Merge branch 'release/dirac-ITT-2020'

.gitignore

@@ -83,6 +83,7 @@ ltmain.sh
 .Trashes
 ehthumbs.db
 Thumbs.db
+.dirstamp
 
 # build directory #
 ###################
@@ -97,11 +98,8 @@ build.sh
 
 # Eigen source #
 ################
-lib/Eigen/*
-
-# FFTW source #
-################
-lib/fftw/*
+Grid/Eigen
+Eigen/*
 
 # libtool macros #
 ##################
@@ -112,21 +110,8 @@ m4/libtool.m4
 ################
 gh-pages/
 
-# Buck files #
-##############
-.buck*
-buck-out
-BUCK
-make-bin-BUCK.sh
-
 # generated sources #
 #####################
-lib/qcd/spin/gamma-gen/*.h
-lib/qcd/spin/gamma-gen/*.cc
-lib/version.h
-
-# vs code editor files #
-########################
-.vscode/
-.vscode/settings.json
-settings.json
+Grid/qcd/spin/gamma-gen/*.h
+Grid/qcd/spin/gamma-gen/*.cc
+Grid/util/Version.h

.travis.yml

@@ -16,7 +16,7 @@ before_install:
     - if [[ "$TRAVIS_OS_NAME" == "linux" ]] && [[ "$CC" == "clang" ]]; then export PATH="${GRIDDIR}/clang/bin:${PATH}"; fi
     - if [[ "$TRAVIS_OS_NAME" == "linux" ]] && [[ "$CC" == "clang" ]]; then export LD_LIBRARY_PATH="${GRIDDIR}/clang/lib:${LD_LIBRARY_PATH}"; fi
     - if [[ "$TRAVIS_OS_NAME" == "osx" ]]; then brew update; fi
-    - if [[ "$TRAVIS_OS_NAME" == "osx" ]]; then brew install libmpc; fi
+    - if [[ "$TRAVIS_OS_NAME" == "osx" ]]; then brew install libmpc openssl; fi
     
 install:
     - export CWD=`pwd`
@@ -33,6 +33,7 @@ install:
     - which $CXX
     - $CXX --version
     - if [[ "$TRAVIS_OS_NAME" == "osx" ]]; then export LDFLAGS='-L/usr/local/lib'; fi
+    - if [[ "$TRAVIS_OS_NAME" == "osx" ]]; then export EXTRACONF='--with-openssl=/usr/local/opt/openssl'; fi
     
 script:
     - ./bootstrap.sh
@@ -49,12 +50,7 @@ script:
     - make -j4
     - make install
     - cd $CWD/build
-    - ../configure --enable-precision=single --enable-simd=SSE4 --enable-comms=none --with-lime=$CWD/build/lime/install
-    - make -j4 
-    - ./benchmarks/Benchmark_dwf --threads 1 --debug-signals
-    - echo make clean
-    - ../configure --enable-precision=double --enable-simd=SSE4 --enable-comms=none --with-lime=$CWD/build/lime/install
+    - ../configure --enable-simd=SSE4 --enable-comms=none --with-lime=$CWD/build/lime/install ${EXTRACONF}
     - make -j4 
     - ./benchmarks/Benchmark_dwf --threads 1 --debug-signals
     - make check
-

ChangeLog

@@ -0,0 +1,5 @@
+Version : 0.8.0
+
+- Clang 3.5 and above, ICPC v16 and above, GCC 6.3 and above recommended
+- MPI and MPI3 comms optimisations for KNL and OPA finished
+- Half precision comms

Grid/DisableWarnings.h

@@ -0,0 +1,63 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/DisableWarnings.h
+
+Copyright (C) 2016
+
+Author: Guido Cossu <guido.cossu@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 DISABLE_WARNINGS_H
+#define DISABLE_WARNINGS_H
+
+
+
+#if defined __GNUC__ && __GNUC__>=6
+#pragma GCC diagnostic ignored "-Wignored-attributes"
+#endif
+
+ //disables and intel compiler specific warning (in json.hpp)
+#pragma warning disable 488  
+
+#ifdef __NVCC__
+ //disables nvcc specific warning in json.hpp
+#pragma clang diagnostic ignored "-Wdeprecated-register"
+#pragma diag_suppress unsigned_compare_with_zero
+#pragma diag_suppress cast_to_qualified_type
+
+ //disables nvcc specific warning in many files
+#pragma diag_suppress esa_on_defaulted_function_ignored
+#pragma diag_suppress extra_semicolon
+
+//Eigen only
+#endif
+
+// Disable vectorisation in Eigen on the Power8/9 and PowerPC
+#ifdef  __ALTIVEC__
+#define  EIGEN_DONT_VECTORIZE
+#endif
+#ifdef  __VSX__
+#define  EIGEN_DONT_VECTORIZE
+#endif
+
+#endif

Grid/Grid.h

@@ -42,6 +42,7 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
 #include <Grid/GridQCDcore.h>
 #include <Grid/qcd/action/Action.h>
 #include <Grid/qcd/utils/GaugeFix.h>
+#include <Grid/qcd/utils/CovariantSmearing.h>
 #include <Grid/qcd/smearing/Smearing.h>
 #include <Grid/parallelIO/MetaData.h>
 #include <Grid/qcd/hmc/HMC_aggregate.h>

Grid/GridCore.h

@@ -38,16 +38,20 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
 #ifndef GRID_BASE_H
 #define GRID_BASE_H
 
-#include <Grid/GridStd.h>
 
+#include <Grid/DisableWarnings.h>
+#include <Grid/Namespace.h>
+#include <Grid/GridStd.h>
+#include <Grid/threads/Pragmas.h>
 #include <Grid/perfmon/Timer.h>
 #include <Grid/perfmon/PerfCount.h>
-#include <Grid/log/Log.h>
-#include <Grid/allocator/AlignedAllocator.h>
-#include <Grid/simd/Simd.h>
-#include <Grid/serialisation/Serialisation.h>
-#include <Grid/threads/Threads.h>
 #include <Grid/util/Util.h>
+#include <Grid/log/Log.h>
+#include <Grid/allocator/Allocator.h>
+#include <Grid/simd/Simd.h>
+#include <Grid/threads/ThreadReduction.h>
+#include <Grid/serialisation/Serialisation.h>
+#include <Grid/util/Sha.h>
 #include <Grid/communicator/Communicator.h> 
 #include <Grid/cartesian/Cartesian.h>    
 #include <Grid/tensors/Tensors.h>      
@@ -56,5 +60,6 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
 #include <Grid/stencil/Stencil.h>      
 #include <Grid/parallelIO/BinaryIO.h>
 #include <Grid/algorithms/Algorithms.h>   
+NAMESPACE_CHECK(GridCore)
 
 #endif

Grid/GridQCDcore.h

@@ -38,5 +38,6 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
 #include <Grid/qcd/spin/Spin.h>
 #include <Grid/qcd/utils/Utils.h>
 #include <Grid/qcd/representations/Representations.h>
+NAMESPACE_CHECK(GridQCDCore);
 
 #endif

Grid/GridStd.h

@@ -6,7 +6,9 @@
 ///////////////////
 #include <cassert>
 #include <complex>
+#include <memory>
 #include <vector>
+#include <array>
 #include <string>
 #include <iostream>
 #include <iomanip>

Grid/Grid_Eigen_Dense.h

@@ -0,0 +1,71 @@
+#include <Grid/GridCore.h>
+#pragma once
+// Force Eigen to use MKL if Grid has been configured with --enable-mkl
+#ifdef USE_MKL
+#define EIGEN_USE_MKL_ALL
+#endif
+
+
+#if defined __GNUC__
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+#endif
+
+/* NVCC save and restore compile environment*/
+#ifdef __NVCC__
+#pragma push
+#pragma diag_suppress code_is_unreachable
+#pragma push_macro("__CUDA_ARCH__")
+#pragma push_macro("__NVCC__")
+#pragma push_macro("__CUDACC__")
+#undef __CUDA_ARCH__
+#undef __NVCC__
+#undef __CUDACC__
+#define __NVCC__REDEFINE__
+#endif 
+
+/* SYCL save and restore compile environment*/
+#ifdef GRID_SYCL
+#pragma push
+#pragma push_macro("__SYCL_DEVICE_ONLY__")
+#undef __SYCL_DEVICE_ONLY__
+#define EIGEN_DONT_VECTORIZE
+//#undef EIGEN_USE_SYCL
+#define __SYCL__REDEFINE__
+#endif
+
+/* HIP save and restore compile environment*/
+#ifdef GRID_HIP
+#pragma push
+#pragma push_macro("__HIP_DEVICE_COMPILE__")
+#endif
+#define EIGEN_NO_HIP
+
+#include <Grid/Eigen/Dense>
+#include <Grid/Eigen/unsupported/CXX11/Tensor>
+
+/* NVCC restore */
+#ifdef __NVCC__REDEFINE__
+#pragma pop_macro("__CUDACC__")
+#pragma pop_macro("__NVCC__")
+#pragma pop_macro("__CUDA_ARCH__")
+#pragma pop
+#endif
+
+/*SYCL restore*/
+#ifdef __SYCL__REDEFINE__
+#pragma pop_macro("__SYCL_DEVICE_ONLY__")
+#pragma pop
+#endif
+
+/*HIP restore*/
+#ifdef __HIP__REDEFINE__
+#pragma pop_macro("__HIP_DEVICE_COMPILE__")
+#pragma pop
+#endif
+
+#if defined __GNUC__
+#pragma GCC diagnostic pop
+#endif
+
+

Grid/Grid_Eigen_Tensor.h

@@ -0,0 +1 @@
+#include <Grid/Grid_Eigen_Dense.h>

Grid/Makefile.am

@@ -21,6 +21,32 @@ if BUILD_HDF5
   extra_headers+=serialisation/Hdf5Type.h
 endif
 
+all: version-cache Version.h
+
+version-cache:
+	@if [ `git status --porcelain | grep -v '??' | wc -l` -gt 0 ]; then\
+		a="uncommited changes";\
+	else\
+		a="clean";\
+	fi;\
+	echo "`git log -n 1 --format=format:"#define GITHASH \\"%H:%d $$a\\"%n" HEAD`" > vertmp;\
+	if [ -e version-cache ]; then\
+		d=`diff vertmp version-cache`;\
+		if [ "$${d}" != "" ]; then\
+			mv vertmp version-cache;\
+			rm -f Version.h;\
+		fi;\
+	else\
+		mv vertmp version-cache;\
+		rm -f Version.h;\
+	fi;\
+	rm -f vertmp
+
+Version.h: version-cache
+	cp version-cache Version.h
+
+.PHONY: version-cache
+
 #
 # Libraries
 #
@@ -30,8 +56,8 @@ include Eigen.inc
 lib_LIBRARIES = libGrid.a
 
 CCFILES += $(extra_sources)
-HFILES  += $(extra_headers)
+HFILES  += $(extra_headers) Config.h Version.h
 
 libGrid_a_SOURCES              = $(CCFILES)
-libGrid_adir                   = $(pkgincludedir)
-nobase_dist_pkginclude_HEADERS = $(HFILES) $(eigen_files) Config.h
+libGrid_adir                   = $(includedir)/Grid
+nobase_dist_pkginclude_HEADERS = $(HFILES) $(eigen_files) $(eigen_unsupp_files)

Grid/Namespace.h

@@ -0,0 +1,38 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/Namespace.h
+
+Copyright (C) 2016
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+#include <type_traits>
+#include <cassert>
+
+#define NAMESPACE_BEGIN(A) namespace A {
+#define NAMESPACE_END(A)   }
+#define GRID_NAMESPACE_BEGIN NAMESPACE_BEGIN(Grid)
+#define GRID_NAMESPACE_END   NAMESPACE_END(Grid)
+#define NAMESPACE_CHECK(x) struct namespaceTEST##x {};  static_assert(std::is_same<namespaceTEST##x, ::namespaceTEST##x>::value,"Not in :: at"  ); 

Grid/algorithms/Algorithms.h

@@ -29,33 +29,46 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 #ifndef GRID_ALGORITHMS_H
 #define GRID_ALGORITHMS_H
 
+NAMESPACE_CHECK(algorithms);
 #include <Grid/algorithms/SparseMatrix.h>
 #include <Grid/algorithms/LinearOperator.h>
 #include <Grid/algorithms/Preconditioner.h>
+NAMESPACE_CHECK(SparseMatrix);
 
 #include <Grid/algorithms/approx/Zolotarev.h>
 #include <Grid/algorithms/approx/Chebyshev.h>
+#include <Grid/algorithms/approx/JacobiPolynomial.h>
 #include <Grid/algorithms/approx/Remez.h>
 #include <Grid/algorithms/approx/MultiShiftFunction.h>
 #include <Grid/algorithms/approx/Forecast.h>
-
+#include <Grid/algorithms/approx/RemezGeneral.h>
+#include <Grid/algorithms/approx/ZMobius.h>
+NAMESPACE_CHECK(approx);
 #include <Grid/algorithms/iterative/Deflation.h>
 #include <Grid/algorithms/iterative/ConjugateGradient.h>
+NAMESPACE_CHECK(ConjGrad);
+#include <Grid/algorithms/iterative/BiCGSTAB.h>
+NAMESPACE_CHECK(BiCGSTAB);
 #include <Grid/algorithms/iterative/ConjugateResidual.h>
 #include <Grid/algorithms/iterative/NormalEquations.h>
 #include <Grid/algorithms/iterative/SchurRedBlack.h>
 #include <Grid/algorithms/iterative/ConjugateGradientMultiShift.h>
 #include <Grid/algorithms/iterative/ConjugateGradientMixedPrec.h>
+#include <Grid/algorithms/iterative/BiCGSTABMixedPrec.h>
 #include <Grid/algorithms/iterative/BlockConjugateGradient.h>
 #include <Grid/algorithms/iterative/ConjugateGradientReliableUpdate.h>
+#include <Grid/algorithms/iterative/MinimalResidual.h>
+#include <Grid/algorithms/iterative/GeneralisedMinimalResidual.h>
+#include <Grid/algorithms/iterative/CommunicationAvoidingGeneralisedMinimalResidual.h>
+#include <Grid/algorithms/iterative/FlexibleGeneralisedMinimalResidual.h>
+#include <Grid/algorithms/iterative/FlexibleCommunicationAvoidingGeneralisedMinimalResidual.h>
+#include <Grid/algorithms/iterative/MixedPrecisionFlexibleGeneralisedMinimalResidual.h>
 #include <Grid/algorithms/iterative/ImplicitlyRestartedLanczos.h>
+#include <Grid/algorithms/iterative/PowerMethod.h>
+
+NAMESPACE_CHECK(PowerMethod);
 #include <Grid/algorithms/CoarsenedMatrix.h>
+NAMESPACE_CHECK(CoarsendMatrix);
 #include <Grid/algorithms/FFT.h>
 
-// EigCg
-// Pcg
-// Hdcg
-// GCR
-// etc..
-
 #endif

Grid/algorithms/CoarsenedMatrix.h

@@ -0,0 +1,635 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/CoarsenedMatrix.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef  GRID_ALGORITHM_COARSENED_MATRIX_H
+#define  GRID_ALGORITHM_COARSENED_MATRIX_H
+
+
+NAMESPACE_BEGIN(Grid);
+
+template<class vobj,class CComplex>
+inline void blockMaskedInnerProduct(Lattice<CComplex> &CoarseInner,
+				    const Lattice<decltype(innerProduct(vobj(),vobj()))> &FineMask,
+				    const Lattice<vobj> &fineX,
+				    const Lattice<vobj> &fineY)
+{
+  typedef decltype(innerProduct(vobj(),vobj())) dotp;
+
+  GridBase *coarse(CoarseInner.Grid());
+  GridBase *fine  (fineX.Grid());
+
+  Lattice<dotp> fine_inner(fine); fine_inner.Checkerboard() = fineX.Checkerboard();
+  Lattice<dotp> fine_inner_msk(fine);
+
+  // Multiply could be fused with innerProduct
+  // Single block sum kernel could do both masks.
+  fine_inner = localInnerProduct(fineX,fineY);
+  mult(fine_inner_msk, fine_inner,FineMask);
+  blockSum(CoarseInner,fine_inner_msk);
+}
+
+
+class Geometry {
+public:
+  int npoint;
+  std::vector<int> directions   ;
+  std::vector<int> displacements;
+
+  Geometry(int _d)  {
+    
+    int base = (_d==5) ? 1:0;
+
+    // make coarse grid stencil for 4d , not 5d
+    if ( _d==5 ) _d=4;
+
+    npoint = 2*_d+1;
+    directions.resize(npoint);
+    displacements.resize(npoint);
+    for(int d=0;d<_d;d++){
+      directions[d   ] = d+base;
+      directions[d+_d] = d+base;
+      displacements[d  ] = +1;
+      displacements[d+_d]= -1;
+    }
+    directions   [2*_d]=0;
+    displacements[2*_d]=0;
+  }
+
+};
+  
+template<class Fobj,class CComplex,int nbasis>
+class Aggregation   {
+public:
+  typedef iVector<CComplex,nbasis >             siteVector;
+  typedef Lattice<siteVector>                 CoarseVector;
+  typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
+
+  typedef Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj >        FineField;
+
+  GridBase *CoarseGrid;
+  GridBase *FineGrid;
+  std::vector<Lattice<Fobj> > subspace;
+  int checkerboard;
+  int Checkerboard(void){return checkerboard;}
+  Aggregation(GridBase *_CoarseGrid,GridBase *_FineGrid,int _checkerboard) : 
+    CoarseGrid(_CoarseGrid),
+    FineGrid(_FineGrid),
+    subspace(nbasis,_FineGrid),
+    checkerboard(_checkerboard)
+  {
+  };
+  
+  void Orthogonalise(void){
+    CoarseScalar InnerProd(CoarseGrid); 
+    std::cout << GridLogMessage <<" Block Gramm-Schmidt pass 1"<<std::endl;
+    blockOrthogonalise(InnerProd,subspace);
+  } 
+  void ProjectToSubspace(CoarseVector &CoarseVec,const FineField &FineVec){
+    blockProject(CoarseVec,FineVec,subspace);
+  }
+  void PromoteFromSubspace(const CoarseVector &CoarseVec,FineField &FineVec){
+    FineVec.Checkerboard() = subspace[0].Checkerboard();
+    blockPromote(CoarseVec,FineVec,subspace);
+  }
+
+  virtual void CreateSubspace(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,int nn=nbasis) {
+
+    RealD scale;
+
+    ConjugateGradient<FineField> CG(1.0e-2,100,false);
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+
+    for(int b=0;b<nn;b++){
+      
+      subspace[b] = Zero();
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+      
+      hermop.Op(noise,Mn); std::cout<<GridLogMessage << "noise   ["<<b<<"] <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+
+      for(int i=0;i<1;i++){
+
+	CG(hermop,noise,subspace[b]);
+
+	noise = subspace[b];
+	scale = std::pow(norm2(noise),-0.5); 
+	noise=noise*scale;
+
+      }
+
+      hermop.Op(noise,Mn); std::cout<<GridLogMessage << "filtered["<<b<<"] <f|MdagM|f> "<<norm2(Mn)<<std::endl;
+      subspace[b]   = noise;
+
+    }
+  }
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  // World of possibilities here. But have tried quite a lot of experiments (250+ jobs run on Summit)
+  // and this is the best I found
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+
+  virtual void CreateSubspaceChebyshev(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,
+				       int nn,
+				       double hi,
+				       double lo,
+				       int orderfilter,
+				       int ordermin,
+				       int orderstep,
+				       double filterlo
+				       ) {
+
+    RealD scale;
+
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+    FineField tmp(FineGrid);
+
+    // New normalised noise
+    gaussian(RNG,noise);
+    scale = std::pow(norm2(noise),-0.5); 
+    noise=noise*scale;
+
+    // Initial matrix element
+    hermop.Op(noise,Mn); std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+
+    int b =0;
+    {
+      // Filter
+      Chebyshev<FineField> Cheb(lo,hi,orderfilter);
+      Cheb(hermop,noise,Mn);
+      // normalise
+      scale = std::pow(norm2(Mn),-0.5); 	Mn=Mn*scale;
+      subspace[b]   = Mn;
+      hermop.Op(Mn,tmp); 
+      std::cout<<GridLogMessage << "filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+      b++;
+    }
+
+    // Generate a full sequence of Chebyshevs
+    {
+      lo=filterlo;
+      noise=Mn;
+
+      FineField T0(FineGrid); T0 = noise;  
+      FineField T1(FineGrid); 
+      FineField T2(FineGrid);
+      FineField y(FineGrid);
+      
+      FineField *Tnm = &T0;
+      FineField *Tn  = &T1;
+      FineField *Tnp = &T2;
+
+      // Tn=T1 = (xscale M + mscale)in
+      RealD xscale = 2.0/(hi-lo);
+      RealD mscale = -(hi+lo)/(hi-lo);
+      hermop.HermOp(T0,y);
+      T1=y*xscale+noise*mscale;
+
+      for(int n=2;n<=ordermin+orderstep*(nn-2);n++){
+	
+	hermop.HermOp(*Tn,y);
+
+	autoView( y_v , y, AcceleratorWrite);
+	autoView( Tn_v , (*Tn), AcceleratorWrite);
+	autoView( Tnp_v , (*Tnp), AcceleratorWrite);
+	autoView( Tnm_v , (*Tnm), AcceleratorWrite);
+	const int Nsimd = CComplex::Nsimd();
+	accelerator_forNB(ss, FineGrid->oSites(), Nsimd, {
+	  coalescedWrite(y_v[ss],xscale*y_v(ss)+mscale*Tn_v(ss));
+	  coalescedWrite(Tnp_v[ss],2.0*y_v(ss)-Tnm_v(ss));
+        });
+
+	// Possible more fine grained control is needed than a linear sweep,
+	// but huge productivity gain if this is simple algorithm and not a tunable
+	int m =1;
+	if ( n>=ordermin ) m=n-ordermin;
+	if ( (m%orderstep)==0 ) { 
+	  Mn=*Tnp;
+	  scale = std::pow(norm2(Mn),-0.5);         Mn=Mn*scale;
+	  subspace[b] = Mn;
+	  hermop.Op(Mn,tmp); 
+	  std::cout<<GridLogMessage << n<<" filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+	  b++;
+	}
+
+	// Cycle pointers to avoid copies
+	FineField *swizzle = Tnm;
+	Tnm    =Tn;
+	Tn     =Tnp;
+	Tnp    =swizzle;
+	  
+      }
+    }
+    assert(b==nn);
+  }
+
+};
+
+// Fine Object == (per site) type of fine field
+// nbasis      == number of deflation vectors
+template<class Fobj,class CComplex,int nbasis>
+class CoarsenedMatrix : public SparseMatrixBase<Lattice<iVector<CComplex,nbasis > > >  {
+public:
+    
+  typedef iVector<CComplex,nbasis >           siteVector;
+  typedef Lattice<CComplex >                  CoarseComplexField;
+  typedef Lattice<siteVector>                 CoarseVector;
+  typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
+  typedef iMatrix<CComplex,nbasis >  Cobj;
+  typedef Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj >        FineField;
+
+  ////////////////////
+  // Data members
+  ////////////////////
+  Geometry         geom;
+  GridBase *       _grid; 
+  int hermitian;
+
+  CartesianStencil<siteVector,siteVector,int> Stencil; 
+
+  std::vector<CoarseMatrix> A;
+    
+  ///////////////////////
+  // Interface
+  ///////////////////////
+  GridBase * Grid(void)         { return _grid; };   // this is all the linalg routines need to know
+
+  void M (const CoarseVector &in, CoarseVector &out)
+  {
+    conformable(_grid,in.Grid());
+    conformable(in.Grid(),out.Grid());
+
+    SimpleCompressor<siteVector> compressor;
+
+    Stencil.HaloExchange(in,compressor);
+    autoView( in_v , in, AcceleratorRead);
+    autoView( out_v , out, AcceleratorWrite);
+    typedef LatticeView<Cobj> Aview;
+      
+    Vector<Aview> AcceleratorViewContainer;
+  
+    for(int p=0;p<geom.npoint;p++) AcceleratorViewContainer.push_back(A[p].View(AcceleratorRead));
+    Aview *Aview_p = & AcceleratorViewContainer[0];
+
+    const int Nsimd = CComplex::Nsimd();
+    typedef decltype(coalescedRead(in_v[0])) calcVector;
+    typedef decltype(coalescedRead(in_v[0](0))) calcComplex;
+
+    int osites=Grid()->oSites();
+
+    accelerator_for(sss, Grid()->oSites()*nbasis, Nsimd, {
+      int ss = sss/nbasis;
+      int b  = sss%nbasis;
+      calcComplex res = Zero();
+      calcVector nbr;
+      int ptype;
+      StencilEntry *SE;
+
+      for(int point=0;point<geom.npoint;point++){
+
+	SE=Stencil.GetEntry(ptype,point,ss);
+	  
+	if(SE->_is_local) { 
+	  nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+	} else {
+	  nbr = coalescedRead(Stencil.CommBuf()[SE->_offset]);
+	}
+	acceleratorSynchronise();
+
+	for(int bb=0;bb<nbasis;bb++) {
+	  res = res + coalescedRead(Aview_p[point][ss](b,bb))*nbr(bb);
+	}
+      }
+      coalescedWrite(out_v[ss](b),res);
+      });
+
+    for(int p=0;p<geom.npoint;p++) AcceleratorViewContainer[p].ViewClose();
+  };
+
+  void Mdag (const CoarseVector &in, CoarseVector &out)
+  {
+    if(hermitian) {
+      // corresponds to Petrov-Galerkin coarsening
+      return M(in,out);
+    } else {
+      // corresponds to Galerkin coarsening
+      CoarseVector tmp(Grid());
+      G5C(tmp, in); 
+      M(tmp, out);
+      G5C(out, out);
+    }
+  };
+  void MdirComms(const CoarseVector &in)
+  {
+    SimpleCompressor<siteVector> compressor;
+    Stencil.HaloExchange(in,compressor);
+  }
+  void MdirCalc(const CoarseVector &in, CoarseVector &out, int point)
+  {
+    conformable(_grid,in.Grid());
+    conformable(_grid,out.Grid());
+
+    typedef LatticeView<Cobj> Aview;
+    Vector<Aview> AcceleratorViewContainer;
+    for(int p=0;p<geom.npoint;p++) AcceleratorViewContainer.push_back(A[p].View(AcceleratorRead));
+    Aview *Aview_p = & AcceleratorViewContainer[0];
+
+    autoView( out_v , out, AcceleratorWrite);
+    autoView( in_v  , in, AcceleratorRead);
+
+    const int Nsimd = CComplex::Nsimd();
+    typedef decltype(coalescedRead(in_v[0])) calcVector;
+    typedef decltype(coalescedRead(in_v[0](0))) calcComplex;
+
+    accelerator_for(sss, Grid()->oSites()*nbasis, Nsimd, {
+      int ss = sss/nbasis;
+      int b  = sss%nbasis;
+      calcComplex res = Zero();
+      calcVector nbr;
+      int ptype;
+      StencilEntry *SE;
+
+      SE=Stencil.GetEntry(ptype,point,ss);
+	  
+      if(SE->_is_local) { 
+	nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+      } else {
+	nbr = coalescedRead(Stencil.CommBuf()[SE->_offset]);
+      }
+      acceleratorSynchronise();
+
+      for(int bb=0;bb<nbasis;bb++) {
+	res = res + coalescedRead(Aview_p[point][ss](b,bb))*nbr(bb);
+      }
+      coalescedWrite(out_v[ss](b),res);
+    });
+    for(int p=0;p<geom.npoint;p++) AcceleratorViewContainer[p].ViewClose();
+  }
+  void MdirAll(const CoarseVector &in,std::vector<CoarseVector> &out)
+  {
+    this->MdirComms(in);
+    int ndir=geom.npoint-1;
+    if ((out.size()!=ndir)&&(out.size()!=ndir+1)) { 
+      std::cout <<"MdirAll out size "<< out.size()<<std::endl;
+      std::cout <<"MdirAll ndir "<< ndir<<std::endl;
+      assert(0);
+    }
+    for(int p=0;p<ndir;p++){
+      MdirCalc(in,out[p],p);
+    }
+  };
+  void Mdir(const CoarseVector &in, CoarseVector &out, int dir, int disp){
+
+    this->MdirComms(in);
+
+    int ndim = in.Grid()->Nd();
+
+    //////////////
+    // 4D action like wilson
+    // 0+ => 0 
+    // 0- => 1
+    // 1+ => 2 
+    // 1- => 3
+    // etc..
+    //////////////
+    // 5D action like DWF
+    // 1+ => 0 
+    // 1- => 1
+    // 2+ => 2 
+    // 2- => 3
+    // etc..
+    auto point = [dir, disp, ndim](){
+      if(dir == 0 and disp == 0)
+	return 8;
+      else if ( ndim==4 ) { 
+	return (4 * dir + 1 - disp) / 2;
+      } else { 
+	return (4 * (dir-1) + 1 - disp) / 2;
+      }
+    }();
+
+    MdirCalc(in,out,point);
+
+  };
+
+  void Mdiag(const CoarseVector &in, CoarseVector &out)
+  {
+    int point=geom.npoint-1;
+    MdirCalc(in, out, point); // No comms
+  };
+
+  
+ CoarsenedMatrix(GridCartesian &CoarseGrid, int hermitian_=0) 	: 
+
+    _grid(&CoarseGrid),
+    geom(CoarseGrid._ndimension),
+    hermitian(hermitian_),
+    Stencil(&CoarseGrid,geom.npoint,Even,geom.directions,geom.displacements,0),
+      A(geom.npoint,&CoarseGrid)
+  {
+  };
+
+  void CoarsenOperator(GridBase *FineGrid,LinearOperatorBase<Lattice<Fobj> > &linop,
+		       Aggregation<Fobj,CComplex,nbasis> & Subspace)
+  {
+    typedef Lattice<typename Fobj::tensor_reduced> FineComplexField;
+    typedef typename Fobj::scalar_type scalar_type;
+
+    FineComplexField one(FineGrid); one=scalar_type(1.0,0.0);
+    FineComplexField zero(FineGrid); zero=scalar_type(0.0,0.0);
+
+    std::vector<FineComplexField> masks(geom.npoint,FineGrid);
+    FineComplexField imask(FineGrid); // contributions from within this block
+    FineComplexField omask(FineGrid); // contributions from outwith this block
+
+    FineComplexField evenmask(FineGrid);
+    FineComplexField oddmask(FineGrid); 
+
+    FineField     phi(FineGrid);
+    FineField     tmp(FineGrid);
+    FineField     zz(FineGrid); zz=Zero();
+    FineField    Mphi(FineGrid);
+    FineField    Mphie(FineGrid);
+    FineField    Mphio(FineGrid);
+    std::vector<FineField>     Mphi_p(geom.npoint,FineGrid);
+
+    Lattice<iScalar<vInteger> > coor (FineGrid);
+    Lattice<iScalar<vInteger> > bcoor(FineGrid);
+    Lattice<iScalar<vInteger> > bcb  (FineGrid); bcb = Zero();
+
+    CoarseVector iProj(Grid()); 
+    CoarseVector oProj(Grid()); 
+    CoarseVector SelfProj(Grid()); 
+    CoarseComplexField iZProj(Grid()); 
+    CoarseComplexField oZProj(Grid()); 
+
+    CoarseScalar InnerProd(Grid()); 
+
+    // Orthogonalise the subblocks over the basis
+    blockOrthogonalise(InnerProd,Subspace.subspace);
+
+    // Compute the matrix elements of linop between this orthonormal
+    // set of vectors.
+    int self_stencil=-1;
+    for(int p=0;p<geom.npoint;p++)
+    { 
+      int dir   = geom.directions[p];
+      int disp  = geom.displacements[p];
+      A[p]=Zero();
+      if( geom.displacements[p]==0){
+	self_stencil=p;
+      }
+
+      Integer block=(FineGrid->_rdimensions[dir])/(Grid()->_rdimensions[dir]);
+
+      LatticeCoordinate(coor,dir);
+
+      ///////////////////////////////////////////////////////
+      // Work out even and odd block checkerboarding for fast diagonal term
+      ///////////////////////////////////////////////////////
+      if ( disp==1 ) {
+	bcb   = bcb + div(coor,block);
+      }
+	
+      if ( disp==0 ) {
+	  masks[p]= Zero();
+      } else if ( disp==1 ) {
+	masks[p] = where(mod(coor,block)==(block-1),one,zero);
+      } else if ( disp==-1 ) {
+	masks[p] = where(mod(coor,block)==(Integer)0,one,zero);
+      }
+    }
+    evenmask = where(mod(bcb,2)==(Integer)0,one,zero);
+    oddmask  = one-evenmask;
+
+    assert(self_stencil!=-1);
+
+    for(int i=0;i<nbasis;i++){
+
+      phi=Subspace.subspace[i];
+
+      //      std::cout << GridLogMessage<< "CoarsenMatrix vector "<<i << std::endl;
+      linop.OpDirAll(phi,Mphi_p);
+      linop.OpDiag  (phi,Mphi_p[geom.npoint-1]);
+
+      for(int p=0;p<geom.npoint;p++){ 
+
+	Mphi = Mphi_p[p];
+
+	int dir   = geom.directions[p];
+	int disp  = geom.displacements[p];
+
+	if ( (disp==-1) || (!hermitian ) ) {
+
+	  ////////////////////////////////////////////////////////////////////////
+	  // Pick out contributions coming from this cell and neighbour cell
+	  ////////////////////////////////////////////////////////////////////////
+	  omask = masks[p];
+	  imask = one-omask;
+	
+	  for(int j=0;j<nbasis;j++){
+	    
+	    blockMaskedInnerProduct(oZProj,omask,Subspace.subspace[j],Mphi);
+	    
+	    autoView( iZProj_v , iZProj, AcceleratorRead) ;
+	    autoView( oZProj_v , oZProj, AcceleratorRead) ;
+	    autoView( A_p     ,  A[p], AcceleratorWrite);
+	    autoView( A_self  , A[self_stencil], AcceleratorWrite);
+
+	    accelerator_for(ss, Grid()->oSites(), Fobj::Nsimd(),{ coalescedWrite(A_p[ss](j,i),oZProj_v(ss)); });
+
+	  }
+	}
+      }
+
+      ///////////////////////////////////////////
+      // Faster alternate self coupling.. use hermiticity to save 2x
+      ///////////////////////////////////////////
+      {
+	mult(tmp,phi,evenmask);  linop.Op(tmp,Mphie);
+	mult(tmp,phi,oddmask );  linop.Op(tmp,Mphio);
+
+	{
+	  autoView( tmp_      , tmp, AcceleratorWrite);
+	  autoView( evenmask_ , evenmask, AcceleratorRead);
+	  autoView( oddmask_  ,  oddmask, AcceleratorRead);
+	  autoView( Mphie_    ,  Mphie, AcceleratorRead);
+	  autoView( Mphio_    ,  Mphio, AcceleratorRead);
+	  accelerator_for(ss, FineGrid->oSites(), Fobj::Nsimd(),{ 
+	      coalescedWrite(tmp_[ss],evenmask_(ss)*Mphie_(ss) + oddmask_(ss)*Mphio_(ss));
+	    });
+	}
+
+	blockProject(SelfProj,tmp,Subspace.subspace);
+
+	autoView( SelfProj_ , SelfProj, AcceleratorRead);
+	autoView( A_self  , A[self_stencil], AcceleratorWrite);
+
+	accelerator_for(ss, Grid()->oSites(), Fobj::Nsimd(),{
+	  for(int j=0;j<nbasis;j++){
+	    coalescedWrite(A_self[ss](j,i), SelfProj_(ss)(j));
+	  }
+	});
+
+      }
+    }
+    if(hermitian) {
+      std::cout << GridLogMessage << " ForceHermitian, new code "<<std::endl;
+      ForceHermitian();
+    }
+  }
+
+  void ForceHermitian(void) {
+    CoarseMatrix Diff  (Grid());
+    for(int p=0;p<geom.npoint;p++){
+      int dir   = geom.directions[p];
+      int disp  = geom.displacements[p];
+      if(disp==-1) {
+	// Find the opposite link
+	for(int pp=0;pp<geom.npoint;pp++){
+	  int dirp   = geom.directions[pp];
+	  int dispp  = geom.displacements[pp];
+	  if ( (dirp==dir) && (dispp==1) ){
+	    //	    Diff = adj(Cshift(A[p],dir,1)) - A[pp]; 
+	    //	    std::cout << GridLogMessage<<" Replacing stencil leg "<<pp<<" with leg "<<p<< " diff "<<norm2(Diff) <<std::endl;
+	    A[pp] = adj(Cshift(A[p],dir,1));
+	  }
+	}
+      }
+    }
+  }
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/FFT.h

@@ -0,0 +1,296 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/Cshift.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef _GRID_FFT_H_
+#define _GRID_FFT_H_
+
+#ifdef HAVE_FFTW
+#ifdef USE_MKL
+#include <fftw/fftw3.h>
+#else
+#include <fftw3.h>
+#endif
+#endif
+
+NAMESPACE_BEGIN(Grid);
+
+template<class scalar> struct FFTW { };
+
+#ifdef HAVE_FFTW	
+template<> struct FFTW<ComplexD> {
+public:
+
+  typedef fftw_complex FFTW_scalar;
+  typedef fftw_plan    FFTW_plan;
+
+  static FFTW_plan fftw_plan_many_dft(int rank, const int *n,int howmany,
+				      FFTW_scalar *in, const int *inembed,		
+				      int istride, int idist,		
+				      FFTW_scalar *out, const int *onembed,		
+				      int ostride, int odist,		
+				      int sign, unsigned flags) {
+    return ::fftw_plan_many_dft(rank,n,howmany,in,inembed,istride,idist,out,onembed,ostride,odist,sign,flags);
+  }	  
+    
+  static void fftw_flops(const FFTW_plan p,double *add, double *mul, double *fmas){
+    ::fftw_flops(p,add,mul,fmas);
+  }
+
+  inline static void fftw_execute_dft(const FFTW_plan p,FFTW_scalar *in,FFTW_scalar *out) {
+    ::fftw_execute_dft(p,in,out);
+  }
+  inline static void fftw_destroy_plan(const FFTW_plan p) {
+    ::fftw_destroy_plan(p);
+  }
+};
+
+template<> struct FFTW<ComplexF> {
+public:
+
+  typedef fftwf_complex FFTW_scalar;
+  typedef fftwf_plan    FFTW_plan;
+
+  static FFTW_plan fftw_plan_many_dft(int rank, const int *n,int howmany,
+				      FFTW_scalar *in, const int *inembed,		
+				      int istride, int idist,		
+				      FFTW_scalar *out, const int *onembed,		
+				      int ostride, int odist,		
+				      int sign, unsigned flags) {
+    return ::fftwf_plan_many_dft(rank,n,howmany,in,inembed,istride,idist,out,onembed,ostride,odist,sign,flags);
+  }	  
+    
+  static void fftw_flops(const FFTW_plan p,double *add, double *mul, double *fmas){
+    ::fftwf_flops(p,add,mul,fmas);
+  }
+
+  inline static void fftw_execute_dft(const FFTW_plan p,FFTW_scalar *in,FFTW_scalar *out) {
+    ::fftwf_execute_dft(p,in,out);
+  }
+  inline static void fftw_destroy_plan(const FFTW_plan p) {
+    ::fftwf_destroy_plan(p);
+  }
+};
+
+#endif
+
+#ifndef FFTW_FORWARD
+#define FFTW_FORWARD (-1)
+#define FFTW_BACKWARD (+1)
+#endif
+
+class FFT {
+private:
+    
+  GridCartesian *vgrid;
+  GridCartesian *sgrid;
+    
+  int Nd;
+  double flops;
+  double flops_call;
+  uint64_t usec;
+    
+  Coordinate dimensions;
+  Coordinate processors;
+  Coordinate processor_coor;
+    
+public:
+    
+  static const int forward=FFTW_FORWARD;
+  static const int backward=FFTW_BACKWARD;
+    
+  double Flops(void) {return flops;}
+  double MFlops(void) {return flops/usec;}
+  double USec(void)   {return (double)usec;}    
+
+  FFT ( GridCartesian * grid ) :
+    vgrid(grid),
+    Nd(grid->_ndimension),
+    dimensions(grid->_fdimensions),
+    processors(grid->_processors),
+    processor_coor(grid->_processor_coor)
+  {
+    flops=0;
+    usec =0;
+    Coordinate layout(Nd,1);
+    sgrid = new GridCartesian(dimensions,layout,processors);
+  };
+    
+  ~FFT ( void)  {
+    delete sgrid;
+  }
+    
+  template<class vobj>
+  void FFT_dim_mask(Lattice<vobj> &result,const Lattice<vobj> &source,Coordinate mask,int sign){
+
+    conformable(result.Grid(),vgrid);
+    conformable(source.Grid(),vgrid);
+    Lattice<vobj> tmp(vgrid);
+    tmp = source;
+    for(int d=0;d<Nd;d++){
+      if( mask[d] ) {
+	FFT_dim(result,tmp,d,sign);
+	tmp=result;
+      }
+    }
+  }
+
+  template<class vobj>
+  void FFT_all_dim(Lattice<vobj> &result,const Lattice<vobj> &source,int sign){
+    Coordinate mask(Nd,1);
+    FFT_dim_mask(result,source,mask,sign);
+  }
+
+
+  template<class vobj>
+  void FFT_dim(Lattice<vobj> &result,const Lattice<vobj> &source,int dim, int sign){
+#ifndef HAVE_FFTW
+    assert(0);
+#else
+    conformable(result.Grid(),vgrid);
+    conformable(source.Grid(),vgrid);
+
+    int L = vgrid->_ldimensions[dim];
+    int G = vgrid->_fdimensions[dim];
+      
+    Coordinate layout(Nd,1);
+    Coordinate pencil_gd(vgrid->_fdimensions);
+      
+    pencil_gd[dim] = G*processors[dim];
+      
+    // Pencil global vol LxLxGxLxL per node
+    GridCartesian pencil_g(pencil_gd,layout,processors);
+      
+    // Construct pencils
+    typedef typename vobj::scalar_object sobj;
+    typedef typename sobj::scalar_type   scalar;
+      
+    Lattice<sobj> pgbuf(&pencil_g);
+    autoView(pgbuf_v , pgbuf, CpuWrite);
+
+    typedef typename FFTW<scalar>::FFTW_scalar FFTW_scalar;
+    typedef typename FFTW<scalar>::FFTW_plan   FFTW_plan;
+      
+    int Ncomp = sizeof(sobj)/sizeof(scalar);
+    int Nlow  = 1;
+    for(int d=0;d<dim;d++){
+      Nlow*=vgrid->_ldimensions[d];
+    }
+      
+    int rank = 1;  /* 1d transforms */
+    int n[] = {G}; /* 1d transforms of length G */
+    int howmany = Ncomp;
+    int odist,idist,istride,ostride;
+    idist   = odist   = 1;          /* Distance between consecutive FT's */
+    istride = ostride = Ncomp*Nlow; /* distance between two elements in the same FT */
+    int *inembed = n, *onembed = n;
+      
+    scalar div;
+    if ( sign == backward ) div = 1.0/G;
+    else if ( sign == forward ) div = 1.0;
+    else assert(0);
+      
+    FFTW_plan p;
+    {
+      FFTW_scalar *in = (FFTW_scalar *)&pgbuf_v[0];
+      FFTW_scalar *out= (FFTW_scalar *)&pgbuf_v[0];
+      p = FFTW<scalar>::fftw_plan_many_dft(rank,n,howmany,
+					   in,inembed,
+					   istride,idist,
+					   out,onembed,
+					   ostride, odist,
+					   sign,FFTW_ESTIMATE);
+    }
+      
+    // Barrel shift and collect global pencil
+    Coordinate lcoor(Nd), gcoor(Nd);
+    result = source;
+    int pc = processor_coor[dim];
+    for(int p=0;p<processors[dim];p++) {
+      {
+	autoView(r_v,result,CpuRead);
+	autoView(p_v,pgbuf,CpuWrite);
+	thread_for(idx, sgrid->lSites(),{
+          Coordinate cbuf(Nd);
+          sobj s;
+	  sgrid->LocalIndexToLocalCoor(idx,cbuf);
+	  peekLocalSite(s,r_v,cbuf);
+	  cbuf[dim]+=((pc+p) % processors[dim])*L;
+	  pokeLocalSite(s,p_v,cbuf);
+        });
+      }
+      if (p != processors[dim] - 1) {
+	result = Cshift(result,dim,L);
+      }
+    }
+      
+    // Loop over orthog coords
+    int NN=pencil_g.lSites();
+    GridStopWatch timer;
+    timer.Start();
+    thread_for( idx,NN,{
+        Coordinate cbuf(Nd);
+	pencil_g.LocalIndexToLocalCoor(idx, cbuf);
+	if ( cbuf[dim] == 0 ) {  // restricts loop to plane at lcoor[dim]==0
+	  FFTW_scalar *in = (FFTW_scalar *)&pgbuf_v[idx];
+	  FFTW_scalar *out= (FFTW_scalar *)&pgbuf_v[idx];
+	  FFTW<scalar>::fftw_execute_dft(p,in,out);
+	}
+    });
+    timer.Stop();
+      
+    // performance counting
+    double add,mul,fma;
+    FFTW<scalar>::fftw_flops(p,&add,&mul,&fma);
+    flops_call = add+mul+2.0*fma;
+    usec += timer.useconds();
+    flops+= flops_call*NN;
+      
+    // writing out result
+    {
+      autoView(pgbuf_v,pgbuf,CpuRead);
+      autoView(result_v,result,CpuWrite);
+      thread_for(idx,sgrid->lSites(),{
+	Coordinate clbuf(Nd), cgbuf(Nd);
+	sobj s;
+	sgrid->LocalIndexToLocalCoor(idx,clbuf);
+	cgbuf = clbuf;
+	cgbuf[dim] = clbuf[dim]+L*pc;
+	peekLocalSite(s,pgbuf_v,cgbuf);
+	pokeLocalSite(s,result_v,clbuf);
+      });
+    }
+    result = result*div;
+      
+    // destroying plan
+    FFTW<scalar>::fftw_destroy_plan(p);
+#endif
+  }
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/algorithms/LinearOperator.h

@@ -0,0 +1,626 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/LinearOperator.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once 
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////////////////////////////////////
+// LinearOperators Take a something and return a something.
+/////////////////////////////////////////////////////////////////////////////////////////////
+//
+// Hopefully linearity is satisfied and the AdjOp is indeed the Hermitian Conjugateugate (transpose if real):
+//SBase
+//   i)  F(a x + b y) = aF(x) + b F(y).
+//  ii)  <x|Op|y> = <y|AdjOp|x>^\ast
+//
+// Would be fun to have a test linearity & Herm Conj function!
+/////////////////////////////////////////////////////////////////////////////////////////////
+template<class Field> class LinearOperatorBase {
+public:
+  // Support for coarsening to a multigrid
+  virtual void OpDiag (const Field &in, Field &out) = 0; // Abstract base
+  virtual void OpDir  (const Field &in, Field &out,int dir,int disp) = 0; // Abstract base
+  virtual void OpDirAll  (const Field &in, std::vector<Field> &out) = 0; // Abstract base
+
+  virtual void Op     (const Field &in, Field &out) = 0; // Abstract base
+  virtual void AdjOp  (const Field &in, Field &out) = 0; // Abstract base
+  virtual void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2)=0;
+  virtual void HermOp(const Field &in, Field &out)=0;
+};
+
+
+/////////////////////////////////////////////////////////////////////////////////////////////
+// By sharing the class for Sparse Matrix across multiple operator wrappers, we can share code
+// between RB and non-RB variants. Sparse matrix is like the fermion action def, and then
+// the wrappers implement the specialisation of "Op" and "AdjOp" to the cases minimising
+// replication of code.
+//
+// I'm not entirely happy with implementation; to share the Schur code between herm and non-herm
+// while still having a "OpAndNorm" in the abstract base I had to implement it in both cases
+// with an assert trap in the non-herm. This isn't right; there must be a better C++ way to
+// do it, but I fear it required multiple inheritance and mixed in abstract base classes
+/////////////////////////////////////////////////////////////////////////////////////////////
+
+////////////////////////////////////////////////////////////////////
+// Construct herm op from non-herm matrix
+////////////////////////////////////////////////////////////////////
+template<class Matrix,class Field>
+class MdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+public:
+  MdagMLinearOperator(Matrix &Mat): _Mat(Mat){};
+
+  // Support for coarsening to a multigrid
+  void OpDiag (const Field &in, Field &out) {
+    _Mat.Mdiag(in,out);
+  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {
+    _Mat.Mdir(in,out,dir,disp);
+  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){
+    _Mat.MdirAll(in,out);
+  };
+  void Op     (const Field &in, Field &out){
+    _Mat.M(in,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    _Mat.Mdag(in,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    _Mat.MdagM(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    _Mat.MdagM(in,out);
+  }
+};
+
+////////////////////////////////////////////////////////////////////
+// Construct herm op and shift it for mgrid smoother
+////////////////////////////////////////////////////////////////////
+template<class Matrix,class Field>
+class ShiftedMdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  RealD _shift;
+public:
+  ShiftedMdagMLinearOperator(Matrix &Mat,RealD shift): _Mat(Mat), _shift(shift){};
+  // Support for coarsening to a multigrid
+  void OpDiag (const Field &in, Field &out) {
+    _Mat.Mdiag(in,out);
+    assert(0);
+  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {
+    _Mat.Mdir(in,out,dir,disp);
+    assert(0);
+  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){
+    assert(0);
+  };
+  void Op     (const Field &in, Field &out){
+    _Mat.M(in,out);
+    assert(0);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    _Mat.Mdag(in,out);
+    assert(0);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    _Mat.MdagM(in,out);
+    out = out + _shift*in;
+  }
+};
+
+////////////////////////////////////////////////////////////////////
+// Wrap an already herm matrix
+////////////////////////////////////////////////////////////////////
+template<class Matrix,class Field>
+class HermitianLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+public:
+  HermitianLinearOperator(Matrix &Mat): _Mat(Mat){};
+  // Support for coarsening to a multigrid
+  void OpDiag (const Field &in, Field &out) {
+    _Mat.Mdiag(in,out);
+  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {
+    _Mat.Mdir(in,out,dir,disp);
+  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){
+    _Mat.MdirAll(in,out);
+  };
+  void Op     (const Field &in, Field &out){
+    _Mat.M(in,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    _Mat.M(in,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot= innerProduct(in,out); n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    _Mat.M(in,out);
+  }
+};
+
+template<class Matrix,class Field>
+class NonHermitianLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+public:
+  NonHermitianLinearOperator(Matrix &Mat): _Mat(Mat){};
+  // Support for coarsening to a multigrid
+  void OpDiag (const Field &in, Field &out) {
+    _Mat.Mdiag(in,out);
+  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {
+    _Mat.Mdir(in,out,dir,disp);
+  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){
+    _Mat.MdirAll(in,out);
+  };
+  void Op     (const Field &in, Field &out){
+    _Mat.M(in,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    _Mat.Mdag(in,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    assert(0);
+  }
+  void HermOp(const Field &in, Field &out){
+    assert(0);
+  }
+};
+
+//////////////////////////////////////////////////////////
+// Even Odd Schur decomp operators; there are several
+// ways to introduce the even odd checkerboarding
+//////////////////////////////////////////////////////////
+
+template<class Field>
+class SchurOperatorBase :  public LinearOperatorBase<Field> {
+ public:
+  virtual  void Mpc      (const Field &in, Field &out) =0;
+  virtual  void MpcDag   (const Field &in, Field &out) =0;
+  virtual  void MpcDagMpc(const Field &in, Field &out) {
+    Field tmp(in.Grid());
+    tmp.Checkerboard() = in.Checkerboard();
+    Mpc(in,tmp);
+    MpcDag(tmp,out);
+  }
+  virtual void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    out.Checkerboard() = in.Checkerboard();
+    MpcDagMpc(in,out);
+    ComplexD dot= innerProduct(in,out); 
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  virtual void HermOp(const Field &in, Field &out){
+    out.Checkerboard() = in.Checkerboard();
+    MpcDagMpc(in,out);
+  }
+  void Op     (const Field &in, Field &out){
+    Mpc(in,out);
+  }
+  void AdjOp     (const Field &in, Field &out){ 
+    MpcDag(in,out);
+  }
+  // Support for coarsening to a multigrid
+  void OpDiag (const Field &in, Field &out) {
+    assert(0); // must coarsen the unpreconditioned system
+  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {
+    assert(0);
+  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){
+    assert(0);
+  };
+};
+template<class Matrix,class Field>
+  class SchurDiagMooeeOperator :  public SchurOperatorBase<Field> {
+ public:
+    Matrix &_Mat;
+    SchurDiagMooeeOperator (Matrix &Mat): _Mat(Mat){};
+    virtual  void Mpc      (const Field &in, Field &out) {
+      Field tmp(in.Grid());
+      tmp.Checkerboard() = !in.Checkerboard();
+      
+      _Mat.Meooe(in,tmp);
+      _Mat.MooeeInv(tmp,out);
+      _Mat.Meooe(out,tmp);
+      _Mat.Mooee(in,out);
+      axpy(out,-1.0,tmp,out);
+    }
+    virtual void MpcDag   (const Field &in, Field &out){
+      Field tmp(in.Grid());
+	
+      _Mat.MeooeDag(in,tmp);
+      _Mat.MooeeInvDag(tmp,out);
+      _Mat.MeooeDag(out,tmp);
+      _Mat.MooeeDag(in,out);
+      axpy(out,-1.0,tmp,out);
+    }
+};
+template<class Matrix,class Field>
+  class SchurDiagOneOperator :  public SchurOperatorBase<Field> {
+ protected:
+    Matrix &_Mat;
+ public:
+    SchurDiagOneOperator (Matrix &Mat): _Mat(Mat){};
+    
+    virtual void Mpc      (const Field &in, Field &out) {
+      Field tmp(in.Grid());
+
+      _Mat.Meooe(in,out);
+      _Mat.MooeeInv(out,tmp);
+      _Mat.Meooe(tmp,out);
+      _Mat.MooeeInv(out,tmp);
+      axpy(out,-1.0,tmp,in);
+    }
+    virtual void MpcDag   (const Field &in, Field &out){
+      Field tmp(in.Grid());
+      
+      _Mat.MooeeInvDag(in,out);
+      _Mat.MeooeDag(out,tmp);
+      _Mat.MooeeInvDag(tmp,out);
+      _Mat.MeooeDag(out,tmp);
+      axpy(out,-1.0,tmp,in);
+    }
+};
+template<class Matrix,class Field>
+  class SchurDiagTwoOperator :  public SchurOperatorBase<Field> {
+ protected:
+    Matrix &_Mat;
+ public:
+    SchurDiagTwoOperator (Matrix &Mat): _Mat(Mat){};
+    
+    virtual void Mpc      (const Field &in, Field &out) {
+      Field tmp(in.Grid());
+      
+      _Mat.MooeeInv(in,out);
+      _Mat.Meooe(out,tmp);
+      _Mat.MooeeInv(tmp,out);
+      _Mat.Meooe(out,tmp);
+      
+      axpy(out,-1.0,tmp,in);
+    }
+    virtual  void MpcDag   (const Field &in, Field &out){
+      Field tmp(in.Grid());
+
+      _Mat.MeooeDag(in,out);
+      _Mat.MooeeInvDag(out,tmp);
+      _Mat.MeooeDag(tmp,out);
+      _Mat.MooeeInvDag(out,tmp);
+
+      axpy(out,-1.0,tmp,in);
+    }
+};
+
+template<class Field>
+class NonHermitianSchurOperatorBase :  public LinearOperatorBase<Field> 
+{
+ public:
+  virtual void  Mpc      (const Field& in, Field& out) = 0;
+  virtual void  MpcDag   (const Field& in, Field& out) = 0;
+  virtual void  MpcDagMpc(const Field& in, Field& out) {
+    Field tmp(in.Grid());
+    tmp.Checkerboard() = in.Checkerboard();
+    Mpc(in,tmp);
+    MpcDag(tmp,out);
+  }
+  virtual void HermOpAndNorm(const Field& in, Field& out, RealD& n1, RealD& n2) {
+    assert(0);
+  }
+  virtual void HermOp(const Field& in, Field& out) {
+    assert(0);
+  }
+  void Op(const Field& in, Field& out) {
+    Mpc(in, out);
+  }
+  void AdjOp(const Field& in, Field& out) { 
+    MpcDag(in, out);
+  }
+  // Support for coarsening to a multigrid
+  void OpDiag(const Field& in, Field& out) {
+    assert(0); // must coarsen the unpreconditioned system
+  }
+  void OpDir(const Field& in, Field& out, int dir, int disp) {
+    assert(0);
+  }
+  void OpDirAll(const Field& in, std::vector<Field>& out){
+    assert(0);
+  };
+};
+
+template<class Matrix, class Field>
+class NonHermitianSchurDiagMooeeOperator :  public NonHermitianSchurOperatorBase<Field> 
+{
+ public:
+  Matrix& _Mat;
+ NonHermitianSchurDiagMooeeOperator(Matrix& Mat): _Mat(Mat){};
+  virtual void Mpc(const Field& in, Field& out) {
+    Field tmp(in.Grid());
+    tmp.Checkerboard() = !in.Checkerboard();
+    
+    _Mat.Meooe(in, tmp);
+    _Mat.MooeeInv(tmp, out);
+    _Mat.Meooe(out, tmp);
+    
+    _Mat.Mooee(in, out);
+    
+    axpy(out, -1.0, tmp, out);
+  }
+  virtual void MpcDag(const Field& in, Field& out) {
+    Field tmp(in.Grid());
+    
+    _Mat.MeooeDag(in, tmp);
+    _Mat.MooeeInvDag(tmp, out);
+    _Mat.MeooeDag(out, tmp);
+	  
+    _Mat.MooeeDag(in, out);
+    
+    axpy(out, -1.0, tmp, out);
+  }
+};
+    
+template<class Matrix,class Field>
+class NonHermitianSchurDiagOneOperator : public NonHermitianSchurOperatorBase<Field> 
+{
+ protected:
+  Matrix &_Mat;
+  
+ public:
+  NonHermitianSchurDiagOneOperator (Matrix& Mat): _Mat(Mat){};
+  virtual void Mpc(const Field& in, Field& out) {
+    Field tmp(in.Grid());
+	  
+    _Mat.Meooe(in, out);
+    _Mat.MooeeInv(out, tmp);
+    _Mat.Meooe(tmp, out);
+    _Mat.MooeeInv(out, tmp);
+
+    axpy(out, -1.0, tmp, in);
+  }
+  virtual void MpcDag(const Field& in, Field& out) {
+    Field tmp(in.Grid());
+    
+    _Mat.MooeeInvDag(in, out);
+    _Mat.MeooeDag(out, tmp);
+    _Mat.MooeeInvDag(tmp, out);
+    _Mat.MeooeDag(out, tmp);
+    
+    axpy(out, -1.0, tmp, in);
+  }
+};
+
+template<class Matrix, class Field>
+class NonHermitianSchurDiagTwoOperator : public NonHermitianSchurOperatorBase<Field> 
+{
+ protected:
+  Matrix& _Mat;
+  
+ public:
+ NonHermitianSchurDiagTwoOperator(Matrix& Mat): _Mat(Mat){};
+
+  virtual void Mpc(const Field& in, Field& out) {
+    Field tmp(in.Grid());
+    
+    _Mat.MooeeInv(in, out);
+    _Mat.Meooe(out, tmp);
+    _Mat.MooeeInv(tmp, out);
+    _Mat.Meooe(out, tmp);
+
+    axpy(out, -1.0, tmp, in);
+  }
+  virtual void MpcDag(const Field& in, Field& out) {
+    Field tmp(in.Grid());
+    
+    _Mat.MeooeDag(in, out);
+    _Mat.MooeeInvDag(out, tmp);
+    _Mat.MeooeDag(tmp, out);
+    _Mat.MooeeInvDag(out, tmp);
+
+    axpy(out, -1.0, tmp, in);
+  }
+};
+
+///////////////////////////////////////////////////////////////////////////////////////////////////
+// Left  handed Moo^-1 ; (Moo - Moe Mee^-1 Meo) psi = eta  -->  ( 1 - Moo^-1 Moe Mee^-1 Meo ) psi = Moo^-1 eta
+// Right handed Moo^-1 ; (Moo - Moe Mee^-1 Meo) Moo^-1 Moo psi = eta  -->  ( 1 - Moe Mee^-1 Meo Moo^-1) phi=eta ; psi = Moo^-1 phi
+///////////////////////////////////////////////////////////////////////////////////////////////////
+template<class Matrix,class Field> using SchurDiagOneRH = SchurDiagTwoOperator<Matrix,Field> ;
+template<class Matrix,class Field> using SchurDiagOneLH = SchurDiagOneOperator<Matrix,Field> ;
+///////////////////////////////////////////////////////////////////////////////////////////////////
+//  Staggered use
+///////////////////////////////////////////////////////////////////////////////////////////////////
+template<class Matrix,class Field>
+class SchurStaggeredOperator :  public SchurOperatorBase<Field> {
+ protected:
+  Matrix &_Mat;
+  Field tmp;
+  RealD mass;
+ public:
+  SchurStaggeredOperator (Matrix &Mat): _Mat(Mat), tmp(_Mat.RedBlackGrid()) 
+  { 
+    assert( _Mat.isTrivialEE() );
+    mass = _Mat.Mass();
+  }
+  virtual void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    Mpc(in,out);
+    ComplexD dot= innerProduct(in,out);
+    n1 = real(dot);
+    n2 =0.0;
+  }
+  virtual void HermOp(const Field &in, Field &out){
+    Mpc(in,out);
+    //    _Mat.Meooe(in,out);
+    //    _Mat.Meooe(out,tmp);
+    //    axpby(out,-1.0,mass*mass,tmp,in);
+  }
+  virtual  void Mpc      (const Field &in, Field &out) 
+  {
+    Field tmp(in.Grid());
+    Field tmp2(in.Grid());
+	
+    //    _Mat.Mooee(in,out);
+    //    _Mat.Mooee(out,tmp);
+
+    _Mat.Meooe(in,out);
+    _Mat.Meooe(out,tmp);
+    axpby(out,-1.0,mass*mass,tmp,in);
+  }
+  virtual  void MpcDag   (const Field &in, Field &out){
+    Mpc(in,out);
+  }
+  virtual void MpcDagMpc(const Field &in, Field &out,RealD &ni,RealD &no) {
+    assert(0);// Never need with staggered
+  }
+};
+template<class Matrix,class Field> using SchurStagOperator = SchurStaggeredOperator<Matrix,Field>;
+
+/////////////////////////////////////////////////////////////
+// Base classes for functions of operators
+/////////////////////////////////////////////////////////////
+template<class Field> class OperatorFunction {
+public:
+  virtual void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) = 0;
+  virtual void operator() (LinearOperatorBase<Field> &Linop, const std::vector<Field> &in,std::vector<Field> &out) {
+    assert(in.size()==out.size());
+    for(int k=0;k<in.size();k++){
+      (*this)(Linop,in[k],out[k]);
+    }
+  };
+};
+
+template<class Field> class LinearFunction {
+public:
+  virtual void operator() (const Field &in, Field &out) = 0;
+};
+
+template<class Field> class IdentityLinearFunction : public LinearFunction<Field> {
+public:
+  void operator() (const Field &in, Field &out){
+    out = in;
+  };
+};
+
+
+/////////////////////////////////////////////////////////////
+// Base classes for Multishift solvers for operators
+/////////////////////////////////////////////////////////////
+template<class Field> class OperatorMultiFunction {
+public:
+  virtual void operator() (LinearOperatorBase<Field> &Linop, const Field &in, std::vector<Field> &out) = 0;
+};
+
+// FIXME : To think about
+
+// Chroma functionality list defining LinearOperator
+/*
+  virtual void operator() (T& chi, const T& psi, enum PlusMinus isign) const = 0;
+  virtual void operator() (T& chi, const T& psi, enum PlusMinus isign, Real epsilon) const
+  virtual const Subset& subset() const = 0;
+  virtual unsigned long nFlops() const { return 0; }
+  virtual void deriv(P& ds_u, const T& chi, const T& psi, enum PlusMinus isign) const
+  class UnprecLinearOperator : public DiffLinearOperator<T,P,Q>
+  const Subset& subset() const {return all;}
+  };
+*/
+
+////////////////////////////////////////////////////////////////////////////////////////////
+// Hermitian operator Linear function and operator function
+////////////////////////////////////////////////////////////////////////////////////////////
+template<class Field>
+class HermOpOperatorFunction : public OperatorFunction<Field> {
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
+    Linop.HermOp(in,out);
+  };
+};
+
+template<typename Field>
+class PlainHermOp : public LinearFunction<Field> {
+public:
+  LinearOperatorBase<Field> &_Linop;
+      
+  PlainHermOp(LinearOperatorBase<Field>& linop) : _Linop(linop) 
+  {}
+      
+  void operator()(const Field& in, Field& out) {
+    _Linop.HermOp(in,out);
+  }
+};
+
+template<typename Field>
+class FunctionHermOp : public LinearFunction<Field> {
+public:
+  OperatorFunction<Field>   & _poly;
+  LinearOperatorBase<Field> &_Linop;
+      
+  FunctionHermOp(OperatorFunction<Field> & poly,LinearOperatorBase<Field>& linop) 
+    : _poly(poly), _Linop(linop) {};
+      
+  void operator()(const Field& in, Field& out) {
+    _poly(_Linop,in,out);
+  }
+};
+
+template<class Field>
+class Polynomial : public OperatorFunction<Field> {
+private:
+  std::vector<RealD> Coeffs;
+public:
+  using OperatorFunction<Field>::operator();
+
+  Polynomial(std::vector<RealD> &_Coeffs) : Coeffs(_Coeffs) { };
+
+  // Implement the required interface
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
+
+    Field AtoN(in.Grid());
+    Field Mtmp(in.Grid());
+    AtoN = in;
+    out = AtoN*Coeffs[0];
+    for(int n=1;n<Coeffs.size();n++){
+      Mtmp = AtoN;
+      Linop.HermOp(Mtmp,AtoN);
+      out=out+AtoN*Coeffs[n];
+    }
+  };
+};
+
+NAMESPACE_END(Grid);

Grid/algorithms/Preconditioner.h

@@ -1,4 +1,4 @@
-    /*************************************************************************************
+/*************************************************************************************
 
     Grid physics library, www.github.com/paboyle/Grid 
 
@@ -23,24 +23,24 @@ Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
     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 */
+*************************************************************************************/
+/*  END LEGAL */
 #ifndef GRID_PRECONDITIONER_H
 #define GRID_PRECONDITIONER_H
 
-namespace Grid {
+NAMESPACE_BEGIN(Grid);
 
-  template<class Field> class Preconditioner :  public LinearFunction<Field> { 
-    virtual void operator()(const Field &src, Field & psi)=0;
-  };
+template<class Field> class Preconditioner :  public LinearFunction<Field> { 
+  virtual void operator()(const Field &src, Field & psi)=0;
+};
 
-  template<class Field> class TrivialPrecon :  public Preconditioner<Field> { 
-  public:
-    void operator()(const Field &src, Field & psi){
-      psi = src;
-    }
-    TrivialPrecon(void){};
-  };
+template<class Field> class TrivialPrecon :  public Preconditioner<Field> { 
+public:
+  void operator()(const Field &src, Field & psi){
+    psi = src;
+  }
+  TrivialPrecon(void){};
+};
 
-}
+NAMESPACE_END(Grid);
 #endif

Grid/algorithms/SparseMatrix.h

@@ -0,0 +1,80 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/SparseMatrix.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef  GRID_ALGORITHM_SPARSE_MATRIX_H
+#define  GRID_ALGORITHM_SPARSE_MATRIX_H
+
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////////////////////////////////////
+// Interface defining what I expect of a general sparse matrix, such as a Fermion action
+/////////////////////////////////////////////////////////////////////////////////////////////
+template<class Field> class SparseMatrixBase {
+public:
+  virtual GridBase *Grid(void) =0;
+  // Full checkerboar operations
+  virtual void  M    (const Field &in, Field &out)=0;
+  virtual void  Mdag (const Field &in, Field &out)=0;
+  virtual void  MdagM(const Field &in, Field &out) {
+    Field tmp (in.Grid());
+    M(in,tmp);
+    Mdag(tmp,out);
+  }
+  virtual  void Mdiag    (const Field &in, Field &out)=0;
+  virtual  void Mdir     (const Field &in, Field &out,int dir, int disp)=0;
+  virtual  void MdirAll  (const Field &in, std::vector<Field> &out)=0;
+};
+
+/////////////////////////////////////////////////////////////////////////////////////////////
+// Interface augmented by a red black sparse matrix, such as a Fermion action
+/////////////////////////////////////////////////////////////////////////////////////////////
+template<class Field> class CheckerBoardedSparseMatrixBase : public SparseMatrixBase<Field> {
+public:
+  virtual GridBase *RedBlackGrid(void)=0;
+
+  //////////////////////////////////////////////////////////////////////
+  // Query the even even properties to make algorithmic decisions
+  //////////////////////////////////////////////////////////////////////
+  virtual RealD  Mass(void)        { return 0.0; };
+  virtual int    ConstEE(void)     { return 1; }; // Disable assumptions unless overridden
+  virtual int    isTrivialEE(void) { return 0; }; // by a derived class that knows better
+
+  // half checkerboard operaions
+  virtual  void Meooe    (const Field &in, Field &out)=0;
+  virtual  void Mooee    (const Field &in, Field &out)=0;
+  virtual  void MooeeInv (const Field &in, Field &out)=0;
+
+  virtual  void MeooeDag    (const Field &in, Field &out)=0;
+  virtual  void MooeeDag    (const Field &in, Field &out)=0;
+  virtual  void MooeeInvDag (const Field &in, Field &out)=0;
+
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/algorithms/approx/Chebyshev.h

