>
-Author: paboyle <paboyle@ph.ed.ac.uk>
-Author: Patrick Oare <poare@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 */
-#ifndef GRID_ARNOLDI_H
-#define GRID_ARNOLDI_H
-
-NAMESPACE_BEGIN(Grid); 
-
-//Moved to KrylovSchur
-#if 0
-/**
-<<<<<<< HEAD
- * Options for which Ritz values to keep in implicit restart.
- */
-enum RitzFilter {
-  EvalNormSmall,           // Keep evals with smallest norm
-  EvalNormLarge,           // Keep evals with largest norm
-  EvalReSmall,             // Keep evals with smallest real part
-  EvalReLarge              // Keep evals with largest real part
-};
-
-// Select comparison function from RitzFilter
-struct ComplexComparator
-{
-  RitzFilter f;
-  ComplexComparator (RitzFilter _f) : f(_f) {}
-  bool operator()(std::complex<double> z1, std::complex<double> z2) { 
-    switch (f) {
-      RealD tmp1, tmp2;
-      tmp1=std::abs(std::imag(z1));
-      tmp2=std::abs(std::imag(z2));
-      case EvalNormSmall:
-        return std::abs(z1) < std::abs(z2);
-      case EvalNormLarge:
-        return std::abs(z1) > std::abs(z2);
-// Terrible hack
-//        return std::abs(std::real(z1)) < std::abs(std::real(z2));
-//	if ( std::abs(std::real(z1))  >4.) tmp1 +=1.;
-//	if ( std::abs(std::real(z2))  >4.) tmp2 +=1.;
-      case EvalReSmall:
-	  return tmp1 < tmp2;
-//        return std::abs(std::imag(z1)) < std::abs(std::imag(z2));
-      case EvalReLarge:
-	  return tmp1 > tmp2;
-//        return std::abs(std::real(z1)) > std::abs(std::real(z2));
-      default:
-        assert(0);
-    }
-  }
-};
-
-=======
->>>>>>> 68af1bba67dd62881ead5ab1e54962a5486a0791
-#endif
-
-/**
- * Implementation of the Arnoldi algorithm.
- */
-template<class Field> 
-class Arnoldi {
-
-  private:
-  
-    std::string cname = std::string("Arnoldi");
-    int MaxIter;   // Max iterations
-    RealD Tolerance;
-    RealD ssq;
-    RealD rtol;
-    int Nm;           // Number of basis vectors to track (equals MaxIter if no restart)
-    int Nk;           // Number of basis vectors to keep every restart (equals -1 if no restart)
-    int Nstop;       // Stop after converging Nstop eigenvectors.
-
-    LinearOperatorBase<Field> &Linop;
-    GridBase *Grid;
-
-    RealD approxLambdaMax;
-    RealD beta_k;
-    Field f;
-    std::vector<Field> basis;               // orthonormal Arnoldi basis
-    Eigen::MatrixXcd Hess;                  // Hessenberg matrix of size Nbasis (after construction)
-    Eigen::MatrixXcd Qt;                    // Transpose of basis rotation which projects out high modes.
-
-    Eigen::VectorXcd evals;                 // evals of Hess
-    Eigen::MatrixXcd littleEvecs;           // Nm x Nm evecs matrix
-    std::vector<Field> evecs;               // Vector of evec fields
-
-    RitzFilter ritzFilter;                        // how to sort evals
-
-  public:       
-
-    Arnoldi(LinearOperatorBase<Field> &_Linop, GridBase *_Grid, RealD _Tolerance, RitzFilter filter = EvalReSmall)
-      : Linop(_Linop), Grid(_Grid), Tolerance(_Tolerance), ritzFilter(filter), f(_Grid), MaxIter(-1), Nm(-1), Nk(-1), 
-          Nstop (-1), evals (0), evecs (), ssq (0.0), rtol (0.0), beta_k (0.0), approxLambdaMax (0.0)
-    {
-      f = Zero();
-    };
-
-    /**
-     * Runs the Arnoldi loop with(out) implicit restarting. For each iteration:
-     *   - Runs an Arnoldi step.
-     *   - Computes the eigensystem of the Hessenberg matrix.
-     *   - Performs implicit restarting.
-     */
-    void operator()(const Field& v0, int _maxIter, int _Nm, int _Nk, int _Nstop, bool doubleOrthog = false) {
-      MaxIter = _maxIter;
-      Nm = _Nm; Nk = _Nk;
-      Nstop = _Nstop;
-      
-      ssq = norm2(v0);
-      RealD approxLambdaMax = approxMaxEval(v0);
-      rtol = Tolerance * approxLambdaMax;
-
-      ComplexComparator compareComplex (ritzFilter);
-      std::cout << GridLogMessage << "Comparing Ritz values with: " << ritzFilter << std::endl;
-
-      int start = 1;
-      Field startVec = v0;
-      littleEvecs = Eigen::MatrixXcd::Zero(Nm, Nm);
-      for (int i = 0; i < MaxIter; i++) {
-        std::cout << GridLogMessage << "Restart Iteration " << i << std::endl;
-
-        // Perform Arnoldi steps to compute Krylov basis and Rayleigh quotient (Hess)
-        arnoldiIteration(startVec, Nm, start, doubleOrthog);
-        startVec = f;
-
-        // compute eigensystem and sort evals
-        // compute_eigensystem();
-        compute_eigensystem(Hess);
-        std::cout << GridLogMessage << "Eigenvalues after Arnoldi step: " << std::endl << evals << std::endl;
-
-        std::sort(evals.begin(), evals.end(), compareComplex);
-        std::cout << GridLogMessage << "Ritz values after sorting (first Nk preserved): " << std::endl << evals << std::endl;
-        // SU(N)::tepidConfiguration
-
-        // Implicit restart to de-weight unwanted eigenvalues
-        implicitRestart(_Nm, _Nk);      // probably can delete _Nm and _Nk from function args
-        start = Nk;
-
-        // check convergence and return if needed.
-        int Nconv = converged();
-        std::cout << GridLogMessage << "Number of evecs converged: " << Nconv << std::endl;
-        if (Nconv >= Nstop || i == MaxIter - 1) {
-          std::cout << GridLogMessage << "Converged with " << Nconv << " / " << Nstop << " eigenvectors on iteration " 
-                        << i << "." << std::endl;
-          basisRotate(evecs, Qt, 0, Nk, 0, Nk, Nm);
-          std::cout << GridLogMessage << "Eigenvalues [first " << Nconv << " converged]: " << std::endl << evals << std::endl;
-          return;
-        }
-      }      
-    }
-
-    /**
-     * Approximates the maximum eigenvalue of Linop.Op to normalize the residual and test for convergence. 
-     * 
-     * Parameters
-     * ----------
-     * Field& v0
-     *  Source field to start with. Must have non-zero norm.
-     * int MAX_ITER (default = 50)
-     *  Maximum number of iterations for power approximation. 
-     * 
-     * Returns
-     * -------
-     * RealD lamApprox
-     *  Approximation of largest eigenvalue. 
-     */
-    RealD approxMaxEval(const Field& v0, int MAX_ITER = 50) {
-      assert (norm2(v0) > 1e-8);                        // must have relatively large source norm to start
-      RealD lamApprox = 0.0;
-      RealD denom = 1.0; RealD num = 1.0;
-      Field v0cp (Grid); Field tmp (Grid);
-      v0cp = v0;
-      denom = std::sqrt(norm2(v0cp));
-      for (int i = 0; i < MAX_ITER; i++) {
-        Linop.Op(v0cp, tmp);                               // CAREFUL: do not do Op(tmp, tmp)
-        v0cp = tmp;
-        num = std::sqrt(norm2(v0cp));                      // num = |A^{n+1} v0|
-        lamApprox = num / denom;                           // lam = |A^{n+1} v0| / |A^n v0|
-        std::cout << GridLogDebug << "Approx for max eval: " << lamApprox << std::endl;
-        denom = num;                                       // denom = |A^{n} v0|
-      }
-      return lamApprox;
-    }
-
-    /**
-     * Constructs the Arnoldi basis for the Krylov space K_n(D, src). (TODO make private)
-     * 
-     * Parameters
-     * ----------
-     * v0 : Field&
-     *  Source to generate Krylov basis. 
-     * Nm : int
-     *  Final size of the basis desired. If the basis becomes complete before a basis of size Nm is constructed 
-     *  (determined by relative tolerance Tolerance), stops iteration there. 
-     * doubleOrthog : bool (default = false)
-     *  Whether to double orthogonalize the basis (for numerical cancellations) or not. 
-     * start        : int (default = 0)
-     *  If non-zero, assumes part of the Arnoldi basis has already been constructed. 
-     */
-    void arnoldiIteration(const Field& v0, int Nm, int start = 1, bool doubleOrthog = false)
-    {
-
-      ComplexD coeff;
-      Field w (Grid);           // A acting on last Krylov vector. 
-
-      if (start == 1) {       // initialize everything that we need.
-        RealD v0Norm = 1 / std::sqrt(ssq);
-        basis.push_back(v0Norm * v0);                // normalized source
-
-        Hess = Eigen::MatrixXcd::Zero(Nm, Nm);
-        f = Zero();
-      } else {
-        assert( start == basis.size() );      // should be starting at the end of basis (start = Nk)
-        Eigen::MatrixXcd HessCp = Hess;
-        Hess = Eigen::MatrixXcd::Zero(Nm, Nm);
-        Hess(Eigen::seqN(0, Nk), Eigen::seqN(0, Nk)) = HessCp;
-      }
-
-      // Construct next Arnoldi vector by normalizing w_i = Dv_i - \sum_j v_j h_{ji}
-      for (int i = start - 1; i < Nm; i++) {
-
-        Linop.Op(basis.back(), w);
-        for (int j = 0; j < basis.size(); j++) {
-          coeff = innerProduct(basis[j], w);       // coeff = h_{ij}. Note that since {vi} is ONB it's OK to subtract it off after. 
-          Hess(j, i) = coeff;
-          w -= coeff * basis[j];
-        }
-
-        if (doubleOrthog) {
-          // TODO implement
-        }
-
-        // add w_i to the pile
-        if (i < Nm - 1) {
-          coeff = std::sqrt(norm2(w));
-          Hess(i+1, i) = coeff;
-          basis.push_back(
-            (1.0/coeff) * w
-          );
-        }
-
-        // after iterations, update f and beta_k = ||f||
-        f = w;                                // make sure f is not normalized
-        beta_k = std::sqrt(norm2(f));         // beta_k = ||f_k|| determines convergence.
-      }
-
-      std::cout << GridLogMessage << "|f|^2 after Arnoldi step = " << norm2(f) << std::endl;
-      std::cout << GridLogDebug << "Computed Hessenberg matrix = " << std::endl << Hess << std::endl;
-
-      return;
-    }
-
-    /**
-     * Approximates the eigensystem of the linear operator by computing the eigensystem of 
-     * the Hessenberg matrix. Assumes that the Hessenberg matrix has already been constructed (by 
-     * calling the operator() function).
-     * 
-     * TODO implement in parent class eventually.
-     * 
-     * Parameters
-     * ----------
-     * Eigen::MatrixXcd& S
-     *  Schur matrix (upper triangular) similar to original Rayleigh quotient.
-     */
-    void compute_eigensystem(Eigen::MatrixXcd& S)
-    {
-
-      std::cout << GridLogMessage << "Computing eigenvalues." << std::endl;
-
-      evecs.clear();
-
-      Eigen::ComplexEigenSolver<Eigen::MatrixXcd> es;
-      es.compute(S);
-      evals = es.eigenvalues();
-      littleEvecs = es.eigenvectors();
-
-      // Convert evecs to lattice fields
-      for (int k = 0; k < evals.size(); k++) {
-        Eigen::VectorXcd vec = littleEvecs.col(k);
-        Field tmp (basis[0].Grid());
-        tmp = Zero();
-        for (int j = 0; j < basis.size(); j++) {
-          tmp = tmp + vec[j] * basis[j];
-        }
-        evecs.push_back(tmp);
-      }
-
-      std::cout << GridLogMessage << "Eigenvalues: " << std::endl << evals << std::endl;
-
-    }
-
-    /**
-     * Verifies the factorization DV = V^\dag H + f e^\dag with the last-computed 
-     * V, H, f. 
-     */
-    // RealD verifyFactorization() {
-    //   int k = basis.size();         // number of basis vectors, also the size of H.
-    //   std::vector<Field> factorized (k, Zero());
-    //   Field tmp (FGrid); tmp = Zero();
-    //   for (int i = 0; i < basis.size(); i++) {
-    //     Linop.Op(basis[i], tmp);
-    //   }
-    //   // basisRotate(basis, Q, 0, Nk, 0, Nk, Nm);
-    //   // Linop.Op(, )
-    // }
-
-    /* Getters */
-    Eigen::MatrixXcd    getHessenbergMat()  { return Hess; }
-    Field               getF()              { return f; }
-    std::vector<Field>  getBasis()          { return basis; }
-    Eigen::VectorXcd    getEvals()          { return evals; }
-    std::vector<Field>  getEvecs()          { return evecs; }
-
-    /**
-     * Implements implicit restarting for Arnoldi. Assumes eigenvalues are sorted. 
-     * 
-     * Parameters
-     * ----------
-     * int _Nm
-     *  Size of basis to keep (Hessenberg is MxM).
-     * int Nk
-     *  Number of basis vectors to keep at each restart.
-     */
-    void implicitRestart(int _Nm, int _Nk) {
-      assert ( _Nk <= _Nm );
-      Nm = _Nm; Nk = _Nk;
-      int Np = Nm - Nk;       // keep Nk smallest (or largest, depends on sort function) evecs
-      
-      std::cout << GridLogMessage << "Computing QR Factorizations." << std::endl;
-
-      Eigen::MatrixXcd Q = Eigen::MatrixXcd::Identity(Nm, Nm);
-      Eigen::MatrixXcd Qi (Nm, Nm);
-      Eigen::MatrixXcd R (Nm, Nm);
-
-      for (int i = Nk; i < Nm; i++) {        // keep the first Nk eigenvalues and iterate through the last Np. Should loop Np times
-
-        // Useful debugging output
-        std::cout << GridLogDebug << "Computing QR factorization for i = " << i << std::endl;
-        std::cout << GridLogDebug << "Eval shift = " << evals[i] << std::endl;
-        std::cout << GridLogDebug << "Hess before rotation: " << Hess << std::endl;
-
-        // QR factorize 
-        Eigen::HouseholderQR<Eigen::MatrixXcd> QR (Hess - evals[i] * Eigen::MatrixXcd::Identity(Nm, Nm));
-        Qi = QR.householderQ();
-        Q = Q * Qi;
-        Hess = Qi.adjoint() * Hess * Qi;
-
-        std::cout << GridLogDebug << "Qt up to i = " << Q.transpose() << std::endl;
-
-      }
-
-      std::cout << GridLogDebug << "Hess after all rotations: " << std::endl << Hess << std::endl; 
-
-      // form Arnoldi vector f: f is normal to the basis vectors and its norm \beta is used to determine the Ritz estimate. 
-      std::complex<double> beta = Hess(Nk, Nk-1);
-      std::complex<double> sigma = Q(Nm-1, Nk-1);
-      f = basis[Nk] * beta + f * sigma;
-      RealD betak = std::sqrt(norm2(f));
-      std::cout << GridLogMessage << "|f|^2 after implicit restart = " << norm2(f) << std::endl;
-
-      // Rotate basis by Qt
-      Qt = Q.transpose();
-      basisRotate(basis, Qt, 0, Nk + 1, 0, Nm, Nm);
-
-      // rotate
-      basisRotate(evecs, Qt, 0, Nk + 1, 0, Nm, Nm);
-
-      // Truncate the basis and restart
-      basis = std::vector<Field> (basis.begin(), basis.begin() + Nk);
-      // evecs = std::vector<Field> (evecs.begin(), evecs.begin() + Nk);
-      Hess = Hess(Eigen::seqN(0, Nk), Eigen::seqN(0, Nk));
-
-      std::cout << "evecs size: " << evecs.size() << std::endl;
-
-    }
-  
-    /**
-     * Computes the number of Arnoldi eigenvectors that have converged. An eigenvector s is considered converged 
-     * for a tolerance epsilon if 
-     *    r(s) := |\beta e_m^T s| < epsilon
-     * where beta is the norm of f_{m+1}.
-     * 
-     * Parameters
-     * ----------
-     * 
-     * Returns
-     * -------
-     * int : Number of converged eigenvectors.
-     */
-    int converged() {
-      int Nconv = 0;
-      for (int k = 0; k < evecs.size(); k++) {
-        RealD emTs = std::abs(littleEvecs(Nm - 1, k));           // e_m^T s
-        RealD ritzEstimate = beta_k * emTs;
-        // TODO should be ritzEstimate < Tolerance * lambda_max
-        std::cout << GridLogMessage << "Ritz estimate for evec " << k << " = " << ritzEstimate << std::endl;
-        if (ritzEstimate < rtol) {
-          Nconv++;
-        }
-      }
-      return Nconv;
-    }
-
-};
-    
-NAMESPACE_END(Grid);
-#endif

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/ConjugateGradientTimeslice.h

@@ -1,277 +0,0 @@
-/*************************************************************************************
-
-Grid physics library, www.github.com/paboyle/Grid
-
-Source file: ./lib/algorithms/iterative/ConjugateGradientTimeslice.h
-
-Copyright (C) 2015
-
-Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
-Author: Peter Boyle <paboyle@ph.ed.ac.uk>
-Author: paboyle <paboyle@ph.ed.ac.uk>
-
-This program is free software; you can redistribute it and/or modify
-it under the terms of the GNU General Public License as published by
-the Free Software Foundation; either version 2 of the License, or
-(at your option) any later version.
-
-This program is distributed in the hope that it will be useful,
-but WITHOUT ANY WARRANTY; without even the implied warranty of
-MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-GNU General Public License for more details.
-
-You should have received a copy of the GNU General Public License along
-with this program; if not, write to the Free Software Foundation, Inc.,
-51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
-
-See the full license in the file "LICENSE" in the top level distribution
-directory
-*************************************************************************************/
-			   /*  END LEGAL */
-#ifndef GRID_CONJUGATE_GRADIENT_TIMESLICE_H
-#define GRID_CONJUGATE_GRADIENT_TIMESLICE_H
-
-NAMESPACE_BEGIN(Grid);
-
-/////////////////////////////////////////////////////////////
-// Base classes for iterative processes based on operators
-// single input vec, single output vec.
-/////////////////////////////////////////////////////////////
-
-/**
- * Simple modification of conjugate gradient that outputs the residual as a function 
- * of time, in order to study the large wavelength behavior of the solver. 
- */
-
-
-template <class Field>
-class ConjugateGradientTimeslice : public OperatorFunction<Field> {
-public:
-
-  using OperatorFunction<Field>::operator();
-  
-  bool ErrorOnNoConverge;  // throw an assert when the CG fails to converge.
-                           // Defaults true.
-  RealD Tolerance;
-  Integer MaxIterations;
-  Integer IterationsToComplete; //Number of iterations the CG took to finish. Filled in upon completion
-  RealD TrueResidual;
-  
-  ConjugateGradientTimeslice(RealD tol, Integer maxit, bool err_on_no_conv = true)
-    : Tolerance(tol),
-      MaxIterations(maxit),
-      ErrorOnNoConverge(err_on_no_conv)
-  {};
-
-  virtual void LogIteration(int k,RealD a,RealD b){
-    //    std::cout << "ConjugageGradient::LogIteration() "<<std::endl;
-  };
-  virtual void LogBegin(void){
-    std::cout << "ConjugageGradient::LogBegin() "<<std::endl;
-  };
-
-    void operator()(LinearOperatorBase<Field> &Linop, const Field &src, Field &psi) {
-
-      this->LogBegin();
-
-      GRID_TRACE("ConjugateGradientTimeslice");
-    GridStopWatch PreambleTimer;
-    GridStopWatch ConstructTimer;
-    GridStopWatch NormTimer;
-    GridStopWatch AssignTimer;
-    PreambleTimer.Start();
-    psi.Checkerboard() = src.Checkerboard();
-
-    conformable(psi, src);
-
-    RealD cp, c, a, d, b, ssq, qq;
-    //RealD b_pred;
-
-    // Was doing copies
-    ConstructTimer.Start();
-    Field p  (src.Grid());
-    Field mmp(src.Grid());
-    Field r  (src.Grid());
-    ConstructTimer.Stop();
-
-    // Initial residual computation & set up
-    NormTimer.Start();
-    ssq = norm2(src);                 // Norm of source vector ||b||^2
-
-    ssqtx = localNorm2(src);          // Norm |b(x, t)|^2 as a field
-    std::vector<RealD> ssqt;          // Norm of source not summed over time slices, ssq(t) = \sum_x |b(x, t)|^2
-    sliceSum(ssqtx, ssqt, Tdir);      // TODO make sure Tdir is globally defined
-
-    RealD guess = norm2(psi);         // Norm of initial guess ||psi||^2
-    NormTimer.Stop();
-    assert(std::isnan(guess) == 0);
-    AssignTimer.Start();
-    if ( guess == 0.0 ) {
-      r = src;
-      p = r;
-      a = ssq;
-    } else { 
-      Linop.HermOpAndNorm(psi, mmp, d, b);        // 
-      r = src - mmp;      // Initial residual r0 = b - A guess
-      p = r;              // initial conj vector p0 = r0
-      a = norm2(p);
-    }
-    cp = a;
-    AssignTimer.Stop();
-
-    // Handle trivial case of zero src
-    if (ssq == 0.){
-      psi = Zero();
-      IterationsToComplete = 1;
-      TrueResidual = 0.;
-      return;
-    }
-
-    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient: guess " << guess << std::endl;
-    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:   src " << ssq << std::endl;
-    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:    mp " << d << std::endl;
-    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:   mmp " << b << std::endl;
-    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:  cp,r " << cp << std::endl;
-    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:     p " << a << std::endl;
-
-    RealD rsq = Tolerance * Tolerance * ssq;
-
-    // Check if guess is really REALLY good :)
-    if (cp <= rsq) {
-      TrueResidual = std::sqrt(a/ssq);
-      std::cout << GridLogMessage << "ConjugateGradient guess is converged already " << std::endl;
-      IterationsToComplete = 0;	
-      return;
-    }
-
-    std::cout << GridLogIterative << std::setprecision(8)
-              << "ConjugateGradient: k=0 residual " << cp << " target " << rsq << std::endl;
-
-    PreambleTimer.Stop();
-    GridStopWatch LinalgTimer;
-    GridStopWatch InnerTimer;
-    GridStopWatch AxpyNormTimer;
-    GridStopWatch LinearCombTimer;
-    GridStopWatch MatrixTimer;
-    GridStopWatch SolverTimer;
-
-    RealD usecs = -usecond();
-    SolverTimer.Start();
-    int k;
-    for (k = 1; k <= MaxIterations; k++) {
-
-      GridStopWatch IterationTimer;
-      IterationTimer.Start();
-      c = cp;
-
-      MatrixTimer.Start();
-      Linop.HermOp(p, mmp);         // Computes mmp = Ap
-      MatrixTimer.Stop();
-
-      LinalgTimer.Start();
-
-      InnerTimer.Start();
-      ComplexD dc  = innerProduct(p,mmp);         // p^\dagger A p
-      InnerTimer.Stop();
-      d = dc.real();
-      a = c / d;
-
-      // What is axpy? Some accelerator or something? Check Lattice_arith.h
-      AxpyNormTimer.Start();
-
-      // axpy_norm computes ax+by for vectors x and y compatible with a GPU. Here b is set to 1 (see the function in Lattice_reduction.h). 
-      // The first argument passes r by reference, so it stores r --> -a * Ap + 1 * r, i.e. it performs an update on 
-      // r_k --> r_{k+1} = r_k - \alpha_k A p_k. The function returns the norm squared of the first variable, i.e. ||r_{k+1}||^2.
-      cp = axpy_norm(r, -a, mmp, r);
-      AxpyNormTimer.Stop();
-      b = cp / c;
-
-      LinearCombTimer.Start();
-      {
-        autoView( psi_v , psi, AcceleratorWrite);
-        autoView( p_v   , p,   AcceleratorWrite);
-        autoView( r_v   , r,   AcceleratorWrite);
-        accelerator_for(ss,p_v.size(), Field::vector_object::Nsimd(),{
-            coalescedWrite(psi_v[ss], a      *  p_v(ss) + psi_v(ss));
-            coalescedWrite(p_v[ss]  , b      *  p_v(ss) + r_v  (ss));
-        });
-      }
-      LinearCombTimer.Stop();
-      LinalgTimer.Stop();
-      LogIteration(k,a,b);
-
-      IterationTimer.Stop();
-      if ( (k % 500) == 0 ) {
-        std::cout << GridLogMessage << "ConjugateGradient: Iteration " << k
-                << " residual " << sqrt(cp/ssq) << " target " << Tolerance << std::endl;
-      } else { 
-        std::cout << GridLogIterative << "ConjugateGradient: Iteration " << k
-                << " residual " << sqrt(cp/ssq) << " target " << Tolerance << " took " << IterationTimer.Elapsed() << std::endl;
-      }
-
-      // Stopping condition
-      if (cp <= rsq) {
-        usecs +=usecond();
-        SolverTimer.Stop();
-        Linop.HermOpAndNorm(psi, mmp, d, qq);
-        p = mmp - src;
-        GridBase *grid = src.Grid();
-        RealD DwfFlops = (1452. )*grid->gSites()*4*k
-   	               + (8+4+8+4+4)*12*grid->gSites()*k; // CG linear algebra
-        RealD srcnorm = std::sqrt(norm2(src));
-        RealD resnorm = std::sqrt(norm2(p));
-        RealD true_residual = resnorm / srcnorm;
-        std::cout << GridLogMessage << "ConjugateGradient Converged on iteration " << k 
-          << "\tComputed residual " << std::sqrt(cp / ssq)
-          << "\tTrue residual " << true_residual
-          << "\tTarget " << Tolerance << std::endl;
-
-        // GridLogMessage logs the message to the terminal output; GridLogPerformance probably writes to a log file?
-        //	std::cout << GridLogMessage << "\tPreamble   " << PreambleTimer.Elapsed() <<std::endl;
-        std::cout << GridLogMessage << "\tSolver Elapsed    " << SolverTimer.Elapsed() <<std::endl;
-        std::cout << GridLogPerformance << "Time breakdown "<<std::endl;
-        std::cout << GridLogPerformance << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
-        std::cout << GridLogPerformance << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
-        std::cout << GridLogPerformance << "\t\tInner      " << InnerTimer.Elapsed() <<std::endl;
-        std::cout << GridLogPerformance << "\t\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
-        std::cout << GridLogPerformance << "\t\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
-
-        std::cout << GridLogDebug << "\tMobius flop rate " << DwfFlops/ usecs<< " Gflops " <<std::endl;
-
-        if (ErrorOnNoConverge) assert(true_residual / Tolerance < 10000.0);
-
-        IterationsToComplete = k;	
-        TrueResidual = true_residual;
-
-        return;
-      }
-    }
-    // Failed. Calculate true residual before giving up                                                         
-    // Linop.HermOpAndNorm(psi, mmp, d, qq);
-    //    p = mmp - src;
-    //TrueResidual = sqrt(norm2(p)/ssq);
-    //    TrueResidual = 1;
-
-    std::cout << GridLogMessage << "ConjugateGradient did NOT converge "<<k<<" / "<< MaxIterations
-    	      <<" residual "<< std::sqrt(cp / ssq)<< std::endl;
-    SolverTimer.Stop();
-    std::cout << GridLogMessage << "\tPreamble   " << PreambleTimer.Elapsed() <<std::endl;
-    std::cout << GridLogMessage << "\tConstruct  " << ConstructTimer.Elapsed() <<std::endl;
-    std::cout << GridLogMessage << "\tNorm       " << NormTimer.Elapsed() <<std::endl;
-    std::cout << GridLogMessage << "\tAssign     " << AssignTimer.Elapsed() <<std::endl;
-    std::cout << GridLogMessage << "\tSolver     " << SolverTimer.Elapsed() <<std::endl;
-    std::cout << GridLogMessage << "Solver breakdown "<<std::endl;
-    std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
-    std::cout << GridLogMessage<< "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
-    std::cout << GridLogPerformance << "\t\tInner      " << InnerTimer.Elapsed() <<std::endl;
-    std::cout << GridLogPerformance << "\t\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
-    std::cout << GridLogPerformance << "\t\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
-
-    if (ErrorOnNoConverge) assert(0);
-    IterationsToComplete = k;
-
-  }
-};
-
-NAMESPACE_END(Grid);
-#endif

Grid/algorithms/iterative/ImplicitlyRestartedLanczos.h

@@ -53,18 +53,6 @@ enum IRLdiagonalisation {
   IRLdiagonaliseWithEigen
 };
 
-enum IRLeigsort { 
-  IRLeigsortMax,
-  IRLeigsortSqMin
-};
-
-#if 0
-bool square_comp(RealD a, RealD b){
-	if (a*a<b*b) return true;
-	return false;
-}
-#endif
-
 template<class Field> class ImplicitlyRestartedLanczosHermOpTester  : public ImplicitlyRestartedLanczosTester<Field>
 {
  public:
@@ -131,9 +119,8 @@ class ImplicitlyRestartedLanczos {
   /////////////////////////
   // Constructor
   /////////////////////////
- public:
-  IRLeigsort EigSort;
   
+public:       
 
   //////////////////////////////////////////////////////////////////
   // PAB:
@@ -167,7 +154,6 @@ class ImplicitlyRestartedLanczos {
     Nstop(_Nstop)  ,      Nk(_Nk),      Nm(_Nm),
     eresid(_eresid),      betastp(_betastp),
     MaxIter(_MaxIter)  ,      MinRestart(_MinRestart),
-    EigSort(IRLeigsortMax), 
     orth_period(_orth_period), diagonalisation(_diagonalisation)  { };
 
     ImplicitlyRestartedLanczos(LinearFunction<Field> & PolyOp,
@@ -184,7 +170,6 @@ class ImplicitlyRestartedLanczos {
     Nstop(_Nstop)  ,      Nk(_Nk),      Nm(_Nm),
     eresid(_eresid),      betastp(_betastp),
     MaxIter(_MaxIter)  ,      MinRestart(_MinRestart),
-    EigSort(IRLeigsortMax), 
     orth_period(_orth_period), diagonalisation(_diagonalisation)  { };
 
   ////////////////////////////////
@@ -331,12 +316,8 @@ until convergence
       // sorting
       //////////////////////////////////
       eval2_copy = eval2;
-//      if (EigSort==IRLeigsortMax)
-//      std::partial_sort(eval2.begin(),eval2.begin()+Nm,eval2.end(),square_comp);
-//      else
       std::partial_sort(eval2.begin(),eval2.begin()+Nm,eval2.end(),std::greater<RealD>());
       std::cout<<GridLogIRL <<" evals sorted "<<std::endl;
-//      eval2_copy = eval2;
       const int chunk=8;
       for(int io=0; io<k2;io+=chunk){
 	std::cout<<GridLogIRL << "eval "<< std::setw(3) << io ;
@@ -352,7 +333,6 @@ until convergence
       //////////////////////////////////
       Qt = Eigen::MatrixXd::Identity(Nm,Nm);
       for(int ip=k2; ip<Nm; ++ip){ 
-//        std::cout<<GridLogIRL <<"QR decompose "<<eval2[ip]<<std::endl;
 	QR_decomp(eval,lme,Nm,Nm,Qt,eval2[ip],k1,Nm);
       }
       std::cout<<GridLogIRL <<"QR decomposed "<<std::endl;
@@ -395,8 +375,7 @@ until convergence
 
 	//  power of two search pattern;  not every evalue in eval2 is assessed.
 	int allconv =1;
-//	for(int jj = 1; jj<=Nstop; jj*=2){
+	for(int jj = 1; jj<=Nstop; jj*=2){
-	for(int jj = 1; jj<=Nstop; jj++){
 	  int j = Nstop-jj;
 	  RealD e = eval2_copy[j]; // Discard the evalue
 	  basisRotateJ(B,evec,Qt,j,0,Nk,Nm);	    

Grid/algorithms/iterative/LanczosBidiagonalization.h

@@ -1,276 +0,0 @@
-/*************************************************************************************
-
-Grid physics library, www.github.com/paboyle/Grid
-
-Source file: ./Grid/algorithms/iterative/LanczosBidiagonalization.h
-
-Copyright (C) 2015
-
-Author: Chulwoo Jung <chulwoo@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 */
-#ifndef GRID_LANCZOS_BIDIAGONALIZATION_H
-#define GRID_LANCZOS_BIDIAGONALIZATION_H
-
-NAMESPACE_BEGIN(Grid);
-
-/**
- * Lanczos Bidiagonalization (Golub-Kahan)
- *
- * For a linear operator A with adjoint A^dag, constructs the bidiagonal
- * decomposition:
- *
- *   A  V_m = U_m B_m
- *   A^dag U_m = V_m B_m^T + beta_{m+1} v_{m+1} e_m^T
- *
- * where:
- *   V_m = [v_1, ..., v_m]  right Lanczos vectors (orthonormal)
- *   U_m = [u_1, ..., u_m]  left  Lanczos vectors (orthonormal)
- *   B_m is upper bidiagonal with diag(alpha_1,...,alpha_m) and
- *       superdiag(beta_2,...,beta_m)
- *
- * The singular values of A are approximated by those of B_m.
- * The singular values of B_m are the square roots of the eigenvalues of
- * the symmetric tridiagonal matrix B_m^T B_m.
- *
- * Usage:
- *   LanczosBidiagonalization<Field> lb(Linop, grid);
- *   lb.run(src, Nm, tol);
- *   // Access results via getters.
- */
-template <class Field>
-class LanczosBidiagonalization {
-
-  public: 
-  LinearOperatorBase<Field> &Linop;
-  GridBase *Grid;
-
-  int Nm;           // number of Lanczos steps taken
-  RealD Tolerance;  // convergence threshold on beta_{k+1} / alpha_k
-
-  std::vector<Field>  V;       // right Lanczos vectors v_1 ... v_m
-  std::vector<Field>  U;       // left  Lanczos vectors u_1 ... u_m
-  std::vector<RealD>  alpha;   // diagonal of bidiagonal matrix
-  std::vector<RealD>  beta;    // super-diagonal (beta[k] couples u_k and v_{k+1})
-
-  // SVD of the bidiagonal matrix (filled after computeSVD())
-  Eigen::VectorXd  singularValues;
-  Eigen::MatrixXd  leftSVecs;   // columns are left  singular vectors of B
-  Eigen::MatrixXd  rightSVecs;  // columns are right singular vectors of B
-
-public:
-
-  LanczosBidiagonalization(LinearOperatorBase<Field> &_Linop, GridBase *_Grid,
-                           RealD _tol = 1.0e-8)
-    : Linop(_Linop), Grid(_Grid), Tolerance(_tol), Nm(0)
-  {}
-
-  /**
-   * Run the Golub-Kahan Lanczos bidiagonalization.
-   *
-   * Parameters
-   * ----------
-   * src  : starting vector (need not be normalised)
-   * Nmax : maximum number of Lanczos steps
-   * reorth : if true, full reorthogonalisation of both V and U bases
-   */
-  void run(const Field &src, int Nmax, bool reorth = true)
-  {
-    assert(norm2(src) > 0.0);
-
-    V.clear(); U.clear();
-    alpha.clear(); beta.clear();
-    Nm = 0;
-
-    Field p(Grid), r(Grid);
-
-    // --- initialise: v_1 = src / ||src|| ---
-    Field v(Grid);
-    v = src;
-    RealD nrm = std::sqrt(norm2(v));
-    v = (1.0 / nrm) * v;
-    V.push_back(v);
-
-    for (int k = 0; k < Nmax; ++k) {
-
-      // p = A v_k
-      Linop.Op(V[k], p);
-
-      // p = p - beta_k * u_{k-1}   (remove previous left vector)
-      if (k > 0) {
-        p = p - beta[k-1] * U[k-1];
-      }
-
-      // alpha_k = ||p||
-      RealD ak = std::sqrt(norm2(p));
-      if (ak < 1.0e-14) {
-        std::cout << GridLogMessage
-                  << "LanczosBidiagonalization: lucky breakdown at step "
-                  << k << " (alpha = " << ak << ")" << std::endl;
-        break;
-      }
-      alpha.push_back(ak);
-
-      // u_k = p / alpha_k
-      Field u(Grid);
-      u = (1.0 / ak) * p;
-
-      // full reorthogonalisation of u against previous U
-      if (reorth) {
-        for (int j = 0; j < (int)U.size(); ++j) {
-          ComplexD ip = innerProduct(U[j], u);
-          u = u - ip * U[j];
-        }
-        RealD unrm = std::sqrt(norm2(u));
-        if (unrm > 1.0e-14) u = (1.0 / unrm) * u;
-      }
-      U.push_back(u);
-
-      // r = A^dag u_k - alpha_k * v_k
-      Linop.AdjOp(U[k], r);
-      r = r - ak * V[k];
-
-      // full reorthogonalisation of r against previous V
-      if (reorth) {
-        for (int j = 0; j < (int)V.size(); ++j) {
-          ComplexD ip = innerProduct(V[j], r);
-          r = r - ip * V[j];
-        }
-      }
-
-      // beta_{k+1} = ||r||
-      RealD bk = std::sqrt(norm2(r));
-      beta.push_back(bk);
-
-      Nm = k + 1;
-
-      std::cout << GridLogMessage
-                << "LanczosBidiagonalization step " << k
-                << "  alpha = " << ak
-                << "  beta  = " << bk << std::endl;
-
-      // convergence: residual beta / alpha small enough
-      if (bk / ak < Tolerance) {
-        std::cout << GridLogMessage
-                  << "LanczosBidiagonalization converged at step " << k
-                  << "  (beta/alpha = " << bk / ak << ")" << std::endl;
-        break;
-      }
-
-      if (k == Nmax - 1) break;   // no v_{k+2} needed after last step
-
-      // v_{k+1} = r / beta_{k+1}
-      Field vnext(Grid);
-      vnext = (1.0 / bk) * r;
-      V.push_back(vnext);
-    }
-  }
-
-  /**
-   * Compute the SVD of the bidiagonal matrix B using Eigen.
-   * Singular values are stored in descending order.
-   */
-  void computeSVD()
-  {
-    int m = Nm;
-    Eigen::MatrixXd B = Eigen::MatrixXd::Zero(m, m);
-
-    for (int k = 0; k < m; ++k) {
-      B(k, k) = alpha[k];
-      if (k + 1 < m && k < (int)beta.size())
-        B(k, k+1) = beta[k];
-    }
-
-    Eigen::JacobiSVD<Eigen::MatrixXd> svd(B,
-        Eigen::ComputeThinU | Eigen::ComputeThinV);
-
-    singularValues = svd.singularValues();   // already sorted descending
-    leftSVecs      = svd.matrixU();
-    rightSVecs     = svd.matrixV();
-
-    std::cout << GridLogMessage
-              << "LanczosBidiagonalization: singular values of B_" << m
-              << std::endl;
-    for (int k = 0; k < m; ++k)
-      std::cout << GridLogMessage << "  sigma[" << k << "] = "
-                << singularValues(k) << std::endl;
-  }
-
-  /**
-   * Return the k-th approximate left singular vector of A in the full
-   * lattice space.  computeSVD() must have been called first.
-   */
-  Field leftSingularVector(int k)
-  {
-    assert(k < (int)leftSVecs.cols());
-    Field svec(Grid);
-    svec = Zero();
-    for (int j = 0; j < Nm; ++j)
-      svec = svec + leftSVecs(j, k) * U[j];
-    return svec;
-  }
-
-  /**
-   * Return the k-th approximate right singular vector of A in the full
-   * lattice space.  computeSVD() must have been called first.
-   */
-  Field rightSingularVector(int k)
-  {
-    assert(k < (int)rightSVecs.cols());
-    Field svec(Grid);
-    svec = Zero();
-    for (int j = 0; j < Nm; ++j)
-      svec = svec + rightSVecs(j, k) * V[j];
-    return svec;
-  }
-
-  /**
-   * Verify the bidiagonalization: returns max residual
-   *   max_k || A v_k - alpha_k u_k - beta_k u_{k-1} ||
-   */
-  RealD verify()
-  {
-    Field tmp(Grid);
-    RealD maxres = 0.0;
-    for (int k = 0; k < Nm; ++k) {
-      Linop.Op(V[k], tmp);
-      tmp = tmp - alpha[k] * U[k];
-      if (k > 0 && k-1 < (int)beta.size())
-        tmp = tmp - beta[k-1] * U[k-1];
-      RealD res = std::sqrt(norm2(tmp));
-      if (res > maxres) maxres = res;
-      std::cout << GridLogMessage
-                << "LanczosBidiagonalization verify step " << k
-                << "  ||A v_k - alpha_k u_k - beta_{k-1} u_{k-1}|| = "
-                << res << std::endl;
-    }
-    return maxres;
-  }
-
-  /* Getters */
-  int                       getNm()           const { return Nm; }
-  const std::vector<Field>& getV()            const { return V; }
-  const std::vector<Field>& getU()            const { return U; }
-  const std::vector<RealD>& getAlpha()        const { return alpha; }
-  const std::vector<RealD>& getBeta()         const { return beta; }
-  Eigen::VectorXd           getSingularValues() const { return singularValues; }
-};
-
-NAMESPACE_END(Grid);
-#endif

