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@ -10,7 +10,7 @@ examples.
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MPI initialization
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------------------
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--------------------
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Grid supports threaded MPI sends and receives and, if running with
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more than one thread, requires the MPI_THREAD_MULTIPLE mode of message
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@ -21,7 +21,7 @@ appropriate initialization call is::
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assert(MPI_THREAD_MULTIPLE == provided);
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Grid Initialization
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-------------------
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---------------------
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Grid itself is initialized with a call::
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@ -44,6 +44,8 @@ properly initialized.
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std::vector<int> GridDefaultSimd(int Nd,vComplex::Nsimd()); SIMD layout
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std::vector<int> GridDefaultMpi(); MPI layout
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int Grid::GridThread::GetThreads(); number of threads
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============================================================= ===========================================================================================================
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MPI coordination
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----------------
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@ -96,7 +98,7 @@ returns a rank that agrees with Grid's `peRank`.
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Mapping fields between Grid and user layouts
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-------------------------------------------
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---------------------------------------------
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In order to map data between layouts, it is important to know
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how the lattice sites are distributed across the processor grid. A
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@ -90,7 +90,8 @@ or any codes directly interacting with the
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* Stencil
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will make use of facilities provided by to assist the creation of high performance code. The internal data layout complexities
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will make use of facilities provided by to assist the creation of high performance code.
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The internal data layout complexities
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will be exposed to some degree and the interfaces are subject to change without notice as HPC architectures change.
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Since some of the internal implementation details are needed to explain the design strategy of grid these will be
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@ -585,18 +586,18 @@ to Grid to choose the specific word size.
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Type definitions are provided in qcd/QCD.h to give the internal index structures
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of QCD codes. For example::
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template<typename vtype> using iSinglet = iScalar<iScalar<iScalar<vtype> > >;
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template<typename vtype> using iSpinMatrix = iScalar<iMatrix<iScalar<vtype>, Ns> >;
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template<typename vtype> using iColourMatrix = iScalar<iScalar<iMatrix<vtype, Nc> > > ;
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template<typename vtype> using iSpinColourMatrix = iScalar<iMatrix<iMatrix<vtype, Nc>, Ns> >;
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template<typename vtype> using iLorentzColourMatrix = iVector<iScalar<iMatrix<vtype, Nc> >, Nd > ;
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template<typename vtype> using iDoubleStoredColourMatrix = iVector<iScalar<iMatrix<vtype, Nc> >, Nds > ;
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template<typename vtype> using iSpinVector = iScalar<iVector<iScalar<vtype>, Ns> >;
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template<typename vtype> using iColourVector = iScalar<iScalar<iVector<vtype, Nc> > >;
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template<typename vtype> using iSpinColourVector = iScalar<iVector<iVector<vtype, Nc>, Ns> >;
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template<typename vtype> using iHalfSpinVector = iScalar<iVector<iScalar<vtype>, Nhs> >;
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template<typename vtype> using iHalfSpinColourVector = iScalar<iVector<iVector<vtype, Nc>, Nhs> >;
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template<typename vtype>
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using iSinglet = iScalar<iScalar<iScalar<vtype> > >;
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using iSpinMatrix = iScalar<iMatrix<iScalar<vtype>, Ns> >;
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using iColourMatrix = iScalar<iScalar<iMatrix<vtype, Nc> > > ;
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using iSpinColourMatrix = iScalar<iMatrix<iMatrix<vtype, Nc>, Ns> >;
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using iLorentzColourMatrix = iVector<iScalar<iMatrix<vtype, Nc> >, Nd > ;
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using iDoubleStoredColourMatrix = iVector<iScalar<iMatrix<vtype, Nc> >, Nds > ;
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using iSpinVector = iScalar<iVector<iScalar<vtype>, Ns> >;
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using iColourVector = iScalar<iScalar<iVector<vtype, Nc> > >;
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using iSpinColourVector = iScalar<iVector<iVector<vtype, Nc>, Ns> >;
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using iHalfSpinVector = iScalar<iVector<iScalar<vtype>, Nhs> >;
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using iHalfSpinColourVector = iScalar<iVector<iVector<vtype, Nc>, Nhs> >;
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Giving the type table:
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@ -1021,26 +1022,6 @@ This enables the coordinates to be manipulated without heap allocation or thread
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and avoids introducing STL functions into GPU code, but does so at the expense of introducing
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a maximum dimensionality. This limit is easy to change (lib/util/Coordinate.h).
