Merge pull request #459 from dbollweg/sycl_slicesum_update

Sycl slicesum bugfix

.github/ISSUE_TEMPLATE/bug-report.yml

@@ -0,0 +1,54 @@
+name: Bug report
+description: Report a bug.
+title: "<insert title>"
+labels: [bug]
+
+body:
+  - type: markdown
+    attributes:
+      value: >
+        Thank you for taking the time to file a bug report.
+        Please check that the code is pointing to the HEAD of develop
+        or any commit in master which is tagged with a version number.
+
+  - type: textarea
+    attributes:
+      label: "Describe the issue:"
+      description: >
+        Describe the issue and any previous attempt to solve it.
+    validations:
+      required: true
+
+  - type: textarea
+    attributes:
+      label: "Code example:"
+      description: >
+        If relevant, show how to reproduce the issue using a minimal working
+        example.
+      placeholder: |
+        << your code here >>
+      render: shell
+    validations:
+      required: false
+
+  - type: textarea
+    attributes:
+      label: "Target platform:"
+      description: >
+        Give a description of the target platform (CPU, network, compiler).
+        Please give the full CPU part description, using for example
+        `cat /proc/cpuinfo | grep 'model name' | uniq` (Linux)
+        or `sysctl machdep.cpu.brand_string` (macOS) and the full output
+        the `--version` option of your compiler.
+    validations:
+      required: true
+
+  - type: textarea
+    attributes:
+      label: "Configure options:"
+      description: >
+        Please give the exact configure command used and attach
+        `config.log`, `grid.config.summary` and the output of `make V=1`.
+      render: shell
+    validations:
+      required: true

.gitignore

@@ -1,3 +1,7 @@
+# Doxygen stuff
+html/*
+latex/*
+
 # Compiled Object files #
 #########################
 *.slo
@@ -83,37 +87,36 @@ ltmain.sh
 .Trashes
 ehthumbs.db
 Thumbs.db
+.dirstamp
 
 # build directory #
 ###################
 build*/*
+Documentation/_build
 
 # IDE related files #
 #####################
 *.xcodeproj/*
 build.sh
+.vscode
+*.code-workspace
 
 # Eigen source #
 ################
-lib/Eigen/*
-
-# FFTW source #
-################
-lib/fftw/*
+Grid/Eigen
+Eigen/*
 
 # libtool macros #
 ##################
 m4/lt*
 m4/libtool.m4
 
-# Buck files #
-##############
-.buck*
-buck-out
-BUCK
-make-bin-BUCK.sh
+# github pages #
+################
+gh-pages/
 
 # generated sources #
 #####################
-lib/qcd/spin/gamma-gen/*.h
-lib/qcd/spin/gamma-gen/*.cc
+Grid/qcd/spin/gamma-gen/*.h
+Grid/qcd/spin/gamma-gen/*.cc
+Grid/util/Version.h

.travis.yml

@@ -1,106 +0,0 @@
-language: cpp
-
-cache:
-  directories:
-    - clang
-
-matrix:
-  include:
-    - os:        osx
-      osx_image: xcode7.2
-      compiler: clang
-    - compiler: gcc
-      addons:
-        apt:
-          sources:
-            - ubuntu-toolchain-r-test
-          packages:
-            - g++-4.9
-            - libmpfr-dev
-            - libgmp-dev
-            - libmpc-dev
-            - libopenmpi-dev
-            - openmpi-bin
-            - binutils-dev
-      env: VERSION=-4.9
-    - compiler: gcc
-      addons:
-        apt:
-          sources:
-            - ubuntu-toolchain-r-test
-          packages:
-            - g++-5
-            - libmpfr-dev
-            - libgmp-dev
-            - libmpc-dev
-            - libopenmpi-dev
-            - openmpi-bin
-            - binutils-dev
-      env: VERSION=-5
-    - compiler: clang
-      addons:
-        apt:
-          sources:
-            - ubuntu-toolchain-r-test
-          packages:
-            - g++-4.8
-            - libmpfr-dev
-            - libgmp-dev
-            - libmpc-dev
-            - libopenmpi-dev
-            - openmpi-bin
-            - binutils-dev
-      env: CLANG_LINK=http://llvm.org/releases/3.8.0/clang+llvm-3.8.0-x86_64-linux-gnu-ubuntu-14.04.tar.xz
-    - compiler: clang
-      addons:
-        apt:
-          sources:
-            - ubuntu-toolchain-r-test
-          packages:
-            - g++-4.8
-            - libmpfr-dev
-            - libgmp-dev
-            - libmpc-dev
-            - libopenmpi-dev
-            - openmpi-bin
-            - binutils-dev
-      env: CLANG_LINK=http://llvm.org/releases/3.7.0/clang+llvm-3.7.0-x86_64-linux-gnu-ubuntu-14.04.tar.xz
-      
-before_install:
-    - export GRIDDIR=`pwd`
-    - if [[ "$TRAVIS_OS_NAME" == "linux" ]] && [[ "$CC" == "clang" ]] && [ ! -e clang/bin ]; then wget $CLANG_LINK; tar -xf `basename $CLANG_LINK`; mkdir clang; mv clang+*/* clang/; fi
-    - if [[ "$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 openmpi; fi
-    - if [[ "$TRAVIS_OS_NAME" == "osx" ]] && [[ "$CC" == "gcc" ]]; then brew install gcc5; fi
-    
-install:
-    - export CC=$CC$VERSION
-    - export CXX=$CXX$VERSION
-    - echo $PATH
-    - which $CC
-    - $CC  --version
-    - which $CXX
-    - $CXX --version
-    - if [[ "$TRAVIS_OS_NAME" == "osx" ]]; then export LDFLAGS='-L/usr/local/lib'; fi
-    
-script:
-    - ./bootstrap.sh
-    - mkdir build
-    - cd build
-    - ../configure --enable-precision=single --enable-simd=SSE4 --enable-comms=none
-    - make -j4 
-    - ./benchmarks/Benchmark_dwf --threads 1
-    - echo make clean
-    - ../configure --enable-precision=double --enable-simd=SSE4 --enable-comms=none
-    - make -j4
-    - ./benchmarks/Benchmark_dwf --threads 1
-    - echo make clean
-    - if [[ "$TRAVIS_OS_NAME" == "linux" ]]; then export CXXFLAGS='-DMPI_UINT32_T=MPI_UNSIGNED -DMPI_UINT64_T=MPI_UNSIGNED_LONG'; fi
-    - ../configure --enable-precision=single --enable-simd=SSE4 --enable-comms=mpi-auto
-    - make -j4
-    - if [[ "$TRAVIS_OS_NAME" == "linux" ]]; then mpirun.openmpi -n 2 ./benchmarks/Benchmark_dwf --threads 1 --mpi 2.1.1.1; fi
-
-

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 +1,73 @@
+/*************************************************************************************
+
+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)
+#ifdef __ICC
+#pragma warning disable 488  
+#endif
+
+#ifdef __NVCC__
+ //disables nvcc specific warning in json.hpp
+#pragma clang diagnostic ignored "-Wdeprecated-register"
+
+#ifdef __NVCC_DIAG_PRAGMA_SUPPORT__
+ //disables nvcc specific warning in json.hpp
+#pragma nv_diag_suppress unsigned_compare_with_zero
+#pragma nv_diag_suppress cast_to_qualified_type
+ //disables nvcc specific warning in many files
+#pragma nv_diag_suppress esa_on_defaulted_function_ignored
+#pragma nv_diag_suppress extra_semicolon
+#else
+ //disables nvcc specific warning in json.hpp
+#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
+#endif
+#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

@@ -41,7 +41,10 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
 #include <Grid/GridCore.h>
 #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>
 
 #endif

Grid/GridCore.h

@@ -38,44 +38,30 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
 #ifndef GRID_BASE_H
 #define GRID_BASE_H
 
-///////////////////
-// Std C++ dependencies
-///////////////////
-#include <cassert>
-#include <complex>
-#include <vector>
-#include <iostream>
-#include <iomanip>
-#include <random>
-#include <functional>
-#include <stdio.h>
-#include <stdlib.h>
-#include <stdio.h>
-#include <signal.h>
-#include <ctime>
-#include <sys/time.h>
-#include <chrono>
-
-///////////////////
-// Grid headers
-///////////////////
-#include "Config.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/perfmon/PerfCount.h>
 #include <Grid/util/Util.h>
+#include <Grid/log/Log.h>
+#include <Grid/perfmon/Tracing.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>      
 #include <Grid/lattice/Lattice.h>      
 #include <Grid/cshift/Cshift.h>       
 #include <Grid/stencil/Stencil.h>      
+#include <Grid/stencil/GeneralLocalStencil.h>      
 #include <Grid/parallelIO/BinaryIO.h>
 #include <Grid/algorithms/Algorithms.h>   
+NAMESPACE_CHECK(GridCore)
 
 #endif

Grid/GridQCDcore.h

@@ -36,7 +36,9 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
 #include <Grid/GridCore.h>
 #include <Grid/qcd/QCD.h>
 #include <Grid/qcd/spin/Spin.h>
+#include <Grid/qcd/gparity/Gparity.h>
 #include <Grid/qcd/utils/Utils.h>
 #include <Grid/qcd/representations/Representations.h>
+NAMESPACE_CHECK(GridQCDCore);
 
 #endif

Grid/GridStd.h

@@ -0,0 +1,35 @@
+#ifndef GRID_STD_H
+#define GRID_STD_H
+
+///////////////////
+// Std C++ dependencies
+///////////////////
+#include <cassert>
+#include <complex>
+#include <memory>
+#include <vector>
+#include <array>
+#include <string>
+#include <iostream>
+#include <iomanip>
+#include <random>
+#include <functional>
+#include <stdio.h>
+#include <stdlib.h>
+#include <strings.h>
+#include <stdio.h>
+#include <signal.h>
+#include <ctime>
+#include <sys/time.h>
+#include <chrono>
+#include <zlib.h>
+
+///////////////////
+// Grid config
+///////////////////
+#include "Config.h"
+
+#ifdef TOFU
+#undef GRID_COMMS_THREADS
+#endif
+#endif /* GRID_STD_H */

Grid/Grid_Eigen_Dense.h

@@ -0,0 +1,75 @@
+#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
+#ifdef __NVCC_DIAG_PRAGMA_SUPPORT__
+#pragma nv_diag_suppress code_is_unreachable
+#else
+#pragma diag_suppress code_is_unreachable
+#endif
+#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

@@ -0,0 +1,81 @@
+extra_sources=
+extra_headers=
+
+if BUILD_COMMS_MPI3
+  extra_sources+=communicator/Communicator_mpi3.cc
+  extra_sources+=communicator/Communicator_base.cc
+  extra_sources+=communicator/SharedMemoryMPI.cc
+  extra_sources+=communicator/SharedMemory.cc
+endif
+
+if BUILD_COMMS_NONE
+  extra_sources+=communicator/Communicator_none.cc
+  extra_sources+=communicator/Communicator_base.cc
+  extra_sources+=communicator/SharedMemoryNone.cc
+  extra_sources+=communicator/SharedMemory.cc
+endif
+
+if BUILD_HDF5
+  extra_sources+=serialisation/Hdf5IO.cc 
+  extra_headers+=serialisation/Hdf5IO.h
+  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
+#
+include Make.inc
+include Eigen.inc
+
+extra_sources+=$(WILS_FERMION_FILES)
+extra_sources+=$(STAG_FERMION_FILES)
+if BUILD_ZMOBIUS
+  extra_sources+=$(ZWILS_FERMION_FILES)
+endif
+if BUILD_GPARITY
+  extra_sources+=$(GP_FERMION_FILES)
+endif
+if BUILD_FERMION_REPS
+  extra_sources+=$(ADJ_FERMION_FILES)
+  extra_sources+=$(TWOIND_FERMION_FILES)
+endif
+if BUILD_SP
+    extra_sources+=$(SP_FERMION_FILES)
+    extra_sources+=$(SP_TWOIND_FERMION_FILES)
+endif
+
+lib_LIBRARIES = libGrid.a
+
+CCFILES += $(extra_sources)
+HFILES  += $(extra_headers) Config.h Version.h
+
+libGrid_a_SOURCES              = $(CCFILES)
+libGrid_adir                   = $(includedir)/Grid
+nobase_dist_pkginclude_HEADERS = $(HFILES) $(eigen_files) $(eigen_unsupp_files)

Grid/Namespace.h

@@ -1,13 +1,12 @@
 /*************************************************************************************
 
-Grid physics library, www.github.com/paboyle/Grid 
+Grid physics library, www.github.com/paboyle/Grid
 
-Source file: extras/Hadrons/Modules.hpp
+Source file: ./lib/Namespace.h
 
-Copyright (C) 2015
 Copyright (C) 2016
 
-Author: Antonin Portelli <antonin.portelli@me.com>
+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
@@ -23,18 +22,17 @@ 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
+See the full license in the file "LICENSE" in the top level distribution
+directory
 *************************************************************************************/
 /*  END LEGAL */
-#include <Grid/Hadrons/Modules/MAction/DWF.hpp>
-#include <Grid/Hadrons/Modules/MAction/Wilson.hpp>
-#include <Grid/Hadrons/Modules/MContraction/Baryon.hpp>
-#include <Grid/Hadrons/Modules/MContraction/Meson.hpp>
-#include <Grid/Hadrons/Modules/MGauge/Load.hpp>
-#include <Grid/Hadrons/Modules/MGauge/Random.hpp>
-#include <Grid/Hadrons/Modules/MGauge/Unit.hpp>
-#include <Grid/Hadrons/Modules/MSolver/RBPrecCG.hpp>
-#include <Grid/Hadrons/Modules/MSource/Point.hpp>
-#include <Grid/Hadrons/Modules/MSource/SeqGamma.hpp>
-#include <Grid/Hadrons/Modules/MSource/Z2.hpp>
-#include <Grid/Hadrons/Modules/Quark.hpp>
+#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

@@ -1,6 +1,6 @@
     /*************************************************************************************
 
-    Grid physics library, www.github.com/paboyle/Grid 
+    Grid physics library, www.github.com/paboyle/Grid
 
     Source file: ./lib/Algorithms.h
 
@@ -29,45 +29,55 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 #ifndef GRID_ALGORITHMS_H
 #define GRID_ALGORITHMS_H
 
+NAMESPACE_CHECK(blas);
+#include <Grid/algorithms/blas/BatchedBlas.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/deflation/Deflation.h>
+#include <Grid/algorithms/deflation/MultiRHSBlockProject.h>
+#include <Grid/algorithms/deflation/MultiRHSDeflation.h>
+NAMESPACE_CHECK(deflation);
 #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>
-
-// Lanczos support
-#include <Grid/algorithms/iterative/MatrixUtils.h>
+#include <Grid/algorithms/iterative/ConjugateGradientMultiShiftMixedPrec.h>
+#include <Grid/algorithms/iterative/ConjugateGradientMixedPrecBatched.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/CoarsenedMatrix.h>
+#include <Grid/algorithms/iterative/PowerMethod.h>
+#include <Grid/algorithms/iterative/AdefGeneric.h>
+#include <Grid/algorithms/iterative/AdefMrhs.h>
+NAMESPACE_CHECK(PowerMethod);
+#include <Grid/algorithms/multigrid/MultiGrid.h>
+NAMESPACE_CHECK(multigrid);
 #include <Grid/algorithms/FFT.h>
 
-// Eigen/lanczos
-// EigCg
-// MCR
-// Pcg
-// Multishift CG
-// Hdcg
-// GCR
-// etc..
-
-// integrator/Leapfrog
-// integrator/Omelyan
-// integrator/ForceGradient
-
-// montecarlo/hmc
-// montecarlo/rhmc
-// montecarlo/metropolis
-// etc...
-
-
 #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
+#if defined(USE_MKL) || defined(GRID_SYCL)
+#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,*grid);
+  };
+    
+  ~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,*vgrid);
+      
+    // 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 +1,679 @@
+/*************************************************************************************
+
+    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;
+  virtual ~LinearOperatorBase(){};
+};
+
+
+/////////////////////////////////////////////////////////////////////////////////////////////
+// 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;
+  }
+};
+
+////////////////////////////////////////////////////////////////////
+// Create a shifted HermOp
+////////////////////////////////////////////////////////////////////
+template<class Field>
+class ShiftedHermOpLinearOperator : public LinearOperatorBase<Field> {
+  LinearOperatorBase<Field> &_Mat;
+  RealD _shift;
+public:
+  ShiftedHermOpLinearOperator(LinearOperatorBase<Field> &Mat,RealD shift): _Mat(Mat), _shift(shift){};
+  // Support for coarsening to a multigrid
+  void OpDiag (const Field &in, Field &out) {
+    assert(0);
+  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {
+    assert(0);
+  }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){
+    assert(0);
+  };
+  void Op     (const Field &in, Field &out){
+    HermOp(in,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    HermOp(in,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    HermOp(in,out);
+    ComplexD dot = innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    _Mat.HermOp(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) {
+    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]);
+    }
+  };
+  virtual ~OperatorFunction(){};
+};
+
+template<class Field> class LinearFunction {
+public:
+  virtual void operator() (const Field &in, Field &out) = 0;
+
+  virtual void operator() (const std::vector<Field> &in, std::vector<Field> &out)
+  {
+    assert(in.size() == out.size());
+
+    for (unsigned int i = 0; i < in.size(); ++i)
+    {
+      (*this)(in[i], out[i]);
+    }
+  }
+  virtual ~LinearFunction(){};
+};
+
+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:
+  using LinearFunction<Field>::operator();
+  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:
+  using LinearFunction<Field>::operator(); 
+  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

@@ -0,0 +1,52 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/Preconditioner.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.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_PRECONDITIONER_H
+#define GRID_PRECONDITIONER_H
+
+NAMESPACE_BEGIN(Grid);
+
+template<class Field> using Preconditioner =  LinearFunction<Field> ;
+
+/*
+template<class Field> class Preconditioner :  public LinearFunction<Field> {
+  using LinearFunction<Field>::operator();
+  virtual void operator()(const Field &src, Field & psi)=0;
+};
+*/
+
+template<class Field> class TrivialPrecon :  public Preconditioner<Field> { 
+public:
+  using Preconditioner<Field>::operator();
+  virtual void operator()(const Field &src, Field & psi){
+    psi = src;
+  }
+  TrivialPrecon(void){};
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/SparseMatrix.h

@@ -0,0 +1,81 @@
+/*************************************************************************************
+
+    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;
+  virtual ~SparseMatrixBase() {};
+};
+
+/////////////////////////////////////////////////////////////////////////////////////////////
+// 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;
+  virtual ~CheckerBoardedSparseMatrixBase() {};
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/algorithms/approx/Chebyshev.h

@@ -0,0 +1,394 @@
+/*************************************************************************************
+
+    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,0.0);
+    Coeffs[order-1] = 1.0;
+  };
+  
+  // 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);
+      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);
+      }
+
+      // 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:
@@ -40,7 +40,7 @@ public:
   RealD norm;
   RealD lo,hi;
 
-  MultiShiftFunction(int n,RealD _lo,RealD _hi): poles(n), residues(n), lo(_lo), hi(_hi) {;};
+  MultiShiftFunction(int n,RealD _lo,RealD _hi): poles(n), residues(n), tolerances(n), lo(_lo), hi(_hi) {;};
   RealD approx(RealD x);
   void csv(std::ostream &out);
   void gnuplot(std::ostream &out);
@@ -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/Remez.h

@@ -16,7 +16,7 @@
 #define INCLUDED_ALG_REMEZ_H
 
 #include <stddef.h>
-#include <Config.h>
+#include <Grid/GridStd.h>
 
 #ifdef HAVE_LIBGMP
 #include "bigfloat.h"

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;
@@ -293,7 +293,7 @@ static void sncndnFK(INTERNAL_PRECISION u, INTERNAL_PRECISION k,
  * Set type = 0 for the Zolotarev approximation, which is zero at x = 0, and
  * type = 1 for the approximation which is infinite at x = 0. */
 
-zolotarev_data* zolotarev(PRECISION epsilon, int n, int type) {
+zolotarev_data* zolotarev(ZOLO_PRECISION epsilon, int n, int type) {
   INTERNAL_PRECISION A, c, cp, kp, ksq, sn, cn, dn, Kp, Kj, z, z0, t, M, F,
     l, invlambda, xi, xisq, *tv, s, opl;
   int m, czero, ts;
@@ -375,12 +375,12 @@ zolotarev_data* zolotarev(PRECISION epsilon, int n, int type) {
   construct_partfrac(d);
   construct_contfrac(d);
 
-  /* Converting everything to PRECISION for external use only */
+  /* Converting everything to ZOLO_PRECISION for external use only */
 
   zd = (zolotarev_data*) malloc(sizeof(zolotarev_data));
-  zd -> A = (PRECISION) d -> A;
-  zd -> Delta = (PRECISION) d -> Delta;
-  zd -> epsilon = (PRECISION) d -> epsilon;
+  zd -> A = (ZOLO_PRECISION) d -> A;
+  zd -> Delta = (ZOLO_PRECISION) d -> Delta;
+  zd -> epsilon = (ZOLO_PRECISION) d -> epsilon;
   zd -> n = d -> n;
   zd -> type = d -> type;
   zd -> dn = d -> dn;
@@ -390,24 +390,24 @@ zolotarev_data* zolotarev(PRECISION epsilon, int n, int type) {
   zd -> deg_num = d -> deg_num;
   zd -> deg_denom = d -> deg_denom;
 
-  zd -> a = (PRECISION*) malloc(zd -> dn * sizeof(PRECISION));
-  for (m = 0; m < zd -> dn; m++) zd -> a[m] = (PRECISION) d -> a[m];
+  zd -> a = (ZOLO_PRECISION*) malloc(zd -> dn * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> dn; m++) zd -> a[m] = (ZOLO_PRECISION) d -> a[m];
   free(d -> a);
 
-  zd -> ap = (PRECISION*) malloc(zd -> dd * sizeof(PRECISION));
-  for (m = 0; m < zd -> dd; m++) zd -> ap[m] = (PRECISION) d -> ap[m];
+  zd -> ap = (ZOLO_PRECISION*) malloc(zd -> dd * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> dd; m++) zd -> ap[m] = (ZOLO_PRECISION) d -> ap[m];
   free(d -> ap);
 
-  zd -> alpha = (PRECISION*) malloc(zd -> da * sizeof(PRECISION));
-  for (m = 0; m < zd -> da; m++) zd -> alpha[m] = (PRECISION) d -> alpha[m];
+  zd -> alpha = (ZOLO_PRECISION*) malloc(zd -> da * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> da; m++) zd -> alpha[m] = (ZOLO_PRECISION) d -> alpha[m];
   free(d -> alpha);
 
-  zd -> beta = (PRECISION*) malloc(zd -> db * sizeof(PRECISION));
-  for (m = 0; m < zd -> db; m++) zd -> beta[m] = (PRECISION) d -> beta[m];
+  zd -> beta = (ZOLO_PRECISION*) malloc(zd -> db * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> db; m++) zd -> beta[m] = (ZOLO_PRECISION) d -> beta[m];
   free(d -> beta);
 
-  zd -> gamma = (PRECISION*) malloc(zd -> n * sizeof(PRECISION));
-  for (m = 0; m < zd -> n; m++) zd -> gamma[m] = (PRECISION) d -> gamma[m];
+  zd -> gamma = (ZOLO_PRECISION*) malloc(zd -> n * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> n; m++) zd -> gamma[m] = (ZOLO_PRECISION) d -> gamma[m];
   free(d -> gamma);
 
   free(d);
@@ -426,7 +426,7 @@ void zolotarev_free(zolotarev_data *zdata)
 }
 
 
-zolotarev_data* higham(PRECISION epsilon, int n) {
+zolotarev_data* higham(ZOLO_PRECISION epsilon, int n) {
   INTERNAL_PRECISION A, M, c, cp, z, z0, t, epssq;
   int m, czero;
   zolotarev_data *zd;
@@ -481,9 +481,9 @@ zolotarev_data* higham(PRECISION epsilon, int n) {
   /* Converting everything to PRECISION for external use only */
 
   zd = (zolotarev_data*) malloc(sizeof(zolotarev_data));
-  zd -> A = (PRECISION) d -> A;
-  zd -> Delta = (PRECISION) d -> Delta;
-  zd -> epsilon = (PRECISION) d -> epsilon;
+  zd -> A = (ZOLO_PRECISION) d -> A;
+  zd -> Delta = (ZOLO_PRECISION) d -> Delta;
+  zd -> epsilon = (ZOLO_PRECISION) d -> epsilon;
   zd -> n = d -> n;
   zd -> type = d -> type;
   zd -> dn = d -> dn;
@@ -493,45 +493,47 @@ zolotarev_data* higham(PRECISION epsilon, int n) {
   zd -> deg_num = d -> deg_num;
   zd -> deg_denom = d -> deg_denom;
 
-  zd -> a = (PRECISION*) malloc(zd -> dn * sizeof(PRECISION));
-  for (m = 0; m < zd -> dn; m++) zd -> a[m] = (PRECISION) d -> a[m];
+  zd -> a = (ZOLO_PRECISION*) malloc(zd -> dn * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> dn; m++) zd -> a[m] = (ZOLO_PRECISION) d -> a[m];
   free(d -> a);
 
-  zd -> ap = (PRECISION*) malloc(zd -> dd * sizeof(PRECISION));
-  for (m = 0; m < zd -> dd; m++) zd -> ap[m] = (PRECISION) d -> ap[m];
+  zd -> ap = (ZOLO_PRECISION*) malloc(zd -> dd * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> dd; m++) zd -> ap[m] = (ZOLO_PRECISION) d -> ap[m];
   free(d -> ap);
 
-  zd -> alpha = (PRECISION*) malloc(zd -> da * sizeof(PRECISION));
-  for (m = 0; m < zd -> da; m++) zd -> alpha[m] = (PRECISION) d -> alpha[m];
+  zd -> alpha = (ZOLO_PRECISION*) malloc(zd -> da * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> da; m++) zd -> alpha[m] = (ZOLO_PRECISION) d -> alpha[m];
   free(d -> alpha);
 
-  zd -> beta = (PRECISION*) malloc(zd -> db * sizeof(PRECISION));
-  for (m = 0; m < zd -> db; m++) zd -> beta[m] = (PRECISION) d -> beta[m];
+  zd -> beta = (ZOLO_PRECISION*) malloc(zd -> db * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> db; m++) zd -> beta[m] = (ZOLO_PRECISION) d -> beta[m];
   free(d -> beta);
 
-  zd -> gamma = (PRECISION*) malloc(zd -> n * sizeof(PRECISION));
-  for (m = 0; m < zd -> n; m++) zd -> gamma[m] = (PRECISION) d -> gamma[m];
+  zd -> gamma = (ZOLO_PRECISION*) malloc(zd -> n * sizeof(ZOLO_PRECISION));
+  for (m = 0; m < zd -> n; m++) zd -> gamma[m] = (ZOLO_PRECISION) d -> gamma[m];
   free(d -> gamma);
 
   free(d);
   return zd;
 }
-}}
+
+NAMESPACE_END(Approx);
+NAMESPACE_END(Grid);
 
 #ifdef TEST
 
 #undef ZERO
-#define ZERO ((PRECISION) 0)
+#define ZERO ((ZOLO_PRECISION) 0)
 #undef ONE
-#define ONE ((PRECISION) 1)
+#define ONE ((ZOLO_PRECISION) 1)
 #undef TWO
-#define TWO ((PRECISION) 2)
+#define TWO ((ZOLO_PRECISION) 2)
 
 /* Evaluate the rational approximation R(x) using the factored form */
 
-static PRECISION zolotarev_eval(PRECISION x, zolotarev_data* rdata) {
+static ZOLO_PRECISION zolotarev_eval(ZOLO_PRECISION x, zolotarev_data* rdata) {
   int m;
-  PRECISION R;
+  ZOLO_PRECISION R;
 
   if (rdata -> type == 0) {
     R = rdata -> A * x;
@@ -549,9 +551,9 @@ static PRECISION zolotarev_eval(PRECISION x, zolotarev_data* rdata) {
 
 /* Evaluate the rational approximation R(x) using the partial fraction form */
 
-static PRECISION zolotarev_partfrac_eval(PRECISION x, zolotarev_data* rdata) {
+static ZOLO_PRECISION zolotarev_partfrac_eval(ZOLO_PRECISION x, zolotarev_data* rdata) {
   int m;
-  PRECISION R = rdata -> alpha[rdata -> da - 1];
+  ZOLO_PRECISION R = rdata -> alpha[rdata -> da - 1];
   for (m = 0; m < rdata -> dd; m++)
     R += rdata -> alpha[m] / (x * x - rdata -> ap[m]);
   if (rdata -> type == 1) R += rdata -> alpha[rdata -> dd] / (x * x);
@@ -566,18 +568,18 @@ static PRECISION zolotarev_partfrac_eval(PRECISION x, zolotarev_data* rdata) {
  * non-signalling overflow this will work correctly since 1/(1/0) = 1/INF = 0,
  * but with signalling overflow you will get an error message. */
 
-static PRECISION zolotarev_contfrac_eval(PRECISION x, zolotarev_data* rdata) {
+static ZOLO_PRECISION zolotarev_contfrac_eval(ZOLO_PRECISION x, zolotarev_data* rdata) {
   int m;
-  PRECISION R = rdata -> beta[0] * x;
+  ZOLO_PRECISION R = rdata -> beta[0] * x;
   for (m = 1; m < rdata -> db; m++) R = rdata -> beta[m] * x + ONE / R;
   return R;
 }    
 
 /* Evaluate the rational approximation R(x) using Cayley form */
 
-static PRECISION zolotarev_cayley_eval(PRECISION x, zolotarev_data* rdata) {
+static ZOLO_PRECISION zolotarev_cayley_eval(ZOLO_PRECISION x, zolotarev_data* rdata) {
   int m;
-  PRECISION T;
+  ZOLO_PRECISION T;
 
   T = rdata -> type == 0 ? ONE : -ONE;
   for (m = 0; m < rdata -> n; m++)
@@ -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):
  *
@@ -604,7 +607,7 @@ int main(int argc, char** argv) {
   int m, n, plotpts = 5000, type = 0;
   float eps, x, ypferr, ycferr, ycaylerr, maxypferr, maxycferr, maxycaylerr;
   zolotarev_data *rdata;
-  PRECISION y;
+  ZOLO_PRECISION y;
   FILE *plot_function, *plot_error, 
     *plot_partfrac, *plot_contfrac, *plot_cayley;
 
@@ -623,13 +626,13 @@ int main(int argc, char** argv) {
   }
 
   rdata = type == 2 
-    ? higham((PRECISION) eps, n) 
-    : zolotarev((PRECISION) eps, n, type);
+    ? higham((ZOLO_PRECISION) eps, n) 
+    : zolotarev((ZOLO_PRECISION) eps, n, type);
 
   printf("Zolotarev Test: R(epsilon = %g, n = %d, type = %d)\n\t" 
 	 STRINGIFY(VERSION) "\n\t" STRINGIFY(HVERSION)
 	 "\n\tINTERNAL_PRECISION = " STRINGIFY(INTERNAL_PRECISION)
-	 "\tPRECISION = " STRINGIFY(PRECISION)
+	 "\tZOLO_PRECISION = " STRINGIFY(ZOLO_PRECISION)
 	 "\n\n\tRational approximation of degree (%d,%d), %s at x = 0\n"
 	 "\tDelta = %g (maximum error)\n\n"
 	 "\tA = %g (overall factor)\n",
@@ -678,15 +681,15 @@ int main(int argc, char** argv) {
     x = 2.4 * (float) m / plotpts - 1.2;
     if (rdata -> type == 0 || fabs(x) * (float) plotpts > 1.0) {
       /* skip x = 0 for type 1, as R(0) is singular */
-      y = zolotarev_eval((PRECISION) x, rdata);
+      y = zolotarev_eval((ZOLO_PRECISION) x, rdata);
       fprintf(plot_function, "%g %g\n", x, (float) y);
       fprintf(plot_error, "%g %g\n",
 	      x, (float)((y - ((x > 0.0 ? ONE : -ONE))) / rdata -> Delta));
-      ypferr = (float)((zolotarev_partfrac_eval((PRECISION) x, rdata) - y)
+      ypferr = (float)((zolotarev_partfrac_eval((ZOLO_PRECISION) x, rdata) - y)
 		       / rdata -> Delta);
-      ycferr = (float)((zolotarev_contfrac_eval((PRECISION) x, rdata) - y)
+      ycferr = (float)((zolotarev_contfrac_eval((ZOLO_PRECISION) x, rdata) - y)
 		       / rdata -> Delta);
-      ycaylerr = (float)((zolotarev_cayley_eval((PRECISION) x, rdata) - y)
+      ycaylerr = (float)((zolotarev_cayley_eval((ZOLO_PRECISION) x, rdata) - y)
 		       / rdata -> Delta);
       if (fabs(x) < 1.0 && fabs(x) > rdata -> epsilon) {
 	maxypferr = MAX(maxypferr, fabs(ypferr));
@@ -723,5 +726,5 @@ int main(int argc, char** argv) {
   return EXIT_SUCCESS;
 }
 
-
 #endif /* TEST */
+

Grid/algorithms/approx/Zolotarev.h

@@ -1,18 +1,18 @@
 /* -*- 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
+#ifndef ZOLO_PRECISION
+#define ZOLO_PRECISION double
 #endif
-#define ZPRECISION PRECISION
+#define ZPRECISION ZOLO_PRECISION
 #define ZOLOTAREV_DATA zolotarev_data
 #endif
 
@@ -77,11 +77,13 @@ typedef struct {
  * zolotarev_data structure. The arguments must satisfy the constraints that
  * epsilon > 0, n > 0, and type = 0 or 1. */
 
-ZOLOTAREV_DATA* higham(PRECISION epsilon, int n) ;
-ZOLOTAREV_DATA* zolotarev(PRECISION epsilon, int n, int type);
+ZOLOTAREV_DATA* higham(ZOLO_PRECISION epsilon, int n) ;
+ZOLOTAREV_DATA* zolotarev(ZOLO_PRECISION epsilon, int n, int type);
 void zolotarev_free(zolotarev_data *zdata);
 #endif
 
 #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/blas/BatchedBlas.cc

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

Grid/algorithms/blas/BatchedBlas.h

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

Grid/algorithms/deflation/Deflation.h

@@ -0,0 +1,157 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ImplicitlyRestartedLanczos.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_DEFLATION_H
+#define GRID_DEFLATION_H
+
+namespace Grid { 
+
+template<class Field>
+class ZeroGuesser: public LinearFunction<Field> {
+public:
+  using LinearFunction<Field>::operator();
+    virtual void operator()(const Field &src, Field &guess) { guess = Zero(); };
+};
+template<class Field>
+class DoNothingGuesser: public LinearFunction<Field> {
+public:
+  using LinearFunction<Field>::operator();
+  virtual void operator()(const Field &src, Field &guess) {  };
+};
+template<class Field>
+class SourceGuesser: public LinearFunction<Field> {
+public:
+  using LinearFunction<Field>::operator();
+  virtual void operator()(const Field &src, Field &guess) { guess = src; };
+};
+
+////////////////////////////////
+// Fine grid deflation
+////////////////////////////////
+template<class Field>
+class DeflatedGuesser: public LinearFunction<Field> {
+private:
+  const std::vector<Field> &evec;
+  const std::vector<RealD> &eval;
+  const unsigned int       N;
+
+public:
+  using LinearFunction<Field>::operator();
+
+  DeflatedGuesser(const std::vector<Field> & _evec,const std::vector<RealD> & _eval)
+  : DeflatedGuesser(_evec, _eval, _evec.size())
+  {}
+
+  DeflatedGuesser(const std::vector<Field> & _evec, const std::vector<RealD> & _eval, const unsigned int _N)
+  : evec(_evec), eval(_eval), N(_N)
+  {
+    assert(evec.size()==eval.size());
+    assert(N <= evec.size());
+  } 
+
+  virtual void operator()(const Field &src,Field &guess) {
+    guess = Zero();
+    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: public LinearFunction<FineField> {
+private:
+  const std::vector<FineField>   &subspace;
+  const std::vector<CoarseField> &evec_coarse;
+  const std::vector<RealD>       &eval_coarse;
+public:
+  
+  using LinearFunction<FineField>::operator();
+  LocalCoherenceDeflatedGuesser(const std::vector<FineField>   &_subspace,
+				const std::vector<CoarseField> &_evec_coarse,
+				const std::vector<RealD>       &_eval_coarse)
+    : subspace(_subspace), 
+      evec_coarse(_evec_coarse), 
+      eval_coarse(_eval_coarse)  
+  {
+  }
+  
+  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();
+    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();
+  };
+
+  void operator()(const std::vector<FineField> &src,std::vector<FineField> &guess) {
+    int Nevec = (int)evec_coarse.size();
+    int Nsrc = (int)src.size();
+    // make temp variables
+    std::vector<CoarseField> src_coarse(Nsrc,evec_coarse[0].Grid());
+    std::vector<CoarseField> guess_coarse(Nsrc,evec_coarse[0].Grid());    
+    //Preporcessing
+    std::cout << GridLogMessage << "Start BlockProject for loop" << std::endl;
+    for (int j=0;j<Nsrc;j++)
+    {
+    guess_coarse[j] = Zero();
+    std::cout << GridLogMessage << "BlockProject iter: " << j << std::endl;
+    blockProject(src_coarse[j],src[j],subspace);
+    }
+    //deflation set up for eigen vector batchsize 1 and source batch size equal number of sources
+    std::cout << GridLogMessage << "Start ProjectAccum for loop" << std::endl;
+    for (int i=0;i<Nevec;i++)
+    {
+      std::cout << GridLogMessage << "ProjectAccum Nvec: " << i << std::endl;
+      const CoarseField & tmp = evec_coarse[i];
+      for (int j=0;j<Nsrc;j++)
+      {
+        axpy(guess_coarse[j],TensorRemove(innerProduct(tmp,src_coarse[j])) / eval_coarse[i],tmp,guess_coarse[j]);
+      }
+    }
+    //postprocessing
+    std::cout << GridLogMessage << "Start BlockPromote for loop" << std::endl;
+    for (int j=0;j<Nsrc;j++)
+    {
+    std::cout << GridLogMessage << "BlockProject iter: " << j << std::endl;
+    blockPromote(guess_coarse[j],guess[j],subspace);
+    guess[j].Checkerboard() = src[j].Checkerboard();
+    }
+  };
+
+  };
+
+
+
+}
+#endif

Grid/algorithms/deflation/MultiRHSBlockProject.h

@@ -0,0 +1,513 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: MultiRHSDeflation.h
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+
+/* 
+   MultiRHS block projection
+
+   Import basis -> nblock x nbasis x  (block x internal) 
+   Import vector of fine lattice objects -> nblock x nrhs x (block x internal) 
+
+   => coarse_(nrhs x nbasis )^block = via batched GEMM
+
+//template<class vobj,class CComplex,int nbasis,class VLattice>
+//inline void blockProject(Lattice<iVector<CComplex,nbasis > > &coarseData,
+//			   const VLattice &fineData,
+//			   const VLattice &Basis)
+*/
+
+template<class Field>
+class MultiRHSBlockProject
+{
+public:
+
+  typedef typename Field::scalar_type   scalar;
+  typedef typename Field::scalar_object scalar_object;
+  typedef Field Fermion;
+
+  int nbasis;
+  GridBase *coarse_grid;
+  GridBase *fine_grid;
+  uint64_t block_vol;
+  uint64_t fine_vol;
+  uint64_t coarse_vol;
+  uint64_t words;
+
+  // Row major layout "C" order:
+  // BLAS_V[coarse_vol][nbasis][block_vol][words]
+  // BLAS_F[coarse_vol][nrhs][block_vol][words]
+  // BLAS_C[coarse_vol][nrhs][nbasis]
+  /*
+   * in Fortran column major notation (cuBlas order)
+   *
+   * Vxb = [v1(x)][..][vn(x)] ... x coarse vol
+   *
+   * Fxr = [r1(x)][..][rm(x)] ... x coarse vol
+   *
+   * Block project:
+   * C_br = V^dag F x coarse vol
+   *
+   * Block promote:
+   * F_xr = Vxb Cbr x coarse_vol
+   */  
+  deviceVector<scalar> BLAS_V;      // words * block_vol * nbasis x coarse_vol 
+  deviceVector<scalar> BLAS_F;      // nrhs x fine_vol * words   -- the sources
+  deviceVector<scalar> BLAS_C;      // nrhs x coarse_vol * nbasis -- the coarse coeffs
+
+  RealD blasNorm2(deviceVector<scalar> &blas)
+  {
+    scalar ss(0.0);
+    std::vector<scalar> tmp(blas.size());
+    acceleratorCopyFromDevice(&blas[0],&tmp[0],blas.size()*sizeof(scalar));
+    for(int64_t s=0;s<blas.size();s++){
+      ss=ss+tmp[s]*adj(tmp[s]);
+    }
+    coarse_grid->GlobalSum(ss);
+    return real(ss);
+  }
+  
+  MultiRHSBlockProject(){};
+ ~MultiRHSBlockProject(){ Deallocate(); };
+  
+  void Deallocate(void)
+  {
+    nbasis=0;
+    coarse_grid=nullptr;
+    fine_grid=nullptr;
+    fine_vol=0;
+    block_vol=0;
+    coarse_vol=0;
+    words=0;
+    BLAS_V.resize(0);
+    BLAS_F.resize(0);
+    BLAS_C.resize(0);
+  }
+  void Allocate(int _nbasis,GridBase *_fgrid,GridBase *_cgrid)
+  {
+    nbasis=_nbasis;
+
+    fine_grid=_fgrid;
+    coarse_grid=_cgrid;
+
+    fine_vol   = fine_grid->lSites();
+    coarse_vol = coarse_grid->lSites();
+    block_vol = fine_vol/coarse_vol;
+    
+    words = sizeof(scalar_object)/sizeof(scalar);
+
+    BLAS_V.resize (fine_vol * words * nbasis );
+  }
+  void ImportFineGridVectors(std::vector <Field > &vecs, deviceVector<scalar> &blas)
+  {
+    int nvec = vecs.size();
+    typedef typename Field::vector_object vobj;
+    //    std::cout << GridLogMessage <<" BlockProjector importing "<<nvec<< " fine grid vectors" <<std::endl;
+
+    assert(vecs[0].Grid()==fine_grid);
+
+    subdivides(coarse_grid,fine_grid); // require they map
+
+    int _ndimension = coarse_grid->_ndimension;
+    assert(block_vol == fine_grid->oSites() / coarse_grid->oSites());
+    
+    Coordinate  block_r      (_ndimension);
+    for(int d=0 ; d<_ndimension;d++){
+      block_r[d] = fine_grid->_rdimensions[d] / coarse_grid->_rdimensions[d];
+    }
+
+    uint64_t sz = blas.size();
+
+    acceleratorMemSet(&blas[0],0,blas.size()*sizeof(scalar));
+
+    Coordinate fine_rdimensions = fine_grid->_rdimensions;
+    Coordinate coarse_rdimensions = coarse_grid->_rdimensions;
+    int64_t bv= block_vol;
+    for(int v=0;v<vecs.size();v++){
+
+      //      std::cout << " BlockProjector importing vector"<<v<<" "<<norm2(vecs[v])<<std::endl;
+      autoView( fineData   , vecs[v], AcceleratorRead);
+
+      auto blasData_p  = &blas[0];
+      auto fineData_p  = &fineData[0];
+
+      int64_t osites = fine_grid->oSites();
+
+      // loop over fine sites
+      const int Nsimd = vobj::Nsimd();
+      //      std::cout << "sz "<<sz<<std::endl;
+      //      std::cout << "prod "<<Nsimd * coarse_grid->oSites() * block_vol * nvec * words<<std::endl;
+      assert(sz == Nsimd * coarse_grid->oSites() * block_vol * nvec * words);
+      uint64_t lwords= words; // local variable for copy in to GPU
+      accelerator_for(sf,osites,Nsimd,{
+#ifdef GRID_SIMT
+        {
+	  int lane=acceleratorSIMTlane(Nsimd); // buffer lane
+#else
+	  for(int lane=0;lane<Nsimd;lane++) {
+#endif
+	  // One thread per fine site
+	  Coordinate coor_f(_ndimension);
+	  Coordinate coor_b(_ndimension);
+	  Coordinate coor_c(_ndimension);
+
+	  // Fine site to fine coor
+	  Lexicographic::CoorFromIndex(coor_f,sf,fine_rdimensions);
+
+	  for(int d=0;d<_ndimension;d++) coor_b[d] = coor_f[d]%block_r[d];
+	  for(int d=0;d<_ndimension;d++) coor_c[d] = coor_f[d]/block_r[d];
+	  
+	  int sc;// coarse site
+	  int sb;// block site
+	  Lexicographic::IndexFromCoor(coor_c,sc,coarse_rdimensions);
+	  Lexicographic::IndexFromCoor(coor_b,sb,block_r);
+
+          scalar_object data = extractLane(lane,fineData[sf]);
+
+	  // BLAS layout address calculation
+	  // words * block_vol * nbasis x coarse_vol
+	  // coarse oSite x block vole x lanes
+	  int64_t site = (lane*osites + sc*bv)*nvec
+   	               + v*bv
+	               + sb;
+
+	  //	  assert(site*lwords<sz);
+
+	  scalar_object * ptr = (scalar_object *)&blasData_p[site*lwords];
+
+	  *ptr = data;
+#ifdef GRID_SIMT
+	}
+#else
+	}
+#endif
+      });
+      //      std::cout << " import fine Blas norm "<<blasNorm2(blas)<<std::endl;
+      //      std::cout << " BlockProjector imported vector"<<v<<std::endl;
+    }
+  }
+  void ExportFineGridVectors(std::vector <Field> &vecs, deviceVector<scalar> &blas)
+  {
+    typedef typename Field::vector_object vobj;
+
+    int nvec = vecs.size();
+
+    assert(vecs[0].Grid()==fine_grid);
+
+    subdivides(coarse_grid,fine_grid); // require they map
+
+    int _ndimension = coarse_grid->_ndimension;
+    assert(block_vol == fine_grid->oSites() / coarse_grid->oSites());
+    
+    Coordinate  block_r      (_ndimension);
+    for(int d=0 ; d<_ndimension;d++){
+      block_r[d] = fine_grid->_rdimensions[d] / coarse_grid->_rdimensions[d];
+    }
+    Coordinate fine_rdimensions = fine_grid->_rdimensions;
+    Coordinate coarse_rdimensions = coarse_grid->_rdimensions;
+
+    //    std::cout << " export fine Blas norm "<<blasNorm2(blas)<<std::endl;
+
+    int64_t bv= block_vol;
+    for(int v=0;v<vecs.size();v++){
+
+      autoView( fineData   , vecs[v], AcceleratorWrite);
+
+      auto blasData_p  = &blas[0];
+      auto fineData_p    = &fineData[0];
+
+      int64_t osites = fine_grid->oSites();
+      uint64_t lwords = words;
+      //      std::cout << " Nsimd is "<<vobj::Nsimd() << std::endl;
+      //      std::cout << " lwords is "<<lwords << std::endl;
+      //      std::cout << " sizeof(scalar_object) is "<<sizeof(scalar_object) << std::endl;
+      // loop over fine sites
+      accelerator_for(sf,osites,vobj::Nsimd(),{
+      
+#ifdef GRID_SIMT
+        {
+	  int lane=acceleratorSIMTlane(vobj::Nsimd()); // buffer lane
+#else
+	  for(int lane=0;lane<vobj::Nsimd();lane++) {
+#endif
+	  // One thread per fine site
+	  Coordinate coor_f(_ndimension);
+	  Coordinate coor_b(_ndimension);
+	  Coordinate coor_c(_ndimension);
+
+	  Lexicographic::CoorFromIndex(coor_f,sf,fine_rdimensions);
+
+	  for(int d=0;d<_ndimension;d++) coor_b[d] = coor_f[d]%block_r[d];
+	  for(int d=0;d<_ndimension;d++) coor_c[d] = coor_f[d]/block_r[d];
+	  
+	  int sc;
+	  int sb;
+	  Lexicographic::IndexFromCoor(coor_c,sc,coarse_rdimensions);
+	  Lexicographic::IndexFromCoor(coor_b,sb,block_r);
+
+	  // BLAS layout address calculation
+	  // words * block_vol * nbasis x coarse_vol 	  
+	  int64_t site = (lane*osites + sc*bv)*nvec
+   	               + v*bv
+	               + sb;
+
+	  scalar_object * ptr = (scalar_object *)&blasData_p[site*lwords];
+
+	  scalar_object data = *ptr;
+
+	  insertLane(lane,fineData[sf],data);
+#ifdef GRID_SIMT
+	}
+#else
+	}
+#endif
+      });
+    }
+  }
+  template<class vobj>
+  void ImportCoarseGridVectors(std::vector <Lattice<vobj> > &vecs, deviceVector<scalar> &blas)
+  {
+    int nvec = vecs.size();
+    typedef typename vobj::scalar_object coarse_scalar_object;
+
+    //    std::cout << " BlockProjector importing "<<nvec<< " coarse grid vectors" <<std::endl;
+
+    assert(vecs[0].Grid()==coarse_grid);
+
+    int _ndimension = coarse_grid->_ndimension;
+
+    uint64_t sz = blas.size();
+
+    Coordinate coarse_rdimensions = coarse_grid->_rdimensions;
+    
+    for(int v=0;v<vecs.size();v++){
+
+      //      std::cout << " BlockProjector importing coarse vector"<<v<<" "<<norm2(vecs[v])<<std::endl;
+      autoView( coarseData   , vecs[v], AcceleratorRead);
+
+      auto blasData_p  = &blas[0];
+      auto coarseData_p  = &coarseData[0];
+
+      int64_t osites = coarse_grid->oSites();
+
+      // loop over fine sites
+      const int Nsimd = vobj::Nsimd();
+      uint64_t cwords=sizeof(typename vobj::scalar_object)/sizeof(scalar);
+      assert(cwords==nbasis);
+      
+      accelerator_for(sc,osites,Nsimd,{
+#ifdef GRID_SIMT
+        {
+	  int lane=acceleratorSIMTlane(Nsimd); // buffer lane
+#else
+	  for(int lane=0;lane<Nsimd;lane++) {
+#endif
+           // C_br per site
+	    int64_t blas_site = (lane*osites + sc)*nvec*cwords + v*cwords;
+	    
+	    coarse_scalar_object data = extractLane(lane,coarseData[sc]);
+
+	    coarse_scalar_object * ptr = (coarse_scalar_object *)&blasData_p[blas_site];
+
+	    *ptr = data;
+#ifdef GRID_SIMT
+	}
+#else
+	}
+#endif
+      });
+      //      std::cout << " import coarsee Blas norm "<<blasNorm2(blas)<<std::endl;
+    }
+  }
+  template<class vobj>
+  void ExportCoarseGridVectors(std::vector <Lattice<vobj> > &vecs, deviceVector<scalar> &blas)
+  {
+    int nvec = vecs.size();
+    typedef typename vobj::scalar_object coarse_scalar_object;
+    //    std::cout << GridLogMessage<<" BlockProjector exporting "<<nvec<< " coarse grid vectors" <<std::endl;
+
+    assert(vecs[0].Grid()==coarse_grid);
+
+    int _ndimension = coarse_grid->_ndimension;
+    
+    uint64_t sz = blas.size();
+
+    Coordinate coarse_rdimensions = coarse_grid->_rdimensions;
+    
+    //    std::cout << " export coarsee Blas norm "<<blasNorm2(blas)<<std::endl;
+    for(int v=0;v<vecs.size();v++){
+
+      //  std::cout << " BlockProjector exporting coarse vector"<<v<<std::endl;
+      autoView( coarseData   , vecs[v], AcceleratorWrite);
+
+      auto blasData_p  = &blas[0];
+      auto coarseData_p  = &coarseData[0];
+
+      int64_t osites = coarse_grid->oSites();
+
+      // loop over fine sites
+      const int Nsimd = vobj::Nsimd();
+      uint64_t cwords=sizeof(typename vobj::scalar_object)/sizeof(scalar);
+      assert(cwords==nbasis);
+      
+      accelerator_for(sc,osites,Nsimd,{
+	  // Wrap in a macro "FOR_ALL_LANES(lane,{ ... });
+#ifdef GRID_SIMT
+        {
+	  int lane=acceleratorSIMTlane(Nsimd); // buffer lane
+#else
+	  for(int lane=0;lane<Nsimd;lane++) {
+#endif
+	    int64_t blas_site = (lane*osites + sc)*nvec*cwords + v*cwords;
+	    coarse_scalar_object * ptr = (coarse_scalar_object *)&blasData_p[blas_site];
+	    coarse_scalar_object data = *ptr;
+	    insertLane(lane,coarseData[sc],data);
+#ifdef GRID_SIMT
+	}
+#else
+	}
+#endif
+      });
+    }
+  }
+  void ImportBasis(std::vector < Field > &vecs)
+  {
+    //    std::cout << " BlockProjector Import basis size "<<vecs.size()<<std::endl;
+    ImportFineGridVectors(vecs,BLAS_V);
+  }
+
+  template<class cobj>
+  void blockProject(std::vector<Field> &fine,std::vector< Lattice<cobj> > & coarse)
+  {
+    int nrhs=fine.size();
+    int _nbasis = sizeof(typename cobj::scalar_object)/sizeof(scalar);
+    //    std::cout << "blockProject nbasis " <<nbasis<<" " << _nbasis<<std::endl;
+    assert(nbasis==_nbasis);
+    
+    BLAS_F.resize (fine_vol * words * nrhs );
+    BLAS_C.resize (coarse_vol * nbasis * nrhs );
+
+    /////////////////////////////////////////////
+    // Copy in the multi-rhs sources to same data layout
+    /////////////////////////////////////////////
+    //    std::cout << "BlockProject import fine"<<std::endl;
+    ImportFineGridVectors(fine,BLAS_F);
+    
+    deviceVector<scalar *> Vd(coarse_vol);
+    deviceVector<scalar *> Fd(coarse_vol);
+    deviceVector<scalar *> Cd(coarse_vol);
+
+    //    std::cout << "BlockProject pointers"<<std::endl;
+    for(int c=0;c<coarse_vol;c++){
+      // BLAS_V[coarse_vol][nbasis][block_vol][words]
+      // BLAS_F[coarse_vol][nrhs][block_vol][words]
+      // BLAS_C[coarse_vol][nrhs][nbasis]
+      scalar * Vh = & BLAS_V[c*nbasis*block_vol*words];
+      scalar * Fh = & BLAS_F[c*nrhs*block_vol*words];
+      scalar * Ch = & BLAS_C[c*nrhs*nbasis];
+
+      acceleratorPut(Vd[c],Vh);
+      acceleratorPut(Fd[c],Fh);
+      acceleratorPut(Cd[c],Ch);
+    }
+
+    GridBLAS BLAS;
+
+    //    std::cout << "BlockProject BLAS"<<std::endl;
+    int64_t vw = block_vol * words;
+    /////////////////////////////////////////
+    // C_br = V^dag R
+    /////////////////////////////////////////
+    BLAS.gemmBatched(GridBLAS_OP_C,GridBLAS_OP_N, 
+    		     nbasis,nrhs,vw,
+		     ComplexD(1.0),
+		     Vd,
+		     Fd,
+		     ComplexD(0.0),  // wipe out C
+		     Cd);
+    BLAS.synchronise();
+    //    std::cout << "BlockProject done"<<std::endl;
+    ExportCoarseGridVectors(coarse, BLAS_C);
+    //    std::cout << "BlockProject done"<<std::endl;
+
+  }
+
+  template<class cobj>
+  void blockPromote(std::vector<Field> &fine,std::vector<Lattice<cobj> > & coarse)
+  {
+    int nrhs=fine.size();
+    int _nbasis = sizeof(typename cobj::scalar_object)/sizeof(scalar);
+    assert(nbasis==_nbasis);
+    
+    BLAS_F.resize (fine_vol * words * nrhs );
+    BLAS_C.resize (coarse_vol * nbasis * nrhs );
+
+    ImportCoarseGridVectors(coarse, BLAS_C);
+
+    GridBLAS BLAS;
+
+    deviceVector<scalar *> Vd(coarse_vol);
+    deviceVector<scalar *> Fd(coarse_vol);
+    deviceVector<scalar *> Cd(coarse_vol);
+
+    for(int c=0;c<coarse_vol;c++){
+      // BLAS_V[coarse_vol][nbasis][block_vol][words]
+      // BLAS_F[coarse_vol][nrhs][block_vol][words]
+      // BLAS_C[coarse_vol][nrhs][nbasis]
+      scalar * Vh = & BLAS_V[c*nbasis*block_vol*words];
+      scalar * Fh = & BLAS_F[c*nrhs*block_vol*words];
+      scalar * Ch = & BLAS_C[c*nrhs*nbasis];
+      acceleratorPut(Vd[c],Vh);
+      acceleratorPut(Fd[c],Fh);
+      acceleratorPut(Cd[c],Ch);
+    }
+
+    /////////////////////////////////////////
+    // Block promote:
+    // F_xr = Vxb Cbr (x coarse_vol)
+    /////////////////////////////////////////
+
+    int64_t vw = block_vol * words;
+    BLAS.gemmBatched(GridBLAS_OP_N,GridBLAS_OP_N, 
+    		     vw,nrhs,nbasis,
+		     ComplexD(1.0),
+		     Vd,
+		     Cd,
+		     ComplexD(0.0),  // wipe out C
+		     Fd);
+    BLAS.synchronise();
+    //    std::cout << " blas call done"<<std::endl;
+    
+    ExportFineGridVectors(fine, BLAS_F);
+    //    std::cout << " exported "<<std::endl;
+  }
+};
+
+NAMESPACE_END(Grid);