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), 
@@ -66,28 +74,18 @@ public:
     Linop(_Linop),
     Preconditioner(Prec),
     mmax(_mmax),
-    nstep(_nstep)         // what is nstep vs mmax? one is the number of inner iterations
+    nstep(_nstep)
   {
-    level=1;
+    Level(1);
     verbose=1;
   };
 
-  // virtual method stubs for updating GCR polynomial
-  virtual void LogBegin(void){
-    std::cout << "GCR::LogBegin() "<<std::endl;
-  };
-  virtual void LogIteration(int k, ComplexD a, std::vector<ComplexD> betas){
-    std::cout << "GCR::LogIteration() "<<std::endl;
-  };
-  virtual void LogComplete(std::vector<ComplexD>& alphas, std::vector<std::vector<ComplexD>>& betas) {
-    std::cout << "GCR::LogComplete() "<<std::endl;
-  };
-
   void operator() (const Field &src, Field &psi){
 
     //    psi=Zero();
     RealD cp, ssq,rsq;
     ssq=norm2(src);
+    SSQ=ssq;
     rsq=Tolerance*Tolerance*ssq;
       
     Field r(src.Grid());
@@ -100,13 +98,15 @@ 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) {
+
 	SolverTimer.Stop();
 
 	Linop.Op(psi,r);
@@ -145,29 +145,31 @@ public:
     ////////////////////////////////
     // history for flexible orthog
     ////////////////////////////////
-    std::vector<Field> q(mmax,grid);        // q = Ap
+    std::vector<Field> q(mmax,grid);
-    std::vector<Field> p(mmax,grid);        // store mmax conjugate momenta
+    std::vector<Field> p(mmax,grid);
-    std::vector<RealD> qq(mmax);            // qq = (Ap)^2 = <p|A^\dagger A |p> (denom of \alpha)
+    std::vector<RealD> qq(mmax);
       
     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.
     //////////////////////////////////
+    if (ZeroGuess && FirstCycle) {
+      psi = Zero();
+      LinalgTimer.Start();
+      r = src;
+      LinalgTimer.Stop();
+    } else {
       MatTimer.Start();
       Linop.Op(psi,Az);
-    //    zAz = innerProduct(Az,psi);
-    zAAz= norm2(Az);
       MatTimer.Stop();
-    
-
       LinalgTimer.Start();
       r=src-Az;
       LinalgTimer.Stop();
-    GCRLogLevel<< "PGCR true residual r = src - A psi   "<< norm2(r) <<std::endl;
+    }
-
+    FirstCycle=0;
-    this->LogBegin();       // initialize polynomial GCR if needed (TODO think about placement of this)
 
     /////////////////////
     // p = Prec(r)
@@ -191,45 +193,32 @@ public:
     q[0]= Az;
     qq[0]= zAAz;
     
-    std::cout << "||init p - src||: " << norm2(p[0] - src) << std::endl;   // for debugging
-    
     cp =norm2(r);
     LinalgTimer.Stop();
-
+    GCRLogLevel<< "PGCR true residual "<< sqrt(cp/SSQ)     <<std::endl;
-    std::vector<ComplexD> all_alphas;
-    std::vector<std::vector<ComplexD>> all_betas;
 
     for(int k=0;k<nstep;k++){
 
       steps++;
 
       int kp     = k+1;
-      int peri_k = k %mmax;     // only store mmax vectors; just roll around if needed
+      int peri_k = k %mmax;
       int peri_kp= kp%mmax;
 
-      // std::cout << "peri_kp = " << peri_kp << std::endl;
-
       LinalgTimer.Start();
       rq= innerProduct(q[peri_k],r); // what if rAr not real?
-      a = rq/qq[peri_k];              // compute alpha_j
+      a = rq/qq[peri_k];
 
-      all_alphas.push_back(a);
+      axpy(psi,a,p[peri_k],psi);         
 
-      axpy(psi,a,p[peri_k],psi);      // update psi --> psi + \alpha p
+      cp = axpy_norm(r,-a,q[peri_k],r);
-
-      cp = axpy_norm(r,-a,q[peri_k],r);       // update r --> r - \alpha D p. Note q = Dp
       LinalgTimer.Stop();
 
-      // LogIterationA(k + 1, a);
+      GCRLogLevel<< "PGCR step["<<steps<<"]  resid " << sqrt(cp/SSQ)<<std::endl;
-
-      GCRLogLevel<< "GCR step["<<steps<<"]  resid " << cp << " target " <<rsq<<std::endl; 
-
-      // moving this to end of loop so that it doesn't exit beforehand
-      // TODO if I want to uncomment this, I have to split the LogIteration again and put LogIterationA() beforehand
-      // if((k==nstep-1)||(cp<rsq)){
-      //   return cp;
-      // }
 
+      if((k==nstep-1)||(cp<rsq)){
+	return cp;
+      }
 
       PrecTimer.Start();
       Preconditioner(r,z);// solve Az = r
@@ -246,205 +235,24 @@ public:
       q[peri_kp]=Az;
       p[peri_kp]=z;
 
-      // Field Dsrc (grid);
-      // Linop.Op(src, Dsrc);
-      // std::cout << "||q[peri_kp] - D(src)||: " << norm2(q[peri_kp] - Dsrc) << std::endl;   // for debugging
-
-          // // delete after testing
-          // std::cout << "Testing Dsq on one for GCR: " << std::endl;
-          // Field myField (grid);
-          // myField = 1.0;
-          // Field out1 (grid); Field out2 (grid);
-          // Linop.HermOp(myField, out1);
-          // Linop.Op(myField, out2);
-          // std::cout << "Dsq.Hermop(ones) has norm " << norm2(out1) << std::endl;
-          // std::cout << "Dsq.Op(ones) has norm " << norm2(out2) << std::endl;
-
-      // basically northog = k+1 if mmax is large
       int northog = ((kp)>(mmax-1))?(mmax-1):(kp);  // if more than mmax done, we orthog all mmax history.
-      // std::cout << "northog: " << northog << std::endl;
-      std::vector<ComplexD> betas (northog);
-      // std::cout << "peri_kp: " << peri_kp << std::endl;
-      // we iterate backwards counting down from the current k+1 index (peri_kp) because we 
       for(int back=0;back<northog;back++){
 
 	int peri_back=(k-back)%mmax;   	  GRID_ASSERT((k-back)>=0);
 
-        // b=-real(innerProduct(q[peri_back],Az))/qq[peri_back];
+	b=-real(innerProduct(q[peri_back],Az))/qq[peri_back];
-        b=-(innerProduct(q[peri_back],Az))/qq[peri_back];     // TODO try complex beta
 	p[peri_kp]=p[peri_kp]+b*p[peri_back];
 	q[peri_kp]=q[peri_kp]+b*q[peri_back];
 
-        // LogIterationB(peri_back, b);
-        // betas[back] = b;    // may need to change the indexing if I ever do it with restarts
-        // std::cout << "[DEBUG] pushing beta for back = " << back << ", peri_back = " << peri_back << std::endl;
-
-        betas[peri_back] = b;    // may need to change the indexing if I ever do it with restarts
-
       }
       qq[peri_kp]=norm2(q[peri_kp]); // could use axpy_norm
       LinalgTimer.Stop();
-
-      // log iteration and update GCR polynomial if necessary.
-      all_betas.push_back(betas);
-      LogIteration(k + 1, a, betas);
-
-      // finish if necessary
-      if((k==nstep-1)||(cp<rsq)){
-        std::cout << "All alphas: " << std::endl << all_alphas << std::endl;
-        std::cout << "All betas: " << std::endl << all_betas << std::endl;
-        LogComplete(all_alphas, all_betas);
-        std::cout << "Exiting GCR." << std::endl;
-        return cp;
-      }
-
     }
     GRID_ASSERT(0); // never reached
     return cp;
   }
 };
-
-class PolynomialFile: Serializable {
-  public:
-    GRID_SERIALIZABLE_CLASS_MEMBERS(PolynomialFile, 
-      std::vector<std::vector<std::complex<double>>>, data,
-      std::vector<std::vector<std::complex<double>>>, betas,
-      std::vector<std::complex<double>>,              alphas
-    );
-};
-
-// Optionally record the GCR polynomial. [PO]: TODO
-template <class Field>
-class PGCRPolynomial : public PrecGeneralisedConjugateResidualNonHermitian<Field> {
-public:
-  std::vector<ComplexD> ak;
-  std::vector<std::vector<ComplexD>> bk;
-  // std::vector<ComplexD> poly_p;
-  std::vector<std::vector<ComplexD>> poly_p;
-  std::vector<ComplexD> poly_Ap;        // polynomial in Ap_j (only store it for last p)
-  std::vector<ComplexD> poly_r;
-  std::vector<ComplexD> polynomial;
-
-  PolynomialFile& PF;
-
-public:
-  PGCRPolynomial(RealD tol, Integer maxit,LinearOperatorBase<Field> &_Linop, LinearFunction<Field> &Prec, int _mmax, int _nstep, PolynomialFile& _PF)
-    : PrecGeneralisedConjugateResidualNonHermitian<Field>(tol, maxit, _Linop, Prec, _mmax, _nstep), PF(_PF)
-  {};
-
-  // think this applies the polynomial in A = Linop to a field src. The coeffs are 
-  // stored in the vector `polynomial`.
-  void PolyOp(const Field &src, Field &psi)
-  {
-    Field tmp(src.Grid());
-    Field AtoN(src.Grid());
-    AtoN = src;
-    psi=AtoN*polynomial[0];
-    for(int n=1;n<polynomial.size();n++){
-      tmp = AtoN;
-      this->Linop.Op(tmp,AtoN);               // iterate A^n
-      psi = psi + polynomial[n]*AtoN;       // psi += poly_n A^n src
-    }
-  }
-
-  // [PO TODO] debug this
-  void PGCRsequence(const Field &src, Field &x)
-  {
-    Field Ap(src.Grid());
-    Field r(src.Grid());
-    // Field p(src.Grid());
-    // p=src;
-    std::vector<Field> p;
-    p.push_back(src);
-    r=src;
-    x=Zero();
-    x.Checkerboard()=src.Checkerboard();
-    for(int k=0;k<ak.size();k++){
-      x = x + ak[k]*p[k];
-      this->Linop.Op(p[k], Ap);
-      r = r - ak[k] * Ap;
-      // p[k] = r;
-      p.push_back(r);
-      for (int i = 0; i < k; i++) {     // [PO TODO] check indices
-        p[k+1] += bk[i, k+1] * p[i];
-      }
-      // p = r + bk[k] * p;
-    }
-  }
-
-  void Solve(const Field &src, Field &psi)
-  {
-    psi=Zero();
-    this->operator()(src, psi);
-  }
-
-  virtual void LogBegin(void)
-  {
-    std::cout << "PGCR::LogBegin() "<<std::endl;
-    ak.resize(0);
-    bk.resize(0);
-    polynomial.resize(0);
-    poly_Ap.push_back(0.0);     // start with (0.0); during first iteration should change to (0.0, 1.0)
-    std::vector<ComplexD> p0_tmp;
-    p0_tmp.push_back(1.0);
-    poly_p.push_back(p0_tmp);
-    poly_r.push_back(1.0);
-  };
-
-  // Updates vector psi and r and initializes vector p[k+1]
-  virtual void LogIteration(int k, ComplexD a, std::vector<ComplexD> betas){
-    std::cout << "PGCR::LogIteration(k = " << k << ")" << std::endl;
-    ak.push_back(a);
-    bk.push_back(betas);
-
-    // update Ap by pushing p[k] to the right
-    poly_Ap.push_back(0.0);   // need to pad the end with an element
-    poly_Ap[0] = 0.0;         // technically this should be unnecessary, as the first component is never set
-    for(int i = 0; i < k; i++){
-      poly_Ap[i+1]=poly_p[k-1][i];        // A\vec{p} = (0, \vec{p}) bc A shifts components of p to the right
-    }
-
-    // update psi_{k+1} --> psi_k + a_k p_k
-    polynomial.push_back(0.0);
-    for(int i = 0; i < k; i++) {
-      polynomial[i] += a * poly_p[k-1][i];
-    }
-    {
-      std::vector<std::complex<double>> poly_stdcmplx(polynomial.begin(), polynomial.end());
-      PF.data.push_back(poly_stdcmplx);
-    }
-
-    //  r_{k+1} --> r_k - a_k A p_k
-    //  p_{k+1} --> r_k + \sum_{i=0}^k \beta_{ik} p_i, input betas = (\beta_{ik})_i
-    poly_r.push_back(0.0);        // should be of size k+1 if we start with k = 1
-    std::vector<ComplexD> p_next (k + 1, ComplexD(0.0));     // p_{k+1} = same size as r_{k+1}
-    for(int i = 0; i < k + 1; i++){
-      poly_r[i] = poly_r[i] - a * poly_Ap[i];     // update r_{k+1} --> r_k - \alpha_k A p_k
-      p_next[i] = poly_r[i];                 // init new vector as r_{k+1}
-    }
-
-    // p_{k+1} --> p_{k+1} + \sum_i \beta_{ij} p_i
-    int nbeta = betas.size();
-    std::cout << "Betas: " << betas << std::endl;
-    for (int j = 0; j < nbeta; j++) {
-      for (int i = 0; i < j+1; i++) {
-        p_next[i] += betas[j] * poly_p[j][i];
-      }
-    }
-    poly_p.push_back(p_next);                 // add p_{k+1} to the list of p's
-  }
-
-  virtual void LogComplete(std::vector<ComplexD>& alphas, std::vector<std::vector<ComplexD>>& betas) {
-    /** Logs all alphas and betas to complete the iterations. */
-    std::cout << "PGCR::LogComplete() "<<std::endl;
-    for (int i = 0; i < alphas.size(); i++) {
-      PF.alphas.push_back(std::complex<double>(alphas[i].real(), alphas[i].imag()));
-      std::vector<std::complex<double>> beta_stdcmplx(betas[i].begin(), betas[i].end());
-      PF.betas.push_back(beta_stdcmplx);
-    }
-  };
-
-};
-
 NAMESPACE_END(Grid);
+
+#undef GCRLogLevel
 #endif

Grid/algorithms/iterative/RestartedLanczosBidiagonalization.h

@@ -1,623 +0,0 @@
-/*************************************************************************************
-
-Grid physics library, www.github.com/paboyle/Grid
-
-Source file: ./Grid/algorithms/iterative/RestartedLanczosBidiagonalization.h
-
-Copyright (C) 2015
-
-Author: Chulwoo Jung <chulwoo@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 */
-#ifndef GRID_RESTARTED_LANCZOS_BIDIAGONALIZATION_H
-#define GRID_RESTARTED_LANCZOS_BIDIAGONALIZATION_H
-
-NAMESPACE_BEGIN(Grid);
-
-/**
- * Implicitly Restarted Lanczos Bidiagonalization (IRLBA)
- *
- * Computes the p largest (or p smallest) singular triplets of a linear
- * operator A using the Golub-Kahan-Lanczos bidiagonalization with implicit
- * restart via thick-restart / QR shifts.
- *
- * Algorithm (Baglama & Reichel, SIAM J. Sci. Comput. 27(1):19-42, 2005):
- *
- *   Outer loop:
- *     1. Extend the p-step (or seed) bidiagonalization to k steps:
- *           A  V_k = U_k B_k
- *           A^dag U_k = V_k B_k^T + beta_{k+1} v_{k+1} e_k^T
- *     2. Compute SVD:  B_k = X Sigma Y^T
- *     3. Check convergence of the p desired singular values via
- *           |beta_{k+1} * y_{k,i}|  <  tol * sigma_i
- *        where y_{k,i} is the last component of the i-th right singular vector.
- *     4. Apply k-p implicit QR shifts to implicitly compress the basis
- *        to p steps (Sorensen-Lehoucq thick restart):
- *           B_p^+ = X_p^T B_k Y_p   (upper bidiagonal, p x p)
- *        and update the lattice vectors:
- *           V_p^+ = V_k Y_p
- *           U_p^+ = U_k X_p
- *        The new residual coupling is
- *           beta_p^+ v_{p+1}^+ = beta_{k+1} v_{k+1} * (e_k^T Y_p)_p
- *                               + B_k(p,p+1) * (orthogonal tail from QR)
- *     5. Go to step 1.
- *
- * Template parameter
- * ------------------
- *   Field : lattice field type (must support Grid algebra operations)
- *
- * Usage
- * -----
- *   RestartedLanczosBidiagonalization<Field> irlba(Linop, grid, p, k, tol, maxIter);
- *   irlba.run(src);
- *   // Results available via getters.
- */
-template <class Field>
-class RestartedLanczosBidiagonalization {
-
-public:
-  LinearOperatorBase<Field> &Linop;
-  GridBase *Grid;
-
-  int    Nk;       // number of desired singular triplets
-  int    Nm;       // Lanczos basis size (Nm > Nk)
-  RealD  Tolerance;
-  int    MaxIter;
-  bool   largest; // if true, target largest singular values; otherwise smallest
-
-  // Converged singular triplets (filled after run())
-  std::vector<RealD>  singularValues;   // sigma_0 >= sigma_1 >= ...
-  std::vector<Field>  leftVectors;      // approximate left singular vectors
-  std::vector<Field>  rightVectors;     // approximate right singular vectors
-
-private:
-  // Working bases (size up to Nm+1)
-  std::vector<Field>  V;    // right Lanczos vectors
-  std::vector<Field>  U;    // left  Lanczos vectors
-  std::vector<RealD>  alpha;
-  std::vector<RealD>  beta;
-
-  // After a thick restart, the column at index restart_col of U^dag A V
-  // has extra non-zero entries (rows 0..restart_col-2) beyond what the
-  // upper bidiagonal captures.  fvec[j] = <U[j] | A V[restart_col]> for
-  // j = 0..restart_col-1.  (fvec[restart_col-1] == beta[restart_col-1].)
-  // reset_col == -1 means no restart has occurred yet (pure bidiagonal).
-  std::vector<RealD>  fvec;
-  int                 restart_col;
-
-public:
-
-  RestartedLanczosBidiagonalization(LinearOperatorBase<Field> &_Linop,
-                                    GridBase *_Grid,
-                                    int _Nk, int _Nm,
-                                    RealD _tol   = 1.0e-8,
-                                    int   _maxIt = 300,
-                                    bool  _largest = true)
-    : Linop(_Linop), Grid(_Grid),
-      Nk(_Nk), Nm(_Nm),
-      Tolerance(_tol), MaxIter(_maxIt),
-      largest(_largest)
-  {
-    assert(Nm > Nk);
-  }
-
-  /**
-   * Run IRLBA starting from src.
-   * On exit, singularValues, leftVectors, rightVectors are filled with
-   * the Nk converged singular triplets.
-   */
-  void run(const Field &src)
-  {
-    assert(norm2(src) > 0.0);
-
-    singularValues.clear();
-    leftVectors.clear();
-    rightVectors.clear();
-
-    // Allocate working bases
-    V.clear(); U.clear();
-    alpha.clear(); beta.clear();
-    fvec.clear(); restart_col = -1;
-    V.reserve(Nm + 1);
-    U.reserve(Nm);
-
-    // Seed: v_0 = src / ||src||
-    Field vtmp(Grid);
-    vtmp = src;
-    RealD nrm = std::sqrt(norm2(vtmp));
-    vtmp = (1.0 / nrm) * vtmp;
-    V.push_back(vtmp);
-
-    int pStart = 0;  // current basis size at start of extension
-    RealD betaRestart = 0.0; // coupling from previous restart
-
-    for (int iter = 0; iter < MaxIter; ++iter) {
-
-      // ----------------------------------------------------------------
-      // Step 1: extend from pStart steps to Nm steps
-      // ----------------------------------------------------------------
-      extendBasis(pStart, Nm, betaRestart);
-      verify();
-
-      // ----------------------------------------------------------------
-      // Step 2: SVD of the Nm x Nm B matrix.
-      // iter=0 (pStart==0): B is exactly bidiagonal — use buildBidiagonal.
-      // iter>0 (pStart==Nk): after a thick restart, column restart_col of
-      // U^dag A V has extra off-diagonal entries captured by fvec; use
-      // buildFullB so the Ritz values and restart vectors are computed from
-      // the exact projected matrix A V = U B_full.
-      // ----------------------------------------------------------------
-      Eigen::MatrixXd B = (pStart == 0) ? buildBidiagonal(Nm) : buildFullB(Nm);
-      Eigen::JacobiSVD<Eigen::MatrixXd> svd(B,
-          Eigen::ComputeThinU | Eigen::ComputeThinV);
-
-      Eigen::VectorXd sigma = svd.singularValues();  // descending
-      Eigen::MatrixXd X     = svd.matrixU();          // Nm x Nm left SVecs of B
-      Eigen::MatrixXd Y     = svd.matrixV();          // Nm x Nm right SVecs of B
-
-      // If targeting smallest, reorder so desired ones come first
-      Eigen::VectorXi order = sortOrder(sigma);
-
-      // ----------------------------------------------------------------
-      // Step 3: check convergence of the Nk desired singular values
-      // ----------------------------------------------------------------
-      RealD betaK = beta.back();  // beta_{k+1}
-      // In our convention A V = U B (exact), the residual is in the A^dag
-      // direction: A^dag u_j - sigma_j v_j = betaK * X[Nm-1,j] * V[Nm].
-      // Convergence criterion: |betaK * X[Nm-1, idx]| < tol * sigma_idx.
-      int nconv = 0;
-      for (int i = 0; i < Nk; ++i) {
-        int idx = order(i);
-        RealD res = std::abs(betaK * X(Nm - 1, idx));
-        RealD thr = Tolerance * std::max(sigma(idx), 1.0e-14);
-        std::cout << GridLogMessage
-                  << "IRLBA iter " << iter
-                  << "  sigma[" << i << "] = " << sigma(idx)
-                  << "  res = " << res
-                  << "  thr = " << thr << std::endl;
-        if (res < thr) ++nconv;
-        else break;  // residuals not strictly ordered but break is conservative
-      }
-
-      if (nconv >= Nk) {
-        std::cout << GridLogMessage
-                  << "IRLBA converged: " << nconv << " singular values after "
-                  << iter + 1 << " iterations." << std::endl;
-        // Collect converged triplets
-        extractTriplets(Nm, sigma, X, Y, order, Nk);
-        return;
-      }
-
-      // ----------------------------------------------------------------
-      // Step 4: implicit restart — compress to Nk steps
-      // ----------------------------------------------------------------
-      implicitRestart(Nm, Nk, sigma, X, Y, order, betaK, betaRestart);
-      verify();
-
-      // Lucky breakdown: exact invariant subspace found; convergence is exact.
-      // B_p^+ = diag(alpha[0..Nk-1]); extract directly from restart basis.
-      if (betaRestart < 1.0e-14) {
-        std::cout << GridLogMessage
-                  << "IRLBA: lucky breakdown after restart (betaRestart = 0)."
-                  << " Extracting " << Nk << " exact Ritz triplets." << std::endl;
-        // Re-run SVD on the p-step diagonal B^+ to get sorted Ritz triplets.
-        Eigen::MatrixXd Bp = buildBidiagonal(Nk);
-        Eigen::JacobiSVD<Eigen::MatrixXd> svdp(Bp,
-            Eigen::ComputeThinU | Eigen::ComputeThinV);
-        Eigen::VectorXi ordp = sortOrder(svdp.singularValues());
-        extractTriplets(Nk, svdp.singularValues(), svdp.matrixU(),
-                        svdp.matrixV(), ordp, Nk);
-        return;
-      }
-
-      pStart = Nk;
-    }
-
-    std::cout << GridLogMessage
-              << "IRLBA: did not converge in " << MaxIter
-              << " iterations. Returning best approximations." << std::endl;
-
-    // Return best available approximations
-    Eigen::MatrixXd B = buildFullB((int)alpha.size());
-    Eigen::JacobiSVD<Eigen::MatrixXd> svd(B,
-        Eigen::ComputeThinU | Eigen::ComputeThinV);
-    Eigen::VectorXd sigma = svd.singularValues();
-    Eigen::MatrixXd X     = svd.matrixU();
-    Eigen::MatrixXd Y     = svd.matrixV();
-    Eigen::VectorXi order = sortOrder(sigma);
-    int nout = std::min(Nk, (int)alpha.size());
-    extractTriplets((int)alpha.size(), sigma, X, Y, order, nout);
-  }
-
-  /* Getters */
-  int getNk() const { return (int)singularValues.size(); }
-  const std::vector<RealD>&  getSingularValues() const { return singularValues; }
-  const std::vector<Field>&  getLeftVectors()    const { return leftVectors; }
-  const std::vector<Field>&  getRightVectors()   const { return rightVectors; }
-
-  /**
-   * Print B_k and U^dag A V to verify the bidiagonalization relation
-   *   A V_m = U_m B_m   (exact in our GK convention)
-   * On the first call (pStart=0), max|B - U^dag A V| should be ~machine epsilon.
-   * After a restart and extension, the column p of U^dag A V deviates from B
-   * by O(betaK): this is expected because the thick restart breaks the Krylov
-   * structure at column p, introducing off-diagonal terms proportional to betaK.
-   * These terms vanish as betaK -> 0 (convergence), so the algorithm is correct.
-   */
-  void verify()
-  {
-    int m  = (int)alpha.size();
-    int nU = (int)U.size();
-    int nV = (int)V.size();
-    if (m == 0) { std::cout << GridLogMessage << "IRLBA verify: empty basis" << std::endl; return; }
-
-    // Build reference matrix Bref (nU x nV):
-    //   Columns 0..m-1 : buildFullB(m)  (bidiagonal + fvec column at restart_col)
-    //   Column  m      : residual column, two cases:
-    //     (a) restart_col == m (right after implicitRestart, before extendBasis):
-    //         V[m] = sgn*V_old[Nm], so <U[i]|A|V[m]> = fvec[i] for all i
-    //     (b) otherwise (pure GK or after extendBasis):
-    //         only entry (m-1, m) = beta[m-1]  (GK recurrence residual)
-    Eigen::MatrixXd Bref = Eigen::MatrixXd::Zero(nU, nV);
-    {
-      Eigen::MatrixXd Bfull = buildFullB(m);
-      int cols = std::min(m, nV);
-      Bref.block(0, 0, m, cols) = Bfull.block(0, 0, m, cols);
-    }
-    if (nV > m && m > 0) {
-      if (restart_col == m && (int)fvec.size() == m) {
-        // Case (a): right after implicitRestart
-        for (int i = 0; i < m; ++i) Bref(i, m) = fvec[i];
-      } else if ((int)beta.size() >= m) {
-        // Case (b): standard GK residual column
-        Bref(m - 1, m) = beta[m - 1];
-      }
-    }
-
-    // Compute M[i,j] = <U[i] | A | V[j]>
-    Eigen::MatrixXd M = Eigen::MatrixXd::Zero(nU, nV);
-    Field Avj(Grid);
-    for (int j = 0; j < nV; ++j) {
-      Linop.Op(V[j], Avj);
-      for (int i = 0; i < nU; ++i) {
-        ComplexD ip = innerProduct(U[i], Avj);
-        M(i, j) = ip.real();
-      }
-    }
-
-    // Print Bref
-    std::cout << GridLogMessage
-              << "IRLBA verify: Bref (" << nU << "x" << nV << "):" << std::endl;
-    for (int i = 0; i < nU; ++i) {
-      std::cout << GridLogMessage << "  row " << i << ": ";
-      for (int j = 0; j < nV; ++j) std::cout << Bref(i,j) << " ";
-      std::cout << std::endl;
-    }
-
-    // Print U^dag A V
-    std::cout << GridLogMessage
-              << "IRLBA verify: U^dag A V (" << nU << "x" << nV << "):" << std::endl;
-    for (int i = 0; i < nU; ++i) {
-      std::cout << GridLogMessage << "  row " << i << ": ";
-      for (int j = 0; j < nV; ++j) std::cout << M(i,j) << " ";
-      std::cout << std::endl;
-    }
-
-    // Max deviation over the full nU x nV matrix
-    RealD maxdev = (Bref - M).cwiseAbs().maxCoeff();
-    std::cout << GridLogMessage
-              << "IRLBA verify: max|Bref - U^dag A V| = " << maxdev << std::endl;
-
-    // Beta
-    std::cout << GridLogMessage << "IRLBA verify: beta[0.." << (int)beta.size()-1 << "] = ";
-    for (auto b : beta) std::cout << b << " ";
-    std::cout << std::endl;
-  }
-
-private:
-
-  // ------------------------------------------------------------------
-  // Build the m x m upper-bidiagonal matrix from alpha[0..m-1], beta[0..m-2]
-  // ------------------------------------------------------------------
-  Eigen::MatrixXd buildBidiagonal(int m) const
-  {
-    Eigen::MatrixXd B = Eigen::MatrixXd::Zero(m, m);
-    for (int k = 0; k < m; ++k) {
-      B(k, k) = alpha[k];
-      if (k + 1 < m && k < (int)beta.size())
-        B(k, k + 1) = beta[k];
-    }
-    return B;
-  }
-
-  // ------------------------------------------------------------------
-  // Build the full m x m B matrix, including the non-bidiagonal column
-  // at restart_col that arises after a thick restart.
-  //
-  // After restart, A V[restart_col] has projections onto all U[0..restart_col-1]
-  // (not just U[restart_col-1]).  These are stored in fvec[0..restart_col-1]
-  // and make column restart_col of U^dag A V non-bidiagonal.
-  // ------------------------------------------------------------------
-  Eigen::MatrixXd buildFullB(int m) const
-  {
-    Eigen::MatrixXd B = buildBidiagonal(m);
-    if (restart_col >= 0 && restart_col < m && (int)fvec.size() > 0) {
-      for (int j = 0; j < restart_col && j < (int)fvec.size(); ++j){
-        B(j, restart_col) = fvec[j];
-        std::cout << GridLogMessage << "buildFullB: B  " <<j<<" "<<restart_col<<B(j, restart_col);
-      }
-    }
-    return B;
-  }
-
-  // ------------------------------------------------------------------
-  // Return a permutation vector that puts the desired Nk singular values
-  // first (largest first if largest==true, smallest first otherwise).
-  // Eigen's JacobiSVD already returns sigma in descending order, so for
-  // largest we just return 0,1,...,m-1; for smallest we reverse.
-  // ------------------------------------------------------------------
-  Eigen::VectorXi sortOrder(const Eigen::VectorXd &sigma) const
-  {
-    int m = (int)sigma.size();
-    Eigen::VectorXi ord(m);
-    if (largest) {
-      for (int i = 0; i < m; ++i) ord(i) = i;
-    } else {
-      for (int i = 0; i < m; ++i) ord(i) = m - 1 - i;
-    }
-    return ord;
-  }
-
-  // ------------------------------------------------------------------
-  // Extend the Lanczos bidiagonalization from pStart to kEnd steps.
-  // On first call pStart==0 (V[0] already set).
-  // On restart calls V[0..pStart], U[0..pStart-1], alpha[0..pStart-1],
-  // beta[0..pStart-1] are already set; betaRestart is the coupling
-  // beta_{pStart} that drives the first new U step.
-  // ------------------------------------------------------------------
-  void extendBasis(int pStart, int kEnd, RealD betaRestart)
-  {
-    // Truncate containers to pStart (Lattice has no default constructor)
-    if ((int)V.size() > pStart + 1) V.erase(V.begin() + pStart + 1, V.end());
-    if ((int)U.size() > pStart)     U.erase(U.begin() + pStart,     U.end());
-    alpha.resize(pStart);
-    beta.resize(pStart);
-
-    Field p(Grid), r(Grid);
-
-    for (int k = pStart; k < kEnd; ++k) {
-
-      // p = A v_k
-      Linop.Op(V[k], p);
-
-      // Remove previous left vector coupling
-      if (k > 0) {
-        p = p - beta[k - 1] * U[k - 1];
-      }
-      // On the first step after a restart, beta[pStart-1] was already set;
-      // but V[pStart] was already constructed including the beta correction,
-      // so no extra subtraction needed here beyond the standard recurrence.
-
-      // Reorthogonalize p against U, then alpha_k = ||p||, u_k = p/alpha_k
-      reorthogonalize(p, U);
-      RealD ak = std::sqrt(norm2(p));
-      if (ak < 1.0e-14) {
-        std::cout << GridLogMessage
-                  << "IRLBA extendBasis: lucky breakdown at step " << k
-                  << " (alpha = " << ak << ")" << std::endl;
-        alpha.push_back(ak);
-        Field zero(Grid); zero = Zero();
-        U.push_back(zero);
-        beta.push_back(0.0);
-        V.push_back(zero);
-        break;
-      }
-      alpha.push_back(ak);
-
-      Field u(Grid);
-      u = (1.0 / ak) * p;
-      U.push_back(u);
-
-      // r = A^dag u_k - alpha_k v_k, reorthogonalize, then beta_{k+1} = ||r||
-      Linop.AdjOp(U[k], r);
-      r = r - ak * V[k];
-      reorthogonalize(r, V);
-
-      RealD bk = std::sqrt(norm2(r));
-      beta.push_back(bk);
-
-      std::cout << GridLogMessage
-                << "IRLBA extend step " << k
-                << "  alpha = " << ak
-                << "  beta  = " << bk << std::endl;
-
-      // Always push v_{k+1} (needed as residual direction for restart)
-      if (bk < 1.0e-14) {
-        std::cout << GridLogMessage
-                  << "IRLBA extendBasis: lucky breakdown (beta = 0) at step "
-                  << k << std::endl;
-        Field zero(Grid); zero = Zero();
-        V.push_back(zero);
-        break;
-      }
-      Field vnext(Grid);
-      vnext = (1.0 / bk) * r;
-      V.push_back(vnext);
-
-      if (k == kEnd - 1) break;  // v_{k+1} pushed above; stop here
-    }
-  }
-
-  // ------------------------------------------------------------------
-  // Full reorthogonalization of vec against the vectors in basis.
-  // Subtracts projections only — does NOT normalize.
-  // ------------------------------------------------------------------
-  void reorthogonalize(Field &vec, const std::vector<Field> &basis)
-  {
-    for (int j = 0; j < (int)basis.size(); ++j) {
-      ComplexD ip = innerProduct(basis[j], vec);
-      vec = vec - ip * basis[j];
-    }
-    // Second pass for numerical stability
-    for (int j = 0; j < (int)basis.size(); ++j) {
-      ComplexD ip = innerProduct(basis[j], vec);
-      vec = vec - ip * basis[j];
-    }
-  }
-
-  // ------------------------------------------------------------------
-  // Implicit restart: given the Nm-step bidiagonalization and its SVD,
-  // compress to Nk steps via implicit QR shifts applied to B_k.
-  //
-  // The "shifts" are the Nm - Nk singular values we want to deflate
-  // (those NOT in the desired set).  We apply them as implicit QR steps
-  // to the bidiagonal matrix, then update the lattice bases accordingly.
-  //
-  // After this call:
-  //   V[0..Nk],  U[0..Nk-1],  alpha[0..Nk-1],  beta[0..Nk-1]  are updated.
-  //   betaRestart  ← new beta_Nk coupling for the next extension.
-  // ------------------------------------------------------------------
-  void implicitRestart(int k, int p,
-                       const Eigen::VectorXd &sigma,
-                       const Eigen::MatrixXd &X,
-                       const Eigen::MatrixXd &Y,
-                       const Eigen::VectorXi &order,
-                       RealD betaK,
-                       RealD &betaRestart)
-  {
-    // Thick restart (Baglama & Reichel, Sec. 2.2):
-    //
-    // Given B_k = X Sigma Y^T, define the new p-step basis by:
-    //   V^+_i = V_k * y_{order(i)}      (right sing. vec. of B_k)
-    //   U^+_i = U_k * x_{order(i)}      (left  sing. vec. of B_k)
-    //
-    // Then A V^+_i = A V_k y_{order(i)} = U_k B_k y_{order(i)}
-    //             = sigma_{order(i)} U_k x_{order(i)} = sigma_{order(i)} U^+_i
-    //
-    // So B_p^+ = diag(sigma_{order(0)}, ..., sigma_{order(p-1)}) — DIAGONAL,
-    // all internal betas are zero.
-    //
-    // The residual coupling comes from A^dag U_k = V_k B_k^T + betaK V[k] e_{k-1}^T:
-    //   A^dag U^+_{p-1} - sigma_{order(p-1)} V^+_{p-1}
-    //     = V_k (B_k^T x_{order(p-1)} - sigma_{order(p-1)} y_{order(p-1)})
-    //       + betaK * X(k-1, order(p-1)) * V[k]
-    //     = betaK * X(k-1, order(p-1)) * V[k]   (since B_k^T x_j = sigma_j y_j)
-    //
-    // Therefore: betaRestart = |betaK * X(k-1, order(p-1))|
-    //            V[p] = sign(X(k-1, order(p-1))) * V[k]
-
-    // ---- Build new lattice vectors ----
-    std::vector<Field> Vnew, Unew;
-    Vnew.reserve(p + 1);
-    Unew.reserve(p);
-
-    for (int i = 0; i < p; ++i) {
-      int idx = order(i);
-      Field vi(Grid); vi = Zero();
-      for (int j = 0; j < k; ++j)
-        vi = vi + Y(j, idx) * V[j];
-      Vnew.push_back(vi);
-    }
-
-    for (int i = 0; i < p; ++i) {
-      int idx = order(i);
-      Field ui(Grid); ui = Zero();
-      for (int j = 0; j < k; ++j)
-        ui = ui + X(j, idx) * U[j];
-      Unew.push_back(ui);
-    }
-
-    // New v_{p} (0-indexed: V[p]) = sign * V[k]
-    // From A^dag U_k = V_k B_k^T + betaK V[k] e_{k-1}^T:
-    //   A^dag U^+_j - sigma_j V^+_j = betaK * X(k-1, order(j)) * V[k]
-    // The last Ritz pair (j=p-1) defines betaRestart and the sign of V[p].
-    // All p couplings (j=0..p-1) are stored in fvec so that buildFullB can
-    // reconstruct the exact column p of U^dag A V after the next extension.
-    RealD coeff = betaK * X(k - 1, order(p - 1));
-    betaRestart  = std::abs(coeff);
-    RealD sgn = (coeff >= 0.0) ? 1.0 : -1.0;
-
-    fvec.resize(p);
-    for (int j = 0; j < p; ++j)
-      fvec[j] = betaK * X(k - 1, order(j)) * sgn;
-    // fvec[p-1] == betaRestart by construction
-    restart_col = p;
-
-    Field vp(Grid);
-    if (betaRestart > 1.0e-14) {
-      vp = sgn * V[k];
-    } else {
-      betaRestart = 0.0;
-      vp = Zero();
-    }
-    Vnew.push_back(vp);  // V[p]
-
-    // ---- New alpha, beta ----
-    // B_p^+ is diagonal: alpha^+_i = sigma_{order(i)}, all internal beta = 0
-    std::vector<RealD> alpha_new(p), beta_new(p);
-    for (int i = 0; i < p; ++i) alpha_new[i] = sigma(order(i));
-    for (int i = 0; i < p - 1; ++i) beta_new[i] = 0.0;
-    beta_new[p - 1] = betaRestart;
-
-    // ---- Commit new state ----
-    V = Vnew;
-    U = Unew;
-    alpha = alpha_new;
-    beta  = beta_new;
-
-    std::cout << GridLogMessage
-              << "IRLBA restart: compressed to " << p << " steps,"
-              << "  new beta_p = " << betaRestart << std::endl;
-  }
-
-  // ------------------------------------------------------------------
-  // Extract the desired singular triplets into the public output vectors.
-  // ------------------------------------------------------------------
-  void extractTriplets(int m,
-                       const Eigen::VectorXd &sigma,
-                       const Eigen::MatrixXd &X,
-                       const Eigen::MatrixXd &Y,
-                       const Eigen::VectorXi &order,
-                       int nout)
-  {
-    singularValues.resize(nout);
-    leftVectors.clear();   leftVectors.reserve(nout);
-    rightVectors.clear();  rightVectors.reserve(nout);
-
-    for (int i = 0; i < nout; ++i) {
-      int idx = order(i);
-      singularValues[i] = sigma(idx);
-
-      // Left singular vector of A:  svec_L = U_m * x_i
-      Field svL(Grid); svL = Zero();
-      for (int j = 0; j < m && j < (int)U.size(); ++j)
-        svL = svL + X(j, idx) * U[j];
-      leftVectors.push_back(svL);
-
-      // Right singular vector of A:  svec_R = V_m * y_i
-      Field svR(Grid); svR = Zero();
-      for (int j = 0; j < m && j < (int)V.size(); ++j)
-        svR = svR + Y(j, idx) * V[j];
-      rightVectors.push_back(svR);
-    }
-  }
-};
-
-NAMESPACE_END(Grid);
-#endif