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**Internals**
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The processor Grid is defined by data values in the Communicator object::
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int _Nprocessors; // How many in all
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std::vector<int> _processors; // Which dimensions get relayed out over processors lanes.
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int _processor; // linear processor rank
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std::vector<int> _processor_coor; // linear processor coordinate
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unsigned long _ndimension;
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Grid_MPI_Comm communicator;
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The final of these is potentially an MPI Cartesian communicator, mapping some total number of processors
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to an N-dimensional coordinate system. This is used by Grid to geometrically decompose the subvolumes of a
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lattice field across processing elements. Grid is aware of multiple ranks per node and attempts to ensure
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that the geometrical decomposition keeps as many neigbours as possible on the same node. This is done
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by reordering the ranks in the constructor of a Communicator object once the topology requested has
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been indicated, via an internal call to the method OptimalCommunicator(). The reordering is chosen
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by Grid to trick MPI, which makes a simple lexicographic assignment of ranks to coordinate, to ensure
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that the simple lexicographic assignment of the reordered ranks is the optimal choice. MPI does not do this
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by default and substantial improvements arise from this design choice.
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Grids
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-------------
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@ -1135,6 +1116,26 @@ are provided to communicate fields between different communicators (e.g. between
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Grid_split (Umu,s_Umu);
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Grid_split (src,s_src);
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**Internals**
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The processor Grid is defined by data values in the Communicator object::
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int _Nprocessors; // How many in all
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std::vector<int> _processors; // Which dimensions get relayed out over processors lanes.
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int _processor; // linear processor rank
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std::vector<int> _processor_coor; // linear processor coordinate
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unsigned long _ndimension;
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Grid_MPI_Comm communicator;
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The final of these is potentially an MPI Cartesian communicator, mapping some total number of processors
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to an N-dimensional coordinate system. This is used by Grid to geometrically decompose the subvolumes of a
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lattice field across processing elements. Grid is aware of multiple ranks per node and attempts to ensure
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that the geometrical decomposition keeps as many neigbours as possible on the same node. This is done
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by reordering the ranks in the constructor of a Communicator object once the topology requested has
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been indicated, via an internal call to the method OptimalCommunicator(). The reordering is chosen
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by Grid to trick MPI, which makes a simple lexicographic assignment of ranks to coordinate, to ensure
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that the simple lexicographic assignment of the reordered ranks is the optimal choice. MPI does not do this
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by default and substantial improvements arise from this design choice.
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Lattice containers
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-----------------------------------------
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@ -1565,62 +1566,6 @@ lattice site :math:`x_\mu = 1` in the rhs to :math:`x_\mu = 0` in the result.
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}
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CovariantCshift
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^^^^^^^^^^^^^^^^^^^^
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Covariant Cshift operations are provided for common cases of the boundary condition. These may be further optimised
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in future::
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template<class covariant,class gauge>
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Lattice<covariant> CovShiftForward(const Lattice<gauge> &Link, int mu,
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const Lattice<covariant> &field);
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template<class covariant,class gauge>
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Lattice<covariant> CovShiftBackward(const Lattice<gauge> &Link, int mu,
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const Lattice<covariant> &field);
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Boundary conditions
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^^^^^^^^^^^^^^^^^^^^
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The covariant shift routines occur in namespaces PeriodicBC and ConjugateBC. The correct covariant shift
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for the boundary condition is passed into the gauge actions and wilson loops via an
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"Impl" template policy class.
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The relevant staples, plaquettes, and loops are formed by using the provided method::
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Impl::CovShiftForward
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Impl::CovShiftBackward
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etc... This makes physics code transform appropriately with externally supplied rules about
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treating the boundary.