Grid/algorithms/deflation/MultiRHSDeflation.h

@@ -0,0 +1,233 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: MultiRHSDeflation.h
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+
+/* Need helper object for BLAS accelerated mrhs projection
+
+   i) MultiRHS Deflation
+
+   Import Evecs -> nev x vol x internal 
+   Import vector of Lattice objects -> nrhs x vol x internal
+   => Cij (nrhs x Nev) via GEMM.
+   => Guess  (nrhs x vol x internal)  = C x evecs (via GEMM)
+   Export
+
+   
+   ii) MultiRHS block projection
+
+   Import basis -> nblock x nbasis x  (block x internal) 
+   Import vector of fine lattice objects -> nblock x nrhs x (block x internal) 
+
+   => coarse_(nrhs x nbasis )^block = via batched GEMM
+
+   iii)   Alternate interface: 
+   Import higher dim Lattice object-> vol x nrhs layout
+   
+*/
+template<class Field>
+class MultiRHSDeflation
+{
+public:
+
+  typedef typename Field::scalar_type   scalar;
+  typedef typename Field::scalar_object scalar_object;
+
+  int nev;
+  std::vector<RealD> eval;
+  GridBase *grid;
+  uint64_t vol;
+  uint64_t words;
+  
+  deviceVector<scalar> BLAS_E;      //  nev x vol -- the eigenbasis   (up to a 1/sqrt(lambda))
+  deviceVector<scalar> BLAS_R;      // nrhs x vol -- the sources
+  deviceVector<scalar> BLAS_G;      // nrhs x vol -- the guess
+  deviceVector<scalar> BLAS_C;      // nrhs x nev -- the coefficients 
+  
+  MultiRHSDeflation(){};
+  ~MultiRHSDeflation(){ Deallocate(); };
+  
+  void Deallocate(void)
+  {
+    nev=0;
+    grid=nullptr;
+    vol=0;
+    words=0;
+    BLAS_E.resize(0);
+    BLAS_R.resize(0);
+    BLAS_C.resize(0);
+    BLAS_G.resize(0);
+  }
+  void Allocate(int _nev,GridBase *_grid)
+  {
+    nev=_nev;
+    grid=_grid;
+    vol   = grid->lSites();
+    words = sizeof(scalar_object)/sizeof(scalar);
+    eval.resize(nev);
+    BLAS_E.resize (vol * words * nev );
+    std::cout << GridLogMessage << " Allocate for "<<nev<<" eigenvectors and volume "<<vol<<std::endl;
+  }
+  void ImportEigenVector(Field &evec,RealD &_eval, int ev)
+  {
+    //    std::cout << " ev " <<ev<<" eval "<<_eval<< std::endl;
+    assert(ev<eval.size());
+    eval[ev] = _eval;
+
+    int64_t offset = ev*vol*words;
+    autoView(v,evec,AcceleratorRead);
+    acceleratorCopyDeviceToDevice(&v[0],&BLAS_E[offset],sizeof(scalar_object)*vol);
+
+  }
+  void ImportEigenBasis(std::vector<Field> &evec,std::vector<RealD> &_eval)
+  {
+    ImportEigenBasis(evec,_eval,0,evec.size());
+  }
+  // Could use to import a batch of eigenvectors
+  void ImportEigenBasis(std::vector<Field> &evec,std::vector<RealD> &_eval, int _ev0, int _nev)
+  {
+    assert(_ev0+_nev<=evec.size());
+
+    Allocate(_nev,evec[0].Grid());
+    
+    // Imports a sub-batch of eigenvectors, _ev0, ..., _ev0+_nev-1
+    for(int e=0;e<nev;e++){
+      std::cout << "Importing eigenvector "<<e<<" evalue "<<_eval[_ev0+e]<<std::endl;
+      ImportEigenVector(evec[_ev0+e],_eval[_ev0+e],e);
+    }
+  }
+  void DeflateSources(std::vector<Field> &source,std::vector<Field> & guess)
+  {
+    int nrhs = source.size();
+    assert(source.size()==guess.size());
+    assert(grid == guess[0].Grid());
+    conformable(guess[0],source[0]);
+
+    int64_t vw = vol * words;
+
+    RealD t0 = usecond();
+    BLAS_R.resize(nrhs * vw); // cost free if size doesn't change
+    BLAS_G.resize(nrhs * vw); // cost free if size doesn't change
+    BLAS_C.resize(nev * nrhs);// cost free if size doesn't change
+
+    /////////////////////////////////////////////
+    // Copy in the multi-rhs sources
+    /////////////////////////////////////////////
+    //    for(int r=0;r<nrhs;r++){
+    //      std::cout << " source["<<r<<"] = "<<norm2(source[r])<<std::endl;
+    //    }
+    for(int r=0;r<nrhs;r++){
+      int64_t offset = r*vw;
+      autoView(v,source[r],AcceleratorRead);
+      acceleratorCopyDeviceToDevice(&v[0],&BLAS_R[offset],sizeof(scalar_object)*vol);
+    }
+
+  /*
+   * in Fortran column major notation (cuBlas order)
+   *
+   * Exe = [e1(x)][..][en(x)]
+   *
+   * Rxr = [r1(x)][..][rm(x)]
+   *
+   * C_er = E^dag R
+   * C_er = C_er / lambda_e 
+   * G_xr = Exe Cer
+   */
+    deviceVector<scalar *> Ed(1);
+    deviceVector<scalar *> Rd(1);
+    deviceVector<scalar *> Cd(1);
+    deviceVector<scalar *> Gd(1);
+
+    scalar * Eh = & BLAS_E[0];
+    scalar * Rh = & BLAS_R[0];
+    scalar * Ch = & BLAS_C[0];
+    scalar * Gh = & BLAS_G[0];
+
+    acceleratorPut(Ed[0],Eh);
+    acceleratorPut(Rd[0],Rh);
+    acceleratorPut(Cd[0],Ch);
+    acceleratorPut(Gd[0],Gh);
+
+    GridBLAS BLAS;
+
+    /////////////////////////////////////////
+    // C_er = E^dag R
+    /////////////////////////////////////////
+    BLAS.gemmBatched(GridBLAS_OP_C,GridBLAS_OP_N, 
+    		     nev,nrhs,vw,
+		     ComplexD(1.0),
+		     Ed,
+		     Rd,
+		     ComplexD(0.0),  // wipe out C
+		     Cd);
+    BLAS.synchronise();
+
+    assert(BLAS_C.size()==nev*nrhs);
+
+    std::vector<scalar> HOST_C(BLAS_C.size());      // nrhs . nev -- the coefficients 
+    acceleratorCopyFromDevice(&BLAS_C[0],&HOST_C[0],BLAS_C.size()*sizeof(scalar));
+    grid->GlobalSumVector(&HOST_C[0],nev*nrhs);
+    for(int e=0;e<nev;e++){
+      RealD lam(1.0/eval[e]);
+      for(int r=0;r<nrhs;r++){
+	int off = e+nev*r;
+	HOST_C[off]=HOST_C[off] * lam;
+	//	std::cout << "C["<<e<<"]["<<r<<"] ="<<HOST_C[off]<< " eval[e] "<<eval[e] <<std::endl;
+      }
+    }
+    acceleratorCopyToDevice(&HOST_C[0],&BLAS_C[0],BLAS_C.size()*sizeof(scalar));
+
+    
+    /////////////////////////////////////////
+    // Guess G_xr = Exe Cer
+    /////////////////////////////////////////
+    BLAS.gemmBatched(GridBLAS_OP_N,GridBLAS_OP_N, 
+		     vw,nrhs,nev,
+		     ComplexD(1.0),
+		     Ed, // x . nev
+		     Cd, // nev . nrhs
+		     ComplexD(0.0),
+		     Gd);
+    BLAS.synchronise();
+
+    ///////////////////////////////////////
+    // Copy out the multirhs
+    ///////////////////////////////////////
+    for(int r=0;r<nrhs;r++){
+      int64_t offset = r*vw;
+      autoView(v,guess[r],AcceleratorWrite);
+      acceleratorCopyDeviceToDevice(&BLAS_G[offset],&v[0],sizeof(scalar_object)*vol);
+    }
+    RealD t1 = usecond();
+    std::cout << GridLogMessage << "MultiRHSDeflation for "<<nrhs<<" sources with "<<nev<<" eigenvectors took " << (t1-t0)/1e3 <<" ms"<<std::endl;
+  }
+};
+
+NAMESPACE_END(Grid);

Grid/algorithms/iterative/AdefGeneric.h

@@ -0,0 +1,599 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/AdefGeneric.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_ALGORITHMS_ITERATIVE_GENERIC_PCG
+#define GRID_ALGORITHMS_ITERATIVE_GENERIC_PCG
+
+  /*
+   * Compared to Tang-2009:  P=Pleft. P^T = PRight Q=MssInv. 
+   * Script A = SolverMatrix 
+   * Script P = Preconditioner
+   *
+   * Implement ADEF-2
+   *
+   * Vstart = P^Tx + Qb
+   * M1 = P^TM + Q
+   * M2=M3=1
+   */
+NAMESPACE_BEGIN(Grid);
+
+
+template<class Field>
+class TwoLevelCG : public LinearFunction<Field>
+{
+ public:
+  RealD   Tolerance;
+  Integer MaxIterations;
+  GridBase *grid;
+
+  // Fine operator, Smoother, CoarseSolver
+  LinearOperatorBase<Field>   &_FineLinop;
+  LinearFunction<Field>   &_Smoother;
+  
+  // more most opertor functions
+  TwoLevelCG(RealD tol,
+	     Integer maxit,
+	     LinearOperatorBase<Field>   &FineLinop,
+	     LinearFunction<Field>       &Smoother,
+	     GridBase *fine) : 
+      Tolerance(tol), 
+      MaxIterations(maxit),
+      _FineLinop(FineLinop),
+      _Smoother(Smoother)
+  {
+    grid       = fine;
+  };
+  
+  virtual void operator() (const Field &src, Field &x)
+  {
+    std::cout << GridLogMessage<<"HDCG: fPcg starting single RHS"<<std::endl;
+    RealD f;
+    RealD rtzp,rtz,a,d,b;
+    RealD rptzp;
+
+    /////////////////////////////
+    // Set up history vectors
+    /////////////////////////////
+    int mmax = 5;
+    std::cout << GridLogMessage<<"HDCG: fPcg allocating"<<std::endl;
+    std::vector<Field> p(mmax,grid);
+    std::vector<Field> mmp(mmax,grid);
+    std::vector<RealD> pAp(mmax);
+    Field z(grid);
+    Field tmp(grid);
+    Field  mp (grid);
+    Field  r  (grid);
+    Field  mu (grid);
+    
+    std::cout << GridLogMessage<<"HDCG: fPcg allocated"<<std::endl;
+    //Initial residual computation & set up
+    RealD guess   = norm2(x);
+    std::cout << GridLogMessage<<"HDCG: fPcg guess nrm "<<guess<<std::endl;
+    RealD src_nrm = norm2(src);
+    std::cout << GridLogMessage<<"HDCG: fPcg src nrm "<<src_nrm<<std::endl;
+    
+    if ( src_nrm == 0.0 ) {
+      std::cout << GridLogMessage<<"HDCG: fPcg given trivial source norm "<<src_nrm<<std::endl;
+      x=Zero();
+    }
+    RealD tn;
+    
+    GridStopWatch HDCGTimer;
+    HDCGTimer.Start();
+    //////////////////////////
+    // x0 = Vstart -- possibly modify guess
+    //////////////////////////
+    Vstart(x,src);
+    
+    // r0 = b -A x0
+    _FineLinop.HermOp(x,mmp[0]);
+    axpy (r, -1.0,mmp[0], src);    // Recomputes r=src-Ax0
+    {
+      double n1 = norm2(x);
+      double n2 = norm2(mmp[0]);
+      double n3 = norm2(r);
+      std::cout<<GridLogMessage<<"x,vstart,r = "<<n1<<" "<<n2<<" "<<n3<<std::endl;
+    }
+
+    //////////////////////////////////
+    // Compute z = M1 x
+    //////////////////////////////////
+    PcgM1(r,z);
+    rtzp =real(innerProduct(r,z));
+    
+    ///////////////////////////////////////
+    // Solve for Mss mu = P A z and set p = z-mu
+    // Def2 p = 1 - Q Az = Pright z
+    // Other algos M2 is trivial
+    ///////////////////////////////////////
+    PcgM2(z,p[0]);
+
+    RealD ssq =  norm2(src);
+    RealD rsq =  ssq*Tolerance*Tolerance;
+
+    std::cout << GridLogMessage<<"HDCG: k=0 residual "<<rtzp<<" rsq "<<rsq<<"\n";
+
+    Field pp(grid);
+
+    for (int k=0;k<=MaxIterations;k++){
+    
+      int peri_k  = k % mmax;
+      int peri_kp = (k+1) % mmax;
+
+      rtz=rtzp;
+      d= PcgM3(p[peri_k],mmp[peri_k]);
+      a = rtz/d;
+    
+      // Memorise this
+      pAp[peri_k] = d;
+      
+      axpy(x,a,p[peri_k],x);
+      RealD rn = axpy_norm(r,-a,mmp[peri_k],r);
+
+      // Compute z = M x
+      PcgM1(r,z);
+      
+      {
+	RealD n1,n2;
+	n1=norm2(r);
+	n2=norm2(z);
+	std::cout << GridLogMessage<<"HDCG::fPcg iteration "<<k<<" : vector r,z "<<n1<<" "<<n2<<"\n";
+      }
+      rtzp =real(innerProduct(r,z));
+      std::cout << GridLogMessage<<"HDCG::fPcg iteration "<<k<<" : inner rtzp "<<rtzp<<"\n";
+
+      //    PcgM2(z,p[0]);
+      PcgM2(z,mu); // ADEF-2 this is identity. Axpy possible to eliminate
+      
+      p[peri_kp]=mu;
+
+      // Standard search direction  p -> z + b p    
+      b = (rtzp)/rtz;
+      
+      int northog;
+      // k=zero  <=> peri_kp=1;        northog = 1
+      // k=1     <=> peri_kp=2;        northog = 2
+      // ...               ...                  ...
+      // k=mmax-2<=> peri_kp=mmax-1;   northog = mmax-1
+      // k=mmax-1<=> peri_kp=0;        northog = 1
+
+      //    northog     = (peri_kp==0)?1:peri_kp; // This is the fCG(mmax) algorithm
+      northog     = (k>mmax-1)?(mmax-1):k;        // This is the fCG-Tr(mmax-1) algorithm
+    
+      std::cout<<GridLogMessage<<"HDCG::fPcg iteration "<<k<<" : orthogonalising to last "<<northog<<" vectors\n";
+      for(int back=0; back < northog; back++){
+	int peri_back = (k-back)%mmax;
+	RealD pbApk= real(innerProduct(mmp[peri_back],p[peri_kp]));
+	RealD beta = -pbApk/pAp[peri_back];
+	axpy(p[peri_kp],beta,p[peri_back],p[peri_kp]);
+      }
+
+      RealD rrn=sqrt(rn/ssq);
+      RealD rtn=sqrt(rtz/ssq);
+      RealD rtnp=sqrt(rtzp/ssq);
+
+      std::cout<<GridLogMessage<<"HDCG: fPcg k= "<<k<<" residual = "<<rrn<<"\n";
+
+      // Stopping condition
+      if ( rn <= rsq ) { 
+
+	HDCGTimer.Stop();
+	std::cout<<GridLogMessage<<"HDCG: fPcg converged in "<<k<<" iterations and "<<HDCGTimer.Elapsed()<<std::endl;;
+	
+	_FineLinop.HermOp(x,mmp[0]);			  
+	axpy(tmp,-1.0,src,mmp[0]);
+	
+	RealD  mmpnorm = sqrt(norm2(mmp[0]));
+	RealD  xnorm   = sqrt(norm2(x));
+	RealD  srcnorm = sqrt(norm2(src));
+	RealD  tmpnorm = sqrt(norm2(tmp));
+	RealD  true_residual = tmpnorm/srcnorm;
+	std::cout<<GridLogMessage
+	       <<"HDCG: true residual is "<<true_residual
+	       <<" solution "<<xnorm
+	       <<" source "<<srcnorm
+	       <<" mmp "<<mmpnorm	  
+	       <<std::endl;
+      
+	return;
+      }
+
+    }
+    HDCGTimer.Stop();
+    std::cout<<GridLogMessage<<"HDCG: not converged "<<HDCGTimer.Elapsed()<<std::endl;
+    RealD  xnorm   = sqrt(norm2(x));
+    RealD  srcnorm = sqrt(norm2(src));
+    std::cout<<GridLogMessage<<"HDCG: non-converged solution "<<xnorm<<" source "<<srcnorm<<std::endl;
+  }
+
+
+
+  virtual void operator() (std::vector<Field> &src, std::vector<Field> &x)
+  {
+    std::cout << GridLogMessage<<"HDCG: mrhs fPcg starting"<<std::endl;
+    src[0].Grid()->Barrier();
+    int nrhs = src.size();
+    std::vector<RealD> f(nrhs);
+    std::vector<RealD> rtzp(nrhs);
+    std::vector<RealD> rtz(nrhs);
+    std::vector<RealD> a(nrhs);
+    std::vector<RealD> d(nrhs);
+    std::vector<RealD> b(nrhs);
+    std::vector<RealD> rptzp(nrhs);
+    /////////////////////////////
+    // Set up history vectors
+    /////////////////////////////
+    int mmax = 3;
+    std::cout << GridLogMessage<<"HDCG: fPcg allocating"<<std::endl;
+    src[0].Grid()->Barrier();
+    std::vector<std::vector<Field> > p(nrhs);   for(int r=0;r<nrhs;r++)  p[r].resize(mmax,grid);
+    std::cout << GridLogMessage<<"HDCG: fPcg allocated p"<<std::endl;
+    src[0].Grid()->Barrier();
+    std::vector<std::vector<Field> > mmp(nrhs); for(int r=0;r<nrhs;r++) mmp[r].resize(mmax,grid);
+    std::cout << GridLogMessage<<"HDCG: fPcg allocated mmp"<<std::endl;
+    src[0].Grid()->Barrier();
+    std::vector<std::vector<RealD> > pAp(nrhs); for(int r=0;r<nrhs;r++) pAp[r].resize(mmax);
+    std::cout << GridLogMessage<<"HDCG: fPcg allocated pAp"<<std::endl;
+    src[0].Grid()->Barrier();
+    std::vector<Field> z(nrhs,grid);
+    std::vector<Field>  mp (nrhs,grid);
+    std::vector<Field>  r  (nrhs,grid);
+    std::vector<Field>  mu (nrhs,grid);
+    std::cout << GridLogMessage<<"HDCG: fPcg allocated z,mp,r,mu"<<std::endl;
+    src[0].Grid()->Barrier();
+
+    //Initial residual computation & set up
+    std::vector<RealD> src_nrm(nrhs);
+    for(int rhs=0;rhs<nrhs;rhs++) {
+      src_nrm[rhs]=norm2(src[rhs]);
+      assert(src_nrm[rhs]!=0.0);
+    }
+    std::vector<RealD> tn(nrhs);
+
+    GridStopWatch HDCGTimer;
+    HDCGTimer.Start();
+    //////////////////////////
+    // x0 = Vstart -- possibly modify guess
+    //////////////////////////
+    Vstart(x,src);
+
+    for(int rhs=0;rhs<nrhs;rhs++){
+      // r0 = b -A x0
+      _FineLinop.HermOp(x[rhs],mmp[rhs][0]);
+      axpy (r[rhs], -1.0,mmp[rhs][0], src[rhs]);    // Recomputes r=src-Ax0
+    }
+
+    //////////////////////////////////
+    // Compute z = M1 x
+    //////////////////////////////////
+    // This needs a multiRHS version for acceleration
+    PcgM1(r,z);
+
+    std::vector<RealD> ssq(nrhs);
+    std::vector<RealD> rsq(nrhs);
+    std::vector<Field> pp(nrhs,grid);
+
+    for(int rhs=0;rhs<nrhs;rhs++){
+      rtzp[rhs] =real(innerProduct(r[rhs],z[rhs]));
+      p[rhs][0]=z[rhs];
+      ssq[rhs]=norm2(src[rhs]);
+      rsq[rhs]=  ssq[rhs]*Tolerance*Tolerance;
+      std::cout << GridLogMessage<<"mrhs HDCG: "<<rhs<<" k=0 residual "<<rtzp[rhs]<<" rsq "<<rsq[rhs]<<"\n";
+    }
+
+    std::vector<RealD> rn(nrhs);
+    for (int k=0;k<=MaxIterations;k++){
+    
+      int peri_k  = k % mmax;
+      int peri_kp = (k+1) % mmax;
+
+      for(int rhs=0;rhs<nrhs;rhs++){
+	rtz[rhs]=rtzp[rhs];
+	d[rhs]= PcgM3(p[rhs][peri_k],mmp[rhs][peri_k]);
+	a[rhs] = rtz[rhs]/d[rhs];
+    
+	// Memorise this
+	pAp[rhs][peri_k] = d[rhs];
+
+	axpy(x[rhs],a[rhs],p[rhs][peri_k],x[rhs]);
+	rn[rhs] = axpy_norm(r[rhs],-a[rhs],mmp[rhs][peri_k],r[rhs]);
+      }
+
+      // Compute z = M x (for *all* RHS)
+      PcgM1(r,z);
+      std::cout << GridLogMessage<<"HDCG::fPcg M1 complete"<<std::endl;
+      grid->Barrier();
+      
+      RealD max_rn=0.0;
+      for(int rhs=0;rhs<nrhs;rhs++){
+
+	rtzp[rhs] =real(innerProduct(r[rhs],z[rhs]));
+
+	std::cout << GridLogMessage<<"HDCG::fPcg rhs"<<rhs<<" iteration "<<k<<" : inner rtzp "<<rtzp[rhs]<<"\n";
+	
+	mu[rhs]=z[rhs];
+
+	p[rhs][peri_kp]=mu[rhs];
+
+	// Standard search direction p == z + b p 
+	b[rhs] = (rtzp[rhs])/rtz[rhs];
+
+	int northog = (k>mmax-1)?(mmax-1):k;        // This is the fCG-Tr(mmax-1) algorithm
+	std::cout<<GridLogMessage<<"HDCG::fPcg iteration "<<k<<" : orthogonalising to last "<<northog<<" vectors\n";
+	for(int back=0; back < northog; back++){
+	  int peri_back = (k-back)%mmax;
+	  RealD pbApk= real(innerProduct(mmp[rhs][peri_back],p[rhs][peri_kp]));
+	  RealD beta = -pbApk/pAp[rhs][peri_back];
+	  axpy(p[rhs][peri_kp],beta,p[rhs][peri_back],p[rhs][peri_kp]);
+	}
+
+	RealD rrn=sqrt(rn[rhs]/ssq[rhs]);
+	RealD rtn=sqrt(rtz[rhs]/ssq[rhs]);
+	RealD rtnp=sqrt(rtzp[rhs]/ssq[rhs]);
+	
+	std::cout<<GridLogMessage<<"HDCG: rhs "<<rhs<<"fPcg k= "<<k<<" residual = "<<rrn<<"\n";
+	if ( rrn > max_rn ) max_rn = rrn;
+      }
+
+      // Stopping condition based on worst case
+      if ( max_rn <= Tolerance ) { 
+
+	HDCGTimer.Stop();
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg converged in "<<k<<" iterations and "<<HDCGTimer.Elapsed()<<std::endl;;
+
+	for(int rhs=0;rhs<nrhs;rhs++){
+	  _FineLinop.HermOp(x[rhs],mmp[rhs][0]);			  
+	  Field tmp(grid);
+	  axpy(tmp,-1.0,src[rhs],mmp[rhs][0]);
+      
+	  RealD  mmpnorm = sqrt(norm2(mmp[rhs][0]));
+	  RealD  xnorm   = sqrt(norm2(x[rhs]));
+	  RealD  srcnorm = sqrt(norm2(src[rhs]));
+	  RealD  tmpnorm = sqrt(norm2(tmp));
+	  RealD  true_residual = tmpnorm/srcnorm;
+	  std::cout<<GridLogMessage
+		   <<"HDCG: true residual ["<<rhs<<"] is "<<true_residual
+		   <<" solution "<<xnorm
+		   <<" source "<<srcnorm
+		   <<" mmp "<<mmpnorm	  
+		   <<std::endl;
+	}
+	return;
+      }
+      
+    }
+    HDCGTimer.Stop();
+    std::cout<<GridLogMessage<<"HDCG: not converged "<<HDCGTimer.Elapsed()<<std::endl;
+    for(int rhs=0;rhs<nrhs;rhs++){
+      RealD  xnorm   = sqrt(norm2(x[rhs]));
+      RealD  srcnorm = sqrt(norm2(src[rhs]));
+      std::cout<<GridLogMessage<<"HDCG: non-converged solution "<<xnorm<<" source "<<srcnorm<<std::endl;
+    }
+  }
+  
+
+ public:
+
+  virtual void PcgM1(std::vector<Field> & in,std::vector<Field> & out)
+  {
+    std::cout << "PcgM1 default (cheat) mrhs version"<<std::endl;
+    for(int rhs=0;rhs<in.size();rhs++){
+      this->PcgM1(in[rhs],out[rhs]);
+    }
+  }
+  virtual void PcgM1(Field & in, Field & out)     =0;
+  virtual void Vstart(std::vector<Field> & x,std::vector<Field> & src)
+  {
+    std::cout << "Vstart default (cheat) mrhs version"<<std::endl;
+    for(int rhs=0;rhs<x.size();rhs++){
+      this->Vstart(x[rhs],src[rhs]);
+    }
+  }
+  virtual void Vstart(Field & x,const Field & src)=0;
+
+  virtual void PcgM2(const Field & in, Field & out) {
+    out=in;
+  }
+
+  virtual RealD PcgM3(const Field & p, Field & mmp){
+    RealD dd;
+    _FineLinop.HermOp(p,mmp);
+    ComplexD dot = innerProduct(p,mmp);
+    dd=real(dot);
+    return dd;
+  }
+
+  /////////////////////////////////////////////////////////////////////
+  // Only Def1 has non-trivial Vout.
+  /////////////////////////////////////////////////////////////////////
+
+};
+  
+template<class Field, class CoarseField, class Aggregation>
+class TwoLevelADEF2 : public TwoLevelCG<Field>
+{
+ public:
+  ///////////////////////////////////////////////////////////////////////////////////
+  // Need something that knows how to get from Coarse to fine and back again
+  //  void ProjectToSubspace(CoarseVector &CoarseVec,const FineField &FineVec){
+  //  void PromoteFromSubspace(const CoarseVector &CoarseVec,FineField &FineVec){
+  ///////////////////////////////////////////////////////////////////////////////////
+  GridBase *coarsegrid;
+  Aggregation &_Aggregates;                    
+  LinearFunction<CoarseField> &_CoarseSolver;
+  LinearFunction<CoarseField> &_CoarseSolverPrecise;
+  ///////////////////////////////////////////////////////////////////////////////////
+  
+  // more most opertor functions
+  TwoLevelADEF2(RealD tol,
+		Integer maxit,
+		LinearOperatorBase<Field>    &FineLinop,
+		LinearFunction<Field>        &Smoother,
+		LinearFunction<CoarseField>  &CoarseSolver,
+		LinearFunction<CoarseField>  &CoarseSolverPrecise,
+		Aggregation &Aggregates
+		) :
+      TwoLevelCG<Field>(tol,maxit,FineLinop,Smoother,Aggregates.FineGrid),
+      _CoarseSolver(CoarseSolver),
+      _CoarseSolverPrecise(CoarseSolverPrecise),
+      _Aggregates(Aggregates)
+  {
+    coarsegrid = Aggregates.CoarseGrid;
+  };
+
+  virtual void PcgM1(Field & in, Field & out)
+  {
+    GRID_TRACE("MultiGridPreconditioner ");
+    // [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
+
+    Field tmp(this->grid);
+    Field Min(this->grid);
+    CoarseField PleftProj(this->coarsegrid);
+    CoarseField PleftMss_proj(this->coarsegrid);
+
+    GridStopWatch SmootherTimer;
+    GridStopWatch MatrixTimer;
+    SmootherTimer.Start();
+    this->_Smoother(in,Min);
+    SmootherTimer.Stop();
+
+    MatrixTimer.Start();
+    this->_FineLinop.HermOp(Min,out);
+    MatrixTimer.Stop();
+    axpy(tmp,-1.0,out,in);          // tmp  = in - A Min
+
+    GridStopWatch ProjTimer;
+    GridStopWatch CoarseTimer;
+    GridStopWatch PromTimer;
+    ProjTimer.Start();
+    this->_Aggregates.ProjectToSubspace(PleftProj,tmp);     
+    ProjTimer.Stop();
+    CoarseTimer.Start();
+    this->_CoarseSolver(PleftProj,PleftMss_proj); // Ass^{-1} [in - A Min]_s
+    CoarseTimer.Stop();
+    PromTimer.Start();
+    this->_Aggregates.PromoteFromSubspace(PleftMss_proj,tmp);// tmp = Q[in - A Min]  
+    PromTimer.Stop();
+    std::cout << GridLogPerformance << "PcgM1 breakdown "<<std::endl;
+    std::cout << GridLogPerformance << "\tSmoother   " << SmootherTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\tProj       " << ProjTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\tCoarse     " << CoarseTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\tProm       " << PromTimer.Elapsed() <<std::endl;
+
+    axpy(out,1.0,Min,tmp); // Min+tmp
+  }
+
+  virtual void Vstart(Field & x,const Field & src)
+  {
+    std::cout << GridLogMessage<<"HDCG: fPcg Vstart "<<std::endl;
+    ///////////////////////////////////
+    // Choose x_0 such that 
+    // x_0 = guess +  (A_ss^inv) r_s = guess + Ass_inv [src -Aguess]
+    //                               = [1 - Ass_inv A] Guess + Assinv src
+    //                               = P^T guess + Assinv src 
+    //                               = Vstart  [Tang notation]
+    // This gives:
+    // W^T (src - A x_0) = src_s - A guess_s - r_s
+    //                   = src_s - (A guess)_s - src_s  + (A guess)_s 
+    //                   = 0 
+    ///////////////////////////////////
+    Field r(this->grid);
+    Field mmp(this->grid);
+    CoarseField PleftProj(this->coarsegrid);
+    CoarseField PleftMss_proj(this->coarsegrid);
+
+    std::cout << GridLogMessage<<"HDCG: fPcg Vstart projecting "<<std::endl;
+    this->_Aggregates.ProjectToSubspace(PleftProj,src);     
+    std::cout << GridLogMessage<<"HDCG: fPcg Vstart coarse solve "<<std::endl;
+    this->_CoarseSolverPrecise(PleftProj,PleftMss_proj); // Ass^{-1} r_s
+    std::cout << GridLogMessage<<"HDCG: fPcg Vstart promote "<<std::endl;
+    this->_Aggregates.PromoteFromSubspace(PleftMss_proj,x);  
+
+  }
+
+};
+
+  
+template<class Field>
+class TwoLevelADEF1defl : public TwoLevelCG<Field>
+{
+public:
+  const std::vector<Field> &evec;
+  const std::vector<RealD> &eval;
+  
+  TwoLevelADEF1defl(RealD tol,
+		   Integer maxit,
+		   LinearOperatorBase<Field>   &FineLinop,
+		   LinearFunction<Field>   &Smoother,
+		   std::vector<Field> &_evec,
+		   std::vector<RealD> &_eval) : 
+    TwoLevelCG<Field>(tol,maxit,FineLinop,Smoother,_evec[0].Grid()),
+    evec(_evec),
+    eval(_eval)
+  {};
+
+  // Can just inherit existing M2
+  // Can just inherit existing M3
+
+  // Simple vstart - do nothing
+  virtual void Vstart(Field & x,const Field & src){
+    x=src; // Could apply Q
+  };
+
+  // Override PcgM1
+  virtual void PcgM1(Field & in, Field & out)
+  {
+    GRID_TRACE("EvecPreconditioner ");
+    int N=evec.size();
+    Field Pin(this->grid);
+    Field Qin(this->grid);
+
+    //MP  + Q = M(1-AQ) + Q = M
+    // // If we are eigenvector deflating in coarse space
+    // // Q   = Sum_i |phi_i> 1/lambda_i <phi_i|
+    // // A Q = Sum_i |phi_i> <phi_i|
+    // // M(1-AQ) = M(1-proj) + Q
+    Qin.Checkerboard()=in.Checkerboard();
+    Qin = Zero();
+    Pin = in;
+    for (int i=0;i<N;i++) {
+      const Field& tmp = evec[i];
+      auto ip = TensorRemove(innerProduct(tmp,in));
+      axpy(Qin, ip / eval[i],tmp,Qin);
+      axpy(Pin, -ip ,tmp,Pin);
+    }
+
+    this->_Smoother(Pin,out);
+
+    out = out + Qin;
+  }
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/algorithms/iterative/AdefMrhs.h

@@ -0,0 +1,414 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/AdefGeneric.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
+
+
+  /*
+   * Compared to Tang-2009:  P=Pleft. P^T = PRight Q=MssInv. 
+   * Script A = SolverMatrix 
+   * Script P = Preconditioner
+   *
+   * Implement ADEF-2
+   *
+   * Vstart = P^Tx + Qb
+   * M1 = P^TM + Q
+   * M2=M3=1
+   */
+NAMESPACE_BEGIN(Grid);
+
+
+template<class Field>
+class TwoLevelCGmrhs
+{
+ public:
+  RealD   Tolerance;
+  Integer MaxIterations;
+  GridBase *grid;
+
+  // Fine operator, Smoother, CoarseSolver
+  LinearOperatorBase<Field>   &_FineLinop;
+  LinearFunction<Field>   &_Smoother;
+
+  GridStopWatch ProjectTimer;
+  GridStopWatch PromoteTimer;
+  GridStopWatch DeflateTimer;
+  GridStopWatch CoarseTimer;
+  GridStopWatch FineTimer;
+  GridStopWatch SmoothTimer;
+  GridStopWatch InsertTimer;
+
+  
+  // more most opertor functions
+  TwoLevelCGmrhs(RealD tol,
+		 Integer maxit,
+		 LinearOperatorBase<Field>   &FineLinop,
+		 LinearFunction<Field>       &Smoother,
+		 GridBase *fine) : 
+    Tolerance(tol), 
+    MaxIterations(maxit),
+    _FineLinop(FineLinop),
+    _Smoother(Smoother)
+  {
+    grid       = fine;
+  };
+  
+  // Vector case
+  virtual void operator() (std::vector<Field> &src, std::vector<Field> &x)
+  {
+    std::cout << GridLogMessage<<"HDCG: mrhs fPcg starting"<<std::endl;
+    src[0].Grid()->Barrier();
+    int nrhs = src.size();
+    std::vector<RealD> f(nrhs);
+    std::vector<RealD> rtzp(nrhs);
+    std::vector<RealD> rtz(nrhs);
+    std::vector<RealD> a(nrhs);
+    std::vector<RealD> d(nrhs);
+    std::vector<RealD> b(nrhs);
+    std::vector<RealD> rptzp(nrhs);
+    /////////////////////////////
+    // Set up history vectors
+    /////////////////////////////
+    int mmax = 3;
+
+    std::vector<std::vector<Field> > p(nrhs);   for(int r=0;r<nrhs;r++)  p[r].resize(mmax,grid);
+    std::vector<std::vector<Field> > mmp(nrhs); for(int r=0;r<nrhs;r++) mmp[r].resize(mmax,grid);
+    std::vector<std::vector<RealD> > pAp(nrhs); for(int r=0;r<nrhs;r++) pAp[r].resize(mmax);
+
+    std::vector<Field> z(nrhs,grid);
+    std::vector<Field>  mp (nrhs,grid);
+    std::vector<Field>  r  (nrhs,grid);
+    std::vector<Field>  mu (nrhs,grid);
+
+    //Initial residual computation & set up
+    std::vector<RealD> src_nrm(nrhs);
+    for(int rhs=0;rhs<nrhs;rhs++) {
+      src_nrm[rhs]=norm2(src[rhs]);
+      assert(src_nrm[rhs]!=0.0);
+    }
+    std::vector<RealD> tn(nrhs);
+
+    GridStopWatch HDCGTimer;
+    //////////////////////////
+    // x0 = Vstart -- possibly modify guess
+    //////////////////////////
+    Vstart(x,src);
+
+    for(int rhs=0;rhs<nrhs;rhs++){
+      // r0 = b -A x0
+      _FineLinop.HermOp(x[rhs],mmp[rhs][0]);
+      axpy (r[rhs], -1.0,mmp[rhs][0], src[rhs]);    // Recomputes r=src-Ax0
+    }
+
+    //////////////////////////////////
+    // Compute z = M1 x
+    //////////////////////////////////
+    // This needs a multiRHS version for acceleration
+    PcgM1(r,z);
+
+    std::vector<RealD> ssq(nrhs);
+    std::vector<RealD> rsq(nrhs);
+    std::vector<Field> pp(nrhs,grid);
+
+    for(int rhs=0;rhs<nrhs;rhs++){
+      rtzp[rhs] =real(innerProduct(r[rhs],z[rhs]));
+      p[rhs][0]=z[rhs];
+      ssq[rhs]=norm2(src[rhs]);
+      rsq[rhs]=  ssq[rhs]*Tolerance*Tolerance;
+      //      std::cout << GridLogMessage<<"mrhs HDCG: "<<rhs<<" k=0 residual "<<rtzp[rhs]<<" rsq "<<rsq[rhs]<<"\n";
+    }
+
+    ProjectTimer.Reset();
+    PromoteTimer.Reset();
+    DeflateTimer.Reset();
+    CoarseTimer.Reset();
+    SmoothTimer.Reset();
+    FineTimer.Reset();
+    InsertTimer.Reset();
+
+    GridStopWatch M1Timer;
+    GridStopWatch M2Timer;
+    GridStopWatch M3Timer;
+    GridStopWatch LinalgTimer;
+
+    HDCGTimer.Start();
+
+    std::vector<RealD> rn(nrhs);
+    for (int k=0;k<=MaxIterations;k++){
+    
+      int peri_k  = k % mmax;
+      int peri_kp = (k+1) % mmax;
+
+      for(int rhs=0;rhs<nrhs;rhs++){
+	rtz[rhs]=rtzp[rhs];
+	M3Timer.Start();
+	d[rhs]= PcgM3(p[rhs][peri_k],mmp[rhs][peri_k]);
+	M3Timer.Stop();
+	a[rhs] = rtz[rhs]/d[rhs];
+
+	LinalgTimer.Start();
+	// Memorise this
+	pAp[rhs][peri_k] = d[rhs];
+
+	axpy(x[rhs],a[rhs],p[rhs][peri_k],x[rhs]);
+	rn[rhs] = axpy_norm(r[rhs],-a[rhs],mmp[rhs][peri_k],r[rhs]);
+	LinalgTimer.Stop();
+      }
+
+      // Compute z = M x (for *all* RHS)
+      M1Timer.Start();
+      PcgM1(r,z);
+      M1Timer.Stop();
+      
+      RealD max_rn=0.0;
+      LinalgTimer.Start();
+      for(int rhs=0;rhs<nrhs;rhs++){
+
+	rtzp[rhs] =real(innerProduct(r[rhs],z[rhs]));
+
+	//	std::cout << GridLogMessage<<"HDCG::fPcg rhs"<<rhs<<" iteration "<<k<<" : inner rtzp "<<rtzp[rhs]<<"\n";
+	mu[rhs]=z[rhs];
+
+	p[rhs][peri_kp]=mu[rhs];
+
+	// Standard search direction p == z + b p 
+	b[rhs] = (rtzp[rhs])/rtz[rhs];
+
+	int northog = (k>mmax-1)?(mmax-1):k;        // This is the fCG-Tr(mmax-1) algorithm
+	for(int back=0; back < northog; back++){
+	  int peri_back = (k-back)%mmax;
+	  RealD pbApk= real(innerProduct(mmp[rhs][peri_back],p[rhs][peri_kp]));
+	  RealD beta = -pbApk/pAp[rhs][peri_back];
+	  axpy(p[rhs][peri_kp],beta,p[rhs][peri_back],p[rhs][peri_kp]);
+	}
+
+	RealD rrn=sqrt(rn[rhs]/ssq[rhs]);
+	RealD rtn=sqrt(rtz[rhs]/ssq[rhs]);
+	RealD rtnp=sqrt(rtzp[rhs]/ssq[rhs]);
+	
+	std::cout<<GridLogMessage<<"HDCG:fPcg rhs "<<rhs<<" k= "<<k<<" residual = "<<rrn<<"\n";
+	if ( rrn > max_rn ) max_rn = rrn;
+      }
+      LinalgTimer.Stop();
+
+      // Stopping condition based on worst case
+      if ( max_rn <= Tolerance ) { 
+
+	HDCGTimer.Stop();
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg converged in "<<k<<" iterations and "<<HDCGTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Linalg  "<<LinalgTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : fine M3 "<<M3Timer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : prec M1 "<<M1Timer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"**** M1 breakdown:"<<std::endl;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Project "<<ProjectTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Promote "<<PromoteTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Deflate "<<DeflateTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Coarse  "<<CoarseTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Fine    "<<FineTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Smooth  "<<SmoothTimer.Elapsed()<<std::endl;;
+	std::cout<<GridLogMessage<<"HDCG: mrhs fPcg : Insert  "<<InsertTimer.Elapsed()<<std::endl;;
+
+	for(int rhs=0;rhs<nrhs;rhs++){
+	  _FineLinop.HermOp(x[rhs],mmp[rhs][0]);			  
+	  Field tmp(grid);
+	  axpy(tmp,-1.0,src[rhs],mmp[rhs][0]);
+      
+	  RealD  mmpnorm = sqrt(norm2(mmp[rhs][0]));
+	  RealD  xnorm   = sqrt(norm2(x[rhs]));
+	  RealD  srcnorm = sqrt(norm2(src[rhs]));
+	  RealD  tmpnorm = sqrt(norm2(tmp));
+	  RealD  true_residual = tmpnorm/srcnorm;
+	  std::cout<<GridLogMessage
+		   <<"HDCG: true residual ["<<rhs<<"] is "<<true_residual
+		   <<" solution "<<xnorm
+		   <<" source "<<srcnorm
+		   <<" mmp "<<mmpnorm	  
+		   <<std::endl;
+	}
+	return;
+      }
+      
+    }
+    HDCGTimer.Stop();
+    std::cout<<GridLogMessage<<"HDCG: not converged "<<HDCGTimer.Elapsed()<<std::endl;
+    for(int rhs=0;rhs<nrhs;rhs++){
+      RealD  xnorm   = sqrt(norm2(x[rhs]));
+      RealD  srcnorm = sqrt(norm2(src[rhs]));
+      std::cout<<GridLogMessage<<"HDCG: non-converged solution "<<xnorm<<" source "<<srcnorm<<std::endl;
+    }
+  }
+  
+
+ public:
+
+  virtual void PcgM1(std::vector<Field> & in,std::vector<Field> & out) = 0;
+  virtual void Vstart(std::vector<Field> & x,std::vector<Field> & src) = 0;
+  virtual void PcgM2(const Field & in, Field & out) {
+    out=in;
+  }
+
+  virtual RealD PcgM3(const Field & p, Field & mmp){
+    RealD dd;
+    _FineLinop.HermOp(p,mmp);
+    ComplexD dot = innerProduct(p,mmp);
+    dd=real(dot);
+    return dd;
+  }
+
+};
+
+template<class Field, class CoarseField>
+class TwoLevelADEF2mrhs : public TwoLevelCGmrhs<Field>
+{
+public:
+  GridBase *coarsegrid;
+  GridBase *coarsegridmrhs;
+  LinearFunction<CoarseField> &_CoarseSolverMrhs;
+  LinearFunction<CoarseField> &_CoarseSolverPreciseMrhs;
+  MultiRHSBlockProject<Field>    &_Projector;
+  MultiRHSDeflation<CoarseField> &_Deflator;
+
+  
+  TwoLevelADEF2mrhs(RealD tol,
+		    Integer maxit,
+		    LinearOperatorBase<Field>    &FineLinop,
+		    LinearFunction<Field>        &Smoother,
+		    LinearFunction<CoarseField>  &CoarseSolverMrhs,
+		    LinearFunction<CoarseField>  &CoarseSolverPreciseMrhs,
+		    MultiRHSBlockProject<Field>    &Projector,
+		    MultiRHSDeflation<CoarseField> &Deflator,
+		    GridBase *_coarsemrhsgrid) :
+    TwoLevelCGmrhs<Field>(tol, maxit,FineLinop,Smoother,Projector.fine_grid),
+    _CoarseSolverMrhs(CoarseSolverMrhs),
+    _CoarseSolverPreciseMrhs(CoarseSolverPreciseMrhs),
+    _Projector(Projector),
+    _Deflator(Deflator)
+  {
+    coarsegrid = Projector.coarse_grid;
+    coarsegridmrhs = _coarsemrhsgrid;// Thi could be in projector
+  };
+
+  // Override Vstart
+  virtual void Vstart(std::vector<Field> & x,std::vector<Field> & src)
+  {
+    int nrhs=x.size();
+    ///////////////////////////////////
+    // Choose x_0 such that 
+    // x_0 = guess +  (A_ss^inv) r_s = guess + Ass_inv [src -Aguess]
+    //                               = [1 - Ass_inv A] Guess + Assinv src
+    //                               = P^T guess + Assinv src 
+    //                               = Vstart  [Tang notation]
+    // This gives:
+    // W^T (src - A x_0) = src_s - A guess_s - r_s
+    //                   = src_s - (A guess)_s - src_s  + (A guess)_s 
+    //                   = 0 
+    ///////////////////////////////////
+    std::vector<CoarseField> PleftProj(nrhs,this->coarsegrid);
+    std::vector<CoarseField> PleftMss_proj(nrhs,this->coarsegrid);
+    CoarseField PleftProjMrhs(this->coarsegridmrhs);
+    CoarseField PleftMss_projMrhs(this->coarsegridmrhs);
+
+    this->_Projector.blockProject(src,PleftProj);
+    this->_Deflator.DeflateSources(PleftProj,PleftMss_proj);
+    for(int rhs=0;rhs<nrhs;rhs++) {
+      InsertSliceFast(PleftProj[rhs],PleftProjMrhs,rhs,0);
+      InsertSliceFast(PleftMss_proj[rhs],PleftMss_projMrhs,rhs,0); // the guess
+    }
+    
+    this->_CoarseSolverPreciseMrhs(PleftProjMrhs,PleftMss_projMrhs); // Ass^{-1} r_s
+
+    for(int rhs=0;rhs<nrhs;rhs++) {
+      ExtractSliceFast(PleftMss_proj[rhs],PleftMss_projMrhs,rhs,0);
+    }
+    this->_Projector.blockPromote(x,PleftMss_proj);
+  }
+
+  virtual void PcgM1(std::vector<Field> & in,std::vector<Field> & out){
+
+    int nrhs=in.size();
+
+    // [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
+    std::vector<Field> tmp(nrhs,this->grid);
+    std::vector<Field> Min(nrhs,this->grid);
+
+    std::vector<CoarseField> PleftProj(nrhs,this->coarsegrid);
+    std::vector<CoarseField> PleftMss_proj(nrhs,this->coarsegrid);
+
+    CoarseField PleftProjMrhs(this->coarsegridmrhs);
+    CoarseField PleftMss_projMrhs(this->coarsegridmrhs);
+
+    for(int rhs=0;rhs<nrhs;rhs++) {
+
+      this->SmoothTimer.Start();
+      this->_Smoother(in[rhs],Min[rhs]);
+      this->SmoothTimer.Stop();
+
+      this->FineTimer.Start();
+      this->_FineLinop.HermOp(Min[rhs],out[rhs]);
+
+      axpy(tmp[rhs],-1.0,out[rhs],in[rhs]);          // resid  = in - A Min
+      this->FineTimer.Stop();
+
+    }
+
+    this->ProjectTimer.Start();
+    this->_Projector.blockProject(tmp,PleftProj);
+    this->ProjectTimer.Stop();
+    this->DeflateTimer.Start();
+    this->_Deflator.DeflateSources(PleftProj,PleftMss_proj);
+    this->DeflateTimer.Stop();
+    this->InsertTimer.Start();
+    for(int rhs=0;rhs<nrhs;rhs++) {
+      InsertSliceFast(PleftProj[rhs],PleftProjMrhs,rhs,0);
+      InsertSliceFast(PleftMss_proj[rhs],PleftMss_projMrhs,rhs,0); // the guess
+    }
+    this->InsertTimer.Stop();
+
+    this->CoarseTimer.Start();
+    this->_CoarseSolverMrhs(PleftProjMrhs,PleftMss_projMrhs); // Ass^{-1} [in - A Min]_s
+    this->CoarseTimer.Stop();
+
+    this->InsertTimer.Start();
+    for(int rhs=0;rhs<nrhs;rhs++) {
+      ExtractSliceFast(PleftMss_proj[rhs],PleftMss_projMrhs,rhs,0);
+    }
+    this->InsertTimer.Stop();
+    this->PromoteTimer.Start();
+    this->_Projector.blockPromote(tmp,PleftMss_proj);// tmp= Q[in - A Min]  
+    this->PromoteTimer.Stop();
+    this->FineTimer.Start();
+    for(int rhs=0;rhs<nrhs;rhs++) {
+      axpy(out[rhs],1.0,Min[rhs],tmp[rhs]); // Min+tmp
+    }
+    this->FineTimer.Stop();
+  }
+};
+  
+
+NAMESPACE_END(Grid);
+
+