Grid/algorithms/iterative/SimpleLanczos.h

@@ -1,931 +0,0 @@
-    /*************************************************************************************
-
-    Grid physics library, www.github.com/paboyle/Grid 
-
-    Source file: ./lib/algorithms/iterative/ImplicitlyRestartedLanczos.h
-
-    Copyright (C) 2015
-
-Author: Chulwoo Jung <chulwoo@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 */
-#ifndef GRID_LANC_H
-#define GRID_LANC_H
-
-#include <string.h>		//memset
-
-#ifdef USE_LAPACK
-#ifdef USE_MKL
-#include<mkl_lapack.h>
-#else
-void LAPACK_dstegr (char *jobz, char *range, int *n, double *d, double *e,
-		    double *vl, double *vu, int *il, int *iu, double *abstol,
-		    int *m, double *w, double *z, int *ldz, int *isuppz,
-		    double *work, int *lwork, int *iwork, int *liwork,
-		    int *info);
-//#include <lapacke/lapacke.h>
-#endif
-#endif
-
-//#include <Grid/algorithms/densematrix/DenseMatrix.h>
-
-// eliminate temorary vector in calc()
-#define MEM_SAVE
-
-namespace Grid
-{
-
-  struct Bisection
-  {
-
-#if 0
-    static void get_eig2 (int row_num, std::vector < RealD > &ALPHA,
-			  std::vector < RealD > &BETA,
-			  std::vector < RealD > &eig)
-    {
-      int i, j;
-        std::vector < RealD > evec1 (row_num + 3);
-        std::vector < RealD > evec2 (row_num + 3);
-      RealD eps2;
-        ALPHA[1] = 0.;
-        BETHA[1] = 0.;
-      for (i = 0; i < row_num - 1; i++)
-	{
-	  ALPHA[i + 1] = A[i * (row_num + 1)].real ();
-	  BETHA[i + 2] = A[i * (row_num + 1) + 1].real ();
-	}
-      ALPHA[row_num] = A[(row_num - 1) * (row_num + 1)].real ();
-        bisec (ALPHA, BETHA, row_num, 1, row_num, 1e-10, 1e-10, evec1, eps2);
-        bisec (ALPHA, BETHA, row_num, 1, row_num, 1e-16, 1e-16, evec2, eps2);
-
-      // Do we really need to sort here?
-      int begin = 1;
-      int end = row_num;
-      int swapped = 1;
-      while (swapped)
-	{
-	  swapped = 0;
-	  for (i = begin; i < end; i++)
-	    {
-	      if (mag (evec2[i]) > mag (evec2[i + 1]))
-		{
-		  swap (evec2 + i, evec2 + i + 1);
-		  swapped = 1;
-		}
-	    }
-	  end--;
-	  for (i = end - 1; i >= begin; i--)
-	    {
-	      if (mag (evec2[i]) > mag (evec2[i + 1]))
-		{
-		  swap (evec2 + i, evec2 + i + 1);
-		  swapped = 1;
-		}
-	    }
-	  begin++;
-	}
-
-      for (i = 0; i < row_num; i++)
-	{
-	  for (j = 0; j < row_num; j++)
-	    {
-	      if (i == j)
-		H[i * row_num + j] = evec2[i + 1];
-	      else
-		H[i * row_num + j] = 0.;
-	    }
-	}
-    }
-#endif
-
-    static void bisec (std::vector < RealD > &c,
-		       std::vector < RealD > &b,
-		       int n,
-		       int m1,
-		       int m2,
-		       RealD eps1,
-		       RealD relfeh, std::vector < RealD > &x, RealD & eps2)
-    {
-      std::vector < RealD > wu (n + 2);
-
-      RealD h, q, x1, xu, x0, xmin, xmax;
-      int i, a, k;
-
-      b[1] = 0.0;
-      xmin = c[n] - fabs (b[n]);
-      xmax = c[n] + fabs (b[n]);
-      for (i = 1; i < n; i++)
-	{
-	  h = fabs (b[i]) + fabs (b[i + 1]);
-	  if (c[i] + h > xmax)
-	    xmax = c[i] + h;
-	  if (c[i] - h < xmin)
-	    xmin = c[i] - h;
-	}
-      xmax *= 2.;
-
-      eps2 = relfeh * ((xmin + xmax) > 0.0 ? xmax : -xmin);
-      if (eps1 <= 0.0)
-	eps1 = eps2;
-      eps2 = 0.5 * eps1 + 7.0 * (eps2);
-      x0 = xmax;
-      for (i = m1; i <= m2; i++)
-	{
-	  x[i] = xmax;
-	  wu[i] = xmin;
-	}
-
-      for (k = m2; k >= m1; k--)
-	{
-	  xu = xmin;
-	  i = k;
-	  do
-	    {
-	      if (xu < wu[i])
-		{
-		  xu = wu[i];
-		  i = m1 - 1;
-		}
-	      i--;
-	    }
-	  while (i >= m1);
-	  if (x0 > x[k])
-	    x0 = x[k];
-	  while ((x0 - xu) > 2 * relfeh * (fabs (xu) + fabs (x0)) + eps1)
-	    {
-	      x1 = (xu + x0) / 2;
-
-	      a = 0;
-	      q = 1.0;
-	      for (i = 1; i <= n; i++)
-		{
-		  q =
-		    c[i] - x1 -
-		    ((q != 0.0) ? b[i] * b[i] / q : fabs (b[i]) / relfeh);
-		  if (q < 0)
-		    a++;
-		}
-//      printf("x1=%0.14e a=%d\n",x1,a);
-	      if (a < k)
-		{
-		  if (a < m1)
-		    {
-		      xu = x1;
-		      wu[m1] = x1;
-		    }
-		  else
-		    {
-		      xu = x1;
-		      wu[a + 1] = x1;
-		      if (x[a] > x1)
-			x[a] = x1;
-		    }
-		}
-	      else
-		x0 = x1;
-	    }
-	  printf ("x0=%0.14e xu=%0.14e k=%d\n", x0, xu, k);
-	  x[k] = (x0 + xu) / 2;
-	}
-    }
-  };
-
-/////////////////////////////////////////////////////////////
-// Implicitly restarted lanczos
-/////////////////////////////////////////////////////////////
-
-
-  template < class Field > class SimpleLanczos
-  {
-
-    const RealD small = 1.0e-16;
-  public:
-    int lock;
-    int get;
-    int Niter;
-    int converged;
-
-    int Nstop;			// Number of evecs checked for convergence
-    int Nk;			// Number of converged sought
-    int Np;			// Np -- Number of spare vecs in kryloc space
-    int Nm;			// Nm -- total number of vectors
-
-
-    RealD OrthoTime;
-
-    RealD eresid;
-
-//    SortEigen < Field > _sort;
-
-    LinearFunction < Field > &_Linop;
-
-//    OperatorFunction < Field > &_poly;
-
-    /////////////////////////
-    // Constructor
-    /////////////////////////
-    void init (void)
-    {
-    };
-//    void Abort (int ff, std::vector < RealD > &evals, DenseVector < Denstd::vector  < RealD > >&evecs);
-
-    SimpleLanczos (LinearFunction < Field > &Linop,	// op
-//		   OperatorFunction < Field > &poly,	// polynmial
-		   int _Nstop,	// sought vecs
-		   int _Nk,	// sought vecs
-		   int _Nm,	// spare vecs
-		   RealD _eresid,	// resid in lmdue deficit 
-		   int _Niter):	// Max iterations
-     
-      _Linop (Linop),
- //     _poly (poly),
-      Nstop (_Nstop), Nk (_Nk), Nm (_Nm), eresid (_eresid), Niter (_Niter)
-    {
-      Np = Nm - Nk;
-      assert (Np > 0);
-    };
-
-    /////////////////////////
-    // Sanity checked this routine (step) against Saad.
-    /////////////////////////
-    void RitzMatrix (std::vector < Field > &evec, int k)
-    {
-
-      if (1)
-	return;
-
-      GridBase *grid = evec[0].Grid();
-      Field w (grid);
-      std::cout << GridLogMessage << "RitzMatrix " << std::endl;
-      for (int i = 0; i < k; i++)
-	{
-	  _Linop(evec[i], w);
-//      _poly(_Linop,evec[i],w);
-	  std::cout << GridLogMessage << "[" << i << "] ";
-	  for (int j = 0; j < k; j++)
-	    {
-	      ComplexD in = innerProduct (evec[j], w);
-	      if (fabs ((double) i - j) > 1)
-		{
-		  if (abs (in) > 1.0e-9)
-		    {
-		      std::cout << GridLogMessage << "oops" << std::endl;
-		      abort ();
-		    }
-		  else
-		    std::cout << GridLogMessage << " 0 ";
-		}
-	      else
-		{
-		  std::cout << GridLogMessage << " " << in << " ";
-		}
-	    }
-	  std::cout << GridLogMessage << std::endl;
-	}
-    }
-
-    void step (std::vector < RealD > &lmd,
-	       std::vector < RealD > &lme,
-	       Field & last, Field & current, Field & next, uint64_t k)
-    {
-      if (lmd.size () <= k)
-	lmd.resize (k + Nm);
-      if (lme.size () <= k)
-	lme.resize (k + Nm);
-
-
-//      _poly(_Linop,current,next );   // 3. wk:=Avk−βkv_{k−1}
-      _Linop(current, next);	// 3. wk:=Avk−βkv_{k−1}
-      if (k > 0)
-	{
-	  next -= lme[k - 1] * last;
-	}
-//      std::cout<<GridLogMessage << "<last|next>" << innerProduct(last,next) <<std::endl;
-
-      ComplexD zalph = innerProduct (current, next);	// 4. αk:=(wk,vk)
-      RealD alph = real (zalph);
-
-      next = next - alph * current;	// 5. wk:=wk−αkvk
-//      std::cout<<GridLogMessage << "<current|next>" << innerProduct(current,next) <<std::endl;
-
-      RealD beta = normalise (next);	// 6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
-      // 7. vk+1 := wk/βk+1
-//       norm=beta;
-
-      int interval = Nm / 100 + 1;
-      if ((k % interval) == 0)
-	std::
-	  cout << GridLogMessage << k << " : alpha = " << zalph << " beta " <<
-	  beta << std::endl;
-      const RealD tiny = 1.0e-20;
-      if (beta < tiny)
-	{
-	  std::cout << GridLogMessage << " beta is tiny " << beta << std::
-	    endl;
-	}
-      lmd[k] = alph;
-      lme[k] = beta;
-
-    }
-
-    void qr_decomp (std::vector < RealD > &lmd,
-		    std::vector  < RealD > &lme,
-		    int Nk,
-		    int Nm,
-		    std::vector  < RealD > &Qt, RealD Dsh, int kmin, int kmax)
-    {
-      int k = kmin - 1;
-      RealD x;
-
-      RealD Fden = 1.0 / hypot (lmd[k] - Dsh, lme[k]);
-      RealD c = (lmd[k] - Dsh) * Fden;
-      RealD s = -lme[k] * Fden;
-
-      RealD tmpa1 = lmd[k];
-      RealD tmpa2 = lmd[k + 1];
-      RealD tmpb = lme[k];
-
-      lmd[k] = c * c * tmpa1 + s * s * tmpa2 - 2.0 * c * s * tmpb;
-      lmd[k + 1] = s * s * tmpa1 + c * c * tmpa2 + 2.0 * c * s * tmpb;
-      lme[k] = c * s * (tmpa1 - tmpa2) + (c * c - s * s) * tmpb;
-      x = -s * lme[k + 1];
-      lme[k + 1] = c * lme[k + 1];
-
-      for (int i = 0; i < Nk; ++i)
-	{
-	  RealD Qtmp1 = Qt[i + Nm * k];
-	  RealD Qtmp2 = Qt[i + Nm * (k + 1)];
-	  Qt[i + Nm * k] = c * Qtmp1 - s * Qtmp2;
-	  Qt[i + Nm * (k + 1)] = s * Qtmp1 + c * Qtmp2;
-	}
-
-      // Givens transformations
-      for (int k = kmin; k < kmax - 1; ++k)
-	{
-
-	  RealD Fden = 1.0 / hypot (x, lme[k - 1]);
-	  RealD c = lme[k - 1] * Fden;
-	  RealD s = -x * Fden;
-
-	  RealD tmpa1 = lmd[k];
-	  RealD tmpa2 = lmd[k + 1];
-	  RealD tmpb = lme[k];
-
-	  lmd[k] = c * c * tmpa1 + s * s * tmpa2 - 2.0 * c * s * tmpb;
-	  lmd[k + 1] = s * s * tmpa1 + c * c * tmpa2 + 2.0 * c * s * tmpb;
-	  lme[k] = c * s * (tmpa1 - tmpa2) + (c * c - s * s) * tmpb;
-	  lme[k - 1] = c * lme[k - 1] - s * x;
-
-	  if (k != kmax - 2)
-	    {
-	      x = -s * lme[k + 1];
-	      lme[k + 1] = c * lme[k + 1];
-	    }
-
-	  for (int i = 0; i < Nk; ++i)
-	    {
-	      RealD Qtmp1 = Qt[i + Nm * k];
-	      RealD Qtmp2 = Qt[i + Nm * (k + 1)];
-	      Qt[i + Nm * k] = c * Qtmp1 - s * Qtmp2;
-	      Qt[i + Nm * (k + 1)] = s * Qtmp1 + c * Qtmp2;
-	    }
-	}
-    }
-
-#if 0
-#ifdef USE_LAPACK
-#ifdef USE_MKL
-#define LAPACK_INT MKL_INT
-#else
-#define LAPACK_INT long long
-#endif
-    void diagonalize_lapack (std::vector  < RealD > &lmd, std::vector  < RealD > &lme, int N1,	// all
-			     int N2,	// get
-			     GridBase * grid)
-    {
-      const int size = Nm;
-      LAPACK_INT NN = N1;
-      double evals_tmp[NN];
-      double DD[NN];
-      double EE[NN];
-      for (int i = 0; i < NN; i++)
-	for (int j = i - 1; j <= i + 1; j++)
-	  if (j < NN && j >= 0)
-	    {
-	      if (i == j)
-		DD[i] = lmd[i];
-	      if (i == j)
-		evals_tmp[i] = lmd[i];
-	      if (j == (i - 1))
-		EE[j] = lme[j];
-	    }
-      LAPACK_INT evals_found;
-      LAPACK_INT lwork =
-	((18 * NN) >
-	 (1 + 4 * NN + NN * NN) ? (18 * NN) : (1 + 4 * NN + NN * NN));
-      LAPACK_INT liwork = 3 + NN * 10;
-      LAPACK_INT iwork[liwork];
-      double work[lwork];
-      LAPACK_INT isuppz[2 * NN];
-      char jobz = 'N';		// calculate evals only
-      char range = 'I';		// calculate il-th to iu-th evals
-      //    char range = 'A'; // calculate all evals
-      char uplo = 'U';		// refer to upper half of original matrix
-      char compz = 'I';		// Compute eigenvectors of tridiagonal matrix
-      int ifail[NN];
-      LAPACK_INT info;
-//  int total = QMP_get_number_of_nodes();
-//  int node = QMP_get_node_number();
-//  GridBase *grid = evec[0]._grid;
-      int total = grid->_Nprocessors;
-      int node = grid->_processor;
-      int interval = (NN / total) + 1;
-      double vl = 0.0, vu = 0.0;
-      LAPACK_INT il = interval * node + 1, iu = interval * (node + 1);
-      if (iu > NN)
-	iu = NN;
-      double tol = 0.0;
-      if (1)
-	{
-	  memset (evals_tmp, 0, sizeof (double) * NN);
-	  if (il <= NN)
-	    {
-	      printf ("total=%d node=%d il=%d iu=%d\n", total, node, il, iu);
-#ifdef USE_MKL
-	      dstegr (&jobz, &range, &NN,
-#else
-	      LAPACK_dstegr (&jobz, &range, &NN,
-#endif
-			     (double *) DD, (double *) EE, &vl, &vu, &il, &iu,	// these four are ignored if second parameteris 'A'
-			     &tol,	// tolerance
-			     &evals_found, evals_tmp, (double *) NULL, &NN,
-			     isuppz, work, &lwork, iwork, &liwork, &info);
-	      for (int i = iu - 1; i >= il - 1; i--)
-		{
-		  printf ("node=%d evals_found=%d evals_tmp[%d] = %g\n", node,
-			  evals_found, i - (il - 1), evals_tmp[i - (il - 1)]);
-		  evals_tmp[i] = evals_tmp[i - (il - 1)];
-		  if (il > 1)
-		    evals_tmp[i - (il - 1)] = 0.;
-		}
-	    }
-	  {
-	    grid->GlobalSumVector (evals_tmp, NN);
-	  }
-	}
-// cheating a bit. It is better to sort instead of just reversing it, but the document of the routine says evals are sorted in increasing order. qr gives evals in decreasing order.
-    }
-#undef LAPACK_INT
-#endif
-
-
-    void diagonalize (std::vector  < RealD > &lmd,
-		      std::vector  < RealD > &lme,
-		      int N2, int N1, GridBase * grid)
-    {
-
-#ifdef USE_LAPACK
-      const int check_lapack = 0;	// just use lapack if 0, check against lapack if 1
-
-      if (!check_lapack)
-	return diagonalize_lapack (lmd, lme, N2, N1, grid);
-
-//      diagonalize_lapack(lmd2,lme2,Nm2,Nm,Qt,grid);
-#endif
-    }
-#endif
-
-    static RealD normalise (Field & v)
-    {
-      RealD nn = norm2 (v);
-      nn = sqrt (nn);
-      v = v * (1.0 / nn);
-      return nn;
-    }
-
-    void orthogonalize (Field & w, std::vector < Field > &evec, int k)
-    {
-      double t0 = -usecond () / 1e6;
-      typedef typename Field::scalar_type MyComplex;
-      MyComplex ip;
-
-      if (0)
-	{
-	  for (int j = 0; j < k; ++j)
-	    {
-	      normalise (evec[j]);
-	      for (int i = 0; i < j; i++)
-		{
-		  ip = innerProduct (evec[i], evec[j]);	// are the evecs normalised? ; this assumes so.
-		  evec[j] = evec[j] - ip * evec[i];
-		}
-	    }
-	}
-
-      for (int j = 0; j < k; ++j)
-	{
-	  ip = innerProduct (evec[j], w);	// are the evecs normalised? ; this assumes so.
-	  w = w - ip * evec[j];
-	}
-      normalise (w);
-      t0 += usecond () / 1e6;
-      OrthoTime += t0;
-    }
-
-    void setUnit_Qt (int Nm, std::vector < RealD > &Qt)
-    {
-      for (int i = 0; i < Qt.size (); ++i)
-	Qt[i] = 0.0;
-      for (int k = 0; k < Nm; ++k)
-	Qt[k + k * Nm] = 1.0;
-    }
-
-
-    void calc (std::vector < RealD > &eval, const Field & src, int &Nconv)
-    {
-
-      GridBase *grid = src.Grid();
-//      assert(grid == src._grid);
-
-      std::
-	cout << GridLogMessage << " -- Nk = " << Nk << " Np = " << Np << std::
-	endl;
-      std::cout << GridLogMessage << " -- Nm = " << Nm << std::endl;
-      std::cout << GridLogMessage << " -- size of eval   = " << eval.
-	size () << std::endl;
-
-//      assert(c.size() && Nm == eval.size());
-
-      std::vector < RealD > lme (Nm);
-      std::vector < RealD > lmd (Nm);
-
-
-      Field current (grid);
-      Field last (grid);
-      Field next (grid);
-
-      Nconv = 0;
-
-      RealD beta_k;
-
-      // Set initial vector
-      // (uniform vector) Why not src??
-      //      evec[0] = 1.0;
-      current = src;
-      std::cout << GridLogMessage << "norm2(src)= " << norm2 (src) << std::
-	endl;
-      normalise (current);
-      std::
-	cout << GridLogMessage << "norm2(evec[0])= " << norm2 (current) <<
-	std::endl;
-
-      // Initial Nk steps
-      OrthoTime = 0.;
-      double t0 = usecond () / 1e6;
-      RealD norm;		// sqrt norm of last vector
-
-      uint64_t iter = 0;
-
-      bool initted = false;
-      std::vector < RealD > low (Nstop * 10);
-      std::vector < RealD > high (Nstop * 10);
-      RealD cont = 0.;
-      while (1) {
-	  cont = 0.;
-	  std::vector < RealD > lme2 (Nm);
-	  std::vector < RealD > lmd2 (Nm);
-	  for (uint64_t k = 0; k < Nm; ++k, iter++) {
-	      step (lmd, lme, last, current, next, iter);
-	      last = current;
-	      current = next;
-	    }
-	  double t1 = usecond () / 1e6;
-	  std::cout << GridLogMessage << "IRL::Initial steps: " << t1 -
-	    t0 << "seconds" << std::endl;
-	  t0 = t1;
-	  std::
-	    cout << GridLogMessage << "IRL::Initial steps:OrthoTime " <<
-	    OrthoTime << "seconds" << std::endl;
-
-	  // getting eigenvalues
-	  lmd2.resize (iter + 2);
-	  lme2.resize (iter + 2);
-	  for (uint64_t k = 0; k < iter; ++k) {
-	      lmd2[k + 1] = lmd[k];
-	      lme2[k + 2] = lme[k];
-	    }
-	  t1 = usecond () / 1e6;
-	  std::cout << GridLogMessage << "IRL:: copy: " << t1 -
-	    t0 << "seconds" << std::endl;
-	  t0 = t1;
-	  {
-	    int total = grid->_Nprocessors;
-	    int node = grid->_processor;
-	    int interval = (Nstop / total) + 1;
-	    int iu = (iter + 1) - (interval * node + 1);
-	    int il = (iter + 1) - (interval * (node + 1));
-	    std::vector < RealD > eval2 (iter + 3);
-	    RealD eps2;
-	    Bisection::bisec (lmd2, lme2, iter, il, iu, 1e-16, 1e-10, eval2,
-			      eps2);
-//        diagonalize(eval2,lme2,iter,Nk,grid);
-	    RealD diff = 0.;
-	    for (int i = il; i <= iu; i++) {
-		if (initted)
-		  diff =
-		    fabs (eval2[i] - high[iu-i]) / (fabs (eval2[i]) +
-						      fabs (high[iu-i]));
-		if (initted && (diff > eresid))
-		  cont = 1.;
-		if (initted)
-		  printf ("eval[%d]=%0.14e %0.14e, %0.14e\n", i, eval2[i],
-			  high[iu-i], diff);
-		high[iu-i] = eval2[i];
-	      }
-	    il = (interval * node + 1);
-	    iu = (interval * (node + 1));
-	    Bisection::bisec (lmd2, lme2, iter, il, iu, 1e-16, 1e-10, eval2,
-			      eps2);
-	    for (int i = il; i <= iu; i++) {
-		if (initted)
-		  diff =
-		    fabs (eval2[i] - low[i]) / (fabs (eval2[i]) +
-						fabs (low[i]));
-		if (initted && (diff > eresid))
-		  cont = 1.;
-		if (initted)
-		  printf ("eval[%d]=%0.14e %0.14e, %0.14e\n", i, eval2[i],
-			  low[i], diff);
-		low[i] = eval2[i];
-	      }
-	    t1 = usecond () / 1e6;
-	    std::cout << GridLogMessage << "IRL:: diagonalize: " << t1 -
-	      t0 << "seconds" << std::endl;
-	    t0 = t1;
-	  }
-
-	  for (uint64_t k = 0; k < Nk; ++k) {
-//          eval[k] = eval2[k];
-	    }
-	  if (initted)
-	    {
-	      grid->GlobalSumVector (&cont, 1);
-	      if (cont < 1.) return;
-	    }
-	  initted = true;
-	}
-
-    }
-
-
-
-
-
-#if 0
-
-/**
-   There is some matrix Q such that for any vector y
-   Q.e_1 = y and Q is unitary.
-**/
-    template < class T >
-      static T orthQ (DenseMatrix < T > &Q, std::vector < T > y)
-    {
-      int N = y.size ();	//Matrix Size
-      Fill (Q, 0.0);
-      T tau;
-      for (int i = 0; i < N; i++)
-	{
-	  Q[i][0] = y[i];
-	}
-      T sig = conj (y[0]) * y[0];
-      T tau0 = fabs (sqrt (sig));
-
-      for (int j = 1; j < N; j++)
-	{
-	  sig += conj (y[j]) * y[j];
-	  tau = abs (sqrt (sig));
-
-	  if (abs (tau0) > 0.0)
-	    {
-
-	      T gam = conj ((y[j] / tau) / tau0);
-	      for (int k = 0; k <= j - 1; k++)
-		{
-		  Q[k][j] = -gam * y[k];
-		}
-	      Q[j][j] = tau0 / tau;
-	    }
-	  else
-	    {
-	      Q[j - 1][j] = 1.0;
-	    }
-	  tau0 = tau;
-	}
-      return tau;
-    }
-
-/**
-	There is some matrix Q such that for any vector y
-	Q.e_k = y and Q is unitary.
-**/
-    template < class T >
-      static T orthU (DenseMatrix < T > &Q, std::vector < T > y)
-    {
-      T tau = orthQ (Q, y);
-      SL (Q);
-      return tau;
-    }
-
-
-/**
-	Wind up with a matrix with the first con rows untouched
-
-say con = 2
-	Q is such that Qdag H Q has {x, x, val, 0, 0, 0, 0, ...} as 1st colum
-	and the matrix is upper hessenberg
-	and with f and Q appropriately modidied with Q is the arnoldi factorization
-
-**/
-
-    template < class T > static void Lock (DenseMatrix < T > &H,	///Hess mtx     
-					   DenseMatrix < T > &Q,	///Lock Transform
-					   T val,	///value to be locked
-					   int con,	///number already locked
-					   RealD small, int dfg, bool herm)
-    {
-      //ForceTridiagonal(H);
-
-      int M = H.dim;
-      DenseVector < T > vec;
-      Resize (vec, M - con);
-
-      DenseMatrix < T > AH;
-      Resize (AH, M - con, M - con);
-      AH = GetSubMtx (H, con, M, con, M);
-
-      DenseMatrix < T > QQ;
-      Resize (QQ, M - con, M - con);
-
-      Unity (Q);
-      Unity (QQ);
-
-      DenseVector < T > evals;
-      Resize (evals, M - con);
-      DenseMatrix < T > evecs;
-      Resize (evecs, M - con, M - con);
-
-      Wilkinson < T > (AH, evals, evecs, small);
-
-      int k = 0;
-      RealD cold = abs (val - evals[k]);
-      for (int i = 1; i < M - con; i++)
-	{
-	  RealD cnew = abs (val - evals[i]);
-	  if (cnew < cold)
-	    {
-	      k = i;
-	      cold = cnew;
-	    }
-	}
-      vec = evecs[k];
-
-      ComplexD tau;
-      orthQ (QQ, vec);
-      //orthQM(QQ,AH,vec);
-
-      AH = Hermitian (QQ) * AH;
-      AH = AH * QQ;
-
-      for (int i = con; i < M; i++)
-	{
-	  for (int j = con; j < M; j++)
-	    {
-	      Q[i][j] = QQ[i - con][j - con];
-	      H[i][j] = AH[i - con][j - con];
-	    }
-	}
-
-      for (int j = M - 1; j > con + 2; j--)
-	{
-
-	  DenseMatrix < T > U;
-	  Resize (U, j - 1 - con, j - 1 - con);
-	  DenseVector < T > z;
-	  Resize (z, j - 1 - con);
-	  T nm = norm (z);
-	  for (int k = con + 0; k < j - 1; k++)
-	    {
-	      z[k - con] = conj (H (j, k + 1));
-	    }
-	  normalise (z);
-
-	  RealD tmp = 0;
-	  for (int i = 0; i < z.size () - 1; i++)
-	    {
-	      tmp = tmp + abs (z[i]);
-	    }
-
-	  if (tmp < small / ((RealD) z.size () - 1.0))
-	    {
-	      continue;
-	    }
-
-	  tau = orthU (U, z);
-
-	  DenseMatrix < T > Hb;
-	  Resize (Hb, j - 1 - con, M);
-
-	  for (int a = 0; a < M; a++)
-	    {
-	      for (int b = 0; b < j - 1 - con; b++)
-		{
-		  T sum = 0;
-		  for (int c = 0; c < j - 1 - con; c++)
-		    {
-		      sum += H[a][con + 1 + c] * U[c][b];
-		    }		//sum += H(a,con+1+c)*U(c,b);}
-		  Hb[b][a] = sum;
-		}
-	    }
-
-	  for (int k = con + 1; k < j; k++)
-	    {
-	      for (int l = 0; l < M; l++)
-		{
-		  H[l][k] = Hb[k - 1 - con][l];
-		}
-	    }			//H(Hb[k-1-con][l] , l,k);}}
-
-	  DenseMatrix < T > Qb;
-	  Resize (Qb, M, M);
-
-	  for (int a = 0; a < M; a++)
-	    {
-	      for (int b = 0; b < j - 1 - con; b++)
-		{
-		  T sum = 0;
-		  for (int c = 0; c < j - 1 - con; c++)
-		    {
-		      sum += Q[a][con + 1 + c] * U[c][b];
-		    }		//sum += Q(a,con+1+c)*U(c,b);}
-		  Qb[b][a] = sum;
-		}
-	    }
-
-	  for (int k = con + 1; k < j; k++)
-	    {
-	      for (int l = 0; l < M; l++)
-		{
-		  Q[l][k] = Qb[k - 1 - con][l];
-		}
-	    }			//Q(Qb[k-1-con][l] , l,k);}}
-
-	  DenseMatrix < T > Hc;
-	  Resize (Hc, M, M);
-
-	  for (int a = 0; a < j - 1 - con; a++)
-	    {
-	      for (int b = 0; b < M; b++)
-		{
-		  T sum = 0;
-		  for (int c = 0; c < j - 1 - con; c++)
-		    {
-		      sum += conj (U[c][a]) * H[con + 1 + c][b];
-		    }		//sum += conj( U(c,a) )*H(con+1+c,b);}
-		  Hc[b][a] = sum;
-		}
-	    }
-
-	  for (int k = 0; k < M; k++)
-	    {
-	      for (int l = con + 1; l < j; l++)
-		{
-		  H[l][k] = Hc[k][l - 1 - con];
-		}
-	    }			//H(Hc[k][l-1-con] , l,k);}}
-
-	}
-    }
-#endif
-
-
-  };
-
-}
-#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;
@@ -110,7 +124,7 @@ 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]);
 
@@ -118,6 +132,8 @@ public:
 	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);
@@ -168,12 +185,15 @@ public:
 	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;
+
       }
 
       DiracOp.Op(noise,Mn); std::cout<<GridLogMessage << "filtered["<<b<<"] <f|Op|f> "<<innerProduct(noise,Mn)<<" <f|OpDagOp|f>"<<norm2(Mn)<<std::endl;
       subspace[b]   = noise;
 
     }
+    GlobalOrthonormalise();
   }
 
   ////////////////////////////////////////////////////////////////////////////////////////////////

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);
-    //    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)
   {
@@ -227,25 +233,24 @@ 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);
@@ -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 +452,19 @@ 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, {
+#ifdef GRID_SIMT
+	    int j = acceleratorSIMTlane(nbasis);
+	    A_v[sss](i,j) = FT_v[sss](j);
+#else
+	    // CPU build: acceleratorSIMTlane()==0 -- an un-looped SIMT tensor
+	    // index writes ONLY j=0 and silently drops the other nbasis-1
+	    // columns (caught by Test_schur_dense_coarse import certificate,
+	    // 2026-08-14).  Loop explicitly.
 	    for(int j=0;j<nbasis;j++){
 	      A_v[sss](i,j) = FT_v[sss](j);
 	    }
+#endif
         });
       }
       tinv+=usecond();
@@ -428,8 +472,8 @@ 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 +561,9 @@ 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();
@@ -546,33 +586,48 @@ public:
     }
     tphase+=usecond();
 