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**Example** (lib/qcd/util/WilsonLoops.h)::
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static void dirPlaquette(GaugeMat &plaq, const std::vector<GaugeMat> &U,
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const int mu, const int nu) {
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// ___
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//| |
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//|<__|
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plaq = Gimpl::CovShiftForward(U[mu],mu,
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Gimpl::CovShiftForward(U[nu],nu,
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Gimpl::CovShiftBackward(U[mu],mu,
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Gimpl::CovShiftIdentityBackward(U[nu], nu))));
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}
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Currently provided predefined implementations are (qcd/action/gauge/GaugeImplementations.h)::
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typedef PeriodicGaugeImpl<GimplTypesR> PeriodicGimplR; // Real.. whichever prec
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typedef PeriodicGaugeImpl<GimplTypesF> PeriodicGimplF; // Float
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typedef PeriodicGaugeImpl<GimplTypesD> PeriodicGimplD; // Double
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typedef PeriodicGaugeImpl<GimplAdjointTypesR> PeriodicGimplAdjR; // Real.. whichever prec
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typedef PeriodicGaugeImpl<GimplAdjointTypesF> PeriodicGimplAdjF; // Float
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typedef PeriodicGaugeImpl<GimplAdjointTypesD> PeriodicGimplAdjD; // Double
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typedef ConjugateGaugeImpl<GimplTypesR> ConjugateGimplR; // Real.. whichever prec
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typedef ConjugateGaugeImpl<GimplTypesF> ConjugateGimplF; // Float
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typedef ConjugateGaugeImpl<GimplTypesD> ConjugateGimplD; // Double
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Inter-grid transfer operations
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@ -1694,11 +1639,6 @@ Growing a lattice by a multiple factor, with periodic replication::
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That latter is useful to, for example, pre-thermalise a smaller volume and then grow the volume in HMC.
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It was written while debugging G-parity boundary conditions.
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Input/Output facilities
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---------------------------------------------
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Random number generators
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=========================================
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@ -1732,18 +1672,32 @@ The interface is as follows::
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class GridSerialRNG {
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GridSerialRNG();
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void SeedFixedIntegers(const std::vector<int> &seeds);
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void SeedUniqueString(const std::string &s);
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}
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class GridParallelRNG {
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GridParallelRNG(GridBase *grid);
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void SeedFixedIntegers(const std::vector<int> &seeds);
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void SeedUniqueString(const std::string &s);
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}
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template <class vobj> void random(GridParallelRNG &rng,Lattice<vobj> &l) { rng.fill(l,rng._uniform); }
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template <class vobj> void gaussian(GridParallelRNG &rng,Lattice<vobj> &l) { rng.fill(l,rng._gaussian); }
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* Seeding
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template <class sobj> void random(GridSerialRNG &rng,sobj &l) { rng.fill(l,rng._uniform ); }
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template <class sobj> void gaussian(GridSerialRNG &rng,sobj &l) { rng.fill(l,rng._gaussian ); }
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The SeedUniqueString uses a 256bit SHA from the OpenSSL library to construct integer seeds.
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The reason for this is to enable reproducible seeding in the measurement sector of physics codes.
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For example, labelling a random drawn by a string representation the physics information, and the
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appending trajectory number will give a unique set of seeds for each measurement on each trajectory.
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This string based functionality is probably not expected to be used in a lattice evolution, except for
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possibly the initial state. Subsequent evolution should checkpoint and restore lattice RNG state using
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the interfaces below.
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These may be drawn as follows::
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void random(GridParallelRNG &rng,Lattice<vobj> &l) { rng.fill(l,rng._uniform); }
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void gaussian(GridParallelRNG &rng,Lattice<vobj> &l) { rng.fill(l,rng._gaussian); }
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void random(GridSerialRNG &rng,sobj &l) { rng.fill(l,rng._uniform ); }
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void gaussian(GridSerialRNG &rng,sobj &l) { rng.fill(l,rng._gaussian ); }
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* Serial RNG's are used to assign scalar fields.
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@ -2435,13 +2389,52 @@ Class::
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class AlgRemez
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Iterative
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------------
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Iterative solvers and algorithms
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-----------------------------------
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We document a number of iterative algorithms of topical relevance to Lattice Gauge theory.
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These are written for application to arbitrary fields and arbitrary operators using type
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templating, by implementating them as arbitrary OperatorFunctions.
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Most of these algorithms these algorithms operate on a generic matrix class, which
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derives from LinearOperatorBase.
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Linear operators
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^^^^^^^^^^^^^^^^^
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By sharing the class for Sparse Matrix across multiple operator wrappers, we can share code
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between RB and non-RB variants. Sparse matrix is an abstract fermion action def, and then
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the LinearOperator wrappers implement the specialisation of "Op" and "AdjOp" to the cases minimising
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replication of code.