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 +1,159 @@
+/*************************************************************************************
+
+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:
+    using LinearFunction<FieldD>::operator();
+    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

@@ -0,0 +1,698 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithms/iterative/BlockConjugateGradient.h
+
+Copyright (C) 2017
+
+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);
+
+enum BlockCGtype { BlockCG, BlockCGrQ, CGmultiRHS, BlockCGVec, BlockCGrQVec };
+
+//////////////////////////////////////////////////////////////////////////
+// Block conjugate gradient. Dimension zero should be the block direction
+//////////////////////////////////////////////////////////////////////////
+template <class Field>
+class BlockConjugateGradient : public OperatorFunction<Field> {
+ public:
+
+  typedef typename Field::scalar_type scomplex;
+
+  int blockDim ;
+  int Nblock;
+
+  BlockCGtype CGtype;
+  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 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),PrintInterval(100)
+  {};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+// Thin QR factorisation (google it)
+////////////////////////////////////////////////////////////////////////////////////////////////////
+  ////////////////////////////////////////////////////////////////////////////////////////////////////
+  //Dimensions
+  // R_{ferm x Nblock} =  Q_{ferm x Nblock} x  C_{Nblock x Nblock} -> ferm x Nblock
+  //
+  // Rdag R = m_rr = Herm = L L^dag        <-- Cholesky decomposition (LLT routine in Eigen)
+  //
+  //   Q  C = R => Q = R C^{-1}
+  //
+  // Want  Ident = Q^dag Q = C^{-dag} R^dag R C^{-1} = C^{-dag} L L^dag C^{-1} = 1_{Nblock x Nblock} 
+  //
+  // Set C = L^{dag}, and then Q^dag Q = ident 
+  //
+  // Checks:
+  // 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());
+
+  Eigen::MatrixXcd L    = m_rr.llt().matrixL(); 
+
+  C    = L.adjoint();
+  Cinv = C.inverse();
+  ////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Q = R C^{-1}
+  //
+  // Q_j  = R_i Cinv(i,j) 
+  //
+  // NB maddMatrix conventions are Right multiplication X[j] a[j,i] already
+  ////////////////////////////////////////////////////////////////////////////////////////////////////
+  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
+////////////////////////////////////////////////////////////////////////////////////////////////////
+void operator()(LinearOperatorBase<Field> &Linop, const Field &Src, Field &Psi) 
+{
+  if ( CGtype == BlockCGrQ ) {
+    BlockCGrQsolve(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:
+//--------------------------
+// X is guess/Solution
+// B is RHS
+// Solve A X_i = B_i    ;        i refers to Nblock index
+////////////////////////////////////////////////////////////////////////////
+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];
+/* FAKE */
+  Nblock=8;
+  std::cout<<GridLogMessage<<" Block Conjugate Gradient : Orthog "<<Orthog<<" Nblock "<<Nblock<<std::endl;
+
+  X.Checkerboard() = B.Checkerboard();
+  conformable(X, B);
+
+  Field tmp(B);
+  Field Q(B);
+  Field D(B);
+  Field Z(B);
+  Field AD(B);
+
+  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);
+
+  sliceNorm(ssq,B,Orthog);
+  RealD sssum=0;
+  for(int b=0;b<Nblock;b++) sssum+=ssq[b];
+
+  sliceNorm(residuals,B,Orthog);
+  for(int b=0;b<Nblock;b++){ assert(std::isnan(residuals[b])==0); }
+
+  sliceNorm(residuals,X,Orthog);
+  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<<"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;  
+
+  ThinQRfact (m_rr, m_C, m_Cinv, Q, tmp);
+  D=Q;
+
+  std::cout << GridLogMessage<<"BlockCGrQ 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();
+    Linop.HermOp(D, Z);      
+    MatrixTimer.Stop();
+
+    //4. M  = [D^dag Z]^{-1}
+    sliceInnerTimer.Start();
+    sliceInnerProductMatrix(m_DZ,D,Z,Orthog);
+    sliceInnerTimer.Stop();
+    m_M       = m_DZ.inverse();
+    
+    //5. X  = X + D MC
+    m_tmp     = m_M * m_C;
+    sliceMaddTimer.Start();
+    sliceMaddMatrix(X,m_tmp, D,X,Orthog);     
+    sliceMaddTimer.Stop();
+
+    //6. QS = Q - ZM
+    sliceMaddTimer.Start();
+    sliceMaddMatrix(tmp,m_M,Z,Q,Orthog,-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();
+    sliceMaddMatrix(D,m_tmp,D,Q,Orthog);
+    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 << "\titeration "<<k<<" rr_sum "<<rrsum<<" ssq_sum "<< sssum
+	      <<" ave "<<std::sqrt(rrsum/sssum) << " max "<< 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;
+
+      Linop.HermOp(X, AD);
+      AD = AD-B;
+      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;
+      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;
+}
+//////////////////////////////////////////////////////////////////////////
+// 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];
+
+  std::cout<<GridLogMessage<<"MultiRHS Conjugate Gradient : Orthog "<<Orthog<<" Nblock "<<Nblock<<std::endl;
+
+  Psi.Checkerboard() = Src.Checkerboard();
+  conformable(Psi, Src);
+
+  Field P(Src);
+  Field AP(Src);
+  Field R(Src);
+  
+  std::vector<ComplexD> v_pAp(Nblock);
+  std::vector<RealD> v_rr (Nblock);
+  std::vector<RealD> v_rr_inv(Nblock);
+  std::vector<RealD> v_alpha(Nblock);
+  std::vector<RealD> v_beta(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);
+
+  R = Src - AP;  
+  P = R;
+  sliceNorm(v_rr,R,Orthog);
+
+  GridStopWatch sliceInnerTimer;
+  GridStopWatch sliceMaddTimer;
+  GridStopWatch sliceNormTimer;
+  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(v_rr[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();
+    sliceInnerProductVector(v_pAp,P,AP,Orthog);
+    sliceInnerTimer.Stop();
+    for(int b=0;b<Nblock;b++){
+      v_alpha[b] = v_rr[b]/real(v_pAp[b]);
+    }
+
+    // Psi, R update
+    sliceMaddTimer.Start();
+    sliceMaddVector(Psi,v_alpha, P,Psi,Orthog);     // add alpha *  P to psi
+    sliceMaddVector(R  ,v_alpha,AP,  R,Orthog,-1.0);// sub alpha * AP to resid
+    sliceMaddTimer.Stop();
+
+    // Beta
+    for(int b=0;b<Nblock;b++){
+      v_rr_inv[b] = 1.0/v_rr[b];
+    }
+    sliceNormTimer.Start();
+    sliceNorm(v_rr,R,Orthog);
+    sliceNormTimer.Stop();
+    for(int b=0;b<Nblock;b++){
+      v_beta[b] = v_rr_inv[b] *v_rr[b];
+    }
+
+    // Search update
+    sliceMaddTimer.Start();
+    sliceMaddVector(P,v_beta,P,R,Orthog);
+    sliceMaddTimer.Stop();
+
+    /*********************
+     * convergence monitor
+     *********************
+     */
+    RealD max_resid=0;
+    for(int b=0;b<Nblock;b++){
+      RealD rr = v_rr[b]/ssq[b];
+      if ( rr > max_resid ) max_resid = rr;
+    }
+    
+    if ( max_resid < Tolerance*Tolerance ) { 
+
+      SolverTimer.Stop();
+
+      std::cout << GridLogMessage<<"MultiRHS solver converged in " <<k<<" iterations"<<std::endl;
+      for(int b=0;b<Nblock;b++){
+	std::cout << GridLogMessage<< "\t\tBlock "<<b<<" computed resid "<< std::sqrt(v_rr[b]/ssq[b])<<std::endl;
+      }
+      std::cout << GridLogMessage<<"\tMax residual is "<<std::sqrt(max_resid)<<std::endl;
+
+      Linop.HermOp(Psi, AP);
+      AP = AP-Src;
+      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;
+      std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tInnerProd  " << sliceInnerTimer.Elapsed() <<std::endl;
+      std::cout << GridLogMessage << "\tNorm       " << sliceNormTimer.Elapsed() <<std::endl;
+      std::cout << GridLogMessage << "\tMaddMatrix " << sliceMaddTimer.Elapsed()  <<std::endl;
+
+
+      IterationsToComplete = k;
+      return;
+    }
+
+  }
+  std::cout << GridLogMessage << "MultiRHSConjugateGradient did NOT converge" << std::endl;
+
+  if (ErrorOnNoConverge) assert(0);
+  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;
+}
+
+};
+
+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

@@ -0,0 +1,237 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithms/iterative/ConjugateGradient.h
+
+Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+			   /*  END LEGAL */
+#ifndef GRID_CONJUGATE_GRADIENT_H
+#define GRID_CONJUGATE_GRADIENT_H
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////
+// Base classes for iterative processes based on operators
+// single input vec, single output vec.
+/////////////////////////////////////////////////////////////
+
+template <class Field>
+class ConjugateGradient : public OperatorFunction<Field> {
+public:
+
+  using OperatorFunction<Field>::operator();
+
+  bool ErrorOnNoConverge;  // throw an assert when the CG fails to converge.
+                           // Defaults true.
+  RealD Tolerance;
+  Integer MaxIterations;
+  Integer IterationsToComplete; //Number of iterations the CG took to finish. Filled in upon completion
+  RealD TrueResidual;
+  
+  ConjugateGradient(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) {
+
+    GRID_TRACE("ConjugateGradient");
+    GridStopWatch PreambleTimer;
+    PreambleTimer.Start();
+    psi.Checkerboard() = src.Checkerboard();
+
+    conformable(psi, src);
+
+    RealD cp, c, a, d, b, ssq, qq;
+    //RealD b_pred;
+
+    // Was doing copies
+    Field p(src.Grid());
+    Field mmp(src.Grid());
+    Field r(src.Grid());
+
+    // Initial residual computation & set up
+    ssq = norm2(src);
+    RealD guess = norm2(psi);
+    assert(std::isnan(guess) == 0);
+    if ( guess == 0.0 ) {
+      r = src;
+      p = r;
+      a = ssq;
+    } else { 
+      Linop.HermOpAndNorm(psi, mmp, d, b);
+      r = src - mmp;
+      p = r;
+      a = norm2(p);
+    }
+    cp = a;
+
+    // Handle trivial case of zero src
+    if (ssq == 0.){
+      psi = Zero();
+      IterationsToComplete = 1;
+      TrueResidual = 0.;
+      return;
+    }
+
+    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient: guess " << guess << std::endl;
+    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:   src " << ssq << std::endl;
+    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:    mp " << d << std::endl;
+    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:   mmp " << b << std::endl;
+    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:  cp,r " << cp << std::endl;
+    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:     p " << a << std::endl;
+
+    RealD rsq = Tolerance * Tolerance * ssq;
+
+    // Check if guess is really REALLY good :)
+    if (cp <= rsq) {
+      TrueResidual = std::sqrt(a/ssq);
+      std::cout << GridLogMessage << "ConjugateGradient guess is converged already " << std::endl;
+      IterationsToComplete = 0;	
+      return;
+    }
+
+    std::cout << GridLogIterative << std::setprecision(8)
+              << "ConjugateGradient: k=0 residual " << cp << " target " << rsq << std::endl;
+
+    PreambleTimer.Stop();
+    GridStopWatch LinalgTimer;
+    GridStopWatch InnerTimer;
+    GridStopWatch AxpyNormTimer;
+    GridStopWatch LinearCombTimer;
+    GridStopWatch MatrixTimer;
+    GridStopWatch SolverTimer;
+
+    RealD usecs = -usecond();
+    SolverTimer.Start();
+    int k;
+    for (k = 1; k <= MaxIterations; k++) {
+
+      GridStopWatch IterationTimer;
+      IterationTimer.Start();
+      c = cp;
+
+      MatrixTimer.Start();
+      Linop.HermOp(p, mmp);
+      MatrixTimer.Stop();
+
+      LinalgTimer.Start();
+
+      InnerTimer.Start();
+      ComplexD dc  = innerProduct(p,mmp);
+      InnerTimer.Stop();
+      d = dc.real();
+      a = c / d;
+
+      AxpyNormTimer.Start();
+      cp = axpy_norm(r, -a, mmp, r);
+      AxpyNormTimer.Stop();
+      b = cp / c;
+
+      LinearCombTimer.Start();
+      {
+	autoView( psi_v , psi, AcceleratorWrite);
+	autoView( p_v   , p,   AcceleratorWrite);
+	autoView( r_v   , r,   AcceleratorWrite);
+	accelerator_for(ss,p_v.size(), Field::vector_object::Nsimd(),{
+	    coalescedWrite(psi_v[ss], a      *  p_v(ss) + psi_v(ss));
+	    coalescedWrite(p_v[ss]  , b      *  p_v(ss) + r_v  (ss));
+	});
+      }
+      LinearCombTimer.Stop();
+      LinalgTimer.Stop();
+
+      IterationTimer.Stop();
+      if ( (k % 500) == 0 ) {
+	std::cout << GridLogMessage << "ConjugateGradient: Iteration " << k
+                << " residual " << sqrt(cp/ssq) << " target " << Tolerance << std::endl;
+      } else { 
+	std::cout << GridLogIterative << "ConjugateGradient: Iteration " << k
+		  << " residual " << sqrt(cp/ssq) << " target " << Tolerance << " took " << IterationTimer.Elapsed() << std::endl;
+      }
+
+      // Stopping condition
+      if (cp <= rsq) {
+	usecs +=usecond();
+        SolverTimer.Stop();
+        Linop.HermOpAndNorm(psi, mmp, d, qq);
+        p = mmp - src;
+	GridBase *grid = src.Grid();
+	RealD DwfFlops = (1452. )*grid->gSites()*4*k
+   	               + (8+4+8+4+4)*12*grid->gSites()*k; // CG linear algebra
+        RealD srcnorm = std::sqrt(norm2(src));
+        RealD resnorm = std::sqrt(norm2(p));
+        RealD true_residual = resnorm / srcnorm;
+        std::cout << GridLogMessage << "ConjugateGradient Converged on iteration " << k 
+		  << "\tComputed residual " << std::sqrt(cp / ssq)
+		  << "\tTrue residual " << true_residual
+		  << "\tTarget " << Tolerance << std::endl;
+
+	//	std::cout << GridLogMessage << "\tPreamble   " << PreambleTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tSolver Elapsed    " << SolverTimer.Elapsed() <<std::endl;
+        std::cout << GridLogPerformance << "Time breakdown "<<std::endl;
+	std::cout << GridLogPerformance << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+	std::cout << GridLogPerformance << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
+	std::cout << GridLogPerformance << "\t\tInner      " << InnerTimer.Elapsed() <<std::endl;
+	std::cout << GridLogPerformance << "\t\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
+	std::cout << GridLogPerformance << "\t\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
+
+	std::cout << GridLogDebug << "\tMobius flop rate " << DwfFlops/ usecs<< " Gflops " <<std::endl;
+
+        if (ErrorOnNoConverge) assert(true_residual / Tolerance < 10000.0);
+
+	IterationsToComplete = k;	
+	TrueResidual = true_residual;
+
+        return;
+      }
+    }
+    // Failed. Calculate true residual before giving up                                                         
+    // Linop.HermOpAndNorm(psi, mmp, d, qq);
+    //    p = mmp - src;
+    //TrueResidual = sqrt(norm2(p)/ssq);
+    //    TrueResidual = 1;
+
+    std::cout << GridLogMessage << "ConjugateGradient did NOT converge "<<k<<" / "<< MaxIterations
+    	      <<" residual "<< std::sqrt(cp / ssq)<< std::endl;
+    SolverTimer.Stop();
+    std::cout << GridLogMessage << "\tPreamble   " << PreambleTimer.Elapsed() <<std::endl;
+    std::cout << GridLogMessage << "\tSolver     " << SolverTimer.Elapsed() <<std::endl;
+    std::cout << GridLogMessage << "Solver breakdown "<<std::endl;
+    std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+    std::cout << GridLogMessage<< "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\t\tInner      " << InnerTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\t\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\t\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
+
+    if (ErrorOnNoConverge) assert(0);
+    IterationsToComplete = k;
+
+  }
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/ConjugateGradientMixedPrec.h

@@ -0,0 +1,170 @@
+/*************************************************************************************
+
+    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:
+    using LinearFunction<FieldD>::operator();
+    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
+    RealD TrueResidual;
+
+    //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){
+    std::cout << GridLogMessage << "MixedPrecisionConjugateGradient: Starting mixed precision CG with outer tolerance " << Tolerance << " and inner tolerance " << InnerTolerance << std::endl;
+    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;
+    
+    std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradient: Starting initial inner CG with tolerance " << inner_tol << std::endl;
+    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
+
+    precisionChangeWorkspace pc_wk_sp_to_dp(DoublePrecGrid, SinglePrecGrid);
+    precisionChangeWorkspace pc_wk_dp_to_sp(SinglePrecGrid, DoublePrecGrid);
+    
+    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, pc_wk_dp_to_sp);
+      PrecChangeTimer.Stop();
+      
+      sol_f = Zero();
+
+      //Optionally improve inner solver guess (eg using known eigenvectors)
+      if(guesser != NULL)
+	(*guesser)(src_f, sol_f);
+
+      //Inner CG
+      std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradient: Outer iteration " << outer_iter << " starting inner CG with tolerance " << inner_tol << std::endl;
+      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, pc_wk_sp_to_dp);
+      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;
+    TrueResidual = CG_d.TrueResidual;
+
+    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/ConjugateGradientMixedPrecBatched.h

@@ -0,0 +1,213 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ConjugateGradientMixedPrecBatched.h
+
+    Copyright (C) 2015
+
+    Author: Raoul Hodgson <raoul.hodgson@ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CONJUGATE_GRADIENT_MIXED_PREC_BATCHED_H
+#define GRID_CONJUGATE_GRADIENT_MIXED_PREC_BATCHED_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 MixedPrecisionConjugateGradientBatched : public LinearFunction<FieldD> {
+public:
+  using LinearFunction<FieldD>::operator();
+  RealD   Tolerance;
+  RealD   InnerTolerance; //Initial tolerance for inner CG. Defaults to Tolerance but can be changed
+  Integer MaxInnerIterations;
+  Integer MaxOuterIterations;
+  Integer MaxPatchupIterations;
+  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;
+
+  //Option to speed up *inner single precision* solves using a LinearFunction that produces a guess
+  LinearFunction<FieldF> *guesser;
+  bool updateResidual;
+  
+  MixedPrecisionConjugateGradientBatched(RealD tol, 
+          Integer maxinnerit, 
+          Integer maxouterit, 
+          Integer maxpatchit,
+          GridBase* _sp_grid, 
+          LinearOperatorBase<FieldF> &_Linop_f, 
+          LinearOperatorBase<FieldD> &_Linop_d,
+          bool _updateResidual=true) :
+    Linop_f(_Linop_f), Linop_d(_Linop_d),
+    Tolerance(tol), InnerTolerance(tol), MaxInnerIterations(maxinnerit), MaxOuterIterations(maxouterit), MaxPatchupIterations(maxpatchit), SinglePrecGrid(_sp_grid),
+    OuterLoopNormMult(100.), guesser(NULL), updateResidual(_updateResidual) { };
+
+  void useGuesser(LinearFunction<FieldF> &g){
+    guesser = &g;
+  }
+  
+  void operator() (const FieldD &src_d_in, FieldD &sol_d){
+    std::vector<FieldD> srcs_d_in{src_d_in};
+    std::vector<FieldD> sols_d{sol_d};
+
+    (*this)(srcs_d_in,sols_d);
+
+    sol_d = sols_d[0];
+  }
+
+  void operator() (const std::vector<FieldD> &src_d_in, std::vector<FieldD> &sol_d){
+    assert(src_d_in.size() == sol_d.size());
+    int NBatch = src_d_in.size();
+
+    std::cout << GridLogMessage << "NBatch = " << NBatch << std::endl;
+
+    Integer TotalOuterIterations = 0; //Number of restarts
+    std::vector<Integer> TotalInnerIterations(NBatch,0);     //Number of inner CG iterations
+    std::vector<Integer> TotalFinalStepIterations(NBatch,0); //Number of CG iterations in final patch-up step
+  
+    GridStopWatch TotalTimer;
+    TotalTimer.Start();
+
+    GridStopWatch InnerCGtimer;
+    GridStopWatch PrecChangeTimer;
+    
+    int cb = src_d_in[0].Checkerboard();
+    
+    std::vector<RealD> src_norm;
+    std::vector<RealD> norm;
+    std::vector<RealD> stop;
+    
+    GridBase* DoublePrecGrid = src_d_in[0].Grid();
+    FieldD tmp_d(DoublePrecGrid);
+    tmp_d.Checkerboard() = cb;
+    
+    FieldD tmp2_d(DoublePrecGrid);
+    tmp2_d.Checkerboard() = cb;
+
+    std::vector<FieldD> src_d;
+    std::vector<FieldF> src_f;
+    std::vector<FieldF> sol_f;
+
+    for (int i=0; i<NBatch; i++) {
+      sol_d[i].Checkerboard() = cb;
+
+      src_norm.push_back(norm2(src_d_in[i]));
+      norm.push_back(0.);
+      stop.push_back(src_norm[i] * Tolerance*Tolerance);
+
+      src_d.push_back(src_d_in[i]); //source for next inner iteration, computed from residual during operation
+
+      src_f.push_back(SinglePrecGrid);
+      src_f[i].Checkerboard() = cb;
+
+      sol_f.push_back(SinglePrecGrid);
+      sol_f[i].Checkerboard() = cb;
+    }
+    
+    RealD inner_tol = InnerTolerance;
+    
+    ConjugateGradient<FieldF> CG_f(inner_tol, MaxInnerIterations);
+    CG_f.ErrorOnNoConverge = false;
+    
+    Integer &outer_iter = TotalOuterIterations; //so it will be equal to the final iteration count
+      
+    for(outer_iter = 0; outer_iter < MaxOuterIterations; outer_iter++){
+      std::cout << GridLogMessage << std::endl;
+      std::cout << GridLogMessage << "Outer iteration " << outer_iter << std::endl;
+      
+      bool allConverged = true;
+      
+      for (int i=0; i<NBatch; i++) {
+        //Compute double precision rsd and also new RHS vector.
+        Linop_d.HermOp(sol_d[i], tmp_d);
+        norm[i] = axpy_norm(src_d[i], -1., tmp_d, src_d_in[i]); //src_d is residual vector
+        
+        std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradientBatched: Outer iteration " << outer_iter <<" solve " << i << " residual "<< norm[i] << " target "<< stop[i] <<std::endl;
+
+        PrecChangeTimer.Start();
+        precisionChange(src_f[i], src_d[i]);
+        PrecChangeTimer.Stop();
+        
+        sol_f[i] = Zero();
+      
+        if(norm[i] > OuterLoopNormMult * stop[i]) {
+          allConverged = false;
+        }
+      }
+      if (allConverged) break;
+
+      if (updateResidual) {
+        RealD normMax = *std::max_element(std::begin(norm), std::end(norm));
+        RealD stopMax = *std::max_element(std::begin(stop), std::end(stop));
+        while( normMax * inner_tol * inner_tol < stopMax) inner_tol *= 2;  // inner_tol = sqrt(stop/norm) ??
+        CG_f.Tolerance = inner_tol;
+      }
+
+      //Optionally improve inner solver guess (eg using known eigenvectors)
+      if(guesser != NULL) {
+        (*guesser)(src_f, sol_f);
+      }
+
+      for (int i=0; i<NBatch; i++) {
+        //Inner CG
+        InnerCGtimer.Start();
+        CG_f(Linop_f, src_f[i], sol_f[i]);
+        InnerCGtimer.Stop();
+        TotalInnerIterations[i] += CG_f.IterationsToComplete;
+        
+        //Convert sol back to double and add to double prec solution
+        PrecChangeTimer.Start();
+        precisionChange(tmp_d, sol_f[i]);
+        PrecChangeTimer.Stop();
+        
+        axpy(sol_d[i], 1.0, tmp_d, sol_d[i]);
+      }
+
+    }
+    
+    //Final trial CG
+    std::cout << GridLogMessage << std::endl;
+    std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradientBatched: Starting final patch-up double-precision solve"<<std::endl;
+    
+    for (int i=0; i<NBatch; i++) {
+      ConjugateGradient<FieldD> CG_d(Tolerance, MaxPatchupIterations);
+      CG_d(Linop_d, src_d_in[i], sol_d[i]);
+      TotalFinalStepIterations[i] += CG_d.IterationsToComplete;
+    }
+
+    TotalTimer.Stop();
+
+    std::cout << GridLogMessage << std::endl;
+    for (int i=0; i<NBatch; i++) {
+      std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradientBatched: solve " << i << " Inner CG iterations " << TotalInnerIterations[i] << " Restarts " << TotalOuterIterations << " Final CG iterations " << TotalFinalStepIterations[i] << std::endl;
+    }
+    std::cout << GridLogMessage << std::endl;
+    std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradientBatched: 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 +1,346 @@
+/*************************************************************************************
+
+    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, const 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)
+  {
+    GRID_TRACE("ConjugateGradientMultiShift");
+  
+    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^2 "<<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);
+    }
+
+    std::cout << GridLogIterative << "ConjugateGradientMultiShift: initial rn (|src|^2) =" << rn << " qq (|MdagM src|^2) =" << qq << " d ( dot(src, [MdagM + m_0]src) ) =" << d << " c=" << c << std::endl;
+    
+  
+  ///////////////////////////////////////
+  // 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 << "\tMatrix   " << 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/ConjugateGradientMultiShiftCleanup.h

@@ -0,0 +1,373 @@
+/*************************************************************************************
+
+    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>
+Author: Christopher Kelly <ckelly@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+//CK 2020: A variant of the multi-shift conjugate gradient with the matrix multiplication in single precision. 
+//The residual is stored in single precision, but the search directions and solution are stored in double precision. 
+//Every update_freq iterations the residual is corrected in double precision. 
+//For safety the a final regular CG is applied to clean up if necessary
+
+//PB Pure single, then double fixup
+
+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 ConjugateGradientMultiShiftMixedPrecCleanup : public OperatorMultiFunction<FieldD>,
+					     public OperatorFunction<FieldD>
+{
+public:                                                
+
+  using OperatorFunction<FieldD>::operator();
+
+  RealD   Tolerance;
+  Integer MaxIterationsMshift;
+  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;
+
+  int ReliableUpdateFreq; //number of iterations between reliable updates
+
+  GridBase* SinglePrecGrid; //Grid for single-precision fields
+  LinearOperatorBase<FieldF> &Linop_f; //single precision
+
+  ConjugateGradientMultiShiftMixedPrecCleanup(Integer maxit, const MultiShiftFunction &_shifts,
+				       GridBase* _SinglePrecGrid, LinearOperatorBase<FieldF> &_Linop_f,
+				       int _ReliableUpdateFreq) : 
+    MaxIterationsMshift(maxit),  shifts(_shifts), SinglePrecGrid(_SinglePrecGrid), Linop_f(_Linop_f), ReliableUpdateFreq(_ReliableUpdateFreq),
+    MaxIterations(20000)
+  { 
+    verbose=1;
+    IterationsToCompleteShift.resize(_shifts.order);
+    TrueResidualShift.resize(_shifts.order);
+  }
+
+  void operator() (LinearOperatorBase<FieldD> &Linop, const FieldD &src, FieldD &psi)
+  {
+    GridBase *grid = src.Grid();
+    int nshift = shifts.order;
+    std::vector<FieldD> results(nshift,grid);
+    (*this)(Linop,src,results,psi);
+  }
+  void operator() (LinearOperatorBase<FieldD> &Linop, const FieldD &src, std::vector<FieldD> &results, FieldD &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<FieldD> &Linop_d, const FieldD &src_d, std::vector<FieldD> &psi_d)
+  { 
+    GRID_TRACE("ConjugateGradientMultiShiftMixedPrecCleanup");
+    GridBase *DoublePrecGrid = src_d.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);
+
+    //Double precision search directions
+    FieldD p_d(DoublePrecGrid);
+    std::vector<FieldF> ps_f (nshift, SinglePrecGrid);// Search directions (single precision)
+    std::vector<FieldF> psi_f(nshift, SinglePrecGrid);// solutions (single precision)
+
+    FieldD tmp_d(DoublePrecGrid);
+    FieldD r_d(DoublePrecGrid);
+    FieldF r_f(SinglePrecGrid);
+    FieldD mmp_d(DoublePrecGrid);
+
+    assert(psi_d.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  rsqf[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
+    FieldF p_f(SinglePrecGrid);
+    FieldF mmp_f(SinglePrecGrid);
+
+    // 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_d);
+
+    // Handle trivial case of zero src.
+    if( cp == 0. ){
+      for(int s=0;s<nshift;s++){
+	psi_d[s] = Zero();
+	psi_f[s] = Zero();
+	IterationsToCompleteShift[s] = 1;
+	TrueResidualShift[s] = 0.;
+      }
+      return;
+    }
+
+    for(int s=0;s<nshift;s++){
+      rsq[s] = cp * mresidual[s] * mresidual[s];
+      rsqf[s] =rsq[s];
+      std::cout<<GridLogMessage<<"ConjugateGradientMultiShiftMixedPrecCleanup: shift "<< s <<" target resid "<<rsq[s]<<std::endl;
+      //      ps_d[s] = src_d;
+      precisionChange(ps_f[s],src_d);
+    }
+    // r and p for primary
+    p_d = src_d; //primary copy --- make this a reference to ps_d to save axpys
+    r_d = p_d;
+    
+    //MdagM+m[0]
+    precisionChange(p_f,p_d);
+    Linop_f.HermOpAndNorm(p_f,mmp_f,d,qq); // mmp = MdagM p        d=real(dot(p, mmp)),  qq=norm2(mmp)
+    precisionChange(tmp_d,mmp_f);
+    Linop_d.HermOpAndNorm(p_d,mmp_d,d,qq); // mmp = MdagM p        d=real(dot(p, mmp)),  qq=norm2(mmp)
+    tmp_d = tmp_d - mmp_d;
+    std::cout << " Testing operators match "<<norm2(mmp_d)<<" f "<<norm2(mmp_f)<<" diff "<< norm2(tmp_d)<<std::endl;
+    //    assert(norm2(tmp_d)< 1.0e-4);
+
+    axpy(mmp_d,mass[0],p_d,mmp_d);
+    RealD rn = norm2(p_d);
+    d += rn*mass[0];
+
+    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_d,b,mmp_d,r_d);
+  
+    for(int s=0;s<nshift;s++) {
+      axpby(psi_d[s],0.,-bs[s]*alpha[s],src_d,src_d);
+      precisionChange(psi_f[s],psi_d[s]);
+    }
+  
+    ///////////////////////////////////////
+    // Timers
+    ///////////////////////////////////////
+    GridStopWatch AXPYTimer, ShiftTimer, QRTimer, MatrixTimer, SolverTimer, PrecChangeTimer, CleanupTimer;
+
+    SolverTimer.Start();
+  
+    // Iteration loop
+    int k;
+  
+    for (k=1;k<=MaxIterationsMshift;k++){    
+
+      a = c /cp;
+      AXPYTimer.Start();
+      axpy(p_d,a,p_d,r_d); 
+      AXPYTimer.Stop();
+
+      PrecChangeTimer.Start();
+      precisionChange(r_f, r_d);
+      PrecChangeTimer.Stop();
+
+      AXPYTimer.Start();
+      for(int s=0;s<nshift;s++){
+	if ( ! converged[s] ) { 
+	  if (s==0){
+	    axpy(ps_f[s],a,ps_f[s],r_f);
+	  } else{
+	    RealD as =a *z[s][iz]*bs[s] /(z[s][1-iz]*b);
+	    axpby(ps_f[s],z[s][iz],as,r_f,ps_f[s]);
+	  }
+	}
+      }
+      AXPYTimer.Stop();
+
+      cp=c;
+      PrecChangeTimer.Start();
+      precisionChange(p_f, p_d); //get back single prec search direction for linop
+      PrecChangeTimer.Stop();
+      MatrixTimer.Start();  
+      Linop_f.HermOp(p_f,mmp_f);
+      MatrixTimer.Stop();  
+      PrecChangeTimer.Start();
+      precisionChange(mmp_d, mmp_f); // From Float to Double
+      PrecChangeTimer.Stop();
+
+      d=real(innerProduct(p_d,mmp_d));    
+      axpy(mmp_d,mass[0],p_d,mmp_d);
+      RealD rn = norm2(p_d);
+      d += rn*mass[0];
+    
+      bp=b;
+      b=-cp/d;
+
+      // 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();
+
+      //Update single precision solutions
+      AXPYTimer.Start();
+      for(int s=0;s<nshift;s++){
+	int ss = s;
+	if( (!converged[s]) ) { 
+	  axpy(psi_f[ss],-bs[s]*alpha[s],ps_f[s],psi_f[ss]);
+	}
+      }
+      c = axpy_norm(r_d,b,mmp_d,r_d);
+      AXPYTimer.Stop();
+    
+      // 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<rsqf[s]){
+	    if ( ! converged[s] )
+	      std::cout<<GridLogMessage<<"ConjugateGradientMultiShiftMixedPrecCleanup k="<<k<<" Shift "<<s<<" has converged"<<std::endl;
+	    converged[s]=1;
+	  } else {
+	    all_converged=0;
+	  }
+
+	}
+      }
+
+      if ( all_converged || k == MaxIterationsMshift-1){
+
+	SolverTimer.Stop();
+
+	for(int s=0;s<nshift;s++){
+	  precisionChange(psi_d[s],psi_f[s]);
+	}
+
+	
+	if ( all_converged ){
+	  std::cout<<GridLogMessage<< "ConjugateGradientMultiShiftMixedPrecCleanup: All shifts have converged iteration "<<k<<std::endl;
+	  std::cout<<GridLogMessage<< "ConjugateGradientMultiShiftMixedPrecCleanup: Checking solutions"<<std::endl;
+	} else {
+	  std::cout<<GridLogMessage<< "ConjugateGradientMultiShiftMixedPrecCleanup: Not all shifts have converged iteration "<<k<<std::endl;
+	}
+	
+	// Check answers 
+	for(int s=0; s < nshift; s++) { 
+	  Linop_d.HermOpAndNorm(psi_d[s],mmp_d,d,qq);
+	  axpy(tmp_d,mass[s],psi_d[s],mmp_d);
+	  axpy(r_d,-alpha[s],src_d,tmp_d);
+	  RealD rn = norm2(r_d);
+	  RealD cn = norm2(src_d);
+	  TrueResidualShift[s] = std::sqrt(rn/cn);
+	  std::cout<<GridLogMessage<<"ConjugateGradientMultiShiftMixedPrecCleanup: shift["<<s<<"] true residual "<< TrueResidualShift[s] << " target " << mresidual[s] << std::endl;
+
+	  //If we have not reached the desired tolerance, do a (mixed precision) CG cleanup
+	  if(rn >= rsq[s]){
+	    CleanupTimer.Start();
+	    std::cout<<GridLogMessage<<"ConjugateGradientMultiShiftMixedPrecCleanup: performing cleanup step for shift " << s << std::endl;
+
+	    //Setup linear operators for final cleanup
+	    ConjugateGradientMultiShiftMixedPrecSupport::ShiftedLinop<FieldD> Linop_shift_d(Linop_d, mass[s]);
+	    ConjugateGradientMultiShiftMixedPrecSupport::ShiftedLinop<FieldF> Linop_shift_f(Linop_f, mass[s]);
+					       
+	    MixedPrecisionConjugateGradient<FieldD,FieldF> cg(mresidual[s], MaxIterations, MaxIterations, SinglePrecGrid, Linop_shift_f, Linop_shift_d); 
+	    cg(src_d, psi_d[s]);
+	    
+	    TrueResidualShift[s] = cg.TrueResidual;
+	    CleanupTimer.Stop();
+	  }
+	}
+
+	std::cout << GridLogMessage << "ConjugateGradientMultiShiftMixedPrecCleanup: Time Breakdown for body"<<std::endl;
+	std::cout << GridLogMessage << "\tSolver    " << SolverTimer.Elapsed()     <<std::endl;
+	std::cout << GridLogMessage << "\t\tAXPY    " << AXPYTimer.Elapsed()     <<std::endl;
+	std::cout << GridLogMessage << "\t\tMatrix    " << MatrixTimer.Elapsed()     <<std::endl;
+	std::cout << GridLogMessage << "\t\tShift    " << ShiftTimer.Elapsed()     <<std::endl;
+	std::cout << GridLogMessage << "\t\tPrecision Change " << PrecChangeTimer.Elapsed()     <<std::endl;
+	std::cout << GridLogMessage << "\tFinal Cleanup " << CleanupTimer.Elapsed()     <<std::endl;
+	std::cout << GridLogMessage << "\tSolver+Cleanup " << SolverTimer.Elapsed() + CleanupTimer.Elapsed() << std::endl;
+
+	IterationsToComplete = k;	
+
+	return;
+      }
+   
+    }
+    std::cout<<GridLogMessage<<"CG multi shift did not converge"<<std::endl;
+    assert(0);
+  }
+
+};
+NAMESPACE_END(Grid);
+

Grid/algorithms/iterative/ConjugateGradientMultiShiftMixedPrec.h

@@ -0,0 +1,416 @@
+/*************************************************************************************
+
+    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>
+Author: Christopher Kelly <ckelly@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_CONJUGATE_GRADIENT_MULTI_SHIFT_MIXEDPREC_H
+#define GRID_CONJUGATE_GRADIENT_MULTI_SHIFT_MIXEDPREC_H
+
+NAMESPACE_BEGIN(Grid);
+
+//CK 2020: A variant of the multi-shift conjugate gradient with the matrix multiplication in single precision. 
+//The residual is stored in single precision, but the search directions and solution are stored in double precision. 
+//Every update_freq iterations the residual is corrected in double precision. 
+    
+//For safety the a final regular CG is applied to clean up if necessary
+
+//Linop to add shift to input linop, used in cleanup CG
+namespace ConjugateGradientMultiShiftMixedPrecSupport{
+template<typename Field>
+class ShiftedLinop: public LinearOperatorBase<Field>{
+public:
+  LinearOperatorBase<Field> &linop_base;
+  RealD shift;
+
+  ShiftedLinop(LinearOperatorBase<Field> &_linop_base, RealD _shift): linop_base(_linop_base), shift(_shift){}
+
+  void OpDiag (const Field &in, Field &out){ assert(0); }
+  void OpDir  (const Field &in, Field &out,int dir,int disp){ assert(0); }
+  void OpDirAll  (const Field &in, std::vector<Field> &out){ assert(0); }
+  
+  void Op     (const Field &in, Field &out){ assert(0); }
+  void AdjOp  (const Field &in, Field &out){ assert(0); }
+
+  void HermOp(const Field &in, Field &out){
+    linop_base.HermOp(in, out);
+    axpy(out, shift, 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);
+  }
+};
+};
+
+
+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 ConjugateGradientMultiShiftMixedPrec : public OperatorMultiFunction<FieldD>,
+					     public OperatorFunction<FieldD>
+{
+public:                                                
+
+  using OperatorFunction<FieldD>::operator();
+
+  RealD   Tolerance;
+  Integer MaxIterationsMshift;
+  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;
+
+  int ReliableUpdateFreq; //number of iterations between reliable updates
+
+  GridBase* SinglePrecGrid; //Grid for single-precision fields
+  LinearOperatorBase<FieldF> &Linop_f; //single precision
+
+  ConjugateGradientMultiShiftMixedPrec(Integer maxit, const MultiShiftFunction &_shifts,
+				       GridBase* _SinglePrecGrid, LinearOperatorBase<FieldF> &_Linop_f,
+				       int _ReliableUpdateFreq) : 
+    MaxIterationsMshift(maxit),  shifts(_shifts), SinglePrecGrid(_SinglePrecGrid), Linop_f(_Linop_f), ReliableUpdateFreq(_ReliableUpdateFreq),
+    MaxIterations(20000)
+  { 
+    verbose=1;
+    IterationsToCompleteShift.resize(_shifts.order);
+    TrueResidualShift.resize(_shifts.order);
+  }
+
+  void operator() (LinearOperatorBase<FieldD> &Linop, const FieldD &src, FieldD &psi)
+  {
+    GridBase *grid = src.Grid();
+    int nshift = shifts.order;
+    std::vector<FieldD> results(nshift,grid);
+    (*this)(Linop,src,results,psi);
+  }
+  void operator() (LinearOperatorBase<FieldD> &Linop, const FieldD &src, std::vector<FieldD> &results, FieldD &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<FieldD> &Linop_d, const FieldD &src_d, std::vector<FieldD> &psi_d)
+  { 
+    GRID_TRACE("ConjugateGradientMultiShiftMixedPrec");
+    GridBase *DoublePrecGrid = src_d.Grid();
+
+    precisionChangeWorkspace pc_wk_s_to_d(DoublePrecGrid,SinglePrecGrid);
+    precisionChangeWorkspace pc_wk_d_to_s(SinglePrecGrid,DoublePrecGrid);
+    
+    ////////////////////////////////////////////////////////////////////////
+    // 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);
+
+    //Double precision search directions
+    FieldD p_d(DoublePrecGrid);
+    std::vector<FieldD> ps_d(nshift, DoublePrecGrid);// Search directions (double precision)
+
+    FieldD tmp_d(DoublePrecGrid);
+    FieldD r_d(DoublePrecGrid);
+    FieldD mmp_d(DoublePrecGrid);
+
+    assert(psi_d.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  rsqf[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
+    FieldF p_f(SinglePrecGrid);
+    FieldF mmp_f(SinglePrecGrid);
+
+    // 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_d);
+
+    // Handle trivial case of zero src.
+    if( cp == 0. ){
+      for(int s=0;s<nshift;s++){
+	psi_d[s] = Zero();
+	IterationsToCompleteShift[s] = 1;
+	TrueResidualShift[s] = 0.;
+      }
+      return;
+    }
+
+    for(int s=0;s<nshift;s++){
+      rsq[s] = cp * mresidual[s] * mresidual[s];
+      rsqf[s] =rsq[s];
+      std::cout<<GridLogMessage<<"ConjugateGradientMultiShiftMixedPrec: shift "<< s <<" target resid "<<rsq[s]<<std::endl;
+      ps_d[s] = src_d;
+    }
+    // r and p for primary
+    p_d = src_d; //primary copy --- make this a reference to ps_d to save axpys
+    r_d = p_d;
+    
+    //MdagM+m[0]
+    precisionChange(p_f, p_d, pc_wk_d_to_s);
+
+    Linop_f.HermOpAndNorm(p_f,mmp_f,d,qq); // mmp = MdagM p        d=real(dot(p, mmp)),  qq=norm2(mmp)
+    precisionChange(tmp_d, mmp_f, pc_wk_s_to_d);
+    Linop_d.HermOpAndNorm(p_d,mmp_d,d,qq); // mmp = MdagM p        d=real(dot(p, mmp)),  qq=norm2(mmp)
+    tmp_d = tmp_d - mmp_d;
+    std::cout << " Testing operators match "<<norm2(mmp_d)<<" f "<<norm2(mmp_f)<<" diff "<< norm2(tmp_d)<<std::endl;
+    assert(norm2(tmp_d)< 1.0);
+
+    axpy(mmp_d,mass[0],p_d,mmp_d);
+    RealD rn = norm2(p_d);
+    d += rn*mass[0];
+
+    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_d,b,mmp_d,r_d);
+  
+    for(int s=0;s<nshift;s++) {
+      axpby(psi_d[s],0.,-bs[s]*alpha[s],src_d,src_d);
+    }
+  
+    ///////////////////////////////////////
+    // Timers
+    ///////////////////////////////////////
+    GridStopWatch AXPYTimer, ShiftTimer, QRTimer, MatrixTimer, SolverTimer, PrecChangeTimer, CleanupTimer;
+
+    SolverTimer.Start();
+  
+    // Iteration loop
+    int k;
+  
+    for (k=1;k<=MaxIterationsMshift;k++){    
+
+      a = c /cp;
+      AXPYTimer.Start();
+      axpy(p_d,a,p_d,r_d); 
+
+      for(int s=0;s<nshift;s++){
+	if ( ! converged[s] ) { 
+	  if (s==0){
+	    axpy(ps_d[s],a,ps_d[s],r_d);
+	  } else{
+	    RealD as =a *z[s][iz]*bs[s] /(z[s][1-iz]*b);
+	    axpby(ps_d[s],z[s][iz],as,r_d,ps_d[s]);
+	  }
+	}
+      }
+      AXPYTimer.Stop();
+
+      PrecChangeTimer.Start();
+      precisionChange(p_f, p_d, pc_wk_d_to_s); //get back single prec search direction for linop
+      PrecChangeTimer.Stop();
+
+      cp=c;
+      MatrixTimer.Start();  
+      Linop_f.HermOp(p_f,mmp_f);
+      MatrixTimer.Stop();  
+
+      PrecChangeTimer.Start();
+      precisionChange(mmp_d, mmp_f, pc_wk_s_to_d); // From Float to Double
+      PrecChangeTimer.Stop();
+
+      AXPYTimer.Start();
+      d=real(innerProduct(p_d,mmp_d));    
+      axpy(mmp_d,mass[0],p_d,mmp_d);
+      AXPYTimer.Stop();
+      RealD rn = norm2(p_d);
+      d += rn*mass[0];
+    
+      bp=b;
+      b=-cp/d;
+
+      // 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();
+
+      //Update double precision solutions
+      AXPYTimer.Start();
+      for(int s=0;s<nshift;s++){
+	int ss = s;
+	if( (!converged[s]) ) { 
+	  axpy(psi_d[ss],-bs[s]*alpha[s],ps_d[s],psi_d[ss]);
+	}
+      }
+
+      //Perform reliable update if necessary; otherwise update residual from single-prec mmp
+      c = axpy_norm(r_d,b,mmp_d,r_d);
+
+      AXPYTimer.Stop();
+
+      if(k % ReliableUpdateFreq == 0){
+	RealD c_old = c;
+	//Replace r with true residual
+	MatrixTimer.Start();  
+	Linop_d.HermOp(psi_d[0],mmp_d); 
+	MatrixTimer.Stop();  
+
+	AXPYTimer.Start();
+	axpy(mmp_d,mass[0],psi_d[0],mmp_d);
+
+	c = axpy_norm(r_d, -1.0, mmp_d, src_d);
+	AXPYTimer.Stop();
+
+	std::cout<<GridLogMessage<<"ConjugateGradientMultiShiftMixedPrec k="<<k<< ", replaced |r|^2 = "<<c_old <<" with |r|^2 = "<<c<<std::endl;
+      }
+    
+      // 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<rsqf[s]){
+	    if ( ! converged[s] )
+	      std::cout<<GridLogMessage<<"ConjugateGradientMultiShiftMixedPrec k="<<k<<" Shift "<<s<<" has converged"<<std::endl;
+	    converged[s]=1;
+	  } else {
+	    all_converged=0;
+	  }
+
+	}
+      }
+
+      if ( all_converged || k == MaxIterationsMshift-1){
+
+	SolverTimer.Stop();
+
+	if ( all_converged ){
+	  std::cout<<GridLogMessage<< "ConjugateGradientMultiShiftMixedPrec: All shifts have converged iteration "<<k<<std::endl;
+	  std::cout<<GridLogMessage<< "ConjugateGradientMultiShiftMixedPrec: Checking solutions"<<std::endl;
+	} else {
+	  std::cout<<GridLogMessage<< "ConjugateGradientMultiShiftMixedPrec: Not all shifts have converged iteration "<<k<<std::endl;
+	}
+	
+	// Check answers 
+	for(int s=0; s < nshift; s++) { 
+	  Linop_d.HermOpAndNorm(psi_d[s],mmp_d,d,qq);
+	  axpy(tmp_d,mass[s],psi_d[s],mmp_d);
+	  axpy(r_d,-alpha[s],src_d,tmp_d);
+	  RealD rn = norm2(r_d);
+	  RealD cn = norm2(src_d);
+	  TrueResidualShift[s] = std::sqrt(rn/cn);
+	  std::cout<<GridLogMessage<<"ConjugateGradientMultiShiftMixedPrec: shift["<<s<<"] true residual "<< TrueResidualShift[s] << " target " << mresidual[s] << std::endl;
+
+	  //If we have not reached the desired tolerance, do a (mixed precision) CG cleanup
+	  if(rn >= rsq[s]){
+	    CleanupTimer.Start();
+	    std::cout<<GridLogMessage<<"ConjugateGradientMultiShiftMixedPrec: performing cleanup step for shift " << s << std::endl;
+
+	    //Setup linear operators for final cleanup
+	    ConjugateGradientMultiShiftMixedPrecSupport::ShiftedLinop<FieldD> Linop_shift_d(Linop_d, mass[s]);
+	    ConjugateGradientMultiShiftMixedPrecSupport::ShiftedLinop<FieldF> Linop_shift_f(Linop_f, mass[s]);
+					       
+	    MixedPrecisionConjugateGradient<FieldD,FieldF> cg(mresidual[s], MaxIterations, MaxIterations, SinglePrecGrid, Linop_shift_f, Linop_shift_d); 
+	    cg(src_d, psi_d[s]);
+	    
+	    TrueResidualShift[s] = cg.TrueResidual;
+	    CleanupTimer.Stop();
+	  }
+	}
+
+	std::cout << GridLogMessage << "ConjugateGradientMultiShiftMixedPrec: Time Breakdown for body"<<std::endl;
+	std::cout << GridLogMessage << "\tSolver    " << SolverTimer.Elapsed()     <<std::endl;
+	std::cout << GridLogMessage << "\t\tAXPY    " << AXPYTimer.Elapsed()     <<std::endl;
+	std::cout << GridLogMessage << "\t\tMatrix    " << MatrixTimer.Elapsed()     <<std::endl;
+	std::cout << GridLogMessage << "\t\tShift    " << ShiftTimer.Elapsed()     <<std::endl;
+	std::cout << GridLogMessage << "\t\tPrecision Change " << PrecChangeTimer.Elapsed()     <<std::endl;
+	std::cout << GridLogMessage << "\tFinal Cleanup " << CleanupTimer.Elapsed()     <<std::endl;
+	std::cout << GridLogMessage << "\tSolver+Cleanup " << SolverTimer.Elapsed() + CleanupTimer.Elapsed() << std::endl;
+
+	IterationsToComplete = k;	
+
+	return;
+      }
+   
+    }
+    std::cout<<GridLogMessage<<"CG multi shift did not converge"<<std::endl;
+    assert(0);
+  }
+
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/ConjugateGradientReliableUpdate.h