@@ -0,0 +1,409 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/approx/Chebyshev.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+Author: Christoph Lehner <clehner@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CHEBYSHEV_H
+#define GRID_CHEBYSHEV_H
+
+#include <Grid/algorithms/LinearOperator.h>
+
+NAMESPACE_BEGIN(Grid);
+
+struct ChebyParams : Serializable {
+  GRID_SERIALIZABLE_CLASS_MEMBERS(ChebyParams,
+				  RealD, alpha,  
+				  RealD, beta,   
+				  int, Npoly);
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////
+// Generic Chebyshev approximations
+////////////////////////////////////////////////////////////////////////////////////////////
+template<class Field>
+class Chebyshev : public OperatorFunction<Field> {
+private:
+  using OperatorFunction<Field>::operator();
+
+  std::vector<RealD> Coeffs;
+  int order;
+  RealD hi;
+  RealD lo;
+
+public:
+  void csv(std::ostream &out){
+    RealD diff = hi-lo;
+    RealD delta = diff*1.0e-9;
+    for (RealD x=lo; x<hi; x+=delta) {
+      delta*=1.1;
+      RealD f = approx(x);
+      out<< x<<" "<<f<<std::endl;
+    }
+    return;
+  }
+
+  // Convenience for plotting the approximation
+  void   PlotApprox(std::ostream &out) {
+    out<<"Polynomial approx ["<<lo<<","<<hi<<"]"<<std::endl;
+    for(RealD x=lo;x<hi;x+=(hi-lo)/50.0){
+      out <<x<<"\t"<<approx(x)<<std::endl;
+    }
+  };
+
+  Chebyshev(){};
+  Chebyshev(ChebyParams p){ Init(p.alpha,p.beta,p.Npoly);};
+  Chebyshev(RealD _lo,RealD _hi,int _order, RealD (* func)(RealD) ) {Init(_lo,_hi,_order,func);};
+  Chebyshev(RealD _lo,RealD _hi,int _order) {Init(_lo,_hi,_order);};
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////////
+  // c.f. numerical recipes "chebft"/"chebev". This is sec 5.8 "Chebyshev approximation".
+  ////////////////////////////////////////////////////////////////////////////////////////////////////
+  // CJ: the one we need for Lanczos
+  void Init(RealD _lo,RealD _hi,int _order)
+  {
+    lo=_lo;
+    hi=_hi;
+    order=_order;
+      
+    if(order < 2) exit(-1);
+    Coeffs.resize(order);
+    Coeffs.assign(0.,order);
+    Coeffs[order-1] = 1.;
+  };
+  
+  // PB - more efficient low pass drops high modes above the low as 1/x uses all Chebyshev's.
+  // Similar kick effect below the threshold as Lanczos filter approach
+  void InitLowPass(RealD _lo,RealD _hi,int _order)
+  {
+    lo=_lo;
+    hi=_hi;
+    order=_order;
+      
+    if(order < 2) exit(-1);
+    Coeffs.resize(order);
+    for(int j=0;j<order;j++){
+      RealD k=(order-1.0);
+      RealD s=std::cos( j*M_PI*(k+0.5)/order );
+      Coeffs[j] = s * 2.0/order;
+    }
+    
+  };
+
+  void Init(RealD _lo,RealD _hi,int _order, RealD (* func)(RealD))
+  {
+    lo=_lo;
+    hi=_hi;
+    order=_order;
+      
+    if(order < 2) exit(-1);
+    Coeffs.resize(order);
+    for(int j=0;j<order;j++){
+      RealD s=0;
+      for(int k=0;k<order;k++){
+	RealD y=std::cos(M_PI*(k+0.5)/order);
+	RealD x=0.5*(y*(hi-lo)+(hi+lo));
+	RealD f=func(x);
+	s=s+f*std::cos( j*M_PI*(k+0.5)/order );
+      }
+      Coeffs[j] = s * 2.0/order;
+    }
+  };
+
+    
+  void JacksonSmooth(void){
+    RealD M=order;
+    RealD alpha = M_PI/(M+2);
+    RealD lmax = std::cos(alpha);
+    RealD sumUsq =0;
+    std::vector<RealD> U(M);
+    std::vector<RealD> a(M);
+    std::vector<RealD> g(M);
+    for(int n=0;n<=M;n++){
+      U[n] = std::sin((n+1)*std::acos(lmax))/std::sin(std::acos(lmax));
+      sumUsq += U[n]*U[n];
+    }      
+    sumUsq = std::sqrt(sumUsq);
+
+    for(int i=1;i<=M;i++){
+      a[i] = U[i]/sumUsq;
+    }
+    g[0] = 1.0;
+    for(int m=1;m<=M;m++){
+      g[m] = 0;
+      for(int i=0;i<=M-m;i++){
+	g[m]+= a[i]*a[m+i];
+      }
+    }
+    for(int m=1;m<=M;m++){
+      Coeffs[m]*=g[m];
+    }
+  }
+  RealD approx(RealD x) // Convenience for plotting the approximation
+  {
+    RealD Tn;
+    RealD Tnm;
+    RealD Tnp;
+      
+    RealD y=( x-0.5*(hi+lo))/(0.5*(hi-lo));
+      
+    RealD T0=1;
+    RealD T1=y;
+      
+    RealD sum;
+    sum = 0.5*Coeffs[0]*T0;
+    sum+= Coeffs[1]*T1;
+      
+    Tn =T1;
+    Tnm=T0;
+    for(int i=2;i<order;i++){
+      Tnp=2*y*Tn-Tnm;
+      Tnm=Tn;
+      Tn =Tnp;
+      sum+= Tn*Coeffs[i];
+    }
+    return sum;
+  };
+
+  RealD approxD(RealD x)
+  {
+    RealD Un;
+    RealD Unm;
+    RealD Unp;
+      
+    RealD y=( x-0.5*(hi+lo))/(0.5*(hi-lo));
+      
+    RealD U0=1;
+    RealD U1=2*y;
+      
+    RealD sum;
+    sum = Coeffs[1]*U0;
+    sum+= Coeffs[2]*U1*2.0;
+      
+    Un =U1;
+    Unm=U0;
+    for(int i=2;i<order-1;i++){
+      Unp=2*y*Un-Unm;
+      Unm=Un;
+      Un =Unp;
+      sum+= Un*Coeffs[i+1]*(i+1.0);
+    }
+    return sum/(0.5*(hi-lo));
+  };
+    
+  RealD approxInv(RealD z, RealD x0, int maxiter, RealD resid) {
+    RealD x = x0;
+    RealD eps;
+      
+    int i;
+    for (i=0;i<maxiter;i++) {
+      eps = approx(x) - z;
+      if (fabs(eps / z) < resid)
+	return x;
+      x = x - eps / approxD(x);
+    }
+      
+    return std::numeric_limits<double>::quiet_NaN();
+  }
+    
+  // Implement the required interface
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
+
+    GridBase *grid=in.Grid();
+
+    int vol=grid->gSites();
+    typedef typename Field::vector_type vector_type;
+
+    Field T0(grid); T0 = in;  
+    Field T1(grid); 
+    Field T2(grid);
+    Field y(grid);
+      
+    Field *Tnm = &T0;
+    Field *Tn  = &T1;
+    Field *Tnp = &T2;
+
+    // Tn=T1 = (xscale M + mscale)in
+    RealD xscale = 2.0/(hi-lo);
+    RealD mscale = -(hi+lo)/(hi-lo);
+    Linop.HermOp(T0,y);
+    axpby(T1,xscale,mscale,y,in);
+
+    // sum = .5 c[0] T0 + c[1] T1
+    //    out = ()*T0 + Coeffs[1]*T1;
+    axpby(out,0.5*Coeffs[0],Coeffs[1],T0,T1);
+    for(int n=2;n<order;n++){
+
+      Linop.HermOp(*Tn,y);
+#if 0
+      auto y_v = y.View();
+      auto Tn_v = Tn->View();
+      auto Tnp_v = Tnp->View();
+      auto Tnm_v = Tnm->View();
+      constexpr int Nsimd = vector_type::Nsimd();
+      accelerator_forNB(ss, in.Grid()->oSites(), Nsimd, {
+	  coalescedWrite(y_v[ss],xscale*y_v(ss)+mscale*Tn_v(ss));
+	  coalescedWrite(Tnp_v[ss],2.0*y_v(ss)-Tnm_v(ss));
+      });
+      if ( Coeffs[n] != 0.0) {
+	axpy(out,Coeffs[n],*Tnp,out);
+      }
+#else
+      axpby(y,xscale,mscale,y,(*Tn));
+      axpby(*Tnp,2.0,-1.0,y,(*Tnm));
+      if ( Coeffs[n] != 0.0) {
+	axpy(out,Coeffs[n],*Tnp,out);
+      }
+#endif
+      // Cycle pointers to avoid copies
+      Field *swizzle = Tnm;
+      Tnm    =Tn;
+      Tn     =Tnp;
+      Tnp    =swizzle;
+	  
+    }
+  }
+};
+
+
+template<class Field>
+class ChebyshevLanczos : public Chebyshev<Field> {
+private:
+  std::vector<RealD> Coeffs;
+  int order;
+  RealD alpha;
+  RealD beta;
+  RealD mu;
+
+public:
+  ChebyshevLanczos(RealD _alpha,RealD _beta,RealD _mu,int _order) :
+    alpha(_alpha),
+    beta(_beta),
+    mu(_mu)
+  {
+    order=_order;
+    Coeffs.resize(order);
+    for(int i=0;i<_order;i++){
+      Coeffs[i] = 0.0;
+    }
+    Coeffs[order-1]=1.0;
+  };
+
+  void csv(std::ostream &out){
+    for (RealD x=-1.2*alpha; x<1.2*alpha; x+=(2.0*alpha)/10000) {
+      RealD f = approx(x);
+      out<< x<<" "<<f<<std::endl;
+    }
+    return;
+  }
+
+  RealD approx(RealD xx) // Convenience for plotting the approximation
+  {
+    RealD Tn;
+    RealD Tnm;
+    RealD Tnp;
+    Real aa = alpha * alpha;
+    Real bb = beta  *  beta;
+      
+    RealD x = ( 2.0 * (xx-mu)*(xx-mu) - (aa+bb) ) / (aa-bb);
+
+    RealD y= x;
+      
+    RealD T0=1;
+    RealD T1=y;
+      
+    RealD sum;
+    sum = 0.5*Coeffs[0]*T0;
+    sum+= Coeffs[1]*T1;
+      
+    Tn =T1;
+    Tnm=T0;
+    for(int i=2;i<order;i++){
+      Tnp=2*y*Tn-Tnm;
+      Tnm=Tn;
+      Tn =Tnp;
+      sum+= Tn*Coeffs[i];
+    }
+    return sum;
+  };
+
+  // shift_Multiply in Rudy's code
+  void AminusMuSq(LinearOperatorBase<Field> &Linop, const Field &in, Field &out) 
+  {
+    GridBase *grid=in.Grid();
+    Field tmp(grid);
+
+    RealD aa= alpha*alpha;
+    RealD bb= beta * beta;
+
+    Linop.HermOp(in,out);
+    out = out - mu*in;
+
+    Linop.HermOp(out,tmp);
+    tmp = tmp - mu * out;
+
+    out = (2.0/ (aa-bb) ) * tmp -  ((aa+bb)/(aa-bb))*in;
+  };
+  // Implement the required interface
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
+
+    GridBase *grid=in.Grid();
+
+    int vol=grid->gSites();
+
+    Field T0(grid); T0 = in;  
+    Field T1(grid); 
+    Field T2(grid);
+    Field  y(grid);
+      
+    Field *Tnm = &T0;
+    Field *Tn  = &T1;
+    Field *Tnp = &T2;
+
+    // Tn=T1 = (xscale M )*in
+    AminusMuSq(Linop,T0,T1);
+
+    // sum = .5 c[0] T0 + c[1] T1
+    out = (0.5*Coeffs[0])*T0 + Coeffs[1]*T1;
+    for(int n=2;n<order;n++){
+	
+      AminusMuSq(Linop,*Tn,y);
+
+      *Tnp=2.0*y-(*Tnm);
+
+      out=out+Coeffs[n]* (*Tnp);
+
+      // Cycle pointers to avoid copies
+      Field *swizzle = Tnm;
+      Tnm    =Tn;
+      Tn     =Tnp;
+      Tnp    =swizzle;
+	  
+    }
+  }
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/approx/Forecast.h

@@ -0,0 +1,152 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithms/approx/Forecast.h
+
+Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+Author: David Murphy <dmurphy@phys.columbia.edu>
+
+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 INCLUDED_FORECAST_H
+#define INCLUDED_FORECAST_H
+
+NAMESPACE_BEGIN(Grid);
+
+// Abstract base class.
+// Takes a matrix (Mat), a source (phi), and a vector of Fields (chi)
+// and returns a forecasted solution to the system D*psi = phi (psi).
+template<class Matrix, class Field>
+class Forecast
+{
+public:
+  virtual Field operator()(Matrix &Mat, const Field& phi, const std::vector<Field>& chi) = 0;
+};
+
+// Implementation of Brower et al.'s chronological inverter (arXiv:hep-lat/9509012),
+// used to forecast solutions across poles of the EOFA heatbath.
+//
+// Modified from CPS (cps_pp/src/util/dirac_op/d_op_base/comsrc/minresext.C)
+template<class Matrix, class Field>
+class ChronoForecast : public Forecast<Matrix,Field>
+{
+public:
+  Field operator()(Matrix &Mat, const Field& phi, const std::vector<Field>& prev_solns)
+  {
+    int degree = prev_solns.size();
+    Field chi(phi); // forecasted solution
+
+    // Trivial cases
+    if(degree == 0){ chi = Zero(); return chi; }
+    else if(degree == 1){ return prev_solns[0]; }
+
+    //    RealD dot;
+    ComplexD xp;
+    Field r(phi); // residual
+    Field Mv(phi);
+    std::vector<Field> v(prev_solns); // orthonormalized previous solutions
+    std::vector<Field> MdagMv(degree,phi);
+
+    // Array to hold the matrix elements
+    std::vector<std::vector<ComplexD>> G(degree, std::vector<ComplexD>(degree));
+
+    // Solution and source vectors
+    std::vector<ComplexD> a(degree);
+    std::vector<ComplexD> b(degree);
+
+    // Orthonormalize the vector basis
+    for(int i=0; i<degree; i++){
+      v[i] *= 1.0/std::sqrt(norm2(v[i]));
+      for(int j=i+1; j<degree; j++){ v[j] -= innerProduct(v[i],v[j]) * v[i]; }
+    }
+
+    // Perform sparse matrix multiplication and construct rhs
+    for(int i=0; i<degree; i++){
+      b[i] = innerProduct(v[i],phi);
+      Mat.M(v[i],Mv);
+      Mat.Mdag(Mv,MdagMv[i]);
+      G[i][i] = innerProduct(v[i],MdagMv[i]);
+    }
+
+    // Construct the matrix
+    for(int j=0; j<degree; j++){
+      for(int k=j+1; k<degree; k++){
+	G[j][k] = innerProduct(v[j],MdagMv[k]);
+	G[k][j] = conjugate(G[j][k]);
+      }}
+
+    // Gauss-Jordan elimination with partial pivoting
+    for(int i=0; i<degree; i++){
+
+      // Perform partial pivoting
+      int k = i;
+      for(int j=i+1; j<degree; j++){ if(abs(G[j][j]) > abs(G[k][k])){ k = j; } }
+      if(k != i){
+	xp = b[k];
+	b[k] = b[i];
+	b[i] = xp;
+	for(int j=0; j<degree; j++){
+	  xp = G[k][j];
+	  G[k][j] = G[i][j];
+	  G[i][j] = xp;
+	}
+      }
+
+      // Convert matrix to upper triangular form
+      for(int j=i+1; j<degree; j++){
+	xp = G[j][i]/G[i][i];
+	b[j] -= xp * b[i];
+	for(int k=0; k<degree; k++){ G[j][k] -= xp*G[i][k]; }
+      }
+    }
+
+    // Use Gaussian elimination to solve equations and calculate initial guess
+    chi = Zero();
+    r = phi;
+    for(int i=degree-1; i>=0; i--){
+      a[i] = 0.0;
+      for(int j=i+1; j<degree; j++){ a[i] += G[i][j] * a[j]; }
+      a[i] = (b[i]-a[i])/G[i][i];
+      chi += a[i]*v[i];
+      r -= a[i]*MdagMv[i];
+    }
+
+    RealD true_r(0.0);
+    ComplexD tmp;
+    for(int i=0; i<degree; i++){
+      tmp = -b[i];
+      for(int j=0; j<degree; j++){ tmp += G[i][j]*a[j]; }
+      tmp = conjugate(tmp)*tmp;
+      true_r += std::sqrt(tmp.real());
+    }
+
+    RealD error = std::sqrt(norm2(r)/norm2(phi));
+    std::cout << GridLogMessage << "ChronoForecast: |res|/|src| = " << error << std::endl;
+
+    return chi;
+  };
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/algorithms/approx/JacobiPolynomial.h

@@ -0,0 +1,129 @@
+#ifndef GRID_JACOBIPOLYNOMIAL_H
+#define GRID_JACOBIPOLYNOMIAL_H
+
+#include <Grid/algorithms/LinearOperator.h>
+
+NAMESPACE_BEGIN(Grid);
+
+template<class Field>
+class JacobiPolynomial : public OperatorFunction<Field> {
+ private:
+  using OperatorFunction<Field>::operator();
+
+  int order;
+  RealD hi;
+  RealD lo;
+  RealD alpha;
+  RealD beta;
+
+ public:
+  void csv(std::ostream &out){
+    csv(out,lo,hi);
+  }
+  void csv(std::ostream &out,RealD llo,RealD hhi){
+    RealD diff = hhi-llo;
+    RealD delta = diff*1.0e-5;
+    for (RealD x=llo-delta; x<=hhi; x+=delta) {
+      RealD f = approx(x);
+      out<< x<<" "<<f <<std::endl;
+    }
+    return;
+  }
+
+  JacobiPolynomial(){};
+  JacobiPolynomial(RealD _lo,RealD _hi,int _order,RealD _alpha, RealD _beta)
+  {
+      lo=_lo;
+      hi=_hi;
+      alpha=_alpha;
+      beta=_beta;
+      order=_order;
+  };
+
+  RealD approx(RealD x) // Convenience for plotting the approximation                                                       
+  {
+    RealD Tn;
+    RealD Tnm;
+    RealD Tnp;
+
+    RealD y=( x-0.5*(hi+lo))/(0.5*(hi-lo));
+
+    RealD T0=1.0;
+    RealD T1=(alpha-beta)*0.5+(alpha+beta+2.0)*0.5*y;
+
+    Tn =T1;
+    Tnm=T0;
+    for(int n=2;n<=order;n++){
+      RealD cnp = 2.0*n*(n+alpha+beta)*(2.0*n-2.0+alpha+beta);
+      RealD cny = (2.0*n-2.0+alpha+beta)*(2.0*n-1.0+alpha+beta)*(2.0*n+alpha+beta);
+      RealD cn1 = (2.0*n+alpha+beta-1.0)*(alpha*alpha-beta*beta);
+      RealD cnm = - 2.0*(n+alpha-1.0)*(n+beta-1.0)*(2.0*n+alpha+beta);
+      Tnp= ( cny * y *Tn + cn1 * Tn + cnm * Tnm )/ cnp;
+      Tnm=Tn;
+      Tn =Tnp;
+    }
+    return Tnp;
+  };
+
+  // Implement the required interface                                                                                       
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
+    GridBase *grid=in.Grid();
+
+    int vol=grid->gSites();
+
+    Field T0(grid);
+    Field T1(grid);
+    Field T2(grid);
+    Field y(grid);
+
+
+    Field *Tnm = &T0;
+    Field *Tn  = &T1;
+    Field *Tnp = &T2;
+
+    //    RealD T0=1.0;                                                                                                     
+    T0=in;
+
+    //    RealD y=( x-0.5*(hi+lo))/(0.5*(hi-lo));                                                                           
+    //           = x * 2/(hi-lo) - (hi+lo)/(hi-lo)                                                                          
+    Linop.HermOp(T0,y);
+    RealD xscale = 2.0/(hi-lo);
+    RealD mscale = -(hi+lo)/(hi-lo);
+    Linop.HermOp(T0,y);
+    y=y*xscale+in*mscale;
+
+    // RealD T1=(alpha-beta)*0.5+(alpha+beta+2.0)*0.5*y;
+    RealD halfAmB  = (alpha-beta)*0.5;
+    RealD halfApBp2= (alpha+beta+2.0)*0.5;
+    T1 = halfAmB * in + halfApBp2*y;
+
+    for(int n=2;n<=order;n++){
+
+      Linop.HermOp(*Tn,y);
+      y=xscale*y+mscale*(*Tn);
+
+      RealD cnp = 2.0*n*(n+alpha+beta)*(2.0*n-2.0+alpha+beta);
+      RealD cny = (2.0*n-2.0+alpha+beta)*(2.0*n-1.0+alpha+beta)*(2.0*n+alpha+beta);
+      RealD cn1 = (2.0*n+alpha+beta-1.0)*(alpha*alpha-beta*beta);
+      RealD cnm = - 2.0*(n+alpha-1.0)*(n+beta-1.0)*(2.0*n+alpha+beta);
+
+      //      Tnp= ( cny * y *Tn + cn1 * Tn + cnm * Tnm )/ cnp;                                                             
+      cny=cny/cnp;
+      cn1=cn1/cnp;
+      cn1=cn1/cnp;
+      cnm=cnm/cnp;
+
+      *Tnp=cny*y + cn1 *(*Tn) + cnm * (*Tnm);
+
+      // Cycle pointers to avoid copies                                                                                     
+      Field *swizzle = Tnm;
+      Tnm    =Tn;
+      Tn     =Tnp;
+      Tnp    =swizzle;
+    }
+    out=*Tnp;
+
+  }
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/approx/MultiShiftFunction.cc

@@ -27,7 +27,8 @@ Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
     /*  END LEGAL */
 #include <Grid/GridCore.h>
 
-namespace Grid {
+NAMESPACE_BEGIN(Grid);
+
 double MultiShiftFunction::approx(double x)
 {
   double a = norm;
@@ -53,4 +54,4 @@ void MultiShiftFunction::csv(std::ostream &out)
   }
   return;
 }
-}
+NAMESPACE_END(Grid);

Grid/algorithms/approx/MultiShiftFunction.h

@@ -29,7 +29,7 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 #ifndef MULTI_SHIFT_FUNCTION
 #define MULTI_SHIFT_FUNCTION
 
-namespace Grid {
+NAMESPACE_BEGIN(Grid);
 
 class MultiShiftFunction {
 public:
@@ -63,5 +63,5 @@ public:
   }
 
 };
-}
+NAMESPACE_END(Grid);
 #endif

Grid/algorithms/approx/Remez.cc

@@ -298,7 +298,7 @@ void AlgRemez::stpini(bigfloat *step) {
 // Search for error maxima and minima
 void AlgRemez::search(bigfloat *step) {
   bigfloat a, q, xm, ym, xn, yn, xx0, xx1;
-  int i, j, meq, emsign, ensign, steps;
+  int i, meq, emsign, ensign, steps;
 
   meq = neq + 1;
   bigfloat *yy = new bigfloat[meq];
@@ -306,7 +306,6 @@ void AlgRemez::search(bigfloat *step) {
   bigfloat eclose = 1.0e30;
   bigfloat farther = 0l;
 
-  j = 1;
   xx0 = apstrt;
 
   for (i = 0; i < meq; i++) {

Grid/algorithms/approx/RemezGeneral.cc

@@ -0,0 +1,473 @@
+#include<math.h>
+#include<stdio.h>
+#include<stdlib.h>
+#include<string>
+#include<iostream>
+#include<iomanip>
+#include<cassert>
+
+#include<Grid/algorithms/approx/RemezGeneral.h>
+
+
+// Constructor
+AlgRemezGeneral::AlgRemezGeneral(double lower, double upper, long precision,
+				 bigfloat (*f)(bigfloat x, void *data), void *data): f(f), 
+										     data(data), 
+										     prec(precision),
+										     apstrt(lower), apend(upper), apwidt(upper - lower),
+										     n(0), d(0), pow_n(0), pow_d(0)
+{
+  bigfloat::setDefaultPrecision(prec);
+
+  std::cout<<"Approximation bounds are ["<<apstrt<<","<<apend<<"]\n";
+  std::cout<<"Precision of arithmetic is "<<precision<<std::endl;
+}
+
+//Determine the properties of the numerator and denominator polynomials
+void AlgRemezGeneral::setupPolyProperties(int num_degree, int den_degree, PolyType num_type_in, PolyType den_type_in){
+  pow_n = num_degree;
+  pow_d = den_degree;
+
+  if(pow_n % 2 == 0 && num_type_in == PolyType::Odd) assert(0);
+  if(pow_n % 2 == 1 && num_type_in == PolyType::Even) assert(0);
+
+  if(pow_d % 2 == 0 && den_type_in == PolyType::Odd) assert(0);
+  if(pow_d % 2 == 1 && den_type_in == PolyType::Even) assert(0);
+
+  num_type = num_type_in;
+  den_type = den_type_in;
+
+  num_pows.resize(pow_n+1);
+  den_pows.resize(pow_d+1);
+
+  int n_in = 0;
+  bool odd = num_type == PolyType::Full || num_type == PolyType::Odd;
+  bool even = num_type == PolyType::Full || num_type == PolyType::Even;
+  for(int i=0;i<=pow_n;i++){
+    num_pows[i] = -1;
+    if(i % 2 == 0 && even) num_pows[i] = n_in++;
+    if(i % 2 == 1 && odd) num_pows[i] = n_in++;
+  }
+
+  std::cout << n_in << " terms in numerator" << std::endl;
+  --n_in; //power is 1 less than the number of terms, eg  pow=1   a x^1  + b x^0
+
+  int d_in = 0;
+  odd = den_type == PolyType::Full || den_type == PolyType::Odd;
+  even = den_type == PolyType::Full || den_type == PolyType::Even;
+  for(int i=0;i<=pow_d;i++){
+    den_pows[i] = -1;
+    if(i % 2 == 0 && even) den_pows[i] = d_in++;
+    if(i % 2 == 1 && odd) den_pows[i] = d_in++;
+  }
+
+  std::cout << d_in << " terms in denominator" << std::endl;
+  --d_in;
+
+  n = n_in;
+  d = d_in;
+}
+
+//Setup algorithm
+void AlgRemezGeneral::reinitializeAlgorithm(){
+  spread = 1.0e37;
+  iter = 0;
+
+  neq = n + d + 1; //not +2 because highest-power term in denominator is fixed to 1
+
+  param.resize(neq);
+  yy.resize(neq+1);
+
+  //Initialize linear equation temporaries
+  A.resize(neq*neq);
+  B.resize(neq);
+  IPS.resize(neq);
+
+  //Initialize maximum and minimum errors
+  xx.resize(neq+2);
+  mm.resize(neq+1);
+  initialGuess();
+
+  //Initialize search steps
+  step.resize(neq+1);
+  stpini();
+}
+
+double AlgRemezGeneral::generateApprox(const int num_degree, const int den_degree, 
+				       const PolyType num_type_in, const PolyType den_type_in, 
+				       const double _tolerance, const int report_freq){
+  //Setup the properties of the polynomial
+  setupPolyProperties(num_degree, den_degree, num_type_in, den_type_in);
+
+  //Setup the algorithm
+  reinitializeAlgorithm();
+
+  bigfloat tolerance = _tolerance;
+
+  //Iterate until convergance
+  while (spread > tolerance) { 
+    if (iter++ % report_freq==0)
+      std::cout<<"Iteration " <<iter-1<<" spread "<<(double)spread<<" delta "<<(double)delta << std::endl; 
+
+    equations();
+    if (delta < tolerance) {
+      std::cout<<"Iteration " << iter-1 << " delta too small (" << delta << "<" << tolerance << "), try increasing precision\n";
+      assert(0);
+    };    
+    assert( delta>= tolerance );
+
+    search();
+  }
+
+  int sign;
+  double error = (double)getErr(mm[0],&sign);
+  std::cout<<"Converged at "<<iter<<" iterations; error = "<<error<<std::endl;
+
+  // Return the maximum error in the approximation
+  return error;
+}
+
+
+// Initial values of maximal and minimal errors
+void AlgRemezGeneral::initialGuess(){
+  // Supply initial guesses for solution points
+  long ncheb = neq;			// Degree of Chebyshev error estimate
+
+  // Find ncheb+1 extrema of Chebyshev polynomial
+  bigfloat a = ncheb;
+  bigfloat r;
+
+  mm[0] = apstrt;
+  for (long i = 1; i < ncheb; i++) {
+    r = 0.5 * (1 - cos((M_PI * i)/(double) a));
+    //r *= sqrt_bf(r);
+    r = (exp((double)r)-1.0)/(exp(1.0)-1.0);
+    mm[i] = apstrt + r * apwidt;
+  }
+  mm[ncheb] = apend;
+
+  a = 2.0 * ncheb;
+  for (long i = 0; i <= ncheb; i++) {
+    r = 0.5 * (1 - cos(M_PI * (2*i+1)/(double) a));
+    //r *= sqrt_bf(r); // Squeeze to low end of interval
+    r = (exp((double)r)-1.0)/(exp(1.0)-1.0);
+    xx[i] = apstrt + r * apwidt;
+  }
+}
+
+// Initialise step sizes
+void AlgRemezGeneral::stpini(){
+  xx[neq+1] = apend;
+  delta = 0.25;
+  step[0] = xx[0] - apstrt;
+  for (int i = 1; i < neq; i++) step[i] = xx[i] - xx[i-1];
+  step[neq] = step[neq-1];
+}
+
+// Search for error maxima and minima
+void AlgRemezGeneral::search(){
+  bigfloat a, q, xm, ym, xn, yn, xx1;
+  int emsign, ensign, steps;
+
+  int meq = neq + 1;
+
+  bigfloat eclose = 1.0e30;
+  bigfloat farther = 0l;
+
+  bigfloat xx0 = apstrt;
+
+  for (int i = 0; i < meq; i++) {
+    steps = 0;
+    xx1 = xx[i]; // Next zero
+    if (i == meq-1) xx1 = apend;
+    xm = mm[i];
+    ym = getErr(xm,&emsign);
+    q = step[i];
+    xn = xm + q;
+    if (xn < xx0 || xn >= xx1) {	// Cannot skip over adjacent boundaries
+      q = -q;
+      xn = xm;
+      yn = ym;
+      ensign = emsign;
+    } else {
+      yn = getErr(xn,&ensign);
+      if (yn < ym) {
+	q = -q;
+	xn = xm;
+	yn = ym;
+	ensign = emsign;
+      }
+    }
+  
+    while(yn >= ym) {		// March until error becomes smaller.
+      if (++steps > 10)
+      	break;
+      
+      ym = yn;
+      xm = xn;
+      emsign = ensign;
+      a = xm + q;
+      if (a == xm || a <= xx0 || a >= xx1)
+	break;// Must not skip over the zeros either side.      
+
+      xn = a;
+      yn = getErr(xn,&ensign);
+    }
+
+    mm[i] = xm;			// Position of maximum
+    yy[i] = ym;			// Value of maximum
+
+    if (eclose > ym) eclose = ym;
+    if (farther < ym) farther = ym;
+
+    xx0 = xx1; // Walk to next zero.
+  } // end of search loop
+
+  q = (farther - eclose);	// Decrease step size if error spread increased
+
+  if (eclose != 0.0) q /= eclose; // Relative error spread
+
+  if (q >= spread)
+    delta *= 0.5; // Spread is increasing; decrease step size
+  
+  spread = q;
+
+  for (int i = 0; i < neq; i++) {
+    q = yy[i+1];
+    if (q != 0.0) q = yy[i] / q  - (bigfloat)1l;
+    else q = 0.0625;
+    if (q > (bigfloat)0.25) q = 0.25;
+    q *= mm[i+1] - mm[i];
+    step[i] = q * delta;
+  }
+  step[neq] = step[neq-1];
+  
+  for (int i = 0; i < neq; i++) {	// Insert new locations for the zeros.
+    xm = xx[i] - step[i];
+
+    if (xm <= apstrt)
+      continue;
+
+    if (xm >= apend)
+      continue;
+
+    if (xm <= mm[i])
+      xm = (bigfloat)0.5 * (mm[i] + xx[i]);    
+
+    if (xm >= mm[i+1])
+      xm = (bigfloat)0.5 * (mm[i+1] + xx[i]);
+    
+    xx[i] = xm;
+  }
+}
+
+// Solve the equations
+void AlgRemezGeneral::equations(){
+  bigfloat x, y, z;
+  bigfloat *aa;
+  
+  for (int i = 0; i < neq; i++) {	// set up the equations for solution by simq()
+    int ip = neq * i;		// offset to 1st element of this row of matrix
+    x = xx[i];			// the guess for this row
+    y = func(x);		// right-hand-side vector
+
+    z = (bigfloat)1l;
+    aa = A.data()+ip;
+    int t = 0;
+    for (int j = 0; j <= pow_n; j++) {
+      if(num_pows[j] != -1){ *aa++ = z; t++; }
+      z *= x;
+    }
+    assert(t == n+1);
+
+    z = (bigfloat)1l;
+    t = 0;
+    for (int j = 0; j < pow_d; j++) {
+      if(den_pows[j] != -1){ *aa++ = -y * z; t++; }
+      z *= x;
+    }
+    assert(t == d);
+
+    B[i] = y * z;		// Right hand side vector
+  }
+
+  // Solve the simultaneous linear equations.
+  if (simq()){
+    std::cout<<"simq failed\n";
+    exit(0);
+  }
+}
+
+
+// Evaluate the rational form P(x)/Q(x) using coefficients
+// from the solution vector param
+bigfloat AlgRemezGeneral::approx(const bigfloat x) const{
+  // Work backwards toward the constant term.
+  int c = n;
+  bigfloat yn = param[c--];		// Highest order numerator coefficient
+  for (int i = pow_n-1; i >= 0; i--) yn = x * yn  +  (num_pows[i] != -1 ? param[c--] : bigfloat(0l));  
+
+  c = n+d;
+  bigfloat yd = 1l; //Highest degree coefficient is 1.0
+  for (int i = pow_d-1; i >= 0; i--) yd = x * yd  +  (den_pows[i] != -1 ? param[c--] : bigfloat(0l)); 
+
+  return(yn/yd);
+}
+
+// Compute size and sign of the approximation error at x
+bigfloat AlgRemezGeneral::getErr(bigfloat x, int *sign) const{
+  bigfloat f = func(x);
+  bigfloat e = approx(x) - f;
+  if (f != 0) e /= f;
+  if (e < (bigfloat)0.0) {
+    *sign = -1;
+    e = -e;
+  }
+  else *sign = 1;
+  
+  return(e);
+}
+
+// Solve the system AX=B
+int AlgRemezGeneral::simq(){
+
+  int ip, ipj, ipk, ipn;
+  int idxpiv;
+  int kp, kp1, kpk, kpn;
+  int nip, nkp;
+  bigfloat em, q, rownrm, big, size, pivot, sum;
+  bigfloat *aa;
+  bigfloat *X = param.data();
+
+  int n = neq;
+  int nm1 = n - 1;
+  // Initialize IPS and X
+  
+  int ij = 0;
+  for (int i = 0; i < n; i++) {
+    IPS[i] = i;
+    rownrm = 0.0;
+    for(int j = 0; j < n; j++) {
+      q = abs_bf(A[ij]);
+      if(rownrm < q) rownrm = q;
+      ++ij;
+    }
+    if (rownrm == (bigfloat)0l) {
+      std::cout<<"simq rownrm=0\n";
+      return(1);
+    }
+    X[i] = (bigfloat)1.0 / rownrm;
+  }
+  
+  for (int k = 0; k < nm1; k++) {
+    big = 0.0;
+    idxpiv = 0;
+    
+    for (int i = k; i < n; i++) {
+      ip = IPS[i];
+      ipk = n*ip + k;
+      size = abs_bf(A[ipk]) * X[ip];
+      if (size > big) {
+	big = size;
+	idxpiv = i;
+      }
+    }
+    
+    if (big == (bigfloat)0l) {
+      std::cout<<"simq big=0\n";
+      return(2);
+    }
+    if (idxpiv != k) {
+      int j = IPS[k];
+      IPS[k] = IPS[idxpiv];
+      IPS[idxpiv] = j;
+    }
+    kp = IPS[k];
+    kpk = n*kp + k;
+    pivot = A[kpk];
+    kp1 = k+1;
+    for (int i = kp1; i < n; i++) {
+      ip = IPS[i];
+      ipk = n*ip + k;
+      em = -A[ipk] / pivot;
+      A[ipk] = -em;
+      nip = n*ip;
+      nkp = n*kp;
+      aa = A.data()+nkp+kp1;
+      for (int j = kp1; j < n; j++) {
+	ipj = nip + j;
+	A[ipj] = A[ipj] + em * *aa++;
+      }
+    }
+  }
+  kpn = n * IPS[n-1] + n - 1;	// last element of IPS[n] th row
+  if (A[kpn] == (bigfloat)0l) {
+    std::cout<<"simq A[kpn]=0\n";
+    return(3);
+  }
+
+  
+  ip = IPS[0];
+  X[0] = B[ip];
+  for (int i = 1; i < n; i++) {
+    ip = IPS[i];
+    ipj = n * ip;
+    sum = 0.0;
+    for (int j = 0; j < i; j++) {
+      sum += A[ipj] * X[j];
+      ++ipj;
+    }
+    X[i] = B[ip] - sum;
+  }
+  
+  ipn = n * IPS[n-1] + n - 1;
+  X[n-1] = X[n-1] / A[ipn];
+  
+  for (int iback = 1; iback < n; iback++) {
+    //i goes (n-1),...,1
+    int i = nm1 - iback;
+    ip = IPS[i];
+    nip = n*ip;
+    sum = 0.0;
+    aa = A.data()+nip+i+1;
+    for (int j= i + 1; j < n; j++) 
+      sum += *aa++ * X[j];
+    X[i] = (X[i] - sum) / A[nip+i];
+  }
+  
+  return(0);
+}
+
+void AlgRemezGeneral::csv(std::ostream & os) const{
+  os << "Numerator" << std::endl;
+  for(int i=0;i<=pow_n;i++){
+    os << getCoeffNum(i) << "*x^" << i;
+    if(i!=pow_n) os << " + ";
+  }
+  os << std::endl;
+
+  os << "Denominator" << std::endl;
+  for(int i=0;i<=pow_d;i++){
+    os << getCoeffDen(i) << "*x^" << i;
+    if(i!=pow_d) os << " + ";
+  }
+  os << std::endl;
+
+  //For a true minimax solution the errors should all be equal and the signs should oscillate +-+-+- etc
+  int sign;
+  os << "Errors at maxima: coordinate, error, (sign)" << std::endl;
+  for(int i=0;i<neq+1;i++){ 
+    os << mm[i] << " " << getErr(mm[i],&sign) << " (" << sign << ")" << std::endl;
+  }
+
+  os << "Scan over range:" << std::endl;
+  int npt = 60;
+  bigfloat dlt = (apend - apstrt)/bigfloat(npt-1);
+
+  for (bigfloat x=apstrt; x<=apend; x = x + dlt) {
+    double f = evaluateFunc(x);
+    double r = evaluateApprox(x);
+    os<< x<<","<<r<<","<<f<<","<<r-f<<std::endl;
+  }
+  return;
+}

Grid/algorithms/approx/RemezGeneral.h

@@ -0,0 +1,170 @@
+/*
+  C.Kelly Jan 2020 based on implementation by M. Clark May 2005
+
+  AlgRemezGeneral is an implementation of the Remez algorithm for approximating an arbitrary function by a rational polynomial 
+  It includes optional restriction to odd/even polynomials for the numerator and/or denominator
+*/
+
+#ifndef INCLUDED_ALG_REMEZ_GENERAL_H
+#define INCLUDED_ALG_REMEZ_GENERAL_H
+
+#include <stddef.h>
+#include <Grid/GridStd.h>
+
+#ifdef HAVE_LIBGMP
+#include "bigfloat.h"
+#else
+#include "bigfloat_double.h"
+#endif
+
+
+class AlgRemezGeneral{
+ public:
+  enum PolyType { Even, Odd, Full };
+
+ private:
+
+  // In GSL-style, pass the function as a function pointer. Any data required to evaluate the function is passed in as a void pointer
+  bigfloat (*f)(bigfloat x, void *data);
+  void *data;
+
+  // The approximation parameters
+  std::vector<bigfloat> param;
+  bigfloat norm;
+
+  // The number of non-zero terms in the numerator and denominator
+  int n, d;
+  // The numerator and denominator degree (i.e.  the largest power)
+  int pow_n, pow_d;
+  
+  // Specify if the numerator and/or denominator are odd/even polynomials
+  PolyType num_type;
+  PolyType den_type;
+  std::vector<int> num_pows; //contains the mapping, with -1 if not present
+  std::vector<int> den_pows;
+
+  // The bounds of the approximation
+  bigfloat apstrt, apwidt, apend;
+
+  // Variables used to calculate the approximation
+  int nd1, iter;
+  std::vector<bigfloat> xx;
+  std::vector<bigfloat> mm;
+  std::vector<bigfloat> step;
+
+  bigfloat delta, spread;
+  
+  // Variables used in search
+  std::vector<bigfloat> yy;
+
+  // Variables used in solving linear equations
+  std::vector<bigfloat> A;
+  std::vector<bigfloat> B;
+  std::vector<int> IPS;
+
+  // The number of equations we must solve at each iteration (n+d+1)
+  int neq;
+
+  // The precision of the GNU MP library
+  long prec;
+
+  // Initialize member variables associated with the polynomial's properties
+  void setupPolyProperties(int num_degree, int den_degree, PolyType num_type_in, PolyType den_type_in);
+
+  // Initial values of maximal and minmal errors
+  void initialGuess();
+
+  // Initialise step sizes
+  void stpini();
+
+  // Initialize the algorithm
+  void reinitializeAlgorithm();
+
+  // Solve the equations
+  void equations();
+
+  // Search for error maxima and minima
+  void search(); 
+
+  // Calculate function required for the approximation
+  inline bigfloat func(bigfloat x) const{
+    return f(x, data);
+  }
+
+  // Compute size and sign of the approximation error at x
+  bigfloat getErr(bigfloat x, int *sign) const;
+
+  // Solve the system AX=B   where X = param
+  int simq();
+
+  // Evaluate the rational form P(x)/Q(x) using coefficients from the solution vector param
+  bigfloat approx(bigfloat x) const;
+
+ public:
+  
+  AlgRemezGeneral(double lower, double upper, long prec,
+		  bigfloat (*f)(bigfloat x, void *data), void *data);
+
+  inline int getDegree(void) const{ 
+    assert(n==d);
+    return n;
+  }
+  // Reset the bounds of the approximation
+  inline void setBounds(double lower, double upper) {
+    apstrt = lower;
+    apend = upper;
+    apwidt = apend - apstrt;
+  }
+
+  // Get the bounds of the approximation
+  inline void getBounds(double &lower, double &upper) const{ 
+    lower=(double)apstrt;
+    upper=(double)apend;
+  }
+
+  // Run the algorithm to generate the rational approximation
+  double generateApprox(int num_degree, int den_degree, 
+			PolyType num_type, PolyType den_type,
+			const double tolerance = 1e-15, const int report_freq = 1000);
+  
+  inline double generateApprox(int num_degree, int den_degree, 
+			       const double tolerance = 1e-15, const int report_freq = 1000){
+    return generateApprox(num_degree, den_degree, Full, Full, tolerance, report_freq);
+  }
+  
+  // Evaluate the rational form P(x)/Q(x) using coefficients from the
+  // solution vector param
+  inline double evaluateApprox(double x) const{
+    return (double)approx((bigfloat)x);
+  }
+
+  // Evaluate the rational form Q(x)/P(x) using coefficients from the solution vector param
+  inline double evaluateInverseApprox(double x) const{
+    return 1.0/(double)approx((bigfloat)x);
+  }  
+
+  // Calculate function required for the approximation
+  inline double evaluateFunc(double x) const{
+    return (double)func((bigfloat)x);
+  }
+
+  // Calculate inverse function required for the approximation
+  inline double evaluateInverseFunc(double x) const{
+    return 1.0/(double)func((bigfloat)x);
+  }
+
+  // Dump csv of function, approx and error
+  void csv(std::ostream &os = std::cout) const;
+
+  // Get the coefficient of the term x^i in the numerator
+  inline double getCoeffNum(const int i) const{    
+    return num_pows[i] == -1 ? 0. : double(param[num_pows[i]]);
+  }
+  // Get the coefficient of the term x^i in the denominator
+  inline double getCoeffDen(const int i) const{ 
+    if(i == pow_d) return 1.0;
+    else return den_pows[i] == -1 ? 0. : double(param[den_pows[i]+n+1]); 
+  }
+};
+
+#endif

Grid/algorithms/approx/ZMobius.cc

@@ -0,0 +1,183 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/approx/ZMobius.cc
+
+    Copyright (C) 2015
+
+Author: Christopher Kelly <ckelly@phys.columbia.edu>
+
+    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/algorithms/approx/ZMobius.h>
+#include <Grid/algorithms/approx/RemezGeneral.h>
+
+NAMESPACE_BEGIN(Grid);
+NAMESPACE_BEGIN(Approx);
+
+//Compute the tanh approximation
+inline double epsilonMobius(const double x, const std::vector<ComplexD> &w){
+  int Ls = w.size();
+
+  ComplexD fxp = 1., fmp = 1.;
+  for(int i=0;i<Ls;i++){
+    fxp = fxp * ( w[i] + x );
+    fmp = fmp * ( w[i] - x );
+  }
+  return ((fxp - fmp)/(fxp + fmp)).real();
+}
+inline double epsilonMobius(const double x, const std::vector<RealD> &w){
+  int Ls = w.size();
+
+  double fxp = 1., fmp = 1.;
+  for(int i=0;i<Ls;i++){
+    fxp = fxp * ( w[i] + x );
+    fmp = fmp * ( w[i] - x );
+  }
+  return (fxp - fmp)/(fxp + fmp);
+}
+
+
+
+//Compute the tanh approximation in a form suitable for the Remez
+bigfloat epsilonMobius(bigfloat x, void* data){
+  const std::vector<RealD> &omega = *( (std::vector<RealD> const*)data );
+  bigfloat fxp(1.0);
+  bigfloat fmp(1.0);
+
+  for(int i=0;i<omega.size();i++){
+    fxp = fxp * ( bigfloat(omega[i]) + x);
+    fmp = fmp * ( bigfloat(omega[i]) - x);
+  }
+  return (fxp - fmp)/(fxp + fmp);
+}
+
+//Compute the Zmobius Omega parameters suitable for eigenvalue range   -lambda_bound <= lambda <= lambda_bound
+//Note omega_i = 1/(b_i + c_i)   where b_i and c_i are the Mobius parameters
+void computeZmobiusOmega(std::vector<ComplexD> &omega_out, const int Ls_out,
+			 const std::vector<RealD> &omega_in, const int Ls_in,
+			 const RealD lambda_bound){
+  assert(omega_in.size() == Ls_in);
+  omega_out.resize(Ls_out);
+
+  //Use the Remez algorithm to generate the appropriate rational polynomial
+  //For odd polynomial, to satisfy Haar condition must take either positive or negative half of range (cf https://arxiv.org/pdf/0803.0439.pdf page 6)  
+  AlgRemezGeneral remez(0, lambda_bound, 64, &epsilonMobius, (void*)&omega_in); 
+  remez.generateApprox(Ls_out-1, Ls_out,AlgRemezGeneral::Odd, AlgRemezGeneral::Even, 1e-15, 100);
+  remez.csv(std::cout);
+
+  //The rational approximation has the form  [ f(x) - f(-x) ] / [ f(x) + f(-x) ]  where  f(x) = \Prod_{i=0}^{L_s-1} ( \omega_i + x )
+  //cf https://academiccommons.columbia.edu/doi/10.7916/D8T72HD7  pg 102
+  //omega_i are therefore the negative of the complex roots of f(x)
+
+  //We can find the roots by recognizing that the eigenvalues of a matrix A are the roots of the characteristic polynomial
+  // \rho(\lambda) = det( A - \lambda I )    where I is the unit matrix
+  //The matrix whose characteristic polynomial is an arbitrary monic polynomial a0 + a1 x + a2 x^2 + ... x^n   is the companion matrix 
+  // A = | 0    1   0    0 0 .... 0 |
+  //     | 0    0   1    0 0 .... 0 |
+  //     | :    :   :    : :      : |
+  //     | 0    0   0    0 0      1
+  //     | -a0 -a1 -a2  ...  ... -an|
+
+
+  //Note the Remez defines the largest power to have unit coefficient
+  std::vector<RealD> coeffs(Ls_out+1);
+  for(int i=0;i<Ls_out+1;i+=2) coeffs[i] = coeffs[i] = remez.getCoeffDen(i); //even powers
+  for(int i=1;i<Ls_out+1;i+=2) coeffs[i] = coeffs[i] = remez.getCoeffNum(i); //odd powers
+
+  std::vector<std::complex<RealD> > roots(Ls_out);
+
+  //Form the companion matrix
+  Eigen::MatrixXd compn(Ls_out,Ls_out);
+  for(int i=0;i<Ls_out-1;i++) compn(i,0) = 0.;
+  compn(Ls_out - 1, 0) = -coeffs[0];
+  
+  for(int j=1;j<Ls_out;j++){
+    for(int i=0;i<Ls_out-1;i++) compn(i,j) = i == j-1 ? 1. : 0.;
+    compn(Ls_out - 1, j) = -coeffs[j];
+  }
+
+  //Eigensolve
+  Eigen::EigenSolver<Eigen::MatrixXd> slv(compn, false);
+
+  const auto & ev = slv.eigenvalues();
+  for(int i=0;i<Ls_out;i++)
+    omega_out[i] = -ev(i);
+
+  //Sort ascending (smallest at start of vector!)
+  std::sort(omega_out.begin(), omega_out.end(), 
+	    [&](const ComplexD &a, const ComplexD &b){ return a.real() < b.real() || (a.real() == b.real() && a.imag() < b.imag()); });
+
+  //McGlynn thesis pg 122 suggest improved iteration counts if magnitude of omega diminishes towards the center of the 5th dimension
+  std::vector<ComplexD> omega_tmp = omega_out;
+  int s_low=0, s_high=Ls_out-1, ss=0;
+  for(int s_from = Ls_out-1; s_from >= 0; s_from--){ //loop from largest omega
+    int s_to;
+    if(ss % 2 == 0){
+      s_to = s_low++;
+    }else{
+      s_to = s_high--;
+    }
+    omega_out[s_to] = omega_tmp[s_from];
+    ++ss;
+  }
+  
+  std::cout << "Resulting omega_i:" << std::endl;  
+  for(int i=0;i<Ls_out;i++)
+    std::cout << omega_out[i] << std::endl;
+
+  std::cout << "Test result matches the approximate polynomial found by the Remez" << std::endl;
+  std::cout << "<x> <remez approx> <poly approx> <diff poly approx remez approx> <exact> <diff poly approx exact>\n";
+  
+  int npt = 60;
+  double dlt = lambda_bound/double(npt-1);
+
+  for (int i =0; i<npt; i++){
+    double x = i*dlt;
+    double r = remez.evaluateApprox(x);
+    double p = epsilonMobius(x, omega_out);
+    double e = epsilonMobius(x, omega_in);
+
+    std::cout << x<< " " << r << " " << p <<" " <<r-p << " " << e << " " << e-p << std::endl;
+  }
+
+}
+  
+//mobius_param = b+c   with b-c=1
+void computeZmobiusOmega(std::vector<ComplexD> &omega_out, const int Ls_out, const RealD mobius_param, const int Ls_in, const RealD lambda_bound){
+  std::vector<RealD> omega_in(Ls_in, 1./mobius_param);
+  computeZmobiusOmega(omega_out, Ls_out, omega_in, Ls_in, lambda_bound);
+}
+
+//ZMobius class takes  gamma_i = (b+c) omega_i as its input, where b, c are factored out
+void computeZmobiusGamma(std::vector<ComplexD> &gamma_out, 
+			 const RealD mobius_param_out, const int Ls_out, 
+			 const RealD mobius_param_in, const int Ls_in,
+			 const RealD lambda_bound){
+  computeZmobiusOmega(gamma_out, Ls_out, mobius_param_in, Ls_in, lambda_bound);
+  for(int i=0;i<Ls_out;i++) gamma_out[i] = gamma_out[i] * mobius_param_out;
+}
+//Assumes mobius_param_out == mobius_param_in
+void computeZmobiusGamma(std::vector<ComplexD> &gamma_out, const int Ls_out, const RealD mobius_param, const int Ls_in, const RealD lambda_bound){
+  computeZmobiusGamma(gamma_out, mobius_param, Ls_out, mobius_param, Ls_in, lambda_bound);
+}
+
+NAMESPACE_END(Approx);
+NAMESPACE_END(Grid);

Grid/algorithms/approx/ZMobius.h

@@ -0,0 +1,57 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/approx/ZMobius.h
+
+    Copyright (C) 2015
+
+Author: Christopher Kelly <ckelly@phys.columbia.edu>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_ZMOBIUS_APPROX_H
+#define GRID_ZMOBIUS_APPROX_H
+
+#include <Grid/GridCore.h>
+
+NAMESPACE_BEGIN(Grid);
+NAMESPACE_BEGIN(Approx);
+
+//Compute the Zmobius Omega parameters suitable for eigenvalue range   -lambda_bound <= lambda <= lambda_bound
+//Note omega_i = 1/(b_i + c_i)   where b_i and c_i are the Mobius parameters
+void computeZmobiusOmega(std::vector<ComplexD> &omega_out, const int Ls_out,
+			 const std::vector<RealD> &omega_in, const int Ls_in,
+			 const RealD lambda_bound);
+  
+//mobius_param = b+c   with b-c=1
+void computeZmobiusOmega(std::vector<ComplexD> &omega_out, const int Ls_out, const RealD mobius_param, const int Ls_in, const RealD lambda_bound);
+
+//ZMobius class takes  gamma_i = (b+c) omega_i as its input, where b, c are factored out
+void computeZmobiusGamma(std::vector<ComplexD> &gamma_out, 
+			 const RealD mobius_param_out, const int Ls_out, 
+			 const RealD mobius_param_in, const int Ls_in,
+			 const RealD lambda_bound);
+
+//Assumes mobius_param_out == mobius_param_in
+void computeZmobiusGamma(std::vector<ComplexD> &gamma_out, const int Ls_out, const RealD mobius_param, const int Ls_in, const RealD lambda_bound);
+
+NAMESPACE_END(Approx);
+NAMESPACE_END(Grid);
+
+#endif

Grid/algorithms/approx/Zolotarev.cc

@@ -58,8 +58,8 @@
 
 /* Compute the partial fraction expansion coefficients (alpha) from the
  * factored form */
-namespace Grid {
-namespace Approx {
+NAMESPACE_BEGIN(Grid);
+NAMESPACE_BEGIN(Approx);
 
 static void construct_partfrac(izd *z) {
   int dn = z -> dn, dd = z -> dd, type = z -> type;
@@ -516,7 +516,9 @@ zolotarev_data* higham(PRECISION epsilon, int n) {
   free(d);
   return zd;
 }
-}}
+
+NAMESPACE_END(Approx);
+NAMESPACE_END(Grid);
 
 #ifdef TEST
 
@@ -585,6 +587,7 @@ static PRECISION zolotarev_cayley_eval(PRECISION x, zolotarev_data* rdata) {
   return (ONE - T) / (ONE + T);
 }
 
+
 /* Test program. Apart from printing out the parameters for R(x) it produces
  * the following data files for plotting (unless NPLOT is defined):
  *
@@ -723,5 +726,5 @@ int main(int argc, char** argv) {
   return EXIT_SUCCESS;
 }
 
-
 #endif /* TEST */
+

Grid/algorithms/approx/Zolotarev.h

@@ -1,13 +1,13 @@
 /* -*- Mode: C; comment-column: 22; fill-column: 79; -*- */
 
 #ifdef __cplusplus
-namespace Grid {
-namespace Approx {
+#include <Grid/Namespace.h>
+NAMESPACE_BEGIN(Grid);
+NAMESPACE_BEGIN(Approx);
 #endif
 
 #define HVERSION Header Time-stamp: <14-OCT-2004 09:26:51.00 adk@MISSCONTRARY>
 
-
 #ifndef ZOLOTAREV_INTERNAL
 #ifndef PRECISION
 #define PRECISION double
@@ -83,5 +83,6 @@ void zolotarev_free(zolotarev_data *zdata);
 #endif
 
 #ifdef __cplusplus
-}}
+NAMESPACE_END(Approx);
+NAMESPACE_END(Grid);
 #endif

Grid/algorithms/approx/bigfloat.h

@@ -10,10 +10,12 @@
 #ifndef INCLUDED_BIGFLOAT_H
 #define INCLUDED_BIGFLOAT_H
 
-
+#define __GMP_WITHIN_CONFIGURE
 #include <gmp.h>
 #include <mpf2mpfr.h>
 #include <mpfr.h>
+#undef  __GMP_WITHIN_CONFIGURE
+
 class bigfloat {
 
 private:

Grid/algorithms/approx/bigfloat_double.h

@@ -25,6 +25,10 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     See the full license in the file "LICENSE" in the top level distribution directory
     *************************************************************************************/
     /*  END LEGAL */
+
+#ifndef INCLUDED_BIGFLOAT_DOUBLE_H
+#define INCLUDED_BIGFLOAT_DOUBLE_H
+
 #include <math.h>
 
 typedef double mfloat; 
@@ -186,4 +190,6 @@ public:
   //  friend bigfloat& random(void);
 };
 
+#endif
+
 

Grid/algorithms/iterative/AdefGeneric.h

@@ -90,8 +90,8 @@ class TwoLevelFlexiblePcg : public LinearFunction<Field>
   void operator() (const Field &src, Field &psi){
   void operator() (const Field &src, Field &psi){
 
-    psi.checkerboard = src.checkerboard;
-    grid             = src._grid;
+    psi.Checkerboard() = src.Checkerboard();
+    grid             = src.Grid();
 
     RealD f;
     RealD rtzp,rtz,a,d,b;

Grid/algorithms/iterative/BiCGSTAB.h

@@ -0,0 +1,234 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithms/iterative/BiCGSTAB.h
+
+Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+Author: juettner <juettner@soton.ac.uk>
+Author: David Murphy <djmurphy@mit.edu>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+
+#ifndef GRID_BICGSTAB_H
+#define GRID_BICGSTAB_H
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////
+// Base classes for iterative processes based on operators
+// single input vec, single output vec.
+/////////////////////////////////////////////////////////////
+
+template <class Field>
+class BiCGSTAB : public OperatorFunction<Field> 
+{
+  public:
+    using OperatorFunction<Field>::operator();
+    
+    bool ErrorOnNoConverge;  // throw an assert when the CG fails to converge.
+                             // Defaults true.
+    RealD Tolerance;
+    Integer MaxIterations;
+    Integer IterationsToComplete; //Number of iterations the CG took to finish. Filled in upon completion
+  
+    BiCGSTAB(RealD tol, Integer maxit, bool err_on_no_conv = true) : 
+      Tolerance(tol), MaxIterations(maxit), ErrorOnNoConverge(err_on_no_conv){};
+
+    void operator()(LinearOperatorBase<Field>& Linop, const Field& src, Field& psi) 
+    {
+      psi.Checkerboard() = src.Checkerboard();
+      conformable(psi, src);
+
+      RealD cp(0), rho(1), rho_prev(0), alpha(1), beta(0), omega(1);
+      RealD a(0), bo(0), b(0), ssq(0);
+
+      Field p(src);
+      Field r(src);
+      Field rhat(src);
+      Field v(src);
+      Field s(src);
+      Field t(src);
+      Field h(src);
+
+      v = Zero();
+      p = Zero();
+
+      // Initial residual computation & set up
+      RealD guess = norm2(psi);
+      assert(std::isnan(guess) == 0);
+    
+      Linop.Op(psi, v);
+      b = norm2(v);
+
+      r = src - v;
+      rhat = r;
+      a = norm2(r);
+      ssq = norm2(src);
+
+      std::cout << GridLogIterative << std::setprecision(8) << "BiCGSTAB: guess " << guess << std::endl;
+      std::cout << GridLogIterative << std::setprecision(8) << "BiCGSTAB:   src " << ssq << std::endl;
+      std::cout << GridLogIterative << std::setprecision(8) << "BiCGSTAB:    mp " << b << std::endl;
+      std::cout << GridLogIterative << std::setprecision(8) << "BiCGSTAB:     r " << a << std::endl;
+
+      RealD rsq = Tolerance * Tolerance * ssq;
+
+      // Check if guess is really REALLY good :)
+      if(a <= rsq){ return; }
+
+      std::cout << GridLogIterative << std::setprecision(8) << "BiCGSTAB: k=0 residual " << a << " target " << rsq << std::endl;
+
+      GridStopWatch LinalgTimer;
+      GridStopWatch InnerTimer;
+      GridStopWatch AxpyNormTimer;
+      GridStopWatch LinearCombTimer;
+      GridStopWatch MatrixTimer;
+      GridStopWatch SolverTimer;
+
+      SolverTimer.Start();
+      int k;
+      for (k = 1; k <= MaxIterations; k++) 
+      {
+        rho_prev = rho;
+
+        LinalgTimer.Start();
+        InnerTimer.Start();
+        ComplexD Crho  = innerProduct(rhat,r);
+        InnerTimer.Stop();
+        rho = Crho.real();
+
+        beta = (rho / rho_prev) * (alpha / omega);
+
+        LinearCombTimer.Start();
+        bo = beta * omega;
+	{
+	  autoView( p_v , p, AcceleratorWrite);
+	  autoView( r_v , r, AcceleratorRead);
+	  autoView( v_v , v, AcceleratorRead);
+	  accelerator_for(ss, p_v.size(), Field::vector_object::Nsimd(),{
+	      coalescedWrite(p_v[ss], beta*p_v(ss) - bo*v_v(ss) + r_v(ss));
+	    });
+	}
+        LinearCombTimer.Stop();
+        LinalgTimer.Stop();
+
+        MatrixTimer.Start();
+        Linop.Op(p,v);
+        MatrixTimer.Stop();
+
+        LinalgTimer.Start();
+        InnerTimer.Start();
+        ComplexD Calpha = innerProduct(rhat,v);
+        InnerTimer.Stop();
+        alpha = rho / Calpha.real();
+
+        LinearCombTimer.Start();
+	{
+	  autoView( p_v , p, AcceleratorRead);
+	  autoView( r_v , r, AcceleratorRead);
+	  autoView( v_v , v, AcceleratorRead);
+	  autoView( psi_v,psi, AcceleratorRead);
+	  autoView( h_v  ,  h, AcceleratorWrite);
+	  autoView( s_v  ,  s, AcceleratorWrite);
+	  accelerator_for(ss, h_v.size(), Field::vector_object::Nsimd(),{
+	      coalescedWrite(h_v[ss], alpha*p_v(ss) + psi_v(ss));
+	    });
+	  accelerator_for(ss, s_v.size(), Field::vector_object::Nsimd(),{
+	      coalescedWrite(s_v[ss], -alpha*v_v(ss) + r_v(ss));
+ 	  });
+        }
+        LinearCombTimer.Stop();
+        LinalgTimer.Stop();
+
+        MatrixTimer.Start();
+        Linop.Op(s,t);
+        MatrixTimer.Stop();
+
+        LinalgTimer.Start();
+        InnerTimer.Start();
+        ComplexD Comega = innerProduct(t,s);
+        InnerTimer.Stop();
+        omega = Comega.real() / norm2(t);
+
+        LinearCombTimer.Start();
+	{
+	  autoView( psi_v,psi, AcceleratorWrite);
+	  autoView( r_v , r, AcceleratorWrite);
+	  autoView( h_v , h, AcceleratorRead);
+	  autoView( s_v , s, AcceleratorRead);
+	  autoView( t_v , t, AcceleratorRead);
+	  accelerator_for(ss, psi_v.size(), Field::vector_object::Nsimd(),{
+	      coalescedWrite(psi_v[ss], h_v(ss) + omega * s_v(ss));
+	      coalescedWrite(r_v[ss], -omega * t_v(ss) + s_v(ss));
+	    });
+	}
+        LinearCombTimer.Stop();
+	
+        cp = norm2(r);
+        LinalgTimer.Stop();
+
+        std::cout << GridLogIterative << "BiCGSTAB: Iteration " << k << " residual " << sqrt(cp/ssq) << " target " << Tolerance << std::endl;
+
+        // Stopping condition
+        if(cp <= rsq) 
+        {
+          SolverTimer.Stop();
+          Linop.Op(psi, v);
+          p = v - src;
+
+          RealD srcnorm = sqrt(norm2(src));
+          RealD resnorm = sqrt(norm2(p));
+          RealD true_residual = resnorm / srcnorm;
+
+          std::cout << GridLogMessage << "BiCGSTAB Converged on iteration " << k << std::endl;
+          std::cout << GridLogMessage << "\tComputed residual " << sqrt(cp/ssq) << std::endl;
+          std::cout << GridLogMessage << "\tTrue residual " << true_residual << std::endl;
+          std::cout << GridLogMessage << "\tTarget " << Tolerance << std::endl;
+
+          std::cout << GridLogMessage << "Time breakdown " << std::endl;
+          std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed() << std::endl;
+          std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed() << std::endl;
+          std::cout << GridLogMessage << "\tLinalg     " << LinalgTimer.Elapsed() << std::endl;
+          std::cout << GridLogMessage << "\tInner      " << InnerTimer.Elapsed() << std::endl;
+          std::cout << GridLogMessage << "\tAxpyNorm   " << AxpyNormTimer.Elapsed() << std::endl;
+          std::cout << GridLogMessage << "\tLinearComb " << LinearCombTimer.Elapsed() << std::endl;
+
+          if(ErrorOnNoConverge){ assert(true_residual / Tolerance < 10000.0); }
+
+          IterationsToComplete = k;	
+
+          return;
+        }
+      }
+      
+      std::cout << GridLogMessage << "BiCGSTAB did NOT converge" << std::endl;
+
+      if(ErrorOnNoConverge){ assert(0); }
+      IterationsToComplete = k;
+    }
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/algorithms/iterative/BiCGSTABMixedPrec.h

@@ -0,0 +1,158 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid 
+
+Source file: ./lib/algorithms/iterative/BiCGSTABMixedPrec.h
+
+Copyright (C) 2015
+
+Author: Christopher Kelly <ckelly@phys.columbia.edu>
+Author: David Murphy <djmurphy@mit.edu>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+
+#ifndef GRID_BICGSTAB_MIXED_PREC_H
+#define GRID_BICGSTAB_MIXED_PREC_H
+
+NAMESPACE_BEGIN(Grid);
+
+// Mixed precision restarted defect correction BiCGSTAB
+template<class FieldD, class FieldF, typename std::enable_if< getPrecision<FieldD>::value == 2, int>::type = 0, typename std::enable_if< getPrecision<FieldF>::value == 1, int>::type = 0> 
+class MixedPrecisionBiCGSTAB : public LinearFunction<FieldD> 
+{
+  public:                                                
+    RealD   Tolerance;
+    RealD   InnerTolerance; // Initial tolerance for inner CG. Defaults to Tolerance but can be changed
+    Integer MaxInnerIterations;
+    Integer MaxOuterIterations;
+    GridBase* SinglePrecGrid; // Grid for single-precision fields
+    RealD OuterLoopNormMult; // Stop the outer loop and move to a final double prec solve when the residual is OuterLoopNormMult * Tolerance
+    LinearOperatorBase<FieldF> &Linop_f;
+    LinearOperatorBase<FieldD> &Linop_d;
+
+    Integer TotalInnerIterations; //Number of inner CG iterations
+    Integer TotalOuterIterations; //Number of restarts
+    Integer TotalFinalStepIterations; //Number of CG iterations in final patch-up step
+
+    //Option to speed up *inner single precision* solves using a LinearFunction that produces a guess
+    LinearFunction<FieldF> *guesser;
+    
+    MixedPrecisionBiCGSTAB(RealD tol, Integer maxinnerit, Integer maxouterit, GridBase* _sp_grid, 
+        LinearOperatorBase<FieldF>& _Linop_f, LinearOperatorBase<FieldD>& _Linop_d) : 
+      Linop_f(_Linop_f), Linop_d(_Linop_d), Tolerance(tol), InnerTolerance(tol), MaxInnerIterations(maxinnerit), 
+      MaxOuterIterations(maxouterit), SinglePrecGrid(_sp_grid), OuterLoopNormMult(100.), guesser(NULL) {};
+
+    void useGuesser(LinearFunction<FieldF>& g){
+      guesser = &g;
+    }
+  
+    void operator() (const FieldD& src_d_in, FieldD& sol_d)
+    {
+      TotalInnerIterations = 0;
+    
+      GridStopWatch TotalTimer;
+      TotalTimer.Start();
+      
+      int cb = src_d_in.Checkerboard();
+      sol_d.Checkerboard() = cb;
+      
+      RealD src_norm = norm2(src_d_in);
+      RealD stop = src_norm * Tolerance*Tolerance;
+
+      GridBase* DoublePrecGrid = src_d_in.Grid();
+      FieldD tmp_d(DoublePrecGrid);
+      tmp_d.Checkerboard() = cb;
+      
+      FieldD tmp2_d(DoublePrecGrid);
+      tmp2_d.Checkerboard() = cb;
+      
+      FieldD src_d(DoublePrecGrid);
+      src_d = src_d_in; //source for next inner iteration, computed from residual during operation
+      
+      RealD inner_tol = InnerTolerance;
+      
+      FieldF src_f(SinglePrecGrid);
+      src_f.Checkerboard() = cb;
+      
+      FieldF sol_f(SinglePrecGrid);
+      sol_f.Checkerboard() = cb;
+      
+      BiCGSTAB<FieldF> CG_f(inner_tol, MaxInnerIterations);
+      CG_f.ErrorOnNoConverge = false;
+
+      GridStopWatch InnerCGtimer;
+
+      GridStopWatch PrecChangeTimer;
+      
+      Integer &outer_iter = TotalOuterIterations; //so it will be equal to the final iteration count
+        
+      for(outer_iter = 0; outer_iter < MaxOuterIterations; outer_iter++)
+      {
+        // Compute double precision rsd and also new RHS vector.
+        Linop_d.Op(sol_d, tmp_d);
+        RealD norm = axpy_norm(src_d, -1., tmp_d, src_d_in); //src_d is residual vector
+        
+        std::cout << GridLogMessage << "MixedPrecisionBiCGSTAB: Outer iteration " << outer_iter << " residual " << norm << " target " << stop << std::endl;
+
+        if(norm < OuterLoopNormMult * stop){
+          std::cout << GridLogMessage << "MixedPrecisionBiCGSTAB: Outer iteration converged on iteration " << outer_iter << std::endl;
+          break;
+        }
+        while(norm * inner_tol * inner_tol < stop){ inner_tol *= 2; } // inner_tol = sqrt(stop/norm) ??
+
+        PrecChangeTimer.Start();
+        precisionChange(src_f, src_d);
+        PrecChangeTimer.Stop();
+        
+        sol_f = Zero();
+
+        //Optionally improve inner solver guess (eg using known eigenvectors)
+        if(guesser != NULL){ (*guesser)(src_f, sol_f); }
+
+        //Inner CG
+        CG_f.Tolerance = inner_tol;
+        InnerCGtimer.Start();
+        CG_f(Linop_f, src_f, sol_f);
+        InnerCGtimer.Stop();
+        TotalInnerIterations += CG_f.IterationsToComplete;
+        
+        //Convert sol back to double and add to double prec solution
+        PrecChangeTimer.Start();
+        precisionChange(tmp_d, sol_f);
+        PrecChangeTimer.Stop();
+        
+        axpy(sol_d, 1.0, tmp_d, sol_d);
+      }
+      
+      //Final trial CG
+      std::cout << GridLogMessage << "MixedPrecisionBiCGSTAB: Starting final patch-up double-precision solve" << std::endl;
+      
+      BiCGSTAB<FieldD> CG_d(Tolerance, MaxInnerIterations);
+      CG_d(Linop_d, src_d_in, sol_d);
+      TotalFinalStepIterations = CG_d.IterationsToComplete;
+
+      TotalTimer.Stop();
+      std::cout << GridLogMessage << "MixedPrecisionBiCGSTAB: Inner CG iterations " << TotalInnerIterations << " Restarts " << TotalOuterIterations << " Final CG iterations " << TotalFinalStepIterations << std::endl;
+      std::cout << GridLogMessage << "MixedPrecisionBiCGSTAB: Total time " << TotalTimer.Elapsed() << " Precision change " << PrecChangeTimer.Elapsed() << " Inner CG total " << InnerCGtimer.Elapsed() << std::endl;
+  }
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/algorithms/iterative/BlockConjugateGradient.h

@@ -27,13 +27,11 @@ See the full license in the file "LICENSE" in the top level distribution
 directory
 *************************************************************************************/
 /*  END LEGAL */
-#ifndef GRID_BLOCK_CONJUGATE_GRADIENT_H
-#define GRID_BLOCK_CONJUGATE_GRADIENT_H
+#pragma once
 
+NAMESPACE_BEGIN(Grid);
 
-namespace Grid {
-
-enum BlockCGtype { BlockCG, BlockCGrQ, CGmultiRHS };
+enum BlockCGtype { BlockCG, BlockCGrQ, CGmultiRHS, BlockCGVec, BlockCGrQVec };
 
 //////////////////////////////////////////////////////////////////////////
 // Block conjugate gradient. Dimension zero should be the block direction
@@ -42,7 +40,6 @@ template <class Field>
 class BlockConjugateGradient : public OperatorFunction<Field> {
  public:
 
-
   typedef typename Field::scalar_type scomplex;
 
   int blockDim ;
@@ -54,21 +51,16 @@ class BlockConjugateGradient : public OperatorFunction<Field> {
   RealD Tolerance;
   Integer MaxIterations;
   Integer IterationsToComplete; //Number of iterations the CG took to finish. Filled in upon completion
+  Integer PrintInterval; //GridLogMessages or Iterative
+  RealD TrueResidual;
   
   BlockConjugateGradient(BlockCGtype cgtype,int _Orthog,RealD tol, Integer maxit, bool err_on_no_conv = true)
-    : Tolerance(tol), CGtype(cgtype),   blockDim(_Orthog),  MaxIterations(maxit), ErrorOnNoConverge(err_on_no_conv)
+    : Tolerance(tol), CGtype(cgtype),   blockDim(_Orthog),  MaxIterations(maxit), ErrorOnNoConverge(err_on_no_conv),PrintInterval(100)
   {};
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 // Thin QR factorisation (google it)
 ////////////////////////////////////////////////////////////////////////////////////////////////////
-void ThinQRfact (Eigen::MatrixXcd &m_rr,
-		 Eigen::MatrixXcd &C,
-		 Eigen::MatrixXcd &Cinv,
-		 Field & Q,
-		 const Field & R)
-{
-  int Orthog = blockDim; // First dimension is block dim; this is an assumption
   ////////////////////////////////////////////////////////////////////////////////////////////////////
   //Dimensions
   // R_{ferm x Nblock} =  Q_{ferm x Nblock} x  C_{Nblock x Nblock} -> ferm x Nblock
@@ -85,22 +77,20 @@ void ThinQRfact (Eigen::MatrixXcd &m_rr,
   // Cdag C = Rdag R ; passes.
   // QdagQ  = 1      ; passes
   ////////////////////////////////////////////////////////////////////////////////////////////////////
+void ThinQRfact (Eigen::MatrixXcd &m_rr,
+		 Eigen::MatrixXcd &C,
+		 Eigen::MatrixXcd &Cinv,
+		 Field & Q,
+		 const Field & R)
+{
+  int Orthog = blockDim; // First dimension is block dim; this is an assumption
   sliceInnerProductMatrix(m_rr,R,R,Orthog);
 
   // Force manifest hermitian to avoid rounding related
   m_rr = 0.5*(m_rr+m_rr.adjoint());
 
-#if 0
-  std::cout << " Calling Cholesky  ldlt on m_rr "  << m_rr <<std::endl;
-  Eigen::MatrixXcd L_ldlt = m_rr.ldlt().matrixL(); 
-  std::cout << " Called Cholesky  ldlt on m_rr "  << L_ldlt <<std::endl;
-  auto  D_ldlt = m_rr.ldlt().vectorD(); 
-  std::cout << " Called Cholesky  ldlt on m_rr "  << D_ldlt <<std::endl;
-#endif
-
-  //  std::cout << " Calling Cholesky  llt on m_rr "  <<std::endl;
   Eigen::MatrixXcd L    = m_rr.llt().matrixL(); 
-  //  std::cout << " Called Cholesky  llt on m_rr "  << L <<std::endl;
+
   C    = L.adjoint();
   Cinv = C.inverse();
   ////////////////////////////////////////////////////////////////////////////////////////////////////
@@ -112,6 +102,25 @@ void ThinQRfact (Eigen::MatrixXcd &m_rr,
   ////////////////////////////////////////////////////////////////////////////////////////////////////
   sliceMulMatrix(Q,Cinv,R,Orthog);
 }
+// see comments above
+void ThinQRfact (Eigen::MatrixXcd &m_rr,
+		 Eigen::MatrixXcd &C,
+		 Eigen::MatrixXcd &Cinv,
+		 std::vector<Field> & Q,
+		 const std::vector<Field> & R)
+{
+  InnerProductMatrix(m_rr,R,R);
+
+  m_rr = 0.5*(m_rr+m_rr.adjoint());
+
+  Eigen::MatrixXcd L    = m_rr.llt().matrixL(); 
+
+  C    = L.adjoint();
+  Cinv = C.inverse();
+
+  MulMatrix(Q,Cinv,R);
+}
+
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 // Call one of several implementations
 ////////////////////////////////////////////////////////////////////////////////////////////////////
@@ -119,14 +128,20 @@ void operator()(LinearOperatorBase<Field> &Linop, const Field &Src, Field &Psi)
 {
   if ( CGtype == BlockCGrQ ) {
     BlockCGrQsolve(Linop,Src,Psi);
-  } else if (CGtype == BlockCG ) {
-    BlockCGsolve(Linop,Src,Psi);
   } else if (CGtype == CGmultiRHS ) {
     CGmultiRHSsolve(Linop,Src,Psi);
   } else {
     assert(0);
   }
 }
+virtual void operator()(LinearOperatorBase<Field> &Linop, const std::vector<Field> &Src, std::vector<Field> &Psi) 
+{
+  if ( CGtype == BlockCGrQVec ) {
+    BlockCGrQsolveVec(Linop,Src,Psi);
+  } else {
+    assert(0);
+  }
+}
 
 ////////////////////////////////////////////////////////////////////////////
 // BlockCGrQ implementation:
@@ -138,11 +153,12 @@ void operator()(LinearOperatorBase<Field> &Linop, const Field &Src, Field &Psi)
 void BlockCGrQsolve(LinearOperatorBase<Field> &Linop, const Field &B, Field &X) 
 {
   int Orthog = blockDim; // First dimension is block dim; this is an assumption
-  Nblock = B._grid->_fdimensions[Orthog];
-
+  Nblock = B.Grid()->_fdimensions[Orthog];
+/* FAKE */
+  Nblock=8;
   std::cout<<GridLogMessage<<" Block Conjugate Gradient : Orthog "<<Orthog<<" Nblock "<<Nblock<<std::endl;
 
-  X.checkerboard = B.checkerboard;
+  X.Checkerboard() = B.Checkerboard();
   conformable(X, B);
 
   Field tmp(B);
@@ -202,15 +218,10 @@ void BlockCGrQsolve(LinearOperatorBase<Field> &Linop, const Field &B, Field &X)
   std::cout << GridLogMessage<<"BlockCGrQ algorithm initialisation " <<std::endl;
 
   //1.  QC = R = B-AX, D = Q     ; QC => Thin QR factorisation (google it)
-
   Linop.HermOp(X, AD);
   tmp = B - AD;  
-  //std::cout << GridLogMessage << " initial tmp " << norm2(tmp)<< std::endl;
+
   ThinQRfact (m_rr, m_C, m_Cinv, Q, tmp);
-  //std::cout << GridLogMessage << " initial Q " << norm2(Q)<< std::endl;
-  //std::cout << GridLogMessage << " m_rr " << m_rr<<std::endl;
-  //std::cout << GridLogMessage << " m_C " << m_C<<std::endl;
-  //std::cout << GridLogMessage << " m_Cinv " << m_Cinv<<std::endl;
   D=Q;
 
   std::cout << GridLogMessage<<"BlockCGrQ computed initial residual and QR fact " <<std::endl;
@@ -232,14 +243,12 @@ void BlockCGrQsolve(LinearOperatorBase<Field> &Linop, const Field &B, Field &X)
     MatrixTimer.Start();
     Linop.HermOp(D, Z);      
     MatrixTimer.Stop();
-    //std::cout << GridLogMessage << " norm2 Z " <<norm2(Z)<<std::endl;
 
     //4. M  = [D^dag Z]^{-1}
     sliceInnerTimer.Start();
     sliceInnerProductMatrix(m_DZ,D,Z,Orthog);
     sliceInnerTimer.Stop();
     m_M       = m_DZ.inverse();
-    //std::cout << GridLogMessage << " m_DZ " <<m_DZ<<std::endl;
     
