Merge 461cd045c6 into da59379612

--disable-accelerator-aware-mpi

.gitignore

@@ -1,3 +1,7 @@
+# Doxygen stuff
+html/*
+latex/*
+
 # Compiled Object files #
 #########################
 *.slo

Grid/Grid_Eigen_Dense.h

@@ -34,7 +34,7 @@
 #pragma push_macro("__SYCL_DEVICE_ONLY__")
 #undef __SYCL_DEVICE_ONLY__
 #define EIGEN_DONT_VECTORIZE
-//#undef EIGEN_USE_SYCL
+#undef EIGEN_USE_SYCL
 #define __SYCL__REDEFINE__
 #endif
 

Grid/Makefile.am

@@ -66,6 +66,10 @@ if BUILD_FERMION_REPS
   extra_sources+=$(ADJ_FERMION_FILES)
   extra_sources+=$(TWOIND_FERMION_FILES)
 endif
+if BUILD_SP
+    extra_sources+=$(SP_FERMION_FILES)
+    extra_sources+=$(SP_TWOIND_FERMION_FILES)
+endif
 
 lib_LIBRARIES = libGrid.a
 

Grid/algorithms/FFT.h

@@ -29,7 +29,7 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 #define _GRID_FFT_H_
 
 #ifdef HAVE_FFTW
-#ifdef USE_MKL
+#if defined(USE_MKL) || defined(GRID_SYCL)
 #include <fftw/fftw3.h>
 #else
 #include <fftw3.h>

Grid/algorithms/approx/Zolotarev.cc

@@ -293,7 +293,7 @@ static void sncndnFK(INTERNAL_PRECISION u, INTERNAL_PRECISION k,
  * Set type = 0 for the Zolotarev approximation, which is zero at x = 0, and
  * type = 1 for the approximation which is infinite at x = 0. */
 
-zolotarev_data* zolotarev(PRECISION epsilon, int n, int type) {
+zolotarev_data* zolotarev(ZOLO_PRECISION epsilon, int n, int type) {
   INTERNAL_PRECISION A, c, cp, kp, ksq, sn, cn, dn, Kp, Kj, z, z0, t, M, F,
     l, invlambda, xi, xisq, *tv, s, opl;
   int m, czero, ts;
@@ -375,12 +375,12 @@ zolotarev_data* zolotarev(PRECISION epsilon, int n, int type) {
   construct_partfrac(d);
   construct_contfrac(d);
 
-  /* Converting everything to PRECISION for external use only */
+  /* Converting everything to ZOLO_PRECISION for external use only */
 
   zd = (zolotarev_data*) malloc(sizeof(zolotarev_data));
-  zd -> A = (PRECISION) d -> A;
-  zd -> Delta = (PRECISION) d -> Delta;
-  zd -> epsilon = (PRECISION) d -> epsilon;
+  zd -> A = (ZOLO_PRECISION) d -> A;
+  zd -> Delta = (ZOLO_PRECISION) d -> Delta;
+  zd -> epsilon = (ZOLO_PRECISION) d -> epsilon;
   zd -> n = d -> n;
   zd -> type = d -> type;
   zd -> dn = d -> dn;
@@ -390,24 +390,24 @@ zolotarev_data* zolotarev(PRECISION epsilon, int n, int type) {
   zd -> deg_num = d -> deg_num;
   zd -> deg_denom = d -> deg_denom;
 
-  zd -> a = (PRECISION*) malloc(zd -> dn * sizeof(PRECISION));
-  for (m = 0; m < zd -> dn; m++) zd -> a[m] = (PRECISION) d -> a[m];
+  zd -> a = (ZOLO_PRECISION*) malloc(zd -> dn * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> dn; m++) zd -> a[m] = (ZOLO_PRECISION) d -> a[m];
   free(d -> a);
 
-  zd -> ap = (PRECISION*) malloc(zd -> dd * sizeof(PRECISION));
-  for (m = 0; m < zd -> dd; m++) zd -> ap[m] = (PRECISION) d -> ap[m];
+  zd -> ap = (ZOLO_PRECISION*) malloc(zd -> dd * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> dd; m++) zd -> ap[m] = (ZOLO_PRECISION) d -> ap[m];
   free(d -> ap);
 
-  zd -> alpha = (PRECISION*) malloc(zd -> da * sizeof(PRECISION));
-  for (m = 0; m < zd -> da; m++) zd -> alpha[m] = (PRECISION) d -> alpha[m];
+  zd -> alpha = (ZOLO_PRECISION*) malloc(zd -> da * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> da; m++) zd -> alpha[m] = (ZOLO_PRECISION) d -> alpha[m];
   free(d -> alpha);
 
-  zd -> beta = (PRECISION*) malloc(zd -> db * sizeof(PRECISION));
-  for (m = 0; m < zd -> db; m++) zd -> beta[m] = (PRECISION) d -> beta[m];
+  zd -> beta = (ZOLO_PRECISION*) malloc(zd -> db * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> db; m++) zd -> beta[m] = (ZOLO_PRECISION) d -> beta[m];
   free(d -> beta);
 
-  zd -> gamma = (PRECISION*) malloc(zd -> n * sizeof(PRECISION));
-  for (m = 0; m < zd -> n; m++) zd -> gamma[m] = (PRECISION) d -> gamma[m];
+  zd -> gamma = (ZOLO_PRECISION*) malloc(zd -> n * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> n; m++) zd -> gamma[m] = (ZOLO_PRECISION) d -> gamma[m];
   free(d -> gamma);
 
   free(d);
@@ -426,7 +426,7 @@ void zolotarev_free(zolotarev_data *zdata)
 }
 
 
-zolotarev_data* higham(PRECISION epsilon, int n) {
+zolotarev_data* higham(ZOLO_PRECISION epsilon, int n) {
   INTERNAL_PRECISION A, M, c, cp, z, z0, t, epssq;
   int m, czero;
   zolotarev_data *zd;
@@ -481,9 +481,9 @@ zolotarev_data* higham(PRECISION epsilon, int n) {
   /* Converting everything to PRECISION for external use only */
 
   zd = (zolotarev_data*) malloc(sizeof(zolotarev_data));
-  zd -> A = (PRECISION) d -> A;
-  zd -> Delta = (PRECISION) d -> Delta;
-  zd -> epsilon = (PRECISION) d -> epsilon;
+  zd -> A = (ZOLO_PRECISION) d -> A;
+  zd -> Delta = (ZOLO_PRECISION) d -> Delta;
+  zd -> epsilon = (ZOLO_PRECISION) d -> epsilon;
   zd -> n = d -> n;
   zd -> type = d -> type;
   zd -> dn = d -> dn;
@@ -493,24 +493,24 @@ zolotarev_data* higham(PRECISION epsilon, int n) {
   zd -> deg_num = d -> deg_num;
   zd -> deg_denom = d -> deg_denom;
 
-  zd -> a = (PRECISION*) malloc(zd -> dn * sizeof(PRECISION));
-  for (m = 0; m < zd -> dn; m++) zd -> a[m] = (PRECISION) d -> a[m];
+  zd -> a = (ZOLO_PRECISION*) malloc(zd -> dn * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> dn; m++) zd -> a[m] = (ZOLO_PRECISION) d -> a[m];
   free(d -> a);
 
-  zd -> ap = (PRECISION*) malloc(zd -> dd * sizeof(PRECISION));
-  for (m = 0; m < zd -> dd; m++) zd -> ap[m] = (PRECISION) d -> ap[m];
+  zd -> ap = (ZOLO_PRECISION*) malloc(zd -> dd * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> dd; m++) zd -> ap[m] = (ZOLO_PRECISION) d -> ap[m];
   free(d -> ap);
 
-  zd -> alpha = (PRECISION*) malloc(zd -> da * sizeof(PRECISION));
-  for (m = 0; m < zd -> da; m++) zd -> alpha[m] = (PRECISION) d -> alpha[m];
+  zd -> alpha = (ZOLO_PRECISION*) malloc(zd -> da * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> da; m++) zd -> alpha[m] = (ZOLO_PRECISION) d -> alpha[m];
   free(d -> alpha);
 
-  zd -> beta = (PRECISION*) malloc(zd -> db * sizeof(PRECISION));
-  for (m = 0; m < zd -> db; m++) zd -> beta[m] = (PRECISION) d -> beta[m];
+  zd -> beta = (ZOLO_PRECISION*) malloc(zd -> db * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> db; m++) zd -> beta[m] = (ZOLO_PRECISION) d -> beta[m];
   free(d -> beta);
 
-  zd -> gamma = (PRECISION*) malloc(zd -> n * sizeof(PRECISION));
-  for (m = 0; m < zd -> n; m++) zd -> gamma[m] = (PRECISION) d -> gamma[m];
+  zd -> gamma = (ZOLO_PRECISION*) malloc(zd -> n * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> n; m++) zd -> gamma[m] = (ZOLO_PRECISION) d -> gamma[m];
   free(d -> gamma);
 
   free(d);
@@ -523,17 +523,17 @@ NAMESPACE_END(Grid);
 #ifdef TEST
 
 #undef ZERO
-#define ZERO ((PRECISION) 0)
+#define ZERO ((ZOLO_PRECISION) 0)
 #undef ONE
-#define ONE ((PRECISION) 1)
+#define ONE ((ZOLO_PRECISION) 1)
 #undef TWO
-#define TWO ((PRECISION) 2)
+#define TWO ((ZOLO_PRECISION) 2)
 
 /* Evaluate the rational approximation R(x) using the factored form */
 
-static PRECISION zolotarev_eval(PRECISION x, zolotarev_data* rdata) {
+static ZOLO_PRECISION zolotarev_eval(ZOLO_PRECISION x, zolotarev_data* rdata) {
   int m;
-  PRECISION R;
+  ZOLO_PRECISION R;
 
   if (rdata -> type == 0) {
     R = rdata -> A * x;
@@ -551,9 +551,9 @@ static PRECISION zolotarev_eval(PRECISION x, zolotarev_data* rdata) {
 
 /* Evaluate the rational approximation R(x) using the partial fraction form */
 
-static PRECISION zolotarev_partfrac_eval(PRECISION x, zolotarev_data* rdata) {
+static ZOLO_PRECISION zolotarev_partfrac_eval(ZOLO_PRECISION x, zolotarev_data* rdata) {
   int m;
-  PRECISION R = rdata -> alpha[rdata -> da - 1];
+  ZOLO_PRECISION R = rdata -> alpha[rdata -> da - 1];
   for (m = 0; m < rdata -> dd; m++)
     R += rdata -> alpha[m] / (x * x - rdata -> ap[m]);
   if (rdata -> type == 1) R += rdata -> alpha[rdata -> dd] / (x * x);
@@ -568,18 +568,18 @@ static PRECISION zolotarev_partfrac_eval(PRECISION x, zolotarev_data* rdata) {
  * non-signalling overflow this will work correctly since 1/(1/0) = 1/INF = 0,
  * but with signalling overflow you will get an error message. */
 
-static PRECISION zolotarev_contfrac_eval(PRECISION x, zolotarev_data* rdata) {
+static ZOLO_PRECISION zolotarev_contfrac_eval(ZOLO_PRECISION x, zolotarev_data* rdata) {
   int m;
-  PRECISION R = rdata -> beta[0] * x;
+  ZOLO_PRECISION R = rdata -> beta[0] * x;
   for (m = 1; m < rdata -> db; m++) R = rdata -> beta[m] * x + ONE / R;
   return R;
 }    
 
 /* Evaluate the rational approximation R(x) using Cayley form */
 
-static PRECISION zolotarev_cayley_eval(PRECISION x, zolotarev_data* rdata) {
+static ZOLO_PRECISION zolotarev_cayley_eval(ZOLO_PRECISION x, zolotarev_data* rdata) {
   int m;
-  PRECISION T;
+  ZOLO_PRECISION T;
 
   T = rdata -> type == 0 ? ONE : -ONE;
   for (m = 0; m < rdata -> n; m++)
@@ -607,7 +607,7 @@ int main(int argc, char** argv) {
   int m, n, plotpts = 5000, type = 0;
   float eps, x, ypferr, ycferr, ycaylerr, maxypferr, maxycferr, maxycaylerr;
   zolotarev_data *rdata;
-  PRECISION y;
+  ZOLO_PRECISION y;
   FILE *plot_function, *plot_error, 
     *plot_partfrac, *plot_contfrac, *plot_cayley;
 
@@ -626,13 +626,13 @@ int main(int argc, char** argv) {
   }
 
   rdata = type == 2 
-    ? higham((PRECISION) eps, n) 
-    : zolotarev((PRECISION) eps, n, type);
+    ? higham((ZOLO_PRECISION) eps, n) 
+    : zolotarev((ZOLO_PRECISION) eps, n, type);
 
   printf("Zolotarev Test: R(epsilon = %g, n = %d, type = %d)\n\t" 
 	 STRINGIFY(VERSION) "\n\t" STRINGIFY(HVERSION)
 	 "\n\tINTERNAL_PRECISION = " STRINGIFY(INTERNAL_PRECISION)
-	 "\tPRECISION = " STRINGIFY(PRECISION)
+	 "\tZOLO_PRECISION = " STRINGIFY(ZOLO_PRECISION)
 	 "\n\n\tRational approximation of degree (%d,%d), %s at x = 0\n"
 	 "\tDelta = %g (maximum error)\n\n"
 	 "\tA = %g (overall factor)\n",
@@ -681,15 +681,15 @@ int main(int argc, char** argv) {
     x = 2.4 * (float) m / plotpts - 1.2;
     if (rdata -> type == 0 || fabs(x) * (float) plotpts > 1.0) {
       /* skip x = 0 for type 1, as R(0) is singular */
-      y = zolotarev_eval((PRECISION) x, rdata);
+      y = zolotarev_eval((ZOLO_PRECISION) x, rdata);
       fprintf(plot_function, "%g %g\n", x, (float) y);
       fprintf(plot_error, "%g %g\n",
 	      x, (float)((y - ((x > 0.0 ? ONE : -ONE))) / rdata -> Delta));
-      ypferr = (float)((zolotarev_partfrac_eval((PRECISION) x, rdata) - y)
+      ypferr = (float)((zolotarev_partfrac_eval((ZOLO_PRECISION) x, rdata) - y)
 		       / rdata -> Delta);
-      ycferr = (float)((zolotarev_contfrac_eval((PRECISION) x, rdata) - y)
+      ycferr = (float)((zolotarev_contfrac_eval((ZOLO_PRECISION) x, rdata) - y)
 		       / rdata -> Delta);
-      ycaylerr = (float)((zolotarev_cayley_eval((PRECISION) x, rdata) - y)
+      ycaylerr = (float)((zolotarev_cayley_eval((ZOLO_PRECISION) x, rdata) - y)
 		       / rdata -> Delta);
       if (fabs(x) < 1.0 && fabs(x) > rdata -> epsilon) {
 	maxypferr = MAX(maxypferr, fabs(ypferr));

Grid/algorithms/approx/Zolotarev.h

@@ -9,10 +9,10 @@ NAMESPACE_BEGIN(Approx);
 #define HVERSION Header Time-stamp: <14-OCT-2004 09:26:51.00 adk@MISSCONTRARY>
 
 #ifndef ZOLOTAREV_INTERNAL
-#ifndef PRECISION
-#define PRECISION double
+#ifndef ZOLO_PRECISION
+#define ZOLO_PRECISION double
 #endif
-#define ZPRECISION PRECISION
+#define ZPRECISION ZOLO_PRECISION
 #define ZOLOTAREV_DATA zolotarev_data
 #endif
 
@@ -77,8 +77,8 @@ typedef struct {
  * zolotarev_data structure. The arguments must satisfy the constraints that
  * epsilon > 0, n > 0, and type = 0 or 1. */
 
-ZOLOTAREV_DATA* higham(PRECISION epsilon, int n) ;
-ZOLOTAREV_DATA* zolotarev(PRECISION epsilon, int n, int type);
+ZOLOTAREV_DATA* higham(ZOLO_PRECISION epsilon, int n) ;
+ZOLOTAREV_DATA* zolotarev(ZOLO_PRECISION epsilon, int n, int type);
 void zolotarev_free(zolotarev_data *zdata);
 #endif
 
@@ -86,3 +86,4 @@ void zolotarev_free(zolotarev_data *zdata);
 NAMESPACE_END(Approx);
 NAMESPACE_END(Grid);
 #endif
+

Grid/algorithms/blas/BatchedBlas.cc

@@ -0,0 +1,34 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: BatchedBlas.h
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#include <Grid/GridCore.h>
+#include <Grid/algorithms/blas/BatchedBlas.h>
+NAMESPACE_BEGIN(Grid);
+gridblasHandle_t GridBLAS::gridblasHandle;
+int              GridBLAS::gridblasInit;
+NAMESPACE_END(Grid);
+

Grid/algorithms/blas/BatchedBlas.h

@@ -0,0 +1,727 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: BatchedBlas.h
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+#ifdef GRID_HIP
+#include <hipblas/hipblas.h>
+#endif
+#ifdef GRID_CUDA
+#include <cublas_v2.h>
+#endif
+#ifdef GRID_SYCL
+#include <oneapi/mkl.hpp>
+#endif
+#if 0
+#define GRID_ONE_MKL
+#endif
+#ifdef GRID_ONE_MKL
+#include <oneapi/mkl.hpp>
+#endif
+///////////////////////////////////////////////////////////////////////	  
+// Need to rearrange lattice data to be in the right format for a
+// batched multiply. Might as well make these static, dense packed
+///////////////////////////////////////////////////////////////////////
+NAMESPACE_BEGIN(Grid);
+#ifdef GRID_HIP
+  typedef hipblasHandle_t gridblasHandle_t;
+#endif
+#ifdef GRID_CUDA
+  typedef cublasHandle_t gridblasHandle_t;
+#endif
+#ifdef GRID_SYCL
+  typedef cl::sycl::queue *gridblasHandle_t;
+#endif
+#ifdef GRID_ONE_MKL
+  typedef cl::sycl::queue *gridblasHandle_t;
+#endif
+#if !defined(GRID_SYCL) && !defined(GRID_CUDA) && !defined(GRID_HIP) && !defined(GRID_ONE_MKL)
+  typedef int32_t gridblasHandle_t;
+#endif
+
+enum GridBLASOperation_t { GridBLAS_OP_N, GridBLAS_OP_T, GridBLAS_OP_C } ;
+
+class GridBLAS {
+public:
+
+  
+  static gridblasHandle_t gridblasHandle;
+  static int            gridblasInit;
+  
+  static void Init(void)
+  {
+    if ( ! gridblasInit ) {
+#ifdef GRID_CUDA
+      std::cout << "cublasCreate"<<std::endl;
+      cublasCreate(&gridblasHandle);
+      cublasSetPointerMode(gridblasHandle, CUBLAS_POINTER_MODE_DEVICE);
+#endif
+#ifdef GRID_HIP
+      std::cout << "hipblasCreate"<<std::endl;
+      hipblasCreate(&gridblasHandle);
+#endif
+#ifdef GRID_SYCL
+      gridblasHandle = theGridAccelerator;
+#endif
+#ifdef GRID_ONE_MKL
+      cl::sycl::cpu_selector selector;
+      cl::sycl::device selectedDevice { selector };
+      gridblasHandle =new sycl::queue (selectedDevice);
+#endif
+      gridblasInit=1;
+    }
+  }
+  
+  // Force construct once
+  GridBLAS() { Init(); };
+  ~GridBLAS() { };
+  
+  /////////////////////////////////////////////////////////////////////////////////////
+  // BLAS GEMM conventions:
+  /////////////////////////////////////////////////////////////////////////////////////
+  // - C = alpha A * B + beta C
+  // Dimensions:
+  // - C_m.n
+  // - A_m.k
+  // - B_k.n
+  // - Flops = 8 M N K
+  // - Bytes = 2*sizeof(word) * (MN+MK+KN)
+  // M=60, N=12
+  // Flop/Byte = 8 . 60.60.12 / (60.12+60.60+60.12)/16 = 4 so expect about 4 TF/s on a GCD
+  /////////////////////////////////////////////////////////////////////////////////////
+  void synchronise(void)
+  {
+#ifdef GRID_HIP
+    auto err = hipDeviceSynchronize();
+    assert(err==hipSuccess);
+#endif
+#ifdef GRID_CUDA
+    auto err = cudaDeviceSynchronize();
+    assert(err==cudaSuccess);
+#endif
+#ifdef GRID_SYCL
+    accelerator_barrier();
+#endif
+#ifdef GRID_ONE_MKL
+    gridblasHandle->wait();
+#endif
+  }
+  
+  void gemmBatched(int m,int n, int k,
+		   ComplexD alpha,
+		   deviceVector<ComplexD*> &Amk,  // pointer list to matrices
+		   deviceVector<ComplexD*> &Bkn,
+		   ComplexD beta,
+		   deviceVector<ComplexD*> &Cmn)
+  {
+    gemmBatched(GridBLAS_OP_N,GridBLAS_OP_N,
+		m,n,k,
+		alpha,
+		Amk,
+		Bkn,
+		beta,
+		Cmn);
+  }
+  void gemmBatched(int m,int n, int k,
+		   ComplexF alpha,
+		   deviceVector<ComplexF*> &Amk,  // pointer list to matrices
+		   deviceVector<ComplexF*> &Bkn,
+		   ComplexF beta,
+		   deviceVector<ComplexF*> &Cmn)
+  {
+    gemmBatched(GridBLAS_OP_N,GridBLAS_OP_N,
+		m,n,k,
+		alpha,
+		Amk,
+		Bkn,
+		beta,
+		Cmn);
+  }
+  void gemmBatched(int m,int n, int k,
+		   RealD alpha,
+		   deviceVector<RealD*> &Amk,  // pointer list to matrices
+		   deviceVector<RealD*> &Bkn,
+		   RealD beta,
+		   deviceVector<RealD*> &Cmn)
+  {
+    gemmBatched(GridBLAS_OP_N,GridBLAS_OP_N,
+		m,n,k,
+		alpha,
+		Amk,
+		Bkn,
+		beta,
+		Cmn);
+  }
+  void gemmBatched(int m,int n, int k,
+		   RealF alpha,
+		   deviceVector<RealF*> &Amk,  // pointer list to matrices
+		   deviceVector<RealF*> &Bkn,
+		   RealF beta,
+		   deviceVector<RealF*> &Cmn)
+  {
+    gemmBatched(GridBLAS_OP_N,GridBLAS_OP_N,
+		m,n,k,
+		alpha,
+		Amk,
+		Bkn,
+		beta,
+		Cmn);
+  }
+
+  void gemmBatched(GridBLASOperation_t OpA,
+		   GridBLASOperation_t OpB,
+		   int m,int n, int k,
+		   ComplexD alpha,
+		   deviceVector<ComplexD*> &Amk,  // pointer list to matrices
+		   deviceVector<ComplexD*> &Bkn,
+		   ComplexD beta,
+		   deviceVector<ComplexD*> &Cmn)
+  {
+    RealD t2=usecond();
+    int32_t batchCount = Amk.size();
+    assert(Bkn.size()==batchCount);
+    assert(Cmn.size()==batchCount);
+
+    int lda = m; // m x k column major
+    int ldb = k; // k x n column major
+    int ldc = m; // m x b column major
+    if(OpA!=GridBLAS_OP_N)
+      lda = k;
+    if(OpB!=GridBLAS_OP_N)
+      ldb = n;
+    
+    static deviceVector<ComplexD> alpha_p(1);
+    static deviceVector<ComplexD> beta_p(1);
+    // can prestore the 1 and the zero on device
+    acceleratorCopyToDevice((void *)&alpha,(void *)&alpha_p[0],sizeof(ComplexD));
+    acceleratorCopyToDevice((void *)&beta ,(void *)&beta_p[0],sizeof(ComplexD));
+    RealD t0=usecond();
+    //    std::cout << "ZgemmBatched mnk  "<<m<<","<<n<<","<<k<<" count "<<batchCount<<std::endl;
+#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;
+    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);
+    //	 std::cout << " hipblas return code " <<(int)err<<std::endl;
+    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);
+    assert(err==CUBLAS_STATUS_SUCCESS);
+#endif
+#ifdef GRID_SYCL
+    //MKL’s cblas_<T>gemm_batch & OneAPI
+#warning "oneMKL implementation not built "
+#endif
+#if !defined(GRID_SYCL) && !defined(GRID_CUDA) && !defined(GRID_HIP)
+    // Need a default/reference implementation
+    int sda = lda*k;
+    int sdb = ldb*k;
+    int sdc = ldc*n;
+    for (int p = 0; p < batchCount; ++p) {
+      for (int mm = 0; mm < m; ++mm) {
+	for (int nn = 0; nn < n; ++nn) {
+	  ComplexD c_mn(0.0);
+	  for (int kk = 0; kk < k; ++kk)
+	    c_mn += Amk[p][mm + kk*lda ] * Bkn[p][kk + nn*ldb];
+	  Cmn[p][mm + nn*ldc] =  (alpha)*c_mn + (beta)*Cmn[p][mm + nn*ldc ];
+	}
+      }
+    }
+#endif
+    //    synchronise();
+     RealD t1=usecond();
+     RealD flops = 8.0*m*n*k*batchCount;
+     RealD bytes = 1.0*sizeof(ComplexD)*(m*k+k*n+m*n)*batchCount;
+     //     std::cout <<GridLogMessage<< " batched Blas copy "<<(t0-t2)/1.e3 <<" ms "<<std::endl;
+     //     std::cout <<GridLogMessage<< " batched Blas zGemm call "<<m<<","<<n<<","<<k<<" "<< flops/(t1-t0)/1.e3 <<" GF/s "<<(t1-t0)/1.e3<<" ms "<<std::endl;
+     //     std::cout <<GridLogMessage<< " batched Blas zGemm call "<<m<<","<<n<<","<<k<<" "<< bytes/(t1-t0)/1.e3 <<" GB/s "<<(t1-t0)/1.e3<<" ms "<<std::endl;
+  }
+
+  void gemmBatched(GridBLASOperation_t OpA,
+		   GridBLASOperation_t OpB,
+		   int m,int n, int k,
+		   ComplexF alpha,
+		   deviceVector<ComplexF*> &Amk,  // pointer list to matrices
+		   deviceVector<ComplexF*> &Bkn,
+		   ComplexF beta,
+		   deviceVector<ComplexF*> &Cmn)
+  {
+    RealD t2=usecond();
+    int32_t batchCount = Amk.size();
+
+    int lda = m; // m x k column major
+    int ldb = k; // k x n column major
+    int ldc = m; // m x b column major
+    if(OpA!=GridBLAS_OP_N)
+      lda = k;
+    if(OpB!=GridBLAS_OP_N)
+      ldb = n;
+    static deviceVector<ComplexF> alpha_p(1);
+    static deviceVector<ComplexF> beta_p(1);
+    // can prestore the 1 and the zero on device
+    acceleratorCopyToDevice((void *)&alpha,(void *)&alpha_p[0],sizeof(ComplexF));
+    acceleratorCopyToDevice((void *)&beta ,(void *)&beta_p[0],sizeof(ComplexF));
+    RealD t0=usecond();
+
+    assert(Bkn.size()==batchCount);
+    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;
+    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);
+
+    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 = 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);
+    assert(err==CUBLAS_STATUS_SUCCESS);
+#endif
+#ifdef GRID_SYCL
+    //MKL’s cblas_<T>gemm_batch & OneAPI
+#warning "oneMKL implementation not built "
+#endif
+#if !defined(GRID_SYCL) && !defined(GRID_CUDA) && !defined(GRID_HIP)
+    int sda = lda*k;
+    int sdb = ldb*k;
+    int sdc = ldc*n;
+    ComplexF alphaf(real(alpha),imag(alpha));
+    ComplexF betaf(real(beta),imag(beta));
+    // Need a default/reference implementation
+    for (int p = 0; p < batchCount; ++p) {
+      for (int mm = 0; mm < m; ++mm) {
+	for (int nn = 0; nn < n; ++nn) {
+	  ComplexF c_mn(0.0);
+	  for (int kk = 0; kk < k; ++kk)
+	    c_mn += Amk[p][mm + kk*lda ] * Bkn[p][kk + nn*ldb];
+	  Cmn[p][mm + nn*ldc] =  (alphaf)*c_mn + (betaf)*Cmn[p][mm + nn*ldc ];
+	}
+      }
+    }
+#endif
+     RealD t1=usecond();
+     RealD flops = 8.0*m*n*k*batchCount;
+     RealD bytes = 1.0*sizeof(ComplexF)*(m*k+k*n+m*n)*batchCount;
+  }
+  
+  ///////////////////////////////////////////////////////////////////////////
+  // Single precision real GEMM
+  ///////////////////////////////////////////////////////////////////////////
+
+  void gemmBatched(GridBLASOperation_t OpA,
+		   GridBLASOperation_t OpB,
+		   int m,int n, int k,
+		   RealF alpha,
+		   deviceVector<RealF*> &Amk,  // pointer list to matrices
+		   deviceVector<RealF*> &Bkn,
+		   RealF beta,
+		   deviceVector<RealF*> &Cmn)
+  {
+    RealD t2=usecond();
+    int32_t batchCount = Amk.size();
+
+    int lda = m; // m x k column major
+    int ldb = k; // k x n column major
+    int ldc = m; // m x b column major
+    if(OpA!=GridBLAS_OP_N)
+      lda = k;
+    if(OpB!=GridBLAS_OP_N)
+      ldb = n;
+    static deviceVector<RealF> alpha_p(1);
+    static deviceVector<RealF> beta_p(1);
+    // can prestore the 1 and the zero on device
+    acceleratorCopyToDevice((void *)&alpha,(void *)&alpha_p[0],sizeof(RealF));
+    acceleratorCopyToDevice((void *)&beta ,(void *)&beta_p[0],sizeof(RealF));
+    RealD t0=usecond();
+
+    assert(Bkn.size()==batchCount);
+    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;
+    auto err = hipblasSgemmBatched(gridblasHandle,
+				   hOpA,
+				   hOpB,
+				   m,n,k,
+				   (float *) &alpha_p[0],
+				   (float **)&Amk[0], lda,
+				   (float **)&Bkn[0], ldb,
+				   (float *) &beta_p[0],
+				   (float **)&Cmn[0], ldc,
+				   batchCount);
+    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 = cublasSgemmBatched(gridblasHandle,
+				  hOpA,
+				  hOpB,
+				  m,n,k,
+				  (float *) &alpha_p[0],
+				  (float **)&Amk[0], lda,
+				  (float **)&Bkn[0], ldb,
+				  (float *) &beta_p[0],
+				  (float **)&Cmn[0], ldc,
+				  batchCount);
+    assert(err==CUBLAS_STATUS_SUCCESS);
+#endif
+#ifdef GRID_SYCL
+    //MKL’s cblas_<T>gemm_batch & OneAPI
+#warning "oneMKL implementation not built "
+#endif
+#if !defined(GRID_SYCL) && !defined(GRID_CUDA) && !defined(GRID_HIP)
+    int sda = lda*k;
+    int sdb = ldb*k;
+    int sdc = ldc*n;
+    // Need a default/reference implementation
+    for (int p = 0; p < batchCount; ++p) {
+      for (int mm = 0; mm < m; ++mm) {
+	for (int nn = 0; nn < n; ++nn) {
+	  RealD c_mn(0.0);
+	  for (int kk = 0; kk < k; ++kk)
+	    c_mn += Amk[p][mm + kk*lda ] * Bkn[p][kk + nn*ldb];
+	  Cmn[p][mm + nn*ldc] =  (alpha)*c_mn + (beta)*Cmn[p][mm + nn*ldc ];
+	}
+      }
+    }
+#endif
+     RealD t1=usecond();
+     RealD flops = 2.0*m*n*k*batchCount;
+     RealD bytes = 1.0*sizeof(RealF)*(m*k+k*n+m*n)*batchCount;
+  }
+  
+  
+  ///////////////////////////////////////////////////////////////////////////
+  // Double precision real GEMM
+  ///////////////////////////////////////////////////////////////////////////
+
+  void gemmBatched(GridBLASOperation_t OpA,
+		   GridBLASOperation_t OpB,
+		   int m,int n, int k,
+		   RealD alpha,
+		   deviceVector<RealD*> &Amk,  // pointer list to matrices
+		   deviceVector<RealD*> &Bkn,
+		   RealD beta,
+		   deviceVector<RealD*> &Cmn)
+  {
+    RealD t2=usecond();
+    int32_t batchCount = Amk.size();
+
+    int lda = m; // m x k column major
+    int ldb = k; // k x n column major
+    int ldc = m; // m x b column major
+    if(OpA!=GridBLAS_OP_N)
+      lda = k;
+    if(OpB!=GridBLAS_OP_N)
+      ldb = n;
+    
+    static deviceVector<RealD> alpha_p(1);
+    static deviceVector<RealD> beta_p(1);
+    // can prestore the 1 and the zero on device
+    acceleratorCopyToDevice((void *)&alpha,(void *)&alpha_p[0],sizeof(RealD));
+    acceleratorCopyToDevice((void *)&beta ,(void *)&beta_p[0],sizeof(RealD));
+    RealD t0=usecond();
+
+    assert(Bkn.size()==batchCount);
+    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;
+    auto err = hipblasDgemmBatched(gridblasHandle,
+				   HIPBLAS_OP_N,
+				   HIPBLAS_OP_N,
+				   m,n,k,
+				   (double *) &alpha_p[0],
+				   (double **)&Amk[0], lda,
+				   (double **)&Bkn[0], ldb,
+				   (double *) &beta_p[0],
+				   (double **)&Cmn[0], ldc,
+				   batchCount);
+    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 = cublasDgemmBatched(gridblasHandle,
+				  hOpA,
+				  hOpB,
+				  m,n,k,
+				  (double *) &alpha_p[0],
+				  (double **)&Amk[0], lda,
+				  (double **)&Bkn[0], ldb,
+				  (double *) &beta_p[0],
+				  (double **)&Cmn[0], ldc,
+				  batchCount);
+    assert(err==CUBLAS_STATUS_SUCCESS);
+#endif
+#ifdef GRID_SYCL
+    /*
+      int64_t m64=m;
+      int64_t n64=n;
+      int64_t k64=k;
+      int64_t batchCount64=batchCount;
+      oneapi::mkl::blas::column_major::gemm_batch(*theGridAccelerator,
+      onemkl::transpose::N,
+      onemkl::transpose::N,
+      &m64,&n64,&k64,
+      (double *) &alpha_p[0],
+      (double **)&Amk[0], lda,
+      (double **)&Bkn[0], ldb,
+      (double *) &beta_p[0],
+      (double **)&Cmn[0], ldc,
+      1,&batchCount64);
+     */
+    //MKL’s cblas_<T>gemm_batch & OneAPI
+#warning "oneMKL implementation not built "
+#endif
+#if !defined(GRID_SYCL) && !defined(GRID_CUDA) && !defined(GRID_HIP)
+    int sda = lda*k;
+    int sdb = ldb*k;
+    int sdc = ldc*n;
+    // Need a default/reference implementation
+    for (int p = 0; p < batchCount; ++p) {
+      for (int mm = 0; mm < m; ++mm) {
+	for (int nn = 0; nn < n; ++nn) {
+	  RealD c_mn(0.0);
+	  for (int kk = 0; kk < k; ++kk)
+	    c_mn += Amk[p][mm + kk*lda ] * Bkn[p][kk + nn*ldb];
+	  Cmn[p][mm + nn*ldc] =  (alpha)*c_mn + (beta)*Cmn[p][mm + nn*ldc ];
+	}
+      }
+    }
+#endif
+     RealD t1=usecond();
+     RealD flops = 2.0*m*n*k*batchCount;
+     RealD bytes = 1.0*sizeof(RealD)*(m*k+k*n+m*n)*batchCount;
+  }
+  
+
+  
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  // Strided case used by benchmark, but generally unused in Grid
+  // Keep a code example in double complex, but don't generate the single and real variants for now
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  
+  void gemmStridedBatched(int m,int n, int k,
+			  ComplexD alpha,
+			  ComplexD* Amk,  // pointer list to matrices
+			  ComplexD* Bkn,
+			  ComplexD beta,
+			  ComplexD* Cmn,
+			  int batchCount)
+  {
+    // Use C-row major storage, so transpose calls
+    int lda = m; // m x k column major
+    int ldb = k; // k x n column major
+    int ldc = m; // m x b column major
+    int sda = m*k;
+    int sdb = k*n;
+    int sdc = m*n;
+    deviceVector<ComplexD> alpha_p(1);
+    deviceVector<ComplexD> beta_p(1);
+    acceleratorCopyToDevice((void *)&alpha,(void *)&alpha_p[0],sizeof(ComplexD));
+    acceleratorCopyToDevice((void *)&beta ,(void *)&beta_p[0],sizeof(ComplexD));
+
+    //    std::cout << "blasZgemmStridedBatched mnk  "<<m<<","<<n<<","<<k<<" count "<<batchCount<<std::endl;
+    //    std::cout << "blasZgemmStridedBatched ld   "<<lda<<","<<ldb<<","<<ldc<<std::endl;
+    //    std::cout << "blasZgemmStridedBatched sd   "<<sda<<","<<sdb<<","<<sdc<<std::endl;
+#ifdef GRID_HIP
+    auto err = hipblasZgemmStridedBatched(gridblasHandle,
+					  HIPBLAS_OP_N,
+					  HIPBLAS_OP_N,
+					  m,n,k,
+					  (hipblasDoubleComplex *) &alpha_p[0],
+					  (hipblasDoubleComplex *) Amk, lda, sda,
+					  (hipblasDoubleComplex *) Bkn, ldb, sdb,
+					  (hipblasDoubleComplex *) &beta_p[0],
+					  (hipblasDoubleComplex *) Cmn, ldc, sdc,
+					  batchCount);
+    assert(err==HIPBLAS_STATUS_SUCCESS);
+#endif
+#ifdef GRID_CUDA
+    cublasZgemmStridedBatched(gridblasHandle,
+			      CUBLAS_OP_N,
+			      CUBLAS_OP_N,
+			      m,n,k,
+			      (cuDoubleComplex *) &alpha_p[0],
+			      (cuDoubleComplex *) Amk, lda, sda,
+			      (cuDoubleComplex *) Bkn, ldb, sdb,
+			      (cuDoubleComplex *) &beta_p[0],
+			      (cuDoubleComplex *) Cmn, ldc, sdc,
+			      batchCount);
+#endif
+#if defined(GRID_SYCL) || defined(GRID_ONE_MKL)
+    oneapi::mkl::blas::column_major::gemm_batch(*gridblasHandle,
+						oneapi::mkl::transpose::N,
+						oneapi::mkl::transpose::N,
+						m,n,k,
+						alpha,
+						(const ComplexD *)Amk,lda,sda,
+						(const ComplexD *)Bkn,ldb,sdb,
+						beta,
+						(ComplexD *)Cmn,ldc,sdc,
+						batchCount);
+#endif
+#if !defined(GRID_SYCL) && !defined(GRID_CUDA) && !defined(GRID_HIP) && !defined(GRID_ONE_MKL)
+     // Need a default/reference implementation
+     for (int p = 0; p < batchCount; ++p) {
+       for (int mm = 0; mm < m; ++mm) {
+	 for (int nn = 0; nn < n; ++nn) {
+	   ComplexD c_mn(0.0);
+	   for (int kk = 0; kk < k; ++kk)
+	     c_mn += Amk[mm + kk*lda + p*sda] * Bkn[kk + nn*ldb + p*sdb];
+	   Cmn[mm + nn*ldc + p*sdc] =  (alpha)*c_mn + (beta)*Cmn[mm + nn*ldc + p*sdc];
+	 }
+       }
+     }
+#endif
+  }
+
+  double benchmark(int M, int N, int K, int BATCH)
+  {
+    int32_t N_A = M*K*BATCH;
+    int32_t N_B = K*N*BATCH;
+    int32_t N_C = M*N*BATCH;
+    deviceVector<ComplexD> A(N_A); acceleratorMemSet(&A[0],0,N_A*sizeof(ComplexD));
+    deviceVector<ComplexD> B(N_B); acceleratorMemSet(&B[0],0,N_B*sizeof(ComplexD));
+    deviceVector<ComplexD> C(N_C); acceleratorMemSet(&C[0],0,N_C*sizeof(ComplexD));
+    ComplexD alpha(1.0);
+    ComplexD beta (1.0);
+    RealD flops = 8.0*M*N*K*BATCH;
+    int ncall=10;
+    RealD t0 = usecond();
+    for(int i=0;i<ncall;i++){
+      gemmStridedBatched(M,N,K,
+			 alpha,
+			 &A[0], // m x k 
+			 &B[0], // k x n
+			 beta, 
+			 &C[0], // m x n
+			 BATCH);
+    }
+    synchronise();
+    RealD t1 = usecond();
+    RealD bytes = 1.0*sizeof(ComplexD)*(M*N*2+N*K+M*K)*BATCH;
+    flops = 8.0*M*N*K*BATCH*ncall;
+    flops = flops/(t1-t0)/1.e3;
+    return flops; // Returns gigaflops
+  }
+
+
+
+
+};
+
+NAMESPACE_END(Grid);

Grid/allocator/AlignedAllocator.h

@@ -176,6 +176,7 @@ template<class T> using cshiftAllocator = std::allocator<T>;
 template<class T> using Vector        = std::vector<T,uvmAllocator<T> >;           
 template<class T> using stencilVector = std::vector<T,alignedAllocator<T> >;           
 template<class T> using commVector = std::vector<T,devAllocator<T> >;
+template<class T> using deviceVector  = std::vector<T,devAllocator<T> >;
 template<class T> using cshiftVector = std::vector<T,cshiftAllocator<T> >;
 
 NAMESPACE_END(Grid);

Grid/communicator/Communicator_mpi3.cc

@@ -348,6 +348,7 @@ double CartesianCommunicator::StencilSendToRecvFrom( void *xmit,
   return offbytes;
 }
 
+#undef NVLINK_GET // Define to use get instead of put DMA
 double CartesianCommunicator::StencilSendToRecvFromBegin(std::vector<CommsRequest_t> &list,
 							 void *xmit,
 							 int dest,int dox,
@@ -380,9 +381,15 @@ double CartesianCommunicator::StencilSendToRecvFromBegin(std::vector<CommsReques
       list.push_back(rrq);
       off_node_bytes+=rbytes;
     }
+#ifdef NVLINK_GET
+      void *shm = (void *) this->ShmBufferTranslate(from,xmit);
+      assert(shm!=NULL);
+      acceleratorCopyDeviceToDeviceAsynch(shm,recv,rbytes);
+#endif
   }
   
   if (dox) {
+    //  rcrc = crc32(rcrc,(unsigned char *)recv,bytes);
     if ( (gdest == MPI_UNDEFINED) || Stencil_force_mpi ) {
       tag= dir+_processor*32;
       ierr =MPI_Isend(xmit, xbytes, MPI_CHAR,dest,tag,communicator_halo[commdir],&xrq);
@@ -390,9 +397,12 @@ double CartesianCommunicator::StencilSendToRecvFromBegin(std::vector<CommsReques
       list.push_back(xrq);
       off_node_bytes+=xbytes;
     } else {
+#ifndef NVLINK_GET
       void *shm = (void *) this->ShmBufferTranslate(dest,recv);
       assert(shm!=NULL);
       acceleratorCopyDeviceToDeviceAsynch(xmit,shm,xbytes);
+#endif
+      
     }
   }
 