+    // Import basis into BLAS layout once; blockProject then reads it once per
+    // 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];
+      for(int p=0;p<npoint;p++)
+	phaV_batch[p] = phaF[p] * V.subspace[i];
       tphaseBZ+=usecond();
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<" phaseBZ done"<< std::endl;
 
-	/////////////////////////////////////////////////////////////////////
-	// Multiple phased subspace vector by matrix and project to subspace
-	// Remove local bulk phase to leave relative phases
-	/////////////////////////////////////////////////////////////////////
       tmat-=usecond();
-	linop.Op(phaV,MphaV);
+      for(int p=0;p<npoint;p++)
+	linop.Op(phaV_batch[p], MphaV_batch[p]);
       tmat+=usecond();
-	//	std::cout << i << " " <<p << " MphaV "<<norm2(MphaV)<<" "<<norm2(phaV)<<std::endl;
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<" mat done"<< std::endl;
 
+      // One batched GEMM reads BLAS_V once for all npoint vectors.
       tproj-=usecond();
-	blockProject(coarseInner,MphaV,U.subspace);
+      Projector.blockProject(MphaV_batch, proj_batch);
-	coarseInner = conjugate(pha[p]) * coarseInner;
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<" blockProject done"<< std::endl;
-
+      for(int p=0;p<npoint;p++)
-	ComputeProj[p] = coarseInner;
+	ComputeProj[p] = conjugate(pha[p]) * proj_batch[p];
       tproj+=usecond();
-	//	std::cout << i << " " <<p << " ComputeProj "<<norm2(ComputeProj[p])<<std::endl;
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<" proj done"<< std::endl;
-
-      }
 
       tinv-=usecond();
       for(int k=0;k<npoint;k++){
@@ -584,10 +639,19 @@ 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, {
+#ifdef GRID_SIMT
+	    int j = acceleratorSIMTlane(nbasis);
+	    A_v[sss](i,j) = FT_v[sss](j);
+#else
+	    // CPU build: acceleratorSIMTlane()==0 -- an un-looped SIMT tensor
+	    // index writes ONLY j=0 and silently drops the other nbasis-1
+	    // columns (caught by Test_schur_dense_coarse import certificate,
+	    // 2026-08-14).  Loop explicitly.
 	    for(int j=0;j<nbasis;j++){
 	      A_v[sss](i,j) = FT_v[sss](j);
 	    }
+#endif
         });
       }
       tinv+=usecond();
@@ -595,13 +659,13 @@ 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 +680,7 @@ 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/algorithms/multigrid/GeneralCoarsenedMatrixMultiRHSV2.h

@@ -0,0 +1,851 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/GeneralCoarsenedMatrixMultiRHS.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+
+NAMESPACE_BEGIN(Grid);
+
+
+// Fine Object == (per site) type of fine field
+// nbasis      == number of deflation vectors
+template<class Fobj,class CComplex,int nbasis>
+class MultiGeneralCoarsenedOperatorV2 : public SparseMatrixBase<Lattice<iVector<CComplex,nbasis > > >  {
+public:
+  typedef typename CComplex::scalar_object SComplex;
+  typedef GeneralCoarsenedMatrix<Fobj,CComplex,nbasis> GeneralCoarseOp;
+  typedef MultiGeneralCoarsenedOperatorV2<Fobj,CComplex,nbasis> MultiGeneralCoarseOp;
+
+  typedef iVector<CComplex,nbasis >           siteVector;
+  typedef iMatrix<CComplex,nbasis >           siteMatrix;
+  typedef iVector<SComplex,nbasis >           calcVector;
+  typedef iMatrix<SComplex,nbasis >           calcMatrix;
+  typedef Lattice<iScalar<CComplex> >         CoarseComplexField;
+  typedef Lattice<siteVector>                 CoarseVector;
+  typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
+  typedef iMatrix<CComplex,nbasis >  Cobj;
+  typedef iVector<CComplex,nbasis >  Cvec;
+  typedef Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj >        FineField;
+  typedef CoarseVector Field;
+
+  // Block operations on the fine vectors carry the fine layout, which need
+  // not be the coarse one
+  typedef decltype(innerProduct(Fobj(),Fobj())) FineInner;
+  typedef Lattice<FineInner>                    FineComplexField;
+  typedef Lattice<FineInner>                    BlockComplexField;
+
+  ////////////////////
+  // Data members
+  //
+  // Nrhs independent: the D dimensional coarse grid, the geometry, the padded
+  // cell that supplies the stencil grid, the stencil, and the matrix elements.
+  //
+  // Nrhs dependent: the D+1 grid, its padded cell, and the BLAS B/C buffers
+  // with their pointer tables. Owned by SetNRHS().
+  ////////////////////
+  GridCartesian *       _CoarseGrid;        // D dimensional
+  NonLocalStencilGeometry geom;
+  NonLocalStencilGeometry geom_srhs;
+  PaddedCell CellD;                         // D dimensional, supplies stencil grid
+  GeneralLocalStencil Stencil;              // D dimensional
+
+  int                   _Nrhs;
+  GridCartesian *       _CoarseGridMulti;   // D+1 dimensional, SetNRHS
+  PaddedCell *          CellMulti;          // D+1 dimensional, SetNRHS
+
+  deviceVector<calcVector> BLAS_B;
+  deviceVector<calcVector> BLAS_C;
+  std::vector<deviceVector<calcMatrix> > BLAS_A;
+
+  std::vector<deviceVector<ComplexD *> > BLAS_AP;
+  std::vector<deviceVector<ComplexD *> > BLAS_BP;
+  deviceVector<ComplexD *>               BLAS_CP;
+
+  ///////////////////////
+  // Interface
+  ///////////////////////
+  GridBase      * Grid(void)           { CheckGridSet(); return _CoarseGridMulti; };
+  GridCartesian * CoarseGrid(void)     { CheckGridSet(); return _CoarseGridMulti; };
+  GridCartesian * CoarseGridD(void)    { return _CoarseGrid; };        // lower dimensional grid
+  int             Nrhs(void)           { CheckGridSet(); return _Nrhs; };
+
+  void CheckGridSet(void)
+  {
+    if ( _CoarseGridMulti == nullptr ) {
+      std::cout << GridLogError
+		<< "MultiGeneralCoarsenedOperatorV2: the multiRHS grid has not been set."
+		<< std::endl;
+      std::cout << GridLogError
+		<< "  Call SetGrid(CoarseGridMulti) with the D+1 dimensional grid your"
+		<< std::endl;
+      std::cout << GridLogError
+		<< "  coarse vectors live on, before Grid(), Nrhs() or M()."
+		<< std::endl;
+      GRID_ASSERT(_CoarseGridMulti != nullptr);
+    }
+  }
+
+  // Can be used to do I/O on the operator matrices externally
+  void SetMatrix (int p,CoarseMatrix & A)
+  {
+    GRID_ASSERT(A.size()==geom_srhs.npoint);
+    GridtoBLAS(A[p],BLAS_A[p]);
+  }
+  void GetMatrix (int p,CoarseMatrix & A)
+  {
+    GRID_ASSERT(A.size()==geom_srhs.npoint);
+    BLAStoGrid(A[p],BLAS_A[p]);
+  }
+  void CopyMatrix (GeneralCoarseOp &_Op)
+  {
+    for(int p=0;p<geom.npoint;p++){
+      auto Aup = _Op.Cell.Extract(_Op._A[p]);
+      //Unpadded
+      GridtoBLAS(Aup,BLAS_A[p]);
+    }
+  }
+  /*
+  void CheckMatrix (GeneralCoarseOp &_Op)
+  {
+    std::cout <<"************* Checking the little direc operator mRHS"<<std::endl;
+    for(int p=0;p<geom.npoint;p++){
+      //Unpadded
+      auto Aup = _Op.Cell.Extract(_Op._A[p]);
+      auto Ack = Aup;
+      BLAStoGrid(Ack,BLAS_A[p]);
+      std::cout << p<<" Ack "<<norm2(Ack)<<std::endl;
+      std::cout << p<<" Aup "<<norm2(Aup)<<std::endl;
+    }
+    std::cout <<"************* "<<std::endl;
+  }
+  */
+  
+  ///////////////////////////////////////////////////////////////////////////
+  // Constructor takes the D dimensional coarse grid. Everything built here
+  // is independent of Nrhs, in particular the matrix elements, which must
+  // survive a change of Nrhs untouched.
+  ///////////////////////////////////////////////////////////////////////////
+  MultiGeneralCoarsenedOperatorV2(NonLocalStencilGeometry &_geom,GridCartesian *CoarseGrid) :
+    _CoarseGrid(CoarseGrid),
+    geom_srhs(_geom),
+    geom(CoarseGrid,_geom.hops,_geom.skip),
+    CellD(geom.Depth(),CoarseGrid),
+    Stencil(CellD.grids.back(),geom.shifts), // D dimensional padded cell stencil
+    _Nrhs(-1),
+    _CoarseGridMulti(nullptr),
+    CellMulti(nullptr)
+  {
+    int32_t unpadded_sites = _CoarseGrid->lSites();
+
+    /////////////////////////////////////////////////
+    // Matrix elements and their pointer table
+    /////////////////////////////////////////////////
+    BLAS_A.resize(geom.npoint);
+    BLAS_AP.resize(geom.npoint);
+    for(int p=0;p<geom.npoint;p++){
+      BLAS_A[p].resize (unpadded_sites); // no ghost zone, npoint elements
+      BLAS_AP[p].resize(unpadded_sites);
+    }
+
+    // Site identity mapping for A
+    for(int p=0;p<geom.npoint;p++){
+      for(int ss=0;ss<unpadded_sites;ss++){
+	ComplexD *ptr = (ComplexD *)&BLAS_A[p][ss];
+	acceleratorPut(BLAS_AP[p][ss],ptr);
+      }
+    }
+  }
+
+  virtual ~MultiGeneralCoarsenedOperatorV2()
+  {
+    ReleaseGrid();
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // Free everything SetGrid allocated. The D+1 grid is borrowed from the
+  // caller and is never deleted here. Safe to call repeatedly and before
+  // the destructor.
+  ///////////////////////////////////////////////////////////////////////////
+  void ReleaseGrid(void)
+  {
+    if ( CellMulti != nullptr ) { delete CellMulti; CellMulti = nullptr; }
+
+    _CoarseGridMulti = nullptr;  // borrowed, not owned
+    _Nrhs            = -1;
+
+    BLAS_B.resize(0);
+    BLAS_C.resize(0);
+    for(int p=0;p<BLAS_BP.size();p++){
+      BLAS_BP[p].resize(0);
+    }
+    BLAS_BP.resize(0);
+    BLAS_CP.resize(0);
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // Everything that depends on Nrhs. Idempotent; lazy called on demand.
+  //
+  // The stencil lives on the D dimensional padded grid. PaddedCell only pads
+  // a dimension when it is distributed, and the rhs direction never is, so
+  // the D+1 padded grid is exactly Nrhs copies of the D dimensional padded
+  // grid with rhs innermost. The neighbour offset therefore carries an Nrhs
+  // factor, in the same way the Nsimd factor is carried.
+  ///////////////////////////////////////////////////////////////////////////
+  void SetGrid(GridCartesian *CoarseGridMulti)
+  {
+    GRID_ASSERT(CoarseGridMulti != nullptr);
+
+    if ( CoarseGridMulti == _CoarseGridMulti ) return; // idempotent on identity
+
+    ReleaseGrid();
+
+    /////////////////////////////////////////////////
+    // The D+1 grid is supplied and owned by the caller. Two operators over
+    // the same coarse space must share one grid object or their fields will
+    // not conform, so this is never manufactured internally.
+    /////////////////////////////////////////////////
+    int nd = _CoarseGrid->_ndimension;
+
+    GRID_ASSERT(CoarseGridMulti->_ndimension == nd+1);
+    GRID_ASSERT(CoarseGridMulti->_processors[0] == 1);   // rhs is not distributed
+    for(int d=0;d<nd;d++){
+      GRID_ASSERT(CoarseGridMulti->_fdimensions[d+1] == _CoarseGrid->_fdimensions[d]);
+      GRID_ASSERT(CoarseGridMulti->_processors [d+1] == _CoarseGrid->_processors [d]);
+      GRID_ASSERT(CoarseGridMulti->_simd_layout[d+1] == _CoarseGrid->_simd_layout[d]);
+    }
+
+    _CoarseGridMulti = CoarseGridMulti;
+    _Nrhs            = CoarseGridMulti->_fdimensions[0];
+    GRID_ASSERT(_Nrhs>=1);
+
+    int nrhs = _Nrhs;
+
+    CellMulti = new PaddedCell(geom.Depth(),_CoarseGridMulti);
+
+    int32_t padded_sites   = CellD.grids.back()->lSites(); // D dimensional
+    int32_t unpadded_sites = _CoarseGrid->lSites();        // D dimensional
+
+    // The neighbour offset multiplication by nrhs is exact only if the D+1
+    // padded volume is nrhs copies of the D dimensional one. Check it.
+    GRID_ASSERT(CellMulti->grids.back()->lSites() == nrhs*padded_sites);
+    GRID_ASSERT(_CoarseGridMulti->lSites()        == nrhs*unpadded_sites);
+
+    /////////////////////////////////////////////////
+    // Device data vector storage
+    /////////////////////////////////////////////////
+    BLAS_B.resize(nrhs *padded_sites);   // includes ghost zone
+    BLAS_C.resize(nrhs *unpadded_sites); // no ghost zone
+    BLAS_BP.resize(geom.npoint);
+    for(int p=0;p<geom.npoint;p++){
+      BLAS_BP[p].resize(unpadded_sites);
+    }
+    BLAS_CP.resize(unpadded_sites);
+
+    // Site identity mapping for C
+    for(int ss=0;ss<unpadded_sites;ss++){
+      ComplexD *ptr = (ComplexD *)&BLAS_C[ss*nrhs];
+      acceleratorPut(BLAS_CP[ss],ptr);
+    }
+
+    // Neighbour table is more complicated
+    int32_t j=0; // Interior point counter (unpadded)
+    for(int32_t s=0;s<padded_sites;s++){ // D volume, padded
+      int ghost_zone=0;
+      for(int32_t point = 0 ; point < geom.npoint; point++){
+	int i=s*geom.npoint+point;
+	if( Stencil._entries[i]._wrap ) { // stencil is indexed by the oSite of the D dim grid
+	  ghost_zone=1; // If general stencil wrapped in any direction, wrap=1
+	}
+      }
+
+      if( ghost_zone==0) {
+	for(int32_t point = 0 ; point < geom.npoint; point++){
+	  int i=s*geom.npoint+point;
+ 	  int32_t nbr = Stencil._entries[i]._offset*CComplex::Nsimd(); // oSite -> lSite, D dim
+	  nbr = nbr*nrhs;                                              // D -> D+1, rhs innermost
+	  GRID_ASSERT(nbr<BLAS_B.size());
+	  ComplexD * ptr = (ComplexD *)&BLAS_B[nbr];
+	  acceleratorPut(BLAS_BP[point][j],ptr); // neighbour indexing in ghost zone volume
+	}
+	j++;
+      }
+    }
+    GRID_ASSERT(j==unpadded_sites);
+  }
+  template<class vobj> void GridtoBLAS(const Lattice<vobj> &from,deviceVector<typename vobj::scalar_object> &to)
+  {
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  GridBase *Fg = from.Grid();
+  GRID_ASSERT(!Fg->_isCheckerBoarded);
+  int nd = Fg->_ndimension;
+
+  to.resize(Fg->lSites());
+
+  Coordinate LocalLatt = Fg->LocalDimensions();
+  size_t nsite = 1;
+  for(int i=0;i<nd;i++) nsite *= LocalLatt[i];
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  // do the index calc on the GPU
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  Coordinate f_ostride = Fg->_ostride;
+  Coordinate f_istride = Fg->_istride;
+  Coordinate f_rdimensions = Fg->_rdimensions;
+
+  autoView(from_v,from,AcceleratorRead);
+  auto to_v = &to[0];
+
+  const int words=sizeof(vobj)/sizeof(vector_type);
+  accelerator_for(idx,nsite,1,{
+      
+      Coordinate from_coor, base;
+      Lexicographic::CoorFromIndex(base,idx,LocalLatt);
+      for(int i=0;i<nd;i++){
+	from_coor[i] = base[i];
+      }
+      int from_oidx = 0; for(int d=0;d<nd;d++) from_oidx+=f_ostride[d]*(from_coor[d]%f_rdimensions[d]);
+      int from_lane = 0; for(int d=0;d<nd;d++) from_lane+=f_istride[d]*(from_coor[d]/f_rdimensions[d]);
+
+      const vector_type* from = (const vector_type *)&from_v[from_oidx];
+      scalar_type* to = (scalar_type *)&to_v[idx];
+      
+      scalar_type stmp;
+      for(int w=0;w<words;w++){
+	stmp = getlane(from[w], from_lane);
+	to[w] = stmp;
+      }
+    });
+  }    
+  template<class vobj> void BLAStoGrid(Lattice<vobj> &grid,deviceVector<typename vobj::scalar_object> &in)
+  {
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  GridBase *Tg = grid.Grid();
+  GRID_ASSERT(!Tg->_isCheckerBoarded);
+  int nd = Tg->_ndimension;
+  
+  GRID_ASSERT(in.size()==Tg->lSites());
+
+  Coordinate LocalLatt = Tg->LocalDimensions();
+  size_t nsite = 1;
+  for(int i=0;i<nd;i++) nsite *= LocalLatt[i];
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  // do the index calc on the GPU
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  Coordinate t_ostride = Tg->_ostride;
+  Coordinate t_istride = Tg->_istride;
+  Coordinate t_rdimensions = Tg->_rdimensions;
+
+  autoView(to_v,grid,AcceleratorWrite);
+  auto from_v = &in[0];
+
+  const int words=sizeof(vobj)/sizeof(vector_type);
+  accelerator_for(idx,nsite,1,{
+      
+      Coordinate to_coor, base;
+      Lexicographic::CoorFromIndex(base,idx,LocalLatt);
+      for(int i=0;i<nd;i++){
+	to_coor[i] = base[i];
+      }
+      int to_oidx = 0; for(int d=0;d<nd;d++) to_oidx+=t_ostride[d]*(to_coor[d]%t_rdimensions[d]);
+      int to_lane = 0; for(int d=0;d<nd;d++) to_lane+=t_istride[d]*(to_coor[d]/t_rdimensions[d]);
+
+      vector_type* to = (vector_type *)&to_v[to_oidx];
+      scalar_type* from = (scalar_type *)&from_v[idx];
+      
+      scalar_type stmp;
+      for(int w=0;w<words;w++){
+	stmp=from[w];
+	putlane(to[w], stmp, to_lane);
+      }
+    });
+  }
+  ///////////////////////////////////////////////////////////////////////////
+  // Shared by both CoarsenOperator variants
+  //
+  //     conj(pha[block]) proj[k (which mom)][j (basis vec cpt)][block]
+  //       =  \sum_{l in ball}  e^{i q_k . delta_l} < phi_{block,j} | MdagM | phi_{(block+delta_l),i} >
+  //       =  \sum_{l in ball} e^{iqk.delta_l} A_ji^{b.b+l}
+  //       = M_{kl} A_ji^{b.b+l}
+  //
+  //     Where q_k = delta_k . (2*M_PI/global_nb[mu])
+  //     Then A{ji}^{b,b+l} = M^{-1}_{lm} ComputeProj_{m,b,i,j}
+  ///////////////////////////////////////////////////////////////////////////
+  void CoarsenFourierMatrix(GridBase *CoarseGrid,Eigen::MatrixXcd &invMkl)
+  {
+    const int npoint = geom_srhs.npoint;
+    Coordinate clatt = CoarseGrid->GlobalDimensions();
+    int Nd = CoarseGrid->Nd();
+
+    Eigen::MatrixXcd Mkl = Eigen::MatrixXcd::Zero(npoint,npoint);
+    ComplexD ci(0.0,1.0);
+    for(int k=0;k<npoint;k++){ // Loop over momenta
+      for(int l=0;l<npoint;l++){ // Loop over nbr relative
+	ComplexD phase(0.0,0.0);
+	for(int mu=0;mu<Nd;mu++){
+	  RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	  phase=phase+TwoPiL*geom_srhs.shifts[k][mu]*geom_srhs.shifts[l][mu];
+	}
+	phase=exp(phase*ci);
+	Mkl(k,l) = phase;
+      }
+    }
+    invMkl = Mkl.inverse();
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // blockOrthogonalise and blockZAXPY are block operations on the fine
+  // vectors, using a coarse shaped field only as an index set. They need a
+  // grid carrying the fine SIMD layout, which the coarse space no longer
+  // does. Constructed local to the caller so it cannot be mistaken for the
+  // coarse grid.
+  ///////////////////////////////////////////////////////////////////////////
+  void CoarsenBlockGridLayout(GridBase *grid,GridBase *CoarseGrid,
+			      Coordinate &latt,Coordinate &simd,Coordinate &mpi)
+  {
+    int nd = CoarseGrid->_ndimension;
+    latt.resize(nd); simd.resize(nd); mpi.resize(nd);
+    for(int d=0;d<nd;d++){
+      latt[d] = CoarseGrid->_fdimensions[d];
+      simd[d] = grid->_simd_layout[d];
+      mpi [d] = CoarseGrid->_processors[d];
+    }
+  }
+
+  // D+1 coarse grid holding the batch, rhs innermost and unvectorised
+  void CoarsenBatchGridLayout(GridBase *CoarseGrid,int batch,
+			      Coordinate &latt,Coordinate &simd,Coordinate &mpi)
+  {
+    latt.resize(1,batch); simd.resize(1,1); mpi.resize(1,1);
+    latt[0]=batch; simd[0]=1; mpi[0]=1;
+    for(int d=0;d<CoarseGrid->_ndimension;d++){
+      latt.push_back(CoarseGrid->_fdimensions[d]);
+      simd.push_back(CoarseGrid->_simd_layout[d]);
+      mpi .push_back(CoarseGrid->_processors[d]);
+    }
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // The Fourier inverse needs the phase in the coarse layout and the basis
+  // phasing needs it in the fine layout; each is built from its own
+  // coordinates rather than transferred.
+  ///////////////////////////////////////////////////////////////////////////
+  void CoarsenPhases(GridBase *grid,GridBase *CoarseGrid,GridCartesian *BlockGrid,
+		     std::vector<CoarseComplexField> &pha,
+		     std::vector<FineComplexField> &phaF)
+  {
+    const int npoint = geom_srhs.npoint;
+    Coordinate clatt = CoarseGrid->GlobalDimensions();
+    int Nd = CoarseGrid->Nd();
+    ComplexD ci(0.0,1.0);
+
+    typedef typename CComplex::scalar_type SComplex;
+    FineComplexField one(grid); one=SComplex(1.0);
+    FineComplexField zz(grid);  zz = Zero();
+    BlockComplexField pha_blk (BlockGrid);
+    BlockComplexField blk_coor(BlockGrid);
+
+    for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
+      CoarseComplexField coor(CoarseGrid);
+      pha[p] =Zero();
+      pha_blk=Zero();
+      for(int mu=0;mu<Nd;mu++){
+	RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	LatticeCoordinate(coor,mu);
+	pha[p]  = pha[p]  + (TwoPiL * geom_srhs.shifts[p][mu]) * coor;
+	LatticeCoordinate(blk_coor,mu);
+	pha_blk = pha_blk + (TwoPiL * geom_srhs.shifts[p][mu]) * blk_coor;
+      }
+      pha[p] =exp(pha[p] *ci);
+      pha_blk=exp(pha_blk*ci);
+
+      blockZAXPY(phaF[p],pha_blk,one,zz);
+    }
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // Remove the bulk phase from the batch of coarse projections and
+  // accumulate the Fourier inverse into A. Both variants reach here with
+  // TmpProj in the same batch coarse order, so this is shared verbatim.
+  ///////////////////////////////////////////////////////////////////////////
+  void CoarsenAccumulate(int p,int i0,int nbv,int batch,
+			 Eigen::MatrixXcd &invMkl,
+			 std::vector<CoarseComplexField> &pha,
+			 CoarseComplexField &phaB,
+			 CoarseVector &TmpProj,
+			 std::vector<CoarseMatrix> &_A,
+			 GridBase *CoarseGrid)
+  {
+    typedef typename CComplex::scalar_type SComplex;
+    const int npoint = geom_srhs.npoint;
+
+    for(int b=0;b<batch;b++) InsertSliceFast(pha[p],phaB,b,0);
+    TmpProj = conjugate(phaB)*TmpProj;
+
+    int osites=CoarseGrid->oSites();
+    for(int k=0;k<npoint;k++){
+      SComplex sc(invMkl(p,k).real(),invMkl(p,k).imag());
+      CComplex coef(sc);
+      autoView( A_v  , _A[k], AcceleratorWrite);
+      autoView( TP_v , TmpProj, AcceleratorRead);
+      accelerator_for(sss, osites, 1, {
+	  for(int b=0;b<nbv;b++){
+	    for(int j=0;j<nbasis;j++){
+	      A_v[sss](i0+b,j) = A_v[sss](i0+b,j) + coef*TP_v[b+batch*sss](j);
+	    }
+	  }
+      });
+    }
+  }
+
+  void CoarsenReport(RealD tphase,RealD tphaseBZ,RealD tslice,
+		     RealD tmat,RealD tproj,RealD tinv)
+  {
+    std::cout << GridLogMessage<<"CoarsenOperator phase  "<<tphase<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator phaseBZ "<<tphaseBZ<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator slice  "<<tslice <<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator mat    "<<tmat <<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator proj   "<<tproj<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator inv    "<<tinv<<" us"<<std::endl;
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // Coarsen a NATIVELY multiRHS fine operator.
+  //
+  // linop acts on the D+1 dimensional fine grid FineGridMulti, with the batch
+  // of phased basis vectors carried in the rhs direction. A single RHS
+  // operator can be promoted with MrhsPromotedOperator, but that pays an
+  // ExtractSlice/InsertSlice pair per rhs; prefer the single RHS variant
+  // below in that case.
+  ///////////////////////////////////////////////////////////////////////////
+  void CoarsenOperator(LinearOperatorBase<Lattice<Fobj> > &linop,
+		       GridCartesian *FineGridMulti,
+		       std::vector<FineField> &Subspace,
+		       GridBase *CoarseGrid)
+  {
+    RealD tproj=0.0, tmat=0.0, tphase=0.0, tphaseBZ=0.0, tslice=0.0, tinv=0.0;
+
+    std::cout << GridLogMessage<< "GeneralCoarsenMatrixMrhs (multiRHS fine operator)"<< std::endl;
+
+    GRID_ASSERT(Subspace.size()==nbasis);
+    GridBase *grid = Subspace[0].Grid();
+
+    GRID_ASSERT(FineGridMulti->_ndimension == grid->_ndimension+1);
+    GRID_ASSERT(FineGridMulti->_processors[0] == 1);
+    for(int d=0;d<grid->_ndimension;d++){
+      GRID_ASSERT(FineGridMulti->_fdimensions[d+1] == grid->_fdimensions[d]);
+      GRID_ASSERT(FineGridMulti->_processors [d+1] == grid->_processors [d]);
+    }
+    int batch = FineGridMulti->_fdimensions[0];
+
+    Coordinate blatt,bsimd,bmpi;
+    CoarsenBlockGridLayout(grid,CoarseGrid,blatt,bsimd,bmpi);
+    GridCartesian BlockGrid(blatt,bsimd,bmpi);
+
+    BlockComplexField InnerProd(&BlockGrid);
+    blockOrthogonalise(InnerProd,Subspace);
+
+    MultiRHSBlockProject<Lattice<Fobj> >    Projector;
+    Projector.Allocate(nbasis,grid,CoarseGrid);
+    Projector.ImportBasis(Subspace);
+
+    const int npoint = geom_srhs.npoint;
+
+    Eigen::MatrixXcd invMkl;
+    CoarsenFourierMatrix(CoarseGrid,invMkl);
+
+    FineField phaV(grid);
+    std::vector<FineComplexField>   phaF(npoint,grid);
+    std::vector<CoarseComplexField> pha (npoint,CoarseGrid);
+
+    tphase=-usecond();
+    CoarsenPhases(grid,CoarseGrid,&BlockGrid,pha,phaF);
+    tphase+=usecond();
+
+    std::vector<CoarseMatrix> _A;
+    _A.resize(npoint,CoarseGrid);
+    for(int k=0;k<npoint;k++) _A[k] = Zero();
+
+    Coordinate cmlatt,cmsimd,cmmpi;
+    CoarsenBatchGridLayout(CoarseGrid,batch,cmlatt,cmsimd,cmmpi);
+    GridCartesian CoarseBatchGrid(cmlatt,cmsimd,cmmpi);
+
+    CoarseVector       TmpProj(&CoarseBatchGrid);
+    CoarseComplexField phaB(&CoarseBatchGrid);
+
+    FineField hi_in (FineGridMulti);
+    FineField hi_out(FineGridMulti);
+    FineField zzF(grid); zzF = Zero();
+
+    for(int i0=0;i0<nbasis;i0+=batch){ // Loop over batches of basis vectors
+
+      int nbv = MIN(batch,nbasis-i0);
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i0<<"/"<<nbasis<< std::endl;
+
+      for(int p=0;p<npoint;p++){ // Loop over momenta
+
+	// One phase, applied to the whole batch. Tail slices are zeroed so
+	// the operator never sees undefined data.
+	for(int b=0;b<nbv;b++){
+	  tphaseBZ-=usecond();
+	  phaV = phaF[p]*Subspace[i0+b];
+	  tphaseBZ+=usecond();
+	  tslice-=usecond();
+	  InsertSliceFast(phaV,hi_in,b,0);
+	  tslice+=usecond();
+	}
+	tslice-=usecond();
+	for(int b=nbv;b<batch;b++){
+	  InsertSliceFast(zzF,hi_in,b,0);
+	}
+	tslice+=usecond();
+
+	tmat-=usecond();
+	linop.Op(hi_in,hi_out);
+	tmat+=usecond();
+
+	tproj-=usecond();
+	Projector.blockProject(hi_out,TmpProj);
+	tproj+=usecond();
+
+	tinv-=usecond();
+	CoarsenAccumulate(p,i0,nbv,batch,invMkl,pha,phaB,TmpProj,_A,CoarseGrid);
+	tinv+=usecond();
+      }
+    }
+
+    for(int p=0;p<npoint;p++){
+      GridtoBLAS(_A[p],BLAS_A[p]);
+    }
+    CoarsenReport(tphase,tphaseBZ,tslice,tmat,tproj,tinv);
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // Coarsen a SINGLE RHS fine operator.
+  //
+  // No multiRHS packing: the operator is applied once per phased basis
+  // vector and the batch is assembled on the coarse side by the mixed
+  // blockProject, which takes a vector of fine fields and writes the batch
+  // coarse field the accumulate expects. Only nbv applications per momentum,
+  // so a batch that does not divide nbasis wastes nothing, and the live fine
+  // storage is batch fields rather than two D+1 fields of extent batch.
+  ///////////////////////////////////////////////////////////////////////////
+  void CoarsenOperator(LinearOperatorBase<Lattice<Fobj> > &linop,
+		       std::vector<FineField> &Subspace,
+		       GridBase *CoarseGrid,
+		       int batch)
+  {
+    RealD tproj=0.0, tmat=0.0, tphase=0.0, tphaseBZ=0.0, tslice=0.0, tinv=0.0;
+
+    std::cout << GridLogMessage<< "GeneralCoarsenMatrixMrhs (single RHS fine operator)"<< std::endl;
+
+    GRID_ASSERT(Subspace.size()==nbasis);
+    GRID_ASSERT(batch>=1);
+    GridBase *grid = Subspace[0].Grid();
+
+    Coordinate blatt,bsimd,bmpi;
+    CoarsenBlockGridLayout(grid,CoarseGrid,blatt,bsimd,bmpi);
+    GridCartesian BlockGrid(blatt,bsimd,bmpi);
+
+    BlockComplexField InnerProd(&BlockGrid);
+    blockOrthogonalise(InnerProd,Subspace);
+
+    MultiRHSBlockProject<Lattice<Fobj> >    Projector;
+    Projector.Allocate(nbasis,grid,CoarseGrid);
+    Projector.ImportBasis(Subspace);
+
+    const int npoint = geom_srhs.npoint;
+
+    Eigen::MatrixXcd invMkl;
+    CoarsenFourierMatrix(CoarseGrid,invMkl);
+
+    FineField phaV(grid);
+    std::vector<FineComplexField>   phaF(npoint,grid);
+    std::vector<CoarseComplexField> pha (npoint,CoarseGrid);
+
+    tphase=-usecond();
+    CoarsenPhases(grid,CoarseGrid,&BlockGrid,pha,phaF);
+    tphase+=usecond();
+
+    std::vector<CoarseMatrix> _A;
+    _A.resize(npoint,CoarseGrid);
+    for(int k=0;k<npoint;k++) _A[k] = Zero();
+
+    Coordinate cmlatt,cmsimd,cmmpi;
+    CoarsenBatchGridLayout(CoarseGrid,batch,cmlatt,cmsimd,cmmpi);
+    GridCartesian CoarseBatchGrid(cmlatt,cmsimd,cmmpi);
+
+    CoarseVector       TmpProj(&CoarseBatchGrid);
+    CoarseComplexField phaB(&CoarseBatchGrid);
+
+    std::vector<FineField> MphaV(batch,grid);
+
+    for(int i0=0;i0<nbasis;i0+=batch){ // Loop over batches of basis vectors
+
+      int nbv = MIN(batch,nbasis-i0);
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i0<<"/"<<nbasis<< std::endl;
+
+      for(int p=0;p<npoint;p++){ // Loop over momenta
+
+	for(int b=0;b<nbv;b++){
+	  tphaseBZ-=usecond();
+	  phaV = phaF[p]*Subspace[i0+b];
+	  tphaseBZ+=usecond();
+	  tmat-=usecond();
+	  linop.Op(phaV,MphaV[b]);
+	  tmat+=usecond();
+	}
+	// The accumulate reads only the first nbv slices, but the projector
+	// sees the whole vector, so the tail must not be undefined.
+	for(int b=nbv;b<batch;b++) MphaV[b] = Zero();
+
+	tproj-=usecond();
+	Projector.blockProject(MphaV,TmpProj);
+	tproj+=usecond();
+
+	tinv-=usecond();
+	CoarsenAccumulate(p,i0,nbv,batch,invMkl,pha,phaB,TmpProj,_A,CoarseGrid);
+	tinv+=usecond();
+      }
+    }
+
+    for(int p=0;p<npoint;p++){
+      GridtoBLAS(_A[p],BLAS_A[p]);
+    }
+    CoarsenReport(tphase,tphaseBZ,tslice,tmat,tproj,tinv);
+  }
+  void Mdag(const CoarseVector &in, CoarseVector &out)
+  {
+    this->M(in,out);
+  }
+  void M (const CoarseVector &in, CoarseVector &out)
+  {
+    //    std::cout << GridLogMessage << "New Mrhs coarse"<<std::endl;
+    conformable(CoarseGrid(),in.Grid());
+    conformable(in.Grid(),out.Grid());
+    out.Checkerboard() = in.Checkerboard();
+
+    RealD t_tot;
+    RealD t_exch;
+    RealD t_GtoB;
+    RealD t_BtoG;
+    RealD t_mult;
+
+    CheckGridSet();
+    if ( in.Grid() != _CoarseGridMulti ) {
+      std::cout << GridLogError
+		<< "MultiGeneralCoarsenedOperatorV2::M called with a field on a"
+		<< std::endl;
+      std::cout << GridLogError
+		<< "  different grid object from the one given to SetGrid(). Two"
+		<< std::endl;
+      std::cout << GridLogError
+		<< "  grids of identical shape do not conform; share one object."
+		<< std::endl;
+      GRID_ASSERT(in.Grid() == _CoarseGridMulti);
+    }
+
+    t_tot=-usecond();
+    CoarseVector tin=in;
+    t_exch=-usecond();
+    CoarseVector pin = CellMulti->ExchangePeriodic(tin); //padded input
+    t_exch+=usecond();
+
+    CoarseVector pout(pin.Grid());
+
+    int npoint = geom.npoint;
+    typedef calcMatrix* Aview;
+    typedef LatticeView<Cvec> Vview;
+      
+    const int Nsimd = CComplex::Nsimd();
+
+    int64_t nrhs  =pin.Grid()->GlobalDimensions()[0];
+    GRID_ASSERT(nrhs>=1);
+
+    RealD flops,bytes;
+    int64_t osites=in.Grid()->oSites(); // unpadded
+    int64_t unpadded_vol = CoarseGrid()->lSites()/nrhs;
+    
+    flops = 1.0* npoint * nbasis * nbasis * 8.0 * osites * CComplex::Nsimd();
+    bytes = 1.0*osites*sizeof(siteMatrix)*npoint/pin.Grid()->GlobalDimensions()[0]
+          + 2.0*osites*sizeof(siteVector)*npoint;
+    
+
+    t_GtoB=-usecond();
+    GridtoBLAS(pin,BLAS_B);
+    t_GtoB+=usecond();
+
+    GridBLAS BLAS;
+
+    t_mult=-usecond();
+    for(int p=0;p<geom.npoint;p++){
+      RealD c = 1.0;
+      if (p==0) c = 0.0;
+      ComplexD beta(c);
+
+      BLAS.gemmBatched(nbasis,nrhs,nbasis,
+		       ComplexD(1.0),
+		       BLAS_AP[p], 
+		       BLAS_BP[p], 
+		       ComplexD(c), 
+		       BLAS_CP);
+    }
+    BLAS.synchronise();
+    t_mult+=usecond();
+
+    t_BtoG=-usecond();
+    BLAStoGrid(out,BLAS_C);
+    t_BtoG+=usecond();
+    t_tot+=usecond();
+    /*
+    std::cout << GridLogMessage << "New Mrhs coarse DONE "<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult exch "<<t_exch<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult mult "<<t_mult<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult GtoB  "<<t_GtoB<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult BtoG  "<<t_BtoG<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult tot  "<<t_tot<<" us"<<std::endl;
+    */
+    //    std::cout << GridLogMessage<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse Kernel flops "<< flops<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse Kernel flop/s "<< flops/t_mult<<" mflop/s"<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse Kernel bytes/s "<< bytes/t_mult/1000<<" GB/s"<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse overall flops/s "<< flops/t_tot<<" mflop/s"<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse total bytes   "<< bytes/1e6<<" MB"<<std::endl;
+  };
+  virtual  void Mdiag    (const Field &in, Field &out){ GRID_ASSERT(0);};
+  virtual  void Mdir     (const Field &in, Field &out,int dir, int disp){assert(0);};
+  virtual  void MdirAll  (const Field &in, std::vector<Field> &out){assert(0);};
+};
+  
+NAMESPACE_END(Grid);