     //5. X  = X + D MC
     m_tmp     = m_M * m_C;
@@ -257,6 +266,7 @@ void BlockCGrQsolve(LinearOperatorBase<Field> &Linop, const Field &B, Field &X)
     
     //7. D  = Q + D S^dag
     m_tmp = m_S.adjoint();
+
     sliceMaddTimer.Start();
     sliceMaddMatrix(D,m_tmp,D,Q,Orthog);
     sliceMaddTimer.Stop();
@@ -297,7 +307,8 @@ void BlockCGrQsolve(LinearOperatorBase<Field> &Linop, const Field &B, Field &X)
 
       Linop.HermOp(X, AD);
       AD = AD-B;
-      std::cout << GridLogMessage <<"\t True residual is " << std::sqrt(norm2(AD)/norm2(B)) <<std::endl;
+      TrueResidual = std::sqrt(norm2(AD)/norm2(B));
+      std::cout << GridLogMessage <<"\tTrue residual is " << TrueResidual <<std::endl;
 
       std::cout << GridLogMessage << "Time Breakdown "<<std::endl;
       std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed()     <<std::endl;
@@ -317,163 +328,17 @@ void BlockCGrQsolve(LinearOperatorBase<Field> &Linop, const Field &B, Field &X)
   IterationsToComplete = k;
 }
 //////////////////////////////////////////////////////////////////////////
-// Block conjugate gradient; Original O'Leary Dimension zero should be the block direction
-//////////////////////////////////////////////////////////////////////////
-void BlockCGsolve(LinearOperatorBase<Field> &Linop, const Field &Src, Field &Psi) 
-{
-  int Orthog = blockDim; // First dimension is block dim; this is an assumption
-  Nblock = Src._grid->_fdimensions[Orthog];
-
-  std::cout<<GridLogMessage<<" Block Conjugate Gradient : Orthog "<<Orthog<<" Nblock "<<Nblock<<std::endl;
-
-  Psi.checkerboard = Src.checkerboard;
-  conformable(Psi, Src);
-
-  Field P(Src);
-  Field AP(Src);
-  Field R(Src);
-  
-  Eigen::MatrixXcd m_pAp    = Eigen::MatrixXcd::Identity(Nblock,Nblock);
-  Eigen::MatrixXcd m_pAp_inv= Eigen::MatrixXcd::Identity(Nblock,Nblock);
-  Eigen::MatrixXcd m_rr     = Eigen::MatrixXcd::Zero(Nblock,Nblock);
-  Eigen::MatrixXcd m_rr_inv = Eigen::MatrixXcd::Zero(Nblock,Nblock);
-
-  Eigen::MatrixXcd m_alpha      = Eigen::MatrixXcd::Zero(Nblock,Nblock);
-  Eigen::MatrixXcd m_beta   = Eigen::MatrixXcd::Zero(Nblock,Nblock);
-
-  // Initial residual computation & set up
-  std::vector<RealD> residuals(Nblock);
-  std::vector<RealD> ssq(Nblock);
-
-  sliceNorm(ssq,Src,Orthog);
-  RealD sssum=0;
-  for(int b=0;b<Nblock;b++) sssum+=ssq[b];
-
-  sliceNorm(residuals,Src,Orthog);
-  for(int b=0;b<Nblock;b++){ assert(std::isnan(residuals[b])==0); }
-
-  sliceNorm(residuals,Psi,Orthog);
-  for(int b=0;b<Nblock;b++){ assert(std::isnan(residuals[b])==0); }
-
-  // Initial search dir is guess
-  Linop.HermOp(Psi, AP);
-  
-
-  /************************************************************************
-   * Block conjugate gradient (Stephen Pickles, thesis 1995, pp 71, O Leary 1980)
-   ************************************************************************
-   * O'Leary : R = B - A X
-   * O'Leary : P = M R ; preconditioner M = 1
-   * O'Leary : alpha = PAP^{-1} RMR
-   * O'Leary : beta  = RMR^{-1}_old RMR_new
-   * O'Leary : X=X+Palpha
-   * O'Leary : R_new=R_old-AP alpha
-   * O'Leary : P=MR_new+P beta
-   */
-
-  R = Src - AP;  
-  P = R;
-  sliceInnerProductMatrix(m_rr,R,R,Orthog);
-
-  GridStopWatch sliceInnerTimer;
-  GridStopWatch sliceMaddTimer;
-  GridStopWatch MatrixTimer;
-  GridStopWatch SolverTimer;
-  SolverTimer.Start();
-
-  int k;
-  for (k = 1; k <= MaxIterations; k++) {
-
-    RealD rrsum=0;
-    for(int b=0;b<Nblock;b++) rrsum+=real(m_rr(b,b));
-
-    std::cout << GridLogIterative << "\titeration "<<k<<" rr_sum "<<rrsum<<" ssq_sum "<< sssum
-	      <<" / "<<std::sqrt(rrsum/sssum) <<std::endl;
-
-    MatrixTimer.Start();
-    Linop.HermOp(P, AP);
-    MatrixTimer.Stop();
-
-    // Alpha
-    sliceInnerTimer.Start();
-    sliceInnerProductMatrix(m_pAp,P,AP,Orthog);
-    sliceInnerTimer.Stop();
-    m_pAp_inv = m_pAp.inverse();
-    m_alpha   = m_pAp_inv * m_rr ;
-
-    // Psi, R update
-    sliceMaddTimer.Start();
-    sliceMaddMatrix(Psi,m_alpha, P,Psi,Orthog);     // add alpha *  P to psi
-    sliceMaddMatrix(R  ,m_alpha,AP,  R,Orthog,-1.0);// sub alpha * AP to resid
-    sliceMaddTimer.Stop();
-
-    // Beta
-    m_rr_inv = m_rr.inverse();
-    sliceInnerTimer.Start();
-    sliceInnerProductMatrix(m_rr,R,R,Orthog);
-    sliceInnerTimer.Stop();
-    m_beta = m_rr_inv *m_rr;
-
-    // Search update
-    sliceMaddTimer.Start();
-    sliceMaddMatrix(AP,m_beta,P,R,Orthog);
-    sliceMaddTimer.Stop();
-    P= AP;
-
-    /*********************
-     * convergence monitor
-     *********************
-     */
-    RealD max_resid=0;
-    RealD rr;
-    for(int b=0;b<Nblock;b++){
-      rr = real(m_rr(b,b))/ssq[b];
-      if ( rr > max_resid ) max_resid = rr;
-    }
-    
-    if ( max_resid < Tolerance*Tolerance ) { 
-
-      SolverTimer.Stop();
-
-      std::cout << GridLogMessage<<"BlockCG converged in "<<k<<" iterations"<<std::endl;
-      for(int b=0;b<Nblock;b++){
-	std::cout << GridLogMessage<< "\t\tblock "<<b<<" computed resid "
-		  << std::sqrt(real(m_rr(b,b))/ssq[b])<<std::endl;
-      }
-      std::cout << GridLogMessage<<"\tMax residual is "<<std::sqrt(max_resid)<<std::endl;
-
-      Linop.HermOp(Psi, AP);
-      AP = AP-Src;
-      std::cout << GridLogMessage <<"\t True residual is " << std::sqrt(norm2(AP)/norm2(Src)) <<std::endl;
-
-      std::cout << GridLogMessage << "Time Breakdown "<<std::endl;
-      std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed()     <<std::endl;
-      std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed()     <<std::endl;
-      std::cout << GridLogMessage << "\tInnerProd  " << sliceInnerTimer.Elapsed() <<std::endl;
-      std::cout << GridLogMessage << "\tMaddMatrix " << sliceMaddTimer.Elapsed()  <<std::endl;
-	    
-      IterationsToComplete = k;
-      return;
-    }
-
-  }
-  std::cout << GridLogMessage << "BlockConjugateGradient did NOT converge" << std::endl;
-
-  if (ErrorOnNoConverge) assert(0);
-  IterationsToComplete = k;
-}
-//////////////////////////////////////////////////////////////////////////
 // multiRHS conjugate gradient. Dimension zero should be the block direction
 // Use this for spread out across nodes
 //////////////////////////////////////////////////////////////////////////
 void CGmultiRHSsolve(LinearOperatorBase<Field> &Linop, const Field &Src, Field &Psi) 
 {
   int Orthog = blockDim; // First dimension is block dim
-  Nblock = Src._grid->_fdimensions[Orthog];
+  Nblock = Src.Grid()->_fdimensions[Orthog];
 
   std::cout<<GridLogMessage<<"MultiRHS Conjugate Gradient : Orthog "<<Orthog<<" Nblock "<<Nblock<<std::endl;
 
-  Psi.checkerboard = Src.checkerboard;
+  Psi.Checkerboard() = Src.Checkerboard();
   conformable(Psi, Src);
 
   Field P(Src);
@@ -579,7 +444,8 @@ void CGmultiRHSsolve(LinearOperatorBase<Field> &Linop, const Field &Src, Field &
 
       Linop.HermOp(Psi, AP);
       AP = AP-Src;
-      std::cout <<GridLogMessage << "\tTrue residual is " << std::sqrt(norm2(AP)/norm2(Src)) <<std::endl;
+      TrueResidual = std::sqrt(norm2(AP)/norm2(Src));
+      std::cout <<GridLogMessage << "\tTrue residual is " << TrueResidual <<std::endl;
 
       std::cout << GridLogMessage << "Time Breakdown "<<std::endl;
       std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed()     <<std::endl;
@@ -600,7 +466,233 @@ void CGmultiRHSsolve(LinearOperatorBase<Field> &Linop, const Field &Src, Field &
   IterationsToComplete = k;
 }
 
+void InnerProductMatrix(Eigen::MatrixXcd &m , const std::vector<Field> &X, const std::vector<Field> &Y){
+  for(int b=0;b<Nblock;b++){
+  for(int bp=0;bp<Nblock;bp++) {
+    m(b,bp) = innerProduct(X[b],Y[bp]);  
+  }}
+}
+void MaddMatrix(std::vector<Field> &AP, Eigen::MatrixXcd &m , const std::vector<Field> &X,const std::vector<Field> &Y,RealD scale=1.0){
+  // Should make this cache friendly with site outermost, parallel_for
+  // Deal with case AP aliases with either Y or X
+  std::vector<Field> tmp(Nblock,X[0]);
+  for(int b=0;b<Nblock;b++){
+    tmp[b]   = Y[b];
+    for(int bp=0;bp<Nblock;bp++) {
+      tmp[b] = tmp[b] + scomplex(scale*m(bp,b))*X[bp]; 
+    }
+  }
+  for(int b=0;b<Nblock;b++){
+    AP[b] = tmp[b];
+  }
+}
+void MulMatrix(std::vector<Field> &AP, Eigen::MatrixXcd &m , const std::vector<Field> &X){
+  // Should make this cache friendly with site outermost, parallel_for
+  for(int b=0;b<Nblock;b++){
+    AP[b] = Zero();
+    for(int bp=0;bp<Nblock;bp++) {
+      AP[b] += scomplex(m(bp,b))*X[bp]; 
+    }
+  }
+}
+double normv(const std::vector<Field> &P){
+  double nn = 0.0;
+  for(int b=0;b<Nblock;b++) {
+    nn+=norm2(P[b]);
+  }
+  return nn;
+}
+
+////////////////////////////////////////////////////////////////////////////
+// BlockCGrQvec implementation:
+//--------------------------
+// X is guess/Solution
+// B is RHS
+// Solve A X_i = B_i    ;        i refers to Nblock index
+////////////////////////////////////////////////////////////////////////////
+void BlockCGrQsolveVec(LinearOperatorBase<Field> &Linop, const std::vector<Field> &B, std::vector<Field> &X) 
+{
+  Nblock = B.size();
+  assert(Nblock == X.size());
+
+  std::cout<<GridLogMessage<<" Block Conjugate Gradient Vec rQ : Nblock "<<Nblock<<std::endl;
+
+  for(int b=0;b<Nblock;b++){ 
+    X[b].Checkerboard() = B[b].Checkerboard();
+    conformable(X[b], B[b]);
+    conformable(X[b], X[0]); 
+  }
+
+  Field Fake(B[0]);
+
+  std::vector<Field> tmp(Nblock,Fake);
+  std::vector<Field>   Q(Nblock,Fake);
+  std::vector<Field>   D(Nblock,Fake);
+  std::vector<Field>   Z(Nblock,Fake);
+  std::vector<Field>  AD(Nblock,Fake);
+
+  Eigen::MatrixXcd m_DZ     = Eigen::MatrixXcd::Identity(Nblock,Nblock);
+  Eigen::MatrixXcd m_M      = Eigen::MatrixXcd::Identity(Nblock,Nblock);
+  Eigen::MatrixXcd m_rr     = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+
+  Eigen::MatrixXcd m_C      = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+  Eigen::MatrixXcd m_Cinv   = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+  Eigen::MatrixXcd m_S      = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+  Eigen::MatrixXcd m_Sinv   = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+
+  Eigen::MatrixXcd m_tmp    = Eigen::MatrixXcd::Identity(Nblock,Nblock);
+  Eigen::MatrixXcd m_tmp1   = Eigen::MatrixXcd::Identity(Nblock,Nblock);
+
+  // Initial residual computation & set up
+  std::vector<RealD> residuals(Nblock);
+  std::vector<RealD> ssq(Nblock);
+
+  RealD sssum=0;
+  for(int b=0;b<Nblock;b++){ ssq[b] = norm2(B[b]);}
+  for(int b=0;b<Nblock;b++) sssum+=ssq[b];
+
+  for(int b=0;b<Nblock;b++){ residuals[b] = norm2(B[b]);}
+  for(int b=0;b<Nblock;b++){ assert(std::isnan(residuals[b])==0); }
+
+  for(int b=0;b<Nblock;b++){ residuals[b] = norm2(X[b]);}
+  for(int b=0;b<Nblock;b++){ assert(std::isnan(residuals[b])==0); }
+
+  /************************************************************************
+   * Block conjugate gradient rQ (Sebastien Birk Thesis, after Dubrulle 2001)
+   ************************************************************************
+   * Dimensions:
+   *
+   *   X,B==(Nferm x Nblock)
+   *   A==(Nferm x Nferm)
+   *  
+   * Nferm = Nspin x Ncolour x Ncomplex x Nlattice_site
+   * 
+   * QC = R = B-AX, D = Q     ; QC => Thin QR factorisation (google it)
+   * for k: 
+   *   Z  = AD
+   *   M  = [D^dag Z]^{-1}
+   *   X  = X + D MC
+   *   QS = Q - ZM
+   *   D  = Q + D S^dag
+   *   C  = S C
+   */
+  ///////////////////////////////////////
+  // Initial block: initial search dir is guess
+  ///////////////////////////////////////
+  std::cout << GridLogMessage<<"BlockCGrQvec algorithm initialisation " <<std::endl;
+
+  //1.  QC = R = B-AX, D = Q     ; QC => Thin QR factorisation (google it)
+  for(int b=0;b<Nblock;b++) {
+    Linop.HermOp(X[b], AD[b]);
+    tmp[b] = B[b] - AD[b];  
+  }
+
+  ThinQRfact (m_rr, m_C, m_Cinv, Q, tmp);
+
+  for(int b=0;b<Nblock;b++) D[b]=Q[b];
+
+  std::cout << GridLogMessage<<"BlockCGrQ vec computed initial residual and QR fact " <<std::endl;
+
+  ///////////////////////////////////////
+  // Timers
+  ///////////////////////////////////////
+  GridStopWatch sliceInnerTimer;
+  GridStopWatch sliceMaddTimer;
+  GridStopWatch QRTimer;
+  GridStopWatch MatrixTimer;
+  GridStopWatch SolverTimer;
+  SolverTimer.Start();
+
+  int k;
+  for (k = 1; k <= MaxIterations; k++) {
+
+    //3. Z  = AD
+    MatrixTimer.Start();
+    for(int b=0;b<Nblock;b++) Linop.HermOp(D[b], Z[b]);      
+    MatrixTimer.Stop();
+
+    //4. M  = [D^dag Z]^{-1}
+    sliceInnerTimer.Start();
+    InnerProductMatrix(m_DZ,D,Z);
+    sliceInnerTimer.Stop();
+    m_M       = m_DZ.inverse();
+    
+    //5. X  = X + D MC
+    m_tmp     = m_M * m_C;
+    sliceMaddTimer.Start();
+    MaddMatrix(X,m_tmp, D,X);     
+    sliceMaddTimer.Stop();
+
+    //6. QS = Q - ZM
+    sliceMaddTimer.Start();
+    MaddMatrix(tmp,m_M,Z,Q,-1.0);
+    sliceMaddTimer.Stop();
+    QRTimer.Start();
+    ThinQRfact (m_rr, m_S, m_Sinv, Q, tmp);
+    QRTimer.Stop();
+    
+    //7. D  = Q + D S^dag
+    m_tmp = m_S.adjoint();
+    sliceMaddTimer.Start();
+    MaddMatrix(D,m_tmp,D,Q);
+    sliceMaddTimer.Stop();
+
+    //8. C  = S C
+    m_C = m_S*m_C;
+    
+    /*********************
+     * convergence monitor
+     *********************
+     */
+    m_rr = m_C.adjoint() * m_C;
+
+    RealD max_resid=0;
+    RealD rrsum=0;
+    RealD rr;
+
+    for(int b=0;b<Nblock;b++) {
+      rrsum+=real(m_rr(b,b));
+      rr = real(m_rr(b,b))/ssq[b];
+      if ( rr > max_resid ) max_resid = rr;
+    }
+
+    std::cout << GridLogIterative << "\t Block Iteration "<<k<<" ave resid "<< std::sqrt(rrsum/sssum) << " max "<< std::sqrt(max_resid) <<std::endl;
+
+    if ( max_resid < Tolerance*Tolerance ) { 
+
+      SolverTimer.Stop();
+
+      std::cout << GridLogMessage<<"BlockCGrQ converged in "<<k<<" iterations"<<std::endl;
+
+      for(int b=0;b<Nblock;b++){
+	std::cout << GridLogMessage<< "\t\tblock "<<b<<" computed resid "<< std::sqrt(real(m_rr(b,b))/ssq[b])<<std::endl;
+      }
+      std::cout << GridLogMessage<<"\tMax residual is "<<std::sqrt(max_resid)<<std::endl;
+
+      for(int b=0;b<Nblock;b++) Linop.HermOp(X[b], AD[b]);
+      for(int b=0;b<Nblock;b++) AD[b] = AD[b]-B[b];
+      TrueResidual = std::sqrt(normv(AD)/normv(B));
+      std::cout << GridLogMessage << "\tTrue residual is " << TrueResidual <<std::endl;
+
+      std::cout << GridLogMessage << "Time Breakdown "<<std::endl;
+      std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tInnerProd  " << sliceInnerTimer.Elapsed() <<std::endl;
+      std::cout << GridLogMessage << "\tMaddMatrix " << sliceMaddTimer.Elapsed()  <<std::endl;
+      std::cout << GridLogMessage << "\tThinQRfact " << QRTimer.Elapsed()  <<std::endl;
+	    
+      IterationsToComplete = k;
+      return;
+    }
+
+  }
+  std::cout << GridLogMessage << "BlockConjugateGradient(rQ) did NOT converge" << std::endl;
+
+  if (ErrorOnNoConverge) assert(0);
+  IterationsToComplete = k;
+}
+
 };
 
-}
-#endif
+NAMESPACE_END(Grid);
+

Grid/algorithms/iterative/CommunicationAvoidingGeneralisedMinimalResidual.h

@@ -0,0 +1,248 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithms/iterative/CommunicationAvoidingGeneralisedMinimalResidual.h
+
+Copyright (C) 2015
+
+Author: Daniel Richtmann <daniel.richtmann@ur.de>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_COMMUNICATION_AVOIDING_GENERALISED_MINIMAL_RESIDUAL_H
+#define GRID_COMMUNICATION_AVOIDING_GENERALISED_MINIMAL_RESIDUAL_H
+
+namespace Grid {
+
+template<class Field>
+class CommunicationAvoidingGeneralisedMinimalResidual : public OperatorFunction<Field> {
+ public:
+  using OperatorFunction<Field>::operator();
+
+  bool ErrorOnNoConverge; // Throw an assert when CAGMRES fails to converge,
+                          // defaults to true
+
+  RealD   Tolerance;
+
+  Integer MaxIterations;
+  Integer RestartLength;
+  Integer MaxNumberOfRestarts;
+  Integer IterationCount; // Number of iterations the CAGMRES took to finish,
+                          // filled in upon completion
+
+  GridStopWatch MatrixTimer;
+  GridStopWatch LinalgTimer;
+  GridStopWatch QrTimer;
+  GridStopWatch CompSolutionTimer;
+
+  Eigen::MatrixXcd H;
+
+  std::vector<ComplexD> y;
+  std::vector<ComplexD> gamma;
+  std::vector<ComplexD> c;
+  std::vector<ComplexD> s;
+
+  CommunicationAvoidingGeneralisedMinimalResidual(RealD   tol,
+                                                  Integer maxit,
+                                                  Integer restart_length,
+                                                  bool    err_on_no_conv = true)
+      : Tolerance(tol)
+      , MaxIterations(maxit)
+      , RestartLength(restart_length)
+      , MaxNumberOfRestarts(MaxIterations/RestartLength + ((MaxIterations%RestartLength == 0) ? 0 : 1))
+      , ErrorOnNoConverge(err_on_no_conv)
+      , H(Eigen::MatrixXcd::Zero(RestartLength, RestartLength + 1)) // sizes taken from DD-αAMG code base
+      , y(RestartLength + 1, 0.)
+      , gamma(RestartLength + 1, 0.)
+      , c(RestartLength + 1, 0.)
+      , s(RestartLength + 1, 0.) {};
+
+  void operator()(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi) {
+
+    std::cout << GridLogWarning << "This algorithm currently doesn't differ from regular GMRES" << std::endl;
+
+    psi.Checkerboard() = src.Checkerboard();
+    conformable(psi, src);
+
+    RealD guess = norm2(psi);
+    assert(std::isnan(guess) == 0);
+
+    RealD cp;
+    RealD ssq = norm2(src);
+    RealD rsq = Tolerance * Tolerance * ssq;
+
+    Field r(src.Grid());
+
+    std::cout << std::setprecision(4) << std::scientific;
+    std::cout << GridLogIterative << "CommunicationAvoidingGeneralisedMinimalResidual: guess " << guess << std::endl;
+    std::cout << GridLogIterative << "CommunicationAvoidingGeneralisedMinimalResidual:   src " << ssq   << std::endl;
+
+    MatrixTimer.Reset();
+    LinalgTimer.Reset();
+    QrTimer.Reset();
+    CompSolutionTimer.Reset();
+
+    GridStopWatch SolverTimer;
+    SolverTimer.Start();
+
+    IterationCount = 0;
+
+    for (int k=0; k<MaxNumberOfRestarts; k++) {
+
+      cp = outerLoopBody(LinOp, src, psi, rsq);
+
+      // Stopping condition
+      if (cp <= rsq) {
+
+        SolverTimer.Stop();
+
+        LinOp.Op(psi,r);
+        axpy(r,-1.0,src,r);
+
+        RealD srcnorm       = sqrt(ssq);
+        RealD resnorm       = sqrt(norm2(r));
+        RealD true_residual = resnorm / srcnorm;
+
+        std::cout << GridLogMessage        << "CommunicationAvoidingGeneralisedMinimalResidual: Converged on iteration " << IterationCount
+                  << " computed residual " << sqrt(cp / ssq)
+                  << " true residual "     << true_residual
+                  << " target "            << Tolerance << std::endl;
+
+        std::cout << GridLogMessage << "CAGMRES Time elapsed: Total   " <<       SolverTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "CAGMRES Time elapsed: Matrix  " <<       MatrixTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "CAGMRES Time elapsed: Linalg  " <<       LinalgTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "CAGMRES Time elapsed: QR      " <<           QrTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "CAGMRES Time elapsed: CompSol " << CompSolutionTimer.Elapsed() << std::endl;
+        return;
+      }
+    }
+
+    std::cout << GridLogMessage << "CommunicationAvoidingGeneralisedMinimalResidual did NOT converge" << std::endl;
+
+    if (ErrorOnNoConverge)
+      assert(0);
+  }
+
+  RealD outerLoopBody(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi, RealD rsq) {
+
+    RealD cp = 0;
+
+    Field w(src.Grid());
+    Field r(src.Grid());
+
+    // this should probably be made a class member so that it is only allocated once, not in every restart
+    std::vector<Field> v(RestartLength + 1, src.Grid()); for (auto &elem : v) elem = Zero();
+
+    MatrixTimer.Start();
+    LinOp.Op(psi, w);
+    MatrixTimer.Stop();
+
+    LinalgTimer.Start();
+    r = src - w;
+
+    gamma[0] = sqrt(norm2(r));
+
+    ComplexD scale = 1.0/gamma[0];
+    v[0] = scale * r;
+
+    LinalgTimer.Stop();
+
+    for (int i=0; i<RestartLength; i++) {
+
+      IterationCount++;
+
+      arnoldiStep(LinOp, v, w, i);
+
+      qrUpdate(i);
+
+      cp = norm(gamma[i+1]);
+
+      std::cout << GridLogIterative << "CommunicationAvoidingGeneralisedMinimalResidual: Iteration " << IterationCount
+                << " residual " << cp << " target " << rsq << std::endl;
+
+      if ((i == RestartLength - 1) || (IterationCount == MaxIterations) || (cp <= rsq)) {
+
+        computeSolution(v, psi, i);
+
+        return cp;
+      }
+    }
+
+    assert(0); // Never reached
+    return cp;
+  }
+
+  void arnoldiStep(LinearOperatorBase<Field> &LinOp, std::vector<Field> &v, Field &w, int iter) {
+
+    MatrixTimer.Start();
+    LinOp.Op(v[iter], w);
+    MatrixTimer.Stop();
+
+    LinalgTimer.Start();
+    for (int i = 0; i <= iter; ++i) {
+      H(iter, i) = innerProduct(v[i], w);
+      w = w - ComplexD(H(iter, i)) * v[i];
+    }
+
+    H(iter, iter + 1) = sqrt(norm2(w));
+    v[iter + 1] = ComplexD(1. / H(iter, iter + 1)) * w;
+    LinalgTimer.Stop();
+  }
+
+  void qrUpdate(int iter) {
+
+    QrTimer.Start();
+    for (int i = 0; i < iter ; ++i) {
+      auto tmp       = -s[i] * ComplexD(H(iter, i)) + c[i] * ComplexD(H(iter, i + 1));
+      H(iter, i)     = conjugate(c[i]) * ComplexD(H(iter, i)) + conjugate(s[i]) * ComplexD(H(iter, i + 1));
+      H(iter, i + 1) = tmp;
+    }
+
+    // Compute new Givens Rotation
+    auto nu     = sqrt(std::norm(H(iter, iter)) + std::norm(H(iter, iter + 1)));
+    c[iter]     = H(iter, iter) / nu;
+    s[iter]     = H(iter, iter + 1) / nu;
+
+    // Apply new Givens rotation
+    H(iter, iter)     = nu;
+    H(iter, iter + 1) = 0.;
+
+    gamma[iter + 1] = -s[iter] * gamma[iter];
+    gamma[iter]     = conjugate(c[iter]) * gamma[iter];
+    QrTimer.Stop();
+  }
+
+  void computeSolution(std::vector<Field> const &v, Field &psi, int iter) {
+
+    CompSolutionTimer.Start();
+    for (int i = iter; i >= 0; i--) {
+      y[i] = gamma[i];
+      for (int k = i + 1; k <= iter; k++)
+        y[i] = y[i] - ComplexD(H(k, i)) * y[k];
+      y[i] = y[i] / ComplexD(H(i, i));
+    }
+
+    for (int i = 0; i <= iter; i++)
+      psi = psi + v[i] * y[i];
+    CompSolutionTimer.Stop();
+  }
+};
+}
+#endif

Grid/algorithms/iterative/ConjugateGradient.h

@@ -27,11 +27,11 @@ with this program; if not, write to the Free Software Foundation, Inc.,
 See the full license in the file "LICENSE" in the top level distribution
 directory
 *************************************************************************************/
-/*  END LEGAL */
+			   /*  END LEGAL */
 #ifndef GRID_CONJUGATE_GRADIENT_H
 #define GRID_CONJUGATE_GRADIENT_H
 
-namespace Grid {
+NAMESPACE_BEGIN(Grid);
 
 /////////////////////////////////////////////////////////////
 // Base classes for iterative processes based on operators
@@ -40,25 +40,30 @@ namespace Grid {
 
 template <class Field>
 class ConjugateGradient : public OperatorFunction<Field> {
- public:
+public:
+
+  using OperatorFunction<Field>::operator();
+
   bool ErrorOnNoConverge;  // throw an assert when the CG fails to converge.
                            // Defaults true.
   RealD Tolerance;
   Integer MaxIterations;
   Integer IterationsToComplete; //Number of iterations the CG took to finish. Filled in upon completion
+  RealD TrueResidual;
   
   ConjugateGradient(RealD tol, Integer maxit, bool err_on_no_conv = true)
-      : Tolerance(tol),
-        MaxIterations(maxit),
-        ErrorOnNoConverge(err_on_no_conv){};
+    : Tolerance(tol),
+      MaxIterations(maxit),
+      ErrorOnNoConverge(err_on_no_conv){};
 
   void operator()(LinearOperatorBase<Field> &Linop, const Field &src, Field &psi) {
 
+    psi.Checkerboard() = src.Checkerboard();
 
-    psi.checkerboard = src.checkerboard;
     conformable(psi, src);
 
-    RealD cp, c, a, d, b, ssq, qq, b_pred;
+    RealD cp, c, a, d, b, ssq, qq;
+    //RealD b_pred;
 
     Field p(src);
     Field mmp(src);
@@ -68,7 +73,6 @@ class ConjugateGradient : public OperatorFunction<Field> {
     RealD guess = norm2(psi);
     assert(std::isnan(guess) == 0);
     
-    
     Linop.HermOpAndNorm(psi, mmp, d, b);
     
     r = src - mmp;
@@ -78,6 +82,14 @@ class ConjugateGradient : public OperatorFunction<Field> {
     cp = a;
     ssq = norm2(src);
 
+    // Handle trivial case of zero src
+    if (ssq == 0.){
+      psi = Zero();
+      IterationsToComplete = 1;
+      TrueResidual = 0.;
+      return;
+    }
+
     std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient: guess " << guess << std::endl;
     std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:   src " << ssq << std::endl;
     std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:    mp " << d << std::endl;
@@ -89,6 +101,9 @@ class ConjugateGradient : public OperatorFunction<Field> {
 
     // Check if guess is really REALLY good :)
     if (cp <= rsq) {
+      TrueResidual = std::sqrt(a/ssq);
+      std::cout << GridLogMessage << "ConjugateGradient guess is converged already " << std::endl;
+      IterationsToComplete = 0;	
       return;
     }
 
@@ -104,7 +119,7 @@ class ConjugateGradient : public OperatorFunction<Field> {
 
     SolverTimer.Start();
     int k;
-    for (k = 1; k <= MaxIterations*1000; k++) {
+    for (k = 1; k <= MaxIterations; k++) {
       c = cp;
 
       MatrixTimer.Start();
@@ -125,15 +140,20 @@ class ConjugateGradient : public OperatorFunction<Field> {
       b = cp / c;
 
       LinearCombTimer.Start();
-      parallel_for(int ss=0;ss<src._grid->oSites();ss++){
-	vstream(psi[ss], a      *  p[ss] + psi[ss]);
-	vstream(p  [ss], b      *  p[ss] + r[ss]);
+      {
+	autoView( psi_v , psi, AcceleratorWrite);
+	autoView( p_v   , p,   AcceleratorWrite);
+	autoView( r_v   , r,   AcceleratorWrite);
+	accelerator_for(ss,p_v.size(), Field::vector_object::Nsimd(),{
+	    coalescedWrite(psi_v[ss], a      *  p_v(ss) + psi_v(ss));
+	    coalescedWrite(p_v[ss]  , b      *  p_v(ss) + r_v  (ss));
+	});
       }
       LinearCombTimer.Stop();
       LinalgTimer.Stop();
 
       std::cout << GridLogIterative << "ConjugateGradient: Iteration " << k
-                << " residual " << cp << " target " << rsq << std::endl;
+                << " residual " << sqrt(cp/ssq) << " target " << Tolerance << std::endl;
 
       // Stopping condition
       if (cp <= rsq) {
@@ -141,37 +161,43 @@ class ConjugateGradient : public OperatorFunction<Field> {
         Linop.HermOpAndNorm(psi, mmp, d, qq);
         p = mmp - src;
 
-        RealD srcnorm = sqrt(norm2(src));
-        RealD resnorm = sqrt(norm2(p));
+        RealD srcnorm = std::sqrt(norm2(src));
+        RealD resnorm = std::sqrt(norm2(p));
         RealD true_residual = resnorm / srcnorm;
 
-        std::cout << GridLogMessage << "ConjugateGradient Converged on iteration " << k << std::endl;
-        std::cout << GridLogMessage << "\tComputed residual " << sqrt(cp / ssq)<<std::endl;
-	std::cout << GridLogMessage << "\tTrue residual " << true_residual<<std::endl;
-	std::cout << GridLogMessage << "\tTarget " << Tolerance << std::endl;
+        std::cout << GridLogMessage << "ConjugateGradient Converged on iteration " << k 
+		  << "\tComputed residual " << std::sqrt(cp / ssq)
+		  << "\tTrue residual " << true_residual
+		  << "\tTarget " << Tolerance << std::endl;
 
-        std::cout << GridLogMessage << "Time breakdown "<<std::endl;
-	std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tInner      " << InnerTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
+        std::cout << GridLogIterative << "Time breakdown "<<std::endl;
+	std::cout << GridLogIterative << "\tElapsed    " << SolverTimer.Elapsed() <<std::endl;
+	std::cout << GridLogIterative << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+	std::cout << GridLogIterative << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
+	std::cout << GridLogIterative << "\tInner      " << InnerTimer.Elapsed() <<std::endl;
+	std::cout << GridLogIterative << "\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
+	std::cout << GridLogIterative << "\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
 
         if (ErrorOnNoConverge) assert(true_residual / Tolerance < 10000.0);
 
 	IterationsToComplete = k;	
+	TrueResidual = true_residual;
 
         return;
       }
     }
-    std::cout << GridLogMessage << "ConjugateGradient did NOT converge"
-              << std::endl;
+    // Failed. Calculate true residual before giving up                                                         
+    Linop.HermOpAndNorm(psi, mmp, d, qq);
+    p = mmp - src;
+
+    TrueResidual = sqrt(norm2(p)/ssq);
+
+    std::cout << GridLogMessage << "ConjugateGradient did NOT converge "<<k<<" / "<< MaxIterations<< std::endl;
 
     if (ErrorOnNoConverge) assert(0);
     IterationsToComplete = k;
 
   }
 };
-}
+NAMESPACE_END(Grid);
 #endif

Grid/algorithms/iterative/ConjugateGradientMixedPrec.h

@@ -0,0 +1,161 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ConjugateGradientMixedPrec.h
+
+    Copyright (C) 2015
+
+Author: Christopher Kelly <ckelly@phys.columbia.edu>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CONJUGATE_GRADIENT_MIXED_PREC_H
+#define GRID_CONJUGATE_GRADIENT_MIXED_PREC_H
+
+NAMESPACE_BEGIN(Grid);
+
+  //Mixed precision restarted defect correction CG
+  template<class FieldD,class FieldF, 
+    typename std::enable_if< getPrecision<FieldD>::value == 2, int>::type = 0,
+    typename std::enable_if< getPrecision<FieldF>::value == 1, int>::type = 0> 
+  class MixedPrecisionConjugateGradient : public LinearFunction<FieldD> {
+  public:                                                
+    RealD   Tolerance;
+    RealD   InnerTolerance; //Initial tolerance for inner CG. Defaults to Tolerance but can be changed
+    Integer MaxInnerIterations;
+    Integer MaxOuterIterations;
+    GridBase* SinglePrecGrid; //Grid for single-precision fields
+    RealD OuterLoopNormMult; //Stop the outer loop and move to a final double prec solve when the residual is OuterLoopNormMult * Tolerance
+    LinearOperatorBase<FieldF> &Linop_f;
+    LinearOperatorBase<FieldD> &Linop_d;
+
+    Integer TotalInnerIterations; //Number of inner CG iterations
+    Integer TotalOuterIterations; //Number of restarts
+    Integer TotalFinalStepIterations; //Number of CG iterations in final patch-up step
+
+    //Option to speed up *inner single precision* solves using a LinearFunction that produces a guess
+    LinearFunction<FieldF> *guesser;
+    
+    MixedPrecisionConjugateGradient(RealD tol, 
+				    Integer maxinnerit, 
+				    Integer maxouterit, 
+				    GridBase* _sp_grid, 
+				    LinearOperatorBase<FieldF> &_Linop_f, 
+				    LinearOperatorBase<FieldD> &_Linop_d) :
+      Linop_f(_Linop_f), Linop_d(_Linop_d),
+      Tolerance(tol), InnerTolerance(tol), MaxInnerIterations(maxinnerit), MaxOuterIterations(maxouterit), SinglePrecGrid(_sp_grid),
+      OuterLoopNormMult(100.), guesser(NULL){ };
+
+    void useGuesser(LinearFunction<FieldF> &g){
+      guesser = &g;
+    }
+  
+  void operator() (const FieldD &src_d_in, FieldD &sol_d){
+    TotalInnerIterations = 0;
+	
+    GridStopWatch TotalTimer;
+    TotalTimer.Start();
+    
+    int cb = src_d_in.Checkerboard();
+    sol_d.Checkerboard() = cb;
+    
+    RealD src_norm = norm2(src_d_in);
+    RealD stop = src_norm * Tolerance*Tolerance;
+
+    GridBase* DoublePrecGrid = src_d_in.Grid();
+    FieldD tmp_d(DoublePrecGrid);
+    tmp_d.Checkerboard() = cb;
+    
+    FieldD tmp2_d(DoublePrecGrid);
+    tmp2_d.Checkerboard() = cb;
+    
+    FieldD src_d(DoublePrecGrid);
+    src_d = src_d_in; //source for next inner iteration, computed from residual during operation
+    
+    RealD inner_tol = InnerTolerance;
+    
+    FieldF src_f(SinglePrecGrid);
+    src_f.Checkerboard() = cb;
+    
+    FieldF sol_f(SinglePrecGrid);
+    sol_f.Checkerboard() = cb;
+    
+    ConjugateGradient<FieldF> CG_f(inner_tol, MaxInnerIterations);
+    CG_f.ErrorOnNoConverge = false;
+
+    GridStopWatch InnerCGtimer;
+
+    GridStopWatch PrecChangeTimer;
+    
+    Integer &outer_iter = TotalOuterIterations; //so it will be equal to the final iteration count
+      
+    for(outer_iter = 0; outer_iter < MaxOuterIterations; outer_iter++){
+      //Compute double precision rsd and also new RHS vector.
+      Linop_d.HermOp(sol_d, tmp_d);
+      RealD norm = axpy_norm(src_d, -1., tmp_d, src_d_in); //src_d is residual vector
+      
+      std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradient: Outer iteration " <<outer_iter<<" residual "<< norm<< " target "<< stop<<std::endl;
+
+      if(norm < OuterLoopNormMult * stop){
+	std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradient: Outer iteration converged on iteration " <<outer_iter <<std::endl;
+	break;
+      }
+      while(norm * inner_tol * inner_tol < stop) inner_tol *= 2;  // inner_tol = sqrt(stop/norm) ??
+
+      PrecChangeTimer.Start();
+      precisionChange(src_f, src_d);
+      PrecChangeTimer.Stop();
+      
+      sol_f = Zero();
+
+      //Optionally improve inner solver guess (eg using known eigenvectors)
+      if(guesser != NULL)
+	(*guesser)(src_f, sol_f);
+
+      //Inner CG
+      CG_f.Tolerance = inner_tol;
+      InnerCGtimer.Start();
+      CG_f(Linop_f, src_f, sol_f);
+      InnerCGtimer.Stop();
+      TotalInnerIterations += CG_f.IterationsToComplete;
+      
+      //Convert sol back to double and add to double prec solution
+      PrecChangeTimer.Start();
+      precisionChange(tmp_d, sol_f);
+      PrecChangeTimer.Stop();
+      
+      axpy(sol_d, 1.0, tmp_d, sol_d);
+    }
+    
+    //Final trial CG
+    std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradient: Starting final patch-up double-precision solve"<<std::endl;
+    
+    ConjugateGradient<FieldD> CG_d(Tolerance, MaxInnerIterations);
+    CG_d(Linop_d, src_d_in, sol_d);
+    TotalFinalStepIterations = CG_d.IterationsToComplete;
+
+    TotalTimer.Stop();
+    std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradient: Inner CG iterations " << TotalInnerIterations << " Restarts " << TotalOuterIterations << " Final CG iterations " << TotalFinalStepIterations << std::endl;
+    std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradient: Total time " << TotalTimer.Elapsed() << " Precision change " << PrecChangeTimer.Elapsed() << " Inner CG total " << InnerCGtimer.Elapsed() << std::endl;
+  }
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/algorithms/iterative/ConjugateGradientMultiShift.h

@@ -0,0 +1,342 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ConjugateGradientMultiShift.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CONJUGATE_MULTI_SHIFT_GRADIENT_H
+#define GRID_CONJUGATE_MULTI_SHIFT_GRADIENT_H
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////
+// Base classes for iterative processes based on operators
+// single input vec, single output vec.
+/////////////////////////////////////////////////////////////
+
+template<class Field> 
+class ConjugateGradientMultiShift : public OperatorMultiFunction<Field>,
+				    public OperatorFunction<Field>
+{
+public:                                                
+
+  using OperatorFunction<Field>::operator();
+
+  RealD   Tolerance;
+  Integer MaxIterations;
+  Integer IterationsToComplete; //Number of iterations the CG took to finish. Filled in upon completion
+  std::vector<int> IterationsToCompleteShift;  // Iterations for this shift
+  int verbose;
+  MultiShiftFunction shifts;
+  std::vector<RealD> TrueResidualShift;
+
+  ConjugateGradientMultiShift(Integer maxit,MultiShiftFunction &_shifts) : 
+    MaxIterations(maxit),
+    shifts(_shifts)
+  { 
+    verbose=1;
+    IterationsToCompleteShift.resize(_shifts.order);
+    TrueResidualShift.resize(_shifts.order);
+  }
+
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &src, Field &psi)
+  {
+    GridBase *grid = src.Grid();
+    int nshift = shifts.order;
+    std::vector<Field> results(nshift,grid);
+    (*this)(Linop,src,results,psi);
+  }
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &src, std::vector<Field> &results, Field &psi)
+  {
+    int nshift = shifts.order;
+
+    (*this)(Linop,src,results);
+  
+    psi = shifts.norm*src;
+    for(int i=0;i<nshift;i++){
+      psi = psi + shifts.residues[i]*results[i];
+    }
+
+    return;
+  }
+
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &src, std::vector<Field> &psi)
+  {
+  
+    GridBase *grid = src.Grid();
+  
+    ////////////////////////////////////////////////////////////////////////
+    // Convenience references to the info stored in "MultiShiftFunction"
+    ////////////////////////////////////////////////////////////////////////
+    int nshift = shifts.order;
+
+    std::vector<RealD> &mass(shifts.poles); // Make references to array in "shifts"
+    std::vector<RealD> &mresidual(shifts.tolerances);
+    std::vector<RealD> alpha(nshift,1.0);
+    std::vector<Field>   ps(nshift,grid);// Search directions
+
+    assert(psi.size()==nshift);
+    assert(mass.size()==nshift);
+    assert(mresidual.size()==nshift);
+  
+    // dynamic sized arrays on stack; 2d is a pain with vector
+    RealD  bs[nshift];
+    RealD  rsq[nshift];
+    RealD  z[nshift][2];
+    int     converged[nshift];
+  
+    const int       primary =0;
+  
+    //Primary shift fields CG iteration
+    RealD a,b,c,d;
+    RealD cp,bp,qq; //prev
+  
+    // Matrix mult fields
+    Field r(grid);
+    Field p(grid);
+    Field tmp(grid);
+    Field mmp(grid);
+  
+    // Check lightest mass
+    for(int s=0;s<nshift;s++){
+      assert( mass[s]>= mass[primary] );
+      converged[s]=0;
+    }
+  
+    // Wire guess to zero
+    // Residuals "r" are src
+    // First search direction "p" is also src
+    cp = norm2(src);
+
+    // Handle trivial case of zero src.
+    if( cp == 0. ){
+      for(int s=0;s<nshift;s++){
+	psi[s] = Zero();
+	IterationsToCompleteShift[s] = 1;
+	TrueResidualShift[s] = 0.;
+      }
+      return;
+    }
+
+    for(int s=0;s<nshift;s++){
+      rsq[s] = cp * mresidual[s] * mresidual[s];
+      std::cout<<GridLogMessage<<"ConjugateGradientMultiShift: shift "<<s
+	       <<" target resid "<<rsq[s]<<std::endl;
+      ps[s] = src;
+    }
+    // r and p for primary
+    r=src;
+    p=src;
+  
+    //MdagM+m[0]
+    Linop.HermOpAndNorm(p,mmp,d,qq);
+    axpy(mmp,mass[0],p,mmp);
+    RealD rn = norm2(p);
+    d += rn*mass[0];
+  
+    // have verified that inner product of 
+    // p and mmp is equal to d after this since
+    // the d computation is tricky
+    //  qq = real(innerProduct(p,mmp));
+    //  std::cout<<GridLogMessage << "debug equal ?  qq "<<qq<<" d "<< d<<std::endl;
+  
+    b = -cp /d;
+  
+    // Set up the various shift variables
+    int       iz=0;
+    z[0][1-iz] = 1.0;
+    z[0][iz]   = 1.0;
+    bs[0]      = b;
+    for(int s=1;s<nshift;s++){
+      z[s][1-iz] = 1.0;
+      z[s][iz]   = 1.0/( 1.0 - b*(mass[s]-mass[0]));
+      bs[s]      = b*z[s][iz]; 
+    }
+  
+    // r += b[0] A.p[0]
+    // c= norm(r)
+    c=axpy_norm(r,b,mmp,r);
+  
+    for(int s=0;s<nshift;s++) {
+      axpby(psi[s],0.,-bs[s]*alpha[s],src,src);
+    }
+  
+  ///////////////////////////////////////
+  // Timers
+  ///////////////////////////////////////
+  GridStopWatch AXPYTimer;
+  GridStopWatch ShiftTimer;
+  GridStopWatch QRTimer;
+  GridStopWatch MatrixTimer;
+  GridStopWatch SolverTimer;
+  SolverTimer.Start();
+  
+    // Iteration loop
+    int k;
+  
+    for (k=1;k<=MaxIterations;k++){
+    
+      a = c /cp;
+    AXPYTimer.Start();
+      axpy(p,a,p,r);
+    AXPYTimer.Stop();
+    
+      // Note to self - direction ps is iterated seperately
+      // for each shift. Does not appear to have any scope
+      // for avoiding linear algebra in "single" case.
+      // 
+      // However SAME r is used. Could load "r" and update
+      // ALL ps[s]. 2/3 Bandwidth saving
+      // New Kernel: Load r, vector of coeffs, vector of pointers ps
+    AXPYTimer.Start();
+      for(int s=0;s<nshift;s++){
+	if ( ! converged[s] ) { 
+	  if (s==0){
+	    axpy(ps[s],a,ps[s],r);
+	  } else{
+	    RealD as =a *z[s][iz]*bs[s] /(z[s][1-iz]*b);
+	    axpby(ps[s],z[s][iz],as,r,ps[s]);
+	  }
+	}
+      }
+    AXPYTimer.Stop();
+    
+      cp=c;
+    MatrixTimer.Start();  
+    //Linop.HermOpAndNorm(p,mmp,d,qq); // d is used
+    // The below is faster on KNL
+    Linop.HermOp(p,mmp); 
+    d=real(innerProduct(p,mmp));
+    
+    MatrixTimer.Stop();  
+
+    AXPYTimer.Start();
+      axpy(mmp,mass[0],p,mmp);
+    AXPYTimer.Stop();
+      RealD rn = norm2(p);
+      d += rn*mass[0];
+    
+      bp=b;
+      b=-cp/d;
+    
+    AXPYTimer.Start();
+      c=axpy_norm(r,b,mmp,r);
+    AXPYTimer.Stop();
+
+      // Toggle the recurrence history
+      bs[0] = b;
+      iz = 1-iz;
+    ShiftTimer.Start();
+      for(int s=1;s<nshift;s++){
+	if((!converged[s])){
+	  RealD z0 = z[s][1-iz];
+	  RealD z1 = z[s][iz];
+	  z[s][iz] = z0*z1*bp
+	    / (b*a*(z1-z0) + z1*bp*(1- (mass[s]-mass[0])*b)); 
+	  bs[s] = b*z[s][iz]/z0; // NB sign  rel to Mike
+	}
+      }
+    ShiftTimer.Stop();
+    
+      for(int s=0;s<nshift;s++){
+	int ss = s;
+	// Scope for optimisation here in case of "single".
+	// Could load psi[0] and pull all ps[s] in.
+	//      if ( single ) ss=primary;
+	// Bandwith saving in single case is Ls * 3 -> 2+Ls, so ~ 3x saving
+	// Pipelined CG gain:
+	//
+	// New Kernel: Load r, vector of coeffs, vector of pointers ps
+	// New Kernel: Load psi[0], vector of coeffs, vector of pointers ps
+	// If can predict the coefficient bs then we can fuse these and avoid write reread cyce
+	//  on ps[s].
+	// Before:  3 x npole  + 3 x npole
+	// After :  2 x npole (ps[s])        => 3x speed up of multishift CG.
+      
+	if( (!converged[s]) ) { 
+	  axpy(psi[ss],-bs[s]*alpha[s],ps[s],psi[ss]);
+	}
+      }
+    
+      // Convergence checks
+      int all_converged = 1;
+      for(int s=0;s<nshift;s++){
+      
+	if ( (!converged[s]) ){
+	  IterationsToCompleteShift[s] = k;
+	
+	  RealD css  = c * z[s][iz]* z[s][iz];
+	
+	  if(css<rsq[s]){
+	    if ( ! converged[s] )
+	      std::cout<<GridLogMessage<<"ConjugateGradientMultiShift k="<<k<<" Shift "<<s<<" has converged"<<std::endl;
+	    converged[s]=1;
+	  } else {
+	    all_converged=0;
+	  }
+
+	}
+      }
+    
+      if ( all_converged ){
+
+    SolverTimer.Stop();
+
+
+	std::cout<<GridLogMessage<< "CGMultiShift: All shifts have converged iteration "<<k<<std::endl;
+	std::cout<<GridLogMessage<< "CGMultiShift: Checking solutions"<<std::endl;
+      
+	// Check answers 
+	for(int s=0; s < nshift; s++) { 
+	  Linop.HermOpAndNorm(psi[s],mmp,d,qq);
+	  axpy(tmp,mass[s],psi[s],mmp);
+	  axpy(r,-alpha[s],src,tmp);
+	  RealD rn = norm2(r);
+	  RealD cn = norm2(src);
+	  TrueResidualShift[s] = std::sqrt(rn/cn);
+	  std::cout<<GridLogMessage<<"CGMultiShift: shift["<<s<<"] true residual "<< TrueResidualShift[s] <<std::endl;
+	}
+
+      std::cout << GridLogMessage << "Time Breakdown "<<std::endl;
+      std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tAXPY    " << AXPYTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tMarix    " << MatrixTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tShift    " << ShiftTimer.Elapsed()     <<std::endl;
+
+      IterationsToComplete = k;	
+
+	return;
+      }
+
+   
+    }
+    // ugly hack
+    std::cout<<GridLogMessage<<"CG multi shift did not converge"<<std::endl;
+    //  assert(0);
+  }
+
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/ConjugateGradientReliableUpdate.h

@@ -0,0 +1,258 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ConjugateGradientReliableUpdate.h
+
+    Copyright (C) 2015
+
+Author: Christopher Kelly <ckelly@phys.columbia.edu>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CONJUGATE_GRADIENT_RELIABLE_UPDATE_H
+#define GRID_CONJUGATE_GRADIENT_RELIABLE_UPDATE_H
+
+NAMESPACE_BEGIN(Grid);
+
+template<class FieldD,class FieldF, 
+	 typename std::enable_if< getPrecision<FieldD>::value == 2, int>::type = 0,
+	 typename std::enable_if< getPrecision<FieldF>::value == 1, int>::type = 0> 
+class ConjugateGradientReliableUpdate : public LinearFunction<FieldD> {
+public:
+  bool ErrorOnNoConverge;  // throw an assert when the CG fails to converge.
+  // Defaults true.
+  RealD Tolerance;
+  Integer MaxIterations;
+  Integer IterationsToComplete; //Number of iterations the CG took to finish. Filled in upon completion
+  Integer ReliableUpdatesPerformed;
+
+  bool DoFinalCleanup; //Final DP cleanup, defaults to true
+  Integer IterationsToCleanup; //Final DP cleanup step iterations
+    
+  LinearOperatorBase<FieldF> &Linop_f;
+  LinearOperatorBase<FieldD> &Linop_d;
+  GridBase* SinglePrecGrid;
+  RealD Delta; //reliable update parameter
+
+  //Optional ability to switch to a different linear operator once the tolerance reaches a certain point. Useful for single/half -> single/single
+  LinearOperatorBase<FieldF> *Linop_fallback;
+  RealD fallback_transition_tol;
+
+    
+  ConjugateGradientReliableUpdate(RealD tol, Integer maxit, RealD _delta, GridBase* _sp_grid, LinearOperatorBase<FieldF> &_Linop_f, LinearOperatorBase<FieldD> &_Linop_d, bool err_on_no_conv = true)
+    : Tolerance(tol),
+      MaxIterations(maxit),
+      Delta(_delta),
+      Linop_f(_Linop_f),
+      Linop_d(_Linop_d),
+      SinglePrecGrid(_sp_grid),
+      ErrorOnNoConverge(err_on_no_conv),
+      DoFinalCleanup(true),
+      Linop_fallback(NULL)
+  {};
+
+  void setFallbackLinop(LinearOperatorBase<FieldF> &_Linop_fallback, const RealD _fallback_transition_tol){
+    Linop_fallback = &_Linop_fallback;
+    fallback_transition_tol = _fallback_transition_tol;      
+  }
+    
+  void operator()(const FieldD &src, FieldD &psi) {
+    LinearOperatorBase<FieldF> *Linop_f_use = &Linop_f;
+    bool using_fallback = false;
+      
+    psi.Checkerboard() = src.Checkerboard();
+    conformable(psi, src);
+
+    RealD cp, c, a, d, b, ssq, qq, b_pred;
+
+    FieldD p(src);
+    FieldD mmp(src);
+    FieldD r(src);
+
+    // Initial residual computation & set up
+    RealD guess = norm2(psi);
+    assert(std::isnan(guess) == 0);
+    
+    Linop_d.HermOpAndNorm(psi, mmp, d, b);
+    
+    r = src - mmp;
+    p = r;
+
+    a = norm2(p);
+    cp = a;
+    ssq = norm2(src);
+
+    std::cout << GridLogIterative << std::setprecision(4) << "ConjugateGradientReliableUpdate: guess " << guess << std::endl;
+    std::cout << GridLogIterative << std::setprecision(4) << "ConjugateGradientReliableUpdate:   src " << ssq << std::endl;
+    std::cout << GridLogIterative << std::setprecision(4) << "ConjugateGradientReliableUpdate:    mp " << d << std::endl;
+    std::cout << GridLogIterative << std::setprecision(4) << "ConjugateGradientReliableUpdate:   mmp " << b << std::endl;
+    std::cout << GridLogIterative << std::setprecision(4) << "ConjugateGradientReliableUpdate:  cp,r " << cp << std::endl;
+    std::cout << GridLogIterative << std::setprecision(4) << "ConjugateGradientReliableUpdate:     p " << a << std::endl;
+
+    RealD rsq = Tolerance * Tolerance * ssq;
+
+    // Check if guess is really REALLY good :)
+    if (cp <= rsq) {
+      std::cout << GridLogMessage << "ConjugateGradientReliableUpdate guess was REALLY good\n";
+      std::cout << GridLogMessage << "\tComputed residual " << std::sqrt(cp / ssq)<<std::endl;
+      return;
+    }
+
+    //Single prec initialization
+    FieldF r_f(SinglePrecGrid);
+    r_f.Checkerboard() = r.Checkerboard();
+    precisionChange(r_f, r);
+
+    FieldF psi_f(r_f);
+    psi_f = Zero();
+
+    FieldF p_f(r_f);
+    FieldF mmp_f(r_f);
+
+    RealD MaxResidSinceLastRelUp = cp; //initial residual    
+    
+    std::cout << GridLogIterative << std::setprecision(4)
+	      << "ConjugateGradient: k=0 residual " << cp << " target " << rsq << std::endl;
+
+    GridStopWatch LinalgTimer;
+    GridStopWatch MatrixTimer;
+    GridStopWatch SolverTimer;
+
+    SolverTimer.Start();
+    int k = 0;
+    int l = 0;
+    
+    for (k = 1; k <= MaxIterations; k++) {
+      c = cp;
+
+      MatrixTimer.Start();
+      Linop_f_use->HermOpAndNorm(p_f, mmp_f, d, qq);
+      MatrixTimer.Stop();
+
+      LinalgTimer.Start();
+
+      a = c / d;
+      b_pred = a * (a * qq - d) / c;
+
+      cp = axpy_norm(r_f, -a, mmp_f, r_f);
+      b = cp / c;
+
+      // Fuse these loops ; should be really easy
+      psi_f = a * p_f + psi_f;
+      //p_f = p_f * b + r_f;
+
+      LinalgTimer.Stop();
+
+      std::cout << GridLogIterative << "ConjugateGradientReliableUpdate: Iteration " << k
+		<< " residual " << cp << " target " << rsq << std::endl;
+      std::cout << GridLogDebug << "a = "<< a << " b_pred = "<< b_pred << "  b = "<< b << std::endl;
+      std::cout << GridLogDebug << "qq = "<< qq << " d = "<< d << "  c = "<< c << std::endl;
+
+      if(cp > MaxResidSinceLastRelUp){
+	std::cout << GridLogIterative << "ConjugateGradientReliableUpdate: updating MaxResidSinceLastRelUp : " << MaxResidSinceLastRelUp << " -> " << cp << std::endl;
+	MaxResidSinceLastRelUp = cp;
+      }
+	  
+      // Stopping condition
+      if (cp <= rsq) {
+	//Although not written in the paper, I assume that I have to add on the final solution
+	precisionChange(mmp, psi_f);
+	psi = psi + mmp;
+	
+	
+	SolverTimer.Stop();
+	Linop_d.HermOpAndNorm(psi, mmp, d, qq);
+	p = mmp - src;
+
+	RealD srcnorm = std::sqrt(norm2(src));
+	RealD resnorm = std::sqrt(norm2(p));
+	RealD true_residual = resnorm / srcnorm;
+
+	std::cout << GridLogMessage << "ConjugateGradientReliableUpdate Converged on iteration " << k << " after " << l << " reliable updates" << std::endl;
+	std::cout << GridLogMessage << "\tComputed residual " << std::sqrt(cp / ssq)<<std::endl;
+	std::cout << GridLogMessage << "\tTrue residual " << true_residual<<std::endl;
+	std::cout << GridLogMessage << "\tTarget " << Tolerance << std::endl;
+
+	std::cout << GridLogMessage << "Time breakdown "<<std::endl;
+	std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
+
+	IterationsToComplete = k;	
+	ReliableUpdatesPerformed = l;
+	  
+	if(DoFinalCleanup){
+	  //Do a final CG to cleanup
+	  std::cout << GridLogMessage << "ConjugateGradientReliableUpdate performing final cleanup.\n";
+	  ConjugateGradient<FieldD> CG(Tolerance,MaxIterations);
+	  CG.ErrorOnNoConverge = ErrorOnNoConverge;
+	  CG(Linop_d,src,psi);
+	  IterationsToCleanup = CG.IterationsToComplete;
+	}
+	else if (ErrorOnNoConverge) assert(true_residual / Tolerance < 10000.0);
+
+	std::cout << GridLogMessage << "ConjugateGradientReliableUpdate complete.\n";
+	return;
+      }
+      else if(cp < Delta * MaxResidSinceLastRelUp) { //reliable update
+	std::cout << GridLogMessage << "ConjugateGradientReliableUpdate "
+		  << cp << "(residual) < " << Delta << "(Delta) * " << MaxResidSinceLastRelUp << "(MaxResidSinceLastRelUp) on iteration " << k << " : performing reliable update\n";
+	precisionChange(mmp, psi_f);
+	psi = psi + mmp;
+
+	Linop_d.HermOpAndNorm(psi, mmp, d, qq);
+	r = src - mmp;
+
+	psi_f = Zero();
+	precisionChange(r_f, r);
+	cp = norm2(r);
+	MaxResidSinceLastRelUp = cp;
+
+	b = cp/c;
+	  
+	std::cout << GridLogMessage << "ConjugateGradientReliableUpdate new residual " << cp << std::endl;
+	  
+	l = l+1;
+      }
+
+      p_f = p_f * b + r_f; //update search vector after reliable update appears to help convergence
+
+      if(!using_fallback && Linop_fallback != NULL && cp < fallback_transition_tol){
+	std::cout << GridLogMessage << "ConjugateGradientReliableUpdate switching to fallback linear operator on iteration " << k << " at residual " << cp << std::endl;
+	Linop_f_use = Linop_fallback;
+	using_fallback = true;
+      }
+
+	
+    }
+    std::cout << GridLogMessage << "ConjugateGradientReliableUpdate did NOT converge"
+	      << std::endl;
+      
+    if (ErrorOnNoConverge) assert(0);
+    IterationsToComplete = k;
+    ReliableUpdatesPerformed = l;      
+  }    
+};
+
+
+NAMESPACE_END(Grid);
+
+
+
+#endif

Grid/algorithms/iterative/ConjugateResidual.h

@@ -0,0 +1,113 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ConjugateResidual.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CONJUGATE_RESIDUAL_H
+#define GRID_CONJUGATE_RESIDUAL_H
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////
+// Base classes for iterative processes based on operators
+// single input vec, single output vec.
+/////////////////////////////////////////////////////////////
+
+template<class Field> 
+class ConjugateResidual : public OperatorFunction<Field> {
+public:                                                
+  using OperatorFunction<Field>::operator();
+
+  RealD   Tolerance;
+  Integer MaxIterations;
+  int verbose;
+
+  ConjugateResidual(RealD tol,Integer maxit) : Tolerance(tol), MaxIterations(maxit) { 
+    verbose=0;
+  };
+
+  void operator() (LinearOperatorBase<Field> &Linop,const Field &src, Field &psi){
+
+    RealD a, b; // c, d;
+    RealD cp, ssq,rsq;
+      
+    RealD rAr, rAAr, rArp;
+    RealD pAp, pAAp;
+
+    GridBase *grid = src.Grid();
+    psi=Zero();
+    Field r(grid),  p(grid), Ap(grid), Ar(grid);
+      
+    r=src;
+    p=src;
+
+    Linop.HermOpAndNorm(p,Ap,pAp,pAAp);
+    Linop.HermOpAndNorm(r,Ar,rAr,rAAr);
+
+    cp =norm2(r);
+    ssq=norm2(src);
+    rsq=Tolerance*Tolerance*ssq;
+
+    if (verbose) std::cout<<GridLogMessage<<"ConjugateResidual: iteration " <<0<<" residual "<<cp<< " target"<< rsq<<std::endl;
+
+    for(int k=1;k<MaxIterations;k++){
+
+      a = rAr/pAAp;
+
+      axpy(psi,a,p,psi);
+
+      cp = axpy_norm(r,-a,Ap,r);
+
+      rArp=rAr;
+
+      Linop.HermOpAndNorm(r,Ar,rAr,rAAr);
+
+      b   =rAr/rArp;
+ 
+      axpy(p,b,p,r);
+      pAAp=axpy_norm(Ap,b,Ap,Ar);
+	
+      if(verbose) std::cout<<GridLogMessage<<"ConjugateResidual: iteration " <<k<<" residual "<<cp<< " target"<< rsq<<std::endl;
+
+      if(cp<rsq) {
+	Linop.HermOp(psi,Ap);
+	axpy(r,-1.0,src,Ap);
+	RealD true_resid = norm2(r)/ssq;
+	std::cout<<GridLogMessage<<"ConjugateResidual: Converged on iteration " <<k
+		 << " computed residual "<<std::sqrt(cp/ssq)
+		 << " true residual "<<std::sqrt(true_resid)
+		 << " target "       <<Tolerance <<std::endl;
+	return;
+      }
+
+    }
+
+    std::cout<<GridLogMessage<<"ConjugateResidual did NOT converge"<<std::endl;
+    assert(0);
+  }
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/Deflation.h

@@ -30,22 +30,27 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 
 namespace Grid { 
 
-struct ZeroGuesser {
+template<class Field>
+class ZeroGuesser: public LinearFunction<Field> {
 public:
-  template<class Field> 
-  void operator()(const Field &src,Field &guess) { guess = Zero(); };
+    virtual void operator()(const Field &src, Field &guess) { guess = Zero(); };
 };
-struct SourceGuesser {
+template<class Field>
+class DoNothingGuesser: public LinearFunction<Field> {
 public:
-  template<class Field> 
-  void operator()(const Field &src,Field &guess) { guess = src; };
+  virtual void operator()(const Field &src, Field &guess) {  };
+};
+template<class Field>
+class SourceGuesser: public LinearFunction<Field> {
+public:
+  virtual void operator()(const Field &src, Field &guess) { guess = src; };
 };
 
 ////////////////////////////////
 // Fine grid deflation
 ////////////////////////////////
 template<class Field>
-struct DeflatedGuesser {
+class DeflatedGuesser: public LinearFunction<Field> {
 private:
   const std::vector<Field> &evec;
   const std::vector<RealD> &eval;
@@ -54,19 +59,20 @@ public:
 
   DeflatedGuesser(const std::vector<Field> & _evec,const std::vector<RealD> & _eval) : evec(_evec), eval(_eval) {};
 
-  void operator()(const Field &src,Field &guess) { 
-    guess = zero;
+  virtual void operator()(const Field &src,Field &guess) {
+    guess = Zero();
     assert(evec.size()==eval.size());
     auto N = evec.size();
     for (int i=0;i<N;i++) {
       const Field& tmp = evec[i];
       axpy(guess,TensorRemove(innerProduct(tmp,src)) / eval[i],tmp,guess);
     }
+    guess.Checkerboard() = src.Checkerboard();
   }
 };
 
 template<class FineField, class CoarseField>
-class LocalCoherenceDeflatedGuesser {
+class LocalCoherenceDeflatedGuesser: public LinearFunction<FineField> {
 private:
   const std::vector<FineField>   &subspace;
   const std::vector<CoarseField> &evec_coarse;
@@ -84,14 +90,15 @@ public:
   
   void operator()(const FineField &src,FineField &guess) { 
     int N = (int)evec_coarse.size();
-    CoarseField src_coarse(evec_coarse[0]._grid);
-    CoarseField guess_coarse(evec_coarse[0]._grid);    guess_coarse = zero;
+    CoarseField src_coarse(evec_coarse[0].Grid());
+    CoarseField guess_coarse(evec_coarse[0].Grid());    guess_coarse = Zero();
     blockProject(src_coarse,src,subspace);    
     for (int i=0;i<N;i++) {
       const CoarseField & tmp = evec_coarse[i];
       axpy(guess_coarse,TensorRemove(innerProduct(tmp,src_coarse)) / eval_coarse[i],tmp,guess_coarse);
     }
     blockPromote(guess_coarse,guess,subspace);
+    guess.Checkerboard() = src.Checkerboard();
   };
 };
 

Grid/algorithms/iterative/FlexibleCommunicationAvoidingGeneralisedMinimalResidual.h

@@ -0,0 +1,258 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithms/iterative/FlexibleCommunicationAvoidingGeneralisedMinimalResidual.h
+
+Copyright (C) 2015
+
+Author: Daniel Richtmann <daniel.richtmann@ur.de>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_FLEXIBLE_COMMUNICATION_AVOIDING_GENERALISED_MINIMAL_RESIDUAL_H
+#define GRID_FLEXIBLE_COMMUNICATION_AVOIDING_GENERALISED_MINIMAL_RESIDUAL_H
+
+namespace Grid {
+
+template<class Field>
+class FlexibleCommunicationAvoidingGeneralisedMinimalResidual : public OperatorFunction<Field> {
+ public:
+  using OperatorFunction<Field>::operator();
+
+  bool ErrorOnNoConverge; // Throw an assert when FCAGMRES fails to converge,
+                          // defaults to true
+
+  RealD   Tolerance;
+
+  Integer MaxIterations;
+  Integer RestartLength;
+  Integer MaxNumberOfRestarts;
+  Integer IterationCount; // Number of iterations the FCAGMRES took to finish,
+                          // filled in upon completion
+
+  GridStopWatch MatrixTimer;
+  GridStopWatch PrecTimer;
+  GridStopWatch LinalgTimer;
+  GridStopWatch QrTimer;
+  GridStopWatch CompSolutionTimer;
+
+  Eigen::MatrixXcd H;
+
+  std::vector<ComplexD> y;
+  std::vector<ComplexD> gamma;
+  std::vector<ComplexD> c;
+  std::vector<ComplexD> s;
+
+  LinearFunction<Field> &Preconditioner;
+
+  FlexibleCommunicationAvoidingGeneralisedMinimalResidual(RealD   tol,
+                                                          Integer maxit,
+                                                          LinearFunction<Field> &Prec,
+                                                          Integer restart_length,
+                                                          bool    err_on_no_conv = true)
+      : Tolerance(tol)
+      , MaxIterations(maxit)
+      , RestartLength(restart_length)
+      , MaxNumberOfRestarts(MaxIterations/RestartLength + ((MaxIterations%RestartLength == 0) ? 0 : 1))
+      , ErrorOnNoConverge(err_on_no_conv)
+      , H(Eigen::MatrixXcd::Zero(RestartLength, RestartLength + 1)) // sizes taken from DD-αAMG code base
+      , y(RestartLength + 1, 0.)
+      , gamma(RestartLength + 1, 0.)
+      , c(RestartLength + 1, 0.)
+      , s(RestartLength + 1, 0.)
+      , Preconditioner(Prec) {};
+
+  void operator()(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi) {
+
+    std::cout << GridLogWarning << "This algorithm currently doesn't differ from regular FGMRES" << std::endl;
+
+    psi.Checkerboard() = src.Checkerboard();
+    conformable(psi, src);
+
+    RealD guess = norm2(psi);
+    assert(std::isnan(guess) == 0);
+
+    RealD cp;
+    RealD ssq = norm2(src);
+    RealD rsq = Tolerance * Tolerance * ssq;
+
+    Field r(src.Grid());
+
+    std::cout << std::setprecision(4) << std::scientific;
+    std::cout << GridLogIterative << "FlexibleCommunicationAvoidingGeneralisedMinimalResidual: guess " << guess << std::endl;
+    std::cout << GridLogIterative << "FlexibleCommunicationAvoidingGeneralisedMinimalResidual:   src " << ssq   << std::endl;
+
+    PrecTimer.Reset();
+    MatrixTimer.Reset();
+    LinalgTimer.Reset();
+    QrTimer.Reset();
+    CompSolutionTimer.Reset();
+
+    GridStopWatch SolverTimer;
+    SolverTimer.Start();
+
+    IterationCount = 0;
+
+    for (int k=0; k<MaxNumberOfRestarts; k++) {
+
+      cp = outerLoopBody(LinOp, src, psi, rsq);
+
+      // Stopping condition
+      if (cp <= rsq) {
+
+        SolverTimer.Stop();
+
+        LinOp.Op(psi,r);
+        axpy(r,-1.0,src,r);
+
+        RealD srcnorm       = sqrt(ssq);
+        RealD resnorm       = sqrt(norm2(r));
+        RealD true_residual = resnorm / srcnorm;
+
+        std::cout << GridLogMessage        << "FlexibleCommunicationAvoidingGeneralisedMinimalResidual: Converged on iteration " << IterationCount
+                  << " computed residual " << sqrt(cp / ssq)
+                  << " true residual "     << true_residual
+                  << " target "            << Tolerance << std::endl;
+
+        std::cout << GridLogMessage << "FCAGMRES Time elapsed: Total   " <<       SolverTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "FCAGMRES Time elapsed: Precon  " <<         PrecTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "FCAGMRES Time elapsed: Matrix  " <<       MatrixTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "FCAGMRES Time elapsed: Linalg  " <<       LinalgTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "FCAGMRES Time elapsed: QR      " <<           QrTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "FCAGMRES Time elapsed: CompSol " << CompSolutionTimer.Elapsed() << std::endl;
+        return;
+      }
+    }
+
+    std::cout << GridLogMessage << "FlexibleCommunicationAvoidingGeneralisedMinimalResidual did NOT converge" << std::endl;
+
+    if (ErrorOnNoConverge)
+      assert(0);
+  }
+
+  RealD outerLoopBody(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi, RealD rsq) {
+
+    RealD cp = 0;
+
+    Field w(src.Grid());
+    Field r(src.Grid());
+
+    // these should probably be made class members so that they are only allocated once, not in every restart
+    std::vector<Field> v(RestartLength + 1, src.Grid()); for (auto &elem : v) elem = Zero();
+    std::vector<Field> z(RestartLength + 1, src.Grid()); for (auto &elem : z) elem = Zero();
+
+    MatrixTimer.Start();
+    LinOp.Op(psi, w);
+    MatrixTimer.Stop();
+
+    LinalgTimer.Start();
+    r = src - w;
+
+    gamma[0] = sqrt(norm2(r));
+
+    v[0] = (1. / gamma[0]) * r;
+    LinalgTimer.Stop();
+
+    for (int i=0; i<RestartLength; i++) {
+
+      IterationCount++;
+
+      arnoldiStep(LinOp, v, z, w, i);
+
+      qrUpdate(i);
+
+      cp = norm(gamma[i+1]);
+
+      std::cout << GridLogIterative << "FlexibleCommunicationAvoidingGeneralisedMinimalResidual: Iteration " << IterationCount
+                << " residual " << cp << " target " << rsq << std::endl;
+
+      if ((i == RestartLength - 1) || (IterationCount == MaxIterations) || (cp <= rsq)) {
+
+        computeSolution(z, psi, i);
+
+        return cp;
+      }
+    }
+
+    assert(0); // Never reached
+    return cp;
+  }
+
+  void arnoldiStep(LinearOperatorBase<Field> &LinOp, std::vector<Field> &v, std::vector<Field> &z, Field &w, int iter) {
+
+    PrecTimer.Start();
+    Preconditioner(v[iter], z[iter]);
+    PrecTimer.Stop();
+
+    MatrixTimer.Start();
+    LinOp.Op(z[iter], w);
+    MatrixTimer.Stop();
+
+    LinalgTimer.Start();
+    for (int i = 0; i <= iter; ++i) {
+      H(iter, i) = innerProduct(v[i], w);
+      w = w - ComplexD(H(iter, i)) * v[i];
+    }
+
+    H(iter, iter + 1) = sqrt(norm2(w));
+    v[iter + 1] = ComplexD(1. / H(iter, iter + 1)) * w;
+    LinalgTimer.Stop();
+  }
+
+  void qrUpdate(int iter) {
+
+    QrTimer.Start();
+    for (int i = 0; i < iter ; ++i) {
+      auto tmp       = -s[i] * ComplexD(H(iter, i)) + c[i] * ComplexD(H(iter, i + 1));
+      H(iter, i)     = conjugate(c[i]) * ComplexD(H(iter, i)) + conjugate(s[i]) * ComplexD(H(iter, i + 1));
+      H(iter, i + 1) = tmp;
+    }
+
+    // Compute new Givens Rotation
+    auto nu = sqrt(std::norm(H(iter, iter)) + std::norm(H(iter, iter + 1)));
+    c[iter]     = H(iter, iter) / nu;
+    s[iter]     = H(iter, iter + 1) / nu;
+
+    // Apply new Givens rotation
+    H(iter, iter)     = nu;
+    H(iter, iter + 1) = 0.;
+
+    gamma[iter + 1] = -s[iter] * gamma[iter];
+    gamma[iter]     = conjugate(c[iter]) * gamma[iter];
+    QrTimer.Stop();
+  }
+
+  void computeSolution(std::vector<Field> const &z, Field &psi, int iter) {
+
+    CompSolutionTimer.Start();
+    for (int i = iter; i >= 0; i--) {
+      y[i] = gamma[i];
+      for (int k = i + 1; k <= iter; k++)
+        y[i] = y[i] - ComplexD(H(k, i)) * y[k];
+      y[i] = y[i] / ComplexD(H(i, i));
+    }
+
+    for (int i = 0; i <= iter; i++)
+      psi = psi + z[i] * y[i];
+    CompSolutionTimer.Stop();
+  }
+};
+}
+#endif