@@ -402,6 +412,8 @@ void CartesianCommunicator::StencilSendToRecvFromComplete(std::vector<CommsReque
 {
   int nreq=list.size();
 
+  acceleratorCopySynchronise();
+
   if (nreq==0) return;
 
   std::vector<MPI_Status> status(nreq);

Grid/communicator/SharedMemory.cc

@@ -40,6 +40,9 @@ int                 GlobalSharedMemory::_ShmAlloc;
 uint64_t            GlobalSharedMemory::_ShmAllocBytes;
 
 std::vector<void *> GlobalSharedMemory::WorldShmCommBufs;
+#ifndef ACCELERATOR_AWARE_MPI
+void * GlobalSharedMemory::HostCommBuf;
+#endif
 
 Grid_MPI_Comm       GlobalSharedMemory::WorldShmComm;
 int                 GlobalSharedMemory::WorldShmRank;
@@ -66,6 +69,26 @@ void GlobalSharedMemory::SharedMemoryFree(void)
 /////////////////////////////////
 // Alloc, free shmem region
 /////////////////////////////////
+#ifndef ACCELERATOR_AWARE_MPI
+void *SharedMemory::HostBufferMalloc(size_t bytes){
+  void *ptr = (void *)host_heap_top;
+  host_heap_top  += bytes;
+  host_heap_bytes+= bytes;
+  if (host_heap_bytes >= host_heap_size) {
+    std::cout<< " HostBufferMalloc exceeded heap size -- try increasing with --shm <MB> flag" <<std::endl;
+    std::cout<< " Parameter specified in units of MB (megabytes) " <<std::endl;
+    std::cout<< " Current alloc is " << (bytes/(1024*1024)) <<"MB"<<std::endl;
+    std::cout<< " Current bytes is " << (host_heap_bytes/(1024*1024)) <<"MB"<<std::endl;
+    std::cout<< " Current heap  is " << (host_heap_size/(1024*1024)) <<"MB"<<std::endl;
+    assert(host_heap_bytes<host_heap_size);
+  }
+  return ptr;
+}
+void SharedMemory::HostBufferFreeAll(void) { 
+  host_heap_top  =(size_t)HostCommBuf;
+  host_heap_bytes=0;
+}
+#endif
 void *SharedMemory::ShmBufferMalloc(size_t bytes){
   //  bytes = (bytes+sizeof(vRealD))&(~(sizeof(vRealD)-1));// align up bytes
   void *ptr = (void *)heap_top;

Grid/communicator/SharedMemory.h

@@ -75,7 +75,9 @@ public:
   static int           Hugepages;
 
   static std::vector<void *> WorldShmCommBufs;
-
+#ifndef ACCELERATOR_AWARE_MPI
+  static void *HostCommBuf;
+#endif
   static Grid_MPI_Comm WorldComm;
   static int           WorldRank;
   static int           WorldSize;
@@ -120,6 +122,13 @@ private:
   size_t heap_bytes;
   size_t heap_size;
 
+#ifndef ACCELERATOR_AWARE_MPI
+  size_t host_heap_top;  // set in free all
+  size_t host_heap_bytes;// set in free all
+  void *HostCommBuf;     // set in SetCommunicator
+  size_t host_heap_size; // set in SetCommunicator
+#endif
+  
 protected:
 
   Grid_MPI_Comm    ShmComm; // for barriers
@@ -151,7 +160,10 @@ public:
   void *ShmBufferTranslate(int rank,void * local_p);
   void *ShmBufferMalloc(size_t bytes);
   void  ShmBufferFreeAll(void) ;
-  
+#ifndef ACCELERATOR_AWARE_MPI
+  void *HostBufferMalloc(size_t bytes);
+  void HostBufferFreeAll(void);
+#endif  
   //////////////////////////////////////////////////////////////////////////
   // Make info on Nodes & ranks and Shared memory available
   //////////////////////////////////////////////////////////////////////////

Grid/communicator/SharedMemoryMPI.cc

@@ -39,10 +39,12 @@ Author: Christoph Lehner <christoph@lhnr.de>
 #include <hip/hip_runtime_api.h>
 #endif
 #ifdef GRID_SYCL
+#ifdef ACCELERATOR_AWARE_MPI
 #define GRID_SYCL_LEVEL_ZERO_IPC
-#include <syscall.h>
 #define SHM_SOCKETS
 #endif 
+#include <syscall.h>
+#endif
 
 #include <sys/socket.h>
 #include <sys/un.h>
@@ -511,46 +513,6 @@ void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
 ////////////////////////////////////////////////////////////////////////////////////////////
 // Hugetlbfs mapping intended
 ////////////////////////////////////////////////////////////////////////////////////////////
-#if defined(GRID_CUDA) ||defined(GRID_HIP)  || defined(GRID_SYCL)
-
-//if defined(GRID_SYCL)
-#if 0
-void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
-{
-  void * ShmCommBuf ; 
-  assert(_ShmSetup==1);
-  assert(_ShmAlloc==0);
-
-  //////////////////////////////////////////////////////////////////////////////////////////////////////////
-  // allocate the pointer array for shared windows for our group
-  //////////////////////////////////////////////////////////////////////////////////////////////////////////
-  MPI_Barrier(WorldShmComm);
-  WorldShmCommBufs.resize(WorldShmSize);
-
-  ///////////////////////////////////////////////////////////////////////////////////////////////////////////
-  // Each MPI rank should allocate our own buffer
-  ///////////////////////////////////////////////////////////////////////////////////////////////////////////
-  ShmCommBuf = acceleratorAllocDevice(bytes);
-
-  if (ShmCommBuf == (void *)NULL ) {
-    std::cerr << " SharedMemoryMPI.cc acceleratorAllocDevice failed NULL pointer for " << bytes<<" bytes " << std::endl;
-    exit(EXIT_FAILURE);  
-  }
-
-  std::cout << WorldRank << Mheader " SharedMemoryMPI.cc acceleratorAllocDevice "<< bytes 
-	    << "bytes at "<< std::hex<< ShmCommBuf <<std::dec<<" for comms buffers " <<std::endl;
-
-  SharedMemoryZero(ShmCommBuf,bytes);
-
-  assert(WorldShmSize == 1);
-  for(int r=0;r<WorldShmSize;r++){
-    WorldShmCommBufs[r] = ShmCommBuf;
-  }
-  _ShmAllocBytes=bytes;
-  _ShmAlloc=1;
-}
-#endif
-
 #if defined(GRID_CUDA) ||defined(GRID_HIP)  || defined(GRID_SYCL)
 void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
 {
@@ -574,6 +536,9 @@ void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
   ///////////////////////////////////////////////////////////////////////////////////////////////////////////
   // Each MPI rank should allocate our own buffer
   ///////////////////////////////////////////////////////////////////////////////////////////////////////////
+#ifndef ACCELERATOR_AWARE_MPI
+  HostCommBuf= malloc(bytes);
+#endif  
   ShmCommBuf = acceleratorAllocDevice(bytes);
   if (ShmCommBuf == (void *)NULL ) {
     std::cerr << " SharedMemoryMPI.cc acceleratorAllocDevice failed NULL pointer for " << bytes<<" bytes " << std::endl;
@@ -604,8 +569,8 @@ void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
 #ifdef GRID_SYCL_LEVEL_ZERO_IPC
     typedef struct { int fd; pid_t pid ; ze_ipc_mem_handle_t ze; } clone_mem_t;
 
-    auto zeDevice    = cl::sycl::get_native<cl::sycl::backend::level_zero>(theGridAccelerator->get_device());
-    auto zeContext   = cl::sycl::get_native<cl::sycl::backend::level_zero>(theGridAccelerator->get_context());
+    auto zeDevice    = cl::sycl::get_native<cl::sycl::backend::ext_oneapi_level_zero>(theGridAccelerator->get_device());
+    auto zeContext   = cl::sycl::get_native<cl::sycl::backend::ext_oneapi_level_zero>(theGridAccelerator->get_context());
       
     ze_ipc_mem_handle_t ihandle;
     clone_mem_t handle;
@@ -738,7 +703,6 @@ void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
   _ShmAllocBytes=bytes;
   _ShmAlloc=1;
 }
-#endif
 
 #else 
 #ifdef GRID_MPI3_SHMMMAP
@@ -962,6 +926,12 @@ void SharedMemory::SetCommunicator(Grid_MPI_Comm comm)
   }
   ShmBufferFreeAll();
 
+#ifndef ACCELERATOR_AWARE_MPI
+  host_heap_size = heap_size;
+  HostCommBuf= GlobalSharedMemory::HostCommBuf;
+  HostBufferFreeAll();
+#endif  
+
   /////////////////////////////////////////////////////////////////////
   // find comm ranks in our SHM group (i.e. which ranks are on our node)
   /////////////////////////////////////////////////////////////////////

Grid/cshift/Cshift_common.h

@@ -29,8 +29,27 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 
 NAMESPACE_BEGIN(Grid);
 
-extern Vector<std::pair<int,int> > Cshift_table; 
+extern std::vector<std::pair<int,int> > Cshift_table; 
+extern commVector<std::pair<int,int> > Cshift_table_device; 
 
+inline std::pair<int,int> *MapCshiftTable(void)
+{
+  // GPU version
+#ifdef ACCELERATOR_CSHIFT    
+  uint64_t sz=Cshift_table.size();
+  if (Cshift_table_device.size()!=sz )    {
+    Cshift_table_device.resize(sz);
+  }
+  acceleratorCopyToDevice((void *)&Cshift_table[0],
+			  (void *)&Cshift_table_device[0],
+			  sizeof(Cshift_table[0])*sz);
+
+  return &Cshift_table_device[0];
+#else 
+  return &Cshift_table[0];
+#endif
+  // CPU version use identify map
+}
 ///////////////////////////////////////////////////////////////////
 // Gather for when there is no need to SIMD split 
 ///////////////////////////////////////////////////////////////////
@@ -74,7 +93,7 @@ Gather_plane_simple (const Lattice<vobj> &rhs,cshiftVector<vobj> &buffer,int dim
   }
   {
     auto buffer_p = & buffer[0];
-    auto table = &Cshift_table[0];
+    auto table = MapCshiftTable();
 #ifdef ACCELERATOR_CSHIFT
     autoView(rhs_v , rhs, AcceleratorRead);
     accelerator_for(i,ent,vobj::Nsimd(),{
@@ -225,7 +244,7 @@ template<class vobj> void Scatter_plane_simple (Lattice<vobj> &rhs,cshiftVector<
   
   {
     auto buffer_p = & buffer[0];
-    auto table = &Cshift_table[0];
+    auto table = MapCshiftTable();
 #ifdef ACCELERATOR_CSHIFT    
     autoView( rhs_v, rhs, AcceleratorWrite);
     accelerator_for(i,ent,vobj::Nsimd(),{
@@ -297,30 +316,6 @@ template<class vobj> void Scatter_plane_merge(Lattice<vobj> &rhs,ExtractPointerA
   }
 }
 
-#if (defined(GRID_CUDA) || defined(GRID_HIP)) && defined(ACCELERATOR_CSHIFT)
-
-template <typename T>
-T iDivUp(T a, T b) // Round a / b to nearest higher integer value
-{ return (a % b != 0) ? (a / b + 1) : (a / b); }
-
-template <typename T>
-__global__ void populate_Cshift_table(T* vector, T lo, T ro, T e1, T e2, T stride)
-{
-    int idx = blockIdx.x*blockDim.x + threadIdx.x;
-    if (idx >= e1*e2) return;
-
-    int n, b, o;
-
-    n = idx / e2;
-    b = idx % e2;
-    o = n*stride + b;
-
-    vector[2*idx + 0] = lo + o;
-    vector[2*idx + 1] = ro + o;
-}
-
-#endif
-
 //////////////////////////////////////////////////////
 // local to node block strided copies
 //////////////////////////////////////////////////////
@@ -345,20 +340,12 @@ template<class vobj> void Copy_plane(Lattice<vobj>& lhs,const Lattice<vobj> &rhs
   int ent=0;
 
   if(cbmask == 0x3 ){
-#if (defined(GRID_CUDA) || defined(GRID_HIP)) && defined(ACCELERATOR_CSHIFT)
-    ent = e1*e2;
-    dim3 blockSize(acceleratorThreads());
-    dim3 gridSize(iDivUp((unsigned int)ent, blockSize.x));
-    populate_Cshift_table<<<gridSize, blockSize>>>(&Cshift_table[0].first, lo, ro, e1, e2, stride);
-    accelerator_barrier();
-#else
     for(int n=0;n<e1;n++){
       for(int b=0;b<e2;b++){
         int o =n*stride+b;
 	Cshift_table[ent++] = std::pair<int,int>(lo+o,ro+o);
       }
     }
-#endif
   } else { 
     for(int n=0;n<e1;n++){
       for(int b=0;b<e2;b++){
@@ -372,7 +359,7 @@ template<class vobj> void Copy_plane(Lattice<vobj>& lhs,const Lattice<vobj> &rhs
   }
 
   {
-    auto table = &Cshift_table[0];
+    auto table = MapCshiftTable();
 #ifdef ACCELERATOR_CSHIFT    
     autoView(rhs_v , rhs, AcceleratorRead);
     autoView(lhs_v , lhs, AcceleratorWrite);
@@ -409,19 +396,11 @@ template<class vobj> void Copy_plane_permute(Lattice<vobj>& lhs,const Lattice<vo
   int ent=0;
 
   if ( cbmask == 0x3 ) {
-#if (defined(GRID_CUDA) || defined(GRID_HIP)) && defined(ACCELERATOR_CSHIFT)
-    ent = e1*e2;
-    dim3 blockSize(acceleratorThreads());
-    dim3 gridSize(iDivUp((unsigned int)ent, blockSize.x));
-    populate_Cshift_table<<<gridSize, blockSize>>>(&Cshift_table[0].first, lo, ro, e1, e2, stride);
-    accelerator_barrier();
-#else
     for(int n=0;n<e1;n++){
     for(int b=0;b<e2;b++){
       int o  =n*stride;
       Cshift_table[ent++] = std::pair<int,int>(lo+o+b,ro+o+b);
     }}
-#endif
   } else {
     for(int n=0;n<e1;n++){
     for(int b=0;b<e2;b++){
@@ -432,7 +411,7 @@ template<class vobj> void Copy_plane_permute(Lattice<vobj>& lhs,const Lattice<vo
   }
 
   {
-    auto table = &Cshift_table[0];
+    auto table = MapCshiftTable();
 #ifdef ACCELERATOR_CSHIFT    
     autoView( rhs_v, rhs, AcceleratorRead);
     autoView( lhs_v, lhs, AcceleratorWrite);

Grid/cshift/Cshift_mpi.h

@@ -52,7 +52,8 @@ template<class vobj> Lattice<vobj> Cshift(const Lattice<vobj> &rhs,int dimension
   int comm_dim        = rhs.Grid()->_processors[dimension] >1 ;
   int splice_dim      = rhs.Grid()->_simd_layout[dimension]>1 && (comm_dim);
 
-
+  RealD t1,t0;
+  t0=usecond();
   if ( !comm_dim ) {
     //std::cout << "CSHIFT: Cshift_local" <<std::endl;
     Cshift_local(ret,rhs,dimension,shift); // Handles checkerboarding
@@ -63,6 +64,8 @@ template<class vobj> Lattice<vobj> Cshift(const Lattice<vobj> &rhs,int dimension
     //std::cout << "CSHIFT: Cshift_comms" <<std::endl;
     Cshift_comms(ret,rhs,dimension,shift);
   }
+  t1=usecond();
+  //  std::cout << GridLogPerformance << "Cshift took "<< (t1-t0)/1e3 << " ms"<<std::endl;
   return ret;
 }
 
@@ -127,16 +130,20 @@ template<class vobj> void Cshift_comms(Lattice<vobj> &ret,const Lattice<vobj> &r
     
   int cb= (cbmask==0x2)? Odd : Even;
   int sshift= rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,cb);
-
+  RealD tcopy=0.0;
+  RealD tgather=0.0;
+  RealD tscatter=0.0;
+  RealD tcomms=0.0;
+  uint64_t xbytes=0;
   for(int x=0;x<rd;x++){       
 
     int sx        =  (x+sshift)%rd;
     int comm_proc = ((x+sshift)/rd)%pd;
     
     if (comm_proc==0) {
-
+      tcopy-=usecond();
       Copy_plane(ret,rhs,dimension,x,sx,cbmask); 
-
+      tcopy+=usecond();
     } else {
 
       int words = buffer_size;
@@ -144,26 +151,39 @@ template<class vobj> void Cshift_comms(Lattice<vobj> &ret,const Lattice<vobj> &r
 
       int bytes = words * sizeof(vobj);
 
+      tgather-=usecond();
       Gather_plane_simple (rhs,send_buf,dimension,sx,cbmask);
+      tgather+=usecond();
 
       //      int rank           = grid->_processor;
       int recv_from_rank;
       int xmit_to_rank;
       grid->ShiftedRanks(dimension,comm_proc,xmit_to_rank,recv_from_rank);
       
-      grid->Barrier();
+      tcomms-=usecond();
+      //      grid->Barrier();
 
       grid->SendToRecvFrom((void *)&send_buf[0],
 			   xmit_to_rank,
 			   (void *)&recv_buf[0],
 			   recv_from_rank,
 			   bytes);
+      xbytes+=bytes;
+      //      grid->Barrier();
+      tcomms+=usecond();
 
-      grid->Barrier();
-
+      tscatter-=usecond();
       Scatter_plane_simple (ret,recv_buf,dimension,x,cbmask);
+      tscatter+=usecond();
     }
   }
+  /*
+  std::cout << GridLogPerformance << " Cshift copy    "<<tcopy/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift gather  "<<tgather/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift scatter "<<tscatter/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift comm    "<<tcomms/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift BW      "<<(2.0*xbytes)/tcomms<<" MB/s "<<2*xbytes<< " Bytes "<<std::endl;
+  */
 }
 
 template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vobj> &rhs,int dimension,int shift,int cbmask)
@@ -190,6 +210,12 @@ template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vo
   assert(shift>=0);
   assert(shift<fd);
 
+  RealD tcopy=0.0;
+  RealD tgather=0.0;
+  RealD tscatter=0.0;
+  RealD tcomms=0.0;
+  uint64_t xbytes=0;
+  
   int permute_type=grid->PermuteType(dimension);
 
   ///////////////////////////////////////////////
@@ -227,7 +253,9 @@ template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vo
       pointers[i] = &send_buf_extract[i][0];
     }
     int sx   = (x+sshift)%rd;
+    tgather-=usecond();
     Gather_plane_extract(rhs,pointers,dimension,sx,cbmask);
+    tgather+=usecond();
 
     for(int i=0;i<Nsimd;i++){
       
@@ -252,7 +280,8 @@ template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vo
       if(nbr_proc){
 	grid->ShiftedRanks(dimension,nbr_proc,xmit_to_rank,recv_from_rank); 
 
-	grid->Barrier();
+	tcomms-=usecond();
+	//	grid->Barrier();
 
 	send_buf_extract_mpi = &send_buf_extract[nbr_lane][0];
 	recv_buf_extract_mpi = &recv_buf_extract[i][0];
@@ -262,7 +291,9 @@ template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vo
 			     recv_from_rank,
 			     bytes);
 
-	grid->Barrier();
+	xbytes+=bytes;
+	//	grid->Barrier();
+	tcomms+=usecond();
 
 	rpointers[i] = &recv_buf_extract[i][0];
       } else { 
@@ -270,9 +301,17 @@ template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vo
       }
 
     }
+    tscatter-=usecond();
     Scatter_plane_merge(ret,rpointers,dimension,x,cbmask);
+    tscatter+=usecond();
   }
-
+  /*
+  std::cout << GridLogPerformance << " Cshift (s) copy    "<<tcopy/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift (s) gather  "<<tgather/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift (s) scatter "<<tscatter/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift (s) comm    "<<tcomms/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift BW      "<<(2.0*xbytes)/tcomms<<" MB/s "<<2*xbytes<< " Bytes "<<std::endl;
+  */
 }
 #else 
 template<class vobj> void Cshift_comms(Lattice<vobj> &ret,const Lattice<vobj> &rhs,int dimension,int shift,int cbmask)
@@ -292,6 +331,11 @@ template<class vobj> void Cshift_comms(Lattice<vobj> &ret,const Lattice<vobj> &r
   assert(comm_dim==1);
   assert(shift>=0);
   assert(shift<fd);
+  RealD tcopy=0.0;
+  RealD tgather=0.0;
+  RealD tscatter=0.0;
+  RealD tcomms=0.0;
+  uint64_t xbytes=0;
   
   int buffer_size = rhs.Grid()->_slice_nblock[dimension]*rhs.Grid()->_slice_block[dimension];
   static cshiftVector<vobj> send_buf_v; send_buf_v.resize(buffer_size);
@@ -315,7 +359,9 @@ template<class vobj> void Cshift_comms(Lattice<vobj> &ret,const Lattice<vobj> &r
     
     if (comm_proc==0) {
 
+      tcopy-=usecond();
       Copy_plane(ret,rhs,dimension,x,sx,cbmask); 
+      tcopy+=usecond();
 
     } else {
 
@@ -324,7 +370,9 @@ template<class vobj> void Cshift_comms(Lattice<vobj> &ret,const Lattice<vobj> &r
 
       int bytes = words * sizeof(vobj);
 
+      tgather-=usecond();
       Gather_plane_simple (rhs,send_buf_v,dimension,sx,cbmask);
+      tgather+=usecond();
 
       //      int rank           = grid->_processor;
       int recv_from_rank;
@@ -332,7 +380,8 @@ template<class vobj> void Cshift_comms(Lattice<vobj> &ret,const Lattice<vobj> &r
       grid->ShiftedRanks(dimension,comm_proc,xmit_to_rank,recv_from_rank);
 
 
-      grid->Barrier();
+      tcomms-=usecond();
+      //      grid->Barrier();
 
       acceleratorCopyDeviceToDevice((void *)&send_buf_v[0],(void *)&send_buf[0],bytes);
       grid->SendToRecvFrom((void *)&send_buf[0],
@@ -340,13 +389,24 @@ template<class vobj> void Cshift_comms(Lattice<vobj> &ret,const Lattice<vobj> &r
 			   (void *)&recv_buf[0],
 			   recv_from_rank,
 			   bytes);
+      xbytes+=bytes;
       acceleratorCopyDeviceToDevice((void *)&recv_buf[0],(void *)&recv_buf_v[0],bytes);
 
-      grid->Barrier();
+      //      grid->Barrier();
+      tcomms+=usecond();
 
+      tscatter-=usecond();
       Scatter_plane_simple (ret,recv_buf_v,dimension,x,cbmask);
+      tscatter+=usecond();
     }
   }
+  /*
+  std::cout << GridLogPerformance << " Cshift copy    "<<tcopy/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift gather  "<<tgather/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift scatter "<<tscatter/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift comm    "<<tcomms/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift BW      "<<(2.0*xbytes)/tcomms<<" MB/s "<<2*xbytes<< " Bytes "<<std::endl;
+  */
 }
 
 template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vobj> &rhs,int dimension,int shift,int cbmask)
@@ -372,6 +432,11 @@ template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vo
   assert(simd_layout==2);
   assert(shift>=0);
   assert(shift<fd);
+  RealD tcopy=0.0;
+  RealD tgather=0.0;
+  RealD tscatter=0.0;
+  RealD tcomms=0.0;
+  uint64_t xbytes=0;
 
   int permute_type=grid->PermuteType(dimension);
 
@@ -414,8 +479,10 @@ template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vo
     for(int i=0;i<Nsimd;i++){       
       pointers[i] = &send_buf_extract[i][0];
     }
+    tgather-=usecond();
     int sx   = (x+sshift)%rd;
     Gather_plane_extract(rhs,pointers,dimension,sx,cbmask);
+    tgather+=usecond();
 
     for(int i=0;i<Nsimd;i++){
       
@@ -440,7 +507,8 @@ template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vo
       if(nbr_proc){
 	grid->ShiftedRanks(dimension,nbr_proc,xmit_to_rank,recv_from_rank); 
 
-	grid->Barrier();
+	tcomms-=usecond();
+	//	grid->Barrier();
 
 	acceleratorCopyDeviceToDevice((void *)&send_buf_extract[nbr_lane][0],(void *)send_buf_extract_mpi,bytes);
 	grid->SendToRecvFrom((void *)send_buf_extract_mpi,
@@ -449,18 +517,29 @@ template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vo
 			     recv_from_rank,
 			     bytes);
 	acceleratorCopyDeviceToDevice((void *)recv_buf_extract_mpi,(void *)&recv_buf_extract[i][0],bytes);
+	xbytes+=bytes;
 
-	grid->Barrier();
+	//	grid->Barrier();
+	tcomms+=usecond();
 	rpointers[i] = &recv_buf_extract[i][0];
       } else { 
 	rpointers[i] = &send_buf_extract[nbr_lane][0];
       }
 
     }
+    tscatter-=usecond();
     Scatter_plane_merge(ret,rpointers,dimension,x,cbmask);
-  }
+    tscatter+=usecond();
 
   }
+  /*
+  std::cout << GridLogPerformance << " Cshift (s) copy    "<<tcopy/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift (s) gather  "<<tgather/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift (s) scatter "<<tscatter/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift (s) comm    "<<tcomms/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift BW      "<<(2.0*xbytes)/tcomms<<" MB/s"<<std::endl;
+  */
+}
 #endif
 NAMESPACE_END(Grid); 
 

Grid/cshift/Cshift_table.cc

@@ -1,4 +1,5 @@
 #include <Grid/GridCore.h>       
 NAMESPACE_BEGIN(Grid);
-Vector<std::pair<int,int> > Cshift_table; 
+std::vector<std::pair<int,int> > Cshift_table; 
+commVector<std::pair<int,int> > Cshift_table_device; 
 NAMESPACE_END(Grid);

Grid/lattice/Lattice.h

@@ -35,6 +35,7 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 #include <Grid/lattice/Lattice_transpose.h>
 #include <Grid/lattice/Lattice_local.h>
 #include <Grid/lattice/Lattice_reduction.h>
+#include <Grid/lattice/Lattice_crc.h>
 #include <Grid/lattice/Lattice_peekpoke.h>
 #include <Grid/lattice/Lattice_reality.h>
 #include <Grid/lattice/Lattice_real_imag.h>
@@ -46,4 +47,4 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 #include <Grid/lattice/Lattice_unary.h>
 #include <Grid/lattice/Lattice_transfer.h>
 #include <Grid/lattice/Lattice_basis.h>
-#include <Grid/lattice/Lattice_crc.h>
+#include <Grid/lattice/PaddedCell.h>

Grid/lattice/Lattice_ET.h

@@ -345,7 +345,9 @@ GridUnopClass(UnaryNot, Not(a));
 GridUnopClass(UnaryTrace, trace(a));
 GridUnopClass(UnaryTranspose, transpose(a));
 GridUnopClass(UnaryTa, Ta(a));
+GridUnopClass(UnarySpTa, SpTa(a));
 GridUnopClass(UnaryProjectOnGroup, ProjectOnGroup(a));
+GridUnopClass(UnaryProjectOnSpGroup, ProjectOnSpGroup(a));
 GridUnopClass(UnaryTimesI, timesI(a));
 GridUnopClass(UnaryTimesMinusI, timesMinusI(a));
 GridUnopClass(UnaryAbs, abs(a));
@@ -456,7 +458,9 @@ GRID_DEF_UNOP(operator!, UnaryNot);
 GRID_DEF_UNOP(trace, UnaryTrace);
 GRID_DEF_UNOP(transpose, UnaryTranspose);
 GRID_DEF_UNOP(Ta, UnaryTa);
+GRID_DEF_UNOP(SpTa, UnarySpTa);
 GRID_DEF_UNOP(ProjectOnGroup, UnaryProjectOnGroup);
+GRID_DEF_UNOP(ProjectOnSpGroup, UnaryProjectOnSpGroup);
 GRID_DEF_UNOP(timesI, UnaryTimesI);
 GRID_DEF_UNOP(timesMinusI, UnaryTimesMinusI);
 GRID_DEF_UNOP(abs, UnaryAbs);  // abs overloaded in cmath C++98; DON'T do the

Grid/lattice/Lattice_arith.h

@@ -270,5 +270,42 @@ RealD axpby_norm(Lattice<vobj> &ret,sobj a,sobj b,const Lattice<vobj> &x,const L
     return axpby_norm_fast(ret,a,b,x,y);
 }
 
+/// Trace product
+template<class obj> auto traceProduct(const Lattice<obj> &rhs_1,const Lattice<obj> &rhs_2)
+  -> Lattice<decltype(trace(obj()))>
+{
+  typedef decltype(trace(obj())) robj;
+  Lattice<robj> ret_i(rhs_1.Grid());
+  autoView( rhs1 , rhs_1, AcceleratorRead);
+  autoView( rhs2 , rhs_2, AcceleratorRead);
+  autoView( ret , ret_i, AcceleratorWrite);
+  ret.Checkerboard() = rhs_1.Checkerboard();
+  accelerator_for(ss,rhs1.size(),obj::Nsimd(),{
+      coalescedWrite(ret[ss],traceProduct(rhs1(ss),rhs2(ss)));
+  });
+  return ret_i;
+}
+
+template<class obj1,class obj2> auto traceProduct(const Lattice<obj1> &rhs_1,const obj2 &rhs2)
+  -> Lattice<decltype(trace(obj1()))>
+{
+  typedef decltype(trace(obj1())) robj;
+  Lattice<robj> ret_i(rhs_1.Grid());
+  autoView( rhs1 , rhs_1, AcceleratorRead);
+  autoView( ret , ret_i, AcceleratorWrite);
+  ret.Checkerboard() = rhs_1.Checkerboard();
+  accelerator_for(ss,rhs1.size(),obj1::Nsimd(),{
+      coalescedWrite(ret[ss],traceProduct(rhs1(ss),rhs2));
+  });
+  return ret_i;
+}
+template<class obj1,class obj2> auto traceProduct(const obj2 &rhs_2,const Lattice<obj1> &rhs_1)
+  -> Lattice<decltype(trace(obj1()))>
+{
+  return traceProduct(rhs_1,rhs_2);
+}
+
+
+
 NAMESPACE_END(Grid);
 #endif

Grid/lattice/Lattice_basis.h

@@ -62,7 +62,7 @@ void basisRotate(VField &basis,Matrix& Qt,int j0, int j1, int k0,int k1,int Nm)
     basis_v.push_back(basis[k].View(AcceleratorWrite));
   }
 
-#if ( (!defined(GRID_CUDA)) )
+#if ( !(defined(GRID_CUDA) || defined(GRID_HIP) || defined(GRID_SYCL)) )
   int max_threads = thread_max();
   Vector < vobj > Bt(Nm * max_threads);
   thread_region

Grid/lattice/Lattice_crc.h

@@ -42,13 +42,13 @@ template<class vobj> void DumpSliceNorm(std::string s,Lattice<vobj> &f,int mu=-1
   }
 }
 
-template<class vobj> uint32_t crc(Lattice<vobj> & buf)
+template<class vobj> uint32_t crc(const Lattice<vobj> & buf)
 {
   autoView( buf_v , buf, CpuRead);
   return ::crc32(0L,(unsigned char *)&buf_v[0],(size_t)sizeof(vobj)*buf.oSites());
 }
 
-#define CRC(U) std::cout << "FingerPrint "<<__FILE__ <<" "<< __LINE__ <<" "<< #U <<" "<<crc(U)<<std::endl;
+#define CRC(U) std::cerr << "FingerPrint "<<__FILE__ <<" "<< __LINE__ <<" "<< #U <<" "<<crc(U)<<std::endl;
 
 NAMESPACE_END(Grid);
 

Grid/lattice/Lattice_reduction.h

@@ -31,6 +31,7 @@ Author: Christoph Lehner <christoph@lhnr.de>
 #if defined(GRID_SYCL)
 #include <Grid/lattice/Lattice_reduction_sycl.h>
 #endif
+#include <Grid/lattice/Lattice_slicesum_core.h>
 
 NAMESPACE_BEGIN(Grid);
 
@@ -280,11 +281,29 @@ inline ComplexD rankInnerProduct(const Lattice<vobj> &left,const Lattice<vobj> &
   return nrm;
 }
 
+
 template<class vobj>
 inline ComplexD innerProduct(const Lattice<vobj> &left,const Lattice<vobj> &right) {
   GridBase *grid = left.Grid();
+
+#ifdef GRID_SYCL
+  uint64_t csum=0;
+  if ( FlightRecorder::LoggingMode != FlightRecorder::LoggingModeNone)
+  {
+    // Hack
+    // Fast integer xor checksum. Can also be used in comms now.
+    autoView(l_v,left,AcceleratorRead);
+    Integer words = left.Grid()->oSites()*sizeof(vobj)/sizeof(uint64_t);
+    uint64_t *base= (uint64_t *)&l_v[0];
+    csum=svm_xor(base,words);
+  }
+  FlightRecorder::CsumLog(csum);
+#endif
   ComplexD nrm = rankInnerProduct(left,right);
+  RealD local = real(nrm);
+  FlightRecorder::NormLog(real(nrm)); 
   grid->GlobalSum(nrm);
+  FlightRecorder::ReductionLog(local,real(nrm)); 
   return nrm;
 }
 
@@ -448,19 +467,10 @@ template<class vobj> inline void sliceSum(const Lattice<vobj> &Data,std::vector<
   int e1=    grid->_slice_nblock[orthogdim];
   int e2=    grid->_slice_block [orthogdim];
   int stride=grid->_slice_stride[orthogdim];
+  int ostride=grid->_ostride[orthogdim];
   
-  // sum over reduced dimension planes, breaking out orthog dir
-  // Parallel over orthog direction
-  autoView( Data_v, Data, CpuRead);
-  thread_for( r,rd, {
-    int so=r*grid->_ostride[orthogdim]; // base offset for start of plane 
-    for(int n=0;n<e1;n++){
-      for(int b=0;b<e2;b++){
-	int ss= so+n*stride+b;
-	lvSum[r]=lvSum[r]+Data_v[ss];
-      }
-    }
-  });
+  //Reduce Data down to lvSum
+  sliceSumReduction(Data,lvSum,rd, e1,e2,stride,ostride,Nsimd);
 
   // Sum across simd lanes in the plane, breaking out orthog dir.
   Coordinate icoor(Nd);
@@ -504,6 +514,7 @@ sliceSum(const Lattice<vobj> &Data,int orthogdim)
   return result;
 }
 
+
 template<class vobj>
 static void sliceInnerProductVector( std::vector<ComplexD> & result, const Lattice<vobj> &lhs,const Lattice<vobj> &rhs,int orthogdim) 
 {

Grid/lattice/Lattice_reduction_gpu.h

@@ -30,7 +30,7 @@ int getNumBlocksAndThreads(const Iterator n, const size_t sizeofsobj, Iterator &
   cudaGetDevice(&device);
 #endif
 #ifdef GRID_HIP
-  hipGetDevice(&device);
+  auto r=hipGetDevice(&device);
 #endif
   
   Iterator warpSize            = gpu_props[device].warpSize;

Grid/lattice/Lattice_reduction_sycl.h

@@ -69,29 +69,30 @@ inline typename vobj::scalar_object sum_gpu_large(const vobj *lat, Integer osite
   return result;
 }
 
-NAMESPACE_END(Grid);
 
-/*
-template<class Double> Double svm_reduce(Double *vec,uint64_t L)
+template<class Word> Word svm_xor(Word *vec,uint64_t L)
 {
-  Double sumResult; zeroit(sumResult);
-  Double *d_sum =(Double *)cl::sycl::malloc_shared(sizeof(Double),*theGridAccelerator);
-  Double identity;  zeroit(identity);
+  Word xorResult; xorResult = 0;
+  Word *d_sum =(Word *)cl::sycl::malloc_shared(sizeof(Word),*theGridAccelerator);
+  Word identity;  identity=0;
   theGridAccelerator->submit([&](cl::sycl::handler &cgh) {
-     auto Reduction = cl::sycl::reduction(d_sum,identity,std::plus<>());
+     auto Reduction = cl::sycl::reduction(d_sum,identity,std::bit_xor<>());
      cgh.parallel_for(cl::sycl::range<1>{L},
 		      Reduction,
 		      [=] (cl::sycl::id<1> index, auto &sum) {
-	 sum +=vec[index];
+	 sum ^=vec[index];
      });
    });
   theGridAccelerator->wait();
-  Double ret = d_sum[0];
+  Word ret = d_sum[0];
   free(d_sum,*theGridAccelerator);
-  std::cout << " svm_reduce finished "<<L<<" sites sum = " << ret <<std::endl;
   return ret;
 }
 
+NAMESPACE_END(Grid);
+
+/*
+
 template <class vobj>
 inline typename vobj::scalar_objectD sumD_gpu_repack(const vobj *lat, Integer osites)
 {

Grid/lattice/Lattice_rng.h

@@ -152,6 +152,7 @@ public:
 #ifdef RNG_FAST_DISCARD
   static void Skip(RngEngine &eng,uint64_t site)
   {
+#if 0
     /////////////////////////////////////////////////////////////////////////////////////
     // Skip by 2^40 elements between successive lattice sites
     // This goes by 10^12.
@@ -179,6 +180,9 @@ public:
     assert((skip >> shift)==site); // check for overflow
 
     eng.discard(skip);
+#else
+    eng.discardhi(site);
+#endif
     //      std::cout << " Engine  " <<site << " state " <<eng<<std::endl;
   } 
 #endif
@@ -407,7 +411,7 @@ public:
       std::cout << GridLogMessage << "Seed SHA256: " << GridChecksum::sha256_string(seeds) << std::endl;
       SeedFixedIntegers(seeds);
     }
-  void SeedFixedIntegers(const std::vector<int> &seeds){
+  void SeedFixedIntegers(const std::vector<int> &seeds, int britney=0){
 
     // Everyone generates the same seed_seq based on input seeds
     CartesianCommunicator::BroadcastWorld(0,(void *)&seeds[0],sizeof(int)*seeds.size());
@@ -424,7 +428,6 @@ public:
     // MT implementation does not implement fast discard even though
     // in principle this is possible
     ////////////////////////////////////////////////
-#if 1
     thread_for( lidx, _grid->lSites(), {
 
 	int gidx;
@@ -445,29 +448,12 @@ public:
 	
 	int l_idx=generator_idx(o_idx,i_idx);
 	_generators[l_idx] = master_engine;
-	Skip(_generators[l_idx],gidx); // Skip to next RNG sequence
-    });
-#else
-    // Everybody loops over global volume.
-    thread_for( gidx, _grid->_gsites, {
-
-	// Where is it?
-	int rank;
-	int o_idx;
-	int i_idx;
-
-	Coordinate gcoor;
-	_grid->GlobalIndexToGlobalCoor(gidx,gcoor);
-	_grid->GlobalCoorToRankIndex(rank,o_idx,i_idx,gcoor);
-	
-	// If this is one of mine we take it
-	if( rank == _grid->ThisRank() ){
-	  int l_idx=generator_idx(o_idx,i_idx);
-	  _generators[l_idx] = master_engine;
+	if ( britney ) { 
+	  Skip(_generators[l_idx],l_idx); // Skip to next RNG sequence
+	} else { 	
 	  Skip(_generators[l_idx],gidx); // Skip to next RNG sequence
 	}
     });
-#endif
 #else 
     ////////////////////////////////////////////////////////////////
     // Machine and thread decomposition dependent seeding is efficient