Grid/algorithms/multigrid/MrhsPromotedOperator.h

@@ -0,0 +1,161 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./lib/algorithms/multigrid/MrhsPromotedOperator.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);
+
+///////////////////////////////////////////////////////////////////////////////
+// Present a D dimensional operator as a D+1 dimensional operator with Nrhs in
+// dimension 0.  Field type is unchanged; only the Grid differs, so this is a
+// LinearOperatorBase and callers need no template parameter: a native mrhs
+// operator derives from the same base and substitutes without a call site
+// change.
+//
+// Slices in and out around the wrapped operator.  No arithmetic beyond the
+// wrapped call, but one ExtractSliceFast/InsertSliceFast pair per right hand
+// side: data motion, not work.
+//
+// AdjOp is carried so that A^dag may be coarsened as a separate coarse
+// operator when needed, rather than doubling coarse storage.
+///////////////////////////////////////////////////////////////////////////////
+template<class Field>
+class MrhsPromotedOperator : public LinearOperatorBase<Field>
+{
+private:
+
+  LinearOperatorBase<Field> &_LinOp;
+  GridBase                  *_LowGrid;
+  int                        _Nrhs;
+
+public:
+
+  MrhsPromotedOperator(LinearOperatorBase<Field> &LinOp,GridBase *LowGrid,int Nrhs)
+    : _LinOp(LinOp), _LowGrid(LowGrid), _Nrhs(Nrhs)
+  {
+    GRID_ASSERT(_Nrhs>=1);
+  }
+
+  GridBase *LowGrid(void) { return _LowGrid; }
+  int       Nrhs(void)    { return _Nrhs;    }
+
+  // Reset on each call; retrieve and accumulate in the caller
+  RealD tslice;
+  RealD top;
+
+  void OpDiag (const Field &in, Field &out)
+  {
+    SliceLoop(in,out,[&](Field &i,Field &o){ _LinOp.OpDiag(i,o); });
+  }
+
+  void Op     (const Field &in, Field &out)
+  {
+    SliceLoop(in,out,[&](Field &i,Field &o){ _LinOp.Op(i,o); });
+  }
+
+  void AdjOp  (const Field &in, Field &out)
+  {
+    SliceLoop(in,out,[&](Field &i,Field &o){ _LinOp.AdjOp(i,o); });
+  }
+
+  void HermOp (const Field &in, Field &out)
+  {
+    SliceLoop(in,out,[&](Field &i,Field &o){ _LinOp.HermOp(i,o); });
+  }
+
+  void OpDir  (const Field &in, Field &out,int dir,int disp)
+  {
+    SliceLoop(in,out,[&](Field &i,Field &o){ _LinOp.OpDir(i,o,dir,disp); });
+  }
+
+  //////////////////////////////////////////////////////////////////
+  // Norms of the D+1 field are the sums over slices
+  //////////////////////////////////////////////////////////////////
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2)
+  {
+    Conformable(in,out);
+    Field lo_in (_LowGrid);
+    Field lo_out(_LowGrid);
+    n1=0.0;
+    n2=0.0;
+    for(int r=0;r<_Nrhs;r++){
+      RealD r1,r2;
+      ExtractSliceFast(lo_in,in,r,0);
+      _LinOp.HermOpAndNorm(lo_in,lo_out,r1,r2);
+      InsertSliceFast(lo_out,out,r,0);
+      n1=n1+r1;
+      n2=n2+r2;
+    }
+  }
+
+  void OpDirAll(const Field &in, std::vector<Field> &out)
+  {
+    int npoint = out.size();
+    Field lo_in(_LowGrid);
+    std::vector<Field> lo_out(npoint,_LowGrid);
+    for(int r=0;r<_Nrhs;r++){
+      ExtractSliceFast(lo_in,in,r,0);
+      _LinOp.OpDirAll(lo_in,lo_out);
+      for(int p=0;p<npoint;p++){
+        InsertSliceFast(lo_out[p],out[p],r,0);
+      }
+    }
+  }
+
+private:
+
+  void Conformable(const Field &in,const Field &out)
+  {
+    conformable(in.Grid(),out.Grid());
+    GRID_ASSERT(in.Grid()->_ndimension == _LowGrid->_ndimension+1);
+    GRID_ASSERT(in.Grid()->_fdimensions[0] == _Nrhs);
+  }
+
+  template<class Kernel>
+  void SliceLoop(const Field &in,Field &out,Kernel K)
+  {
+    Conformable(in,out);
+    Field lo_in (_LowGrid);
+    Field lo_out(_LowGrid);
+    tslice=0.0;
+    top=0.0;
+    for(int r=0;r<_Nrhs;r++){
+      tslice-=usecond();
+      ExtractSliceFast(lo_in,in,r,0);
+      tslice+=usecond();
+      top-=usecond();
+      K(lo_in,lo_out);
+      top+=usecond();
+      tslice-=usecond();
+      InsertSliceFast(lo_out,out,r,0);
+      tslice+=usecond();
+    }
+  }
+
+};
+
+NAMESPACE_END(Grid);

Grid/algorithms/multigrid/MultiGrid.h

@@ -32,3 +32,5 @@ Author: Peter Boyle <pboyle@bnl.gov>
 #include <Grid/algorithms/multigrid/CoarsenedMatrix.h>
 #include <Grid/algorithms/multigrid/GeneralCoarsenedMatrix.h>
 #include <Grid/algorithms/multigrid/GeneralCoarsenedMatrixMultiRHS.h>
+#include <Grid/algorithms/multigrid/GeneralCoarsenedMatrixMultiRHSV2.h>
+#include <Grid/algorithms/multigrid/MrhsPromotedOperator.h>

Grid/algorithms/multigrid/RecursiveSchurInverse.h

@@ -0,0 +1,617 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: RecursiveSchurInverse.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>
+
+NAMESPACE_BEGIN(Grid);
+
+///////////////////////////////////////////////////////////////////////////////
+// RecursiveSchurInverse: distributed dense inversion by recursive Schur
+// complement over a binary rank-range tree.
+//
+// Contract: rank r owns global rows [rowStart[r], rowStart[r+1]) of an
+// N x N matrix in rank-major ordering, and receives its rows of the
+// inverse in the same layout.  Consumes GridBase collectives, GridBLAS
+// and GridBLASInverse only; Eigen reference backends permit CPU unit
+// testing under mpirun (Test_schur_inverse).
+//
+// Arithmetic is fp64 throughout; the caller rounds once into fp32 storage.
+//
+// Execution: SPMD full-tree walk.  Every rank makes the identical call
+// sequence; data participation is ownership-gated; all collectives are
+// world-wide, so no deadlock surface exists.
+//
+// Storage: BlockRows is column-major, ld = rows; element (i,j) at
+// data[i + j*ld]; a column window is the contiguous slice at data[col0*ld].
+///////////////////////////////////////////////////////////////////////////////
+
+///////////////////////////////////////////////////////////////////////////////
+// My rows of a distributed dense matrix: rows x cols, column major, ld = rows.
+///////////////////////////////////////////////////////////////////////////////
+class BlockRows
+{
+public:
+  deviceVector<ComplexD> data;
+  int64_t                rows;
+  int64_t                cols;
+  int64_t                ld;
+
+  BlockRows()
+  {
+    rows = 0;
+    cols = 0;
+    ld   = 0;
+  }
+  void Resize(int64_t r, int64_t c)
+  {
+    rows = r;
+    cols = c;
+    ld   = r;
+    data.resize((uint64_t)r*c);
+  }
+  ComplexD *ColumnWindow(int64_t col0)
+  {
+    GRID_ASSERT( col0 >= 0 );
+    GRID_ASSERT( col0 <= cols );
+    return &data[(uint64_t)col0*ld];
+  }
+};
+
+class RecursiveSchurInverse
+{
+public:
+  GridBase             *grid;       // world collectives only
+  int64_t               N;          // global matrix dimension
+  int                   P;          // ranks
+  int                   me;         // this rank
+  std::vector<int64_t>  rowStart;   // P+1 entries: rank-major row ownership
+  int64_t               myRow0;
+  int64_t               myNrows;
+  int64_t               panelBytes; // gather panel budget (DENSE_PANEL_BYTES)
+
+  GridBLAS              BLAS;
+  GridBLASInverse       INV;
+
+  // Growth telemetry: one entry per merge node, walk order
+  std::vector<double>   telNormB;      // ||B||_F = ||A11inv A12||_F
+  std::vector<double>   telSratio;     // ||S||_F / ||A22||_F
+  double                telLeafMaxInv; // max |(leaf inverse)_ij| over leaves
+
+  // Phase timers/counters, reported by ReportTelemetry
+  double                tMemset;       // device panel zero-fill
+  double                tDeposit;      // owner rows -> panel (device kernel)
+  double                tAllreduce;    // GlobalSumVector on device panels
+  double                tGemm;         // strided gemm + synchronise
+  double                tLeaf;         // leaf inversions
+  double                tARmin;        // fastest single panel collective
+  double                tARmax;        // slowest single panel collective
+  uint64_t              bytesAllreduce;
+  uint64_t              nAllreduce;    // panel collectives
+  uint64_t              nGatherGemm;   // GatherGemm calls
+
+  // Persistent grow-only device panel; assembly and collectives are
+  // device-resident.  Device builds require GPU-aware MPI.
+  deviceVector<ComplexD> dPanelBuf;
+
+  ///////////////////////////////////////////////////////////////////////////
+  // Ownership-table validation: a proper partition of [0,N).
+  // Static and communicator-free so synthetic tables unit-test directly.
+  ///////////////////////////////////////////////////////////////////////////
+  static void CheckRowStart(const std::vector<int64_t> &table, int64_t N)
+  {
+    int P = (int)table.size() - 1;
+    GRID_ASSERT( P >= 1 );
+    GRID_ASSERT( table[0] == 0 );
+    GRID_ASSERT( table[P] == N );
+    for(int r=0; r<P; r++)
+    {
+      GRID_ASSERT( table[r+1] >= table[r] );  // zero-row ranks permitted
+    }
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // Build the ownership table from each rank's local row count: zero-fill
+  // allgather (the standing comms idiom) then prefix sum.  Every rank
+  // returns the identical table.
+  ///////////////////////////////////////////////////////////////////////////
+  static std::vector<int64_t> MakeRowStart(GridBase *g, int64_t myNrows)
+  {
+    int P  = g->ProcessorCount();
+    int me = g->ThisRank();
+
+    std::vector<uint64_t> counts(P, 0);
+    counts[me] = (uint64_t)myNrows;
+    g->GlobalSumVector(&counts[0], P);
+
+    std::vector<int64_t> table(P+1);
+    table[0] = 0;
+    for(int r=0; r<P; r++)
+    {
+      table[r+1] = table[r] + (int64_t)counts[r];
+    }
+    CheckRowStart(table, table[P]);
+    return table;
+  }
+
+  RecursiveSchurInverse(GridBase *g,
+                        int64_t N_,
+                        std::vector<int64_t> &rowStart_,
+                        int64_t panelBytes_)
+  {
+    grid       = g;
+    N          = N_;
+    P          = g->ProcessorCount();
+    me         = g->ThisRank();
+    rowStart   = rowStart_;
+    panelBytes = panelBytes_;
+
+    GRID_ASSERT( (int)rowStart.size() == P+1 );
+    CheckRowStart(rowStart, N);
+
+    myRow0  = rowStart[me];
+    myNrows = rowStart[me+1] - rowStart[me];
+
+    telLeafMaxInv = 0.0;
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // The communication primitive.
+  //
+  //   C(:, colC : colC+widthB) <-   beta  * C(:, colC : colC+widthB)
+  //                               + alpha * A(:, colA : colA+widthA) * Bsub
+  //
+  // Bsub is the widthA x widthB sub-block of a row-distributed operand
+  // owned by ranks [rB0, rB1): owner r contributes its rows of
+  // B(:, colB : colB+widthB) at sub-block row offset
+  // rowStart[r] - rowStart[rB0], gathered in panelBytes row-chunks by
+  // device zero-fill + deposit kernel + GlobalSumVector.
+  //
+  // Every rank calls; non-owners of B add zeros; ranks with A.rows == 0
+  // skip local compute but make every collective call.  Column offsets
+  // are local buffer offsets -- non-participants pass 0.
+  ///////////////////////////////////////////////////////////////////////////
+  void GatherGemm(ComplexD alpha,
+                  BlockRows &A, int64_t colA, int64_t widthA,
+                  int rB0, int rB1,
+                  BlockRows &B, int64_t colB, int64_t widthB,
+                  ComplexD beta,
+                  BlockRows &C, int64_t colC)
+  {
+    GRID_ASSERT( rB0 >= 0 );
+    GRID_ASSERT( rB1 >  rB0 );
+    GRID_ASSERT( rB1 <= P );
+
+    int64_t k = rowStart[rB1] - rowStart[rB0];
+    int64_t m = A.rows;
+    int64_t n = widthB;
+    GRID_ASSERT( widthA == k );
+    GRID_ASSERT( n >= 1 );
+
+    int owner = ( me >= rB0 ) && ( me < rB1 ) && ( B.rows > 0 );
+    int64_t myOff = 0;
+    if ( owner )
+    {
+      myOff = rowStart[me] - rowStart[rB0];
+    }
+
+    if ( m > 0 )
+    {
+      GRID_ASSERT( colA + widthA <= A.cols );
+      GRID_ASSERT( colC + widthB <= C.cols );
+      GRID_ASSERT( C.rows == m );
+    }
+
+    nGatherGemm++;
+    GRID_TRACE("GatherGemm");
+
+    if ( owner )
+    {
+      GRID_ASSERT( colB + widthB <= B.cols );
+    }
+
+    int64_t kc = panelBytes / ( (int64_t)sizeof(ComplexD) * n );
+    if ( kc < 1 ) kc = 1;
+    if ( kc > k ) kc = k;
+    GRID_ASSERT( kc*n < 2147483647L );   // GlobalSumVector count is int
+
+    deviceVector<ComplexD> &dPanel = dPanelBuf;
+    if ( dPanel.size() < (uint64_t)kc*n ) dPanel.resize((uint64_t)kc*n);
+    deviceVector<ComplexD*> ap(1);
+    deviceVector<ComplexD*> bp(1);
+    deviceVector<ComplexD*> cp(1);
+    std::vector<ComplexD*>  ptr(1);
+
+    for(int64_t k0=0; k0<k; k0+=kc)
+    {
+      int64_t kchunk = std::min(kc, k-k0);
+
+      // Zeroing must complete before MPI reads the panel; it is the sole
+      // producer on non-owner ranks.
+      tMemset -= usecond();
+      acceleratorMemSet(&dPanel[0], 0, (uint64_t)kchunk*n*sizeof(ComplexD));
+      tMemset += usecond();
+      if ( owner )
+      {
+        int64_t i0 = std::max(k0,        myOff);
+        int64_t i1 = std::min(k0+kchunk, myOff+B.rows);
+        if ( i1 > i0 )
+        {
+          // Deposit my rows: strided block copy, len rows x n columns
+          int64_t   len   = i1-i0;
+          int64_t   brows = B.rows;
+          int64_t   dof   = i0-k0;
+          int64_t   sof   = i0-myOff;
+          ComplexD *src   = B.ColumnWindow(colB);
+          ComplexD *dst   = &dPanel[0];
+          tDeposit -= usecond();
+          accelerator_for(idx, (uint64_t)(len*n), 1, {
+            int64_t j = idx / len;
+            int64_t i = idx % len;
+            dst[(uint64_t)(dof + i + j*kchunk)] = src[(uint64_t)(sof + i + j*brows)];
+          });
+          tDeposit += usecond();
+        }
+      }
+      double tar = -usecond();
+      grid->GlobalSumVector(&dPanel[0], (int)(kchunk*n));
+      tar += usecond();
+      tAllreduce += tar;
+      tARmin = std::min(tARmin, tar);
+      tARmax = std::max(tARmax, tar);
+      bytesAllreduce += (uint64_t)kchunk*n*sizeof(ComplexD);
+      nAllreduce++;
+
+      if ( m > 0 )
+      {
+        ComplexD beta_use = ( k0==0 ) ? beta : ComplexD(1.0,0.0);
+
+        ptr[0] = A.ColumnWindow(colA + k0);
+        acceleratorCopyToDevice(&ptr[0], &ap[0], sizeof(ComplexD*));
+        ptr[0] = &dPanel[0];
+        acceleratorCopyToDevice(&ptr[0], &bp[0], sizeof(ComplexD*));
+        ptr[0] = C.ColumnWindow(colC);
+        acceleratorCopyToDevice(&ptr[0], &cp[0], sizeof(ComplexD*));
+
+        tGemm -= usecond();
+        BLAS.gemmBatched(GridBLAS_OP_N, GridBLAS_OP_N,
+                         (int)m, (int)n, (int)kchunk,
+                         alpha,    ap, (int)A.ld,
+                                   bp, (int)kchunk,
+                         beta_use, cp, (int)C.ld);
+        BLAS.synchronise();
+        tGemm += usecond();
+      }
+    }
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // Local Frobenius norm-squared of a full-height column window.
+  // NO comms; callers GlobalSum the result.  Host staging, setup-scale.
+  ///////////////////////////////////////////////////////////////////////////
+  double FrobNorm2Local(BlockRows &X, int64_t col0, int64_t w)
+  {
+    if ( X.rows == 0 ) return 0.0;
+    GRID_ASSERT( col0 + w <= X.cols );
+    uint64_t len = (uint64_t)X.rows*w;
+    std::vector<ComplexD> h(len);
+    acceleratorCopyFromDevice(X.ColumnWindow(col0), &h[0], len*sizeof(ComplexD));
+    // Member real()/imag(): portable across std::complex (CPU) and
+    // thrust::complex (HIP), where std::norm does not resolve.
+    double s = 0.0;
+    for(uint64_t i=0; i<len; i++)
+    {
+      double re = h[i].real();
+      double im = h[i].imag();
+      s += re*re + im*im;
+    }
+    return s;
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // dst(:, dcol0 : dcol0+w) = - src(:, 0:w).  Both operands have ld == rows
+  // so full-height windows are contiguous: flat elementwise device copy.
+  ///////////////////////////////////////////////////////////////////////////
+  void NegateCopy(BlockRows &src, BlockRows &dst, int64_t dcol0, int64_t w)
+  {
+    GRID_ASSERT( src.rows == dst.rows );
+    GRID_ASSERT( w <= src.cols );
+    GRID_ASSERT( dcol0 + w <= dst.cols );
+    if ( src.rows == 0 ) return;
+    uint64_t len = (uint64_t)src.rows*w;
+    ComplexD *s = &src.data[0];
+    ComplexD *d = dst.ColumnWindow(dcol0);
+    accelerator_for(i, len, 1, {
+      d[i] = -s[i];
+    });
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // Leaf inversion: local, in place on the contiguous diagonal window.
+  // No collectives.
+  ///////////////////////////////////////////////////////////////////////////
+  void LeafInvert(int64_t col0, int64_t width, BlockRows &Arows)
+  {
+    GRID_TRACE("SchurLeaf");
+    GRID_ASSERT( width == Arows.rows );
+    GRID_ASSERT( col0 + width <= Arows.cols );
+    int64_t  w   = width;
+    uint64_t len = (uint64_t)w*w;
+    tLeaf -= usecond();
+
+    deviceVector<ComplexD*> bp(1);
+    std::vector<ComplexD*>  ptr(1);
+    ptr[0] = Arows.ColumnWindow(col0);
+    acceleratorCopyToDevice(&ptr[0], &bp[0], sizeof(ComplexD*));
+    INV.inverseBatched(w, bp);
+
+    // Telemetry: max |element| of the leaf inverse
+    {
+      std::vector<ComplexD> h(len);
+      acceleratorCopyFromDevice(Arows.ColumnWindow(col0), &h[0], len*sizeof(ComplexD));
+      double mx = 0.0;
+      for(uint64_t i=0; i<len; i++)
+      {
+        double re = h[i].real();
+        double im = h[i].imag();
+        mx = std::max(mx, re*re + im*im);
+      }
+      telLeafMaxInv = std::max(telLeafMaxInv, std::sqrt(mx));
+    }
+    tLeaf += usecond();
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // The recursion (plan 3.5 / 4B.3).  Inverts the diagonal block of the
+  // rank-major matrix spanned by ranks [r0, r1), living in every member
+  // rank's column window [col0, col0+width) -- IN PLACE.
+  //
+  // SPMD: every rank calls with IDENTICAL (r0, r1, width) and its own
+  // local (col0, Arows); ranks outside [r0, r1) participate in the
+  // collectives only (dummy operands, zero contributions).  The collective
+  // sequence -- 5 GatherGemm calls + 3 scalar GlobalSums per merge node --
+  // is identical on every rank by construction.
+  //
+  //   I = [r0, mid)   J = [mid, r1)   widths WI, WJ
+  //   1. recurse I:      A11 -> A11inv
+  //   2. B = A11inv.A12                     (I rows)
+  //   3. C = A21.A11inv                     (J rows)
+  //   4. S = A22 - A21.B    in place        (J rows)   [alpha=-1, beta=1]
+  //   5. recurse J:      S -> Sinv
+  //   6. T = Sinv.C                         (J rows)
+  //   7. U = B.Sinv                         (I rows)
+  //   8. X11 = A11inv + U.C  in place       (I rows)   [beta=1]
+  //   9. X12 = -U, X21 = -T  local negates; X22 = Sinv already in place
+  ///////////////////////////////////////////////////////////////////////////
+  void SchurNode(int r0, int r1, int64_t col0, int64_t width, BlockRows &Arows)
+  {
+    int span = r1 - r0;
+    GRID_ASSERT( span >= 1 );
+    GRID_ASSERT( width == rowStart[r1] - rowStart[r0] );
+
+    if ( span == 1 )
+    {
+      if ( ( me == r0 ) && ( myNrows > 0 ) )
+      {
+        LeafInvert(col0, width, Arows);
+      }
+      return;
+    }
+
+    int     mid = ( r0 + r1 ) / 2;
+    int64_t WI  = rowStart[mid] - rowStart[r0];
+    int64_t WJ  = rowStart[r1]  - rowStart[mid];
+
+    // Zero-width child ranges (all ranks of a half owning no rows) are a
+    // KNOWN LIMITATION: fail loudly rather than divide mysteriously.
+    GRID_ASSERT( WI > 0 );
+    GRID_ASSERT( WJ > 0 );
+
+    int inI = ( me >= r0  ) && ( me < mid );
+    int inJ = ( me >= mid ) && ( me < r1  );
+
+    ComplexD one  ( 1.0,0.0);
+    ComplexD mone (-1.0,0.0);
+    ComplexD zero ( 0.0,0.0);
+
+    BlockRows dummy;
+
+    // 1. A11 -> A11inv
+    SchurNode(r0, mid, col0, WI, Arows);
+
+    // 2. B = A11inv . A12   (I rows; gather A12 from I owners)
+    BlockRows Bbuf;
+    if ( inI ) Bbuf.Resize(myNrows, WJ);
+    {
+      BlockRows &Aop = inI ? Arows : dummy;
+      BlockRows &Cop = inI ? Bbuf  : dummy;
+      int64_t    cA  = inI ? col0  : 0;
+      GatherGemm(one, Aop, cA, WI,
+                 r0, mid,
+                 Arows, col0+WI, WJ,
+                 zero, Cop, 0);
+    }
+    double nB = FrobNorm2Local(Bbuf, 0, inI ? WJ : 0);
+    grid->GlobalSumVector(&nB, 1);
+    telNormB.push_back(std::sqrt(nB));
+
+    // 3. C = A21 . A11inv   (J rows; gather A11inv from I owners)
+    BlockRows Cbuf;
+    if ( inJ ) Cbuf.Resize(myNrows, WI);
+    {
+      BlockRows &Aop = inJ ? Arows : dummy;
+      BlockRows &Cop = inJ ? Cbuf  : dummy;
+      int64_t    cA  = inJ ? col0  : 0;
+      GatherGemm(one, Aop, cA, WI,
+                 r0, mid,
+                 Arows, col0, WI,
+                 zero, Cop, 0);
+    }
+
+    // 4. S = A22 - A21 . B  in place on my A22 window (J rows)
+    double nA22 = FrobNorm2Local( inJ ? Arows : dummy, inJ ? col0+WI : 0, inJ ? WJ : 0 );
+    grid->GlobalSumVector(&nA22, 1);
+    {
+      BlockRows &Aop = inJ ? Arows   : dummy;
+      BlockRows &Cop = inJ ? Arows   : dummy;
+      int64_t    cA  = inJ ? col0    : 0;
+      int64_t    cC  = inJ ? col0+WI : 0;
+      GatherGemm(mone, Aop, cA, WI,
+                 r0, mid,
+                 Bbuf, 0, WJ,
+                 one, Cop, cC);
+    }
+    double nS = FrobNorm2Local( inJ ? Arows : dummy, inJ ? col0+WI : 0, inJ ? WJ : 0 );
+    grid->GlobalSumVector(&nS, 1);
+    telSratio.push_back( std::sqrt(nS) / ( std::sqrt(nA22) + 1.0e-300 ) );
+
+    // 5. S -> Sinv
+    SchurNode(mid, r1, col0+WI, WJ, Arows);
+
+    // 6. T = Sinv . C       (J rows; gather C from J owners)
+    BlockRows Tbuf;
+    if ( inJ ) Tbuf.Resize(myNrows, WI);
+    {
+      BlockRows &Aop = inJ ? Arows   : dummy;
+      BlockRows &Cop = inJ ? Tbuf    : dummy;
+      int64_t    cA  = inJ ? col0+WI : 0;
+      GatherGemm(one, Aop, cA, WJ,
+                 mid, r1,
+                 Cbuf, 0, WI,
+                 zero, Cop, 0);
+    }
+
+    // 7. U = B . Sinv       (I rows; gather Sinv from J owners)
+    BlockRows Ubuf;
+    if ( inI ) Ubuf.Resize(myNrows, WJ);
+    {
+      BlockRows &Aop = inI ? Bbuf : dummy;
+      BlockRows &Cop = inI ? Ubuf : dummy;
+      GatherGemm(one, Aop, 0, WJ,
+                 mid, r1,
+                 Arows, col0+WI, WJ,
+                 zero, Cop, 0);
+    }
+
+    // 8. X11 = A11inv + U . C  in place (I rows; gather C from J owners)
+    {
+      BlockRows &Aop = inI ? Ubuf  : dummy;
+      BlockRows &Cop = inI ? Arows : dummy;
+      int64_t    cC  = inI ? col0  : 0;
+      GatherGemm(one, Aop, 0, WJ,
+                 mid, r1,
+                 Cbuf, 0, WI,
+                 one, Cop, cC);
+    }
+
+    // 9. Off-diagonal signs, local
+    if ( inI ) NegateCopy(Ubuf, Arows, col0+WI, WJ);
+    if ( inJ ) NegateCopy(Tbuf, Arows, col0,    WI);
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // PUBLIC ENTRY.  Arows: my rows of the rank-major N x N matrix (fp64).
+  // On exit Arows holds my rows of the inverse, still fp64; the caller
+  // owns the single terminal rounding into its fp32 apply storage.
+  ///////////////////////////////////////////////////////////////////////////
+  void Invert(BlockRows &Arows)
+  {
+    GRID_ASSERT( Arows.rows == myNrows );
+    GRID_ASSERT( Arows.cols == N );
+
+    telNormB.resize(0);
+    telSratio.resize(0);
+    telLeafMaxInv = 0.0;
+
+    tMemset        = 0.0;
+    tDeposit       = 0.0;
+    tAllreduce     = 0.0;
+    tGemm          = 0.0;
+    tLeaf          = 0.0;
+    tARmin         = 1.0e30;
+    tARmax         = 0.0;
+    bytesAllreduce = 0;
+    nAllreduce     = 0;
+    nGatherGemm    = 0;
+
+    SchurNode(0, P, 0, N, Arows);
+
+    RealD mx = telLeafMaxInv;
+    grid->GlobalMax(mx);
+    telLeafMaxInv = mx;
+  }
+
+  // All telemetry values are globally reduced or boss-local; safe to
+  // stream on every rank (Grid quiesces stdout to the boss unless
+  // --debug-stdout).  NOTE: tAllreduce INCLUDES wait/imbalance -- a rank
+  // arriving early books its wait here; the min/max spread across ranks
+  // separates true wire time (~min) from skew (max-min).
+  void ReportTelemetry(void)
+  {
+    for(uint64_t i=0; i<telNormB.size(); i++)
+    {
+      std::cout << GridLogPerformance
+                << "SchurNode " << i
+                << " ||B||_F "       << telNormB[i]
+                << " ||S||/||A22|| " << telSratio[i]
+                << std::endl;
+    }
+    std::cout << GridLogPerformance
+              << "Schur leaves max|Ainv| " << telLeafMaxInv
+              << std::endl;
+
+    RealD armax =  tAllreduce;
+    RealD armin = -tAllreduce;
+    grid->GlobalMax(armax);
+    grid->GlobalMax(armin);
+    armin = -armin;
+
+    std::cout << GridLogMessage << "Schur phases (boss rank, seconds):"
+              << "  memset "    << tMemset/1.0e6
+              << "  deposit "   << tDeposit/1.0e6
+              << "  allreduce " << tAllreduce/1.0e6
+              << "  gemm "      << tGemm/1.0e6
+              << "  leaf "      << tLeaf/1.0e6
+              << std::endl;
+    std::cout << GridLogMessage << "Schur comms:"
+              << "  GatherGemm calls " << nGatherGemm
+              << "  panel allreduces " << nAllreduce
+              << "  allreduce GB "     << bytesAllreduce/1024./1024./1024.
+              << "  allreduce s min/max over ranks " << armin/1.0e6
+              << " / " << armax/1.0e6
+              << std::endl;
+    std::cout << GridLogMessage << "Schur comms per-call (boss):"
+              << "  min " << (nAllreduce ? tARmin/1.0e3 : 0.0) << " ms"
+              << "  avg " << (nAllreduce ? tAllreduce/nAllreduce/1.0e3 : 0.0) << " ms"
+              << "  max " << tARmax/1.0e3 << " ms"
+              << std::endl;
+  }
+};
+
+NAMESPACE_END(Grid);

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

@@ -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

@@ -239,6 +239,16 @@ 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)
   {
     Broadcast(root,(void *)&data,sizeof(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_ET.h

@@ -74,7 +74,7 @@ accelerator_inline vobj predicatedWhere(const iobj &predicate,
 
   extract(iftrue, truevals);
   extract(iffalse, falsevals);
-  extract<vInteger, Integer>(TensorRemove(predicate), mask);
+  extract(TensorRemove(predicate), mask);
 
   for (int s = 0; s < Nsimd; s++) {
     if (mask[s]) falsevals[s] = truevals[s];

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_comparison.h

@@ -40,16 +40,16 @@ NAMESPACE_BEGIN(Grid);
 //Query supporting logical &&, ||, 
 //////////////////////////////////////////////////////////////////////////
 
-typedef iScalar<vInteger> vPredicate ;
+template<class vobj> using vPredicate = iScalar<IntegerPredicate<vobj> > ;
 
 //////////////////////////////////////////////////////////////////////////
 // compare lattice to lattice
 //////////////////////////////////////////////////////////////////////////
 
 template<class vfunctor,class lobj,class robj>  
-inline Lattice<vPredicate> LLComparison(vfunctor op,const Lattice<lobj> &lhs,const Lattice<robj> &rhs)
+inline Lattice<vPredicate<lobj> > LLComparison(vfunctor op,const Lattice<lobj> &lhs,const Lattice<robj> &rhs)
 {
-  Lattice<vPredicate> ret(rhs.Grid());
+  Lattice<vPredicate<lobj> > ret(rhs.Grid());
   autoView( lhs_v, lhs, CpuRead);
   autoView( rhs_v, rhs, CpuRead);
   autoView( ret_v, ret, CpuWrite);
@@ -62,9 +62,9 @@ inline Lattice<vPredicate> LLComparison(vfunctor op,const Lattice<lobj> &lhs,con
 // compare lattice to scalar
 //////////////////////////////////////////////////////////////////////////
 template<class vfunctor,class lobj,class robj> 
-inline Lattice<vPredicate> LSComparison(vfunctor op,const Lattice<lobj> &lhs,const robj &rhs)
+inline Lattice<vPredicate<lobj> > LSComparison(vfunctor op,const Lattice<lobj> &lhs,const robj &rhs)
 {
-  Lattice<vPredicate> ret(lhs.Grid());
+  Lattice<vPredicate<lobj> > ret(lhs.Grid());
   autoView( lhs_v, lhs, CpuRead);
   autoView( ret_v, ret, CpuWrite);
   thread_for( ss, lhs_v.size(), {
@@ -76,9 +76,9 @@ inline Lattice<vPredicate> LSComparison(vfunctor op,const Lattice<lobj> &lhs,con
 // compare scalar to lattice
 //////////////////////////////////////////////////////////////////////////
 template<class vfunctor,class lobj,class robj> 
-inline Lattice<vPredicate> SLComparison(vfunctor op,const lobj &lhs,const Lattice<robj> &rhs)
+inline Lattice<vPredicate<robj> > SLComparison(vfunctor op,const lobj &lhs,const Lattice<robj> &rhs)
 {
-  Lattice<vPredicate> ret(rhs.Grid());
+  Lattice<vPredicate<robj> > ret(rhs.Grid());
   autoView( rhs_v, rhs, CpuRead);
   autoView( ret_v, ret, CpuWrite);
   thread_for( ss, rhs_v.size(), {
@@ -92,87 +92,87 @@ inline Lattice<vPredicate> SLComparison(vfunctor op,const lobj &lhs,const Lattic
 //////////////////////////////////////////////////////////////////////////
 // Less than
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator < (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+inline Lattice<vPredicate<lobj> > operator < (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
   return LLComparison(vlt<lobj,robj>(),lhs,rhs);
 }
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator < (const Lattice<lobj> & lhs, const robj & rhs) {
+inline Lattice<vPredicate<lobj> > operator < (const Lattice<lobj> & lhs, const robj & rhs) {
   return LSComparison(vlt<lobj,robj>(),lhs,rhs);
 }
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator < (const lobj & lhs, const Lattice<robj> & rhs) {
+inline Lattice<vPredicate<robj> > operator < (const lobj & lhs, const Lattice<robj> & rhs) {
   return SLComparison(vlt<lobj,robj>(),lhs,rhs);
 }
   
 // Less than equal
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator <= (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+inline Lattice<vPredicate<lobj> > operator <= (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
   return LLComparison(vle<lobj,robj>(),lhs,rhs);
 }
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator <= (const Lattice<lobj> & lhs, const robj & rhs) {
+inline Lattice<vPredicate<lobj> > operator <= (const Lattice<lobj> & lhs, const robj & rhs) {
   return LSComparison(vle<lobj,robj>(),lhs,rhs);
 }
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator <= (const lobj & lhs, const Lattice<robj> & rhs) {
+inline Lattice<vPredicate<robj> > operator <= (const lobj & lhs, const Lattice<robj> & rhs) {
   return SLComparison(vle<lobj,robj>(),lhs,rhs);
 }
   
 // Greater than 
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator > (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+inline Lattice<vPredicate<lobj> > operator > (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
   return LLComparison(vgt<lobj,robj>(),lhs,rhs);
 }
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator > (const Lattice<lobj> & lhs, const robj & rhs) {
+inline Lattice<vPredicate<lobj> > operator > (const Lattice<lobj> & lhs, const robj & rhs) {
   return LSComparison(vgt<lobj,robj>(),lhs,rhs);
 }
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator > (const lobj & lhs, const Lattice<robj> & rhs) {
+inline Lattice<vPredicate<robj> > operator > (const lobj & lhs, const Lattice<robj> & rhs) {
   return SLComparison(vgt<lobj,robj>(),lhs,rhs);
 }
   
   
 // Greater than equal
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator >= (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+inline Lattice<vPredicate<lobj> > operator >= (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
   return LLComparison(vge<lobj,robj>(),lhs,rhs);
 }
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator >= (const Lattice<lobj> & lhs, const robj & rhs) {
+inline Lattice<vPredicate<lobj> > operator >= (const Lattice<lobj> & lhs, const robj & rhs) {
   return LSComparison(vge<lobj,robj>(),lhs,rhs);
 }
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator >= (const lobj & lhs, const Lattice<robj> & rhs) {
+inline Lattice<vPredicate<robj> > operator >= (const lobj & lhs, const Lattice<robj> & rhs) {
   return SLComparison(vge<lobj,robj>(),lhs,rhs);
 }
    