Grid/algorithms/iterative/FlexibleGeneralisedMinimalResidual.h

@@ -0,0 +1,256 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithms/iterative/FlexibleGeneralisedMinimalResidual.h
+
+Copyright (C) 2015
+
+Author: Daniel Richtmann <daniel.richtmann@ur.de>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_FLEXIBLE_GENERALISED_MINIMAL_RESIDUAL_H
+#define GRID_FLEXIBLE_GENERALISED_MINIMAL_RESIDUAL_H
+
+namespace Grid {
+
+template<class Field>
+class FlexibleGeneralisedMinimalResidual : public OperatorFunction<Field> {
+ public:
+  using OperatorFunction<Field>::operator();
+
+  bool ErrorOnNoConverge; // Throw an assert when FGMRES fails to converge,
+                          // defaults to true
+
+  RealD   Tolerance;
+
+  Integer MaxIterations;
+  Integer RestartLength;
+  Integer MaxNumberOfRestarts;
+  Integer IterationCount; // Number of iterations the FGMRES took to finish,
+                          // filled in upon completion
+
+  GridStopWatch MatrixTimer;
+  GridStopWatch PrecTimer;
+  GridStopWatch LinalgTimer;
+  GridStopWatch QrTimer;
+  GridStopWatch CompSolutionTimer;
+
+  Eigen::MatrixXcd H;
+
+  std::vector<ComplexD> y;
+  std::vector<ComplexD> gamma;
+  std::vector<ComplexD> c;
+  std::vector<ComplexD> s;
+
+  LinearFunction<Field> &Preconditioner;
+
+  FlexibleGeneralisedMinimalResidual(RealD   tol,
+                                     Integer maxit,
+                                     LinearFunction<Field> &Prec,
+                                     Integer restart_length,
+                                     bool    err_on_no_conv = true)
+      : Tolerance(tol)
+      , MaxIterations(maxit)
+      , RestartLength(restart_length)
+      , MaxNumberOfRestarts(MaxIterations/RestartLength + ((MaxIterations%RestartLength == 0) ? 0 : 1))
+      , ErrorOnNoConverge(err_on_no_conv)
+      , H(Eigen::MatrixXcd::Zero(RestartLength, RestartLength + 1)) // sizes taken from DD-αAMG code base
+      , y(RestartLength + 1, 0.)
+      , gamma(RestartLength + 1, 0.)
+      , c(RestartLength + 1, 0.)
+      , s(RestartLength + 1, 0.)
+      , Preconditioner(Prec) {};
+
+  void operator()(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi) {
+
+    psi.Checkerboard() = src.Checkerboard();
+    conformable(psi, src);
+
+    RealD guess = norm2(psi);
+    assert(std::isnan(guess) == 0);
+
+    RealD cp;
+    RealD ssq = norm2(src);
+    RealD rsq = Tolerance * Tolerance * ssq;
+
+    Field r(src.Grid());
+
+    std::cout << std::setprecision(4) << std::scientific;
+    std::cout << GridLogIterative << "FlexibleGeneralisedMinimalResidual: guess " << guess << std::endl;
+    std::cout << GridLogIterative << "FlexibleGeneralisedMinimalResidual:   src " << ssq   << std::endl;
+
+    PrecTimer.Reset();
+    MatrixTimer.Reset();
+    LinalgTimer.Reset();
+    QrTimer.Reset();
+    CompSolutionTimer.Reset();
+
+    GridStopWatch SolverTimer;
+    SolverTimer.Start();
+
+    IterationCount = 0;
+
+    for (int k=0; k<MaxNumberOfRestarts; k++) {
+
+      cp = outerLoopBody(LinOp, src, psi, rsq);
+
+      // Stopping condition
+      if (cp <= rsq) {
+
+        SolverTimer.Stop();
+
+        LinOp.Op(psi,r);
+        axpy(r,-1.0,src,r);
+
+        RealD srcnorm       = sqrt(ssq);
+        RealD resnorm       = sqrt(norm2(r));
+        RealD true_residual = resnorm / srcnorm;
+
+        std::cout << GridLogMessage        << "FlexibleGeneralisedMinimalResidual: Converged on iteration " << IterationCount
+                  << " computed residual " << sqrt(cp / ssq)
+                  << " true residual "     << true_residual
+                  << " target "            << Tolerance << std::endl;
+
+        std::cout << GridLogMessage << "FGMRES Time elapsed: Total   " <<       SolverTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "FGMRES Time elapsed: Precon  " <<         PrecTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "FGMRES Time elapsed: Matrix  " <<       MatrixTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "FGMRES Time elapsed: Linalg  " <<       LinalgTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "FGMRES Time elapsed: QR      " <<           QrTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "FGMRES Time elapsed: CompSol " << CompSolutionTimer.Elapsed() << std::endl;
+        return;
+      }
+    }
+
+    std::cout << GridLogMessage << "FlexibleGeneralisedMinimalResidual did NOT converge" << std::endl;
+
+    if (ErrorOnNoConverge)
+      assert(0);
+  }
+
+  RealD outerLoopBody(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi, RealD rsq) {
+
+    RealD cp = 0;
+
+    Field w(src.Grid());
+    Field r(src.Grid());
+
+    // these should probably be made class members so that they are only allocated once, not in every restart
+    std::vector<Field> v(RestartLength + 1, src.Grid()); for (auto &elem : v) elem = Zero();
+    std::vector<Field> z(RestartLength + 1, src.Grid()); for (auto &elem : z) elem = Zero();
+
+    MatrixTimer.Start();
+    LinOp.Op(psi, w);
+    MatrixTimer.Stop();
+
+    LinalgTimer.Start();
+    r = src - w;
+
+    gamma[0] = sqrt(norm2(r));
+
+    v[0] = (1. / gamma[0]) * r;
+    LinalgTimer.Stop();
+
+    for (int i=0; i<RestartLength; i++) {
+
+      IterationCount++;
+
+      arnoldiStep(LinOp, v, z, w, i);
+
+      qrUpdate(i);
+
+      cp = norm(gamma[i+1]);
+
+      std::cout << GridLogIterative << "FlexibleGeneralisedMinimalResidual: Iteration " << IterationCount
+                << " residual " << cp << " target " << rsq << std::endl;
+
+      if ((i == RestartLength - 1) || (IterationCount == MaxIterations) || (cp <= rsq)) {
+
+        computeSolution(z, psi, i);
+
+        return cp;
+      }
+    }
+
+    assert(0); // Never reached
+    return cp;
+  }
+
+  void arnoldiStep(LinearOperatorBase<Field> &LinOp, std::vector<Field> &v, std::vector<Field> &z, Field &w, int iter) {
+
+    PrecTimer.Start();
+    Preconditioner(v[iter], z[iter]);
+    PrecTimer.Stop();
+
+    MatrixTimer.Start();
+    LinOp.Op(z[iter], w);
+    MatrixTimer.Stop();
+
+    LinalgTimer.Start();
+    for (int i = 0; i <= iter; ++i) {
+      H(iter, i) = innerProduct(v[i], w);
+      w = w - ComplexD(H(iter, i)) * v[i];
+    }
+
+    H(iter, iter + 1) = sqrt(norm2(w));
+    v[iter + 1] = ComplexD(1. / H(iter, iter + 1)) * w;
+    LinalgTimer.Stop();
+  }
+
+  void qrUpdate(int iter) {
+
+    QrTimer.Start();
+    for (int i = 0; i < iter ; ++i) {
+      auto tmp       = -s[i] * ComplexD(H(iter, i)) + c[i] * ComplexD(H(iter, i + 1));
+      H(iter, i)     = conjugate(c[i]) * ComplexD(H(iter, i)) + conjugate(s[i]) * ComplexD(H(iter, i + 1));
+      H(iter, i + 1) = tmp;
+    }
+
+    // Compute new Givens Rotation
+    auto nu = sqrt(std::norm(H(iter, iter)) + std::norm(H(iter, iter + 1)));
+    c[iter]     = H(iter, iter) / nu;
+    s[iter]     = H(iter, iter + 1) / nu;
+
+    // Apply new Givens rotation
+    H(iter, iter)     = nu;
+    H(iter, iter + 1) = 0.;
+
+    gamma[iter + 1] = -s[iter] * gamma[iter];
+    gamma[iter]     = conjugate(c[iter]) * gamma[iter];
+    QrTimer.Stop();
+  }
+
+  void computeSolution(std::vector<Field> const &z, Field &psi, int iter) {
+
+    CompSolutionTimer.Start();
+    for (int i = iter; i >= 0; i--) {
+      y[i] = gamma[i];
+      for (int k = i + 1; k <= iter; k++)
+        y[i] = y[i] - ComplexD(H(k, i)) * y[k];
+      y[i] = y[i] / ComplexD(H(i, i));
+    }
+
+    for (int i = 0; i <= iter; i++)
+      psi = psi + z[i] * y[i];
+    CompSolutionTimer.Stop();
+  }
+};
+}
+#endif

Grid/algorithms/iterative/GeneralisedMinimalResidual.h

@@ -0,0 +1,244 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithms/iterative/GeneralisedMinimalResidual.h
+
+Copyright (C) 2015
+
+Author: Daniel Richtmann <daniel.richtmann@ur.de>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_GENERALISED_MINIMAL_RESIDUAL_H
+#define GRID_GENERALISED_MINIMAL_RESIDUAL_H
+
+namespace Grid {
+
+template<class Field>
+class GeneralisedMinimalResidual : public OperatorFunction<Field> {
+ public:
+  using OperatorFunction<Field>::operator();
+
+  bool ErrorOnNoConverge; // Throw an assert when GMRES fails to converge,
+                          // defaults to true
+
+  RealD   Tolerance;
+
+  Integer MaxIterations;
+  Integer RestartLength;
+  Integer MaxNumberOfRestarts;
+  Integer IterationCount; // Number of iterations the GMRES took to finish,
+                          // filled in upon completion
+
+  GridStopWatch MatrixTimer;
+  GridStopWatch LinalgTimer;
+  GridStopWatch QrTimer;
+  GridStopWatch CompSolutionTimer;
+
+  Eigen::MatrixXcd H;
+
+  std::vector<ComplexD> y;
+  std::vector<ComplexD> gamma;
+  std::vector<ComplexD> c;
+  std::vector<ComplexD> s;
+
+  GeneralisedMinimalResidual(RealD   tol,
+                             Integer maxit,
+                             Integer restart_length,
+                             bool    err_on_no_conv = true)
+      : Tolerance(tol)
+      , MaxIterations(maxit)
+      , RestartLength(restart_length)
+      , MaxNumberOfRestarts(MaxIterations/RestartLength + ((MaxIterations%RestartLength == 0) ? 0 : 1))
+      , ErrorOnNoConverge(err_on_no_conv)
+      , H(Eigen::MatrixXcd::Zero(RestartLength, RestartLength + 1)) // sizes taken from DD-αAMG code base
+      , y(RestartLength + 1, 0.)
+      , gamma(RestartLength + 1, 0.)
+      , c(RestartLength + 1, 0.)
+      , s(RestartLength + 1, 0.) {};
+
+  void operator()(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi) {
+
+    psi.Checkerboard() = src.Checkerboard();
+    conformable(psi, src);
+
+    RealD guess = norm2(psi);
+    assert(std::isnan(guess) == 0);
+
+    RealD cp;
+    RealD ssq = norm2(src);
+    RealD rsq = Tolerance * Tolerance * ssq;
+
+    Field r(src.Grid());
+
+    std::cout << std::setprecision(4) << std::scientific;
+    std::cout << GridLogIterative << "GeneralisedMinimalResidual: guess " << guess << std::endl;
+    std::cout << GridLogIterative << "GeneralisedMinimalResidual:   src " << ssq   << std::endl;
+
+    MatrixTimer.Reset();
+    LinalgTimer.Reset();
+    QrTimer.Reset();
+    CompSolutionTimer.Reset();
+
+    GridStopWatch SolverTimer;
+    SolverTimer.Start();
+
+    IterationCount = 0;
+
+    for (int k=0; k<MaxNumberOfRestarts; k++) {
+
+      cp = outerLoopBody(LinOp, src, psi, rsq);
+
+      // Stopping condition
+      if (cp <= rsq) {
+
+        SolverTimer.Stop();
+
+        LinOp.Op(psi,r);
+        axpy(r,-1.0,src,r);
+
+        RealD srcnorm       = sqrt(ssq);
+        RealD resnorm       = sqrt(norm2(r));
+        RealD true_residual = resnorm / srcnorm;
+
+        std::cout << GridLogMessage        << "GeneralisedMinimalResidual: Converged on iteration " << IterationCount
+                  << " computed residual " << sqrt(cp / ssq)
+                  << " true residual "     << true_residual
+                  << " target "            << Tolerance << std::endl;
+
+        std::cout << GridLogMessage << "GMRES Time elapsed: Total   " <<       SolverTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "GMRES Time elapsed: Matrix  " <<       MatrixTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "GMRES Time elapsed: Linalg  " <<       LinalgTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "GMRES Time elapsed: QR      " <<           QrTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "GMRES Time elapsed: CompSol " << CompSolutionTimer.Elapsed() << std::endl;
+        return;
+      }
+    }
+
+    std::cout << GridLogMessage << "GeneralisedMinimalResidual did NOT converge" << std::endl;
+
+    if (ErrorOnNoConverge)
+      assert(0);
+  }
+
+  RealD outerLoopBody(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi, RealD rsq) {
+
+    RealD cp = 0;
+
+    Field w(src.Grid());
+    Field r(src.Grid());
+
+    // this should probably be made a class member so that it is only allocated once, not in every restart
+    std::vector<Field> v(RestartLength + 1, src.Grid()); for (auto &elem : v) elem = Zero();
+
+    MatrixTimer.Start();
+    LinOp.Op(psi, w);
+    MatrixTimer.Stop();
+
+    LinalgTimer.Start();
+    r = src - w;
+
+    gamma[0] = sqrt(norm2(r));
+
+    v[0] = (1. / gamma[0]) * r;
+    LinalgTimer.Stop();
+
+    for (int i=0; i<RestartLength; i++) {
+
+      IterationCount++;
+
+      arnoldiStep(LinOp, v, w, i);
+
+      qrUpdate(i);
+
+      cp = norm(gamma[i+1]);
+
+      std::cout << GridLogIterative << "GeneralisedMinimalResidual: Iteration " << IterationCount
+                << " residual " << cp << " target " << rsq << std::endl;
+
+      if ((i == RestartLength - 1) || (IterationCount == MaxIterations) || (cp <= rsq)) {
+
+        computeSolution(v, psi, i);
+
+        return cp;
+      }
+    }
+
+    assert(0); // Never reached
+    return cp;
+  }
+
+  void arnoldiStep(LinearOperatorBase<Field> &LinOp, std::vector<Field> &v, Field &w, int iter) {
+
+    MatrixTimer.Start();
+    LinOp.Op(v[iter], w);
+    MatrixTimer.Stop();
+
+    LinalgTimer.Start();
+    for (int i = 0; i <= iter; ++i) {
+      H(iter, i) = innerProduct(v[i], w);
+      w = w - ComplexD(H(iter, i)) * v[i];
+    }
+
+    H(iter, iter + 1) = sqrt(norm2(w));
+    v[iter + 1] = ComplexD(1. / H(iter, iter + 1)) * w;
+    LinalgTimer.Stop();
+  }
+
+  void qrUpdate(int iter) {
+
+    QrTimer.Start();
+    for (int i = 0; i < iter ; ++i) {
+      auto tmp       = -s[i] * ComplexD(H(iter, i)) + c[i] * ComplexD(H(iter, i + 1));
+      H(iter, i)     = conjugate(c[i]) * ComplexD(H(iter, i)) + conjugate(s[i]) * ComplexD(H(iter, i + 1));
+      H(iter, i + 1) = tmp;
+    }
+
+    // Compute new Givens Rotation
+    auto nu = sqrt(std::norm(H(iter, iter)) + std::norm(H(iter, iter + 1)));
+    c[iter]     = H(iter, iter) / nu;
+    s[iter]     = H(iter, iter + 1) / nu;
+
+    // Apply new Givens rotation
+    H(iter, iter)     = nu;
+    H(iter, iter + 1) = 0.;
+
+    gamma[iter + 1] = -s[iter] * gamma[iter];
+    gamma[iter]     = conjugate(c[iter]) * gamma[iter];
+    QrTimer.Stop();
+  }
+
+  void computeSolution(std::vector<Field> const &v, Field &psi, int iter) {
+
+    CompSolutionTimer.Start();
+    for (int i = iter; i >= 0; i--) {
+      y[i] = gamma[i];
+      for (int k = i + 1; k <= iter; k++)
+        y[i] = y[i] - ComplexD(H(k, i)) * y[k];
+      y[i] = y[i] / ComplexD(H(i, i));
+    }
+
+    for (int i = 0; i <= iter; i++)
+      psi = psi + v[i] * y[i];
+    CompSolutionTimer.Stop();
+  }
+};
+}
+#endif

Grid/algorithms/iterative/ImplicitlyRestartedLanczos.h

@@ -35,120 +35,7 @@ Author: Christoph Lehner <clehner@bnl.gov>
 //#include <zlib.h>
 #include <sys/stat.h>
 
-namespace Grid { 
-
-  ////////////////////////////////////////////////////////
-  // Move following 100 LOC to lattice/Lattice_basis.h
-  ////////////////////////////////////////////////////////
-template<class Field>
-void basisOrthogonalize(std::vector<Field> &basis,Field &w,int k) 
-{
-  for(int j=0; j<k; ++j){
-    auto ip = innerProduct(basis[j],w);
-    w = w - ip*basis[j];
-  }
-}
-
-template<class Field>
-void basisRotate(std::vector<Field> &basis,Eigen::MatrixXd& Qt,int j0, int j1, int k0,int k1,int Nm) 
-{
-  typedef typename Field::vector_object vobj;
-  GridBase* grid = basis[0]._grid;
-      
-  parallel_region
-  {
-
-    std::vector < vobj , commAllocator<vobj> > B(Nm); // Thread private
-       
-    parallel_for_internal(int ss=0;ss < grid->oSites();ss++){
-      for(int j=j0; j<j1; ++j) B[j]=0.;
-      
-      for(int j=j0; j<j1; ++j){
-	for(int k=k0; k<k1; ++k){
-	  B[j] +=Qt(j,k) * basis[k]._odata[ss];
-	}
-      }
-      for(int j=j0; j<j1; ++j){
-	  basis[j]._odata[ss] = B[j];
-      }
-    }
-  }
-}
-
-// Extract a single rotated vector
-template<class Field>
-void basisRotateJ(Field &result,std::vector<Field> &basis,Eigen::MatrixXd& Qt,int j, int k0,int k1,int Nm) 
-{
-  typedef typename Field::vector_object vobj;
-  GridBase* grid = basis[0]._grid;
-
-  result.checkerboard = basis[0].checkerboard;
-  parallel_for(int ss=0;ss < grid->oSites();ss++){
-    vobj B = zero;
-    for(int k=k0; k<k1; ++k){
-      B +=Qt(j,k) * basis[k]._odata[ss];
-    }
-    result._odata[ss] = B;
-  }
-}
-
-template<class Field>
-void basisReorderInPlace(std::vector<Field> &_v,std::vector<RealD>& sort_vals, std::vector<int>& idx) 
-{
-  int vlen = idx.size();
-
-  assert(vlen>=1);
-  assert(vlen<=sort_vals.size());
-  assert(vlen<=_v.size());
-
-  for (size_t i=0;i<vlen;i++) {
-
-    if (idx[i] != i) {
-
-      //////////////////////////////////////
-      // idx[i] is a table of desired sources giving a permutation.
-      // Swap v[i] with v[idx[i]].
-      // Find  j>i for which _vnew[j] = _vold[i],
-      // track the move idx[j] => idx[i]
-      // track the move idx[i] => i
-      //////////////////////////////////////
-      size_t j;
-      for (j=i;j<idx.size();j++)
-	if (idx[j]==i)
-	  break;
-
-      assert(idx[i] > i);     assert(j!=idx.size());      assert(idx[j]==i);
-
-      std::swap(_v[i]._odata,_v[idx[i]]._odata); // should use vector move constructor, no data copy
-      std::swap(sort_vals[i],sort_vals[idx[i]]);
-
-      idx[j] = idx[i];
-      idx[i] = i;
-    }
-  }
-}
-
-inline std::vector<int> basisSortGetIndex(std::vector<RealD>& sort_vals) 
-{
-  std::vector<int> idx(sort_vals.size());
-  std::iota(idx.begin(), idx.end(), 0);
-
-  // sort indexes based on comparing values in v
-  std::sort(idx.begin(), idx.end(), [&sort_vals](int i1, int i2) {
-    return ::fabs(sort_vals[i1]) < ::fabs(sort_vals[i2]);
-  });
-  return idx;
-}
-
-template<class Field>
-void basisSortInPlace(std::vector<Field> & _v,std::vector<RealD>& sort_vals, bool reverse) 
-{
-  std::vector<int> idx = basisSortGetIndex(sort_vals);
-  if (reverse)
-    std::reverse(idx.begin(), idx.end());
-  
-  basisReorderInPlace(_v,sort_vals,idx);
-}
+NAMESPACE_BEGIN(Grid); 
 
 /////////////////////////////////////////////////////////////
 // Implicitly restarted lanczos
@@ -259,7 +146,7 @@ public:
 			    RealD _eresid, // resid in lmdue deficit 
 			    int _MaxIter, // Max iterations
 			    RealD _betastp=0.0, // if beta(k) < betastp: converged
-			    int _MinRestart=1, int _orth_period = 1,
+			    int _MinRestart=0, int _orth_period = 1,
 			    IRLdiagonalisation _diagonalisation= IRLdiagonaliseWithEigen) :
     SimpleTester(HermOp), _PolyOp(PolyOp),      _HermOp(HermOp), _Tester(Tester),
     Nstop(_Nstop)  ,      Nk(_Nk),      Nm(_Nm),
@@ -275,7 +162,7 @@ public:
 			       RealD _eresid, // resid in lmdue deficit 
 			       int _MaxIter, // Max iterations
 			       RealD _betastp=0.0, // if beta(k) < betastp: converged
-			       int _MinRestart=1, int _orth_period = 1,
+			       int _MinRestart=0, int _orth_period = 1,
 			       IRLdiagonalisation _diagonalisation= IRLdiagonaliseWithEigen) :
     SimpleTester(HermOp),  _PolyOp(PolyOp),      _HermOp(HermOp), _Tester(SimpleTester),
     Nstop(_Nstop)  ,      Nk(_Nk),      Nm(_Nm),
@@ -289,7 +176,7 @@ public:
   template<typename T>  static RealD normalise(T& v) 
   {
     RealD nn = norm2(v);
-    nn = sqrt(nn);
+    nn = std::sqrt(nn);
     v = v * (1.0/nn);
     return nn;
   }
@@ -321,10 +208,10 @@ until convergence
 */
   void calc(std::vector<RealD>& eval, std::vector<Field>& evec,  const Field& src, int& Nconv, bool reverse=false)
   {
-    GridBase *grid = src._grid;
-    assert(grid == evec[0]._grid);
+    GridBase *grid = src.Grid();
+    assert(grid == evec[0].Grid());
     
-    GridLogIRL.TimingMode(1);
+    //    GridLogIRL.TimingMode(1);
     std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
     std::cout << GridLogIRL <<" ImplicitlyRestartedLanczos::calc() starting iteration 0 /  "<< MaxIter<< std::endl;
     std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
@@ -349,14 +236,17 @@ until convergence
     {
       auto src_n = src;
       auto tmp = src;
+      std::cout << GridLogIRL << " IRL source norm " << norm2(src) << std::endl;
       const int _MAX_ITER_IRL_MEVAPP_ = 50;
       for (int i=0;i<_MAX_ITER_IRL_MEVAPP_;i++) {
 	normalise(src_n);
 	_HermOp(src_n,tmp);
+	//	std::cout << GridLogMessage<< tmp<<std::endl; exit(0);
+	//	std::cout << GridLogIRL << " _HermOp " << norm2(tmp) << std::endl;
 	RealD vnum = real(innerProduct(src_n,tmp)); // HermOp.
 	RealD vden = norm2(src_n);
 	RealD na = vnum/vden;
-	if (fabs(evalMaxApprox/na - 1.0) < 0.05)
+	if (fabs(evalMaxApprox/na - 1.0) < 0.0001)
 	  i=_MAX_ITER_IRL_MEVAPP_;
 	evalMaxApprox = na;
 	std::cout << GridLogIRL << " Approximation of largest eigenvalue: " << evalMaxApprox << std::endl;
@@ -446,7 +336,7 @@ until convergence
       assert(k2<Nm);      assert(k2<Nm);      assert(k1>0);
 
       basisRotate(evec,Qt,k1-1,k2+1,0,Nm,Nm); /// big constraint on the basis
-      std::cout<<GridLogIRL <<"basisRotated  by Qt"<<std::endl;
+      std::cout<<GridLogIRL <<"basisRotated  by Qt *"<<k1-1<<","<<k2+1<<")"<<std::endl;
       
       ////////////////////////////////////////////////////
       // Compressed vector f and beta(k2)
@@ -454,7 +344,7 @@ until convergence
       f *= Qt(k2-1,Nm-1);
       f += lme[k2-1] * evec[k2];
       beta_k = norm2(f);
-      beta_k = sqrt(beta_k);
+      beta_k = std::sqrt(beta_k);
       std::cout<<GridLogIRL<<" beta(k) = "<<beta_k<<std::endl;
 	  
       RealD betar = 1.0/beta_k;
@@ -477,7 +367,7 @@ until convergence
 
 	std::cout << GridLogIRL << "Test convergence: rotate subset of vectors to test convergence " << std::endl;
 
-	Field B(grid); B.checkerboard = evec[0].checkerboard;
+	Field B(grid); B.Checkerboard() = evec[0].Checkerboard();
 
 	//  power of two search pattern;  not every evalue in eval2 is assessed.
 	int allconv =1;
@@ -515,7 +405,7 @@ until convergence
 	
   converged:
     {
-      Field B(grid); B.checkerboard = evec[0].checkerboard;
+      Field B(grid); B.Checkerboard() = evec[0].Checkerboard();
       basisRotate(evec,Qt,0,Nk,0,Nk,Nm);	    
       std::cout << GridLogIRL << " Rotated basis"<<std::endl;
       Nconv=0;
@@ -554,11 +444,11 @@ until convergence
 /* Saad PP. 195
 1. Choose an initial vector v1 of 2-norm unity. Set β1 ≡ 0, v0 ≡ 0
 2. For k = 1,2,...,m Do:
-3. wk:=Avk−βkv_{k−1}      
-4. αk:=(wk,vk)       // 
-5. wk:=wk−αkvk       // wk orthog vk 
-6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
-7. vk+1 := wk/βk+1
+3. wk:=Avk - b_k v_{k-1}      
+4. ak:=(wk,vk)       // 
+5. wk:=wk-akvk       // wk orthog vk 
+6. bk+1 := ||wk||_2. If b_k+1 = 0 then Stop
+7. vk+1 := wk/b_k+1
 8. EndDo
  */
   void step(std::vector<RealD>& lmd,
@@ -566,6 +456,7 @@ until convergence
 	    std::vector<Field>& evec,
 	    Field& w,int Nm,int k)
   {
+    std::cout<<GridLogIRL << "Lanczos step " <<k<<std::endl;
     const RealD tiny = 1.0e-20;
     assert( k< Nm );
 
@@ -577,20 +468,20 @@ until convergence
 
     if(k>0) w -= lme[k-1] * evec[k-1];
 
-    ComplexD zalph = innerProduct(evec_k,w); // 4. αk:=(wk,vk)
+    ComplexD zalph = innerProduct(evec_k,w);
     RealD     alph = real(zalph);
 
-    w = w - alph * evec_k;// 5. wk:=wk−αkvk
+    w = w - alph * evec_k;
 
-    RealD beta = normalise(w); // 6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
-    // 7. vk+1 := wk/βk+1
+    RealD beta = normalise(w); 
 
     lmd[k] = alph;
     lme[k] = beta;
 
-    if (k>0 && k % orth_period == 0) {
+    if ( (k>0) && ( (k % orth_period) == 0 )) {
+      std::cout<<GridLogIRL << "Orthogonalising " <<k<<std::endl;
       orthogonalize(w,evec,k); // orthonormalise
-      std::cout<<GridLogIRL << "Orthogonalised " <<std::endl;
+      std::cout<<GridLogIRL << "Orthogonalised " <<k<<std::endl;
     }
 
     if(k < Nm-1) evec[k+1] = w;
@@ -598,6 +489,8 @@ until convergence
     std::cout<<GridLogIRL << "alpha[" << k << "] = " << zalph << " beta[" << k << "] = "<<beta<<std::endl;
     if ( beta < tiny ) 
       std::cout<<GridLogIRL << " beta is tiny "<<beta<<std::endl;
+
+    std::cout<<GridLogIRL << "Lanczos step complete " <<k<<std::endl;
   }
 
   void diagonalize_Eigen(std::vector<RealD>& lmd, std::vector<RealD>& lme, 
@@ -807,7 +700,7 @@ void diagonalize_QR(std::vector<RealD>& lmd, std::vector<RealD>& lme,
     
     // determination of 2x2 leading submatrix
     RealD dsub = lmd[kmax-1]-lmd[kmax-2];
-    RealD dd = sqrt(dsub*dsub + 4.0*lme[kmax-2]*lme[kmax-2]);
+    RealD dd = std::sqrt(dsub*dsub + 4.0*lme[kmax-2]*lme[kmax-2]);
     RealD Dsh = 0.5*(lmd[kmax-2]+lmd[kmax-1] +dd*(dsub/fabs(dsub)));
     // (Dsh: shift)
     
@@ -838,5 +731,6 @@ void diagonalize_QR(std::vector<RealD>& lmd, std::vector<RealD>& lme,
   abort();
 }
 };
-}
+
+NAMESPACE_END(Grid);
 #endif

Grid/algorithms/iterative/LocalCoherenceLanczos.h

@@ -1,4 +1,4 @@
-    /*************************************************************************************
+/*************************************************************************************
 
     Grid physics library, www.github.com/paboyle/Grid 
 
@@ -24,16 +24,15 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
     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 */
+*************************************************************************************/
+/*  END LEGAL */
 #ifndef GRID_LOCAL_COHERENCE_IRL_H
 #define GRID_LOCAL_COHERENCE_IRL_H
 
-namespace Grid { 
-
+NAMESPACE_BEGIN(Grid); 
 
 struct LanczosParams : Serializable {
- public:
+public:
   GRID_SERIALIZABLE_CLASS_MEMBERS(LanczosParams,
 				  ChebyParams, Cheby,/*Chebyshev*/
 				  int, Nstop,    /*Vecs in Lanczos must converge Nstop < Nk < Nm*/
@@ -46,7 +45,7 @@ struct LanczosParams : Serializable {
 };
 
 struct LocalCoherenceLanczosParams : Serializable {
- public:
+public:
   GRID_SERIALIZABLE_CLASS_MEMBERS(LocalCoherenceLanczosParams,
 				  bool, saveEvecs,
 				  bool, doFine,
@@ -59,7 +58,7 @@ struct LocalCoherenceLanczosParams : Serializable {
 				  RealD        , coarse_relax_tol,
 				  std::vector<int>, blockSize,
 				  std::string, config,
-				  std::vector < std::complex<double>  >, omega,
+				  std::vector < ComplexD  >, omega,
 				  RealD, mass,
 				  RealD, M5);
 };
@@ -83,14 +82,14 @@ public:
   };
 
   void operator()(const CoarseField& in, CoarseField& out) {
-    GridBase *FineGrid = subspace[0]._grid;    
-    int   checkerboard = subspace[0].checkerboard;
+    GridBase *FineGrid = subspace[0].Grid();    
+    int   checkerboard = subspace[0].Checkerboard();
 
-    FineField fin (FineGrid);     fin.checkerboard= checkerboard;
-    FineField fout(FineGrid);   fout.checkerboard = checkerboard;
+    FineField fin (FineGrid);     fin.Checkerboard()= checkerboard;
+    FineField fout(FineGrid);   fout.Checkerboard() = checkerboard;
 
     blockPromote(in,fin,subspace);       std::cout<<GridLogIRL<<"ProjectedHermop : Promote to fine"<<std::endl;
-    _Linop.HermOp(fin,fout);             std::cout<<GridLogIRL<<"ProjectedHermop : HermOp (fine) "<<std::endl;
+    _Linop.HermOp(fin,fout);                   std::cout<<GridLogIRL<<"ProjectedHermop : HermOp (fine) "<<std::endl;
     blockProject(out,fout,subspace);     std::cout<<GridLogIRL<<"ProjectedHermop : Project to coarse "<<std::endl;
   }
 };
@@ -118,11 +117,11 @@ public:
 
   void operator()(const CoarseField& in, CoarseField& out) {
 
-    GridBase *FineGrid = subspace[0]._grid;    
-    int   checkerboard = subspace[0].checkerboard;
+    GridBase *FineGrid = subspace[0].Grid();    
+    int   checkerboard = subspace[0].Checkerboard();
 
-    FineField fin (FineGrid); fin.checkerboard =checkerboard;
-    FineField fout(FineGrid);fout.checkerboard =checkerboard;
+    FineField fin (FineGrid); fin.Checkerboard() =checkerboard;
+    FineField fout(FineGrid);fout.Checkerboard() =checkerboard;
     
     blockPromote(in,fin,subspace);             std::cout<<GridLogIRL<<"ProjectedFunctionHermop : Promote to fine"<<std::endl;
     _poly(_Linop,fin,fout);                    std::cout<<GridLogIRL<<"ProjectedFunctionHermop : Poly "<<std::endl;
@@ -133,7 +132,7 @@ public:
 template<class Fobj,class CComplex,int nbasis>
 class ImplicitlyRestartedLanczosSmoothedTester  : public ImplicitlyRestartedLanczosTester<Lattice<iVector<CComplex,nbasis > > >
 {
- public:
+public:
   typedef iVector<CComplex,nbasis >           CoarseSiteVector;
   typedef Lattice<CoarseSiteVector>           CoarseField;
   typedef Lattice<CComplex>   CoarseScalar; // used for inner products on fine field
@@ -142,7 +141,7 @@ class ImplicitlyRestartedLanczosSmoothedTester  : public ImplicitlyRestartedLanc
   LinearFunction<CoarseField> & _Poly;
   OperatorFunction<FineField>   & _smoother;
   LinearOperatorBase<FineField> &_Linop;
-  RealD                          _coarse_relax_tol;
+  RealD                             _coarse_relax_tol;
   std::vector<FineField>        &_subspace;
   
   ImplicitlyRestartedLanczosSmoothedTester(LinearFunction<CoarseField>   &Poly,
@@ -182,10 +181,10 @@ class ImplicitlyRestartedLanczosSmoothedTester  : public ImplicitlyRestartedLanc
   }
   int ReconstructEval(int j,RealD eresid,CoarseField &B, RealD &eval,RealD evalMaxApprox)
   {
-    GridBase *FineGrid = _subspace[0]._grid;    
-    int checkerboard   = _subspace[0].checkerboard;
-    FineField fB(FineGrid);fB.checkerboard =checkerboard;
-    FineField fv(FineGrid);fv.checkerboard =checkerboard;
+    GridBase *FineGrid = _subspace[0].Grid();    
+    int checkerboard   = _subspace[0].Checkerboard();
+    FineField fB(FineGrid);fB.Checkerboard() =checkerboard;
+    FineField fv(FineGrid);fv.Checkerboard() =checkerboard;
 
     blockPromote(B,fv,_subspace);  
     
@@ -286,8 +285,10 @@ public:
 
   void Orthogonalise(void ) {
     CoarseScalar InnerProd(_CoarseGrid);
-    blockOrthogonalise(InnerProd,subspace);std::cout << GridLogMessage <<" Gramm-Schmidt pass 1"<<std::endl;
-    blockOrthogonalise(InnerProd,subspace);std::cout << GridLogMessage <<" Gramm-Schmidt pass 2"<<std::endl;
+    std::cout << GridLogMessage <<" Gramm-Schmidt pass 1"<<std::endl;
+    blockOrthogonalise(InnerProd,subspace);
+    std::cout << GridLogMessage <<" Gramm-Schmidt pass 2"<<std::endl;
+    blockOrthogonalise(InnerProd,subspace);
   };
 
   template<typename T>  static RealD normalise(T& v) 
@@ -303,11 +304,11 @@ public:
     int Nk = nbasis;
     subspace.resize(Nk,_FineGrid);
     subspace[0]=1.0;
-    subspace[0].checkerboard=_checkerboard;
+    subspace[0].Checkerboard()=_checkerboard;
     normalise(subspace[0]);
     PlainHermOp<FineField>    Op(_FineOp);
     for(int k=1;k<Nk;k++){
-      subspace[k].checkerboard=_checkerboard;
+      subspace[k].Checkerboard()=_checkerboard;
       Op(subspace[k-1],subspace[k]);
       normalise(subspace[k]);
     }
@@ -333,7 +334,7 @@ public:
     // create a smoother and see if we can get a cheap convergence test and smooth inside the IRL
     //////////////////////////////////////////////////////////////////////////////////////////////////
     Chebyshev<FineField>                          ChebySmooth(cheby_smooth);
-    ProjectedFunctionHermOp<Fobj,CComplex,nbasis> ChebyOp (ChebySmooth,_FineOp,_subspace);
+    ProjectedFunctionHermOp<Fobj,CComplex,nbasis> ChebyOp (ChebySmooth,_FineOp,subspace);
     ImplicitlyRestartedLanczosSmoothedTester<Fobj,CComplex,nbasis> ChebySmoothTester(ChebyOp,ChebySmooth,_FineOp,subspace,relax);
 
     for(int k=0;k<evec_coarse.size();k++){
@@ -358,7 +359,11 @@ public:
 
     ImplicitlyRestartedLanczos<FineField> IRL(ChebyOp,Op,Nstop,Nk,Nm,resid,MaxIt,betastp,MinRes);
 
-    FineField src(_FineGrid); src=1.0; src.checkerboard = _checkerboard;
+    FineField src(_FineGrid); 
+    typedef typename FineField::scalar_type Scalar;
+    // src=1.0; 
+    src=Scalar(1.0); 
+    src.Checkerboard() = _checkerboard;
 
     int Nconv;
     IRL.calc(evals_fine,subspace,src,Nconv,false);
@@ -374,14 +379,14 @@ public:
 		  RealD MaxIt, RealD betastp, int MinRes)
   {
     Chebyshev<FineField>                          Cheby(cheby_op);
-    ProjectedHermOp<Fobj,CComplex,nbasis>         Op(_FineOp,_subspace);
-    ProjectedFunctionHermOp<Fobj,CComplex,nbasis> ChebyOp (Cheby,_FineOp,_subspace);
+    ProjectedHermOp<Fobj,CComplex,nbasis>         Op(_FineOp,subspace);
+    ProjectedFunctionHermOp<Fobj,CComplex,nbasis> ChebyOp (Cheby,_FineOp,subspace);
     //////////////////////////////////////////////////////////////////////////////////////////////////
     // create a smoother and see if we can get a cheap convergence test and smooth inside the IRL
     //////////////////////////////////////////////////////////////////////////////////////////////////
 
     Chebyshev<FineField>                                           ChebySmooth(cheby_smooth);
-    ImplicitlyRestartedLanczosSmoothedTester<Fobj,CComplex,nbasis> ChebySmoothTester(ChebyOp,ChebySmooth,_FineOp,_subspace,relax);
+    ImplicitlyRestartedLanczosSmoothedTester<Fobj,CComplex,nbasis> ChebySmoothTester(ChebyOp,ChebySmooth,_FineOp,subspace,relax);
 
     evals_coarse.resize(Nm);
     evec_coarse.resize(Nm,_CoarseGrid);
@@ -400,5 +405,5 @@ public:
   }
 };
 
-}
+NAMESPACE_END(Grid);
 #endif

Grid/algorithms/iterative/MinimalResidual.h

@@ -0,0 +1,157 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithms/iterative/MinimalResidual.h
+
+Copyright (C) 2015
+
+Author: Daniel Richtmann <daniel.richtmann@ur.de>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_MINIMAL_RESIDUAL_H
+#define GRID_MINIMAL_RESIDUAL_H
+
+namespace Grid {
+
+template<class Field> class MinimalResidual : public OperatorFunction<Field> {
+ public:
+  using OperatorFunction<Field>::operator();
+
+  bool ErrorOnNoConverge; // throw an assert when the MR fails to converge.
+                          // Defaults true.
+  RealD   Tolerance;
+  Integer MaxIterations;
+  RealD   overRelaxParam;
+  Integer IterationsToComplete; // Number of iterations the MR took to finish.
+                                // Filled in upon completion
+
+  MinimalResidual(RealD tol, Integer maxit, Real ovrelparam = 1.0, bool err_on_no_conv = true)
+    : Tolerance(tol), MaxIterations(maxit), overRelaxParam(ovrelparam), ErrorOnNoConverge(err_on_no_conv){};
+
+  void operator()(LinearOperatorBase<Field> &Linop, const Field &src, Field &psi) {
+
+    psi.Checkerboard() = src.Checkerboard();
+    conformable(psi, src);
+
+    ComplexD a, c;
+    RealD    d;
+
+    Field Mr(src);
+    Field r(src);
+
+    // Initial residual computation & set up
+    RealD guess = norm2(psi);
+    assert(std::isnan(guess) == 0);
+
+    RealD ssq = norm2(src);
+    RealD rsq = Tolerance * Tolerance * ssq;
+
+    Linop.Op(psi, Mr);
+
+    r = src - Mr;
+
+    RealD cp = norm2(r);
+
+    std::cout << std::setprecision(4) << std::scientific;
+    std::cout << GridLogIterative << "MinimalResidual: guess " << guess << std::endl;
+    std::cout << GridLogIterative << "MinimalResidual:   src " << ssq << std::endl;
+    std::cout << GridLogIterative << "MinimalResidual:  cp,r " << cp << std::endl;
+
+    if (cp <= rsq) {
+      return;
+    }
+
+    std::cout << GridLogIterative << "MinimalResidual: k=0 residual " << cp << " target " << rsq << std::endl;
+
+    GridStopWatch LinalgTimer;
+    GridStopWatch MatrixTimer;
+    GridStopWatch SolverTimer;
+
+    SolverTimer.Start();
+    int k;
+    for (k = 1; k <= MaxIterations; k++) {
+
+      MatrixTimer.Start();
+      Linop.Op(r, Mr);
+      MatrixTimer.Stop();
+
+      LinalgTimer.Start();
+
+      c = innerProduct(Mr, r);
+
+      d = norm2(Mr);
+
+      a = c / d;
+
+      a = a * overRelaxParam;
+
+      psi = psi + r * a;
+
+      r = r - Mr * a;
+
+      cp = norm2(r);
+
+      LinalgTimer.Stop();
+
+      std::cout << GridLogIterative << "MinimalResidual: Iteration " << k
+                << " residual " << cp << " target " << rsq << std::endl;
+      std::cout << GridLogDebug << "a = " << a << " c = " << c << " d = " << d << std::endl;
+
+      // Stopping condition
+      if (cp <= rsq) {
+        SolverTimer.Stop();
+
+        Linop.Op(psi, Mr);
+        r = src - Mr;
+
+        RealD srcnorm       = sqrt(ssq);
+        RealD resnorm       = sqrt(norm2(r));
+        RealD true_residual = resnorm / srcnorm;
+
+        std::cout << GridLogMessage        << "MinimalResidual Converged on iteration " << k
+                  << " computed residual " << sqrt(cp / ssq)
+                  << " true residual "     << true_residual
+                  << " target "            << Tolerance << std::endl;
+
+        std::cout << GridLogMessage << "MR Time elapsed: Total   " << SolverTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "MR Time elapsed: Matrix  " << MatrixTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "MR Time elapsed: Linalg  " << LinalgTimer.Elapsed() << std::endl;
+
+        if (ErrorOnNoConverge)
+          assert(true_residual / Tolerance < 10000.0);
+
+        IterationsToComplete = k;
+
+        return;
+      }
+    }
+
+    std::cout << GridLogMessage << "MinimalResidual did NOT converge"
+              << std::endl;
+
+    if (ErrorOnNoConverge)
+      assert(0);
+
+    IterationsToComplete = k;
+  }
+};
+} // namespace Grid
+#endif

Grid/algorithms/iterative/MixedPrecisionFlexibleGeneralisedMinimalResidual.h

@@ -0,0 +1,276 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithms/iterative/MixedPrecisionFlexibleGeneralisedMinimalResidual.h
+
+Copyright (C) 2015
+
+Author: Daniel Richtmann <daniel.richtmann@ur.de>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_MIXED_PRECISION_FLEXIBLE_GENERALISED_MINIMAL_RESIDUAL_H
+#define GRID_MIXED_PRECISION_FLEXIBLE_GENERALISED_MINIMAL_RESIDUAL_H
+
+namespace Grid {
+
+template<class FieldD, class FieldF, typename std::enable_if<getPrecision<FieldD>::value == 2, int>::type = 0, typename std::enable_if< getPrecision<FieldF>::value == 1, int>::type = 0>
+class MixedPrecisionFlexibleGeneralisedMinimalResidual : public OperatorFunction<FieldD> {
+ public:
+
+  using OperatorFunction<FieldD>::operator();
+
+  bool ErrorOnNoConverge; // Throw an assert when MPFGMRES fails to converge,
+                          // defaults to true
+
+  RealD   Tolerance;
+
+  Integer MaxIterations;
+  Integer RestartLength;
+  Integer MaxNumberOfRestarts;
+  Integer IterationCount; // Number of iterations the MPFGMRES took to finish,
+                          // filled in upon completion
+
+  GridStopWatch MatrixTimer;
+  GridStopWatch PrecTimer;
+  GridStopWatch LinalgTimer;
+  GridStopWatch QrTimer;
+  GridStopWatch CompSolutionTimer;
+  GridStopWatch ChangePrecTimer;
+
+  Eigen::MatrixXcd H;
+
+  std::vector<ComplexD> y;
+  std::vector<ComplexD> gamma;
+  std::vector<ComplexD> c;
+  std::vector<ComplexD> s;
+
+  GridBase* SinglePrecGrid;
+
+  LinearFunction<FieldF> &Preconditioner;
+
+  MixedPrecisionFlexibleGeneralisedMinimalResidual(RealD   tol,
+                                                   Integer maxit,
+                                                   GridBase * sp_grid,
+                                                   LinearFunction<FieldF> &Prec,
+                                                   Integer restart_length,
+                                                   bool    err_on_no_conv = true)
+      : Tolerance(tol)
+      , MaxIterations(maxit)
+      , RestartLength(restart_length)
+      , MaxNumberOfRestarts(MaxIterations/RestartLength + ((MaxIterations%RestartLength == 0) ? 0 : 1))
+      , ErrorOnNoConverge(err_on_no_conv)
+      , H(Eigen::MatrixXcd::Zero(RestartLength, RestartLength + 1)) // sizes taken from DD-αAMG code base
+      , y(RestartLength + 1, 0.)
+      , gamma(RestartLength + 1, 0.)
+      , c(RestartLength + 1, 0.)
+      , s(RestartLength + 1, 0.)
+      , SinglePrecGrid(sp_grid)
+      , Preconditioner(Prec) {};
+
+  void operator()(LinearOperatorBase<FieldD> &LinOp, const FieldD &src, FieldD &psi) {
+
+    psi.Checkerboard() = src.Checkerboard();
+    conformable(psi, src);
+
+    RealD guess = norm2(psi);
+    assert(std::isnan(guess) == 0);
+
+    RealD cp;
+    RealD ssq = norm2(src);
+    RealD rsq = Tolerance * Tolerance * ssq;
+
+    FieldD r(src.Grid());
+
+    std::cout << std::setprecision(4) << std::scientific;
+    std::cout << GridLogIterative << "MPFGMRES: guess " << guess << std::endl;
+    std::cout << GridLogIterative << "MPFGMRES:   src " << ssq   << std::endl;
+
+    PrecTimer.Reset();
+    MatrixTimer.Reset();
+    LinalgTimer.Reset();
+    QrTimer.Reset();
+    CompSolutionTimer.Reset();
+    ChangePrecTimer.Reset();
+
+    GridStopWatch SolverTimer;
+    SolverTimer.Start();
+
+    IterationCount = 0;
+
+    for (int k=0; k<MaxNumberOfRestarts; k++) {
+
+      cp = outerLoopBody(LinOp, src, psi, rsq);
+
+      // Stopping condition
+      if (cp <= rsq) {
+
+        SolverTimer.Stop();
+
+        LinOp.Op(psi,r);
+        axpy(r,-1.0,src,r);
+
+        RealD srcnorm       = sqrt(ssq);
+        RealD resnorm       = sqrt(norm2(r));
+        RealD true_residual = resnorm / srcnorm;
+
+        std::cout << GridLogMessage        << "MPFGMRES: Converged on iteration " << IterationCount
+                  << " computed residual " << sqrt(cp / ssq)
+                  << " true residual "     << true_residual
+                  << " target "            << Tolerance << std::endl;
+
+        std::cout << GridLogMessage << "MPFGMRES Time elapsed: Total      " <<       SolverTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "MPFGMRES Time elapsed: Precon     " <<         PrecTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "MPFGMRES Time elapsed: Matrix     " <<       MatrixTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "MPFGMRES Time elapsed: Linalg     " <<       LinalgTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "MPFGMRES Time elapsed: QR         " <<           QrTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "MPFGMRES Time elapsed: CompSol    " << CompSolutionTimer.Elapsed() << std::endl;
+        std::cout << GridLogMessage << "MPFGMRES Time elapsed: PrecChange " <<   ChangePrecTimer.Elapsed() << std::endl;
+        return;
+      }
+    }
+
+    std::cout << GridLogMessage << "MPFGMRES did NOT converge" << std::endl;
+
+    if (ErrorOnNoConverge)
+      assert(0);
+  }
+
+  RealD outerLoopBody(LinearOperatorBase<FieldD> &LinOp, const FieldD &src, FieldD &psi, RealD rsq) {
+
+    RealD cp = 0;
+
+    FieldD w(src.Grid());
+    FieldD r(src.Grid());
+
+    // these should probably be made class members so that they are only allocated once, not in every restart
+    std::vector<FieldD> v(RestartLength + 1, src.Grid()); for (auto &elem : v) elem = Zero();
+    std::vector<FieldD> z(RestartLength + 1, src.Grid()); for (auto &elem : z) elem = Zero();
+
+    MatrixTimer.Start();
+    LinOp.Op(psi, w);
+    MatrixTimer.Stop();
+
+    LinalgTimer.Start();
+    r = src - w;
+
+    gamma[0] = sqrt(norm2(r));
+
+    v[0] = (1. / gamma[0]) * r;
+    LinalgTimer.Stop();
+
+    for (int i=0; i<RestartLength; i++) {
+
+      IterationCount++;
+
+      arnoldiStep(LinOp, v, z, w, i);
+
+      qrUpdate(i);
+
+      cp = norm(gamma[i+1]);
+
+      std::cout << GridLogIterative << "MPFGMRES: Iteration " << IterationCount
+                << " residual " << cp << " target " << rsq << std::endl;
+
+      if ((i == RestartLength - 1) || (IterationCount == MaxIterations) || (cp <= rsq)) {
+
+        computeSolution(z, psi, i);
+
+        return cp;
+      }
+    }
+
+    assert(0); // Never reached
+    return cp;
+  }
+
+  void arnoldiStep(LinearOperatorBase<FieldD> &LinOp, std::vector<FieldD> &v, std::vector<FieldD> &z, FieldD &w, int iter) {
+
+    FieldF v_f(SinglePrecGrid);
+    FieldF z_f(SinglePrecGrid);
+
+    ChangePrecTimer.Start();
+    precisionChange(v_f, v[iter]);
+    precisionChange(z_f, z[iter]);
+    ChangePrecTimer.Stop();
+
+    PrecTimer.Start();
+    Preconditioner(v_f, z_f);
+    PrecTimer.Stop();
+
+    ChangePrecTimer.Start();
+    precisionChange(z[iter], z_f);
+    ChangePrecTimer.Stop();
+
+    MatrixTimer.Start();
+    LinOp.Op(z[iter], w);
+    MatrixTimer.Stop();
+
+    LinalgTimer.Start();
+    for (int i = 0; i <= iter; ++i) {
+      H(iter, i) = innerProduct(v[i], w);
+      w = w - ComplexD(H(iter, i)) * v[i];
+    }
+
+    H(iter, iter + 1) = sqrt(norm2(w));
+    v[iter + 1] = ComplexD(1. / H(iter, iter + 1)) * w;
+    LinalgTimer.Stop();
+  }
+
+  void qrUpdate(int iter) {
+
+    QrTimer.Start();
+    for (int i = 0; i < iter ; ++i) {
+      auto tmp       = -s[i] * ComplexD(H(iter, i)) + c[i] * ComplexD(H(iter, i + 1));
+      H(iter, i)     = conjugate(c[i]) * ComplexD(H(iter, i)) + conjugate(s[i]) * ComplexD(H(iter, i + 1));
+      H(iter, i + 1) = tmp;
+    }
+
+    // Compute new Givens Rotation
+    auto nu = sqrt(std::norm(H(iter, iter)) + std::norm(H(iter, iter + 1)));
+    c[iter]     = H(iter, iter) / nu;
+    s[iter]     = H(iter, iter + 1) / nu;
+
+    // Apply new Givens rotation
+    H(iter, iter)     = nu;
+    H(iter, iter + 1) = 0.;
+
+    gamma[iter + 1] = -s[iter] * gamma[iter];
+    gamma[iter]     = conjugate(c[iter]) * gamma[iter];
+    QrTimer.Stop();
+  }
+
+  void computeSolution(std::vector<FieldD> const &z, FieldD &psi, int iter) {
+
+    CompSolutionTimer.Start();
+    for (int i = iter; i >= 0; i--) {
+      y[i] = gamma[i];
+      for (int k = i + 1; k <= iter; k++)
+        y[i] = y[i] - ComplexD(H(k, i)) * y[k];
+      y[i] = y[i] / ComplexD(H(i, i));
+    }
+
+    for (int i = 0; i <= iter; i++)
+      psi = psi + z[i] * y[i];
+    CompSolutionTimer.Stop();
+  }
+};
+}
+#endif

Grid/algorithms/iterative/NormalEquations.h

@@ -0,0 +1,112 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/NormalEquations.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_NORMAL_EQUATIONS_H
+#define GRID_NORMAL_EQUATIONS_H
+
+NAMESPACE_BEGIN(Grid);
+
+///////////////////////////////////////////////////////////////////////////////////////////////////////
+// Take a matrix and form an NE solver calling a Herm solver
+///////////////////////////////////////////////////////////////////////////////////////////////////////
+template<class Field> class NormalEquations {
+private:
+  SparseMatrixBase<Field> & _Matrix;
+  OperatorFunction<Field> & _HermitianSolver;
+  LinearFunction<Field>   & _Guess;
+public:
+
+  /////////////////////////////////////////////////////
+  // Wrap the usual normal equations trick
+  /////////////////////////////////////////////////////
+ NormalEquations(SparseMatrixBase<Field> &Matrix, OperatorFunction<Field> &HermitianSolver,
+		 LinearFunction<Field> &Guess) 
+   :  _Matrix(Matrix), _HermitianSolver(HermitianSolver), _Guess(Guess) {}; 
+
+  void operator() (const Field &in, Field &out){
+ 
+    Field src(in.Grid());
+    Field tmp(in.Grid());
+
+    MdagMLinearOperator<SparseMatrixBase<Field>,Field> MdagMOp(_Matrix);
+    _Matrix.Mdag(in,src);
+    _Guess(src,out);
+    _HermitianSolver(MdagMOp,src,out);  // Mdag M out = Mdag in
+
+  }     
+};
+
+template<class Field> class HPDSolver {
+private:
+  LinearOperatorBase<Field> & _Matrix;
+  OperatorFunction<Field> & _HermitianSolver;
+  LinearFunction<Field>   & _Guess;
+public:
+
+  /////////////////////////////////////////////////////
+  // Wrap the usual normal equations trick
+  /////////////////////////////////////////////////////
+ HPDSolver(LinearOperatorBase<Field> &Matrix,
+	   OperatorFunction<Field> &HermitianSolver,
+	   LinearFunction<Field> &Guess) 
+   :  _Matrix(Matrix), _HermitianSolver(HermitianSolver), _Guess(Guess) {}; 
+
+  void operator() (const Field &in, Field &out){
+ 
+    _Guess(in,out);
+    _HermitianSolver(_Matrix,in,out);  // Mdag M out = Mdag in
+
+  }     
+};
+
+
+template<class Field> class MdagMSolver {
+private:
+  SparseMatrixBase<Field> & _Matrix;
+  OperatorFunction<Field> & _HermitianSolver;
+  LinearFunction<Field>   & _Guess;
+public:
+
+  /////////////////////////////////////////////////////
+  // Wrap the usual normal equations trick
+  /////////////////////////////////////////////////////
+ MdagMSolver(SparseMatrixBase<Field> &Matrix, OperatorFunction<Field> &HermitianSolver,
+	     LinearFunction<Field> &Guess) 
+   :  _Matrix(Matrix), _HermitianSolver(HermitianSolver), _Guess(Guess) {}; 
+
+  void operator() (const Field &in, Field &out){
+ 
+    MdagMLinearOperator<SparseMatrixBase<Field>,Field> MdagMOp(_Matrix);
+    _Guess(in,out);
+
+    _HermitianSolver(MdagMOp,in,out);  // Mdag M out = Mdag in
+
+  }     
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/PowerMethod.h

@@ -0,0 +1,45 @@
+#pragma once
+namespace Grid {
+template<class Field> class PowerMethod  
+{ 
+ public: 
+
+  template<typename T>  static RealD normalise(T& v) 
+  {
+    RealD nn = norm2(v);
+    nn = sqrt(nn);
+    v = v * (1.0/nn);
+    return nn;
+  }
+
+  RealD operator()(LinearOperatorBase<Field> &HermOp, const Field &src) 
+  { 
+    GridBase *grid = src.Grid(); 
+    
+    // quickly get an idea of the largest eigenvalue to more properly normalize the residuum 
+    RealD evalMaxApprox = 0.0; 
+    auto src_n = src; 
+    auto tmp = src; 
+    const int _MAX_ITER_EST_ = 50; 
+
+    for (int i=0;i<_MAX_ITER_EST_;i++) { 
+      
+      normalise(src_n); 
+      HermOp.HermOp(src_n,tmp); 
+      RealD vnum = real(innerProduct(src_n,tmp)); // HermOp. 
+      RealD vden = norm2(src_n); 
+      RealD na = vnum/vden; 
+      
+      if ( (fabs(evalMaxApprox/na - 1.0) < 0.001) || (i==_MAX_ITER_EST_-1) ) { 
+ 	evalMaxApprox = na; 
+	std::cout << GridLogMessage << " Approximation of largest eigenvalue: " << evalMaxApprox << std::endl;
+ 	return evalMaxApprox; 
+      } 
+      evalMaxApprox = na; 
+      src_n = tmp;
+    }
+    assert(0);
+    return 0;
+  }
+};
+}

Grid/algorithms/iterative/PrecConjugateResidual.h

@@ -0,0 +1,119 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/PrecConjugateResidual.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_PREC_CONJUGATE_RESIDUAL_H
+#define GRID_PREC_CONJUGATE_RESIDUAL_H
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////
+// Base classes for iterative processes based on operators
+// single input vec, single output vec.
+/////////////////////////////////////////////////////////////
+
+template<class Field> 
+class PrecConjugateResidual : public OperatorFunction<Field> {
+public:                                                
+  RealD   Tolerance;
+  Integer MaxIterations;
+  int verbose;
+  LinearFunction<Field> &Preconditioner;
+
+  PrecConjugateResidual(RealD tol,Integer maxit,LinearFunction<Field> &Prec) : Tolerance(tol), MaxIterations(maxit),      Preconditioner(Prec)
+  { 
+    verbose=1;
+  };
+
+  void operator() (LinearOperatorBase<Field> &Linop,const Field &src, Field &psi){
+
+    RealD a, b, c, d;
+    RealD cp, ssq,rsq;
+      
+    RealD rAr, rAAr, rArp;
+    RealD pAp, pAAp;
+
+    GridBase *grid = src.Grid();
+    Field r(grid),  p(grid), Ap(grid), Ar(grid), z(grid);
+      
+    psi=zero;
+    r  = src;
+    Preconditioner(r,p);
+
+      
+
+    Linop.HermOpAndNorm(p,Ap,pAp,pAAp);
+    Ar=Ap;
+    rAr=pAp;
+    rAAr=pAAp;
+
+    cp =norm2(r);
+    ssq=norm2(src);
+    rsq=Tolerance*Tolerance*ssq;
+
+    if (verbose) std::cout<<GridLogMessage<<"PrecConjugateResidual: iteration " <<0<<" residual "<<cp<< " target"<< rsq<<std::endl;
+
+    for(int k=0;k<MaxIterations;k++){
+
+
+      Preconditioner(Ap,z);
+      RealD rq= real(innerProduct(Ap,z)); 
+
+      a = rAr/rq;
+
+      axpy(psi,a,p,psi);
+      cp = axpy_norm(r,-a,z,r);
+
+      rArp=rAr;
+
+      Linop.HermOpAndNorm(r,Ar,rAr,rAAr);
+
+      b   =rAr/rArp;
+ 
+      axpy(p,b,p,r);
+      pAAp=axpy_norm(Ap,b,Ap,Ar);
+	
+      if(verbose) std::cout<<GridLogMessage<<"PrecConjugateResidual: iteration " <<k<<" residual "<<cp<< " target"<< rsq<<std::endl;
+
+      if(cp<rsq) {
+	Linop.HermOp(psi,Ap);
+	axpy(r,-1.0,src,Ap);
+	RealD true_resid = norm2(r)/ssq;
+	std::cout<<GridLogMessage<<"PrecConjugateResidual: Converged on iteration " <<k
+		 << " computed residual "<<sqrt(cp/ssq)
+		 << " true residual "<<sqrt(true_resid)
+		 << " target "       <<Tolerance <<std::endl;
+	return;
+      }
+
+    }
+
+    std::cout<<GridLogMessage<<"PrecConjugateResidual did NOT converge"<<std::endl;
+    assert(0);
+  }
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/PrecGeneralisedConjugateResidual.h

@@ -0,0 +1,239 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/PrecGeneralisedConjugateResidual.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_PREC_GCR_H
+#define GRID_PREC_GCR_H
+
+///////////////////////////////////////////////////////////////////////////////////////////////////////
+//VPGCR Abe and Zhang, 2005.
+//INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
+//Computing and Information Volume 2, Number 2, Pages 147-161
+//NB. Likely not original reference since they are focussing on a preconditioner variant.
+//    but VPGCR was nicely written up in their paper
+///////////////////////////////////////////////////////////////////////////////////////////////////////
+NAMESPACE_BEGIN(Grid);
+
+#define GCRLogLevel std::cout << GridLogMessage <<std::string(level,'\t')<< " Level "<<level<<" " 
+
+template<class Field>
+class PrecGeneralisedConjugateResidual : public LinearFunction<Field> {
+public:                                                
+
+  RealD   Tolerance;
+  Integer MaxIterations;
+  int verbose;
+  int mmax;
+  int nstep;
+  int steps;
+  int level;
+  GridStopWatch PrecTimer;
+  GridStopWatch MatTimer;
+  GridStopWatch LinalgTimer;
+
+  LinearFunction<Field>     &Preconditioner;
+  LinearOperatorBase<Field> &Linop;
+
+  void Level(int lv) { level=lv; };
+
+  PrecGeneralisedConjugateResidual(RealD tol,Integer maxit,LinearOperatorBase<Field> &_Linop,LinearFunction<Field> &Prec,int _mmax,int _nstep) : 
+    Tolerance(tol), 
+    MaxIterations(maxit),
+    Linop(_Linop),
+    Preconditioner(Prec),
+    mmax(_mmax),
+    nstep(_nstep)
+  { 
+    level=1;
+    verbose=1;
+  };
+
+  void operator() (const Field &src, Field &psi){
+
+    psi=Zero();
+    RealD cp, ssq,rsq;
+    ssq=norm2(src);
+    rsq=Tolerance*Tolerance*ssq;
+      
+    Field r(src.Grid());
+
+    PrecTimer.Reset();
+    MatTimer.Reset();
+    LinalgTimer.Reset();
+
+    GridStopWatch SolverTimer;
+    SolverTimer.Start();
+
+    steps=0;
+    for(int k=0;k<MaxIterations;k++){
+
+      cp=GCRnStep(src,psi,rsq);
+
+      GCRLogLevel <<"PGCR("<<mmax<<","<<nstep<<") "<< steps <<" steps cp = "<<cp<<" target "<<rsq <<std::endl;
+
+      if(cp<rsq) {
+
+	SolverTimer.Stop();
+
+	Linop.HermOp(psi,r);
+	axpy(r,-1.0,src,r);
+	RealD tr = norm2(r);
+	GCRLogLevel<<"PGCR: Converged on iteration " <<steps
+		 << " computed residual "<<sqrt(cp/ssq)
+		 << " true residual "    <<sqrt(tr/ssq)
+		 << " target "           <<Tolerance <<std::endl;
+
+	GCRLogLevel<<"PGCR Time elapsed: Total  "<< SolverTimer.Elapsed() <<std::endl;
+	/*
+	  GCRLogLevel<<"PGCR Time elapsed: Precon "<<   PrecTimer.Elapsed() <<std::endl;
+	  GCRLogLevel<<"PGCR Time elapsed: Matrix "<<    MatTimer.Elapsed() <<std::endl;
+	  GCRLogLevel<<"PGCR Time elapsed: Linalg "<< LinalgTimer.Elapsed() <<std::endl;
+	*/
+	return;
+      }
+
+    }
+    GCRLogLevel<<"Variable Preconditioned GCR did not converge"<<std::endl;
+    //    assert(0);
+  }
+
+  RealD GCRnStep(const Field &src, Field &psi,RealD rsq){
+
+    RealD cp;
+    RealD a, b;
+    RealD zAz, zAAz;
+    RealD rq;
+
+    GridBase *grid = src.Grid();
+
+    Field r(grid);
+    Field z(grid);
+    Field tmp(grid);
+    Field ttmp(grid);
+    Field Az(grid);
+
+    ////////////////////////////////
+    // history for flexible orthog
+    ////////////////////////////////
+    std::vector<Field> q(mmax,grid);
+    std::vector<Field> p(mmax,grid);
+    std::vector<RealD> qq(mmax);
+      
+    GCRLogLevel<< "PGCR nStep("<<nstep<<")"<<std::endl;
+
+    //////////////////////////////////
+    // initial guess x0 is taken as nonzero.
+    // r0=src-A x0 = src
+    //////////////////////////////////
+    MatTimer.Start();
+    Linop.HermOpAndNorm(psi,Az,zAz,zAAz); 
+    MatTimer.Stop();
+    
+
+    LinalgTimer.Start();
+    r=src-Az;
+    LinalgTimer.Stop();
+    GCRLogLevel<< "PGCR true residual r = src - A psi   "<<norm2(r) <<std::endl;
+    
+    /////////////////////
+    // p = Prec(r)
+    /////////////////////
+
+    PrecTimer.Start();
+    Preconditioner(r,z);
+    PrecTimer.Stop();
+
+    MatTimer.Start();
+    Linop.HermOpAndNorm(z,Az,zAz,zAAz); 
+    MatTimer.Stop();
+
+    LinalgTimer.Start();
+
+    //p[0],q[0],qq[0] 
+    p[0]= z;
+    q[0]= Az;
+    qq[0]= zAAz;
+    
+    cp =norm2(r);
+    LinalgTimer.Stop();
+
+    for(int k=0;k<nstep;k++){
+
+      steps++;
+
+      int kp     = k+1;
+      int peri_k = k %mmax;
+      int peri_kp= kp%mmax;
+
+      LinalgTimer.Start();
+      rq= real(innerProduct(r,q[peri_k])); // what if rAr not real?
+      a = rq/qq[peri_k];
+
+      axpy(psi,a,p[peri_k],psi);         
+
+      cp = axpy_norm(r,-a,q[peri_k],r);
+      LinalgTimer.Stop();
+
+      GCRLogLevel<< "PGCR step["<<steps<<"]  resid " << cp << " target " <<rsq<<std::endl; 
+
+      if((k==nstep-1)||(cp<rsq)){
+	return cp;
+      }
+
+
+      PrecTimer.Start();
+      Preconditioner(r,z);// solve Az = r
+      PrecTimer.Stop();
+
+      MatTimer.Start();
+      Linop.HermOpAndNorm(z,Az,zAz,zAAz);
+      MatTimer.Stop();
+
+      LinalgTimer.Start();
+
+      q[peri_kp]=Az;
+      p[peri_kp]=z;
+
+      int northog = ((kp)>(mmax-1))?(mmax-1):(kp);  // if more than mmax done, we orthog all mmax history.
+      for(int back=0;back<northog;back++){
+
+	int peri_back=(k-back)%mmax;   	  assert((k-back)>=0);
+
+	b=-real(innerProduct(q[peri_back],Az))/qq[peri_back];
+	p[peri_kp]=p[peri_kp]+b*p[peri_back];
+	q[peri_kp]=q[peri_kp]+b*q[peri_back];
+
+      }
+      qq[peri_kp]=norm2(q[peri_kp]); // could use axpy_norm
+      LinalgTimer.Stop();
+    }
+    assert(0); // never reached
+    return cp;
+  }
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.h

@@ -0,0 +1,241 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/PrecGeneralisedConjugateResidual.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_PREC_GCR_NON_HERM_H
+#define GRID_PREC_GCR_NON_HERM_H
+
+///////////////////////////////////////////////////////////////////////////////////////////////////////
+//VPGCR Abe and Zhang, 2005.
+//INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
+//Computing and Information Volume 2, Number 2, Pages 147-161
+//NB. Likely not original reference since they are focussing on a preconditioner variant.
+//    but VPGCR was nicely written up in their paper
+///////////////////////////////////////////////////////////////////////////////////////////////////////
+NAMESPACE_BEGIN(Grid);
+
+#define GCRLogLevel std::cout << GridLogMessage <<std::string(level,'\t')<< " Level "<<level<<" " 
+
+template<class Field>
+class PrecGeneralisedConjugateResidualNonHermitian : public LinearFunction<Field> {
+public:                                                
+
+  RealD   Tolerance;
+  Integer MaxIterations;
+  int verbose;
+  int mmax;
+  int nstep;
+  int steps;
+  int level;
+  GridStopWatch PrecTimer;
+  GridStopWatch MatTimer;
+  GridStopWatch LinalgTimer;
+
+  LinearFunction<Field>     &Preconditioner;
+  LinearOperatorBase<Field> &Linop;
+
+  void Level(int lv) { level=lv; };
+
+  PrecGeneralisedConjugateResidualNonHermitian(RealD tol,Integer maxit,LinearOperatorBase<Field> &_Linop,LinearFunction<Field> &Prec,int _mmax,int _nstep) : 
+    Tolerance(tol), 
+    MaxIterations(maxit),
+    Linop(_Linop),
+    Preconditioner(Prec),
+    mmax(_mmax),
+    nstep(_nstep)
+  { 
+    level=1;
+    verbose=1;
+  };
+
+  void operator() (const Field &src, Field &psi){
+
+    psi=Zero();
+    RealD cp, ssq,rsq;
+    ssq=norm2(src);
+    rsq=Tolerance*Tolerance*ssq;
+      
+    Field r(src.Grid());
+
+    PrecTimer.Reset();
+    MatTimer.Reset();
+    LinalgTimer.Reset();
+
+    GridStopWatch SolverTimer;
+    SolverTimer.Start();
+
+    steps=0;
+    for(int k=0;k<MaxIterations;k++){
+
+      cp=GCRnStep(src,psi,rsq);
+
+      GCRLogLevel <<"PGCR("<<mmax<<","<<nstep<<") "<< steps <<" steps cp = "<<cp<<" target "<<rsq <<std::endl;
+
+      if(cp<rsq) {
+
+	SolverTimer.Stop();
+
+	Linop.Op(psi,r);
+	axpy(r,-1.0,src,r);
+	RealD tr = norm2(r);
+	GCRLogLevel<<"PGCR: Converged on iteration " <<steps
+		 << " computed residual "<<sqrt(cp/ssq)
+		 << " true residual "    <<sqrt(tr/ssq)
+		 << " target "           <<Tolerance <<std::endl;
+
+	GCRLogLevel<<"PGCR Time elapsed: Total  "<< SolverTimer.Elapsed() <<std::endl;
+	return;
+      }
+
+    }
+    GCRLogLevel<<"Variable Preconditioned GCR did not converge"<<std::endl;
+    //    assert(0);
+  }
+
+  RealD GCRnStep(const Field &src, Field &psi,RealD rsq){
+
+    RealD cp;
+    ComplexD a, b, zAz;
+    RealD zAAz;
+    ComplexD rq;
+
+    GridBase *grid = src.Grid();
+
+    Field r(grid);
+    Field z(grid);
+    Field tmp(grid);
+    Field ttmp(grid);
+    Field Az(grid);
+
+    ////////////////////////////////
+    // history for flexible orthog
+    ////////////////////////////////
+    std::vector<Field> q(mmax,grid);
+    std::vector<Field> p(mmax,grid);
+    std::vector<RealD> qq(mmax);
+      
+    GCRLogLevel<< "PGCR nStep("<<nstep<<")"<<std::endl;
+
+    //////////////////////////////////
+    // initial guess x0 is taken as nonzero.
+    // r0=src-A x0 = src
+    //////////////////////////////////
+    MatTimer.Start();
+    Linop.Op(psi,Az);
+    zAz = innerProduct(Az,psi);
+    zAAz= norm2(Az);
+    MatTimer.Stop();
+    
+
+    LinalgTimer.Start();
+    r=src-Az;
+    LinalgTimer.Stop();
+    GCRLogLevel<< "PGCR true residual r = src - A psi   "<<norm2(r) <<std::endl;
+    
+    /////////////////////
+    // p = Prec(r)
+    /////////////////////
+
+    PrecTimer.Start();
+    Preconditioner(r,z);
+    PrecTimer.Stop();
+
+    MatTimer.Start();
+    Linop.Op(z,Az);
+    MatTimer.Stop();
+
+    LinalgTimer.Start();
+
+    zAz = innerProduct(Az,psi);
+    zAAz= norm2(Az);
+
+    //p[0],q[0],qq[0] 
+    p[0]= z;
+    q[0]= Az;
+    qq[0]= zAAz;
+    
+    cp =norm2(r);
+    LinalgTimer.Stop();
+
+    for(int k=0;k<nstep;k++){
+
+      steps++;
+
+      int kp     = k+1;
+      int peri_k = k %mmax;
+      int peri_kp= kp%mmax;
+
+      LinalgTimer.Start();
+      rq= innerProduct(q[peri_k],r); // what if rAr not real?
+      a = rq/qq[peri_k];
+
+      axpy(psi,a,p[peri_k],psi);         
+
+      cp = axpy_norm(r,-a,q[peri_k],r);
+      LinalgTimer.Stop();
+
+      GCRLogLevel<< "PGCR step["<<steps<<"]  resid " << cp << " target " <<rsq<<std::endl; 
+
+      if((k==nstep-1)||(cp<rsq)){
+	return cp;
+      }
+
+
+      PrecTimer.Start();
+      Preconditioner(r,z);// solve Az = r
+      PrecTimer.Stop();
+
+      MatTimer.Start();
+      Linop.Op(z,Az);
+      MatTimer.Stop();
+      zAz = innerProduct(Az,psi);
+      zAAz= norm2(Az);
+
+      LinalgTimer.Start();
+
+      q[peri_kp]=Az;
+      p[peri_kp]=z;
+
+      int northog = ((kp)>(mmax-1))?(mmax-1):(kp);  // if more than mmax done, we orthog all mmax history.
+      for(int back=0;back<northog;back++){
+
+	int peri_back=(k-back)%mmax;   	  assert((k-back)>=0);
+
+	b=-real(innerProduct(q[peri_back],Az))/qq[peri_back];
+	p[peri_kp]=p[peri_kp]+b*p[peri_back];
+	q[peri_kp]=q[peri_kp]+b*q[peri_back];
+
+      }
+      qq[peri_kp]=norm2(q[peri_kp]); // could use axpy_norm
+      LinalgTimer.Stop();
+    }
+    assert(0); // never reached
+    return cp;
+  }
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/QuasiMinimalResidual.h