Grid/lattice/Lattice_slicesum_core.h

@@ -0,0 +1,224 @@
+#pragma once
+
+#if defined(GRID_CUDA)
+
+#include <cub/cub.cuh>
+#define gpucub cub
+#define gpuError_t cudaError_t
+#define gpuSuccess cudaSuccess
+
+#elif defined(GRID_HIP)
+
+#include <hipcub/hipcub.hpp>
+#define gpucub hipcub
+#define gpuError_t hipError_t
+#define gpuSuccess hipSuccess
+
+#endif
+
+
+NAMESPACE_BEGIN(Grid);
+
+
+#if defined(GRID_CUDA) || defined(GRID_HIP)
+template<class vobj> inline void sliceSumReduction_cub_small(const vobj *Data, Vector<vobj> &lvSum, const int rd, const int e1, const int e2, const int stride, const int ostride, const int Nsimd) {
+  size_t subvol_size = e1*e2;
+  commVector<vobj> reduction_buffer(rd*subvol_size);
+  auto rb_p = &reduction_buffer[0];
+  vobj zero_init;
+  zeroit(zero_init);
+
+  
+  void *temp_storage_array = NULL;
+  size_t temp_storage_bytes = 0;
+  vobj *d_out;
+  int* d_offsets;
+
+  std::vector<int> offsets(rd+1,0);
+
+  for (int i = 0; i < offsets.size(); i++) {
+    offsets[i] = i*subvol_size;
+  }
+  
+  //Allocate memory for output and offset arrays on device
+  d_out = static_cast<vobj*>(acceleratorAllocDevice(rd*sizeof(vobj)));
+  
+  d_offsets = static_cast<int*>(acceleratorAllocDevice((rd+1)*sizeof(int)));
+  
+  //copy offsets to device
+  acceleratorCopyToDeviceAsync(&offsets[0],d_offsets,sizeof(int)*(rd+1),computeStream);
+  
+  
+  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);
+  if (gpuErr!=gpuSuccess) {
+    std::cout << GridLogError << "Lattice_slicesum_gpu.h: Encountered error during gpucub::DeviceSegmentedReduce::Reduce (setup)! Error: " << gpuErr <<std::endl;
+    exit(EXIT_FAILURE);
+  }
+
+  //allocate memory for temp_storage_array  
+  temp_storage_array = acceleratorAllocDevice(temp_storage_bytes);
+  
+  //prepare buffer for reduction
+  //use non-blocking accelerator_for to avoid syncs (ok because we submit to same computeStream)
+  //use 2d accelerator_for to avoid launch latencies found when serially looping over rd 
+  accelerator_for2dNB( s,subvol_size, r,rd, Nsimd,{ 
+  
+    int n = s / e2;
+    int b = s % e2;
+    int so=r*ostride; // base offset for start of plane 
+    int ss= so+n*stride+b;
+
+    coalescedWrite(rb_p[r*subvol_size+s], coalescedRead(Data[ss]));
+
+  });
+  
+  //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);
+  if (gpuErr!=gpuSuccess) {
+    std::cout << GridLogError << "Lattice_slicesum_gpu.h: Encountered error during gpucub::DeviceSegmentedReduce::Reduce! Error: " << gpuErr <<std::endl;
+    exit(EXIT_FAILURE);
+  }
+  
+  acceleratorCopyFromDeviceAsync(d_out,&lvSum[0],rd*sizeof(vobj),computeStream);
+  
+  //sync after copy
+  accelerator_barrier();
+ 
+  acceleratorFreeDevice(temp_storage_array);
+  acceleratorFreeDevice(d_out);
+  acceleratorFreeDevice(d_offsets);
+  
+
+}
+#endif 
+
+
+#if defined(GRID_SYCL)
+template<class vobj> inline void sliceSumReduction_sycl_small(const vobj *Data, Vector <vobj> &lvSum, const int  &rd, const int &e1, const int &e2, const int &stride, const int &ostride, const int &Nsimd)
+{
+  size_t subvol_size = e1*e2;
+
+  vobj *mysum = (vobj *) malloc_shared(rd*sizeof(vobj),*theGridAccelerator);
+  vobj vobj_zero;
+  zeroit(vobj_zero);
+  for (int r = 0; r<rd; r++) { 
+    mysum[r] = vobj_zero; 
+  }
+
+  commVector<vobj> reduction_buffer(rd*subvol_size);    
+
+  auto rb_p = &reduction_buffer[0];
+
+  // autoView(Data_v, Data, AcceleratorRead);
+
+  //prepare reduction buffer 
+  accelerator_for2d( s,subvol_size, r,rd, (size_t)Nsimd,{ 
+  
+      int n = s / e2;
+      int b = s % e2;
+      int so=r*ostride; // base offset for start of plane 
+      int ss= so+n*stride+b;
+
+      coalescedWrite(rb_p[r*subvol_size+s], coalescedRead(Data[ss]));
+
+  });
+
+  for (int r = 0; r < rd; r++) {
+      theGridAccelerator->submit([&](cl::sycl::handler &cgh) {
+          auto Reduction = cl::sycl::reduction(&mysum[r],std::plus<>());
+          cgh.parallel_for(cl::sycl::range<1>{subvol_size},
+          Reduction,
+          [=](cl::sycl::id<1> item, auto &sum) {
+              auto s = item[0];
+              sum += rb_p[r*subvol_size+s];
+          });
+      });
+      
+     
+  }
+  theGridAccelerator->wait();
+  for (int r = 0; r < rd; r++) {
+    lvSum[r] = mysum[r];
+  }
+  free(mysum,*theGridAccelerator);
+}
+#endif
+
+template<class vobj> inline void sliceSumReduction_large(const vobj *Data, Vector<vobj> &lvSum, const int rd, const int e1, const int e2, const int stride, const int ostride, const int Nsimd) {
+  typedef typename vobj::vector_type vector;
+  const int words = sizeof(vobj)/sizeof(vector);
+  const int osites = rd*e1*e2;
+  commVector<vector>buffer(osites);
+  vector *dat = (vector *)Data;
+  vector *buf = &buffer[0];
+  Vector<vector> lvSum_small(rd);
+  vector *lvSum_ptr = (vector *)&lvSum[0];
+
+  for (int w = 0; w < words; w++) {
+    accelerator_for(ss,osites,1,{
+	    buf[ss] = dat[ss*words+w];
+    });
+
+    #if defined(GRID_CUDA) || defined(GRID_HIP)
+      sliceSumReduction_cub_small(buf,lvSum_small,rd,e1,e2,stride, ostride,Nsimd);
+    #elif defined(GRID_SYCL)
+      sliceSumReduction_sycl_small(buf,lvSum_small,rd,e1,e2,stride, ostride,Nsimd);
+    #endif
+
+    for (int r = 0; r < rd; r++) {
+      lvSum_ptr[w+words*r]=lvSum_small[r];
+    }
+
+  }
+
+  
+}
+
+template<class vobj> inline void sliceSumReduction_gpu(const Lattice<vobj> &Data, Vector<vobj> &lvSum, const int rd, const int e1, const int e2, const int stride, const int ostride, const int Nsimd)
+{
+  autoView(Data_v, Data, AcceleratorRead); //reduction libraries cannot deal with large vobjs so we split into small/large case.
+    if constexpr (sizeof(vobj) <= 256) { 
+
+      #if defined(GRID_CUDA) || defined(GRID_HIP)
+        sliceSumReduction_cub_small(&Data_v[0], lvSum, rd, e1, e2, stride, ostride, Nsimd);
+      #elif defined (GRID_SYCL)
+        sliceSumReduction_sycl_small(&Data_v[0], lvSum, rd, e1, e2, stride, ostride, Nsimd);
+      #endif
+
+    }
+    else {
+      sliceSumReduction_large(&Data_v[0], lvSum, rd, e1, e2, stride, ostride, Nsimd);
+    }
+}
+
+
+template<class vobj> inline void sliceSumReduction_cpu(const Lattice<vobj> &Data, Vector<vobj> &lvSum, const int &rd, const int &e1, const int &e2, const int &stride, const int &ostride, const int &Nsimd)
+{
+  // sum over reduced dimension planes, breaking out orthog dir
+  // Parallel over orthog direction
+  autoView( Data_v, Data, CpuRead);
+  thread_for( r,rd, {
+    int so=r*ostride; // base offset for start of plane 
+    for(int n=0;n<e1;n++){
+      for(int b=0;b<e2;b++){
+        int ss= so+n*stride+b;
+        lvSum[r]=lvSum[r]+Data_v[ss];
+      }
+    }
+  });
+}
+
+template<class vobj> inline void sliceSumReduction(const Lattice<vobj> &Data, Vector<vobj> &lvSum, const int &rd, const int &e1, const int &e2, const int &stride, const int &ostride, const int &Nsimd) 
+{
+  #if defined(GRID_CUDA) || defined(GRID_HIP) || defined(GRID_SYCL)
+  
+  sliceSumReduction_gpu(Data, lvSum, rd, e1, e2, stride, ostride, Nsimd);
+  
+  #else
+  sliceSumReduction_cpu(Data, lvSum, rd, e1, e2, stride, ostride, Nsimd);
+
+  #endif
+}
+
+
+NAMESPACE_END(Grid);

Grid/lattice/Lattice_trace.h

@@ -66,6 +66,65 @@ inline auto TraceIndex(const Lattice<vobj> &lhs) -> Lattice<decltype(traceIndex<
   return ret;
 };
 
+template<int N, class Vec>
+Lattice<iScalar<iScalar<iScalar<Vec> > > > Determinant(const Lattice<iScalar<iScalar<iMatrix<Vec, N> > > > &Umu)
+{
+  GridBase *grid=Umu.Grid();
+  auto lvol = grid->lSites();
+  Lattice<iScalar<iScalar<iScalar<Vec> > > > ret(grid);
+  typedef typename Vec::scalar_type scalar;
+  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);
+    iScalar<iScalar<iMatrix<scalar, N> > > Us;
+    peekLocalSite(Us, Umu_v, lcoor);
+    for(int i=0;i<N;i++){
+      for(int j=0;j<N;j++){
+	scalar tmp= Us()()(i,j);
+	ComplexD ztmp(real(tmp),imag(tmp));
+	EigenU(i,j)=ztmp;
+      }}
+    ComplexD detD  = EigenU.determinant();
+    typename Vec::scalar_type det(detD.real(),detD.imag());
+    pokeLocalSite(det,ret_v,lcoor);
+  });
+  return ret;
+}
+
+template<int N>
+Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > Inverse(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
+{
+  GridBase *grid=Umu.Grid();
+  auto lvol = grid->lSites();
+  Lattice<iScalar<iScalar<iMatrix<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);
+    iScalar<iScalar<iMatrix<ComplexD, N> > > Us;
+    iScalar<iScalar<iMatrix<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

@@ -469,15 +469,13 @@ inline void blockSum(Lattice<vobj> &coarseData,const Lattice<vobj> &fineData)
   Coordinate fine_rdimensions = fine->_rdimensions;
   Coordinate coarse_rdimensions = coarse->_rdimensions;
 
-  vobj zz = Zero();
-  
   accelerator_for(sc,coarse->oSites(),1,{
 
       // One thread per sub block
       Coordinate coor_c(_ndimension);
       Lexicographic::CoorFromIndex(coor_c,sc,coarse_rdimensions);  // Block coordinate
 
-      vobj cd = zz;
+      vobj cd = Zero();
       
       for(int sb=0;sb<blockVol;sb++){
 
@@ -697,8 +695,68 @@ void localCopyRegion(const Lattice<vobj> &From,Lattice<vobj> & To,Coordinate Fro
   for(int d=0;d<nd;d++){
     assert(Fg->_processors[d]  == Tg->_processors[d]);
   }
-
   // the above should guarantee that the operations are local
+  
+#if 1
+
+  size_t nsite = 1;
+  for(int i=0;i<nd;i++) nsite *= RegionSize[i];
+  
+  size_t tbytes = 4*nsite*sizeof(int);
+  int *table = (int*)malloc(tbytes);
+ 
+  thread_for(idx, nsite, {
+      Coordinate from_coor, to_coor;
+      size_t rem = idx;
+      for(int i=0;i<nd;i++){
+	size_t base_i  = rem % RegionSize[i]; rem /= RegionSize[i];
+	from_coor[i] = base_i + FromLowerLeft[i];
+	to_coor[i] = base_i + ToLowerLeft[i];
+      }
+      
+      int foidx = Fg->oIndex(from_coor);
+      int fiidx = Fg->iIndex(from_coor);
+      int toidx = Tg->oIndex(to_coor);
+      int tiidx = Tg->iIndex(to_coor);
+      int* tt = table + 4*idx;
+      tt[0] = foidx;
+      tt[1] = fiidx;
+      tt[2] = toidx;
+      tt[3] = tiidx;
+    });
+  
+  int* table_d = (int*)acceleratorAllocDevice(tbytes);
+  acceleratorCopyToDevice(table,table_d,tbytes);
+
+  typedef typename vobj::vector_type vector_type;
+  typedef typename vobj::scalar_type scalar_type;
+
+  autoView(from_v,From,AcceleratorRead);
+  autoView(to_v,To,AcceleratorWrite);
+  
+  accelerator_for(idx,nsite,1,{
+      static const int words=sizeof(vobj)/sizeof(vector_type);
+      int* tt = table_d + 4*idx;
+      int from_oidx = *tt++;
+      int from_lane = *tt++;
+      int to_oidx = *tt++;
+      int to_lane = *tt;
+
+      const vector_type* from = (const vector_type *)&from_v[from_oidx];
+      vector_type* to = (vector_type *)&to_v[to_oidx];
+      
+      scalar_type stmp;
+      for(int w=0;w<words;w++){
+	stmp = getlane(from[w], from_lane);
+	putlane(to[w], stmp, to_lane);
+      }
+    });
+  
+  acceleratorFreeDevice(table_d);    
+  free(table);
+  
+
+#else  
   Coordinate ldf = Fg->_ldimensions;
   Coordinate rdf = Fg->_rdimensions;
   Coordinate isf = Fg->_istride;
@@ -738,6 +796,8 @@ void localCopyRegion(const Lattice<vobj> &From,Lattice<vobj> & To,Coordinate Fro
 #endif
     }
   });
+
+#endif
 }
 
 
@@ -830,6 +890,8 @@ void ExtractSlice(Lattice<vobj> &lowDim,const Lattice<vobj> & higherDim,int slic
 }
 
 
+//Insert subvolume orthogonal to direction 'orthog' with slice index 'slice_lo' from 'lowDim' onto slice index 'slice_hi' of higherDim
+//The local dimensions of both 'lowDim' and 'higherDim' orthogonal to 'orthog' should be the same
 template<class vobj>
 void InsertSliceLocal(const Lattice<vobj> &lowDim, Lattice<vobj> & higherDim,int slice_lo,int slice_hi, int orthog)
 {
@@ -851,6 +913,65 @@ void InsertSliceLocal(const Lattice<vobj> &lowDim, Lattice<vobj> & higherDim,int
     }
   }
 
+#if 1
+  size_t nsite = lg->lSites()/lg->LocalDimensions()[orthog];
+  size_t tbytes = 4*nsite*sizeof(int);
+  int *table = (int*)malloc(tbytes);
+  
+  thread_for(idx,nsite,{
+    Coordinate lcoor(nl);
+    Coordinate hcoor(nh);
+    lcoor[orthog] = slice_lo;
+    hcoor[orthog] = slice_hi;
+    size_t rem = idx;
+    for(int mu=0;mu<nl;mu++){
+      if(mu != orthog){
+	int xmu = rem % lg->LocalDimensions()[mu];  rem /= lg->LocalDimensions()[mu];
+	lcoor[mu] = hcoor[mu] = xmu;
+      }
+    }
+    int loidx = lg->oIndex(lcoor);
+    int liidx = lg->iIndex(lcoor);
+    int hoidx = hg->oIndex(hcoor);
+    int hiidx = hg->iIndex(hcoor);
+    int* tt = table + 4*idx;
+    tt[0] = loidx;
+    tt[1] = liidx;
+    tt[2] = hoidx;
+    tt[3] = hiidx;
+    });
+   
+  int* table_d = (int*)acceleratorAllocDevice(tbytes);
+  acceleratorCopyToDevice(table,table_d,tbytes);
+
+  typedef typename vobj::vector_type vector_type;
+  typedef typename vobj::scalar_type scalar_type;
+
+  autoView(lowDim_v,lowDim,AcceleratorRead);
+  autoView(higherDim_v,higherDim,AcceleratorWrite);
+  
+  accelerator_for(idx,nsite,1,{
+      static const int words=sizeof(vobj)/sizeof(vector_type);
+      int* tt = table_d + 4*idx;
+      int from_oidx = *tt++;
+      int from_lane = *tt++;
+      int to_oidx = *tt++;
+      int to_lane = *tt;
+
+      const vector_type* from = (const vector_type *)&lowDim_v[from_oidx];
+      vector_type* to = (vector_type *)&higherDim_v[to_oidx];
+      
+      scalar_type stmp;
+      for(int w=0;w<words;w++){
+	stmp = getlane(from[w], from_lane);
+	putlane(to[w], stmp, to_lane);
+      }
+    });
+  
+  acceleratorFreeDevice(table_d);    
+  free(table);
+  
+#else
   // the above should guarantee that the operations are local
   autoView(lowDimv,lowDim,CpuRead);
   autoView(higherDimv,higherDim,CpuWrite);
@@ -866,6 +987,7 @@ void InsertSliceLocal(const Lattice<vobj> &lowDim, Lattice<vobj> & higherDim,int
       pokeLocalSite(s,higherDimv,hcoor);
     }
   });
+#endif
 }
 
 

Grid/lattice/Lattice_view.h

@@ -45,6 +45,7 @@ public:
   };
   // Host only
   GridBase * getGrid(void) const { return _grid; };
+  vobj* getHostPointer(void) const { return _odata; };
 };
 
 /////////////////////////////////////////////////////////////////////////////////////////

Grid/lattice/PaddedCell.h

@@ -26,14 +26,32 @@ Author: Peter Boyle pboyle@bnl.gov
 /*  END LEGAL */
 #pragma once
 
+#include<Grid/cshift/Cshift.h>
+
 NAMESPACE_BEGIN(Grid);
 
+//Allow the user to specify how the C-shift is performed, e.g. to respect the appropriate boundary conditions
+template<typename vobj>
+struct CshiftImplBase{
+  virtual Lattice<vobj> Cshift(const Lattice<vobj> &in, int dir, int shift) const = 0;
+  virtual ~CshiftImplBase(){}
+};
+template<typename vobj>
+struct CshiftImplDefault: public CshiftImplBase<vobj>{
+  Lattice<vobj> Cshift(const Lattice<vobj> &in, int dir, int shift) const override{ return Grid::Cshift(in,dir,shift); }
+};
+template<typename Gimpl>
+struct CshiftImplGauge: public CshiftImplBase<typename Gimpl::GaugeLinkField::vector_object>{
+  typename Gimpl::GaugeLinkField Cshift(const typename Gimpl::GaugeLinkField &in, int dir, int shift) const override{ return Gimpl::CshiftLink(in,dir,shift); }
+};  
+
 class PaddedCell {
 public:
   GridCartesian * unpadded_grid;
   int dims;
   int depth;
   std::vector<GridCartesian *> grids;
+
   ~PaddedCell()
   {
     DeleteGrids();
@@ -77,7 +95,7 @@ public:
     }
   };
   template<class vobj>
-  inline Lattice<vobj> Extract(Lattice<vobj> &in)
+  inline Lattice<vobj> Extract(const Lattice<vobj> &in) const
   {
     Lattice<vobj> out(unpadded_grid);
 
@@ -88,19 +106,19 @@ public:
     return out;
   }
   template<class vobj>
-  inline Lattice<vobj> Exchange(Lattice<vobj> &in)
+  inline Lattice<vobj> Exchange(const Lattice<vobj> &in, const CshiftImplBase<vobj> &cshift = CshiftImplDefault<vobj>()) const
   {
     GridBase *old_grid = in.Grid();
     int dims = old_grid->Nd();
     Lattice<vobj> tmp = in;
     for(int d=0;d<dims;d++){
-      tmp = Expand(d,tmp); // rvalue && assignment
+      tmp = Expand(d,tmp,cshift); // rvalue && assignment
     }
     return tmp;
   }
   // expand up one dim at a time
   template<class vobj>
-  inline Lattice<vobj> Expand(int dim,Lattice<vobj> &in)
+  inline Lattice<vobj> Expand(int dim, const Lattice<vobj> &in, const CshiftImplBase<vobj> &cshift = CshiftImplDefault<vobj>()) const
   {
     GridBase *old_grid = in.Grid();
     GridCartesian *new_grid = grids[dim];//These are new grids
@@ -112,20 +130,40 @@ public:
     else       conformable(old_grid,grids[dim-1]);
 
     std::cout << " dim "<<dim<<" local "<<local << " padding to "<<plocal<<std::endl;
+
+    double tins=0, tshift=0;
+    
     // Middle bit
+    double t = usecond();
     for(int x=0;x<local[dim];x++){
       InsertSliceLocal(in,padded,x,depth+x,dim);
     }
+    tins += usecond() - t;
+    
     // High bit
-    shifted = Cshift(in,dim,depth);
+    t = usecond();
+    shifted = cshift.Cshift(in,dim,depth);
+    tshift += usecond() - t;
+
+    t=usecond();
     for(int x=0;x<depth;x++){
       InsertSliceLocal(shifted,padded,local[dim]-depth+x,depth+local[dim]+x,dim);
     }
+    tins += usecond() - t;
+    
     // Low bit
-    shifted = Cshift(in,dim,-depth);
+    t = usecond();
+    shifted = cshift.Cshift(in,dim,-depth);
+    tshift += usecond() - t;
+    
+    t = usecond();
     for(int x=0;x<depth;x++){
       InsertSliceLocal(shifted,padded,x,x,dim);
     }
+    tins += usecond() - t;
+
+    std::cout << GridLogPerformance << "PaddedCell::Expand timings: cshift:" << tshift/1000 << "ms, insert-slice:" << tins/1000 << "ms" << std::endl;
+    
     return padded;
   }
 

Grid/log/Log.h

@@ -191,6 +191,41 @@ extern Colours    GridLogColours;
 
 std::string demangle(const char* name) ;
 
+template<typename... Args>
+inline std::string sjoin(Args&&... args) noexcept {
+    std::ostringstream msg;
+    (msg << ... << args);
+    return msg.str();
+}
+
+/*!  @brief make log messages work like python print */
+template <typename... Args>
+inline void Grid_log(Args&&... args) {
+    std::string msg = sjoin(std::forward<Args>(args)...);
+    std::cout << GridLogMessage << msg << std::endl;
+}
+
+/*!  @brief make warning messages work like python print */
+template <typename... Args>
+inline void Grid_warn(Args&&... args) {
+    std::string msg = sjoin(std::forward<Args>(args)...);
+    std::cout << "\033[33m" << GridLogWarning << msg << "\033[0m" << std::endl;
+}
+
+/*!  @brief make error messages work like python print */
+template <typename... Args>
+inline void Grid_error(Args&&... args) {
+    std::string msg = sjoin(std::forward<Args>(args)...);
+    std::cout << "\033[31m" << GridLogError << msg << "\033[0m" << std::endl;
+}
+
+/*!  @brief make pass messages work like python print */
+template <typename... Args>
+inline void Grid_pass(Args&&... args) {
+    std::string msg = sjoin(std::forward<Args>(args)...);
+    std::cout << "\033[32m" << GridLogMessage << msg << "\033[0m" << std::endl;
+}
+
 #define _NBACKTRACE (256)
 extern void * Grid_backtrace_buffer[_NBACKTRACE];
 

Grid/perfmon/Tracing.h

@@ -34,7 +34,7 @@ class GridTracer {
 };
 inline void tracePush(const char *name) { roctxRangePushA(name); }
 inline void tracePop(const char *name) { roctxRangePop(); }
-inline int  traceStart(const char *name) { roctxRangeStart(name); }
+inline int  traceStart(const char *name) { return roctxRangeStart(name); }
 inline void traceStop(int ID) { roctxRangeStop(ID); }
 #endif
 

Grid/qcd/action/ActionBase.h

@@ -129,6 +129,22 @@ public:
   virtual ~Action(){}
 };
 
+template <class GaugeField >
+class EmptyAction : public Action <GaugeField>
+{
+  virtual void refresh(const GaugeField& U, GridSerialRNG &sRNG, GridParallelRNG& pRNG) { assert(0);}; // refresh pseudofermions
+  virtual RealD S(const GaugeField& U) { return 0.0;};                             // evaluate the action
+  virtual void deriv(const GaugeField& U, GaugeField& dSdU) { assert(0); };        // evaluate the action derivative
+
+  ///////////////////////////////
+  // Logging
+  ///////////////////////////////
+  virtual std::string action_name()    { return std::string("Level Force Log"); };
+  virtual std::string LogParameters()  { return std::string("No parameters");};
+};
+
+
+
 NAMESPACE_END(Grid);
 
 #endif // ACTION_BASE_H

Grid/qcd/action/fermion/CayleyFermion5D.h

@@ -124,11 +124,6 @@ public:
   RealD                _b;
   RealD                _c;
 
-  // possible boost
-  std::vector<ComplexD> qmu;
-  void set_qmu(std::vector<ComplexD> _qmu) { qmu=_qmu; assert(qmu.size()==Nd);};
-  void addQmu(const FermionField &in, FermionField &out, int dag);
-  
   // Cayley form Moebius (tanh and zolotarev)
   Vector<Coeff_t> omega;
   Vector<Coeff_t> bs;    // S dependent coeffs

Grid/qcd/action/fermion/ContinuedFractionFermion5D.h

@@ -60,50 +60,6 @@ public:
   //      virtual void   Instantiatable(void)=0;
   virtual void   Instantiatable(void) =0;
 
-  void FreePropagator(const FermionField &in,FermionField &out,RealD mass,std::vector<Complex> boundary, std::vector<double> twist)
-  {
-    std::cout << "Free Propagator for PartialFraction"<<std::endl;
-    FermionField in_k(in.Grid());
-    FermionField prop_k(in.Grid());
-    
-    FFT theFFT((GridCartesian *) in.Grid());
-
-    //phase for boundary condition
-    ComplexField coor(in.Grid());
-    ComplexField ph(in.Grid());  ph = Zero();
-    FermionField in_buf(in.Grid()); in_buf = Zero();
-    typedef typename Simd::scalar_type Scalar;
-    Scalar ci(0.0,1.0);
-    assert(twist.size() == Nd);//check that twist is Nd
-    assert(boundary.size() == Nd);//check that boundary conditions is Nd
-    int shift = 0;
-    for(unsigned int nu = 0; nu < Nd; nu++)
-      {
-	// Shift coordinate lattice index by 1 to account for 5th dimension.
-	LatticeCoordinate(coor, nu + shift);
-	double boundary_phase = ::acos(real(boundary[nu]));
-	ph = ph + boundary_phase*coor*((1./(in.Grid()->_fdimensions[nu+shift])));
-	//momenta for propagator shifted by twist+boundary
-	twist[nu] = twist[nu] + boundary_phase/((2.0*M_PI));
-      }
-    in_buf = exp(ci*ph*(-1.0))*in;
-
-    theFFT.FFT_all_dim(in_k,in,FFT::forward);
-    this->MomentumSpacePropagatorHw(prop_k,in_k,mass,twist);
-    theFFT.FFT_all_dim(out,prop_k,FFT::backward);
-    
-    //phase for boundary condition
-    out = out * exp(ci*ph);
-  };
-
-  virtual void FreePropagator(const FermionField &in,FermionField &out,RealD mass) {
-    std::vector<double> twist(Nd,0.0); //default: periodic boundarys in all directions
-    std::vector<Complex> boundary;
-    for(int i=0;i<Nd;i++) boundary.push_back(1);//default: periodic boundary conditions
-    FreePropagator(in,out,mass,boundary,twist);
-  };
-
-  
   // Efficient support for multigrid coarsening
   virtual void  Mdir (const FermionField &in, FermionField &out,int dir,int disp);
   virtual void  MdirAll(const FermionField &in, std::vector<FermionField> &out);

Grid/qcd/action/fermion/Fermion.h

@@ -126,6 +126,16 @@ typedef WilsonFermion<WilsonTwoIndexSymmetricImplD> WilsonTwoIndexSymmetricFermi
 typedef WilsonFermion<WilsonTwoIndexAntiSymmetricImplF> WilsonTwoIndexAntiSymmetricFermionF;
 typedef WilsonFermion<WilsonTwoIndexAntiSymmetricImplD> WilsonTwoIndexAntiSymmetricFermionD;
 
+// Sp(2n)
+typedef WilsonFermion<SpWilsonImplF> SpWilsonFermionF;
+typedef WilsonFermion<SpWilsonImplD> SpWilsonFermionD;
+
+typedef WilsonFermion<SpWilsonTwoIndexAntiSymmetricImplF> SpWilsonTwoIndexAntiSymmetricFermionF;
+typedef WilsonFermion<SpWilsonTwoIndexAntiSymmetricImplD> SpWilsonTwoIndexAntiSymmetricFermionD;
+
+typedef WilsonFermion<SpWilsonTwoIndexSymmetricImplF> SpWilsonTwoIndexSymmetricFermionF;
+typedef WilsonFermion<SpWilsonTwoIndexSymmetricImplD> SpWilsonTwoIndexSymmetricFermionD;
+
 // Twisted mass fermion
 typedef WilsonTMFermion<WilsonImplD2> WilsonTMFermionD2;
 typedef WilsonTMFermion<WilsonImplF> WilsonTMFermionF;

Grid/qcd/action/fermion/PartialFractionFermion5D.h

@@ -39,7 +39,7 @@ class PartialFractionFermion5D : public WilsonFermion5D<Impl>
 public:
   INHERIT_IMPL_TYPES(Impl);
 
-  const int part_frac_chroma_convention=0;
+  const int part_frac_chroma_convention=1;
 
   void   Meooe_internal(const FermionField &in, FermionField &out,int dag);
   void   Mooee_internal(const FermionField &in, FermionField &out,int dag);
@@ -83,63 +83,12 @@ public:
 			   GridRedBlackCartesian &FourDimRedBlackGrid,
 			   RealD _mass,RealD M5,const ImplParams &p= ImplParams());
 
-  PartialFractionFermion5D(GaugeField &_Umu,
-			   GridCartesian         &FiveDimGrid,
-			   GridRedBlackCartesian &FiveDimRedBlackGrid,
-			   GridCartesian         &FourDimGrid,
-			   GridRedBlackCartesian &FourDimRedBlackGrid,
-			   RealD _mass,RealD M5,std::vector<RealD> &_qmu,const ImplParams &p= ImplParams());
-
-  void FreePropagator(const FermionField &in,FermionField &out,RealD mass,std::vector<Complex> boundary, std::vector<double> twist)
-  {
-    std::cout << "Free Propagator for PartialFraction"<<std::endl;
-    FermionField in_k(in.Grid());
-    FermionField prop_k(in.Grid());
-    
-    FFT theFFT((GridCartesian *) in.Grid());
-
-    //phase for boundary condition
-    ComplexField coor(in.Grid());
-    ComplexField ph(in.Grid());  ph = Zero();
-    FermionField in_buf(in.Grid()); in_buf = Zero();
-    typedef typename Simd::scalar_type Scalar;
-    Scalar ci(0.0,1.0);
-    assert(twist.size() == Nd);//check that twist is Nd
-    assert(boundary.size() == Nd);//check that boundary conditions is Nd
-    int shift = 0;
-    for(unsigned int nu = 0; nu < Nd; nu++)
-      {
-	// Shift coordinate lattice index by 1 to account for 5th dimension.
-	LatticeCoordinate(coor, nu + shift);
-	double boundary_phase = ::acos(real(boundary[nu]));
-	ph = ph + boundary_phase*coor*((1./(in.Grid()->_fdimensions[nu+shift])));
-	//momenta for propagator shifted by twist+boundary
-	twist[nu] = twist[nu] + boundary_phase/((2.0*M_PI));
-      }
-    in_buf = exp(ci*ph*(-1.0))*in;
-
-    theFFT.FFT_all_dim(in_k,in,FFT::forward);
-    this->MomentumSpacePropagatorHw(prop_k,in_k,mass,twist);
-    theFFT.FFT_all_dim(out,prop_k,FFT::backward);
-    
-    //phase for boundary condition
-    out = out * exp(ci*ph);
-  };
-
-  virtual void FreePropagator(const FermionField &in,FermionField &out,RealD mass) {
-    std::vector<double> twist(Nd,0.0); //default: periodic boundarys in all directions
-    std::vector<Complex> boundary;
-    for(int i=0;i<Nd;i++) boundary.push_back(1);//default: periodic boundary conditions
-    FreePropagator(in,out,mass,boundary,twist);
-  };
-  
 protected:
 
   virtual void SetCoefficientsTanh(Approx::zolotarev_data *zdata,RealD scale);
   virtual void SetCoefficientsZolotarev(RealD zolo_hi,Approx::zolotarev_data *zdata);
 
   // Part frac
-  std::vector<RealD> qmu;
   RealD mass;
   RealD dw_diag;
   RealD R;

Grid/qcd/action/fermion/WilsonImpl.h

@@ -261,6 +261,22 @@ typedef WilsonImpl<vComplex,  TwoIndexAntiSymmetricRepresentation, CoeffReal > W
 typedef WilsonImpl<vComplexF, TwoIndexAntiSymmetricRepresentation, CoeffReal > WilsonTwoIndexAntiSymmetricImplF;  // Float
 typedef WilsonImpl<vComplexD, TwoIndexAntiSymmetricRepresentation, CoeffReal > WilsonTwoIndexAntiSymmetricImplD;  // Double
 
+//sp 2n
+
+typedef WilsonImpl<vComplex,  SpFundamentalRepresentation, CoeffReal > SpWilsonImplR;  // Real.. whichever prec
+typedef WilsonImpl<vComplexF, SpFundamentalRepresentation, CoeffReal > SpWilsonImplF;  // Float
+typedef WilsonImpl<vComplexD, SpFundamentalRepresentation, CoeffReal > SpWilsonImplD;  // Double
+
+typedef WilsonImpl<vComplex,  SpTwoIndexAntiSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexAntiSymmetricImplR;  // Real.. whichever prec
+typedef WilsonImpl<vComplexF, SpTwoIndexAntiSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexAntiSymmetricImplF;  // Float
+typedef WilsonImpl<vComplexD, SpTwoIndexAntiSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexAntiSymmetricImplD;  // Double
+
+typedef WilsonImpl<vComplex,  SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexSymmetricImplR;  // Real.. whichever prec
+typedef WilsonImpl<vComplexF, SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexSymmetricImplF;  // Float
+typedef WilsonImpl<vComplexD, SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexSymmetricImplD;  // Double
+
+typedef WilsonImpl<vComplex,  SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonAdjImplR;  // Real.. whichever prec    // adj = 2indx symmetric for Sp(2N)
+typedef WilsonImpl<vComplexF, SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonAdjImplF;  // Float     // adj = 2indx symmetric for Sp(2N)
+typedef WilsonImpl<vComplexD, SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonAdjImplD;  // Double    // adj = 2indx symmetric for Sp(2N)
 
 NAMESPACE_END(Grid);
-

Grid/qcd/action/fermion/WilsonTMFermion.h

@@ -63,6 +63,8 @@ public:
   virtual void MooeeDag(const FermionField &in, FermionField &out) ;
   virtual void MooeeInv(const FermionField &in, FermionField &out) ;
   virtual void MooeeInvDag(const FermionField &in, FermionField &out) ;
+  virtual void M(const FermionField &in, FermionField &out) ;
+  virtual void Mdag(const FermionField &in, FermionField &out) ;
   
 private:
   RealD mu; // TwistedMass parameter

Grid/qcd/action/fermion/implementation/CayleyFermion5DImplementation.h

@@ -49,7 +49,6 @@ CayleyFermion5D<Impl>::CayleyFermion5D(GaugeField &_Umu,
 			FourDimRedBlackGrid,_M5,p),
   mass_plus(_mass), mass_minus(_mass)
 { 
-  // qmu defaults to zero size;
 }
 
 ///////////////////////////////////////////////////////////////
@@ -271,34 +270,6 @@ void CayleyFermion5D<Impl>::MeooeDag5D    (const FermionField &psi, FermionField
   M5Ddag(psi,psi,Din,lower,diag,upper);
 }
 
-template<class Impl>
-void CayleyFermion5D<Impl>::addQmu(const FermionField &psi,FermionField &chi, int dag)
-{
-  if ( qmu.size() ) {
-
-    Gamma::Algebra Gmu [] = {
-      Gamma::Algebra::GammaX,
-      Gamma::Algebra::GammaY,
-      Gamma::Algebra::GammaZ,
-      Gamma::Algebra::GammaT
-    };
-    std::vector<ComplexD> coeff(Nd);
-    ComplexD ci(0,1);
-
-    assert(qmu.size()==Nd);
-
-    for(int mu=0;mu<Nd;mu++){
-       coeff[mu] = ci*qmu[mu];
-       if ( dag ) coeff[mu] = conjugate(coeff[mu]);
-    }
-
-    chi = chi + Gamma(Gmu[0])*psi*coeff[0];
-    for(int mu=1;mu<Nd;mu++){
-      chi = chi + Gamma(Gmu[mu])*psi*coeff[mu];
-    }
-  }
-}
-
 template<class Impl>
 void CayleyFermion5D<Impl>::M    (const FermionField &psi, FermionField &chi)
 {
@@ -308,10 +279,6 @@ void CayleyFermion5D<Impl>::M    (const FermionField &psi, FermionField &chi)
   Meooe5D(psi,Din);
   
   this->DW(Din,chi,DaggerNo);
-
-  // add i q_mu gamma_mu here
-  addQmu(Din,chi,DaggerNo);
-  
   // ((b D_W + D_w hop terms +1) on s-diag
   axpby(chi,1.0,1.0,chi,psi); 
   
@@ -329,9 +296,6 @@ void CayleyFermion5D<Impl>::Mdag (const FermionField &psi, FermionField &chi)
   // Apply Dw
   this->DW(psi,Din,DaggerYes); 
   
-  // add -i conj(q_mu) gamma_mu here ... if qmu is real, gammm_5 hermitian, otherwise not.
-  addQmu(psi,Din,DaggerYes);
-  
   MeooeDag5D(Din,chi);
   
   M5Ddag(psi,chi);

Grid/qcd/action/fermion/implementation/ContinuedFractionFermion5DImplementation.h

@@ -42,13 +42,13 @@ template<class Impl>
 void ContinuedFractionFermion5D<Impl>::SetCoefficientsZolotarev(RealD zolo_hi,Approx::zolotarev_data *zdata)
 {
   // How to check Ls matches??
-  std::cout<<GridLogMessage << zdata->n  << " - n"<<std::endl;
-  std::cout<<GridLogMessage << zdata->da << " -da "<<std::endl;
-  std::cout<<GridLogMessage << zdata->db << " -db"<<std::endl;
-  std::cout<<GridLogMessage << zdata->dn << " -dn"<<std::endl;
-  std::cout<<GridLogMessage << zdata->dd << " -dd"<<std::endl;
+  //      std::cout<<GridLogMessage << Ls << " Ls"<<std::endl;
+  //      std::cout<<GridLogMessage << zdata->n  << " - n"<<std::endl;
+  //      std::cout<<GridLogMessage << zdata->da << " -da "<<std::endl;
+  //      std::cout<<GridLogMessage << zdata->db << " -db"<<std::endl;
+  //      std::cout<<GridLogMessage << zdata->dn << " -dn"<<std::endl;
+  //      std::cout<<GridLogMessage << zdata->dd << " -dd"<<std::endl;
   int Ls = this->Ls;
-  std::cout<<GridLogMessage << Ls << " Ls"<<std::endl;
   assert(zdata->db==Ls);// Beta has Ls coeffs
 
   R=(1+this->mass)/(1-this->mass);
@@ -320,7 +320,7 @@ ContinuedFractionFermion5D<Impl>::ContinuedFractionFermion5D(
       int Ls = this->Ls;
       conformable(solution5d.Grid(),this->FermionGrid());
       conformable(exported4d.Grid(),this->GaugeGrid());
-      ExtractSlice(exported4d, solution5d, Ls-1, 0);
+      ExtractSlice(exported4d, solution5d, Ls-1, Ls-1);
     }
     template<class Impl>
     void ContinuedFractionFermion5D<Impl>::ImportPhysicalFermionSource(const FermionField &input4d,FermionField &imported5d)
@@ -330,7 +330,7 @@ ContinuedFractionFermion5D<Impl>::ContinuedFractionFermion5D(
       conformable(input4d.Grid()   ,this->GaugeGrid());
       FermionField tmp(this->FermionGrid());
       tmp=Zero();
-      InsertSlice(input4d, tmp, Ls-1, 0);
+      InsertSlice(input4d, tmp, Ls-1, Ls-1);
       tmp=Gamma(Gamma::Algebra::Gamma5)*tmp;
       this->Dminus(tmp,imported5d);
     }

Grid/qcd/action/fermion/implementation/PartialFractionFermion5DImplementation.h

@@ -255,45 +255,6 @@ void   PartialFractionFermion5D<Impl>::M_internal(const FermionField &psi, Fermi
   }
 	
   {
-    // The 'conventional' Cayley overlap operator is
-    //
-    // Dov = (1+m)/2 + (1-m)/2 g5 sgn Hw
-    //
-    //
-    // With massless limit 1/2(1+g5 sgnHw)
-    //
-    // Luscher shows quite neatly that 1+g5 sgn Hw has tree level propagator i qslash +O(a^2)
-    //
-    // However, the conventional normalisation has both a leading order factor of 2 in Zq
-    // at tree level AND a mass dependent (1-m) that are convenient to absorb.
-    //
-    // In WilsonFermion5DImplementation.h, the tree level propagator for Hw is
-    //
-    // num = -i sin kmu gmu
-    //
-    // denom ( sqrt(sk^2 + (2shk^2 - 1)^2
-    //    b_k = sk2 - M5;
-    //     
-    //    w_k = sqrt(sk + b_k*b_k);
-    //
-    //    denom= ( w_k + b_k + mass*mass) ;
-    //
-    //    denom= one/denom;
-    //    out = num*denom;
-    //
-    // Chroma, and Grid define partial fraction via 4d operator
-    //
-    //   Dpf = 2/(1-m) x Dov = (1+m)/(1-m) + g5 sgn Hw
-    //
-    // Now since:
-    //
-    //      (1+m)/(1-m) = (1-m)/(1-m) + 2m/(1-m) = 1 + 2m/(1-m)
-    //
-    // This corresponds to a modified mass parameter
-    //
-    // It has an annoying 
-    //
-    // 
     double R=(1+this->mass)/(1-this->mass);
     //R g5 psi[Ls] + p[0] H
     ag5xpbg5y_ssp(chi,R*scale,psi,p[nblock]*scale/amax,D,Ls-1,Ls-1);
@@ -303,28 +264,6 @@ void   PartialFractionFermion5D<Impl>::M_internal(const FermionField &psi, Fermi
       double pp = p[nblock-1-b];
       axpby_ssp(chi,1.0,chi,-sqrt(amax*pp)*scale*sign,psi,Ls-1,s);
     }
-
-    if ( qmu.size() ) {
-
-      FermionField qslash_psi(psi.Grid());
-      
-      Gamma::Algebra Gmu [] = {
-			 Gamma::Algebra::GammaX,
-			 Gamma::Algebra::GammaY,
-			 Gamma::Algebra::GammaZ,
-			 Gamma::Algebra::GammaT
-      };
-      ComplexD ci(0,1);
-      assert(qmu.size()==Nd);
-      qslash_psi = Gamma(Gmu[0])*psi;
-      for(int mu=1;mu<Nd;mu++){
-	qslash_psi = Gamma(Gmu[mu])*psi;
-      }
-      //      RealD coeff = 1.0;
-      qslash_psi = Gamma(Gamma::Algebra::Gamma5)*qslash_psi*ci ; // i g5 qslash -- 1-m factor???
-      axpby_ssp(chi,1.0,chi,1.0, qslash_psi,Ls-1,Ls-1);
-    }
-    
   }
 
 }
@@ -472,7 +411,7 @@ void  PartialFractionFermion5D<Impl>::SetCoefficientsZolotarev(RealD zolo_hi,App
       int Ls = this->Ls;
       conformable(solution5d.Grid(),this->FermionGrid());
       conformable(exported4d.Grid(),this->GaugeGrid());
-      ExtractSlice(exported4d, solution5d, Ls-1, 0);
+      ExtractSlice(exported4d, solution5d, Ls-1, Ls-1);
     }
     template<class Impl>
     void PartialFractionFermion5D<Impl>::ImportPhysicalFermionSource(const FermionField &input4d,FermionField &imported5d)
@@ -482,8 +421,7 @@ void  PartialFractionFermion5D<Impl>::SetCoefficientsZolotarev(RealD zolo_hi,App
       conformable(input4d.Grid()   ,this->GaugeGrid());
       FermionField tmp(this->FermionGrid());
       tmp=Zero();
-      std::cout << " importing to slice " << Ls-1 <<std::endl;
-      InsertSlice(input4d, tmp, Ls-1, 0);
+      InsertSlice(input4d, tmp, Ls-1, Ls-1);
       tmp=Gamma(Gamma::Algebra::Gamma5)*tmp;
       this->Dminus(tmp,imported5d);
     }
@@ -504,7 +442,7 @@ PartialFractionFermion5D<Impl>::PartialFractionFermion5D(GaugeField &_Umu,
 
 {
   int Ls = this->Ls;
-  qmu.resize(0);
+
   assert((Ls&0x1)==1); // Odd Ls required
   int nrational=Ls-1;
 
@@ -522,22 +460,6 @@ PartialFractionFermion5D<Impl>::PartialFractionFermion5D(GaugeField &_Umu,
   Approx::zolotarev_free(zdata);
 
 }
-template<class Impl>
-PartialFractionFermion5D<Impl>::PartialFractionFermion5D(GaugeField &_Umu,
-							 GridCartesian         &FiveDimGrid,
-							 GridRedBlackCartesian &FiveDimRedBlackGrid,
-							 GridCartesian         &FourDimGrid,
-							 GridRedBlackCartesian &FourDimRedBlackGrid,
-							 RealD _mass,RealD M5,
-							 std::vector<RealD> &_qmu,
-							 const ImplParams &p)
-  : PartialFractionFermion5D<Impl>(_Umu,
-			     FiveDimGrid,FiveDimRedBlackGrid,
-			     FourDimGrid,FourDimRedBlackGrid,
-			     _mass,M5,p)
-{
-  qmu=_qmu;
-}
 