 // equal
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator == (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+inline Lattice<vPredicate<lobj> > operator == (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
   return LLComparison(veq<lobj,robj>(),lhs,rhs);
 }
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator == (const Lattice<lobj> & lhs, const robj & rhs) {
+inline Lattice<vPredicate<lobj> > operator == (const Lattice<lobj> & lhs, const robj & rhs) {
   return LSComparison(veq<lobj,robj>(),lhs,rhs);
 }
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator == (const lobj & lhs, const Lattice<robj> & rhs) {
+inline Lattice<vPredicate<robj> > operator == (const lobj & lhs, const Lattice<robj> & rhs) {
   return SLComparison(veq<lobj,robj>(),lhs,rhs);
 }
    
    
 // not equal
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator != (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+inline Lattice<vPredicate<lobj> > operator != (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
   return LLComparison(vne<lobj,robj>(),lhs,rhs);
 }
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator != (const Lattice<lobj> & lhs, const robj & rhs) {
+inline Lattice<vPredicate<lobj> > operator != (const Lattice<lobj> & lhs, const robj & rhs) {
   return LSComparison(vne<lobj,robj>(),lhs,rhs);
 }
 template<class lobj,class robj>
-inline Lattice<vPredicate> operator != (const lobj & lhs, const Lattice<robj> & rhs) {
+inline Lattice<vPredicate<robj> > operator != (const lobj & lhs, const Lattice<robj> & rhs) {
   return SLComparison(vne<lobj,robj>(),lhs,rhs);
 }
 NAMESPACE_END(Grid);

Grid/lattice/Lattice_comparison_utils.h

@@ -39,47 +39,53 @@ NAMESPACE_BEGIN(Grid);
   //
   // Should guard this with isGridTensor<> enable if?
   /////////////////////////////////////////
+  //
+  // Predicate type matching the operand's vectorisation
+  //
+  template<class obj> using IntegerPredicate =
+    typename GridTypeMapper<typename GridTypeMapper<obj>::vector_type>::Integerified;
+
   //
   // Generic list of functors
   //
   template<class lobj,class robj> class veq {
   public:
-    accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
+    accelerator IntegerPredicate<lobj> operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) == (rhs);
     }
   };
   template<class lobj,class robj> class vne {
   public:
-    accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
+    accelerator IntegerPredicate<lobj> operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) != (rhs);
     }
   };
   template<class lobj,class robj> class vlt {
   public:
-    accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
+    accelerator IntegerPredicate<lobj> operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) < (rhs);
     }
   };
   template<class lobj,class robj> class vle {
   public:
-    accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
+    accelerator IntegerPredicate<lobj> operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) <= (rhs);
     }
   };
   template<class lobj,class robj> class vgt {
   public:
-    accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
+    accelerator IntegerPredicate<lobj> operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) > (rhs);
     }
   };
   template<class lobj,class robj> class vge {
     public:
-    accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
+    accelerator IntegerPredicate<lobj> operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) >= (rhs);
     }
@@ -133,78 +139,78 @@ NAMESPACE_BEGIN(Grid);
   // Integer and real get extra relational functions.
   //////////////////////////////////////////////////////////////////////////////////////////////////////
   template<class sfunctor, class vsimd,IfNotComplex<vsimd> = 0> 
-    accelerator_inline vInteger Comparison(sfunctor sop,const vsimd & lhs, const vsimd & rhs)
+    accelerator_inline IntegerPredicate<vsimd> Comparison(sfunctor sop,const vsimd & lhs, const vsimd & rhs)
     {
       typedef typename vsimd::scalar_type scalar;
       ExtractBuffer<scalar> vlhs(vsimd::Nsimd());   // Use functors to reduce this to single implementation
       ExtractBuffer<scalar> vrhs(vsimd::Nsimd());
       ExtractBuffer<Integer> vpred(vsimd::Nsimd());
-      vInteger ret;
+      IntegerPredicate<vsimd> ret;
       extract<vsimd,scalar>(lhs,vlhs);
       extract<vsimd,scalar>(rhs,vrhs);
       for(int s=0;s<vsimd::Nsimd();s++){
 	vpred[s] = sop(vlhs[s],vrhs[s]);
       }
-      merge<vInteger,Integer>(ret,vpred);
+      merge<IntegerPredicate<vsimd>,Integer>(ret,vpred);
       return ret;
     }
 
   template<class sfunctor, class vsimd,IfNotComplex<vsimd> = 0> 
-    accelerator_inline vInteger Comparison(sfunctor sop,const vsimd & lhs, const typename vsimd::scalar_type & rhs)
+    accelerator_inline IntegerPredicate<vsimd> Comparison(sfunctor sop,const vsimd & lhs, const typename vsimd::scalar_type & rhs)
     {
       typedef typename vsimd::scalar_type scalar;
       ExtractBuffer<scalar> vlhs(vsimd::Nsimd());   // Use functors to reduce this to single implementation
       ExtractBuffer<Integer> vpred(vsimd::Nsimd());
-      vInteger ret;
+      IntegerPredicate<vsimd> ret;
       extract<vsimd,scalar>(lhs,vlhs);
       for(int s=0;s<vsimd::Nsimd();s++){
 	vpred[s] = sop(vlhs[s],rhs);
       }
-      merge<vInteger,Integer>(ret,vpred);
+      merge<IntegerPredicate<vsimd>,Integer>(ret,vpred);
       return ret;
     }
 
   template<class sfunctor, class vsimd,IfNotComplex<vsimd> = 0> 
-    accelerator_inline vInteger Comparison(sfunctor sop,const typename vsimd::scalar_type & lhs, const vsimd & rhs)
+    accelerator_inline IntegerPredicate<vsimd> Comparison(sfunctor sop,const typename vsimd::scalar_type & lhs, const vsimd & rhs)
     {
       typedef typename vsimd::scalar_type scalar;
       ExtractBuffer<scalar> vrhs(vsimd::Nsimd());   // Use functors to reduce this to single implementation
       ExtractBuffer<Integer> vpred(vsimd::Nsimd());
-      vInteger ret;
+      IntegerPredicate<vsimd> ret;
       extract<vsimd,scalar>(rhs,vrhs);
       for(int s=0;s<vsimd::Nsimd();s++){
 	vpred[s] = sop(lhs,vrhs[s]);
       }
-      merge<vInteger,Integer>(ret,vpred);
+      merge<IntegerPredicate<vsimd>,Integer>(ret,vpred);
       return ret;
     }
 
 #define DECLARE_RELATIONAL_EQ(op,functor) \
   template<class vsimd,IfSimd<vsimd> = 0>\
-    accelerator_inline vInteger operator op (const vsimd & lhs, const vsimd & rhs)\
+    accelerator_inline IntegerPredicate<vsimd> operator op (const vsimd & lhs, const vsimd & rhs)\
     {\
       typedef typename vsimd::scalar_type scalar;\
       return Comparison(functor<scalar,scalar>(),lhs,rhs);\
     }\
   template<class vsimd,IfSimd<vsimd> = 0>\
-    accelerator_inline vInteger operator op (const vsimd & lhs, const typename vsimd::scalar_type & rhs) \
+    accelerator_inline IntegerPredicate<vsimd> operator op (const vsimd & lhs, const typename vsimd::scalar_type & rhs) \
     {\
       typedef typename vsimd::scalar_type scalar;\
       return Comparison(functor<scalar,scalar>(),lhs,rhs);\
     }\
   template<class vsimd,IfSimd<vsimd> = 0>\
-    accelerator_inline vInteger operator op (const typename vsimd::scalar_type & lhs, const vsimd & rhs) \
+    accelerator_inline IntegerPredicate<vsimd> operator op (const typename vsimd::scalar_type & lhs, const vsimd & rhs) \
     {\
       typedef typename vsimd::scalar_type scalar;\
       return Comparison(functor<scalar,scalar>(),lhs,rhs);\
     }\
   template<class vsimd>\
-    accelerator_inline vInteger operator op(const iScalar<vsimd> &lhs,const typename vsimd::scalar_type &rhs) \
+    accelerator_inline IntegerPredicate<vsimd> operator op(const iScalar<vsimd> &lhs,const typename vsimd::scalar_type &rhs) \
     {									\
       return lhs._internal op rhs;					\
     }									\
   template<class vsimd>\
-    accelerator_inline vInteger operator op(const typename vsimd::scalar_type &lhs,const iScalar<vsimd> &rhs) \
+    accelerator_inline IntegerPredicate<vsimd> operator op(const typename vsimd::scalar_type &lhs,const iScalar<vsimd> &rhs) \
     {									\
       return lhs op rhs._internal;					\
     }									\
@@ -212,7 +218,7 @@ NAMESPACE_BEGIN(Grid);
 #define DECLARE_RELATIONAL(op,functor) \
   DECLARE_RELATIONAL_EQ(op,functor)    \
   template<class vsimd>\
-    accelerator_inline vInteger operator op(const iScalar<vsimd> &lhs,const iScalar<vsimd> &rhs)\
+    accelerator_inline IntegerPredicate<vsimd> operator op(const iScalar<vsimd> &lhs,const iScalar<vsimd> &rhs)\
     {									\
       return lhs._internal op rhs._internal;				\
     }									

Grid/lattice/Lattice_reduction_gpu.h

@@ -197,6 +197,9 @@ __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)
 {
@@ -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::scalar_typeD   scalarD;
-  typedef typename vobj::scalar_objectD sobj;
+  typedef typename vobj::scalar_objectD sobjD;
-  sobj ret;
-  scalarD *ret_p = (scalarD *)&ret;
 
   const int words = sizeof(vobj) / sizeof(vector);
+  sobjD ret; zeroit(ret);
+  scalarD *ret_p = (scalarD *)&ret;
 
-  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

@@ -11,23 +11,22 @@ inline typename vobj::scalar_objectD sumD_gpu_tensor(const vobj *lat, Integer os
   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<sobj, 1> abuff(&ret, {1});
+    sycl::buffer<sobjD, 1> abuff(&ret, {1});
     theGridAccelerator->submit([&](sycl::handler &cgh) {
       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,
                        [=](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);
@@ -82,12 +86,14 @@ 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);
   
   //sync after copy

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/lattice/Lattice_transfer.h

@@ -191,6 +191,15 @@ accelerator_inline void convertType(vComplexD & out, const ComplexD & in) {
 accelerator_inline void convertType(vComplexD2 & out, const ComplexD & in) {
   ((ComplexD*)&out)[acceleratorSIMTlane(vComplexD::Nsimd()*2)] = in;
 }
+// Lex chart: one lane, so there is no lane to select. Needed because the
+// coalesced accessor hands the kernel a scalar object while the destination
+// is still the vector type.
+accelerator_inline void convertType(sComplexF & out, const ComplexF & in) {
+  out.v = in;
+}
+accelerator_inline void convertType(sComplexD & out, const ComplexD & in) {
+  out.v = in;
+}
 #endif
 
 accelerator_inline void convertType(vComplexF & out, const vComplexD2 & in) {

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 +255,402 @@ 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;
 
+  // Single point of control for the aggregated path. Setting
+  // GRID_BINARYIO_NOAGGREGATE falls back to plain lexicographic I/O.
+  static int DefaultControl(void)
+  {
+    static int ctrl = getenv("GRID_BINARYIO_NOAGGREGATE")
+                    ? BINARYIO_LEXICOGRAPHIC
+                    : BINARYIO_LEXICOGRAPHIC|BINARYIO_AGGREGATE;
+    return ctrl;
+  }
+
+#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 +694,18 @@ 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 +733,8 @@ 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 +746,7 @@ 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 +765,19 @@ 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 +835,25 @@ 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 +898,26 @@ class BinaryIO {
         
 	std::ofstream fout; 
 	fout.exceptions ( std::fstream::failbit | std::fstream::badbit );
-	try {
+
-	  if (offset) { // Must already exist and contain data
+        ////////////////////////////////////////////////////////////////////
-	    fout.open(file,std::ios::binary|std::ios::out|std::ios::in);
+        // Grid's model is that the boss rank performs the metadata
-	  } else {     // Allow create
+        // operations and every other rank only seeks and writes into a file
-	    fout.open(file,std::ios::binary|std::ios::out);
+        // 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 {
+	  fout.open(file,std::ios::binary|std::ios::out|std::ios::in);
 	} 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;
@@ -548,7 +999,7 @@ class BinaryIO {
 				       uint32_t &nersc_csum,
 				       uint32_t &scidac_csuma,
 				       uint32_t &scidac_csumb,
-				       int control=BINARYIO_LEXICOGRAPHIC
+				       int control=DefaultControl()
 				       )
   {
     typedef typename vobj::scalar_object sobj;
@@ -587,7 +1038,7 @@ class BinaryIO {
 					  uint32_t &nersc_csum,
 					  uint32_t &scidac_csuma,
 					  uint32_t &scidac_csumb,
-					  int control=BINARYIO_LEXICOGRAPHIC)
+					  int control=DefaultControl())
   {
     typedef typename vobj::scalar_object sobj;
     typedef typename vobj::Realified::scalar_type word;    word w=0;
@@ -674,7 +1125,7 @@ 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|DefaultControl(),
 	     nersc_csum,scidac_csuma,scidac_csumb);
 
     timer.Start();
@@ -753,7 +1204,7 @@ class BinaryIO {
     });
     timer.Stop();
 
-    IOobject(w,grid,iodata,file,offset,format,BINARYIO_WRITE|BINARYIO_LEXICOGRAPHIC,
+    IOobject(w,grid,iodata,file,offset,format,BINARYIO_WRITE|DefaultControl(),
 	     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_;
@@ -260,8 +260,7 @@ class GridLimeReader : public BinaryIO {
               << " / field= " << n2ck << " / rdiff= " << GRID_FIELD_NORM_CALC(FieldNormMetaData_,n2ck) << std::endl;
 	  GRID_FIELD_NORM_CHECK(FieldNormMetaData_,n2ck);
 	}
-//	assert(scidacChecksumVerify(scidacChecksum_,scidac_csuma,scidac_csumb)==1);
+	assert(scidacChecksumVerify(scidacChecksum_,scidac_csuma,scidac_csumb)==1);
-	scidacChecksumVerify(scidacChecksum_,scidac_csuma,scidac_csumb);
 
 	// find out if next field is a GridFieldNorm
 	return;
@@ -415,7 +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
@@ -520,7 +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();
 
@@ -562,7 +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/parallelIO/MetaData.h

@@ -180,7 +180,7 @@ template<class Impl>
 class GaugeStatistics
 {
 public:
-  void operator()(Lattice<vLorentzColourMatrixD> & data,FieldMetaData &header)
+  void operator()(typename Impl::Field & data,FieldMetaData &header)
   {
     header.link_trace = WilsonLoops<Impl>::linkTrace(data);
     header.plaquette  = WilsonLoops<Impl>::avgPlaquette(data);
@@ -188,6 +188,8 @@ public:
 };
 typedef GaugeStatistics<PeriodicGimplD> PeriodicGaugeStatistics;
 typedef GaugeStatistics<ConjugateGimplD> ConjugateGaugeStatistics;
+typedef GaugeStatistics<lexPeriodicGimplD> lexPeriodicGaugeStatistics;
+typedef GaugeStatistics<lexConjugateGimplD> lexConjugateGaugeStatistics;
 template<> inline void PrepareMetaData<vLorentzColourMatrixD>(Lattice<vLorentzColourMatrixD> & field, FieldMetaData &header)
 {
   GridBase *grid = field.Grid();
@@ -197,6 +199,15 @@ template<> inline void PrepareMetaData<vLorentzColourMatrixD>(Lattice<vLorentzCo
   GridMetaData(grid,header);
   MachineCharacteristics(header);
 }
+template<> inline void PrepareMetaData<sLorentzColourMatrixD>(Lattice<sLorentzColourMatrixD> & field, FieldMetaData &header)
+{
+  GridBase *grid = field.Grid();
+  std::string format = getFormatString<sLorentzColourMatrixD>();
+  header.floating_point = format;
+  header.checksum = 0x0; // Nersc checksum unused in ILDG, Scidac
+  GridMetaData(grid,header);
+  MachineCharacteristics(header);
+}
 
 //////////////////////////////////////////////////////////////////////
 // Utilities ; these are QCD aware

Grid/parallelIO/NerscIO.h

@@ -122,7 +122,7 @@ public:
     field.checksum = std::stoul(header["CHECKSUM"],0,16);
     field.ensemble_id      = header["ENSEMBLE_ID"];
     field.ensemble_label   = header["ENSEMBLE_LABEL"];
-//    field.sequence_number  = std::stol(header["SEQUENCE_NUMBER"]);
+    field.sequence_number  = std::stol(header["SEQUENCE_NUMBER"]);
     field.creator          = header["CREATOR"];
     field.creator_hardware = header["CREATOR_HARDWARE"];
     field.creation_date    = header["CREATION_DATE"];
@@ -136,12 +136,14 @@ public:
   // Now the meat: the object readers
   /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 
-  template<class GaugeStats=PeriodicGaugeStatistics>
+  template<class GaugeFieldType,class GaugeStats>
-  static inline void readConfiguration(GaugeField &Umu,
+  static inline void readConfigurationInternal(GaugeFieldType &Umu,
 					       FieldMetaData& header,
 					       std::string file,
-				       GaugeStats GaugeStatisticsCalculator=GaugeStats())
+					       GaugeStats GaugeStatisticsCalculator)
   {
+    typedef typename GaugeFieldType::vector_object vobj;
+    typedef typename GaugeFieldType::scalar_object sobj;
 
     GridBase *grid = Umu.Grid();
     uint64_t offset = readHeader(file,Umu.Grid(),header);
@@ -162,24 +164,24 @@ public:
     const std::string stNC = std::to_string( Nc ) ;
     if ( header.data_type == std::string("4D_SU"+stNC+"_GAUGE") ) {
       if ( ieee32 || ieee32big ) {
-	BinaryIO::readLatticeObject<vLorentzColourMatrixD, LorentzColour2x3F> 
+	BinaryIO::readLatticeObject<vobj, LorentzColour2x3F> 
-	  (Umu,file,Gauge3x2munger<LorentzColour2x3F,LorentzColourMatrix>(), offset,format,
+	  (Umu,file,Gauge3x2munger<LorentzColour2x3F,sobj>(), offset,format,
 	   nersc_csum,scidac_csuma,scidac_csumb);
       }
       if ( ieee64 || ieee64big ) {
-	BinaryIO::readLatticeObject<vLorentzColourMatrixD, LorentzColour2x3D> 
+	BinaryIO::readLatticeObject<vobj, LorentzColour2x3D> 
-	  (Umu,file,Gauge3x2munger<LorentzColour2x3D,LorentzColourMatrix>(),offset,format,
+	  (Umu,file,Gauge3x2munger<LorentzColour2x3D,sobj>(),offset,format,
 	   nersc_csum,scidac_csuma,scidac_csumb);
       }
     } else if ( header.data_type == std::string("4D_SU"+stNC+"_GAUGE_"+stNC+"x"+stNC) ) {
       if ( ieee32 || ieee32big ) {
-	BinaryIO::readLatticeObject<vLorentzColourMatrixD,LorentzColourMatrixF>
+	BinaryIO::readLatticeObject<vobj,LorentzColourMatrixF>
-	  (Umu,file,GaugeSimpleMunger<LorentzColourMatrixF,LorentzColourMatrix>(),offset,format,
+	  (Umu,file,GaugeSimpleMunger<LorentzColourMatrixF,sobj>(),offset,format,
 	   nersc_csum,scidac_csuma,scidac_csumb);
       }
       if ( ieee64 || ieee64big ) {
-	BinaryIO::readLatticeObject<vLorentzColourMatrixD,LorentzColourMatrixD>
+	BinaryIO::readLatticeObject<vobj,LorentzColourMatrixD>
-	  (Umu,file,GaugeSimpleMunger<LorentzColourMatrixD,LorentzColourMatrix>(),offset,format,
+	  (Umu,file,GaugeSimpleMunger<LorentzColourMatrixD,sobj>(),offset,format,
 	   nersc_csum,scidac_csuma,scidac_csumb);
       }
     } else {
@@ -203,7 +205,6 @@ public:
       std::cerr << " plaqs " << clone.plaquette << " " << header.plaquette << std::endl;
       std::cerr << " trace " << clone.link_trace<< " " << header.link_trace<< std::endl;
       std::cerr << " nersc_csum  " <<std::hex<< nersc_csum << " " << header.checksum<< std::dec<< std::endl;
-      exit(0);
     }
     if(exitOnReadPlaquetteMismatch()) GRID_ASSERT(fabs(clone.plaquette -header.plaquette ) < 1.0e-5 );
     GRID_ASSERT(fabs(clone.link_trace-header.link_trace) < 1.0e-6 );
@@ -212,6 +213,26 @@ public:
     std::cout<<GridLogMessage <<"NERSC Configuration "<<file<< " and plaquette, link trace, and checksum agree"<<std::endl;
   }
 
+  //////////////////////////////////////////////////////////////////////////
+  // Constrained frontends: vectorised and lexicographic gauge fields
+  //////////////////////////////////////////////////////////////////////////
+  template<class GaugeStats=PeriodicGaugeStatistics>
+  static inline void readConfiguration(Lattice<vLorentzColourMatrixD> &Umu,
+				       FieldMetaData& header,
+				       std::string file,
+				       GaugeStats GaugeStatisticsCalculator=GaugeStats())
+  {
+    readConfigurationInternal(Umu,header,file,GaugeStatisticsCalculator);
+  }
+  template<class GaugeStats=lexPeriodicGaugeStatistics>
+  static inline void readConfiguration(Lattice<sLorentzColourMatrixD> &Umu,
+				       FieldMetaData& header,
+				       std::string file,
+				       GaugeStats GaugeStatisticsCalculator=GaugeStats())
+  {
+    readConfigurationInternal(Umu,header,file,GaugeStatisticsCalculator);
+  }
+
   // Preferred interface
   template<class GaugeStats=PeriodicGaugeStatistics>
   static inline void writeConfiguration(Lattice<vLorentzColourMatrixD > &Umu,
@@ -220,7 +241,16 @@ public:
 					std::string ens_id = std::string("UKQCD"),
 					unsigned int sequence_number = 1)
   {
-    writeConfiguration(Umu,file,0,1,ens_label,ens_id,sequence_number);
+    writeConfigurationInternal<Lattice<vLorentzColourMatrixD>,GaugeStats>(Umu,file,0,1,ens_label,ens_id,sequence_number);
+  }
+  template<class GaugeStats=lexPeriodicGaugeStatistics>
+  static inline void writeConfiguration(Lattice<sLorentzColourMatrixD > &Umu,
+					std::string file, 
+					std::string ens_label = std::string("DWF"),
+					std::string ens_id = std::string("UKQCD"),
+					unsigned int sequence_number = 1)
+  {
+    writeConfigurationInternal<Lattice<sLorentzColourMatrixD>,GaugeStats>(Umu,file,0,1,ens_label,ens_id,sequence_number);
   }
   template<class GaugeStats=PeriodicGaugeStatistics>
   static inline void writeConfiguration(Lattice<vLorentzColourMatrixD > &Umu,
@@ -231,7 +261,29 @@ public:
 					std::string ens_id = std::string("UKQCD"),
 					unsigned int sequence_number = 1)
   {
-    typedef vLorentzColourMatrixD vobj;
+    writeConfigurationInternal<Lattice<vLorentzColourMatrixD>,GaugeStats>(Umu,file,two_row,bits32,ens_label,ens_id,sequence_number);
+  }
+  template<class GaugeStats=lexPeriodicGaugeStatistics>
+  static inline void writeConfiguration(Lattice<sLorentzColourMatrixD > &Umu,
+					std::string file, 
+					int two_row,
+					int bits32,
+					std::string ens_label = std::string("DWF"),
+					std::string ens_id = std::string("UKQCD"),
+					unsigned int sequence_number = 1)
+  {
+    writeConfigurationInternal<Lattice<sLorentzColourMatrixD>,GaugeStats>(Umu,file,two_row,bits32,ens_label,ens_id,sequence_number);
+  }
+  template<class GaugeFieldType,class GaugeStats>
+  static inline void writeConfigurationInternal(GaugeFieldType &Umu,
+					std::string file, 
+					int two_row,
+					int bits32,
+					std::string ens_label = std::string("DWF"),
+					std::string ens_id = std::string("UKQCD"),
+					unsigned int sequence_number = 1)
+  {
+    typedef typename GaugeFieldType::vector_object vobj;
     typedef typename vobj::scalar_object sobj;
 
     FieldMetaData header;
@@ -280,6 +332,9 @@ public:
     if ( grid->IsBoss() ) {
       writeHeader(header,file);
     }
+    // The header is written twice; the checksum is only known after the data.
+    // Other ranks must not proceed to read it until the rewrite has landed.
+    grid->Barrier();
 
     std::cout<<GridLogMessage <<"Written NERSC Configuration on "<< file << " checksum "
 	     <<std::hex<<header.checksum
@@ -333,6 +388,9 @@ public:
 	if ( grid->IsBoss() ) {
     offset = writeHeader(header,file);
 	}
+    // As for the gauge field: the checksum is only known after the data, so
+    // the header is rewritten. Hold the other ranks until that has landed.
+    grid->Barrier();
 
     std::cout<<GridLogMessage
 	     <<"Written NERSC RNG STATE "<<file<< " checksum "
@@ -374,7 +432,6 @@ public:
 
     if ( nersc_csum != header.checksum ) {
       std::cerr << "checksum mismatch "<<std::hex<< nersc_csum <<" "<<header.checksum<<std::dec<<std::endl;
-      exit(0);
     }
     GRID_ASSERT(nersc_csum == header.checksum );
 

Grid/perfmon/PerfCount.h

@@ -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/QCD.h

@@ -127,7 +127,6 @@ typedef iSpinMatrix<ComplexD >          SpinMatrixD;
 typedef iSpinMatrix<vComplex >          vSpinMatrix;
 typedef iSpinMatrix<vComplexF>          vSpinMatrixF;
 typedef iSpinMatrix<vComplexD>          vSpinMatrixD;
-typedef iSpinMatrix<vComplexD2>         vSpinMatrixD2;
 
 // Colour Matrix
 typedef iColourMatrix<Complex  >        ColourMatrix;
@@ -137,7 +136,6 @@ typedef iColourMatrix<ComplexD >        ColourMatrixD;
 typedef iColourMatrix<vComplex >        vColourMatrix;
 typedef iColourMatrix<vComplexF>        vColourMatrixF;
 typedef iColourMatrix<vComplexD>        vColourMatrixD;
-typedef iColourMatrix<vComplexD2>       vColourMatrixD2;
 
 // SpinColour matrix
 typedef iSpinColourMatrix<Complex  >    SpinColourMatrix;
@@ -147,7 +145,6 @@ typedef iSpinColourMatrix<ComplexD >    SpinColourMatrixD;
 typedef iSpinColourMatrix<vComplex >    vSpinColourMatrix;
 typedef iSpinColourMatrix<vComplexF>    vSpinColourMatrixF;
 typedef iSpinColourMatrix<vComplexD>    vSpinColourMatrixD;
-typedef iSpinColourMatrix<vComplexD2>   vSpinColourMatrixD2;
 
 // SpinColourSpinColour matrix
 typedef iSpinColourSpinColourMatrix<Complex  >    SpinColourSpinColourMatrix;
@@ -157,17 +154,6 @@ typedef iSpinColourSpinColourMatrix<ComplexD >    SpinColourSpinColourMatrixD;
 typedef iSpinColourSpinColourMatrix<vComplex >    vSpinColourSpinColourMatrix;
 typedef iSpinColourSpinColourMatrix<vComplexF>    vSpinColourSpinColourMatrixF;
 typedef iSpinColourSpinColourMatrix<vComplexD>    vSpinColourSpinColourMatrixD;
-typedef iSpinColourSpinColourMatrix<vComplexD2>   vSpinColourSpinColourMatrixD2;
-
-// SpinColourSpinColour matrix
-typedef iSpinColourSpinColourMatrix<Complex  >    SpinColourSpinColourMatrix;
-typedef iSpinColourSpinColourMatrix<ComplexF >    SpinColourSpinColourMatrixF;
-typedef iSpinColourSpinColourMatrix<ComplexD >    SpinColourSpinColourMatrixD;
-
-typedef iSpinColourSpinColourMatrix<vComplex >    vSpinColourSpinColourMatrix;
-typedef iSpinColourSpinColourMatrix<vComplexF>    vSpinColourSpinColourMatrixF;
-typedef iSpinColourSpinColourMatrix<vComplexD>    vSpinColourSpinColourMatrixD;
-typedef iSpinColourSpinColourMatrix<vComplexD2>   vSpinColourSpinColourMatrixD2;
 
 // LorentzColour
 typedef iLorentzColourMatrix<Complex  > LorentzColourMatrix;
@@ -177,7 +163,6 @@ typedef iLorentzColourMatrix<ComplexD > LorentzColourMatrixD;
 typedef iLorentzColourMatrix<vComplex >  vLorentzColourMatrix;
 typedef iLorentzColourMatrix<vComplexF>  vLorentzColourMatrixF;
 typedef iLorentzColourMatrix<vComplexD>  vLorentzColourMatrixD;
-typedef iLorentzColourMatrix<vComplexD2> vLorentzColourMatrixD2;
 
 // LorentzComplex
 typedef iLorentzComplex<Complex  > LorentzComplex;
@@ -196,7 +181,6 @@ typedef iDoubleStoredColourMatrix<ComplexD > DoubleStoredColourMatrixD;
 typedef iDoubleStoredColourMatrix<vComplex >  vDoubleStoredColourMatrix;
 typedef iDoubleStoredColourMatrix<vComplexF>  vDoubleStoredColourMatrixF;
 typedef iDoubleStoredColourMatrix<vComplexD>  vDoubleStoredColourMatrixD;
-typedef iDoubleStoredColourMatrix<vComplexD2> vDoubleStoredColourMatrixD2;
 
 //G-parity flavour matrix
 typedef iGparityFlavourMatrix<Complex> GparityFlavourMatrix;
@@ -206,7 +190,6 @@ typedef iGparityFlavourMatrix<ComplexD> GparityFlavourMatrixD;
 typedef iGparityFlavourMatrix<vComplex>   vGparityFlavourMatrix;
 typedef iGparityFlavourMatrix<vComplexF>  vGparityFlavourMatrixF;
 typedef iGparityFlavourMatrix<vComplexD>  vGparityFlavourMatrixD;
-typedef iGparityFlavourMatrix<vComplexD2> vGparityFlavourMatrixD2;
 
 
 // Spin vector
@@ -217,7 +200,6 @@ typedef iSpinVector<ComplexD>           SpinVectorD;
 typedef iSpinVector<vComplex >           vSpinVector;
 typedef iSpinVector<vComplexF>           vSpinVectorF;
 typedef iSpinVector<vComplexD>           vSpinVectorD;
-typedef iSpinVector<vComplexD2>          vSpinVectorD2;
 
 // Colour vector
 typedef iColourVector<Complex >         ColourVector;
@@ -227,7 +209,6 @@ typedef iColourVector<ComplexD>         ColourVectorD;
 typedef iColourVector<vComplex >         vColourVector;
 typedef iColourVector<vComplexF>         vColourVectorF;
 typedef iColourVector<vComplexD>         vColourVectorD;
-typedef iColourVector<vComplexD2>        vColourVectorD2;
 
 // SpinColourVector
 typedef iSpinColourVector<Complex >     SpinColourVector;
@@ -237,7 +218,6 @@ typedef iSpinColourVector<ComplexD>     SpinColourVectorD;
 typedef iSpinColourVector<vComplex >     vSpinColourVector;
 typedef iSpinColourVector<vComplexF>     vSpinColourVectorF;
 typedef iSpinColourVector<vComplexD>     vSpinColourVectorD;
-typedef iSpinColourVector<vComplexD2>    vSpinColourVectorD2;
 
 // HalfSpin vector
 typedef iHalfSpinVector<Complex >       HalfSpinVector;
@@ -247,7 +227,6 @@ typedef iHalfSpinVector<ComplexD>       HalfSpinVectorD;
 typedef iHalfSpinVector<vComplex >       vHalfSpinVector;
 typedef iHalfSpinVector<vComplexF>       vHalfSpinVectorF;
 typedef iHalfSpinVector<vComplexD>       vHalfSpinVectorD;
-typedef iHalfSpinVector<vComplexD2>      vHalfSpinVectorD2;
 
 // HalfSpinColour vector
 typedef iHalfSpinColourVector<Complex > HalfSpinColourVector;
@@ -257,7 +236,6 @@ typedef iHalfSpinColourVector<ComplexD> HalfSpinColourVectorD;
 typedef iHalfSpinColourVector<vComplex >  vHalfSpinColourVector;
 typedef iHalfSpinColourVector<vComplexF>  vHalfSpinColourVectorF;
 typedef iHalfSpinColourVector<vComplexD>  vHalfSpinColourVectorD;
-typedef iHalfSpinColourVector<vComplexD2> vHalfSpinColourVectorD2;
 
 //G-parity flavour vector
 typedef iGparityFlavourVector<Complex >         GparityFlavourVector;
@@ -267,7 +245,6 @@ typedef iGparityFlavourVector<ComplexD>         GparityFlavourVectorD;
 typedef iGparityFlavourVector<vComplex >         vGparityFlavourVector;
 typedef iGparityFlavourVector<vComplexF>         vGparityFlavourVectorF;
 typedef iGparityFlavourVector<vComplexD>         vGparityFlavourVectorD;
-typedef iGparityFlavourVector<vComplexD2>        vGparityFlavourVectorD2;
     
 // singlets
 typedef iSinglet<Complex >         TComplex;     // FIXME This is painful. Tensor singlet complex type.
@@ -277,7 +254,6 @@ typedef iSinglet<ComplexD>         TComplexD;    // FIXME This is painful. Tenso
 typedef iSinglet<vComplex >        vTComplex ;   // what if we don't know the tensor structure
 typedef iSinglet<vComplexF>        vTComplexF;   // what if we don't know the tensor structure
 typedef iSinglet<vComplexD>        vTComplexD;   // what if we don't know the tensor structure
-typedef iSinglet<vComplexD2>       vTComplexD2;   // what if we don't know the tensor structure
 
 typedef iSinglet<Real >            TReal;        // Shouldn't need these; can I make it work without?
 typedef iSinglet<RealF>            TRealF;       // Shouldn't need these; can I make it work without?
@@ -295,27 +271,22 @@ typedef iSinglet<Integer >         TInteger;
 typedef Lattice<vColourMatrix>          LatticeColourMatrix;
 typedef Lattice<vColourMatrixF>         LatticeColourMatrixF;
 typedef Lattice<vColourMatrixD>         LatticeColourMatrixD;
-typedef Lattice<vColourMatrixD2>        LatticeColourMatrixD2;
 
 typedef Lattice<vSpinMatrix>            LatticeSpinMatrix;
 typedef Lattice<vSpinMatrixF>           LatticeSpinMatrixF;
 typedef Lattice<vSpinMatrixD>           LatticeSpinMatrixD;
-typedef Lattice<vSpinMatrixD2>          LatticeSpinMatrixD2;
 
 typedef Lattice<vSpinColourMatrix>      LatticeSpinColourMatrix;
 typedef Lattice<vSpinColourMatrixF>     LatticeSpinColourMatrixF;
 typedef Lattice<vSpinColourMatrixD>     LatticeSpinColourMatrixD;
-typedef Lattice<vSpinColourMatrixD2>    LatticeSpinColourMatrixD2;
 
 typedef Lattice<vSpinColourSpinColourMatrix>      LatticeSpinColourSpinColourMatrix;
 typedef Lattice<vSpinColourSpinColourMatrixF>     LatticeSpinColourSpinColourMatrixF;
 typedef Lattice<vSpinColourSpinColourMatrixD>     LatticeSpinColourSpinColourMatrixD;
-typedef Lattice<vSpinColourSpinColourMatrixD2>    LatticeSpinColourSpinColourMatrixD2;
 
 typedef Lattice<vLorentzColourMatrix>   LatticeLorentzColourMatrix;
 typedef Lattice<vLorentzColourMatrixF>  LatticeLorentzColourMatrixF;
 typedef Lattice<vLorentzColourMatrixD>  LatticeLorentzColourMatrixD;
-typedef Lattice<vLorentzColourMatrixD2> LatticeLorentzColourMatrixD2;
 
 typedef Lattice<vLorentzComplex>  LatticeLorentzComplex;
 typedef Lattice<vLorentzComplexF> LatticeLorentzComplexF;
@@ -325,32 +296,26 @@ typedef Lattice<vLorentzComplexD> LatticeLorentzComplexD;
 typedef Lattice<vDoubleStoredColourMatrix>   LatticeDoubleStoredColourMatrix;
 typedef Lattice<vDoubleStoredColourMatrixF>  LatticeDoubleStoredColourMatrixF;
 typedef Lattice<vDoubleStoredColourMatrixD>  LatticeDoubleStoredColourMatrixD;
-typedef Lattice<vDoubleStoredColourMatrixD2> LatticeDoubleStoredColourMatrixD2;
 
 typedef Lattice<vSpinVector>            LatticeSpinVector;
 typedef Lattice<vSpinVectorF>           LatticeSpinVectorF;
 typedef Lattice<vSpinVectorD>           LatticeSpinVectorD;
-typedef Lattice<vSpinVectorD2>          LatticeSpinVectorD2;
 
 typedef Lattice<vColourVector>          LatticeColourVector;
 typedef Lattice<vColourVectorF>         LatticeColourVectorF;
 typedef Lattice<vColourVectorD>         LatticeColourVectorD;
-typedef Lattice<vColourVectorD2>        LatticeColourVectorD2;
 
 typedef Lattice<vSpinColourVector>      LatticeSpinColourVector;
 typedef Lattice<vSpinColourVectorF>     LatticeSpinColourVectorF;
 typedef Lattice<vSpinColourVectorD>     LatticeSpinColourVectorD;
-typedef Lattice<vSpinColourVectorD2>    LatticeSpinColourVectorD2;
 
 typedef Lattice<vHalfSpinVector>        LatticeHalfSpinVector;
 typedef Lattice<vHalfSpinVectorF>       LatticeHalfSpinVectorF;
 typedef Lattice<vHalfSpinVectorD>       LatticeHalfSpinVectorD;
-typedef Lattice<vHalfSpinVectorD2>      LatticeHalfSpinVectorD2;
 
 typedef Lattice<vHalfSpinColourVector>   LatticeHalfSpinColourVector;
 typedef Lattice<vHalfSpinColourVectorF>  LatticeHalfSpinColourVectorF;
 typedef Lattice<vHalfSpinColourVectorD>  LatticeHalfSpinColourVectorD;
-typedef Lattice<vHalfSpinColourVectorD2> LatticeHalfSpinColourVectorD2;
 
 typedef Lattice<vTReal>            LatticeReal;
 typedef Lattice<vTRealF>           LatticeRealF;
@@ -359,7 +324,6 @@ typedef Lattice<vTRealD>           LatticeRealD;
 typedef Lattice<vTComplex>         LatticeComplex;
 typedef Lattice<vTComplexF>        LatticeComplexF;
 typedef Lattice<vTComplexD>        LatticeComplexD;
-typedef Lattice<vTComplexD2>       LatticeComplexD2;
 
 typedef Lattice<vTInteger>         LatticeInteger; // Predicates for "where"
 