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algorithms/LinearOperator.h
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Class::
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template<class Field> class LinearOperatorBase {
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public:
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// Support for coarsening to a multigrid
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virtual void OpDiag (const Field &in, Field &out) = 0; // Abstract base
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virtual void OpDir (const Field &in, Field &out,int dir,int disp) = 0; // Abstract base
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virtual void Op (const Field &in, Field &out) = 0; // Abstract base
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virtual void AdjOp (const Field &in, Field &out) = 0; // Abstract base
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virtual void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2) = 0;
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virtual void HermOp(const Field &in, Field &out)=0;
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};
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The specific operators are:
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template<class Matrix,class Field> class MdagMLinearOperator : public LinearOperatorBase<Field>
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template<class Matrix,class Field> class ShiftedMdagMLinearOperator : public LinearOperatorBase<Field>
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template<class Matrix,class Field> class HermitianLinearOperator : public LinearOperatorBase<Field>
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template<class Field> class SchurOperatorBase : public LinearOperatorBase<Field>
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template<class Matrix,class Field> class SchurDiagOneRH : public SchurOperatorBase<Field>
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template<class Matrix,class Field> class SchurDiagOneLH : public SchurOperatorBase<Field>
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template<class Matrix,class Field> class SchurStaggeredOperator : public SchurOperatorBase<Field>
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Conjugate Gradient
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^^^^^^^^^^^^^^^^^^^
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@ -2558,41 +2551,6 @@ Solve method::
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void calc(std::vector<RealD>& eval, std::vector<Field>& evec, const Field& src, int& Nconv, bool reverse=false)
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Linear operators
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^^^^^^^^^^^^^^^^^
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By sharing the class for Sparse Matrix across multiple operator wrappers, we can share code
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between RB and non-RB variants. Sparse matrix is an abstract fermion action def, and then
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the LinearOperator wrappers implement the specialisation of "Op" and "AdjOp" to the cases minimising
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replication of code.
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algorithms/LinearOperator.h
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Class::
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template<class Field> class LinearOperatorBase {
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public:
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// Support for coarsening to a multigrid
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virtual void OpDiag (const Field &in, Field &out) = 0; // Abstract base
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virtual void OpDir (const Field &in, Field &out,int dir,int disp) = 0; // Abstract base
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virtual void Op (const Field &in, Field &out) = 0; // Abstract base
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virtual void AdjOp (const Field &in, Field &out) = 0; // Abstract base
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virtual void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2) = 0;
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virtual void HermOp(const Field &in, Field &out)=0;
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};
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The specific operators are:
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template<class Matrix,class Field> class MdagMLinearOperator : public LinearOperatorBase<Field>
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template<class Matrix,class Field> class ShiftedMdagMLinearOperator : public LinearOperatorBase<Field>
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template<class Matrix,class Field> class HermitianLinearOperator : public LinearOperatorBase<Field>
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template<class Field> class SchurOperatorBase : public LinearOperatorBase<Field>
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template<class Matrix,class Field> class SchurDiagOneRH : public SchurOperatorBase<Field>
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template<class Matrix,class Field> class SchurDiagOneLH : public SchurOperatorBase<Field>
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template<class Matrix,class Field> class SchurStaggeredOperator : public SchurOperatorBase<Field>
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Schur decomposition
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^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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@ -2647,37 +2605,15 @@ Grid Dirac algebra, spin projectors, and Gamma multiplication table.