 NAMESPACE_END(Grid);
 

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

@@ -280,20 +280,16 @@ void StaggeredKernels<Impl>::DhopImproved(StencilImpl &st, LebesgueOrder &lo,
 
   if( interior && exterior ) { 
     if (Opt == OptGeneric    ) { KERNEL_CALL(DhopSiteGeneric,1); return;}
-#ifndef GRID_CUDA
     if (Opt == OptHandUnroll ) { KERNEL_CALL(DhopSiteHand,1);    return;}
+#ifndef GRID_CUDA
     if (Opt == OptInlineAsm  ) {  ASM_CALL(DhopSiteAsm);     return;}
 #endif
   } else if( interior ) {
     if (Opt == OptGeneric    ) { KERNEL_CALL(DhopSiteGenericInt,1); return;}
-#ifndef GRID_CUDA
     if (Opt == OptHandUnroll ) { KERNEL_CALL(DhopSiteHandInt,1);    return;}
-#endif
   } else if( exterior ) { 
     if (Opt == OptGeneric    ) { KERNEL_CALL(DhopSiteGenericExt,1); return;}
-#ifndef GRID_CUDA
     if (Opt == OptHandUnroll ) { KERNEL_CALL(DhopSiteHandExt,1);    return;}
-#endif
   }
   assert(0 && " Kernel optimisation case not covered ");
 }
@@ -322,19 +318,13 @@ void StaggeredKernels<Impl>::DhopNaive(StencilImpl &st, LebesgueOrder &lo,
   
   if( interior && exterior ) { 
     if (Opt == OptGeneric    ) { KERNEL_CALL(DhopSiteGeneric,0); return;}
-#ifndef GRID_CUDA
     if (Opt == OptHandUnroll ) { KERNEL_CALL(DhopSiteHand,0);    return;}
-#endif
   } else if( interior ) {
     if (Opt == OptGeneric    ) { KERNEL_CALL(DhopSiteGenericInt,0); return;}
-#ifndef GRID_CUDA
     if (Opt == OptHandUnroll ) { KERNEL_CALL(DhopSiteHandInt,0);    return;}
-#endif
   } else if( exterior ) { 
     if (Opt == OptGeneric    ) { KERNEL_CALL(DhopSiteGenericExt,0); return;}
-#ifndef GRID_CUDA
     if (Opt == OptHandUnroll ) { KERNEL_CALL(DhopSiteHandExt,0);    return;}
-#endif
   }
 }
 

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

@@ -462,6 +462,7 @@ void WilsonKernels<Impl>::DhopKernel(int Opt,StencilImpl &st,  DoubledGaugeField
     autoView(st_v , st,AcceleratorRead);
 
    if( interior && exterior ) {
+     acceleratorFenceComputeStream();
      if (Opt == WilsonKernelsStatic::OptGeneric    ) { KERNEL_CALL(GenericDhopSite); return;}
      if (Opt == WilsonKernelsStatic::OptHandUnroll ) { KERNEL_CALL(HandDhopSite);    return;}
 #ifndef GRID_CUDA
@@ -495,6 +496,7 @@ void WilsonKernels<Impl>::DhopKernel(int Opt,StencilImpl &st,  DoubledGaugeField
     autoView(st_v ,st,AcceleratorRead);
 
    if( interior && exterior ) {
+     acceleratorFenceComputeStream();
      if (Opt == WilsonKernelsStatic::OptGeneric    ) { KERNEL_CALL(GenericDhopSiteDag); return;}
      if (Opt == WilsonKernelsStatic::OptHandUnroll ) { KERNEL_CALL(HandDhopSiteDag);    return;}
 #ifndef GRID_CUDA

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

@@ -93,5 +93,25 @@ void WilsonTMFermion<Impl>::MooeeInvDag(const FermionField &in, FermionField &ou
   RealD b    = tm /sq;
   axpibg5x(out,in,a,b);
 }
+template<class Impl>
+void WilsonTMFermion<Impl>::M(const FermionField &in, FermionField &out) {
+  out.Checkerboard() = in.Checkerboard();
+  this->Dhop(in, out, DaggerNo);
+  FermionField tmp(out.Grid());
+  RealD a = 4.0+this->mass;
+  RealD b = this->mu;
+  axpibg5x(tmp,in,a,b);
+  axpy(out, 1.0, tmp, out);
+}
+template<class Impl>
+void WilsonTMFermion<Impl>::Mdag(const FermionField &in, FermionField &out) {
+  out.Checkerboard() = in.Checkerboard();
+  this->Dhop(in, out, DaggerYes);
+  FermionField tmp(out.Grid());
+  RealD a = 4.0+this->mass;
+  RealD b = -this->mu;
+  axpibg5x(tmp,in,a,b);
+  axpy(out, 1.0, tmp, out);
+}
 
 NAMESPACE_END(Grid);

Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonCloverFermionInstantiationSpWilsonImplD.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonFermionInstantiationSpWilsonImplD.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonKernelsInstantiationSpWilsonImplD.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonTMFermionInstantiationSpWilsonImplD.cc

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

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

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

Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonCloverFermionInstantiationSpWilsonImplF.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonFermionInstantiationSpWilsonImplF.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonKernelsInstantiationSpWilsonImplF.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonTMFermionInstantiationSpWilsonImplF.cc

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

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

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc

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

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

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc

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

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

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc

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

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

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc

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

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc

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

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

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

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

@@ -10,12 +10,18 @@ WILSON_IMPL_LIST=" \
 	   WilsonImplF \
 	   WilsonImplD \
 	   WilsonImplD2 \
+	   SpWilsonImplF \
+	   SpWilsonImplD \
 	   WilsonAdjImplF \
 	   WilsonAdjImplD \
 	   WilsonTwoIndexSymmetricImplF \
 	   WilsonTwoIndexSymmetricImplD \
 	   WilsonTwoIndexAntiSymmetricImplF \
 	   WilsonTwoIndexAntiSymmetricImplD \
+	   SpWilsonTwoIndexAntiSymmetricImplF \
+	   SpWilsonTwoIndexAntiSymmetricImplD \
+	   SpWilsonTwoIndexSymmetricImplF \
+	   SpWilsonTwoIndexSymmetricImplD \
 	   GparityWilsonImplF \
 	   GparityWilsonImplD "
 

Grid/qcd/action/gauge/Gauge.h

@@ -39,6 +39,9 @@ NAMESPACE_BEGIN(Grid);
 typedef WilsonGaugeAction<PeriodicGimplR>          WilsonGaugeActionR;
 typedef WilsonGaugeAction<PeriodicGimplF>          WilsonGaugeActionF;
 typedef WilsonGaugeAction<PeriodicGimplD>          WilsonGaugeActionD;
+typedef WilsonGaugeAction<SpPeriodicGimplR>        SpWilsonGaugeActionR;
+typedef WilsonGaugeAction<SpPeriodicGimplF>        SpWilsonGaugeActionF;
+typedef WilsonGaugeAction<SpPeriodicGimplD>        SpWilsonGaugeActionD;
 typedef PlaqPlusRectangleAction<PeriodicGimplR>    PlaqPlusRectangleActionR;
 typedef PlaqPlusRectangleAction<PeriodicGimplF>    PlaqPlusRectangleActionF;
 typedef PlaqPlusRectangleAction<PeriodicGimplD>    PlaqPlusRectangleActionD;

Grid/qcd/action/gauge/GaugeImplTypes.h

@@ -61,7 +61,7 @@ NAMESPACE_BEGIN(Grid);
   typedef typename Impl::Field Field;
 
 // hardcodes the exponential approximation in the template
-template <class S, int Nrepresentation = Nc, int Nexp = 12 > class GaugeImplTypes {
+template <class S, int Nrepresentation = Nc, int Nexp = 12, class Group = SU<Nc> > class GaugeImplTypes {
 public:
   typedef S Simd;
   typedef typename Simd::scalar_type scalar_type;
@@ -78,8 +78,6 @@ public:
   typedef Lattice<SiteLink>    LinkField; 
   typedef Lattice<SiteField>   Field;
 
-  typedef SU<Nrepresentation> Group;
-
   // Guido: we can probably separate the types from the HMC functions
   // this will create 2 kind of implementations
   // probably confusing the users
@@ -119,6 +117,7 @@ public:
     //
     LinkField Pmu(P.Grid());
     Pmu = Zero();
+
     for (int mu = 0; mu < Nd; mu++) {
       Group::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
       RealD scale = ::sqrt(HMC_MOMENTUM_DENOMINATOR) ;
@@ -127,7 +126,11 @@ public:
     }
   }
     
-  static inline Field projectForce(Field &P) { return Ta(P); }
+  static inline Field projectForce(Field &P) {
+      Field ret(P.Grid());
+      Group::taProj(P, ret);
+      return ret;
+    }
 
   static inline void update_field(Field& P, Field& U, double ep){
     //static std::chrono::duration<double> diff;
@@ -137,7 +140,8 @@ public:
     autoView(P_v,P,AcceleratorRead);
     accelerator_for(ss, P.Grid()->oSites(),1,{
       for (int mu = 0; mu < Nd; mu++) {
-        U_v[ss](mu) = ProjectOnGroup(Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu));
+          U_v[ss](mu) = Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu);
+          U_v[ss](mu) = Group::ProjectOnGeneralGroup(U_v[ss](mu));
       }
     });
    //auto end = std::chrono::high_resolution_clock::now();
@@ -157,7 +161,7 @@ public:
   }
 
   static inline void Project(Field &U) {
-    ProjectSUn(U);
+    Group::ProjectOnSpecialGroup(U);
   }
 
   static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U) {
@@ -171,6 +175,7 @@ public:
   static inline void ColdConfiguration(GridParallelRNG &pRNG, Field &U) {
     Group::ColdConfiguration(pRNG, U);
   }
+
 };
 
 
@@ -178,10 +183,17 @@ 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<vComplexF, Nc, 12, Sp<Nc> > SpGimplTypesF;
+typedef GaugeImplTypes<vComplexD, Nc, 12, Sp<Nc> > SpGimplTypesD;
+
 typedef GaugeImplTypes<vComplex, SU<Nc>::AdjointDimension> GimplAdjointTypesR;
 typedef GaugeImplTypes<vComplexF, SU<Nc>::AdjointDimension> GimplAdjointTypesF;
 typedef GaugeImplTypes<vComplexD, SU<Nc>::AdjointDimension> GimplAdjointTypesD;
 
+
+
+
 NAMESPACE_END(Grid);
 
 #endif // GRID_GAUGE_IMPL_TYPES_H

Grid/qcd/action/gauge/GaugeImplementations.h

@@ -176,7 +176,7 @@ public:
       return PeriodicBC::CshiftLink(Link,mu,shift);
   }
 
-  static inline void       setDirections(std::vector<int> &conjDirs) { _conjDirs=conjDirs; }
+  static inline void       setDirections(const std::vector<int> &conjDirs) { _conjDirs=conjDirs; }
   static inline std::vector<int> getDirections(void) { return _conjDirs; }
   static inline bool isPeriodicGaugeField(void) { return false; }
 };
@@ -193,6 +193,11 @@ typedef ConjugateGaugeImpl<GimplTypesR> ConjugateGimplR; // Real.. whichever pre
 typedef ConjugateGaugeImpl<GimplTypesF> ConjugateGimplF; // Float
 typedef ConjugateGaugeImpl<GimplTypesD> ConjugateGimplD; // Double
 
+typedef PeriodicGaugeImpl<SpGimplTypesR> SpPeriodicGimplR; // Real.. whichever prec
+typedef PeriodicGaugeImpl<SpGimplTypesF> SpPeriodicGimplF; // Float
+typedef PeriodicGaugeImpl<SpGimplTypesD> SpPeriodicGimplD; // Double
+
+
 NAMESPACE_END(Grid);
 
 #endif

Grid/qcd/action/gauge/PlaqPlusRectangleAction.h

@@ -43,7 +43,7 @@ public:
 private:
   RealD c_plaq;
   RealD c_rect;
-
+  typename WilsonLoops<Gimpl>::StapleAndRectStapleAllWorkspace workspace;
 public:
   PlaqPlusRectangleAction(RealD b,RealD c): c_plaq(b),c_rect(c){};
 
@@ -79,27 +79,18 @@ public:
     GridBase *grid = Umu.Grid();
 
     std::vector<GaugeLinkField> U (Nd,grid);
-    std::vector<GaugeLinkField> U2(Nd,grid);
-
     for(int mu=0;mu<Nd;mu++){
       U[mu] = PeekIndex<LorentzIndex>(Umu,mu);
-      WilsonLoops<Gimpl>::RectStapleDouble(U2[mu],U[mu],mu);
     }
+    std::vector<GaugeLinkField> RectStaple(Nd,grid), Staple(Nd,grid);
+    WilsonLoops<Gimpl>::StapleAndRectStapleAll(Staple, RectStaple, U, workspace);
 
     GaugeLinkField dSdU_mu(grid);
     GaugeLinkField staple(grid);
 
     for (int mu=0; mu < Nd; mu++){
-
-      // Staple in direction mu
-
-      WilsonLoops<Gimpl>::Staple(staple,Umu,mu);
-
-      dSdU_mu = Ta(U[mu]*staple)*factor_p;
-
-      WilsonLoops<Gimpl>::RectStaple(Umu,staple,U2,U,mu);
-
-      dSdU_mu = dSdU_mu + Ta(U[mu]*staple)*factor_r;
+      dSdU_mu = Ta(U[mu]*Staple[mu])*factor_p;
+      dSdU_mu = dSdU_mu + Ta(U[mu]*RectStaple[mu])*factor_r;
 	  
       PokeIndex<LorentzIndex>(dSdU, dSdU_mu, mu);
     }

Grid/qcd/hmc/GenericHMCrunner.h

@@ -225,6 +225,18 @@ template <class RepresentationsPolicy,
 using GenericHMCRunnerHirep =
 				     HMCWrapperTemplate<PeriodicGimplR, Integrator, RepresentationsPolicy>;
 
+// sp2n
+
+template <template <typename, typename, typename> class Integrator>
+using GenericSpHMCRunner = HMCWrapperTemplate<SpPeriodicGimplR, Integrator>;
+
+template <class RepresentationsPolicy,
+          template <typename, typename, typename> class Integrator>
+using GenericSpHMCRunnerHirep =
+                     HMCWrapperTemplate<SpPeriodicGimplR, Integrator, RepresentationsPolicy>;
+
+
+
 template <class Implementation, class RepresentationsPolicy, 
           template <typename, typename, typename> class Integrator>
 using GenericHMCRunnerTemplate = HMCWrapperTemplate<Implementation, Integrator, RepresentationsPolicy>;

Grid/qcd/hmc/integrators/Integrator.h

@@ -87,6 +87,8 @@ public:
 
   const ActionSet<Field, RepresentationPolicy> as;
 
+  ActionSet<Field,RepresentationPolicy> LevelForces;
+  
   //Get a pointer to a shared static instance of the "do-nothing" momentum filter to serve as a default
   static MomentumFilterBase<MomentaField> const* getDefaultMomFilter(){ 
     static MomentumFilterNone<MomentaField> filter;
@@ -124,6 +126,9 @@ public:
     // input U actually not used in the fundamental case
     // Fundamental updates, include smearing
 
+    assert(as.size()==LevelForces.size());
+    
+    Field level_force(U.Grid()); level_force =Zero();
     for (int a = 0; a < as[level].actions.size(); ++a) {
 
       double start_full = usecond();
@@ -145,6 +150,9 @@ public:
 
       std::cout << GridLogIntegrator << " update_P : Level [" << level <<"]["<<a <<"] "<<name<<" dt "<<ep<<  std::endl;
 
+      // track the total
+      level_force = level_force+force;
+
       Real force_abs   = std::sqrt(norm2(force)/U.Grid()->gSites()); //average per-site norm.  nb. norm2(latt) = \sum_x norm2(latt[x]) 
       Real impulse_abs = force_abs * ep * HMC_MOMENTUM_DENOMINATOR;    
 
@@ -167,6 +175,16 @@ public:
 
     }
 
+    {
+      // total force
+      Real force_abs   = std::sqrt(norm2(level_force)/U.Grid()->gSites()); //average per-site norm.  nb. norm2(latt) = \sum_x norm2(latt[x]) 
+      Real impulse_abs = force_abs * ep * HMC_MOMENTUM_DENOMINATOR;    
+
+      Real force_max   = std::sqrt(maxLocalNorm2(level_force));
+      Real impulse_max = force_max * ep * HMC_MOMENTUM_DENOMINATOR;    
+      LevelForces[level].actions.at(0)->deriv_log(force_abs,force_max,impulse_abs,impulse_max);
+    }
+
     // Force from the other representations
     as[level].apply(update_P_hireps, Representations, Mom, U, ep);
 
@@ -216,6 +234,16 @@ public:
 
     //Default the momentum filter to "do-nothing"
     MomFilter = getDefaultMomFilter();
+
+    for (int level = 0; level < as.size(); ++level) {
+      int multiplier = as.at(level).multiplier;
+      ActionLevel<Field, RepresentationPolicy> * Level = new ActionLevel<Field, RepresentationPolicy>(multiplier);
+      Level->push_back(new EmptyAction<Field>); 
+      LevelForces.push_back(*Level);
+      // does it copy by value or reference??
+      // - answer it copies by value, BUT the action level contains a reference that is NOT updated.
+      // Unsafe code in Guido's area
+    }
   };
 
   virtual ~Integrator() {}
@@ -233,10 +261,14 @@ public:
 
   void reset_timer(void)
   {
+    assert(as.size()==LevelForces.size());
     for (int level = 0; level < as.size(); ++level) {
       for (int actionID = 0; actionID < as[level].actions.size(); ++actionID) {
         as[level].actions.at(actionID)->reset_timer();
       }
+      int actionID=0;
+      assert(LevelForces.at(level).actions.size()==1);
+      LevelForces.at(level).actions.at(actionID)->reset_timer();
     }
   }
   void print_timer(void)
@@ -298,6 +330,16 @@ public:
 		  <<" calls "     << as[level].actions.at(actionID)->deriv_num
 		  << std::endl;
       }
+      int actionID=0;
+      std::cout << GridLogMessage 
+		  << LevelForces[level].actions.at(actionID)->action_name()
+		  <<"["<<level<<"]["<< actionID<<"] :\n\t\t "
+		  <<" force max " << LevelForces[level].actions.at(actionID)->deriv_max_average()
+		  <<" norm "      << LevelForces[level].actions.at(actionID)->deriv_norm_average()
+		  <<" Fdt max  "  << LevelForces[level].actions.at(actionID)->Fdt_max_average()
+		  <<" Fdt norm "  << LevelForces[level].actions.at(actionID)->Fdt_norm_average()
+		  <<" calls "     << LevelForces[level].actions.at(actionID)->deriv_num
+		  << std::endl;
     }
     std::cout << GridLogMessage << ":::::::::::::::::::::::::::::::::::::::::"<< std::endl;
   }
@@ -319,6 +361,13 @@ public:
 	std::cout << as[level].actions.at(actionID)->LogParameters();
       }
     }
+    std::cout << " [Integrator] Total Force loggers: "<< LevelForces.size() <<std::endl;
+    for (int level = 0; level < LevelForces.size(); ++level) {
+      std::cout << GridLogMessage << "[Integrator] ---- Level: "<< level << std::endl;
+      for (int actionID = 0; actionID < LevelForces[level].actions.size(); ++actionID) {
+	std::cout << GridLogMessage << "["<< LevelForces[level].actions.at(actionID)->action_name() << "] ID: " << actionID << std::endl;
+      }
+    }
     std::cout << GridLogMessage << ":::::::::::::::::::::::::::::::::::::::::"<< std::endl;
   }
 
@@ -400,6 +449,7 @@ public:
   RealD S(Field& U) 
   {  // here also U not used
 
+    assert(as.size()==LevelForces.size());
     std::cout << GridLogIntegrator << "Integrator action\n";
 
     RealD H = - FieldImplementation::FieldSquareNorm(P)/HMC_MOMENTUM_DENOMINATOR; // - trace (P*P)/denom

Grid/qcd/representations/fundamental.h

@@ -13,7 +13,7 @@ NAMESPACE_BEGIN(Grid);
  * Empty since HMC updates already the fundamental representation 
  */
 
-template <int ncolour>
+template <int ncolour, class group_name>
 class FundamentalRep {
 public:
   static const int Dimension = ncolour;
@@ -21,7 +21,7 @@ public:
 
   // typdef to be used by the Representations class in HMC to get the
   // types for the higher representation fields
-  typedef typename SU<ncolour>::LatticeMatrix LatticeMatrix;
+  typedef typename GaugeGroup<ncolour,group_name>::LatticeMatrix LatticeMatrix;
   typedef LatticeGaugeField LatticeField;
   
   explicit FundamentalRep(GridBase* grid) {} //do nothing
@@ -45,7 +45,8 @@ public:
     
 
   
-typedef	 FundamentalRep<Nc> FundamentalRepresentation;
+typedef	 FundamentalRep<Nc,GroupName::SU> FundamentalRepresentation;
+typedef	 FundamentalRep<Nc,GroupName::Sp> SpFundamentalRepresentation;
 
 NAMESPACE_END(Grid);  
 

Grid/qcd/representations/two_index.h

@@ -20,14 +20,14 @@ NAMESPACE_BEGIN(Grid);
  * in the SUnTwoIndex.h file
  */
 
-template <int ncolour, TwoIndexSymmetry S>
+template <int ncolour, TwoIndexSymmetry S, class group_name = GroupName::SU>
 class TwoIndexRep {
 public:
   // typdef to be used by the Representations class in HMC to get the
   // types for the higher representation fields
-  typedef typename SU_TwoIndex<ncolour, S>::LatticeTwoIndexMatrix LatticeMatrix;
-  typedef typename SU_TwoIndex<ncolour, S>::LatticeTwoIndexField LatticeField;
-  static const int Dimension = ncolour * (ncolour + S) / 2;
+  typedef typename GaugeGroupTwoIndex<ncolour, S, group_name>::LatticeTwoIndexMatrix LatticeMatrix;
+  typedef typename GaugeGroupTwoIndex<ncolour, S, group_name>::LatticeTwoIndexField LatticeField;
+  static const int Dimension = GaugeGroupTwoIndex<ncolour,S,group_name>::Dimension;
   static const bool isFundamental = false;
 
   LatticeField U;
@@ -43,10 +43,10 @@ public:
     U = Zero();
     LatticeColourMatrix tmp(Uin.Grid());
 
-    Vector<typename SU<ncolour>::Matrix> eij(Dimension);
+    Vector<typename GaugeGroup<ncolour,group_name>::Matrix> eij(Dimension);
 
     for (int a = 0; a < Dimension; a++)
-      SU_TwoIndex<ncolour, S>::base(a, eij[a]);
+      GaugeGroupTwoIndex<ncolour, S, group_name>::base(a, eij[a]);
 
     for (int mu = 0; mu < Nd; mu++) {
       auto Uin_mu = peekLorentz(Uin, mu);
@@ -71,7 +71,7 @@ public:
 
       out_mu = Zero();
 
-      typename SU<ncolour>::LatticeAlgebraVector h(in.Grid());
+      typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector h(in.Grid());
       projectOnAlgebra(h, in_mu, double(Nc + 2 * S));  // factor T(r)/T(fund)
       FundamentalLieAlgebraMatrix(h, out_mu);          // apply scale only once
       pokeLorentz(out, out_mu, mu);
@@ -80,20 +80,23 @@ public:
   }
 
 private:
-  void projectOnAlgebra(typename SU<ncolour>::LatticeAlgebraVector &h_out,
+  void projectOnAlgebra(typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
                         const LatticeMatrix &in, Real scale = 1.0) const {
-    SU_TwoIndex<ncolour, S>::projectOnAlgebra(h_out, in, scale);
+    GaugeGroupTwoIndex<ncolour, S,group_name>::projectOnAlgebra(h_out, in, scale);
   }
 
   void FundamentalLieAlgebraMatrix(
-				   typename SU<ncolour>::LatticeAlgebraVector &h,
-				   typename SU<ncolour>::LatticeMatrix &out, Real scale = 1.0) const {
-    SU<ncolour>::FundamentalLieAlgebraMatrix(h, out, scale);
+				   typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h,
+				   typename GaugeGroup<ncolour, group_name>::LatticeMatrix &out, Real scale = 1.0) const {
+    GaugeGroup<ncolour,group_name>::FundamentalLieAlgebraMatrix(h, out, scale);
   }
 };
 
-typedef TwoIndexRep<Nc, Symmetric> TwoIndexSymmetricRepresentation;
-typedef TwoIndexRep<Nc, AntiSymmetric> TwoIndexAntiSymmetricRepresentation;
+typedef TwoIndexRep<Nc, Symmetric, GroupName::SU> TwoIndexSymmetricRepresentation;
+typedef TwoIndexRep<Nc, AntiSymmetric, GroupName::SU> TwoIndexAntiSymmetricRepresentation;
+
+typedef TwoIndexRep<Nc, Symmetric, GroupName::Sp> SpTwoIndexSymmetricRepresentation;
+typedef TwoIndexRep<Nc, AntiSymmetric, GroupName::Sp> SpTwoIndexAntiSymmetricRepresentation;
 
 NAMESPACE_END(Grid);
 

Grid/qcd/smearing/GaugeConfigurationMasked.h

@@ -1,3 +1,4 @@
+
 /*!
   @file GaugeConfiguration.h
   @brief Declares the GaugeConfiguration class
@@ -6,6 +7,15 @@
 
 NAMESPACE_BEGIN(Grid);
 
+
+template<class T> void Dump(const Lattice<T> & lat,
+			    std::string s,
+			    Coordinate site = Coordinate({0,0,0,0}))
+{
+  typename T::scalar_object tmp;
+  peekSite(tmp,lat,site);
+  std::cout << " Dump "<<s<<" "<<tmp<<std::endl;
+}
 /*!
   @brief Smeared configuration masked container
   Modified for a multi-subset smearing (aka Luscher Flowed HMC)
@@ -28,6 +38,101 @@ private:
   typedef typename SU3Adjoint::LatticeAdjMatrix  AdjMatrixField;
   typedef typename SU3Adjoint::LatticeAdjVector  AdjVectorField;
 
+  void BaseSmearDerivative(GaugeField& SigmaTerm,
+			   const GaugeField& iLambda,
+			   const GaugeField& U,
+			   int mmu, RealD rho)
+  {
+    // Reference
+    // Morningstar, Peardon, Phys.Rev.D69,054501(2004)
+    // Equation 75
+    // Computing Sigma_mu, derivative of S[fat links] with respect to the thin links
+    // Output SigmaTerm
+
+    GridBase *grid = U.Grid();
+
+    WilsonLoops<Gimpl> WL;
+    GaugeLinkField staple(grid), u_tmp(grid);
+    GaugeLinkField iLambda_mu(grid), iLambda_nu(grid);
+    GaugeLinkField U_mu(grid), U_nu(grid);
+    GaugeLinkField sh_field(grid), temp_Sigma(grid);
+    Real rho_munu, rho_numu;
+
+    rho_munu = rho;
+    rho_numu = rho;
+    for(int mu = 0; mu < Nd; ++mu){
+      U_mu       = peekLorentz(      U, mu);
+      iLambda_mu = peekLorentz(iLambda, mu);
+
+      for(int nu = 0; nu < Nd; ++nu){
+	if(nu==mu) continue;
+
+	U_nu       = peekLorentz(      U, nu);
+
+	// Nd(nd-1) = 12 staples normally.
+	// We must compute 6 of these
+	// in FTHMC case
+	if ( (mu==mmu)||(nu==mmu) )
+	  WL.StapleUpper(staple, U, mu, nu);
+	
+	if(nu==mmu) {
+	  iLambda_nu = peekLorentz(iLambda, nu);
+
+	  temp_Sigma = -rho_numu*staple*iLambda_nu;  //ok
+	  //-r_numu*U_nu(x+mu)*Udag_mu(x+nu)*Udag_nu(x)*Lambda_nu(x)
+	  Gimpl::AddLink(SigmaTerm, temp_Sigma, mu);
+
+	  sh_field = Cshift(iLambda_nu, mu, 1);// general also for Gparity?
+
+	  temp_Sigma = rho_numu*sh_field*staple; //ok
+	  //r_numu*Lambda_nu(mu)*U_nu(x+mu)*Udag_mu(x+nu)*Udag_nu(x)
+	  Gimpl::AddLink(SigmaTerm, temp_Sigma, mu);
+	}
+
+	if ( mu == mmu ) { 
+	  sh_field = Cshift(iLambda_mu, nu, 1);
+
+	  temp_Sigma = -rho_munu*staple*U_nu*sh_field*adj(U_nu); //ok
+	  //-r_munu*U_nu(x+mu)*Udag_mu(x+nu)*Lambda_mu(x+nu)*Udag_nu(x)
+	  Gimpl::AddLink(SigmaTerm, temp_Sigma, mu);
+	}
+
+	//	staple = Zero();
+	sh_field = Cshift(U_nu, mu, 1);
+
+	temp_Sigma = Zero();
+
+	if ( mu == mmu )
+	  temp_Sigma = -rho_munu*adj(sh_field)*adj(U_mu)*iLambda_mu*U_nu;
+
+	if ( nu == mmu ) {
+	  temp_Sigma += rho_numu*adj(sh_field)*adj(U_mu)*iLambda_nu*U_nu;
+
+	  u_tmp = adj(U_nu)*iLambda_nu;
+	  sh_field = Cshift(u_tmp, mu, 1);
+	  temp_Sigma += -rho_numu*sh_field*adj(U_mu)*U_nu;
+	}
+	
+	sh_field = Cshift(temp_Sigma, nu, -1);
+	Gimpl::AddLink(SigmaTerm, sh_field, mu);
+
+      }
+    }
+  }
+  
+  void BaseSmear(GaugeLinkField& Cup, const GaugeField& U,int mu,RealD rho) {
+    GridBase *grid = U.Grid();
+    GaugeLinkField tmp_stpl(grid);
+    WilsonLoops<Gimpl> WL;
+    Cup = Zero();
+    for(int nu=0; nu<Nd; ++nu){
+      if (nu != mu) {
+	// get the staple in direction mu, nu
+	WL.Staple(tmp_stpl, U, mu, nu);  //nb staple conventions of IroIro and Grid differ by a dagger
+	Cup += adj(tmp_stpl*rho);
+      }
+    }
+  }
   // Adjoint vector to GaugeField force
   void InsertForce(GaugeField &Fdet,AdjVectorField &Fdet_nu,int nu)
   {
@@ -47,27 +152,54 @@ private:
     GaugeLinkField UtaU(PlaqL.Grid());
     GaugeLinkField D(PlaqL.Grid());
     AdjMatrixField Dbc(PlaqL.Grid());
+    AdjMatrixField Dbc_opt(PlaqL.Grid());
     LatticeComplex tmp(PlaqL.Grid());
     const int Ngen = SU3Adjoint::Dimension;
     Complex ci(0,1);
     ColourMatrix   ta,tb,tc;
-    
+    RealD t=0;
+    RealD tp=0;
+    RealD tta=0;
+    RealD tpk=0;
+    t-=usecond();
     for(int a=0;a<Ngen;a++) {
+      tta-=usecond();
       SU3::generator(a, ta);
+      ta = 2.0 * ci * ta;
       // Qlat Tb = 2i Tb^Grid
-      UtaU= 2.0*ci*adj(PlaqL)*ta*PlaqR;
+      UtaU= adj(PlaqL)*ta*PlaqR; // 6ms
+      tta+=usecond();
+      ////////////////////////////////////////////
+      // Could add this entire C-loop to a projection routine
+      // for performance. Could also pick checkerboard on UtaU
+      // and set checkerboard on result for 2x perf
+      ////////////////////////////////////////////
       for(int c=0;c<Ngen;c++) {
 	SU3::generator(c, tc);
-	D = Ta( (2.0)*ci*tc *UtaU);
+	tc = 2.0*ci*tc;
+	tp-=usecond(); 
+	D = Ta( tc *UtaU); // 2ms
+#if 1
+	SU3::LieAlgebraProject(Dbc_opt,D,c); // 5.5ms
+#else
 	for(int b=0;b<Ngen;b++){
 	  SU3::generator(b, tb);
 	  tmp =-trace(ci*tb*D); 
 	  PokeIndex<ColourIndex>(Dbc,tmp,b,c);  // Adjoint rep
 	}
+#endif
+	tp+=usecond();
       }
-      tmp = trace(MpInvJx * Dbc);
+      //      Dump(Dbc_opt,"Dbc_opt");
+      //      Dump(Dbc,"Dbc");
+      tpk-=usecond();
+      tmp = trace(MpInvJx * Dbc_opt);
       PokeIndex<ColourIndex>(Fdet2,tmp,a);
+      tpk+=usecond();
     }
+    t+=usecond();
+    std::cout << GridLogPerformance << " Compute_MpInvJx_dNxxdSy " << t/1e3 << " ms  proj "<<tp/1e3<< " ms"
+	      << " ta "<<tta/1e3<<" ms" << " poke "<<tpk/1e3<< " ms"<<std::endl;
   }
   
   void ComputeNxy(const GaugeLinkField &PlaqL,const GaugeLinkField &PlaqR,AdjMatrixField &NxAd)
@@ -79,12 +211,17 @@ private:
     ColourMatrix   tc;
     for(int b=0;b<Ngen;b++) {
       SU3::generator(b, tb);
-      Nx = (2.0)*Ta( adj(PlaqL)*ci*tb * PlaqR );
+      tb = 2.0 * ci * tb;
+      Nx = Ta( adj(PlaqL)*tb * PlaqR );
+#if 1
+      SU3::LieAlgebraProject(NxAd,Nx,b);
+#else
       for(int c=0;c<Ngen;c++) {
 	SU3::generator(c, tc);
 	auto tmp =closure( -trace(ci*tc*Nx)); 
 	PokeIndex<ColourIndex>(NxAd,tmp,c,b); 
       }
+#endif
     }
   }
   void ApplyMask(GaugeField &U,int smr)
@@ -164,8 +301,7 @@ public:
     // Computes ALL the staples -- could compute one only and do it here
     RealD time;
     time=-usecond();
-    this->StoutSmearing->BaseSmear(C, U);
-    Cmu = peekLorentz(C, mu);
+    BaseSmear(Cmu, U,mu,rho);
 
     //////////////////////////////////////////////////////////////////
     // Assemble Luscher exp diff map J matrix 
@@ -209,6 +345,36 @@ public:
     // dJ(x)/dxe
     //////////////////////////////////////
     time=-usecond();
+#if 1
+    std::vector<AdjMatrixField>  dJdX;    dJdX.resize(8,grid);
+    std::vector<AdjMatrix> TRb_s; TRb_s.resize(8);
+    AdjMatrixField tbXn(grid);
+    AdjMatrixField sumXtbX(grid);
+    AdjMatrixField t2(grid);
+    AdjMatrixField dt2(grid);
+    AdjMatrixField t3(grid);
+    AdjMatrixField dt3(grid);
+    AdjMatrixField aunit(grid);
+
+    for(int b=0;b<8;b++){
+      SU3Adjoint::generator(b, TRb_s[b]);
+      dJdX[b] = TRb_s[b];
+    }
+    aunit = ComplexD(1.0);
+    // Could put into an accelerator_for
+    X  = (-1.0)*ZxAd; 
+    t2 = X;
+    for (int j = 12; j > 1; --j) {
+      t3  = t2*(1.0 / (j + 1))  + aunit;
+      t2  = X * t3;
+      for(int b=0;b<8;b++){
+	dJdX[b]= TRb_s[b] * t3 + X * dJdX[b]*(1.0 / (j + 1));
+      }
+    }
+    for(int b=0;b<8;b++){
+      dJdX[b] = -dJdX[b];
+    }
+#else
     std::vector<AdjMatrixField>  dJdX;    dJdX.resize(8,grid);
     AdjMatrixField tbXn(grid);
     AdjMatrixField sumXtbX(grid);
@@ -224,7 +390,7 @@ public:
       X  = (-1.0)*ZxAd; 
       t2 = X;
       dt2 = TRb;
-      for (int j = 20; j > 1; --j) {
+      for (int j = 12; j > 1; --j) {
 	t3  = t2*(1.0 / (j + 1))  + aunit;
 	dt3 = dt2*(1.0 / (j + 1));
 	t2 = X * t3;
@@ -232,6 +398,7 @@ public:
       }
       dJdX[b] = -dt2; 
     }
+#endif  
     time+=usecond();
     std::cout << GridLogMessage << "dJx took "<<time<< " us"<<std::endl;
     /////////////////////////////////////////////////////////////////
@@ -281,8 +448,8 @@ public:
     
     for(int e =0 ; e<8 ; e++){
       LatticeComplexD tr(grid);
-      ColourMatrix te;
-      SU3::generator(e, te);
+      //      ColourMatrix te;
+      //      SU3::generator(e, te);
       tr = trace(dJdX[e] * nMpInv);
       pokeColour(dJdXe_nMpInv,tr,e);
     }
@@ -493,20 +660,25 @@ public:
     //////////////////////////////////////////////////////////////////
     // Assemble the N matrix
     //////////////////////////////////////////////////////////////////
-    // Computes ALL the staples -- could compute one only here
-    this->StoutSmearing->BaseSmear(C, U);
-    Cmu = peekLorentz(C, mu);
+    double rho=this->StoutSmearing->SmearRho[1];
+    BaseSmear(Cmu, U,mu,rho);
+
     Umu = peekLorentz(U, mu);
     Complex ci(0,1);
     for(int b=0;b<Ngen;b++) {
       SU3::generator(b, Tb);
       // Qlat Tb = 2i Tb^Grid
       Nb = (2.0)*Ta( ci*Tb * Umu * adj(Cmu));
+      // FIXME -- replace this with LieAlgebraProject
+#if 0
+      SU3::LieAlgebraProject(Ncb,tmp,b);
+#else
       for(int c=0;c<Ngen;c++) {
 	SU3::generator(c, Tc);
 	auto tmp = -trace(ci*Tc*Nb); // Luchang's norm: (2Tc) (2Td) N^db = -2 delta cd N^db // - was important
 	PokeIndex<ColourIndex>(Ncb,tmp,c,b); 
       }
+#endif
     }      
 
     //////////////////////////////////////////////////////////////////
@@ -693,7 +865,7 @@ private:
 					  const GaugeField& GaugeK,int level) 
   {
     GridBase* grid = GaugeK.Grid();
-    GaugeField C(grid), SigmaK(grid), iLambda(grid);
+    GaugeField SigmaK(grid), iLambda(grid);
     GaugeField SigmaKPrimeA(grid);
     GaugeField SigmaKPrimeB(grid);
     GaugeLinkField iLambda_mu(grid);
@@ -701,7 +873,11 @@ private:
     GaugeLinkField SigmaKPrime_mu(grid);
     GaugeLinkField GaugeKmu(grid), Cmu(grid);
 
-    this->StoutSmearing->BaseSmear(C, GaugeK);
+    int mmu= (level/2) %Nd;
+    int cb= (level%2);
+    double rho=this->StoutSmearing->SmearRho[1];
+
+    // Can override this to do one direction only.
     SigmaK = Zero();
     iLambda = Zero();
 
@@ -712,18 +888,38 @@ private:
     // Could get away with computing only one polarisation here
     // int mu= (smr/2) %Nd;
     // SigmaKprime_A has only one component
-    for (int mu = 0; mu < Nd; mu++)
-    {
-      Cmu = peekLorentz(C, mu);
+#if 0
+    BaseSmear(Cmu, GaugeK,mu,rho);
     GaugeKmu = peekLorentz(GaugeK, mu);
     SigmaKPrime_mu = peekLorentz(SigmaKPrimeA, mu);
     iQ = Ta(Cmu * adj(GaugeKmu));
     this->set_iLambda(iLambda_mu, e_iQ, iQ, SigmaKPrime_mu, GaugeKmu);
     pokeLorentz(SigmaK, SigmaKPrime_mu * e_iQ + adj(Cmu) * iLambda_mu, mu);
     pokeLorentz(iLambda, iLambda_mu, mu);
+    BaseSmearDerivative(SigmaK, iLambda,GaugeK,mu,rho);  // derivative of SmearBase
+#else
+    //    GaugeField C(grid);
+    //    this->StoutSmearing->BaseSmear(C, GaugeK);
+    //    for (int mu = 0; mu < Nd; mu++)
+    int mu =mmu;
+    BaseSmear(Cmu, GaugeK,mu,rho);
+    {
+      // Cmu = peekLorentz(C, mu);
+      GaugeKmu = peekLorentz(GaugeK, mu);
+      SigmaKPrime_mu = peekLorentz(SigmaKPrimeA, mu);
+      iQ = Ta(Cmu * adj(GaugeKmu));
+      this->set_iLambda(iLambda_mu, e_iQ, iQ, SigmaKPrime_mu, GaugeKmu);
+      pokeLorentz(SigmaK, SigmaKPrime_mu * e_iQ + adj(Cmu) * iLambda_mu, mu);
+      pokeLorentz(iLambda, iLambda_mu, mu);
+      std::cout << " mu "<<mu<<" SigmaKPrime_mu"<<norm2(SigmaKPrime_mu)<< " iLambda_mu " <<norm2(iLambda_mu)<<std::endl;
     }
-    this->StoutSmearing->derivative(SigmaK, iLambda,GaugeK);  // derivative of SmearBase
-
+    //    GaugeField SigmaKcopy(grid);
+    //    SigmaKcopy = SigmaK;
+    BaseSmearDerivative(SigmaK, iLambda,GaugeK,mu,rho);  // derivative of SmearBase
+    //    this->StoutSmearing->derivative(SigmaK, iLambda,GaugeK);  // derivative of SmearBase
+    //    SigmaKcopy = SigmaKcopy - SigmaK;
+    //    std::cout << " BaseSmearDerivative fast path error" <<norm2(SigmaKcopy)<<std::endl;
+#endif
     ////////////////////////////////////////////////////////////////////////////////////
     // propagate the rest of the force as identity map, just add back
     ////////////////////////////////////////////////////////////////////////////////////