@@ -370,39 +334,124 @@ typedef Lattice<vTInteger>         LatticeInteger; // Predicates for "where"
 typedef LatticeHalfSpinColourVector   LatticeHalfFermion;
 typedef LatticeHalfSpinColourVectorF  LatticeHalfFermionF;
 typedef LatticeHalfSpinColourVectorD  LatticeHalfFermionD;
-typedef LatticeHalfSpinColourVectorD2 LatticeHalfFermionD2;
 
 typedef LatticeSpinColourVector      LatticeFermion;
 typedef LatticeSpinColourVectorF     LatticeFermionF;
 typedef LatticeSpinColourVectorD     LatticeFermionD;
-typedef LatticeSpinColourVectorD2    LatticeFermionD2;
 
 typedef LatticeSpinColourMatrix                LatticePropagator;
 typedef LatticeSpinColourMatrixF               LatticePropagatorF;
 typedef LatticeSpinColourMatrixD               LatticePropagatorD;
-typedef LatticeSpinColourMatrixD2              LatticePropagatorD2;
 
 typedef LatticeLorentzColourMatrix             LatticeGaugeField;
 typedef LatticeLorentzColourMatrixF            LatticeGaugeFieldF;
 typedef LatticeLorentzColourMatrixD            LatticeGaugeFieldD;
-typedef LatticeLorentzColourMatrixD2           LatticeGaugeFieldD2;
 
 typedef LatticeDoubleStoredColourMatrix        LatticeDoubledGaugeField;
 typedef LatticeDoubleStoredColourMatrixF       LatticeDoubledGaugeFieldF;
 typedef LatticeDoubleStoredColourMatrixD       LatticeDoubledGaugeFieldD;
-typedef LatticeDoubleStoredColourMatrixD2      LatticeDoubledGaugeFieldD2;
 
 template<class GF> using LorentzScalar = Lattice<iScalar<typename GF::vector_object::element> >;
 
 typedef Lattice<vColourVector>          LatticeStaggeredFermion;    
 typedef Lattice<vColourVectorF>         LatticeStaggeredFermionF;    
 typedef Lattice<vColourVectorD>         LatticeStaggeredFermionD;    
-typedef Lattice<vColourVectorD2>        LatticeStaggeredFermionD2;    
 
 typedef Lattice<vColourMatrix>          LatticeStaggeredPropagator; 
 typedef Lattice<vColourMatrixF>         LatticeStaggeredPropagatorF; 
 typedef Lattice<vColourMatrixD>         LatticeStaggeredPropagatorD; 
-typedef Lattice<vColourMatrixD2>        LatticeStaggeredPropagatorD2; 
+
+
+/////////////////////////////////////////////////////////////////////////////
+// Lexicographic lattice types: Nsimd()==1 containers of the same tensors.
+// Single and double precision only; no default precision alias.
+/////////////////////////////////////////////////////////////////////////////
+
+// Site objects over the width one simd types
+typedef iSpinMatrix<sComplexF>                        sSpinMatrixF;
+typedef iSpinMatrix<sComplexD>                        sSpinMatrixD;
+typedef iColourMatrix<sComplexF>                      sColourMatrixF;
+typedef iColourMatrix<sComplexD>                      sColourMatrixD;
+typedef iSpinColourMatrix<sComplexF>                  sSpinColourMatrixF;
+typedef iSpinColourMatrix<sComplexD>                  sSpinColourMatrixD;
+typedef iSpinColourSpinColourMatrix<sComplexF>        sSpinColourSpinColourMatrixF;
+typedef iSpinColourSpinColourMatrix<sComplexD>        sSpinColourSpinColourMatrixD;
+typedef iLorentzColourMatrix<sComplexF>               sLorentzColourMatrixF;
+typedef iLorentzColourMatrix<sComplexD>               sLorentzColourMatrixD;
+typedef iLorentzComplex<sComplexF>                    sLorentzComplexF;
+typedef iLorentzComplex<sComplexD>                    sLorentzComplexD;
+typedef iDoubleStoredColourMatrix<sComplexF>          sDoubleStoredColourMatrixF;
+typedef iDoubleStoredColourMatrix<sComplexD>          sDoubleStoredColourMatrixD;
+typedef iGparityFlavourMatrix<sComplexF>              sGparityFlavourMatrixF;
+typedef iGparityFlavourMatrix<sComplexD>              sGparityFlavourMatrixD;
+typedef iSpinVector<sComplexF>                        sSpinVectorF;
+typedef iSpinVector<sComplexD>                        sSpinVectorD;
+typedef iColourVector<sComplexF>                      sColourVectorF;
+typedef iColourVector<sComplexD>                      sColourVectorD;
+typedef iSpinColourVector<sComplexF>                  sSpinColourVectorF;
+typedef iSpinColourVector<sComplexD>                  sSpinColourVectorD;
+typedef iHalfSpinVector<sComplexF>                    sHalfSpinVectorF;
+typedef iHalfSpinVector<sComplexD>                    sHalfSpinVectorD;
+typedef iHalfSpinColourVector<sComplexF>              sHalfSpinColourVectorF;
+typedef iHalfSpinColourVector<sComplexD>              sHalfSpinColourVectorD;
+typedef iGparityFlavourVector<sComplexF>              sGparityFlavourVectorF;
+typedef iGparityFlavourVector<sComplexD>              sGparityFlavourVectorD;
+typedef iSinglet<sComplexF>                           sTComplexF;
+typedef iSinglet<sComplexD>                           sTComplexD;
+typedef iSinglet<sRealF>                              sTRealF;
+typedef iSinglet<sRealD>                              sTRealD;
+typedef iSinglet<sInteger>                            sTInteger;
+
+// Lattices of these
+typedef Lattice<sColourMatrixF>                       lexLatticeColourMatrixF;
+typedef Lattice<sColourMatrixD>                       lexLatticeColourMatrixD;
+typedef Lattice<sSpinMatrixF>                         lexLatticeSpinMatrixF;
+typedef Lattice<sSpinMatrixD>                         lexLatticeSpinMatrixD;
+typedef Lattice<sSpinColourMatrixF>                   lexLatticeSpinColourMatrixF;
+typedef Lattice<sSpinColourMatrixD>                   lexLatticeSpinColourMatrixD;
+typedef Lattice<sSpinColourSpinColourMatrixF>         lexLatticeSpinColourSpinColourMatrixF;
+typedef Lattice<sSpinColourSpinColourMatrixD>         lexLatticeSpinColourSpinColourMatrixD;
+typedef Lattice<sLorentzColourMatrixF>                lexLatticeLorentzColourMatrixF;
+typedef Lattice<sLorentzColourMatrixD>                lexLatticeLorentzColourMatrixD;
+typedef Lattice<sLorentzComplexF>                     lexLatticeLorentzComplexF;
+typedef Lattice<sLorentzComplexD>                     lexLatticeLorentzComplexD;
+typedef Lattice<sDoubleStoredColourMatrixF>           lexLatticeDoubleStoredColourMatrixF;
+typedef Lattice<sDoubleStoredColourMatrixD>           lexLatticeDoubleStoredColourMatrixD;
+typedef Lattice<sSpinVectorF>                         lexLatticeSpinVectorF;
+typedef Lattice<sSpinVectorD>                         lexLatticeSpinVectorD;
+typedef Lattice<sColourVectorF>                       lexLatticeColourVectorF;
+typedef Lattice<sColourVectorD>                       lexLatticeColourVectorD;
+typedef Lattice<sSpinColourVectorF>                   lexLatticeSpinColourVectorF;
+typedef Lattice<sSpinColourVectorD>                   lexLatticeSpinColourVectorD;
+typedef Lattice<sHalfSpinVectorF>                     lexLatticeHalfSpinVectorF;
+typedef Lattice<sHalfSpinVectorD>                     lexLatticeHalfSpinVectorD;
+typedef Lattice<sHalfSpinColourVectorF>               lexLatticeHalfSpinColourVectorF;
+typedef Lattice<sHalfSpinColourVectorD>               lexLatticeHalfSpinColourVectorD;
+typedef Lattice<sTRealF>                              lexLatticeRealF;
+typedef Lattice<sTRealD>                              lexLatticeRealD;
+typedef Lattice<sTComplexF>                           lexLatticeComplexF;
+typedef Lattice<sTComplexD>                           lexLatticeComplexD;
+typedef Lattice<sTInteger>                            lexLatticeInteger;
+typedef Lattice<sColourVectorF>                       lexLatticeStaggeredFermionF;
+typedef Lattice<sColourVectorD>                       lexLatticeStaggeredFermionD;
+typedef Lattice<sColourMatrixF>                       lexLatticeStaggeredPropagatorF;
+typedef Lattice<sColourMatrixD>                       lexLatticeStaggeredPropagatorD;
+
+// Physical names for things
+typedef lexLatticeHalfSpinColourVectorF               lexLatticeHalfFermionF;
+typedef lexLatticeHalfSpinColourVectorD               lexLatticeHalfFermionD;
+typedef lexLatticeSpinColourVectorF                   lexLatticeFermionF;
+typedef lexLatticeSpinColourVectorD                   lexLatticeFermionD;
+typedef lexLatticeSpinColourMatrixF                   lexLatticePropagatorF;
+typedef lexLatticeSpinColourMatrixD                   lexLatticePropagatorD;
+typedef lexLatticeLorentzColourMatrixF                lexLatticeGaugeFieldF;
+typedef lexLatticeLorentzColourMatrixD                lexLatticeGaugeFieldD;
+typedef lexLatticeDoubleStoredColourMatrixF           lexLatticeDoubledGaugeFieldF;
+typedef lexLatticeDoubleStoredColourMatrixD           lexLatticeDoubledGaugeFieldD;
+
+/////////////////////////////////////////////////////////////////////////////
+// End lexicographic lattice types
+/////////////////////////////////////////////////////////////////////////////
 
 //////////////////////////////////////////////////////////////////////////////
 // Peek and Poke named after physics attributes

Grid/qcd/action/fermion/CloverHelpers.h

@@ -143,6 +143,8 @@ public:
   static int getNMAX(Lattice<iImplClover<vComplexD2>> &t, RealD R) {return getNMAX(1e-12,R);}
   static int getNMAX(Lattice<iImplClover<vComplexD>> &t, RealD R) {return getNMAX(1e-12,R);}
   static int getNMAX(Lattice<iImplClover<vComplexF>> &t, RealD R) {return getNMAX(1e-6,R);}
+  static int getNMAX(Lattice<iImplClover<sComplexD>> &t, RealD R) {return getNMAX(1e-12,R);}
+  static int getNMAX(Lattice<iImplClover<sComplexF>> &t, RealD R) {return getNMAX(1e-6,R);}
 
   static void Instantiate(CloverField& Clover, CloverField& CloverInv, RealD csw_t, RealD diag_mass) {
     GridBase* grid = Clover.Grid();
@@ -268,6 +270,8 @@ public:
 
   static int getNMAX(Lattice<iImplClover<vComplexD>> &t, RealD R) {return getNMAX(1e-12,R);}
   static int getNMAX(Lattice<iImplClover<vComplexF>> &t, RealD R) {return getNMAX(1e-6,R);}
+  static int getNMAX(Lattice<iImplClover<sComplexD>> &t, RealD R) {return getNMAX(1e-12,R);}
+  static int getNMAX(Lattice<iImplClover<sComplexF>> &t, RealD R) {return getNMAX(1e-6,R);}
 
   static void InstantiateClover(CloverField& Clover, CloverField& CloverInv, RealD csw_t, RealD diag_mass) {
 

Grid/qcd/action/fermion/DomainWallVec5dImpl.h

@@ -40,15 +40,12 @@ public:
   static const int Dimension = Representation::Dimension;
   static const bool isFundamental = Representation::isFundamental;
   static const bool LsVectorised=true;
-  static const int Nhcs = Options::Nhcs;
       
   typedef typename Options::_Coeff_t Coeff_t;      
-  typedef typename Options::template PrecisionMapper<Simd>::LowerPrecVector SimdL;
   
   template <typename vtype> using iImplSpinor            = iScalar<iVector<iVector<vtype, Dimension>, Ns> >;
   template <typename vtype> using iImplPropagator        = iScalar<iMatrix<iMatrix<vtype, Dimension>, Ns> >;
   template <typename vtype> using iImplHalfSpinor        = iScalar<iVector<iVector<vtype, Dimension>, Nhs> >;
-  template <typename vtype> using iImplHalfCommSpinor    = iScalar<iVector<iVector<vtype, Dimension>, Nhcs> >;
   template <typename vtype> using iImplDoubledGaugeField = iVector<iScalar<iMatrix<vtype, Dimension> >, Nds>;
   template <typename vtype> using iImplGaugeField        = iVector<iScalar<iMatrix<vtype, Dimension> >, Nd>;
   template <typename vtype> using iImplGaugeLink         = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
@@ -56,7 +53,6 @@ public:
   typedef iImplSpinor<Simd>            SiteSpinor;
   typedef iImplPropagator<Simd>        SitePropagator;
   typedef iImplHalfSpinor<Simd>        SiteHalfSpinor;
-  typedef iImplHalfCommSpinor<SimdL>   SiteHalfCommSpinor;
   typedef Lattice<SiteSpinor>          FermionField;
   typedef Lattice<SitePropagator>      PropagatorField;
 
@@ -68,7 +64,7 @@ public:
   typedef iImplGaugeLink<typename Simd::scalar_type>          SiteScalarGaugeLink;  // scalar
   typedef Lattice<SiteDoubledGaugeField>                      DoubledGaugeField;
       
-  typedef WilsonCompressor<SiteHalfCommSpinor,SiteHalfSpinor, SiteSpinor> Compressor;
+  typedef WilsonCompressor<SiteHalfSpinor, SiteSpinor> Compressor;
   typedef WilsonImplParams ImplParams;
   typedef WilsonStencil<SiteSpinor, SiteHalfSpinor,ImplParams> StencilImpl;
   typedef typename StencilImpl::View_type StencilView;
@@ -201,16 +197,8 @@ typedef DomainWallVec5dImpl<vComplex ,FundamentalRepresentation, CoeffReal> Doma
 typedef DomainWallVec5dImpl<vComplexF,FundamentalRepresentation, CoeffReal> DomainWallVec5dImplF; // Float
 typedef DomainWallVec5dImpl<vComplexD,FundamentalRepresentation, CoeffReal> DomainWallVec5dImplD; // Double
  
-typedef DomainWallVec5dImpl<vComplex ,FundamentalRepresentation, CoeffRealHalfComms> DomainWallVec5dImplRL; // Real.. whichever prec
-typedef DomainWallVec5dImpl<vComplexF,FundamentalRepresentation, CoeffRealHalfComms> DomainWallVec5dImplFH; // Float
-typedef DomainWallVec5dImpl<vComplexD,FundamentalRepresentation, CoeffRealHalfComms> DomainWallVec5dImplDF; // Double
- 
 typedef DomainWallVec5dImpl<vComplex ,FundamentalRepresentation,CoeffComplex> ZDomainWallVec5dImplR; // Real.. whichever prec
 typedef DomainWallVec5dImpl<vComplexF,FundamentalRepresentation,CoeffComplex> ZDomainWallVec5dImplF; // Float
 typedef DomainWallVec5dImpl<vComplexD,FundamentalRepresentation,CoeffComplex> ZDomainWallVec5dImplD; // Double
 
-typedef DomainWallVec5dImpl<vComplex ,FundamentalRepresentation,CoeffComplexHalfComms> ZDomainWallVec5dImplRL; // Real.. whichever prec
-typedef DomainWallVec5dImpl<vComplexF,FundamentalRepresentation,CoeffComplexHalfComms> ZDomainWallVec5dImplFH; // Float
-typedef DomainWallVec5dImpl<vComplexD,FundamentalRepresentation,CoeffComplexHalfComms> ZDomainWallVec5dImplDF; // Double
-
 NAMESPACE_END(Grid);

Grid/qcd/action/fermion/Fermion.h

@@ -114,7 +114,7 @@ NAMESPACE_CHECK(DWFutils);
 // Cayley 5d
 NAMESPACE_BEGIN(Grid);
 
-typedef WilsonFermion<WilsonImplD2> WilsonFermionD2;
+//typedef WilsonFermion<WilsonImplD2> WilsonFermionD2;
 typedef WilsonFermion<WilsonImplF> WilsonFermionF;
 typedef WilsonFermion<WilsonImplD> WilsonFermionD;
 
@@ -138,7 +138,7 @@ typedef WilsonFermion<SpWilsonTwoIndexSymmetricImplF> SpWilsonTwoIndexSymmetricF
 typedef WilsonFermion<SpWilsonTwoIndexSymmetricImplD> SpWilsonTwoIndexSymmetricFermionD;
 
 // Twisted mass fermion
-typedef WilsonTMFermion<WilsonImplD2> WilsonTMFermionD2;
+//typedef WilsonTMFermion<WilsonImplD2> WilsonTMFermionD2;
 typedef WilsonTMFermion<WilsonImplF> WilsonTMFermionF;
 typedef WilsonTMFermion<WilsonImplD> WilsonTMFermionD;
 
@@ -146,11 +146,11 @@ typedef WilsonTMFermion<WilsonImplD> WilsonTMFermionD;
 template <typename WImpl> using WilsonClover = WilsonCloverFermion<WImpl, CloverHelpers<WImpl>>;
 template <typename WImpl> using WilsonExpClover = WilsonCloverFermion<WImpl, ExpCloverHelpers<WImpl>>;
 
-typedef WilsonClover<WilsonImplD2> WilsonCloverFermionD2;
+//typedef WilsonClover<WilsonImplD2> WilsonCloverFermionD2;
 typedef WilsonClover<WilsonImplF> WilsonCloverFermionF;
 typedef WilsonClover<WilsonImplD> WilsonCloverFermionD;
 
-typedef WilsonExpClover<WilsonImplD2> WilsonExpCloverFermionD2;
+//typedef WilsonExpClover<WilsonImplD2> WilsonExpCloverFermionD2;
 typedef WilsonExpClover<WilsonImplF> WilsonExpCloverFermionF;
 typedef WilsonExpClover<WilsonImplD> WilsonExpCloverFermionD;
 
@@ -168,15 +168,15 @@ template <typename WImpl> using CompactWilsonClover = CompactWilsonCloverFermion
 template <typename WImpl> using CompactWilsonClover5D = CompactWilsonCloverFermion5D<WImpl, CompactCloverHelpers<WImpl>>;
 template <typename WImpl> using CompactWilsonExpClover = CompactWilsonCloverFermion<WImpl, CompactExpCloverHelpers<WImpl>>;
 
-typedef CompactWilsonClover<WilsonImplD2> CompactWilsonCloverFermionD2;
+//typedef CompactWilsonClover<WilsonImplD2> CompactWilsonCloverFermionD2;
 typedef CompactWilsonClover<WilsonImplF> CompactWilsonCloverFermionF;
 typedef CompactWilsonClover<WilsonImplD> CompactWilsonCloverFermionD;
 
-typedef CompactWilsonClover5D<WilsonImplD2> CompactWilsonCloverFermion5DD2;
+//typedef CompactWilsonClover5D<WilsonImplD2> CompactWilsonCloverFermion5DD2;
 typedef CompactWilsonClover5D<WilsonImplF> CompactWilsonCloverFermion5DF;
 typedef CompactWilsonClover5D<WilsonImplD> CompactWilsonCloverFermion5DD;
 
-typedef CompactWilsonExpClover<WilsonImplD2> CompactWilsonExpCloverFermionD2;
+//typedef CompactWilsonExpClover<WilsonImplD2> CompactWilsonExpCloverFermionD2;
 typedef CompactWilsonExpClover<WilsonImplF> CompactWilsonExpCloverFermionF;
 typedef CompactWilsonExpClover<WilsonImplD> CompactWilsonExpCloverFermionD;
 
@@ -192,56 +192,56 @@ typedef CompactWilsonClover<WilsonTwoIndexAntiSymmetricImplD> CompactWilsonClove
 // Domain Wall fermions
 typedef DomainWallFermion<WilsonImplF> DomainWallFermionF;
 typedef DomainWallFermion<WilsonImplD> DomainWallFermionD;
-typedef DomainWallFermion<WilsonImplD2> DomainWallFermionD2;
+//typedef DomainWallFermion<WilsonImplD2> DomainWallFermionD2;
 
-typedef DomainWallEOFAFermion<WilsonImplD2> DomainWallEOFAFermionD2;
+//typedef DomainWallEOFAFermion<WilsonImplD2> DomainWallEOFAFermionD2;
 typedef DomainWallEOFAFermion<WilsonImplF> DomainWallEOFAFermionF;
 typedef DomainWallEOFAFermion<WilsonImplD> DomainWallEOFAFermionD;
 
-typedef MobiusFermion<WilsonImplD2> MobiusFermionD2;
+//typedef MobiusFermion<WilsonImplD2> MobiusFermionD2;
 typedef MobiusFermion<WilsonImplF> MobiusFermionF;
 typedef MobiusFermion<WilsonImplD> MobiusFermionD;
 
-typedef MobiusEOFAFermion<WilsonImplD2> MobiusEOFAFermionD2;
+//typedef MobiusEOFAFermion<WilsonImplD2> MobiusEOFAFermionD2;
 typedef MobiusEOFAFermion<WilsonImplF> MobiusEOFAFermionF;
 typedef MobiusEOFAFermion<WilsonImplD> MobiusEOFAFermionD;
 
-typedef ZMobiusFermion<ZWilsonImplD2> ZMobiusFermionD2;
+//typedef ZMobiusFermion<ZWilsonImplD2> ZMobiusFermionD2;
 typedef ZMobiusFermion<ZWilsonImplF> ZMobiusFermionF;
 typedef ZMobiusFermion<ZWilsonImplD> ZMobiusFermionD;
 
-typedef ScaledShamirFermion<WilsonImplD2> ScaledShamirFermionD2;
+//typedef ScaledShamirFermion<WilsonImplD2> ScaledShamirFermionD2;
 typedef ScaledShamirFermion<WilsonImplF> ScaledShamirFermionF;
 typedef ScaledShamirFermion<WilsonImplD> ScaledShamirFermionD;
 
-typedef MobiusZolotarevFermion<WilsonImplD2> MobiusZolotarevFermionD2;
+//typedef MobiusZolotarevFermion<WilsonImplD2> MobiusZolotarevFermionD2;
 typedef MobiusZolotarevFermion<WilsonImplF> MobiusZolotarevFermionF;
 typedef MobiusZolotarevFermion<WilsonImplD> MobiusZolotarevFermionD;
-typedef ShamirZolotarevFermion<WilsonImplD2> ShamirZolotarevFermionD2;
+//typedef ShamirZolotarevFermion<WilsonImplD2> ShamirZolotarevFermionD2;
 typedef ShamirZolotarevFermion<WilsonImplF> ShamirZolotarevFermionF;
 typedef ShamirZolotarevFermion<WilsonImplD> ShamirZolotarevFermionD;
 
-typedef OverlapWilsonCayleyTanhFermion<WilsonImplD2> OverlapWilsonCayleyTanhFermionD2;
+//typedef OverlapWilsonCayleyTanhFermion<WilsonImplD2> OverlapWilsonCayleyTanhFermionD2;
 typedef OverlapWilsonCayleyTanhFermion<WilsonImplF> OverlapWilsonCayleyTanhFermionF;
 typedef OverlapWilsonCayleyTanhFermion<WilsonImplD> OverlapWilsonCayleyTanhFermionD;
-typedef OverlapWilsonCayleyZolotarevFermion<WilsonImplD2> OverlapWilsonCayleyZolotarevFermionD2;
+//typedef OverlapWilsonCayleyZolotarevFermion<WilsonImplD2> OverlapWilsonCayleyZolotarevFermionD2;
 typedef OverlapWilsonCayleyZolotarevFermion<WilsonImplF> OverlapWilsonCayleyZolotarevFermionF;
 typedef OverlapWilsonCayleyZolotarevFermion<WilsonImplD> OverlapWilsonCayleyZolotarevFermionD;
 
 // Continued fraction
-typedef OverlapWilsonContFracTanhFermion<WilsonImplD2> OverlapWilsonContFracTanhFermionD2;
+//typedef OverlapWilsonContFracTanhFermion<WilsonImplD2> OverlapWilsonContFracTanhFermionD2;
 typedef OverlapWilsonContFracTanhFermion<WilsonImplF> OverlapWilsonContFracTanhFermionF;
 typedef OverlapWilsonContFracTanhFermion<WilsonImplD> OverlapWilsonContFracTanhFermionD;
-typedef OverlapWilsonContFracZolotarevFermion<WilsonImplD2> OverlapWilsonContFracZolotarevFermionD2;
+//typedef OverlapWilsonContFracZolotarevFermion<WilsonImplD2> OverlapWilsonContFracZolotarevFermionD2;
 typedef OverlapWilsonContFracZolotarevFermion<WilsonImplF> OverlapWilsonContFracZolotarevFermionF;
 typedef OverlapWilsonContFracZolotarevFermion<WilsonImplD> OverlapWilsonContFracZolotarevFermionD;
 
 // Partial fraction
-typedef OverlapWilsonPartialFractionTanhFermion<WilsonImplD2> OverlapWilsonPartialFractionTanhFermionD2;
+//typedef OverlapWilsonPartialFractionTanhFermion<WilsonImplD2> OverlapWilsonPartialFractionTanhFermionD2;
 typedef OverlapWilsonPartialFractionTanhFermion<WilsonImplF> OverlapWilsonPartialFractionTanhFermionF;
 typedef OverlapWilsonPartialFractionTanhFermion<WilsonImplD> OverlapWilsonPartialFractionTanhFermionD;
 
-typedef OverlapWilsonPartialFractionZolotarevFermion<WilsonImplD2> OverlapWilsonPartialFractionZolotarevFermionD2;
+//typedef OverlapWilsonPartialFractionZolotarevFermion<WilsonImplD2> OverlapWilsonPartialFractionZolotarevFermionD2;
 typedef OverlapWilsonPartialFractionZolotarevFermion<WilsonImplF> OverlapWilsonPartialFractionZolotarevFermionF;
 typedef OverlapWilsonPartialFractionZolotarevFermion<WilsonImplD> OverlapWilsonPartialFractionZolotarevFermionD;
 
@@ -252,19 +252,19 @@ typedef WilsonFermion<GparityWilsonImplD>     GparityWilsonFermionD;
 typedef DomainWallFermion<GparityWilsonImplF> GparityDomainWallFermionF;
 typedef DomainWallFermion<GparityWilsonImplD> GparityDomainWallFermionD;
 
-typedef DomainWallEOFAFermion<GparityWilsonImplR> GparityDomainWallEOFAFermionD2;
+//typedef DomainWallEOFAFermion<GparityWilsonImplR> GparityDomainWallEOFAFermionD2;
 typedef DomainWallEOFAFermion<GparityWilsonImplF> GparityDomainWallEOFAFermionF;
 typedef DomainWallEOFAFermion<GparityWilsonImplD> GparityDomainWallEOFAFermionD;
 
-typedef WilsonTMFermion<GparityWilsonImplR> GparityWilsonTMFermionD2;
+//typedef WilsonTMFermion<GparityWilsonImplR> GparityWilsonTMFermionD2;
 typedef WilsonTMFermion<GparityWilsonImplF> GparityWilsonTMFermionF;
 typedef WilsonTMFermion<GparityWilsonImplD> GparityWilsonTMFermionD;
 
-typedef MobiusFermion<GparityWilsonImplR> GparityMobiusFermionD2;
+//typedef MobiusFermion<GparityWilsonImplR> GparityMobiusFermionD2;
 typedef MobiusFermion<GparityWilsonImplF> GparityMobiusFermionF;
 typedef MobiusFermion<GparityWilsonImplD> GparityMobiusFermionD;
 
-typedef MobiusEOFAFermion<GparityWilsonImplR> GparityMobiusEOFAFermionD2;
+//typedef MobiusEOFAFermion<GparityWilsonImplR> GparityMobiusEOFAFermionD2;
 typedef MobiusEOFAFermion<GparityWilsonImplF> GparityMobiusEOFAFermionF;
 typedef MobiusEOFAFermion<GparityWilsonImplD> GparityMobiusEOFAFermionD;
 

Grid/qcd/action/fermion/FermionOperatorImpl.h

@@ -88,51 +88,14 @@ NAMESPACE_BEGIN(Grid);
 //  }
 //////////////////////////////////////////////
 
-template <class T> struct SamePrecisionMapper {
-  typedef T HigherPrecVector ;
-  typedef T LowerPrecVector ;
-};
-template <class T> struct LowerPrecisionMapper {  };
-template <> struct LowerPrecisionMapper<vRealF> {
-  typedef vRealF HigherPrecVector ;
-  typedef vRealH LowerPrecVector ;
-};
-template <> struct LowerPrecisionMapper<vRealD> {
-  typedef vRealD HigherPrecVector ;
-  typedef vRealF LowerPrecVector ;
-};
-template <> struct LowerPrecisionMapper<vComplexF> {
-  typedef vComplexF HigherPrecVector ;
-  typedef vComplexH LowerPrecVector ;
-};
-template <> struct LowerPrecisionMapper<vComplexD> {
-  typedef vComplexD HigherPrecVector ;
-  typedef vComplexF LowerPrecVector ;
-};
 
 struct CoeffReal {
 public:
   typedef RealD _Coeff_t;
-  static const int Nhcs = 2;
-  template<class Simd> using PrecisionMapper = SamePrecisionMapper<Simd>;
-};
-struct CoeffRealHalfComms {
-public:
-  typedef RealD _Coeff_t;
-  static const int Nhcs = 1;
-  template<class Simd> using PrecisionMapper = LowerPrecisionMapper<Simd>;
 };
 struct CoeffComplex {
 public:
   typedef ComplexD _Coeff_t;
-  static const int Nhcs = 2;
-  template<class Simd> using PrecisionMapper = SamePrecisionMapper<Simd>;
-};
-struct CoeffComplexHalfComms {
-public:
-  typedef ComplexD _Coeff_t;
-  static const int Nhcs = 1;
-  template<class Simd> using PrecisionMapper = LowerPrecisionMapper<Simd>;
 };
 
 ////////////////////////////////////////////////////////////////////////

Grid/qcd/action/fermion/GparityWilsonImpl.h

@@ -48,7 +48,6 @@ public:
 
  static const int Dimension = Representation::Dimension;
  static const bool isFundamental = Representation::isFundamental;
- static const int Nhcs = Options::Nhcs;
  static const bool LsVectorised=false;
  static const bool isGparity=true;
 
@@ -56,18 +55,15 @@ public:
  INHERIT_GIMPL_TYPES(Gimpl);
  
  typedef typename Options::_Coeff_t Coeff_t;
- typedef typename Options::template PrecisionMapper<Simd>::LowerPrecVector SimdL;
       
  template <typename vtype> using iImplSpinor            = iVector<iVector<iVector<vtype, Dimension>, Ns>,   Ngp>;
  template <typename vtype> using iImplPropagator        = iMatrix<iMatrix<iMatrix<vtype, Dimension>, Ns>,   Ngp>;
  template <typename vtype> using iImplHalfSpinor        = iVector<iVector<iVector<vtype, Dimension>, Nhs>,  Ngp>;
- template <typename vtype> using iImplHalfCommSpinor    = iVector<iVector<iVector<vtype, Dimension>, Nhcs>, Ngp>;
  template <typename vtype> using iImplDoubledGaugeField = iVector<iVector<iScalar<iMatrix<vtype, Dimension> >, Nds>, Ngp>;
 
   typedef iImplSpinor<Simd>            SiteSpinor;
   typedef iImplPropagator<Simd>        SitePropagator;
   typedef iImplHalfSpinor<Simd>        SiteHalfSpinor;
-  typedef iImplHalfCommSpinor<SimdL>   SiteHalfCommSpinor;
   typedef iImplDoubledGaugeField<Simd> SiteDoubledGaugeField;
 
   typedef Lattice<SiteSpinor> FermionField;
@@ -75,7 +71,7 @@ public:
   typedef Lattice<SiteDoubledGaugeField> DoubledGaugeField;
  
   typedef GparityWilsonImplParams ImplParams;
-  typedef WilsonCompressor<SiteHalfCommSpinor,SiteHalfSpinor, SiteSpinor> Compressor;
+  typedef WilsonCompressor<SiteHalfSpinor, SiteSpinor> Compressor;
   typedef WilsonStencil<SiteSpinor, SiteHalfSpinor, ImplParams> StencilImpl;
   typedef typename StencilImpl::View_type StencilView;
       
@@ -409,8 +405,4 @@ typedef GparityWilsonImpl<vComplex , FundamentalRepresentation,CoeffReal> Gparit
 typedef GparityWilsonImpl<vComplexF, FundamentalRepresentation,CoeffReal> GparityWilsonImplF;  // Float
 typedef GparityWilsonImpl<vComplexD, FundamentalRepresentation,CoeffReal> GparityWilsonImplD;  // Double
 
-//typedef GparityWilsonImpl<vComplex , FundamentalRepresentation,CoeffRealHalfComms> GparityWilsonImplRL;  // Real.. whichever prec
-//typedef GparityWilsonImpl<vComplexF, FundamentalRepresentation,CoeffRealHalfComms> GparityWilsonImplFH;  // Float
-//typedef GparityWilsonImpl<vComplexD, FundamentalRepresentation,CoeffRealHalfComms> GparityWilsonImplDF;  // Double
-
 NAMESPACE_END(Grid);

Grid/qcd/action/fermion/StaggeredImpl.h

@@ -176,4 +176,13 @@ typedef StaggeredImpl<vComplex,  FundamentalRepresentation > StaggeredImplR;   /
 typedef StaggeredImpl<vComplexF, FundamentalRepresentation > StaggeredImplF;  // Float
 typedef StaggeredImpl<vComplexD, FundamentalRepresentation > StaggeredImplD;  // Double
 
+/////////////////////////////////////////////////////////////////////////////
+// Lexicographic staggered implementations
+/////////////////////////////////////////////////////////////////////////////
+typedef StaggeredImpl<sComplexF, FundamentalRepresentation > lexStaggeredImplF;
+typedef StaggeredImpl<sComplexD, FundamentalRepresentation > lexStaggeredImplD;
+/////////////////////////////////////////////////////////////////////////////
+// End lexicographic staggered implementations
+/////////////////////////////////////////////////////////////////////////////
+
 NAMESPACE_END(Grid);

Grid/qcd/action/fermion/WilsonCompressor.h

@@ -38,7 +38,7 @@ NAMESPACE_BEGIN(Grid);
 
 
 //Could make FaceGather a template param, but then behaviour is runtime not compile time
-template<class _HCspinor,class _Hspinor,class _Spinor, class projector>
+template<class _Hspinor,class _Spinor, class projector>
 class WilsonCompressorTemplate : public FaceGatherSimple
 {
 public:
@@ -53,13 +53,11 @@ public:
 
   typedef _Spinor         SiteSpinor;
   typedef _Hspinor     SiteHalfSpinor;
-  typedef _HCspinor SiteHalfCommSpinor;
+  typedef typename SiteHalfSpinor::vector_type vector_type;    
-  typedef typename SiteHalfCommSpinor::vector_type vComplexLow;
+  constexpr static int Nw=sizeof(SiteHalfSpinor)/sizeof(vector_type);
-  typedef typename SiteHalfSpinor::vector_type     vComplexHigh;
-  constexpr static int Nw=sizeof(SiteHalfSpinor)/sizeof(vComplexHigh);
 
   accelerator_inline int CommDatumSize(void) const {
-    return sizeof(SiteHalfCommSpinor);
+    return sizeof(SiteHalfSpinor);
   }
 
   /*****************************************************/
@@ -159,7 +157,7 @@ public:
     spProj(result,in);							\
   }									\
   };									\
-  template<typename HCS,typename HS,typename S> using Compressor = WilsonCompressorTemplate<HCS,HS,S,Projector>;
+  template<typename HS,typename S> using Compressor = WilsonCompressorTemplate<HS,S,Projector>;
 
 DECLARE_PROJ(WilsonXpProjector,WilsonXpCompressor,spProjXp);
 DECLARE_PROJ(WilsonYpProjector,WilsonYpCompressor,spProjYp);
@@ -188,7 +186,7 @@ public:
     }
   }
 };
-template<typename HCS,typename HS,typename S> using WilsonCompressor = WilsonCompressorTemplate<HCS,HS,S,WilsonProjector>;
+template<typename HS,typename S> using WilsonCompressor = WilsonCompressorTemplate<HS,S,WilsonProjector>;
 
 // Fast comms buffer manipulation which should inline right through (avoid direction
 // dependent logic that prevents inlining
@@ -237,7 +235,6 @@ public:
     // Use types to select the write direction by directon compressor
     typedef typename compressor::SiteSpinor         SiteSpinor;
     typedef typename compressor::SiteHalfSpinor     SiteHalfSpinor;
-    typedef typename compressor::SiteHalfCommSpinor SiteHalfCommSpinor;
 
     this->_grid->StencilBarrier();
 