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The spin basis is:
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* :math:`\gamma_x`
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==== == == ==
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( 0 0 0 i)
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( 0 0 i 0)
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( 0 -i 0 0)
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(-i 0 0 0)
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==== == == ==
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.. math:: \gamma_x= \left(\begin{array}{cccc} 0& 0& 0& i\\ 0& 0& i& 0\\ 0&-i& 0& 0\\ -i& 0& 0& 0 \end{array}\right)
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* :math:`\gamma_y`
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==== == == ==
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( 0 0 0 -1)
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( 0 0 1 0)
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( 0 1 0 0)
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(-1 0 0 0)
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==== == == ==
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.. math:: \gamma_y= \left(\begin{array}{cccc} 0& 0& 0&-1\\ 0& 0& 1& 0\\ 0& 1& 0& 0\\ -1& 0& 0& 0 \end{array}\right)
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* :math:`\gamma_z`
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==== == == ==
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( 0 0 i 0)
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( 0 0 0 -i)
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(-i 0 0 0)
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( 0 i 0 0)
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==== == == ==
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.. math:: \gamma_z= \left(\begin{array}{cccc} 0& 0& i& 0\\ 0& 0& 0&-i\\ -i& 0& 0& 0\\ 0& i& 0& 0 \end{array}\right)
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* :math:`\gamma_t`
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==== == == ==
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( 0 0 1 0)
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( 0 0 0 1)
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( 1 0 0 0)
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( 0 1 0 0)
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==== == == ==
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.. math:: \gamma_t= \left(\begin{array}{cccc} 0& 0& 1& 0\\ 0& 0& 0& 1\\ 1& 0& 0& 0\\ 0& 1& 0& 0 \end{array}\right)
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.. math:: \gamma_5= \left(\begin{array}{cccc} 1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0&-1 &0\\ 0& 0& 0&-1 \end{array}\right)
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These can be accessed via a strongly typed enumeration to avoid multiplication by zeros.
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The values are considered opaque, and symbolic names must be used.
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@ -2733,73 +2669,523 @@ They can be used, for example (benchmarks/Benchmark_wilson.cc)::
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Two spin projection is also possible on non-lattice fields, and used to build high performance routines
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such as the Wilson kernel::
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template<class vtype> strong_inline void spProjXp (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
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template<class vtype> strong_inline void spProjYp (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
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template<class vtype> strong_inline void spProjZp (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
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template<class vtype> strong_inline void spProjTp (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
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template<class vtype> strong_inline void spProj5p (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
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template<class vtype> strong_inline void spProjXm (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
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template<class vtype> strong_inline void spProjYm (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
|
||||
template<class vtype> strong_inline void spProjZm (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
|
||||
template<class vtype> strong_inline void spProjTm (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
|
||||
template<class vtype> strong_inline void spProj5m (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
|
||||
template<class vtype> void spProjXp (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
|
||||
template<class vtype> void spProjYp (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
|
||||
template<class vtype> void spProjZp (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
|
||||
template<class vtype> void spProjTp (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
|
||||
template<class vtype> void spProj5p (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
|
||||
template<class vtype> void spProjXm (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
|
||||
template<class vtype> void spProjYm (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
|
||||
template<class vtype> void spProjZm (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
|
||||
template<class vtype> void spProjTm (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
|
||||
template<class vtype> void spProj5m (iVector<vtype,Nhs> &hspin,const iVector<vtype,Ns> &fspin)
|
||||
|
||||
and there are associated reconstruction routines for assembling four spinors from these two spinors::
|
||||
|
||||