@@ -0,0 +1,277 @@
+/*************************************************************************************
+
+    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. A reliable update is performed when the residual drops by a factor of Delta relative to its value at the last update
+
+  //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)
+  {
+    assert(Delta > 0. && Delta < 1. && "Expect  0 < Delta < 1");
+  };
+
+  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) {
+    GRID_TRACE("ConjugateGradientReliableUpdate");
+    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
+    precisionChangeWorkspace pc_wk_sp_to_dp(src.Grid(), SinglePrecGrid);
+    precisionChangeWorkspace pc_wk_dp_to_sp(SinglePrecGrid, src.Grid());
+    
+    FieldF r_f(SinglePrecGrid);
+    r_f.Checkerboard() = r.Checkerboard();
+    precisionChange(r_f, r, pc_wk_dp_to_sp);
+
+    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;
+    GridStopWatch PrecChangeTimer;
+    
+    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
+	PrecChangeTimer.Start();
+	precisionChange(mmp, psi_f, pc_wk_sp_to_dp);
+	PrecChangeTimer.Stop();
+	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;
+	std::cout << GridLogMessage << "\tPrecChange " << PrecChangeTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tPrecChange avg time " << PrecChangeTimer.Elapsed()/(2*l+1) <<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";
+	PrecChangeTimer.Start();
+	precisionChange(mmp, psi_f, pc_wk_sp_to_dp);
+	PrecChangeTimer.Stop();
+	psi = psi + mmp;
+
+	MatrixTimer.Start();
+	Linop_d.HermOpAndNorm(psi, mmp, d, qq);
+	MatrixTimer.Stop();
+	
+	r = src - mmp;
+
+	psi_f = Zero();
+	PrecChangeTimer.Start();
+	precisionChange(r_f, r, pc_wk_dp_to_sp);
+	PrecChangeTimer.Stop();
+	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/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

@@ -0,0 +1,739 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ImplicitlyRestartedLanczos.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+Author: Chulwoo Jung <chulwoo@bnl.gov>
+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_BIRL_H
+#define GRID_BIRL_H
+
+#include <string.h> //memset
+//#include <zlib.h>
+#include <sys/stat.h>
+
+NAMESPACE_BEGIN(Grid); 
+
+/////////////////////////////////////////////////////////////
+// Implicitly restarted lanczos
+/////////////////////////////////////////////////////////////
+template<class Field> class ImplicitlyRestartedLanczosTester 
+{
+ public:
+  virtual int TestConvergence(int j,RealD resid,Field &evec, RealD &eval,RealD evalMaxApprox)=0;
+  virtual int ReconstructEval(int j,RealD resid,Field &evec, RealD &eval,RealD evalMaxApprox)=0;
+};
+
+enum IRLdiagonalisation { 
+  IRLdiagonaliseWithDSTEGR,
+  IRLdiagonaliseWithQR,
+  IRLdiagonaliseWithEigen
+};
+
+template<class Field> class ImplicitlyRestartedLanczosHermOpTester  : public ImplicitlyRestartedLanczosTester<Field>
+{
+ public:
+
+  LinearFunction<Field>       &_HermOp;
+  ImplicitlyRestartedLanczosHermOpTester(LinearFunction<Field> &HermOp) : _HermOp(HermOp)  {  };
+  int ReconstructEval(int j,RealD resid,Field &B, RealD &eval,RealD evalMaxApprox)
+  {
+    return TestConvergence(j,resid,B,eval,evalMaxApprox);
+  }
+  int TestConvergence(int j,RealD eresid,Field &B, RealD &eval,RealD evalMaxApprox)
+  {
+    Field v(B);
+    RealD eval_poly = eval;
+    // Apply operator
+    _HermOp(B,v);
+
+    RealD vnum = real(innerProduct(B,v)); // HermOp.
+    RealD vden = norm2(B);
+    RealD vv0  = norm2(v);
+    eval   = vnum/vden;
+    v -= eval*B;
+
+    RealD vv = norm2(v) / ::pow(evalMaxApprox,2.0);
+
+    std::cout.precision(13);
+
+    int conv=0;
+    if( (vv<eresid*eresid) ) conv = 1;
+
+    std::cout<<GridLogIRL  << "[" << std::setw(3)<<j<<"] "
+	     <<"eval = "<<std::setw(25)<< eval << " (" << eval_poly << ")"
+	     <<" |H B[i] - eval[i]B[i]|^2 / evalMaxApprox^2 " << std::setw(25) << vv
+	     <<" target " << eresid*eresid << " conv " <<conv
+	     <<std::endl;
+
+    return conv;
+  }
+};
+
+template<class Field> 
+class ImplicitlyRestartedLanczos {
+ private:
+  const RealD small = 1.0e-8;
+  int MaxIter;
+  int MinRestart; // Minimum number of restarts; only check for convergence after
+  int Nstop;   // Number of evecs checked for convergence
+  int Nk;      // Number of converged sought
+  //  int Np;      // Np -- Number of spare vecs in krylov space //  == Nm - Nk
+  int Nm;      // Nm -- total number of vectors
+  IRLdiagonalisation diagonalisation;
+  int orth_period;
+    
+  RealD OrthoTime;
+  RealD eresid, betastp;
+  ////////////////////////////////
+  // Embedded objects
+  ////////////////////////////////
+  LinearFunction<Field>       &_PolyOp;
+  LinearFunction<Field>       &_HermOp;
+  ImplicitlyRestartedLanczosTester<Field> &_Tester;
+  // Default tester provided (we need a ref to something in default case)
+  ImplicitlyRestartedLanczosHermOpTester<Field> SimpleTester;
+  /////////////////////////
+  // Constructor
+  /////////////////////////
+  
+public:       
+
+  //////////////////////////////////////////////////////////////////
+  // PAB:
+  //////////////////////////////////////////////////////////////////
+  // Too many options  & knobs. 
+  // Eliminate:
+  //   orth_period
+  //   betastp
+  //   MinRestart
+  //
+  // Do we really need orth_period
+  // What is the theoretical basis & guarantees of betastp ?
+  // Nstop=Nk viable?
+  // MinRestart avoidable with new convergence test?
+  // Could cut to PolyOp, HermOp, Tester, Nk, Nm, resid, maxiter (+diagonalisation)
+  // HermOp could be eliminated if we dropped the Power method for max eval.
+  // -- also: The eval, eval2, eval2_copy stuff is still unnecessarily unclear
+  //////////////////////////////////////////////////////////////////
+ ImplicitlyRestartedLanczos(LinearFunction<Field> & PolyOp,
+			    LinearFunction<Field> & HermOp,
+			    ImplicitlyRestartedLanczosTester<Field> & Tester,
+			    int _Nstop, // sought vecs
+			    int _Nk, // sought vecs
+			    int _Nm, // spare vecs
+			    RealD _eresid, // resid in lmdue deficit 
+			    int _MaxIter, // Max iterations
+			    RealD _betastp=0.0, // if beta(k) < betastp: converged
+			    int _MinRestart=0, int _orth_period = 1,
+			    IRLdiagonalisation _diagonalisation= IRLdiagonaliseWithEigen) :
+    SimpleTester(HermOp), _PolyOp(PolyOp),      _HermOp(HermOp), _Tester(Tester),
+    Nstop(_Nstop)  ,      Nk(_Nk),      Nm(_Nm),
+    eresid(_eresid),      betastp(_betastp),
+    MaxIter(_MaxIter)  ,      MinRestart(_MinRestart),
+    orth_period(_orth_period), diagonalisation(_diagonalisation)  { };
+
+    ImplicitlyRestartedLanczos(LinearFunction<Field> & PolyOp,
+			       LinearFunction<Field> & HermOp,
+			       int _Nstop, // sought vecs
+			       int _Nk, // sought vecs
+			       int _Nm, // spare vecs
+			       RealD _eresid, // resid in lmdue deficit 
+			       int _MaxIter, // Max iterations
+			       RealD _betastp=0.0, // if beta(k) < betastp: converged
+			       int _MinRestart=0, int _orth_period = 1,
+			       IRLdiagonalisation _diagonalisation= IRLdiagonaliseWithEigen) :
+    SimpleTester(HermOp),  _PolyOp(PolyOp),      _HermOp(HermOp), _Tester(SimpleTester),
+    Nstop(_Nstop)  ,      Nk(_Nk),      Nm(_Nm),
+    eresid(_eresid),      betastp(_betastp),
+    MaxIter(_MaxIter)  ,      MinRestart(_MinRestart),
+    orth_period(_orth_period), diagonalisation(_diagonalisation)  { };
+
+  ////////////////////////////////
+  // Helpers
+  ////////////////////////////////
+  template<typename T>  static RealD normalise(T& v) 
+  {
+    RealD nn = norm2(v);
+    nn = std::sqrt(nn);
+    v = v * (1.0/nn);
+    return nn;
+  }
+
+  void orthogonalize(Field& w, std::vector<Field>& evec,int k)
+  {
+    OrthoTime-=usecond()/1e6;
+    basisOrthogonalize(evec,w,k);
+    normalise(w);
+    OrthoTime+=usecond()/1e6;
+  }
+
+/* Rudy Arthur's thesis pp.137
+------------------------
+Require: M > K P = M − K †
+Compute the factorization AVM = VM HM + fM eM 
+repeat
+  Q=I
+  for i = 1,...,P do
+    QiRi =HM −θiI Q = QQi
+    H M = Q †i H M Q i
+  end for
+  βK =HM(K+1,K) σK =Q(M,K)
+  r=vK+1βK +rσK
+  VK =VM(1:M)Q(1:M,1:K)
+  HK =HM(1:K,1:K)
+  →AVK =VKHK +fKe†K † Extend to an M = K + P step factorization AVM = VMHM + fMeM
+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());
+    
+    //    GridLogIRL.TimingMode(1);
+    std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
+    std::cout << GridLogIRL <<" ImplicitlyRestartedLanczos::calc() starting iteration 0 /  "<< MaxIter<< std::endl;
+    std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
+    std::cout << GridLogIRL <<" -- seek   Nk    = " << Nk    <<" vectors"<< std::endl;
+    std::cout << GridLogIRL <<" -- accept Nstop = " << Nstop <<" vectors"<< std::endl;
+    std::cout << GridLogIRL <<" -- total  Nm    = " << Nm    <<" vectors"<< std::endl;
+    std::cout << GridLogIRL <<" -- size of eval = " << eval.size() << std::endl;
+    std::cout << GridLogIRL <<" -- size of evec = " << evec.size() << std::endl;
+    if ( diagonalisation == IRLdiagonaliseWithDSTEGR ) {
+      std::cout << GridLogIRL << "Diagonalisation is DSTEGR "<<std::endl;
+    } else if ( diagonalisation == IRLdiagonaliseWithQR ) { 
+      std::cout << GridLogIRL << "Diagonalisation is QR "<<std::endl;
+    }  else if ( diagonalisation == IRLdiagonaliseWithEigen ) { 
+      std::cout << GridLogIRL << "Diagonalisation is Eigen "<<std::endl;
+    }
+    std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
+	
+    assert(Nm <= evec.size() && Nm <= eval.size());
+    
+    // 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;
+      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) < 0.0001)
+	  i=_MAX_ITER_IRL_MEVAPP_;
+	evalMaxApprox = na;
+	std::cout << GridLogIRL << " Approximation of largest eigenvalue: " << evalMaxApprox << std::endl;
+	src_n = tmp;
+      }
+    }
+	
+    std::vector<RealD> lme(Nm);  
+    std::vector<RealD> lme2(Nm);
+    std::vector<RealD> eval2(Nm);
+    std::vector<RealD> eval2_copy(Nm);
+    Eigen::MatrixXd Qt = Eigen::MatrixXd::Zero(Nm,Nm);
+
+    Field f(grid);
+    Field v(grid);
+    int k1 = 1;
+    int k2 = Nk;
+    RealD beta_k;
+
+    Nconv = 0;
+  
+    // Set initial vector
+    evec[0] = src;
+    normalise(evec[0]);
+	
+    // Initial Nk steps
+    OrthoTime=0.;
+    for(int k=0; k<Nk; ++k) step(eval,lme,evec,f,Nm,k);
+    std::cout<<GridLogIRL <<"Initial "<< Nk <<"steps done "<<std::endl;
+    std::cout<<GridLogIRL <<"Initial steps:OrthoTime "<<OrthoTime<< "seconds"<<std::endl;
+
+    //////////////////////////////////
+    // Restarting loop begins
+    //////////////////////////////////
+    int iter;
+    for(iter = 0; iter<MaxIter; ++iter){
+      
+      OrthoTime=0.;
+
+      std::cout<< GridLogMessage <<" **********************"<< std::endl;
+      std::cout<< GridLogMessage <<" Restart iteration = "<< iter << std::endl;
+      std::cout<< GridLogMessage <<" **********************"<< std::endl;
+
+      std::cout<<GridLogIRL <<" running "<<Nm-Nk <<" steps: "<<std::endl;
+      for(int k=Nk; k<Nm; ++k) step(eval,lme,evec,f,Nm,k);
+      f *= lme[Nm-1];
+
+      std::cout<<GridLogIRL <<" "<<Nm-Nk <<" steps done "<<std::endl;
+      std::cout<<GridLogIRL <<"Initial steps:OrthoTime "<<OrthoTime<< "seconds"<<std::endl;
+	  
+      //////////////////////////////////
+      // getting eigenvalues
+      //////////////////////////////////
+      for(int k=0; k<Nm; ++k){
+	eval2[k] = eval[k+k1-1];
+	lme2[k] = lme[k+k1-1];
+      }
+      Qt = Eigen::MatrixXd::Identity(Nm,Nm);
+      diagonalize(eval2,lme2,Nm,Nm,Qt,grid);
+      std::cout<<GridLogIRL <<" diagonalized "<<std::endl;
+
+      //////////////////////////////////
+      // sorting
+      //////////////////////////////////
+      eval2_copy = eval2;
+      std::partial_sort(eval2.begin(),eval2.begin()+Nm,eval2.end(),std::greater<RealD>());
+      std::cout<<GridLogIRL <<" evals sorted "<<std::endl;
+      const int chunk=8;
+      for(int io=0; io<k2;io+=chunk){
+	std::cout<<GridLogIRL << "eval "<< std::setw(3) << io ;
+	for(int ii=0;ii<chunk;ii++){
+	  if ( (io+ii)<k2 )
+	    std::cout<< " "<< std::setw(12)<< eval2[io+ii];
+	}
+	std::cout << std::endl;
+      }
+
+      //////////////////////////////////
+      // Implicitly shifted QR transformations
+      //////////////////////////////////
+      Qt = Eigen::MatrixXd::Identity(Nm,Nm);
+      for(int ip=k2; ip<Nm; ++ip){ 
+	QR_decomp(eval,lme,Nm,Nm,Qt,eval2[ip],k1,Nm);
+      }
+      std::cout<<GridLogIRL <<"QR decomposed "<<std::endl;
+
+      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 *"<<k1-1<<","<<k2+1<<")"<<std::endl;
+      
+      ////////////////////////////////////////////////////
+      // Compressed vector f and beta(k2)
+      ////////////////////////////////////////////////////
+      f *= Qt(k2-1,Nm-1);
+      f += lme[k2-1] * evec[k2];
+      beta_k = norm2(f);
+      beta_k = std::sqrt(beta_k);
+      std::cout<<GridLogIRL<<" beta(k) = "<<beta_k<<std::endl;
+	  
+      RealD betar = 1.0/beta_k;
+      evec[k2] = betar * f;
+      lme[k2-1] = beta_k;
+	  
+      ////////////////////////////////////////////////////
+      // Convergence test
+      ////////////////////////////////////////////////////
+      for(int k=0; k<Nm; ++k){    
+	eval2[k] = eval[k];
+	lme2[k] = lme[k];
+      }
+      Qt = Eigen::MatrixXd::Identity(Nm,Nm);
+      diagonalize(eval2,lme2,Nk,Nm,Qt,grid);
+      std::cout<<GridLogIRL <<" Diagonalized "<<std::endl;
+	  
+      Nconv = 0;
+      if (iter >= MinRestart) {
+
+	std::cout << GridLogIRL << "Test convergence: rotate subset of vectors to test convergence " << std::endl;
+
+	Field B(grid); B.Checkerboard() = evec[0].Checkerboard();
+
+	//  power of two search pattern;  not every evalue in eval2 is assessed.
+	int allconv =1;
+	for(int jj = 1; jj<=Nstop; jj*=2){
+	  int j = Nstop-jj;
+	  RealD e = eval2_copy[j]; // Discard the evalue
+	  basisRotateJ(B,evec,Qt,j,0,Nk,Nm);	    
+	  if( !_Tester.TestConvergence(j,eresid,B,e,evalMaxApprox) ) {
+	    allconv=0;
+	  }
+	}
+	// Do evec[0] for good measure
+	{ 
+	  int j=0;
+	  RealD e = eval2_copy[0]; 
+	  basisRotateJ(B,evec,Qt,j,0,Nk,Nm);	    
+	  if( !_Tester.TestConvergence(j,eresid,B,e,evalMaxApprox) ) allconv=0;
+	}
+	if ( allconv ) Nconv = Nstop;
+
+	// test if we converged, if so, terminate
+	std::cout<<GridLogIRL<<" #modes converged: >= "<<Nconv<<"/"<<Nstop<<std::endl;
+	//	if( Nconv>=Nstop || beta_k < betastp){
+	if( Nconv>=Nstop){
+	  goto converged;
+	}
+	  
+      } else {
+	std::cout << GridLogIRL << "iter < MinRestart: do not yet test for convergence\n";
+      } // end of iter loop
+    }
+
+    std::cout<<GridLogError<<"\n NOT converged.\n";
+    abort();
+	
+  converged:
+    {
+      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;
+      //////////////////////////////////////////////////////////////////////
+      // Full final convergence test; unconditionally applied
+      //////////////////////////////////////////////////////////////////////
+      for(int j = 0; j<=Nk; j++){
+	B=evec[j];
+	if( _Tester.ReconstructEval(j,eresid,B,eval2[j],evalMaxApprox) ) {
+	  Nconv++;
+	}
+      }
+
+      if ( Nconv < Nstop ) {
+	std::cout << GridLogIRL << "Nconv ("<<Nconv<<") < Nstop ("<<Nstop<<")"<<std::endl;
+	std::cout << GridLogIRL << "returning Nstop vectors, the last "<< Nstop-Nconv << "of which might meet convergence criterion only approximately" <<std::endl;
+      }
+      eval=eval2;
+      
+      //Keep only converged
+      eval.resize(Nstop);// was Nconv
+      evec.resize(Nstop,grid);// was Nconv
+      basisSortInPlace(evec,eval,reverse);
+      
+    }
+       
+    std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
+    std::cout << GridLogIRL << "ImplicitlyRestartedLanczos CONVERGED ; Summary :\n";
+    std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
+    std::cout << GridLogIRL << " -- Iterations  = "<< iter   << "\n";
+    std::cout << GridLogIRL << " -- beta(k)     = "<< beta_k << "\n";
+    std::cout << GridLogIRL << " -- Nconv       = "<< Nconv  << "\n";
+    std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
+  }
+
+ private:
+/* 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 - 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,
+	    std::vector<RealD>& lme, 
+	    std::vector<Field>& evec,
+	    Field& w,int Nm,int k)
+  {
+    std::cout<<GridLogDebug << "Lanczos step " <<k<<std::endl;
+    const RealD tiny = 1.0e-20;
+    assert( k< Nm );
+
+    GridStopWatch gsw_op,gsw_o;
+
+    Field& evec_k = evec[k];
+
+    _PolyOp(evec_k,w);    std::cout<<GridLogDebug << "PolyOp" <<std::endl;
+
+    if(k>0) w -= lme[k-1] * evec[k-1];
+
+    ComplexD zalph = innerProduct(evec_k,w);
+    RealD     alph = real(zalph);
+
+    w = w - alph * evec_k;
+
+    RealD beta = normalise(w); 
+
+    lmd[k] = alph;
+    lme[k] = beta;
+
+    if ( (k>0) && ( (k % orth_period) == 0 )) {
+      std::cout<<GridLogDebug << "Orthogonalising " <<k<<std::endl;
+      orthogonalize(w,evec,k); // orthonormalise
+      std::cout<<GridLogDebug << "Orthogonalised " <<k<<std::endl;
+    }
+
+    if(k < Nm-1) evec[k+1] = w;
+
+    std::cout<<GridLogIRL << "Lanczos step alpha[" << k << "] = " << zalph << " beta[" << k << "] = "<<beta<<std::endl;
+    if ( beta < tiny ) 
+      std::cout<<GridLogIRL << " beta is tiny "<<beta<<std::endl;
+
+    std::cout<<GridLogDebug << "Lanczos step complete " <<k<<std::endl;
+  }
+
+  void diagonalize_Eigen(std::vector<RealD>& lmd, std::vector<RealD>& lme, 
+			 int Nk, int Nm,  
+			 Eigen::MatrixXd & Qt, // Nm x Nm
+			 GridBase *grid)
+  {
+    Eigen::MatrixXd TriDiag = Eigen::MatrixXd::Zero(Nk,Nk);
+
+    for(int i=0;i<Nk;i++)   TriDiag(i,i)   = lmd[i];
+    for(int i=0;i<Nk-1;i++) TriDiag(i,i+1) = lme[i];
+    for(int i=0;i<Nk-1;i++) TriDiag(i+1,i) = lme[i];
+    
+    Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eigensolver(TriDiag);
+
+    for (int i = 0; i < Nk; i++) {
+      lmd[Nk-1-i] = eigensolver.eigenvalues()(i);
+    }
+    for (int i = 0; i < Nk; i++) {
+      for (int j = 0; j < Nk; j++) {
+	Qt(Nk-1-i,j) = eigensolver.eigenvectors()(j,i);
+      }
+    }
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // File could end here if settle on Eigen ??? !!!
+  ///////////////////////////////////////////////////////////////////////////
+  void QR_decomp(std::vector<RealD>& lmd,   // Nm 
+		 std::vector<RealD>& lme,   // Nm 
+		 int Nk, int Nm,            // Nk, Nm
+		 Eigen::MatrixXd& Qt,       // Nm x Nm matrix
+		 RealD Dsh, int kmin, int kmax)
+  {
+    int k = kmin-1;
+    RealD x;
+    
+    RealD Fden = 1.0/hypot(lmd[k]-Dsh,lme[k]);
+    RealD c = ( lmd[k] -Dsh) *Fden;
+    RealD s = -lme[k] *Fden;
+      
+    RealD tmpa1 = lmd[k];
+    RealD tmpa2 = lmd[k+1];
+    RealD tmpb  = lme[k];
+
+    lmd[k]   = c*c*tmpa1 +s*s*tmpa2 -2.0*c*s*tmpb;
+    lmd[k+1] = s*s*tmpa1 +c*c*tmpa2 +2.0*c*s*tmpb;
+    lme[k]   = c*s*(tmpa1-tmpa2) +(c*c-s*s)*tmpb;
+    x        =-s*lme[k+1];
+    lme[k+1] = c*lme[k+1];
+      
+    for(int i=0; i<Nk; ++i){
+      RealD Qtmp1 = Qt(k,i);
+      RealD Qtmp2 = Qt(k+1,i);
+      Qt(k,i)  = c*Qtmp1 - s*Qtmp2;
+      Qt(k+1,i)= s*Qtmp1 + c*Qtmp2; 
+    }
+
+    // Givens transformations
+    for(int k = kmin; k < kmax-1; ++k){
+      
+      RealD Fden = 1.0/hypot(x,lme[k-1]);
+      RealD c = lme[k-1]*Fden;
+      RealD s = - x*Fden;
+	
+      RealD tmpa1 = lmd[k];
+      RealD tmpa2 = lmd[k+1];
+      RealD tmpb  = lme[k];
+
+      lmd[k]   = c*c*tmpa1 +s*s*tmpa2 -2.0*c*s*tmpb;
+      lmd[k+1] = s*s*tmpa1 +c*c*tmpa2 +2.0*c*s*tmpb;
+      lme[k]   = c*s*(tmpa1-tmpa2) +(c*c-s*s)*tmpb;
+      lme[k-1] = c*lme[k-1] -s*x;
+
+      if(k != kmax-2){
+	x = -s*lme[k+1];
+	lme[k+1] = c*lme[k+1];
+      }
+
+      for(int i=0; i<Nk; ++i){
+	RealD Qtmp1 = Qt(k,i);
+	RealD Qtmp2 = Qt(k+1,i);
+	Qt(k,i)     = c*Qtmp1 -s*Qtmp2;
+	Qt(k+1,i)   = s*Qtmp1 +c*Qtmp2;
+      }
+    }
+  }
+
+  void diagonalize(std::vector<RealD>& lmd, std::vector<RealD>& lme, 
+		   int Nk, int Nm,   
+		   Eigen::MatrixXd & Qt,
+		   GridBase *grid)
+  {
+    Qt = Eigen::MatrixXd::Identity(Nm,Nm);
+    if ( diagonalisation == IRLdiagonaliseWithDSTEGR ) {
+      diagonalize_lapack(lmd,lme,Nk,Nm,Qt,grid);
+    } else if ( diagonalisation == IRLdiagonaliseWithQR ) { 
+      diagonalize_QR(lmd,lme,Nk,Nm,Qt,grid);
+    }  else if ( diagonalisation == IRLdiagonaliseWithEigen ) { 
+      diagonalize_Eigen(lmd,lme,Nk,Nm,Qt,grid);
+    } else { 
+      assert(0);
+    }
+  }
+
+#ifdef USE_LAPACK
+void LAPACK_dstegr(char *jobz, char *range, int *n, double *d, double *e,
+                   double *vl, double *vu, int *il, int *iu, double *abstol,
+                   int *m, double *w, double *z, int *ldz, int *isuppz,
+                   double *work, int *lwork, int *iwork, int *liwork,
+                   int *info);
+#endif
+
+void diagonalize_lapack(std::vector<RealD>& lmd,
+			std::vector<RealD>& lme, 
+			int Nk, int Nm,  
+			Eigen::MatrixXd& Qt,
+			GridBase *grid)
+{
+#ifdef USE_LAPACK
+  const int size = Nm;
+  int NN = Nk;
+  double evals_tmp[NN];
+  double evec_tmp[NN][NN];
+  memset(evec_tmp[0],0,sizeof(double)*NN*NN);
+  double DD[NN];
+  double EE[NN];
+  for (int i = 0; i< NN; i++) {
+    for (int j = i - 1; j <= i + 1; j++) {
+      if ( j < NN && j >= 0 ) {
+	if (i==j) DD[i] = lmd[i];
+	if (i==j) evals_tmp[i] = lmd[i];
+	if (j==(i-1)) EE[j] = lme[j];
+      }
+    }
+  }
+  int evals_found;
+  int lwork = ( (18*NN) > (1+4*NN+NN*NN)? (18*NN):(1+4*NN+NN*NN)) ;
+  int liwork =  3+NN*10 ;
+  int iwork[liwork];
+  double work[lwork];
+  int isuppz[2*NN];
+  char jobz = 'V'; // calculate evals & evecs
+  char range = 'I'; // calculate all evals
+  //    char range = 'A'; // calculate all evals
+  char uplo = 'U'; // refer to upper half of original matrix
+  char compz = 'I'; // Compute eigenvectors of tridiagonal matrix
+  int ifail[NN];
+  int info;
+  int total = grid->_Nprocessors;
+  int node  = grid->_processor;
+  int interval = (NN/total)+1;
+  double vl = 0.0, vu = 0.0;
+  int il = interval*node+1 , iu = interval*(node+1);
+  if (iu > NN)  iu=NN;
+  double tol = 0.0;
+  if (1) {
+    memset(evals_tmp,0,sizeof(double)*NN);
+    if ( il <= NN){
+      LAPACK_dstegr(&jobz, &range, &NN,
+		    (double*)DD, (double*)EE,
+		    &vl, &vu, &il, &iu, // these four are ignored if second parameteris 'A'
+		    &tol, // tolerance
+		    &evals_found, evals_tmp, (double*)evec_tmp, &NN,
+		    isuppz,
+		    work, &lwork, iwork, &liwork,
+		    &info);
+      for (int i = iu-1; i>= il-1; i--){
+	evals_tmp[i] = evals_tmp[i - (il-1)];
+	if (il>1) evals_tmp[i-(il-1)]=0.;
+	for (int j = 0; j< NN; j++){
+	  evec_tmp[i][j] = evec_tmp[i - (il-1)][j];
+	  if (il>1) evec_tmp[i-(il-1)][j]=0.;
+	}
+      }
+    }
+    {
+      grid->GlobalSumVector(evals_tmp,NN);
+      grid->GlobalSumVector((double*)evec_tmp,NN*NN);
+    }
+  } 
+  // Safer to sort instead of just reversing it, 
+  // but the document of the routine says evals are sorted in increasing order. 
+  // qr gives evals in decreasing order.
+  for(int i=0;i<NN;i++){
+    lmd [NN-1-i]=evals_tmp[i];
+    for(int j=0;j<NN;j++){
+      Qt((NN-1-i),j)=evec_tmp[i][j];
+    }
+  }
+#else 
+  assert(0);
+#endif
+}
+
+void diagonalize_QR(std::vector<RealD>& lmd, std::vector<RealD>& lme, 
+		    int Nk, int Nm,   
+		    Eigen::MatrixXd & Qt,
+		    GridBase *grid)
+{
+  int QRiter = 100*Nm;
+  int kmin = 1;
+  int kmax = Nk;
+  
+  // (this should be more sophisticated)
+  for(int iter=0; iter<QRiter; ++iter){
+    
+    // determination of 2x2 leading submatrix
+    RealD dsub = lmd[kmax-1]-lmd[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)
+    
+    // transformation
+    QR_decomp(lmd,lme,Nk,Nm,Qt,Dsh,kmin,kmax); // Nk, Nm
+    
+    // Convergence criterion (redef of kmin and kamx)
+    for(int j=kmax-1; j>= kmin; --j){
+      RealD dds = fabs(lmd[j-1])+fabs(lmd[j]);
+      if(fabs(lme[j-1])+dds > dds){
+	kmax = j+1;
+	goto continued;
+      }
+    }
+    QRiter = iter;
+    return;
+    
+  continued:
+    for(int j=0; j<kmax-1; ++j){
+      RealD dds = fabs(lmd[j])+fabs(lmd[j+1]);
+      if(fabs(lme[j])+dds > dds){
+	kmin = j+1;
+	break;
+      }
+    }
+  }
+  std::cout << GridLogError << "[QL method] Error - Too many iteration: "<<QRiter<<"\n";
+  abort();
+}
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/LocalCoherenceLanczos.h

@@ -0,0 +1,454 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/LocalCoherenceLanczos.h
+
+    Copyright (C) 2015
+
+Author: Christoph Lehner <clehner@bnl.gov>
+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_LOCAL_COHERENCE_IRL_H
+#define GRID_LOCAL_COHERENCE_IRL_H
+
+NAMESPACE_BEGIN(Grid); 
+
+struct LanczosParams : Serializable {
+public:
+  GRID_SERIALIZABLE_CLASS_MEMBERS(LanczosParams,
+				  ChebyParams, Cheby,/*Chebyshev*/
+				  int, Nstop,    /*Vecs in Lanczos must converge Nstop < Nk < Nm*/
+				  int, Nk,       /*Vecs in Lanczos seek converge*/
+				  int, Nm,       /*Total vecs in Lanczos include restart*/
+				  RealD, resid,  /*residual*/
+ 				  int, MaxIt, 
+				  RealD, betastp,  /* ? */
+				  int, MinRes);    // Must restart
+};
+
+//This class is the input parameter class for some testing programs
+struct LocalCoherenceLanczosParams : Serializable {
+public:
+  GRID_SERIALIZABLE_CLASS_MEMBERS(LocalCoherenceLanczosParams,
+				  bool, saveEvecs,
+				  bool, doFine,
+				  bool, doFineRead,
+				  bool, doCoarse,
+	       			  bool, doCoarseRead,
+				  LanczosParams, FineParams,
+				  LanczosParams, CoarseParams,
+				  ChebyParams,   Smoother,
+				  RealD        , coarse_relax_tol,
+				  std::vector<int>, blockSize,
+				  std::string, config,
+				  std::vector < ComplexD  >, omega,
+				  RealD, mass,
+				  RealD, M5);
+};
+
+// Duplicate functionality; ProjectedFunctionHermOp could be used with the trivial function
+template<class Fobj,class CComplex,int nbasis>
+class ProjectedHermOp : public LinearFunction<Lattice<iVector<CComplex,nbasis > > > {
+public:
+  using LinearFunction<Lattice<iVector<CComplex,nbasis > > >::operator();
+  typedef iVector<CComplex,nbasis >           CoarseSiteVector;
+  typedef Lattice<CoarseSiteVector>           CoarseField;
+  typedef Lattice<CComplex>   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj>          FineField;
+
+  LinearOperatorBase<FineField> &_Linop;
+  std::vector<FineField>        &subspace;
+
+  ProjectedHermOp(LinearOperatorBase<FineField>& linop, std::vector<FineField> & _subspace) : 
+    _Linop(linop), subspace(_subspace)
+  {  
+    assert(subspace.size() >0);
+  };
+
+  void operator()(const CoarseField& in, CoarseField& out) {
+    GridBase *FineGrid = subspace[0].Grid();    
+    int   checkerboard = subspace[0].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;
+    blockProject(out,fout,subspace);     std::cout<<GridLogIRL<<"ProjectedHermop : Project to coarse "<<std::endl;
+  }
+};
+
+template<class Fobj,class CComplex,int nbasis>
+class ProjectedFunctionHermOp : public LinearFunction<Lattice<iVector<CComplex,nbasis > > > {
+public:
+  using LinearFunction<Lattice<iVector<CComplex,nbasis > > >::operator();
+  typedef iVector<CComplex,nbasis >           CoarseSiteVector;
+  typedef Lattice<CoarseSiteVector>           CoarseField;
+  typedef Lattice<CComplex>   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj>          FineField;
+
+
+  OperatorFunction<FineField>   & _poly;
+  LinearOperatorBase<FineField> &_Linop;
+  std::vector<FineField>        &subspace;
+
+  ProjectedFunctionHermOp(OperatorFunction<FineField> & poly,
+			  LinearOperatorBase<FineField>& linop, 
+			  std::vector<FineField> & _subspace) :
+    _poly(poly),
+    _Linop(linop),
+    subspace(_subspace)
+  {  };
+
+  void operator()(const CoarseField& in, CoarseField& out) {
+
+    GridBase *FineGrid = subspace[0].Grid();    
+    int   checkerboard = subspace[0].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;
+    blockProject(out,fout,subspace);           std::cout<<GridLogIRL<<"ProjectedFunctionHermop : Project to coarse "<<std::endl;
+  }
+};
+
+template<class Fobj,class CComplex,int nbasis>
+class ImplicitlyRestartedLanczosSmoothedTester  : public ImplicitlyRestartedLanczosTester<Lattice<iVector<CComplex,nbasis > > >
+{
+public:
+  typedef iVector<CComplex,nbasis >           CoarseSiteVector;
+  typedef Lattice<CoarseSiteVector>           CoarseField;
+  typedef Lattice<CComplex>   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj>          FineField;
+
+  LinearFunction<CoarseField> & _Poly;
+  OperatorFunction<FineField>   & _smoother;
+  LinearOperatorBase<FineField> &_Linop;
+  RealD                             _coarse_relax_tol;
+  std::vector<FineField>        &_subspace;
+
+  int _largestEvalIdxForReport; //The convergence of the LCL is based on the evals of the coarse grid operator, not those of the underlying fine grid operator
+                                //As a result we do not know what the eval range of the fine operator is until the very end, making tuning the Cheby bounds very difficult
+                                //To work around this issue, every restart we separately reconstruct the fine operator eval for the lowest and highest evec and print these
+                                //out alongside the evals of the coarse operator. To do so we need to know the index of the largest eval (i.e. Nstop-1)
+                                //NOTE: If largestEvalIdxForReport=-1 (default) then this is not performed
+  
+  ImplicitlyRestartedLanczosSmoothedTester(LinearFunction<CoarseField>   &Poly,
+					   OperatorFunction<FineField>   &smoother,
+					   LinearOperatorBase<FineField> &Linop,
+					   std::vector<FineField>        &subspace,
+					   RealD coarse_relax_tol=5.0e3,
+					   int largestEvalIdxForReport=-1) 
+    : _smoother(smoother), _Linop(Linop), _Poly(Poly), _subspace(subspace),
+      _coarse_relax_tol(coarse_relax_tol), _largestEvalIdxForReport(largestEvalIdxForReport)
+  {    };
+
+  //evalMaxApprox: approximation of largest eval of the fine Chebyshev operator (suitably wrapped by block projection)
+  int TestConvergence(int j,RealD eresid,CoarseField &B, RealD &eval,RealD evalMaxApprox)
+  {
+    CoarseField v(B);
+    RealD eval_poly = eval;
+
+    // Apply operator
+    _Poly(B,v);
+
+    RealD vnum = real(innerProduct(B,v)); // HermOp.
+    RealD vden = norm2(B);
+    RealD vv0  = norm2(v);
+    eval   = vnum/vden;
+    v -= eval*B;
+
+    RealD vv = norm2(v) / ::pow(evalMaxApprox,2.0);
+
+    std::cout.precision(13);
+    std::cout<<GridLogIRL  << "[" << std::setw(3)<<j<<"] "
+	     <<"eval = "<<std::setw(25)<< eval << " (" << eval_poly << ")"
+	     <<" |H B[i] - eval[i]B[i]|^2 / evalMaxApprox^2 " << std::setw(25) << vv
+	     <<std::endl;
+
+    if(_largestEvalIdxForReport != -1 && (j==0 || j==_largestEvalIdxForReport)){
+      std::cout<<GridLogIRL << "Estimating true eval of fine grid operator for eval idx " << j << std::endl;
+      RealD tmp_eval;
+      ReconstructEval(j,eresid,B,tmp_eval,1.0); //don't use evalMaxApprox of coarse operator! (cf below)
+    }
+    
+    int conv=0;
+    if( (vv<eresid*eresid) ) conv = 1;
+    return conv;
+  }
+
+  //This function is called at the end of the coarse grid Lanczos. It promotes the coarse eigenvector 'B' to the fine grid,
+  //applies a smoother to the result then computes the computes the *fine grid* eigenvalue (output as 'eval').
+
+  //evalMaxApprox should be the approximation of the largest eval of the fine Hermop. However when this function is called by IRL it actually passes the largest eval of the *Chebyshev* operator (as this is the max approx used for the TestConvergence above)
+  //As the largest eval of the Chebyshev is typically several orders of magnitude larger this makes the convergence test pass even when it should not.
+  //We therefore ignore evalMaxApprox here and use a value of 1.0 (note this value is already used by TestCoarse)
+  int ReconstructEval(int j,RealD eresid,CoarseField &B, RealD &eval,RealD evalMaxApprox)  
+  {
+    evalMaxApprox = 1.0; //cf above
+    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);  
+    
+    _smoother(_Linop,fv,fB); 
+
+    RealD eval_poly = eval;
+    _Linop.HermOp(fB,fv);
+
+    RealD vnum = real(innerProduct(fB,fv)); // HermOp.
+    RealD vden = norm2(fB);
+    RealD vv0  = norm2(fv);
+    eval   = vnum/vden;
+    fv -= eval*fB;
+    RealD vv = norm2(fv) / ::pow(evalMaxApprox,2.0);
+    if ( j > nbasis ) eresid = eresid*_coarse_relax_tol;
+    
+    std::cout.precision(13);
+    std::cout<<GridLogIRL  << "[" << std::setw(3)<<j<<"] "
+	     <<"eval = "<<std::setw(25)<< eval << " (" << eval_poly << ")"
+	     <<" |H B[i] - eval[i]B[i]|^2 / evalMaxApprox^2 " << std::setw(25) << vv << " target " << eresid*eresid
+	     <<std::endl;
+    if( (vv<eresid*eresid) ) return 1;
+    return 0;
+  }
+};
+
+////////////////////////////////////////////
+// Make serializable Lanczos params
+////////////////////////////////////////////
+template<class Fobj,class CComplex,int nbasis>
+class LocalCoherenceLanczos 
+{
+public:
+  typedef iVector<CComplex,nbasis >           CoarseSiteVector;
+  typedef Lattice<CComplex>                   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<CoarseSiteVector>           CoarseField;
+  typedef Lattice<Fobj>                       FineField;
+
+protected:
+  GridBase *_CoarseGrid;
+  GridBase *_FineGrid;
+  int _checkerboard;
+  LinearOperatorBase<FineField>                 & _FineOp;
+  
+  std::vector<RealD>                              &evals_fine;
+  std::vector<RealD>                              &evals_coarse; 
+  std::vector<FineField>                          &subspace;
+  std::vector<CoarseField>                        &evec_coarse;
+
+private:
+  std::vector<RealD>                              _evals_fine;
+  std::vector<RealD>                              _evals_coarse; 
+  std::vector<FineField>                          _subspace;
+  std::vector<CoarseField>                        _evec_coarse;
+
+public:
+
+  LocalCoherenceLanczos(GridBase *FineGrid,
+			GridBase *CoarseGrid,
+			LinearOperatorBase<FineField> &FineOp,
+			int checkerboard) :
+    _CoarseGrid(CoarseGrid),
+    _FineGrid(FineGrid),
+    _FineOp(FineOp),
+    _checkerboard(checkerboard),
+    evals_fine  (_evals_fine),
+    evals_coarse(_evals_coarse),
+    subspace    (_subspace),
+    evec_coarse(_evec_coarse)
+  {
+    evals_fine.resize(0);
+    evals_coarse.resize(0);
+  };
+  //////////////////////////////////////////////////////////////////////////
+  // Alternate constructore, external storage for use by Hadrons module
+  //////////////////////////////////////////////////////////////////////////
+  LocalCoherenceLanczos(GridBase *FineGrid,
+			GridBase *CoarseGrid,
+			LinearOperatorBase<FineField> &FineOp,
+			int checkerboard,
+			std::vector<FineField>   &ext_subspace,
+			std::vector<CoarseField> &ext_coarse,
+			std::vector<RealD>       &ext_eval_fine,
+			std::vector<RealD>       &ext_eval_coarse
+			) :
+    _CoarseGrid(CoarseGrid),
+    _FineGrid(FineGrid),
+    _FineOp(FineOp),
+    _checkerboard(checkerboard),
+    evals_fine  (ext_eval_fine), 
+    evals_coarse(ext_eval_coarse),
+    subspace    (ext_subspace),
+    evec_coarse (ext_coarse)
+  {
+    evals_fine.resize(0);
+    evals_coarse.resize(0);
+  };
+
+  //The block inner product is the inner product on the fine grid locally summed over the blocks
+  //to give a Lattice<Scalar> on the coarse grid. This function orthnormalizes the fine-grid subspace
+  //vectors under the block inner product. This step must be performed after computing the fine grid
+  //eigenvectors and before computing the coarse grid eigenvectors.    
+  void Orthogonalise(void ) {
+    CoarseScalar InnerProd(_CoarseGrid);
+    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) 
+  {
+    RealD nn = norm2(v);
+    nn = ::sqrt(nn);
+    v = v * (1.0/nn);
+    return nn;
+  }
+  /*
+  void fakeFine(void)
+  {
+    int Nk = nbasis;
+    subspace.resize(Nk,_FineGrid);
+    subspace[0]=1.0;
+    subspace[0].Checkerboard()=_checkerboard;
+    normalise(subspace[0]);
+    PlainHermOp<FineField>    Op(_FineOp);
+    for(int k=1;k<Nk;k++){
+      subspace[k].Checkerboard()=_checkerboard;
+      Op(subspace[k-1],subspace[k]);
+      normalise(subspace[k]);
+    }
+  }
+  */
+
+  void testFine(RealD resid) 
+  {
+    assert(evals_fine.size() == nbasis);
+    assert(subspace.size() == nbasis);
+    PlainHermOp<FineField>    Op(_FineOp);
+    ImplicitlyRestartedLanczosHermOpTester<FineField> SimpleTester(Op);
+    for(int k=0;k<nbasis;k++){
+      assert(SimpleTester.ReconstructEval(k,resid,subspace[k],evals_fine[k],1.0)==1);
+    }
+  }
+
+  //While this method serves to check the coarse eigenvectors, it also recomputes the eigenvalues from the smoothed reconstructed eigenvectors
+  //hence the smoother can be tuned after running the coarse Lanczos by using a different smoother here
+  void testCoarse(RealD resid,ChebyParams cheby_smooth,RealD relax) 
+  {
+    assert(evals_fine.size() == nbasis);
+    assert(subspace.size() == nbasis);
+    //////////////////////////////////////////////////////////////////////////////////////////////////
+    // 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);
+    ImplicitlyRestartedLanczosSmoothedTester<Fobj,CComplex,nbasis> ChebySmoothTester(ChebyOp,ChebySmooth,_FineOp,subspace,relax);
+
+    for(int k=0;k<evec_coarse.size();k++){
+      if ( k < nbasis ) { 
+	assert(ChebySmoothTester.ReconstructEval(k,resid,evec_coarse[k],evals_coarse[k],1.0)==1);
+      } else { 
+	assert(ChebySmoothTester.ReconstructEval(k,resid*relax,evec_coarse[k],evals_coarse[k],1.0)==1);
+      }
+    }
+  }
+
+  void calcFine(ChebyParams cheby_parms,int Nstop,int Nk,int Nm,RealD resid, 
+		RealD MaxIt, RealD betastp, int MinRes)
+  {
+    assert(nbasis<=Nm);
+    Chebyshev<FineField>      Cheby(cheby_parms);
+    FunctionHermOp<FineField> ChebyOp(Cheby,_FineOp);
+    PlainHermOp<FineField>    Op(_FineOp);
+
+    evals_fine.resize(Nm);
+    subspace.resize(Nm,_FineGrid);
+
+    ImplicitlyRestartedLanczos<FineField> IRL(ChebyOp,Op,Nstop,Nk,Nm,resid,MaxIt,betastp,MinRes);
+
+    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);
+    
+    // Shrink down to number saved
+    assert(Nstop>=nbasis);
+    assert(Nconv>=nbasis);
+    evals_fine.resize(nbasis);
+    subspace.resize(nbasis,_FineGrid);
+  }
+
+
+  //cheby_op: Parameters of the fine grid Chebyshev polynomial used for the Lanczos acceleration
+  //cheby_smooth: Parameters of a separate Chebyshev polynomial used after the Lanczos has completed to smooth out high frequency noise in the reconstructed fine grid eigenvectors prior to computing the eigenvalue
+  //relax: Reconstructed eigenvectors (post smoothing) are naturally not as precise as true eigenvectors. This factor acts as a multiplier on the stopping condition when determining whether the results satisfy the user provided stopping condition
+  void calcCoarse(ChebyParams cheby_op,ChebyParams cheby_smooth,RealD relax,
+		  int Nstop, int Nk, int Nm,RealD resid, 
+		  RealD MaxIt, RealD betastp, int MinRes)
+  {
+    Chebyshev<FineField>                          Cheby(cheby_op); //Chebyshev of fine operator on fine grid
+    ProjectedHermOp<Fobj,CComplex,nbasis>         Op(_FineOp,subspace); //Fine operator on coarse grid with intermediate fine grid conversion
+    ProjectedFunctionHermOp<Fobj,CComplex,nbasis> ChebyOp (Cheby,_FineOp,subspace); //Chebyshev of fine operator on coarse grid with intermediate fine grid conversion
+    //////////////////////////////////////////////////////////////////////////////////////////////////
+    // create a smoother and see if we can get a cheap convergence test and smooth inside the IRL
+    //////////////////////////////////////////////////////////////////////////////////////////////////
+
+    Chebyshev<FineField>                                           ChebySmooth(cheby_smooth); //lower order Chebyshev of fine operator on fine grid used to smooth regenerated eigenvectors
+    ImplicitlyRestartedLanczosSmoothedTester<Fobj,CComplex,nbasis> ChebySmoothTester(ChebyOp,ChebySmooth,_FineOp,subspace,relax,Nstop-1); 
+
+    evals_coarse.resize(Nm);
+    evec_coarse.resize(Nm,_CoarseGrid);
+
+    CoarseField src(_CoarseGrid);     src=1.0; 
+
+    //Note the "tester" here is also responsible for generating the fine grid eigenvalues which are output into the "evals_coarse" array
+    ImplicitlyRestartedLanczos<CoarseField> IRL(ChebyOp,ChebyOp,ChebySmoothTester,Nstop,Nk,Nm,resid,MaxIt,betastp,MinRes);
+    int Nconv=0;
+    IRL.calc(evals_coarse,evec_coarse,src,Nconv,false);
+    assert(Nconv>=Nstop);
+    evals_coarse.resize(Nstop);
+    evec_coarse.resize (Nstop,_CoarseGrid);
+    for (int i=0;i<Nstop;i++){
+      std::cout << i << " Coarse eval = " << evals_coarse[i]  << std::endl;
+    }
+  }
+
+  //Get the fine eigenvector 'i' by reconstruction
+  void getFineEvecEval(FineField &evec, RealD &eval, const int i) const{
+    blockPromote(evec_coarse[i],evec,subspace);  
+    eval = evals_coarse[i];
+  }
+    
+    
+};
+
+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 : public LinearFunction<Field>{
+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 : public LinearFunction<Field> {
+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);  //M out = in
+
+  }     
+};
+
+
+template<class Field> class MdagMSolver : public LinearFunction<Field> {
+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 +1,47 @@
+#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_ = 100; 
+
+    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; 
+
+      std::cout << GridLogIterative << "PowerMethod: Current approximation of largest eigenvalue " << na << std::endl;
+      
+      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:                                                
+  using LinearFunction<Field>::operator();
+  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 +1,242 @@
+/*************************************************************************************
+
+    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:                                                
+  using LinearFunction<Field>::operator();
+  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;
+    //    ComplexD 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 +1,651 @@
+    /*************************************************************************************
+
+    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);
+    }
+
+    void RedBlackSource(Matrix &_Matrix, const std::vector<Field> &in, std::vector<Field> &src_o) 
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      Field tmp(grid);
+      int nblock = in.size();
+      for(int b=0;b<nblock;b++){
+	RedBlackSource(_Matrix,in[b],tmp,src_o[b]);
+      }
+    }
+    // James can write his own deflated guesser
+    // with optimised code for the inner products
+    //    RedBlackSolveSplitGrid();
+    //    RedBlackSolve(_Matrix,src_o,sol_o); 
+
+    void RedBlackSolution(Matrix &_Matrix, const std::vector<Field> &in, const std::vector<Field> &sol_o, std::vector<Field> &out)
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      Field tmp(grid);
+      int nblock = in.size();
+      for(int b=0;b<nblock;b++) {
+	pickCheckerboard(Even,tmp,in[b]);
+	RedBlackSolution(_Matrix,sol_o[b],tmp,out[b]);
+      }
+    }
+
+    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
+      ////////////////////////////////////////////////
+      RedBlackSource(_Matrix,in,src_o);
+	//      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);
+
+      
+      if(useSolnAsInitGuess) {
+        for(int b=0;b<nblock;b++){
+          pickCheckerboard(Odd, sol_o[b], out[b]);
+        }
+      } else {
+        guess(src_o, sol_o); 
+      }
+
+	    if ( subGuess ) { 
+        for(int b=0;b<nblock;b++){
+          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/algorithms/multigrid/Aggregates.h