@@ -245,14 +242,14 @@ public:
     
     this->u_comm_offset=0;
       
-    WilsonXpCompressor<SiteHalfCommSpinor,SiteHalfSpinor,SiteSpinor> XpCompress; 
+    WilsonXpCompressor<SiteHalfSpinor,SiteSpinor> XpCompress; 
-    WilsonYpCompressor<SiteHalfCommSpinor,SiteHalfSpinor,SiteSpinor> YpCompress; 
+    WilsonYpCompressor<SiteHalfSpinor,SiteSpinor> YpCompress; 
-    WilsonZpCompressor<SiteHalfCommSpinor,SiteHalfSpinor,SiteSpinor> ZpCompress; 
+    WilsonZpCompressor<SiteHalfSpinor,SiteSpinor> ZpCompress; 
-    WilsonTpCompressor<SiteHalfCommSpinor,SiteHalfSpinor,SiteSpinor> TpCompress;
+    WilsonTpCompressor<SiteHalfSpinor,SiteSpinor> TpCompress;
-    WilsonXmCompressor<SiteHalfCommSpinor,SiteHalfSpinor,SiteSpinor> XmCompress; 
+    WilsonXmCompressor<SiteHalfSpinor,SiteSpinor> XmCompress; 
-    WilsonYmCompressor<SiteHalfCommSpinor,SiteHalfSpinor,SiteSpinor> YmCompress; 
+    WilsonYmCompressor<SiteHalfSpinor,SiteSpinor> YmCompress; 
-    WilsonZmCompressor<SiteHalfCommSpinor,SiteHalfSpinor,SiteSpinor> ZmCompress; 
+    WilsonZmCompressor<SiteHalfSpinor,SiteSpinor> ZmCompress; 
-    WilsonTmCompressor<SiteHalfCommSpinor,SiteHalfSpinor,SiteSpinor> TmCompress;
+    WilsonTmCompressor<SiteHalfSpinor,SiteSpinor> TmCompress;
 
     int dag = compress.dag;
     int face_idx=0;

Grid/qcd/action/fermion/WilsonImpl.h

@@ -42,7 +42,6 @@ public:
   static const bool isFundamental = Representation::isFundamental;
   static const bool LsVectorised=false;
   static const bool isGparity=false;
-  static const int Nhcs = Options::Nhcs;
 
   typedef PeriodicGaugeImpl<GaugeImplTypes<S, Dimension > > Gimpl;
   INHERIT_GIMPL_TYPES(Gimpl);
@@ -51,25 +50,22 @@ public:
   constexpr bool is_fundamental() const{return Dimension == Nc ? 1 : 0;}
     
   typedef typename Options::_Coeff_t Coeff_t;
-  typedef typename Options::template PrecisionMapper<Simd>::LowerPrecVector SimdL;
       
   template <typename vtype> using iImplSpinor            = iScalar<iVector<iVector<vtype, Dimension>, Ns> >;
   template <typename vtype> using iImplPropagator        = iScalar<iMatrix<iMatrix<vtype, Dimension>, Ns> >;
   template <typename vtype> using iImplHalfSpinor        = iScalar<iVector<iVector<vtype, Dimension>, Nhs> >;
-  template <typename vtype> using iImplHalfCommSpinor    = iScalar<iVector<iVector<vtype, Dimension>, Nhcs> >;
   template <typename vtype> using iImplDoubledGaugeField = iVector<iScalar<iMatrix<vtype, Dimension> >, Nds>;
     
   typedef iImplSpinor<Simd>            SiteSpinor;
   typedef iImplPropagator<Simd>        SitePropagator;
   typedef iImplHalfSpinor<Simd>        SiteHalfSpinor;
-  typedef iImplHalfCommSpinor<SimdL>   SiteHalfCommSpinor;
   typedef iImplDoubledGaugeField<Simd> SiteDoubledGaugeField;
     
   typedef Lattice<SiteSpinor>            FermionField;
   typedef Lattice<SitePropagator>        PropagatorField;
   typedef Lattice<SiteDoubledGaugeField> DoubledGaugeField;
     
-  typedef WilsonCompressor<SiteHalfCommSpinor,SiteHalfSpinor, SiteSpinor> Compressor;
+  typedef WilsonCompressor<SiteHalfSpinor, SiteSpinor> Compressor;
   typedef WilsonImplParams ImplParams;
   typedef WilsonStencil<SiteSpinor, SiteHalfSpinor,ImplParams> StencilImpl;
   typedef const typename StencilImpl::View_type StencilView;
@@ -242,12 +238,19 @@ public:
 typedef WilsonImpl<vComplex,  FundamentalRepresentation, CoeffReal > WilsonImplR;  // Real.. whichever prec
 typedef WilsonImpl<vComplexF, FundamentalRepresentation, CoeffReal > WilsonImplF;  // Float
 typedef WilsonImpl<vComplexD, FundamentalRepresentation, CoeffReal > WilsonImplD;  // Double
-typedef WilsonImpl<vComplexD2, FundamentalRepresentation, CoeffReal > WilsonImplD2;  // Double
+
+/////////////////////////////////////////////////////////////////////////////
+// Lexicographic Wilson implementations
+/////////////////////////////////////////////////////////////////////////////
+typedef WilsonImpl<sComplexF, FundamentalRepresentation, CoeffReal > lexWilsonImplF;
+typedef WilsonImpl<sComplexD, FundamentalRepresentation, CoeffReal > lexWilsonImplD;
+/////////////////////////////////////////////////////////////////////////////
+// End lexicographic Wilson implementations
+/////////////////////////////////////////////////////////////////////////////
 
 typedef WilsonImpl<vComplex,  FundamentalRepresentation, CoeffComplex > ZWilsonImplR; // Real.. whichever prec
 typedef WilsonImpl<vComplexF, FundamentalRepresentation, CoeffComplex > ZWilsonImplF; // Float
 typedef WilsonImpl<vComplexD, FundamentalRepresentation, CoeffComplex > ZWilsonImplD; // Double
-typedef WilsonImpl<vComplexD2, FundamentalRepresentation, CoeffComplex > ZWilsonImplD2; // Double
 
 typedef WilsonImpl<vComplex,  AdjointRepresentation, CoeffReal > WilsonAdjImplR;   // Real.. whichever prec
 typedef WilsonImpl<vComplexF, AdjointRepresentation, CoeffReal > WilsonAdjImplF;  // Float

Grid/qcd/action/fermion/implementation/StaggeredKernelsAsm.h

@@ -684,7 +684,7 @@ void StaggeredKernels<Impl>::DhopSiteAsm(StencilView &st,
 #ifdef STAG_VEC5D
   // This is the single precision 5th direction vectorised kernel
 #include <Grid/simd/Intel512single.h>
-template <> void StaggeredKernels<StaggeredVec5dImplF>::DhopSiteAsm(StencilView &st,
+template <> inline void StaggeredKernels<StaggeredVec5dImplF>::DhopSiteAsm(StencilView &st,
 								    DoubledGaugeFieldView &U,
 								    DoubledGaugeFieldView &UUU,
 								    SiteSpinor *buf, int sF,
@@ -739,7 +739,7 @@ template <> void StaggeredKernels<StaggeredVec5dImplF>::DhopSiteAsm(StencilView
 }
 
 #include <Grid/simd/Intel512double.h>
-template <> void StaggeredKernels<StaggeredVec5dImplD>::DhopSiteAsm(StencilView &st, 
+template <> inline void StaggeredKernels<StaggeredVec5dImplD>::DhopSiteAsm(StencilView &st, 
 								    DoubledGaugeFieldView &U,
 								    DoubledGaugeFieldView &UUU,
 								    SiteSpinor *buf, int sF,
@@ -825,7 +825,7 @@ template <> void StaggeredKernels<StaggeredVec5dImplD>::DhopSiteAsm(StencilView
   // This is the single precision 5th direction vectorised kernel
 
 #include <Grid/simd/Intel512single.h>
-template <> void StaggeredKernels<StaggeredImplF>::DhopSiteAsm(StencilView &st, 
+template <> inline void StaggeredKernels<StaggeredImplF>::DhopSiteAsm(StencilView &st, 
 							       DoubledGaugeFieldView &U,
 							       DoubledGaugeFieldView &UUU,
 							       SiteSpinor *buf, int sF,
@@ -894,7 +894,7 @@ template <> void StaggeredKernels<StaggeredImplF>::DhopSiteAsm(StencilView &st,
 }
 
 #include <Grid/simd/Intel512double.h>
-template <> void StaggeredKernels<StaggeredImplD>::DhopSiteAsm(StencilView &st, 
+template <> inline void StaggeredKernels<StaggeredImplD>::DhopSiteAsm(StencilView &st, 
 							       DoubledGaugeFieldView &U,
 							       DoubledGaugeFieldView &UUU,
 							       SiteSpinor *buf, int sF,

Grid/qcd/action/fermion/instantiation/StaggeredKernelsInstantiation.cc.master

@@ -29,6 +29,7 @@ directory
 #include <Grid/qcd/action/fermion/FermionCore.h>
 #include <Grid/qcd/action/fermion/implementation/StaggeredKernelsImplementation.h>
 #include <Grid/qcd/action/fermion/implementation/StaggeredKernelsHand.h>
+#include <Grid/qcd/action/fermion/implementation/StaggeredKernelsAsm.h>
 
 NAMESPACE_BEGIN(Grid);
 

Grid/qcd/action/fermion/instantiation/generate_instantiations.sh

@@ -2,14 +2,15 @@
 
 STAG_IMPL_LIST=" \
 	   StaggeredImplF \
-	   StaggeredImplD  "
+	   StaggeredImplD \
-
+	   lexStaggeredImplF \
-STAG5_IMPL_LIST=""
+	   lexStaggeredImplD  "
 
 WILSON_IMPL_LIST=" \
 	   WilsonImplF \
 	   WilsonImplD \
-	   WilsonImplD2 \
+	   lexWilsonImplF \
+	   lexWilsonImplD \
 	   SpWilsonImplF \
 	   SpWilsonImplD \
 	   WilsonAdjImplF \
@@ -32,9 +33,10 @@ COMPACT_WILSON_IMPL_LIST=" \
 DWF_IMPL_LIST=" \
 	   WilsonImplF \
 	   WilsonImplD \
-	   WilsonImplD2 \
+	   lexWilsonImplF \
+	   lexWilsonImplD \
 	   ZWilsonImplF \
-	   ZWilsonImplD2 "
+	   ZWilsonImplD "
 
 GDWF_IMPL_LIST=" \
 	   GparityWilsonImplF \
@@ -109,8 +111,3 @@ do
   ln -f -s ../$f.cc.master $impl/$f$impl.cc
 done
 done
-
-CC_LIST=" \
-  ImprovedStaggeredFermion5DInstantiation \
-  StaggeredKernelsInstantiation "
-

Grid/qcd/action/fermion/instantiation/lexStaggeredImplD/ImprovedStaggeredFermion5DInstantiationlexStaggeredImplD.cc

@@ -0,0 +1 @@
+../ImprovedStaggeredFermion5DInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexStaggeredImplD/ImprovedStaggeredFermionInstantiationlexStaggeredImplD.cc

@@ -0,0 +1 @@
+../ImprovedStaggeredFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexStaggeredImplD/NaiveStaggeredFermionInstantiationlexStaggeredImplD.cc

@@ -0,0 +1 @@
+../NaiveStaggeredFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexStaggeredImplD/StaggeredKernelsInstantiationlexStaggeredImplD.cc

@@ -0,0 +1 @@
+../StaggeredKernelsInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexStaggeredImplD/impl.h

@@ -0,0 +1 @@
+#define IMPLEMENTATION lexStaggeredImplD

Grid/qcd/action/fermion/instantiation/lexStaggeredImplF/ImprovedStaggeredFermion5DInstantiationlexStaggeredImplF.cc

@@ -0,0 +1 @@
+../ImprovedStaggeredFermion5DInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexStaggeredImplF/ImprovedStaggeredFermionInstantiationlexStaggeredImplF.cc

@@ -0,0 +1 @@
+../ImprovedStaggeredFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexStaggeredImplF/NaiveStaggeredFermionInstantiationlexStaggeredImplF.cc

@@ -0,0 +1 @@
+../NaiveStaggeredFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexStaggeredImplF/StaggeredKernelsInstantiationlexStaggeredImplF.cc

@@ -0,0 +1 @@
+../StaggeredKernelsInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexStaggeredImplF/impl.h

@@ -0,0 +1 @@
+#define IMPLEMENTATION lexStaggeredImplF

Grid/qcd/action/fermion/instantiation/lexWilsonImplD/CayleyFermion5DInstantiationlexWilsonImplD.cc

@@ -0,0 +1 @@
+../CayleyFermion5DInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplD/ContinuedFractionFermion5DInstantiationlexWilsonImplD.cc

@@ -0,0 +1 @@
+../ContinuedFractionFermion5DInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplD/DomainWallEOFAFermionInstantiationlexWilsonImplD.cc

@@ -0,0 +1 @@
+../DomainWallEOFAFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplD/MobiusEOFAFermionInstantiationlexWilsonImplD.cc

@@ -0,0 +1 @@
+../MobiusEOFAFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplD/PartialFractionFermion5DInstantiationlexWilsonImplD.cc

@@ -0,0 +1 @@
+../PartialFractionFermion5DInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplD/WilsonCloverFermionInstantiationlexWilsonImplD.cc

@@ -0,0 +1 @@
+../WilsonCloverFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplD/WilsonFermion5DInstantiationlexWilsonImplD.cc

@@ -0,0 +1 @@
+../WilsonFermion5DInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplD/WilsonFermionInstantiationlexWilsonImplD.cc

@@ -0,0 +1 @@
+../WilsonFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplD/WilsonKernelsInstantiationlexWilsonImplD.cc

@@ -0,0 +1 @@
+../WilsonKernelsInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplD/WilsonTMFermionInstantiationlexWilsonImplD.cc

@@ -0,0 +1 @@
+../WilsonTMFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplD/impl.h

@@ -0,0 +1 @@
+#define IMPLEMENTATION lexWilsonImplD

Grid/qcd/action/fermion/instantiation/lexWilsonImplF/CayleyFermion5DInstantiationlexWilsonImplF.cc

@@ -0,0 +1 @@
+../CayleyFermion5DInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplF/ContinuedFractionFermion5DInstantiationlexWilsonImplF.cc

@@ -0,0 +1 @@
+../ContinuedFractionFermion5DInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplF/DomainWallEOFAFermionInstantiationlexWilsonImplF.cc

@@ -0,0 +1 @@
+../DomainWallEOFAFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplF/MobiusEOFAFermionInstantiationlexWilsonImplF.cc

@@ -0,0 +1 @@
+../MobiusEOFAFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplF/PartialFractionFermion5DInstantiationlexWilsonImplF.cc

@@ -0,0 +1 @@
+../PartialFractionFermion5DInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplF/WilsonCloverFermionInstantiationlexWilsonImplF.cc

@@ -0,0 +1 @@
+../WilsonCloverFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplF/WilsonFermion5DInstantiationlexWilsonImplF.cc

@@ -0,0 +1 @@
+../WilsonFermion5DInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplF/WilsonFermionInstantiationlexWilsonImplF.cc

@@ -0,0 +1 @@
+../WilsonFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplF/WilsonKernelsInstantiationlexWilsonImplF.cc

@@ -0,0 +1 @@
+../WilsonKernelsInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplF/WilsonTMFermionInstantiationlexWilsonImplF.cc

@@ -0,0 +1 @@
+../WilsonTMFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/lexWilsonImplF/impl.h

@@ -0,0 +1 @@
+#define IMPLEMENTATION lexWilsonImplF

Grid/qcd/action/gauge/GaugeImplTypes.h

@@ -60,8 +60,10 @@ NAMESPACE_BEGIN(Grid);
   typedef typename Impl::SiteField SiteField;	    \
   typedef typename Impl::Field Field;
 
-// hardcodes the exponential approximation in the template
+// Order of the exponential approximation
-template <class S, int Nrepresentation = Nc, int Nexp = 12, class Group = SU<Nc> > class GaugeImplTypes {
+const int NexpDefault = 12;
+
+template <class S, int Nrepresentation = Nc, int Nexp = NexpDefault, class Group = SU<Nc> > class GaugeImplTypes {
 public:
   typedef S Simd;
   typedef typename Simd::scalar_type scalar_type;
@@ -188,14 +190,29 @@ typedef GaugeImplTypes<vComplex, Nc> GimplTypesR;
 typedef GaugeImplTypes<vComplexF, Nc> GimplTypesF;
 typedef GaugeImplTypes<vComplexD, Nc> GimplTypesD;
 
-typedef GaugeImplTypes<vComplex, Nc, 12, Sp<Nc> > SpGimplTypesR;
+typedef GaugeImplTypes<vComplex, Nc, NexpDefault, Sp<Nc> > SpGimplTypesR;
-typedef GaugeImplTypes<vComplexF, Nc, 12, Sp<Nc> > SpGimplTypesF;
+typedef GaugeImplTypes<vComplexF, Nc, NexpDefault, Sp<Nc> > SpGimplTypesF;
-typedef GaugeImplTypes<vComplexD, Nc, 12, Sp<Nc> > SpGimplTypesD;
+typedef GaugeImplTypes<vComplexD, Nc, NexpDefault, Sp<Nc> > SpGimplTypesD;
 
 typedef GaugeImplTypes<vComplex, SU<Nc>::AdjointDimension> GimplAdjointTypesR;
 typedef GaugeImplTypes<vComplexF, SU<Nc>::AdjointDimension> GimplAdjointTypesF;
 typedef GaugeImplTypes<vComplexD, SU<Nc>::AdjointDimension> GimplAdjointTypesD;
 
+/////////////////////////////////////////////////////////////////////////////
+// Lexicographic gauge implementation types
+/////////////////////////////////////////////////////////////////////////////
+typedef GaugeImplTypes<sComplexF, Nc> lexGimplTypesF;
+typedef GaugeImplTypes<sComplexD, Nc> lexGimplTypesD;
+
+typedef GaugeImplTypes<sComplexF, Nc, NexpDefault, Sp<Nc> > lexSpGimplTypesF;
+typedef GaugeImplTypes<sComplexD, Nc, NexpDefault, Sp<Nc> > lexSpGimplTypesD;
+
+typedef GaugeImplTypes<sComplexF, SU<Nc>::AdjointDimension> lexGimplAdjointTypesF;
+typedef GaugeImplTypes<sComplexD, SU<Nc>::AdjointDimension> lexGimplAdjointTypesD;
+/////////////////////////////////////////////////////////////////////////////
+// End lexicographic gauge implementation types
+/////////////////////////////////////////////////////////////////////////////
+
 
 
 

Grid/qcd/action/gauge/GaugeImplementations.h

@@ -197,6 +197,24 @@ typedef PeriodicGaugeImpl<SpGimplTypesR> SpPeriodicGimplR; // Real.. whichever p
 typedef PeriodicGaugeImpl<SpGimplTypesF> SpPeriodicGimplF; // Float
 typedef PeriodicGaugeImpl<SpGimplTypesD> SpPeriodicGimplD; // Double
 
+/////////////////////////////////////////////////////////////////////////////
+// Lexicographic gauge implementations
+/////////////////////////////////////////////////////////////////////////////
+typedef PeriodicGaugeImpl<lexGimplTypesF> lexPeriodicGimplF;
+typedef PeriodicGaugeImpl<lexGimplTypesD> lexPeriodicGimplD;
+
+typedef PeriodicGaugeImpl<lexGimplAdjointTypesF> lexPeriodicGimplAdjF;
+typedef PeriodicGaugeImpl<lexGimplAdjointTypesD> lexPeriodicGimplAdjD;
+
+typedef ConjugateGaugeImpl<lexGimplTypesF> lexConjugateGimplF;
+typedef ConjugateGaugeImpl<lexGimplTypesD> lexConjugateGimplD;
+
+typedef PeriodicGaugeImpl<lexSpGimplTypesF> lexSpPeriodicGimplF;
+typedef PeriodicGaugeImpl<lexSpGimplTypesD> lexSpPeriodicGimplD;
+/////////////////////////////////////////////////////////////////////////////
+// End lexicographic gauge implementations
+/////////////////////////////////////////////////////////////////////////////
+
 
 NAMESPACE_END(Grid);
 

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/TwoFlavourPVdagMPseudoFermion.h

@@ -0,0 +1,183 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./lib/qcd/action/pseudofermion/TwoFlavourPVdagMPseudoFermion.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 pseudofermion on the COMPOSITE operator  F = PVdag M :
+//
+//    S1 = phi^dag (Fdag F)^-1 phi
+//
+//    integral  ==>  det( Mdag PV PVdag M ) = |det M|^2 |det PV|^2
+//
+// i.e. the target two-flavour |det M|^2 TIMES an excess |det PV|^2, to be
+// cancelled by compensator monomials (two TwoFlavourBosonPseudoFermionAction
+// instances on PV, each contributing |det PV|^-2, net |det PV|^-4; together
+// with this action's |det PV|^2 the ensemble carries |det M|^2/|det PV|^2 --
+// the standard DWF quotient).
+//
+// Why this shape: F = PVdag M is exactly the operator the non-Hermitian
+// multigrid coarsens, so its cycles precondition (Fdag F) natively.  The
+// outer solve is CG on a Hermitian positive definite system -- the
+// non-normality is quarantined inside the preconditioner.  One solve per
+// force evaluation; all other force ingredients are matrix multiplies.
+//
+// Heatbath is exact by OPERATOR ALGEBRA (no wall/projection identity):
+//    refresh:  phi = Fdag eta   ==>   S1 = eta^dag F (Fdag F)^-1 Fdag eta
+//                                        = |eta|^2       (to solver tol)
+//
+// Hasenbusch: nothing here requires PVOp to have mass one.  Any
+// (heavier,lighter) pair F(m1,m2) = D^dag(m1) D(m2) works, each rung
+// coarsenable by the same machinery; compensate intermediate-mass excess
+// dets with boson monomials on the heavier operator.
+//
+// Solver slots map  b -> (Fdag F)^-1 b  (full grid, zero guess imposed
+// internally).  The class is agnostic to the implementation: plain CG on
+// the normal equations for testing; sequential MG solves of Fdag and F, or
+// preconditioned CG with a frozen-cycle G Gdag preconditioner in production.
+///////////////////////////////////////////////////////////////////////////////
+template<class Impl>
+class TwoFlavourPVdagMPseudoFermionAction : public Action<typename Impl::GaugeField> {
+public:
+  INHERIT_IMPL_TYPES(Impl);
+
+private:
+  FermionOperator<Impl> & PVOp; // the heavier / Pauli-Villars operator
+  FermionOperator<Impl> & MOp;  // the lighter operator
+
+  LinearFunction<FermionField> &DerivSolver;  // b -> (FdagF)^-1 b, MD tolerance
+  LinearFunction<FermionField> &ActionSolver; // b -> (FdagF)^-1 b, accept/reject tolerance
+
+  FermionField Phi; // the pseudo fermion field for this trajectory
+
+  ////////////////////////////////////////////////////////////////////
+  // F = PVdag M  and  Fdag = Mdag PV
+  ////////////////////////////////////////////////////////////////////
+  void Fapply(const FermionField &in, FermionField &out) {
+    FermionField tmp(MOp.FermionGrid());
+    MOp.M(in,tmp);
+    PVOp.Mdag(tmp,out);
+  }
+  void FdagApply(const FermionField &in, FermionField &out) {
+    FermionField tmp(MOp.FermionGrid());
+    PVOp.M(in,tmp);
+    MOp.Mdag(tmp,out);
+  }
+
+public:
+  TwoFlavourPVdagMPseudoFermionAction(FermionOperator<Impl>  &_PVOp,
+				      FermionOperator<Impl>  &_MOp,
+				      LinearFunction<FermionField> & DS,
+				      LinearFunction<FermionField> & AS
+				      ) : PVOp(_PVOp),
+					  MOp(_MOp),
+					  DerivSolver(DS),
+					  ActionSolver(AS),
+					  Phi(_MOp.FermionGrid())
+  {};
+
+  virtual std::string action_name(){return "TwoFlavourPVdagMPseudoFermionAction";}
+
+  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 (FdagF)^-1 phi} ; phi = Fdag 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(MOp.FermionGrid());
+    gaussian(pRNG,eta);
+    eta = eta * scale;
+    refresh(U,eta);
+  }
+
+  // Deterministic-noise variant (test hook, TwoFlavourEvenOddRatio idiom):
+  // after this,  S(U) == norm2(eta)  exactly (to solver tolerance).
+  void refresh(const GaugeField &U, const FermionField &eta) {
+    PVOp.ImportGauge(U);
+    MOp.ImportGauge(U);
+    FdagApply(eta,Phi);            // NO solve: heatbath is two matmuls
+    std::cout << GridLogMessage << action_name() << " refresh |Phi|^2 = "<< norm2(Phi)<<std::endl;
+  }
+
+  //////////////////////////////////////////////////////
+  // S1 = phi^dag (FdagF)^-1 phi
+  //////////////////////////////////////////////////////
+  virtual RealD S(const GaugeField &U) {
+    PVOp.ImportGauge(U);
+    MOp.ImportGauge(U);
+
+    FermionField X(MOp.FermionGrid());
+    X = Zero();
+    ActionSolver(Phi,X);                       // X = (FdagF)^-1 phi
+
+    RealD action = real(innerProduct(Phi,X));  // Hermitian positive kernel
+    return action;
+  }
+
+  //////////////////////////////////////////////////////
+  // dS1 = - X^dag [ dFdag F + Fdag dF ] X ,   X = (FdagF)^-1 phi,  Y = F X
+  //
+  // dF    = dPVdag M + PVdag dM   ==>  with A = M X,  B = PV Y :
+  //
+  // dS1 = - X^dag dMdag B - B^dag dM X - A^dag dPV Y - Y^dag dPVdag A
+  //
+  // ONE solve; A,Y,B by matrix multiply (Y = PVdag A reuses A).
+  //////////////////////////////////////////////////////
+  virtual void deriv(const GaugeField &U,GaugeField & dSdU) {
+    PVOp.ImportGauge(U);
+    MOp.ImportGauge(U);
+
+    FermionField X(MOp.FermionGrid());
+    FermionField Y(MOp.FermionGrid());
+    FermionField A(MOp.FermionGrid());
+    FermionField B(MOp.FermionGrid());
+
+    GaugeField force(MOp.GaugeGrid());
+
+    X = Zero();
+    DerivSolver(Phi,X);            // X = (FdagF)^-1 phi
+    MOp.M(X,A);                    // A = M X
+    PVOp.Mdag(A,Y);                // Y = PVdag A = F X
+    PVOp.M(Y,B);                   // B = PV Y
+
+    // dS1 = -( X^dag dMdag B + B^dag dM X + A^dag dPV Y + Y^dag dPVdag A )
+    MOp.MDeriv (force, X, B, DaggerYes); dSdU =      -force;
+    MOp.MDeriv (force, B, X, DaggerNo ); dSdU = dSdU -force;
+    PVOp.MDeriv(force, A, Y, DaggerNo ); dSdU = dSdU -force;
+    PVOp.MDeriv(force, Y, A, DaggerYes); 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/qcd/utils/GaugeGroup.h

@@ -89,10 +89,8 @@ template <int ncolour, class group_name>
 class GaugeGroup {
  public:
   static const int Dimension = ncolour;
-  static const int AdjointDimension =
+  static const int AdjointDimension = compute_adjoint_dimension<group_name>(ncolour);
-      compute_adjoint_dimension<group_name>(ncolour);
+  static const int AlgebraDimension = compute_adjoint_dimension<group_name>(ncolour);
-  static const int AlgebraDimension =
-      compute_adjoint_dimension<group_name>(ncolour);
 
   template <typename vtype>
   using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
@@ -101,8 +99,7 @@ class GaugeGroup {
   template <typename vtype>
   using iAlgebraVector = iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
   template <typename vtype>
-  using iSUnAlgebraMatrix =
+  using iSUnAlgebraMatrix = iScalar<iScalar<iMatrix<vtype, AdjointDimension> > >;
-    iScalar<iScalar<iMatrix<vtype, AdjointDimension> > >;
   static int su2subgroups(void) { return su2subgroups(group_name()); }
 
   //////////////////////////////////////////////////////////////////////////////////////////////////
@@ -297,15 +294,17 @@ class GaugeGroup {
     }
   }
   
-
-  
   template <int N,class vComplex_t>
-  static Lattice<iScalar<iScalar<iMatrix<vComplex_t, N> > > > ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vComplex_t, N> > > > &Umu) {
+  static Lattice<iScalar<iScalar<iMatrix<vComplex_t, N> > > >
+  ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vComplex_t, N> > > > &Umu)
+  {
     return ProjectOnGeneralGroup(Umu, group_name());
   }
 
-  template <int N,class vComplex_t>       // Projects on SU(N), Sp(2N), with unit determinant, by first projecting on general group and then enforcing unit determinant
+  // Projects on SU(N), Sp(2N), with unit determinant, by first projecting on general group and then enforcing unit determinant
-  static void ProjectOnSpecialGroup(Lattice<iScalar<iScalar<iMatrix<vComplex_t, N> > > > &Umu) {
+  template <int N,class vComplex_t>  
+  static void ProjectOnSpecialGroup(Lattice<iScalar<iScalar<iMatrix<vComplex_t, N> > > > &Umu)
+  {
        Umu = ProjectOnGeneralGroup(Umu);
        auto det = Determinant(Umu);
 
@@ -319,7 +318,8 @@ class GaugeGroup {
    }
 
   template <int N,class vComplex_t>    // reunitarise, resimplectify... previously ProjectSUn
-    static void ProjectOnSpecialGroup(Lattice<iVector<iScalar<iMatrix<vComplex_t, N> >, Nd> > &U) {
+  static void ProjectOnSpecialGroup(Lattice<iVector<iScalar<iMatrix<vComplex_t, N> >, Nd> > &U)
+  {
       // Reunitarise
       for (int mu = 0; mu < Nd; mu++) {
         auto Umu = PeekIndex<LorentzIndex>(U, mu);

Grid/simd/Grid_a64fx-2.h

@@ -933,6 +933,8 @@ typedef Optimization::Div            DivSIMD;
 typedef Optimization::Mult           MultSIMD;
 typedef Optimization::MultComplex    MultComplexSIMD;
 typedef Optimization::MultAddComplex MultAddComplexSIMD;
+// Asserts MultAddComplexSIMD and a three argument MultSIMD operator()
+#define GRID_ARCH_HAS_COMPLEX_MULT_ADD 1
 typedef Optimization::MultRealPart   MultRealPartSIMD;
 typedef Optimization::MaddRealPart   MaddRealPartSIMD;
 typedef Optimization::Conj           ConjSIMD;

Grid/simd/Grid_a64fx-fixedsize.h

@@ -760,6 +760,8 @@ typedef Optimization::Div            DivSIMD;
 typedef Optimization::Mult           MultSIMD;
 typedef Optimization::MultComplex    MultComplexSIMD;
 typedef Optimization::MultAddComplex MultAddComplexSIMD;
+// Asserts MultAddComplexSIMD and a three argument MultSIMD operator()
+#define GRID_ARCH_HAS_COMPLEX_MULT_ADD 1
 typedef Optimization::MultRealPart   MultRealPartSIMD;
 typedef Optimization::MaddRealPart   MaddRealPartSIMD;
 typedef Optimization::Conj           ConjSIMD;

Grid/simd/Grid_doubled_vector.h

@@ -339,54 +339,6 @@ typedef Grid_simd2<complex<double>  , vComplexD>  vComplexD2;
 typedef Grid_simd2<double           , vRealD>     vRealD2;
 
 
-
-/////////////////////////////////////////
-// Some traits to recognise the types
-/////////////////////////////////////////
-template <typename T>
-struct is_simd : public std::false_type {};
-template <> struct is_simd<vRealF>     : public std::true_type {};
-template <> struct is_simd<vRealD>     : public std::true_type {};
-template <> struct is_simd<vRealH>     : public std::true_type {};
-template <> struct is_simd<vComplexF>  : public std::true_type {};
-template <> struct is_simd<vComplexD>  : public std::true_type {};
-template <> struct is_simd<vComplexH>  : public std::true_type {};
-template <> struct is_simd<vInteger>   : public std::true_type {};
-template <> struct is_simd<vRealD2>    : public std::true_type {};
-template <> struct is_simd<vComplexD2> : public std::true_type {};
-
-template <typename T> using IfSimd    = Invoke<std::enable_if<is_simd<T>::value, int> >;
-template <typename T> using IfNotSimd = Invoke<std::enable_if<!is_simd<T>::value, unsigned> >;
-
-///////////////////////////////////////////////
-// insert / extract with complex support
-///////////////////////////////////////////////
-template <class S, class V>
-accelerator_inline S getlane(const Grid_simd<S, V> &in,int lane) {
-  return in.getlane(lane);
-}
-template <class S, class V>
-accelerator_inline void putlane(Grid_simd<S, V> &vec,const S &_S, int lane){
-  vec.putlane(_S,lane);
-}
-template <class S,IfNotSimd<S> = 0 >
-accelerator_inline S getlane(const S &in,int lane) {
-  return in;
-}
-template <class S,IfNotSimd<S> = 0 >
-accelerator_inline void putlane(S &vec,const S &_S, int lane){
-  vec = _S;
-}
-template <class S, class V>
-accelerator_inline S getlane(const Grid_simd2<S, V> &in,int lane) {
-  return in.getlane(lane);
-}
-template <class S, class V>
-accelerator_inline void putlane(Grid_simd2<S, V> &vec,const S &_S, int lane){
-  vec.putlane(_S,lane);
-}
-
-
 ////////////////////////////////////////////////////////////////////
 // General rotate
 ////////////////////////////////////////////////////////////////////

Grid/simd/Grid_neon.h

@@ -42,6 +42,16 @@
 #define GEN_SIMD_WIDTH 16u
 #endif
 
+//////////////////////////////////////////////////////////////////////////////
+// ARMv8.3 complex assist (FCMLA). Kept separate from the ACLE
+// __ARM_FEATURE_COMPLEX: the instructions are also present on A64FX, where
+// their throughput is 1:4 and this path would be a regression. Revisit the
+// rule once measured per target.
+//////////////////////////////////////////////////////////////////////////////
+#ifdef __ARM_FEATURE_COMPLEX
+#define GRID_ARM_FEATURE_COMPLEX 1
+#endif
+
 #include "Grid_generic_types.h"
 #include <arm_neon.h>
 
@@ -226,6 +236,22 @@ struct Div{
 };
 
 struct MultComplex{
+#ifdef GRID_ARM_FEATURE_COMPLEX
+  // fcmla #0  : r += (ar,ar)*(br,bi) = ( ar*br, ar*bi)
+  // fcmla #90 : r += (-ai,ai)*(bi,br) = (-ai*bi, ai*br)
+  // Complex float: two products, two instructions
+  inline float32x4_t operator()(float32x4_t a, float32x4_t b){
+    float32x4_t r = vdupq_n_f32(0.0f);
+    r = vcmlaq_f32(r, a, b);
+    return vcmlaq_rot90_f32(r, a, b);
+  }
+  // Complex double
+  inline float64x2_t operator()(float64x2_t a, float64x2_t b){
+    float64x2_t r = vdupq_n_f64(0.0);
+    r = vcmlaq_f64(r, a, b);
+    return vcmlaq_rot90_f64(r, a, b);
+  }
+#else
   // Complex float
   inline float32x4_t operator()(float32x4_t a, float32x4_t b){
 
@@ -273,8 +299,23 @@ struct MultComplex{
     // r5 = vmulq_f64(r0, a);
     // return vaddq_f64(r4, r5);
   }
+#endif
 };
 
+#ifdef GRID_ARM_FEATURE_COMPLEX
+struct MultAddComplex{
+  // Complex a*b+c
+  inline float32x4_t operator()(float32x4_t a, float32x4_t b, float32x4_t c){
+    c = vcmlaq_f32(c, a, b);
+    return vcmlaq_rot90_f32(c, a, b);
+  }
+  inline float64x2_t operator()(float64x2_t a, float64x2_t b, float64x2_t c){
+    c = vcmlaq_f64(c, a, b);
+    return vcmlaq_rot90_f64(c, a, b);
+  }
+};
+#endif
+
 struct Mult{
   // Real float
   inline float32x4_t mac(float32x4_t a, float32x4_t b, float32x4_t c){
@@ -285,6 +326,13 @@ struct Mult{
     //return vaddq_f64(vmulq_f64(b,c),a);
     return vfmaq_f64(a, b, c);
   }
+  // Real a*b+c
+  inline float32x4_t operator()(float32x4_t a, float32x4_t b, float32x4_t c){
+    return vfmaq_f32(c, a, b);
+  }
+  inline float64x2_t operator()(float64x2_t a, float64x2_t b, float64x2_t c){
+    return vfmaq_f64(c, a, b);
+  }
   inline float32x4_t operator()(float32x4_t a, float32x4_t b){
     return vmulq_f32(a,b);
   }
@@ -585,6 +633,11 @@ typedef Optimization::Sub         SubSIMD;
 typedef Optimization::Div         DivSIMD;
 typedef Optimization::Mult        MultSIMD;
 typedef Optimization::MultComplex MultComplexSIMD;
+#ifdef GRID_ARM_FEATURE_COMPLEX
+typedef Optimization::MultAddComplex MultAddComplexSIMD;
+// Asserts MultAddComplexSIMD and a three argument MultSIMD operator()
+#define GRID_ARCH_HAS_COMPLEX_MULT_ADD 1
+#endif
 typedef Optimization::MultRealPart MultRealPartSIMD;
 typedef Optimization::MaddRealPart MaddRealPartSIMD;
 typedef Optimization::Conj        ConjSIMD;