template<class vtype> strong_inline void spReconXp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void spReconYp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void spReconZp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void spReconTp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void spRecon5p (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void spReconXm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void spReconYm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void spReconZm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void spReconTm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void spRecon5m (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void spReconXp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void spReconYp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void spReconZp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void spReconTp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void spRecon5p (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void spReconXm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void spReconYm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void spReconZm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void spReconTm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void spRecon5m (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
|
||||
template<class vtype> strong_inline void accumReconXp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void accumReconYp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void accumReconZp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void accumReconTp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void accumRecon5p (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void accumReconXm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void accumReconYm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void accumReconZm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void accumReconTm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> strong_inline void accumRecon5m (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void accumReconXp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void accumReconYp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void accumReconZp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void accumReconTp (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void accumRecon5p (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void accumReconXm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void accumReconYm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void accumReconZm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void accumReconTm (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
template<class vtype> void accumRecon5m (iVector<vtype,Ns> &fspin,const iVector<vtype,Nhs> &hspin)
|
||||
|
||||
These ca
|
||||
|
||||
|
||||
SU(N)
|
||||
--------
|
||||
|
||||
A generic Nc qcd/utils/SUn.h is provided. This defines a template class::
|
||||
|
||||
template <int ncolour> class SU ;
|
||||
|
||||
The most important external methods are::
|
||||
|
||||
static void printGenerators(void) ;
|
||||
template <class cplx> static void generator(int lieIndex, iSUnMatrix<cplx> &ta) ;
|
||||
|
||||
static void SubGroupHeatBath(GridSerialRNG &sRNG, GridParallelRNG &pRNG, RealD beta, // coeff multiplying staple in action (with no 1/Nc)
|
||||
LatticeMatrix &link,
|
||||
const LatticeMatrix &barestaple, // multiplied by action coeffs so th
|
||||
int su2_subgroup, int nheatbath, LatticeInteger &wheremask);
|
||||
|
||||
static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
|
||||
LatticeMatrix &out,
|
||||
Real scale = 1.0) ;
|
||||
static void GaugeTransform( GaugeField &Umu, GaugeMat &g)
|
||||
static void RandomGaugeTransform(GridParallelRNG &pRNG, GaugeField &Umu, GaugeMat &g);
|
||||
|
||||
static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) ;
|
||||
static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out);
|
||||
static void ColdConfiguration(GaugeField &out);
|
||||
|
||||
static void taProj( const LatticeMatrixType &in, LatticeMatrixType &out);
|
||||
static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) ;
|
||||
|
||||
static int su2subgroups(void) ; // returns how many subgroups
|
||||
|
||||
|
||||
Specific instantiations are defined::
|
||||
|
||||
typedef SU<2> SU2;
|
||||
typedef SU<3> SU3;
|
||||
typedef SU<4> SU4;
|
||||
typedef SU<5> SU5;
|
||||
|
||||
For example, Quenched QCD updating may be run as (tests/core/Test_quenched_update.cc)::
|
||||
|
||||
for(int sweep=0;sweep<1000;sweep++){
|
||||
|
||||
RealD plaq = ColourWilsonLoops::avgPlaquette(Umu);
|
||||
|
||||
std::cout<<GridLogMessage<<"sweep "<<sweep<<" PLAQUETTE "<<plaq<<std::endl;
|
||||
|
||||
for( int cb=0;cb<2;cb++ ) {
|
||||
|
||||
one.checkerboard=subsets[cb];
|
||||
mask= zero;
|
||||
setCheckerboard(mask,one);
|
||||
|
||||
// std::cout<<GridLogMessage<<mask<<std::endl;
|
||||
for(int mu=0;mu<Nd;mu++){
|
||||
|
||||
// Get Link and Staple term in action; must contain Beta and
|
||||
// any other coeffs
|
||||
ColourWilsonLoops::Staple(staple,Umu,mu);
|
||||
|
||||
link = PeekIndex<LorentzIndex>(Umu,mu);
|
||||
|
||||
for( int subgroup=0;subgroup<SU3::su2subgroups();subgroup++ ) {
|
||||
|
||||
// update Even checkerboard
|
||||
SU3::SubGroupHeatBath(sRNG,pRNG,beta,link,staple,subgroup,20,mask);
|
||||
|
||||
}
|
||||
|
||||
PokeIndex<LorentzIndex>(Umu,link,mu);
|
||||
|
||||
//reunitarise link;
|
||||
ProjectOnGroup(Umu);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
Space time grids
|
||||
----------------
|
||||
|
||||
Random configurations and random gauge transforms
|
||||
---------------------------------------------------
|
||||
|
||||
|
||||
Wilson loops
|
||||
--------------
|
||||
|
||||
|
||||
Lattice actions
|
||||
=========================================
|
||||
|
||||
.. todo:: CD: The whole section needs to be completed, of course
|
||||
We discuss in some detail the implementation of the lattice actions.
|
||||
The action is a sum of terms, each of which must inherit from and provide the following interface.
|
||||
|
||||
WilsonCloverFermionR Dwc(Umu, Grid, RBGrid, mass, csw_r, csw_t, anis, params);
|
||||
lib/qcd/action/ActionBase.h::
|
||||
|
||||
class Action
|
||||
{
|
||||
|
||||
public:
|
||||
bool is_smeared = false;
|
||||
// Heatbath?
|
||||
virtual void refresh(const GaugeField& U, GridParallelRNG& pRNG) = 0; // refresh pseudofermions
|
||||
virtual RealD S(const GaugeField& U) = 0; // evaluate the action
|
||||
virtual void deriv(const GaugeField& U, GaugeField& dSdU) = 0; // evaluate the action derivative
|
||||
virtual std::string action_name() = 0; // return the action name
|
||||
virtual std::string LogParameters() = 0; // prints action parameters
|
||||
virtual ~Action(){}
|
||||
};
|
||||
|
||||
Fermion Lattice actions are defined in the qcd/action/fermion subdirectory and in the
|
||||
qcd/action/gauge subdirectories. For Hybrid Monte Carlo and derivative sampling algorithm
|
||||
Pseudofermoin actions are defined in the qcd/action/pseudofermion subdirectory.