@@ -0,0 +1,478 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/Aggregates.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 */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+inline RealD AggregatePowerLaw(RealD x)
+{
+  //  return std::pow(x,-4);
+  //  return std::pow(x,-3);
+  return std::pow(x,-5);
+}
+
+template<class Fobj,class CComplex,int nbasis>
+class Aggregation {
+public:
+  constexpr int Nbasis(void) { return nbasis; };
+  
+  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 CreateSubspaceRandom(GridParallelRNG  &RNG) {
+    int nn=nbasis;
+    RealD scale;
+    FineField noise(FineGrid);
+    for(int b=0;b<nn;b++){
+      subspace[b] = Zero();
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+      subspace[b] = noise;
+    }
+  }
+  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;
+
+    std::cout << GridLogMessage<<" Chebyshev subspace pass-1 : ord "<<orderfilter<<" ["<<lo<<","<<hi<<"]"<<std::endl;
+    std::cout << GridLogMessage<<" Chebyshev subspace pass-2 : nbasis"<<nn<<" min "
+	      <<ordermin<<" step "<<orderstep
+	      <<" lo"<<filterlo<<std::endl;
+
+    // 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_for(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);
+  }
+  virtual void CreateSubspaceChebyshev(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,
+				       int nn,
+				       double hi,
+				       double lo,
+				       int orderfilter
+				       ) {
+
+    RealD scale;
+
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+    FineField tmp(FineGrid);
+
+    // New normalised noise
+    std::cout << GridLogMessage<<" Chebyshev subspace pure noise : ord "<<orderfilter<<" ["<<lo<<","<<hi<<"]"<<std::endl;
+    std::cout << GridLogMessage<<" Chebyshev subspace pure noise  : nbasis "<<nn<<std::endl;
+
+
+    for(int b =0;b<nbasis;b++)
+    {
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+
+      // Initial matrix element
+      hermop.Op(noise,Mn);
+      if(b==0) std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+
+      // Filter
+      Chebyshev<FineField> Cheb(lo,hi,orderfilter);
+      Cheb(hermop,noise,Mn);
+      scale = std::pow(norm2(Mn),-0.5); 	Mn=Mn*scale;
+
+      // Refine
+      Chebyshev<FineField> PowerLaw(lo,hi,1000,AggregatePowerLaw);
+      noise = Mn;
+      PowerLaw(hermop,noise,Mn);
+      scale = std::pow(norm2(Mn),-0.5); 	Mn=Mn*scale;
+
+      // normalise
+      subspace[b]   = Mn;
+      hermop.Op(Mn,tmp); 
+      std::cout<<GridLogMessage << "filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+    }
+
+  }
+
+  virtual void CreateSubspaceChebyshevPowerLaw(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,
+					       int nn,
+					       double hi,
+					       int orderfilter
+					       ) {
+
+    RealD scale;
+
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+    FineField tmp(FineGrid);
+
+    // New normalised noise
+    std::cout << GridLogMessage<<" Chebyshev subspace pure noise : ord "<<orderfilter<<" [0,"<<hi<<"]"<<std::endl;
+    std::cout << GridLogMessage<<" Chebyshev subspace pure noise  : nbasis "<<nn<<std::endl;
+
+    for(int b =0;b<nbasis;b++)
+    {
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+
+      // Initial matrix element
+      hermop.Op(noise,Mn);
+      if(b==0) std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+      // Filter
+      Chebyshev<FineField> Cheb(0.0,hi,orderfilter,AggregatePowerLaw);
+      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;
+    }
+
+  }
+  virtual void CreateSubspaceChebyshevNew(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,
+					  double hi
+					  ) {
+
+    RealD scale;
+
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+    FineField tmp(FineGrid);
+
+    // New normalised noise
+    for(int b =0;b<nbasis;b++)
+    {
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+
+      // Initial matrix element
+      hermop.Op(noise,Mn);
+      if(b==0) std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+      // Filter
+      //#opt2(x) =  acheb(x,3,90,300)* acheb(x,1,90,50) * acheb(x,0.5,90,200) * acheb(x,0.05,90,400) * acheb(x,0.01,90,1500)
+      /*266
+      Chebyshev<FineField> Cheb1(3.0,hi,300);
+      Chebyshev<FineField> Cheb2(1.0,hi,50);
+      Chebyshev<FineField> Cheb3(0.5,hi,300);
+      Chebyshev<FineField> Cheb4(0.05,hi,500);
+      Chebyshev<FineField> Cheb5(0.01,hi,2000);
+      */
+      /* 242 */
+      /*
+      Chebyshev<FineField> Cheb3(0.1,hi,300);
+      Chebyshev<FineField> Cheb2(0.02,hi,1000);
+      Chebyshev<FineField> Cheb1(0.003,hi,2000);
+      8?
+      */
+      /* How many??
+      */
+      Chebyshev<FineField> Cheb2(0.001,hi,2500); // 169 iters on HDCG after refine
+      Chebyshev<FineField> Cheb1(0.02,hi,600);
+
+      //      Chebyshev<FineField> Cheb2(0.001,hi,1500);
+      //      Chebyshev<FineField> Cheb1(0.02,hi,600);
+      Cheb1(hermop,noise,Mn); scale = std::pow(norm2(Mn),-0.5); 	noise=Mn*scale;
+      hermop.Op(noise,tmp); std::cout<<GridLogMessage << "Cheb1 <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+      Cheb2(hermop,noise,Mn); scale = std::pow(norm2(Mn),-0.5); 	noise=Mn*scale;
+      hermop.Op(noise,tmp); std::cout<<GridLogMessage << "Cheb2 <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+      //      Cheb3(hermop,noise,Mn); scale = std::pow(norm2(Mn),-0.5); 	noise=Mn*scale;
+      //      hermop.Op(noise,tmp); std::cout<<GridLogMessage << "Cheb3 <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+      //      Cheb4(hermop,noise,Mn); scale = std::pow(norm2(Mn),-0.5); 	noise=Mn*scale;
+      //      hermop.Op(noise,tmp); std::cout<<GridLogMessage << "Cheb4 <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+      //      Cheb5(hermop,noise,Mn); scale = std::pow(norm2(Mn),-0.5); 	noise=Mn*scale;
+      //      hermop.Op(noise,tmp); std::cout<<GridLogMessage << "Cheb5 <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+      subspace[b]   = noise;
+      hermop.Op(subspace[b],tmp); 
+      std::cout<<GridLogMessage << "filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<< " norm " << norm2(noise)<<std::endl;
+    }
+
+  }
+
+  virtual void CreateSubspaceMultishift(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,
+					double Lo,double tol,int maxit)
+  {
+
+    RealD scale;
+
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+    FineField tmp(FineGrid);
+
+    // New normalised noise
+    std::cout << GridLogMessage<<" Multishift subspace : Lo "<<Lo<<std::endl;
+
+    // Filter
+    // [ 1/6(x+Lo)  - 1/2(x+2Lo) + 1/2(x+3Lo)  -1/6(x+4Lo) = Lo^3 /[ (x+1Lo)(x+2Lo)(x+3Lo)(x+4Lo) ]
+    //
+    // 1/(x+Lo)  - 1/(x+2 Lo)
+    double epsilon      = Lo/3;
+    std::vector<RealD> alpha({1.0/6.0,-1.0/2.0,1.0/2.0,-1.0/6.0});
+    std::vector<RealD> shifts({Lo,Lo+epsilon,Lo+2*epsilon,Lo+3*epsilon});
+    std::vector<RealD> tols({tol,tol,tol,tol});
+    std::cout << "sizes "<<alpha.size()<<" "<<shifts.size()<<" "<<tols.size()<<std::endl;
+
+    MultiShiftFunction msf(4,0.0,95.0);
+    std::cout << "msf constructed "<<std::endl;
+    msf.poles=shifts;
+    msf.residues=alpha;
+    msf.tolerances=tols;
+    msf.norm=0.0;
+    msf.order=alpha.size();
+    ConjugateGradientMultiShift<FineField> MSCG(maxit,msf);
+    
+    for(int b =0;b<nbasis;b++)
+    {
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+
+      // Initial matrix element
+      hermop.Op(noise,Mn);
+      if(b==0) std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+
+      MSCG(hermop,noise,Mn);
+      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;
+
+    }
+
+  }
+  virtual void RefineSubspace(LinearOperatorBase<FineField> &hermop,
+			      double Lo,double tol,int maxit)
+  {
+    FineField tmp(FineGrid);
+    for(int b =0;b<nbasis;b++)
+    {
+      ConjugateGradient<FineField>  CGsloppy(tol,maxit,false);
+      ShiftedHermOpLinearOperator<FineField> ShiftedFineHermOp(hermop,Lo);
+      tmp=Zero();
+      CGsloppy(hermop,subspace[b],tmp);
+      RealD scale = std::pow(norm2(tmp),-0.5); 	tmp=tmp*scale;
+      subspace[b]=tmp;
+      hermop.Op(subspace[b],tmp);
+      std::cout<<GridLogMessage << "filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+    }
+  }
+  virtual void RefineSubspaceHDCG(LinearOperatorBase<FineField> &hermop,
+				  TwoLevelADEF2mrhs<FineField,CoarseVector> & theHDCG,
+				  int nrhs)
+  {
+    std::vector<FineField> src_mrhs(nrhs,FineGrid);
+    std::vector<FineField> res_mrhs(nrhs,FineGrid);
+    FineField tmp(FineGrid);
+    for(int b =0;b<nbasis;b+=nrhs)
+    {
+      tmp = subspace[b];
+      RealD scale = std::pow(norm2(tmp),-0.5); 	tmp=tmp*scale;
+      subspace[b] =tmp;
+      hermop.Op(subspace[b],tmp);
+      std::cout<<GridLogMessage << "before filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+
+      for(int r=0;r<MIN(nbasis-b,nrhs);r++){
+	src_mrhs[r] = subspace[b+r];
+      }
+      for(int r=0;r<nrhs;r++){
+	res_mrhs[r] = Zero();
+      }
+      theHDCG(src_mrhs,res_mrhs);
+
+      for(int r=0;r<MIN(nbasis-b,nrhs);r++){
+	tmp = res_mrhs[r];
+	RealD scale = std::pow(norm2(tmp),-0.5); tmp=tmp*scale;
+	subspace[b+r]=tmp;
+      }
+      hermop.Op(subspace[b],tmp);
+      std::cout<<GridLogMessage << "after filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+    }
+  }
+
+  
+  
+};
+NAMESPACE_END(Grid);
+

Grid/algorithms/multigrid/CoarsenedMatrix.h

@@ -0,0 +1,814 @@
+/*************************************************************************************
+
+    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
+
+#include <Grid/qcd/QCD.h> // needed for Dagger(Yes|No), Inverse(Yes|No)
+
+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);
+}
+
+// Fine Object == (per site) type of fine field
+// nbasis      == number of deflation vectors
+template<class Fobj,class CComplex,int nbasis>
+class CoarsenedMatrix : public CheckerBoardedSparseMatrixBase<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;
+  typedef CoarseVector FermionField;
+
+  // enrich interface, use default implementation as in FermionOperator ///////
+  void Dminus(CoarseVector const& in, CoarseVector& out) { out = in; }
+  void DminusDag(CoarseVector const& in, CoarseVector& out) { out = in; }
+  void ImportPhysicalFermionSource(CoarseVector const& input, CoarseVector& imported) { imported = input; }
+  void ImportUnphysicalFermion(CoarseVector const& input, CoarseVector& imported) { imported = input; }
+  void ExportPhysicalFermionSolution(CoarseVector const& solution, CoarseVector& exported) { exported = solution; };
+  void ExportPhysicalFermionSource(CoarseVector const& solution, CoarseVector& exported) { exported = solution; };
+
+  ////////////////////
+  // Data members
+  ////////////////////
+  Geometry         geom;
+  GridBase *       _grid; 
+  GridBase*        _cbgrid;
+  int hermitian;
+
+  CartesianStencil<siteVector,siteVector,DefaultImplParams> Stencil; 
+  CartesianStencil<siteVector,siteVector,DefaultImplParams> StencilEven;
+  CartesianStencil<siteVector,siteVector,DefaultImplParams> StencilOdd;
+
+  std::vector<CoarseMatrix> A;
+  std::vector<CoarseMatrix> Aeven;
+  std::vector<CoarseMatrix> Aodd;
+
+  CoarseMatrix AselfInv;
+  CoarseMatrix AselfInvEven;
+  CoarseMatrix AselfInvOdd;
+
+  Vector<RealD> dag_factor;
+
+  ///////////////////////
+  // Interface
+  ///////////////////////
+  GridBase * Grid(void)         { return _grid; };   // this is all the linalg routines need to know
+  GridBase * RedBlackGrid()     { return _cbgrid; };
+
+  int ConstEE() { return 0; }
+
+  void M (const CoarseVector &in, CoarseVector &out)
+  {
+    conformable(_grid,in.Grid());
+    conformable(in.Grid(),out.Grid());
+    out.Checkerboard() = in.Checkerboard();
+
+    SimpleCompressor<siteVector> compressor;
+
+    Stencil.HaloExchange(in,compressor);
+    autoView( in_v , in, AcceleratorRead);
+    autoView( out_v , out, AcceleratorWrite);
+    autoView( Stencil_v  , Stencil, AcceleratorRead);
+    int npoint = geom.npoint;
+    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<npoint;point++){
+
+	SE=Stencil_v.GetEntry(ptype,point,ss);
+	  
+	if(SE->_is_local) { 
+	  nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+	} else {
+	  nbr = coalescedRead(Stencil_v.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
+      return MdagNonHermitian(in, out);
+    }
+  };
+
+  void MdagNonHermitian(const CoarseVector &in, CoarseVector &out)
+  {
+    conformable(_grid,in.Grid());
+    conformable(in.Grid(),out.Grid());
+    out.Checkerboard() = in.Checkerboard();
+
+    SimpleCompressor<siteVector> compressor;
+
+    Stencil.HaloExchange(in,compressor);
+    autoView( in_v , in, AcceleratorRead);
+    autoView( out_v , out, AcceleratorWrite);
+    autoView( Stencil_v  , Stencil, AcceleratorRead);
+    int npoint = geom.npoint;
+    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();
+
+    Vector<int> points(geom.npoint, 0);
+    for(int p=0; p<geom.npoint; p++)
+      points[p] = geom.points_dagger[p];
+
+    auto points_p = &points[0];
+
+    RealD* dag_factor_p = &dag_factor[0];
+
+    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 p=0;p<npoint;p++){
+        int point = points_p[p];
+
+	SE=Stencil_v.GetEntry(ptype,point,ss);
+
+	if(SE->_is_local) {
+	  nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+	} else {
+	  nbr = coalescedRead(Stencil_v.CommBuf()[SE->_offset]);
+	}
+	acceleratorSynchronise();
+
+	for(int bb=0;bb<nbasis;bb++) {
+	  res = res + dag_factor_p[b*nbasis+bb]*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 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());
+    out.Checkerboard() = in.Checkerboard();
+
+    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);
+    autoView( Stencil_v  , Stencil, 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_v.GetEntry(ptype,point,ss);
+	  
+      if(SE->_is_local) { 
+	nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+      } else {
+	nbr = coalescedRead(Stencil_v.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);
+
+    MdirCalc(in,out,geom.point(dir,disp));
+  };
+
+  void Mdiag(const CoarseVector &in, CoarseVector &out)
+  {
+    int point=geom.npoint-1;
+    MdirCalc(in, out, point); // No comms
+  };
+
+  void Mooee(const CoarseVector &in, CoarseVector &out) {
+    MooeeInternal(in, out, DaggerNo, InverseNo);
+  }
+
+  void MooeeInv(const CoarseVector &in, CoarseVector &out) {
+    MooeeInternal(in, out, DaggerNo, InverseYes);
+  }
+
+  void MooeeDag(const CoarseVector &in, CoarseVector &out) {
+    MooeeInternal(in, out, DaggerYes, InverseNo);
+  }
+
+  void MooeeInvDag(const CoarseVector &in, CoarseVector &out) {
+    MooeeInternal(in, out, DaggerYes, InverseYes);
+  }
+
+  void Meooe(const CoarseVector &in, CoarseVector &out) {
+    if(in.Checkerboard() == Odd) {
+      DhopEO(in, out, DaggerNo);
+    } else {
+      DhopOE(in, out, DaggerNo);
+    }
+  }
+
+  void MeooeDag(const CoarseVector &in, CoarseVector &out) {
+    if(in.Checkerboard() == Odd) {
+      DhopEO(in, out, DaggerYes);
+    } else {
+      DhopOE(in, out, DaggerYes);
+    }
+  }
+
+  void Dhop(const CoarseVector &in, CoarseVector &out, int dag) {
+    conformable(in.Grid(), _grid); // verifies full grid
+    conformable(in.Grid(), out.Grid());
+
+    out.Checkerboard() = in.Checkerboard();
+
+    DhopInternal(Stencil, A, in, out, dag);
+  }
+
+  void DhopOE(const CoarseVector &in, CoarseVector &out, int dag) {
+    conformable(in.Grid(), _cbgrid);    // verifies half grid
+    conformable(in.Grid(), out.Grid()); // drops the cb check
+
+    assert(in.Checkerboard() == Even);
+    out.Checkerboard() = Odd;
+
+    DhopInternal(StencilEven, Aodd, in, out, dag);
+  }
+
+  void DhopEO(const CoarseVector &in, CoarseVector &out, int dag) {
+    conformable(in.Grid(), _cbgrid);    // verifies half grid
+    conformable(in.Grid(), out.Grid()); // drops the cb check
+
+    assert(in.Checkerboard() == Odd);
+    out.Checkerboard() = Even;
+
+    DhopInternal(StencilOdd, Aeven, in, out, dag);
+  }
+
+  void MooeeInternal(const CoarseVector &in, CoarseVector &out, int dag, int inv) {
+    out.Checkerboard() = in.Checkerboard();
+    assert(in.Checkerboard() == Odd || in.Checkerboard() == Even);
+
+    CoarseMatrix *Aself = nullptr;
+    if(in.Grid()->_isCheckerBoarded) {
+      if(in.Checkerboard() == Odd) {
+        Aself = (inv) ? &AselfInvOdd : &Aodd[geom.npoint-1];
+        DselfInternal(StencilOdd, *Aself, in, out, dag);
+      } else {
+        Aself = (inv) ? &AselfInvEven : &Aeven[geom.npoint-1];
+        DselfInternal(StencilEven, *Aself, in, out, dag);
+      }
+    } else {
+      Aself = (inv) ? &AselfInv : &A[geom.npoint-1];
+      DselfInternal(Stencil, *Aself, in, out, dag);
+    }
+    assert(Aself != nullptr);
+  }
+
+  void DselfInternal(CartesianStencil<siteVector,siteVector,DefaultImplParams> &st, CoarseMatrix &a,
+                       const CoarseVector &in, CoarseVector &out, int dag) {
+    int point = geom.npoint-1;
+    autoView( out_v, out, AcceleratorWrite);
+    autoView( in_v,  in,  AcceleratorRead);
+    autoView( st_v,  st,  AcceleratorRead);
+    autoView( a_v,   a,   AcceleratorRead);
+
+    const int Nsimd = CComplex::Nsimd();
+    typedef decltype(coalescedRead(in_v[0])) calcVector;
+    typedef decltype(coalescedRead(in_v[0](0))) calcComplex;
+
+    RealD* dag_factor_p = &dag_factor[0];
+
+    if(dag) {
+      accelerator_for(sss, in.Grid()->oSites()*nbasis, Nsimd, {
+        int ss = sss/nbasis;
+        int b  = sss%nbasis;
+        calcComplex res = Zero();
+        calcVector nbr;
+        int ptype;
+        StencilEntry *SE;
+
+        SE=st_v.GetEntry(ptype,point,ss);
+
+        if(SE->_is_local) {
+          nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+        } else {
+          nbr = coalescedRead(st_v.CommBuf()[SE->_offset]);
+        }
+        acceleratorSynchronise();
+
+        for(int bb=0;bb<nbasis;bb++) {
+          res = res + dag_factor_p[b*nbasis+bb]*coalescedRead(a_v[ss](b,bb))*nbr(bb);
+        }
+        coalescedWrite(out_v[ss](b),res);
+      });
+    } else {
+      accelerator_for(sss, in.Grid()->oSites()*nbasis, Nsimd, {
+        int ss = sss/nbasis;
+        int b  = sss%nbasis;
+        calcComplex res = Zero();
+        calcVector nbr;
+        int ptype;
+        StencilEntry *SE;
+
+        SE=st_v.GetEntry(ptype,point,ss);
+
+        if(SE->_is_local) {
+          nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+        } else {
+          nbr = coalescedRead(st_v.CommBuf()[SE->_offset]);
+        }
+        acceleratorSynchronise();
+
+        for(int bb=0;bb<nbasis;bb++) {
+          res = res + coalescedRead(a_v[ss](b,bb))*nbr(bb);
+        }
+        coalescedWrite(out_v[ss](b),res);
+      });
+    }
+  }
+
+  void DhopInternal(CartesianStencil<siteVector,siteVector,DefaultImplParams> &st, std::vector<CoarseMatrix> &a,
+                    const CoarseVector &in, CoarseVector &out, int dag) {
+    SimpleCompressor<siteVector> compressor;
+
+    st.HaloExchange(in,compressor);
+    autoView( in_v,  in,  AcceleratorRead);
+    autoView( out_v, out, AcceleratorWrite);
+    autoView( st_v , st,  AcceleratorRead);
+    typedef LatticeView<Cobj> Aview;
+
+    // determine in what order we need the points
+    int npoint = geom.npoint-1;
+    Vector<int> points(npoint, 0);
+    for(int p=0; p<npoint; p++)
+      points[p] = (dag && !hermitian) ? geom.points_dagger[p] : p;
+
+    auto points_p = &points[0];
+
+    Vector<Aview> AcceleratorViewContainer;
+    for(int p=0;p<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;
+
+    RealD* dag_factor_p = &dag_factor[0];
+
+    if(dag) {
+      accelerator_for(sss, in.Grid()->oSites()*nbasis, Nsimd, {
+        int ss = sss/nbasis;
+        int b  = sss%nbasis;
+        calcComplex res = Zero();
+        calcVector nbr;
+        int ptype;
+        StencilEntry *SE;
+
+        for(int p=0;p<npoint;p++){
+          int point = points_p[p];
+          SE=st_v.GetEntry(ptype,point,ss);
+
+          if(SE->_is_local) {
+            nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+          } else {
+            nbr = coalescedRead(st_v.CommBuf()[SE->_offset]);
+          }
+          acceleratorSynchronise();
+
+          for(int bb=0;bb<nbasis;bb++) {
+            res = res + dag_factor_p[b*nbasis+bb]*coalescedRead(Aview_p[point][ss](b,bb))*nbr(bb);
+          }
+        }
+        coalescedWrite(out_v[ss](b),res);
+      });
+    } else {
+      accelerator_for(sss, in.Grid()->oSites()*nbasis, Nsimd, {
+        int ss = sss/nbasis;
+        int b  = sss%nbasis;
+        calcComplex res = Zero();
+        calcVector nbr;
+        int ptype;
+        StencilEntry *SE;
+
+        for(int p=0;p<npoint;p++){
+          int point = points_p[p];
+          SE=st_v.GetEntry(ptype,point,ss);
+
+          if(SE->_is_local) {
+            nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+          } else {
+            nbr = coalescedRead(st_v.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<npoint;p++) AcceleratorViewContainer[p].ViewClose();
+  }
+  
+  CoarsenedMatrix(GridCartesian &CoarseGrid, int hermitian_=0) 	:
+    _grid(&CoarseGrid),
+    _cbgrid(new GridRedBlackCartesian(&CoarseGrid)),
+    geom(CoarseGrid._ndimension),
+    hermitian(hermitian_),
+    Stencil(&CoarseGrid,geom.npoint,Even,geom.directions,geom.displacements),
+    StencilEven(_cbgrid,geom.npoint,Even,geom.directions,geom.displacements),
+    StencilOdd(_cbgrid,geom.npoint,Odd,geom.directions,geom.displacements),
+    A(geom.npoint,&CoarseGrid),
+    Aeven(geom.npoint,_cbgrid),
+    Aodd(geom.npoint,_cbgrid),
+    AselfInv(&CoarseGrid),
+    AselfInvEven(_cbgrid),
+    AselfInvOdd(_cbgrid),
+    dag_factor(nbasis*nbasis)
+  {
+    fillFactor();
+  };
+
+  CoarsenedMatrix(GridCartesian &CoarseGrid, GridRedBlackCartesian &CoarseRBGrid, int hermitian_=0) 	:
+
+    _grid(&CoarseGrid),
+    _cbgrid(&CoarseRBGrid),
+    geom(CoarseGrid._ndimension),
+    hermitian(hermitian_),
+    Stencil(&CoarseGrid,geom.npoint,Even,geom.directions,geom.displacements),
+    StencilEven(&CoarseRBGrid,geom.npoint,Even,geom.directions,geom.displacements),
+    StencilOdd(&CoarseRBGrid,geom.npoint,Odd,geom.directions,geom.displacements),
+    A(geom.npoint,&CoarseGrid),
+    Aeven(geom.npoint,&CoarseRBGrid),
+    Aodd(geom.npoint,&CoarseRBGrid),
+    AselfInv(&CoarseGrid),
+    AselfInvEven(&CoarseRBGrid),
+    AselfInvOdd(&CoarseRBGrid),
+    dag_factor(nbasis*nbasis)
+  {
+    fillFactor();
+  };
+
+  void fillFactor() {
+    Eigen::MatrixXd dag_factor_eigen = Eigen::MatrixXd::Ones(nbasis, nbasis);
+    if(!hermitian) {
+      const int nb = nbasis/2;
+      dag_factor_eigen.block(0,nb,nb,nb) *= -1.0;
+      dag_factor_eigen.block(nb,0,nb,nb) *= -1.0;
+    }
+
+    // GPU readable prefactor
+    thread_for(i, nbasis*nbasis, {
+      int j = i/nbasis;
+      int k = i%nbasis;
+      dag_factor[i] = dag_factor_eigen(j, k);
+    });
+  }
+
+  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;
+
+    std::cout << GridLogMessage<< "CoarsenMatrix "<< std::endl;
+
+    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()); 
+
+    std::cout << GridLogMessage<< "CoarsenMatrix Orthog "<< std::endl;
+    // Orthogonalise the subblocks over the basis
+    blockOrthogonalise(InnerProd,Subspace.subspace);
+
+    // Compute the matrix elements of linop between this orthonormal
+    // set of vectors.
+    std::cout << GridLogMessage<< "CoarsenMatrix masks "<< std::endl;
+    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)); });
+	    if ( hermitian && (disp==-1) ) {
+	      for(int pp=0;pp<geom.npoint;pp++){// Find the opposite link and set <j|A|i> = <i|A|j>*
+		int dirp   = geom.directions[pp];
+		int dispp  = geom.displacements[pp];
+		if ( (dirp==dir) && (dispp==1) ){
+		  auto sft = conjugate(Cshift(oZProj,dir,1));
+		  autoView( sft_v    ,  sft  , AcceleratorWrite);
+		  autoView( A_pp     ,  A[pp], AcceleratorWrite);
+		  accelerator_for(ss, Grid()->oSites(), Fobj::Nsimd(),{ coalescedWrite(A_pp[ss](i,j),sft_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;
+    }
+
+    InvertSelfStencilLink(); std::cout << GridLogMessage << "Coarse self link inverted" << std::endl;
+    FillHalfCbs(); std::cout << GridLogMessage << "Coarse half checkerboards filled" << std::endl;
+  }
+
+  void InvertSelfStencilLink() {
+    std::cout << GridLogDebug << "CoarsenedMatrix::InvertSelfStencilLink" << std::endl;
+    int localVolume = Grid()->lSites();
+
+    typedef typename Cobj::scalar_object scalar_object;
+
+    autoView(Aself_v,    A[geom.npoint-1], CpuRead);
+    autoView(AselfInv_v, AselfInv,         CpuWrite);
+    thread_for(site, localVolume, { // NOTE: Not able to bring this to GPU because of Eigen + peek/poke
+      Eigen::MatrixXcd selfLinkEigen    = Eigen::MatrixXcd::Zero(nbasis, nbasis);
+      Eigen::MatrixXcd selfLinkInvEigen = Eigen::MatrixXcd::Zero(nbasis, nbasis);
+
+      scalar_object selfLink    = Zero();
+      scalar_object selfLinkInv = Zero();
+
+      Coordinate lcoor;
+
+      Grid()->LocalIndexToLocalCoor(site, lcoor);
+      peekLocalSite(selfLink, Aself_v, lcoor);
+
+      for (int i = 0; i < nbasis; ++i)
+        for (int j = 0; j < nbasis; ++j)
+          selfLinkEigen(i, j) = static_cast<ComplexD>(TensorRemove(selfLink(i, j)));
+
+      selfLinkInvEigen = selfLinkEigen.inverse();
+
+      for(int i = 0; i < nbasis; ++i)
+        for(int j = 0; j < nbasis; ++j)
+          selfLinkInv(i, j) = selfLinkInvEigen(i, j);
+
+      pokeLocalSite(selfLinkInv, AselfInv_v, lcoor);
+    });
+  }
+
+  void FillHalfCbs() {
+    std::cout << GridLogDebug << "CoarsenedMatrix::FillHalfCbs" << std::endl;
+    for(int p = 0; p < geom.npoint; ++p) {
+      pickCheckerboard(Even, Aeven[p], A[p]);
+      pickCheckerboard(Odd, Aodd[p], A[p]);
+    }
+    pickCheckerboard(Even, AselfInvEven, AselfInv);
+    pickCheckerboard(Odd, AselfInvOdd, AselfInv);
+  }
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/multigrid/GeneralCoarsenedMatrix.h

@@ -0,0 +1,619 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/GeneralCoarsenedMatrix.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+#include <Grid/qcd/QCD.h> // needed for Dagger(Yes|No), Inverse(Yes|No)
+
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+NAMESPACE_BEGIN(Grid);
+
+// Fine Object == (per site) type of fine field
+// nbasis      == number of deflation vectors
+template<class Fobj,class CComplex,int nbasis>
+class GeneralCoarsenedMatrix : public SparseMatrixBase<Lattice<iVector<CComplex,nbasis > > >  {
+public:
+
+  typedef GeneralCoarsenedMatrix<Fobj,CComplex,nbasis> GeneralCoarseOp;
+  typedef iVector<CComplex,nbasis >           siteVector;
+  typedef iMatrix<CComplex,nbasis >           siteMatrix;
+  typedef Lattice<iScalar<CComplex> >         CoarseComplexField;
+  typedef Lattice<siteVector>                 CoarseVector;
+  typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
+  typedef iMatrix<CComplex,nbasis >  Cobj;
+  typedef iVector<CComplex,nbasis >  Cvec;
+  typedef Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj >        FineField;
+  typedef Lattice<CComplex >    FineComplexField;
+  typedef CoarseVector Field;
+  ////////////////////
+  // Data members
+  ////////////////////
+  int hermitian;
+  GridBase      *       _FineGrid; 
+  GridCartesian *       _CoarseGrid; 
+  NonLocalStencilGeometry &geom;
+  PaddedCell Cell;
+  GeneralLocalStencil Stencil;
+  
+  std::vector<CoarseMatrix> _A;
+  std::vector<CoarseMatrix> _Adag;
+  std::vector<CoarseVector> MultTemporaries;
+
+  ///////////////////////
+  // Interface
+  ///////////////////////
+  GridBase      * Grid(void)           { return _CoarseGrid; };   // this is all the linalg routines need to know
+  GridBase      * FineGrid(void)       { return _FineGrid; };   // this is all the linalg routines need to know
+  GridCartesian * CoarseGrid(void)     { return _CoarseGrid; };   // this is all the linalg routines need to know
+
+  /*  void ShiftMatrix(RealD shift)
+  {
+    int Nd=_FineGrid->Nd(); 
+    Coordinate zero_shift(Nd,0);
+    for(int p=0;p<geom.npoint;p++){
+      if ( zero_shift==geom.shifts[p] ) {
+	_A[p] = _A[p]+shift;
+	//	_Adag[p] = _Adag[p]+shift;
+      }
+    }    
+  }
+  void ProjectNearestNeighbour(RealD shift, GeneralCoarseOp &CopyMe)
+  {
+    int nfound=0;
+    std::cout << GridLogMessage <<"GeneralCoarsenedMatrix::ProjectNearestNeighbour "<< CopyMe._A[0].Grid()<<std::endl;
+    for(int p=0;p<geom.npoint;p++){
+      for(int pp=0;pp<CopyMe.geom.npoint;pp++){
+ 	// Search for the same relative shift
+	// Avoids brutal handling of Grid pointers
+	if ( CopyMe.geom.shifts[pp]==geom.shifts[p] ) {
+	  _A[p] = CopyMe.Cell.Extract(CopyMe._A[pp]);
+	  //	  _Adag[p] = CopyMe.Cell.Extract(CopyMe._Adag[pp]);
+	  nfound++;
+	}
+      }
+    }
+    assert(nfound==geom.npoint);
+    ExchangeCoarseLinks();
+  }
+  */
+  
+  GeneralCoarsenedMatrix(NonLocalStencilGeometry &_geom,GridBase *FineGrid, GridCartesian * CoarseGrid)
+    : geom(_geom),
+      _FineGrid(FineGrid),
+      _CoarseGrid(CoarseGrid),
+      hermitian(1),
+      Cell(_geom.Depth(),_CoarseGrid),
+      Stencil(Cell.grids.back(),geom.shifts)
+  {
+    {
+      int npoint = _geom.npoint;
+    }
+    _A.resize(geom.npoint,CoarseGrid);
+    //    _Adag.resize(geom.npoint,CoarseGrid);
+  }
+  void M (const CoarseVector &in, CoarseVector &out)
+  {
+    Mult(_A,in,out);
+  }
+  void Mdag (const CoarseVector &in, CoarseVector &out)
+  {
+    assert(hermitian);
+    Mult(_A,in,out);
+    //    if ( hermitian ) M(in,out);
+    //    else Mult(_Adag,in,out);
+  }
+  void Mult (std::vector<CoarseMatrix> &A,const CoarseVector &in, CoarseVector &out)
+  {
+    RealD tviews=0;    RealD ttot=0;    RealD tmult=0;   RealD texch=0;    RealD text=0; RealD ttemps=0; RealD tcopy=0;
+    RealD tmult2=0;
+
+    ttot=-usecond();
+    conformable(CoarseGrid(),in.Grid());
+    conformable(in.Grid(),out.Grid());
+    out.Checkerboard() = in.Checkerboard();
+    CoarseVector tin=in;
+
+    texch-=usecond();
+    CoarseVector pin = Cell.ExchangePeriodic(tin);
+    texch+=usecond();
+
+    CoarseVector pout(pin.Grid());
+
+    int npoint = geom.npoint;
+    typedef LatticeView<Cobj> Aview;
+    typedef LatticeView<Cvec> Vview;
+      
+    const int Nsimd = CComplex::Nsimd();
+    
+    int64_t osites=pin.Grid()->oSites();
+
+    RealD flops = 1.0* npoint * nbasis * nbasis * 8.0 * osites * CComplex::Nsimd();
+    RealD bytes = 1.0*osites*sizeof(siteMatrix)*npoint
+                + 2.0*osites*sizeof(siteVector)*npoint;
+      
+    {
+      tviews-=usecond();
+      autoView( in_v , pin, AcceleratorRead);
+      autoView( out_v , pout, AcceleratorWriteDiscard);
+      autoView( Stencil_v  , Stencil, AcceleratorRead);
+      tviews+=usecond();
+
+      // Static and prereserve to keep UVM region live and not resized across multiple calls
+      ttemps-=usecond();
+      MultTemporaries.resize(npoint,pin.Grid());       
+      ttemps+=usecond();
+      std::vector<Aview> AcceleratorViewContainer_h;
+      std::vector<Vview> AcceleratorVecViewContainer_h; 
+
+      tviews-=usecond();
+      for(int p=0;p<npoint;p++) {
+	AcceleratorViewContainer_h.push_back(      A[p].View(AcceleratorRead));
+	AcceleratorVecViewContainer_h.push_back(MultTemporaries[p].View(AcceleratorWrite));
+      }
+      tviews+=usecond();
+
+      static deviceVector<Aview> AcceleratorViewContainer; AcceleratorViewContainer.resize(npoint);
+      static deviceVector<Vview> AcceleratorVecViewContainer; AcceleratorVecViewContainer.resize(npoint); 
+      
+      auto Aview_p = &AcceleratorViewContainer[0];
+      auto Vview_p = &AcceleratorVecViewContainer[0];
+      tcopy-=usecond();
+      acceleratorCopyToDevice(&AcceleratorViewContainer_h[0],&AcceleratorViewContainer[0],npoint *sizeof(Aview));
+      acceleratorCopyToDevice(&AcceleratorVecViewContainer_h[0],&AcceleratorVecViewContainer[0],npoint *sizeof(Vview));
+      tcopy+=usecond();
+
+      tmult-=usecond();
+      accelerator_for(spb, osites*nbasis*npoint, Nsimd, {
+	  typedef decltype(coalescedRead(in_v[0](0))) calcComplex;
+	  int32_t ss   = spb/(nbasis*npoint);
+	  int32_t bp   = spb%(nbasis*npoint);
+	  int32_t point= bp/nbasis;
+	  int32_t b    = bp%nbasis;
+	  auto SE  = Stencil_v.GetEntry(point,ss);
+	  auto nbr = coalescedReadGeneralPermute(in_v[SE->_offset],SE->_permute,Nd);
+	  auto res = coalescedRead(Aview_p[point][ss](0,b))*nbr(0);
+	  for(int bb=1;bb<nbasis;bb++) {
+	    res = res + coalescedRead(Aview_p[point][ss](bb,b))*nbr(bb);
+	  }
+	  coalescedWrite(Vview_p[point][ss](b),res);
+      });
+      tmult2-=usecond();
+      accelerator_for(sb, osites*nbasis, Nsimd, {
+	  int ss = sb/nbasis;
+	  int b  = sb%nbasis;
+	  auto res = coalescedRead(Vview_p[0][ss](b));
+	  for(int point=1;point<npoint;point++){
+	    res = res + coalescedRead(Vview_p[point][ss](b));
+	  }
+	  coalescedWrite(out_v[ss](b),res);
+      });
+      tmult2+=usecond();
+      tmult+=usecond();
+      for(int p=0;p<npoint;p++) {
+	AcceleratorViewContainer_h[p].ViewClose();
+	AcceleratorVecViewContainer_h[p].ViewClose();
+      }
+    }
+
+    text-=usecond();
+    out = Cell.Extract(pout);
+    text+=usecond();
+    ttot+=usecond();
+    
+    std::cout << GridLogPerformance<<"Coarse 1rhs Mult Aviews "<<tviews<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Mult exch "<<texch<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Mult mult "<<tmult<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<" of which mult2  "<<tmult2<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Mult ext  "<<text<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Mult temps "<<ttemps<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Mult copy  "<<tcopy<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Mult tot  "<<ttot<<" us"<<std::endl;
+    //    std::cout << GridLogPerformance<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Kernel flops "<< flops<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Kernel flop/s "<< flops/tmult<<" mflop/s"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Kernel bytes/s "<< bytes/tmult<<" MB/s"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse overall flops/s "<< flops/ttot<<" mflop/s"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse total bytes   "<< bytes/1e6<<" MB"<<std::endl;
+
+  };
+  
+  void PopulateAdag(void)
+  {
+    for(int64_t bidx=0;bidx<CoarseGrid()->gSites() ;bidx++){
+      Coordinate bcoor;
+      CoarseGrid()->GlobalIndexToGlobalCoor(bidx,bcoor);
+      
+      for(int p=0;p<geom.npoint;p++){
+	Coordinate scoor = bcoor;
+	for(int mu=0;mu<bcoor.size();mu++){
+	  int L = CoarseGrid()->GlobalDimensions()[mu];
+	  scoor[mu] = (bcoor[mu] - geom.shifts[p][mu] + L) % L; // Modulo arithmetic
+	}
+	// Flip to poke/peekLocalSite and not too bad
+	auto link = peekSite(_A[p],scoor);
+	int pp = geom.Reverse(p);
+	pokeSite(adj(link),_Adag[pp],bcoor);
+      }
+    }
+  }
+  /////////////////////////////////////////////////////////////
+  // 
+  // A) Only reduced flops option is to use a padded cell of depth 4
+  // and apply MpcDagMpc in the padded cell.
+  //
+  // Makes for ONE application of MpcDagMpc per vector instead of 30 or 80.
+  // With the effective cell size around (B+8)^4 perhaps 12^4/4^4 ratio
+  // Cost is 81x more, same as stencil size.
+  //
+  // But: can eliminate comms and do as local dirichlet.
+  //
+  // Local exchange gauge field once.
+  // Apply to all vectors, local only computation.
+  // Must exchange ghost subcells in reverse process of PaddedCell to take inner products
+  //
+  // B) Can reduce cost: pad by 1, apply Deo      (4^4+6^4+8^4+8^4 )/ (4x 4^4)
+  //                     pad by 2, apply Doe
+  //                     pad by 3, apply Deo
+  //                     then break out 8x directions; cost is ~10x MpcDagMpc per vector
+  //
+  // => almost factor of 10 in setup cost, excluding data rearrangement
+  //
+  // Intermediates -- ignore the corner terms, leave approximate and force Hermitian
+  // Intermediates -- pad by 2 and apply 1+8+24 = 33 times.
+  /////////////////////////////////////////////////////////////
+
+    //////////////////////////////////////////////////////////
+    // BFM HDCG style approach: Solve a system of equations to get Aij
+    //////////////////////////////////////////////////////////
+    /*
+     *     Here, k,l index which possible shift within the 3^Nd "ball" connected by MdagM.
+     *
+     *     conj(phases[block]) proj[k][ block*Nvec+j ] =  \sum_ball  e^{i q_k . delta} < phi_{block,j} | MdagM | phi_{(block+delta),i} > 
+     *                                                 =  \sum_ball e^{iqk.delta} A_ji
+     *
+     *     Must invert matrix M_k,l = e^[i q_k . delta_l]
+     *
+     *     Where q_k = delta_k . (2*M_PI/global_nb[mu])
+     */
+#if 0
+  void CoarsenOperator(LinearOperatorBase<Lattice<Fobj> > &linop,
+		       Aggregation<Fobj,CComplex,nbasis> & Subspace)
+  {
+    std::cout << GridLogMessage<< "GeneralCoarsenMatrix "<< std::endl;
+    GridBase *grid = FineGrid();
+
+    RealD tproj=0.0;
+    RealD teigen=0.0;
+    RealD tmat=0.0;
+    RealD tphase=0.0;
+    RealD tinv=0.0;
+
+    /////////////////////////////////////////////////////////////
+    // Orthogonalise the subblocks over the basis
+    /////////////////////////////////////////////////////////////
+    CoarseScalar InnerProd(CoarseGrid()); 
+    blockOrthogonalise(InnerProd,Subspace.subspace);
+
+    const int npoint = geom.npoint;
+      
+    Coordinate clatt = CoarseGrid()->GlobalDimensions();
+    int Nd = CoarseGrid()->Nd();
+
+      /*
+       *     Here, k,l index which possible momentum/shift within the N-points connected by MdagM.
+       *     Matrix index i is mapped to this shift via 
+       *               geom.shifts[i]
+       *
+       *     conj(pha[block]) proj[k (which mom)][j (basis vec cpt)][block] 
+       *       =  \sum_{l in ball}  e^{i q_k . delta_l} < phi_{block,j} | MdagM | phi_{(block+delta_l),i} > 
+       *       =  \sum_{l in ball} e^{iqk.delta_l} A_ji^{b.b+l}
+       *       = M_{kl} A_ji^{b.b+l}
+       *
+       *     Must assemble and invert matrix M_k,l = e^[i q_k . delta_l]
+       *  
+       *     Where q_k = delta_k . (2*M_PI/global_nb[mu])
+       *
+       *     Then A{ji}^{b,b+l} = M^{-1}_{lm} ComputeProj_{m,b,i,j}
+       */
+    teigen-=usecond();
+    Eigen::MatrixXcd Mkl    = Eigen::MatrixXcd::Zero(npoint,npoint);
+    Eigen::MatrixXcd invMkl = Eigen::MatrixXcd::Zero(npoint,npoint);
+    ComplexD ci(0.0,1.0);
+    for(int k=0;k<npoint;k++){ // Loop over momenta
+
+      for(int l=0;l<npoint;l++){ // Loop over nbr relative
+	ComplexD phase(0.0,0.0);
+	for(int mu=0;mu<Nd;mu++){
+	  RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	  phase=phase+TwoPiL*geom.shifts[k][mu]*geom.shifts[l][mu];
+	}
+	phase=exp(phase*ci);
+	Mkl(k,l) = phase;
+      }
+    }
+    invMkl = Mkl.inverse();
+    teigen+=usecond();
+
+    ///////////////////////////////////////////////////////////////////////
+    // Now compute the matrix elements of linop between the orthonormal
+    // set of vectors.
+    ///////////////////////////////////////////////////////////////////////
+    FineField phaV(grid); // Phased block basis vector
+    FineField MphaV(grid);// Matrix applied
+    CoarseVector coarseInner(CoarseGrid());
+
+    std::vector<CoarseVector> ComputeProj(npoint,CoarseGrid());
+    std::vector<CoarseVector>          FT(npoint,CoarseGrid());
+    for(int i=0;i<nbasis;i++){// Loop over basis vectors
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<"/"<<nbasis<< std::endl;
+      for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
+	/////////////////////////////////////////////////////
+	// Stick a phase on every block
+	/////////////////////////////////////////////////////
+	tphase-=usecond();
+	CoarseComplexField coor(CoarseGrid());
+	CoarseComplexField pha(CoarseGrid());	pha=Zero();
+	for(int mu=0;mu<Nd;mu++){
+	  LatticeCoordinate(coor,mu);
+	  RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	  pha = pha + (TwoPiL * geom.shifts[p][mu]) * coor;
+	}
+	pha  =exp(pha*ci);
+	phaV=Zero();
+	blockZAXPY(phaV,pha,Subspace.subspace[i],phaV);
+	tphase+=usecond();
+
+	/////////////////////////////////////////////////////////////////////
+	// Multiple phased subspace vector by matrix and project to subspace
+	// Remove local bulk phase to leave relative phases
+	/////////////////////////////////////////////////////////////////////
+	tmat-=usecond();
+	linop.Op(phaV,MphaV);
+	tmat+=usecond();
+
+	tproj-=usecond();
+	blockProject(coarseInner,MphaV,Subspace.subspace);
+	coarseInner = conjugate(pha) * coarseInner;
+
+	ComputeProj[p] = coarseInner;
+	tproj+=usecond();
+
+      }
+
+      tinv-=usecond();
+      for(int k=0;k<npoint;k++){
+	FT[k] = Zero();
+	for(int l=0;l<npoint;l++){
+	  FT[k]= FT[k]+ invMkl(l,k)*ComputeProj[l];
+	}
+      
+	int osites=CoarseGrid()->oSites();
+	autoView( A_v  , _A[k], AcceleratorWrite);
+	autoView( FT_v  , FT[k], AcceleratorRead);
+	accelerator_for(sss, osites, 1, {
+	    for(int j=0;j<nbasis;j++){
+	      A_v[sss](i,j) = FT_v[sss](j);
+	    }
+        });
+      }
+      tinv+=usecond();
+    }
+
+    // Only needed if nonhermitian
+    if ( ! hermitian ) {
+      //      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
+      //      PopulateAdag();
+    }
+
+    // Need to write something to populate Adag from A
+    ExchangeCoarseLinks();
+    std::cout << GridLogMessage<<"CoarsenOperator eigen  "<<teigen<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator phase  "<<tphase<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator mat    "<<tmat <<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator proj   "<<tproj<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator inv    "<<tinv<<" us"<<std::endl;
+  }
+#else
+  void CoarsenOperator(LinearOperatorBase<Lattice<Fobj> > &linop,
+		       Aggregation<Fobj,CComplex,nbasis> & Subspace)
+  {
+    std::cout << GridLogMessage<< "GeneralCoarsenMatrix "<< std::endl;
+    GridBase *grid = FineGrid();
+
+    RealD tproj=0.0;
+    RealD teigen=0.0;
+    RealD tmat=0.0;
+    RealD tphase=0.0;
+    RealD tphaseBZ=0.0;
+    RealD tinv=0.0;
+
+    /////////////////////////////////////////////////////////////
+    // Orthogonalise the subblocks over the basis
+    /////////////////////////////////////////////////////////////
+    CoarseScalar InnerProd(CoarseGrid()); 
+    blockOrthogonalise(InnerProd,Subspace.subspace);
+
+    //    for(int s=0;s<Subspace.subspace.size();s++){
+      //      std::cout << " subspace norm "<<norm2(Subspace.subspace[s])<<std::endl;
+    //    }
+    const int npoint = geom.npoint;
+      
+    Coordinate clatt = CoarseGrid()->GlobalDimensions();
+    int Nd = CoarseGrid()->Nd();
+
+      /*
+       *     Here, k,l index which possible momentum/shift within the N-points connected by MdagM.
+       *     Matrix index i is mapped to this shift via 
+       *               geom.shifts[i]
+       *
+       *     conj(pha[block]) proj[k (which mom)][j (basis vec cpt)][block] 
+       *       =  \sum_{l in ball}  e^{i q_k . delta_l} < phi_{block,j} | MdagM | phi_{(block+delta_l),i} > 
+       *       =  \sum_{l in ball} e^{iqk.delta_l} A_ji^{b.b+l}
+       *       = M_{kl} A_ji^{b.b+l}
+       *
+       *     Must assemble and invert matrix M_k,l = e^[i q_k . delta_l]
+       *  
+       *     Where q_k = delta_k . (2*M_PI/global_nb[mu])
+       *
+       *     Then A{ji}^{b,b+l} = M^{-1}_{lm} ComputeProj_{m,b,i,j}
+       */
+    teigen-=usecond();
+    Eigen::MatrixXcd Mkl    = Eigen::MatrixXcd::Zero(npoint,npoint);
+    Eigen::MatrixXcd invMkl = Eigen::MatrixXcd::Zero(npoint,npoint);
+    ComplexD ci(0.0,1.0);
+    for(int k=0;k<npoint;k++){ // Loop over momenta
+
+      for(int l=0;l<npoint;l++){ // Loop over nbr relative
+	ComplexD phase(0.0,0.0);
+	for(int mu=0;mu<Nd;mu++){
+	  RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	  phase=phase+TwoPiL*geom.shifts[k][mu]*geom.shifts[l][mu];
+	}
+	phase=exp(phase*ci);
+	Mkl(k,l) = phase;
+      }
+    }
+    invMkl = Mkl.inverse();
+    teigen+=usecond();
+
+    ///////////////////////////////////////////////////////////////////////
+    // Now compute the matrix elements of linop between the orthonormal
+    // set of vectors.
+    ///////////////////////////////////////////////////////////////////////
+    FineField phaV(grid); // Phased block basis vector
+    FineField MphaV(grid);// Matrix applied
+    std::vector<FineComplexField> phaF(npoint,grid);
+    std::vector<CoarseComplexField> pha(npoint,CoarseGrid());
+    
+    CoarseVector coarseInner(CoarseGrid());
+    
+    typedef typename CComplex::scalar_type SComplex;
+    FineComplexField one(grid); one=SComplex(1.0);
+    FineComplexField zz(grid); zz = Zero();
+    tphase=-usecond();
+    for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
+      /////////////////////////////////////////////////////
+      // Stick a phase on every block
+      /////////////////////////////////////////////////////
+      CoarseComplexField coor(CoarseGrid());
+      pha[p]=Zero();
+      for(int mu=0;mu<Nd;mu++){
+	LatticeCoordinate(coor,mu);
+	RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	pha[p] = pha[p] + (TwoPiL * geom.shifts[p][mu]) * coor;
+      }
+      pha[p]  =exp(pha[p]*ci);
+
+      blockZAXPY(phaF[p],pha[p],one,zz);
+      
+    }
+    tphase+=usecond();
+    
+    std::vector<CoarseVector> ComputeProj(npoint,CoarseGrid());
+    std::vector<CoarseVector>          FT(npoint,CoarseGrid());
+    for(int i=0;i<nbasis;i++){// Loop over basis vectors
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<"/"<<nbasis<< std::endl;
+      for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
+	tphaseBZ-=usecond();
+	phaV = phaF[p]*Subspace.subspace[i];
+	tphaseBZ+=usecond();
+
+	/////////////////////////////////////////////////////////////////////
+	// Multiple phased subspace vector by matrix and project to subspace
+	// Remove local bulk phase to leave relative phases
+	/////////////////////////////////////////////////////////////////////
+	tmat-=usecond();
+	linop.Op(phaV,MphaV);
+	tmat+=usecond();
+	//	std::cout << i << " " <<p << " MphaV "<<norm2(MphaV)<<" "<<norm2(phaV)<<std::endl;
+
+	tproj-=usecond();
+	blockProject(coarseInner,MphaV,Subspace.subspace);
+	coarseInner = conjugate(pha[p]) * coarseInner;
+
+	ComputeProj[p] = coarseInner;
+	tproj+=usecond();
+	//	std::cout << i << " " <<p << " ComputeProj "<<norm2(ComputeProj[p])<<std::endl;
+
+      }
+
+      tinv-=usecond();
+      for(int k=0;k<npoint;k++){
+	FT[k] = Zero();
+	for(int l=0;l<npoint;l++){
+	  FT[k]= FT[k]+ invMkl(l,k)*ComputeProj[l];
+	}
+      
+	int osites=CoarseGrid()->oSites();
+	autoView( A_v  , _A[k], AcceleratorWrite);
+	autoView( FT_v  , FT[k], AcceleratorRead);
+	accelerator_for(sss, osites, 1, {
+	    for(int j=0;j<nbasis;j++){
+	      A_v[sss](i,j) = FT_v[sss](j);
+	    }
+        });
+      }
+      tinv+=usecond();
+    }
+
+    // Only needed if nonhermitian
+    if ( ! hermitian ) {
+      //      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
+      //      PopulateAdag();
+    }
+
+    for(int p=0;p<geom.npoint;p++){
+      std::cout << " _A["<<p<<"] "<<norm2(_A[p])<<std::endl;
+    }
+
+    // Need to write something to populate Adag from A
+    ExchangeCoarseLinks();
+    std::cout << GridLogMessage<<"CoarsenOperator eigen  "<<teigen<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator phase  "<<tphase<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator phaseBZ "<<tphaseBZ<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator mat    "<<tmat <<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator proj   "<<tproj<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator inv    "<<tinv<<" us"<<std::endl;
+  }
+#endif  
+  void ExchangeCoarseLinks(void){
+    for(int p=0;p<geom.npoint;p++){
+      _A[p] = Cell.ExchangePeriodic(_A[p]);
+      //      _Adag[p]= Cell.ExchangePeriodic(_Adag[p]);
+    }
+  }
+  virtual  void Mdiag    (const Field &in, Field &out){ assert(0);};
+  virtual  void Mdir     (const Field &in, Field &out,int dir, int disp){assert(0);};
+  virtual  void MdirAll  (const Field &in, std::vector<Field> &out){assert(0);};
+};
+
+
+  
+NAMESPACE_END(Grid);