Grid/qcd/smearing/HISQSmearing.h

@@ -0,0 +1,389 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/qcd/smearing/HISQSmearing.h
+
+Copyright (C) 2023
+
+Author: D. A. Clarke <clarke.davida@gmail.com> 
+
+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
+*************************************************************************************/
+/*
+    @file HISQSmearing.h
+    @brief Declares classes related to HISQ smearing 
+*/
+
+
+#pragma once
+#include <Grid/Grid.h>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+
+NAMESPACE_BEGIN(Grid);
+
+
+// TODO: find a way to fold this into the stencil header. need to access grid to get
+// Nd, since you don't want to inherit from QCD.h
+/*!  @brief append arbitrary shift path to shifts */
+template<typename... Args>
+void appendShift(std::vector<Coordinate>& shifts, int dir, Args... args) {
+    Coordinate shift(Nd,0);
+    generalShift(shift, dir, args...); 
+    // push_back creates an element at the end of shifts and
+    // assigns the data in the argument to it.
+    shifts.push_back(shift);
+}
+
+
+/*!  @brief figure out the stencil index from mu and nu */
+accelerator_inline int stencilIndex(int mu, int nu) {
+    // Nshifts depends on how you built the stencil
+    int Nshifts = 6;
+    return Nshifts*nu + Nd*Nshifts*mu;
+}
+
+
+/*!  @brief structure holding the link treatment */
+struct SmearingParameters{
+    SmearingParameters(){}
+    Real c_1;               // 1 link
+    Real c_naik;            // Naik term
+    Real c_3;               // 3 link
+    Real c_5;               // 5 link
+    Real c_7;               // 7 link
+    Real c_lp;              // 5 link Lepage
+    SmearingParameters(Real c1, Real cnaik, Real c3, Real c5, Real c7, Real clp) 
+        : c_1(c1),
+          c_naik(cnaik),
+          c_3(c3),
+          c_5(c5),
+          c_7(c7),
+          c_lp(clp){}
+};
+
+
+/*!  @brief create fat links from link variables */
+template<class Gimpl> 
+class Smear_HISQ : public Gimpl {
+
+private:
+    GridCartesian* const _grid;
+    SmearingParameters _linkTreatment;
+
+public:
+
+    INHERIT_GIMPL_TYPES(Gimpl);
+    typedef typename Gimpl::GaugeField     GF;
+    typedef typename Gimpl::GaugeLinkField LF;
+    typedef typename Gimpl::ComplexField   CF;
+
+    // Don't allow default values here.
+    Smear_HISQ(GridCartesian* grid, Real c1, Real cnaik, Real c3, Real c5, Real c7, Real clp) 
+        : _grid(grid), 
+          _linkTreatment(c1,cnaik,c3,c5,c7,clp) {
+        assert(Nc == 3 && "HISQ smearing currently implemented only for Nc==3");
+        assert(Nd == 4 && "HISQ smearing only defined for Nd==4");
+    }
+
+    // Allow to pass a pointer to a C-style, double array for MILC convenience
+    Smear_HISQ(GridCartesian* grid, double* coeff) 
+        : _grid(grid), 
+          _linkTreatment(coeff[0],coeff[1],coeff[2],coeff[3],coeff[4],coeff[5]) {
+        assert(Nc == 3 && "HISQ smearing currently implemented only for Nc==3");
+        assert(Nd == 4 && "HISQ smearing only defined for Nd==4");
+    }
+
+    ~Smear_HISQ() {}
+
+    // Intent: OUT--u_smr, u_naik
+    //          IN--u_thin
+    void smear(GF& u_smr, GF& u_naik, GF& u_thin) const {
+
+        SmearingParameters lt = this->_linkTreatment;
+        auto grid = this->_grid;
+
+        // Create a padded cell of extra padding depth=1 and fill the padding.
+        int depth = 1;
+        PaddedCell Ghost(depth,grid);
+        GF Ughost = Ghost.Exchange(u_thin);
+
+        // This is where auxiliary N-link fields and the final smear will be stored. 
+        GF Ughost_fat(Ughost.Grid());
+        GF Ughost_3link(Ughost.Grid());
+        GF Ughost_5linkA(Ughost.Grid());
+        GF Ughost_5linkB(Ughost.Grid());
+
+        // mu-nu plane stencil. We allow mu==nu to make indexing the stencil easier,
+        // but these entries will not be used. 
+        std::vector<Coordinate> shifts;
+        for(int mu=0;mu<Nd;mu++)
+        for(int nu=0;nu<Nd;nu++) {
+            appendShift(shifts,mu);
+            appendShift(shifts,nu);
+            appendShift(shifts,shiftSignal::NO_SHIFT);
+            appendShift(shifts,mu,Back(nu));
+            appendShift(shifts,Back(nu));
+            appendShift(shifts,Back(mu));
+        }
+
+        // A GeneralLocalStencil has two indices: a site and stencil index 
+        GeneralLocalStencil gStencil(Ughost.Grid(),shifts);
+
+        // This is where contributions from the smearing get added together
+        Ughost_fat=Zero();
+
+        // This loop handles 3-, 5-, and 7-link constructs, minus Lepage and Naik.
+        for(int mu=0;mu<Nd;mu++) {
+
+            // TODO: This approach is slightly memory inefficient. It uses 25% extra memory 
+            Ughost_3link =Zero();
+            Ughost_5linkA=Zero();
+            Ughost_5linkB=Zero();
+
+            // Create the accessors
+            autoView(U_v       , Ughost       , AcceleratorRead);
+            autoView(U_fat_v   , Ughost_fat   , AcceleratorWrite);
+            autoView(U_3link_v , Ughost_3link , AcceleratorWrite);
+            autoView(U_5linkA_v, Ughost_5linkA, AcceleratorWrite);
+            autoView(U_5linkB_v, Ughost_5linkB, AcceleratorWrite);
+
+            // We infer some types that will be needed in the calculation.
+            typedef decltype(gStencil.GetEntry(0,0)) stencilElement;
+            typedef decltype(coalescedReadGeneralPermute(U_v[0](0),gStencil.GetEntry(0,0)->_permute,Nd)) U3matrix;
+
+            int Nsites = U_v.size();
+            auto gStencil_v = gStencil.View(); 
+
+            accelerator_for(site,Nsites,Simd::Nsimd(),{ // ----------- 3-link constructs
+                stencilElement SE0, SE1, SE2, SE3, SE4, SE5;
+                U3matrix U0, U1, U2, U3, U4, U5, W;
+                for(int nu=0;nu<Nd;nu++) {
+                    if(nu==mu) continue;
+                    int s = stencilIndex(mu,nu);
+
+                    // The stencil gives us support points in the mu-nu plane that we will use to
+                    // grab the links we need.
+                    SE0 = gStencil_v.GetEntry(s+0,site); int x_p_mu      = SE0->_offset;
+                    SE1 = gStencil_v.GetEntry(s+1,site); int x_p_nu      = SE1->_offset;
+                    SE2 = gStencil_v.GetEntry(s+2,site); int x           = SE2->_offset;
+                    SE3 = gStencil_v.GetEntry(s+3,site); int x_p_mu_m_nu = SE3->_offset;
+                    SE4 = gStencil_v.GetEntry(s+4,site); int x_m_nu      = SE4->_offset;
+                    SE5 = gStencil_v.GetEntry(s+5,site); int x_m_mu      = SE5->_offset;
+
+                    // When you're deciding whether to take an adjoint, the question is: how is the
+                    // stored link oriented compared to the one you want? If I imagine myself travelling
+                    // with the to-be-updated link, I have two possible, alternative 3-link paths I can
+                    // take, one starting by going to the left, the other starting by going to the right.
+                    U0 = coalescedReadGeneralPermute(U_v[x_p_mu     ](nu),SE0->_permute,Nd);
+                    U1 = coalescedReadGeneralPermute(U_v[x_p_nu     ](mu),SE1->_permute,Nd);
+                    U2 = coalescedReadGeneralPermute(U_v[x          ](nu),SE2->_permute,Nd);
+                    U3 = coalescedReadGeneralPermute(U_v[x_p_mu_m_nu](nu),SE3->_permute,Nd);
+                    U4 = coalescedReadGeneralPermute(U_v[x_m_nu     ](mu),SE4->_permute,Nd);
+                    U5 = coalescedReadGeneralPermute(U_v[x_m_nu     ](nu),SE4->_permute,Nd);
+
+                    //  "left"          "right"
+                    W = U2*U1*adj(U0) + adj(U5)*U4*U3;
+
+                    // Save 3-link construct for later and add to smeared field.
+                    coalescedWrite(U_3link_v[x](nu), W);
+
+                    // The index operator (x) returns the coalesced read on GPU. The view [] index returns 
+                    // a reference to the vector object. The [x](mu) returns a reference to the densely 
+                    // packed (contiguous in memory) mu-th element of the vector object. On CPU, 
+                    // coalescedRead/Write is the identity mapping assigning vector object to vector object.
+                    // But on GPU it's non-trivial and maps scalar object to vector object and vice versa.
+                    coalescedWrite(U_fat_v[x](mu), U_fat_v(x)(mu) + lt.c_3*W);
+                }
+            })
+
+            accelerator_for(site,Nsites,Simd::Nsimd(),{ // ----------- 5-link 
+                stencilElement SE0, SE1, SE2, SE3, SE4, SE5;
+                U3matrix U0, U1, U2, U3, U4, U5, W;
+                int sigmaIndex = 0;
+                for(int nu=0;nu<Nd;nu++) {
+                    if(nu==mu) continue;
+                    int s = stencilIndex(mu,nu);
+                    for(int rho=0;rho<Nd;rho++) {
+                        if (rho == mu || rho == nu) continue;
+
+                        SE0 = gStencil_v.GetEntry(s+0,site); int x_p_mu      = SE0->_offset;
+                        SE1 = gStencil_v.GetEntry(s+1,site); int x_p_nu      = SE1->_offset;
+                        SE2 = gStencil_v.GetEntry(s+2,site); int x           = SE2->_offset;
+                        SE3 = gStencil_v.GetEntry(s+3,site); int x_p_mu_m_nu = SE3->_offset;
+                        SE4 = gStencil_v.GetEntry(s+4,site); int x_m_nu      = SE4->_offset;
+
+                        U0 = coalescedReadGeneralPermute(      U_v[x_p_mu     ](nu ),SE0->_permute,Nd);
+                        U1 = coalescedReadGeneralPermute(U_3link_v[x_p_nu     ](rho),SE1->_permute,Nd);
+                        U2 = coalescedReadGeneralPermute(      U_v[x          ](nu ),SE2->_permute,Nd);
+                        U3 = coalescedReadGeneralPermute(      U_v[x_p_mu_m_nu](nu ),SE3->_permute,Nd);
+                        U4 = coalescedReadGeneralPermute(U_3link_v[x_m_nu     ](rho),SE4->_permute,Nd);
+                        U5 = coalescedReadGeneralPermute(      U_v[x_m_nu     ](nu ),SE4->_permute,Nd);
+
+                        W  = U2*U1*adj(U0) + adj(U5)*U4*U3;
+
+                        if(sigmaIndex<3) {
+                            coalescedWrite(U_5linkA_v[x](rho), W);
+                        } else {
+                            coalescedWrite(U_5linkB_v[x](rho), W);
+                        }    
+
+                        coalescedWrite(U_fat_v[x](mu), U_fat_v(x)(mu) + lt.c_5*W);
+                        sigmaIndex++;
+                    }
+                }
+            })
+
+            accelerator_for(site,Nsites,Simd::Nsimd(),{ // ----------- 7-link
+                stencilElement SE0, SE1, SE2, SE3, SE4, SE5;
+                U3matrix U0, U1, U2, U3, U4, U5, W;
+                int sigmaIndex = 0;
+                for(int nu=0;nu<Nd;nu++) {
+                    if(nu==mu) continue;
+                    int s = stencilIndex(mu,nu);
+                    for(int rho=0;rho<Nd;rho++) {
+                        if (rho == mu || rho == nu) continue;
+
+                        SE0 = gStencil_v.GetEntry(s+0,site); int x_p_mu      = SE0->_offset;
+                        SE1 = gStencil_v.GetEntry(s+1,site); int x_p_nu      = SE1->_offset;
+                        SE2 = gStencil_v.GetEntry(s+2,site); int x           = SE2->_offset;
+                        SE3 = gStencil_v.GetEntry(s+3,site); int x_p_mu_m_nu = SE3->_offset;
+                        SE4 = gStencil_v.GetEntry(s+4,site); int x_m_nu      = SE4->_offset;
+
+                        U0 = coalescedReadGeneralPermute(U_v[x_p_mu](nu),SE0->_permute,Nd);
+                        if(sigmaIndex<3) {
+                            U1 = coalescedReadGeneralPermute(U_5linkB_v[x_p_nu](rho),SE1->_permute,Nd);
+                        } else {
+                            U1 = coalescedReadGeneralPermute(U_5linkA_v[x_p_nu](rho),SE1->_permute,Nd);
+                        }  
+                        U2 = coalescedReadGeneralPermute(U_v[x](nu),SE2->_permute,Nd);
+                        U3 = coalescedReadGeneralPermute(U_v[x_p_mu_m_nu](nu),SE3->_permute,Nd);
+                        if(sigmaIndex<3) {
+                            U4 = coalescedReadGeneralPermute(U_5linkB_v[x_m_nu](rho),SE4->_permute,Nd);
+                        } else {
+                            U4 = coalescedReadGeneralPermute(U_5linkA_v[x_m_nu](rho),SE4->_permute,Nd);
+                        }  
+                        U5 = coalescedReadGeneralPermute(U_v[x_m_nu](nu),SE4->_permute,Nd);
+
+                        W  = U2*U1*adj(U0) + adj(U5)*U4*U3;
+
+                        coalescedWrite(U_fat_v[x](mu), U_fat_v(x)(mu) + lt.c_7*W);
+                        sigmaIndex++;
+                    }
+                }
+            })
+
+        } // end mu loop
+
+        // c1, c3, c5, c7 construct contributions
+        u_smr = Ghost.Extract(Ughost_fat) + lt.c_1*u_thin;
+
+        // Load up U and V std::vectors to access thin and smeared links.
+        std::vector<LF> U(Nd, grid);
+        std::vector<LF> V(Nd, grid);
+        std::vector<LF> Vnaik(Nd, grid);
+        for (int mu = 0; mu < Nd; mu++) {
+            U[mu] = PeekIndex<LorentzIndex>(u_thin, mu);
+            V[mu] = PeekIndex<LorentzIndex>(u_smr, mu);
+        }
+
+        for(int mu=0;mu<Nd;mu++) {
+
+            // Naik
+            Vnaik[mu] = lt.c_naik*Gimpl::CovShiftForward(U[mu],mu,
+                                    Gimpl::CovShiftForward(U[mu],mu,
+                                      Gimpl::CovShiftIdentityForward(U[mu],mu)));
+
+            // LePage
+            for (int nu_h=1;nu_h<Nd;nu_h++) {
+                int nu=(mu+nu_h)%Nd;
+                                // nu, nu, mu, Back(nu), Back(nu)
+                V[mu] = V[mu] + lt.c_lp*Gimpl::CovShiftForward(U[nu],nu,
+                                          Gimpl::CovShiftForward(U[nu],nu,
+                                            Gimpl::CovShiftForward(U[mu],mu,
+                                              Gimpl::CovShiftBackward(U[nu],nu,
+                                                Gimpl::CovShiftIdentityBackward(U[nu],nu)))))
+                                // Back(nu), Back(nu), mu, nu, nu
+                              + lt.c_lp*Gimpl::CovShiftBackward(U[nu],nu,
+                                          Gimpl::CovShiftBackward(U[nu],nu,
+                                            Gimpl::CovShiftForward(U[mu],mu,
+                                              Gimpl::CovShiftForward(U[nu],nu,
+                                                Gimpl::CovShiftIdentityForward(U[nu],nu)))));
+            }
+        }
+
+        // Put V back into u_smr.
+        for (int mu = 0; mu < Nd; mu++) {
+            PokeIndex<LorentzIndex>(u_smr , V[mu]    , mu);
+            PokeIndex<LorentzIndex>(u_naik, Vnaik[mu], mu);
+        }
+    };
+
+
+    // Intent: OUT--u_proj
+    //          IN--u_mu
+    void projectU3(GF& u_proj, GF& u_mu) const {
+
+        auto grid = this->_grid;
+
+        LF V(grid), Q(grid), sqrtQinv(grid), id_3(grid), diff(grid);
+        CF c0(grid), c1(grid), c2(grid), g0(grid), g1(grid), g2(grid), S(grid), R(grid), theta(grid), 
+           u(grid), v(grid), w(grid), den(grid), f0(grid), f1(grid), f2(grid);
+
+        // Follow MILC 10.1103/PhysRevD.82.074501, eqs (B2-B3) and (C1-C8)
+        for (int mu = 0; mu < Nd; mu++) {
+            V  = PeekIndex<LorentzIndex>(u_mu, mu);
+            Q  = adj(V)*V;
+            c0 =        real(trace(Q));
+            c1 = (1/2.)*real(trace(Q*Q));
+            c2 = (1/3.)*real(trace(Q*Q*Q));
+            S  = (1/3.)*c1-(1/18.)*c0*c0;
+            if (norm2(S)<1e-28) {
+                g0 = (1/3.)*c0; g1 = g0; g2 = g1;
+            } else {
+                R     = (1/2.)*c2-(1/3. )*c0*c1+(1/27.)*c0*c0*c0;
+                theta = acos(R*pow(S,-1.5));
+                g0    = (1/3.)*c0+2.*sqrt(S)*cos((1/3.)*theta-2*M_PI/3.);
+                g1    = (1/3.)*c0+2.*sqrt(S)*cos((1/3.)*theta          );
+                g2    = (1/3.)*c0+2.*sqrt(S)*cos((1/3.)*theta+2*M_PI/3.);
+            }
+//            if (fabs(Q.determinant()/(g0*g1*g2)-1.0) > 1e-5) { SVD }
+            u     = sqrt(g0) + sqrt(g1) + sqrt(g2);
+            v     = sqrt(g0*g1) + sqrt(g0*g2) + sqrt(g1*g2);
+            w     = sqrt(g0*g1*g2);
+            den   = w*(u*v-w);
+            f0    = (-w*(u*u+v)+u*v*v)/den;
+            f1    = (-w-u*u*u+2.*u*v)/den;
+            f2    = u/den;
+            id_3  = 1.;
+
+            sqrtQinv = f0*id_3 + f1*Q + f2*Q*Q;
+
+            PokeIndex<LorentzIndex>(u_proj, V*sqrtQinv, mu);
+        }
+    };
+
+
+//    void derivative(const GaugeField& Gauge) const {
+//    };
+};
+
+
+NAMESPACE_END(Grid);

Grid/qcd/smearing/Smearing.h

@@ -5,4 +5,5 @@
 #include <Grid/qcd/smearing/StoutSmearing.h>
 #include <Grid/qcd/smearing/GaugeConfiguration.h>
 #include <Grid/qcd/smearing/WilsonFlow.h>
+#include <Grid/qcd/smearing/HISQSmearing.h>
 

Grid/qcd/smearing/StoutSmearing.h

@@ -69,7 +69,7 @@ public:
   /*! Construct stout smearing object from explicitly specified rho matrix */
   Smear_Stout(const std::vector<double>& rho_)
     : OwnedBase{new Smear_APE<Gimpl>(rho_)}, SmearBase{OwnedBase.get()} {
-    std::cout << GridLogDebug << "Stout smearing constructor : Smear_Stout(const std::vector<double>& " << rho_ << " )" << std::endl
+    std::cout << GridLogDebug << "Stout smearing constructor : Smear_Stout(const std::vector<double>& " << rho_ << " )" << std::endl;
     assert(Nc == 3 && "Stout smearing currently implemented only for Nc==3");
     }
 

Grid/qcd/utils/CovariantCshift.h

@@ -37,13 +37,14 @@ NAMESPACE_BEGIN(Grid);
 // Make these members of an Impl class for BC's.
 
 namespace PeriodicBC { 
-
+  //Out(x) = Link(x)*field(x+mu)
   template<class covariant,class gauge> Lattice<covariant> CovShiftForward(const Lattice<gauge> &Link, 
 									   int mu,
 									   const Lattice<covariant> &field)
   {
     return Link*Cshift(field,mu,1);// moves towards negative mu
   }
+  //Out(x) = Link^dag(x-mu)*field(x-mu)
   template<class covariant,class gauge> Lattice<covariant> CovShiftBackward(const Lattice<gauge> &Link, 
 									    int mu,
 									    const Lattice<covariant> &field)
@@ -52,19 +53,19 @@ namespace PeriodicBC {
     tmp = adj(Link)*field;
     return Cshift(tmp,mu,-1);// moves towards positive mu
   }
-
+  //Out(x) = Link^dag(x-mu)
   template<class gauge> Lattice<gauge>
   CovShiftIdentityBackward(const Lattice<gauge> &Link, int mu) 
   {
     return Cshift(adj(Link), mu, -1);
   }
-
+  //Out(x) = Link(x)
   template<class gauge> Lattice<gauge>
   CovShiftIdentityForward(const Lattice<gauge> &Link, int mu)
   {
     return Link;
   }
-
+  //Link(x) = Link(x+mu)
   template<class gauge> Lattice<gauge>
   ShiftStaple(const Lattice<gauge> &Link, int mu)
   {

Grid/qcd/utils/GaugeGroup.h

@@ -0,0 +1,528 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/qcd/utils/GaugeGroup.h
+
+Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: neo <cossu@post.kek.jp>
+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 QCD_UTIL_GAUGEGROUP_H
+#define QCD_UTIL_GAUGEGROUP_H
+
+// Important detail: nvcc requires all template parameters to have names.
+// This is the only reason why the second template parameter has a name.
+#define ONLY_IF_SU                                                       \
+  typename dummy_name = group_name,                                      \
+           typename named_dummy = std::enable_if_t <                                 \
+                          std::is_same<dummy_name, group_name>::value && \
+                      is_su<dummy_name>::value >
+
+#define ONLY_IF_Sp                                                       \
+  typename dummy_name = group_name,                                      \
+           typename named_dummy = std::enable_if_t <                                 \
+                          std::is_same<dummy_name, group_name>::value && \
+                      is_sp<dummy_name>::value >
+
+NAMESPACE_BEGIN(Grid);
+namespace GroupName {
+class SU {};
+class Sp {};
+}  // namespace GroupName
+
+template <typename group_name>
+struct is_su {
+  static const bool value = false;
+};
+
+template <>
+struct is_su<GroupName::SU> {
+  static const bool value = true;
+};
+
+template <typename group_name>
+struct is_sp {
+  static const bool value = false;
+};
+
+template <>
+struct is_sp<GroupName::Sp> {
+  static const bool value = true;
+};
+
+template <typename group_name>
+constexpr int compute_adjoint_dimension(int ncolour);
+
+template <>
+constexpr int compute_adjoint_dimension<GroupName::SU>(int ncolour) {
+  return ncolour * ncolour - 1;
+}
+
+template <>
+constexpr int compute_adjoint_dimension<GroupName::Sp>(int ncolour) {
+  return ncolour / 2 * (ncolour + 1);
+}
+
+template <int ncolour, class group_name>
+class GaugeGroup {
+ public:
+  static const int Dimension = ncolour;
+  static const int AdjointDimension =
+      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> > >;
+  template <typename vtype>
+  using iGroupMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
+  template <typename vtype>
+  using iAlgebraVector = iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
+  template <typename vtype>
+  using iSUnAlgebraMatrix =
+    iScalar<iScalar<iMatrix<vtype, AdjointDimension> > >;
+  static int su2subgroups(void) { return su2subgroups(group_name()); }
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+  // Types can be accessed as SU<2>::Matrix , SU<2>::vSUnMatrix,
+  // SU<2>::LatticeMatrix etc...
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+  typedef iGroupMatrix<Complex> Matrix;
+  typedef iGroupMatrix<ComplexF> MatrixF;
+  typedef iGroupMatrix<ComplexD> MatrixD;
+
+  typedef iGroupMatrix<vComplex> vMatrix;
+  typedef iGroupMatrix<vComplexF> vMatrixF;
+  typedef iGroupMatrix<vComplexD> vMatrixD;
+
+  // For the projectors to the algebra
+  // these should be real...
+  // keeping complex for consistency with the SIMD vector types
+  typedef iAlgebraVector<Complex> AlgebraVector;
+  typedef iAlgebraVector<ComplexF> AlgebraVectorF;
+  typedef iAlgebraVector<ComplexD> AlgebraVectorD;
+
+  typedef iAlgebraVector<vComplex> vAlgebraVector;
+  typedef iAlgebraVector<vComplexF> vAlgebraVectorF;
+  typedef iAlgebraVector<vComplexD> vAlgebraVectorD;
+
+  typedef Lattice<vMatrix> LatticeMatrix;
+  typedef Lattice<vMatrixF> LatticeMatrixF;
+  typedef Lattice<vMatrixD> LatticeMatrixD;
+  
+  typedef Lattice<vAlgebraVector> LatticeAlgebraVector;
+  typedef Lattice<vAlgebraVectorF> LatticeAlgebraVectorF;
+  typedef Lattice<vAlgebraVectorD> LatticeAlgebraVectorD;
+   
+  typedef iSUnAlgebraMatrix<vComplex>  vAlgebraMatrix;
+  typedef iSUnAlgebraMatrix<vComplexF> vAlgebraMatrixF;
+  typedef iSUnAlgebraMatrix<vComplexD> vAlgebraMatrixD;
+
+  typedef Lattice<vAlgebraMatrix>  LatticeAlgebraMatrix;
+  typedef Lattice<vAlgebraMatrixF> LatticeAlgebraMatrixF;
+  typedef Lattice<vAlgebraMatrixD> LatticeAlgebraMatrixD;
+  
+
+  typedef iSU2Matrix<Complex> SU2Matrix;
+  typedef iSU2Matrix<ComplexF> SU2MatrixF;
+  typedef iSU2Matrix<ComplexD> SU2MatrixD;
+
+  typedef iSU2Matrix<vComplex> vSU2Matrix;
+  typedef iSU2Matrix<vComplexF> vSU2MatrixF;
+  typedef iSU2Matrix<vComplexD> vSU2MatrixD;
+
+  typedef Lattice<vSU2Matrix> LatticeSU2Matrix;
+  typedef Lattice<vSU2MatrixF> LatticeSU2MatrixF;
+  typedef Lattice<vSU2MatrixD> LatticeSU2MatrixD;
+
+  // Private implementation details are specified in the following files:
+  // Grid/qcd/utils/SUn.impl
+  // Grid/qcd/utils/SUn.impl
+  // The public part of the interface follows below and refers to these
+  // private member functions.
+
+#include <Grid/qcd/utils/SUn.impl.h>
+#include <Grid/qcd/utils/Sp2n.impl.h>
+
+ public:
+  template <class cplx>
+  static void generator(int lieIndex, iGroupMatrix<cplx> &ta) {
+    return generator(lieIndex, ta, group_name());
+  }
+
+  static accelerator_inline void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
+    return su2SubGroupIndex(i1, i2, su2_index, group_name());
+  }
+
+  static void testGenerators(void) { testGenerators(group_name()); }
+
+  static void printGenerators(void) {
+    for (int gen = 0; gen < AlgebraDimension; gen++) {
+      Matrix ta;
+      generator(gen, ta);
+      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
+                << std::endl;
+      std::cout << GridLogMessage << ta << std::endl;
+    }
+  }
+
+  template <typename LatticeMatrixType>
+  static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out,
+                           double scale = 1.0) {
+    GridBase *grid = out.Grid();
+
+    typedef typename LatticeMatrixType::vector_type vector_type;
+
+    typedef iSinglet<vector_type> vTComplexType;
+
+    typedef Lattice<vTComplexType> LatticeComplexType;
+    typedef typename GridTypeMapper<
+        typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
+
+    LatticeComplexType ca(grid);
+    LatticeMatrixType lie(grid);
+    LatticeMatrixType la(grid);
+    ComplexD ci(0.0, scale);
+    MatrixType ta;
+
+    lie = Zero();
+
+    for (int a = 0; a < AlgebraDimension; a++) {
+      random(pRNG, ca);
+
+      ca = (ca + conjugate(ca)) * 0.5;
+      ca = ca - 0.5;
+
+      generator(a, ta);
+
+      la = ci * ca * ta;
+
+      lie = lie + la;  // e^{i la ta}
+    }
+    taExp(lie, out);
+  }
+
+  static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
+                                                  LatticeMatrix &out,
+                                                  Real scale = 1.0) {
+    GridBase *grid = out.Grid();
+    LatticeReal ca(grid);
+    LatticeMatrix la(grid);
+    Complex ci(0.0, scale);
+    Matrix ta;
+
+    out = Zero();
+    for (int a = 0; a < AlgebraDimension; a++) {
+      gaussian(pRNG, ca);
+      generator(a, ta);
+      la = toComplex(ca) * ta;
+      out += la;
+    }
+    out *= ci;
+  }
+
+  static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
+                                          LatticeMatrix &out,
+                                          Real scale = 1.0) {
+    conformable(h, out);
+    GridBase *grid = out.Grid();
+    LatticeMatrix la(grid);
+    Matrix ta;
+
+    out = Zero();
+    for (int a = 0; a < AlgebraDimension; a++) {
+      generator(a, ta);
+      la = peekColour(h, a) * timesI(ta) * scale;
+      out += la;
+    }
+  }
+
+  // Projects the algebra components a lattice matrix (of dimension ncol*ncol -1
+  // ) inverse operation: FundamentalLieAlgebraMatrix
+  static void projectOnAlgebra(LatticeAlgebraVector &h_out,
+                               const LatticeMatrix &in, Real scale = 1.0) {
+    conformable(h_out, in);
+    h_out = Zero();
+    Matrix Ta;
+
+    for (int a = 0; a < AlgebraDimension; a++) {
+      generator(a, Ta);
+      pokeColour(h_out, -2.0 * (trace(timesI(Ta) * in)) * scale, a);
+    }
+  }
+
+   
+  template <class vtype>
+  accelerator_inline static iScalar<vtype> ProjectOnGeneralGroup(const iScalar<vtype> &r) {
+    return ProjectOnGeneralGroup(r, group_name());
+  }
+
+  template <class vtype, int N>
+  accelerator_inline static iVector<vtype,N> ProjectOnGeneralGroup(const iVector<vtype,N> &r) {
+    return ProjectOnGeneralGroup(r, group_name());
+  }
+
+  template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
+  accelerator_inline static iMatrix<vtype,N> ProjectOnGeneralGroup(const iMatrix<vtype,N> &arg) {
+    return ProjectOnGeneralGroup(arg, group_name());
+  }
+
+  template <int N,class vComplex_t>                  // Projects on the general groups U(N), Sp(2N)xZ2 i.e. determinant is allowed a complex phase.
+  static void ProjectOnGeneralGroup(Lattice<iVector<iScalar<iMatrix<vComplex_t, N> >, Nd> > &U) {
+    for (int mu = 0; mu < Nd; mu++) {
+      auto Umu = PeekIndex<LorentzIndex>(U, mu);
+      Umu = ProjectOnGeneralGroup(Umu);
+    }
+  }
+       
+
+  
+  template <int N,class vComplex_t>
+  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
+  static void ProjectOnSpecialGroup(Lattice<iScalar<iScalar<iMatrix<vComplex_t, N> > > > &Umu) {
+       Umu = ProjectOnGeneralGroup(Umu);
+       auto det = Determinant(Umu);
+
+       det = conjugate(det);
+
+       for (int i = 0; i < N; i++) {
+           auto element = PeekIndex<ColourIndex>(Umu, N - 1, i);
+           element = element * det;
+           PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
+       }
+   }
+
+  template <int N,class vComplex_t>    // reunitarise, resimplectify... previously ProjectSUn
+    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);
+        ProjectOnSpecialGroup(Umu);
+        PokeIndex<LorentzIndex>(U, Umu, mu);
+      }
+    }
+    
+  template <typename GaugeField>
+  static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
+    typedef typename GaugeField::vector_type vector_type;
+    typedef iGroupMatrix<vector_type> vMatrixType;
+    typedef Lattice<vMatrixType> LatticeMatrixType;
+
+    LatticeMatrixType Umu(out.Grid());
+    LatticeMatrixType tmp(out.Grid());
+    for (int mu = 0; mu < Nd; mu++) {
+      //      LieRandomize(pRNG, Umu, 1.0);
+      //      PokeIndex<LorentzIndex>(out, Umu, mu);
+      gaussian(pRNG,Umu);
+      tmp = Ta(Umu);
+      taExp(tmp,Umu);
+      ProjectOnSpecialGroup(Umu);
+      //      ProjectSUn(Umu);
+      PokeIndex<LorentzIndex>(out, Umu, mu);
+    }
+  }
+  template <typename GaugeField>
+  static void TepidConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
+    typedef typename GaugeField::vector_type vector_type;
+    typedef iGroupMatrix<vector_type> vMatrixType;
+    typedef Lattice<vMatrixType> LatticeMatrixType;
+
+    LatticeMatrixType Umu(out.Grid());
+    for (int mu = 0; mu < Nd; mu++) {
+      LieRandomize(pRNG, Umu, 0.01);
+      PokeIndex<LorentzIndex>(out, Umu, mu);
+    }
+  }
+    
+  template <typename GaugeField>
+  static void ColdConfiguration(GaugeField &out) {
+    typedef typename GaugeField::vector_type vector_type;
+    typedef iGroupMatrix<vector_type> vMatrixType;
+    typedef Lattice<vMatrixType> LatticeMatrixType;
+
+    LatticeMatrixType Umu(out.Grid());
+    Umu = 1.0;
+    for (int mu = 0; mu < Nd; mu++) {
+      PokeIndex<LorentzIndex>(out, Umu, mu);
+    }
+  }
+    
+  template <typename GaugeField>
+  static void ColdConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
+    ColdConfiguration(out);
+  }
+
+  template <typename LatticeMatrixType>
+  static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out) {
+    taProj(in, out, group_name());
+  }
+    
+  template <typename LatticeMatrixType>
+  static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) {
+    typedef typename LatticeMatrixType::scalar_type ComplexType;
+
+    LatticeMatrixType xn(x.Grid());
+    RealD nfac = 1.0;
+
+    xn = x;
+    ex = xn + ComplexType(1.0);  // 1+x
+
+    // Do a 12th order exponentiation
+    for (int i = 2; i <= 12; ++i) {
+      nfac = nfac / RealD(i);  // 1/2, 1/2.3 ...
+      xn = xn * x;             // x2, x3,x4....
+      ex = ex + xn * nfac;     // x2/2!, x3/3!....
+    }
+  }
+
+// Ta are hermitian (?)
+// Anti herm is i Ta basis
+static void LieAlgebraProject(LatticeAlgebraMatrix &out,const LatticeMatrix &in, int b)
+{
+  conformable(in, out);
+  GridBase *grid = out.Grid();
+  LatticeComplex tmp(grid);
+  Matrix ta;
+  // Using Luchang's projection convention
+  //  2 Tr{Ta Tb} A_b= 2/2 delta ab A_b = A_a
+  autoView(out_v,out,AcceleratorWrite);
+  autoView(in_v,in,AcceleratorRead);
+  int N = ncolour;
+  int NNm1 = N * (N - 1);
+  int hNNm1= NNm1/2;
+  RealD sqrt_2 = sqrt(2.0);
+  Complex ci(0.0,1.0);
+  for(int su2Index=0;su2Index<hNNm1;su2Index++){
+    int i1, i2;
+    su2SubGroupIndex(i1, i2, su2Index);
+    int ax = su2Index*2;
+    int ay = su2Index*2+1;
+    accelerator_for(ss,grid->oSites(),1,{
+	// in is traceless ANTI-hermitian whereas Grid generators are Hermitian.
+	// trace( Ta x Ci in)
+	// Bet I need to move to real part with mult by -i
+	out_v[ss]()()(ax,b) = 0.5*(real(in_v[ss]()()(i2,i1)) - real(in_v[ss]()()(i1,i2)));
+	out_v[ss]()()(ay,b) = 0.5*(imag(in_v[ss]()()(i1,i2)) + imag(in_v[ss]()()(i2,i1)));
+      });
+  }
+  for(int diagIndex=0;diagIndex<N-1;diagIndex++){
+    int k = diagIndex + 1; // diagIndex starts from 0
+    int a = NNm1+diagIndex;
+    RealD scale = 1.0/sqrt(2.0*k*(k+1));
+    accelerator_for(ss,grid->oSites(),vComplex::Nsimd(),{
+	auto tmp = in_v[ss]()()(0,0);
+	for(int i=1;i<k;i++){
+	  tmp=tmp+in_v[ss]()()(i,i);
+	}
+	tmp = tmp - in_v[ss]()()(k,k)*k;
+	out_v[ss]()()(a,b) =imag(tmp) * scale;
+      });
+    }
+}
+
+  
+};
+    
+template <int ncolour>
+using SU = GaugeGroup<ncolour, GroupName::SU>;
+
+template <int ncolour>
+using Sp = GaugeGroup<ncolour, GroupName::Sp>;
+
+typedef SU<2> SU2;
+typedef SU<3> SU3;
+typedef SU<4> SU4;
+typedef SU<5> SU5;
+
+typedef SU<Nc> FundamentalMatrices;
+    
+typedef Sp<2> Sp2;
+typedef Sp<4> Sp4;
+typedef Sp<6> Sp6;
+typedef Sp<8> Sp8;
+
+template <int N,class vComplex_t>
+static void ProjectSUn(Lattice<iScalar<iScalar<iMatrix<vComplex_t, N> > > > &Umu)
+{
+    GaugeGroup<N,GroupName::SU>::ProjectOnSpecialGroup(Umu);
+}
+  
+template <int N,class vComplex_t>
+static void ProjectSUn(Lattice<iVector<iScalar<iMatrix<vComplex_t, N> >,Nd> > &U)
+{
+    GaugeGroup<N,GroupName::SU>::ProjectOnSpecialGroup(U);
+}
+    
+template <int N,class vComplex_t>
+static void ProjectSpn(Lattice<iScalar<iScalar<iMatrix<vComplex_t, N> > > > &Umu)
+{
+    GaugeGroup<N,GroupName::Sp>::ProjectOnSpecialGroup(Umu);
+}
+    
+template <int N,class vComplex_t>
+static void ProjectSpn(Lattice<iVector<iScalar<iMatrix<vComplex_t, N> >,Nd> > &U)
+{
+    GaugeGroup<N,GroupName::Sp>::ProjectOnSpecialGroup(U);
+}
+
+// Explicit specialisation for SU(3).
+static void ProjectSU3(Lattice<iScalar<iScalar<iMatrix<vComplexD, 3> > > > &Umu)
+{
+  GridBase *grid = Umu.Grid();
+  const int x = 0;
+  const int y = 1;
+  const int z = 2;
+  // Reunitarise
+  Umu = ProjectOnGroup(Umu);
+  autoView(Umu_v, Umu, CpuWrite);
+  thread_for(ss, grid->oSites(), {
+    auto cm = Umu_v[ss];
+    cm()()(2, x) = adj(cm()()(0, y) * cm()()(1, z) -
+                       cm()()(0, z) * cm()()(1, y));  // x= yz-zy
+    cm()()(2, y) = adj(cm()()(0, z) * cm()()(1, x) -
+                       cm()()(0, x) * cm()()(1, z));  // y= zx-xz
+    cm()()(2, z) = adj(cm()()(0, x) * cm()()(1, y) -
+                       cm()()(0, y) * cm()()(1, x));  // z= xy-yx
+    Umu_v[ss] = cm;
+  });
+}
+static void ProjectSU3(Lattice<iVector<iScalar<iMatrix<vComplexD, 3> >, Nd> > &U)
+{
+  GridBase *grid = U.Grid();
+  // Reunitarise
+  for (int mu = 0; mu < Nd; mu++) {
+    auto Umu = PeekIndex<LorentzIndex>(U, mu);
+    Umu = ProjectOnGroup(Umu);
+    ProjectSU3(Umu);
+    PokeIndex<LorentzIndex>(U, Umu, mu);
+  }
+}
+
+NAMESPACE_END(Grid);
+#endif