|
||||
|
||||
The simplest lattice action is the Wilson plaquette action, and we start by considering the Wilson loops
|
||||
facilities as this is illustrative of the implementation policy design approach.
|
||||
|
||||
Wilson loops
|
||||
--------------
|
||||
|
||||
Wilson loops are common objects in Lattice Gauge Theory.
|
||||
A utility class is provided to assist assembling these as they occur both in common observable construction but
|
||||
also in actions such as the Wilson plaquette and the rectangle actions.
|
||||
|
||||
Since derivatives with respect to gauge links are required for evolution codes, non-closed staples of
|
||||
various types are also provided. The gauge actions are all assembled consistently from the Wilson loops
|
||||
class.
|
||||
|
||||
**Implementation policies**
|
||||
|
||||
The Wilson loops class is templated to take a implementation policy class parameter. The covarian Cshift is inherity from
|
||||
the policy and implements boundary conditions, such as period, anti-period or charge conjugate. In this
|
||||
way the Wilson loop code can automatically transform with the boundary condition and give the right plaquette,
|
||||
force terms etc... for the boundary conditions passed in external to the class.
|
||||
|
||||
|
||||
This implementation policy class is called an "impl", and a class that bundles together all the required
|
||||
rules to assemble a gauge action is called a Gimpl.
|
||||
|
||||
There are several facilities provided by a Gimpl.
|
||||
|
||||
These include Boundary conditions and consequently a CovariantCshift.
|
||||
|
||||
CovariantCshift
|
||||
^^^^^^^^^^^^^^^^^^
|
||||
|
||||
Covariant Cshift operations are provided for common cases of the boundary condition. These may be further optimised
|
||||
in future::
|
||||
|
||||
template<class covariant,class gauge>
|
||||
Lattice<covariant> CovShiftForward(const Lattice<gauge> &Link, int mu,
|
||||
const Lattice<covariant> &field);
|
||||
|
||||
template<class covariant,class gauge>
|
||||
Lattice<covariant> CovShiftBackward(const Lattice<gauge> &Link, int mu,
|
||||
const Lattice<covariant> &field);
|
||||
|
||||
Boundary conditions
|
||||
^^^^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
The covariant shift routines occur in namespaces PeriodicBC and ConjugateBC. The correct covariant shift
|
||||
for the boundary condition is passed into the gauge actions and wilson loops via an
|
||||
"Impl" template policy class.
|
||||
|
||||
The relevant staples, plaquettes, and loops are formed by using the provided method::
|
||||
|
||||
Impl::CovShiftForward
|
||||
Impl::CovShiftBackward
|
||||
|
||||
etc... This makes physics code transform appropriately with externally supplied rules about
|
||||
treating the boundary.
|
||||
|
||||
**Example** (lib/qcd/util/WilsonLoops.h)::
|
||||
|
||||
static void dirPlaquette(GaugeMat &plaq, const std::vector<GaugeMat> &U,
|
||||
const int mu, const int nu) {
|
||||
// ___
|
||||
//| |
|
||||
//|<__|
|
||||
plaq = Gimpl::CovShiftForward(U[mu],mu,
|
||||
Gimpl::CovShiftForward(U[nu],nu,
|
||||
Gimpl::CovShiftBackward(U[mu],mu,
|
||||
Gimpl::CovShiftIdentityBackward(U[nu], nu))));
|
||||
}
|
||||
|
||||
Currently provided predefined implementations are (qcd/action/gauge/GaugeImplementations.h)::
|
||||
|
||||
typedef PeriodicGaugeImpl<GimplTypesR> PeriodicGimplR; // Real.. whichever prec
|
||||
typedef PeriodicGaugeImpl<GimplTypesF> PeriodicGimplF; // Float
|
||||
typedef PeriodicGaugeImpl<GimplTypesD> PeriodicGimplD; // Double
|
||||
|
||||
typedef PeriodicGaugeImpl<GimplAdjointTypesR> PeriodicGimplAdjR; // Real.. whichever prec
|
||||
typedef PeriodicGaugeImpl<GimplAdjointTypesF> PeriodicGimplAdjF; // Float
|
||||
typedef PeriodicGaugeImpl<GimplAdjointTypesD> PeriodicGimplAdjD; // Double
|
||||
|
||||
typedef ConjugateGaugeImpl<GimplTypesR> ConjugateGimplR; // Real.. whichever prec
|
||||
typedef ConjugateGaugeImpl<GimplTypesF> ConjugateGimplF; // Float
|
||||
typedef ConjugateGaugeImpl<GimplTypesD> ConjugateGimplD; // Double
|
||||
|
||||
Gauge Actions
|
||||
---------------
|
||||
|
||||
lib/qcd/action/gauge/Photon.h defines the U(1) field::
|
||||
|
||||
class Photon
|
||||
|
||||
using Fourier techniques.