Grid/algorithms/multigrid/GeneralCoarsenedMatrixMultiRHS.h

@@ -0,0 +1,729 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/GeneralCoarsenedMatrixMultiRHS.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+
+NAMESPACE_BEGIN(Grid);
+
+
+// Fine Object == (per site) type of fine field
+// nbasis      == number of deflation vectors
+template<class Fobj,class CComplex,int nbasis>
+class MultiGeneralCoarsenedMatrix : public SparseMatrixBase<Lattice<iVector<CComplex,nbasis > > >  {
+public:
+  typedef typename CComplex::scalar_object SComplex;
+  typedef GeneralCoarsenedMatrix<Fobj,CComplex,nbasis> GeneralCoarseOp;
+  typedef MultiGeneralCoarsenedMatrix<Fobj,CComplex,nbasis> MultiGeneralCoarseOp;
+
+  typedef iVector<CComplex,nbasis >           siteVector;
+  typedef iMatrix<CComplex,nbasis >           siteMatrix;
+  typedef iVector<SComplex,nbasis >           calcVector;
+  typedef iMatrix<SComplex,nbasis >           calcMatrix;
+  typedef Lattice<iScalar<CComplex> >         CoarseComplexField;
+  typedef Lattice<siteVector>                 CoarseVector;
+  typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
+  typedef iMatrix<CComplex,nbasis >  Cobj;
+  typedef iVector<CComplex,nbasis >  Cvec;
+  typedef Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj >        FineField;
+  typedef Lattice<CComplex >    FineComplexField;
+  typedef CoarseVector Field;
+
+  ////////////////////
+  // Data members
+  ////////////////////
+  GridCartesian *       _CoarseGridMulti; 
+  NonLocalStencilGeometry geom;
+  NonLocalStencilGeometry geom_srhs;
+  PaddedCell Cell;
+  GeneralLocalStencil Stencil;
+
+  deviceVector<calcVector> BLAS_B;
+  deviceVector<calcVector> BLAS_C;
+  std::vector<deviceVector<calcMatrix> > BLAS_A;
+
+  std::vector<deviceVector<ComplexD *> > BLAS_AP;
+  std::vector<deviceVector<ComplexD *> > BLAS_BP;
+  deviceVector<ComplexD *>               BLAS_CP;
+
+  ///////////////////////
+  // Interface
+  ///////////////////////
+  GridBase      * Grid(void)           { return _CoarseGridMulti; };   // this is all the linalg routines need to know
+  GridCartesian * CoarseGrid(void)     { return _CoarseGridMulti; };   // this is all the linalg routines need to know
+
+  // Can be used to do I/O on the operator matrices externally
+  void SetMatrix (int p,CoarseMatrix & A)
+  {
+    assert(A.size()==geom_srhs.npoint);
+    GridtoBLAS(A[p],BLAS_A[p]);
+  }
+  void GetMatrix (int p,CoarseMatrix & A)
+  {
+    assert(A.size()==geom_srhs.npoint);
+    BLAStoGrid(A[p],BLAS_A[p]);
+  }
+  void CopyMatrix (GeneralCoarseOp &_Op)
+  {
+    for(int p=0;p<geom.npoint;p++){
+      auto Aup = _Op.Cell.Extract(_Op._A[p]);
+      //Unpadded
+      GridtoBLAS(Aup,BLAS_A[p]);
+    }
+  }
+  /*
+  void CheckMatrix (GeneralCoarseOp &_Op)
+  {
+    std::cout <<"************* Checking the little direc operator mRHS"<<std::endl;
+    for(int p=0;p<geom.npoint;p++){
+      //Unpadded
+      auto Aup = _Op.Cell.Extract(_Op._A[p]);
+      auto Ack = Aup;
+      BLAStoGrid(Ack,BLAS_A[p]);
+      std::cout << p<<" Ack "<<norm2(Ack)<<std::endl;
+      std::cout << p<<" Aup "<<norm2(Aup)<<std::endl;
+    }
+    std::cout <<"************* "<<std::endl;
+  }
+  */
+  
+  MultiGeneralCoarsenedMatrix(NonLocalStencilGeometry &_geom,GridCartesian *CoarseGridMulti) :
+    _CoarseGridMulti(CoarseGridMulti),
+    geom_srhs(_geom),
+    geom(_CoarseGridMulti,_geom.hops,_geom.skip+1),
+    Cell(geom.Depth(),_CoarseGridMulti),
+    Stencil(Cell.grids.back(),geom.shifts) // padded cell stencil
+  {
+    int32_t padded_sites   = Cell.grids.back()->lSites();
+    int32_t unpadded_sites = CoarseGridMulti->lSites();
+    
+    int32_t nrhs  = CoarseGridMulti->FullDimensions()[0];  // # RHS
+    int32_t orhs  = nrhs/CComplex::Nsimd();
+
+    padded_sites   = padded_sites/nrhs;
+    unpadded_sites = unpadded_sites/nrhs;
+    
+    /////////////////////////////////////////////////
+    // Device data vector storage
+    /////////////////////////////////////////////////
+    BLAS_A.resize(geom.npoint);
+    for(int p=0;p<geom.npoint;p++){
+      BLAS_A[p].resize (unpadded_sites); // no ghost zone, npoint elements
+    }
+    
+    BLAS_B.resize(nrhs *padded_sites);   // includes ghost zone
+    BLAS_C.resize(nrhs *unpadded_sites); // no ghost zone
+    BLAS_AP.resize(geom.npoint);
+    BLAS_BP.resize(geom.npoint);
+    for(int p=0;p<geom.npoint;p++){
+      BLAS_AP[p].resize(unpadded_sites);
+      BLAS_BP[p].resize(unpadded_sites);
+    }
+    BLAS_CP.resize(unpadded_sites);
+
+    /////////////////////////////////////////////////
+    // Pointers to data
+    /////////////////////////////////////////////////
+
+    // Site identity mapping for A
+    for(int p=0;p<geom.npoint;p++){
+      for(int ss=0;ss<unpadded_sites;ss++){
+	ComplexD *ptr = (ComplexD *)&BLAS_A[p][ss];
+	acceleratorPut(BLAS_AP[p][ss],ptr);
+      }
+    }
+    // Site identity mapping for C
+    for(int ss=0;ss<unpadded_sites;ss++){
+      ComplexD *ptr = (ComplexD *)&BLAS_C[ss*nrhs];
+      acceleratorPut(BLAS_CP[ss],ptr);
+    }
+
+    // Neighbour table is more complicated
+    int32_t j=0; // Interior point counter (unpadded)
+    for(int32_t s=0;s<padded_sites;s++){ // 4 volume, padded
+      int ghost_zone=0;
+      for(int32_t point = 0 ; point < geom.npoint; point++){
+	int i=s*orhs*geom.npoint+point;
+	if( Stencil._entries[i]._wrap ) { // stencil is indexed by the oSite of the CoarseGridMulti, hence orhs factor
+	  ghost_zone=1; // If general stencil wrapped in any direction, wrap=1
+	}
+      }
+
+      if( ghost_zone==0) {
+	for(int32_t point = 0 ; point < geom.npoint; point++){
+	  int i=s*orhs*geom.npoint+point;
+ 	  int32_t nbr = Stencil._entries[i]._offset*CComplex::Nsimd(); // oSite -> lSite
+	  assert(nbr<BLAS_B.size());
+	  ComplexD * ptr = (ComplexD *)&BLAS_B[nbr];
+	  acceleratorPut(BLAS_BP[point][j],ptr); // neighbour indexing in ghost zone volume
+	}
+	j++;
+      }
+    }
+    assert(j==unpadded_sites);
+  }
+  template<class vobj> void GridtoBLAS(const Lattice<vobj> &from,deviceVector<typename vobj::scalar_object> &to)
+  {
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  GridBase *Fg = from.Grid();
+  assert(!Fg->_isCheckerBoarded);
+  int nd = Fg->_ndimension;
+
+  to.resize(Fg->lSites());
+
+  Coordinate LocalLatt = Fg->LocalDimensions();
+  size_t nsite = 1;
+  for(int i=0;i<nd;i++) nsite *= LocalLatt[i];
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  // do the index calc on the GPU
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  Coordinate f_ostride = Fg->_ostride;
+  Coordinate f_istride = Fg->_istride;
+  Coordinate f_rdimensions = Fg->_rdimensions;
+
+  autoView(from_v,from,AcceleratorRead);
+  auto to_v = &to[0];
+
+  const int words=sizeof(vobj)/sizeof(vector_type);
+  accelerator_for(idx,nsite,1,{
+      
+      Coordinate from_coor, base;
+      Lexicographic::CoorFromIndex(base,idx,LocalLatt);
+      for(int i=0;i<nd;i++){
+	from_coor[i] = base[i];
+      }
+      int from_oidx = 0; for(int d=0;d<nd;d++) from_oidx+=f_ostride[d]*(from_coor[d]%f_rdimensions[d]);
+      int from_lane = 0; for(int d=0;d<nd;d++) from_lane+=f_istride[d]*(from_coor[d]/f_rdimensions[d]);
+
+      const vector_type* from = (const vector_type *)&from_v[from_oidx];
+      scalar_type* to = (scalar_type *)&to_v[idx];
+      
+      scalar_type stmp;
+      for(int w=0;w<words;w++){
+	stmp = getlane(from[w], from_lane);
+	to[w] = stmp;
+      }
+    });
+  }    
+  template<class vobj> void BLAStoGrid(Lattice<vobj> &grid,deviceVector<typename vobj::scalar_object> &in)
+  {
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  GridBase *Tg = grid.Grid();
+  assert(!Tg->_isCheckerBoarded);
+  int nd = Tg->_ndimension;
+  
+  assert(in.size()==Tg->lSites());
+
+  Coordinate LocalLatt = Tg->LocalDimensions();
+  size_t nsite = 1;
+  for(int i=0;i<nd;i++) nsite *= LocalLatt[i];
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  // do the index calc on the GPU
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  Coordinate t_ostride = Tg->_ostride;
+  Coordinate t_istride = Tg->_istride;
+  Coordinate t_rdimensions = Tg->_rdimensions;
+
+  autoView(to_v,grid,AcceleratorWrite);
+  auto from_v = &in[0];
+
+  const int words=sizeof(vobj)/sizeof(vector_type);
+  accelerator_for(idx,nsite,1,{
+      
+      Coordinate to_coor, base;
+      Lexicographic::CoorFromIndex(base,idx,LocalLatt);
+      for(int i=0;i<nd;i++){
+	to_coor[i] = base[i];
+      }
+      int to_oidx = 0; for(int d=0;d<nd;d++) to_oidx+=t_ostride[d]*(to_coor[d]%t_rdimensions[d]);
+      int to_lane = 0; for(int d=0;d<nd;d++) to_lane+=t_istride[d]*(to_coor[d]/t_rdimensions[d]);
+
+      vector_type* to = (vector_type *)&to_v[to_oidx];
+      scalar_type* from = (scalar_type *)&from_v[idx];
+      
+      scalar_type stmp;
+      for(int w=0;w<words;w++){
+	stmp=from[w];
+	putlane(to[w], stmp, to_lane);
+      }
+    });
+  }
+  void CoarsenOperator(LinearOperatorBase<Lattice<Fobj> > &linop,
+		       Aggregation<Fobj,CComplex,nbasis> & Subspace,
+		       GridBase *CoarseGrid)
+  {
+#if 0
+    std::cout << GridLogMessage<< "GeneralCoarsenMatrixMrhs "<< std::endl;
+
+    GridBase *grid = Subspace.FineGrid;
+
+    /////////////////////////////////////////////////////////////
+    // Orthogonalise the subblocks over the basis
+    /////////////////////////////////////////////////////////////
+    CoarseScalar InnerProd(CoarseGrid); 
+    blockOrthogonalise(InnerProd,Subspace.subspace);
+
+    const int npoint = geom_srhs.npoint;
+
+    Coordinate clatt = CoarseGrid->GlobalDimensions();
+    int Nd = CoarseGrid->Nd();
+      /*
+       *     Here, k,l index which possible momentum/shift within the N-points connected by MdagM.
+       *     Matrix index i is mapped to this shift via 
+       *               geom.shifts[i]
+       *
+       *     conj(pha[block]) proj[k (which mom)][j (basis vec cpt)][block] 
+       *       =  \sum_{l in ball}  e^{i q_k . delta_l} < phi_{block,j} | MdagM | phi_{(block+delta_l),i} > 
+       *       =  \sum_{l in ball} e^{iqk.delta_l} A_ji^{b.b+l}
+       *       = M_{kl} A_ji^{b.b+l}
+       *
+       *     Must assemble and invert matrix M_k,l = e^[i q_k . delta_l]
+       *  
+       *     Where q_k = delta_k . (2*M_PI/global_nb[mu])
+       *
+       *     Then A{ji}^{b,b+l} = M^{-1}_{lm} ComputeProj_{m,b,i,j}
+       */
+    Eigen::MatrixXcd Mkl    = Eigen::MatrixXcd::Zero(npoint,npoint);
+    Eigen::MatrixXcd invMkl = Eigen::MatrixXcd::Zero(npoint,npoint);
+    ComplexD ci(0.0,1.0);
+    for(int k=0;k<npoint;k++){ // Loop over momenta
+
+      for(int l=0;l<npoint;l++){ // Loop over nbr relative
+	ComplexD phase(0.0,0.0);
+	for(int mu=0;mu<Nd;mu++){
+	  RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	  phase=phase+TwoPiL*geom_srhs.shifts[k][mu]*geom_srhs.shifts[l][mu];
+	}
+	phase=exp(phase*ci);
+	Mkl(k,l) = phase;
+      }
+    }
+    invMkl = Mkl.inverse();
+
+    ///////////////////////////////////////////////////////////////////////
+    // Now compute the matrix elements of linop between the orthonormal
+    // set of vectors.
+    ///////////////////////////////////////////////////////////////////////
+    FineField phaV(grid); // Phased block basis vector
+    FineField MphaV(grid);// Matrix applied
+    std::vector<FineComplexField> phaF(npoint,grid);
+    std::vector<CoarseComplexField> pha(npoint,CoarseGrid);
+    
+    CoarseVector coarseInner(CoarseGrid);
+    
+    typedef typename CComplex::scalar_type SComplex;
+    FineComplexField one(grid); one=SComplex(1.0);
+    FineComplexField zz(grid); zz = Zero();
+    for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
+      /////////////////////////////////////////////////////
+      // Stick a phase on every block
+      /////////////////////////////////////////////////////
+      CoarseComplexField coor(CoarseGrid);
+      pha[p]=Zero();
+      for(int mu=0;mu<Nd;mu++){
+	LatticeCoordinate(coor,mu);
+	RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	pha[p] = pha[p] + (TwoPiL * geom_srhs.shifts[p][mu]) * coor;
+      }
+      pha[p]  =exp(pha[p]*ci);	
+
+      blockZAXPY(phaF[p],pha[p],one,zz);
+    }
+
+    // Could save on temporary storage here
+    std::vector<CoarseMatrix> _A;
+    _A.resize(geom_srhs.npoint,CoarseGrid);
+
+    std::vector<CoarseVector> ComputeProj(npoint,CoarseGrid);
+    CoarseVector          FT(CoarseGrid);
+    for(int i=0;i<nbasis;i++){// Loop over basis vectors
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<"/"<<nbasis<< std::endl;
+      for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
+
+	phaV = phaF[p]*Subspace.subspace[i];
+
+	/////////////////////////////////////////////////////////////////////
+	// Multiple phased subspace vector by matrix and project to subspace
+	// Remove local bulk phase to leave relative phases
+	/////////////////////////////////////////////////////////////////////
+	linop.Op(phaV,MphaV);
+
+	// Fixme, could use batched block projector here
+	blockProject(coarseInner,MphaV,Subspace.subspace);
+
+	coarseInner = conjugate(pha[p]) * coarseInner;
+
+	ComputeProj[p] = coarseInner;
+      }
+
+      // Could do this with a block promote or similar BLAS call via the MultiRHSBlockProjector with a const matrix.
+      for(int k=0;k<npoint;k++){
+
+	FT = Zero();
+	for(int l=0;l<npoint;l++){
+	  FT= FT+ invMkl(l,k)*ComputeProj[l];
+	}
+      
+	int osites=CoarseGrid->oSites();
+	autoView( A_v  , _A[k], AcceleratorWrite);
+	autoView( FT_v  , FT, AcceleratorRead);
+	accelerator_for(sss, osites, 1, {
+	    for(int j=0;j<nbasis;j++){
+	      A_v[sss](i,j) = FT_v[sss](j);
+	    }
+        });
+      }
+    }
+
+    // Only needed if nonhermitian
+    //    if ( ! hermitian ) {
+    //      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
+    //      PopulateAdag();
+    //    }
+    // Need to write something to populate Adag from A
+
+    for(int p=0;p<geom_srhs.npoint;p++){
+      GridtoBLAS(_A[p],BLAS_A[p]);
+    }
+    /*
+Grid : Message : 11698.730546 s : CoarsenOperator eigen  1334 us
+Grid : Message : 11698.730563 s : CoarsenOperator phase  34729 us
+Grid : Message : 11698.730565 s : CoarsenOperator phaseBZ 2423814 us
+Grid : Message : 11698.730566 s : CoarsenOperator mat    127890998 us
+Grid : Message : 11698.730567 s : CoarsenOperator proj   515840840 us
+Grid : Message : 11698.730568 s : CoarsenOperator inv    103948313 us
+Takes 600s to compute matrix elements, DOMINATED by the block project.
+Easy to speed up with the batched block project.
+Store npoint vectors, get npoint x Nbasis block projection, and 81 fold faster.
+
+// Block project below taks to 240s
+Grid : Message : 328.193418 s : CoarsenOperator phase      38338 us
+Grid : Message : 328.193434 s : CoarsenOperator phaseBZ  1711226 us
+Grid : Message : 328.193436 s : CoarsenOperator mat    122213270 us
+//Grid : Message : 328.193438 s : CoarsenOperator proj   1181154 us <-- this is mistimed
+//Grid : Message : 11698.730568 s : CoarsenOperator inv  103948313 us <-- Cut this ~10x if lucky by loop fusion
+     */
+#else
+    RealD tproj=0.0;
+    RealD tmat=0.0;
+    RealD tphase=0.0;
+    RealD tphaseBZ=0.0;
+    RealD tinv=0.0;
+
+    std::cout << GridLogMessage<< "GeneralCoarsenMatrixMrhs "<< std::endl;
+
+    GridBase *grid = Subspace.FineGrid;
+
+    /////////////////////////////////////////////////////////////
+    // Orthogonalise the subblocks over the basis
+    /////////////////////////////////////////////////////////////
+    CoarseScalar InnerProd(CoarseGrid); 
+    blockOrthogonalise(InnerProd,Subspace.subspace);
+
+
+    MultiRHSBlockProject<Lattice<Fobj> >    Projector;
+    Projector.Allocate(nbasis,grid,CoarseGrid);
+    Projector.ImportBasis(Subspace.subspace);
+    
+    const int npoint = geom_srhs.npoint;
+
+    Coordinate clatt = CoarseGrid->GlobalDimensions();
+    int Nd = CoarseGrid->Nd();
+      /*
+       *     Here, k,l index which possible momentum/shift within the N-points connected by MdagM.
+       *     Matrix index i is mapped to this shift via 
+       *               geom.shifts[i]
+       *
+       *     conj(pha[block]) proj[k (which mom)][j (basis vec cpt)][block] 
+       *       =  \sum_{l in ball}  e^{i q_k . delta_l} < phi_{block,j} | MdagM | phi_{(block+delta_l),i} > 
+       *       =  \sum_{l in ball} e^{iqk.delta_l} A_ji^{b.b+l}
+       *       = M_{kl} A_ji^{b.b+l}
+       *
+       *     Must assemble and invert matrix M_k,l = e^[i q_k . delta_l]
+       *  
+       *     Where q_k = delta_k . (2*M_PI/global_nb[mu])
+       *
+       *     Then A{ji}^{b,b+l} = M^{-1}_{lm} ComputeProj_{m,b,i,j}
+       */
+    Eigen::MatrixXcd Mkl    = Eigen::MatrixXcd::Zero(npoint,npoint);
+    Eigen::MatrixXcd invMkl = Eigen::MatrixXcd::Zero(npoint,npoint);
+    ComplexD ci(0.0,1.0);
+    for(int k=0;k<npoint;k++){ // Loop over momenta
+
+      for(int l=0;l<npoint;l++){ // Loop over nbr relative
+	ComplexD phase(0.0,0.0);
+	for(int mu=0;mu<Nd;mu++){
+	  RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	  phase=phase+TwoPiL*geom_srhs.shifts[k][mu]*geom_srhs.shifts[l][mu];
+	}
+	phase=exp(phase*ci);
+	Mkl(k,l) = phase;
+      }
+    }
+    invMkl = Mkl.inverse();
+
+    ///////////////////////////////////////////////////////////////////////
+    // Now compute the matrix elements of linop between the orthonormal
+    // set of vectors.
+    ///////////////////////////////////////////////////////////////////////
+    FineField phaV(grid); // Phased block basis vector
+    FineField MphaV(grid);// Matrix applied
+    std::vector<FineComplexField> phaF(npoint,grid);
+    std::vector<CoarseComplexField> pha(npoint,CoarseGrid);
+    
+    CoarseVector coarseInner(CoarseGrid);
+    
+    tphase=-usecond();
+    typedef typename CComplex::scalar_type SComplex;
+    FineComplexField one(grid); one=SComplex(1.0);
+    FineComplexField zz(grid); zz = Zero();
+    for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
+      /////////////////////////////////////////////////////
+      // Stick a phase on every block
+      /////////////////////////////////////////////////////
+      CoarseComplexField coor(CoarseGrid);
+      pha[p]=Zero();
+      for(int mu=0;mu<Nd;mu++){
+	LatticeCoordinate(coor,mu);
+	RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
+	pha[p] = pha[p] + (TwoPiL * geom_srhs.shifts[p][mu]) * coor;
+      }
+      pha[p]  =exp(pha[p]*ci);	
+
+      blockZAXPY(phaF[p],pha[p],one,zz);
+    }
+    tphase+=usecond();
+
+    // Could save on temporary storage here
+    std::vector<CoarseMatrix> _A;
+    _A.resize(geom_srhs.npoint,CoarseGrid);
+
+    // Count use small chunks than npoint == 81 and save memory
+    int batch = 9;
+    std::vector<FineField>    _MphaV(batch,grid);
+    std::vector<CoarseVector> TmpProj(batch,CoarseGrid);
+
+    std::vector<CoarseVector> ComputeProj(npoint,CoarseGrid);
+    CoarseVector          FT(CoarseGrid);
+    for(int i=0;i<nbasis;i++){// Loop over basis vectors
+      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<"/"<<nbasis<< std::endl;
+
+      //      std::cout << GridLogMessage << " phasing the fine vector "<<std::endl;
+      // Fixme : do this in batches
+      for(int p=0;p<npoint;p+=batch){ // Loop over momenta in npoint
+
+	for(int b=0;b<MIN(batch,npoint-p);b++){
+	  tphaseBZ-=usecond();
+	  phaV = phaF[p+b]*Subspace.subspace[i];
+	  tphaseBZ+=usecond();
+
+	  /////////////////////////////////////////////////////////////////////
+	  // Multiple phased subspace vector by matrix and project to subspace
+	  // Remove local bulk phase to leave relative phases
+	  /////////////////////////////////////////////////////////////////////
+	  // Memory footprint was an issue
+	  tmat-=usecond();
+	  linop.Op(phaV,MphaV);
+	  _MphaV[b] = MphaV;
+	  tmat+=usecond();
+	}      
+
+	//	std::cout << GridLogMessage << " Calling block project "<<std::endl;
+	tproj-=usecond();
+	Projector.blockProject(_MphaV,TmpProj);
+	tproj+=usecond();
+	
+	//	std::cout << GridLogMessage << " conj phasing the coarse vectors "<<std::endl;
+	for(int b=0;b<MIN(batch,npoint-p);b++){
+	  ComputeProj[p+b] = conjugate(pha[p+b])*TmpProj[b];
+	}
+      }
+
+      // Could do this with a block promote or similar BLAS call via the MultiRHSBlockProjector with a const matrix.
+      
+      // std::cout << GridLogMessage << " Starting FT inv "<<std::endl;
+      tinv-=usecond();
+      for(int k=0;k<npoint;k++){
+	FT = Zero();
+	// 81 kernel calls as many ComputeProj vectors
+	// Could fuse with a vector of views, but ugly
+	// Could unroll the expression and run fewer kernels -- much more attractive
+	// Could also do non blocking.
+#if 0	
+	for(int l=0;l<npoint;l++){
+	  FT= FT+ invMkl(l,k)*ComputeProj[l];
+	}
+#else
+	const int radix = 9;
+	int ll;
+	for(ll=0;ll+radix-1<npoint;ll+=radix){
+	  // When ll = npoint-radix, ll+radix-1 = npoint-1, and we do it all.
+	  FT = FT 
+	    + invMkl(ll+0,k)*ComputeProj[ll+0]
+	    + invMkl(ll+1,k)*ComputeProj[ll+1]
+	    + invMkl(ll+2,k)*ComputeProj[ll+2]
+	    + invMkl(ll+3,k)*ComputeProj[ll+3]
+	    + invMkl(ll+4,k)*ComputeProj[ll+4]
+	    + invMkl(ll+5,k)*ComputeProj[ll+5]
+	    + invMkl(ll+6,k)*ComputeProj[ll+6]
+	    + invMkl(ll+7,k)*ComputeProj[ll+7]
+	    + invMkl(ll+8,k)*ComputeProj[ll+8];
+	}
+	for(int l=ll;l<npoint;l++){
+	  FT= FT+ invMkl(l,k)*ComputeProj[l];
+	}
+#endif
+      
+	// 1 kernel call -- must be cheaper
+	int osites=CoarseGrid->oSites();
+	autoView( A_v  , _A[k], AcceleratorWrite);
+	autoView( FT_v  , FT, AcceleratorRead);
+	accelerator_for(sss, osites, 1, {
+	    for(int j=0;j<nbasis;j++){
+	      A_v[sss](i,j) = FT_v[sss](j);
+	    }
+        });
+      }
+      tinv+=usecond();
+    }
+
+    // Only needed if nonhermitian
+    //    if ( ! hermitian ) {
+    //      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
+    //      PopulateAdag();
+    //    }
+    // Need to write something to populate Adag from A
+    //    std::cout << GridLogMessage << " Calling GridtoBLAS "<<std::endl;
+    for(int p=0;p<geom_srhs.npoint;p++){
+      GridtoBLAS(_A[p],BLAS_A[p]);
+    }
+    std::cout << GridLogMessage<<"CoarsenOperator phase  "<<tphase<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator phaseBZ "<<tphaseBZ<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator mat    "<<tmat <<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator proj   "<<tproj<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"CoarsenOperator inv    "<<tinv<<" us"<<std::endl;
+#endif
+  }
+  void Mdag(const CoarseVector &in, CoarseVector &out)
+  {
+    this->M(in,out);
+  }
+  void M (const CoarseVector &in, CoarseVector &out)
+  {
+    //    std::cout << GridLogMessage << "New Mrhs coarse"<<std::endl;
+    conformable(CoarseGrid(),in.Grid());
+    conformable(in.Grid(),out.Grid());
+    out.Checkerboard() = in.Checkerboard();
+
+    RealD t_tot;
+    RealD t_exch;
+    RealD t_GtoB;
+    RealD t_BtoG;
+    RealD t_mult;
+
+    t_tot=-usecond();
+    CoarseVector tin=in;
+    t_exch=-usecond();
+    CoarseVector pin = Cell.ExchangePeriodic(tin); //padded input
+    t_exch+=usecond();
+
+    CoarseVector pout(pin.Grid());
+
+    int npoint = geom.npoint;
+    typedef calcMatrix* Aview;
+    typedef LatticeView<Cvec> Vview;
+      
+    const int Nsimd = CComplex::Nsimd();
+
+    int64_t nrhs  =pin.Grid()->GlobalDimensions()[0];
+    assert(nrhs>=1);
+
+    RealD flops,bytes;
+    int64_t osites=in.Grid()->oSites(); // unpadded
+    int64_t unpadded_vol = CoarseGrid()->lSites()/nrhs;
+    
+    flops = 1.0* npoint * nbasis * nbasis * 8.0 * osites * CComplex::Nsimd();
+    bytes = 1.0*osites*sizeof(siteMatrix)*npoint/pin.Grid()->GlobalDimensions()[0]
+          + 2.0*osites*sizeof(siteVector)*npoint;
+    
+
+    t_GtoB=-usecond();
+    GridtoBLAS(pin,BLAS_B);
+    t_GtoB+=usecond();
+
+    GridBLAS BLAS;
+
+    t_mult=-usecond();
+    for(int p=0;p<geom.npoint;p++){
+      RealD c = 1.0;
+      if (p==0) c = 0.0;
+      ComplexD beta(c);
+
+      BLAS.gemmBatched(nbasis,nrhs,nbasis,
+		       ComplexD(1.0),
+		       BLAS_AP[p], 
+		       BLAS_BP[p], 
+		       ComplexD(c), 
+		       BLAS_CP);
+    }
+    BLAS.synchronise();
+    t_mult+=usecond();
+
+    t_BtoG=-usecond();
+    BLAStoGrid(out,BLAS_C);
+    t_BtoG+=usecond();
+    t_tot+=usecond();
+    /*
+    std::cout << GridLogMessage << "New Mrhs coarse DONE "<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult exch "<<t_exch<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult mult "<<t_mult<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult GtoB  "<<t_GtoB<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult BtoG  "<<t_BtoG<<" us"<<std::endl;
+    std::cout << GridLogMessage<<"Coarse Mult tot  "<<t_tot<<" us"<<std::endl;
+    */
+    //    std::cout << GridLogMessage<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse Kernel flops "<< flops<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse Kernel flop/s "<< flops/t_mult<<" mflop/s"<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse Kernel bytes/s "<< bytes/t_mult/1000<<" GB/s"<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse overall flops/s "<< flops/t_tot<<" mflop/s"<<std::endl;
+    //    std::cout << GridLogMessage<<"Coarse total bytes   "<< bytes/1e6<<" MB"<<std::endl;
+  };
+  virtual  void Mdiag    (const Field &in, Field &out){ assert(0);};
+  virtual  void Mdir     (const Field &in, Field &out,int dir, int disp){assert(0);};
+  virtual  void MdirAll  (const Field &in, std::vector<Field> &out){assert(0);};
+};
+  
+NAMESPACE_END(Grid);

Grid/algorithms/multigrid/Geometry.h

@@ -0,0 +1,238 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/GeneralCoarsenedMatrix.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <pboyle@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+
+/////////////////////////////////////////////////////////////////
+// Geometry class in cartesian case
+/////////////////////////////////////////////////////////////////
+
+class Geometry {
+public:
+  int npoint;
+  int base;
+  std::vector<int> directions   ;
+  std::vector<int> displacements;
+  std::vector<int> points_dagger;
+
+  Geometry(int _d)  {
+    
+    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);
+    points_dagger.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;
+      points_dagger[d   ] = d+_d;
+      points_dagger[d+_d] = d;
+    }
+    directions   [2*_d]=0;
+    displacements[2*_d]=0;
+    points_dagger[2*_d]=2*_d;
+  }
+
+  int point(int dir, int disp) {
+    assert(disp == -1 || disp == 0 || disp == 1);
+    assert(base+0 <= dir && dir < base+4);
+
+    // directions faster index = new indexing
+    // 4d (base = 0):
+    // point 0  1  2  3  4  5  6  7  8
+    // dir   0  1  2  3  0  1  2  3  0
+    // disp +1 +1 +1 +1 -1 -1 -1 -1  0
+    // 5d (base = 1):
+    // point 0  1  2  3  4  5  6  7  8
+    // dir   1  2  3  4  1  2  3  4  0
+    // disp +1 +1 +1 +1 -1 -1 -1 -1  0
+
+    // displacements faster index = old indexing
+    // 4d (base = 0):
+    // point 0  1  2  3  4  5  6  7  8
+    // dir   0  0  1  1  2  2  3  3  0
+    // disp +1 -1 +1 -1 +1 -1 +1 -1  0
+    // 5d (base = 1):
+    // point 0  1  2  3  4  5  6  7  8
+    // dir   1  1  2  2  3  3  4  4  0
+    // disp +1 -1 +1 -1 +1 -1 +1 -1  0
+
+    if(dir == 0 and disp == 0)
+      return 8;
+    else // New indexing
+      return (1 - disp) / 2 * 4 + dir - base;
+    // else // Old indexing
+    //   return (4 * (dir - base) + 1 - disp) / 2;
+  }
+};
+
+/////////////////////////////////////////////////////////////////
+// Less local equivalent of Geometry class in cartesian case
+/////////////////////////////////////////////////////////////////
+class NonLocalStencilGeometry {
+public:
+  //  int depth;
+  int skip;
+  int hops;
+  int npoint;
+  std::vector<Coordinate> shifts;
+  Coordinate stencil_size;
+  Coordinate stencil_lo;
+  Coordinate stencil_hi;
+  GridCartesian *grid;
+  GridCartesian *Grid() {return grid;};
+  int Depth(void){return 1;};   // Ghost zone depth
+  int Hops(void){return hops;}; // # of hops=> level of corner fill in in stencil
+  int DimSkip(void){return skip;};
+
+  virtual ~NonLocalStencilGeometry() {};
+
+  int  Reverse(int point)
+  {
+    int Nd = Grid()->Nd();
+    Coordinate shft = shifts[point];
+    Coordinate rev(Nd);
+    for(int mu=0;mu<Nd;mu++) rev[mu]= -shft[mu];
+    for(int p=0;p<npoint;p++){
+      if(rev==shifts[p]){
+	return p;
+      }
+    }
+    assert(0);
+    return -1;
+  }
+  void BuildShifts(void)
+  {
+    this->shifts.resize(0);
+    int Nd = this->grid->Nd();
+
+    int dd = this->DimSkip();
+    for(int s0=this->stencil_lo[dd+0];s0<=this->stencil_hi[dd+0];s0++){
+    for(int s1=this->stencil_lo[dd+1];s1<=this->stencil_hi[dd+1];s1++){
+    for(int s2=this->stencil_lo[dd+2];s2<=this->stencil_hi[dd+2];s2++){
+    for(int s3=this->stencil_lo[dd+3];s3<=this->stencil_hi[dd+3];s3++){
+      Coordinate sft(Nd,0);
+      sft[dd+0] = s0;
+      sft[dd+1] = s1;
+      sft[dd+2] = s2;
+      sft[dd+3] = s3;
+      int nhops = abs(s0)+abs(s1)+abs(s2)+abs(s3);
+      if(nhops<=this->hops) this->shifts.push_back(sft);
+    }}}}
+    this->npoint = this->shifts.size();
+    std::cout << GridLogMessage << "NonLocalStencilGeometry has "<< this->npoint << " terms in stencil "<<std::endl;
+  }
+  
+  NonLocalStencilGeometry(GridCartesian *_coarse_grid,int _hops,int _skip) : grid(_coarse_grid), hops(_hops), skip(_skip)
+  {
+    Coordinate latt = grid->GlobalDimensions();
+    stencil_size.resize(grid->Nd());
+    stencil_lo.resize(grid->Nd());
+    stencil_hi.resize(grid->Nd());
+    for(int d=0;d<grid->Nd();d++){
+     if ( latt[d] == 1 ) {
+      stencil_lo[d] = 0;
+      stencil_hi[d] = 0;
+      stencil_size[d]= 1;
+     } else if ( latt[d] == 2 ) {
+      stencil_lo[d] = -1;
+      stencil_hi[d] = 0;
+      stencil_size[d]= 2;
+     } else if ( latt[d] > 2 ) {
+       stencil_lo[d] = -1;
+       stencil_hi[d] =  1;
+       stencil_size[d]= 3;
+     }
+    }
+    this->BuildShifts();
+  };
+
+};
+
+// Need to worry about red-black now
+class NonLocalStencilGeometry4D : public NonLocalStencilGeometry {
+public:
+  virtual int DerivedDimSkip(void) { return 0;};
+  NonLocalStencilGeometry4D(GridCartesian *Coarse,int _hops) : NonLocalStencilGeometry(Coarse,_hops,0) { };
+  virtual ~NonLocalStencilGeometry4D() {};
+};
+class NonLocalStencilGeometry5D : public NonLocalStencilGeometry {
+public:
+  virtual int DerivedDimSkip(void) { return 1; }; 
+  NonLocalStencilGeometry5D(GridCartesian *Coarse,int _hops) : NonLocalStencilGeometry(Coarse,_hops,1)  { };
+  virtual ~NonLocalStencilGeometry5D() {};
+};
+/*
+ * Bunch of different options classes
+ */
+class NextToNextToNextToNearestStencilGeometry4D : public NonLocalStencilGeometry4D {
+public:
+  NextToNextToNextToNearestStencilGeometry4D(GridCartesian *Coarse) :  NonLocalStencilGeometry4D(Coarse,4)
+  {
+  };
+};
+class NextToNextToNextToNearestStencilGeometry5D : public  NonLocalStencilGeometry5D {
+public:
+  NextToNextToNextToNearestStencilGeometry5D(GridCartesian *Coarse) :  NonLocalStencilGeometry5D(Coarse,4)
+  {
+  };
+};
+class NextToNearestStencilGeometry4D : public  NonLocalStencilGeometry4D {
+public:
+  NextToNearestStencilGeometry4D(GridCartesian *Coarse) :  NonLocalStencilGeometry4D(Coarse,2)
+  {
+  };
+};
+class NextToNearestStencilGeometry5D : public  NonLocalStencilGeometry5D {
+public:
+  NextToNearestStencilGeometry5D(GridCartesian *Coarse) :  NonLocalStencilGeometry5D(Coarse,2)
+  {
+  };
+};
+class NearestStencilGeometry4D : public  NonLocalStencilGeometry4D {
+public:
+  NearestStencilGeometry4D(GridCartesian *Coarse) :  NonLocalStencilGeometry4D(Coarse,1)
+  {
+  };
+};
+class NearestStencilGeometry5D : public  NonLocalStencilGeometry5D {
+public:
+  NearestStencilGeometry5D(GridCartesian *Coarse) :  NonLocalStencilGeometry5D(Coarse,1)
+  {
+  };
+};
+
+NAMESPACE_END(Grid);

Grid/algorithms/multigrid/MultiGrid.h

@@ -1,12 +1,12 @@
     /*************************************************************************************
 
-    Grid physics library, www.github.com/paboyle/Grid 
+    Grid physics library, www.github.com/paboyle/Grid
 
-    Source file: ./lib/algorithms/Preconditioner.h
+    Source file: Grid/algorithms/multigrid/MultiGrid.h
 
-    Copyright (C) 2015
+    Copyright (C) 2023
 
-Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <pboyle@bnl.gov>
 
     This program is free software; you can redistribute it and/or modify
     it under the terms of the GNU General Public License as published by
@@ -25,22 +25,10 @@ Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
     See the full license in the file "LICENSE" in the top level distribution directory
     *************************************************************************************/
     /*  END LEGAL */
-#ifndef GRID_PRECONDITIONER_H
-#define GRID_PRECONDITIONER_H
+#pragma once
 
-namespace Grid {
-
-  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){};
-  };
-
-}
-#endif
+#include <Grid/algorithms/multigrid/Aggregates.h>
+#include <Grid/algorithms/multigrid/Geometry.h>
+#include <Grid/algorithms/multigrid/CoarsenedMatrix.h>
+#include <Grid/algorithms/multigrid/GeneralCoarsenedMatrix.h>
+#include <Grid/algorithms/multigrid/GeneralCoarsenedMatrixMultiRHS.h>