@@ -0,0 +1,371 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithmsf/iterative/QuasiMinimalResidual.h
+
+Copyright (C) 2019
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+template<class Field> 
+RealD innerG5ProductReal(Field &l, Field &r)
+{
+  Gamma G5(Gamma::Algebra::Gamma5);
+  Field tmp(l.Grid());
+  //  tmp = G5*r;
+  G5R5(tmp,r);
+  ComplexD ip =innerProduct(l,tmp);
+  std::cout << "innerProductRealG5R5 "<<ip<<std::endl;
+  return ip.real();
+}
+
+template<class Field>
+class QuasiMinimalResidual : public OperatorFunction<Field> {
+ public:
+  using OperatorFunction<Field>::operator();
+
+  bool ErrorOnNoConverge; 
+  RealD   Tolerance;
+  Integer MaxIterations;
+  Integer IterationCount;
+
+  QuasiMinimalResidual(RealD   tol,
+		       Integer maxit,
+		       bool    err_on_no_conv = true)
+      : Tolerance(tol)
+      , MaxIterations(maxit)
+      , ErrorOnNoConverge(err_on_no_conv) 
+  {};
+
+#if 1
+  void operator()(LinearOperatorBase<Field> &LinOp, const Field &b, Field &x) 
+  {
+    RealD resid;
+    IterationCount=0;
+
+    RealD  rho, rho_1, xi, gamma, gamma_1, theta, theta_1;
+    RealD  eta, delta, ep, beta; 
+
+    GridBase *Grid = b.Grid();
+    Field r(Grid), d(Grid), s(Grid);
+    Field v(Grid), w(Grid), y(Grid),  z(Grid);
+    Field v_tld(Grid), w_tld(Grid), y_tld(Grid), z_tld(Grid);
+    Field p(Grid), q(Grid), p_tld(Grid);
+
+    Real normb = norm2(b);
+
+    LinOp.Op(x,r); r = b - r;
+
+    assert(normb> 0.0);
+
+    resid = norm2(r)/normb;
+    if (resid <= Tolerance) {
+      return;
+    }
+
+    v_tld = r;
+    y = v_tld;
+    rho = norm2(y);
+
+    // Take Gamma5 conjugate
+    //    Gamma G5(Gamma::Algebra::Gamma5);
+    //    G5R5(w_tld,r);
+    //    w_tld = G5* v_tld;
+    w_tld=v_tld;
+    z = w_tld;
+    xi = norm2(z);
+
+    gamma = 1.0;
+    eta   = -1.0;
+    theta = 0.0;
+
+    for (int i = 1; i <= MaxIterations; i++) {
+
+      // Breakdown tests
+      assert( rho != 0.0);
+      assert( xi  != 0.0);
+
+      v = (1. / rho) * v_tld;
+      y = (1. / rho) * y;
+
+      w = (1. / xi) * w_tld;
+      z = (1. / xi) * z;
+
+      ComplexD Zdelta = innerProduct(z, y); // Complex?
+      std::cout << "Zdelta "<<Zdelta<<std::endl;
+      delta = Zdelta.real();
+
+      y_tld = y; 
+      z_tld = z;
+
+      if (i > 1) {
+	p = y_tld - (xi  * delta / ep) * p;
+	q = z_tld - (rho * delta / ep) * q;
+      } else {
+	p = y_tld;
+	q = z_tld;
+      }
+
+      LinOp.Op(p,p_tld);      //     p_tld = A * p;
+      ComplexD Zep = innerProduct(q, p_tld);
+      ep=Zep.real();
+      std::cout << "Zep "<<Zep <<std::endl;
+      // Complex Audit
+      assert(abs(ep)>0);
+
+      beta = ep / delta;
+      assert(abs(beta)>0);
+
+      v_tld = p_tld - beta * v;
+      y = v_tld;
+
+      rho_1 = rho;
+      rho   = norm2(y);
+      LinOp.AdjOp(q,w_tld);
+      w_tld = w_tld - beta * w;
+      z = w_tld;
+
+      xi = norm2(z);
+
+      gamma_1 = gamma;
+      theta_1 = theta;
+
+      theta   = rho / (gamma_1 * beta);
+      gamma   = 1.0 / sqrt(1.0 + theta * theta);
+      std::cout << "theta "<<theta<<std::endl;
+      std::cout << "gamma "<<gamma<<std::endl;
+
+      assert(abs(gamma)> 0.0);
+
+      eta = -eta * rho_1 * gamma* gamma / (beta * gamma_1 * gamma_1);
+
+      if (i > 1) {
+	d = eta * p + (theta_1 * theta_1 * gamma * gamma) * d;
+	s = eta * p_tld + (theta_1 * theta_1 * gamma * gamma) * s;
+      } else {
+	d = eta * p;
+	s = eta * p_tld;
+      }
+
+      x =x+d;                            // update approximation vector
+      r =r-s;                            // compute residual
+
+      if ((resid = norm2(r) / normb) <= Tolerance) {
+	return;
+      }
+      std::cout << "Iteration "<<i<<" resid " << resid<<std::endl;
+    }
+    assert(0);
+    return;                            // no convergence
+  }
+#else
+  // QMRg5 SMP thesis
+  void operator()(LinearOperatorBase<Field> &LinOp, const Field &b, Field &x) 
+  {
+    // Real scalars
+    GridBase *grid = b.Grid();
+
+    Field    r(grid);
+    Field    p_m(grid), p_m_minus_1(grid), p_m_minus_2(grid);
+    Field    v_m(grid), v_m_minus_1(grid), v_m_plus_1(grid);
+    Field    tmp(grid);
+
+    RealD    w;
+    RealD    z1, z2;
+    RealD    delta_m, delta_m_minus_1;
+    RealD    c_m_plus_1, c_m, c_m_minus_1;
+    RealD    s_m_plus_1, s_m, s_m_minus_1;
+    RealD    alpha, beta, gamma, epsilon;
+    RealD    mu, nu, rho, theta, xi, chi;
+    RealD    mod2r, mod2b;
+    RealD    tau2, target2;
+
+    mod2b=norm2(b);
+
+    /////////////////////////
+    // Initial residual
+    /////////////////////////
+    LinOp.Op(x,tmp);
+    r = b - tmp;
+
+    /////////////////////////
+    // \mu = \rho = |r_0|
+    /////////////////////////
+    mod2r = norm2(r);
+    rho = sqrt( mod2r);
+    mu=rho;
+    
+    std::cout << "QuasiMinimalResidual rho "<< rho<<std::endl;
+    /////////////////////////
+    // Zero negative history
+    /////////////////////////
+    v_m_plus_1  = Zero();
+    v_m_minus_1 = Zero();
+    p_m_minus_1 = Zero();
+    p_m_minus_2 = Zero();
+
+    // v0
+    v_m = (1.0/rho)*r;
+
+    /////////////////////////
+    // Initial coeffs
+    /////////////////////////
+    delta_m_minus_1 = 1.0;
+    c_m_minus_1     = 1.0;
+    c_m             = 1.0;
+    s_m_minus_1     = 0.0;
+    s_m             = 0.0;
+
+    /////////////////////////
+    // Set up convergence check
+    /////////////////////////
+    tau2    = mod2r;
+    target2 = mod2b * Tolerance*Tolerance;
+ 
+    for(int iter = 0 ; iter < MaxIterations; iter++){
+
+      /////////////////////////
+      // \delta_m = (v_m, \gamma_5 v_m) 
+      /////////////////////////
+      delta_m = innerG5ProductReal(v_m,v_m);
+      std::cout << "QuasiMinimalResidual delta_m "<< delta_m<<std::endl;
+
+      /////////////////////////
+      // tmp = A v_m
+      /////////////////////////
+      LinOp.Op(v_m,tmp);
+
+      /////////////////////////
+      // \alpha = (v_m, \gamma_5 temp) / \delta_m 
+      /////////////////////////
+      alpha = innerG5ProductReal(v_m,tmp);
+      alpha = alpha/delta_m ;
+      std::cout << "QuasiMinimalResidual alpha "<< alpha<<std::endl;
+
+      /////////////////////////
+      // \beta = \rho \delta_m / \delta_{m-1}
+      /////////////////////////
+      beta = rho * delta_m / delta_m_minus_1;
+      std::cout << "QuasiMinimalResidual beta "<< beta<<std::endl;
+
+      /////////////////////////
+      // \tilde{v}_{m+1} = temp - \alpha v_m - \beta v_{m-1}
+      /////////////////////////
+      v_m_plus_1 = tmp - alpha*v_m - beta*v_m_minus_1;
+
+      ///////////////////////////////
+      // \rho = || \tilde{v}_{m+1} ||
+      ///////////////////////////////
+      rho = sqrt( norm2(v_m_plus_1) );
+      std::cout << "QuasiMinimalResidual rho "<< rho<<std::endl;
+
+      ///////////////////////////////
+      //      v_{m+1} = \tilde{v}_{m+1}
+      ///////////////////////////////
+      v_m_plus_1 = (1.0 / rho) * v_m_plus_1;
+
+      ////////////////////////////////
+      // QMR recurrence coefficients.
+      ////////////////////////////////
+      theta      = s_m_minus_1 * beta;
+      gamma      = c_m_minus_1 * beta;
+      epsilon    =  c_m * gamma + s_m * alpha;
+      xi         = -s_m * gamma + c_m * alpha;
+      nu         = sqrt( xi*xi + rho*rho );
+      c_m_plus_1 = fabs(xi) / nu;
+      if ( xi == 0.0 ) {
+	s_m_plus_1 = 1.0;
+      } else {
+	s_m_plus_1 = c_m_plus_1 * rho / xi;
+      }
+      chi = c_m_plus_1 * xi + s_m_plus_1 * rho;
+
+      std::cout << "QuasiMinimalResidual coeffs "<< theta <<" "<<gamma<<" "<< epsilon<<" "<< xi<<" "<< nu<<std::endl;
+      std::cout << "QuasiMinimalResidual coeffs "<< chi   <<std::endl;
+
+      ////////////////////////////////
+      //p_m=(v_m - \epsilon p_{m-1} - \theta p_{m-2}) / \chi
+      ////////////////////////////////
+      p_m = (1.0/chi) * v_m - (epsilon/chi) * p_m_minus_1 - (theta/chi) * p_m_minus_2;
+
+      ////////////////////////////////////////////////////////////////
+      //      \psi = \psi + c_{m+1} \mu p_m	
+      ////////////////////////////////////////////////////////////////
+      x = x + ( c_m_plus_1 * mu ) * p_m;
+
+      ////////////////////////////////////////
+      //
+      ////////////////////////////////////////
+      mu              = -s_m_plus_1 * mu;
+      delta_m_minus_1 = delta_m;
+      c_m_minus_1     = c_m;
+      c_m             = c_m_plus_1;
+      s_m_minus_1     = s_m;
+      s_m             = s_m_plus_1;
+
+      ////////////////////////////////////
+      // Could use pointer swizzle games.
+      ////////////////////////////////////
+      v_m_minus_1 = v_m;
+      v_m         = v_m_plus_1;
+      p_m_minus_2 = p_m_minus_1;
+      p_m_minus_1 = p_m;
+
+
+      /////////////////////////////////////
+      // Convergence checks
+      /////////////////////////////////////
+      z1 = RealD(iter+1.0);
+      z2 = z1 + 1.0;
+      tau2 = tau2 *( z2 / z1 ) * s_m * s_m;
+      std::cout << " QuasiMinimumResidual iteration "<< iter<<std::endl;
+      std::cout << " QuasiMinimumResidual tau bound "<< tau2<<std::endl;
+
+      // Compute true residual
+      mod2r = tau2;
+      if ( 1 || (tau2 < (100.0 * target2)) ) {
+	LinOp.Op(x,tmp);
+	r = b - tmp;
+	mod2r = norm2(r);
+	std::cout << " QuasiMinimumResidual true residual is "<< mod2r<<std::endl;
+      }
+
+
+      if ( mod2r < target2 ) { 
+
+	std::cout << " QuasiMinimumResidual has converged"<<std::endl;
+	return;
+
+      }
+
+    }
+
+
+  }
+#endif
+};
+
+NAMESPACE_END(Grid);

Grid/algorithms/iterative/SchurRedBlack.h

@@ -0,0 +1,621 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/SchurRedBlack.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#ifndef GRID_SCHUR_RED_BLACK_H
+#define GRID_SCHUR_RED_BLACK_H
+
+
+  /*
+   * Red black Schur decomposition
+   *
+   *  M = (Mee Meo) =  (1             0 )   (Mee   0               )  (1 Mee^{-1} Meo)
+   *      (Moe Moo)    (Moe Mee^-1    1 )   (0   Moo-Moe Mee^-1 Meo)  (0   1         )
+   *                =         L                     D                     U
+   *
+   * L^-1 = (1              0 )
+   *        (-MoeMee^{-1}   1 )   
+   * L^{dag} = ( 1       Mee^{-dag} Moe^{dag} )
+   *           ( 0       1                    )
+   * L^{-d}  = ( 1      -Mee^{-dag} Moe^{dag} )
+   *           ( 0       1                    )
+   *
+   * U^-1 = (1   -Mee^{-1} Meo)
+   *        (0    1           )
+   * U^{dag} = ( 1                 0)
+   *           (Meo^dag Mee^{-dag} 1)
+   * U^{-dag} = (  1                 0)
+   *            (-Meo^dag Mee^{-dag} 1)
+   ***********************
+   *     M psi = eta
+   ***********************
+   *Odd
+   * i)                 D_oo psi_o =  L^{-1}  eta_o
+   *                        eta_o' = (D_oo)^dag (eta_o - Moe Mee^{-1} eta_e)
+   *
+   * Wilson:
+   *      (D_oo)^{\dag} D_oo psi_o = (D_oo)^dag L^{-1}  eta_o
+   * Stag:
+   *      D_oo psi_o = L^{-1}  eta =    (eta_o - Moe Mee^{-1} eta_e)
+   *
+   * L^-1 eta_o= (1              0 ) (e
+   *             (-MoeMee^{-1}   1 )   
+   *
+   *Even
+   * ii)  Mee psi_e + Meo psi_o = src_e
+   *
+   *   => sol_e = M_ee^-1 * ( src_e - Meo sol_o )...
+   *
+   * 
+   * TODO: Other options:
+   * 
+   * a) change checkerboards for Schur e<->o
+   *
+   * Left precon by Moo^-1
+   * b) Doo^{dag} M_oo^-dag Moo^-1 Doo psi_0 =  (D_oo)^dag M_oo^-dag Moo^-1 L^{-1}  eta_o
+   *                              eta_o'     = (D_oo)^dag  M_oo^-dag Moo^-1 (eta_o - Moe Mee^{-1} eta_e)
+   *
+   * Right precon by Moo^-1
+   * c) M_oo^-dag Doo^{dag} Doo Moo^-1 phi_0 = M_oo^-dag (D_oo)^dag L^{-1}  eta_o
+   *                              eta_o'     = M_oo^-dag (D_oo)^dag (eta_o - Moe Mee^{-1} eta_e)
+   *                              psi_o = M_oo^-1 phi_o
+   * TODO: Deflation 
+   */
+namespace Grid {
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Use base class to share code
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Take a matrix and form a Red Black solver calling a Herm solver
+  // Use of RB info prevents making SchurRedBlackSolve conform to standard interface
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  template<class Field> class SchurRedBlackBase {
+  protected:
+    typedef CheckerBoardedSparseMatrixBase<Field> Matrix;
+    OperatorFunction<Field> & _HermitianRBSolver;
+    int CBfactorise;
+    bool subGuess;
+    bool useSolnAsInitGuess; // if true user-supplied solution vector is used as initial guess for solver
+  public:
+
+    SchurRedBlackBase(OperatorFunction<Field> &HermitianRBSolver, const bool initSubGuess = false,
+        const bool _solnAsInitGuess = false)  :
+    _HermitianRBSolver(HermitianRBSolver),
+    useSolnAsInitGuess(_solnAsInitGuess)
+    { 
+      CBfactorise = 0;
+      subtractGuess(initSubGuess);
+    };
+    void subtractGuess(const bool initSubGuess)
+    {
+      subGuess = initSubGuess;
+    }
+    bool isSubtractGuess(void)
+    {
+      return subGuess;
+    }
+
+    /////////////////////////////////////////////////////////////
+    // Shared code
+    /////////////////////////////////////////////////////////////
+    void operator() (Matrix & _Matrix,const Field &in, Field &out){
+      ZeroGuesser<Field> guess;
+      (*this)(_Matrix,in,out,guess);
+    }
+    void operator()(Matrix &_Matrix, const std::vector<Field> &in, std::vector<Field> &out) 
+    {
+      ZeroGuesser<Field> guess;
+      (*this)(_Matrix,in,out,guess);
+    }
+
+    template<class Guesser>
+    void operator()(Matrix &_Matrix, const std::vector<Field> &in, std::vector<Field> &out,Guesser &guess) 
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+      int nblock = in.size();
+
+      std::vector<Field> src_o(nblock,grid);
+      std::vector<Field> sol_o(nblock,grid);
+      
+      std::vector<Field> guess_save;
+
+      Field resid(fgrid);
+      Field tmp(grid);
+
+      ////////////////////////////////////////////////
+      // Prepare RedBlack source
+      ////////////////////////////////////////////////
+      for(int b=0;b<nblock;b++){
+	RedBlackSource(_Matrix,in[b],tmp,src_o[b]);
+      }
+      ////////////////////////////////////////////////
+      // Make the guesses
+      ////////////////////////////////////////////////
+      if ( subGuess ) guess_save.resize(nblock,grid);
+
+      for(int b=0;b<nblock;b++){
+        if(useSolnAsInitGuess) {
+          pickCheckerboard(Odd, sol_o[b], out[b]);
+        } else {
+          guess(src_o[b],sol_o[b]); 
+        }
+
+	if ( subGuess ) { 
+	  guess_save[b] = sol_o[b];
+	}
+      }
+      //////////////////////////////////////////////////////////////
+      // Call the block solver
+      //////////////////////////////////////////////////////////////
+      std::cout<<GridLogMessage << "SchurRedBlackBase calling the solver for "<<nblock<<" RHS" <<std::endl;
+      RedBlackSolve(_Matrix,src_o,sol_o);
+
+      ////////////////////////////////////////////////
+      // A2A boolean behavioural control & reconstruct other checkerboard
+      ////////////////////////////////////////////////
+      for(int b=0;b<nblock;b++) {
+
+	if (subGuess)   sol_o[b] = sol_o[b] - guess_save[b];
+
+	///////// Needs even source //////////////
+	pickCheckerboard(Even,tmp,in[b]);
+	RedBlackSolution(_Matrix,sol_o[b],tmp,out[b]);
+
+	/////////////////////////////////////////////////
+	// Check unprec residual if possible
+	/////////////////////////////////////////////////
+	if ( ! subGuess ) {
+	  _Matrix.M(out[b],resid); 
+	  resid = resid-in[b];
+	  RealD ns = norm2(in[b]);
+	  RealD nr = norm2(resid);
+	
+	  std::cout<<GridLogMessage<< "SchurRedBlackBase solver true unprec resid["<<b<<"] "<<std::sqrt(nr/ns) << std::endl;
+	} else {
+	  std::cout<<GridLogMessage<< "SchurRedBlackBase Guess subtracted after solve["<<b<<"] " << std::endl;
+	}
+
+      }
+    }
+    template<class Guesser>
+    void operator() (Matrix & _Matrix,const Field &in, Field &out,Guesser &guess){
+
+      // FIXME CGdiagonalMee not implemented virtual function
+      // FIXME use CBfactorise to control schur decomp
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+
+      Field resid(fgrid);
+      Field src_o(grid);
+      Field src_e(grid);
+      Field sol_o(grid);
+
+      ////////////////////////////////////////////////
+      // RedBlack source
+      ////////////////////////////////////////////////
+      RedBlackSource(_Matrix,in,src_e,src_o);
+
+      ////////////////////////////////
+      // Construct the guess
+      ////////////////////////////////
+      if(useSolnAsInitGuess) {
+        pickCheckerboard(Odd, sol_o, out);
+      } else {
+        guess(src_o,sol_o);
+      }
+
+      Field  guess_save(grid);
+      guess_save = sol_o;
+
+      //////////////////////////////////////////////////////////////
+      // Call the red-black solver
+      //////////////////////////////////////////////////////////////
+      RedBlackSolve(_Matrix,src_o,sol_o);
+
+      ////////////////////////////////////////////////
+      // Fionn A2A boolean behavioural control
+      ////////////////////////////////////////////////
+      if (subGuess)      sol_o= sol_o-guess_save;
+
+      ///////////////////////////////////////////////////
+      // RedBlack solution needs the even source
+      ///////////////////////////////////////////////////
+      RedBlackSolution(_Matrix,sol_o,src_e,out);
+
+      // Verify the unprec residual
+      if ( ! subGuess ) {
+        _Matrix.M(out,resid); 
+        resid = resid-in;
+        RealD ns = norm2(in);
+        RealD nr = norm2(resid);
+
+        std::cout<<GridLogMessage << "SchurRedBlackBase solver true unprec resid "<< std::sqrt(nr/ns) << std::endl;
+      } else {
+        std::cout << GridLogMessage << "SchurRedBlackBase Guess subtracted after solve." << std::endl;
+      }
+    }     
+    
+    /////////////////////////////////////////////////////////////
+    // Override in derived. 
+    /////////////////////////////////////////////////////////////
+    virtual void RedBlackSource  (Matrix & _Matrix,const Field &src, Field &src_e,Field &src_o)                =0;
+    virtual void RedBlackSolution(Matrix & _Matrix,const Field &sol_o, const Field &src_e,Field &sol)          =0;
+    virtual void RedBlackSolve   (Matrix & _Matrix,const Field &src_o, Field &sol_o)                           =0;
+    virtual void RedBlackSolve   (Matrix & _Matrix,const std::vector<Field> &src_o,  std::vector<Field> &sol_o)=0;
+
+  };
+
+  template<class Field> class SchurRedBlackStaggeredSolve : public SchurRedBlackBase<Field> {
+  public:
+    typedef CheckerBoardedSparseMatrixBase<Field> Matrix;
+
+    SchurRedBlackStaggeredSolve(OperatorFunction<Field> &HermitianRBSolver, const bool initSubGuess = false,
+        const bool _solnAsInitGuess = false) 
+      :    SchurRedBlackBase<Field> (HermitianRBSolver,initSubGuess,_solnAsInitGuess) 
+    {
+    }
+
+    //////////////////////////////////////////////////////
+    // Override RedBlack specialisation
+    //////////////////////////////////////////////////////
+    virtual void RedBlackSource(Matrix & _Matrix,const Field &src, Field &src_e,Field &src_o)
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+
+      Field   tmp(grid);
+      Field  Mtmp(grid);
+
+      pickCheckerboard(Even,src_e,src);
+      pickCheckerboard(Odd ,src_o,src);
+
+      /////////////////////////////////////////////////////
+      // src_o = (source_o - Moe MeeInv source_e)
+      /////////////////////////////////////////////////////
+      _Matrix.MooeeInv(src_e,tmp);     assert(  tmp.Checkerboard() ==Even);
+      _Matrix.Meooe   (tmp,Mtmp);      assert( Mtmp.Checkerboard() ==Odd);     
+      tmp=src_o-Mtmp;                  assert(  tmp.Checkerboard() ==Odd);     
+
+      _Matrix.Mooee(tmp,src_o); // Extra factor of "m" in source from dumb choice of matrix norm.
+    }
+    virtual void RedBlackSolution(Matrix & _Matrix,const Field &sol_o, const Field &src_e_c,Field &sol)
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+
+      Field   tmp(grid);
+      Field   sol_e(grid);
+      Field   src_e(grid);
+
+      src_e = src_e_c; // Const correctness
+
+      ///////////////////////////////////////////////////
+      // sol_e = M_ee^-1 * ( src_e - Meo sol_o )...
+      ///////////////////////////////////////////////////
+      _Matrix.Meooe(sol_o,tmp);        assert(  tmp.Checkerboard()   ==Even);
+      src_e = src_e-tmp;               assert(  src_e.Checkerboard() ==Even);
+      _Matrix.MooeeInv(src_e,sol_e);   assert(  sol_e.Checkerboard() ==Even);
+     
+      setCheckerboard(sol,sol_e); assert(  sol_e.Checkerboard() ==Even);
+      setCheckerboard(sol,sol_o); assert(  sol_o.Checkerboard() ==Odd );
+    }
+    virtual void RedBlackSolve   (Matrix & _Matrix,const Field &src_o, Field &sol_o)
+    {
+      SchurStaggeredOperator<Matrix,Field> _HermOpEO(_Matrix);
+      this->_HermitianRBSolver(_HermOpEO,src_o,sol_o);  assert(sol_o.Checkerboard()==Odd);
+    };
+    virtual void RedBlackSolve   (Matrix & _Matrix,const std::vector<Field> &src_o,  std::vector<Field> &sol_o)
+    {
+      SchurStaggeredOperator<Matrix,Field> _HermOpEO(_Matrix);
+      this->_HermitianRBSolver(_HermOpEO,src_o,sol_o); 
+    }
+  };
+  template<class Field> using SchurRedBlackStagSolve = SchurRedBlackStaggeredSolve<Field>;
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Site diagonal has Mooee on it.
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  template<class Field> class SchurRedBlackDiagMooeeSolve : public SchurRedBlackBase<Field> {
+  public:
+    typedef CheckerBoardedSparseMatrixBase<Field> Matrix;
+
+    SchurRedBlackDiagMooeeSolve(OperatorFunction<Field> &HermitianRBSolver, const bool initSubGuess = false,
+        const bool _solnAsInitGuess = false)  
+      : SchurRedBlackBase<Field> (HermitianRBSolver,initSubGuess,_solnAsInitGuess) {};
+
+
+    //////////////////////////////////////////////////////
+    // Override RedBlack specialisation
+    //////////////////////////////////////////////////////
+    virtual void RedBlackSource(Matrix & _Matrix,const Field &src, Field &src_e,Field &src_o)
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+
+      Field   tmp(grid);
+      Field  Mtmp(grid);
+
+      pickCheckerboard(Even,src_e,src);
+      pickCheckerboard(Odd ,src_o,src);
+
+      /////////////////////////////////////////////////////
+      // src_o = Mdag * (source_o - Moe MeeInv source_e)
+      /////////////////////////////////////////////////////
+      _Matrix.MooeeInv(src_e,tmp);     assert(  tmp.Checkerboard() ==Even);
+      _Matrix.Meooe   (tmp,Mtmp);      assert( Mtmp.Checkerboard() ==Odd);     
+      tmp=src_o-Mtmp;                  assert(  tmp.Checkerboard() ==Odd);     
+
+      // get the right MpcDag
+      SchurDiagMooeeOperator<Matrix,Field> _HermOpEO(_Matrix);
+      _HermOpEO.MpcDag(tmp,src_o);     assert(src_o.Checkerboard() ==Odd);       
+
+    }
+    virtual void RedBlackSolution(Matrix & _Matrix,const Field &sol_o, const Field &src_e,Field &sol)
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+
+      Field   tmp(grid);
+      Field  sol_e(grid);
+      Field  src_e_i(grid);
+      ///////////////////////////////////////////////////
+      // sol_e = M_ee^-1 * ( src_e - Meo sol_o )...
+      ///////////////////////////////////////////////////
+      _Matrix.Meooe(sol_o,tmp);          assert(  tmp.Checkerboard()   ==Even);
+      src_e_i = src_e-tmp;               assert(  src_e_i.Checkerboard() ==Even);
+      _Matrix.MooeeInv(src_e_i,sol_e);   assert(  sol_e.Checkerboard() ==Even);
+     
+      setCheckerboard(sol,sol_e); assert(  sol_e.Checkerboard() ==Even);
+      setCheckerboard(sol,sol_o); assert(  sol_o.Checkerboard() ==Odd );
+    }
+    virtual void RedBlackSolve   (Matrix & _Matrix,const Field &src_o, Field &sol_o)
+    {
+      SchurDiagMooeeOperator<Matrix,Field> _HermOpEO(_Matrix);
+      this->_HermitianRBSolver(_HermOpEO,src_o,sol_o);  assert(sol_o.Checkerboard()==Odd);
+    };
+    virtual void RedBlackSolve   (Matrix & _Matrix,const std::vector<Field> &src_o,  std::vector<Field> &sol_o)
+    {
+      SchurDiagMooeeOperator<Matrix,Field> _HermOpEO(_Matrix);
+      this->_HermitianRBSolver(_HermOpEO,src_o,sol_o); 
+    }
+  };
+
+  template<class Field> class NonHermitianSchurRedBlackDiagMooeeSolve : public SchurRedBlackBase<Field> 
+  {
+    public:
+      typedef CheckerBoardedSparseMatrixBase<Field> Matrix;
+
+      NonHermitianSchurRedBlackDiagMooeeSolve(OperatorFunction<Field>& RBSolver, const bool initSubGuess = false,
+          const bool _solnAsInitGuess = false)  
+      : SchurRedBlackBase<Field>(RBSolver, initSubGuess, _solnAsInitGuess) {};
+
+      //////////////////////////////////////////////////////
+      // Override RedBlack specialisation
+      //////////////////////////////////////////////////////
+      virtual void RedBlackSource(Matrix& _Matrix, const Field& src, Field& src_e, Field& src_o)
+      {
+        GridBase* grid  = _Matrix.RedBlackGrid();
+        GridBase* fgrid = _Matrix.Grid();
+
+        Field  tmp(grid);
+        Field Mtmp(grid);
+
+        pickCheckerboard(Even, src_e, src);
+        pickCheckerboard(Odd , src_o, src);
+
+        /////////////////////////////////////////////////////
+        // src_o = Mdag * (source_o - Moe MeeInv source_e)
+        /////////////////////////////////////////////////////
+        _Matrix.MooeeInv(src_e, tmp);   assert(   tmp.Checkerboard() == Even );
+        _Matrix.Meooe   (tmp, Mtmp);    assert(  Mtmp.Checkerboard() == Odd  );     
+        src_o -= Mtmp;                  assert( src_o.Checkerboard() == Odd  );     
+      }
+      
+      virtual void RedBlackSolution(Matrix& _Matrix, const Field& sol_o, const Field& src_e, Field& sol)
+      {
+        GridBase* grid  = _Matrix.RedBlackGrid();
+        GridBase* fgrid = _Matrix.Grid();
+
+        Field     tmp(grid);
+        Field   sol_e(grid);
+        Field src_e_i(grid);
+        
+        ///////////////////////////////////////////////////
+        // sol_e = M_ee^-1 * ( src_e - Meo sol_o )...
+        ///////////////////////////////////////////////////
+        _Matrix.Meooe(sol_o, tmp);         assert(     tmp.Checkerboard() == Even );
+        src_e_i = src_e - tmp;             assert( src_e_i.Checkerboard() == Even );
+        _Matrix.MooeeInv(src_e_i, sol_e);  assert(   sol_e.Checkerboard() == Even );
+       
+        setCheckerboard(sol, sol_e); assert( sol_e.Checkerboard() == Even );
+        setCheckerboard(sol, sol_o); assert( sol_o.Checkerboard() == Odd  );
+      }
+
+      virtual void RedBlackSolve(Matrix& _Matrix, const Field& src_o, Field& sol_o)
+      {
+        NonHermitianSchurDiagMooeeOperator<Matrix,Field> _OpEO(_Matrix);
+        this->_HermitianRBSolver(_OpEO, src_o, sol_o);  assert(sol_o.Checkerboard() == Odd);
+      }
+
+      virtual void RedBlackSolve(Matrix& _Matrix, const std::vector<Field>& src_o, std::vector<Field>& sol_o)
+      {
+        NonHermitianSchurDiagMooeeOperator<Matrix,Field> _OpEO(_Matrix);
+        this->_HermitianRBSolver(_OpEO, src_o, sol_o); 
+      }
+  };
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Site diagonal is identity, right preconditioned by Mee^inv
+  // ( 1 - Meo Moo^inv Moe Mee^inv  ) phi =( 1 - Meo Moo^inv Moe Mee^inv  ) Mee psi =  = eta  = eta
+  //=> psi = MeeInv phi
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  template<class Field> class SchurRedBlackDiagTwoSolve : public SchurRedBlackBase<Field> {
+  public:
+    typedef CheckerBoardedSparseMatrixBase<Field> Matrix;
+
+    /////////////////////////////////////////////////////
+    // Wrap the usual normal equations Schur trick
+    /////////////////////////////////////////////////////
+  SchurRedBlackDiagTwoSolve(OperatorFunction<Field> &HermitianRBSolver, const bool initSubGuess = false,
+      const bool _solnAsInitGuess = false)  
+    : SchurRedBlackBase<Field>(HermitianRBSolver,initSubGuess,_solnAsInitGuess) {};
+
+    virtual void RedBlackSource(Matrix & _Matrix,const Field &src, Field &src_e,Field &src_o)
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+
+      SchurDiagTwoOperator<Matrix,Field> _HermOpEO(_Matrix);
+      
+      Field   tmp(grid);
+      Field  Mtmp(grid);
+
+      pickCheckerboard(Even,src_e,src);
+      pickCheckerboard(Odd ,src_o,src);
+    
+      /////////////////////////////////////////////////////
+      // src_o = Mdag * (source_o - Moe MeeInv source_e)
+      /////////////////////////////////////////////////////
+      _Matrix.MooeeInv(src_e,tmp);     assert(  tmp.Checkerboard() ==Even);
+      _Matrix.Meooe   (tmp,Mtmp);      assert( Mtmp.Checkerboard() ==Odd);     
+      tmp=src_o-Mtmp;                  assert(  tmp.Checkerboard() ==Odd);     
+
+      // get the right MpcDag
+      _HermOpEO.MpcDag(tmp,src_o);     assert(src_o.Checkerboard() ==Odd);       
+    }
+
+    virtual void RedBlackSolution(Matrix & _Matrix,const Field &sol_o, const Field &src_e,Field &sol)
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+
+      Field   sol_o_i(grid);
+      Field   tmp(grid);
+      Field   sol_e(grid);
+
+      ////////////////////////////////////////////////
+      // MooeeInv due to pecond
+      ////////////////////////////////////////////////
+      _Matrix.MooeeInv(sol_o,tmp);
+      sol_o_i = tmp;
+
+      ///////////////////////////////////////////////////
+      // sol_e = M_ee^-1 * ( src_e - Meo sol_o )...
+      ///////////////////////////////////////////////////
+      _Matrix.Meooe(sol_o_i,tmp);    assert(  tmp.Checkerboard()   ==Even);
+      tmp = src_e-tmp;               assert(  src_e.Checkerboard() ==Even);
+      _Matrix.MooeeInv(tmp,sol_e);   assert(  sol_e.Checkerboard() ==Even);
+     
+      setCheckerboard(sol,sol_e);    assert(  sol_e.Checkerboard() ==Even);
+      setCheckerboard(sol,sol_o_i);  assert(  sol_o_i.Checkerboard() ==Odd );
+    };
+
+    virtual void RedBlackSolve   (Matrix & _Matrix,const Field &src_o, Field &sol_o)
+    {
+      SchurDiagTwoOperator<Matrix,Field> _HermOpEO(_Matrix);
+      this->_HermitianRBSolver(_HermOpEO,src_o,sol_o);
+    };
+    virtual void RedBlackSolve   (Matrix & _Matrix,const std::vector<Field> &src_o,  std::vector<Field> &sol_o)
+    {
+      SchurDiagTwoOperator<Matrix,Field> _HermOpEO(_Matrix);
+      this->_HermitianRBSolver(_HermOpEO,src_o,sol_o); 
+    }
+  };
+
+  template<class Field> class NonHermitianSchurRedBlackDiagTwoSolve : public SchurRedBlackBase<Field> 
+  {
+    public:
+      typedef CheckerBoardedSparseMatrixBase<Field> Matrix;
+
+      /////////////////////////////////////////////////////
+      // Wrap the usual normal equations Schur trick
+      /////////////////////////////////////////////////////
+      NonHermitianSchurRedBlackDiagTwoSolve(OperatorFunction<Field>& RBSolver, const bool initSubGuess = false,
+          const bool _solnAsInitGuess = false)  
+      : SchurRedBlackBase<Field>(RBSolver, initSubGuess, _solnAsInitGuess) {};
+
+      virtual void RedBlackSource(Matrix& _Matrix, const Field& src, Field& src_e, Field& src_o)
+      {
+        GridBase* grid  = _Matrix.RedBlackGrid();
+        GridBase* fgrid = _Matrix.Grid();
+
+        Field  tmp(grid);
+        Field Mtmp(grid);
+
+        pickCheckerboard(Even, src_e, src);
+        pickCheckerboard(Odd , src_o, src);
+      
+        /////////////////////////////////////////////////////
+        // src_o = Mdag * (source_o - Moe MeeInv source_e)
+        /////////////////////////////////////////////////////
+        _Matrix.MooeeInv(src_e, tmp);   assert(   tmp.Checkerboard() == Even );
+        _Matrix.Meooe   (tmp, Mtmp);    assert(  Mtmp.Checkerboard() == Odd  );     
+        src_o -= Mtmp;                  assert( src_o.Checkerboard() == Odd  );     
+      }
+
+      virtual void RedBlackSolution(Matrix& _Matrix, const Field& sol_o, const Field& src_e, Field& sol)
+      {
+        GridBase* grid  = _Matrix.RedBlackGrid();
+        GridBase* fgrid = _Matrix.Grid();
+
+        Field sol_o_i(grid);
+        Field     tmp(grid);
+        Field   sol_e(grid);
+
+        ////////////////////////////////////////////////
+        // MooeeInv due to pecond
+        ////////////////////////////////////////////////
+        _Matrix.MooeeInv(sol_o, tmp);
+        sol_o_i = tmp;
+
+        ///////////////////////////////////////////////////
+        // sol_e = M_ee^-1 * ( src_e - Meo sol_o )...
+        ///////////////////////////////////////////////////
+        _Matrix.Meooe(sol_o_i, tmp);    assert(   tmp.Checkerboard() == Even );
+        tmp = src_e - tmp;              assert( src_e.Checkerboard() == Even );
+        _Matrix.MooeeInv(tmp, sol_e);   assert( sol_e.Checkerboard() == Even );
+       
+        setCheckerboard(sol, sol_e);    assert(   sol_e.Checkerboard() == Even );
+        setCheckerboard(sol, sol_o_i);  assert( sol_o_i.Checkerboard() == Odd  );
+      };
+
+      virtual void RedBlackSolve(Matrix& _Matrix, const Field& src_o, Field& sol_o)
+      {
+        NonHermitianSchurDiagTwoOperator<Matrix,Field> _OpEO(_Matrix);
+        this->_HermitianRBSolver(_OpEO, src_o, sol_o);
+      };
+
+      virtual void RedBlackSolve(Matrix& _Matrix, const std::vector<Field>& src_o,  std::vector<Field>& sol_o)
+      {
+        NonHermitianSchurDiagTwoOperator<Matrix,Field> _OpEO(_Matrix);
+        this->_HermitianRBSolver(_OpEO, src_o, sol_o); 
+      }
+  };
+}
+
+#endif

Grid/allocator/AlignedAllocator.cc

@@ -1,70 +1,11 @@
 #include <Grid/GridCore.h>
 #include <fcntl.h>
 
-namespace Grid {
+NAMESPACE_BEGIN(Grid);
 
 MemoryStats *MemoryProfiler::stats = nullptr;
 bool         MemoryProfiler::debug = false;
 
-int PointerCache::victim;
-
-PointerCache::PointerCacheEntry PointerCache::Entries[PointerCache::Ncache];
-
-void *PointerCache::Insert(void *ptr,size_t bytes) {
-
-  if (bytes < 4096 ) return ptr;
-
-#ifdef GRID_OMP
-  assert(omp_in_parallel()==0);
-#endif 
-
-  void * ret = NULL;
-  int v = -1;
-
-  for(int e=0;e<Ncache;e++) {
-    if ( Entries[e].valid==0 ) {
-      v=e; 
-      break;
-    }
-  }
-
-  if ( v==-1 ) {
-    v=victim;
-    victim = (victim+1)%Ncache;
-  }
-
-  if ( Entries[v].valid ) {
-    ret = Entries[v].address;
-    Entries[v].valid = 0;
-    Entries[v].address = NULL;
-    Entries[v].bytes = 0;
-  }
-
-  Entries[v].address=ptr;
-  Entries[v].bytes  =bytes;
-  Entries[v].valid  =1;
-
-  return ret;
-}
-
-void *PointerCache::Lookup(size_t bytes) {
-
- if (bytes < 4096 ) return NULL;
-
-#ifdef _OPENMP
-  assert(omp_in_parallel()==0);
-#endif 
-
-  for(int e=0;e<Ncache;e++){
-    if ( Entries[e].valid && ( Entries[e].bytes == bytes ) ) {
-      Entries[e].valid = 0;
-      return Entries[e].address;
-    }
-  }
-  return NULL;
-}
-
-
 void check_huge_pages(void *Buf,uint64_t BYTES)
 {
 #ifdef __linux__
@@ -90,7 +31,7 @@ void check_huge_pages(void *Buf,uint64_t BYTES)
       ++n4ktotal;
       if (pageaddr != baseaddr + j * page_size)
 	++nnothuge;
-      }
+    }
   }
   int rank = CartesianCommunicator::RankWorld();
   printf("rank %d Allocated %d 4k pages, %d not in huge pages\n", rank, n4ktotal, nnothuge);
@@ -106,20 +47,21 @@ std::string sizeString(const size_t bytes)
   double                 count = bytes;
   
   while (count >= 1024 && s < 7)
-  {
+    {
       s++;
       count /= 1024;
-  }
+    }
   if (count - floor(count) == 0.0)
-  {
+    {
       snprintf(buf, bufSize, "%d %sB", (int)count, suffixes[s]);
-  }
+    }
   else
-  {
+    {
       snprintf(buf, bufSize, "%.1f %sB", count, suffixes[s]);
-  }
+    }
   
   return std::string(buf);
 }
 
-}
+NAMESPACE_END(Grid);
+

Grid/allocator/AlignedAllocator.h

@@ -0,0 +1,174 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/AlignedAllocator.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+template<typename _Tp>
+class alignedAllocator {
+public: 
+  typedef std::size_t     size_type;
+  typedef std::ptrdiff_t  difference_type;
+  typedef _Tp*       pointer;
+  typedef const _Tp* const_pointer;
+  typedef _Tp&       reference;
+  typedef const _Tp& const_reference;
+  typedef _Tp        value_type;
+
+  template<typename _Tp1>  struct rebind { typedef alignedAllocator<_Tp1> other; };
+  alignedAllocator() throw() { }
+  alignedAllocator(const alignedAllocator&) throw() { }
+  template<typename _Tp1> alignedAllocator(const alignedAllocator<_Tp1>&) throw() { }
+  ~alignedAllocator() throw() { }
+  pointer       address(reference __x)       const { return &__x; }
+  size_type  max_size() const throw() { return size_t(-1) / sizeof(_Tp); }
+
+  pointer allocate(size_type __n, const void* _p= 0)
+  { 
+    size_type bytes = __n*sizeof(_Tp);
+    profilerAllocate(bytes);
+    _Tp *ptr = (_Tp*) MemoryManager::CpuAllocate(bytes);
+    assert( ( (_Tp*)ptr != (_Tp *)NULL ) );
+    return ptr;
+  }
+
+  void deallocate(pointer __p, size_type __n) 
+  { 
+    size_type bytes = __n * sizeof(_Tp);
+    profilerFree(bytes);
+    MemoryManager::CpuFree((void *)__p,bytes);
+  }
+
+  // FIXME: hack for the copy constructor: it must be avoided to avoid single thread loop
+  void construct(pointer __p, const _Tp& __val) { assert(0);};
+  void construct(pointer __p) { };
+  void destroy(pointer __p) { };
+};
+template<typename _Tp>  inline bool operator==(const alignedAllocator<_Tp>&, const alignedAllocator<_Tp>&){ return true; }
+template<typename _Tp>  inline bool operator!=(const alignedAllocator<_Tp>&, const alignedAllocator<_Tp>&){ return false; }
+
+//////////////////////////////////////////////////////////////////////////////////////
+// Unified virtual memory
+//////////////////////////////////////////////////////////////////////////////////////
+template<typename _Tp>
+class uvmAllocator {
+public: 
+  typedef std::size_t     size_type;
+  typedef std::ptrdiff_t  difference_type;
+  typedef _Tp*       pointer;
+  typedef const _Tp* const_pointer;
+  typedef _Tp&       reference;
+  typedef const _Tp& const_reference;
+  typedef _Tp        value_type;
+
+  template<typename _Tp1>  struct rebind { typedef uvmAllocator<_Tp1> other; };
+  uvmAllocator() throw() { }
+  uvmAllocator(const uvmAllocator&) throw() { }
+  template<typename _Tp1> uvmAllocator(const uvmAllocator<_Tp1>&) throw() { }
+  ~uvmAllocator() throw() { }
+  pointer       address(reference __x)       const { return &__x; }
+  size_type  max_size() const throw() { return size_t(-1) / sizeof(_Tp); }
+
+  pointer allocate(size_type __n, const void* _p= 0)
+  { 
+    size_type bytes = __n*sizeof(_Tp);
+    profilerAllocate(bytes);
+    _Tp *ptr = (_Tp*) MemoryManager::SharedAllocate(bytes);
+    assert( ( (_Tp*)ptr != (_Tp *)NULL ) );
+    return ptr;
+  }
+
+  void deallocate(pointer __p, size_type __n) 
+  { 
+    size_type bytes = __n * sizeof(_Tp);
+    profilerFree(bytes);
+    MemoryManager::SharedFree((void *)__p,bytes);
+  }
+
+  void construct(pointer __p, const _Tp& __val) { new((void *)__p) _Tp(__val); };
+  void construct(pointer __p) { };
+  void destroy(pointer __p) { };
+};
+template<typename _Tp>  inline bool operator==(const uvmAllocator<_Tp>&, const uvmAllocator<_Tp>&){ return true; }
+template<typename _Tp>  inline bool operator!=(const uvmAllocator<_Tp>&, const uvmAllocator<_Tp>&){ return false; }
+
+////////////////////////////////////////////////////////////////////////////////
+// Device memory
+////////////////////////////////////////////////////////////////////////////////
+template<typename _Tp>
+class devAllocator {
+public: 
+  typedef std::size_t     size_type;
+  typedef std::ptrdiff_t  difference_type;
+  typedef _Tp*       pointer;
+  typedef const _Tp* const_pointer;
+  typedef _Tp&       reference;
+  typedef const _Tp& const_reference;
+  typedef _Tp        value_type;
+
+  template<typename _Tp1>  struct rebind { typedef devAllocator<_Tp1> other; };
+  devAllocator() throw() { }
+  devAllocator(const devAllocator&) throw() { }
+  template<typename _Tp1> devAllocator(const devAllocator<_Tp1>&) throw() { }
+  ~devAllocator() throw() { }
+  pointer       address(reference __x)       const { return &__x; }
+  size_type  max_size() const throw() { return size_t(-1) / sizeof(_Tp); }
+
+  pointer allocate(size_type __n, const void* _p= 0)
+  { 
+    size_type bytes = __n*sizeof(_Tp);
+    profilerAllocate(bytes);
+    _Tp *ptr = (_Tp*) MemoryManager::AcceleratorAllocate(bytes);
+    assert( ( (_Tp*)ptr != (_Tp *)NULL ) );
+    return ptr;
+  }
+
+  void deallocate(pointer __p, size_type __n) 
+  { 
+    size_type bytes = __n * sizeof(_Tp);
+    profilerFree(bytes);
+    MemoryManager::AcceleratorFree((void *)__p,bytes);
+  }
+  void construct(pointer __p, const _Tp& __val) { };
+  void construct(pointer __p) { };
+  void destroy(pointer __p) { };
+};
+template<typename _Tp>  inline bool operator==(const devAllocator<_Tp>&, const devAllocator<_Tp>&){ return true; }
+template<typename _Tp>  inline bool operator!=(const devAllocator<_Tp>&, const devAllocator<_Tp>&){ return false; }
+
+////////////////////////////////////////////////////////////////////////////////
+// Template typedefs
+////////////////////////////////////////////////////////////////////////////////
+//template<class T> using commAllocator = devAllocator<T>;
+template<class T> using Vector     = std::vector<T,uvmAllocator<T> >;           
+template<class T> using commVector = std::vector<T,devAllocator<T> >;
+
+NAMESPACE_END(Grid);
+
+

Grid/allocator/Allocator.h

@@ -0,0 +1,4 @@
+#pragma once
+#include <Grid/allocator/MemoryStats.h>
+#include <Grid/allocator/MemoryManager.h>
+#include <Grid/allocator/AlignedAllocator.h>

Grid/allocator/MemoryManager.cc

@@ -0,0 +1,254 @@
+#include <Grid/GridCore.h>
+
+NAMESPACE_BEGIN(Grid);
+
+/*Allocation types, saying which pointer cache should be used*/
+#define Cpu      (0)
+#define CpuSmall (1)
+#define Acc      (2)
+#define AccSmall (3)
+#define Shared   (4)
+#define SharedSmall (5)
+uint64_t total_shared;
+uint64_t total_device;
+uint64_t total_host;;
+void MemoryManager::PrintBytes(void)
+{
+  std::cout << " MemoryManager : "<<total_shared<<" shared      bytes "<<std::endl;
+  std::cout << " MemoryManager : "<<total_device<<" accelerator bytes "<<std::endl;
+  std::cout << " MemoryManager : "<<total_host  <<" cpu         bytes "<<std::endl;
+}
+
+//////////////////////////////////////////////////////////////////////
+// Data tables for recently freed pooiniter caches
+//////////////////////////////////////////////////////////////////////
+MemoryManager::AllocationCacheEntry MemoryManager::Entries[MemoryManager::NallocType][MemoryManager::NallocCacheMax];
+int MemoryManager::Victim[MemoryManager::NallocType];
+int MemoryManager::Ncache[MemoryManager::NallocType] = { 8, 32, 8, 32, 8, 32 };
+
+//////////////////////////////////////////////////////////////////////
+// Actual allocation and deallocation utils
+//////////////////////////////////////////////////////////////////////
+void *MemoryManager::AcceleratorAllocate(size_t bytes)
+{
+  void *ptr = (void *) Lookup(bytes,Acc);
+  if ( ptr == (void *) NULL ) {
+    ptr = (void *) acceleratorAllocDevice(bytes);
+    total_device+=bytes;
+  }
+  return ptr;
+}
+void  MemoryManager::AcceleratorFree    (void *ptr,size_t bytes)
+{
+  void *__freeme = Insert(ptr,bytes,Acc);
+  if ( __freeme ) {
+    acceleratorFreeDevice(__freeme);
+    total_device-=bytes;
+    //    PrintBytes();
+  }
+}
+void *MemoryManager::SharedAllocate(size_t bytes)
+{
+  void *ptr = (void *) Lookup(bytes,Shared);
+  if ( ptr == (void *) NULL ) {
+    ptr = (void *) acceleratorAllocShared(bytes);
+    total_shared+=bytes;
+    //    std::cout <<"AcceleratorAllocate: allocated Shared pointer "<<std::hex<<ptr<<std::dec<<std::endl;
+    //    PrintBytes();
+  }
+  return ptr;
+}
+void  MemoryManager::SharedFree    (void *ptr,size_t bytes)
+{
+  void *__freeme = Insert(ptr,bytes,Shared);
+  if ( __freeme ) {
+    acceleratorFreeShared(__freeme);
+    total_shared-=bytes;
+    //    PrintBytes();
+  }
+}
+#ifdef GRID_UVM
+void *MemoryManager::CpuAllocate(size_t bytes)
+{
+  void *ptr = (void *) Lookup(bytes,Cpu);
+  if ( ptr == (void *) NULL ) {
+    ptr = (void *) acceleratorAllocShared(bytes);
+    total_host+=bytes;
+  }
+  return ptr;
+}
+void  MemoryManager::CpuFree    (void *_ptr,size_t bytes)
+{
+  NotifyDeletion(_ptr);
+  void *__freeme = Insert(_ptr,bytes,Cpu);
+  if ( __freeme ) { 
+    acceleratorFreeShared(__freeme);
+    total_host-=bytes;
+  }
+}
+#else
+void *MemoryManager::CpuAllocate(size_t bytes)
+{
+  void *ptr = (void *) Lookup(bytes,Cpu);
+  if ( ptr == (void *) NULL ) {
+    ptr = (void *) acceleratorAllocCpu(bytes);
+    total_host+=bytes;
+  }
+  return ptr;
+}
+void  MemoryManager::CpuFree    (void *_ptr,size_t bytes)
+{
+  NotifyDeletion(_ptr);
+  void *__freeme = Insert(_ptr,bytes,Cpu);
+  if ( __freeme ) { 
+    acceleratorFreeCpu(__freeme);
+    total_host-=bytes;
+  }
+}
+#endif
+
+//////////////////////////////////////////
+// call only once
+//////////////////////////////////////////
+void MemoryManager::Init(void)
+{
+
+  char * str;
+  int Nc;
+  int NcS;
+  
+  str= getenv("GRID_ALLOC_NCACHE_LARGE");
+  if ( str ) {
+    Nc = atoi(str);
+    if ( (Nc>=0) && (Nc < NallocCacheMax)) {
+      Ncache[Cpu]=Nc;
+      Ncache[Acc]=Nc;
+      Ncache[Shared]=Nc;
+    }
+  }
+
+  str= getenv("GRID_ALLOC_NCACHE_SMALL");
+  if ( str ) {
+    Nc = atoi(str);
+    if ( (Nc>=0) && (Nc < NallocCacheMax)) {
+      Ncache[CpuSmall]=Nc;
+      Ncache[AccSmall]=Nc;
+      Ncache[SharedSmall]=Nc;
+    }
+  }
+
+}
+
+void MemoryManager::InitMessage(void) {
+
+#ifndef GRID_UVM
+  std::cout << GridLogMessage << "MemoryManager Cache "<< MemoryManager::DeviceMaxBytes <<" bytes "<<std::endl;
+#endif
+  
+  std::cout << GridLogMessage<< "MemoryManager::Init() setting up"<<std::endl;
+#ifdef ALLOCATION_CACHE
+  std::cout << GridLogMessage<< "MemoryManager::Init() cache pool for recent allocations: SMALL "<<Ncache[CpuSmall]<<" LARGE "<<Ncache[Cpu]<<std::endl;
+#endif
+  
+#ifdef GRID_UVM
+  std::cout << GridLogMessage<< "MemoryManager::Init() Unified memory space"<<std::endl;
+#ifdef GRID_CUDA
+  std::cout << GridLogMessage<< "MemoryManager::Init() Using cudaMallocManaged"<<std::endl;
+#endif
+#ifdef GRID_HIP
+  std::cout << GridLogMessage<< "MemoryManager::Init() Using hipMallocManaged"<<std::endl;
+#endif
+#ifdef GRID_SYCL
+  std::cout << GridLogMessage<< "MemoryManager::Init() Using SYCL malloc_shared"<<std::endl;
+#endif
+#else
+  std::cout << GridLogMessage<< "MemoryManager::Init() Non unified: Caching accelerator data in dedicated memory"<<std::endl;
+#ifdef GRID_CUDA
+  std::cout << GridLogMessage<< "MemoryManager::Init() Using cudaMalloc"<<std::endl;
+#endif
+#ifdef GRID_HIP
+  std::cout << GridLogMessage<< "MemoryManager::Init() Using hipMalloc"<<std::endl;
+#endif
+#ifdef GRID_SYCL
+  std::cout << GridLogMessage<< "MemoryManager::Init() Using SYCL malloc_device"<<std::endl;
+#endif
+#endif
+
+}
+
+void *MemoryManager::Insert(void *ptr,size_t bytes,int type) 
+{
+#ifdef ALLOCATION_CACHE
+  bool small = (bytes < GRID_ALLOC_SMALL_LIMIT);
+  int cache = type + small;
+  return Insert(ptr,bytes,Entries[cache],Ncache[cache],Victim[cache]);  
+#else
+  return ptr;
+#endif
+}
+
+void *MemoryManager::Insert(void *ptr,size_t bytes,AllocationCacheEntry *entries,int ncache,int &victim) 
+{
+  assert(ncache>0);
+#ifdef GRID_OMP
+  assert(omp_in_parallel()==0);
+#endif 
+
+  void * ret = NULL;
+  int v = -1;
+
+  for(int e=0;e<ncache;e++) {
+    if ( entries[e].valid==0 ) {
+      v=e; 
+      break;
+    }
+  }
+
+  if ( v==-1 ) {
+    v=victim;
+    victim = (victim+1)%ncache;
+  }
+
+  if ( entries[v].valid ) {
+    ret = entries[v].address;
+    entries[v].valid = 0;
+    entries[v].address = NULL;
+    entries[v].bytes = 0;
+  }
+
+  entries[v].address=ptr;
+  entries[v].bytes  =bytes;
+  entries[v].valid  =1;
+
+  return ret;
+}
+
+void *MemoryManager::Lookup(size_t bytes,int type)
+{
+#ifdef ALLOCATION_CACHE
+  bool small = (bytes < GRID_ALLOC_SMALL_LIMIT);
+  int cache = type+small;
+  return Lookup(bytes,Entries[cache],Ncache[cache]);
+#else
+  return NULL;
+#endif
+}
+
+void *MemoryManager::Lookup(size_t bytes,AllocationCacheEntry *entries,int ncache) 
+{
+  assert(ncache>0);
+#ifdef GRID_OMP
+  assert(omp_in_parallel()==0);
+#endif 
+  for(int e=0;e<ncache;e++){
+    if ( entries[e].valid && ( entries[e].bytes == bytes ) ) {
+      entries[e].valid = 0;
+      return entries[e].address;
+    }
+  }
+  return NULL;
+}
+
+
+NAMESPACE_END(Grid);
+

Grid/allocator/MemoryManager.h

@@ -0,0 +1,182 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/MemoryManager.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+#include <list> 
+#include <unordered_map>  
+
+NAMESPACE_BEGIN(Grid);
+
+// Move control to configure.ac and Config.h?
+
+#define ALLOCATION_CACHE
+#define GRID_ALLOC_ALIGN (2*1024*1024)
+#define GRID_ALLOC_SMALL_LIMIT (4096)
+
+/*Pinning pages is costly*/
+////////////////////////////////////////////////////////////////////////////
+// Advise the LatticeAccelerator class
+////////////////////////////////////////////////////////////////////////////
+enum ViewAdvise {
+ AdviseDefault       = 0x0,    // Regular data
+ AdviseInfrequentUse = 0x1     // Advise that the data is used infrequently.  This can
+                               // significantly influence performance of bulk storage.
+ 
+ // AdviseTransient      = 0x2,   // Data will mostly be read.  On some architectures
+                               // enables read-only copies of memory to be kept on
+                               // host and device.
+
+ // AdviseAcceleratorWriteDiscard = 0x4  // Field will be written in entirety on device
+
+};
+
+////////////////////////////////////////////////////////////////////////////
+// View Access Mode
+////////////////////////////////////////////////////////////////////////////
+enum ViewMode {
+  AcceleratorRead  = 0x01,
+  AcceleratorWrite = 0x02,
+  AcceleratorWriteDiscard = 0x04,
+  CpuRead  = 0x08,
+  CpuWrite = 0x10,
+  CpuWriteDiscard = 0x10 // same for now
+};
+
+class MemoryManager {
+private:
+
+  ////////////////////////////////////////////////////////////
+  // For caching recently freed allocations
+  ////////////////////////////////////////////////////////////
+  typedef struct { 
+    void *address;
+    size_t bytes;
+    int valid;
+  } AllocationCacheEntry;
+
+  static const int NallocCacheMax=128; 
+  static const int NallocType=6;
+  static AllocationCacheEntry Entries[NallocType][NallocCacheMax];
+  static int Victim[NallocType];
+  static int Ncache[NallocType];
+
+  /////////////////////////////////////////////////
+  // Free pool
+  /////////////////////////////////////////////////
+  static void *Insert(void *ptr,size_t bytes,int type) ;
+  static void *Lookup(size_t bytes,int type) ;
+  static void *Insert(void *ptr,size_t bytes,AllocationCacheEntry *entries,int ncache,int &victim) ;
+  static void *Lookup(size_t bytes,AllocationCacheEntry *entries,int ncache) ;
+
+  static void PrintBytes(void);
+ public:
+  static void Init(void);
+  static void InitMessage(void);
+  static void *AcceleratorAllocate(size_t bytes);
+  static void  AcceleratorFree    (void *ptr,size_t bytes);
+  static void *SharedAllocate(size_t bytes);
+  static void  SharedFree    (void *ptr,size_t bytes);
+  static void *CpuAllocate(size_t bytes);
+  static void  CpuFree    (void *ptr,size_t bytes);
+
+  ////////////////////////////////////////////////////////
+  // Footprint tracking
+  ////////////////////////////////////////////////////////
+  static uint64_t     DeviceBytes;
+  static uint64_t     DeviceLRUBytes;
+  static uint64_t     DeviceMaxBytes;
+  static uint64_t     HostToDeviceBytes;
+  static uint64_t     DeviceToHostBytes;
+  static uint64_t     HostToDeviceXfer;
+  static uint64_t     DeviceToHostXfer;
+ 
+ private:
+#ifndef GRID_UVM
+  //////////////////////////////////////////////////////////////////////
+  // Data tables for ViewCache
+  //////////////////////////////////////////////////////////////////////
+  typedef std::list<uint64_t> LRU_t;
+  typedef typename LRU_t::iterator LRUiterator;
+  typedef struct { 
+    int        LRU_valid;
+    LRUiterator LRU_entry;
+    uint64_t CpuPtr;
+    uint64_t AccPtr;
+    size_t   bytes;
+    uint32_t transient;
+    uint32_t state;
+    uint32_t accLock;
+    uint32_t cpuLock;
+  } AcceleratorViewEntry;
+  
+  typedef std::unordered_map<uint64_t,AcceleratorViewEntry> AccViewTable_t;
+  typedef typename AccViewTable_t::iterator AccViewTableIterator ;
+
+  static AccViewTable_t AccViewTable;
+  static LRU_t LRU;
+
+  /////////////////////////////////////////////////
+  // Device motion
+  /////////////////////////////////////////////////
+  static void  Create(uint64_t CpuPtr,size_t bytes,ViewMode mode,ViewAdvise hint);
+  static void  EvictVictims(uint64_t bytes); // Frees up <bytes>
+  static void  Evict(AcceleratorViewEntry &AccCache);
+  static void  Flush(AcceleratorViewEntry &AccCache);
+  static void  Clone(AcceleratorViewEntry &AccCache);
+  static void  AccDiscard(AcceleratorViewEntry &AccCache);
+  static void  CpuDiscard(AcceleratorViewEntry &AccCache);
+
+  //  static void  LRUupdate(AcceleratorViewEntry &AccCache);
+  static void  LRUinsert(AcceleratorViewEntry &AccCache);
+  static void  LRUremove(AcceleratorViewEntry &AccCache);
+  
+  // manage entries in the table
+  static int                  EntryPresent(uint64_t CpuPtr);
+  static void                 EntryCreate(uint64_t CpuPtr,size_t bytes,ViewMode mode,ViewAdvise hint);
+  static void                 EntryErase (uint64_t CpuPtr);
+  static AccViewTableIterator EntryLookup(uint64_t CpuPtr);
+  static void                 EntrySet   (uint64_t CpuPtr,AcceleratorViewEntry &entry);
+
+  static void     AcceleratorViewClose(uint64_t AccPtr);
+  static uint64_t AcceleratorViewOpen(uint64_t  CpuPtr,size_t bytes,ViewMode mode,ViewAdvise hint);
+  static void     CpuViewClose(uint64_t Ptr);
+  static uint64_t CpuViewOpen(uint64_t  CpuPtr,size_t bytes,ViewMode mode,ViewAdvise hint);
+#endif
+  static void NotifyDeletion(void * CpuPtr);
+
+ public:
+  static void Print(void);
+  static int   isOpen   (void* CpuPtr);
+  static void  ViewClose(void* CpuPtr,ViewMode mode);
+  static void *ViewOpen (void* CpuPtr,size_t bytes,ViewMode mode,ViewAdvise hint);
+
+};
+
+NAMESPACE_END(Grid);
+
+