Grid/qcd/utils/GaugeGroupTwoIndex.h

@@ -0,0 +1,371 @@
+////////////////////////////////////////////////////////////////////////
+//
+// * Two index representation generators
+//
+// * Normalisation for the fundamental generators:
+//   trace ta tb = 1/2 delta_ab = T_F delta_ab
+//   T_F = 1/2  for SU(N) groups
+//
+//
+//   base for NxN two index (anti-symmetric) matrices
+//   normalized to 1 (d_ij is the kroenecker delta)
+//
+//   (e^(ij)_{kl} = 1 / sqrt(2) (d_ik d_jl +/- d_jk d_il)
+//
+//   Then the generators are written as
+//
+//   (iT_a)^(ij)(lk) = i * ( tr[e^(ij)^dag e^(lk) T^trasp_a] +
+//   tr[e^(lk)e^(ij)^dag T_a] )  //
+//
+//
+////////////////////////////////////////////////////////////////////////
+
+// Authors: David Preti, Guido Cossu
+
+#ifndef QCD_UTIL_GAUGEGROUPTWOINDEX_H
+#define QCD_UTIL_GAUGEGROUPTWOINDEX_H
+
+NAMESPACE_BEGIN(Grid);
+
+enum TwoIndexSymmetry { Symmetric = 1, AntiSymmetric = -1 };
+
+constexpr inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
+
+namespace detail {
+
+template <class cplx, int nc, TwoIndexSymmetry S>
+struct baseOffDiagonalSpHelper;
+
+template <class cplx, int nc>
+struct baseOffDiagonalSpHelper<cplx, nc, AntiSymmetric> {
+  static const int ngroup = nc / 2;
+  static void baseOffDiagonalSp(int i, int j, iScalar<iScalar<iMatrix<cplx, nc> > > &eij) {
+    eij = Zero();
+    RealD tmp;
+
+    if ((i == ngroup + j) && (1 <= j) && (j < ngroup)) {
+      for (int k = 0; k < j+1; k++) {
+        if (k < j) {
+          tmp = 1 / sqrt(j * (j + 1));
+          eij()()(k, k + ngroup) = tmp;
+          eij()()(k + ngroup, k) = -tmp;
+        }
+        if (k == j) {
+          tmp = -j / sqrt(j * (j + 1));
+          eij()()(k, k + ngroup) = tmp;
+          eij()()(k + ngroup, k) = -tmp;
+        }
+      }
+
+    }
+
+    else if (i != ngroup + j) {
+      for (int k = 0; k < nc; k++)
+        for (int l = 0; l < nc; l++) {
+          eij()()(l, k) =
+              delta(i, k) * delta(j, l) - delta(j, k) * delta(i, l);
+        }
+    }
+    RealD nrm = 1. / std::sqrt(2.0);
+    eij = eij * nrm;
+  }
+};
+
+template <class cplx, int nc>
+struct baseOffDiagonalSpHelper<cplx, nc, Symmetric> {
+  static void baseOffDiagonalSp(int i, int j, iScalar<iScalar<iMatrix<cplx, nc> > > &eij) {
+    eij = Zero();
+    for (int k = 0; k < nc; k++)
+      for (int l = 0; l < nc; l++)
+        eij()()(l, k) =
+            delta(i, k) * delta(j, l) + delta(j, k) * delta(i, l);
+
+    RealD nrm = 1. / std::sqrt(2.0);
+    eij = eij * nrm;
+  }
+};
+
+}   // closing detail namespace
+
+template <int ncolour, TwoIndexSymmetry S, class group_name>
+class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
+ public:
+  // The chosen convention is that we are taking ncolour to be N in SU<N> but 2N
+  // in Sp(2N). ngroup is equal to N for SU but 2N/2 = N for Sp(2N).
+  static_assert(std::is_same<group_name, GroupName::SU>::value or
+                    std::is_same<group_name, GroupName::Sp>::value,
+                "ngroup is only implemented for SU and Sp currently.");
+  static const int ngroup =
+      std::is_same<group_name, GroupName::SU>::value ? ncolour : ncolour / 2;
+  static const int Dimension =
+      (ncolour * (ncolour + S) / 2) + (std::is_same<group_name, GroupName::Sp>::value ? (S - 1) / 2 : 0);
+  static const int DimensionAS =
+      (ncolour * (ncolour - 1) / 2) + (std::is_same<group_name, GroupName::Sp>::value ? (- 1) : 0);
+  static const int DimensionS =
+      ncolour * (ncolour + 1) / 2;
+  static const int NumGenerators =
+      GaugeGroup<ncolour, group_name>::AlgebraDimension;
+
+  template <typename vtype>
+  using iGroupTwoIndexMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
+
+  typedef iGroupTwoIndexMatrix<Complex> TIMatrix;
+  typedef iGroupTwoIndexMatrix<ComplexF> TIMatrixF;
+  typedef iGroupTwoIndexMatrix<ComplexD> TIMatrixD;
+
+  typedef iGroupTwoIndexMatrix<vComplex> vTIMatrix;
+  typedef iGroupTwoIndexMatrix<vComplexF> vTIMatrixF;
+  typedef iGroupTwoIndexMatrix<vComplexD> vTIMatrixD;
+
+  typedef Lattice<vTIMatrix> LatticeTwoIndexMatrix;
+  typedef Lattice<vTIMatrixF> LatticeTwoIndexMatrixF;
+  typedef Lattice<vTIMatrixD> LatticeTwoIndexMatrixD;
+
+  typedef Lattice<iVector<iScalar<iMatrix<vComplex, Dimension> >, Nd> >
+      LatticeTwoIndexField;
+  typedef Lattice<iVector<iScalar<iMatrix<vComplexF, Dimension> >, Nd> >
+      LatticeTwoIndexFieldF;
+  typedef Lattice<iVector<iScalar<iMatrix<vComplexD, Dimension> >, Nd> >
+      LatticeTwoIndexFieldD;
+
+  template <typename vtype>
+  using iGroupMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
+
+  typedef iGroupMatrix<Complex> Matrix;
+  typedef iGroupMatrix<ComplexF> MatrixF;
+  typedef iGroupMatrix<ComplexD> MatrixD;
+    
+private:
+  template <class cplx>
+  static void baseDiagonal(int Index, iGroupMatrix<cplx> &eij) {
+    eij = Zero();
+    eij()()(Index - ncolour * (ncolour - 1) / 2,
+            Index - ncolour * (ncolour - 1) / 2) = 1.0;
+  }
+    
+  template <class cplx>
+  static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij, GroupName::SU) {
+    eij = Zero();
+    for (int k = 0; k < ncolour; k++)
+      for (int l = 0; l < ncolour; l++)
+        eij()()(l, k) =
+            delta(i, k) * delta(j, l) + S * delta(j, k) * delta(i, l);
+
+    RealD nrm = 1. / std::sqrt(2.0);
+    eij = eij * nrm;
+  }
+    
+  template <class cplx>
+  static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij, GroupName::Sp) {
+    detail::baseOffDiagonalSpHelper<cplx, ncolour, S>::baseOffDiagonalSp(i, j, eij);
+  }
+
+public:
+    
+  template <class cplx>
+  static void base(int Index, iGroupMatrix<cplx> &eij) {
+  // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
+    assert(Index < Dimension);
+    eij = Zero();
+  // for the linearisation of the 2 indexes
+    static int a[ncolour * (ncolour - 1) / 2][2];  // store the a <-> i,j
+    static bool filled = false;
+    if (!filled) {
+      int counter = 0;
+      for (int i = 1; i < ncolour; i++) {
+      for (int j = 0; j < i; j++) {
+        if (std::is_same<group_name, GroupName::Sp>::value)
+          {
+            if (j==0 && i==ngroup+j && S==-1) {
+            //std::cout << "skipping" << std::endl; // for Sp2n this vanishes identically.
+              j = j+1;
+            }
+          }
+          a[counter][0] = i;
+          a[counter][1] = j;
+          counter++;
+          }
+      }
+      filled = true;
+    }
+    if (Index < ncolour*ncolour - DimensionS)
+    {
+      baseOffDiagonal(a[Index][0], a[Index][1], eij, group_name());
+    } else {
+      baseDiagonal(Index, eij);
+    }
+  }
+    
+  static void printBase(void) {
+    for (int gen = 0; gen < Dimension; gen++) {
+      Matrix tmp;
+      base(gen, tmp);
+      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
+                << std::endl;
+      std::cout << GridLogMessage << tmp << std::endl;
+    }
+  }
+
+  template <class cplx>
+  static void generator(int Index, iGroupTwoIndexMatrix<cplx> &i2indTa) {
+    Vector<iGroupMatrix<cplx> > ta(NumGenerators);
+    Vector<iGroupMatrix<cplx> > eij(Dimension);
+    iGroupMatrix<cplx> tmp;
+
+    for (int a = 0; a < NumGenerators; a++)
+      GaugeGroup<ncolour, group_name>::generator(a, ta[a]);
+
+    for (int a = 0; a < Dimension; a++) base(a, eij[a]);
+
+    for (int a = 0; a < Dimension; a++) {
+      tmp = transpose(eij[a]*ta[Index]) + transpose(eij[a]) * ta[Index];
+      for (int b = 0; b < Dimension; b++) {
+        Complex iTr = TensorRemove(timesI(trace(tmp * eij[b])));
+        i2indTa()()(a, b) = iTr;
+      }
+    }
+  }
+
+  static void printGenerators(void) {
+    for (int gen = 0; gen < NumGenerators; gen++) {
+      TIMatrix i2indTa;
+      generator(gen, i2indTa);
+      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
+                << std::endl;
+      std::cout << GridLogMessage << i2indTa << std::endl;
+    }
+  }
+
+  static void testGenerators(void) {
+    TIMatrix i2indTa, i2indTb;
+    std::cout << GridLogMessage << "2IndexRep - Checking if traceless"
+              << std::endl;
+    for (int a = 0; a < NumGenerators; a++) {
+      generator(a, i2indTa);
+      std::cout << GridLogMessage << a << std::endl;
+      assert(norm2(trace(i2indTa)) < 1.0e-6);
+    }
+    std::cout << GridLogMessage << std::endl;
+
+    std::cout << GridLogMessage << "2IndexRep - Checking if antihermitean"
+              << std::endl;
+    for (int a = 0; a < NumGenerators; a++) {
+      generator(a, i2indTa);
+      std::cout << GridLogMessage << a << std::endl;
+      assert(norm2(adj(i2indTa) + i2indTa) < 1.0e-6);
+    }
+
+    std::cout << GridLogMessage << std::endl;
+    std::cout << GridLogMessage
+              << "2IndexRep - Checking Tr[Ta*Tb]=delta(a,b)*(N +- 2)/2"
+              << std::endl;
+    for (int a = 0; a < NumGenerators; a++) {
+      for (int b = 0; b < NumGenerators; b++) {
+        generator(a, i2indTa);
+        generator(b, i2indTb);
+
+        // generator returns iTa, so we need a minus sign here
+        Complex Tr = -TensorRemove(trace(i2indTa * i2indTb));
+        std::cout << GridLogMessage << "a=" << a << "b=" << b << "Tr=" << Tr
+                  << std::endl;
+        if (a == b) {
+          assert(real(Tr) - ((ncolour + S * 2) * 0.5) < 1e-8);
+        } else {
+          assert(real(Tr) < 1e-8);
+        }
+        assert(imag(Tr) < 1e-8);
+      }
+    }
+    std::cout << GridLogMessage << std::endl;
+  }
+
+  static void TwoIndexLieAlgebraMatrix(
+      const typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h,
+      LatticeTwoIndexMatrix &out, Real scale = 1.0) {
+    conformable(h, out);
+    GridBase *grid = out.Grid();
+    LatticeTwoIndexMatrix la(grid);
+    TIMatrix i2indTa;
+
+    out = Zero();
+    for (int a = 0; a < NumGenerators; a++) {
+      generator(a, i2indTa);
+      la = peekColour(h, a) * i2indTa;
+      out += la;
+    }
+    out *= scale;
+  }
+
+  // Projects the algebra components
+  // of a lattice matrix ( of dimension ncol*ncol -1 )
+  static void projectOnAlgebra(
+      typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
+      const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
+    conformable(h_out, in);
+    h_out = Zero();
+    TIMatrix i2indTa;
+    Real coefficient = -2.0 / (ncolour + 2 * S) * scale;
+    // 2/(Nc +/- 2) for the normalization of the trace in the two index rep
+    for (int a = 0; a < NumGenerators; a++) {
+      generator(a, i2indTa);
+      pokeColour(h_out, real(trace(i2indTa * in)) * coefficient, a);
+    }
+  }
+
+  // a projector that keeps the generators stored to avoid the overhead of
+  // recomputing them
+  static void projector(
+      typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
+      const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
+    conformable(h_out, in);
+    // to store the generators
+    static std::vector<TIMatrix> i2indTa(NumGenerators);
+    h_out = Zero();
+    static bool precalculated = false;
+    if (!precalculated) {
+      precalculated = true;
+      for (int a = 0; a < NumGenerators; a++) generator(a, i2indTa[a]);
+    }
+
+    Real coefficient =
+        -2.0 / (ncolour + 2 * S) * scale;  // 2/(Nc +/- 2) for the normalization
+    // of the trace in the two index rep
+
+    for (int a = 0; a < NumGenerators; a++) {
+      auto tmp = real(trace(i2indTa[a] * in)) * coefficient;
+      pokeColour(h_out, tmp, a);
+    }
+  }
+};
+
+template <int ncolour, TwoIndexSymmetry S>
+using SU_TwoIndex = GaugeGroupTwoIndex<ncolour, S, GroupName::SU>;
+
+// Some useful type names
+typedef SU_TwoIndex<Nc, Symmetric> TwoIndexSymmMatrices;
+typedef SU_TwoIndex<Nc, AntiSymmetric> TwoIndexAntiSymmMatrices;
+
+typedef SU_TwoIndex<2, Symmetric> SU2TwoIndexSymm;
+typedef SU_TwoIndex<3, Symmetric> SU3TwoIndexSymm;
+typedef SU_TwoIndex<4, Symmetric> SU4TwoIndexSymm;
+typedef SU_TwoIndex<5, Symmetric> SU5TwoIndexSymm;
+
+typedef SU_TwoIndex<2, AntiSymmetric> SU2TwoIndexAntiSymm;
+typedef SU_TwoIndex<3, AntiSymmetric> SU3TwoIndexAntiSymm;
+typedef SU_TwoIndex<4, AntiSymmetric> SU4TwoIndexAntiSymm;
+typedef SU_TwoIndex<5, AntiSymmetric> SU5TwoIndexAntiSymm;
+
+template <int ncolour, TwoIndexSymmetry S>
+using Sp_TwoIndex = GaugeGroupTwoIndex<ncolour, S, GroupName::Sp>;
+
+typedef Sp_TwoIndex<Nc, Symmetric> SpTwoIndexSymmMatrices;
+typedef Sp_TwoIndex<Nc, AntiSymmetric> SpTwoIndexAntiSymmMatrices;
+
+typedef Sp_TwoIndex<2, Symmetric> Sp2TwoIndexSymm;
+typedef Sp_TwoIndex<4, Symmetric> Sp4TwoIndexSymm;
+
+typedef Sp_TwoIndex<4, AntiSymmetric> Sp4TwoIndexAntiSymm;
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/qcd/utils/SUn.h

@@ -1,932 +0,0 @@
-/*************************************************************************************
-
-Grid physics library, www.github.com/paboyle/Grid
-
-Source file: ./lib/qcd/utils/SUn.h
-
-Copyright (C) 2015
-
-Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
-Author: Peter Boyle <paboyle@ph.ed.ac.uk>
-Author: neo <cossu@post.kek.jp>
-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 QCD_UTIL_SUN_H
-#define QCD_UTIL_SUN_H
-
-NAMESPACE_BEGIN(Grid);
-
-template<int N, class Vec>
-Lattice<iScalar<iScalar<iScalar<Vec> > > > Determinant(const Lattice<iScalar<iScalar<iMatrix<Vec, N> > > > &Umu)
-{
-  GridBase *grid=Umu.Grid();
-  auto lvol = grid->lSites();
-  Lattice<iScalar<iScalar<iScalar<Vec> > > > ret(grid);
-  typedef typename Vec::scalar_type scalar;
-  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);
-    iScalar<iScalar<iMatrix<scalar, N> > > Us;
-    peekLocalSite(Us, Umu_v, lcoor);
-    for(int i=0;i<N;i++){
-      for(int j=0;j<N;j++){
-	scalar tmp= Us()()(i,j);
-	ComplexD ztmp(real(tmp),imag(tmp));
-	EigenU(i,j)=ztmp;
-      }}
-    ComplexD detD  = EigenU.determinant();
-    typename Vec::scalar_type det(detD.real(),detD.imag());
-    pokeLocalSite(det,ret_v,lcoor);
-  });
-  return ret;
-}
-
-template<int N, class Vec>
-static void ProjectSUn(Lattice<iScalar<iScalar<iMatrix<Vec, N> > > > &Umu)
-{
-  Umu      = ProjectOnGroup(Umu);
-  auto det = Determinant(Umu);
-
-  det = conjugate(det);
-
-  for(int i=0;i<N;i++){
-    auto element = PeekIndex<ColourIndex>(Umu,N-1,i);
-    element = element * det;
-    PokeIndex<ColourIndex>(Umu,element,Nc-1,i);
-  }
-}
-template<int N,class Vec>
-static void ProjectSUn(Lattice<iVector<iScalar<iMatrix<Vec, N> >,Nd> > &U)
-{
-  GridBase *grid=U.Grid();
-  // Reunitarise
-  for(int mu=0;mu<Nd;mu++){
-    auto Umu = PeekIndex<LorentzIndex>(U,mu);
-    Umu      = ProjectOnGroup(Umu);
-    ProjectSUn(Umu);
-    PokeIndex<LorentzIndex>(U,Umu,mu);
-  }
-}
-
-template <int ncolour>
-class SU {
-public:
-  static const int Dimension = ncolour;
-  static const int AdjointDimension = ncolour * ncolour - 1;
-  static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
-
-  template <typename vtype>
-  using iSUnMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
-  template <typename vtype>
-  using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
-  template <typename vtype>
-  using iSUnAlgebraVector =
-    iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
-
-  //////////////////////////////////////////////////////////////////////////////////////////////////
-  // Types can be accessed as SU<2>::Matrix , SU<2>::vSUnMatrix,
-  // SU<2>::LatticeMatrix etc...
-  //////////////////////////////////////////////////////////////////////////////////////////////////
-  typedef iSUnMatrix<Complex> Matrix;
-  typedef iSUnMatrix<ComplexF> MatrixF;
-  typedef iSUnMatrix<ComplexD> MatrixD;
-
-  typedef iSUnMatrix<vComplex> vMatrix;
-  typedef iSUnMatrix<vComplexF> vMatrixF;
-  typedef iSUnMatrix<vComplexD> vMatrixD;
-
-  // For the projectors to the algebra
-  // these should be real...
-  // keeping complex for consistency with the SIMD vector types
-  typedef iSUnAlgebraVector<Complex> AlgebraVector;
-  typedef iSUnAlgebraVector<ComplexF> AlgebraVectorF;
-  typedef iSUnAlgebraVector<ComplexD> AlgebraVectorD;
-
-  typedef iSUnAlgebraVector<vComplex> vAlgebraVector;
-  typedef iSUnAlgebraVector<vComplexF> vAlgebraVectorF;
-  typedef iSUnAlgebraVector<vComplexD> vAlgebraVectorD;
-
-  typedef Lattice<vMatrix> LatticeMatrix;
-  typedef Lattice<vMatrixF> LatticeMatrixF;
-  typedef Lattice<vMatrixD> LatticeMatrixD;
-
-  typedef Lattice<vAlgebraVector> LatticeAlgebraVector;
-  typedef Lattice<vAlgebraVectorF> LatticeAlgebraVectorF;
-  typedef Lattice<vAlgebraVectorD> LatticeAlgebraVectorD;
-
-  typedef iSU2Matrix<Complex> SU2Matrix;
-  typedef iSU2Matrix<ComplexF> SU2MatrixF;
-  typedef iSU2Matrix<ComplexD> SU2MatrixD;
-
-  typedef iSU2Matrix<vComplex> vSU2Matrix;
-  typedef iSU2Matrix<vComplexF> vSU2MatrixF;
-  typedef iSU2Matrix<vComplexD> vSU2MatrixD;
-
-  typedef Lattice<vSU2Matrix> LatticeSU2Matrix;
-  typedef Lattice<vSU2MatrixF> LatticeSU2MatrixF;
-  typedef Lattice<vSU2MatrixD> LatticeSU2MatrixD;
-
-  ////////////////////////////////////////////////////////////////////////
-  // There are N^2-1 generators for SU(N).
-  //
-  // We take a traceless hermitian generator basis as follows
-  //
-  // * Normalisation: trace ta tb = 1/2 delta_ab = T_F delta_ab
-  //   T_F = 1/2  for SU(N) groups
-  //
-  // * Off diagonal
-  //    - pairs of rows i1,i2 behaving like pauli matrices signma_x, sigma_y
-  //
-  //    - there are (Nc-1-i1) slots for i2 on each row [ x  0  x ]
-  //      direct count off each row
-  //
-  //    - Sum of all pairs is Nc(Nc-1)/2: proof arithmetic series
-  //
-  //      (Nc-1) + (Nc-2)+...  1      ==> Nc*(Nc-1)/2
-  //      1+ 2+          +   + Nc-1
-  //
-  //    - There are 2 x Nc (Nc-1)/ 2 of these = Nc^2 - Nc
-  //
-  //    - We enumerate the row-col pairs.
-  //    - for each row col pair there is a (sigma_x) and a (sigma_y) like
-  //    generator
-  //
-  //
-  //   t^a_ij = { in 0.. Nc(Nc-1)/2 -1} =>  1/2(delta_{i,i1} delta_{j,i2} +
-  //   delta_{i,i1} delta_{j,i2})
-  //   t^a_ij = { in Nc(Nc-1)/2 ... Nc(Nc-1) - 1} =>  i/2( delta_{i,i1}
-  //   delta_{j,i2} - i delta_{i,i1} delta_{j,i2})
-  //
-  // * Diagonal; must be traceless and normalised
-  //   - Sequence is
-  //   N  (1,-1,0,0...)
-  //   N  (1, 1,-2,0...)
-  //   N  (1, 1, 1,-3,0...)
-  //   N  (1, 1, 1, 1,-4,0...)
-  //
-  //   where 1/2 = N^2 (1+.. m^2)etc.... for the m-th diagonal generator
-  //   NB this gives the famous SU3 result for su2 index 8
-  //
-  //   N= sqrt(1/2 . 1/6 ) = 1/2 . 1/sqrt(3)
-  //
-  //   ( 1      )
-  //   (    1   ) / sqrt(3) /2  = 1/2 lambda_8
-  //   (      -2)
-  //
-  ////////////////////////////////////////////////////////////////////////
-  template <class cplx>
-  static void generator(int lieIndex, iSUnMatrix<cplx> &ta) {
-    // map lie index to which type of generator
-    int diagIndex;
-    int su2Index;
-    int sigxy;
-    int NNm1 = ncolour * (ncolour - 1);
-    if (lieIndex >= NNm1) {
-      diagIndex = lieIndex - NNm1;
-      generatorDiagonal(diagIndex, ta);
-      return;
-    }
-    sigxy = lieIndex & 0x1;  // even or odd
-    su2Index = lieIndex >> 1;
-    if (sigxy)
-      generatorSigmaY(su2Index, ta);
-    else
-      generatorSigmaX(su2Index, ta);
-  }
-  
-  template <class cplx>
-  static void generatorSigmaY(int su2Index, iSUnMatrix<cplx> &ta) {
-    ta = Zero();
-    int i1, i2;
-    su2SubGroupIndex(i1, i2, su2Index);
-    ta()()(i1, i2) = 1.0;
-    ta()()(i2, i1) = 1.0;
-    ta = ta * 0.5;
-  }
-  
-  template <class cplx>
-  static void generatorSigmaX(int su2Index, iSUnMatrix<cplx> &ta) {
-    ta = Zero();
-    cplx i(0.0, 1.0);
-    int i1, i2;
-    su2SubGroupIndex(i1, i2, su2Index);
-    ta()()(i1, i2) = i;
-    ta()()(i2, i1) = -i;
-    ta = ta * 0.5;
-  }
-
-  template <class cplx>
-  static void generatorDiagonal(int diagIndex, iSUnMatrix<cplx> &ta) {
-    // diag ({1, 1, ..., 1}(k-times), -k, 0, 0, ...)
-    ta = Zero();
-    int k = diagIndex + 1;                  // diagIndex starts from 0
-    for (int i = 0; i <= diagIndex; i++) {  // k iterations
-      ta()()(i, i) = 1.0;
-    }
-    ta()()(k, k) = -k;  // indexing starts from 0
-    RealD nrm = 1.0 / std::sqrt(2.0 * k * (k + 1));
-    ta = ta * nrm;
-  }
-
-
-
-  ////////////////////////////////////////////////////////////////////////
-  // Map a su2 subgroup number to the pair of rows that are non zero
-  ////////////////////////////////////////////////////////////////////////
-  static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
-    assert((su2_index >= 0) && (su2_index < (ncolour * (ncolour - 1)) / 2));
-
-    int spare = su2_index;
-    for (i1 = 0; spare >= (ncolour - 1 - i1); i1++) {
-      spare = spare - (ncolour - 1 - i1);  // remove the Nc-1-i1 terms
-    }
-    i2 = i1 + 1 + spare;
-  }
-
-  //////////////////////////////////////////////////////////////////////////////////////////
-  // Pull out a subgroup and project on to real coeffs x pauli basis
-  //////////////////////////////////////////////////////////////////////////////////////////
-  template <class vcplx>
-  static void su2Extract(Lattice<iSinglet<vcplx> > &Determinant,
-                         Lattice<iSU2Matrix<vcplx> > &subgroup,
-                         const Lattice<iSUnMatrix<vcplx> > &source,
-                         int su2_index) {
-    GridBase *grid(source.Grid());
-    conformable(subgroup, source);
-    conformable(subgroup, Determinant);
-    int i0, i1;
-    su2SubGroupIndex(i0, i1, su2_index);
-
-    autoView( subgroup_v , subgroup,AcceleratorWrite);
-    autoView( source_v   , source,AcceleratorRead);
-    autoView( Determinant_v , Determinant,AcceleratorWrite);
-    accelerator_for(ss, grid->oSites(), 1, {
-
-      subgroup_v[ss]()()(0, 0) = source_v[ss]()()(i0, i0);
-      subgroup_v[ss]()()(0, 1) = source_v[ss]()()(i0, i1);
-      subgroup_v[ss]()()(1, 0) = source_v[ss]()()(i1, i0);
-      subgroup_v[ss]()()(1, 1) = source_v[ss]()()(i1, i1);
-
-      iSU2Matrix<vcplx> Sigma = subgroup_v[ss];
-
-      Sigma = Sigma - adj(Sigma) + trace(adj(Sigma));
-
-      subgroup_v[ss] = Sigma;
-
-      // this should be purely real
-      Determinant_v[ss] =
-	Sigma()()(0, 0) * Sigma()()(1, 1) - Sigma()()(0, 1) * Sigma()()(1, 0);
-    });
-  }
-
-  //////////////////////////////////////////////////////////////////////////////////////////
-  // Set matrix to one and insert a pauli subgroup
-  //////////////////////////////////////////////////////////////////////////////////////////
-  template <class vcplx>
-  static void su2Insert(const Lattice<iSU2Matrix<vcplx> > &subgroup,
-                        Lattice<iSUnMatrix<vcplx> > &dest, int su2_index) {
-    GridBase *grid(dest.Grid());
-    conformable(subgroup, dest);
-    int i0, i1;
-    su2SubGroupIndex(i0, i1, su2_index);
-
-    dest = 1.0;  // start out with identity
-    autoView( dest_v , dest, AcceleratorWrite);
-    autoView( subgroup_v, subgroup, AcceleratorRead);
-    accelerator_for(ss, grid->oSites(),1,
-    {
-      dest_v[ss]()()(i0, i0) = subgroup_v[ss]()()(0, 0);
-      dest_v[ss]()()(i0, i1) = subgroup_v[ss]()()(0, 1);
-      dest_v[ss]()()(i1, i0) = subgroup_v[ss]()()(1, 0);
-      dest_v[ss]()()(i1, i1) = subgroup_v[ss]()()(1, 1);
-    });
-
-  }
-
-  ///////////////////////////////////////////////
-  // Generate e^{ Re Tr Staple Link} dlink
-  //
-  // *** Note Staple should be appropriate linear compbination between all
-  // staples.
-  // *** If already by beta pass coefficient 1.0.
-  // *** This routine applies the additional 1/Nc factor that comes after trace
-  // in action.
-  //
-  ///////////////////////////////////////////////
-  static void SubGroupHeatBath(GridSerialRNG &sRNG, GridParallelRNG &pRNG,
-			       RealD beta,  // coeff multiplying staple in action (with no 1/Nc)
-			       LatticeMatrix &link,
-			       const LatticeMatrix &barestaple,  // multiplied by action coeffs so th
-			       int su2_subgroup, int nheatbath, LatticeInteger &wheremask) 
-  {
-    GridBase *grid = link.Grid();
-
-    const RealD twopi = 2.0 * M_PI;
-
-    LatticeMatrix staple(grid);
-
-    staple = barestaple * (beta / ncolour);
-
-    LatticeMatrix V(grid);
-    V = link * staple;
-
-    // Subgroup manipulation in the lie algebra space
-    LatticeSU2Matrix u(grid);  // Kennedy pendleton "u" real projected normalised Sigma
-    LatticeSU2Matrix uinv(grid);
-    LatticeSU2Matrix ua(grid);  // a in pauli form
-    LatticeSU2Matrix b(grid);   // rotated matrix after hb
-
-    // Some handy constant fields
-    LatticeComplex ones(grid);
-    ones = 1.0;
-    LatticeComplex zeros(grid);
-    zeros = Zero();
-    LatticeReal rones(grid);
-    rones = 1.0;
-    LatticeReal rzeros(grid);
-    rzeros = Zero();
-    LatticeComplex udet(grid);  // determinant of real(staple)
-    LatticeInteger mask_true(grid);
-    mask_true = 1;
-    LatticeInteger mask_false(grid);
-    mask_false = 0;
-
-    /*
-      PLB 156 P393 (1985) (Kennedy and Pendleton)
-
-      Note: absorb "beta" into the def of sigma compared to KP paper; staple
-      passed to this routine has "beta" already multiplied in
-
-      Action linear in links h and of form:
-
-      beta S = beta  Sum_p (1 - 1/Nc Re Tr Plaq )
-
-      Writing Sigma = 1/Nc (beta Sigma') where sum over staples is "Sigma' "
-
-      beta S = const - beta/Nc Re Tr h Sigma'
-      = const - Re Tr h Sigma
-
-      Decompose h and Sigma into (1, sigma_j) ; h_i real, h^2=1, Sigma_i complex
-      arbitrary.
-
-      Tr h Sigma = h_i Sigma_j Tr (sigma_i sigma_j)  = h_i Sigma_j 2 delta_ij
-      Re Tr h Sigma = 2 h_j Re Sigma_j
-
-      Normalised re Sigma_j = xi u_j
-
-      With u_j a unit vector and U can be in SU(2);
-
-      Re Tr h Sigma = 2 h_j Re Sigma_j = 2 xi (h.u)
-
-      4xi^2 = Det [ Sig - Sig^dag  + 1 Tr Sigdag]
-      u   = 1/2xi [ Sig - Sig^dag  + 1 Tr Sigdag]
-
-      xi = sqrt(Det)/2;
-
-      Write a= u h in SU(2); a has pauli decomp a_j;
-
-      Note: Product b' xi is unvariant because scaling Sigma leaves
-      normalised vector "u" fixed; Can rescale Sigma so b' = 1.
-    */
-
-    ////////////////////////////////////////////////////////
-    // Real part of Pauli decomposition
-    // Note a subgroup can project to zero in cold start
-    ////////////////////////////////////////////////////////
-    su2Extract(udet, u, V, su2_subgroup);
-
-    //////////////////////////////////////////////////////
-    // Normalising this vector if possible; else identity
-    //////////////////////////////////////////////////////
-    LatticeComplex xi(grid);
-
-    LatticeSU2Matrix lident(grid);
-
-    SU2Matrix ident = Complex(1.0);
-    SU2Matrix pauli1;
-    SU<2>::generator(0, pauli1);
-    SU2Matrix pauli2;
-    SU<2>::generator(1, pauli2);
-    SU2Matrix pauli3;
-    SU<2>::generator(2, pauli3);
-    pauli1 = timesI(pauli1) * 2.0;
-    pauli2 = timesI(pauli2) * 2.0;
-    pauli3 = timesI(pauli3) * 2.0;
-
-    LatticeComplex cone(grid);
-    LatticeReal adet(grid);
-    adet = abs(toReal(udet));
-    lident = Complex(1.0);
-    cone = Complex(1.0);
-    Real machine_epsilon = 1.0e-7;
-    u = where(adet > machine_epsilon, u, lident);
-    udet = where(adet > machine_epsilon, udet, cone);
-
-    xi = 0.5 * sqrt(udet);  // 4xi^2 = Det [ Sig - Sig^dag  + 1 Tr Sigdag]
-    u = 0.5 * u *
-      pow(xi, -1.0);  //  u   = 1/2xi [ Sig - Sig^dag  + 1 Tr Sigdag]
-
-    // Debug test for sanity
-    uinv = adj(u);
-    b = u * uinv - 1.0;
-    assert(norm2(b) < 1.0e-4);
-
-    /*
-      Measure: Haar measure dh has d^4a delta(1-|a^2|)
-      In polars:
-      da = da0 r^2 sin theta dr dtheta dphi delta( 1 - r^2 -a0^2)
-      = da0 r^2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r)(sqrt(1-a0^) +
-      r) )
-      = da0 r/2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r) )
-
-      Action factor Q(h) dh  = e^-S[h]  dh =  e^{  xi Tr uh} dh    // beta enters
-      through xi
-      =  e^{2 xi (h.u)} dh
-      =  e^{2 xi h0u0}.e^{2 xi h1u1}.e^{2 xi
-      h2u2}.e^{2 xi h3u3} dh
-
-      Therefore for each site, take xi for that site
-      i) generate  |a0|<1 with dist
-      (1-a0^2)^0.5 e^{2 xi a0 } da0
-
-      Take alpha = 2 xi  = 2 xi [ recall 2 beta/Nc unmod staple norm]; hence 2.0/Nc
-      factor in Chroma ]
-      A. Generate two uniformly distributed pseudo-random numbers R and R', R'',
-      R''' in the unit interval;
-      B. Set X = -(ln R)/alpha, X' =-(ln R')/alpha;
-      C. Set C = cos^2(2pi R"), with R" another uniform random number in [0,1] ;
-      D. Set A = XC;
-      E. Let d  = X'+A;
-      F. If R'''^2 :> 1 - 0.5 d,  go back to A;
-      G. Set a0 = 1 - d;
-
-      Note that in step D setting B ~ X - A and using B in place of A in step E will
-      generate a second independent a 0 value.
-    */
-
-    /////////////////////////////////////////////////////////
-    // count the number of sites by picking "1"'s out of hat
-    /////////////////////////////////////////////////////////
-    Integer hit = 0;
-    LatticeReal rtmp(grid);
-    rtmp = where(wheremask, rones, rzeros);
-    RealD numSites = sum(rtmp);
-    RealD numAccepted;
-    LatticeInteger Accepted(grid);
-    Accepted = Zero();
-    LatticeInteger newlyAccepted(grid);
-
-    std::vector<LatticeReal> xr(4, grid);
-    std::vector<LatticeReal> a(4, grid);
-    LatticeReal d(grid);
-    d = Zero();
-    LatticeReal alpha(grid);
-
-    //    std::cout<<GridLogMessage<<"xi "<<xi <<std::endl;
-    xi = 2.0 *xi;
-    alpha = toReal(xi);
-
-    do {
-      // A. Generate two uniformly distributed pseudo-random numbers R and R',
-      // R'', R''' in the unit interval;
-      random(pRNG, xr[0]);
-      random(pRNG, xr[1]);
-      random(pRNG, xr[2]);
-      random(pRNG, xr[3]);
-
-      // B. Set X = - ln R/alpha, X' = -ln R'/alpha
-      xr[1] = -log(xr[1]) / alpha;
-      xr[2] = -log(xr[2]) / alpha;
-
-      // C. Set C = cos^2(2piR'')
-      xr[3] = cos(xr[3] * twopi);
-      xr[3] = xr[3] * xr[3];
-
-      LatticeReal xrsq(grid);
-
-      // D. Set A = XC;
-      // E. Let d  = X'+A;
-      xrsq = xr[2] + xr[1] * xr[3];
-
-      d = where(Accepted, d, xr[2] + xr[1] * xr[3]);
-
-      // F. If R'''^2 :> 1 - 0.5 d,  go back to A;
-      LatticeReal thresh(grid);
-      thresh = 1.0 - d * 0.5;
-      xrsq = xr[0] * xr[0];
-      LatticeInteger ione(grid);
-      ione = 1;
-      LatticeInteger izero(grid);
-      izero = Zero();
-
-      newlyAccepted = where(xrsq < thresh, ione, izero);
-      Accepted = where(newlyAccepted, newlyAccepted, Accepted);
-      Accepted = where(wheremask, Accepted, izero);
-
-      // FIXME need an iSum for integer to avoid overload on return type??
-      rtmp = where(Accepted, rones, rzeros);
-      numAccepted = sum(rtmp);
-
-      hit++;
-
-    } while ((numAccepted < numSites) && (hit < nheatbath));
-
-    // G. Set a0 = 1 - d;
-    a[0] = Zero();
-    a[0] = where(wheremask, 1.0 - d, a[0]);
-
-    //////////////////////////////////////////
-    //    ii) generate a_i uniform on two sphere radius (1-a0^2)^0.5
-    //////////////////////////////////////////
-
-    LatticeReal a123mag(grid);
-    a123mag = sqrt(abs(1.0 - a[0] * a[0]));
-
-    LatticeReal cos_theta(grid);
-    LatticeReal sin_theta(grid);
-    LatticeReal phi(grid);
-
-    random(pRNG, phi);
-    phi = phi * twopi;  // uniform in [0,2pi]
-    random(pRNG, cos_theta);
-    cos_theta = (cos_theta * 2.0) - 1.0;  // uniform in [-1,1]
-    sin_theta = sqrt(abs(1.0 - cos_theta * cos_theta));
-
-    a[1] = a123mag * sin_theta * cos(phi);
-    a[2] = a123mag * sin_theta * sin(phi);
-    a[3] = a123mag * cos_theta;
-
-    ua = toComplex(a[0]) * ident  + toComplex(a[1]) * pauli1 +
-         toComplex(a[2]) * pauli2 + toComplex(a[3]) * pauli3;
-
-    b = 1.0;
-    b = where(wheremask, uinv * ua, b);
-    su2Insert(b, V, su2_subgroup);
-
-    // mask the assignment back based on Accptance
-    link = where(Accepted, V * link, link);
-
-    //////////////////////////////
-    // Debug Checks
-    // SU2 check
-    LatticeSU2Matrix check(grid);  // rotated matrix after hb
-    u = Zero();
-    check = ua * adj(ua) - 1.0;
-    check = where(Accepted, check, u);
-    assert(norm2(check) < 1.0e-4);
-
-    check = b * adj(b) - 1.0;
-    check = where(Accepted, check, u);
-    assert(norm2(check) < 1.0e-4);
-
-    LatticeMatrix Vcheck(grid);
-    Vcheck = Zero();
-    Vcheck = where(Accepted, V * adj(V) - 1.0, Vcheck);
-    //    std::cout<<GridLogMessage << "SU3 check " <<norm2(Vcheck)<<std::endl;
-    assert(norm2(Vcheck) < 1.0e-4);
-
-    // Verify the link stays in SU(3)
-    //    std::cout<<GridLogMessage <<"Checking the modified link"<<std::endl;
-    Vcheck = link * adj(link) - 1.0;
-    assert(norm2(Vcheck) < 1.0e-4);
-    /////////////////////////////////
-  }
-
-  static void printGenerators(void) {
-    for (int gen = 0; gen < AdjointDimension; gen++) {
-      Matrix ta;
-      generator(gen, ta);
-      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
-                << std::endl;
-      std::cout << GridLogMessage << ta << std::endl;
-    }
-  }
-
-
-
-  static void testGenerators(void) {
-    Matrix ta;
-    Matrix tb;
-    std::cout << GridLogMessage
-              << "Fundamental - Checking trace ta tb is 0.5 delta_ab"
-              << std::endl;
-    for (int a = 0; a < AdjointDimension; a++) {
-      for (int b = 0; b < AdjointDimension; b++) {
-        generator(a, ta);
-        generator(b, tb);
-        Complex tr = TensorRemove(trace(ta * tb));
-        std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
-                  << std::endl;
-        if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
-        if (a != b) assert(abs(tr) < 1.0e-6);
-      }
-      std::cout << GridLogMessage << std::endl;
-    }
-    std::cout << GridLogMessage << "Fundamental - Checking if hermitian"
-              << std::endl;
-    for (int a = 0; a < AdjointDimension; a++) {
-      generator(a, ta);
-      std::cout << GridLogMessage << a << std::endl;
-      assert(norm2(ta - adj(ta)) < 1.0e-6);
-    }
-    std::cout << GridLogMessage << std::endl;
-
-    std::cout << GridLogMessage << "Fundamental - Checking if traceless"
-              << std::endl;
-    for (int a = 0; a < AdjointDimension; a++) {
-      generator(a, ta);
-      Complex tr = TensorRemove(trace(ta));
-      std::cout << GridLogMessage << a << " " << std::endl;
-      assert(abs(tr) < 1.0e-6);
-    }
-    std::cout << GridLogMessage << std::endl;
-  }
-
-  // reunitarise??
-  template <typename LatticeMatrixType>
-  static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out, double scale = 1.0) 
-  {
-    GridBase *grid = out.Grid();
-
-    typedef typename LatticeMatrixType::vector_type vector_type;
-
-    typedef iSinglet<vector_type> vTComplexType;
-
-    typedef Lattice<vTComplexType> LatticeComplexType;
-    typedef typename GridTypeMapper<typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
-
-    LatticeComplexType ca(grid);
-    LatticeMatrixType lie(grid);
-    LatticeMatrixType la(grid);
-    ComplexD ci(0.0, scale);
-    //    ComplexD cone(1.0, 0.0);
-    MatrixType ta;
-
-    lie = Zero();
-
-    for (int a = 0; a < AdjointDimension; a++) {
-      random(pRNG, ca);
-
-      ca = (ca + conjugate(ca)) * 0.5;
-      ca = ca - 0.5;
-
-      generator(a, ta);
-
-      la = ci * ca * ta;
-
-      lie = lie + la;  // e^{i la ta}
-
-    }
-    taExp(lie, out);
-  }
-
-  static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
-                                                  LatticeMatrix &out,
-                                                  Real scale = 1.0) {
-    GridBase *grid = out.Grid();
-    LatticeReal ca(grid);
-    LatticeMatrix la(grid);
-    Complex ci(0.0, scale);
-    Matrix ta;
-
-    out = Zero();
-    for (int a = 0; a < AdjointDimension; a++) {
-      gaussian(pRNG, ca);
-      generator(a, ta);
-      la = toComplex(ca) * ta;
-      out += la;
-    }
-    out *= ci;
-  }
-
-  static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
-                                          LatticeMatrix &out,
-                                          Real scale = 1.0) {
-    conformable(h, out);
-    GridBase *grid = out.Grid();
-    LatticeMatrix la(grid);
-    Matrix ta;
-
-    out = Zero();
-    for (int a = 0; a < AdjointDimension; a++) {
-      generator(a, ta);
-      la = peekColour(h, a) * timesI(ta) * scale;
-      out += la;
-    }
-  }
-/*
- * Fundamental rep gauge xform
- */
-  template<typename Fundamental,typename GaugeMat>
-  static void GaugeTransformFundamental( Fundamental &ferm, GaugeMat &g){
-    GridBase *grid = ferm._grid;
-    conformable(grid,g._grid);
-    ferm = g*ferm;
-  }
-/*
- * Adjoint rep gauge xform
- */
-
-  template<typename Gimpl>
-  static void GaugeTransform(typename Gimpl::GaugeField &Umu, typename Gimpl::GaugeLinkField &g){
-    GridBase *grid = Umu.Grid();
-    conformable(grid,g.Grid());
-
-    typename Gimpl::GaugeLinkField U(grid);
-    typename Gimpl::GaugeLinkField ag(grid); ag = adj(g);
-
-    for(int mu=0;mu<Nd;mu++){
-      U= PeekIndex<LorentzIndex>(Umu,mu);
-      U = g*U*Gimpl::CshiftLink(ag, mu, 1); //BC-aware
-      PokeIndex<LorentzIndex>(Umu,U,mu);
-    }
-  }
-  template<typename Gimpl>
-  static void GaugeTransform( std::vector<typename Gimpl::GaugeLinkField> &U, typename Gimpl::GaugeLinkField &g){
-    GridBase *grid = g.Grid();
-    typename Gimpl::GaugeLinkField ag(grid); ag = adj(g);
-    for(int mu=0;mu<Nd;mu++){
-      U[mu] = g*U[mu]*Gimpl::CshiftLink(ag, mu, 1); //BC-aware
-    }
-  }
-  template<typename Gimpl>
-  static void RandomGaugeTransform(GridParallelRNG &pRNG, typename Gimpl::GaugeField &Umu, typename Gimpl::GaugeLinkField &g){
-    LieRandomize(pRNG,g,1.0);
-    GaugeTransform<Gimpl>(Umu,g);
-  }
-
-  // Projects the algebra components a lattice matrix (of dimension ncol*ncol -1 )
-  // inverse operation: FundamentalLieAlgebraMatrix
-  static void projectOnAlgebra(LatticeAlgebraVector &h_out, const LatticeMatrix &in, Real scale = 1.0) {
-    conformable(h_out, in);
-    h_out = Zero();
-    Matrix Ta;
-
-    for (int a = 0; a < AdjointDimension; a++) {
-      generator(a, Ta);
-      pokeColour(h_out, - 2.0 * (trace(timesI(Ta) * in)) * scale, a);
-    }
-  }
-
-  template <typename GaugeField>
-  static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
-    typedef typename GaugeField::vector_type vector_type;
-    typedef iSUnMatrix<vector_type> vMatrixType;
-    typedef Lattice<vMatrixType> LatticeMatrixType;
-
-    LatticeMatrixType Umu(out.Grid());
-    LatticeMatrixType tmp(out.Grid());
-    for (int mu = 0; mu < Nd; mu++) {
-      //      LieRandomize(pRNG, Umu, 1.0);
-      //      PokeIndex<LorentzIndex>(out, Umu, mu);
-      gaussian(pRNG,Umu);
-      tmp = Ta(Umu);
-      taExp(tmp,Umu);
-      ProjectSUn(Umu);
-      PokeIndex<LorentzIndex>(out, Umu, mu);
-    }
-  }
-  template<typename GaugeField>
-  static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out){
-    typedef typename GaugeField::vector_type vector_type;
-    typedef iSUnMatrix<vector_type> vMatrixType;
-    typedef Lattice<vMatrixType> LatticeMatrixType;
-
-    LatticeMatrixType Umu(out.Grid());
-    for(int mu=0;mu<Nd;mu++){
-      LieRandomize(pRNG,Umu,0.01);
-      PokeIndex<LorentzIndex>(out,Umu,mu);
-    }
-  }
-  template<typename GaugeField>
-  static void ColdConfiguration(GaugeField &out){
-    typedef typename GaugeField::vector_type vector_type;
-    typedef iSUnMatrix<vector_type> vMatrixType;
-    typedef Lattice<vMatrixType> LatticeMatrixType;
-
-    LatticeMatrixType Umu(out.Grid());
-    Umu=1.0;
-    for(int mu=0;mu<Nd;mu++){
-      PokeIndex<LorentzIndex>(out,Umu,mu);
-    }
-  }
-  template<typename GaugeField>
-  static void ColdConfiguration(GridParallelRNG &pRNG,GaugeField &out){
-    ColdConfiguration(out);
-  }
-
-  template<typename LatticeMatrixType>
-  static void taProj( const LatticeMatrixType &in,  LatticeMatrixType &out){
-    out = Ta(in);
-  }
-  template <typename LatticeMatrixType>
-  static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) {
-    typedef typename LatticeMatrixType::scalar_type ComplexType;
-
-    LatticeMatrixType xn(x.Grid());
-    RealD nfac = 1.0;
-
-    xn = x;
-    ex = xn + ComplexType(1.0);  // 1+x
-
-    // Do a 12th order exponentiation
-    for (int i = 2; i <= 12; ++i) {
-      nfac = nfac / RealD(i);  // 1/2, 1/2.3 ...
-      xn = xn * x;             // x2, x3,x4....
-      ex = ex + xn * nfac;     // x2/2!, x3/3!....
-    }
-  }
-};
-
-template<int N>
-Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > Inverse(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
-{
-  GridBase *grid=Umu.Grid();
-  auto lvol = grid->lSites();
-  Lattice<iScalar<iScalar<iMatrix<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);
-    iScalar<iScalar<iMatrix<ComplexD, N> > > Us;
-    iScalar<iScalar<iMatrix<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;
-}
-// Explicit specialisation for SU(3).
-// Explicit specialisation for SU(3).
-static void
-ProjectSU3 (Lattice<iScalar<iScalar<iMatrix<vComplexD, 3> > > > &Umu)
-{
-  GridBase *grid=Umu.Grid();
-  const int x=0;
-  const int y=1;
-  const int z=2;
-  // Reunitarise
-  Umu = ProjectOnGroup(Umu);
-  autoView(Umu_v,Umu,CpuWrite);
-  thread_for(ss,grid->oSites(),{
-      auto cm = Umu_v[ss];
-      cm()()(2,x) = adj(cm()()(0,y)*cm()()(1,z)-cm()()(0,z)*cm()()(1,y)); //x= yz-zy
-      cm()()(2,y) = adj(cm()()(0,z)*cm()()(1,x)-cm()()(0,x)*cm()()(1,z)); //y= zx-xz
-      cm()()(2,z) = adj(cm()()(0,x)*cm()()(1,y)-cm()()(0,y)*cm()()(1,x)); //z= xy-yx
-      Umu_v[ss]=cm;
-  });
-}
-static void ProjectSU3(Lattice<iVector<iScalar<iMatrix<vComplexD, 3> >,Nd> > &U)
-{
-  GridBase *grid=U.Grid();
-  // Reunitarise
-  for(int mu=0;mu<Nd;mu++){
-    auto Umu = PeekIndex<LorentzIndex>(U,mu);
-    Umu      = ProjectOnGroup(Umu);
-    ProjectSU3(Umu);
-    PokeIndex<LorentzIndex>(U,Umu,mu);
-  }
-}
-
-typedef SU<2> SU2;
-typedef SU<3> SU3;
-typedef SU<4> SU4;
-typedef SU<5> SU5;
-
-
-typedef SU<Nc> FundamentalMatrices;
-
-NAMESPACE_END(Grid);
-#endif