Grid/allocator/AlignedAllocator.h

@@ -0,0 +1,231 @@
+/*************************************************************************************
+
+    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
+////////////////////////////////////////////////////////////////////////////////
+#ifdef ACCELERATOR_CSHIFT
+// Cshift on device
+template<class T> using cshiftAllocator = devAllocator<T>;
+#else
+// Cshift on host
+template<class T> using cshiftAllocator = std::allocator<T>;
+#endif
+
+template<class T> using Vector        = std::vector<T,uvmAllocator<T> >;           
+template<class T> using stencilVector = std::vector<T,alignedAllocator<T> >;           
+template<class T> using commVector    = std::vector<T,devAllocator<T> >;
+template<class T> using deviceVector  = std::vector<T,devAllocator<T> >;
+template<class T> using cshiftVector  = std::vector<T,cshiftAllocator<T> >;
+
+/*
+template<class T> class vecView
+{
+ protected:
+  T * data;
+  uint64_t size;
+  ViewMode mode;
+  void * cpu_ptr;
+ public:
+  accelerator_inline T & operator[](size_t i) const { return this->data[i]; };
+  vecView(std::vector<T> &refer_to_me,ViewMode _mode)
+  {
+    cpu_ptr = &refer_to_me[0];
+    size = refer_to_me.size();
+    mode = _mode;
+    data =(T *) MemoryManager::ViewOpen(cpu_ptr,
+					size*sizeof(T),
+					mode,
+					AdviseDefault);
+  }
+  void ViewClose(void)
+  { // Inform the manager
+    MemoryManager::ViewClose(this->cpu_ptr,this->mode);    
+  }
+};
+
+template<class T> vecView<T> VectorView(std::vector<T> &vec,ViewMode _mode)
+{
+  vecView<T> ret(vec,_mode); // does the open
+  return ret;                // must be closed
+}
+
+// Little autoscope assister
+template<class View> 
+class VectorViewCloser
+{
+  View v;  // Take a copy of view and call view close when I go out of scope automatically
+ public:
+  VectorViewCloser(View &_v) : v(_v) {};
+  ~VectorViewCloser() { auto ptr = v.cpu_ptr; v.ViewClose();  MemoryManager::NotifyDeletion(ptr);}
+};
+
+#define autoVecView(v_v,v,mode)					\
+  auto v_v = VectorView(v,mode);				\
+  ViewCloser<decltype(v_v)> _autoView##v_v(v_v);
+*/
+
+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 +1,324 @@
+#include <Grid/GridCore.h>
+
+NAMESPACE_BEGIN(Grid);
+
+/*Allocation types, saying which pointer cache should be used*/
+#define Cpu      (0)
+#define CpuHuge  (1)
+#define CpuSmall (2)
+#define Acc      (3)
+#define AccHuge  (4)
+#define AccSmall (5)
+#define Shared   (6)
+#define SharedHuge  (7)
+#define SharedSmall (8)
+#undef GRID_MM_VERBOSE 
+uint64_t total_shared;
+uint64_t total_device;
+uint64_t total_host;;
+void MemoryManager::PrintBytes(void)
+{
+  std::cout << " MemoryManager : ------------------------------------ "<<std::endl;
+  std::cout << " MemoryManager : PrintBytes "<<std::endl;
+  std::cout << " MemoryManager : ------------------------------------ "<<std::endl;
+  std::cout << " MemoryManager : "<<(total_shared>>20)<<" shared      Mbytes "<<std::endl;
+  std::cout << " MemoryManager : "<<(total_device>>20)<<" accelerator Mbytes "<<std::endl;
+  std::cout << " MemoryManager : "<<(total_host>>20)  <<" cpu         Mbytes "<<std::endl;
+  uint64_t cacheBytes;
+  cacheBytes = CacheBytes[Cpu];
+  std::cout << " MemoryManager : "<<(cacheBytes>>20) <<" cpu cache Mbytes "<<std::endl;
+  cacheBytes = CacheBytes[Acc];
+  std::cout << " MemoryManager : "<<(cacheBytes>>20) <<" acc cache Mbytes "<<std::endl;
+  cacheBytes = CacheBytes[Shared];
+  std::cout << " MemoryManager : "<<(cacheBytes>>20) <<" shared cache Mbytes "<<std::endl;
+  
+#ifdef GRID_CUDA
+  cuda_mem();
+#endif
+  
+}
+
+uint64_t MemoryManager::DeviceCacheBytes() { return CacheBytes[Acc] + CacheBytes[AccHuge] + CacheBytes[AccSmall]; }
+uint64_t MemoryManager::HostCacheBytes()   { return CacheBytes[Cpu] + CacheBytes[CpuHuge] + CacheBytes[CpuSmall]; }
+
+//////////////////////////////////////////////////////////////////////
+// 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] = { 2, 0, 8, 8, 0, 16, 8, 0, 16 };
+uint64_t MemoryManager::CacheBytes[MemoryManager::NallocType];
+//////////////////////////////////////////////////////////////////////
+// Actual allocation and deallocation utils
+//////////////////////////////////////////////////////////////////////
+void *MemoryManager::AcceleratorAllocate(size_t bytes)
+{
+  total_device+=bytes;
+  void *ptr = (void *) Lookup(bytes,Acc);
+  if ( ptr == (void *) NULL ) {
+    ptr = (void *) acceleratorAllocDevice(bytes);
+  }
+#ifdef GRID_MM_VERBOSE
+  std::cout <<"AcceleratorAllocate "<<std::endl;
+  PrintBytes();
+#endif
+  return ptr;
+}
+void  MemoryManager::AcceleratorFree    (void *ptr,size_t bytes)
+{
+  total_device-=bytes;
+  void *__freeme = Insert(ptr,bytes,Acc);
+  if ( __freeme ) {
+    acceleratorFreeDevice(__freeme);
+  }
+#ifdef GRID_MM_VERBOSE
+  std::cout <<"AcceleratorFree "<<std::endl;
+  PrintBytes();
+#endif
+}
+void *MemoryManager::SharedAllocate(size_t bytes)
+{
+  total_shared+=bytes;
+  void *ptr = (void *) Lookup(bytes,Shared);
+  if ( ptr == (void *) NULL ) {
+    ptr = (void *) acceleratorAllocShared(bytes);
+  }
+#ifdef GRID_MM_VERBOSE
+  std::cout <<"SharedAllocate "<<std::endl;
+  PrintBytes();
+#endif
+  return ptr;
+}
+void  MemoryManager::SharedFree    (void *ptr,size_t bytes)
+{
+  total_shared-=bytes;
+  void *__freeme = Insert(ptr,bytes,Shared);
+  if ( __freeme ) {
+    acceleratorFreeShared(__freeme);
+  }
+#ifdef GRID_MM_VERBOSE
+  std::cout <<"SharedFree "<<std::endl;
+  PrintBytes();
+#endif
+}
+#ifdef GRID_UVM
+void *MemoryManager::CpuAllocate(size_t bytes)
+{
+  total_host+=bytes;
+  void *ptr = (void *) Lookup(bytes,Cpu);
+  if ( ptr == (void *) NULL ) {
+    ptr = (void *) acceleratorAllocShared(bytes);
+  }
+#ifdef GRID_MM_VERBOSE
+  std::cout <<"CpuAllocate "<<std::endl;
+  PrintBytes();
+#endif
+  return ptr;
+}
+void  MemoryManager::CpuFree    (void *_ptr,size_t bytes)
+{
+  total_host-=bytes;
+  NotifyDeletion(_ptr);
+  void *__freeme = Insert(_ptr,bytes,Cpu);
+  if ( __freeme ) { 
+    acceleratorFreeShared(__freeme);
+  }
+#ifdef GRID_MM_VERBOSE
+  std::cout <<"CpuFree "<<std::endl;
+  PrintBytes();
+#endif
+}
+#else
+void *MemoryManager::CpuAllocate(size_t bytes)
+{
+  total_host+=bytes;
+  void *ptr = (void *) Lookup(bytes,Cpu);
+  if ( ptr == (void *) NULL ) {
+    ptr = (void *) acceleratorAllocCpu(bytes);
+  }
+#ifdef GRID_MM_VERBOSE
+  std::cout <<"CpuAllocate "<<std::endl;
+  PrintBytes();
+#endif
+  return ptr;
+}
+void  MemoryManager::CpuFree    (void *_ptr,size_t bytes)
+{
+  total_host-=bytes;
+  NotifyDeletion(_ptr);
+  void *__freeme = Insert(_ptr,bytes,Cpu);
+  if ( __freeme ) { 
+    acceleratorFreeCpu(__freeme);
+  }
+#ifdef GRID_MM_VERBOSE
+  std::cout <<"CpuFree "<<std::endl;
+  PrintBytes();
+#endif
+}
+#endif
+
+//////////////////////////////////////////
+// call only once
+//////////////////////////////////////////
+void MemoryManager::Init(void)
+{
+
+  char * str;
+  int Nc;
+  
+  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_HUGE");
+  if ( str ) {
+    Nc = atoi(str);
+    if ( (Nc>=0) && (Nc < NallocCacheMax)) {
+      Ncache[CpuHuge]=Nc;
+      Ncache[AccHuge]=Nc;
+      Ncache[SharedHuge]=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 host   allocations: SMALL "<<Ncache[CpuSmall]<<" LARGE "<<Ncache[Cpu]<<" HUGE "<<Ncache[CpuHuge]<<std::endl;
+  std::cout << GridLogMessage<< "MemoryManager::Init() cache pool for recent device allocations: SMALL "<<Ncache[AccSmall]<<" LARGE "<<Ncache[Acc]<<" Huge "<<Ncache[AccHuge]<<std::endl;
+  std::cout << GridLogMessage<< "MemoryManager::Init() cache pool for recent shared allocations: SMALL "<<Ncache[SharedSmall]<<" LARGE "<<Ncache[Shared]<<" Huge "<<Ncache[SharedHuge]<<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
+  int cache;
+  if      (bytes < GRID_ALLOC_SMALL_LIMIT) cache = type + 2;
+  else if (bytes >= GRID_ALLOC_HUGE_LIMIT) cache = type + 1;
+  else                                     cache = type;
+
+  return Insert(ptr,bytes,Entries[cache],Ncache[cache],Victim[cache],CacheBytes[cache]);  
+#else
+  return ptr;
+#endif
+}
+
+void *MemoryManager::Insert(void *ptr,size_t bytes,AllocationCacheEntry *entries,int ncache,int &victim, uint64_t &cacheBytes) 
+{
+#ifdef GRID_OMP
+  assert(omp_in_parallel()==0);
+#endif 
+
+  if (ncache == 0) return ptr;
+
+  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;
+    cacheBytes -= entries[v].bytes;
+    entries[v].valid = 0;
+    entries[v].address = NULL;
+    entries[v].bytes = 0;
+  }
+
+  entries[v].address=ptr;
+  entries[v].bytes  =bytes;
+  entries[v].valid  =1;
+  cacheBytes += bytes;
+
+  return ret;
+}
+
+void *MemoryManager::Lookup(size_t bytes,int type)
+{
+#ifdef ALLOCATION_CACHE
+  int cache;
+  if      (bytes < GRID_ALLOC_SMALL_LIMIT) cache = type + 2;
+  else if (bytes >= GRID_ALLOC_HUGE_LIMIT) cache = type + 1;
+  else                                     cache = type;
+
+  return Lookup(bytes,Entries[cache],Ncache[cache],CacheBytes[cache]);
+#else
+  return NULL;
+#endif
+}
+
+void *MemoryManager::Lookup(size_t bytes,AllocationCacheEntry *entries,int ncache,uint64_t & cacheBytes) 
+{
+#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;
+      cacheBytes -= entries[e].bytes;
+      return entries[e].address;
+    }
+  }
+  return NULL;
+}
+
+
+NAMESPACE_END(Grid);
+

Grid/allocator/MemoryManager.h

@@ -0,0 +1,226 @@
+/*************************************************************************************
+
+    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 GRID_ALLOC_SMALL_LIMIT (4096)
+#define GRID_ALLOC_HUGE_LIMIT  (2147483648)
+
+#define STRINGIFY(x) #x
+#define TOSTRING(x) STRINGIFY(x)
+#define FILE_LINE __FILE__ ":" TOSTRING(__LINE__)
+#define AUDIT(a) MemoryManager::Audit(FILE_LINE)
+
+/*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
+};
+
+struct MemoryStatus {
+  uint64_t     DeviceBytes;
+  uint64_t     DeviceLRUBytes;
+  uint64_t     DeviceMaxBytes;
+  uint64_t     HostToDeviceBytes;
+  uint64_t     DeviceToHostBytes;
+  uint64_t     HostToDeviceXfer;
+  uint64_t     DeviceToHostXfer;
+  uint64_t     DeviceEvictions;
+  uint64_t     DeviceDestroy;
+  uint64_t     DeviceAllocCacheBytes;
+  uint64_t     HostAllocCacheBytes;
+};
+
+
+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=9;
+  static AllocationCacheEntry Entries[NallocType][NallocCacheMax];
+  static int Victim[NallocType];
+  static int Ncache[NallocType];
+  static uint64_t CacheBytes[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,uint64_t &cbytes) ;
+  static void *Lookup(size_t bytes,AllocationCacheEntry *entries,int ncache,uint64_t &cbytes) ;
+
+ public:
+  static void PrintBytes(void);
+  static void Audit(std::string s);
+  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;
+  static uint64_t     DeviceEvictions;
+  static uint64_t     DeviceDestroy;
+  
+  static uint64_t     DeviceCacheBytes();
+  static uint64_t     HostCacheBytes();
+
+  static MemoryStatus GetFootprint(void) {
+    MemoryStatus stat;
+    stat.DeviceBytes       = DeviceBytes;
+    stat.DeviceLRUBytes    = DeviceLRUBytes;
+    stat.DeviceMaxBytes    = DeviceMaxBytes;
+    stat.HostToDeviceBytes = HostToDeviceBytes;
+    stat.DeviceToHostBytes = DeviceToHostBytes;
+    stat.HostToDeviceXfer  = HostToDeviceXfer;
+    stat.DeviceToHostXfer  = DeviceToHostXfer;
+    stat.DeviceEvictions   = DeviceEvictions;
+    stat.DeviceDestroy     = DeviceDestroy;
+    stat.DeviceAllocCacheBytes = DeviceCacheBytes();
+    stat.HostAllocCacheBytes   = HostCacheBytes();
+    return stat;
+  };
+  
+ 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
+
+ public:
+  static void NotifyDeletion(void * CpuPtr);
+  static void Print(void);
+  static void PrintAll(void);
+  static void PrintState( void* CpuPtr);
+  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 +1,602 @@
+#include <Grid/GridCore.h>
+#ifndef GRID_UVM
+
+#warning "Using explicit device memory copies"
+NAMESPACE_BEGIN(Grid);
+
+#define MAXLINE 512
+static char print_buffer [ MAXLINE ];
+
+#define mprintf(...) snprintf (print_buffer,MAXLINE, __VA_ARGS__ ); std::cout << GridLogMemory << print_buffer;
+#define dprintf(...) snprintf (print_buffer,MAXLINE, __VA_ARGS__ ); std::cout << GridLogDebug << print_buffer;
+//#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;
+uint64_t  MemoryManager::DeviceEvictions;
+uint64_t  MemoryManager::DeviceDestroy;
+
+////////////////////////////////////
+// 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(%lx) %lx\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);
+    DeviceDestroy++;
+    DeviceBytes   -=AccCache.bytes;
+    LRUremove(AccCache);
+    AccCache.AccPtr=(uint64_t) NULL;
+    dprintf("MemoryManager: Free(%lx) LRU %ld Total %ld\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 from LRU, LEAVE CPU only entry
+  // Cannot be acclocked. If allocated must be in LRU pool.
+  //
+  // Nov 2022... Felix issue: Allocating two CpuPtrs, can have an entry in LRU-q with CPUlock.
+  //                          and require to evict the AccPtr copy. Eviction was a mistake in CpuViewOpen
+  //                          but there is a weakness where CpuLock entries are attempted for erase
+  //                          Take these OUT LRU queue when CPU locked?
+  //                          Cannot take out the table as cpuLock data is important.
+  ///////////////////////////////////////////////////////////////////////////
+  assert(AccCache.state!=Empty);
+  
+  mprintf("MemoryManager: Evict CpuPtr %lx AccPtr %lx cpuLock %ld accLock %ld\n",
+	  (uint64_t)AccCache.CpuPtr,(uint64_t)AccCache.AccPtr,
+	  (uint64_t)AccCache.cpuLock,(uint64_t)AccCache.accLock); 
+  if (AccCache.accLock!=0) return;
+  if (AccCache.cpuLock!=0) return;
+  if(AccCache.state==AccDirty) {
+    Flush(AccCache);
+  }
+  if(AccCache.AccPtr) {
+    AcceleratorFree((void *)AccCache.AccPtr,AccCache.bytes);
+    LRUremove(AccCache);
+    AccCache.AccPtr=(uint64_t)NULL;
+    AccCache.state=CpuDirty; // CPU primary now
+    DeviceBytes   -=AccCache.bytes;
+    dprintf("MemoryManager: Free(AccPtr %lx) footprint now %ld \n",(uint64_t)AccCache.AccPtr,DeviceBytes);  
+  }
+  //  uint64_t CpuPtr = AccCache.CpuPtr;
+  DeviceEvictions++;
+  //  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);
+  mprintf("MemoryManager: acceleratorCopyFromDevice Flush AccPtr %lx -> CpuPtr %lx\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;
+  }
+  mprintf("MemoryManager: acceleratorCopyToDevice   Clone AccPtr %lx <- CpuPtr %lx\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) ){
+    dprintf("AcceleratorViewClose %lx\n",(uint64_t)Ptr);
+    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) ){
+    dprintf("AcceleratorViewOpen %lx\n",(uint64_t)CpuPtr);
+    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)
+{
+  assert(bytes<DeviceMaxBytes);
+  while(bytes+DeviceLRUBytes > DeviceMaxBytes){
+    if ( DeviceLRUBytes > 0){
+      assert(LRU.size()>0);
+      uint64_t victim = LRU.back(); // From the LRU
+      auto AccCacheIterator = EntryLookup(victim);
+      auto & AccCache = AccCacheIterator->second;
+      Evict(AccCache);
+    } else {
+      return;
+    }
+  }
+}
+uint64_t MemoryManager::AcceleratorViewOpen(uint64_t CpuPtr,size_t bytes,ViewMode mode,ViewAdvise hint)
+{
+  ////////////////////////////////////////////////////////////////////////////
+  // Find if present, otherwise get or force an empty
+  ////////////////////////////////////////////////////////////////////////////
+  if ( EntryPresent(CpuPtr)==0 ){
+    EntryCreate(CpuPtr,bytes,mode,hint);
+  }
+
+  auto AccCacheIterator = EntryLookup(CpuPtr);
+  auto & AccCache = AccCacheIterator->second;
+  if (!AccCache.AccPtr) {
+    EvictVictims(bytes); 
+  } 
+  assert((mode==AcceleratorRead)||(mode==AcceleratorWrite)||(mode==AcceleratorWriteDiscard));
+
+  assert(AccCache.cpuLock==0);  // Programming error
+
+  if(AccCache.state!=Empty) {
+    dprintf("ViewOpen found entry %lx %lx : %ld %ld accLock %ld\n",
+		    (uint64_t)AccCache.CpuPtr,
+		    (uint64_t)CpuPtr,
+		    (uint64_t)AccCache.bytes,
+	            (uint64_t)bytes,
+		    (uint64_t)AccCache.accLock);
+    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;
+    dprintf("Copied Empty entry into device accLock= %d\n",AccCache.accLock);
+  } 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++;
+    dprintf("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++;
+    dprintf("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++;
+    dprintf("AccDirty entry ++accLock= %d\n",AccCache.accLock);
+  } else {
+    assert(0);
+  }
+
+  assert(AccCache.accLock>0);
+  // If view is opened on device must remove from LRU
+  if(AccCache.LRU_valid==1){
+    // must possibly remove from LRU as now locked on GPU
+    dprintf("AccCache entry removed from LRU \n");
+    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) {
+    dprintf("AccleratorViewClose %lx AccLock decremented to %ld move to LRU queue\n",(uint64_t)CpuPtr,(uint64_t)AccCache.accLock);
+    LRUinsert(AccCache);
+  } else {
+    dprintf("AccleratorViewClose %lx AccLock decremented to %ld\n",(uint64_t)CpuPtr,(uint64_t)AccCache.accLock);
+  }
+}
+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 ){
+    EntryCreate(CpuPtr,bytes,mode,transient);
+  }
+
+  auto AccCacheIterator = EntryLookup(CpuPtr);
+  auto & AccCache = AccCacheIterator->second;
+
+  // CPU doesn't need to free space
+  //  if (!AccCache.AccPtr) {
+  //    EvictVictims(bytes);
+  //  }
+
+  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)
+{
+  PrintBytes();
+  std::cout << GridLogMessage << "--------------------------------------------" << std::endl;
+  std::cout << GridLogMessage << "Memory Manager                             " << std::endl;
+  std::cout << GridLogMessage << "--------------------------------------------" << std::endl;
+  std::cout << GridLogMessage << DeviceBytes   << " bytes allocated on device " << std::endl;
+  std::cout << GridLogMessage << DeviceLRUBytes<< " bytes evictable on device " << std::endl;
+  std::cout << GridLogMessage << DeviceMaxBytes<< " bytes max on device       " << std::endl;
+  std::cout << GridLogMessage << HostToDeviceXfer << " transfers        to   device " << std::endl;
+  std::cout << GridLogMessage << DeviceToHostXfer << " transfers        from device " << std::endl;
+  std::cout << GridLogMessage << HostToDeviceBytes<< " bytes transfered to   device " << std::endl;
+  std::cout << GridLogMessage << DeviceToHostBytes<< " bytes transfered from device " << std::endl;
+  std::cout << GridLogMessage << DeviceEvictions  << " Evictions from device " << std::endl;
+  std::cout << GridLogMessage << DeviceDestroy    << " Destroyed vectors on device " << std::endl;
+  std::cout << GridLogMessage << AccViewTable.size()<< " vectors " << LRU.size()<<" evictable"<< std::endl;
+  acceleratorMem();
+  std::cout << GridLogMessage << "--------------------------------------------" << std::endl;
+}
+void  MemoryManager::PrintAll(void)
+{
+  Print();
+  std::cout << GridLogMessage << std::endl;
+  std::cout << GridLogMessage << "--------------------------------------------" << std::endl;
+  std::cout << GridLogMessage << "CpuAddr\t\tAccAddr\t\tState\t\tcpuLock\taccLock\tLRU_valid "<<std::endl;
+  std::cout << GridLogMessage << "--------------------------------------------" << 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 << GridLogMessage << "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 << GridLogMessage << "--------------------------------------------" << 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;
+  }
+}
+void MemoryManager::Audit(std::string s)
+{
+  uint64_t CpuBytes=0;
+  uint64_t AccBytes=0;
+  uint64_t LruBytes1=0;
+  uint64_t LruBytes2=0;
+  uint64_t LruCnt=0;
+  
+  std::cout << " Memory Manager::Audit() from "<<s<<std::endl;
+  for(auto it=LRU.begin();it!=LRU.end();it++){
+    uint64_t cpuPtr = *it;
+    assert(EntryPresent(cpuPtr));
+    auto AccCacheIterator = EntryLookup(cpuPtr);
+    auto & AccCache = AccCacheIterator->second;
+    LruBytes2+=AccCache.bytes;
+    assert(AccCache.LRU_valid==1);
+    assert(AccCache.LRU_entry==it);
+  }
+  std::cout << " Memory Manager::Audit() LRU queue matches table entries "<<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");
+
+    CpuBytes+=AccCache.bytes;
+    if( AccCache.AccPtr )    AccBytes+=AccCache.bytes;
+    if( AccCache.LRU_valid ) LruBytes1+=AccCache.bytes;
+    if( AccCache.LRU_valid ) LruCnt++;
+    
+    if ( AccCache.cpuLock || AccCache.accLock ) {
+      assert(AccCache.LRU_valid==0);
+
+      std::cout << GridLogError << s<< "\n\t 0x"<<std::hex<<AccCache.CpuPtr<<std::dec
+		<< "\t0x"<<std::hex<<AccCache.AccPtr<<std::dec<<"\t" <<str
+		<< "\t cpuLock  " << AccCache.cpuLock
+		<< "\t accLock  " << AccCache.accLock
+		<< "\t LRUvalid " << AccCache.LRU_valid<<std::endl;
+    }
+
+    assert( AccCache.cpuLock== 0 ) ;
+    assert( AccCache.accLock== 0 ) ;
+  }
+  std::cout << " Memory Manager::Audit() no locked table entries "<<std::endl;
+  assert(LruBytes1==LruBytes2);
+  assert(LruBytes1==DeviceLRUBytes);
+  std::cout << " Memory Manager::Audit() evictable bytes matches sum over table "<<std::endl;
+  assert(AccBytes==DeviceBytes);
+  std::cout << " Memory Manager::Audit() device bytes matches sum over table "<<std::endl;
+  assert(LruCnt == LRU.size());
+  std::cout << " Memory Manager::Audit() LRU entry count matches "<<std::endl;
+
+}
+
+void MemoryManager::PrintState(void* _CpuPtr)
+{
+  uint64_t CpuPtr = (uint64_t)_CpuPtr;
+
+  if ( EntryPresent(CpuPtr) ){
+    auto AccCacheIterator = EntryLookup(CpuPtr);
+    auto & AccCache = AccCacheIterator->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");
+    if ( AccCache.state==EvictNext) str = std::string("EvictNext");
+
+    std::cout << GridLogMessage << "CpuAddr\t\tAccAddr\t\tState\t\tcpuLock\taccLock\tLRU_valid "<<std::endl;
+    std::cout << GridLogMessage << "\tx"<<std::hex<<AccCache.CpuPtr<<std::dec
+    << "\tx"<<std::hex<<AccCache.AccPtr<<std::dec<<"\t" <<str
+    << "\t" << AccCache.cpuLock
+    << "\t" << AccCache.accLock
+    << "\t" << AccCache.LRU_valid<<std::endl;
+
+  } else {
+    std::cout << GridLogMessage << "No Entry in AccCache table." << std::endl; 
+  }
+}
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/allocator/MemoryManagerShared.cc

@@ -0,0 +1,31 @@
+#include <Grid/GridCore.h>
+#ifdef GRID_UVM
+
+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;
+uint64_t  MemoryManager::DeviceEvictions;
+uint64_t  MemoryManager::DeviceDestroy;
+
+void  MemoryManager::Audit(std::string s){};
+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::PrintState(void* CpuPtr)
+{
+std::cout << GridLogMessage << "Host<->Device memory movement not currently managed by Grid." << std::endl;
+};
+void  MemoryManager::Print(void){};
+void  MemoryManager::PrintAll(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;
+  int64_t _fsites;                  // _isites*_osites = product(dimensions).
+  int64_t _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 int64_t gSites(void) const { return (int64_t)_isites*(int64_t)_osites*(int64_t)_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(int64_t 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,int64_t & 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,const Coordinate &rdim,const 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 +23,13 @@ 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>
 
 #endif

Grid/communicator/Communicator_base.cc

@@ -0,0 +1,79 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/communicator/Communicator_none.cc
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#include <Grid/GridCore.h>
+#include <fcntl.h>
+#include <unistd.h>
+#include <limits.h>
+#include <sys/mman.h>
+
+NAMESPACE_BEGIN(Grid);
+
+bool Stencil_force_mpi = true;
+
+///////////////////////////////////////////////////////////////
+// Info that is setup once and indept of cartesian layout
+///////////////////////////////////////////////////////////////
+CartesianCommunicator::CommunicatorPolicy_t  
+CartesianCommunicator::CommunicatorPolicy= CartesianCommunicator::CommunicatorPolicyConcurrent;
+int CartesianCommunicator::nCommThreads = -1;
+
+/////////////////////////////////
+// Grid information queries
+/////////////////////////////////
+int                      CartesianCommunicator::Dimensions(void)        { return _ndimension; };
+int                      CartesianCommunicator::IsBoss(void)            { return _processor==0; };
+int                      CartesianCommunicator::BossRank(void)          { return 0; };
+int                      CartesianCommunicator::ThisRank(void)          { return _processor; };
+const Coordinate & CartesianCommunicator::ThisProcessorCoor(void) { return _processor_coor; };
+const Coordinate & CartesianCommunicator::ProcessorGrid(void)     { return _processors; };
+int                      CartesianCommunicator::ProcessorCount(void)    { return _Nprocessors; };
+
+////////////////////////////////////////////////////////////////////////////////
+// very VERY rarely (Log, serial RNG) we need world without a grid
+////////////////////////////////////////////////////////////////////////////////
+
+void CartesianCommunicator::GlobalSum(ComplexF &c)
+{
+  GlobalSumVector((float *)&c,2);
+}
+void CartesianCommunicator::GlobalSumVector(ComplexF *c,int N)
+{
+  GlobalSumVector((float *)c,2*N);
+}
+void CartesianCommunicator::GlobalSum(ComplexD &c)
+{
+  GlobalSumVector((double *)&c,2);
+}
+void CartesianCommunicator::GlobalSumVector(ComplexD *c,int N)
+{
+  GlobalSumVector((double *)c,2*N);
+}
+  
+NAMESPACE_END(Grid);
+
+

Grid/communicator/Communicator_base.h

@@ -1,5 +1,4 @@
-
-    /*************************************************************************************
+/*************************************************************************************
 
     Grid physics library, www.github.com/paboyle/Grid 
 
@@ -24,197 +23,150 @@ 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
 
 ///////////////////////////////////
 // Processor layout information
 ///////////////////////////////////
-#ifdef GRID_COMMS_MPI
-#include <mpi.h>
-#endif
-#ifdef GRID_COMMS_MPI3
-#include <mpi.h>
-#endif
-#ifdef GRID_COMMS_MPI3L
-#include <mpi.h>
-#endif
-#ifdef GRID_COMMS_SHMEM
-#include <mpp/shmem.h>
-#endif
+#include <Grid/communicator/SharedMemory.h>
 
-namespace Grid {
+NAMESPACE_BEGIN(Grid);
 
-class CartesianCommunicator {
-  public:    
+extern bool Stencil_force_mpi ;
 
-  // 65536 ranks per node adequate for now
-  // 128MB shared memory for comms enought for 48^4 local vol comms
-  // Give external control (command line override?) of this
+class CartesianCommunicator : public SharedMemory {
 
-  static const int      MAXLOG2RANKSPERNODE = 16;            
-  static uint64_t MAX_MPI_SHM_BYTES;
+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.
-  int              _processor;       // linear processor rank
-  std::vector<int> _processor_coor;  // linear processor coordinate
-  unsigned long _ndimension;
-
-#if defined (GRID_COMMS_MPI) || defined (GRID_COMMS_MPI3) || defined (GRID_COMMS_MPI3L)
-  static MPI_Comm communicator_world;
-         MPI_Comm communicator;
-  typedef MPI_Request CommsRequest_t;
-#else 
-  typedef int CommsRequest_t;
-#endif
-
-  ////////////////////////////////////////////////////////////////////
-  // Helper functionality for SHM Windows common to all other impls
-  ////////////////////////////////////////////////////////////////////
-  // Longer term; drop this in favour of a master / slave model with 
-  // cartesian communicator on a subset of ranks, slave ranks controlled
-  // by group leader with data xfer via shared memory
-  ////////////////////////////////////////////////////////////////////
-#ifdef GRID_COMMS_MPI3
-
-  static int ShmRank;
-  static int ShmSize;
-  static int GroupRank;
-  static int GroupSize;
-  static int WorldRank;
-  static int WorldSize;
-
-  std::vector<int>  WorldDims;
-  std::vector<int>  GroupDims;
-  std::vector<int>  ShmDims;
-  
-  std::vector<int> GroupCoor;
-  std::vector<int> ShmCoor;
-  std::vector<int> WorldCoor;
-
-  static std::vector<int> GroupRanks; 
-  static std::vector<int> MyGroup;
-  static int ShmSetup;
-  static MPI_Win ShmWindow; 
-  static MPI_Comm ShmComm;
-  
-  std::vector<int>  LexicographicToWorldRank;
-  
-  static std::vector<void *> ShmCommBufs;
-
-#else 
-  static void ShmInitGeneric(void);
-  static commVector<uint8_t> ShmBufStorageVector;
-#endif 
-
-  /////////////////////////////////
-  // Grid information and queries
-  // Implemented in Communicator_base.C
-  /////////////////////////////////
-  static void * ShmCommBuf;
-
-  // Isend/Irecv/Wait, or Sendrecv blocking
+  ////////////////////////////////////////////
+  // Policies
+  ////////////////////////////////////////////
   enum CommunicatorPolicy_t { CommunicatorPolicyConcurrent, CommunicatorPolicySequential };
   static CommunicatorPolicy_t CommunicatorPolicy;
   static void SetCommunicatorPolicy(CommunicatorPolicy_t policy ) { CommunicatorPolicy = policy; }
+  static int       nCommThreads;
 
-  size_t heap_top;
-  size_t heap_bytes;
-
-  void *ShmBufferSelf(void);
-  void *ShmBuffer(int rank);
-  void *ShmBufferTranslate(int rank,void * local_p);
-  void *ShmBufferMalloc(size_t bytes);
-  void ShmBufferFreeAll(void) ;
+  ////////////////////////////////////////////
+  // Communicator should know nothing of the physics grid, only processor grid.
+  ////////////////////////////////////////////
+  int              _Nprocessors;     // How many in all
+  int              _processor;       // linear processor rank
+  unsigned long    _ndimension;
+  Coordinate _shm_processors;  // Which dimensions get relayed out over processors lanes.
+  Coordinate _processors;      // Which dimensions get relayed out over processors lanes.
+  Coordinate _processor_coor;  // linear processor coordinate
+  static Grid_MPI_Comm      communicator_world;
+  Grid_MPI_Comm             communicator;
+  std::vector<Grid_MPI_Comm> communicator_halo;
   
   ////////////////////////////////////////////////
   // Must call in Grid startup
   ////////////////////////////////////////////////
   static void Init(int *argc, char ***argv);
+
+  ////////////////////////////////////////////////
+  // Constructors to sub-divide a parent communicator
+  // and default to comm world
+  ////////////////////////////////////////////////
+  CartesianCommunicator(const Coordinate &processors,const CartesianCommunicator &parent,int &srank);
+  CartesianCommunicator(const Coordinate &pdimensions_in);
+  virtual ~CartesianCommunicator();
+
+private:
+
+  ////////////////////////////////////////////////
+  // Private initialise from an MPI communicator
+  // Can use after an MPI_Comm_split, but hidden from user so private
+  ////////////////////////////////////////////////
+  void InitFromMPICommunicator(const Coordinate &processors, Grid_MPI_Comm communicator_base);
+
+public:
   
-  ////////////////////////////////////////////////
-  // Constructor of any given grid
-  ////////////////////////////////////////////////
-  CartesianCommunicator(const std::vector<int> &pdimensions_in);
   
   ////////////////////////////////////////////////////////////////////////////////////////
   // 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)     ;
-  int                      ProcessorCount(void)    ;
-  int                      NodeCount(void)    ;
+  const Coordinate & ThisProcessorCoor(void) ;
+  const Coordinate & ShmGrid(void)  { return _shm_processors; }  ;
+  const Coordinate & ProcessorGrid(void)     ;
+  int                ProcessorCount(void)    ;
 
   ////////////////////////////////////////////////////////////////////////////////
   // very VERY rarely (Log, serial RNG) we need world without a grid
   ////////////////////////////////////////////////////////////////////////////////
   static int  RankWorld(void) ;
   static void BroadcastWorld(int root,void* data, int bytes);
+  static void BarrierWorld(void);
   
   ////////////////////////////////////////////////////////////
   // Reduction
   ////////////////////////////////////////////////////////////
+  void GlobalMax(RealD &);
+  void GlobalMax(RealF &);
   void GlobalSum(RealF &);
   void GlobalSumVector(RealF *,int N);
   void GlobalSum(RealD &);
   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);
   void GlobalSumVector(ComplexD *c,int N);
+  void GlobalXOR(uint32_t &);
+  void GlobalXOR(uint64_t &);
   
   template<class obj> void GlobalSum(obj &o){
     typedef typename obj::scalar_type scalar_type;
     int words = sizeof(obj)/sizeof(scalar_type);
-    scalar_type * ptr = (scalar_type *)& o;
+    scalar_type * ptr = (scalar_type *)& o; // Safe alias 
     GlobalSumVector(ptr,words);
   }
   
   ////////////////////////////////////////////////////////////
   // Face exchange, buffer swap in translational invariant way
   ////////////////////////////////////////////////////////////
+  void CommsComplete(std::vector<CommsRequest_t> &list);
+  void SendToRecvFromBegin(std::vector<CommsRequest_t> &list,
+			   void *xmit,
+			   int dest,
+			   void *recv,
+			   int from,
+			   int bytes,int dir);
+  
   void SendToRecvFrom(void *xmit,
 		      int xmit_to_rank,
 		      void *recv,
 		      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,int do_xmit,
+			       void *recv,
+			       int recv_from_rank,int do_recv,
+			       int bytes,int dir);
 
   double StencilSendToRecvFromBegin(std::vector<CommsRequest_t> &list,
-				  void *xmit,
-				  int xmit_to_rank,
-				  void *recv,
-				  int recv_from_rank,
-				  int bytes);
+				    void *xmit,
+				    int xmit_to_rank,int do_xmit,
+				    void *recv,
+				    int recv_from_rank,int do_recv,
+				    int xbytes,int rbytes,int dir);
   
-  void StencilSendToRecvFromComplete(std::vector<CommsRequest_t> &waitall);
+  
+  void StencilSendToRecvFromComplete(std::vector<CommsRequest_t> &waitall,int i);
   void StencilBarrier(void);
 
   ////////////////////////////////////////////////////////////
@@ -226,13 +178,31 @@ class CartesianCommunicator {
   // Broadcast a buffer and composite larger
   ////////////////////////////////////////////////////////////
   void Broadcast(int root,void* data, int bytes);
+
+  ////////////////////////////////////////////////////////////
+  // All2All down one dimension
+  ////////////////////////////////////////////////////////////
+  template<class T> void AllToAll(int dim,std::vector<T> &in, std::vector<T> &out){
+    assert(dim>=0);
+    assert(dim<_ndimension);
+    assert(in.size()==out.size());
+    int numnode = _processors[dim];
+    uint64_t bytes=sizeof(T);
+    uint64_t words=in.size()/numnode;
+    assert(numnode * words == in.size());
+    assert(words < (1ULL<<31));
+    AllToAll(dim,(void *)&in[0],(void *)&out[0],words,bytes);
+  }
+  void AllToAll(int dim  ,void *in,void *out,uint64_t words,uint64_t bytes);
+  void AllToAll(void  *in,void *out,uint64_t words         ,uint64_t bytes);
   
   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

@@ -0,0 +1,533 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./lib/communicator/Communicator_mpi.cc
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#include <Grid/GridCore.h>
+#include <Grid/communicator/SharedMemory.h>
+
+NAMESPACE_BEGIN(Grid);
+
+Grid_MPI_Comm       CartesianCommunicator::communicator_world;
+
+////////////////////////////////////////////
+// First initialise of comms system
+////////////////////////////////////////////
+void CartesianCommunicator::Init(int *argc, char ***argv)
+{
+
+  int flag;
+  int provided;
+
+  MPI_Initialized(&flag); // needed to coexist with other libs apparently
+  if ( !flag ) {
+
+#ifndef GRID_COMMS_THREADS
+    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();
+}
+
+///////////////////////////////////////////////////////////////////////////
+// Use cartesian communicators now even in MPI3
+///////////////////////////////////////////////////////////////////////////
+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(Coordinate &coor)
+{
+  int rank;
+  int ierr=MPI_Cart_rank  (communicator, &coor[0], &rank);
+  assert(ierr==0);
+  return rank;
+}
+void  CartesianCommunicator::ProcessorCoorFromRank(int rank, Coordinate &coor)
+{
+  coor.resize(_ndimension);
+  int ierr=MPI_Cart_coords  (communicator, rank, _ndimension,&coor[0]);
+  assert(ierr==0);
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Initialises from communicator_world
+////////////////////////////////////////////////////////////////////////////////////////////////////////
+CartesianCommunicator::CartesianCommunicator(const Coordinate &processors)
+{
+  MPI_Comm optimal_comm;
+  ////////////////////////////////////////////////////
+  // Remap using the shared memory optimising routine
+  // The remap creates a comm which must be freed
+  ////////////////////////////////////////////////////
+  GlobalSharedMemory::OptimalCommunicator    (processors,optimal_comm,_shm_processors);
+  InitFromMPICommunicator(processors,optimal_comm);
+  SetCommunicator(optimal_comm);
+  ///////////////////////////////////////////////////
+  // Free the temp communicator
+  ///////////////////////////////////////////////////
+  MPI_Comm_free(&optimal_comm);
+}
+
+//////////////////////////////////
+// Try to subdivide communicator
+//////////////////////////////////
+CartesianCommunicator::CartesianCommunicator(const Coordinate &processors,const CartesianCommunicator &parent,int &srank)
+{
+  _ndimension = processors.size();  assert(_ndimension>=1);
+  int parent_ndimension = parent._ndimension; assert(_ndimension >= parent._ndimension);
+  Coordinate parent_processor_coor(_ndimension,0);
+  Coordinate parent_processors    (_ndimension,1);
+  Coordinate shm_processors       (_ndimension,1);
+  // Can make 5d grid from 4d etc...
+  int pad = _ndimension-parent_ndimension;
+  for(int d=0;d<parent_ndimension;d++){
+    parent_processor_coor[pad+d]=parent._processor_coor[d];
+    parent_processors    [pad+d]=parent._processors[d];
+    shm_processors       [pad+d]=parent._shm_processors[d];
+  }
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////////
+  // split the communicator
+  //////////////////////////////////////////////////////////////////////////////////////////////////////
+  //  int Nparent = parent._processors ;
+  int Nparent;
+  MPI_Comm_size(parent.communicator,&Nparent);
+
+  int childsize=1;
+  for(int d=0;d<processors.size();d++) {
+    childsize *= processors[d];
+  }
+  int Nchild = Nparent/childsize;
+  assert (childsize * Nchild == Nparent);
+
+  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];
+    scoor[d] = parent_processor_coor[d] / processors[d];
+    ssize[d] = parent_processors[d]     / processors[d];
+    if ( processors[d] < shm_processors[d] ) shm_processors[d] = processors[d]; // subnode splitting.
+  }
+
+  // rank within subcomm ; srank is rank of subcomm within blocks of subcomms
+  int crank;
+  // Mpi uses the reverse Lexico convention to us; so reversed routines called
+  Lexicographic::IndexFromCoorReversed(ccoor,crank,processors); // processors is the split grid dimensions
+  Lexicographic::IndexFromCoorReversed(scoor,srank,ssize);      // ssize is the number of split grids
+
+  MPI_Comm comm_split;
+  if ( Nchild > 1 ) {
+
+    ////////////////////////////////////////////////////////////////
+    // Split the communicator
+    ////////////////////////////////////////////////////////////////
+    int ierr= MPI_Comm_split(parent.communicator,srank,crank,&comm_split);
+    assert(ierr==0);
+
+  } else {
+    srank = 0;
+    int ierr = MPI_Comm_dup (parent.communicator,&comm_split);
+    assert(ierr==0);
+  }
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Set up from the new split communicator
+  //////////////////////////////////////////////////////////////////////////////////////////////////////
+  InitFromMPICommunicator(processors,comm_split);
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Take the right SHM buffers
+  //////////////////////////////////////////////////////////////////////////////////////////////////////
+  SetCommunicator(comm_split);
+
+  ///////////////////////////////////////////////
+  // Free the temp communicator
+  ///////////////////////////////////////////////
+  MPI_Comm_free(&comm_split);
+
+  if(0){
+    std::cout << " ndim " <<_ndimension<<" " << parent._ndimension << std::endl;
+    for(int d=0;d<processors.size();d++){
+      std::cout << d<< " " << _processor_coor[d] <<" " <<  ccoor[d]<<std::endl;
+    }
+  }
+  for(int d=0;d<processors.size();d++){
+    assert(_processor_coor[d] == ccoor[d] );
+  }
+}
+
+void CartesianCommunicator::InitFromMPICommunicator(const Coordinate &processors, MPI_Comm communicator_base)
+{
+  ////////////////////////////////////////////////////
+  // Creates communicator, and the communicator_halo
+  ////////////////////////////////////////////////////
+  _ndimension = processors.size();
+  _processor_coor.resize(_ndimension);
+
+  /////////////////////////////////
+  // Count the requested nodes
+  /////////////////////////////////
+  _Nprocessors=1;
+  _processors = processors;
+  for(int i=0;i<_ndimension;i++){
+    _Nprocessors*=_processors[i];
+  }
+
+  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]);
+
+  if ( 0 && (communicator_base != communicator_world) ) {
+    std::cout << "InitFromMPICommunicator Cartesian communicator created with a non-world communicator"<<std::endl;
+    std::cout << " new communicator rank "<<_processor<< " coor ["<<_ndimension<<"] ";
+    for(int d=0;d<_processors.size();d++){
+      std::cout << _processor_coor[d]<<" ";
+    }
+    std::cout << std::endl;
+  }
+
+  int Size;
+  MPI_Comm_size(communicator,&Size);
+
+  communicator_halo.resize (2*_ndimension);
+  for(int i=0;i<_ndimension*2;i++){
+    MPI_Comm_dup(communicator,&communicator_halo[i]);
+  }
+  assert(Size==_Nprocessors);
+}
+
+CartesianCommunicator::~CartesianCommunicator()
+{
+  int MPI_is_finalised;
+  MPI_Finalized(&MPI_is_finalised);
+  if (communicator && !MPI_is_finalised) {
+    MPI_Comm_free(&communicator);
+    for(int i=0;i<communicator_halo.size();i++){
+      MPI_Comm_free(&communicator_halo[i]);
+    }
+  }
+}
+void CartesianCommunicator::GlobalSum(uint32_t &u){
+  int ierr=MPI_Allreduce(MPI_IN_PLACE,&u,1,MPI_UINT32_T,MPI_SUM,communicator);
+  assert(ierr==0);
+}
+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);
+}
+void CartesianCommunicator::GlobalXOR(uint64_t &u){
+  int ierr=MPI_Allreduce(MPI_IN_PLACE,&u,1,MPI_UINT64_T,MPI_BXOR,communicator);
+  assert(ierr==0);
+}
+void CartesianCommunicator::GlobalMax(float &f)
+{
+  int ierr=MPI_Allreduce(MPI_IN_PLACE,&f,1,MPI_FLOAT,MPI_MAX,communicator);
+  assert(ierr==0);
+}
+void CartesianCommunicator::GlobalMax(double &d)
+{
+  int ierr = MPI_Allreduce(MPI_IN_PLACE,&d,1,MPI_DOUBLE,MPI_MAX,communicator);
+  assert(ierr==0);
+}
+void CartesianCommunicator::GlobalSum(float &f){
+  int ierr=MPI_Allreduce(MPI_IN_PLACE,&f,1,MPI_FLOAT,MPI_SUM,communicator);
+  assert(ierr==0);
+}
+void CartesianCommunicator::GlobalSumVector(float *f,int N)
+{
+  int ierr=MPI_Allreduce(MPI_IN_PLACE,f,N,MPI_FLOAT,MPI_SUM,communicator);
+  assert(ierr==0);
+}
+void CartesianCommunicator::GlobalSum(double &d)
+{
+  int ierr = MPI_Allreduce(MPI_IN_PLACE,&d,1,MPI_DOUBLE,MPI_SUM,communicator);
+  assert(ierr==0);
+}
+void CartesianCommunicator::GlobalSumVector(double *d,int N)
+{
+  int ierr = MPI_Allreduce(MPI_IN_PLACE,d,N,MPI_DOUBLE,MPI_SUM,communicator);
+  assert(ierr==0);
+}
+
+void CartesianCommunicator::SendToRecvFromBegin(std::vector<CommsRequest_t> &list,
+						void *xmit,
+						int dest,
+						void *recv,
+						int from,
+						int bytes,int dir)
+{
+  MPI_Request xrq;
+  MPI_Request rrq;
+
+  assert(dest != _processor);
+  assert(from != _processor);
+
+  int tag;
+
+  tag= dir+from*32;
+  int ierr=MPI_Irecv(recv, bytes, MPI_CHAR,from,tag,communicator,&rrq);
+  assert(ierr==0);
+  list.push_back(rrq);
+  
+  tag= dir+_processor*32;
+  ierr =MPI_Isend(xmit, bytes, MPI_CHAR,dest,tag,communicator,&xrq);
+  assert(ierr==0);
+  list.push_back(xrq);
+}
+void CartesianCommunicator::CommsComplete(std::vector<CommsRequest_t> &list)
+{
+  int nreq=list.size();
+
+  if (nreq==0) return;
+
+  std::vector<MPI_Status> status(nreq);
+  int ierr = MPI_Waitall(nreq,&list[0],&status[0]);
+  assert(ierr==0);
+  list.resize(0);
+}
+
+// Basic Halo comms primitive
+void CartesianCommunicator::SendToRecvFrom(void *xmit,
+					   int dest,
+					   void *recv,
+					   int from,
+					   int bytes)
+{
+  std::vector<CommsRequest_t> reqs(0);
+  unsigned long  xcrc = crc32(0L, Z_NULL, 0);
+  unsigned long  rcrc = crc32(0L, Z_NULL, 0);
+
+  int myrank = _processor;
+  int ierr;
+
+  // Enforce no UVM in comms, device or host OK
+  assert(acceleratorIsCommunicable(xmit));
+  assert(acceleratorIsCommunicable(recv));
+
+  // 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);
+
+  //  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, int dox,
+						     void *recv,
+						     int from, int dor,
+						     int bytes,int dir)
+{
+  std::vector<CommsRequest_t> list;
+  double offbytes = StencilSendToRecvFromBegin(list,xmit,dest,dox,recv,from,dor,bytes,bytes,dir);
+  StencilSendToRecvFromComplete(list,dir);
+  return offbytes;
+}
+
+#undef NVLINK_GET // Define to use get instead of put DMA
+double CartesianCommunicator::StencilSendToRecvFromBegin(std::vector<CommsRequest_t> &list,
+							 void *xmit,
+							 int dest,int dox,
+							 void *recv,
+							 int from,int dor,
+							 int xbytes,int rbytes,int dir)
+{
+  int ncomm  =communicator_halo.size();
+  int commdir=dir%ncomm;
+
+  MPI_Request xrq;
+  MPI_Request rrq;
+
+  int ierr;
+  int gdest = ShmRanks[dest];
+  int gfrom = ShmRanks[from];
+  int gme   = ShmRanks[_processor];
+
+  assert(dest != _processor);
+  assert(from != _processor);
+  assert(gme  == ShmRank);
+  double off_node_bytes=0.0;
+  int tag;
+
+  if ( dor ) {
+    if ( (gfrom ==MPI_UNDEFINED) || Stencil_force_mpi ) {
+      tag= dir+from*32;
+      ierr=MPI_Irecv(recv, rbytes, MPI_CHAR,from,tag,communicator_halo[commdir],&rrq);
+      assert(ierr==0);
+      list.push_back(rrq);
+      off_node_bytes+=rbytes;
+    }
+#ifdef NVLINK_GET
+      void *shm = (void *) this->ShmBufferTranslate(from,xmit);
+      assert(shm!=NULL);
+      acceleratorCopyDeviceToDeviceAsynch(shm,recv,rbytes);
+#endif
+  }
+  
+  if (dox) {
+    //  rcrc = crc32(rcrc,(unsigned char *)recv,bytes);
+    if ( (gdest == MPI_UNDEFINED) || Stencil_force_mpi ) {
+      tag= dir+_processor*32;
+      ierr =MPI_Isend(xmit, xbytes, MPI_CHAR,dest,tag,communicator_halo[commdir],&xrq);
+      assert(ierr==0);
+      list.push_back(xrq);
+      off_node_bytes+=xbytes;
+    } else {
+#ifndef NVLINK_GET
+      void *shm = (void *) this->ShmBufferTranslate(dest,recv);
+      assert(shm!=NULL);
+      acceleratorCopyDeviceToDeviceAsynch(xmit,shm,xbytes);
+#endif
+      
+    }
+  }
+
+  return off_node_bytes;
+}
+void CartesianCommunicator::StencilSendToRecvFromComplete(std::vector<CommsRequest_t> &list,int dir)
+{
+  int nreq=list.size();
+
+  acceleratorCopySynchronise();
+
+  if (nreq==0) return;
+
+  std::vector<MPI_Status> status(nreq);
+  int ierr = MPI_Waitall(nreq,&list[0],&status[0]);
+  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);
+  assert(ierr==0);
+}
+void CartesianCommunicator::Broadcast(int root,void* data, int bytes)
+{
+  int ierr=MPI_Bcast(data,
+		     bytes,
+		     MPI_BYTE,
+		     root,
+		     communicator);
+  assert(ierr==0);
+}
+int CartesianCommunicator::RankWorld(void){
+  int r;
+  MPI_Comm_rank(communicator_world,&r);
+  return r;
+}
+void CartesianCommunicator::BarrierWorld(void){
+  int ierr = MPI_Barrier(communicator_world);
+  assert(ierr==0);
+}
+void CartesianCommunicator::BroadcastWorld(int root,void* data, int bytes)
+{
+  int ierr= MPI_Bcast(data,
+		      bytes,
+		      MPI_BYTE,
+		      root,
+		      communicator_world);
+  assert(ierr==0);
+}
+
+void CartesianCommunicator::AllToAll(int dim,void  *in,void *out,uint64_t words,uint64_t bytes)
+{
+  Coordinate row(_ndimension,1);
+  assert(dim>=0 && dim<_ndimension);
+
+  //  Split the communicator
+  row[dim] = _processors[dim];
+
+  int me;
+  CartesianCommunicator Comm(row,*this,me);
+  Comm.AllToAll(in,out,words,bytes);
+}
+void CartesianCommunicator::AllToAll(void  *in,void *out,uint64_t words,uint64_t bytes)
+{
+  // MPI is a pain and uses "int" arguments
+  // 64*64*64*128*16 == 500Million elements of data.
+  // When 24*4 bytes multiples get 50x 10^9 >>> 2x10^9 Y2K bug.
+  // (Turns up on 32^3 x 64 Gparity too)
+  MPI_Datatype object;
+  int iwords;
+  int ibytes;
+  iwords = words;
+  ibytes = bytes;
+  assert(words == iwords); // safe to cast to int ?
+  assert(bytes == ibytes); // safe to cast to int ?
+  MPI_Type_contiguous(ibytes,MPI_BYTE,&object);
+  MPI_Type_commit(&object);
+  MPI_Alltoall(in,iwords,object,out,iwords,object,communicator);
+  MPI_Type_free(&object);
+}
+
+NAMESPACE_END(Grid);