Grid/allocator/MemoryManagerCache.cc

@@ -0,0 +1,468 @@
+#include <Grid/GridCore.h>
+
+#ifndef GRID_UVM
+
+#warning "Using explicit device memory copies"
+NAMESPACE_BEGIN(Grid);
+#define dprintf(...)
+
+////////////////////////////////////////////////////////////
+// For caching copies of data on device
+////////////////////////////////////////////////////////////
+MemoryManager::AccViewTable_t MemoryManager::AccViewTable;
+MemoryManager::LRU_t MemoryManager::LRU;
+  
+////////////////////////////////////////////////////////
+// Footprint tracking
+////////////////////////////////////////////////////////
+uint64_t  MemoryManager::DeviceBytes;
+uint64_t  MemoryManager::DeviceLRUBytes;
+uint64_t  MemoryManager::DeviceMaxBytes = 1024*1024*128;
+uint64_t  MemoryManager::HostToDeviceBytes;
+uint64_t  MemoryManager::DeviceToHostBytes;
+uint64_t  MemoryManager::HostToDeviceXfer;
+uint64_t  MemoryManager::DeviceToHostXfer;
+
+////////////////////////////////////
+// Priority ordering for unlocked entries
+//  Empty
+//  CpuDirty 
+//  Consistent
+//  AccDirty
+////////////////////////////////////
+#define Empty         (0x0)  /*Entry unoccupied  */
+#define CpuDirty      (0x1)  /*CPU copy is golden, Acc buffer MAY not be allocated*/
+#define Consistent    (0x2)  /*ACC copy AND CPU copy are valid */
+#define AccDirty      (0x4)  /*ACC copy is golden */
+#define EvictNext     (0x8)  /*Priority for eviction*/
+
+/////////////////////////////////////////////////
+// Mechanics of data table maintenance
+/////////////////////////////////////////////////
+int   MemoryManager::EntryPresent(uint64_t CpuPtr)
+{
+  if(AccViewTable.empty()) return 0;
+
+  auto count = AccViewTable.count(CpuPtr);  assert((count==0)||(count==1));
+  return count;
+}
+void  MemoryManager::EntryCreate(uint64_t CpuPtr,size_t bytes,ViewMode mode,ViewAdvise hint)
+{
+  assert(!EntryPresent(CpuPtr));
+  AcceleratorViewEntry AccCache;
+  AccCache.CpuPtr = CpuPtr;
+  AccCache.AccPtr = (uint64_t)NULL;
+  AccCache.bytes  = bytes;
+  AccCache.state  = CpuDirty;
+  AccCache.LRU_valid=0;
+  AccCache.transient=0;
+  AccCache.accLock=0;
+  AccCache.cpuLock=0;
+  AccViewTable[CpuPtr] = AccCache;
+}
+MemoryManager::AccViewTableIterator MemoryManager::EntryLookup(uint64_t CpuPtr)
+{
+  assert(EntryPresent(CpuPtr));
+  auto AccCacheIterator = AccViewTable.find(CpuPtr);
+  assert(AccCacheIterator!=AccViewTable.end());
+  return AccCacheIterator;
+}
+void MemoryManager::EntryErase(uint64_t CpuPtr)
+{
+  auto AccCache = EntryLookup(CpuPtr);
+  AccViewTable.erase(CpuPtr);
+}
+void  MemoryManager::LRUinsert(AcceleratorViewEntry &AccCache)
+{
+  assert(AccCache.LRU_valid==0);
+  if (AccCache.transient) { 
+    LRU.push_back(AccCache.CpuPtr);
+    AccCache.LRU_entry = --LRU.end();
+  } else {
+    LRU.push_front(AccCache.CpuPtr);
+    AccCache.LRU_entry = LRU.begin();
+  }
+  AccCache.LRU_valid = 1;
+  DeviceLRUBytes+=AccCache.bytes;
+}
+void  MemoryManager::LRUremove(AcceleratorViewEntry &AccCache)
+{
+  assert(AccCache.LRU_valid==1);
+  LRU.erase(AccCache.LRU_entry);
+  AccCache.LRU_valid = 0;
+  DeviceLRUBytes-=AccCache.bytes;
+}
+/////////////////////////////////////////////////
+// Accelerator cache motion & consistency logic
+/////////////////////////////////////////////////
+void MemoryManager::AccDiscard(AcceleratorViewEntry &AccCache)
+{
+  ///////////////////////////////////////////////////////////
+  // Remove from Accelerator, remove entry, without flush
+  // Cannot be locked. If allocated Must be in LRU pool.
+  ///////////////////////////////////////////////////////////
+  assert(AccCache.state!=Empty);
+  
+  //  dprintf("MemoryManager: Discard(%llx) %llx\n",(uint64_t)AccCache.CpuPtr,(uint64_t)AccCache.AccPtr); 
+  assert(AccCache.accLock==0);
+  assert(AccCache.cpuLock==0);
+  assert(AccCache.CpuPtr!=(uint64_t)NULL);
+  if(AccCache.AccPtr) {
+    AcceleratorFree((void *)AccCache.AccPtr,AccCache.bytes);
+    DeviceBytes   -=AccCache.bytes;
+    LRUremove(AccCache);
+    //    dprintf("MemoryManager: Free(%llx) LRU %lld Total %lld\n",(uint64_t)AccCache.AccPtr,DeviceLRUBytes,DeviceBytes);  
+  }
+  uint64_t CpuPtr = AccCache.CpuPtr;
+  EntryErase(CpuPtr);
+}
+
+void MemoryManager::Evict(AcceleratorViewEntry &AccCache)
+{
+  ///////////////////////////////////////////////////////////////////////////
+  // Make CPU consistent, remove from Accelerator, remove entry
+  // Cannot be locked. If allocated must be in LRU pool.
+  ///////////////////////////////////////////////////////////////////////////
+  assert(AccCache.state!=Empty);
+  
+  //  dprintf("MemoryManager: Evict(%llx) %llx\n",(uint64_t)AccCache.CpuPtr,(uint64_t)AccCache.AccPtr); 
+  assert(AccCache.accLock==0);
+  assert(AccCache.cpuLock==0);
+  if(AccCache.state==AccDirty) {
+    Flush(AccCache);
+  }
+  assert(AccCache.CpuPtr!=(uint64_t)NULL);
+  if(AccCache.AccPtr) {
+    AcceleratorFree((void *)AccCache.AccPtr,AccCache.bytes);
+    DeviceBytes   -=AccCache.bytes;
+    LRUremove(AccCache);
+    //    dprintf("MemoryManager: Free(%llx) footprint now %lld \n",(uint64_t)AccCache.AccPtr,DeviceBytes);  
+  }
+  uint64_t CpuPtr = AccCache.CpuPtr;
+  EntryErase(CpuPtr);
+}
+void MemoryManager::Flush(AcceleratorViewEntry &AccCache)
+{
+  assert(AccCache.state==AccDirty);
+  assert(AccCache.cpuLock==0);
+  assert(AccCache.accLock==0);
+  assert(AccCache.AccPtr!=(uint64_t)NULL);
+  assert(AccCache.CpuPtr!=(uint64_t)NULL);
+  acceleratorCopyFromDevice((void *)AccCache.AccPtr,(void *)AccCache.CpuPtr,AccCache.bytes);
+  //  dprintf("MemoryManager: Flush  %llx -> %llx\n",(uint64_t)AccCache.AccPtr,(uint64_t)AccCache.CpuPtr); fflush(stdout);
+  DeviceToHostBytes+=AccCache.bytes;
+  DeviceToHostXfer++;
+  AccCache.state=Consistent;
+}
+void MemoryManager::Clone(AcceleratorViewEntry &AccCache)
+{
+  assert(AccCache.state==CpuDirty);
+  assert(AccCache.cpuLock==0);
+  assert(AccCache.accLock==0);
+  assert(AccCache.CpuPtr!=(uint64_t)NULL);
+  if(AccCache.AccPtr==(uint64_t)NULL){
+    AccCache.AccPtr=(uint64_t)AcceleratorAllocate(AccCache.bytes);
+    DeviceBytes+=AccCache.bytes;
+  }
+  //  dprintf("MemoryManager: Clone %llx <- %llx\n",(uint64_t)AccCache.AccPtr,(uint64_t)AccCache.CpuPtr); fflush(stdout);
+  acceleratorCopyToDevice((void *)AccCache.CpuPtr,(void *)AccCache.AccPtr,AccCache.bytes);
+  HostToDeviceBytes+=AccCache.bytes;
+  HostToDeviceXfer++;
+  AccCache.state=Consistent;
+}
+
+void MemoryManager::CpuDiscard(AcceleratorViewEntry &AccCache)
+{
+  assert(AccCache.state!=Empty);
+  assert(AccCache.cpuLock==0);
+  assert(AccCache.accLock==0);
+  assert(AccCache.CpuPtr!=(uint64_t)NULL);
+  if(AccCache.AccPtr==(uint64_t)NULL){
+    AccCache.AccPtr=(uint64_t)AcceleratorAllocate(AccCache.bytes);
+    DeviceBytes+=AccCache.bytes;
+  }
+  AccCache.state=AccDirty;
+}
+
+/////////////////////////////////////////////////////////////////////////////////
+// View management
+/////////////////////////////////////////////////////////////////////////////////
+void MemoryManager::ViewClose(void* Ptr,ViewMode mode)
+{
+  if( (mode==AcceleratorRead)||(mode==AcceleratorWrite)||(mode==AcceleratorWriteDiscard) ){
+    AcceleratorViewClose((uint64_t)Ptr);
+  } else if( (mode==CpuRead)||(mode==CpuWrite)){
+    CpuViewClose((uint64_t)Ptr);
+  } else { 
+    assert(0);
+  }
+}
+void *MemoryManager::ViewOpen(void* _CpuPtr,size_t bytes,ViewMode mode,ViewAdvise hint)
+{
+  uint64_t CpuPtr = (uint64_t)_CpuPtr;
+  if( (mode==AcceleratorRead)||(mode==AcceleratorWrite)||(mode==AcceleratorWriteDiscard) ){
+    return (void *) AcceleratorViewOpen(CpuPtr,bytes,mode,hint);
+  } else if( (mode==CpuRead)||(mode==CpuWrite)){
+    return (void *)CpuViewOpen(CpuPtr,bytes,mode,hint);
+  } else { 
+    assert(0);
+    return NULL;
+  }
+}
+void  MemoryManager::EvictVictims(uint64_t bytes)
+{
+  while(bytes+DeviceLRUBytes > DeviceMaxBytes){
+    if ( DeviceLRUBytes > 0){
+      assert(LRU.size()>0);
+      uint64_t victim = LRU.back();
+      auto AccCacheIterator = EntryLookup(victim);
+      auto & AccCache = AccCacheIterator->second;
+      Evict(AccCache);
+    }
+  }
+}
+uint64_t MemoryManager::AcceleratorViewOpen(uint64_t CpuPtr,size_t bytes,ViewMode mode,ViewAdvise hint)
+{
+  ////////////////////////////////////////////////////////////////////////////
+  // Find if present, otherwise get or force an empty
+  ////////////////////////////////////////////////////////////////////////////
+  if ( EntryPresent(CpuPtr)==0 ){
+    EvictVictims(bytes);
+    EntryCreate(CpuPtr,bytes,mode,hint);
+  }
+
+  auto AccCacheIterator = EntryLookup(CpuPtr);
+  auto & AccCache = AccCacheIterator->second;
+  
+  assert((mode==AcceleratorRead)||(mode==AcceleratorWrite)||(mode==AcceleratorWriteDiscard));
+
+  assert(AccCache.cpuLock==0);  // Programming error
+
+  if(AccCache.state!=Empty) {
+    assert(AccCache.CpuPtr == CpuPtr);
+    assert(AccCache.bytes  ==bytes);
+  }
+/*
+ *  State transitions and actions
+ *
+ *  Action  State   StateNext         Flush    Clone
+ *
+ *  AccRead  Empty   Consistent        -        Y
+ *  AccWrite Empty   AccDirty          -        Y
+ *  AccRead  CpuDirty Consistent       -        Y
+ *  AccWrite CpuDirty AccDirty         -        Y
+ *  AccRead  Consistent Consistent     -        - 
+ *  AccWrite Consistent AccDirty       -        - 
+ *  AccRead  AccDirty   AccDirty       -        - 
+ *  AccWrite AccDirty   AccDirty       -        - 
+ */
+  if(AccCache.state==Empty) {
+    assert(AccCache.LRU_valid==0);
+    AccCache.CpuPtr = CpuPtr;
+    AccCache.AccPtr = (uint64_t)NULL;
+    AccCache.bytes  = bytes;
+    AccCache.state  = CpuDirty;   // Cpu starts primary
+    if(mode==AcceleratorWriteDiscard){
+      CpuDiscard(AccCache);
+      AccCache.state  = AccDirty;   // Empty + AcceleratorWrite=> AccDirty
+    } else if(mode==AcceleratorWrite){
+      Clone(AccCache);
+      AccCache.state  = AccDirty;   // Empty + AcceleratorWrite=> AccDirty
+    } else {
+      Clone(AccCache);
+      AccCache.state  = Consistent; // Empty + AccRead => Consistent
+    }
+    AccCache.accLock= 1;
+  } else if(AccCache.state==CpuDirty ){
+    if(mode==AcceleratorWriteDiscard) {
+      CpuDiscard(AccCache);
+      AccCache.state  = AccDirty;   // CpuDirty + AcceleratorWrite=> AccDirty
+    } else if(mode==AcceleratorWrite) {
+      Clone(AccCache);
+      AccCache.state  = AccDirty;   // CpuDirty + AcceleratorWrite=> AccDirty
+    } else {
+      Clone(AccCache);
+      AccCache.state  = Consistent; // CpuDirty + AccRead => Consistent
+    }
+    AccCache.accLock++;
+    //    printf("Copied CpuDirty entry into device accLock %d\n",AccCache.accLock);
+  } else if(AccCache.state==Consistent) {
+    if((mode==AcceleratorWrite)||(mode==AcceleratorWriteDiscard))
+      AccCache.state  = AccDirty;   // Consistent + AcceleratorWrite=> AccDirty
+    else
+      AccCache.state  = Consistent; // Consistent + AccRead => Consistent
+    AccCache.accLock++;
+    //    printf("Consistent entry into device accLock %d\n",AccCache.accLock);
+  } else if(AccCache.state==AccDirty) {
+    if((mode==AcceleratorWrite)||(mode==AcceleratorWriteDiscard))
+      AccCache.state  = AccDirty; // AccDirty + AcceleratorWrite=> AccDirty
+    else
+      AccCache.state  = AccDirty; // AccDirty + AccRead => AccDirty
+    AccCache.accLock++;
+    //    printf("AccDirty entry into device accLock %d\n",AccCache.accLock);
+  } else {
+    assert(0);
+  }
+
+  // If view is opened on device remove from LRU
+  if(AccCache.LRU_valid==1){
+    // must possibly remove from LRU as now locked on GPU
+    LRUremove(AccCache);
+  }
+
+  int transient =hint;
+  AccCache.transient= transient? EvictNext : 0;
+
+  return AccCache.AccPtr;
+}
+////////////////////////////////////
+// look up & decrement lock count
+////////////////////////////////////
+void MemoryManager::AcceleratorViewClose(uint64_t CpuPtr)
+{
+  auto AccCacheIterator = EntryLookup(CpuPtr);
+  auto & AccCache = AccCacheIterator->second;
+
+  assert(AccCache.cpuLock==0);
+  assert(AccCache.accLock>0);
+
+  AccCache.accLock--;
+
+  // Move to LRU queue if not locked and close on device
+  if(AccCache.accLock==0) {
+    LRUinsert(AccCache);
+  }
+}
+void MemoryManager::CpuViewClose(uint64_t CpuPtr)
+{
+  auto AccCacheIterator = EntryLookup(CpuPtr);
+  auto & AccCache = AccCacheIterator->second;
+
+  assert(AccCache.cpuLock>0);
+  assert(AccCache.accLock==0);
+
+  AccCache.cpuLock--;
+}
+/*
+ *  Action  State   StateNext         Flush    Clone
+ *
+ *  CpuRead  Empty   CpuDirty          -        -
+ *  CpuWrite Empty   CpuDirty          -        -
+ *  CpuRead  CpuDirty CpuDirty         -        -
+ *  CpuWrite CpuDirty CpuDirty         -        - 
+ *  CpuRead  Consistent Consistent     -        - 
+ *  CpuWrite Consistent CpuDirty       -        - 
+ *  CpuRead  AccDirty   Consistent     Y        -
+ *  CpuWrite AccDirty   CpuDirty       Y        -
+ */
+uint64_t MemoryManager::CpuViewOpen(uint64_t CpuPtr,size_t bytes,ViewMode mode,ViewAdvise transient)
+{
+  ////////////////////////////////////////////////////////////////////////////
+  // Find if present, otherwise get or force an empty
+  ////////////////////////////////////////////////////////////////////////////
+  if ( EntryPresent(CpuPtr)==0 ){
+    EvictVictims(bytes);
+    EntryCreate(CpuPtr,bytes,mode,transient);
+  }
+
+  auto AccCacheIterator = EntryLookup(CpuPtr);
+  auto & AccCache = AccCacheIterator->second;
+  
+  assert((mode==CpuRead)||(mode==CpuWrite));
+  assert(AccCache.accLock==0);  // Programming error
+
+  if(AccCache.state!=Empty) {
+    assert(AccCache.CpuPtr == CpuPtr);
+    assert(AccCache.bytes==bytes);
+  }
+
+  if(AccCache.state==Empty) {
+    AccCache.CpuPtr = CpuPtr;
+    AccCache.AccPtr = (uint64_t)NULL;
+    AccCache.bytes  = bytes;
+    AccCache.state  = CpuDirty; // Empty + CpuRead/CpuWrite => CpuDirty
+    AccCache.accLock= 0;
+    AccCache.cpuLock= 1;
+  } else if(AccCache.state==CpuDirty ){
+    // AccPtr dont care, deferred allocate
+    AccCache.state = CpuDirty; // CpuDirty +CpuRead/CpuWrite => CpuDirty
+    AccCache.cpuLock++;
+  } else if(AccCache.state==Consistent) {
+    assert(AccCache.AccPtr != (uint64_t)NULL);
+    if(mode==CpuWrite)
+      AccCache.state = CpuDirty;   // Consistent +CpuWrite => CpuDirty
+    else 
+      AccCache.state = Consistent; // Consistent +CpuRead  => Consistent
+    AccCache.cpuLock++;
+  } else if(AccCache.state==AccDirty) {
+    assert(AccCache.AccPtr != (uint64_t)NULL);
+    Flush(AccCache);
+    if(mode==CpuWrite) AccCache.state = CpuDirty;   // AccDirty +CpuWrite => CpuDirty, Flush
+    else            AccCache.state = Consistent; // AccDirty +CpuRead  => Consistent, Flush
+    AccCache.cpuLock++;
+  } else {
+    assert(0); // should be unreachable
+  }
+
+  AccCache.transient= transient? EvictNext : 0;
+
+  return AccCache.CpuPtr;
+}
+void  MemoryManager::NotifyDeletion(void *_ptr)
+{
+  // Look up in ViewCache
+  uint64_t ptr = (uint64_t)_ptr;
+  if(EntryPresent(ptr)) {
+    auto e = EntryLookup(ptr);
+    AccDiscard(e->second);
+  }
+}
+void  MemoryManager::Print(void)
+{
+  std::cout << GridLogDebug << "--------------------------------------------" << std::endl;
+  std::cout << GridLogDebug << "Memory Manager                             " << std::endl;
+  std::cout << GridLogDebug << "--------------------------------------------" << std::endl;
+  std::cout << GridLogDebug << DeviceBytes   << " bytes allocated on device " << std::endl;
+  std::cout << GridLogDebug << DeviceLRUBytes<< " bytes evictable on device " << std::endl;
+  std::cout << GridLogDebug << DeviceMaxBytes<< " bytes max on device       " << std::endl;
+  std::cout << GridLogDebug << HostToDeviceXfer << " transfers        to   device " << std::endl;
+  std::cout << GridLogDebug << DeviceToHostXfer << " transfers        from device " << std::endl;
+  std::cout << GridLogDebug << HostToDeviceBytes<< " bytes transfered to   device " << std::endl;
+  std::cout << GridLogDebug << DeviceToHostBytes<< " bytes transfered from device " << std::endl;
+  std::cout << GridLogDebug << AccViewTable.size()<< " vectors " << LRU.size()<<" evictable"<< std::endl;
+  std::cout << GridLogDebug << "--------------------------------------------" << std::endl;
+  std::cout << GridLogDebug << "CpuAddr\t\tAccAddr\t\tState\t\tcpuLock\taccLock\tLRU_valid "<<std::endl;
+  std::cout << GridLogDebug << "--------------------------------------------" << std::endl;
+  for(auto it=AccViewTable.begin();it!=AccViewTable.end();it++){
+    auto &AccCache = it->second;
+    
+    std::string str;
+    if ( AccCache.state==Empty    ) str = std::string("Empty");
+    if ( AccCache.state==CpuDirty ) str = std::string("CpuDirty");
+    if ( AccCache.state==AccDirty ) str = std::string("AccDirty");
+    if ( AccCache.state==Consistent)str = std::string("Consistent");
+
+    std::cout << GridLogDebug << "0x"<<std::hex<<AccCache.CpuPtr<<std::dec
+	      << "\t0x"<<std::hex<<AccCache.AccPtr<<std::dec<<"\t" <<str
+	      << "\t" << AccCache.cpuLock
+	      << "\t" << AccCache.accLock
+	      << "\t" << AccCache.LRU_valid<<std::endl;
+  }
+  std::cout << GridLogDebug << "--------------------------------------------" << std::endl;
+
+};
+int   MemoryManager::isOpen   (void* _CpuPtr) 
+{ 
+  uint64_t CpuPtr = (uint64_t)_CpuPtr;
+  if ( EntryPresent(CpuPtr) ){
+    auto AccCacheIterator = EntryLookup(CpuPtr);
+    auto & AccCache = AccCacheIterator->second;
+    return AccCache.cpuLock+AccCache.accLock;
+  } else { 
+    return 0;
+  }
+}
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/allocator/MemoryManagerShared.cc

@@ -0,0 +1,24 @@
+#include <Grid/GridCore.h>
+#ifdef GRID_UVM
+
+#warning "Grid is assuming unified virtual memory address space"
+NAMESPACE_BEGIN(Grid);
+/////////////////////////////////////////////////////////////////////////////////
+// View management is 1:1 address space mapping
+/////////////////////////////////////////////////////////////////////////////////
+uint64_t  MemoryManager::DeviceBytes;
+uint64_t  MemoryManager::DeviceLRUBytes;
+uint64_t  MemoryManager::DeviceMaxBytes = 1024*1024*128;
+uint64_t  MemoryManager::HostToDeviceBytes;
+uint64_t  MemoryManager::DeviceToHostBytes;
+uint64_t  MemoryManager::HostToDeviceXfer;
+uint64_t  MemoryManager::DeviceToHostXfer;
+
+void  MemoryManager::ViewClose(void* AccPtr,ViewMode mode){};
+void *MemoryManager::ViewOpen(void* CpuPtr,size_t bytes,ViewMode mode,ViewAdvise hint){ return CpuPtr; };
+int   MemoryManager::isOpen   (void* CpuPtr) { return 0;}
+void  MemoryManager::Print(void){};
+void  MemoryManager::NotifyDeletion(void *ptr){};
+
+NAMESPACE_END(Grid);
+#endif

Grid/allocator/MemoryStats.cc

@@ -0,0 +1,67 @@
+#include <Grid/GridCore.h>
+#include <fcntl.h>
+
+NAMESPACE_BEGIN(Grid);
+
+MemoryStats *MemoryProfiler::stats = nullptr;
+bool         MemoryProfiler::debug = false;
+
+void check_huge_pages(void *Buf,uint64_t BYTES)
+{
+#ifdef __linux__
+  int fd = open("/proc/self/pagemap", O_RDONLY);
+  assert(fd >= 0);
+  const int page_size = 4096;
+  uint64_t virt_pfn = (uint64_t)Buf / page_size;
+  off_t offset = sizeof(uint64_t) * virt_pfn;
+  uint64_t npages = (BYTES + page_size-1) / page_size;
+  uint64_t pagedata[npages];
+  uint64_t ret = lseek(fd, offset, SEEK_SET);
+  assert(ret == offset);
+  ret = ::read(fd, pagedata, sizeof(uint64_t)*npages);
+  assert(ret == sizeof(uint64_t) * npages);
+  int nhugepages = npages / 512;
+  int n4ktotal, nnothuge;
+  n4ktotal = 0;
+  nnothuge = 0;
+  for (int i = 0; i < nhugepages; ++i) {
+    uint64_t baseaddr = (pagedata[i*512] & 0x7fffffffffffffULL) * page_size;
+    for (int j = 0; j < 512; ++j) {
+      uint64_t pageaddr = (pagedata[i*512+j] & 0x7fffffffffffffULL) * page_size;
+      ++n4ktotal;
+      if (pageaddr != baseaddr + j * page_size)
+	++nnothuge;
+    }
+  }
+  int rank = CartesianCommunicator::RankWorld();
+  printf("rank %d Allocated %d 4k pages, %d not in huge pages\n", rank, n4ktotal, nnothuge);
+#endif
+}
+
+std::string sizeString(const size_t bytes)
+{
+  constexpr unsigned int bufSize = 256;
+  const char             *suffixes[7] = {"", "K", "M", "G", "T", "P", "E"};
+  char                   buf[256];
+  size_t                 s     = 0;
+  double                 count = bytes;
+  
+  while (count >= 1024 && s < 7)
+    {
+      s++;
+      count /= 1024;
+    }
+  if (count - floor(count) == 0.0)
+    {
+      snprintf(buf, bufSize, "%d %sB", (int)count, suffixes[s]);
+    }
+  else
+    {
+      snprintf(buf, bufSize, "%.1f %sB", count, suffixes[s]);
+    }
+  
+  return std::string(buf);
+}
+
+NAMESPACE_END(Grid);
+

Grid/allocator/MemoryStats.h

@@ -0,0 +1,95 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/MemoryStats.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+
+NAMESPACE_BEGIN(Grid);
+
+std::string sizeString(size_t bytes);
+
+struct MemoryStats
+{
+  size_t totalAllocated{0}, maxAllocated{0}, 
+    currentlyAllocated{0}, totalFreed{0};
+};
+    
+class MemoryProfiler
+{
+public:
+  static MemoryStats *stats;
+  static bool        debug;
+};
+
+#define memString(bytes) std::to_string(bytes) + " (" + sizeString(bytes) + ")"
+#define profilerDebugPrint						\
+  if (MemoryProfiler::stats)						\
+    {									\
+      auto s = MemoryProfiler::stats;					\
+      std::cout << GridLogDebug << "[Memory debug] Stats " << MemoryProfiler::stats << std::endl; \
+      std::cout << GridLogDebug << "[Memory debug] total  : " << memString(s->totalAllocated) \
+		<< std::endl;						\
+      std::cout << GridLogDebug << "[Memory debug] max    : " << memString(s->maxAllocated) \
+		<< std::endl;						\
+      std::cout << GridLogDebug << "[Memory debug] current: " << memString(s->currentlyAllocated) \
+		<< std::endl;						\
+      std::cout << GridLogDebug << "[Memory debug] freed  : " << memString(s->totalFreed) \
+		<< std::endl;						\
+    }
+
+#define profilerAllocate(bytes)						\
+  if (MemoryProfiler::stats)						\
+    {									\
+      auto s = MemoryProfiler::stats;					\
+      s->totalAllocated     += (bytes);					\
+      s->currentlyAllocated += (bytes);					\
+      s->maxAllocated        = std::max(s->maxAllocated, s->currentlyAllocated); \
+    }									\
+  if (MemoryProfiler::debug)						\
+    {									\
+      std::cout << GridLogDebug << "[Memory debug] allocating " << memString(bytes) << std::endl; \
+      profilerDebugPrint;						\
+    }
+
+#define profilerFree(bytes)						\
+  if (MemoryProfiler::stats)						\
+    {									\
+      auto s = MemoryProfiler::stats;					\
+      s->totalFreed         += (bytes);					\
+      s->currentlyAllocated -= (bytes);					\
+    }									\
+  if (MemoryProfiler::debug)						\
+    {									\
+      std::cout << GridLogDebug << "[Memory debug] freeing " << memString(bytes) << std::endl; \
+      profilerDebugPrint;						\
+    }
+
+void check_huge_pages(void *Buf,uint64_t BYTES);
+
+NAMESPACE_END(Grid);
+

Grid/cartesian/Cartesian.h

@@ -1,4 +1,4 @@
-    /*************************************************************************************
+/*************************************************************************************
 
     Grid physics library, www.github.com/paboyle/Grid 
 
@@ -23,8 +23,8 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     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 */
+*************************************************************************************/
+/*  END LEGAL */
 #ifndef GRID_CARTESIAN_H
 #define GRID_CARTESIAN_H
 

Grid/cartesian/Cartesian_base.h

@@ -0,0 +1,291 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/cartesian/Cartesian_base.h
+
+    Copyright (C) 2015
+
+    Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+    Author: paboyle <paboyle@ph.ed.ac.uk>
+    Author: Guido Cossu <guido.cossu@ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CARTESIAN_BASE_H
+#define GRID_CARTESIAN_BASE_H
+
+NAMESPACE_BEGIN(Grid);
+
+//////////////////////////////////////////////////////////////////////
+// Commicator provides information on the processor grid
+//////////////////////////////////////////////////////////////////////
+//    unsigned long _ndimension;
+//    Coordinate _processors; // processor grid
+//    int              _processor;  // linear processor rank
+//    Coordinate _processor_coor;  // linear processor rank
+//////////////////////////////////////////////////////////////////////
+class GridBase : public CartesianCommunicator , public GridThread {
+
+public:
+  int dummy;
+  // Give Lattice access
+  template<class object> friend class Lattice;
+
+  GridBase(const Coordinate & processor_grid) : CartesianCommunicator(processor_grid) { LocallyPeriodic=0;}; 
+
+  GridBase(const Coordinate & processor_grid,
+	   const CartesianCommunicator &parent,
+	   int &split_rank) 
+    : CartesianCommunicator(processor_grid,parent,split_rank) {LocallyPeriodic=0;};
+
+  GridBase(const Coordinate & processor_grid,
+	   const CartesianCommunicator &parent) 
+    : CartesianCommunicator(processor_grid,parent,dummy) {LocallyPeriodic=0;};
+
+  virtual ~GridBase() = default;
+
+  // Physics Grid information.
+  Coordinate _simd_layout;// Which dimensions get relayed out over simd lanes.
+  Coordinate _fdimensions;// (full) Global dimensions of array prior to cb removal
+  Coordinate _gdimensions;// Global dimensions of array after cb removal
+  Coordinate _ldimensions;// local dimensions of array with processor images removed
+  Coordinate _rdimensions;// Reduced local dimensions with simd lane images and processor images removed 
+  Coordinate _ostride;    // Outer stride for each dimension
+  Coordinate _istride;    // Inner stride i.e. within simd lane
+  int _osites;                  // _isites*_osites = product(dimensions).
+  int _isites;
+  int _fsites;                  // _isites*_osites = product(dimensions).
+  int _gsites;
+  Coordinate _slice_block;// subslice information
+  Coordinate _slice_stride;
+  Coordinate _slice_nblock;
+
+  Coordinate _lstart;     // local start of array in gcoors _processor_coor[d]*_ldimensions[d]
+  Coordinate _lend  ;     // local end of array in gcoors   _processor_coor[d]*_ldimensions[d]+_ldimensions_[d]-1
+
+  bool _isCheckerBoarded; 
+  int        LocallyPeriodic;
+  Coordinate _checker_dim_mask;
+
+public:
+
+  ////////////////////////////////////////////////////////////////
+  // Checkerboarding interface is virtual and overridden by 
+  // GridCartesian / GridRedBlackCartesian
+  ////////////////////////////////////////////////////////////////
+  virtual int CheckerBoarded(int dim)=0;
+  virtual int CheckerBoard(const Coordinate &site)=0;
+  virtual int CheckerBoardDestination(int source_cb,int shift,int dim)=0;
+  virtual int CheckerBoardShift(int source_cb,int dim,int shift,int osite)=0;
+  virtual int CheckerBoardShiftForCB(int source_cb,int dim,int shift,int cb)=0;
+  virtual int CheckerBoardFromOindex (int Oindex)=0;
+  virtual int CheckerBoardFromOindexTable (int Oindex)=0;
+
+  //////////////////////////////////////////////////////////////////////////////////////////////
+  // Local layout calculations
+  //////////////////////////////////////////////////////////////////////////////////////////////
+  // These routines are key. Subdivide the linearised cartesian index into
+  //      "inner" index identifying which simd lane of object<vFcomplex> is associated with coord
+  //      "outer" index identifying which element of _odata in class "Lattice" is associated with coord.
+  //
+  // Compared to, say, Blitz++ we simply need to store BOTH an inner stride and an outer
+  // stride per dimension. The cost of evaluating the indexing information is doubled for an n-dimensional
+  // coordinate. Note, however, for data parallel operations the "inner" indexing cost is not paid and all
+  // lanes are operated upon simultaneously.
+  
+  virtual int oIndex(Coordinate &coor)
+  {
+    int idx=0;
+    // Works with either global or local coordinates
+    for(int d=0;d<_ndimension;d++) idx+=_ostride[d]*(coor[d]%_rdimensions[d]);
+    return idx;
+  }
+  virtual int iIndex(Coordinate &lcoor)
+  {
+    int idx=0;
+    for(int d=0;d<_ndimension;d++) idx+=_istride[d]*(lcoor[d]/_rdimensions[d]);
+    return idx;
+  }
+  inline int oIndexReduced(Coordinate &ocoor)
+  {
+    int idx=0; 
+    // ocoor is already reduced so can eliminate the modulo operation
+    // for fast indexing and inline the routine
+    for(int d=0;d<_ndimension;d++) idx+=_ostride[d]*ocoor[d];
+    return idx;
+  }
+  inline void oCoorFromOindex (Coordinate& coor,int Oindex){
+    Lexicographic::CoorFromIndex(coor,Oindex,_rdimensions);
+  }
+
+  inline void InOutCoorToLocalCoor (Coordinate &ocoor, Coordinate &icoor, Coordinate &lcoor) {
+    lcoor.resize(_ndimension);
+    for (int d = 0; d < _ndimension; d++)
+      lcoor[d] = ocoor[d] + _rdimensions[d] * icoor[d];
+  }
+
+  //////////////////////////////////////////////////////////
+  // SIMD lane addressing
+  //////////////////////////////////////////////////////////
+  inline void iCoorFromIindex(Coordinate &coor,int lane)
+  {
+    Lexicographic::CoorFromIndex(coor,lane,_simd_layout);
+  }
+
+  inline int PermuteDim(int dimension){
+    return _simd_layout[dimension]>1;
+  }
+  inline int PermuteType(int dimension){
+    int permute_type=0;
+    //
+    // Best way to encode this would be to present a mask 
+    // for which simd dimensions are rotated, and the rotation
+    // size. If there is only one simd dimension rotated, this is just 
+    // a permute. 
+    //
+    // Cases: PermuteType == 1,2,4,8
+    // Distance should be either 0,1,2..
+    //
+    if ( _simd_layout[dimension] > 2 ) { 
+      for(int d=0;d<_ndimension;d++){
+	if ( d != dimension ) assert ( (_simd_layout[d]==1)  );
+      }
+      permute_type = RotateBit; // How to specify distance; this is not just direction.
+      return permute_type;
+    }
+
+    for(int d=_ndimension-1;d>dimension;d--){
+      if (_simd_layout[d]>1 ) permute_type++;
+    }
+    return permute_type;
+  }
+  ////////////////////////////////////////////////////////////////
+  // Array sizing queries
+  ////////////////////////////////////////////////////////////////
+
+  inline int iSites(void) const { return _isites; };
+  inline int Nsimd(void)  const { return _isites; };// Synonymous with iSites
+  inline int oSites(void) const { return _osites; };
+  inline int lSites(void) const { return _isites*_osites; }; 
+  inline int gSites(void) const { return _isites*_osites*_Nprocessors; }; 
+  inline int Nd    (void) const { return _ndimension;};
+
+  inline const Coordinate LocalStarts(void)             { return _lstart;    };
+  inline const Coordinate &FullDimensions(void)         { return _fdimensions;};
+  inline const Coordinate &GlobalDimensions(void)       { return _gdimensions;};
+  inline const Coordinate &LocalDimensions(void)        { return _ldimensions;};
+  inline const Coordinate &VirtualLocalDimensions(void) { return _ldimensions;};
+
+  ////////////////////////////////////////////////////////////////
+  // Utility to print the full decomposition details 
+  ////////////////////////////////////////////////////////////////
+
+  void show_decomposition(){
+    std::cout << GridLogMessage << "\tFull Dimensions    : " << _fdimensions << std::endl;
+    std::cout << GridLogMessage << "\tSIMD layout        : " << _simd_layout << std::endl;
+    std::cout << GridLogMessage << "\tGlobal Dimensions  : " << _gdimensions << std::endl;
+    std::cout << GridLogMessage << "\tLocal Dimensions   : " << _ldimensions << std::endl;
+    std::cout << GridLogMessage << "\tReduced Dimensions : " << _rdimensions << std::endl;
+    std::cout << GridLogMessage << "\tOuter strides      : " << _ostride << std::endl;
+    std::cout << GridLogMessage << "\tInner strides      : " << _istride << std::endl;
+    std::cout << GridLogMessage << "\tiSites             : " << _isites << std::endl;
+    std::cout << GridLogMessage << "\toSites             : " << _osites << std::endl;
+    std::cout << GridLogMessage << "\tlSites             : " << lSites() << std::endl;        
+    std::cout << GridLogMessage << "\tgSites             : " << gSites() << std::endl;
+    std::cout << GridLogMessage << "\tNd                 : " << _ndimension << std::endl;             
+  } 
+
+  ////////////////////////////////////////////////////////////////
+  // Global addressing
+  ////////////////////////////////////////////////////////////////
+  void GlobalIndexToGlobalCoor(int gidx,Coordinate &gcoor){
+    assert(gidx< gSites());
+    Lexicographic::CoorFromIndex(gcoor,gidx,_gdimensions);
+  }
+  void LocalIndexToLocalCoor(int lidx,Coordinate &lcoor){
+    assert(lidx<lSites());
+    Lexicographic::CoorFromIndex(lcoor,lidx,_ldimensions);
+  }
+  void GlobalCoorToGlobalIndex(const Coordinate & gcoor,int & gidx){
+    gidx=0;
+    int mult=1;
+    for(int mu=0;mu<_ndimension;mu++) {
+      gidx+=mult*gcoor[mu];
+      mult*=_gdimensions[mu];
+    }
+  }
+  void GlobalCoorToProcessorCoorLocalCoor(Coordinate &pcoor,Coordinate &lcoor,const Coordinate &gcoor)
+  {
+    pcoor.resize(_ndimension);
+    lcoor.resize(_ndimension);
+    for(int mu=0;mu<_ndimension;mu++){
+      int _fld  = _fdimensions[mu]/_processors[mu];
+      pcoor[mu] = gcoor[mu]/_fld;
+      lcoor[mu] = gcoor[mu]%_fld;
+    }
+  }
+  void GlobalCoorToRankIndex(int &rank, int &o_idx, int &i_idx ,const Coordinate &gcoor)
+  {
+    Coordinate pcoor;
+    Coordinate lcoor;
+    GlobalCoorToProcessorCoorLocalCoor(pcoor,lcoor,gcoor);
+    rank = RankFromProcessorCoor(pcoor);
+    /*
+      Coordinate cblcoor(lcoor);
+      for(int d=0;d<cblcoor.size();d++){
+      if( this->CheckerBoarded(d) ) {
+      cblcoor[d] = lcoor[d]/2;
+      }
+      }
+    */
+    i_idx= iIndex(lcoor);
+    o_idx= oIndex(lcoor);
+  }
+
+  void RankIndexToGlobalCoor(int rank, int o_idx, int i_idx , Coordinate &gcoor)
+  {
+    gcoor.resize(_ndimension);
+    Coordinate coor(_ndimension);
+
+    ProcessorCoorFromRank(rank,coor);
+    for(int mu=0;mu<_ndimension;mu++) gcoor[mu] = _ldimensions[mu]*coor[mu];
+
+    iCoorFromIindex(coor,i_idx);
+    for(int mu=0;mu<_ndimension;mu++) gcoor[mu] += _rdimensions[mu]*coor[mu];
+
+    oCoorFromOindex (coor,o_idx);
+    for(int mu=0;mu<_ndimension;mu++) gcoor[mu] += coor[mu];
+      
+  }
+  void RankIndexCbToFullGlobalCoor(int rank, int o_idx, int i_idx, int cb,Coordinate &fcoor)
+  {
+    RankIndexToGlobalCoor(rank,o_idx,i_idx ,fcoor);
+    if(CheckerBoarded(0)){
+      fcoor[0] = fcoor[0]*2+cb;
+    }
+  }
+  void ProcessorCoorLocalCoorToGlobalCoor(Coordinate &Pcoor,Coordinate &Lcoor,Coordinate &gcoor)
+  {
+    gcoor.resize(_ndimension);
+    for(int mu=0;mu<_ndimension;mu++) gcoor[mu] = Pcoor[mu]*_ldimensions[mu]+Lcoor[mu];
+  }
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/cartesian/Cartesian_full.h

@@ -0,0 +1,178 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/cartesian/Cartesian_full.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CARTESIAN_FULL_H
+#define GRID_CARTESIAN_FULL_H
+
+NAMESPACE_BEGIN(Grid);
+    
+/////////////////////////////////////////////////////////////////////////////////////////
+// Grid Support.
+/////////////////////////////////////////////////////////////////////////////////////////
+
+class GridCartesian: public GridBase {
+
+public:
+  int dummy;
+  Coordinate _checker_dim_mask;
+  virtual int  CheckerBoardFromOindexTable (int Oindex) {
+    return 0;
+  }
+  virtual int  CheckerBoardFromOindex (int Oindex)
+  {
+    return 0;
+  }
+  virtual int CheckerBoarded(int dim){
+    return 0;
+  }
+  virtual int CheckerBoard(const Coordinate &site){
+    return 0;
+  }
+  virtual int CheckerBoardDestination(int cb,int shift,int dim){
+    return 0;
+  }
+  virtual int CheckerBoardShiftForCB(int source_cb,int dim,int shift, int ocb){
+    return shift;
+  }
+  virtual int CheckerBoardShift(int source_cb,int dim,int shift, int osite){
+    return shift;
+  }
+  /////////////////////////////////////////////////////////////////////////
+  // Constructor takes a parent grid and possibly subdivides communicator.
+  /////////////////////////////////////////////////////////////////////////
+  GridCartesian(const Coordinate &dimensions,
+		const Coordinate &simd_layout,
+		const Coordinate &processor_grid,
+		const GridCartesian &parent) : GridBase(processor_grid,parent,dummy)
+  {
+    Init(dimensions,simd_layout,processor_grid);
+  }
+  GridCartesian(const Coordinate &dimensions,
+		const Coordinate &simd_layout,
+		const Coordinate &processor_grid,
+		const GridCartesian &parent,int &split_rank) : GridBase(processor_grid,parent,split_rank)
+  {
+    Init(dimensions,simd_layout,processor_grid);
+  }
+  /////////////////////////////////////////////////////////////////////////
+  // Construct from comm world
+  /////////////////////////////////////////////////////////////////////////
+  GridCartesian(const Coordinate &dimensions,
+		const Coordinate &simd_layout,
+		const Coordinate &processor_grid) : GridBase(processor_grid)
+  {
+    Init(dimensions,simd_layout,processor_grid);
+  }
+
+  virtual ~GridCartesian() = default;
+
+  void Init(const Coordinate &dimensions,
+	    const Coordinate &simd_layout,
+	    const Coordinate &processor_grid)
+  {
+    ///////////////////////
+    // Grid information
+    ///////////////////////
+      _isCheckerBoarded = false;
+    _ndimension = dimensions.size();
+
+    _fdimensions.resize(_ndimension);
+    _gdimensions.resize(_ndimension);
+    _ldimensions.resize(_ndimension);
+    _rdimensions.resize(_ndimension);
+    _simd_layout.resize(_ndimension);
+    _checker_dim_mask.resize(_ndimension);;
+    _lstart.resize(_ndimension);
+    _lend.resize(_ndimension);
+
+    _ostride.resize(_ndimension);
+    _istride.resize(_ndimension);
+
+    _fsites = _gsites = _osites = _isites = 1;
+
+    for (int d = 0; d < _ndimension; d++)
+      {
+	_checker_dim_mask[d]=0;
+
+        _fdimensions[d] = dimensions[d];   // Global dimensions
+        _gdimensions[d] = _fdimensions[d]; // Global dimensions
+        _simd_layout[d] = simd_layout[d];
+        _fsites = _fsites * _fdimensions[d];
+        _gsites = _gsites * _gdimensions[d];
+
+        // Use a reduced simd grid
+        _ldimensions[d] = _gdimensions[d] / _processors[d]; //local dimensions
+        //std::cout << _ldimensions[d] << "  " << _gdimensions[d] << "  " << _processors[d] << std::endl;
+        assert(_ldimensions[d] * _processors[d] == _gdimensions[d]);
+
+        _rdimensions[d] = _ldimensions[d] / _simd_layout[d]; //overdecomposition
+        assert(_rdimensions[d] * _simd_layout[d] == _ldimensions[d]);
+
+        _lstart[d] = _processor_coor[d] * _ldimensions[d];
+        _lend[d] = _processor_coor[d] * _ldimensions[d] + _ldimensions[d] - 1;
+        _osites *= _rdimensions[d];
+        _isites *= _simd_layout[d];
+
+        // Addressing support
+        if (d == 0)
+	  {
+	    _ostride[d] = 1;
+	    _istride[d] = 1;
+	  }
+        else
+	  {
+	    _ostride[d] = _ostride[d - 1] * _rdimensions[d - 1];
+	    _istride[d] = _istride[d - 1] * _simd_layout[d - 1];
+	  }
+      }
+
+    ///////////////////////
+    // subplane information
+    ///////////////////////
+    _slice_block.resize(_ndimension);
+    _slice_stride.resize(_ndimension);
+    _slice_nblock.resize(_ndimension);
+
+    int block = 1;
+    int nblock = 1;
+    for (int d = 0; d < _ndimension; d++)
+      nblock *= _rdimensions[d];
+
+    for (int d = 0; d < _ndimension; d++)
+      {
+        nblock /= _rdimensions[d];
+        _slice_block[d] = block;
+        _slice_stride[d] = _ostride[d] * _rdimensions[d];
+        _slice_nblock[d] = nblock;
+        block = block * _rdimensions[d];
+      }
+  };
+
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/cartesian/Cartesian_red_black.h

@@ -0,0 +1,305 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/cartesian/Cartesian_red_black.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CARTESIAN_RED_BLACK_H
+#define GRID_CARTESIAN_RED_BLACK_H
+
+NAMESPACE_BEGIN(Grid);
+
+static const int CbRed  =0;
+static const int CbBlack=1;
+static const int Even   =CbRed;
+static const int Odd    =CbBlack;
+
+accelerator_inline int RedBlackCheckerBoardFromOindex (int oindex, Coordinate &rdim, Coordinate &chk_dim_msk)
+{
+  int nd=rdim.size();
+  Coordinate coor(nd);
+
+  Lexicographic::CoorFromIndex(coor,oindex,rdim);
+
+  int linear=0;
+  for(int d=0;d<nd;d++){
+    if(chk_dim_msk[d])
+      linear=linear+coor[d];
+  }
+  return (linear&0x1);
+}
+
+    
+// Specialise this for red black grids storing half the data like a chess board.
+class GridRedBlackCartesian : public GridBase
+{
+public:
+  //  Coordinate _checker_dim_mask;
+  int              _checker_dim;
+  std::vector<int> _checker_board;
+
+  virtual int CheckerBoarded(int dim){
+    if( dim==_checker_dim) return 1;
+    else return 0;
+  }
+  virtual int CheckerBoard(const Coordinate &site){
+    int linear=0;
+    assert(site.size()==_ndimension);
+    for(int d=0;d<_ndimension;d++){ 
+      if(_checker_dim_mask[d])
+	linear=linear+site[d];
+    }
+    return (linear&0x1);
+  }
+
+  // Depending on the cb of site, we toggle source cb.
+  // for block #b, element #e = (b, e)
+  // we need 
+  virtual int CheckerBoardShiftForCB(int source_cb,int dim,int shift,int ocb){
+    if(dim != _checker_dim) return shift;
+
+    int fulldim =_fdimensions[dim];
+    shift = (shift+fulldim)%fulldim;
+
+    // Probably faster with table lookup;
+    // or by looping over x,y,z and multiply rather than computing checkerboard.
+	  
+    if ( (source_cb+ocb)&1 ) {
+      return (shift)/2;
+    } else {
+      return (shift+1)/2;
+    }
+  }
+  virtual int  CheckerBoardFromOindexTable (int Oindex) {
+    return _checker_board[Oindex];
+  }
+  virtual int  CheckerBoardFromOindex (int Oindex)
+  {
+    Coordinate ocoor;
+    oCoorFromOindex(ocoor,Oindex);
+    return CheckerBoard(ocoor);
+  }
+  virtual int CheckerBoardShift(int source_cb,int dim,int shift,int osite){
+
+    if(dim != _checker_dim) return shift;
+
+    int ocb=CheckerBoardFromOindex(osite);
+      
+    return CheckerBoardShiftForCB(source_cb,dim,shift,ocb);
+  }
+    
+  virtual int CheckerBoardDestination(int source_cb,int shift,int dim){
+    if ( _checker_dim_mask[dim]  ) {
+      // If _fdimensions[checker_dim] is odd, then shifting by 1 in other dims
+      // does NOT cause a parity hop.
+      int add=(dim==_checker_dim) ? 0 : _fdimensions[_checker_dim];
+      if ( (shift+add) &0x1) {
+	return 1-source_cb;
+      } else {
+	return source_cb;
+      }
+    } else {
+      return source_cb;
+
+    }
+  };
+
+  ////////////////////////////////////////////////////////////
+  // Create Redblack from original grid; require full grid pointer ?
+  ////////////////////////////////////////////////////////////
+  GridRedBlackCartesian(const GridBase *base) : GridBase(base->_processors,*base)
+  {
+    int dims = base->_ndimension;
+    Coordinate checker_dim_mask(dims,1);
+    int checker_dim = 0;
+    Init(base->_fdimensions,base->_simd_layout,base->_processors,checker_dim_mask,checker_dim);
+  };
+
+  ////////////////////////////////////////////////////////////
+  // Create redblack from original grid, with non-trivial checker dim mask
+  ////////////////////////////////////////////////////////////
+  GridRedBlackCartesian(const GridBase *base,
+			const Coordinate &checker_dim_mask,
+			int checker_dim
+			) :  GridBase(base->_processors,*base) 
+  {
+    Init(base->_fdimensions,base->_simd_layout,base->_processors,checker_dim_mask,checker_dim)  ;
+  }
+
+  virtual ~GridRedBlackCartesian() = default;
+
+  void Init(const Coordinate &dimensions,
+	    const Coordinate &simd_layout,
+	    const Coordinate &processor_grid,
+	    const Coordinate &checker_dim_mask,
+	    int checker_dim)
+  {
+
+      _isCheckerBoarded = true;
+    _checker_dim = checker_dim;
+    assert(checker_dim_mask[checker_dim] == 1);
+    _ndimension = dimensions.size();
+    assert(checker_dim_mask.size() == _ndimension);
+    assert(processor_grid.size() == _ndimension);
+    assert(simd_layout.size() == _ndimension);
+
+    _fdimensions.resize(_ndimension);
+    _gdimensions.resize(_ndimension);
+    _ldimensions.resize(_ndimension);
+    _rdimensions.resize(_ndimension);
+    _simd_layout.resize(_ndimension);
+    _lstart.resize(_ndimension);
+    _lend.resize(_ndimension);
+
+    _ostride.resize(_ndimension);
+    _istride.resize(_ndimension);
+
+    _fsites = _gsites = _osites = _isites = 1;
+
+    _checker_dim_mask = checker_dim_mask;
+
+    for (int d = 0; d < _ndimension; d++)
+      {
+        _fdimensions[d] = dimensions[d];
+        _gdimensions[d] = _fdimensions[d];
+        _fsites = _fsites * _fdimensions[d];
+        _gsites = _gsites * _gdimensions[d];
+
+        if (d == _checker_dim)
+	  {
+	    assert((_gdimensions[d] & 0x1) == 0);
+	    _gdimensions[d] = _gdimensions[d] / 2; // Remove a checkerboard
+	    _gsites /= 2;
+	  }
+        _ldimensions[d] = _gdimensions[d] / _processors[d];
+        assert(_ldimensions[d] * _processors[d] == _gdimensions[d]);
+        _lstart[d] = _processor_coor[d] * _ldimensions[d];
+        _lend[d] = _processor_coor[d] * _ldimensions[d] + _ldimensions[d] - 1;
+
+        // Use a reduced simd grid
+        _simd_layout[d] = simd_layout[d];
+        _rdimensions[d] = _ldimensions[d] / _simd_layout[d]; // this is not checking if this is integer
+        assert(_rdimensions[d] * _simd_layout[d] == _ldimensions[d]);
+        assert(_rdimensions[d] > 0);
+
+        // all elements of a simd vector must have same checkerboard.
+        // If Ls vectorised, this must still be the case; e.g. dwf rb5d
+        if (_simd_layout[d] > 1)
+	  {
+	    if (checker_dim_mask[d])
+	      {
+		assert((_rdimensions[d] & 0x1) == 0);
+	      }
+	  }
+
+        _osites *= _rdimensions[d];
+        _isites *= _simd_layout[d];
+
+        // Addressing support
+        if (d == 0)
+	  {
+	    _ostride[d] = 1;
+	    _istride[d] = 1;
+	  }
+        else
+	  {
+	    _ostride[d] = _ostride[d - 1] * _rdimensions[d - 1];
+	    _istride[d] = _istride[d - 1] * _simd_layout[d - 1];
+	  }
+      }
+
+    ////////////////////////////////////////////////////////////////////////////////////////////
+    // subplane information
+    ////////////////////////////////////////////////////////////////////////////////////////////
+    _slice_block.resize(_ndimension);
+    _slice_stride.resize(_ndimension);
+    _slice_nblock.resize(_ndimension);
+
+    int block = 1;
+    int nblock = 1;
+    for (int d = 0; d < _ndimension; d++)
+      nblock *= _rdimensions[d];
+
+    for (int d = 0; d < _ndimension; d++)
+      {
+        nblock /= _rdimensions[d];
+        _slice_block[d] = block;
+        _slice_stride[d] = _ostride[d] * _rdimensions[d];
+        _slice_nblock[d] = nblock;
+        block = block * _rdimensions[d];
+      }
+
+    ////////////////////////////////////////////////
+    // Create a checkerboard lookup table
+    ////////////////////////////////////////////////
+    int rvol = 1;
+    for (int d = 0; d < _ndimension; d++)
+      {
+        rvol = rvol * _rdimensions[d];
+      }
+    _checker_board.resize(rvol);
+    for (int osite = 0; osite < _osites; osite++)
+      {
+        _checker_board[osite] = CheckerBoardFromOindex(osite);
+      }
+  };
+
+protected:
+  virtual int oIndex(Coordinate &coor)
+  {
+    int idx = 0;
+    for (int d = 0; d < _ndimension; d++)
+      {
+        if (d == _checker_dim)
+	  {
+	    idx += _ostride[d] * ((coor[d] / 2) % _rdimensions[d]);
+	  }
+        else
+	  {
+	    idx += _ostride[d] * (coor[d] % _rdimensions[d]);
+	  }
+      }
+    return idx;
+  };
+
+  virtual int iIndex(Coordinate &lcoor)
+  {
+    int idx = 0;
+    for (int d = 0; d < _ndimension; d++)
+      {
+        if (d == _checker_dim)
+	  {
+	    idx += _istride[d] * (lcoor[d] / (2 * _rdimensions[d]));
+	  }
+        else
+	  {
+	    idx += _istride[d] * (lcoor[d] / _rdimensions[d]);
+	  }
+      }
+    return idx;
+  }
+};
+NAMESPACE_END(Grid);
+#endif

Grid/communicator/Communicator.h

@@ -1,4 +1,4 @@
-    /*************************************************************************************
+/*************************************************************************************
 
     Grid physics library, www.github.com/paboyle/Grid 
 
@@ -23,11 +23,12 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     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 */
+*************************************************************************************/
+/*  END LEGAL */
 #ifndef GRID_COMMUNICATOR_H
 #define GRID_COMMUNICATOR_H
 
+#include <Grid/util/Coordinate.h>
 #include <Grid/communicator/SharedMemory.h>
 #include <Grid/communicator/Communicator_base.h>
 

Grid/communicator/Communicator_base.cc

@@ -1,4 +1,4 @@
-    /*************************************************************************************
+/*************************************************************************************
 
     Grid physics library, www.github.com/paboyle/Grid 
 
@@ -23,15 +23,15 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     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 */
+*************************************************************************************/
+/*  END LEGAL */
 #include <Grid/GridCore.h>
 #include <fcntl.h>
 #include <unistd.h>
 #include <limits.h>
 #include <sys/mman.h>
 
-namespace Grid {
+NAMESPACE_BEGIN(Grid);
 
 ///////////////////////////////////////////////////////////////
 // Info that is setup once and indept of cartesian layout
@@ -47,8 +47,8 @@ int                      CartesianCommunicator::Dimensions(void)        { return
 int                      CartesianCommunicator::IsBoss(void)            { return _processor==0; };
 int                      CartesianCommunicator::BossRank(void)          { return 0; };
 int                      CartesianCommunicator::ThisRank(void)          { return _processor; };
-const std::vector<int> & CartesianCommunicator::ThisProcessorCoor(void) { return _processor_coor; };
-const std::vector<int> & CartesianCommunicator::ProcessorGrid(void)     { return _processors; };
+const Coordinate & CartesianCommunicator::ThisProcessorCoor(void) { return _processor_coor; };
+const Coordinate & CartesianCommunicator::ProcessorGrid(void)     { return _processors; };
 int                      CartesianCommunicator::ProcessorCount(void)    { return _Nprocessors; };
 
 ////////////////////////////////////////////////////////////////////////////////
@@ -72,5 +72,6 @@ void CartesianCommunicator::GlobalSumVector(ComplexD *c,int N)
   GlobalSumVector((double *)c,2*N);
 }
   
-}
+NAMESPACE_END(Grid);
+
 

Grid/communicator/Communicator_base.h

@@ -1,5 +1,5 @@
 
-    /*************************************************************************************
+/*************************************************************************************
 
     Grid physics library, www.github.com/paboyle/Grid 
 
@@ -24,8 +24,8 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     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 */
+*************************************************************************************/
+/*  END LEGAL */
 #ifndef GRID_COMMUNICATOR_BASE_H
 #define GRID_COMMUNICATOR_BASE_H
 
@@ -34,7 +34,7 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 ///////////////////////////////////
 #include <Grid/communicator/SharedMemory.h>
 
-namespace Grid {
+NAMESPACE_BEGIN(Grid);
 
 class CartesianCommunicator : public SharedMemory {
 
@@ -52,9 +52,9 @@ public:
   // Communicator should know nothing of the physics grid, only processor grid.
   ////////////////////////////////////////////
   int              _Nprocessors;     // How many in all
-  std::vector<int> _processors;      // Which dimensions get relayed out over processors lanes.
+  Coordinate _processors;      // Which dimensions get relayed out over processors lanes.
   int              _processor;       // linear processor rank
-  std::vector<int> _processor_coor;  // linear processor coordinate
+  Coordinate _processor_coor;  // linear processor coordinate
   unsigned long    _ndimension;
   static Grid_MPI_Comm      communicator_world;
   Grid_MPI_Comm             communicator;
@@ -69,34 +69,34 @@ public:
   // Constructors to sub-divide a parent communicator
   // and default to comm world
   ////////////////////////////////////////////////
-  CartesianCommunicator(const std::vector<int> &processors,const CartesianCommunicator &parent,int &srank);
-  CartesianCommunicator(const std::vector<int> &pdimensions_in);
+  CartesianCommunicator(const Coordinate &processors,const CartesianCommunicator &parent,int &srank);
+  CartesianCommunicator(const Coordinate &pdimensions_in);
   virtual ~CartesianCommunicator();
 
- private:
+private:
 
   ////////////////////////////////////////////////
   // Private initialise from an MPI communicator
   // Can use after an MPI_Comm_split, but hidden from user so private
   ////////////////////////////////////////////////
-  void InitFromMPICommunicator(const std::vector<int> &processors, Grid_MPI_Comm communicator_base);
+  void InitFromMPICommunicator(const Coordinate &processors, Grid_MPI_Comm communicator_base);
 
- public:
+public:
   
   
   ////////////////////////////////////////////////////////////////////////////////////////
   // Wraps MPI_Cart routines, or implements equivalent on other impls
   ////////////////////////////////////////////////////////////////////////////////////////
   void ShiftedRanks(int dim,int shift,int & source, int & dest);
-  int  RankFromProcessorCoor(std::vector<int> &coor);
-  void ProcessorCoorFromRank(int rank,std::vector<int> &coor);
+  int  RankFromProcessorCoor(Coordinate &coor);
+  void ProcessorCoorFromRank(int rank,Coordinate &coor);
   
   int                      Dimensions(void)        ;
   int                      IsBoss(void)            ;
   int                      BossRank(void)          ;
   int                      ThisRank(void)          ;
-  const std::vector<int> & ThisProcessorCoor(void) ;
-  const std::vector<int> & ProcessorGrid(void)     ;
+  const Coordinate & ThisProcessorCoor(void) ;
+  const Coordinate & ProcessorGrid(void)     ;
   int                      ProcessorCount(void)    ;
 
   ////////////////////////////////////////////////////////////////////////////////
@@ -114,6 +114,7 @@ public:
   void GlobalSumVector(RealD *,int N);
   void GlobalSum(uint32_t &);
   void GlobalSum(uint64_t &);
+  void GlobalSumVector(uint64_t*,int N);
   void GlobalSum(ComplexF &c);
   void GlobalSumVector(ComplexF *c,int N);
   void GlobalSum(ComplexD &c);
@@ -137,21 +138,6 @@ public:
 		      int recv_from_rank,
 		      int bytes);
   
-  void SendRecvPacket(void *xmit,
-		      void *recv,
-		      int xmit_to_rank,
-		      int recv_from_rank,
-		      int bytes);
-  
-  void SendToRecvFromBegin(std::vector<CommsRequest_t> &list,
-			   void *xmit,
-			   int xmit_to_rank,
-			   void *recv,
-			   int recv_from_rank,
-			   int bytes);
-  
-  void SendToRecvFromComplete(std::vector<CommsRequest_t> &waitall);
-
   double StencilSendToRecvFrom(void *xmit,
 			       int xmit_to_rank,
 			       void *recv,
@@ -197,11 +183,12 @@ public:
   void AllToAll(void  *in,void *out,uint64_t words         ,uint64_t bytes);
   
   template<class obj> void Broadcast(int root,obj &data)
-    {
-      Broadcast(root,(void *)&data,sizeof(data));
-    };
+  {
+    Broadcast(root,(void *)&data,sizeof(data));
+  }
 
 }; 
-}
+
+NAMESPACE_END(Grid);
 
 #endif

Grid/communicator/Communicator_mpi3.cc

@@ -23,12 +23,12 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     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 */
+*************************************************************************************/
+/*  END LEGAL */
 #include <Grid/GridCore.h>
 #include <Grid/communicator/SharedMemory.h>
 
-namespace Grid {
+NAMESPACE_BEGIN(Grid);
 
 Grid_MPI_Comm       CartesianCommunicator::communicator_world;
 
@@ -43,22 +43,35 @@ void CartesianCommunicator::Init(int *argc, char ***argv)
 
   MPI_Initialized(&flag); // needed to coexist with other libs apparently
   if ( !flag ) {
-    MPI_Init_thread(argc,argv,MPI_THREAD_MULTIPLE,&provided);
-    //If only 1 comms thread we require any threading mode other than SINGLE, but for multiple comms threads we need MULTIPLE
-    if( (nCommThreads == 1 && provided == MPI_THREAD_SINGLE) ||
-        (nCommThreads > 1 && provided != MPI_THREAD_MULTIPLE) )
-      assert(0);
-  }
 
-  Grid_quiesce_nodes();
+#if defined (TOFU) // FUGAKU, credits go to Issaku Kanamori
+    nCommThreads=1;
+    // wrong results here too
+    // For now: comms-overlap leads to wrong results in Benchmark_wilson even on single node MPI runs
+    // other comms schemes are ok
+    MPI_Init_thread(argc,argv,MPI_THREAD_SERIALIZED,&provided);
+#else
+    MPI_Init_thread(argc,argv,MPI_THREAD_MULTIPLE,&provided);
+#endif
+    //If only 1 comms thread we require any threading mode other than SINGLE, but for multiple comms threads we need MULTIPLE
+    if( (nCommThreads == 1) && (provided == MPI_THREAD_SINGLE) ) {
+      assert(0);
+    }
+
+    if( (nCommThreads > 1) && (provided != MPI_THREAD_MULTIPLE) ) {
+      assert(0);
+    }
+  }
 
   // Never clean up as done once.
   MPI_Comm_dup (MPI_COMM_WORLD,&communicator_world);
 
+  Grid_quiesce_nodes();
   GlobalSharedMemory::Init(communicator_world);
   GlobalSharedMemory::SharedMemoryAllocate(
 		   GlobalSharedMemory::MAX_MPI_SHM_BYTES,
 		   GlobalSharedMemory::Hugepages);
+  Grid_unquiesce_nodes();
 }
 
 ///////////////////////////////////////////////////////////////////////////
@@ -69,14 +82,14 @@ void CartesianCommunicator::ShiftedRanks(int dim,int shift,int &source,int &dest
   int ierr=MPI_Cart_shift(communicator,dim,shift,&source,&dest);
   assert(ierr==0);
 }
-int CartesianCommunicator::RankFromProcessorCoor(std::vector<int> &coor)
+int CartesianCommunicator::RankFromProcessorCoor(Coordinate &coor)
 {
   int rank;
   int ierr=MPI_Cart_rank  (communicator, &coor[0], &rank);
   assert(ierr==0);
   return rank;
 }
-void  CartesianCommunicator::ProcessorCoorFromRank(int rank, std::vector<int> &coor)
+void  CartesianCommunicator::ProcessorCoorFromRank(int rank, Coordinate &coor)
 {
   coor.resize(_ndimension);
   int ierr=MPI_Cart_coords  (communicator, rank, _ndimension,&coor[0]);
@@ -86,7 +99,7 @@ void  CartesianCommunicator::ProcessorCoorFromRank(int rank, std::vector<int> &c
 ////////////////////////////////////////////////////////////////////////////////////////////////////////
 // Initialises from communicator_world
 ////////////////////////////////////////////////////////////////////////////////////////////////////////
-CartesianCommunicator::CartesianCommunicator(const std::vector<int> &processors) 
+CartesianCommunicator::CartesianCommunicator(const Coordinate &processors)
 {
   MPI_Comm optimal_comm;
   ////////////////////////////////////////////////////
@@ -105,13 +118,12 @@ CartesianCommunicator::CartesianCommunicator(const std::vector<int> &processors)
 //////////////////////////////////
 // Try to subdivide communicator
 //////////////////////////////////
-CartesianCommunicator::CartesianCommunicator(const std::vector<int> &processors,const CartesianCommunicator &parent,int &srank)    
+CartesianCommunicator::CartesianCommunicator(const Coordinate &processors,const CartesianCommunicator &parent,int &srank)
 {
-  _ndimension = processors.size();
-
+  _ndimension = processors.size();  assert(_ndimension>=1);
   int parent_ndimension = parent._ndimension; assert(_ndimension >= parent._ndimension);
-  std::vector<int> parent_processor_coor(_ndimension,0);
-  std::vector<int> parent_processors    (_ndimension,1);
+  Coordinate parent_processor_coor(_ndimension,0);
+  Coordinate parent_processors    (_ndimension,1);
 
   // Can make 5d grid from 4d etc...
   int pad = _ndimension-parent_ndimension;
@@ -124,10 +136,8 @@ CartesianCommunicator::CartesianCommunicator(const std::vector<int> &processors,
   // split the communicator
   //////////////////////////////////////////////////////////////////////////////////////////////////////
   //  int Nparent = parent._processors ;
-  //  std::cout << " splitting from communicator "<<parent.communicator <<std::endl;
   int Nparent;
   MPI_Comm_size(parent.communicator,&Nparent);
-  //  std::cout << " Parent size  "<<Nparent <<std::endl;
 
   int childsize=1;
   for(int d=0;d<processors.size();d++) {
@@ -136,11 +146,9 @@ CartesianCommunicator::CartesianCommunicator(const std::vector<int> &processors,
   int Nchild = Nparent/childsize;
   assert (childsize * Nchild == Nparent);
 
-  //  std::cout << " child size  "<<childsize <<std::endl;
-
-  std::vector<int> ccoor(_ndimension); // coor within subcommunicator
-  std::vector<int> scoor(_ndimension); // coor of split within parent
-  std::vector<int> ssize(_ndimension); // coor of split within parent
+  Coordinate ccoor(_ndimension); // coor within subcommunicator
+  Coordinate scoor(_ndimension); // coor of split within parent
+  Coordinate ssize(_ndimension); // coor of split within parent
 
   for(int d=0;d<_ndimension;d++){
     ccoor[d] = parent_processor_coor[d] % processors[d];
@@ -157,36 +165,6 @@ CartesianCommunicator::CartesianCommunicator(const std::vector<int> &processors,
   MPI_Comm comm_split;
   if ( Nchild > 1 ) {
 
-    if(0){
-      std::cout << GridLogMessage<<"Child communicator of "<< std::hex << parent.communicator << std::dec<<std::endl;
-      std::cout << GridLogMessage<<" parent grid["<< parent._ndimension<<"]    ";
-      for(int d=0;d<parent._ndimension;d++)  std::cout << parent._processors[d] << " ";
-      std::cout<<std::endl;
-      
-      std::cout << GridLogMessage<<" child grid["<< _ndimension <<"]    ";
-      for(int d=0;d<processors.size();d++)  std::cout << processors[d] << " ";
-      std::cout<<std::endl;
-      
-      std::cout << GridLogMessage<<" old rank "<< parent._processor<<" coor ["<< parent._ndimension <<"]    ";
-      for(int d=0;d<parent._ndimension;d++)  std::cout << parent._processor_coor[d] << " ";
-      std::cout<<std::endl;
-      
-      std::cout << GridLogMessage<<" new split "<< srank<<" scoor ["<< _ndimension <<"]    ";
-      for(int d=0;d<processors.size();d++)  std::cout << scoor[d] << " ";
-      std::cout<<std::endl;
-      
-      std::cout << GridLogMessage<<" new rank "<< crank<<" coor ["<< _ndimension <<"]    ";
-      for(int d=0;d<processors.size();d++)  std::cout << ccoor[d] << " ";
-      std::cout<<std::endl;
-
-      //////////////////////////////////////////////////////////////////////////////////////////////////////
-      // Declare victory
-      //////////////////////////////////////////////////////////////////////////////////////////////////////
-      std::cout << GridLogMessage<<"Divided communicator "<< parent._Nprocessors<<" into "
-		<< Nchild <<" communicators with " << childsize << " ranks"<<std::endl;
-      std::cout << " Split communicator " <<comm_split <<std::endl;
-    }
-
     ////////////////////////////////////////////////////////////////
     // Split the communicator
     ////////////////////////////////////////////////////////////////
@@ -225,7 +203,7 @@ CartesianCommunicator::CartesianCommunicator(const std::vector<int> &processors,
   }
 }
 
-void CartesianCommunicator::InitFromMPICommunicator(const std::vector<int> &processors, MPI_Comm communicator_base)
+void CartesianCommunicator::InitFromMPICommunicator(const Coordinate &processors, MPI_Comm communicator_base)
 {
   ////////////////////////////////////////////////////
   // Creates communicator, and the communicator_halo
@@ -242,7 +220,7 @@ void CartesianCommunicator::InitFromMPICommunicator(const std::vector<int> &proc
     _Nprocessors*=_processors[i];
   }
 
-  std::vector<int> periodic(_ndimension,1);
+  Coordinate periodic(_ndimension,1);
   MPI_Cart_create(communicator_base, _ndimension,&_processors[0],&periodic[0],0,&communicator);
   MPI_Comm_rank(communicator,&_processor);
   MPI_Cart_coords(communicator,_processor,_ndimension,&_processor_coor[0]);
@@ -285,6 +263,10 @@ void CartesianCommunicator::GlobalSum(uint64_t &u){
   int ierr=MPI_Allreduce(MPI_IN_PLACE,&u,1,MPI_UINT64_T,MPI_SUM,communicator);
   assert(ierr==0);
 }
+void CartesianCommunicator::GlobalSumVector(uint64_t* u,int N){
+  int ierr=MPI_Allreduce(MPI_IN_PLACE,u,N,MPI_UINT64_T,MPI_SUM,communicator);
+  assert(ierr==0);
+}
 void CartesianCommunicator::GlobalXOR(uint32_t &u){
   int ierr=MPI_Allreduce(MPI_IN_PLACE,&u,1,MPI_UINT32_T,MPI_BXOR,communicator);
   assert(ierr==0);
@@ -320,60 +302,28 @@ void CartesianCommunicator::SendToRecvFrom(void *xmit,
 					   int bytes)
 {
   std::vector<CommsRequest_t> reqs(0);
-  //    unsigned long  xcrc = crc32(0L, Z_NULL, 0);
-  //    unsigned long  rcrc = crc32(0L, Z_NULL, 0);
-  //    xcrc = crc32(xcrc,(unsigned char *)xmit,bytes);
-  SendToRecvFromBegin(reqs,xmit,dest,recv,from,bytes);
-  SendToRecvFromComplete(reqs);
-  //    rcrc = crc32(rcrc,(unsigned char *)recv,bytes);
-  //    printf("proc %d SendToRecvFrom %d bytes %lx %lx\n",_processor,bytes,xcrc,rcrc);
-}
-void CartesianCommunicator::SendRecvPacket(void *xmit,
-					   void *recv,
-					   int sender,
-					   int receiver,
-					   int bytes)
-{
-  MPI_Status stat;
-  assert(sender != receiver);
-  int tag = sender;
-  if ( _processor == sender ) {
-    MPI_Send(xmit, bytes, MPI_CHAR,receiver,tag,communicator);
-  }
-  if ( _processor == receiver ) { 
-    MPI_Recv(recv, bytes, MPI_CHAR,sender,tag,communicator,&stat);
-  }
-}
-// Basic Halo comms primitive
-void CartesianCommunicator::SendToRecvFromBegin(std::vector<CommsRequest_t> &list,
-						void *xmit,
-						int dest,
-						void *recv,
-						int from,
-						int bytes)
-{
+  unsigned long  xcrc = crc32(0L, Z_NULL, 0);
+  unsigned long  rcrc = crc32(0L, Z_NULL, 0);
+
   int myrank = _processor;
   int ierr;
 
-  if ( CommunicatorPolicy == CommunicatorPolicyConcurrent ) { 
-    MPI_Request xrq;
-    MPI_Request rrq;
+  // Enforce no UVM in comms, device or host OK
+  assert(acceleratorIsCommunicable(xmit));
+  assert(acceleratorIsCommunicable(recv));
 
-    ierr =MPI_Irecv(recv, bytes, MPI_CHAR,from,from,communicator,&rrq);
-    ierr|=MPI_Isend(xmit, bytes, MPI_CHAR,dest,_processor,communicator,&xrq);
+  // Give the CPU to MPI immediately; can use threads to overlap optionally
+  //  printf("proc %d SendToRecvFrom %d bytes Sendrecv \n",_processor,bytes);
+  ierr=MPI_Sendrecv(xmit,bytes,MPI_CHAR,dest,myrank,
+		    recv,bytes,MPI_CHAR,from, from,
+		    communicator,MPI_STATUS_IGNORE);
+  assert(ierr==0);
 
-    assert(ierr==0);
-    list.push_back(xrq);
-    list.push_back(rrq);
-  } else { 
-    // Give the CPU to MPI immediately; can use threads to overlap optionally
-    ierr=MPI_Sendrecv(xmit,bytes,MPI_CHAR,dest,myrank,
-		      recv,bytes,MPI_CHAR,from, from,
-		      communicator,MPI_STATUS_IGNORE);
-    assert(ierr==0);
-  }
+  //  xcrc = crc32(xcrc,(unsigned char *)xmit,bytes);
+  //  rcrc = crc32(rcrc,(unsigned char *)recv,bytes);
+  //  printf("proc %d SendToRecvFrom %d bytes xcrc %lx rcrc %lx\n",_processor,bytes,xcrc,rcrc); fflush
 }
-
+// Basic Halo comms primitive
 double CartesianCommunicator::StencilSendToRecvFrom( void *xmit,
 						     int dest,
 						     void *recv,
@@ -429,15 +379,7 @@ double CartesianCommunicator::StencilSendToRecvFromBegin(std::vector<CommsReques
 
   return off_node_bytes;
 }
-void CartesianCommunicator::StencilSendToRecvFromComplete(std::vector<CommsRequest_t> &waitall,int dir)
-{
-  SendToRecvFromComplete(waitall);
-}
-void CartesianCommunicator::StencilBarrier(void)
-{
-  MPI_Barrier  (ShmComm);
-}
-void CartesianCommunicator::SendToRecvFromComplete(std::vector<CommsRequest_t> &list)
+void CartesianCommunicator::StencilSendToRecvFromComplete(std::vector<CommsRequest_t> &list,int dir)
 {
   int nreq=list.size();
 
@@ -448,6 +390,13 @@ void CartesianCommunicator::SendToRecvFromComplete(std::vector<CommsRequest_t> &
   assert(ierr==0);
   list.resize(0);
 }
+void CartesianCommunicator::StencilBarrier(void)
+{
+  MPI_Barrier  (ShmComm);
+}
+//void CartesianCommunicator::SendToRecvFromComplete(std::vector<CommsRequest_t> &list)
+//{
+//}
 void CartesianCommunicator::Barrier(void)
 {
   int ierr = MPI_Barrier(communicator);
@@ -479,7 +428,7 @@ void CartesianCommunicator::BroadcastWorld(int root,void* data, int bytes)
 
 void CartesianCommunicator::AllToAll(int dim,void  *in,void *out,uint64_t words,uint64_t bytes)
 {
-  std::vector<int> row(_ndimension,1);
+  Coordinate row(_ndimension,1);
   assert(dim>=0 && dim<_ndimension);
 
   //  Split the communicator
@@ -508,7 +457,4 @@ void CartesianCommunicator::AllToAll(void  *in,void *out,uint64_t words,uint64_t
   MPI_Type_free(&object);
 }
 
-
-
-}
-
+NAMESPACE_END(Grid);

Grid/communicator/Communicator_none.cc

@@ -1,4 +1,4 @@
-    /*************************************************************************************
+/*************************************************************************************
 
     Grid physics library, www.github.com/paboyle/Grid 
 
@@ -23,11 +23,11 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     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 */
+*************************************************************************************/
+/*  END LEGAL */
 #include <Grid/GridCore.h>
 
-namespace Grid {
+NAMESPACE_BEGIN(Grid);
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
 // Info that is setup once and indept of cartesian layout
@@ -38,21 +38,21 @@ void CartesianCommunicator::Init(int *argc, char *** arv)
 {
   GlobalSharedMemory::Init(communicator_world);
   GlobalSharedMemory::SharedMemoryAllocate(
-		   GlobalSharedMemory::MAX_MPI_SHM_BYTES,
-		   GlobalSharedMemory::Hugepages);
+					   GlobalSharedMemory::MAX_MPI_SHM_BYTES,
+					   GlobalSharedMemory::Hugepages);
 }
 
-CartesianCommunicator::CartesianCommunicator(const std::vector<int> &processors,const CartesianCommunicator &parent,int &srank) 
+CartesianCommunicator::CartesianCommunicator(const Coordinate &processors,const CartesianCommunicator &parent,int &srank) 
   : CartesianCommunicator(processors) 
 {
   srank=0;
   SetCommunicator(communicator_world);
 }
 
-CartesianCommunicator::CartesianCommunicator(const std::vector<int> &processors)
+CartesianCommunicator::CartesianCommunicator(const Coordinate &processors)
 {
   _processors = processors;
-  _ndimension = processors.size();
+  _ndimension = processors.size();  assert(_ndimension>=1);
   _processor_coor.resize(_ndimension);
   
   // Require 1^N processor grid for fake
@@ -70,21 +70,13 @@ CartesianCommunicator::~CartesianCommunicator(){}
 void CartesianCommunicator::GlobalSum(float &){}
 void CartesianCommunicator::GlobalSumVector(float *,int N){}
 void CartesianCommunicator::GlobalSum(double &){}
+void CartesianCommunicator::GlobalSumVector(double *,int N){}
 void CartesianCommunicator::GlobalSum(uint32_t &){}
 void CartesianCommunicator::GlobalSum(uint64_t &){}
-void CartesianCommunicator::GlobalSumVector(double *,int N){}
+void CartesianCommunicator::GlobalSumVector(uint64_t *,int N){}
 void CartesianCommunicator::GlobalXOR(uint32_t &){}
 void CartesianCommunicator::GlobalXOR(uint64_t &){}
 
-void CartesianCommunicator::SendRecvPacket(void *xmit,
-					   void *recv,
-					   int xmit_to_rank,
-					   int recv_from_rank,
-					   int bytes)
-{
-  assert(0);
-}
-
 
 // Basic Halo comms primitive -- should never call in single node
 void CartesianCommunicator::SendToRecvFrom(void *xmit,
@@ -95,20 +87,6 @@ void CartesianCommunicator::SendToRecvFrom(void *xmit,
 {
   assert(0);
 }
-void CartesianCommunicator::SendToRecvFromBegin(std::vector<CommsRequest_t> &list,
-						void *xmit,
-						int dest,
-						void *recv,
-						int from,
-						int bytes)
-{
-  assert(0);
-}
-
-void CartesianCommunicator::SendToRecvFromComplete(std::vector<CommsRequest_t> &list)
-{
-  assert(0);
-}
 void CartesianCommunicator::AllToAll(int dim,void  *in,void *out,uint64_t words,uint64_t bytes)
 {
   bcopy(in,out,bytes*words);
@@ -122,8 +100,8 @@ int  CartesianCommunicator::RankWorld(void){return 0;}
 void CartesianCommunicator::Barrier(void){}
 void CartesianCommunicator::Broadcast(int root,void* data, int bytes) {}
 void CartesianCommunicator::BroadcastWorld(int root,void* data, int bytes) { }
-int  CartesianCommunicator::RankFromProcessorCoor(std::vector<int> &coor) {  return 0;}
-void CartesianCommunicator::ProcessorCoorFromRank(int rank, std::vector<int> &coor){  coor = _processor_coor; }
+int  CartesianCommunicator::RankFromProcessorCoor(Coordinate &coor) {  return 0;}
+void CartesianCommunicator::ProcessorCoorFromRank(int rank, Coordinate &coor){  coor = _processor_coor; }
 void CartesianCommunicator::ShiftedRanks(int dim,int shift,int &source,int &dest)
 {
   source =0;
@@ -136,10 +114,6 @@ double CartesianCommunicator::StencilSendToRecvFrom( void *xmit,
 						     int recv_from_rank,
 						     int bytes, int dir)
 {
-  std::vector<CommsRequest_t> list;
-  // Discard the "dir"
-  SendToRecvFromBegin   (list,xmit,xmit_to_rank,recv,recv_from_rank,bytes);
-  SendToRecvFromComplete(list);
   return 2.0*bytes;
 }
 double CartesianCommunicator::StencilSendToRecvFromBegin(std::vector<CommsRequest_t> &list,
@@ -149,17 +123,14 @@ double CartesianCommunicator::StencilSendToRecvFromBegin(std::vector<CommsReques
 							 int recv_from_rank,
 							 int bytes, int dir)
 {
-  // Discard the "dir"
-  SendToRecvFromBegin(list,xmit,xmit_to_rank,recv,recv_from_rank,bytes);
   return 2.0*bytes;
 }
 void CartesianCommunicator::StencilSendToRecvFromComplete(std::vector<CommsRequest_t> &waitall,int dir)
 {
-  SendToRecvFromComplete(waitall);
 }
 
 void CartesianCommunicator::StencilBarrier(void){};
 