Grid/qcd/utils/SUn.impl.h

@@ -0,0 +1,580 @@
+// This file is #included into the body of the class template definition of
+// GaugeGroup. So, image there to be
+//
+// template <int ncolour, class group_name>
+// class GaugeGroup {
+//
+// around it.
+//
+// Please note that the unconventional file extension makes sure that it
+// doesn't get found by the scripts/filelist during bootstrapping.
+
+private:
+
+template <ONLY_IF_SU>
+static int su2subgroups(GroupName::SU) { return (ncolour * (ncolour - 1)) / 2; }
+////////////////////////////////////////////////////////////////////////
+// There are N^2-1 generators for SU(N).
+//
+// We take a traceless hermitian generator basis as follows
+//
+// * Normalisation: trace ta tb = 1/2 delta_ab = T_F delta_ab
+//   T_F = 1/2  for SU(N) groups
+//
+// * Off diagonal
+//    - pairs of rows i1,i2 behaving like pauli matrices signma_x, sigma_y
+//
+//    - there are (Nc-1-i1) slots for i2 on each row [ x  0  x ]
+//      direct count off each row
+//
+//    - Sum of all pairs is Nc(Nc-1)/2: proof arithmetic series
+//
+//      (Nc-1) + (Nc-2)+...  1      ==> Nc*(Nc-1)/2
+//      1+ 2+          +   + Nc-1
+//
+//    - There are 2 x Nc (Nc-1)/ 2 of these = Nc^2 - Nc
+//
+//    - We enumerate the row-col pairs.
+//    - for each row col pair there is a (sigma_x) and a (sigma_y) like
+//    generator
+//
+//
+//   t^a_ij = { in 0.. Nc(Nc-1)/2 -1} =>  1/2(delta_{i,i1} delta_{j,i2} +
+//   delta_{i,i1} delta_{j,i2})
+//   t^a_ij = { in Nc(Nc-1)/2 ... Nc(Nc-1) - 1} =>  i/2( delta_{i,i1}
+//   delta_{j,i2} - i delta_{i,i1} delta_{j,i2})
+//
+// * Diagonal; must be traceless and normalised
+//   - Sequence is
+//   N  (1,-1,0,0...)
+//   N  (1, 1,-2,0...)
+//   N  (1, 1, 1,-3,0...)
+//   N  (1, 1, 1, 1,-4,0...)
+//
+//   where 1/2 = N^2 (1+.. m^2)etc.... for the m-th diagonal generator
+//   NB this gives the famous SU3 result for su2 index 8
+//
+//   N= sqrt(1/2 . 1/6 ) = 1/2 . 1/sqrt(3)
+//
+//   ( 1      )
+//   (    1   ) / sqrt(3) /2  = 1/2 lambda_8
+//   (      -2)
+//
+////////////////////////////////////////////////////////////////////////
+template <class cplx, ONLY_IF_SU>
+static void generator(int lieIndex, iGroupMatrix<cplx> &ta, GroupName::SU) {
+  // map lie index to which type of generator
+  int diagIndex;
+  int su2Index;
+  int sigxy;
+  int NNm1 = ncolour * (ncolour - 1);
+  if (lieIndex >= NNm1) {
+    diagIndex = lieIndex - NNm1;
+    generatorDiagonal(diagIndex, ta);
+    return;
+  }
+  sigxy = lieIndex & 0x1;  // even or odd
+  su2Index = lieIndex >> 1;
+  if (sigxy)
+    generatorSigmaY(su2Index, ta);
+  else
+    generatorSigmaX(su2Index, ta);
+}
+
+template <class cplx, ONLY_IF_SU>
+static void generatorSigmaY(int su2Index, iGroupMatrix<cplx> &ta) {
+  ta = Zero();
+  int i1, i2;
+  su2SubGroupIndex(i1, i2, su2Index);
+  ta()()(i1, i2) = 1.0;
+  ta()()(i2, i1) = 1.0;
+  ta = ta * 0.5;
+}
+
+template <class cplx, ONLY_IF_SU>
+static void generatorSigmaX(int su2Index, iGroupMatrix<cplx> &ta) {
+  ta = Zero();
+  cplx i(0.0, 1.0);
+  int i1, i2;
+  su2SubGroupIndex(i1, i2, su2Index);
+  ta()()(i1, i2) = i;
+  ta()()(i2, i1) = -i;
+  ta = ta * 0.5;
+}
+
+template <class cplx, ONLY_IF_SU>
+static void generatorDiagonal(int diagIndex, iGroupMatrix<cplx> &ta) {
+  // diag ({1, 1, ..., 1}(k-times), -k, 0, 0, ...)
+  ta = Zero();
+  int k = diagIndex + 1;                  // diagIndex starts from 0
+  for (int i = 0; i <= diagIndex; i++) {  // k iterations
+    ta()()(i, i) = 1.0;
+  }
+  ta()()(k, k) = -k;  // indexing starts from 0
+  RealD nrm = 1.0 / std::sqrt(2.0 * k * (k + 1));
+  ta = ta * nrm;
+}
+
+////////////////////////////////////////////////////////////////////////
+// Map a su2 subgroup number to the pair of rows that are non zero
+////////////////////////////////////////////////////////////////////////
+static void su2SubGroupIndex(int &i1, int &i2, int su2_index, GroupName::SU) {
+  assert((su2_index >= 0) && (su2_index < (ncolour * (ncolour - 1)) / 2));
+
+  int spare = su2_index;
+  for (i1 = 0; spare >= (ncolour - 1 - i1); i1++) {
+    spare = spare - (ncolour - 1 - i1);  // remove the Nc-1-i1 terms
+  }
+  i2 = i1 + 1 + spare;
+}
+
+public:
+//////////////////////////////////////////////////////////////////////////////////////////
+// Pull out a subgroup and project on to real coeffs x pauli basis
+//////////////////////////////////////////////////////////////////////////////////////////
+template <class vcplx, ONLY_IF_SU>
+static void su2Extract(Lattice<iSinglet<vcplx> > &Determinant,
+                       Lattice<iSU2Matrix<vcplx> > &subgroup,
+                       const Lattice<iGroupMatrix<vcplx> > &source,
+                       int su2_index) {
+  GridBase *grid(source.Grid());
+  conformable(subgroup, source);
+  conformable(subgroup, Determinant);
+  int i0, i1;
+  su2SubGroupIndex(i0, i1, su2_index);
+
+  autoView(subgroup_v, subgroup, AcceleratorWrite);
+  autoView(source_v, source, AcceleratorRead);
+  autoView(Determinant_v, Determinant, AcceleratorWrite);
+  accelerator_for(ss, grid->oSites(), 1, {
+    subgroup_v[ss]()()(0, 0) = source_v[ss]()()(i0, i0);
+    subgroup_v[ss]()()(0, 1) = source_v[ss]()()(i0, i1);
+    subgroup_v[ss]()()(1, 0) = source_v[ss]()()(i1, i0);
+    subgroup_v[ss]()()(1, 1) = source_v[ss]()()(i1, i1);
+
+    iSU2Matrix<vcplx> Sigma = subgroup_v[ss];
+
+    Sigma = Sigma - adj(Sigma) + trace(adj(Sigma));
+
+    subgroup_v[ss] = Sigma;
+
+    // this should be purely real
+    Determinant_v[ss] =
+        Sigma()()(0, 0) * Sigma()()(1, 1) - Sigma()()(0, 1) * Sigma()()(1, 0);
+  });
+}
+
+//////////////////////////////////////////////////////////////////////////////////////////
+// Set matrix to one and insert a pauli subgroup
+//////////////////////////////////////////////////////////////////////////////////////////
+template <class vcplx, ONLY_IF_SU>
+static void su2Insert(const Lattice<iSU2Matrix<vcplx> > &subgroup,
+                      Lattice<iGroupMatrix<vcplx> > &dest, int su2_index) {
+  GridBase *grid(dest.Grid());
+  conformable(subgroup, dest);
+  int i0, i1;
+  su2SubGroupIndex(i0, i1, su2_index);
+
+  dest = 1.0;  // start out with identity
+  autoView(dest_v, dest, AcceleratorWrite);
+  autoView(subgroup_v, subgroup, AcceleratorRead);
+  accelerator_for(ss, grid->oSites(), 1, {
+    dest_v[ss]()()(i0, i0) = subgroup_v[ss]()()(0, 0);
+    dest_v[ss]()()(i0, i1) = subgroup_v[ss]()()(0, 1);
+    dest_v[ss]()()(i1, i0) = subgroup_v[ss]()()(1, 0);
+    dest_v[ss]()()(i1, i1) = subgroup_v[ss]()()(1, 1);
+  });
+}
+
+///////////////////////////////////////////////
+// Generate e^{ Re Tr Staple Link} dlink
+//
+// *** Note Staple should be appropriate linear compbination between all
+// staples.
+// *** If already by beta pass coefficient 1.0.
+// *** This routine applies the additional 1/Nc factor that comes after trace
+// in action.
+//
+///////////////////////////////////////////////
+template <ONLY_IF_SU>
+static void SubGroupHeatBath(
+    GridSerialRNG &sRNG, GridParallelRNG &pRNG,
+    RealD beta,  // coeff multiplying staple in action (with no 1/Nc)
+    LatticeMatrix &link,
+    const LatticeMatrix &barestaple,  // multiplied by action coeffs so th
+    int su2_subgroup, int nheatbath, LatticeInteger &wheremask) {
+  GridBase *grid = link.Grid();
+
+  const RealD twopi = 2.0 * M_PI;
+
+  LatticeMatrix staple(grid);
+
+  staple = barestaple * (beta / ncolour);
+
+  LatticeMatrix V(grid);
+  V = link * staple;
+
+  // Subgroup manipulation in the lie algebra space
+  LatticeSU2Matrix u(
+      grid);  // Kennedy pendleton "u" real projected normalised Sigma
+  LatticeSU2Matrix uinv(grid);
+  LatticeSU2Matrix ua(grid);  // a in pauli form
+  LatticeSU2Matrix b(grid);   // rotated matrix after hb
+
+  // Some handy constant fields
+  LatticeComplex ones(grid);
+  ones = 1.0;
+  LatticeComplex zeros(grid);
+  zeros = Zero();
+  LatticeReal rones(grid);
+  rones = 1.0;
+  LatticeReal rzeros(grid);
+  rzeros = Zero();
+  LatticeComplex udet(grid);  // determinant of real(staple)
+  LatticeInteger mask_true(grid);
+  mask_true = 1;
+  LatticeInteger mask_false(grid);
+  mask_false = 0;
+
+  /*
+    PLB 156 P393 (1985) (Kennedy and Pendleton)
+
+    Note: absorb "beta" into the def of sigma compared to KP paper; staple
+    passed to this routine has "beta" already multiplied in
+
+    Action linear in links h and of form:
+
+    beta S = beta  Sum_p (1 - 1/Nc Re Tr Plaq )
+
+    Writing Sigma = 1/Nc (beta Sigma') where sum over staples is "Sigma' "
+
+    beta S = const - beta/Nc Re Tr h Sigma'
+    = const - Re Tr h Sigma
+
+    Decompose h and Sigma into (1, sigma_j) ; h_i real, h^2=1, Sigma_i complex
+    arbitrary.
+
+    Tr h Sigma = h_i Sigma_j Tr (sigma_i sigma_j)  = h_i Sigma_j 2 delta_ij
+    Re Tr h Sigma = 2 h_j Re Sigma_j
+
+    Normalised re Sigma_j = xi u_j
+
+    With u_j a unit vector and U can be in SU(2);
+
+    Re Tr h Sigma = 2 h_j Re Sigma_j = 2 xi (h.u)
+
+    4xi^2 = Det [ Sig - Sig^dag  + 1 Tr Sigdag]
+    u   = 1/2xi [ Sig - Sig^dag  + 1 Tr Sigdag]
+
+    xi = sqrt(Det)/2;
+
+    Write a= u h in SU(2); a has pauli decomp a_j;
+
+    Note: Product b' xi is unvariant because scaling Sigma leaves
+    normalised vector "u" fixed; Can rescale Sigma so b' = 1.
+  */
+
+  ////////////////////////////////////////////////////////
+  // Real part of Pauli decomposition
+  // Note a subgroup can project to zero in cold start
+  ////////////////////////////////////////////////////////
+  su2Extract(udet, u, V, su2_subgroup);
+
+  //////////////////////////////////////////////////////
+  // Normalising this vector if possible; else identity
+  //////////////////////////////////////////////////////
+  LatticeComplex xi(grid);
+
+  LatticeSU2Matrix lident(grid);
+
+  SU2Matrix ident = Complex(1.0);
+  SU2Matrix pauli1;
+  GaugeGroup<2, GroupName::SU>::generator(0, pauli1);
+  SU2Matrix pauli2;
+  GaugeGroup<2, GroupName::SU>::generator(1, pauli2);
+  SU2Matrix pauli3;
+  GaugeGroup<2, GroupName::SU>::generator(2, pauli3);
+  pauli1 = timesI(pauli1) * 2.0;
+  pauli2 = timesI(pauli2) * 2.0;
+  pauli3 = timesI(pauli3) * 2.0;
+
+  LatticeComplex cone(grid);
+  LatticeReal adet(grid);
+  adet = abs(toReal(udet));
+  lident = Complex(1.0);
+  cone = Complex(1.0);
+  Real machine_epsilon = 1.0e-7;
+  u = where(adet > machine_epsilon, u, lident);
+  udet = where(adet > machine_epsilon, udet, cone);
+
+  xi = 0.5 * sqrt(udet);        // 4xi^2 = Det [ Sig - Sig^dag  + 1 Tr Sigdag]
+  u = 0.5 * u * pow(xi, -1.0);  //  u   = 1/2xi [ Sig - Sig^dag  + 1 Tr Sigdag]
+
+  // Debug test for sanity
+  uinv = adj(u);
+  b = u * uinv - 1.0;
+  assert(norm2(b) < 1.0e-4);
+
+  /*
+    Measure: Haar measure dh has d^4a delta(1-|a^2|)
+    In polars:
+    da = da0 r^2 sin theta dr dtheta dphi delta( 1 - r^2 -a0^2)
+    = da0 r^2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r)(sqrt(1-a0^) +
+    r) )
+    = da0 r/2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r) )
+
+    Action factor Q(h) dh  = e^-S[h]  dh =  e^{  xi Tr uh} dh    // beta
+    enters through xi =  e^{2 xi (h.u)} dh =  e^{2 xi h0u0}.e^{2 xi h1u1}.e^{2
+    xi h2u2}.e^{2 xi h3u3} dh
+
+    Therefore for each site, take xi for that site
+    i) generate  |a0|<1 with dist
+    (1-a0^2)^0.5 e^{2 xi a0 } da0
+
+    Take alpha = 2 xi  = 2 xi [ recall 2 beta/Nc unmod staple norm];
+    hence 2.0/Nc factor in Chroma ] A. Generate two uniformly distributed
+    pseudo-random numbers R and R', R'', R''' in the unit interval; B. Set X =
+    -(ln R)/alpha, X' =-(ln R')/alpha; C. Set C = cos^2(2pi R"), with R"
+    another uniform random number in [0,1] ; D. Set A = XC; E. Let d  = X'+A;
+    F. If R'''^2 :> 1 - 0.5 d,  go back to A;
+    G. Set a0 = 1 - d;
+
+    Note that in step D setting B ~ X - A and using B in place of A in step E
+    will generate a second independent a 0 value.
+  */
+
+  /////////////////////////////////////////////////////////
+  // count the number of sites by picking "1"'s out of hat
+  /////////////////////////////////////////////////////////
+  Integer hit = 0;
+  LatticeReal rtmp(grid);
+  rtmp = where(wheremask, rones, rzeros);
+  RealD numSites = sum(rtmp);
+  RealD numAccepted;
+  LatticeInteger Accepted(grid);
+  Accepted = Zero();
+  LatticeInteger newlyAccepted(grid);
+
+  std::vector<LatticeReal> xr(4, grid);
+  std::vector<LatticeReal> a(4, grid);
+  LatticeReal d(grid);
+  d = Zero();
+  LatticeReal alpha(grid);
+
+  //    std::cout<<GridLogMessage<<"xi "<<xi <<std::endl;
+  xi = 2.0 * xi;
+  alpha = toReal(xi);
+
+  do {
+    // A. Generate two uniformly distributed pseudo-random numbers R and R',
+    // R'', R''' in the unit interval;
+    random(pRNG, xr[0]);
+    random(pRNG, xr[1]);
+    random(pRNG, xr[2]);
+    random(pRNG, xr[3]);
+
+    // B. Set X = - ln R/alpha, X' = -ln R'/alpha
+    xr[1] = -log(xr[1]) / alpha;
+    xr[2] = -log(xr[2]) / alpha;
+
+    // C. Set C = cos^2(2piR'')
+    xr[3] = cos(xr[3] * twopi);
+    xr[3] = xr[3] * xr[3];
+
+    LatticeReal xrsq(grid);
+
+    // D. Set A = XC;
+    // E. Let d  = X'+A;
+    xrsq = xr[2] + xr[1] * xr[3];
+
+    d = where(Accepted, d, xr[2] + xr[1] * xr[3]);
+
+    // F. If R'''^2 :> 1 - 0.5 d,  go back to A;
+    LatticeReal thresh(grid);
+    thresh = 1.0 - d * 0.5;
+    xrsq = xr[0] * xr[0];
+    LatticeInteger ione(grid);
+    ione = 1;
+    LatticeInteger izero(grid);
+    izero = Zero();
+
+    newlyAccepted = where(xrsq < thresh, ione, izero);
+    Accepted = where(newlyAccepted, newlyAccepted, Accepted);
+    Accepted = where(wheremask, Accepted, izero);
+
+    // FIXME need an iSum for integer to avoid overload on return type??
+    rtmp = where(Accepted, rones, rzeros);
+    numAccepted = sum(rtmp);
+
+    hit++;
+
+  } while ((numAccepted < numSites) && (hit < nheatbath));
+
+  // G. Set a0 = 1 - d;
+  a[0] = Zero();
+  a[0] = where(wheremask, 1.0 - d, a[0]);
+
+  //////////////////////////////////////////
+  //    ii) generate a_i uniform on two sphere radius (1-a0^2)^0.5
+  //////////////////////////////////////////
+
+  LatticeReal a123mag(grid);
+  a123mag = sqrt(abs(1.0 - a[0] * a[0]));
+
+  LatticeReal cos_theta(grid);
+  LatticeReal sin_theta(grid);
+  LatticeReal phi(grid);
+
+  random(pRNG, phi);
+  phi = phi * twopi;  // uniform in [0,2pi]
+  random(pRNG, cos_theta);
+  cos_theta = (cos_theta * 2.0) - 1.0;  // uniform in [-1,1]
+  sin_theta = sqrt(abs(1.0 - cos_theta * cos_theta));
+
+  a[1] = a123mag * sin_theta * cos(phi);
+  a[2] = a123mag * sin_theta * sin(phi);
+  a[3] = a123mag * cos_theta;
+
+  ua = toComplex(a[0]) * ident + toComplex(a[1]) * pauli1 +
+       toComplex(a[2]) * pauli2 + toComplex(a[3]) * pauli3;
+
+  b = 1.0;
+  b = where(wheremask, uinv * ua, b);
+  su2Insert(b, V, su2_subgroup);
+
+  // mask the assignment back based on Accptance
+  link = where(Accepted, V * link, link);
+
+  //////////////////////////////
+  // Debug Checks
+  // SU2 check
+  LatticeSU2Matrix check(grid);  // rotated matrix after hb
+  u = Zero();
+  check = ua * adj(ua) - 1.0;
+  check = where(Accepted, check, u);
+  assert(norm2(check) < 1.0e-4);
+
+  check = b * adj(b) - 1.0;
+  check = where(Accepted, check, u);
+  assert(norm2(check) < 1.0e-4);
+
+  LatticeMatrix Vcheck(grid);
+  Vcheck = Zero();
+  Vcheck = where(Accepted, V * adj(V) - 1.0, Vcheck);
+  //    std::cout<<GridLogMessage << "SU3 check " <<norm2(Vcheck)<<std::endl;
+  assert(norm2(Vcheck) < 1.0e-4);
+
+  // Verify the link stays in SU(3)
+  //    std::cout<<GridLogMessage <<"Checking the modified link"<<std::endl;
+  Vcheck = link * adj(link) - 1.0;
+  assert(norm2(Vcheck) < 1.0e-4);
+  /////////////////////////////////
+}
+
+template <ONLY_IF_SU>
+static void testGenerators(GroupName::SU) {
+  Matrix ta;
+  Matrix tb;
+  std::cout << GridLogMessage
+            << "Fundamental - Checking trace ta tb is 0.5 delta_ab"
+            << std::endl;
+  for (int a = 0; a < AdjointDimension; a++) {
+    for (int b = 0; b < AdjointDimension; b++) {
+      generator(a, ta);
+      generator(b, tb);
+      Complex tr = TensorRemove(trace(ta * tb));
+      std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
+                << std::endl;
+      if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
+      if (a != b) assert(abs(tr) < 1.0e-6);
+    }
+    std::cout << GridLogMessage << std::endl;
+  }
+  std::cout << GridLogMessage << "Fundamental - Checking if hermitian"
+            << std::endl;
+  for (int a = 0; a < AdjointDimension; a++) {
+    generator(a, ta);
+    std::cout << GridLogMessage << a << std::endl;
+    assert(norm2(ta - adj(ta)) < 1.0e-6);
+  }
+  std::cout << GridLogMessage << std::endl;
+
+  std::cout << GridLogMessage << "Fundamental - Checking if traceless"
+            << std::endl;
+  for (int a = 0; a < AdjointDimension; a++) {
+    generator(a, ta);
+    Complex tr = TensorRemove(trace(ta));
+    std::cout << GridLogMessage << a << " " << std::endl;
+    assert(abs(tr) < 1.0e-6);
+  }
+  std::cout << GridLogMessage << std::endl;
+}
+
+
+template <int N, class vtype>
+static Lattice<iScalar<iScalar<iMatrix<vtype, N> > > >
+ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vtype, N> > > > &Umu, GroupName::SU) {
+  return ProjectOnGroup(Umu);
+}
+
+template <class vtype>
+accelerator_inline static iScalar<vtype> ProjectOnGeneralGroup(const iScalar<vtype> &r, GroupName::SU) {
+  return ProjectOnGroup(r);
+}
+
+template <class vtype, int N>
+accelerator_inline static iVector<vtype,N> ProjectOnGeneralGroup(const iVector<vtype,N> &r, GroupName::SU) {
+  return ProjectOnGroup(r);
+}
+
+template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
+accelerator_inline static iMatrix<vtype,N> ProjectOnGeneralGroup(const iMatrix<vtype,N> &arg, GroupName::SU) {
+  return ProjectOnGroup(arg);
+}
+
+template <typename LatticeMatrixType>
+static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::SU) {
+  out = Ta(in);
+}
+
+/*
+ * Fundamental rep gauge xform
+ */
+template<typename Fundamental,typename GaugeMat>
+static void GaugeTransformFundamental( Fundamental &ferm, GaugeMat &g){
+  GridBase *grid = ferm._grid;
+  conformable(grid,g._grid);
+  ferm = g*ferm;
+}
+/*
+ * Adjoint rep gauge xform
+ */
+
+template<typename Gimpl>
+static void GaugeTransform(typename Gimpl::GaugeField &Umu, typename Gimpl::GaugeLinkField &g){
+  GridBase *grid = Umu.Grid();
+  conformable(grid,g.Grid());
+
+  typename Gimpl::GaugeLinkField U(grid);
+  typename Gimpl::GaugeLinkField ag(grid); ag = adj(g);
+
+  for(int mu=0;mu<Nd;mu++){
+    U= PeekIndex<LorentzIndex>(Umu,mu);
+    U = g*U*Gimpl::CshiftLink(ag, mu, 1); //BC-aware
+    PokeIndex<LorentzIndex>(Umu,U,mu);
+  }
+}
+template<typename Gimpl>
+static void GaugeTransform( std::vector<typename Gimpl::GaugeLinkField> &U, typename Gimpl::GaugeLinkField &g){
+  GridBase *grid = g.Grid();
+  typename Gimpl::GaugeLinkField ag(grid); ag = adj(g);
+  for(int mu=0;mu<Nd;mu++){
+    U[mu] = g*U[mu]*Gimpl::CshiftLink(ag, mu, 1); //BC-aware
+  }
+}
+template<typename Gimpl>
+static void RandomGaugeTransform(GridParallelRNG &pRNG, typename Gimpl::GaugeField &Umu, typename Gimpl::GaugeLinkField &g){
+  LieRandomize(pRNG,g,1.0);
+  GaugeTransform<Gimpl>(Umu,g);
+}
+

Grid/qcd/utils/SUnAdjoint.h

@@ -51,6 +51,10 @@ public:
   typedef Lattice<iVector<iScalar<iMatrix<vComplexF, Dimension> >, Nd> > LatticeAdjFieldF;
   typedef Lattice<iVector<iScalar<iMatrix<vComplexD, Dimension> >, Nd> > LatticeAdjFieldD;
 
+
+  template <typename vtype>
+  using iSUnMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
+
   typedef Lattice<iScalar<iScalar<iVector<vComplex, Dimension> > > >  LatticeAdjVector;
 
   template <class cplx>
@@ -58,8 +62,8 @@ public:
     // returns i(T_Adj)^index necessary for the projectors
     // see definitions above
     iAdjTa = Zero();
-    Vector<typename SU<ncolour>::template iSUnMatrix<cplx> > ta(ncolour * ncolour - 1);
-    typename SU<ncolour>::template iSUnMatrix<cplx> tmp;
+    Vector<iSUnMatrix<cplx> > ta(ncolour * ncolour - 1);
+    iSUnMatrix<cplx> tmp;
 
     // FIXME not very efficient to get all the generators everytime
     for (int a = 0; a < Dimension; a++) SU<ncolour>::generator(a, ta[a]);
@@ -67,8 +71,7 @@ public:
     for (int a = 0; a < Dimension; a++) {
       tmp = ta[a] * ta[Index] - ta[Index] * ta[a];
       for (int b = 0; b < (ncolour * ncolour - 1); b++) {
-        typename SU<ncolour>::template iSUnMatrix<cplx> tmp1 =
-	  2.0 * tmp * ta[b];  // 2.0 from the normalization
+        iSUnMatrix<cplx> tmp1 = 2.0 * tmp * ta[b];  // 2.0 from the normalization
         Complex iTr = TensorRemove(timesI(trace(tmp1)));
         //iAdjTa()()(b, a) = iTr;
         iAdjTa()()(a, b) = iTr;
@@ -134,8 +137,7 @@ public:
 
     for (int a = 0; a < Dimension; a++) {
       generator(a, iTa);
-      LatticeComplex tmp = real(trace(iTa * in)) * coefficient;
-      pokeColour(h_out, tmp, a);
+      pokeColour(h_out, real(trace(iTa * in)) * coefficient, a);
     }
   }
 

Grid/qcd/utils/SUnTwoIndex.h

@@ -1,273 +0,0 @@
-////////////////////////////////////////////////////////////////////////
-//
-// * Two index representation generators
-//
-// * Normalisation for the fundamental generators:
-//   trace ta tb = 1/2 delta_ab = T_F delta_ab
-//   T_F = 1/2  for SU(N) groups
-//
-//
-//   base for NxN two index (anti-symmetric) matrices
-//   normalized to 1 (d_ij is the kroenecker delta)
-//
-//   (e^(ij)_{kl} = 1 / sqrt(2) (d_ik d_jl +/- d_jk d_il)
-//
-//   Then the generators are written as
-//
-//   (iT_a)^(ij)(lk) = i * ( tr[e^(ij)^dag e^(lk) T^trasp_a] +
-//   tr[e^(lk)e^(ij)^dag T_a] )  //
-//   
-//
-////////////////////////////////////////////////////////////////////////
-
-// Authors: David Preti, Guido Cossu
-
-#ifndef QCD_UTIL_SUN2INDEX_H
-#define QCD_UTIL_SUN2INDEX_H
-
-
-NAMESPACE_BEGIN(Grid);
-
-enum TwoIndexSymmetry { Symmetric = 1, AntiSymmetric = -1 };
-
-inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
-
-template <int ncolour, TwoIndexSymmetry S>
-class SU_TwoIndex : public SU<ncolour> {
-public:
-  static const int Dimension = ncolour * (ncolour + S) / 2;
-  static const int NumGenerators = SU<ncolour>::AdjointDimension;
-
-  template <typename vtype>
-  using iSUnTwoIndexMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
-
-  typedef iSUnTwoIndexMatrix<Complex> TIMatrix;
-  typedef iSUnTwoIndexMatrix<ComplexF> TIMatrixF;
-  typedef iSUnTwoIndexMatrix<ComplexD> TIMatrixD;
-
-  typedef iSUnTwoIndexMatrix<vComplex> vTIMatrix;
-  typedef iSUnTwoIndexMatrix<vComplexF> vTIMatrixF;
-  typedef iSUnTwoIndexMatrix<vComplexD> vTIMatrixD;
-
-  typedef Lattice<vTIMatrix> LatticeTwoIndexMatrix;
-  typedef Lattice<vTIMatrixF> LatticeTwoIndexMatrixF;
-  typedef Lattice<vTIMatrixD> LatticeTwoIndexMatrixD;
-
-  typedef Lattice<iVector<iScalar<iMatrix<vComplex, Dimension> >, Nd> >
-  LatticeTwoIndexField;
-  typedef Lattice<iVector<iScalar<iMatrix<vComplexF, Dimension> >, Nd> >
-  LatticeTwoIndexFieldF;
-  typedef Lattice<iVector<iScalar<iMatrix<vComplexD, Dimension> >, Nd> >
-  LatticeTwoIndexFieldD;
-
-  template <typename vtype>
-  using iSUnMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
-
-  typedef iSUnMatrix<Complex> Matrix;
-  typedef iSUnMatrix<ComplexF> MatrixF;
-  typedef iSUnMatrix<ComplexD> MatrixD;
-
-  template <class cplx>
-  static void base(int Index, iSUnMatrix<cplx> &eij) {
-    // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
-    assert(Index < NumGenerators);
-    eij = Zero();
-
-    // for the linearisation of the 2 indexes 
-    static int a[ncolour * (ncolour - 1) / 2][2]; // store the a <-> i,j
-    static bool filled = false;
-    if (!filled) {
-      int counter = 0;
-      for (int i = 1; i < ncolour; i++) {
-        for (int j = 0; j < i; j++) {
-          a[counter][0] = i;
-          a[counter][1] = j;
-          counter++;
-        }
-      }
-      filled = true;
-    }
-
-    if (Index < ncolour * (ncolour - 1) / 2) {
-      baseOffDiagonal(a[Index][0], a[Index][1], eij);
-    } else {
-      baseDiagonal(Index, eij);
-    }
-  }
-
-  template <class cplx>
-  static void baseDiagonal(int Index, iSUnMatrix<cplx> &eij) {
-    eij = Zero();
-    eij()()(Index - ncolour * (ncolour - 1) / 2,
-            Index - ncolour * (ncolour - 1) / 2) = 1.0;
-  }
-
-  template <class cplx>
-  static void baseOffDiagonal(int i, int j, iSUnMatrix<cplx> &eij) {
-    eij = Zero();
-    for (int k = 0; k < ncolour; k++)
-      for (int l = 0; l < ncolour; l++)
-        eij()()(l, k) = delta(i, k) * delta(j, l) +
-	  S * delta(j, k) * delta(i, l);
-
-    RealD nrm = 1. / std::sqrt(2.0);
-    eij = eij * nrm;
-  }
-
-  static void printBase(void) {
-    for (int gen = 0; gen < Dimension; gen++) {
-      Matrix tmp;
-      base(gen, tmp);
-      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
-                << std::endl;
-      std::cout << GridLogMessage << tmp << std::endl;
-    }
-  }
-
-  template <class cplx>
-  static void generator(int Index, iSUnTwoIndexMatrix<cplx> &i2indTa) {
-    Vector<typename SU<ncolour>::template iSUnMatrix<cplx> > ta(
-								ncolour * ncolour - 1);
-    Vector<typename SU<ncolour>::template iSUnMatrix<cplx> > eij(Dimension);
-    typename SU<ncolour>::template iSUnMatrix<cplx> tmp;
-    i2indTa = Zero();
-    
-    for (int a = 0; a < ncolour * ncolour - 1; a++)
-      SU<ncolour>::generator(a, ta[a]);
-    
-    for (int a = 0; a < Dimension; a++) base(a, eij[a]);
-
-    for (int a = 0; a < Dimension; a++) {
-      tmp = transpose(ta[Index]) * adj(eij[a]) + adj(eij[a]) * ta[Index];
-      for (int b = 0; b < Dimension; b++) {
-        typename SU<ncolour>::template iSUnMatrix<cplx> tmp1 =
-	  tmp * eij[b]; 
-        Complex iTr = TensorRemove(timesI(trace(tmp1)));
-        i2indTa()()(a, b) = iTr;
-      }
-    }
-  }
-
-  static void printGenerators(void) {
-    for (int gen = 0; gen < ncolour * ncolour - 1; gen++) {
-      TIMatrix i2indTa;
-      generator(gen, i2indTa);
-      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
-                << std::endl;
-      std::cout << GridLogMessage << i2indTa << std::endl;
-    }
-  }
-
-  static void testGenerators(void) {
-    TIMatrix i2indTa, i2indTb;
-    std::cout << GridLogMessage << "2IndexRep - Checking if traceless"
-              << std::endl;
-    for (int a = 0; a < ncolour * ncolour - 1; a++) {
-      generator(a, i2indTa);
-      std::cout << GridLogMessage << a << std::endl;
-      assert(norm2(trace(i2indTa)) < 1.0e-6);
-    }
-    std::cout << GridLogMessage << std::endl;
-
-    std::cout << GridLogMessage << "2IndexRep - Checking if antihermitean"
-              << std::endl;
-    for (int a = 0; a < ncolour * ncolour - 1; a++) {
-      generator(a, i2indTa);
-      std::cout << GridLogMessage << a << std::endl;
-      assert(norm2(adj(i2indTa) + i2indTa) < 1.0e-6);
-    }
-
-    std::cout << GridLogMessage << std::endl;
-    std::cout << GridLogMessage
-              << "2IndexRep - Checking Tr[Ta*Tb]=delta(a,b)*(N +- 2)/2"
-              << std::endl;
-    for (int a = 0; a < ncolour * ncolour - 1; a++) {
-      for (int b = 0; b < ncolour * ncolour - 1; b++) {
-        generator(a, i2indTa);
-        generator(b, i2indTb);
-
-        // generator returns iTa, so we need a minus sign here
-        Complex Tr = -TensorRemove(trace(i2indTa * i2indTb));
-        std::cout << GridLogMessage << "a=" << a << "b=" << b << "Tr=" << Tr
-                  << std::endl;
-      }
-    }
-    std::cout << GridLogMessage << std::endl;
-  }
-
-  static void TwoIndexLieAlgebraMatrix(
-				       const typename SU<ncolour>::LatticeAlgebraVector &h,
-				       LatticeTwoIndexMatrix &out, Real scale = 1.0) {
-    conformable(h, out);
-    GridBase *grid = out.Grid();
-    LatticeTwoIndexMatrix la(grid);
-    TIMatrix i2indTa;
-
-    out = Zero();
-    for (int a = 0; a < ncolour * ncolour - 1; a++) {
-      generator(a, i2indTa);
-      la = peekColour(h, a) * i2indTa;
-      out += la;
-    }
-    out *= scale;
-  }
-
-  // Projects the algebra components 
-  // of a lattice matrix ( of dimension ncol*ncol -1 )
-  static void projectOnAlgebra(
-			       typename SU<ncolour>::LatticeAlgebraVector &h_out,
-			       const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
-    conformable(h_out, in);
-    h_out = Zero();
-    TIMatrix i2indTa;
-    Real coefficient = -2.0 / (ncolour + 2 * S) * scale;
-    // 2/(Nc +/- 2) for the normalization of the trace in the two index rep
-    for (int a = 0; a < ncolour * ncolour - 1; a++) {
-      generator(a, i2indTa);
-      auto tmp = real(trace(i2indTa * in)) * coefficient;
-      pokeColour(h_out, tmp, a);
-    }
-  }
-
-  // a projector that keeps the generators stored to avoid the overhead of
-  // recomputing them
-  static void projector(typename SU<ncolour>::LatticeAlgebraVector &h_out,
-                        const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
-    conformable(h_out, in);
-    // to store the generators
-    static std::vector<TIMatrix> i2indTa(ncolour * ncolour -1); 
-    h_out = Zero();
-    static bool precalculated = false;
-    if (!precalculated) {
-      precalculated = true;
-      for (int a = 0; a < ncolour * ncolour - 1; a++) generator(a, i2indTa[a]);
-    }
-
-    Real coefficient =
-      -2.0 / (ncolour + 2 * S) * scale;  // 2/(Nc +/- 2) for the normalization
-    // of the trace in the two index rep
-
-    for (int a = 0; a < ncolour * ncolour - 1; a++) {
-      auto tmp = real(trace(i2indTa[a] * in)) * coefficient;
-      pokeColour(h_out, tmp, a);
-    }
-  }
-};
-
-// Some useful type names
-typedef SU_TwoIndex<Nc, Symmetric> TwoIndexSymmMatrices;
-typedef SU_TwoIndex<Nc, AntiSymmetric> TwoIndexAntiSymmMatrices;
-
-typedef SU_TwoIndex<2, Symmetric> SU2TwoIndexSymm;
-typedef SU_TwoIndex<3, Symmetric> SU3TwoIndexSymm;
-typedef SU_TwoIndex<4, Symmetric> SU4TwoIndexSymm;
-typedef SU_TwoIndex<5, Symmetric> SU5TwoIndexSymm;
-
-typedef SU_TwoIndex<2, AntiSymmetric> SU2TwoIndexAntiSymm;
-typedef SU_TwoIndex<3, AntiSymmetric> SU3TwoIndexAntiSymm;
-typedef SU_TwoIndex<4, AntiSymmetric> SU4TwoIndexAntiSymm;
-typedef SU_TwoIndex<5, AntiSymmetric> SU5TwoIndexAntiSymm;
-
-NAMESPACE_END(Grid);
-
-#endif