Grid/communicator/Communicator_none.cc

@@ -1,4 +1,4 @@
-    /*************************************************************************************
+/*************************************************************************************
 
     Grid physics library, www.github.com/paboyle/Grid 
 
@@ -23,25 +23,38 @@ 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
 ///////////////////////////////////////////////////////////////////////////////////////////////////
+Grid_MPI_Comm       CartesianCommunicator::communicator_world;
 
 void CartesianCommunicator::Init(int *argc, char *** arv)
 {
-  ShmInitGeneric();
+  GlobalSharedMemory::Init(communicator_world);
+  GlobalSharedMemory::SharedMemoryAllocate(
+					   GlobalSharedMemory::MAX_MPI_SHM_BYTES,
+					   GlobalSharedMemory::Hugepages);
 }
 
-CartesianCommunicator::CartesianCommunicator(const std::vector<int> &processors)
+CartesianCommunicator::CartesianCommunicator(const Coordinate &processors,const CartesianCommunicator &parent,int &srank) 
+  : CartesianCommunicator(processors) 
 {
+  _shm_processors = Coordinate(processors.size(),1);
+  srank=0;
+  SetCommunicator(communicator_world);
+}
+
+CartesianCommunicator::CartesianCommunicator(const Coordinate &processors)
+{
+  _shm_processors = Coordinate(processors.size(),1);
   _processors = processors;
-  _ndimension = processors.size();
+  _ndimension = processors.size();  assert(_ndimension>=1);
   _processor_coor.resize(_ndimension);
   
   // Require 1^N processor grid for fake
@@ -51,23 +64,22 @@ CartesianCommunicator::CartesianCommunicator(const std::vector<int> &processors)
     assert(_processors[d]==1);
     _processor_coor[d] = 0;
   }
+  SetCommunicator(communicator_world);
 }
 
+CartesianCommunicator::~CartesianCommunicator(){}
+
+void CartesianCommunicator::GlobalMax(float &){}
+void CartesianCommunicator::GlobalMax(double &){}
 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::SendRecvPacket(void *xmit,
-					   void *recv,
-					   int xmit_to_rank,
-					   int recv_from_rank,
-					   int bytes)
-{
-  assert(0);
-}
+void CartesianCommunicator::GlobalSumVector(uint64_t *,int N){}
+void CartesianCommunicator::GlobalXOR(uint32_t &){}
+void CartesianCommunicator::GlobalXOR(uint64_t &){}
 
 
 // Basic Halo comms primitive -- should never call in single node
@@ -79,33 +91,62 @@ void CartesianCommunicator::SendToRecvFrom(void *xmit,
 {
   assert(0);
 }
+void CartesianCommunicator::CommsComplete(std::vector<CommsRequest_t> &list){ assert(0);}
 void CartesianCommunicator::SendToRecvFromBegin(std::vector<CommsRequest_t> &list,
 						void *xmit,
 						int dest,
 						void *recv,
 						int from,
-						int bytes)
+						int bytes,int dir)
 {
   assert(0);
 }
 
-void CartesianCommunicator::SendToRecvFromComplete(std::vector<CommsRequest_t> &list)
+void CartesianCommunicator::AllToAll(int dim,void  *in,void *out,uint64_t words,uint64_t bytes)
 {
-  assert(0);
+  bcopy(in,out,bytes*words);
+}
+void CartesianCommunicator::AllToAll(void  *in,void *out,uint64_t words,uint64_t bytes)
+{
+  bcopy(in,out,bytes*words);
 }
 
 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; }
+void CartesianCommunicator::BarrierWorld(void) { }
+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;
   dest=0;
 }
 
-
+double CartesianCommunicator::StencilSendToRecvFrom( void *xmit,
+						     int xmit_to_rank,int dox,
+						     void *recv,
+						     int recv_from_rank,int dor,
+						     int bytes, int dir)
+{
+  return 2.0*bytes;
+}
+double CartesianCommunicator::StencilSendToRecvFromBegin(std::vector<CommsRequest_t> &list,
+							 void *xmit,
+							 int xmit_to_rank,int dox,
+							 void *recv,
+							 int recv_from_rank,int dor,
+							 int xbytes,int rbytes, int dir)
+{
+  return xbytes+rbytes;
+}
+void CartesianCommunicator::StencilSendToRecvFromComplete(std::vector<CommsRequest_t> &waitall,int dir)
+{
 }
 
+void CartesianCommunicator::StencilBarrier(void){};
+
+NAMESPACE_END(Grid);
+
+

Grid/communicator/SharedMemory.cc

@@ -0,0 +1,172 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/communicator/SharedMemory.cc
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+
+#include <Grid/GridCore.h>
+
+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;
+int                 GlobalSharedMemory::_ShmAlloc;
+uint64_t            GlobalSharedMemory::_ShmAllocBytes;
+
+std::vector<void *> GlobalSharedMemory::WorldShmCommBufs;
+#ifndef ACCELERATOR_AWARE_MPI
+void * GlobalSharedMemory::HostCommBuf;
+#endif
+
+Grid_MPI_Comm       GlobalSharedMemory::WorldShmComm;
+int                 GlobalSharedMemory::WorldShmRank;
+int                 GlobalSharedMemory::WorldShmSize;
+std::vector<int>    GlobalSharedMemory::WorldShmRanks;
+
+Grid_MPI_Comm       GlobalSharedMemory::WorldComm;
+int                 GlobalSharedMemory::WorldSize;
+int                 GlobalSharedMemory::WorldRank;
+
+int                 GlobalSharedMemory::WorldNodes;
+int                 GlobalSharedMemory::WorldNode;
+
+void GlobalSharedMemory::SharedMemoryFree(void)
+{
+  assert(_ShmAlloc);
+  assert(_ShmAllocBytes>0);
+  for(int r=0;r<WorldShmSize;r++){
+    munmap(WorldShmCommBufs[r],_ShmAllocBytes);
+  }
+  _ShmAlloc = 0;
+  _ShmAllocBytes = 0;
+}
+/////////////////////////////////
+// Alloc, free shmem region
+/////////////////////////////////
+#ifndef ACCELERATOR_AWARE_MPI
+void *SharedMemory::HostBufferMalloc(size_t bytes){
+  void *ptr = (void *)host_heap_top;
+  host_heap_top  += bytes;
+  host_heap_bytes+= bytes;
+  if (host_heap_bytes >= host_heap_size) {
+    std::cout<< " HostBufferMalloc exceeded heap size -- try increasing with --shm <MB> flag" <<std::endl;
+    std::cout<< " Parameter specified in units of MB (megabytes) " <<std::endl;
+    std::cout<< " Current alloc is " << (bytes/(1024*1024)) <<"MB"<<std::endl;
+    std::cout<< " Current bytes is " << (host_heap_bytes/(1024*1024)) <<"MB"<<std::endl;
+    std::cout<< " Current heap  is " << (host_heap_size/(1024*1024)) <<"MB"<<std::endl;
+    assert(host_heap_bytes<host_heap_size);
+  }
+  return ptr;
+}
+void SharedMemory::HostBufferFreeAll(void) { 
+  host_heap_top  =(size_t)HostCommBuf;
+  host_heap_bytes=0;
+}
+#endif
+void *SharedMemory::ShmBufferMalloc(size_t bytes){
+  //  bytes = (bytes+sizeof(vRealD))&(~(sizeof(vRealD)-1));// align up bytes
+  void *ptr = (void *)heap_top;
+  heap_top  += bytes;
+  heap_bytes+= 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 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) { 
+  heap_top  =(size_t)ShmBufferSelf();
+  heap_bytes=0;
+}
+void *SharedMemory::ShmBufferSelf(void)
+{
+  //std::cerr << "ShmBufferSelf "<<ShmRank<<" "<<std::hex<< ShmCommBufs[ShmRank] <<std::dec<<std::endl;
+  return ShmCommBufs[ShmRank];
+}
+static inline int divides(int a,int b)
+{
+  return ( b == ( (b/a)*a ) );
+}
+void GlobalSharedMemory::GetShmDims(const Coordinate &WorldDims,Coordinate &ShmDims)
+{
+  ////////////////////////////////////////////////////////////////
+  // Allow user to configure through environment variable
+  ////////////////////////////////////////////////////////////////
+  char* str = getenv(("GRID_SHM_DIMS_" + std::to_string(ShmDims.size())).c_str());
+  if ( str ) {
+    std::vector<int> IntShmDims;
+    GridCmdOptionIntVector(std::string(str),IntShmDims);
+    assert(IntShmDims.size() == WorldDims.size());
+    long ShmSize = 1;
+    for (int dim=0;dim<WorldDims.size();dim++) {
+      ShmSize *= (ShmDims[dim] = IntShmDims[dim]);
+      assert(divides(ShmDims[dim],WorldDims[dim]));
+    }
+    assert(ShmSize == WorldShmSize);
+    return;
+  }
+  
+  ////////////////////////////////////////////////////////////////
+  // 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;
+  }
+}
+
+NAMESPACE_END(Grid); 
+

Grid/communicator/SharedMemory.h

@@ -0,0 +1,176 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/communicator/SharedMemory.cc
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once 
+
+#include <Grid/GridCore.h>
+
+#if defined (GRID_COMMS_MPI3) 
+#include <mpi.h>
+#endif 
+#include <semaphore.h>
+#include <fcntl.h>
+#include <unistd.h>
+#include <limits.h>
+#include <sys/types.h>
+#include <sys/ipc.h>
+#include <sys/shm.h>
+#include <sys/mman.h>
+#include <zlib.h>
+
+NAMESPACE_BEGIN(Grid);
+
+#if defined (GRID_COMMS_MPI3) 
+typedef MPI_Comm    Grid_MPI_Comm;
+typedef MPI_Request CommsRequest_t;
+#else 
+typedef int CommsRequest_t;
+typedef int Grid_MPI_Comm;
+#endif
+
+class GlobalSharedMemory {
+private:
+  static const int     MAXLOG2RANKSPERNODE = 16;            
+
+
+  // Init once lock on the buffer allocation
+  static int      _ShmSetup;
+  static int      _ShmAlloc;
+  static uint64_t _ShmAllocBytes;
+
+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; }
+  static uint64_t      MAX_MPI_SHM_BYTES;
+  static int           Hugepages;
+
+  static std::vector<void *> WorldShmCommBufs;
+#ifndef ACCELERATOR_AWARE_MPI
+  static void *HostCommBuf;
+#endif
+  static Grid_MPI_Comm WorldComm;
+  static int           WorldRank;
+  static int           WorldSize;
+
+  static Grid_MPI_Comm WorldShmComm;
+  static int           WorldShmRank;
+  static int           WorldShmSize;
+
+  static int           WorldNodes;
+  static int           WorldNode;
+
+  static std::vector<int>  WorldShmRanks;
+
+  //////////////////////////////////////////////////////////////////////////////////////
+  // Create an optimal reordered communicator that makes MPI_Cart_create get it right
+  //////////////////////////////////////////////////////////////////////////////////////
+  static void Init(Grid_MPI_Comm comm); // Typically MPI_COMM_WORLD
+  // Turns MPI_COMM_WORLD into right layout for Cartesian
+  static void OptimalCommunicator            (const Coordinate &processors,Grid_MPI_Comm & optimal_comm,Coordinate &ShmDims); 
+  static void OptimalCommunicatorHypercube   (const Coordinate &processors,Grid_MPI_Comm & optimal_comm,Coordinate &ShmDims); 
+  static void OptimalCommunicatorSharedMemory(const Coordinate &processors,Grid_MPI_Comm & optimal_comm,Coordinate &ShmDims); 
+  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,void *src,size_t bytes);
+  static void SharedMemoryZero(void *dest,size_t bytes);
+
+};
+
+//////////////////////////////
+// one per communicator
+//////////////////////////////
+class SharedMemory 
+{
+private:
+  static const int     MAXLOG2RANKSPERNODE = 16;            
+
+  size_t heap_top;
+  size_t heap_bytes;
+  size_t heap_size;
+
+#ifndef ACCELERATOR_AWARE_MPI
+  size_t host_heap_top;  // set in free all
+  size_t host_heap_bytes;// set in free all
+  void *HostCommBuf;     // set in SetCommunicator
+  size_t host_heap_size; // set in SetCommunicator
+#endif
+  
+protected:
+
+  Grid_MPI_Comm    ShmComm; // for barriers
+  int    ShmRank; 
+  int    ShmSize;
+  std::vector<void *> ShmCommBufs;
+  std::vector<int>    ShmRanks;// Mapping comm ranks to Shm ranks
+
+public:
+  SharedMemory() {};
+  ~SharedMemory();
+  ///////////////////////////////////////////////////////////////////////////////////////
+  // set the buffers & sizes
+  ///////////////////////////////////////////////////////////////////////////////////////
+  void SetCommunicator(Grid_MPI_Comm comm);
+
+  ////////////////////////////////////////////////////////////////////////
+  // For this instance ; disjoint buffer sets between splits if split grid
+  ////////////////////////////////////////////////////////////////////////
+  void ShmBarrier(void); 
+
+  ///////////////////////////////////////////////////
+  // Call on any instance
+  ///////////////////////////////////////////////////
+  void SharedMemoryTest(void);
+  
+  void *ShmBufferSelf(void);
+  void *ShmBuffer    (int rank);
+  void *ShmBufferTranslate(int rank,void * local_p);
+  void *ShmBufferMalloc(size_t bytes);
+  void  ShmBufferFreeAll(void) ;
+#ifndef ACCELERATOR_AWARE_MPI
+  void *HostBufferMalloc(size_t bytes);
+  void HostBufferFreeAll(void);
+#endif  
+  //////////////////////////////////////////////////////////////////////////
+  // Make info on Nodes & ranks and Shared memory available
+  //////////////////////////////////////////////////////////////////////////
+  int NodeCount(void) { return GlobalSharedMemory::WorldNodes;};
+  int RankCount(void) { return GlobalSharedMemory::WorldSize;};
+
+};
+
+NAMESPACE_END(Grid);
+

Grid/communicator/SharedMemoryNone.cc

@@ -0,0 +1,171 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/communicator/SharedMemory.cc
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+
+#include <Grid/GridCore.h>
+
+NAMESPACE_BEGIN(Grid); 
+#define header "SharedMemoryNone: "
+
+/*Construct from an MPI communicator*/
+void GlobalSharedMemory::Init(Grid_MPI_Comm comm)
+{
+  assert(_ShmSetup==0);
+  WorldComm = 0;
+  WorldRank = 0;
+  WorldSize = 1;
+  WorldShmComm = 0 ;
+  WorldShmRank = 0 ;
+  WorldShmSize = 1 ;
+  WorldNodes   = 1 ;
+  WorldNode    = 0 ;
+  WorldShmRanks.resize(WorldSize); WorldShmRanks[0] = 0;
+  WorldShmCommBufs.resize(1);
+  _ShmSetup=1;
+}
+
+void GlobalSharedMemory::OptimalCommunicator(const Coordinate &processors,Grid_MPI_Comm & optimal_comm,Coordinate &SHM)
+{
+  optimal_comm = WorldComm;
+  SHM = Coordinate(processors.size(),1);
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////
+// Hugetlbfs mapping intended, use anonymous mmap
+////////////////////////////////////////////////////////////////////////////////////////////
+#if 1
+void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
+{
+  std::cout << header "SharedMemoryAllocate "<< bytes<< " GPU implementation "<<std::endl;
+  void * ShmCommBuf ; 
+  assert(_ShmSetup==1);
+  assert(_ShmAlloc==0);
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Each MPI rank should allocate our own buffer
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////////
+  ShmCommBuf = acceleratorAllocDevice(bytes);
+
+  if (ShmCommBuf == (void *)NULL ) {
+    std::cerr << " SharedMemoryNone.cc acceleratorAllocDevice failed NULL pointer for " << bytes<<" bytes " << std::endl;
+    exit(EXIT_FAILURE);  
+  }
+  if ( WorldRank == 0 ){
+    std::cout << WorldRank << header " SharedMemoryNone.cc acceleratorAllocDevice "<< bytes 
+	      << "bytes at "<< std::hex<< ShmCommBuf <<std::dec<<" for comms buffers " <<std::endl;
+  }
+  SharedMemoryZero(ShmCommBuf,bytes);
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Loop over ranks/gpu's on our node
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////////
+  WorldShmCommBufs[0] = ShmCommBuf;
+
+  _ShmAllocBytes=bytes;
+  _ShmAlloc=1;
+}
+#else
+void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
+{
+  void * ShmCommBuf ; 
+  assert(_ShmSetup==1);
+  assert(_ShmAlloc==0);
+  int mmap_flag =0;
+#ifdef MAP_ANONYMOUS
+  mmap_flag = mmap_flag| MAP_SHARED | MAP_ANONYMOUS;
+#endif
+#ifdef MAP_ANON
+  mmap_flag = mmap_flag| MAP_SHARED | MAP_ANON;
+#endif
+#ifdef MAP_HUGETLB
+  if ( flags ) mmap_flag |= MAP_HUGETLB;
+#endif
+  ShmCommBuf =(void *) mmap(NULL, bytes, PROT_READ | PROT_WRITE, mmap_flag, -1, 0); 
+  if (ShmCommBuf == (void *)MAP_FAILED) {
+    perror("mmap failed ");
+    exit(EXIT_FAILURE);  
+  }
+#ifdef MADV_HUGEPAGE
+  if (!Hugepages ) madvise(ShmCommBuf,bytes,MADV_HUGEPAGE);
+#endif
+  bzero(ShmCommBuf,bytes);
+  WorldShmCommBufs[0] = ShmCommBuf;
+  _ShmAllocBytes=bytes;
+  _ShmAlloc=1;
+};
+#endif
+void GlobalSharedMemory::SharedMemoryZero(void *dest,size_t bytes)
+{
+  acceleratorMemSet(dest,0,bytes);
+}
+void GlobalSharedMemory::SharedMemoryCopy(void *dest,void *src,size_t bytes)
+{
+  acceleratorCopyToDevice(src,dest,bytes);
+}
+////////////////////////////////////////////////////////
+// Global shared functionality finished
+// Now move to per communicator functionality
+////////////////////////////////////////////////////////
+void SharedMemory::SetCommunicator(Grid_MPI_Comm comm)
+{
+  assert(GlobalSharedMemory::ShmAlloc()==1);
+  ShmRanks.resize(1);
+  ShmCommBufs.resize(1);
+  ShmRanks[0] = 0;
+  ShmRank     = 0;
+  ShmSize     = 1;
+  //////////////////////////////////////////////////////////////////////
+  // Map ShmRank to WorldShmRank and use the right buffer
+  //////////////////////////////////////////////////////////////////////
+  ShmCommBufs[0] = GlobalSharedMemory::WorldShmCommBufs[0];
+  heap_size      = GlobalSharedMemory::ShmAllocBytes();
+  ShmBufferFreeAll();
+  return;
+}
+//////////////////////////////////////////////////////////////////
+// On node barrier
+//////////////////////////////////////////////////////////////////
+void SharedMemory::ShmBarrier(void){ return ; }
+
+//////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Test the shared memory is working
+//////////////////////////////////////////////////////////////////////////////////////////////////////////
+void SharedMemory::SharedMemoryTest(void) { return; }
+
+void *SharedMemory::ShmBuffer(int rank)
+{
+  return NULL;
+}
+void *SharedMemory::ShmBufferTranslate(int rank,void * local_p)
+{
+  return NULL;
+}
+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_
 
@@ -42,11 +42,21 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 #include <Grid/cshift/Cshift_mpi.h>
 #endif 
 
-#ifdef GRID_COMMS_MPI3L
+#ifdef GRID_COMMS_MPIT
 #include <Grid/cshift/Cshift_mpi.h>
 #endif 
 
 #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

@@ -0,0 +1,515 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/cshift/Cshift_common.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);
+
+extern std::vector<std::pair<int,int> > Cshift_table; 
+extern commVector<std::pair<int,int> > Cshift_table_device; 
+
+inline std::pair<int,int> *MapCshiftTable(void)
+{
+  // GPU version
+#ifdef ACCELERATOR_CSHIFT    
+  uint64_t sz=Cshift_table.size();
+  if (Cshift_table_device.size()!=sz )    {
+    Cshift_table_device.resize(sz);
+  }
+  acceleratorCopyToDevice((void *)&Cshift_table[0],
+			  (void *)&Cshift_table_device[0],
+			  sizeof(Cshift_table[0])*sz);
+
+  return &Cshift_table_device[0];
+#else 
+  return &Cshift_table[0];
+#endif
+  // CPU version use identify map
+}
+///////////////////////////////////////////////////////////////////
+// Gather for when there is no need to SIMD split 
+///////////////////////////////////////////////////////////////////
+template<class vobj> void 
+Gather_plane_simple (const Lattice<vobj> &rhs,cshiftVector<vobj> &buffer,int dimension,int plane,int cbmask, int off=0)
+{
+  int rd = rhs.Grid()->_rdimensions[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 ent = 0;
+
+  if(Cshift_table.size()<e1*e2) Cshift_table.resize(e1*e2); // Let it grow to biggest
+
+  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;
+	Cshift_table[ent++] = std::pair<int,int>(off+bo+b,so+o+b);
+      }
+    }
+  } else { 
+     int bo=0;
+     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);
+	 if ( ocb &cbmask ) {
+	   Cshift_table[ent++]=std::pair<int,int> (off+bo++,so+o+b);
+	 }
+       }
+     }
+  }
+  {
+    auto buffer_p = & buffer[0];
+    auto table = MapCshiftTable();
+#ifdef ACCELERATOR_CSHIFT
+    autoView(rhs_v , rhs, AcceleratorRead);
+    accelerator_for(i,ent,vobj::Nsimd(),{
+	coalescedWrite(buffer_p[table[i].first],coalescedRead(rhs_v[table[i].second]));
+    });
+#else
+    autoView(rhs_v , rhs, CpuRead);
+    thread_for(i,ent,{
+      buffer_p[table[i].first]=rhs_v[table[i].second];
+    });
+#endif
+  }
+}
+
+///////////////////////////////////////////////////////////////////
+// Gather for when there *is* need to SIMD split 
+///////////////////////////////////////////////////////////////////
+template<class vobj> void 
+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];
+
+  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 n1=rhs.Grid()->_slice_stride[dimension];
+
+  if ( cbmask ==0x3){
+#ifdef ACCELERATOR_CSHIFT
+    autoView(rhs_v , rhs, AcceleratorRead);
+    accelerator_for(nn,e1*e2,1,{
+	int n = nn%e1;
+	int b = nn/e1;
+	int o      =   n*n1;
+	int offset = b+n*e2;
+	
+	vobj temp =rhs_v[so+o+b];
+	extract<vobj>(temp,pointers,offset);
+      });
+#else
+    autoView(rhs_v , rhs, CpuRead);
+    thread_for2d(n,e1,b,e2,{
+	int o      =   n*n1;
+	int offset = b+n*e2;
+	
+	vobj temp =rhs_v[so+o+b];
+	extract<vobj>(temp,pointers,offset);
+      });
+#endif
+  } else { 
+    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?
+#ifdef ACCELERATOR_CSHIFT    
+    autoView(rhs_v , rhs, AcceleratorRead);
+    accelerator_for(nn,e1*e2,1,{
+	int n = nn%e1;
+	int b = nn/e1;
+
+	Coordinate coor;
+
+	int o=n*n1;
+	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_v[so+o+b];
+	  extract<vobj>(temp,pointers,offset);
+	}
+      });
+#else
+    autoView(rhs_v , rhs, CpuRead);
+    thread_for2d(n,e1,b,e2,{
+
+	Coordinate coor;
+
+	int o=n*n1;
+	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_v[so+o+b];
+	  extract<vobj>(temp,pointers,offset);
+	}
+      });
+#endif
+  }
+}
+
+//////////////////////////////////////////////////////
+// Scatter for when there is no need to SIMD split
+//////////////////////////////////////////////////////
+template<class vobj> void Scatter_plane_simple (Lattice<vobj> &rhs,cshiftVector<vobj> &buffer, int dimension,int plane,int cbmask)
+{
+  int rd = rhs.Grid()->_rdimensions[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 stride=rhs.Grid()->_slice_stride[dimension];
+
+  if(Cshift_table.size()<e1*e2) Cshift_table.resize(e1*e2); // Let it grow to biggest
+
+  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];
+	Cshift_table[ent++] = std::pair<int,int>(so+o+b,bo+b);
+      }
+    }
+
+  } else { 
+    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
+	if ( ocb & cbmask ) {
+	  Cshift_table[ent++]=std::pair<int,int> (so+o+b,bo++);
+	}
+      }
+    }
+  }
+  
+  {
+    auto buffer_p = & buffer[0];
+    auto table = MapCshiftTable();
+#ifdef ACCELERATOR_CSHIFT    
+    autoView( rhs_v, rhs, AcceleratorWrite);
+    accelerator_for(i,ent,vobj::Nsimd(),{
+	coalescedWrite(rhs_v[table[i].first],coalescedRead(buffer_p[table[i].second]));
+    });
+#else
+    autoView( rhs_v, rhs, CpuWrite);
+    thread_for(i,ent,{
+      rhs_v[table[i].first]=buffer_p[table[i].second];
+    });
+#endif
+  }
+}
+
+//////////////////////////////////////////////////////
+// Scatter for when there *is* need to SIMD split
+//////////////////////////////////////////////////////
+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];
+
+  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];
+
+  if(cbmask ==0x3 ) {
+    int _slice_stride = rhs.Grid()->_slice_stride[dimension];
+    int _slice_block = rhs.Grid()->_slice_block[dimension];
+#ifdef ACCELERATOR_CSHIFT    
+    autoView( rhs_v , rhs, AcceleratorWrite);
+    accelerator_for(nn,e1*e2,1,{
+	int n = nn%e1;
+	int b = nn/e1;
+	int o      = n*_slice_stride;
+	int offset = b+n*_slice_block;
+	merge(rhs_v[so+o+b],pointers,offset);
+      });
+#else
+    autoView( rhs_v , rhs, CpuWrite);
+    thread_for2d(n,e1,b,e2,{
+	int o      = n*_slice_stride;
+	int offset = b+n*_slice_block;
+	merge(rhs_v[so+o+b],pointers,offset);
+    });
+#endif
+  } 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);
+	if ( ocb&cbmask ) {
+	  merge(rhs_v[so+o+b],pointers,offset);
+	}
+      }
+    }
+  }
+}
+
+//////////////////////////////////////////////////////
+// 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];
+
+  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 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 ent=0;
+
+  if(cbmask == 0x3 ){
+    for(int n=0;n<e1;n++){
+      for(int b=0;b<e2;b++){
+        int o =n*stride+b;
+	Cshift_table[ent++] = std::pair<int,int>(lo+o,ro+o);
+      }
+    }
+  } 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);
+        if ( ocb&cbmask ) {
+	  Cshift_table[ent++] = std::pair<int,int>(lo+o,ro+o);
+	}
+      }
+    }
+  }
+
+  {
+    auto table = MapCshiftTable();
+#ifdef ACCELERATOR_CSHIFT    
+    autoView(rhs_v , rhs, AcceleratorRead);
+    autoView(lhs_v , lhs, AcceleratorWrite);
+    accelerator_for(i,ent,vobj::Nsimd(),{
+      coalescedWrite(lhs_v[table[i].first],coalescedRead(rhs_v[table[i].second]));
+    });
+#else
+    autoView(rhs_v , rhs, CpuRead);
+    autoView(lhs_v , lhs, CpuWrite);
+    thread_for(i,ent,{
+      lhs_v[table[i].first]=rhs_v[table[i].second];
+    });
+#endif
+  }
+}
+
+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];
+
+  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 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
+
+  int ent=0;
+
+  if ( cbmask == 0x3 ) {
+    for(int n=0;n<e1;n++){
+    for(int b=0;b<e2;b++){
+      int o  =n*stride;
+      Cshift_table[ent++] = std::pair<int,int>(lo+o+b,ro+o+b);
+    }}
+  } 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 ) Cshift_table[ent++] = std::pair<int,int>(lo+o+b,ro+o+b);
+    }}
+  }
+
+  {
+    auto table = MapCshiftTable();
+#ifdef ACCELERATOR_CSHIFT    
+    autoView( rhs_v, rhs, AcceleratorRead);
+    autoView( lhs_v, lhs, AcceleratorWrite);
+    accelerator_for(i,ent,1,{
+      permute(lhs_v[table[i].first],rhs_v[table[i].second],permute_type);
+    });
+#else
+    autoView( rhs_v, rhs, CpuRead);
+    autoView( lhs_v, lhs, CpuWrite);
+    thread_for(i,ent,{
+      permute(lhs_v[table[i].first],rhs_v[table[i].second],permute_type);
+    });
+#endif
+  }
+}
+
+//////////////////////////////////////////////////////
+// Local to node Cshift
+//////////////////////////////////////////////////////
+template<class vobj> void Cshift_local(Lattice<vobj>& ret,const Lattice<vobj> &rhs,int dimension,int shift)
+{
+  int sshift[2];
+
+  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);
+  } else {
+    Cshift_local(ret,rhs,dimension,shift,0x1);// if checkerboard is unfavourable take two passes
+    Cshift_local(ret,rhs,dimension,shift,0x2);// both with block stride loop iteration
+  }
+}
+
+template<class vobj> void Cshift_local(Lattice<vobj> &ret,const Lattice<vobj> &rhs,int dimension,int shift,int cbmask)
+{
+  GridBase *grid = rhs.Grid();
+  int fd = grid->_fdimensions[dimension];
+  int rd = grid->_rdimensions[dimension];
+  int ld = grid->_ldimensions[dimension];
+  int gd = grid->_gdimensions[dimension];
+  int ly = grid->_simd_layout[dimension];
+
+  // Map to always positive shift modulo global full dimension.
+  shift = (shift+fd)%fd;
+
+  // the permute type
+  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 bo  = x * grid->_ostride[dimension];
+    int cb= (cbmask==0x2)? Odd : Even;
+
+    int sshift = grid->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,cb);
+    int sx     = (x+sshift)%rd;
+    
+    // wrap is whether sshift > rd.
+    //  num is sshift mod rd.
+    // 
+    //  shift 7
+    //
+    //  XoXo YcYc 
+    //  oXoX cYcY
+    //  XoXo YcYc
+    //  oXoX cYcY
+    //
+    //  sshift -- 
+    //
+    //  XX YY ; 3
+    //  XX YY ; 0
+    //  XX YY ; 3
+    //  XX YY ; 0
+    //
+    int permute_slice=0;
+    if(permute_dim){
+      int wrap = sshift/rd; wrap=wrap % ly;
+      int  num = sshift%rd;
+
+      if ( x< rd-num ) permute_slice=wrap;
+      else permute_slice = (wrap+1)%ly;
+
+      if ( (ly>2) && (permute_slice) ) {
+	assert(permute_type & RotateBit);
+	permute_type_dist = permute_type|permute_slice;
+      } else {
+	permute_type_dist = permute_type;
+      }
+    }
+
+    if ( permute_slice ) Copy_plane_permute(ret,rhs,dimension,x,sx,cbmask,permute_type_dist);
+    else                 Copy_plane(ret,rhs,dimension,x,sx,cbmask); 
+  
+  }
+}
+NAMESPACE_END(Grid);
+

Grid/cshift/Cshift_mpi.h

@@ -0,0 +1,546 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/cshift/Cshift_mpi.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef _GRID_CSHIFT_MPI_H_
+#define _GRID_CSHIFT_MPI_H_
+
+
+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()); 
+  
+  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);
+        
+  // 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);
+
+  RealD t1,t0;
+  t0=usecond();
+  if ( !comm_dim ) {
+    //std::cout << "CSHIFT: Cshift_local" <<std::endl;
+    Cshift_local(ret,rhs,dimension,shift); // Handles checkerboarding
+  } else if ( splice_dim ) {
+    //std::cout << "CSHIFT: Cshift_comms_simd call - splice_dim = " << splice_dim << " shift " << shift << " dimension = " << dimension << std::endl;
+    Cshift_comms_simd(ret,rhs,dimension,shift);
+  } else {
+    //std::cout << "CSHIFT: Cshift_comms" <<std::endl;
+    Cshift_comms(ret,rhs,dimension,shift);
+  }
+  t1=usecond();
+  //  std::cout << GridLogPerformance << "Cshift took "<< (t1-t0)/1e3 << " ms"<<std::endl;
+  return ret;
+}
+
+template<class vobj> void Cshift_comms(Lattice<vobj>& ret,const Lattice<vobj> &rhs,int dimension,int shift)
+{
+  int sshift[2];
+
+  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;
+  if ( sshift[0] == sshift[1] ) {
+    //    std::cout << "Single pass Cshift_comms" <<std::endl;
+    Cshift_comms(ret,rhs,dimension,shift,0x3);
+  } else {
+    //    std::cout << "Two pass Cshift_comms" <<std::endl;
+    Cshift_comms(ret,rhs,dimension,shift,0x1);// if checkerboard is unfavourable take two passes
+    Cshift_comms(ret,rhs,dimension,shift,0x2);// both with block stride loop iteration
+  }
+}
+
+template<class vobj> void Cshift_comms_simd(Lattice<vobj>& ret,const Lattice<vobj> &rhs,int dimension,int shift)
+{
+  int sshift[2];
+
+  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] ) {
+    //std::cout << "Single pass Cshift_comms" <<std::endl;
+    Cshift_comms_simd(ret,rhs,dimension,shift,0x3);
+  } else {
+    //std::cout << "Two pass Cshift_comms" <<std::endl;
+    Cshift_comms_simd(ret,rhs,dimension,shift,0x1);// if checkerboard is unfavourable take two passes
+    Cshift_comms_simd(ret,rhs,dimension,shift,0x2);// both with block stride loop iteration
+  }
+}
+#define ACCELERATOR_CSHIFT_NO_COPY
+#ifdef ACCELERATOR_CSHIFT_NO_COPY
+template<class vobj> void Cshift_comms(Lattice<vobj> &ret,const Lattice<vobj> &rhs,int dimension,int shift,int cbmask)
+{
+  typedef typename vobj::vector_type vector_type;
+  typedef typename vobj::scalar_type scalar_type;
+
+  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 ;
+  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];
+  static cshiftVector<vobj> send_buf; send_buf.resize(buffer_size);
+  static cshiftVector<vobj> recv_buf; recv_buf.resize(buffer_size);
+    
+  int cb= (cbmask==0x2)? Odd : Even;
+  int sshift= rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,cb);
+  RealD tcopy=0.0;
+  RealD tgather=0.0;
+  RealD tscatter=0.0;
+  RealD tcomms=0.0;
+  uint64_t xbytes=0;
+  for(int x=0;x<rd;x++){       
+
+    int sx        =  (x+sshift)%rd;
+    int comm_proc = ((x+sshift)/rd)%pd;
+    
+    if (comm_proc==0) {
+      tcopy-=usecond();
+      Copy_plane(ret,rhs,dimension,x,sx,cbmask); 
+      tcopy+=usecond();
+    } else {
+
+      int words = buffer_size;
+      if (cbmask != 0x3) words=words>>1;
+
+      int bytes = words * sizeof(vobj);
+
+      tgather-=usecond();
+      Gather_plane_simple (rhs,send_buf,dimension,sx,cbmask);
+      tgather+=usecond();
+
+      //      int rank           = grid->_processor;
+      int recv_from_rank;
+      int xmit_to_rank;
+      grid->ShiftedRanks(dimension,comm_proc,xmit_to_rank,recv_from_rank);
+      
+      tcomms-=usecond();
+      //      grid->Barrier();
+
+      grid->SendToRecvFrom((void *)&send_buf[0],
+			   xmit_to_rank,
+			   (void *)&recv_buf[0],
+			   recv_from_rank,
+			   bytes);
+      xbytes+=bytes;
+      //      grid->Barrier();
+      tcomms+=usecond();
+
+      tscatter-=usecond();
+      Scatter_plane_simple (ret,recv_buf,dimension,x,cbmask);
+      tscatter+=usecond();
+    }
+  }
+  /*
+  std::cout << GridLogPerformance << " Cshift copy    "<<tcopy/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift gather  "<<tgather/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift scatter "<<tscatter/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift comm    "<<tcomms/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift BW      "<<(2.0*xbytes)/tcomms<<" MB/s "<<2*xbytes<< " Bytes "<<std::endl;
+  */
+}
+
+template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vobj> &rhs,int dimension,int shift,int cbmask)
+{
+  GridBase *grid=rhs.Grid();
+  const int Nsimd = grid->Nsimd();
+  typedef typename vobj::vector_type vector_type;
+  typedef typename vobj::scalar_object scalar_object;
+  typedef typename vobj::scalar_type scalar_type;
+   
+  int fd = grid->_fdimensions[dimension];
+  int rd = grid->_rdimensions[dimension];
+  int ld = grid->_ldimensions[dimension];
+  int pd = grid->_processors[dimension];
+  int simd_layout     = grid->_simd_layout[dimension];
+  int comm_dim        = grid->_processors[dimension] >1 ;
+
+  //std::cout << "Cshift_comms_simd dim "<< dimension << " fd "<<fd<<" rd "<<rd
+  //    << " ld "<<ld<<" pd " << pd<<" simd_layout "<<simd_layout 
+  //    << " comm_dim " << comm_dim << " cbmask " << cbmask <<std::endl;
+
+  assert(comm_dim==1);
+  assert(simd_layout==2);
+  assert(shift>=0);
+  assert(shift<fd);
+
+  RealD tcopy=0.0;
+  RealD tgather=0.0;
+  RealD tscatter=0.0;
+  RealD tcomms=0.0;
+  uint64_t xbytes=0;
+  
+  int permute_type=grid->PermuteType(dimension);
+
+  ///////////////////////////////////////////////
+  // 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);
+
+  static std::vector<cshiftVector<scalar_object> >  send_buf_extract; send_buf_extract.resize(Nsimd);
+  static std::vector<cshiftVector<scalar_object> >  recv_buf_extract; recv_buf_extract.resize(Nsimd);
+  scalar_object *  recv_buf_extract_mpi;
+  scalar_object *  send_buf_extract_mpi;
+ 
+  for(int s=0;s<Nsimd;s++){
+    send_buf_extract[s].resize(buffer_size);
+    recv_buf_extract[s].resize(buffer_size);
+  }
+
+  int bytes = buffer_size*sizeof(scalar_object);
+
+  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);
+
+  // loop over outer coord planes orthog to dim
+  for(int x=0;x<rd;x++){       
+
+    // FIXME call local permute copy if none are offnode.
+    for(int i=0;i<Nsimd;i++){       
+      pointers[i] = &send_buf_extract[i][0];
+    }
+    int sx   = (x+sshift)%rd;
+    tgather-=usecond();
+    Gather_plane_extract(rhs,pointers,dimension,sx,cbmask);
+    tgather+=usecond();
+
+    for(int i=0;i<Nsimd;i++){
+      
+      int inner_bit = (Nsimd>>(permute_type+1));
+      int ic= (i&inner_bit)? 1:0;
+
+      int my_coor          = rd*ic + x;
+      int nbr_coor         = my_coor+sshift;
+      int nbr_proc = ((nbr_coor)/ld) % pd;// relative shift in processors
+
+      int nbr_ic   = (nbr_coor%ld)/rd;    // inner coord of peer
+      int nbr_ox   = (nbr_coor%rd);       // outer coord of peer
+      int nbr_lane = (i&(~inner_bit));
+
+      int recv_from_rank;
+      int xmit_to_rank;
+
+      if (nbr_ic) nbr_lane|=inner_bit;
+
+      assert (sx == nbr_ox);
+
+      if(nbr_proc){
+	grid->ShiftedRanks(dimension,nbr_proc,xmit_to_rank,recv_from_rank); 
+
+	tcomms-=usecond();
+	//	grid->Barrier();
+
+	send_buf_extract_mpi = &send_buf_extract[nbr_lane][0];
+	recv_buf_extract_mpi = &recv_buf_extract[i][0];
+	grid->SendToRecvFrom((void *)send_buf_extract_mpi,
+			     xmit_to_rank,
+			     (void *)recv_buf_extract_mpi,
+			     recv_from_rank,
+			     bytes);
+
+	xbytes+=bytes;
+	//	grid->Barrier();
+	tcomms+=usecond();
+
+	rpointers[i] = &recv_buf_extract[i][0];
+      } else { 
+	rpointers[i] = &send_buf_extract[nbr_lane][0];
+      }
+
+    }
+    tscatter-=usecond();
+    Scatter_plane_merge(ret,rpointers,dimension,x,cbmask);
+    tscatter+=usecond();
+  }
+  /*
+  std::cout << GridLogPerformance << " Cshift (s) copy    "<<tcopy/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift (s) gather  "<<tgather/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift (s) scatter "<<tscatter/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift (s) comm    "<<tcomms/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift BW      "<<(2.0*xbytes)/tcomms<<" MB/s "<<2*xbytes<< " Bytes "<<std::endl;
+  */
+}
+#else 
+template<class vobj> void Cshift_comms(Lattice<vobj> &ret,const Lattice<vobj> &rhs,int dimension,int shift,int cbmask)
+{
+  typedef typename vobj::vector_type vector_type;
+  typedef typename vobj::scalar_type scalar_type;
+
+  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 ;
+  assert(simd_layout==1);
+  assert(comm_dim==1);
+  assert(shift>=0);
+  assert(shift<fd);
+  RealD tcopy=0.0;
+  RealD tgather=0.0;
+  RealD tscatter=0.0;
+  RealD tcomms=0.0;
+  uint64_t xbytes=0;
+  
+  int buffer_size = rhs.Grid()->_slice_nblock[dimension]*rhs.Grid()->_slice_block[dimension];
+  static cshiftVector<vobj> send_buf_v; send_buf_v.resize(buffer_size);
+  static cshiftVector<vobj> recv_buf_v; recv_buf_v.resize(buffer_size);
+  vobj *send_buf;
+  vobj *recv_buf;
+  {
+    grid->ShmBufferFreeAll();
+    size_t bytes = buffer_size*sizeof(vobj);
+    send_buf=(vobj *)grid->ShmBufferMalloc(bytes);
+    recv_buf=(vobj *)grid->ShmBufferMalloc(bytes);
+  }
+    
+  int cb= (cbmask==0x2)? Odd : Even;
+  int sshift= rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,cb);
+
+  for(int x=0;x<rd;x++){       
+
+    int sx        =  (x+sshift)%rd;
+    int comm_proc = ((x+sshift)/rd)%pd;
+    
+    if (comm_proc==0) {
+
+      tcopy-=usecond();
+      Copy_plane(ret,rhs,dimension,x,sx,cbmask); 
+      tcopy+=usecond();
+
+    } else {
+
+      int words = buffer_size;
+      if (cbmask != 0x3) words=words>>1;
+
+      int bytes = words * sizeof(vobj);
+
+      tgather-=usecond();
+      Gather_plane_simple (rhs,send_buf_v,dimension,sx,cbmask);
+      tgather+=usecond();
+
+      //      int rank           = grid->_processor;
+      int recv_from_rank;
+      int xmit_to_rank;
+      grid->ShiftedRanks(dimension,comm_proc,xmit_to_rank,recv_from_rank);
+
+
+      tcomms-=usecond();
+      //      grid->Barrier();
+
+      acceleratorCopyDeviceToDevice((void *)&send_buf_v[0],(void *)&send_buf[0],bytes);
+      grid->SendToRecvFrom((void *)&send_buf[0],
+			   xmit_to_rank,
+			   (void *)&recv_buf[0],
+			   recv_from_rank,
+			   bytes);
+      xbytes+=bytes;
+      acceleratorCopyDeviceToDevice((void *)&recv_buf[0],(void *)&recv_buf_v[0],bytes);
+
+      //      grid->Barrier();
+      tcomms+=usecond();
+
+      tscatter-=usecond();
+      Scatter_plane_simple (ret,recv_buf_v,dimension,x,cbmask);
+      tscatter+=usecond();
+    }
+  }
+  /*
+  std::cout << GridLogPerformance << " Cshift copy    "<<tcopy/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift gather  "<<tgather/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift scatter "<<tscatter/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift comm    "<<tcomms/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift BW      "<<(2.0*xbytes)/tcomms<<" MB/s "<<2*xbytes<< " Bytes "<<std::endl;
+  */
+}
+
+template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vobj> &rhs,int dimension,int shift,int cbmask)
+{
+  GridBase *grid=rhs.Grid();
+  const int Nsimd = grid->Nsimd();
+  typedef typename vobj::vector_type vector_type;
+  typedef typename vobj::scalar_object scalar_object;
+  typedef typename vobj::scalar_type scalar_type;
+   
+  int fd = grid->_fdimensions[dimension];
+  int rd = grid->_rdimensions[dimension];
+  int ld = grid->_ldimensions[dimension];
+  int pd = grid->_processors[dimension];
+  int simd_layout     = grid->_simd_layout[dimension];
+  int comm_dim        = grid->_processors[dimension] >1 ;
+
+  //std::cout << "Cshift_comms_simd dim "<< dimension << " fd "<<fd<<" rd "<<rd
+  //    << " ld "<<ld<<" pd " << pd<<" simd_layout "<<simd_layout 
+  //    << " comm_dim " << comm_dim << " cbmask " << cbmask <<std::endl;
+
+  assert(comm_dim==1);
+  assert(simd_layout==2);
+  assert(shift>=0);
+  assert(shift<fd);
+  RealD tcopy=0.0;
+  RealD tgather=0.0;
+  RealD tscatter=0.0;
+  RealD tcomms=0.0;
+  uint64_t xbytes=0;
+
+  int permute_type=grid->PermuteType(dimension);
+
+  ///////////////////////////////////////////////
+  // 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);
+
+  static std::vector<cshiftVector<scalar_object> >  send_buf_extract; send_buf_extract.resize(Nsimd);
+  static std::vector<cshiftVector<scalar_object> >  recv_buf_extract; recv_buf_extract.resize(Nsimd);
+  scalar_object *  recv_buf_extract_mpi;
+  scalar_object *  send_buf_extract_mpi;
+  {
+    size_t bytes = sizeof(scalar_object)*buffer_size;
+    grid->ShmBufferFreeAll();
+    send_buf_extract_mpi = (scalar_object *)grid->ShmBufferMalloc(bytes);
+    recv_buf_extract_mpi = (scalar_object *)grid->ShmBufferMalloc(bytes);
+  }
+  for(int s=0;s<Nsimd;s++){
+    send_buf_extract[s].resize(buffer_size);
+    recv_buf_extract[s].resize(buffer_size);
+  }
+
+  int bytes = buffer_size*sizeof(scalar_object);
+
+  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);
+
+  // loop over outer coord planes orthog to dim
+  for(int x=0;x<rd;x++){       
+
+    // FIXME call local permute copy if none are offnode.
+    for(int i=0;i<Nsimd;i++){       
+      pointers[i] = &send_buf_extract[i][0];
+    }
+    tgather-=usecond();
+    int sx   = (x+sshift)%rd;
+    Gather_plane_extract(rhs,pointers,dimension,sx,cbmask);
+    tgather+=usecond();
+
+    for(int i=0;i<Nsimd;i++){
+      
+      int inner_bit = (Nsimd>>(permute_type+1));
+      int ic= (i&inner_bit)? 1:0;
+
+      int my_coor          = rd*ic + x;
+      int nbr_coor         = my_coor+sshift;
+      int nbr_proc = ((nbr_coor)/ld) % pd;// relative shift in processors
+
+      int nbr_ic   = (nbr_coor%ld)/rd;    // inner coord of peer
+      int nbr_ox   = (nbr_coor%rd);       // outer coord of peer
+      int nbr_lane = (i&(~inner_bit));
+
+      int recv_from_rank;
+      int xmit_to_rank;
+
+      if (nbr_ic) nbr_lane|=inner_bit;
+
+      assert (sx == nbr_ox);
+
+      if(nbr_proc){
+	grid->ShiftedRanks(dimension,nbr_proc,xmit_to_rank,recv_from_rank); 
+
+	tcomms-=usecond();
+	//	grid->Barrier();
+
+	acceleratorCopyDeviceToDevice((void *)&send_buf_extract[nbr_lane][0],(void *)send_buf_extract_mpi,bytes);
+	grid->SendToRecvFrom((void *)send_buf_extract_mpi,
+			     xmit_to_rank,
+			     (void *)recv_buf_extract_mpi,
+			     recv_from_rank,
+			     bytes);
+	acceleratorCopyDeviceToDevice((void *)recv_buf_extract_mpi,(void *)&recv_buf_extract[i][0],bytes);
+	xbytes+=bytes;
+
+	//	grid->Barrier();
+	tcomms+=usecond();
+	rpointers[i] = &recv_buf_extract[i][0];
+      } else { 
+	rpointers[i] = &send_buf_extract[nbr_lane][0];
+      }
+
+    }
+    tscatter-=usecond();
+    Scatter_plane_merge(ret,rpointers,dimension,x,cbmask);
+    tscatter+=usecond();
+
+  }
+  /*
+  std::cout << GridLogPerformance << " Cshift (s) copy    "<<tcopy/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift (s) gather  "<<tgather/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift (s) scatter "<<tscatter/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift (s) comm    "<<tcomms/1e3<<" ms"<<std::endl;
+  std::cout << GridLogPerformance << " Cshift BW      "<<(2.0*xbytes)/tcomms<<" MB/s"<<std::endl;
+  */
+}
+#endif
+NAMESPACE_END(Grid); 
+
+#endif