+NAMESPACE_END(Grid);
 
-}
 

Grid/communicator/SharedMemory.cc

@@ -28,10 +28,11 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 
 #include <Grid/GridCore.h>
 
-namespace Grid { 
+NAMESPACE_BEGIN(Grid); 
 
 // static data
 
+int                 GlobalSharedMemory::HPEhypercube = 1;
 uint64_t            GlobalSharedMemory::MAX_MPI_SHM_BYTES   = 1024LL*1024LL*1024LL; 
 int                 GlobalSharedMemory::Hugepages = 0;
 int                 GlobalSharedMemory::_ShmSetup;
@@ -73,9 +74,12 @@ void *SharedMemory::ShmBufferMalloc(size_t bytes){
   if (heap_bytes >= heap_size) {
     std::cout<< " ShmBufferMalloc exceeded shared heap size -- try increasing with --shm <MB> flag" <<std::endl;
     std::cout<< " Parameter specified in units of MB (megabytes) " <<std::endl;
-    std::cout<< " Current value is " << (heap_size/(1024*1024)) <<std::endl;
+    std::cout<< " Current alloc is " << (bytes/(1024*1024)) <<"MB"<<std::endl;
+    std::cout<< " Current bytes is " << (heap_bytes/(1024*1024)) <<"MB"<<std::endl;
+    std::cout<< " Current heap  is " << (heap_size/(1024*1024)) <<"MB"<<std::endl;
     assert(heap_bytes<heap_size);
   }
+  //std::cerr << "ShmBufferMalloc "<<std::hex<< ptr<<" - "<<((uint64_t)ptr+bytes)<<std::dec<<std::endl;
   return ptr;
 }
 void SharedMemory::ShmBufferFreeAll(void) { 
@@ -84,9 +88,9 @@ void SharedMemory::ShmBufferFreeAll(void) {
 }
 void *SharedMemory::ShmBufferSelf(void)
 {
+  //std::cerr << "ShmBufferSelf "<<ShmRank<<" "<<std::hex<< ShmCommBufs[ShmRank] <<std::dec<<std::endl;
   return ShmCommBufs[ShmRank];
 }
 
+NAMESPACE_END(Grid); 
 
-
-}

Grid/communicator/SharedMemory.h

@@ -25,18 +25,6 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     See the full license in the file "LICENSE" in the top level distribution directory
 *************************************************************************************/
 /*  END LEGAL */
-
-
-// TODO
-// 1) move includes into SharedMemory.cc
-//
-// 2) split shared memory into a) optimal communicator creation from comm world
-// 
-//                             b) shared memory buffers container
-//                                -- static globally shared; init once
-//                                -- per instance set of buffers.
-//                                   
-
 #pragma once 
 
 #include <Grid/GridCore.h>
@@ -53,30 +41,33 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 #include <sys/shm.h>
 #include <sys/mman.h>
 #include <zlib.h>
-#ifdef HAVE_NUMAIF_H
-#include <numaif.h>
-#endif
 
-namespace Grid {
+NAMESPACE_BEGIN(Grid);
 
 #if defined (GRID_COMMS_MPI3) 
-  typedef MPI_Comm    Grid_MPI_Comm;
-  typedef MPI_Request CommsRequest_t;
+typedef MPI_Comm    Grid_MPI_Comm;
+typedef MPI_Request CommsRequest_t;
 #else 
-  typedef int CommsRequest_t;
-  typedef int Grid_MPI_Comm;
+typedef int CommsRequest_t;
+typedef int Grid_MPI_Comm;
 #endif
 
 class GlobalSharedMemory {
- private:
+private:
   static const int     MAXLOG2RANKSPERNODE = 16;            
 
+
   // Init once lock on the buffer allocation
   static int      _ShmSetup;
   static int      _ShmAlloc;
   static uint64_t _ShmAllocBytes;
 
- public:
+public:
+  ///////////////////////////////////////
+  // HPE 8600 hypercube optimisation
+  ///////////////////////////////////////
+  static int HPEhypercube;
+
   static int      ShmSetup(void)      { return _ShmSetup; }
   static int      ShmAlloc(void)      { return _ShmAlloc; }
   static uint64_t ShmAllocBytes(void) { return _ShmAllocBytes; }
@@ -102,12 +93,17 @@ class GlobalSharedMemory {
   // Create an optimal reordered communicator that makes MPI_Cart_create get it right
   //////////////////////////////////////////////////////////////////////////////////////
   static void Init(Grid_MPI_Comm comm); // Typically MPI_COMM_WORLD
-  static void OptimalCommunicator(const std::vector<int> &processors,Grid_MPI_Comm & optimal_comm);  // Turns MPI_COMM_WORLD into right layout for Cartesian
+  static void OptimalCommunicator            (const Coordinate &processors,Grid_MPI_Comm & optimal_comm);  // Turns MPI_COMM_WORLD into right layout for Cartesian
+  static void OptimalCommunicatorHypercube   (const Coordinate &processors,Grid_MPI_Comm & optimal_comm);  // Turns MPI_COMM_WORLD into right layout for Cartesian
+  static void OptimalCommunicatorSharedMemory(const Coordinate &processors,Grid_MPI_Comm & optimal_comm);  // Turns MPI_COMM_WORLD into right layout for Cartesian
+  static void GetShmDims(const Coordinate &WorldDims,Coordinate &ShmDims);
   ///////////////////////////////////////////////////
   // Provide shared memory facilities off comm world
   ///////////////////////////////////////////////////
   static void SharedMemoryAllocate(uint64_t bytes, int flags);
   static void SharedMemoryFree(void);
+  static void SharedMemoryCopy(void *dest,const void *src,size_t bytes);
+  static void SharedMemoryZero(void *dest,size_t bytes);
 
 };
 
@@ -116,14 +112,14 @@ class GlobalSharedMemory {
 //////////////////////////////
 class SharedMemory 
 {
- private:
+private:
   static const int     MAXLOG2RANKSPERNODE = 16;            
 
   size_t heap_top;
   size_t heap_bytes;
   size_t heap_size;
 
- protected:
+protected:
 
   Grid_MPI_Comm    ShmComm; // for barriers
   int    ShmRank; 
@@ -131,7 +127,7 @@ class SharedMemory
   std::vector<void *> ShmCommBufs;
   std::vector<int>    ShmRanks;// Mapping comm ranks to Shm ranks
 
- public:
+public:
   SharedMemory() {};
   ~SharedMemory();
   ///////////////////////////////////////////////////////////////////////////////////////
@@ -148,6 +144,7 @@ class SharedMemory
   // Call on any instance
   ///////////////////////////////////////////////////
   void SharedMemoryTest(void);
+  
   void *ShmBufferSelf(void);
   void *ShmBuffer    (int rank);
   void *ShmBufferTranslate(int rank,void * local_p);
@@ -162,4 +159,5 @@ class SharedMemory
 
 };
 
-}
+NAMESPACE_END(Grid);
+

Grid/communicator/SharedMemoryMPI.cc

@@ -29,8 +29,15 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 #include <Grid/GridCore.h>
 #include <pwd.h>
 
-namespace Grid { 
+#ifdef GRID_CUDA
+#include <cuda_runtime_api.h>
+#endif
+#ifdef GRID_HIP
+#include <hip/hip_runtime_api.h>
+#endif
 
+NAMESPACE_BEGIN(Grid); 
+#define header "SharedMemoryMpi: "
 /*Construct from an MPI communicator*/
 void GlobalSharedMemory::Init(Grid_MPI_Comm comm)
 {
@@ -43,9 +50,19 @@ void GlobalSharedMemory::Init(Grid_MPI_Comm comm)
   /////////////////////////////////////////////////////////////////////
   // Split into groups that can share memory
   /////////////////////////////////////////////////////////////////////
+#ifndef GRID_MPI3_SHM_NONE
   MPI_Comm_split_type(comm, MPI_COMM_TYPE_SHARED, 0, MPI_INFO_NULL,&WorldShmComm);
+#else
+  MPI_Comm_split(comm, WorldRank, 0, &WorldShmComm);
+#endif
+
   MPI_Comm_rank(WorldShmComm     ,&WorldShmRank);
   MPI_Comm_size(WorldShmComm     ,&WorldShmSize);
+
+  if ( WorldRank == 0) {
+    std::cout << header " World communicator of size " <<WorldSize << std::endl;  
+    std::cout << header " Node  communicator of size " <<WorldShmSize << std::endl;
+  }
   // WorldShmComm, WorldShmSize, WorldShmRank
 
   // WorldNodes
@@ -130,10 +147,60 @@ int Log2Size(int TwoToPower,int MAXLOG2)
   }
   return log2size;
 }
-void GlobalSharedMemory::OptimalCommunicator(const std::vector<int> &processors,Grid_MPI_Comm & optimal_comm)
+void GlobalSharedMemory::OptimalCommunicator(const Coordinate &processors,Grid_MPI_Comm & optimal_comm)
+{
+  //////////////////////////////////////////////////////////////////////////////
+  // Look and see if it looks like an HPE 8600 based on hostname conventions
+  //////////////////////////////////////////////////////////////////////////////
+  const int namelen = _POSIX_HOST_NAME_MAX;
+  char name[namelen];
+  int R;
+  int I;
+  int N;
+  gethostname(name,namelen);
+  int nscan = sscanf(name,"r%di%dn%d",&R,&I,&N) ;
+
+  if(nscan==3 && HPEhypercube ) OptimalCommunicatorHypercube(processors,optimal_comm);
+  else                          OptimalCommunicatorSharedMemory(processors,optimal_comm);
+}
+static inline int divides(int a,int b)
+{
+  return ( b == ( (b/a)*a ) );
+}
+void GlobalSharedMemory::GetShmDims(const Coordinate &WorldDims,Coordinate &ShmDims)
+{
+  ////////////////////////////////////////////////////////////////
+  // Powers of 2,3,5 only in prime decomposition for now
+  ////////////////////////////////////////////////////////////////
+  int ndimension = WorldDims.size();
+  ShmDims=Coordinate(ndimension,1);
+
+  std::vector<int> primes({2,3,5});
+
+  int dim = 0;
+  int last_dim = ndimension - 1;
+  int AutoShmSize = 1;
+  while(AutoShmSize != WorldShmSize) {
+    int p;
+    for(p=0;p<primes.size();p++) {
+      int prime=primes[p];
+      if ( divides(prime,WorldDims[dim]/ShmDims[dim])
+        && divides(prime,WorldShmSize/AutoShmSize)  ) {
+	AutoShmSize*=prime;
+	ShmDims[dim]*=prime;
+	last_dim = dim;
+	break;
+      }
+    }
+    if (p == primes.size() && last_dim == dim) {
+      std::cerr << "GlobalSharedMemory::GetShmDims failed" << std::endl;
+      exit(EXIT_FAILURE);
+    }
+    dim=(dim+1) %ndimension;
+  }
+}
+void GlobalSharedMemory::OptimalCommunicatorHypercube(const Coordinate &processors,Grid_MPI_Comm & optimal_comm)
 {
-#undef HYPERCUBE 
-#ifdef HYPERCUBE
   ////////////////////////////////////////////////////////////////
   // Assert power of two shm_size.
   ////////////////////////////////////////////////////////////////
@@ -174,9 +241,9 @@ void GlobalSharedMemory::OptimalCommunicator(const std::vector<int> &processors,
   }
 
   std::string hname(name);
-  std::cout << "hostname "<<hname<<std::endl;
-  std::cout << "R " << R << " I " << I << " N "<< N<<
-            << " hypercoor 0x"<<std::hex<<hypercoor<<std::dec<<std::endl;
+  //  std::cout << "hostname "<<hname<<std::endl;
+  //  std::cout << "R " << R << " I " << I << " N "<< N
+  //            << " hypercoor 0x"<<std::hex<<hypercoor<<std::dec<<std::endl;
 
   //////////////////////////////////////////////////////////////////
   // broadcast node 0's base coordinate for this partition.
@@ -198,16 +265,13 @@ void GlobalSharedMemory::OptimalCommunicator(const std::vector<int> &processors,
   // in a maximally symmetrical way
   ////////////////////////////////////////////////////////////////
   int ndimension              = processors.size();
-  std::vector<int> processor_coor(ndimension);
-  std::vector<int> WorldDims = processors;   std::vector<int> ShmDims  (ndimension,1);  std::vector<int> NodeDims (ndimension);
-  std::vector<int> ShmCoor  (ndimension);    std::vector<int> NodeCoor (ndimension);    std::vector<int> WorldCoor(ndimension);
-  std::vector<int> HyperCoor(ndimension);
-  int dim = 0;
-  for(int l2=0;l2<log2size;l2++){
-    while ( (WorldDims[dim] / ShmDims[dim]) <= 1 ) dim=(dim+1)%ndimension;
-    ShmDims[dim]*=2;
-    dim=(dim+1)%ndimension;
-  }
+  Coordinate processor_coor(ndimension);
+  Coordinate WorldDims = processors;
+  Coordinate ShmDims  (ndimension);  Coordinate NodeDims (ndimension);
+  Coordinate ShmCoor  (ndimension);    Coordinate NodeCoor (ndimension);    Coordinate WorldCoor(ndimension);
+  Coordinate HyperCoor(ndimension);
+
+  GetShmDims(WorldDims,ShmDims);
 
   ////////////////////////////////////////////////////////////////
   // Establish torus of processes and nodes with sub-blockings
@@ -254,28 +318,19 @@ void GlobalSharedMemory::OptimalCommunicator(const std::vector<int> &processors,
   /////////////////////////////////////////////////////////////////
   int ierr= MPI_Comm_split(WorldComm,0,rank,&optimal_comm);
   assert(ierr==0);
-#else 
-  ////////////////////////////////////////////////////////////////
-  // Assert power of two shm_size.
-  ////////////////////////////////////////////////////////////////
-  int log2size = Log2Size(WorldShmSize,MAXLOG2RANKSPERNODE);
-  assert(log2size != -1);
-
+}
+void GlobalSharedMemory::OptimalCommunicatorSharedMemory(const Coordinate &processors,Grid_MPI_Comm & optimal_comm)
+{
   ////////////////////////////////////////////////////////////////
   // Identify subblock of ranks on node spreading across dims
   // in a maximally symmetrical way
   ////////////////////////////////////////////////////////////////
   int ndimension              = processors.size();
-  std::vector<int> processor_coor(ndimension);
-  std::vector<int> WorldDims = processors;   std::vector<int> ShmDims  (ndimension,1);  std::vector<int> NodeDims (ndimension);
-  std::vector<int> ShmCoor  (ndimension);    std::vector<int> NodeCoor (ndimension);    std::vector<int> WorldCoor(ndimension);
-  int dim = 0;
-  for(int l2=0;l2<log2size;l2++){
-    while ( (WorldDims[dim] / ShmDims[dim]) <= 1 ) dim=(dim+1)%ndimension;
-    ShmDims[dim]*=2;
-    dim=(dim+1)%ndimension;
-  }
+  Coordinate processor_coor(ndimension);
+  Coordinate WorldDims = processors; Coordinate ShmDims(ndimension);  Coordinate NodeDims (ndimension);
+  Coordinate ShmCoor(ndimension);    Coordinate NodeCoor(ndimension);   Coordinate WorldCoor(ndimension);
 
+  GetShmDims(WorldDims,ShmDims);
   ////////////////////////////////////////////////////////////////
   // Establish torus of processes and nodes with sub-blockings
   ////////////////////////////////////////////////////////////////
@@ -307,7 +362,6 @@ void GlobalSharedMemory::OptimalCommunicator(const std::vector<int> &processors,
   /////////////////////////////////////////////////////////////////
   int ierr= MPI_Comm_split(WorldComm,0,rank,&optimal_comm);
   assert(ierr==0);
-#endif
 }
 ////////////////////////////////////////////////////////////////////////////////////////////
 // SHMGET
@@ -315,7 +369,7 @@ void GlobalSharedMemory::OptimalCommunicator(const std::vector<int> &processors,
 #ifdef GRID_MPI3_SHMGET
 void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
 {
-  std::cout << "SharedMemoryAllocate "<< bytes<< " shmget implementation "<<std::endl;
+  std::cout << header "SharedMemoryAllocate "<< bytes<< " shmget implementation "<<std::endl;
   assert(_ShmSetup==1);
   assert(_ShmAlloc==0);
 
@@ -338,7 +392,7 @@ void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
         int errsv = errno;
         printf("Errno %d\n",errsv);
         printf("key   %d\n",key);
-        printf("size  %lld\n",size);
+        printf("size  %ld\n",size);
         printf("flags %d\n",flags);
         perror("shmget");
         exit(1);
@@ -374,10 +428,121 @@ void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
 ////////////////////////////////////////////////////////////////////////////////////////////
 // Hugetlbfs mapping intended
 ////////////////////////////////////////////////////////////////////////////////////////////
+#if defined(GRID_CUDA) ||defined(GRID_HIP)
+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);
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // TODO/FIXME : NOT ALL NVLINK BOARDS have full Peer to peer connectivity.
+  // The annoyance is that they have partial peer 2 peer. This occurs on the 8 GPU blades.
+  // e.g. DGX1, supermicro board, 
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////
+  //  cudaDeviceGetP2PAttribute(&perfRank, cudaDevP2PAttrPerformanceRank, device1, device2);
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // 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);  
+  }
+  if ( WorldRank == 0 ){
+    std::cout << header " SharedMemoryMPI.cc cudaMalloc "<< bytes 
+	      << "bytes at "<< std::hex<< ShmCommBuf <<std::dec<<" for comms buffers " <<std::endl;
+  }
+  SharedMemoryZero(ShmCommBuf,bytes);
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Loop over ranks/gpu's on our node
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////////
+  for(int r=0;r<WorldShmSize;r++){
+
+#ifndef GRID_MPI3_SHM_NONE
+    //////////////////////////////////////////////////
+    // If it is me, pass around the IPC access key
+    //////////////////////////////////////////////////
+#ifdef GRID_CUDA
+    cudaIpcMemHandle_t handle;
+    if ( r==WorldShmRank ) { 
+      auto err = cudaIpcGetMemHandle(&handle,ShmCommBuf);
+      if ( err !=  cudaSuccess) {
+	std::cerr << " SharedMemoryMPI.cc cudaIpcGetMemHandle failed for rank" << r <<" "<<cudaGetErrorString(err)<< std::endl;
+	exit(EXIT_FAILURE);
+      }
+    }
+#endif
+#ifdef GRID_HIP
+    hipIpcMemHandle_t handle;    
+    if ( r==WorldShmRank ) { 
+      auto err = hipIpcGetMemHandle(&handle,ShmCommBuf);
+      if ( err !=  hipSuccess) {
+	std::cerr << " SharedMemoryMPI.cc hipIpcGetMemHandle failed for rank" << r <<" "<<hipGetErrorString(err)<< std::endl;
+	exit(EXIT_FAILURE);
+      }
+    }
+#endif
+    //////////////////////////////////////////////////
+    // Share this IPC handle across the Shm Comm
+    //////////////////////////////////////////////////
+    { 
+      int ierr=MPI_Bcast(&handle,
+			 sizeof(handle),
+			 MPI_BYTE,
+			 r,
+			 WorldShmComm);
+      assert(ierr==0);
+    }
+    
+    ///////////////////////////////////////////////////////////////
+    // If I am not the source, overwrite thisBuf with remote buffer
+    ///////////////////////////////////////////////////////////////
+    void * thisBuf = ShmCommBuf;
+#ifdef GRID_CUDA
+    if ( r!=WorldShmRank ) { 
+      auto err = cudaIpcOpenMemHandle(&thisBuf,handle,cudaIpcMemLazyEnablePeerAccess);
+      if ( err !=  cudaSuccess) {
+	std::cerr << " SharedMemoryMPI.cc cudaIpcOpenMemHandle failed for rank" << r <<" "<<cudaGetErrorString(err)<< std::endl;
+	exit(EXIT_FAILURE);
+      }
+    }
+#endif
+#ifdef GRID_HIP
+    if ( r!=WorldShmRank ) { 
+      auto err = hipIpcOpenMemHandle(&thisBuf,handle,hipIpcMemLazyEnablePeerAccess);
+      if ( err !=  hipSuccess) {
+	std::cerr << " SharedMemoryMPI.cc hipIpcOpenMemHandle failed for rank" << r <<" "<<hipGetErrorString(err)<< std::endl;
+	exit(EXIT_FAILURE);
+      }
+    }
+#endif
+    ///////////////////////////////////////////////////////////////
+    // Save a copy of the device buffers
+    ///////////////////////////////////////////////////////////////
+    WorldShmCommBufs[r] = thisBuf;
+#else
+    WorldShmCommBufs[r] = ShmCommBuf;
+#endif
+  }
+
+  _ShmAllocBytes=bytes;
+  _ShmAlloc=1;
+}
+#else 
 #ifdef GRID_MPI3_SHMMMAP
 void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
 {
-  std::cout << "SharedMemoryAllocate "<< bytes<< " MMAP implementation "<< GRID_SHM_PATH <<std::endl;
+  std::cout << header "SharedMemoryAllocate "<< bytes<< " MMAP implementation "<< GRID_SHM_PATH <<std::endl;
   assert(_ShmSetup==1);
   assert(_ShmAlloc==0);
   //////////////////////////////////////////////////////////////////////////////////////////////////////////
@@ -414,7 +579,7 @@ void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
     assert(((uint64_t)ptr&0x3F)==0);
     close(fd);
     WorldShmCommBufs[r] =ptr;
-    std::cout << "Set WorldShmCommBufs["<<r<<"]="<<ptr<< "("<< bytes<< "bytes)"<<std::endl;
+    //    std::cout << header "Set WorldShmCommBufs["<<r<<"]="<<ptr<< "("<< bytes<< "bytes)"<<std::endl;
   }
   _ShmAlloc=1;
   _ShmAllocBytes  = bytes;
@@ -424,7 +589,7 @@ void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
 #ifdef GRID_MPI3_SHM_NONE
 void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
 {
-  std::cout << "SharedMemoryAllocate "<< bytes<< " MMAP anonymous implementation "<<std::endl;
+  std::cout << header "SharedMemoryAllocate "<< bytes<< " MMAP anonymous implementation "<<std::endl;
   assert(_ShmSetup==1);
   assert(_ShmAlloc==0);
   //////////////////////////////////////////////////////////////////////////////////////////////////////////
@@ -456,7 +621,7 @@ void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
     assert(((uint64_t)ptr&0x3F)==0);
     close(fd);
     WorldShmCommBufs[r] =ptr;
-    std::cout << "Set WorldShmCommBufs["<<r<<"]="<<ptr<< "("<< bytes<< "bytes)"<<std::endl;
+    //    std::cout << "Set WorldShmCommBufs["<<r<<"]="<<ptr<< "("<< bytes<< "bytes)"<<std::endl;
   }
   _ShmAlloc=1;
   _ShmAllocBytes  = bytes;
@@ -471,7 +636,7 @@ void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
 ////////////////////////////////////////////////////////////////////////////////////////////
 void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
 { 
-  std::cout << "SharedMemoryAllocate "<< bytes<< " SHMOPEN implementation "<<std::endl;
+  std::cout << header "SharedMemoryAllocate "<< bytes<< " SHMOPEN implementation "<<std::endl;
   assert(_ShmSetup==1);
   assert(_ShmAlloc==0); 
   MPI_Barrier(WorldShmComm);
@@ -500,7 +665,7 @@ void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
 #endif
       void * ptr =  mmap(NULL,size, PROT_READ | PROT_WRITE, mmap_flag, fd, 0);
       
-      std::cout << "Set WorldShmCommBufs["<<r<<"]="<<ptr<< "("<< size<< "bytes)"<<std::endl;
+      //      std::cout << "Set WorldShmCommBufs["<<r<<"]="<<ptr<< "("<< size<< "bytes)"<<std::endl;
       if ( ptr == (void * )MAP_FAILED ) {       
 	perror("failed mmap");     
 	assert(0);    
@@ -537,14 +702,31 @@ void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
   _ShmAllocBytes = bytes;
 }
 #endif
+#endif // End NVCC case for GPU device buffers
 
-
-
-
-  ////////////////////////////////////////////////////////
-  // Global shared functionality finished
-  // Now move to per communicator functionality
-  ////////////////////////////////////////////////////////
+/////////////////////////////////////////////////////////////////////////
+// Routines accessing shared memory should route through for GPU safety
+/////////////////////////////////////////////////////////////////////////
+void GlobalSharedMemory::SharedMemoryZero(void *dest,size_t bytes)
+{
+#ifdef GRID_CUDA
+  cudaMemset(dest,0,bytes);
+#else
+  bzero(dest,bytes);
+#endif
+}
+void GlobalSharedMemory::SharedMemoryCopy(void *dest,const void *src,size_t bytes)
+{
+#ifdef GRID_CUDA
+  cudaMemcpy(dest,src,bytes,cudaMemcpyDefault);
+#else   
+  bcopy(src,dest,bytes);
+#endif
+}
+////////////////////////////////////////////////////////
+// Global shared functionality finished
+// Now move to per communicator functionality
+////////////////////////////////////////////////////////
 void SharedMemory::SetCommunicator(Grid_MPI_Comm comm)
 {
   int rank, size;
@@ -555,7 +737,11 @@ void SharedMemory::SetCommunicator(Grid_MPI_Comm comm)
   /////////////////////////////////////////////////////////////////////
   // Split into groups that can share memory
   /////////////////////////////////////////////////////////////////////
+#ifndef GRID_MPI3_SHM_NONE
   MPI_Comm_split_type(comm, MPI_COMM_TYPE_SHARED, 0, MPI_INFO_NULL,&ShmComm);
+#else
+  MPI_Comm_split(comm, rank, 0, &ShmComm);
+#endif
   MPI_Comm_rank(ShmComm     ,&ShmRank);
   MPI_Comm_size(ShmComm     ,&ShmSize);
   ShmCommBufs.resize(ShmSize);
@@ -572,7 +758,6 @@ void SharedMemory::SetCommunicator(Grid_MPI_Comm comm)
     MPI_Allreduce(MPI_IN_PLACE,&wsr,1,MPI_UINT32_T,MPI_SUM,ShmComm);
 
     ShmCommBufs[r] = GlobalSharedMemory::WorldShmCommBufs[wsr];
-    //    std::cout << "SetCommunicator ShmCommBufs ["<< r<< "] = "<< ShmCommBufs[r]<< "  wsr = "<<wsr<<std::endl;
   }
   ShmBufferFreeAll();
 
@@ -585,6 +770,26 @@ void SharedMemory::SetCommunicator(Grid_MPI_Comm comm)
 
   std::vector<int> ranks(size);   for(int r=0;r<size;r++) ranks[r]=r;
   MPI_Group_translate_ranks (FullGroup,size,&ranks[0],ShmGroup, &ShmRanks[0]); 
+
+#ifdef GRID_IBM_SUMMIT
+  // Hide the shared memory path between sockets 
+  // if even number of nodes
+  if ( (ShmSize & 0x1)==0 ) {
+    int SocketSize = ShmSize/2;
+    int mySocket = ShmRank/SocketSize; 
+    for(int r=0;r<size;r++){
+      int hisRank=ShmRanks[r];
+      if ( hisRank!= MPI_UNDEFINED ) {
+	int hisSocket=hisRank/SocketSize;
+	if ( hisSocket != mySocket ) {
+	  ShmRanks[r] = MPI_UNDEFINED;
+	}
+      }
+    }
+  }
+#endif
+
+  SharedMemoryTest();
 }
 //////////////////////////////////////////////////////////////////
 // On node barrier
@@ -599,24 +804,26 @@ void SharedMemory::ShmBarrier(void)
 void SharedMemory::SharedMemoryTest(void)
 {
   ShmBarrier();
+  uint64_t check[3];
+  uint64_t magic = 0x5A5A5A;
   if ( ShmRank == 0 ) {
-    for(int r=0;r<ShmSize;r++){
-      uint64_t * check = (uint64_t *) ShmCommBufs[r];
-      check[0] = GlobalSharedMemory::WorldNode;
-      check[1] = r;
-      check[2] = 0x5A5A5A;
+    for(uint64_t r=0;r<ShmSize;r++){
+       check[0]=GlobalSharedMemory::WorldNode;
+       check[1]=r;
+       check[2]=magic;
+       GlobalSharedMemory::SharedMemoryCopy( ShmCommBufs[r], check, 3*sizeof(uint64_t));
     }
   }
   ShmBarrier();
-  for(int r=0;r<ShmSize;r++){
-    uint64_t * check = (uint64_t *) ShmCommBufs[r];
-    
+  for(uint64_t r=0;r<ShmSize;r++){
+    ShmBarrier();
+    GlobalSharedMemory::SharedMemoryCopy(check,ShmCommBufs[r], 3*sizeof(uint64_t));
+    ShmBarrier();
     assert(check[0]==GlobalSharedMemory::WorldNode);
     assert(check[1]==r);
-    assert(check[2]==0x5A5A5A);
-    
+    assert(check[2]==magic);
+    ShmBarrier();
   }
-  ShmBarrier();
 }
 
 void *SharedMemory::ShmBuffer(int rank)
@@ -630,7 +837,6 @@ void *SharedMemory::ShmBuffer(int rank)
 }
 void *SharedMemory::ShmBufferTranslate(int rank,void * local_p)
 {
-  static int count =0;
   int gpeer = ShmRanks[rank];
   assert(gpeer!=ShmRank); // never send to self
   if (gpeer == MPI_UNDEFINED){
@@ -649,4 +855,5 @@ SharedMemory::~SharedMemory()
   }
 };
 
-}
+NAMESPACE_END(Grid); 
+

Grid/communicator/SharedMemoryNone.cc

@@ -28,7 +28,7 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 
 #include <Grid/GridCore.h>
 
-namespace Grid { 
+NAMESPACE_BEGIN(Grid); 
 
 /*Construct from an MPI communicator*/
 void GlobalSharedMemory::Init(Grid_MPI_Comm comm)
@@ -47,7 +47,7 @@ void GlobalSharedMemory::Init(Grid_MPI_Comm comm)
   _ShmSetup=1;
 }
 
-void GlobalSharedMemory::OptimalCommunicator(const std::vector<int> &processors,Grid_MPI_Comm & optimal_comm)
+void GlobalSharedMemory::OptimalCommunicator(const Coordinate &processors,Grid_MPI_Comm & optimal_comm)
 {
   optimal_comm = WorldComm;
 }
@@ -84,10 +84,10 @@ void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
   _ShmAlloc=1;
 };
 
-  ////////////////////////////////////////////////////////
-  // Global shared functionality finished
-  // Now move to per communicator functionality
-  ////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////
+// Global shared functionality finished
+// Now move to per communicator functionality
+////////////////////////////////////////////////////////
 void SharedMemory::SetCommunicator(Grid_MPI_Comm comm)
 {
   assert(GlobalSharedMemory::ShmAlloc()==1);
@@ -125,4 +125,5 @@ void *SharedMemory::ShmBufferTranslate(int rank,void * local_p)
 SharedMemory::~SharedMemory()
 {};
 
-}
+NAMESPACE_END(Grid); 
+

Grid/cshift/Cshift.h

@@ -1,4 +1,4 @@
-    /*************************************************************************************
+/*************************************************************************************
 
     Grid physics library, www.github.com/paboyle/Grid 
 
@@ -23,8 +23,8 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     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 */
+*************************************************************************************/
+/*  END LEGAL */
 #ifndef _GRID_CSHIFT_H_
 #define _GRID_CSHIFT_H_
 
@@ -49,4 +49,14 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 #ifdef GRID_COMMS_SHMEM
 #include <Grid/cshift/Cshift_mpi.h> // uses same implementation of communicator
 #endif 
+
+NAMESPACE_BEGIN(Grid);
+
+template<class Expression,typename std::enable_if<is_lattice_expr<Expression>::value,void>::type * = nullptr> 
+auto Cshift(const Expression &expr,int dim,int shift)  -> decltype(closure(expr)) 
+{
+  return Cshift(closure(expr),dim,shift);
+}
+NAMESPACE_END(Grid);
+
 #endif

Grid/cshift/Cshift_common.h

@@ -25,10 +25,11 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     See the full license in the file "LICENSE" in the top level distribution directory
     *************************************************************************************/
     /*  END LEGAL */
-#ifndef _GRID_CSHIFT_COMMON_H_
-#define _GRID_CSHIFT_COMMON_H_
+#pragma once
 
-namespace Grid {
+NAMESPACE_BEGIN(Grid);
+
+extern Vector<std::pair<int,int> > Cshift_table; 
 
 ///////////////////////////////////////////////////////////////////
 // Gather for when there is no need to SIMD split 
@@ -36,26 +37,27 @@ namespace Grid {
 template<class vobj> void 
 Gather_plane_simple (const Lattice<vobj> &rhs,commVector<vobj> &buffer,int dimension,int plane,int cbmask, int off=0)
 {
-  int rd = rhs._grid->_rdimensions[dimension];
+  int rd = rhs.Grid()->_rdimensions[dimension];
 
-  if ( !rhs._grid->CheckerBoarded(dimension) ) {
+  if ( !rhs.Grid()->CheckerBoarded(dimension) ) {
     cbmask = 0x3;
   }
   
-  int so=plane*rhs._grid->_ostride[dimension]; // base offset for start of plane 
-  int e1=rhs._grid->_slice_nblock[dimension];
-  int e2=rhs._grid->_slice_block[dimension];
+  int so=plane*rhs.Grid()->_ostride[dimension]; // base offset for start of plane 
+  int e1=rhs.Grid()->_slice_nblock[dimension];
+  int e2=rhs.Grid()->_slice_block[dimension];
   int ent = 0;
 
-  static std::vector<std::pair<int,int> > table; table.resize(e1*e2);
+  if(Cshift_table.size()<e1*e2) Cshift_table.resize(e1*e2); // Let it grow to biggest
+
+  int stride=rhs.Grid()->_slice_stride[dimension];
 
-  int stride=rhs._grid->_slice_stride[dimension];
   if ( cbmask == 0x3 ) { 
     for(int n=0;n<e1;n++){
       for(int b=0;b<e2;b++){
 	int o  = n*stride;
 	int bo = n*e2;
-	table[ent++] = std::pair<int,int>(off+bo+b,so+o+b);
+	Cshift_table[ent++] = std::pair<int,int>(off+bo+b,so+o+b);
       }
     }
   } else { 
@@ -63,15 +65,20 @@ Gather_plane_simple (const Lattice<vobj> &rhs,commVector<vobj> &buffer,int dimen
      for(int n=0;n<e1;n++){
        for(int b=0;b<e2;b++){
 	 int o  = n*stride;
-	 int ocb=1<<rhs._grid->CheckerBoardFromOindex(o+b);
+	 int ocb=1<<rhs.Grid()->CheckerBoardFromOindex(o+b);
 	 if ( ocb &cbmask ) {
-	   table[ent++]=std::pair<int,int> (off+bo++,so+o+b);
+	   Cshift_table[ent++]=std::pair<int,int> (off+bo++,so+o+b);
 	 }
        }
      }
   }
-  parallel_for(int i=0;i<ent;i++){
-    buffer[table[i].first]=rhs._odata[table[i].second];
+  {
+    autoView(rhs_v , rhs, AcceleratorRead);
+    auto buffer_p = & buffer[0];
+    auto table = &Cshift_table[0];
+    accelerator_for(i,ent,vobj::Nsimd(),{
+	coalescedWrite(buffer_p[table[i].first],coalescedRead(rhs_v[table[i].second]));
+    });
   }
 }
 
@@ -79,50 +86,54 @@ Gather_plane_simple (const Lattice<vobj> &rhs,commVector<vobj> &buffer,int dimen
 // Gather for when there *is* need to SIMD split 
 ///////////////////////////////////////////////////////////////////
 template<class vobj> void 
-Gather_plane_extract(const Lattice<vobj> &rhs,std::vector<typename vobj::scalar_object *> pointers,int dimension,int plane,int cbmask)
+Gather_plane_extract(const Lattice<vobj> &rhs,
+		     ExtractPointerArray<typename vobj::scalar_object> pointers,
+		     int dimension,int plane,int cbmask)
 {
-  int rd = rhs._grid->_rdimensions[dimension];
+  int rd = rhs.Grid()->_rdimensions[dimension];
 
-  if ( !rhs._grid->CheckerBoarded(dimension) ) {
+  if ( !rhs.Grid()->CheckerBoarded(dimension) ) {
     cbmask = 0x3;
   }
 
-  int so  = plane*rhs._grid->_ostride[dimension]; // base offset for start of plane 
+  int so  = plane*rhs.Grid()->_ostride[dimension]; // base offset for start of plane 
 
-  int e1=rhs._grid->_slice_nblock[dimension];
-  int e2=rhs._grid->_slice_block[dimension];
-  int n1=rhs._grid->_slice_stride[dimension];
+  int e1=rhs.Grid()->_slice_nblock[dimension];
+  int e2=rhs.Grid()->_slice_block[dimension];
+  int n1=rhs.Grid()->_slice_stride[dimension];
 
   if ( cbmask ==0x3){
-    parallel_for_nest2(int n=0;n<e1;n++){
-      for(int b=0;b<e2;b++){
-
+    autoView(rhs_v , rhs, AcceleratorRead);
+    accelerator_for2d(n,e1,b,e2,1,{
 	int o      =   n*n1;
 	int offset = b+n*e2;
 	
-	vobj temp =rhs._odata[so+o+b];
+	vobj temp =rhs_v[so+o+b];
 	extract<vobj>(temp,pointers,offset);
-
-      }
-    }
+      });
   } else { 
+    autoView(rhs_v , rhs, AcceleratorRead);
 
-    // Case of SIMD split AND checker dim cannot currently be hit, except in 
-    // Test_cshift_red_black code.
-    std::cout << " Dense packed buffer WARNING " <<std::endl;
-    parallel_for_nest2(int n=0;n<e1;n++){
-      for(int b=0;b<e2;b++){
+    Coordinate rdim=rhs.Grid()->_rdimensions;
+    Coordinate cdm =rhs.Grid()->_checker_dim_mask;
+    std::cout << " Dense packed buffer WARNING " <<std::endl; // Does this get called twice once for each cb?
+    accelerator_for2d(n,e1,b,e2,1,{
+
+	Coordinate coor;
 
 	int o=n*n1;
-	int ocb=1<<rhs._grid->CheckerBoardFromOindex(o+b);
+	int oindex = o+b;
+
+       	int cb = RedBlackCheckerBoardFromOindex(oindex, rdim, cdm);
+
+	int ocb=1<<cb;
 	int offset = b+n*e2;
 
 	if ( ocb & cbmask ) {
-	  vobj temp =rhs._odata[so+o+b];
+	  vobj temp =rhs_v[so+o+b];
 	  extract<vobj>(temp,pointers,offset);
 	}
-      }
-    }
+      });
   }
 }
 
@@ -131,28 +142,29 @@ Gather_plane_extract(const Lattice<vobj> &rhs,std::vector<typename vobj::scalar_
 //////////////////////////////////////////////////////
 template<class vobj> void Scatter_plane_simple (Lattice<vobj> &rhs,commVector<vobj> &buffer, int dimension,int plane,int cbmask)
 {
-  int rd = rhs._grid->_rdimensions[dimension];
+  int rd = rhs.Grid()->_rdimensions[dimension];
 
-  if ( !rhs._grid->CheckerBoarded(dimension) ) {
+  if ( !rhs.Grid()->CheckerBoarded(dimension) ) {
     cbmask=0x3;
   }
 
-  int so  = plane*rhs._grid->_ostride[dimension]; // base offset for start of plane 
+  int so  = plane*rhs.Grid()->_ostride[dimension]; // base offset for start of plane 
     
-  int e1=rhs._grid->_slice_nblock[dimension];
-  int e2=rhs._grid->_slice_block[dimension];
-  int stride=rhs._grid->_slice_stride[dimension];
+  int e1=rhs.Grid()->_slice_nblock[dimension];
+  int e2=rhs.Grid()->_slice_block[dimension];
+  int stride=rhs.Grid()->_slice_stride[dimension];
+
+  if(Cshift_table.size()<e1*e2) Cshift_table.resize(e1*e2); // Let it grow to biggest
 
-  static std::vector<std::pair<int,int> > table; table.resize(e1*e2);
   int ent    =0;
 
   if ( cbmask ==0x3 ) {
 
     for(int n=0;n<e1;n++){
       for(int b=0;b<e2;b++){
-	int o   =n*rhs._grid->_slice_stride[dimension];
-	int bo  =n*rhs._grid->_slice_block[dimension];
-	table[ent++] = std::pair<int,int>(so+o+b,bo+b);
+	int o   =n*rhs.Grid()->_slice_stride[dimension];
+	int bo  =n*rhs.Grid()->_slice_block[dimension];
+	Cshift_table[ent++] = std::pair<int,int>(so+o+b,bo+b);
       }
     }
 
@@ -160,57 +172,65 @@ template<class vobj> void Scatter_plane_simple (Lattice<vobj> &rhs,commVector<vo
     int bo=0;
     for(int n=0;n<e1;n++){
       for(int b=0;b<e2;b++){
-	int o   =n*rhs._grid->_slice_stride[dimension];
-	int ocb=1<<rhs._grid->CheckerBoardFromOindex(o+b);// Could easily be a table lookup
+	int o   =n*rhs.Grid()->_slice_stride[dimension];
+	int ocb=1<<rhs.Grid()->CheckerBoardFromOindex(o+b);// Could easily be a table lookup
 	if ( ocb & cbmask ) {
-	  table[ent++]=std::pair<int,int> (so+o+b,bo++);
+	  Cshift_table[ent++]=std::pair<int,int> (so+o+b,bo++);
 	}
       }
     }
   }
   
-  parallel_for(int i=0;i<ent;i++){
-    rhs._odata[table[i].first]=buffer[table[i].second];
+  {
+    autoView( rhs_v, rhs, AcceleratorWrite);
+    auto buffer_p = & buffer[0];
+    auto table = &Cshift_table[0];
+    accelerator_for(i,ent,vobj::Nsimd(),{
+	coalescedWrite(rhs_v[table[i].first],coalescedRead(buffer_p[table[i].second]));
+    });
   }
 }
 
 //////////////////////////////////////////////////////
 // Scatter for when there *is* need to SIMD split
 //////////////////////////////////////////////////////
-template<class vobj> void Scatter_plane_merge(Lattice<vobj> &rhs,std::vector<typename vobj::scalar_object *> pointers,int dimension,int plane,int cbmask)
+template<class vobj> void Scatter_plane_merge(Lattice<vobj> &rhs,ExtractPointerArray<typename vobj::scalar_object> pointers,int dimension,int plane,int cbmask)
 {
-  int rd = rhs._grid->_rdimensions[dimension];
+  int rd = rhs.Grid()->_rdimensions[dimension];
 
-  if ( !rhs._grid->CheckerBoarded(dimension) ) {
+  if ( !rhs.Grid()->CheckerBoarded(dimension) ) {
     cbmask=0x3;
   }
 
-  int so  = plane*rhs._grid->_ostride[dimension]; // base offset for start of plane 
+  int so  = plane*rhs.Grid()->_ostride[dimension]; // base offset for start of plane 
     
-  int e1=rhs._grid->_slice_nblock[dimension];
-  int e2=rhs._grid->_slice_block[dimension];
+  int e1=rhs.Grid()->_slice_nblock[dimension];
+  int e2=rhs.Grid()->_slice_block[dimension];
 
   if(cbmask ==0x3 ) {
-    parallel_for_nest2(int n=0;n<e1;n++){
-      for(int b=0;b<e2;b++){
-	int o      = n*rhs._grid->_slice_stride[dimension];
-	int offset = b+n*rhs._grid->_slice_block[dimension];
-	merge(rhs._odata[so+o+b],pointers,offset);
-      }
-    }
+    autoView( rhs_v , rhs, AcceleratorWrite);
+    int _slice_stride = rhs.Grid()->_slice_stride[dimension];
+    int _slice_block = rhs.Grid()->_slice_block[dimension];
+    accelerator_for2d(n,e1,b,e2,1,{
+	int o      = n*_slice_stride;
+	int offset = b+n*_slice_block;
+	merge(rhs_v[so+o+b],pointers,offset);
+      });
   } else { 
 
     // Case of SIMD split AND checker dim cannot currently be hit, except in 
     // Test_cshift_red_black code.
     //    std::cout << "Scatter_plane merge assert(0); think this is buggy FIXME "<< std::endl;// think this is buggy FIXME
     std::cout<<" Unthreaded warning -- buffer is not densely packed ??"<<std::endl;
+    assert(0); // This will fail if hit on GPU
+    autoView( rhs_v, rhs, CpuWrite);
     for(int n=0;n<e1;n++){
       for(int b=0;b<e2;b++){
-	int o      = n*rhs._grid->_slice_stride[dimension];
-	int offset = b+n*rhs._grid->_slice_block[dimension];
-	int ocb=1<<rhs._grid->CheckerBoardFromOindex(o+b);
+	int o      = n*rhs.Grid()->_slice_stride[dimension];
+	int offset = b+n*rhs.Grid()->_slice_block[dimension];
+	int ocb=1<<rhs.Grid()->CheckerBoardFromOindex(o+b);
 	if ( ocb&cbmask ) {
-	  merge(rhs._odata[so+o+b],pointers,offset);
+	  merge(rhs_v[so+o+b],pointers,offset);
 	}
       }
     }
@@ -220,85 +240,96 @@ template<class vobj> void Scatter_plane_merge(Lattice<vobj> &rhs,std::vector<typ
 //////////////////////////////////////////////////////
 // local to node block strided copies
 //////////////////////////////////////////////////////
+
 template<class vobj> void Copy_plane(Lattice<vobj>& lhs,const Lattice<vobj> &rhs, int dimension,int lplane,int rplane,int cbmask)
 {
-  int rd = rhs._grid->_rdimensions[dimension];
+  int rd = rhs.Grid()->_rdimensions[dimension];
 
-  if ( !rhs._grid->CheckerBoarded(dimension) ) {
+  if ( !rhs.Grid()->CheckerBoarded(dimension) ) {
     cbmask=0x3;
   }
 
-  int ro  = rplane*rhs._grid->_ostride[dimension]; // base offset for start of plane 
-  int lo  = lplane*lhs._grid->_ostride[dimension]; // base offset for start of plane 
+  int ro  = rplane*rhs.Grid()->_ostride[dimension]; // base offset for start of plane 
+  int lo  = lplane*lhs.Grid()->_ostride[dimension]; // base offset for start of plane 
+
+  int e1=rhs.Grid()->_slice_nblock[dimension]; // clearly loop invariant for icpc
+  int e2=rhs.Grid()->_slice_block[dimension];
+  int stride = rhs.Grid()->_slice_stride[dimension];
+
+  if(Cshift_table.size()<e1*e2) Cshift_table.resize(e1*e2); // Let it grow to biggest
 
-  int e1=rhs._grid->_slice_nblock[dimension]; // clearly loop invariant for icpc
-  int e2=rhs._grid->_slice_block[dimension];
-  int stride = rhs._grid->_slice_stride[dimension];
-  static std::vector<std::pair<int,int> > table; table.resize(e1*e2);
   int ent=0;
 
   if(cbmask == 0x3 ){
     for(int n=0;n<e1;n++){
       for(int b=0;b<e2;b++){
         int o =n*stride+b;
-	table[ent++] = std::pair<int,int>(lo+o,ro+o);
+	Cshift_table[ent++] = std::pair<int,int>(lo+o,ro+o);
       }
     }
   } else { 
     for(int n=0;n<e1;n++){
       for(int b=0;b<e2;b++){
         int o =n*stride+b;
-        int ocb=1<<lhs._grid->CheckerBoardFromOindex(o);
+        int ocb=1<<lhs.Grid()->CheckerBoardFromOindex(o);
         if ( ocb&cbmask ) {
-	  table[ent++] = std::pair<int,int>(lo+o,ro+o);
+	  Cshift_table[ent++] = std::pair<int,int>(lo+o,ro+o);
 	}
       }
     }
   }
 
-  parallel_for(int i=0;i<ent;i++){
-    lhs._odata[table[i].first]=rhs._odata[table[i].second];
+  {
+    autoView(rhs_v , rhs, AcceleratorRead);
+    autoView(lhs_v , lhs, AcceleratorWrite);
+    auto table = &Cshift_table[0];
+    accelerator_for(i,ent,vobj::Nsimd(),{
+      coalescedWrite(lhs_v[table[i].first],coalescedRead(rhs_v[table[i].second]));
+    });
   }
-
 }
 
 template<class vobj> void Copy_plane_permute(Lattice<vobj>& lhs,const Lattice<vobj> &rhs, int dimension,int lplane,int rplane,int cbmask,int permute_type)
 {
+  int rd = rhs.Grid()->_rdimensions[dimension];
 
-  int rd = rhs._grid->_rdimensions[dimension];
-
-  if ( !rhs._grid->CheckerBoarded(dimension) ) {
+  if ( !rhs.Grid()->CheckerBoarded(dimension) ) {
     cbmask=0x3;
   }
 
-  int ro  = rplane*rhs._grid->_ostride[dimension]; // base offset for start of plane 
-  int lo  = lplane*lhs._grid->_ostride[dimension]; // base offset for start of plane 
+  int ro  = rplane*rhs.Grid()->_ostride[dimension]; // base offset for start of plane 
+  int lo  = lplane*lhs.Grid()->_ostride[dimension]; // base offset for start of plane 
 
-  int e1=rhs._grid->_slice_nblock[dimension];
-  int e2=rhs._grid->_slice_block [dimension];
-  int stride = rhs._grid->_slice_stride[dimension];
+  int e1=rhs.Grid()->_slice_nblock[dimension];
+  int e2=rhs.Grid()->_slice_block [dimension];
+  int stride = rhs.Grid()->_slice_stride[dimension];
+
+  if(Cshift_table.size()<e1*e2) Cshift_table.resize(e1*e2); // Let it grow to biggest
 
-  static std::vector<std::pair<int,int> > table;  table.resize(e1*e2);
   int ent=0;
 
-  double t_tab,t_perm;
   if ( cbmask == 0x3 ) {
     for(int n=0;n<e1;n++){
     for(int b=0;b<e2;b++){
       int o  =n*stride;
-      table[ent++] = std::pair<int,int>(lo+o+b,ro+o+b);
+      Cshift_table[ent++] = std::pair<int,int>(lo+o+b,ro+o+b);
     }}
   } else {
     for(int n=0;n<e1;n++){
     for(int b=0;b<e2;b++){
       int o  =n*stride;
-      int ocb=1<<lhs._grid->CheckerBoardFromOindex(o+b);
-      if ( ocb&cbmask ) table[ent++] = std::pair<int,int>(lo+o+b,ro+o+b);
+      int ocb=1<<lhs.Grid()->CheckerBoardFromOindex(o+b);
+      if ( ocb&cbmask ) Cshift_table[ent++] = std::pair<int,int>(lo+o+b,ro+o+b);
     }}
   }
 
-  parallel_for(int i=0;i<ent;i++){
-    permute(lhs._odata[table[i].first],rhs._odata[table[i].second],permute_type);
+  {
+    autoView( rhs_v, rhs, AcceleratorRead);
+    autoView( lhs_v, lhs, AcceleratorWrite);
+    auto table = &Cshift_table[0];
+    accelerator_for(i,ent,1,{
+      permute(lhs_v[table[i].first],rhs_v[table[i].second],permute_type);
+    });
   }
 }
 
@@ -309,10 +340,8 @@ template<class vobj> void Cshift_local(Lattice<vobj>& ret,const Lattice<vobj> &r
 {
   int sshift[2];
 
-  sshift[0] = rhs._grid->CheckerBoardShiftForCB(rhs.checkerboard,dimension,shift,Even);
-  sshift[1] = rhs._grid->CheckerBoardShiftForCB(rhs.checkerboard,dimension,shift,Odd);
-
-  double t_local;
+  sshift[0] = rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,Even);
+  sshift[1] = rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,Odd);
 
   if ( sshift[0] == sshift[1] ) {
     Cshift_local(ret,rhs,dimension,shift,0x3);
@@ -324,7 +353,7 @@ template<class vobj> void Cshift_local(Lattice<vobj>& ret,const Lattice<vobj> &r
 
 template<class vobj> void Cshift_local(Lattice<vobj> &ret,const Lattice<vobj> &rhs,int dimension,int shift,int cbmask)
 {
-  GridBase *grid = rhs._grid;
+  GridBase *grid = rhs.Grid();
   int fd = grid->_fdimensions[dimension];
   int rd = grid->_rdimensions[dimension];
   int ld = grid->_ldimensions[dimension];
@@ -335,18 +364,18 @@ template<class vobj> void Cshift_local(Lattice<vobj> &ret,const Lattice<vobj> &r
   shift = (shift+fd)%fd;
 
   // the permute type
-  ret.checkerboard = grid->CheckerBoardDestination(rhs.checkerboard,shift,dimension);
+  ret.Checkerboard() = grid->CheckerBoardDestination(rhs.Checkerboard(),shift,dimension);
   int permute_dim =grid->PermuteDim(dimension);
   int permute_type=grid->PermuteType(dimension);
   int permute_type_dist;
 
   for(int x=0;x<rd;x++){       
 
-    int o   = 0;
+    //    int o   = 0;
     int bo  = x * grid->_ostride[dimension];
     int cb= (cbmask==0x2)? Odd : Even;
 
-    int sshift = grid->CheckerBoardShiftForCB(rhs.checkerboard,dimension,shift,cb);
+    int sshift = grid->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,cb);
     int sx     = (x+sshift)%rd;
     
     // wrap is whether sshift > rd.
@@ -387,5 +416,5 @@ template<class vobj> void Cshift_local(Lattice<vobj> &ret,const Lattice<vobj> &r
   
   }
 }
-}
-#endif
+NAMESPACE_END(Grid);
+

Grid/cshift/Cshift_mpi.h

@@ -1,4 +1,4 @@
-    /*************************************************************************************
+/*************************************************************************************
 
     Grid physics library, www.github.com/paboyle/Grid 
 
@@ -24,33 +24,33 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
     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 */
+*************************************************************************************/
+/*  END LEGAL */
 #ifndef _GRID_CSHIFT_MPI_H_
 #define _GRID_CSHIFT_MPI_H_
 
 
-namespace Grid { 
+NAMESPACE_BEGIN(Grid); 
 
 template<class vobj> Lattice<vobj> Cshift(const Lattice<vobj> &rhs,int dimension,int shift)
 {
   typedef typename vobj::vector_type vector_type;
   typedef typename vobj::scalar_type scalar_type;
 
-  Lattice<vobj> ret(rhs._grid); 
+  Lattice<vobj> ret(rhs.Grid()); 
   
-  int fd = rhs._grid->_fdimensions[dimension];
-  int rd = rhs._grid->_rdimensions[dimension];
+  int fd = rhs.Grid()->_fdimensions[dimension];
+  int rd = rhs.Grid()->_rdimensions[dimension];
 
   // Map to always positive shift modulo global full dimension.
   shift = (shift+fd)%fd;
 
-  ret.checkerboard = rhs._grid->CheckerBoardDestination(rhs.checkerboard,shift,dimension);
+  ret.Checkerboard() = rhs.Grid()->CheckerBoardDestination(rhs.Checkerboard(),shift,dimension);
         
   // the permute type
-  int simd_layout     = rhs._grid->_simd_layout[dimension];
-  int comm_dim        = rhs._grid->_processors[dimension] >1 ;
-  int splice_dim      = rhs._grid->_simd_layout[dimension]>1 && (comm_dim);
+  int simd_layout     = rhs.Grid()->_simd_layout[dimension];
+  int comm_dim        = rhs.Grid()->_processors[dimension] >1 ;
+  int splice_dim      = rhs.Grid()->_simd_layout[dimension]>1 && (comm_dim);
 
 
   if ( !comm_dim ) {
@@ -70,10 +70,10 @@ template<class vobj> void Cshift_comms(Lattice<vobj>& ret,const Lattice<vobj> &r
 {
   int sshift[2];
 
-  sshift[0] = rhs._grid->CheckerBoardShiftForCB(rhs.checkerboard,dimension,shift,Even);
-  sshift[1] = rhs._grid->CheckerBoardShiftForCB(rhs.checkerboard,dimension,shift,Odd);
+  sshift[0] = rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,Even);
+  sshift[1] = rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,Odd);
 
-  //  std::cout << "Cshift_comms dim "<<dimension<<"cb "<<rhs.checkerboard<<"shift "<<shift<<" sshift " << sshift[0]<<" "<<sshift[1]<<std::endl;
+  //  std::cout << "Cshift_comms dim "<<dimension<<"cb "<<rhs.Checkerboard()<<"shift "<<shift<<" sshift " << sshift[0]<<" "<<sshift[1]<<std::endl;
   if ( sshift[0] == sshift[1] ) {
     //    std::cout << "Single pass Cshift_comms" <<std::endl;
     Cshift_comms(ret,rhs,dimension,shift,0x3);
@@ -88,8 +88,8 @@ template<class vobj> void Cshift_comms_simd(Lattice<vobj>& ret,const Lattice<vob
 {
   int sshift[2];
 
-  sshift[0] = rhs._grid->CheckerBoardShiftForCB(rhs.checkerboard,dimension,shift,Even);
-  sshift[1] = rhs._grid->CheckerBoardShiftForCB(rhs.checkerboard,dimension,shift,Odd);
+  sshift[0] = rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,Even);
+  sshift[1] = rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,Odd);
 
   //std::cout << "Cshift_comms_simd dim "<<dimension<<"cb "<<rhs.checkerboard<<"shift "<<shift<<" sshift " << sshift[0]<<" "<<sshift[1]<<std::endl;
   if ( sshift[0] == sshift[1] ) {
@@ -107,25 +107,25 @@ template<class vobj> void Cshift_comms(Lattice<vobj> &ret,const Lattice<vobj> &r
   typedef typename vobj::vector_type vector_type;
   typedef typename vobj::scalar_type scalar_type;
 
-  GridBase *grid=rhs._grid;
-  Lattice<vobj> temp(rhs._grid);
+  GridBase *grid=rhs.Grid();
+  Lattice<vobj> temp(rhs.Grid());
 
-  int fd              = rhs._grid->_fdimensions[dimension];
-  int rd              = rhs._grid->_rdimensions[dimension];
-  int pd              = rhs._grid->_processors[dimension];
-  int simd_layout     = rhs._grid->_simd_layout[dimension];
-  int comm_dim        = rhs._grid->_processors[dimension] >1 ;
+  int fd              = rhs.Grid()->_fdimensions[dimension];
+  int rd              = rhs.Grid()->_rdimensions[dimension];
+  int pd              = rhs.Grid()->_processors[dimension];
+  int simd_layout     = rhs.Grid()->_simd_layout[dimension];
+  int comm_dim        = rhs.Grid()->_processors[dimension] >1 ;
   assert(simd_layout==1);
   assert(comm_dim==1);
   assert(shift>=0);
   assert(shift<fd);
   
-  int buffer_size = rhs._grid->_slice_nblock[dimension]*rhs._grid->_slice_block[dimension];
+  int buffer_size = rhs.Grid()->_slice_nblock[dimension]*rhs.Grid()->_slice_block[dimension];
   commVector<vobj> send_buf(buffer_size);
   commVector<vobj> recv_buf(buffer_size);
 
   int cb= (cbmask==0x2)? Odd : Even;
-  int sshift= rhs._grid->CheckerBoardShiftForCB(rhs.checkerboard,dimension,shift,cb);
+  int sshift= rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,cb);
 
   for(int x=0;x<rd;x++){       
 
@@ -145,7 +145,7 @@ template<class vobj> void Cshift_comms(Lattice<vobj> &ret,const Lattice<vobj> &r
 
       Gather_plane_simple (rhs,send_buf,dimension,sx,cbmask);
 
-      int rank           = grid->_processor;
+      //      int rank           = grid->_processor;
       int recv_from_rank;
       int xmit_to_rank;
       grid->ShiftedRanks(dimension,comm_proc,xmit_to_rank,recv_from_rank);
@@ -165,7 +165,7 @@ template<class vobj> void Cshift_comms(Lattice<vobj> &ret,const Lattice<vobj> &r
 
 template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vobj> &rhs,int dimension,int shift,int cbmask)
 {
-  GridBase *grid=rhs._grid;
+  GridBase *grid=rhs.Grid();
   const int Nsimd = grid->Nsimd();
   typedef typename vobj::vector_type vector_type;
   typedef typename vobj::scalar_object scalar_object;
@@ -193,21 +193,21 @@ template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vo
   // Simd direction uses an extract/merge pair
   ///////////////////////////////////////////////
   int buffer_size = grid->_slice_nblock[dimension]*grid->_slice_block[dimension];
-  int words = sizeof(vobj)/sizeof(vector_type);
+  //  int words = sizeof(vobj)/sizeof(vector_type);
 
   std::vector<commVector<scalar_object> >   send_buf_extract(Nsimd,commVector<scalar_object>(buffer_size) );
   std::vector<commVector<scalar_object> >   recv_buf_extract(Nsimd,commVector<scalar_object>(buffer_size) );
 
   int bytes = buffer_size*sizeof(scalar_object);
 
-  std::vector<scalar_object *>  pointers(Nsimd); // 
-  std::vector<scalar_object *> rpointers(Nsimd); // received pointers
+  ExtractPointerArray<scalar_object>  pointers(Nsimd); // 
+  ExtractPointerArray<scalar_object> rpointers(Nsimd); // received pointers
 
   ///////////////////////////////////////////
   // Work out what to send where
   ///////////////////////////////////////////
   int cb    = (cbmask==0x2)? Odd : Even;
-  int sshift= grid->CheckerBoardShiftForCB(rhs.checkerboard,dimension,shift,cb);
+  int sshift= grid->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,cb);
 
   // loop over outer coord planes orthog to dim
   for(int x=0;x<rd;x++){       
@@ -257,6 +257,8 @@ template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vo
     Scatter_plane_merge(ret,rpointers,dimension,x,cbmask);
   }
 
- }
 }
+
+NAMESPACE_END(Grid); 
+
 #endif

Grid/cshift/Cshift_none.h

@@ -1,4 +1,4 @@
-    /*************************************************************************************
+/*************************************************************************************
 
     Grid physics library, www.github.com/paboyle/Grid 
 
@@ -23,17 +23,18 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     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 */
+*************************************************************************************/
+/*  END LEGAL */
 #ifndef _GRID_CSHIFT_NONE_H_
 #define _GRID_CSHIFT_NONE_H_
-namespace Grid {
+NAMESPACE_BEGIN(Grid);
 template<class vobj> Lattice<vobj> Cshift(const Lattice<vobj> &rhs,int dimension,int shift)
 {
-  Lattice<vobj> ret(rhs._grid);
-  ret.checkerboard = rhs._grid->CheckerBoardDestination(rhs.checkerboard,shift,dimension);
+  Lattice<vobj> ret(rhs.Grid());
+  ret.Checkerboard() = rhs.Grid()->CheckerBoardDestination(rhs.Checkerboard(),shift,dimension);
   Cshift_local(ret,rhs,dimension,shift);
   return ret;
 }
-}
+NAMESPACE_END(Grid);
+
 #endif

Grid/cshift/Cshift_table.cc

@@ -0,0 +1,4 @@
+#include <Grid/GridCore.h>       
+NAMESPACE_BEGIN(Grid);
+Vector<std::pair<int,int> > Cshift_table; 
+NAMESPACE_END(Grid);

Grid/lattice/Lattice.h

@@ -2,7 +2,7 @@
 
     Grid physics library, www.github.com/paboyle/Grid 
 
-    Source file: ./lib/lattice/Lattice_coordinate.h
+    Source file: ./lib/Lattice.h
 
     Copyright (C) 2015
 
@@ -25,32 +25,24 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     See the full license in the file "LICENSE" in the top level distribution directory
     *************************************************************************************/
     /*  END LEGAL */
-#ifndef GRID_LATTICE_COORDINATE_H
-#define GRID_LATTICE_COORDINATE_H
-
-namespace Grid {
-
-    template<class iobj> inline void LatticeCoordinate(Lattice<iobj> &l,int mu)
-    {
-      typedef typename iobj::scalar_type scalar_type;
-      typedef typename iobj::vector_type vector_type;
-
-      GridBase *grid = l._grid;
-      int Nsimd = grid->iSites();
-
-      std::vector<int> gcoor;
-      std::vector<scalar_type> mergebuf(Nsimd);
-
-      vector_type vI;
-      for(int o=0;o<grid->oSites();o++){
-	for(int i=0;i<grid->iSites();i++){
-	  grid->RankIndexToGlobalCoor(grid->ThisRank(),o,i,gcoor);
-	  mergebuf[i]=(Integer)gcoor[mu];
-	}
-	merge<vector_type,scalar_type>(vI,mergebuf);
-	l._odata[o]=vI;
-      }
-    };
-
-}
-#endif
+#pragma once
+#include <Grid/lattice/Lattice_view.h>
+#include <Grid/lattice/Lattice_base.h>
+#include <Grid/lattice/Lattice_conformable.h>
+#include <Grid/lattice/Lattice_ET.h>
+#include <Grid/lattice/Lattice_arith.h>
+#include <Grid/lattice/Lattice_trace.h>
+#include <Grid/lattice/Lattice_transpose.h>
+#include <Grid/lattice/Lattice_local.h>
+#include <Grid/lattice/Lattice_reduction.h>
+#include <Grid/lattice/Lattice_peekpoke.h>
+//#include <Grid/lattice/Lattice_reality.h>
+#include <Grid/lattice/Lattice_real_imag.h>
+#include <Grid/lattice/Lattice_comparison_utils.h>
+#include <Grid/lattice/Lattice_comparison.h>
+#include <Grid/lattice/Lattice_coordinate.h>
+//#include <Grid/lattice/Lattice_where.h>
+#include <Grid/lattice/Lattice_rng.h>
+#include <Grid/lattice/Lattice_unary.h>
+#include <Grid/lattice/Lattice_transfer.h>
+#include <Grid/lattice/Lattice_basis.h>