Grid/qcd/utils/Sp2n.impl.h

@@ -0,0 +1,317 @@
+// This file is #included into the body of the class template definition of
+// GaugeGroup. So, image there to be
+//
+// template <int ncolour, class group_name>
+// class GaugeGroup {
+//
+// around it.
+//
+// Please note that the unconventional file extension makes sure that it
+// doesn't get found by the scripts/filelist during bootstrapping.
+
+private:
+template <ONLY_IF_Sp>
+static int su2subgroups(GroupName::Sp) { return (ncolour/2 * (ncolour/2 - 1)) / 2; }
+
+// Sp(2N) has N(2N+1) = 2N^2+N generators
+//
+// normalise the generators such that
+// Trace ( Ta Tb) = 1/2 delta_ab
+//
+// N generators in the cartan, 2N^2 off
+// off diagonal:
+//     there are 6 types named a,b,c,d and w,z
+//     abcd are N(N-1)/2 each while wz are N each
+
+template <class cplx, ONLY_IF_Sp>
+static void generator(int lieIndex, iGroupMatrix<cplx> &ta, GroupName::Sp) {
+  // map lie index into type of generators: diagonal, abcd type, wz type
+
+  const int nsp = ncolour/2;
+  int diagIndex;
+  int aIndex, bIndex, cIndex, dIndex;
+  int wIndex, zIndex;  // a,b,c,d are N(N-1)/2 and w,z are N
+  const int mod = nsp * (nsp - 1) * 0.5;
+  const int offdiag =
+      2 * nsp * nsp;  // number of generators not in the cartan subalgebra
+  const int wmod = 4 * mod;
+  const int zmod = wmod + nsp;
+  if (lieIndex >= offdiag) {
+    diagIndex = lieIndex - offdiag;  // 0, ... ,N-1
+    // std::cout << GridLogMessage << "diag type " << std::endl;
+    generatorDiagtype(diagIndex, ta);
+    return;
+  }
+  if ((lieIndex >= wmod) && (lieIndex < zmod)) {
+    // std::cout << GridLogMessage << "w type " << std::endl;
+    wIndex = lieIndex - wmod;  // 0, ... ,N-1
+    generatorWtype(wIndex, ta);
+    return;
+  }
+  if ((lieIndex >= zmod) && (lieIndex < offdiag)) {
+    // std::cout << GridLogMessage << "z type " << std::endl;
+    // std::cout << GridLogMessage << "lie index " << lieIndex << std::endl;
+    // std::cout << GridLogMessage << "z mod " << zmod << std::endl;
+    zIndex = lieIndex - zmod;  // 0, ... ,N-1
+    generatorZtype(zIndex, ta);
+    return;
+  }
+  if (lieIndex < mod) {  // atype 0, ... , N(N-1)/2=mod
+    // std::cout << GridLogMessage << "a type " << std::endl;
+    aIndex = lieIndex;
+    // std::cout << GridLogMessage << "a indx " << aIndex << std::endl;
+    generatorAtype(aIndex, ta);
+    return;
+  }
+  if ((lieIndex >= mod) && lieIndex < 2 * mod) {  // btype mod, ... , 2mod-1
+    // std::cout << GridLogMessage << "b type " << std::endl;
+    bIndex = lieIndex - mod;
+    generatorBtype(bIndex, ta);
+    return;
+  }
+  if ((lieIndex >= 2 * mod) &&
+      lieIndex < 3 * mod) {  // ctype 2mod, ... , 3mod-1
+    // std::cout << GridLogMessage << "c type " << std::endl;
+    cIndex = lieIndex - 2 * mod;
+    generatorCtype(cIndex, ta);
+    return;
+  }
+  if ((lieIndex >= 3 * mod) &&
+      lieIndex < wmod) {  // ctype 3mod, ... , 4mod-1 = wmod-1
+    // std::cout << GridLogMessage << "d type " << std::endl;
+    dIndex = lieIndex - 3 * mod;
+    generatorDtype(dIndex, ta);
+    return;
+  }
+
+}  // end of generator
+
+template <class cplx, ONLY_IF_Sp>
+static void generatorDiagtype(int diagIndex, iGroupMatrix<cplx> &ta) {
+  // ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan subalgebra
+
+  const int nsp=ncolour/2;
+  ta = Zero();
+  RealD nrm = 1.0 / 2;
+
+  ta()()(diagIndex, diagIndex) = nrm;
+  ta()()(diagIndex + nsp, diagIndex + nsp) = -nrm;
+}
+
+template <class cplx, ONLY_IF_Sp>
+static void generatorAtype(int aIndex, iGroupMatrix<cplx> &ta) {
+  // ta(i,j) = ta(j,i) = -ta(i+N,j+N) = -ta(j+N,i+N) = 1 / 2 sqrt(2)
+  // with i<j and i=0,...,N-2
+  // follows that j=i+1, ... , N
+  int i1, i2;
+  const int nsp=ncolour/2;
+  ta = Zero();
+  RealD nrm = 1 / (2 * std::sqrt(2));
+
+  su2SubGroupIndex(i1, i2, aIndex);
+  ta()()(i1, i2) = 1;
+  ta()()(i2, i1) = 1;
+  ta()()(i1 + nsp, i2 + nsp) = -1;
+  ta()()(i2 + nsp, i1 + nsp) = -1;
+
+  ta = ta * nrm;
+}
+
+template <class cplx, ONLY_IF_Sp>
+static void generatorBtype(int bIndex, iGroupMatrix<cplx> &ta) {
+  // ta(i,j) = -ta(j,i) = ta(i+N,j+N) = -ta(j+N,i+N) = i / 1/ 2 sqrt(2)
+  // with i<j and i=0,...,N-2
+  // follows that j=i+1, ... , N-1
+
+  const int nsp=ncolour/2;
+  int i1, i2;
+  ta = Zero();
+  cplx i(0.0, 1.0);
+  RealD nrm = 1 / (2 * std::sqrt(2));
+  su2SubGroupIndex(i1, i2, bIndex);
+
+  ta()()(i1, i2) = i;
+  ta()()(i2, i1) = -i;
+  ta()()(i1 + nsp, i2 + nsp) = i;
+  ta()()(i2 + nsp, i1 + nsp) = -i;
+
+  ta = ta * nrm;
+}
+
+template <class cplx, ONLY_IF_Sp>
+static void generatorCtype(int cIndex, iGroupMatrix<cplx> &ta) {
+  // ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
+
+  const int nsp=ncolour/2;
+  int i1, i2;
+  ta = Zero();
+  RealD nrm = 1 / (2 * std::sqrt(2));
+  su2SubGroupIndex(i1, i2, cIndex);
+
+  ta()()(i1, i2 + nsp) = 1;
+  ta()()(i2, i1 + nsp) = 1;
+  ta()()(i1 + nsp, i2) = 1;
+  ta()()(i2 + nsp, i1) = 1;
+
+  ta = ta * nrm;
+}
+
+template <class cplx, ONLY_IF_Sp>
+static void generatorDtype(int dIndex, iGroupMatrix<cplx> &ta) {
+  // ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i /  2 sqrt(2)
+
+  const int nsp=ncolour/2;
+  int i1, i2;
+  ta = Zero();
+  cplx i(0.0, 1.0);
+  RealD nrm = 1 / (2 * std::sqrt(2));
+  su2SubGroupIndex(i1, i2, dIndex);
+
+  ta()()(i1, i2 + nsp) = i;
+  ta()()(i2, i1 + nsp) = i;
+  ta()()(i1 + nsp, i2) = -i;
+  ta()()(i2 + nsp, i1) = -i;
+
+  ta = ta * nrm;
+}
+
+template <class cplx, ONLY_IF_Sp>
+static void generatorWtype(int wIndex, iGroupMatrix<cplx> &ta) {
+  // ta(i,i+N) =  ta(i+N,i) = 1/2
+
+  const int nsp=ncolour/2;
+  ta = Zero();
+  RealD nrm = 1.0 / 2;  // check
+
+  ta()()(wIndex, wIndex + nsp) = 1;
+  ta()()(wIndex + nsp, wIndex) = 1;
+
+  ta = ta * nrm;
+}
+
+template <class cplx, ONLY_IF_Sp>
+static void generatorZtype(int zIndex, iGroupMatrix<cplx> &ta) {
+  // ta(i,i+N) = - ta(i+N,i) = i/2
+
+  const int nsp=ncolour/2;
+  ta = Zero();
+  RealD nrm = 1.0 / 2;  // check
+  cplx i(0.0, 1.0);
+  ta()()(zIndex, zIndex + nsp) = i;
+  ta()()(zIndex + nsp, zIndex) = -i;
+
+  ta = ta * nrm;
+}
+
+////////////////////////////////////////////////////////////////////////
+// Map a su2 subgroup number to the pair of rows that are non zero
+////////////////////////////////////////////////////////////////////////
+template <ONLY_IF_Sp>
+static void su2SubGroupIndex(int &i1, int &i2, int su2_index, GroupName::Sp) {
+  const int nsp=ncolour/2;
+  assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
+
+  int spare = su2_index;
+  for (i1 = 0; spare >= (nsp - 1 - i1); i1++) {
+    spare = spare - (nsp - 1 - i1);  // remove the Nc-1-i1 terms
+  }
+  i2 = i1 + 1 + spare;
+}
+
+static void testGenerators(GroupName::Sp) {
+  Matrix ta;
+  Matrix tb;
+  std::cout << GridLogMessage
+            << "Fundamental - Checking trace ta tb is 0.5 delta_ab "
+            << std::endl;
+  for (int a = 0; a < AlgebraDimension; a++) {
+    for (int b = 0; b < AlgebraDimension; b++) {
+      generator(a, ta);
+      generator(b, tb);
+      Complex tr = TensorRemove(trace(ta * tb));
+      std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
+                << std::endl;
+      if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
+      if (a != b) assert(abs(tr) < 1.0e-6);
+    }
+  }
+  std::cout << GridLogMessage << std::endl;
+  std::cout << GridLogMessage << "Fundamental - Checking if hermitian"
+            << std::endl;
+  for (int a = 0; a < AlgebraDimension; a++) {
+    generator(a, ta);
+    std::cout << GridLogMessage << a << std::endl;
+    assert(norm2(ta - adj(ta)) < 1.0e-6);
+  }
+  std::cout << GridLogMessage << std::endl;
+  std::cout << GridLogMessage << "Fundamental - Checking if traceless"
+            << std::endl;
+  for (int a = 0; a < AlgebraDimension; a++) {
+    generator(a, ta);
+    Complex tr = TensorRemove(trace(ta));
+    std::cout << GridLogMessage << a << std::endl;
+    assert(abs(tr) < 1.0e-6);
+  }
+}
+
+template <int N>
+static Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > >
+ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::Sp) {
+  return ProjectOnSpGroup(Umu);
+}
+
+template <class vtype>
+accelerator_inline static iScalar<vtype> ProjectOnGeneralGroup(const iScalar<vtype> &r, GroupName::Sp) {
+  return ProjectOnSpGroup(r);
+}
+
+template <class vtype, int N>
+accelerator_inline static iVector<vtype,N> ProjectOnGeneralGroup(const iVector<vtype,N> &r, GroupName::Sp) {
+  return ProjectOnSpGroup(r);
+}
+
+template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
+accelerator_inline static iMatrix<vtype,N> ProjectOnGeneralGroup(const iMatrix<vtype,N> &arg, GroupName::Sp) {
+  return ProjectOnSpGroup(arg);
+}
+
+template <typename LatticeMatrixType>   
+static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::Sp) {
+  out = SpTa(in);
+}
+
+public:
+
+template <ONLY_IF_Sp>
+static void Omega(LatticeColourMatrixD &in) {
+  const int nsp=ncolour/2;
+  LatticeColourMatrixD OmegaLatt(in.Grid());
+  LatticeColourMatrixD identity(in.Grid());
+  ColourMatrix Omega;
+
+  OmegaLatt = Zero();
+  Omega = Zero();
+  identity = 1.;
+
+  for (int i = 0; i < nsp; i++) {
+    Omega()()(i, nsp + i) = 1.;
+    Omega()()(nsp + i, i) = -1;
+  }
+  OmegaLatt = OmegaLatt + (identity * Omega);
+  in = OmegaLatt;
+}
+
+template <ONLY_IF_Sp, class vtype, int N>
+static void Omega(iScalar<iScalar<iMatrix<vtype, N> > > &in) {
+  const int nsp=ncolour/2;
+    
+  iScalar<iScalar<iMatrix<vtype, N> > > Omega;
+  Omega = Zero();
+
+  for (int i = 0; i < nsp; i++) {
+    Omega()()(i, nsp + i) = 1.;
+    Omega()()(nsp + i, i) = -1;
+  }
+    
+  in = Omega;
+}

Grid/qcd/utils/Utils.h

@@ -8,9 +8,9 @@
 #include <Grid/qcd/utils/ScalarObjs.h>
 
 // Include representations
-#include <Grid/qcd/utils/SUn.h>
+#include <Grid/qcd/utils/GaugeGroup.h>
 #include <Grid/qcd/utils/SUnAdjoint.h>
-#include <Grid/qcd/utils/SUnTwoIndex.h>
+#include <Grid/qcd/utils/GaugeGroupTwoIndex.h>
 
 // All-to-all contraction kernels that touch the 
 // internal lattice structure

Grid/qcd/utils/WilsonLoops.h

@@ -290,7 +290,7 @@ public:
   }
 */
   //////////////////////////////////////////////////
-  // the sum over all staples on each site
+  // the sum over all nu-oriented staples for nu != mu on each site
   //////////////////////////////////////////////////
   static void Staple(GaugeMat &staple, const GaugeLorentz &Umu, int mu) {
 
@@ -300,6 +300,10 @@ public:
     for (int d = 0; d < Nd; d++) {
       U[d] = PeekIndex<LorentzIndex>(Umu, d);
     }
+    Staple(staple, U, mu);
+  }
+
+  static void Staple(GaugeMat &staple, const std::vector<GaugeMat> &U, int mu) {
     staple = Zero();
 
     for (int nu = 0; nu < Nd; nu++) {
@@ -335,6 +339,203 @@ public:
     }
   }
 
+  /////////////
+  //Staples for each direction mu, summed over nu != mu
+  //staple: output staples for each mu (Nd)
+  //U: link array (Nd)
+  /////////////
+  static void StapleAll(std::vector<GaugeMat> &staple, const std::vector<GaugeMat> &U) {
+    assert(staple.size() == Nd); assert(U.size() == Nd);
+    for(int mu=0;mu<Nd;mu++) Staple(staple[mu], U, mu);
+  }
+
+
+  //A workspace class allowing reuse of the stencil
+  class WilsonLoopPaddedStencilWorkspace{
+    std::unique_ptr<GeneralLocalStencil> stencil;
+    size_t nshift;
+
+    void generateStencil(GridBase* padded_grid){
+      double t0 = usecond();
+      
+      //Generate shift arrays
+      std::vector<Coordinate> shifts = this->getShifts();
+      nshift = shifts.size();
+      
+      double t1 = usecond();
+      //Generate local stencil
+      stencil.reset(new GeneralLocalStencil(padded_grid,shifts));
+      double t2 = usecond();
+      std::cout << GridLogPerformance << " WilsonLoopPaddedWorkspace timings: coord:" << (t1-t0)/1000 << "ms, stencil:" << (t2-t1)/1000 << "ms" << std::endl;   
+    }
+  public:
+    //Get the stencil. If not already generated, or if generated using a different Grid than in PaddedCell, it will be created on-the-fly
+    const GeneralLocalStencil & getStencil(const PaddedCell &pcell){
+      assert(pcell.depth >= this->paddingDepth());
+      if(!stencil || stencil->Grid() != (GridBase*)pcell.grids.back() ) generateStencil((GridBase*)pcell.grids.back());
+      return *stencil;
+    }
+    size_t Nshift() const{ return nshift; }
+    
+    virtual std::vector<Coordinate> getShifts() const = 0;
+    virtual int paddingDepth() const = 0; //padding depth required
+    
+    virtual ~WilsonLoopPaddedStencilWorkspace(){}
+  };
+
+  //This workspace allows the sharing of a common PaddedCell object between multiple stencil workspaces
+  class WilsonLoopPaddedWorkspace{
+    std::vector<WilsonLoopPaddedStencilWorkspace*> stencil_wk;
+    std::unique_ptr<PaddedCell> pcell;
+
+    void generatePcell(GridBase* unpadded_grid){
+      assert(stencil_wk.size());
+      int max_depth = 0;
+      for(auto const &s : stencil_wk) max_depth=std::max(max_depth, s->paddingDepth());
+      
+      pcell.reset(new PaddedCell(max_depth, dynamic_cast<GridCartesian*>(unpadded_grid)));
+    }
+    
+  public:
+    //Add a stencil definition. This should be done before the first call to retrieve a stencil object.
+    //Takes ownership of the pointer
+    void addStencil(WilsonLoopPaddedStencilWorkspace *stencil){
+      assert(!pcell);
+      stencil_wk.push_back(stencil);
+    }
+
+    const GeneralLocalStencil & getStencil(const size_t stencil_idx, GridBase* unpadded_grid){
+      if(!pcell || pcell->unpadded_grid != unpadded_grid) generatePcell(unpadded_grid);
+      return stencil_wk[stencil_idx]->getStencil(*pcell);
+    }      
+    const PaddedCell & getPaddedCell(GridBase* unpadded_grid){
+      if(!pcell || pcell->unpadded_grid != unpadded_grid) generatePcell(unpadded_grid);
+      return *pcell;
+    }
+    
+    ~WilsonLoopPaddedWorkspace(){
+      for(auto &s : stencil_wk) delete s;
+    }
+  };
+
+  //A workspace class allowing reuse of the stencil
+  class StaplePaddedAllWorkspace: public WilsonLoopPaddedStencilWorkspace{
+  public:
+    std::vector<Coordinate> getShifts() const override{
+      std::vector<Coordinate> shifts;
+      for(int mu=0;mu<Nd;mu++){
+	for(int nu=0;nu<Nd;nu++){
+	  if(nu != mu){
+	    Coordinate shift_0(Nd,0);
+	    Coordinate shift_mu(Nd,0); shift_mu[mu]=1;
+	    Coordinate shift_nu(Nd,0); shift_nu[nu]=1;
+	    Coordinate shift_mnu(Nd,0); shift_mnu[nu]=-1;
+	    Coordinate shift_mnu_pmu(Nd,0); shift_mnu_pmu[nu]=-1; shift_mnu_pmu[mu]=1;
+      
+	    //U_nu(x+mu)U^dag_mu(x+nu) U^dag_nu(x)
+	    shifts.push_back(shift_0);
+	    shifts.push_back(shift_nu);
+	    shifts.push_back(shift_mu);
+      
+	    //U_nu^dag(x-nu+mu) U_mu^dag(x-nu) U_nu(x-nu)
+	    shifts.push_back(shift_mnu);
+	    shifts.push_back(shift_mnu);
+	    shifts.push_back(shift_mnu_pmu);
+	  }
+	}
+      }
+      return shifts;
+    }
+
+    int paddingDepth() const override{ return 1; }
+  }; 
+
+  //Padded cell implementation of the staple method for all mu, summed over nu != mu
+  //staple: output staple for each mu, summed over nu != mu (Nd)
+  //U_padded: the gauge link fields padded out using the PaddedCell class
+  //Cell: the padded cell class
+  static void StaplePaddedAll(std::vector<GaugeMat> &staple, const std::vector<GaugeMat> &U_padded, const PaddedCell &Cell) {
+    StaplePaddedAllWorkspace wk;
+    StaplePaddedAll(staple,U_padded,Cell,wk.getStencil(Cell));
+  }
+  
+  //Padded cell implementation of the staple method for all mu, summed over nu != mu
+  //staple: output staple for each mu, summed over nu != mu (Nd)
+  //U_padded: the gauge link fields padded out using the PaddedCell class
+  //Cell: the padded cell class
+  //gStencil: the precomputed generalized local stencil for the staple
+  static void StaplePaddedAll(std::vector<GaugeMat> &staple, const std::vector<GaugeMat> &U_padded, const PaddedCell &Cell, const GeneralLocalStencil &gStencil)
+  {
+    double t0 = usecond();
+    assert(U_padded.size() == Nd); assert(staple.size() == Nd);
+    assert(U_padded[0].Grid() == (GridBase*)Cell.grids.back());
+    assert(Cell.depth >= 1);
+    GridBase *ggrid = U_padded[0].Grid(); //padded cell grid
+
+    int shift_mu_off = gStencil._npoints/Nd;
+    
+    //Open views to padded gauge links and keep open over mu loop
+    typedef LatticeView<typename GaugeMat::vector_object> GaugeViewType;
+    size_t vsize = Nd*sizeof(GaugeViewType);
+    GaugeViewType* Ug_dirs_v_host = (GaugeViewType*)malloc(vsize);
+    for(int i=0;i<Nd;i++) Ug_dirs_v_host[i] = U_padded[i].View(AcceleratorRead);
+    GaugeViewType* Ug_dirs_v = (GaugeViewType*)acceleratorAllocDevice(vsize);
+    acceleratorCopyToDevice(Ug_dirs_v_host,Ug_dirs_v,vsize);
+    
+    GaugeMat gStaple(ggrid);
+
+    int outer_off = 0;
+    for(int mu=0;mu<Nd;mu++){
+      { //view scope
+	autoView( gStaple_v , gStaple, AcceleratorWrite);
+	auto gStencil_v = gStencil.View();
+	
+	accelerator_for(ss, ggrid->oSites(), (size_t)ggrid->Nsimd(), {
+	    decltype(coalescedRead(Ug_dirs_v[0][0])) stencil_ss;
+	    stencil_ss = Zero();
+	    int off = outer_off;
+	    
+	    for(int nu=0;nu<Nd;nu++){
+	      if(nu != mu){	  
+		GeneralStencilEntry const* e = gStencil_v.GetEntry(off++,ss);
+		auto U0 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(off++,ss);
+		auto U1 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(off++,ss);
+		auto U2 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
+      
+		stencil_ss = stencil_ss + U2 * U1 * U0;
+
+		e = gStencil_v.GetEntry(off++,ss);
+		U0 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
+		e = gStencil_v.GetEntry(off++,ss);
+		U1 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(off++,ss);
+		U2 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
+
+		stencil_ss = stencil_ss + U2 * U1 * U0;
+	      }
+	    }
+		
+	    coalescedWrite(gStaple_v[ss],stencil_ss);
+	  }
+	  );
+      } //ensure views are all closed!
+      
+      staple[mu] = Cell.Extract(gStaple);
+      outer_off += shift_mu_off;
+    }//mu loop
+
+    for(int i=0;i<Nd;i++) Ug_dirs_v_host[i].ViewClose();
+    free(Ug_dirs_v_host);
+    acceleratorFreeDevice(Ug_dirs_v);
+    
+    double t1=usecond();
+    
+    std::cout << GridLogPerformance << "StaplePaddedAll timing:" << (t1-t0)/1000 << "ms" << std::endl;   
+  }
+
+   
   //////////////////////////////////////////////////
   // the sum over all staples on each site in direction mu,nu, upper part
   //////////////////////////////////////////////////
@@ -707,18 +908,14 @@ public:
   // the sum over all staples on each site
   //////////////////////////////////////////////////
   static void RectStapleDouble(GaugeMat &U2, const GaugeMat &U, int mu) {
-    U2 = U * Cshift(U, mu, 1);
+    U2 = U * Gimpl::CshiftLink(U, mu, 1);
   }
 
   ////////////////////////////////////////////////////////////////////////////
-  // Hop by two optimisation strategy does not work nicely with Gparity. (could
-  // do,
-  // but need to track two deep where cross boundary and apply a conjugation).
-  // Must differentiate this in Gimpl, and use Gimpl::isPeriodicGaugeField to do
-  // so .
+  // Hop by two optimisation strategy. Use RectStapleDouble to obtain 'U2'
   ////////////////////////////////////////////////////////////////////////////
-  static void RectStapleOptimised(GaugeMat &Stap, std::vector<GaugeMat> &U2,
-                                  std::vector<GaugeMat> &U, int mu) {
+  static void RectStapleOptimised(GaugeMat &Stap, const std::vector<GaugeMat> &U2,
+                                  const std::vector<GaugeMat> &U, int mu) {
 
     Stap = Zero();
 
@@ -732,9 +929,9 @@ public:
 
         // Up staple    ___ ___
         //             |       |
-        tmp = Cshift(adj(U[nu]), nu, -1);
+        tmp = Gimpl::CshiftLink(adj(U[nu]), nu, -1);
         tmp = adj(U2[mu]) * tmp;
-        tmp = Cshift(tmp, mu, -2);
+        tmp = Gimpl::CshiftLink(tmp, mu, -2);
 
         Staple2x1 = Gimpl::CovShiftForward(U[nu], nu, tmp);
 
@@ -742,14 +939,14 @@ public:
         //             |___ ___|
         //
         tmp = adj(U2[mu]) * U[nu];
-        Staple2x1 += Gimpl::CovShiftBackward(U[nu], nu, Cshift(tmp, mu, -2));
+        Staple2x1 += Gimpl::CovShiftBackward(U[nu], nu, Gimpl::CshiftLink(tmp, mu, -2));
 
         //              ___ ___
         //             |    ___|
         //             |___ ___|
         //
 
-        Stap += Cshift(Gimpl::CovShiftForward(U[mu], mu, Staple2x1), mu, 1);
+        Stap += Gimpl::CshiftLink(Gimpl::CovShiftForward(U[mu], mu, Staple2x1), mu, 1);
 
         //              ___ ___
         //             |___    |
@@ -758,7 +955,7 @@ public:
 
         //  tmp= Staple2x1* Cshift(U[mu],mu,-2);
         //  Stap+= Cshift(tmp,mu,1) ;
-        Stap += Cshift(Staple2x1, mu, 1) * Cshift(U[mu], mu, -1);
+        Stap += Gimpl::CshiftLink(Staple2x1, mu, 1) * Gimpl::CshiftLink(U[mu], mu, -1);
         ;
 
         //       --
@@ -766,10 +963,10 @@ public:
         //
         //      |  |
 
-        tmp = Cshift(adj(U2[nu]), nu, -2);
+        tmp = Gimpl::CshiftLink(adj(U2[nu]), nu, -2);
         tmp = Gimpl::CovShiftBackward(U[mu], mu, tmp);
-        tmp = U2[nu] * Cshift(tmp, nu, 2);
-        Stap += Cshift(tmp, mu, 1);
+        tmp = U2[nu] * Gimpl::CshiftLink(tmp, nu, 2);
+        Stap += Gimpl::CshiftLink(tmp, mu, 1);
 
         //      |  |
         //
@@ -778,25 +975,12 @@ public:
 
         tmp = Gimpl::CovShiftBackward(U[mu], mu, U2[nu]);
         tmp = adj(U2[nu]) * tmp;
-        tmp = Cshift(tmp, nu, -2);
-        Stap += Cshift(tmp, mu, 1);
+        tmp = Gimpl::CshiftLink(tmp, nu, -2);
+        Stap += Gimpl::CshiftLink(tmp, mu, 1);
       }
     }
   }
 
-  static void RectStaple(GaugeMat &Stap, const GaugeLorentz &Umu, int mu) {
-    RectStapleUnoptimised(Stap, Umu, mu);
-  }
-  static void RectStaple(const GaugeLorentz &Umu, GaugeMat &Stap,
-                         std::vector<GaugeMat> &U2, std::vector<GaugeMat> &U,
-                         int mu) {
-    if (Gimpl::isPeriodicGaugeField()) {
-      RectStapleOptimised(Stap, U2, U, mu);
-    } else {
-      RectStapleUnoptimised(Stap, Umu, mu);
-    }
-  }
-
   static void RectStapleUnoptimised(GaugeMat &Stap, const GaugeLorentz &Umu,
                                     int mu) {
     GridBase *grid = Umu.Grid();
@@ -895,6 +1079,288 @@ public:
     }
   }
 
+  static void RectStaple(GaugeMat &Stap, const GaugeLorentz &Umu, int mu) {
+    RectStapleUnoptimised(Stap, Umu, mu);
+  }
+  static void RectStaple(const GaugeLorentz &Umu, GaugeMat &Stap,
+                         std::vector<GaugeMat> &U2, std::vector<GaugeMat> &U,
+                         int mu) {
+    RectStapleOptimised(Stap, U2, U, mu);
+  }
+  //////////////////////////////////////////////////////
+  //Compute the rectangular staples for all orientations
+  //Stap : Array of staples (Nd)
+  //U: Gauge links in each direction (Nd)
+  /////////////////////////////////////////////////////
+  static void RectStapleAll(std::vector<GaugeMat> &Stap, const std::vector<GaugeMat> &U){
+    assert(Stap.size() == Nd); assert(U.size() == Nd);
+    std::vector<GaugeMat> U2(Nd,U[0].Grid());
+    for(int mu=0;mu<Nd;mu++) RectStapleDouble(U2[mu], U[mu], mu);
+    for(int mu=0;mu<Nd;mu++) RectStapleOptimised(Stap[mu], U2, U, mu);
+  }
+
+  //A workspace class allowing reuse of the stencil
+  class RectStaplePaddedAllWorkspace: public WilsonLoopPaddedStencilWorkspace{
+  public:
+    std::vector<Coordinate> getShifts() const override{
+      std::vector<Coordinate> shifts;
+      for (int mu = 0; mu < Nd; mu++){
+	for (int nu = 0; nu < Nd; nu++) {
+	  if (nu != mu) {
+	    auto genShift = [&](int mushift,int nushift){
+	      Coordinate out(Nd,0); out[mu]=mushift; out[nu]=nushift; return out;
+	    };
+
+	    //tmp6 = tmp5(x+mu) = U_mu(x+mu)U_nu(x+2mu)U_mu^dag(x+nu+mu) U_mu^dag(x+nu) U_nu^dag(x)
+	    shifts.push_back(genShift(0,0));
+	    shifts.push_back(genShift(0,+1));
+	    shifts.push_back(genShift(+1,+1));
+	    shifts.push_back(genShift(+2,0));
+	    shifts.push_back(genShift(+1,0));
+
+	    //tmp5 = tmp4(x+mu) = U_mu(x+mu)U^dag_nu(x-nu+2mu)U^dag_mu(x-nu+mu)U^dag_mu(x-nu)U_nu(x-nu)
+	    shifts.push_back(genShift(0,-1));
+	    shifts.push_back(genShift(0,-1));
+	    shifts.push_back(genShift(+1,-1));
+	    shifts.push_back(genShift(+2,-1));
+	    shifts.push_back(genShift(+1,0));
+
+	    //tmp5 = tmp4(x+mu) = U^dag_nu(x-nu+mu)U^dag_mu(x-nu)U^dag_mu(x-mu-nu)U_nu(x-mu-nu)U_mu(x-mu)
+	    shifts.push_back(genShift(-1,0));
+	    shifts.push_back(genShift(-1,-1));
+	    shifts.push_back(genShift(-1,-1));
+	    shifts.push_back(genShift(0,-1));
+	    shifts.push_back(genShift(+1,-1));
+
+	    //tmp5 = tmp4(x+mu) = U_nu(x+mu)U_mu^dag(x+nu)U_mu^dag(x-mu+nu)U_nu^dag(x-mu)U_mu(x-mu)
+	    shifts.push_back(genShift(-1,0));
+	    shifts.push_back(genShift(-1,0));
+	    shifts.push_back(genShift(-1,+1));
+	    shifts.push_back(genShift(0,+1));
+	    shifts.push_back(genShift(+1,0));
+
+	    //tmp6 = tmp5(x+mu) = U_nu(x+mu)U_nu(x+mu+nu)U_mu^dag(x+2nu)U_nu^dag(x+nu)U_nu^dag(x)
+	    shifts.push_back(genShift(0,0));
+	    shifts.push_back(genShift(0,+1));
+	    shifts.push_back(genShift(0,+2));
+	    shifts.push_back(genShift(+1,+1));
+	    shifts.push_back(genShift(+1,0));
+
+	    //tmp5 = tmp4(x+mu) = U_nu^dag(x+mu-nu)U_nu^dag(x+mu-2nu)U_mu^dag(x-2nu)U_nu(x-2nu)U_nu(x-nu)
+	    shifts.push_back(genShift(0,-1));
+	    shifts.push_back(genShift(0,-2));
+	    shifts.push_back(genShift(0,-2));
+	    shifts.push_back(genShift(+1,-2));
+	    shifts.push_back(genShift(+1,-1));
+	  }
+	}
+      }
+      return shifts;
+    }
+
+    int paddingDepth() const override{ return 2; }
+  }; 
+
+  //Padded cell implementation of the rectangular staple method for all mu, summed over nu != mu
+  //staple: output staple for each mu, summed over nu != mu (Nd)
+  //U_padded: the gauge link fields padded out using the PaddedCell class
+  //Cell: the padded cell class
+  static void RectStaplePaddedAll(std::vector<GaugeMat> &staple, const std::vector<GaugeMat> &U_padded, const PaddedCell &Cell) {
+    RectStaplePaddedAllWorkspace wk;
+    RectStaplePaddedAll(staple,U_padded,Cell,wk.getStencil(Cell));
+  }
+  
+  //Padded cell implementation of the rectangular staple method for all mu, summed over nu != mu
+  //staple: output staple for each mu, summed over nu != mu (Nd)
+  //U_padded: the gauge link fields padded out using the PaddedCell class
+  //Cell: the padded cell class
+  //gStencil: the stencil
+  static void RectStaplePaddedAll(std::vector<GaugeMat> &staple, const std::vector<GaugeMat> &U_padded, const PaddedCell &Cell, const GeneralLocalStencil &gStencil) {
+    double t0 = usecond();
+    assert(U_padded.size() == Nd); assert(staple.size() == Nd);
+    assert(U_padded[0].Grid() == (GridBase*)Cell.grids.back());
+    assert(Cell.depth >= 2);
+    GridBase *ggrid = U_padded[0].Grid(); //padded cell grid
+
+    size_t nshift = gStencil._npoints;
+    int mu_off_delta = nshift / Nd;
+    
+    //Open views to padded gauge links and keep open over mu loop
+    typedef LatticeView<typename GaugeMat::vector_object> GaugeViewType;
+    size_t vsize = Nd*sizeof(GaugeViewType);
+    GaugeViewType* Ug_dirs_v_host = (GaugeViewType*)malloc(vsize);
+    for(int i=0;i<Nd;i++) Ug_dirs_v_host[i] = U_padded[i].View(AcceleratorRead);
+    GaugeViewType* Ug_dirs_v = (GaugeViewType*)acceleratorAllocDevice(vsize);
+    acceleratorCopyToDevice(Ug_dirs_v_host,Ug_dirs_v,vsize);
+
+    GaugeMat gStaple(ggrid); //temp staple object on padded grid
+
+    int offset = 0;
+    for(int mu=0; mu<Nd; mu++){
+
+      { //view scope
+	autoView( gStaple_v , gStaple, AcceleratorWrite);
+	auto gStencil_v = gStencil.View();
+
+	accelerator_for(ss, ggrid->oSites(), (size_t)ggrid->Nsimd(), {
+	    decltype(coalescedRead(Ug_dirs_v[0][0])) stencil_ss;
+	    stencil_ss = Zero();
+	    int s=offset;
+	    for(int nu=0;nu<Nd;nu++){
+	      if(nu != mu){
+		//tmp6 = tmp5(x+mu) = U_mu(x+mu)U_nu(x+2mu)U_mu^dag(x+nu+mu) U_mu^dag(x+nu) U_nu^dag(x)
+		GeneralStencilEntry const* e = gStencil_v.GetEntry(s++,ss);
+		auto U0 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		auto U1 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		auto U2 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		auto U3 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
+		e = gStencil_v.GetEntry(s++,ss);
+		auto U4 = coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd);
+	    
+		stencil_ss = stencil_ss + U4*U3*U2*U1*U0;
+
+		//tmp5 = tmp4(x+mu) = U_mu(x+mu)U^dag_nu(x-nu+2mu)U^dag_mu(x-nu+mu)U^dag_mu(x-nu)U_nu(x-nu)
+		e = gStencil_v.GetEntry(s++,ss);
+		U0 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
+		e = gStencil_v.GetEntry(s++,ss);
+		U1 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		U2 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		U3 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		U4 = coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd);
+
+		stencil_ss = stencil_ss + U4*U3*U2*U1*U0;
+
+		//tmp5 = tmp4(x+mu) = U^dag_nu(x-nu+mu)U^dag_mu(x-nu)U^dag_mu(x-mu-nu)U_nu(x-mu-nu)U_mu(x-mu)
+		e = gStencil_v.GetEntry(s++,ss);
+		U0 = coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd);
+		e = gStencil_v.GetEntry(s++,ss);
+		U1 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
+		e = gStencil_v.GetEntry(s++,ss);
+		U2 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		U3 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		U4 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
+
+		stencil_ss = stencil_ss + U4*U3*U2*U1*U0;
+
+		//tmp5 = tmp4(x+mu) = U_nu(x+mu)U_mu^dag(x+nu)U_mu^dag(x-mu+nu)U_nu^dag(x-mu)U_mu(x-mu)
+		e = gStencil_v.GetEntry(s++,ss);
+		U0 = coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd);
+		e = gStencil_v.GetEntry(s++,ss);
+		U1 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		U2 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		U3 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		U4 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
+
+		stencil_ss = stencil_ss + U4*U3*U2*U1*U0;
+
+		//tmp6 = tmp5(x+mu) = U_nu(x+mu)U_nu(x+mu+nu)U_mu^dag(x+2nu)U_nu^dag(x+nu)U_nu^dag(x)
+		e = gStencil_v.GetEntry(s++,ss);
+		U0 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		U1 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		U2 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		U3 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
+		e = gStencil_v.GetEntry(s++,ss);
+		U4 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
+
+		stencil_ss = stencil_ss + U4*U3*U2*U1*U0;   
+
+		//tmp5 = tmp4(x+mu) = U_nu^dag(x+mu-nu)U_nu^dag(x+mu-2nu)U_mu^dag(x-2nu)U_nu(x-2nu)U_nu(x-nu)
+		e = gStencil_v.GetEntry(s++,ss);
+		U0 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
+		e = gStencil_v.GetEntry(s++,ss);
+		U1 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
+		e = gStencil_v.GetEntry(s++,ss);
+		U2 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		U3 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
+		e = gStencil_v.GetEntry(s++,ss);
+		U4 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
+
+		stencil_ss = stencil_ss + U4*U3*U2*U1*U0;   
+
+	      }
+	    }
+	    coalescedWrite(gStaple_v[ss],stencil_ss);
+	  }
+	  );
+	offset += mu_off_delta;
+      }//kernel/view scope
+
+      staple[mu] = Cell.Extract(gStaple);    
+    }//mu loop
+  
+    for(int i=0;i<Nd;i++) Ug_dirs_v_host[i].ViewClose();
+    free(Ug_dirs_v_host);
+    acceleratorFreeDevice(Ug_dirs_v);
+    
+    double t1 = usecond();
+    
+    std::cout << GridLogPerformance << "RectStaplePaddedAll timings:" << (t1-t0)/1000 << "ms" << std::endl;   
+  }
+
+  //A workspace for reusing the PaddedCell and GeneralLocalStencil objects
+  class StapleAndRectStapleAllWorkspace: public WilsonLoopPaddedWorkspace{
+  public:
+    StapleAndRectStapleAllWorkspace(){
+      this->addStencil(new StaplePaddedAllWorkspace);
+      this->addStencil(new RectStaplePaddedAllWorkspace);
+    }
+  };     
+    
+  //////////////////////////////////////////////////////
+  //Compute the 1x1 and 1x2 staples for all orientations
+  //Stap : Array of staples (Nd)
+  //RectStap: Array of rectangular staples (Nd)
+  //U: Gauge links in each direction (Nd)
+  /////////////////////////////////////////////////////
+  static void StapleAndRectStapleAll(std::vector<GaugeMat> &Stap, std::vector<GaugeMat> &RectStap, const std::vector<GaugeMat> &U){
+    StapleAndRectStapleAllWorkspace wk;
+    StapleAndRectStapleAll(Stap,RectStap,U,wk);
+  }
+  
+  //////////////////////////////////////////////////////
+  //Compute the 1x1 and 1x2 staples for all orientations
+  //Stap : Array of staples (Nd)
+  //RectStap: Array of rectangular staples (Nd)
+  //U: Gauge links in each direction (Nd)
+  //wk: a workspace containing stored PaddedCell and GeneralLocalStencil objects to maximize reuse
+  /////////////////////////////////////////////////////
+  static void StapleAndRectStapleAll(std::vector<GaugeMat> &Stap, std::vector<GaugeMat> &RectStap, const std::vector<GaugeMat> &U, StapleAndRectStapleAllWorkspace &wk){
+#if 0
+    StapleAll(Stap, U);
+    RectStapleAll(RectStap, U);
+#else
+    double t0 = usecond();
+
+    GridCartesian* unpadded_grid = dynamic_cast<GridCartesian*>(U[0].Grid());
+    const PaddedCell &Ghost = wk.getPaddedCell(unpadded_grid);
+        
+    CshiftImplGauge<Gimpl> cshift_impl;
+    std::vector<GaugeMat> U_pad(Nd, Ghost.grids.back());
+    for(int mu=0;mu<Nd;mu++) U_pad[mu] = Ghost.Exchange(U[mu], cshift_impl);
+    double t1 = usecond();
+    StaplePaddedAll(Stap, U_pad, Ghost, wk.getStencil(0,unpadded_grid) );
+    double t2 = usecond();
+    RectStaplePaddedAll(RectStap, U_pad, Ghost, wk.getStencil(1,unpadded_grid));
+    double t3 = usecond();
+    std::cout << GridLogPerformance << "StapleAndRectStapleAll timings: pad:" << (t1-t0)/1000 << "ms, staple:" << (t2-t1)/1000 << "ms, rect-staple:" << (t3-t2)/1000 << "ms" << std::endl;
+#endif
+  }
+
   //////////////////////////////////////////////////
   // Wilson loop of size (R1, R2), oriented in mu,nu plane
   //////////////////////////////////////////////////

Grid/simd/Grid_vector_types.h

@@ -1133,4 +1133,13 @@ static_assert(sizeof(SIMD_Ftype) == sizeof(SIMD_Itype), "SIMD vector lengths inc
 
 NAMESPACE_END(Grid);
 
+#ifdef GRID_SYCL
+template<> struct sycl::is_device_copyable<Grid::vComplexF> : public std::true_type {};
+template<> struct sycl::is_device_copyable<Grid::vComplexD> : public std::true_type {};
+template<> struct sycl::is_device_copyable<Grid::vRealF   > : public std::true_type {};
+template<> struct sycl::is_device_copyable<Grid::vRealD   > : public std::true_type {};
+template<> struct sycl::is_device_copyable<Grid::vInteger > : public std::true_type {};
+#endif
+
+
 #endif

Grid/sitmo_rng/sitmo_prng_engine.hpp

@@ -218,6 +218,10 @@ public:
     // -------------------------------------------------
     // misc
     // -------------------------------------------------
+    void discardhi(uint64_t z) {
+      _s[3] += z;
+      encrypt_counter();
+    }
     
     // req: 26.5.1.4 Random number engine requirements, p.908 table 117, row 9
     // Advances e’s state ei to ei+z by any means equivalent to z