Grid/lattice/Lattice_ET.h

@@ -0,0 +1,538 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/lattice/Lattice_ET.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: Christoph Lehner <christoph@lhnr.de
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+			   /*  END LEGAL */
+#ifndef GRID_LATTICE_ET_H
+#define GRID_LATTICE_ET_H
+
+#include <iostream>
+#include <tuple>
+#include <typeinfo>
+#include <vector>
+
+NAMESPACE_BEGIN(Grid);
+
+////////////////////////////////////////////////////
+// Predicated where support
+////////////////////////////////////////////////////
+#ifdef GRID_SIMT
+// drop to scalar in SIMT; cleaner in fact
+template <class iobj, class vobj, class robj>
+accelerator_inline vobj predicatedWhere(const iobj &predicate, 
+					const vobj &iftrue, 
+					const robj &iffalse) 
+{
+  Integer mask = TensorRemove(predicate);
+  typename std::remove_const<vobj>::type ret= iffalse;
+  if (mask) ret=iftrue;
+  return ret;
+}
+#else
+template <class iobj, class vobj, class robj>
+accelerator_inline vobj predicatedWhere(const iobj &predicate, 
+					const vobj &iftrue, 
+					const robj &iffalse) 
+{
+  typename std::remove_const<vobj>::type ret;
+
+  typedef typename vobj::scalar_object scalar_object;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  const int Nsimd = vobj::vector_type::Nsimd();
+
+  ExtractBuffer<Integer> mask(Nsimd);
+  ExtractBuffer<scalar_object> truevals(Nsimd);
+  ExtractBuffer<scalar_object> falsevals(Nsimd);
+
+  extract(iftrue, truevals);
+  extract(iffalse, falsevals);
+  extract<vInteger, Integer>(TensorRemove(predicate), mask);
+
+  for (int s = 0; s < Nsimd; s++) {
+    if (mask[s]) falsevals[s] = truevals[s];
+  }
+
+  merge(ret, falsevals);
+  return ret;
+}
+#endif
+
+/////////////////////////////////////////////////////
+//Specialization of getVectorType for lattices
+/////////////////////////////////////////////////////
+template<typename T>
+struct getVectorType<Lattice<T> >{
+  typedef typename Lattice<T>::vector_object type;
+};
+
+////////////////////////////////////////////
+//--  recursive evaluation of expressions; --
+// handle leaves of syntax tree
+///////////////////////////////////////////////////
+template<class sobj,
+  typename std::enable_if<!is_lattice<sobj>::value&&!is_lattice_expr<sobj>::value,sobj>::type * = nullptr> 
+accelerator_inline 
+sobj eval(const uint64_t ss, const sobj &arg)
+{
+  return arg;
+}
+template <class lobj> accelerator_inline 
+auto eval(const uint64_t ss, const LatticeView<lobj> &arg) -> decltype(arg(ss))
+{
+  return arg(ss);
+}
+
+////////////////////////////////////////////
+//--  recursive evaluation of expressions; --
+// whole vector return, used only for expression return type inference
+///////////////////////////////////////////////////
+template<class sobj> accelerator_inline 
+sobj vecEval(const uint64_t ss, const sobj &arg)
+{
+  return arg;
+}
+template <class lobj> accelerator_inline 
+const lobj & vecEval(const uint64_t ss, const LatticeView<lobj> &arg) 
+{
+  return arg[ss];
+}
+
+///////////////////////////////////////////////////
+// handle nodes in syntax tree- eval one operand
+// vecEval needed (but never called as all expressions offloaded) to infer the return type
+// in SIMT contexts of closure.
+///////////////////////////////////////////////////
+template <typename Op, typename T1> accelerator_inline 
+auto vecEval(const uint64_t ss, const LatticeUnaryExpression<Op, T1> &expr)  
+  -> decltype(expr.op.func( vecEval(ss, expr.arg1)))
+{
+  return expr.op.func( vecEval(ss, expr.arg1) );
+}
+// vecEval two operands
+template <typename Op, typename T1, typename T2> accelerator_inline
+auto vecEval(const uint64_t ss, const LatticeBinaryExpression<Op, T1, T2> &expr)  
+  -> decltype(expr.op.func( vecEval(ss,expr.arg1),vecEval(ss,expr.arg2)))
+{
+  return expr.op.func( vecEval(ss,expr.arg1), vecEval(ss,expr.arg2) );
+}
+// vecEval three operands
+template <typename Op, typename T1, typename T2, typename T3> accelerator_inline
+auto vecEval(const uint64_t ss, const LatticeTrinaryExpression<Op, T1, T2, T3> &expr)  
+  -> decltype(expr.op.func(vecEval(ss, expr.arg1), vecEval(ss, expr.arg2), vecEval(ss, expr.arg3)))
+{
+  return expr.op.func(vecEval(ss, expr.arg1), vecEval(ss, expr.arg2), vecEval(ss, expr.arg3));
+}
+
+///////////////////////////////////////////////////
+// handle nodes in syntax tree- eval one operand coalesced
+///////////////////////////////////////////////////
+template <typename Op, typename T1> accelerator_inline 
+auto eval(const uint64_t ss, const LatticeUnaryExpression<Op, T1> &expr)  
+  -> decltype(expr.op.func( eval(ss, expr.arg1)))
+{
+  return expr.op.func( eval(ss, expr.arg1) );
+}
+// eval two operands
+template <typename Op, typename T1, typename T2> accelerator_inline
+auto eval(const uint64_t ss, const LatticeBinaryExpression<Op, T1, T2> &expr)  
+  -> decltype(expr.op.func( eval(ss,expr.arg1),eval(ss,expr.arg2)))
+{
+  return expr.op.func( eval(ss,expr.arg1), eval(ss,expr.arg2) );
+}
+// eval three operands
+template <typename Op, typename T1, typename T2, typename T3> accelerator_inline
+auto eval(const uint64_t ss, const LatticeTrinaryExpression<Op, T1, T2, T3> &expr)  
+  -> decltype(expr.op.func(eval(ss, expr.arg1), 
+			   eval(ss, expr.arg2), 
+			   eval(ss, expr.arg3)))
+{
+#ifdef GRID_SIMT
+  // Handles Nsimd (vInteger) != Nsimd(ComplexD)
+  typedef decltype(vecEval(ss, expr.arg2)) rvobj;
+  typedef typename std::remove_reference<rvobj>::type vobj;
+
+  const int Nsimd = vobj::vector_type::Nsimd();
+
+  auto vpred = vecEval(ss,expr.arg1);
+
+  ExtractBuffer<Integer> mask(Nsimd);
+  extract<vInteger, Integer>(TensorRemove(vpred), mask);
+
+  int s = acceleratorSIMTlane(Nsimd);
+  return expr.op.func(mask[s],
+		      eval(ss, expr.arg2), 
+		      eval(ss, expr.arg3));
+#else
+  return expr.op.func(eval(ss, expr.arg1),
+		      eval(ss, expr.arg2), 
+		      eval(ss, expr.arg3));
+#endif
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Obtain the grid from an expression, ensuring conformable. This must follow a
+// tree recursion; must retain grid pointer in the LatticeView class which sucks
+// Use a different method, and make it void *.
+// Perhaps a conformable method.
+//////////////////////////////////////////////////////////////////////////
+template <class T1,typename std::enable_if<is_lattice<T1>::value, T1>::type * = nullptr>
+accelerator_inline void GridFromExpression(GridBase *&grid, const T1 &lat)  // Lattice leaf
+{
+  lat.Conformable(grid);
+}
+
+template <class T1,typename std::enable_if<!is_lattice<T1>::value, T1>::type * = nullptr>
+accelerator_inline 
+void GridFromExpression(GridBase *&grid,const T1 &notlat)  // non-lattice leaf
+{}
+
+template <typename Op, typename T1>
+accelerator_inline 
+void GridFromExpression(GridBase *&grid,const LatticeUnaryExpression<Op, T1> &expr) 
+{
+  GridFromExpression(grid, expr.arg1);  // recurse
+}
+
+template <typename Op, typename T1, typename T2>
+accelerator_inline 
+void GridFromExpression(GridBase *&grid, const LatticeBinaryExpression<Op, T1, T2> &expr) 
+{
+  GridFromExpression(grid, expr.arg1);  // recurse
+  GridFromExpression(grid, expr.arg2);
+}
+template <typename Op, typename T1, typename T2, typename T3>
+accelerator_inline 
+void GridFromExpression(GridBase *&grid, const LatticeTrinaryExpression<Op, T1, T2, T3> &expr) 
+{
+  GridFromExpression(grid, expr.arg1);  // recurse
+  GridFromExpression(grid, expr.arg2);  // recurse
+  GridFromExpression(grid, expr.arg3);  // recurse
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Obtain the CB from an expression, ensuring conformable. This must follow a
+// tree recursion
+//////////////////////////////////////////////////////////////////////////
+template <class T1,typename std::enable_if<is_lattice<T1>::value, T1>::type * = nullptr>
+inline void CBFromExpression(int &cb, const T1 &lat)  // Lattice leaf
+{
+  if ((cb == Odd) || (cb == Even)) {
+    assert(cb == lat.Checkerboard());
+  }
+  cb = lat.Checkerboard();
+}
+template <class T1,typename std::enable_if<!is_lattice<T1>::value, T1>::type * = nullptr>
+inline void CBFromExpression(int &cb, const T1 &notlat) {} // non-lattice leaf
+template <typename Op, typename T1> inline 
+void CBFromExpression(int &cb,const LatticeUnaryExpression<Op, T1> &expr) 
+{
+  CBFromExpression(cb, expr.arg1);  // recurse AST
+}
+template <typename Op, typename T1, typename T2> inline 
+void CBFromExpression(int &cb,const LatticeBinaryExpression<Op, T1, T2> &expr) 
+{
+  CBFromExpression(cb, expr.arg1);  // recurse AST
+  CBFromExpression(cb, expr.arg2);  // recurse AST
+}
+template <typename Op, typename T1, typename T2, typename T3>
+inline void CBFromExpression(int &cb, const LatticeTrinaryExpression<Op, T1, T2, T3> &expr) 
+{
+  CBFromExpression(cb, expr.arg1);  // recurse AST
+  CBFromExpression(cb, expr.arg2);  // recurse AST
+  CBFromExpression(cb, expr.arg3);  // recurse AST
+}
+
+
+//////////////////////////////////////////////////////////////////////////
+// ViewOpen
+//////////////////////////////////////////////////////////////////////////
+template <class T1,typename std::enable_if<is_lattice<T1>::value, T1>::type * = nullptr>
+inline void ExpressionViewOpen(T1 &lat)  // Lattice leaf
+{
+  lat.ViewOpen(AcceleratorRead);
+}
+template <class T1,typename std::enable_if<!is_lattice<T1>::value, T1>::type * = nullptr>
+  inline void ExpressionViewOpen(T1 &notlat) {}
+
+template <typename Op, typename T1> inline 
+void ExpressionViewOpen(LatticeUnaryExpression<Op, T1> &expr) 
+{  
+  ExpressionViewOpen(expr.arg1); // recurse AST
+}
+
+template <typename Op, typename T1, typename T2> inline 
+void ExpressionViewOpen(LatticeBinaryExpression<Op, T1, T2> &expr) 
+{
+  ExpressionViewOpen(expr.arg1);  // recurse AST
+  ExpressionViewOpen(expr.arg2);  // rrecurse AST
+}
+template <typename Op, typename T1, typename T2, typename T3>
+inline void ExpressionViewOpen(LatticeTrinaryExpression<Op, T1, T2, T3> &expr) 
+{
+  ExpressionViewOpen(expr.arg1);  // recurse AST
+  ExpressionViewOpen(expr.arg2);  // recurse AST
+  ExpressionViewOpen(expr.arg3);  // recurse AST
+}
+
+//////////////////////////////////////////////////////////////////////////
+// ViewClose
+//////////////////////////////////////////////////////////////////////////
+template <class T1,typename std::enable_if<is_lattice<T1>::value, T1>::type * = nullptr>
+inline void ExpressionViewClose( T1 &lat)  // Lattice leaf
+{
+  lat.ViewClose();
+}
+template <class T1,typename std::enable_if<!is_lattice<T1>::value, T1>::type * = nullptr>
+inline void ExpressionViewClose(T1 &notlat) {}
+
+template <typename Op, typename T1> inline 
+void ExpressionViewClose(LatticeUnaryExpression<Op, T1> &expr) 
+{  
+  ExpressionViewClose(expr.arg1); // recurse AST
+}
+template <typename Op, typename T1, typename T2> inline 
+void ExpressionViewClose(LatticeBinaryExpression<Op, T1, T2> &expr) 
+{
+  ExpressionViewClose(expr.arg1);  // recurse AST
+  ExpressionViewClose(expr.arg2);  // recurse AST
+}
+template <typename Op, typename T1, typename T2, typename T3>
+inline void ExpressionViewClose(LatticeTrinaryExpression<Op, T1, T2, T3> &expr) 
+{
+  ExpressionViewClose(expr.arg1);  // recurse AST
+  ExpressionViewClose(expr.arg2);  // recurse AST
+  ExpressionViewClose(expr.arg3);  // recurse AST
+}
+
+////////////////////////////////////////////
+// Unary operators and funcs
+////////////////////////////////////////////
+#define GridUnopClass(name, ret)					\
+  struct name {								\
+    template<class _arg> static auto accelerator_inline func(const _arg a) -> decltype(ret) { return ret; } \
+  };
+
+GridUnopClass(UnarySub, -a);
+GridUnopClass(UnaryNot, Not(a));
+GridUnopClass(UnaryAdj, adj(a));
+GridUnopClass(UnaryConj, conjugate(a));
+GridUnopClass(UnaryTrace, trace(a));
+GridUnopClass(UnaryTranspose, transpose(a));
+GridUnopClass(UnaryTa, Ta(a));
+GridUnopClass(UnaryProjectOnGroup, ProjectOnGroup(a));
+GridUnopClass(UnaryToReal, toReal(a));
+GridUnopClass(UnaryToComplex, toComplex(a));
+GridUnopClass(UnaryTimesI, timesI(a));
+GridUnopClass(UnaryTimesMinusI, timesMinusI(a));
+GridUnopClass(UnaryAbs, abs(a));
+GridUnopClass(UnarySqrt, sqrt(a));
+GridUnopClass(UnaryRsqrt, rsqrt(a));
+GridUnopClass(UnarySin, sin(a));
+GridUnopClass(UnaryCos, cos(a));
+GridUnopClass(UnaryAsin, asin(a));
+GridUnopClass(UnaryAcos, acos(a));
+GridUnopClass(UnaryLog, log(a));
+GridUnopClass(UnaryExp, exp(a));
+
+////////////////////////////////////////////
+// Binary operators
+////////////////////////////////////////////
+#define GridBinOpClass(name, combination)			\
+  struct name {							\
+    template <class _left, class _right>			\
+    static auto accelerator_inline				\
+    func(const _left &lhs, const _right &rhs)			\
+      -> decltype(combination) const				\
+    {								\
+      return combination;					\
+    }								\
+  };
+
+GridBinOpClass(BinaryAdd, lhs + rhs);
+GridBinOpClass(BinarySub, lhs - rhs);
+GridBinOpClass(BinaryMul, lhs *rhs);
+GridBinOpClass(BinaryDiv, lhs /rhs);
+GridBinOpClass(BinaryAnd, lhs &rhs);
+GridBinOpClass(BinaryOr, lhs | rhs);
+GridBinOpClass(BinaryAndAnd, lhs &&rhs);
+GridBinOpClass(BinaryOrOr, lhs || rhs);
+
+////////////////////////////////////////////////////
+// Trinary conditional op
+////////////////////////////////////////////////////
+#define GridTrinOpClass(name, combination)				\
+  struct name {								\
+    template <class _predicate,class _left, class _right>		\
+    static auto accelerator_inline					\
+    func(const _predicate &pred, const _left &lhs, const _right &rhs)	\
+      -> decltype(combination) const					\
+    {									\
+      return combination;						\
+    }									\
+  };
+
+GridTrinOpClass(TrinaryWhere,
+		(predicatedWhere<
+		 typename std::remove_reference<_predicate>::type, 
+		 typename std::remove_reference<_left>::type,
+		 typename std::remove_reference<_right>::type>(pred, lhs,rhs)));
+
+////////////////////////////////////////////
+// Operator syntactical glue
+////////////////////////////////////////////
+#define GRID_UNOP(name)   name
+#define GRID_BINOP(name)  name
+#define GRID_TRINOP(name) name
+
+#define GRID_DEF_UNOP(op, name)						\
+  template <typename T1, typename std::enable_if<is_lattice<T1>::value||is_lattice_expr<T1>::value,T1>::type * = nullptr> \
+  inline auto op(const T1 &arg) ->decltype(LatticeUnaryExpression<GRID_UNOP(name),T1>(GRID_UNOP(name)(), arg)) \
+  {									\
+    return     LatticeUnaryExpression<GRID_UNOP(name),T1>(GRID_UNOP(name)(), arg); \
+  }
+
+#define GRID_BINOP_LEFT(op, name)					\
+  template <typename T1, typename T2,					\
+            typename std::enable_if<is_lattice<T1>::value||is_lattice_expr<T1>::value,T1>::type * = nullptr> \
+  inline auto op(const T1 &lhs, const T2 &rhs)				\
+    ->decltype(LatticeBinaryExpression<GRID_BINOP(name),T1,T2>(GRID_BINOP(name)(),lhs,rhs)) \
+  {									\
+    return     LatticeBinaryExpression<GRID_BINOP(name),T1,T2>(GRID_BINOP(name)(),lhs,rhs);\
+  }
+
+#define GRID_BINOP_RIGHT(op, name)					\
+  template <typename T1, typename T2,					\
+            typename std::enable_if<!is_lattice<T1>::value&&!is_lattice_expr<T1>::value,T1>::type * = nullptr, \
+            typename std::enable_if< is_lattice<T2>::value|| is_lattice_expr<T2>::value,T2>::type * = nullptr> \
+  inline auto op(const T1 &lhs, const T2 &rhs)				\
+    ->decltype(LatticeBinaryExpression<GRID_BINOP(name),T1,T2>(GRID_BINOP(name)(),lhs, rhs)) \
+  {									\
+    return     LatticeBinaryExpression<GRID_BINOP(name),T1,T2>(GRID_BINOP(name)(),lhs, rhs); \
+  }
+
+#define GRID_DEF_BINOP(op, name)		\
+  GRID_BINOP_LEFT(op, name);			\
+  GRID_BINOP_RIGHT(op, name);
+
+#define GRID_DEF_TRINOP(op, name)					\
+  template <typename T1, typename T2, typename T3>			\
+  inline auto op(const T1 &pred, const T2 &lhs, const T3 &rhs)		\
+    ->decltype(LatticeTrinaryExpression<GRID_TRINOP(name),T1,T2,T3>(GRID_TRINOP(name)(),pred, lhs, rhs)) \
+  {									\
+    return LatticeTrinaryExpression<GRID_TRINOP(name),T1,T2,T3>(GRID_TRINOP(name)(),pred, lhs, rhs); \
+  }
+
+////////////////////////
+// Operator definitions
+////////////////////////
+GRID_DEF_UNOP(operator-, UnarySub);
+GRID_DEF_UNOP(Not, UnaryNot);
+GRID_DEF_UNOP(operator!, UnaryNot);
+GRID_DEF_UNOP(adj, UnaryAdj);
+GRID_DEF_UNOP(conjugate, UnaryConj);
+GRID_DEF_UNOP(trace, UnaryTrace);
+GRID_DEF_UNOP(transpose, UnaryTranspose);
+GRID_DEF_UNOP(Ta, UnaryTa);
+GRID_DEF_UNOP(ProjectOnGroup, UnaryProjectOnGroup);
+GRID_DEF_UNOP(toReal, UnaryToReal);
+GRID_DEF_UNOP(toComplex, UnaryToComplex);
+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
+                               // abs-fabs-dabs-labs thing
+GRID_DEF_UNOP(sqrt, UnarySqrt);
+GRID_DEF_UNOP(rsqrt, UnaryRsqrt);
+GRID_DEF_UNOP(sin, UnarySin);
+GRID_DEF_UNOP(cos, UnaryCos);
+GRID_DEF_UNOP(asin, UnaryAsin);
+GRID_DEF_UNOP(acos, UnaryAcos);
+GRID_DEF_UNOP(log, UnaryLog);
+GRID_DEF_UNOP(exp, UnaryExp);
+
+GRID_DEF_BINOP(operator+, BinaryAdd);
+GRID_DEF_BINOP(operator-, BinarySub);
+GRID_DEF_BINOP(operator*, BinaryMul);
+GRID_DEF_BINOP(operator/, BinaryDiv);
+
+GRID_DEF_BINOP(operator&, BinaryAnd);
+GRID_DEF_BINOP(operator|, BinaryOr);
+GRID_DEF_BINOP(operator&&, BinaryAndAnd);
+GRID_DEF_BINOP(operator||, BinaryOrOr);
+
+GRID_DEF_TRINOP(where, TrinaryWhere);
+
+/////////////////////////////////////////////////////////////
+// Closure convenience to force expression to evaluate
+/////////////////////////////////////////////////////////////
+template <class Op, class T1>
+auto closure(const LatticeUnaryExpression<Op, T1> &expr)
+  -> Lattice<decltype(expr.op.func(vecEval(0, expr.arg1)))> 
+{
+  Lattice<decltype(expr.op.func(vecEval(0, expr.arg1)))> ret(expr);
+  return ret;
+}
+template <class Op, class T1, class T2>
+auto closure(const LatticeBinaryExpression<Op, T1, T2> &expr)
+  -> Lattice<decltype(expr.op.func(vecEval(0, expr.arg1),vecEval(0, expr.arg2)))> 
+{
+  Lattice<decltype(expr.op.func(vecEval(0, expr.arg1),vecEval(0, expr.arg2)))> ret(expr);
+  return ret;
+}
+template <class Op, class T1, class T2, class T3>
+auto closure(const LatticeTrinaryExpression<Op, T1, T2, T3> &expr)
+  -> Lattice<decltype(expr.op.func(vecEval(0, expr.arg1),
+				   vecEval(0, expr.arg2),
+				   vecEval(0, expr.arg3)))> 
+{
+  Lattice<decltype(expr.op.func(vecEval(0, expr.arg1),
+				vecEval(0, expr.arg2),
+			        vecEval(0, expr.arg3)))>  ret(expr);
+  return ret;
+}
+#define EXPRESSION_CLOSURE(function)					\
+  template<class Expression,typename std::enable_if<is_lattice_expr<Expression>::value,void>::type * = nullptr> \
+    auto function(Expression &expr) -> decltype(function(closure(expr))) \
+  {									\
+    return function(closure(expr));					\
+  }
+
+
+#undef GRID_UNOP
+#undef GRID_BINOP
+#undef GRID_TRINOP
+
+#undef GRID_DEF_UNOP
+#undef GRID_DEF_BINOP
+#undef GRID_DEF_TRINOP
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/lattice/Lattice_arith.h

@@ -0,0 +1,258 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_arith.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: Christoph Lehner <christoph@lhnr.de>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LATTICE_ARITH_H
+#define GRID_LATTICE_ARITH_H
+
+NAMESPACE_BEGIN(Grid);
+
+//////////////////////////////////////////////////////////////////////////////////////////////////////
+//  avoid copy back routines for mult, mac, sub, add
+//////////////////////////////////////////////////////////////////////////////////////////////////////
+template<class obj1,class obj2,class obj3> inline
+void mult(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  autoView( ret_v , ret, AcceleratorWrite);
+  autoView( lhs_v , lhs, AcceleratorRead);
+  autoView( rhs_v , rhs, AcceleratorRead);
+  conformable(ret,rhs);
+  conformable(lhs,rhs);
+  accelerator_for(ss,lhs_v.size(),obj1::Nsimd(),{
+    decltype(coalescedRead(obj1())) tmp;
+    auto lhs_t = lhs_v(ss);
+    auto rhs_t = rhs_v(ss);
+    mult(&tmp,&lhs_t,&rhs_t);
+    coalescedWrite(ret_v[ss],tmp);
+  });
+}
+  
+template<class obj1,class obj2,class obj3> inline
+void mac(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  conformable(ret,rhs);
+  conformable(lhs,rhs);
+  autoView( ret_v , ret, AcceleratorWrite);
+  autoView( lhs_v , lhs, AcceleratorRead);
+  autoView( rhs_v , rhs, AcceleratorRead);
+  accelerator_for(ss,lhs_v.size(),obj1::Nsimd(),{
+    auto lhs_t=lhs_v(ss);
+    auto rhs_t=rhs_v(ss);
+    auto tmp  =ret_v(ss);
+    mac(&tmp,&lhs_t,&rhs_t);
+    coalescedWrite(ret_v[ss],tmp);
+  });
+}
+  
+template<class obj1,class obj2,class obj3> inline
+void sub(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  conformable(ret,rhs);
+  conformable(lhs,rhs);
+  autoView( ret_v , ret, AcceleratorWrite);
+  autoView( lhs_v , lhs, AcceleratorRead);
+  autoView( rhs_v , rhs, AcceleratorRead);
+  accelerator_for(ss,lhs_v.size(),obj1::Nsimd(),{
+    decltype(coalescedRead(obj1())) tmp;
+    auto lhs_t=lhs_v(ss);
+    auto rhs_t=rhs_v(ss);
+    sub(&tmp,&lhs_t,&rhs_t);
+    coalescedWrite(ret_v[ss],tmp);
+  });
+}
+template<class obj1,class obj2,class obj3> inline
+void add(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  conformable(ret,rhs);
+  conformable(lhs,rhs);
+  autoView( ret_v , ret, AcceleratorWrite);
+  autoView( lhs_v , lhs, AcceleratorRead);
+  autoView( rhs_v , rhs, AcceleratorRead);
+  accelerator_for(ss,lhs_v.size(),obj1::Nsimd(),{
+    decltype(coalescedRead(obj1())) tmp;
+    auto lhs_t=lhs_v(ss);
+    auto rhs_t=rhs_v(ss);
+    add(&tmp,&lhs_t,&rhs_t);
+    coalescedWrite(ret_v[ss],tmp);
+  });
+}
+  
+//////////////////////////////////////////////////////////////////////////////////////////////////////
+//  avoid copy back routines for mult, mac, sub, add
+//////////////////////////////////////////////////////////////////////////////////////////////////////
+template<class obj1,class obj2,class obj3> inline
+void mult(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const obj3 &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  conformable(lhs,ret);
+  autoView( ret_v , ret, AcceleratorWrite);
+  autoView( lhs_v , lhs, AcceleratorRead);
+  accelerator_for(ss,lhs_v.size(),obj1::Nsimd(),{
+    decltype(coalescedRead(obj1())) tmp;
+    mult(&tmp,&lhs_v(ss),&rhs);
+    coalescedWrite(ret_v[ss],tmp);
+  });
+}
+  
+template<class obj1,class obj2,class obj3> inline
+void mac(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const obj3 &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  conformable(ret,lhs);
+  autoView( ret_v , ret, AcceleratorWrite);
+  autoView( lhs_v , lhs, AcceleratorRead);
+  accelerator_for(ss,lhs_v.size(),obj1::Nsimd(),{
+    auto tmp  =ret_v(ss);
+    auto lhs_t=lhs_v(ss);
+    mac(&tmp,&lhs_t,&rhs);
+    coalescedWrite(ret_v[ss],tmp);
+  });
+}
+  
+template<class obj1,class obj2,class obj3> inline
+void sub(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const obj3 &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  conformable(ret,lhs);
+  autoView( ret_v , ret, AcceleratorWrite);
+  autoView( lhs_v , lhs, AcceleratorRead);
+  accelerator_for(ss,lhs_v.size(),obj1::Nsimd(),{
+    decltype(coalescedRead(obj1())) tmp;
+    auto lhs_t=lhs_v(ss);
+    sub(&tmp,&lhs_t,&rhs);
+    coalescedWrite(ret_v[ss],tmp);
+  });
+}
+template<class obj1,class obj2,class obj3> inline
+void add(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const obj3 &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  conformable(lhs,ret);
+  autoView( ret_v , ret, AcceleratorWrite);
+  autoView( lhs_v , lhs, AcceleratorRead);
+  accelerator_for(ss,lhs_v.size(),obj1::Nsimd(),{
+    decltype(coalescedRead(obj1())) tmp;
+    auto lhs_t=lhs_v(ss);
+    add(&tmp,&lhs_t,&rhs);
+    coalescedWrite(ret_v[ss],tmp);
+  });
+}
+
+//////////////////////////////////////////////////////////////////////////////////////////////////////
+//  avoid copy back routines for mult, mac, sub, add
+//////////////////////////////////////////////////////////////////////////////////////////////////////
+template<class obj1,class obj2,class obj3> inline
+void mult(Lattice<obj1> &ret,const obj2 &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = rhs.Checkerboard();
+  conformable(ret,rhs);
+  autoView( ret_v , ret, AcceleratorWrite);
+  autoView( rhs_v , lhs, AcceleratorRead);
+  accelerator_for(ss,rhs_v.size(),obj1::Nsimd(),{
+    decltype(coalescedRead(obj1())) tmp;
+    auto rhs_t=rhs_v(ss);
+    mult(&tmp,&lhs,&rhs_t);
+    coalescedWrite(ret_v[ss],tmp);
+  });
+}
+  
+template<class obj1,class obj2,class obj3> inline
+void mac(Lattice<obj1> &ret,const obj2 &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = rhs.Checkerboard();
+  conformable(ret,rhs);
+  autoView( ret_v , ret, AcceleratorWrite);
+  autoView( rhs_v , lhs, AcceleratorRead);
+  accelerator_for(ss,rhs_v.size(),obj1::Nsimd(),{
+    auto tmp  =ret_v(ss);
+    auto rhs_t=rhs_v(ss);
+    mac(&tmp,&lhs,&rhs_t);
+    coalescedWrite(ret_v[ss],tmp);
+  });
+}
+  
+template<class obj1,class obj2,class obj3> inline
+void sub(Lattice<obj1> &ret,const obj2 &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = rhs.Checkerboard();
+  conformable(ret,rhs);
+  autoView( ret_v , ret, AcceleratorWrite);
+  autoView( rhs_v , lhs, AcceleratorRead);
+  accelerator_for(ss,rhs_v.size(),obj1::Nsimd(),{
+    decltype(coalescedRead(obj1())) tmp;
+    auto rhs_t=rhs_v(ss);
+    sub(&tmp,&lhs,&rhs_t);
+    coalescedWrite(ret_v[ss],tmp);
+  });
+}
+template<class obj1,class obj2,class obj3> inline
+void add(Lattice<obj1> &ret,const obj2 &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = rhs.Checkerboard();
+  conformable(ret,rhs);
+  autoView( ret_v , ret, AcceleratorWrite);
+  autoView( rhs_v , lhs, AcceleratorRead);
+  accelerator_for(ss,rhs_v.size(),obj1::Nsimd(),{
+    decltype(coalescedRead(obj1())) tmp;
+    auto rhs_t=rhs_v(ss);
+    add(&tmp,&lhs,&rhs_t);
+    coalescedWrite(ret_v[ss],tmp);
+  });
+}
+  
+template<class sobj,class vobj> inline
+void axpy(Lattice<vobj> &ret,sobj a,const Lattice<vobj> &x,const Lattice<vobj> &y){
+  ret.Checkerboard() = x.Checkerboard();
+  conformable(ret,x);
+  conformable(x,y);
+  autoView( ret_v , ret, AcceleratorWrite);
+  autoView( x_v , x, AcceleratorRead);
+  autoView( y_v , y, AcceleratorRead);
+  accelerator_for(ss,x_v.size(),vobj::Nsimd(),{
+    auto tmp = a*x_v(ss)+y_v(ss);
+    coalescedWrite(ret_v[ss],tmp);
+  });
+}
+template<class sobj,class vobj> inline
+void axpby(Lattice<vobj> &ret,sobj a,sobj b,const Lattice<vobj> &x,const Lattice<vobj> &y){
+  ret.Checkerboard() = x.Checkerboard();
+  conformable(ret,x);
+  conformable(x,y);
+  autoView( ret_v , ret, AcceleratorWrite);
+  autoView( x_v , x, AcceleratorRead);
+  autoView( y_v , y, AcceleratorRead);
+  accelerator_for(ss,x_v.size(),vobj::Nsimd(),{
+    auto tmp = a*x_v(ss)+b*y_v(ss);
+    coalescedWrite(ret_v[ss],tmp);
+  });
+}
+
+template<class sobj,class vobj> inline
+RealD axpy_norm(Lattice<vobj> &ret,sobj a,const Lattice<vobj> &x,const Lattice<vobj> &y)
+{
+    return axpy_norm_fast(ret,a,x,y);
+}
+template<class sobj,class vobj> inline
+RealD axpby_norm(Lattice<vobj> &ret,sobj a,sobj b,const Lattice<vobj> &x,const Lattice<vobj> &y)
+{
+    return axpby_norm_fast(ret,a,b,x,y);
+}
+
+NAMESPACE_END(Grid);
+#endif

Grid/lattice/Lattice_base.h

@@ -0,0 +1,372 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/lattice/Lattice_base.h
+
+Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+Author: Christoph Lehner <christoph@lhnr.de>
+
+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 
+
+#define STREAMING_STORES
+
+NAMESPACE_BEGIN(Grid);
+
+extern int GridCshiftPermuteMap[4][16];
+
+/////////////////////////////////////////////////////////////////////////////////////////
+// The real lattice class, with normal copy and assignment semantics.
+// This contains extra (host resident) grid pointer data that may be accessed by host code
+/////////////////////////////////////////////////////////////////////////////////////////
+template<class vobj>
+class Lattice : public LatticeAccelerator<vobj>
+{
+public:
+  GridBase *Grid(void) const { return this->_grid; }
+  ///////////////////////////////////////////////////
+  // Member types
+  ///////////////////////////////////////////////////
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+  typedef typename vobj::scalar_object scalar_object;
+  typedef vobj vector_object;
+
+private:
+  void dealloc(void)
+  {
+    if( this->_odata_size ) {
+      alignedAllocator<vobj> alloc;
+      alloc.deallocate(this->_odata,this->_odata_size);
+      this->_odata=nullptr;
+      this->_odata_size=0;
+    }
+  }
+  void resize(uint64_t size)
+  {
+    if ( this->_odata_size != size ) {
+      alignedAllocator<vobj> alloc;
+
+      dealloc();
+      
+      this->_odata_size = size;
+      if ( size )
+	this->_odata      = alloc.allocate(this->_odata_size);
+      else 
+	this->_odata      = nullptr;
+    }
+  }
+public:
+
+  /////////////////////////////////////////////////////////////////////////////////
+  // Can use to make accelerator dirty without copy from host ; useful for temporaries "dont care" prev contents
+  /////////////////////////////////////////////////////////////////////////////////
+  void SetViewMode(ViewMode mode) {
+    LatticeView<vobj> accessor(*( (LatticeAccelerator<vobj> *) this),mode);
+    accessor.ViewClose();
+  }
+  /////////////////////////////////////////////////////////////////////////////////
+  // Return a view object that may be dereferenced in site loops.
+  // The view is trivially copy constructible and may be copied to an accelerator device
+  // in device lambdas
+  /////////////////////////////////////////////////////////////////////////////////
+
+  LatticeView<vobj> View (ViewMode mode) const 
+  {
+    LatticeView<vobj> accessor(*( (LatticeAccelerator<vobj> *) this),mode);
+    return accessor;
+  }
+
+  ~Lattice() { 
+    if ( this->_odata_size ) {
+      dealloc();
+    }
+   }
+  ////////////////////////////////////////////////////////////////////////////////
+  // Expression Template closure support
+  ////////////////////////////////////////////////////////////////////////////////
+  template <typename Op, typename T1> inline Lattice<vobj> & operator=(const LatticeUnaryExpression<Op,T1> &expr)
+  {
+    GridBase *egrid(nullptr);
+    GridFromExpression(egrid,expr);
+    assert(egrid!=nullptr);
+    conformable(this->_grid,egrid);
+
+    int cb=-1;
+    CBFromExpression(cb,expr);
+    assert( (cb==Odd) || (cb==Even));
+    this->checkerboard=cb;
+    
+    auto exprCopy = expr;
+    ExpressionViewOpen(exprCopy);
+    auto me  = View(AcceleratorWriteDiscard);
+    accelerator_for(ss,me.size(),vobj::Nsimd(),{
+      auto tmp = eval(ss,exprCopy);
+      coalescedWrite(me[ss],tmp);
+    });
+    me.ViewClose();
+    ExpressionViewClose(exprCopy);
+    return *this;
+  }
+  template <typename Op, typename T1,typename T2> inline Lattice<vobj> & operator=(const LatticeBinaryExpression<Op,T1,T2> &expr)
+  {
+    GridBase *egrid(nullptr);
+    GridFromExpression(egrid,expr);
+    assert(egrid!=nullptr);
+    conformable(this->_grid,egrid);
+
+    int cb=-1;
+    CBFromExpression(cb,expr);
+    assert( (cb==Odd) || (cb==Even));
+    this->checkerboard=cb;
+
+    auto exprCopy = expr;
+    ExpressionViewOpen(exprCopy);
+    auto me  = View(AcceleratorWriteDiscard);
+    accelerator_for(ss,me.size(),vobj::Nsimd(),{
+      auto tmp = eval(ss,exprCopy);
+      coalescedWrite(me[ss],tmp);
+    });
+    me.ViewClose();
+    ExpressionViewClose(exprCopy);
+    return *this;
+  }
+  template <typename Op, typename T1,typename T2,typename T3> inline Lattice<vobj> & operator=(const LatticeTrinaryExpression<Op,T1,T2,T3> &expr)
+  {
+    GridBase *egrid(nullptr);
+    GridFromExpression(egrid,expr);
+    assert(egrid!=nullptr);
+    conformable(this->_grid,egrid);
+
+    int cb=-1;
+    CBFromExpression(cb,expr);
+    assert( (cb==Odd) || (cb==Even));
+    this->checkerboard=cb;
+    auto exprCopy = expr;
+    ExpressionViewOpen(exprCopy);
+    auto me  = View(AcceleratorWriteDiscard);
+    accelerator_for(ss,me.size(),vobj::Nsimd(),{
+      auto tmp = eval(ss,exprCopy);
+      coalescedWrite(me[ss],tmp);
+    });
+    me.ViewClose();
+    ExpressionViewClose(exprCopy);
+    return *this;
+  }
+  //GridFromExpression is tricky to do
+  template<class Op,class T1>
+  Lattice(const LatticeUnaryExpression<Op,T1> & expr) {
+    this->_grid = nullptr;
+    GridFromExpression(this->_grid,expr);
+    assert(this->_grid!=nullptr);
+
+    int cb=-1;
+    CBFromExpression(cb,expr);
+    assert( (cb==Odd) || (cb==Even));
+    this->checkerboard=cb;
+
+    resize(this->_grid->oSites());
+
+    *this = expr;
+  }
+  template<class Op,class T1, class T2>
+  Lattice(const LatticeBinaryExpression<Op,T1,T2> & expr) {
+    this->_grid = nullptr;
+    GridFromExpression(this->_grid,expr);
+    assert(this->_grid!=nullptr);
+
+    int cb=-1;
+    CBFromExpression(cb,expr);
+    assert( (cb==Odd) || (cb==Even));
+    this->checkerboard=cb;
+
+    resize(this->_grid->oSites());
+
+    *this = expr;
+  }
+  template<class Op,class T1, class T2, class T3>
+  Lattice(const LatticeTrinaryExpression<Op,T1,T2,T3> & expr) {
+    this->_grid = nullptr;
+    GridFromExpression(this->_grid,expr);
+    assert(this->_grid!=nullptr);
+
+    int cb=-1;
+    CBFromExpression(cb,expr);
+    assert( (cb==Odd) || (cb==Even));
+    this->checkerboard=cb;
+
+    resize(this->_grid->oSites());
+
+    *this = expr;
+  }
+
+  template<class sobj> inline Lattice<vobj> & operator = (const sobj & r){
+    auto me  = View(CpuWrite);
+    thread_for(ss,me.size(),{
+	me[ss]= r;
+    });
+    me.ViewClose();
+    return *this;
+  }
+
+  //////////////////////////////////////////////////////////////////
+  // Follow rule of five, with Constructor requires "grid" passed
+  // to user defined constructor
+  ///////////////////////////////////////////
+  // user defined constructor
+  ///////////////////////////////////////////
+  Lattice(GridBase *grid,ViewMode mode=AcceleratorWriteDiscard) { 
+    this->_grid = grid;
+    resize(this->_grid->oSites());
+    assert((((uint64_t)&this->_odata[0])&0xF) ==0);
+    this->checkerboard=0;
+    SetViewMode(mode);
+  }
+  
+  //  virtual ~Lattice(void) = default;
+    
+  void reset(GridBase* grid) {
+    if (this->_grid != grid) {
+      this->_grid = grid;
+      this->resize(grid->oSites());
+      this->checkerboard = 0;
+    }
+  }
+  ///////////////////////////////////////////
+  // copy constructor
+  ///////////////////////////////////////////
+  Lattice(const Lattice& r){ 
+    this->_grid = r.Grid();
+    resize(this->_grid->oSites());
+    *this = r;
+  }
+  ///////////////////////////////////////////
+  // move constructor
+  ///////////////////////////////////////////
+  Lattice(Lattice && r){ 
+    this->_grid = r.Grid();
+    this->_odata      = r._odata;
+    this->_odata_size = r._odata_size;
+    this->checkerboard= r.Checkerboard();
+    r._odata      = nullptr;
+    r._odata_size = 0;
+  }
+  ///////////////////////////////////////////
+  // assignment template
+  ///////////////////////////////////////////
+  template<class robj> inline Lattice<vobj> & operator = (const Lattice<robj> & r){
+    typename std::enable_if<!std::is_same<robj,vobj>::value,int>::type i=0;
+    conformable(*this,r);
+    this->checkerboard = r.Checkerboard();
+    auto me =   View(AcceleratorWriteDiscard);
+    auto him= r.View(AcceleratorRead);
+    accelerator_for(ss,me.size(),vobj::Nsimd(),{
+      coalescedWrite(me[ss],him(ss));
+    });
+    me.ViewClose();    him.ViewClose();
+    return *this;
+  }
+
+  ///////////////////////////////////////////
+  // Copy assignment 
+  ///////////////////////////////////////////
+  inline Lattice<vobj> & operator = (const Lattice<vobj> & r){
+    this->checkerboard = r.Checkerboard();
+    conformable(*this,r);
+    auto me =   View(AcceleratorWriteDiscard);
+    auto him= r.View(AcceleratorRead);
+    accelerator_for(ss,me.size(),vobj::Nsimd(),{
+      coalescedWrite(me[ss],him(ss));
+    });
+    me.ViewClose();    him.ViewClose();
+    return *this;
+  }
+  ///////////////////////////////////////////
+  // Move assignment possible if same type
+  ///////////////////////////////////////////
+  inline Lattice<vobj> & operator = (Lattice<vobj> && r){
+
+    resize(0); // deletes if appropriate
+    this->_grid       = r.Grid();
+    this->_odata      = r._odata;
+    this->_odata_size = r._odata_size;
+    this->checkerboard= r.Checkerboard();
+
+    r._odata      = nullptr;
+    r._odata_size = 0;
+    
+    return *this;
+  }
+
+  /////////////////////////////////////////////////////////////////////////////
+  // *=,+=,-= operators inherit behvour from correspond */+/- operation
+  /////////////////////////////////////////////////////////////////////////////
+  template<class T> inline Lattice<vobj> &operator *=(const T &r) {
+    *this = (*this)*r;
+    return *this;
+  }
+  
+  template<class T> inline Lattice<vobj> &operator -=(const T &r) {
+    *this = (*this)-r;
+    return *this;
+  }
+  template<class T> inline Lattice<vobj> &operator +=(const T &r) {
+    *this = (*this)+r;
+    return *this;
+  }
+
+  friend inline void swap(Lattice &l, Lattice &r) { 
+    conformable(l,r);
+    LatticeAccelerator<vobj> tmp;
+    LatticeAccelerator<vobj> *lp = (LatticeAccelerator<vobj> *)&l;
+    LatticeAccelerator<vobj> *rp = (LatticeAccelerator<vobj> *)&r;
+    tmp = *lp;    *lp=*rp;    *rp=tmp;
+  }
+
+}; // class Lattice
+
+template<class vobj> std::ostream& operator<< (std::ostream& stream, const Lattice<vobj> &o){
+  typedef typename vobj::scalar_object sobj;
+  for(int g=0;g<o.Grid()->_gsites;g++){
+
+    Coordinate gcoor;
+    o.Grid()->GlobalIndexToGlobalCoor(g,gcoor);
+
+    sobj ss;
+    peekSite(ss,o,gcoor);
+    stream<<"[";
+    for(int d=0;d<gcoor.size();d++){
+      stream<<gcoor[d];
+      if(d!=gcoor.size()-1) stream<<",";
+    }
+    stream<<"]\t";
+    stream<<ss<<std::endl;
+  }
+  return stream;
+}
+  
+NAMESPACE_END(Grid);
+

Grid/lattice/Lattice_basis.h

@@ -0,0 +1,246 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/lattice/Lattice_basis.h
+
+Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+Author: Christoph Lehner <christoph@lhnr.de>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+			   /*  END LEGAL */
+
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+template<class Field>
+void basisOrthogonalize(std::vector<Field> &basis,Field &w,int k) 
+{
+  // If assume basis[j] are already orthonormal,
+  // can take all inner products in parallel saving 2x bandwidth
+  // Save 3x bandwidth on the second line of loop.
+  // perhaps 2.5x speed up.
+  // 2x overall in Multigrid Lanczos  
+  for(int j=0; j<k; ++j){
+    auto ip = innerProduct(basis[j],w);
+    w = w - ip*basis[j];
+  }
+}
+
+template<class VField, class Matrix>
+void basisRotate(VField &basis,Matrix& Qt,int j0, int j1, int k0,int k1,int Nm) 
+{
+  typedef decltype(basis[0]) Field;
+  typedef decltype(basis[0].View(AcceleratorRead)) View;
+
+  Vector<View> basis_v; basis_v.reserve(basis.size());
+  typedef typename std::remove_reference<decltype(basis_v[0][0])>::type vobj;
+  typedef typename std::remove_reference<decltype(Qt(0,0))>::type Coeff_t;
+  GridBase* grid = basis[0].Grid();
+      
+  for(int k=0;k<basis.size();k++){
+    basis_v.push_back(basis[k].View(AcceleratorWrite));
+  }
+
+#if ( (!defined(GRID_SYCL)) && (!defined(GRID_CUDA)) && (!defined(GRID_HIP)) )
+  int max_threads = thread_max();
+  Vector < vobj > Bt(Nm * max_threads);
+  thread_region
+    {
+      vobj* B = &Bt[Nm * thread_num()];
+      thread_for_in_region(ss, grid->oSites(),{
+	  for(int j=j0; j<j1; ++j) B[j]=0.;
+      
+	  for(int j=j0; j<j1; ++j){
+	    for(int k=k0; k<k1; ++k){
+	      B[j] +=Qt(j,k) * basis_v[k][ss];
+	    }
+	  }
+	  for(int j=j0; j<j1; ++j){
+	    basis_v[j][ss] = B[j];
+	  }
+	});
+    }
+#else
+  View *basis_vp = &basis_v[0];
+
+  int nrot = j1-j0;
+  if (!nrot) // edge case not handled gracefully by Cuda
+    return;
+
+  uint64_t oSites   =grid->oSites();
+  uint64_t siteBlock=(grid->oSites()+nrot-1)/nrot; // Maximum 1 additional vector overhead
+
+  Vector <vobj> Bt(siteBlock * nrot); 
+  auto Bp=&Bt[0];
+
+  // GPU readable copy of matrix
+  Vector<Coeff_t> Qt_jv(Nm*Nm);
+  Coeff_t *Qt_p = & Qt_jv[0];
+  thread_for(i,Nm*Nm,{
+      int j = i/Nm;
+      int k = i%Nm;
+      Qt_p[i]=Qt(j,k);
+  });
+
+  // Block the loop to keep storage footprint down
+  for(uint64_t s=0;s<oSites;s+=siteBlock){
+
+    // remaining work in this block
+    int ssites=MIN(siteBlock,oSites-s);
+
+    // zero out the accumulators
+    accelerator_for(ss,siteBlock*nrot,vobj::Nsimd(),{
+	decltype(coalescedRead(Bp[ss])) z;
+	z=Zero();
+	coalescedWrite(Bp[ss],z);
+      });
+
+    accelerator_for(sj,ssites*nrot,vobj::Nsimd(),{
+	
+	int j =sj%nrot;
+	int jj  =j0+j;
+	int ss =sj/nrot;
+	int sss=ss+s;
+
+	for(int k=k0; k<k1; ++k){
+	  auto tmp = coalescedRead(Bp[ss*nrot+j]);
+	  coalescedWrite(Bp[ss*nrot+j],tmp+ Qt_p[jj*Nm+k] * coalescedRead(basis_v[k][sss]));
+	}
+      });
+
+    accelerator_for(sj,ssites*nrot,vobj::Nsimd(),{
+	int j =sj%nrot;
+	int jj  =j0+j;
+	int ss =sj/nrot;
+	int sss=ss+s;
+	coalescedWrite(basis_v[jj][sss],coalescedRead(Bp[ss*nrot+j]));
+      });
+  }
+#endif
+
+  for(int k=0;k<basis.size();k++) basis_v[k].ViewClose();
+}
+
+// Extract a single rotated vector
+template<class Field>
+void basisRotateJ(Field &result,std::vector<Field> &basis,Eigen::MatrixXd& Qt,int j, int k0,int k1,int Nm) 
+{
+  typedef decltype(basis[0].View(AcceleratorRead)) View;
+  typedef typename Field::vector_object vobj;
+  GridBase* grid = basis[0].Grid();
+
+  result.Checkerboard() = basis[0].Checkerboard();
+
+  Vector<View> basis_v; basis_v.reserve(basis.size());
+  for(int k=0;k<basis.size();k++){
+    basis_v.push_back(basis[k].View(AcceleratorRead));
+  }
+  vobj zz=Zero();
+  Vector<double> Qt_jv(Nm);
+  double * Qt_j = & Qt_jv[0];
+  for(int k=0;k<Nm;++k) Qt_j[k]=Qt(j,k);
+
+  autoView(result_v,result,AcceleratorWrite);
+  accelerator_for(ss, grid->oSites(),vobj::Nsimd(),{
+    auto B=coalescedRead(zz);
+    for(int k=k0; k<k1; ++k){
+      B +=Qt_j[k] * coalescedRead(basis_v[k][ss]);
+    }
+    coalescedWrite(result_v[ss], B);
+  });
+  for(int k=0;k<basis.size();k++) basis_v[k].ViewClose();
+}
+
+template<class Field>
+void basisReorderInPlace(std::vector<Field> &_v,std::vector<RealD>& sort_vals, std::vector<int>& idx) 
+{
+  int vlen = idx.size();
+
+  assert(vlen>=1);
+  assert(vlen<=sort_vals.size());
+  assert(vlen<=_v.size());
+
+  for (size_t i=0;i<vlen;i++) {
+
+    if (idx[i] != i) {
+
+      //////////////////////////////////////
+      // idx[i] is a table of desired sources giving a permutation.
+      // Swap v[i] with v[idx[i]].
+      // Find  j>i for which _vnew[j] = _vold[i],
+      // track the move idx[j] => idx[i]
+      // track the move idx[i] => i
+      //////////////////////////////////////
+      size_t j;
+      for (j=i;j<idx.size();j++)
+	if (idx[j]==i)
+	  break;
+
+      assert(idx[i] > i);     assert(j!=idx.size());      assert(idx[j]==i);
+
+      swap(_v[i],_v[idx[i]]); // should use vector move constructor, no data copy
+      std::swap(sort_vals[i],sort_vals[idx[i]]);
+
+      idx[j] = idx[i];
+      idx[i] = i;
+    }
+  }
+}
+
+inline std::vector<int> basisSortGetIndex(std::vector<RealD>& sort_vals) 
+{
+  std::vector<int> idx(sort_vals.size());
+  std::iota(idx.begin(), idx.end(), 0);
+
+  // sort indexes based on comparing values in v
+  std::sort(idx.begin(), idx.end(), [&sort_vals](int i1, int i2) {
+    return ::fabs(sort_vals[i1]) < ::fabs(sort_vals[i2]);
+  });
+  return idx;
+}
+
+template<class Field>
+void basisSortInPlace(std::vector<Field> & _v,std::vector<RealD>& sort_vals, bool reverse) 
+{
+  std::vector<int> idx = basisSortGetIndex(sort_vals);
+  if (reverse)
+    std::reverse(idx.begin(), idx.end());
+  
+  basisReorderInPlace(_v,sort_vals,idx);
+}
+
+// PAB: faster to compute the inner products first then fuse loops.
+// If performance critical can improve.
+template<class Field>
+void basisDeflate(const std::vector<Field> &_v,const std::vector<RealD>& eval,const Field& src_orig,Field& result) {
+  result = Zero();
+  assert(_v.size()==eval.size());
+  int N = (int)_v.size();
+  for (int i=0;i<N;i++) {
+    Field& tmp = _v[i];
+    axpy(result,TensorRemove(innerProduct(tmp,src_orig)) / eval[i],tmp,result);
+  }
+}
+
+NAMESPACE_END(Grid);

Grid/lattice/Lattice_comparison.h

@@ -0,0 +1,179 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_comparison.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LATTICE_COMPARISON_H
+#define GRID_LATTICE_COMPARISON_H
+
+NAMESPACE_BEGIN(Grid);
+
+//////////////////////////////////////////////////////////////////////////
+// relational operators
+// 
+// Support <,>,<=,>=,==,!=
+//
+//Query supporting bitwise &, |, ^, !
+//Query supporting logical &&, ||, 
+//////////////////////////////////////////////////////////////////////////
+
+typedef iScalar<vInteger> vPredicate ;
+
+//////////////////////////////////////////////////////////////////////////
+// compare lattice to lattice
+//////////////////////////////////////////////////////////////////////////
+
+template<class vfunctor,class lobj,class robj>  
+inline Lattice<vPredicate> LLComparison(vfunctor op,const Lattice<lobj> &lhs,const Lattice<robj> &rhs)
+{
+  Lattice<vPredicate> ret(rhs.Grid());
+  autoView( lhs_v, lhs, CpuRead);
+  autoView( rhs_v, rhs, CpuRead);
+  autoView( ret_v, ret, CpuWrite);
+  thread_for( ss, rhs_v.size(), {
+      ret_v[ss]=op(lhs_v[ss],rhs_v[ss]);
+  });
+  return ret;
+}
+//////////////////////////////////////////////////////////////////////////
+// compare lattice to scalar
+//////////////////////////////////////////////////////////////////////////
+template<class vfunctor,class lobj,class robj> 
+inline Lattice<vPredicate> LSComparison(vfunctor op,const Lattice<lobj> &lhs,const robj &rhs)
+{
+  Lattice<vPredicate> ret(lhs.Grid());
+  autoView( lhs_v, lhs, CpuRead);
+  autoView( ret_v, ret, CpuWrite);
+  thread_for( ss, lhs_v.size(), {
+    ret_v[ss]=op(lhs_v[ss],rhs);
+  });
+  return ret;
+}
+//////////////////////////////////////////////////////////////////////////
+// compare scalar to lattice
+//////////////////////////////////////////////////////////////////////////
+template<class vfunctor,class lobj,class robj> 
+inline Lattice<vPredicate> SLComparison(vfunctor op,const lobj &lhs,const Lattice<robj> &rhs)
+{
+  Lattice<vPredicate> ret(rhs.Grid());
+  autoView( rhs_v, rhs, CpuRead);
+  autoView( ret_v, ret, CpuWrite);
+  thread_for( ss, rhs_v.size(), {
+    ret_v[ss]=op(lhs,rhs_v[ss]);
+  });
+  return ret;
+}
+  
+//////////////////////////////////////////////////////////////////////////
+// Map to functors
+//////////////////////////////////////////////////////////////////////////
+// Less than
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator < (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+  return LLComparison(vlt<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator < (const Lattice<lobj> & lhs, const robj & rhs) {
+  return LSComparison(vlt<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator < (const lobj & lhs, const Lattice<robj> & rhs) {
+  return SLComparison(vlt<lobj,robj>(),lhs,rhs);
+}
+  
+// Less than equal
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator <= (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+  return LLComparison(vle<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator <= (const Lattice<lobj> & lhs, const robj & rhs) {
+  return LSComparison(vle<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator <= (const lobj & lhs, const Lattice<robj> & rhs) {
+  return SLComparison(vle<lobj,robj>(),lhs,rhs);
+}
+  
+// Greater than 
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator > (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+  return LLComparison(vgt<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator > (const Lattice<lobj> & lhs, const robj & rhs) {
+  return LSComparison(vgt<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator > (const lobj & lhs, const Lattice<robj> & rhs) {
+  return SLComparison(vgt<lobj,robj>(),lhs,rhs);
+}
+  
+  
+// Greater than equal
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator >= (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+  return LLComparison(vge<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator >= (const Lattice<lobj> & lhs, const robj & rhs) {
+  return LSComparison(vge<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator >= (const lobj & lhs, const Lattice<robj> & rhs) {
+  return SLComparison(vge<lobj,robj>(),lhs,rhs);
+}
+   
+// equal
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator == (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+  return LLComparison(veq<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator == (const Lattice<lobj> & lhs, const robj & rhs) {
+  return LSComparison(veq<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator == (const lobj & lhs, const Lattice<robj> & rhs) {
+  return SLComparison(veq<lobj,robj>(),lhs,rhs);
+}
+   
+   
+// not equal
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator != (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+  return LLComparison(vne<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator != (const Lattice<lobj> & lhs, const robj & rhs) {
+  return LSComparison(vne<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vPredicate> operator != (const lobj & lhs, const Lattice<robj> & rhs) {
+  return SLComparison(vne<lobj,robj>(),lhs,rhs);
+}
+NAMESPACE_END(Grid);
+#endif

Grid/lattice/Lattice_comparison_utils.h

@@ -26,10 +26,10 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     See the full license in the file "LICENSE" in the top level distribution directory
     *************************************************************************************/
     /*  END LEGAL */
-#ifndef GRID_COMPARISON_H
-#define GRID_COMPARISON_H
 
-namespace Grid {
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
 
   /////////////////////////////////////////
   // This implementation is a bit poor.
@@ -44,42 +44,42 @@ namespace Grid {
   //
   template<class lobj,class robj> class veq {
   public:
-    vInteger operator()(const lobj &lhs, const robj &rhs)
+    accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) == (rhs);
     }
   };
   template<class lobj,class robj> class vne {
   public:
-    vInteger operator()(const lobj &lhs, const robj &rhs)
+    accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) != (rhs);
     }
   };
   template<class lobj,class robj> class vlt {
   public:
-    vInteger operator()(const lobj &lhs, const robj &rhs)
+    accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) < (rhs);
     }
   };
   template<class lobj,class robj> class vle {
   public:
-    vInteger operator()(const lobj &lhs, const robj &rhs)
+    accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) <= (rhs);
     }
   };
   template<class lobj,class robj> class vgt {
   public:
-    vInteger operator()(const lobj &lhs, const robj &rhs)
+    accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) > (rhs);
     }
   };
   template<class lobj,class robj> class vge {
     public:
-    vInteger operator()(const lobj &lhs, const robj &rhs)
+    accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) >= (rhs);
     }
@@ -88,42 +88,42 @@ namespace Grid {
   // Generic list of functors
   template<class lobj,class robj> class seq {
   public:
-    Integer operator()(const lobj &lhs, const robj &rhs)
+    accelerator Integer operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) == (rhs);
     }
   };
   template<class lobj,class robj> class sne {
   public:
-    Integer operator()(const lobj &lhs, const robj &rhs)
+    accelerator Integer operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) != (rhs);
     }
   };
   template<class lobj,class robj> class slt {
   public:
-    Integer operator()(const lobj &lhs, const robj &rhs)
+    accelerator Integer operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) < (rhs);
     }
   };
   template<class lobj,class robj> class sle {
   public:
-    Integer operator()(const lobj &lhs, const robj &rhs)
+    accelerator Integer operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) <= (rhs);
     }
   };
   template<class lobj,class robj> class sgt {
   public:
-    Integer operator()(const lobj &lhs, const robj &rhs)
+    accelerator Integer operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) > (rhs);
     }
   };
   template<class lobj,class robj> class sge {
   public:
-    Integer operator()(const lobj &lhs, const robj &rhs)
+    accelerator Integer operator()(const lobj &lhs, const robj &rhs)
     { 
       return (lhs) >= (rhs);
     }
@@ -133,12 +133,12 @@ namespace Grid {
   // Integer and real get extra relational functions.
   //////////////////////////////////////////////////////////////////////////////////////////////////////
   template<class sfunctor, class vsimd,IfNotComplex<vsimd> = 0> 
-    inline vInteger Comparison(sfunctor sop,const vsimd & lhs, const vsimd & rhs)
+    accelerator_inline vInteger Comparison(sfunctor sop,const vsimd & lhs, const vsimd & rhs)
     {
       typedef typename vsimd::scalar_type scalar;
-      std::vector<scalar> vlhs(vsimd::Nsimd());   // Use functors to reduce this to single implementation
-      std::vector<scalar> vrhs(vsimd::Nsimd());
-      std::vector<Integer> vpred(vsimd::Nsimd());
+      ExtractBuffer<scalar> vlhs(vsimd::Nsimd());   // Use functors to reduce this to single implementation
+      ExtractBuffer<scalar> vrhs(vsimd::Nsimd());
+      ExtractBuffer<Integer> vpred(vsimd::Nsimd());
       vInteger ret;
       extract<vsimd,scalar>(lhs,vlhs);
       extract<vsimd,scalar>(rhs,vrhs);
@@ -150,11 +150,11 @@ namespace Grid {
     }
 
   template<class sfunctor, class vsimd,IfNotComplex<vsimd> = 0> 
-    inline vInteger Comparison(sfunctor sop,const vsimd & lhs, const typename vsimd::scalar_type & rhs)
+    accelerator_inline vInteger Comparison(sfunctor sop,const vsimd & lhs, const typename vsimd::scalar_type & rhs)
     {
       typedef typename vsimd::scalar_type scalar;
-      std::vector<scalar> vlhs(vsimd::Nsimd());   // Use functors to reduce this to single implementation
-      std::vector<Integer> vpred(vsimd::Nsimd());
+      ExtractBuffer<scalar> vlhs(vsimd::Nsimd());   // Use functors to reduce this to single implementation
+      ExtractBuffer<Integer> vpred(vsimd::Nsimd());
       vInteger ret;
       extract<vsimd,scalar>(lhs,vlhs);
       for(int s=0;s<vsimd::Nsimd();s++){
@@ -165,11 +165,11 @@ namespace Grid {
     }
 
   template<class sfunctor, class vsimd,IfNotComplex<vsimd> = 0> 
-    inline vInteger Comparison(sfunctor sop,const typename vsimd::scalar_type & lhs, const vsimd & rhs)
+    accelerator_inline vInteger Comparison(sfunctor sop,const typename vsimd::scalar_type & lhs, const vsimd & rhs)
     {
       typedef typename vsimd::scalar_type scalar;
-      std::vector<scalar> vrhs(vsimd::Nsimd());   // Use functors to reduce this to single implementation
-      std::vector<Integer> vpred(vsimd::Nsimd());
+      ExtractBuffer<scalar> vrhs(vsimd::Nsimd());   // Use functors to reduce this to single implementation
+      ExtractBuffer<Integer> vpred(vsimd::Nsimd());
       vInteger ret;
       extract<vsimd,scalar>(rhs,vrhs);
       for(int s=0;s<vsimd::Nsimd();s++){
@@ -181,30 +181,30 @@ namespace Grid {
 
 #define DECLARE_RELATIONAL_EQ(op,functor) \
   template<class vsimd,IfSimd<vsimd> = 0>\
-    inline vInteger operator op (const vsimd & lhs, const vsimd & rhs)\
+    accelerator_inline vInteger operator op (const vsimd & lhs, const vsimd & rhs)\
     {\
       typedef typename vsimd::scalar_type scalar;\
       return Comparison(functor<scalar,scalar>(),lhs,rhs);\
     }\
   template<class vsimd,IfSimd<vsimd> = 0>\
-    inline vInteger operator op (const vsimd & lhs, const typename vsimd::scalar_type & rhs) \
+    accelerator_inline vInteger operator op (const vsimd & lhs, const typename vsimd::scalar_type & rhs) \
     {\
       typedef typename vsimd::scalar_type scalar;\
       return Comparison(functor<scalar,scalar>(),lhs,rhs);\
     }\
   template<class vsimd,IfSimd<vsimd> = 0>\
-    inline vInteger operator op (const typename vsimd::scalar_type & lhs, const vsimd & rhs) \
+    accelerator_inline vInteger operator op (const typename vsimd::scalar_type & lhs, const vsimd & rhs) \
     {\
       typedef typename vsimd::scalar_type scalar;\
       return Comparison(functor<scalar,scalar>(),lhs,rhs);\
     }\
   template<class vsimd>\
-    inline vInteger operator op(const iScalar<vsimd> &lhs,const typename vsimd::scalar_type &rhs) \
+    accelerator_inline vInteger operator op(const iScalar<vsimd> &lhs,const typename vsimd::scalar_type &rhs) \
     {									\
       return lhs._internal op rhs;					\
     }									\
   template<class vsimd>\
-    inline vInteger operator op(const typename vsimd::scalar_type &lhs,const iScalar<vsimd> &rhs) \
+    accelerator_inline vInteger operator op(const typename vsimd::scalar_type &lhs,const iScalar<vsimd> &rhs) \
     {									\
       return lhs op rhs._internal;					\
     }									\
@@ -212,7 +212,7 @@ namespace Grid {
 #define DECLARE_RELATIONAL(op,functor) \
   DECLARE_RELATIONAL_EQ(op,functor)    \
   template<class vsimd>\
-    inline vInteger operator op(const iScalar<vsimd> &lhs,const iScalar<vsimd> &rhs)\
+    accelerator_inline vInteger operator op(const iScalar<vsimd> &lhs,const iScalar<vsimd> &rhs)\
     {									\
       return lhs._internal op rhs._internal;				\
     }									
@@ -226,7 +226,7 @@ DECLARE_RELATIONAL(!=,sne);
 
 #undef DECLARE_RELATIONAL
 
-}
+NAMESPACE_END(Grid);
+
 
 
-#endif

Grid/lattice/Lattice_conformable.h

@@ -1,4 +1,4 @@
-    /*************************************************************************************
+/*************************************************************************************
 
     Grid physics library, www.github.com/paboyle/Grid 
 
@@ -23,18 +23,18 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     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 */
+*************************************************************************************/
+/*  END LEGAL */
 #ifndef GRID_LATTICE_CONFORMABLE_H
 #define GRID_LATTICE_CONFORMABLE_H
 
-namespace Grid {
-
-    template<class obj1,class obj2> void conformable(const Lattice<obj1> &lhs,const Lattice<obj2> &rhs)
-    {
-        assert(lhs._grid == rhs._grid);
-        assert(lhs.checkerboard == rhs.checkerboard);
-    }
+NAMESPACE_BEGIN(Grid);
 
+template<class obj1,class obj2> void conformable(const Lattice<obj1> &lhs,const Lattice<obj2> &rhs)
+{
+  assert(lhs.Grid() == rhs.Grid());
+  assert(lhs.Checkerboard() == rhs.Checkerboard());
 }
+
+NAMESPACE_END(Grid);
 #endif

Grid/lattice/Lattice_coordinate.h

@@ -0,0 +1,55 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_coordinate.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once 
+
+NAMESPACE_BEGIN(Grid);
+
+template<class iobj> inline void LatticeCoordinate(Lattice<iobj> &l,int mu)
+{
+  typedef typename iobj::scalar_type scalar_type;
+  typedef typename iobj::vector_type vector_type;
+
+  GridBase *grid = l.Grid();
+  int Nsimd = grid->iSites();
+
+  autoView(l_v, l, CpuWrite);
+  thread_for( o, grid->oSites(), {
+    vector_type vI;
+    Coordinate gcoor;
+    ExtractBuffer<scalar_type> mergebuf(Nsimd);
+    for(int i=0;i<grid->iSites();i++){
+      grid->RankIndexToGlobalCoor(grid->ThisRank(),o,i,gcoor);
+      mergebuf[i]=(Integer)gcoor[mu];
+    }
+    merge<vector_type,scalar_type>(vI,mergebuf);
+    l_v[o]=vI;
+  });
+};
+
+NAMESPACE_END(Grid);
+

Grid/lattice/Lattice_local.h

@@ -0,0 +1,87 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_local.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LATTICE_LOCALREDUCTION_H
+#define GRID_LATTICE_LOCALREDUCTION_H
+
+///////////////////////////////////////////////
+// localInner, localNorm, outerProduct
+///////////////////////////////////////////////
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////
+// Non site, reduced locally reduced routines
+/////////////////////////////////////////////////////
+  
+// localNorm2,
+template<class vobj>
+inline auto localNorm2 (const Lattice<vobj> &rhs)-> Lattice<typename vobj::tensor_reduced>
+{
+  Lattice<typename vobj::tensor_reduced> ret(rhs.Grid());
+  autoView( rhs_v , rhs, AcceleratorRead);
+  autoView( ret_v , ret, AcceleratorWrite);
+  accelerator_for(ss,rhs_v.size(),vobj::Nsimd(),{
+    coalescedWrite(ret_v[ss],innerProduct(rhs_v(ss),rhs_v(ss)));
+  });
+  return ret;
+}
+  
+// localInnerProduct
+template<class vobj>
+inline auto localInnerProduct (const Lattice<vobj> &lhs,const Lattice<vobj> &rhs) -> Lattice<typename vobj::tensor_reduced>
+{
+  Lattice<typename vobj::tensor_reduced> ret(rhs.Grid());
+  autoView( lhs_v , lhs, AcceleratorRead);
+  autoView( rhs_v , rhs, AcceleratorRead);
+  autoView( ret_v , ret, AcceleratorWrite);
+  accelerator_for(ss,rhs_v.size(),vobj::Nsimd(),{
+    coalescedWrite(ret_v[ss],innerProduct(lhs_v(ss),rhs_v(ss)));
+  });
+  return ret;
+}
+  
+// outerProduct Scalar x Scalar -> Scalar
+//              Vector x Vector -> Matrix
+template<class ll,class rr>
+inline auto outerProduct (const Lattice<ll> &lhs,const Lattice<rr> &rhs) -> Lattice<decltype(outerProduct(ll(),rr()))>
+{
+  typedef decltype(coalescedRead(ll())) sll;
+  typedef decltype(coalescedRead(rr())) srr;
+  Lattice<decltype(outerProduct(ll(),rr()))> ret(rhs.Grid());
+  autoView( lhs_v , lhs, AcceleratorRead);
+  autoView( rhs_v , rhs, AcceleratorRead);
+  autoView( ret_v , ret, AcceleratorWrite);
+  accelerator_for(ss,rhs_v.size(),1,{
+    // FIXME had issues with scalar version of outer 
+    // Use vector [] operator and don't read coalesce this loop
+    ret_v[ss]=outerProduct(lhs_v[ss],rhs_v[ss]);
+  });
+  return ret;
+}
+NAMESPACE_END(Grid);
+#endif

Grid/lattice/Lattice_matrix_reduction.h

@@ -0,0 +1,202 @@
+/*************************************************************************************
+    Grid physics library, www.github.com/paboyle/Grid 
+    Source file: ./lib/lattice/Lattice_reduction.h
+    Copyright (C) 2015
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once 
+#include <Grid/Grid_Eigen_Dense.h>
+
+#ifdef GRID_WARN_SUBOPTIMAL
+#warning "Optimisation alert all these reduction loops are NOT threaded "
+#endif     
+
+NAMESPACE_BEGIN(Grid);
+
+template<class vobj>
+static void sliceMaddMatrix (Lattice<vobj> &R,Eigen::MatrixXcd &aa,const Lattice<vobj> &X,const Lattice<vobj> &Y,int Orthog,RealD scale=1.0) 
+{    
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  int Nblock = X.Grid()->GlobalDimensions()[Orthog];
+
+  GridBase *FullGrid  = X.Grid();
+  //  GridBase *SliceGrid = makeSubSliceGrid(FullGrid,Orthog);
+
+  //  Lattice<vobj> Xslice(SliceGrid);
+  //  Lattice<vobj> Rslice(SliceGrid);
+
+  assert( FullGrid->_simd_layout[Orthog]==1);
+
+  //FIXME package in a convenient iterator
+  //Should loop over a plane orthogonal to direction "Orthog"
+  int stride=FullGrid->_slice_stride[Orthog];
+  int block =FullGrid->_slice_block [Orthog];
+  int nblock=FullGrid->_slice_nblock[Orthog];
+  int ostride=FullGrid->_ostride[Orthog];
+  autoView( X_v , X, CpuRead);
+  autoView( Y_v , Y, CpuRead);
+  autoView( R_v , R, CpuWrite);
+  thread_region
+  {
+    std::vector<vobj> s_x(Nblock);
+
+    thread_loop_collapse2( (int n=0;n<nblock;n++),{
+      for(int b=0;b<block;b++){
+	int o  = n*stride + b;
+
+	for(int i=0;i<Nblock;i++){
+	  s_x[i] = X_v[o+i*ostride];
+	}
+
+	vobj dot;
+	for(int i=0;i<Nblock;i++){
+	  dot = Y_v[o+i*ostride];
+	  for(int j=0;j<Nblock;j++){
+	    dot = dot + s_x[j]*(scale*aa(j,i));
+	  }
+	  R_v[o+i*ostride]=dot;
+	}
+      }});
+  }
+};
+
+template<class vobj>
+static void sliceMulMatrix (Lattice<vobj> &R,Eigen::MatrixXcd &aa,const Lattice<vobj> &X,int Orthog,RealD scale=1.0) 
+{    
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  int Nblock = X.Grid()->GlobalDimensions()[Orthog];
+
+  GridBase *FullGrid  = X.Grid();
+  assert( FullGrid->_simd_layout[Orthog]==1);
+
+  //FIXME package in a convenient iterator
+  //Should loop over a plane orthogonal to direction "Orthog"
+  int stride=FullGrid->_slice_stride[Orthog];
+  int block =FullGrid->_slice_block [Orthog];
+  int nblock=FullGrid->_slice_nblock[Orthog];
+  int ostride=FullGrid->_ostride[Orthog];
+
+  autoView( X_v , X, CpuRead);
+  autoView( R_v , R, CpuWrite);
+
+  thread_region
+  {
+    std::vector<vobj> s_x(Nblock);
+    
+    thread_loop_collapse2( (int n=0;n<nblock;n++),{
+      for(int b=0;b<block;b++){
+	int o  = n*stride + b;
+
+	for(int i=0;i<Nblock;i++){
+	  s_x[i] = X_v[o+i*ostride];
+	}
+
+	vobj dot;
+	for(int i=0;i<Nblock;i++){
+	  dot = s_x[0]*(scale*aa(0,i));
+	  for(int j=1;j<Nblock;j++){
+	    dot = dot + s_x[j]*(scale*aa(j,i));
+	  }
+	  R_v[o+i*ostride]=dot;
+	}
+    }});
+  }
+
+};
+
+
+template<class vobj>
+static void sliceInnerProductMatrix(  Eigen::MatrixXcd &mat, const Lattice<vobj> &lhs,const Lattice<vobj> &rhs,int Orthog) 
+{
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+  
+  GridBase *FullGrid  = lhs.Grid();
+  //  GridBase *SliceGrid = makeSubSliceGrid(FullGrid,Orthog);
+  
+  int Nblock = FullGrid->GlobalDimensions()[Orthog];
+  
+  //  Lattice<vobj> Lslice(SliceGrid);
+  //  Lattice<vobj> Rslice(SliceGrid);
+  
+  mat = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+
+  assert( FullGrid->_simd_layout[Orthog]==1);
+  //  int nh =  FullGrid->_ndimension;
+  //  int nl = SliceGrid->_ndimension;
+  //  int nl = nh-1;
+
+  //FIXME package in a convenient iterator
+  //Should loop over a plane orthogonal to direction "Orthog"
+  int stride=FullGrid->_slice_stride[Orthog];
+  int block =FullGrid->_slice_block [Orthog];
+  int nblock=FullGrid->_slice_nblock[Orthog];
+  int ostride=FullGrid->_ostride[Orthog];
+
+  typedef typename vobj::vector_typeD vector_typeD;
+  autoView( lhs_v , lhs, CpuRead);
+  autoView( rhs_v , rhs, CpuRead);
+  thread_region {
+    std::vector<vobj> Left(Nblock);
+    std::vector<vobj> Right(Nblock);
+    Eigen::MatrixXcd  mat_thread = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+
+    thread_loop_collapse2((int n=0;n<nblock;n++),{
+      for(int b=0;b<block;b++){
+
+	int o  = n*stride + b;
+
+	for(int i=0;i<Nblock;i++){
+	  Left [i] = lhs_v[o+i*ostride];
+	  Right[i] = rhs_v[o+i*ostride];
+	}
+
+	for(int i=0;i<Nblock;i++){
+	  for(int j=0;j<Nblock;j++){
+	    auto tmp = innerProduct(Left[i],Right[j]);
+	    auto rtmp = TensorRemove(tmp);
+	    ComplexD z = Reduce(rtmp);
+	    mat_thread(i,j) += std::complex<double>(real(z),imag(z));
+	  }}
+    }});
+    thread_critical {
+      mat += mat_thread;
+    }  
+  }
+
+  for(int i=0;i<Nblock;i++){
+    for(int j=0;j<Nblock;j++){
+      ComplexD sum = mat(i,j);
+      FullGrid->GlobalSum(sum);
+      mat(i,j)=sum;
+    }}
+
+  return;
+}
+
+NAMESPACE_END(Grid);
+
+
+

Grid/lattice/Lattice_peekpoke.h

@@ -0,0 +1,231 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_peekpoke.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LATTICE_PEEK_H
+#define GRID_LATTICE_PEEK_H
+
+///////////////////////////////////////////////
+// Peeking and poking around
+///////////////////////////////////////////////
+
+NAMESPACE_BEGIN(Grid);
+
+
+// FIXME accelerator_loop and accelerator_inline these
+////////////////////////////////////////////////////////////////////////////////////////////////////
+// Peek internal indices of a Lattice object
+////////////////////////////////////////////////////////////////////////////////////////////////////
+template<int Index,class vobj> 
+auto PeekIndex(const Lattice<vobj> &lhs,int i) -> Lattice<decltype(peekIndex<Index>(vobj(),i))>
+{
+  Lattice<decltype(peekIndex<Index>(vobj(),i))> ret(lhs.Grid());
+  ret.Checkerboard()=lhs.Checkerboard();
+  autoView( ret_v, ret, AcceleratorWrite);
+  autoView( lhs_v, lhs, AcceleratorRead);
+  accelerator_for( ss, lhs_v.size(), 1, {
+    ret_v[ss] = peekIndex<Index>(lhs_v[ss],i);
+  });
+  return ret;
+};
+template<int Index,class vobj> 
+auto PeekIndex(const Lattice<vobj> &lhs,int i,int j) -> Lattice<decltype(peekIndex<Index>(vobj(),i,j))>
+{
+  Lattice<decltype(peekIndex<Index>(vobj(),i,j))> ret(lhs.Grid());
+  ret.Checkerboard()=lhs.Checkerboard();
+  autoView( ret_v, ret, AcceleratorWrite);
+  autoView( lhs_v, lhs, AcceleratorRead);
+  accelerator_for( ss, lhs_v.size(), 1, {
+    ret_v[ss] = peekIndex<Index>(lhs_v[ss],i,j);
+  });
+  return ret;
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+// Poke internal indices of a Lattice object
+////////////////////////////////////////////////////////////////////////////////////////////////////
+template<int Index,class vobj>  
+void PokeIndex(Lattice<vobj> &lhs,const Lattice<decltype(peekIndex<Index>(vobj(),0))> & rhs,int i)
+{
+  autoView( rhs_v, rhs, AcceleratorRead);
+  autoView( lhs_v, lhs, AcceleratorWrite);
+  accelerator_for( ss, lhs_v.size(), 1, {
+    pokeIndex<Index>(lhs_v[ss],rhs_v[ss],i);
+  });
+}
+template<int Index,class vobj> 
+void PokeIndex(Lattice<vobj> &lhs,const Lattice<decltype(peekIndex<Index>(vobj(),0,0))> & rhs,int i,int j)
+{
+  autoView( rhs_v, rhs, AcceleratorRead);
+  autoView( lhs_v, lhs, AcceleratorWrite);
+  accelerator_for( ss, lhs_v.size(), 1, {
+    pokeIndex<Index>(lhs_v[ss],rhs_v[ss],i,j);
+  });
+}
+
+//////////////////////////////////////////////////////
+// Poke a scalar object into the SIMD array
+//////////////////////////////////////////////////////
+template<class vobj,class sobj> 
+void pokeSite(const sobj &s,Lattice<vobj> &l,const Coordinate &site){
+
+  GridBase *grid=l.Grid();
+
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  int Nsimd = grid->Nsimd();
+
+  assert( l.Checkerboard()== l.Grid()->CheckerBoard(site));
+  assert( sizeof(sobj)*Nsimd == sizeof(vobj));
+
+  int rank,odx,idx;
+  // Optional to broadcast from node 0.
+  grid->GlobalCoorToRankIndex(rank,odx,idx,site);
+  grid->Broadcast(grid->BossRank(),s);
+
+  // extract-modify-merge cycle is easiest way and this is not perf critical
+  ExtractBuffer<sobj> buf(Nsimd);
+  autoView( l_v , l, CpuWrite);
+  if ( rank == grid->ThisRank() ) {
+    extract(l_v[odx],buf);
+    buf[idx] = s;
+    merge(l_v[odx],buf);
+  }
+
+  return;
+};
+
+
+//////////////////////////////////////////////////////////
+// Peek a scalar object from the SIMD array
+//////////////////////////////////////////////////////////
+template<class vobj,class sobj>
+void peekSite(sobj &s,const Lattice<vobj> &l,const Coordinate &site){
+        
+  GridBase *grid=l.Grid();
+
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  int Nsimd = grid->Nsimd();
+
+  assert( l.Checkerboard() == l.Grid()->CheckerBoard(site));
+
+  int rank,odx,idx;
+  grid->GlobalCoorToRankIndex(rank,odx,idx,site);
+
+  ExtractBuffer<sobj> buf(Nsimd);
+  autoView( l_v , l, CpuWrite);
+  extract(l_v[odx],buf);
+
+  s = buf[idx];
+
+  grid->Broadcast(rank,s);
+
+  return;
+};
+
+//////////////////////////////////////////////////////////
+// Peek a scalar object from the SIMD array
+//////////////////////////////////////////////////////////
+// Must be CPU read view
+template<class vobj,class sobj>
+inline void peekLocalSite(sobj &s,const LatticeView<vobj> &l,Coordinate &site)
+{
+  GridBase *grid = l.getGrid();
+  assert(l.mode==CpuRead);
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  int Nsimd = grid->Nsimd();
+
+  assert( l.Checkerboard()== grid->CheckerBoard(site));
+  assert( sizeof(sobj)*Nsimd == sizeof(vobj));
+
+  static const int words=sizeof(vobj)/sizeof(vector_type);
+  int odx,idx;
+  idx= grid->iIndex(site);
+  odx= grid->oIndex(site);
+  
+  scalar_type * vp = (scalar_type *)&l[odx];
+  scalar_type * pt = (scalar_type *)&s;
+      
+  for(int w=0;w<words;w++){
+    pt[w] = vp[idx+w*Nsimd];
+  }
+      
+  return;
+};
+template<class vobj,class sobj>
+inline void peekLocalSite(sobj &s,const Lattice<vobj> &l,Coordinate &site)
+{
+  autoView(lv,l,CpuRead);
+  peekLocalSite(s,lv,site);
+  return;
+};
+
+// Must be CPU write view
+template<class vobj,class sobj>
+inline void pokeLocalSite(const sobj &s,LatticeView<vobj> &l,Coordinate &site)
+{
+  GridBase *grid=l.getGrid();
+  assert(l.mode==CpuWrite);
+
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  int Nsimd = grid->Nsimd();
+
+  assert( l.Checkerboard()== grid->CheckerBoard(site));
+  assert( sizeof(sobj)*Nsimd == sizeof(vobj));
+
+  static const int words=sizeof(vobj)/sizeof(vector_type);
+  int odx,idx;
+  idx= grid->iIndex(site);
+  odx= grid->oIndex(site);
+
+  scalar_type * vp = (scalar_type *)&l[odx];
+  scalar_type * pt = (scalar_type *)&s;
+  for(int w=0;w<words;w++){
+    vp[idx+w*Nsimd] = pt[w];
+  }
+  return;
+};
+
+template<class vobj,class sobj>
+inline void pokeLocalSite(const sobj &s, Lattice<vobj> &l,Coordinate &site)
+{
+  autoView(lv,l,CpuWrite);
+  pokeLocalSite(s,lv,site);
+  return;
+};
+
+NAMESPACE_END(Grid);
+#endif
+