|
||||
|
||||
lib/qcd/action/gauge/WilsonGaugeAction.h defines the standard plaquette action::
|
||||
|
||||
template <class Gimpl>
|
||||
class WilsonGaugeAction : public Action<typename Gimpl::GaugeField> ;
|
||||
|
||||
This action is suitable to use in a Hybrid Monte Carlo evolution as an action term and has constructor::
|
||||
|
||||
WilsonGaugeAction(RealD beta_);
|
||||
|
||||
lib/qcd/action/gauge/PlaqPlusRectangleAction.h defines the standard plaquette plus rectangle class of action::
|
||||
|
||||
template<class Gimpl>
|
||||
class PlaqPlusRectangleAction : public Action<typename Gimpl::GaugeField> ;
|
||||
|
||||
The constructor is::
|
||||
|
||||
PlaqPlusRectangleAction(RealD b,RealD c);
|
||||
|
||||
Due to varying conventions, convenience wrappers are provided::
|
||||
|
||||
template<class Gimpl> class RBCGaugeAction : public PlaqPlusRectangleAction<Gimpl>;
|
||||
template<class Gimpl> class IwasakiGaugeAction : public RBCGaugeAction<Gimpl> ;
|
||||
template<class Gimpl> class SymanzikGaugeAction : public RBCGaugeAction<Gimpl> ;
|
||||
template<class Gimpl> class DBW2GaugeAction : public RBCGaugeAction<Gimpl> ;
|
||||
|
||||
With convenience constructors to set the rectangle coefficient automatically to popular values::
|
||||
|
||||
SymanzikGaugeAction(RealD beta) : RBCGaugeAction<Gimpl>(beta,-1.0/12.0) {};
|
||||
IwasakiGaugeAction(RealD beta) : RBCGaugeAction<Gimpl>(beta,-0.331) {};
|
||||
DBW2GaugeAction(RealD beta) : RBCGaugeAction<Gimpl>(beta,-1.4067) {};
|
||||
|
||||
Gauge
|
||||
--------
|
||||
|
||||
Fermion
|
||||
--------
|
||||
|
||||
These classes all make use of a Fermion Implementation (Fimpl) policy class to provide
|
||||
things like boundary conditions, covariant transportation rules etc.
|
||||
|
||||
All Fermion operators actions inherit from a common base class,
|
||||
|
||||
that conforms to the CheckerBoardedSparseMatrix interface and constrains these objects to conform to the
|
||||
interface expected by general algorithms in 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 RealD M (const Field &in, Field &out)=0;
|
||||
virtual RealD Mdag (const Field &in, Field &out)=0;
|
||||
virtual void MdagM(const Field &in, Field &out,RealD &ni,RealD &no) {
|
||||
Field tmp (in._grid);
|
||||
ni=M(in,tmp);
|
||||
no=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;
|
||||
};
|
||||
|
||||
/////////////////////////////////////////////////////////////////////////////////////////////
|
||||
// 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;
|
||||
// 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;
|
||||
|
||||
};
|
||||
|
||||
The base class for Fermion Operators inherits frmo these::
|
||||
|
||||
template<class Impl>
|
||||
class FermionOperator : public CheckerBoardedSparseMatrixBase<typename Impl::FermionField>, public Impl
|
||||
|
||||
These all make use of an implementation template class, and the possible implementations include::
|
||||
|
||||
typedef WilsonImpl<vComplexF, FundamentalRepresentation, CoeffReal > WilsonImplF; // Float
|
||||
typedef WilsonImpl<vComplexD, FundamentalRepresentation, CoeffReal > WilsonImplD; // Double
|
||||
|
||||
Staggered fermions make us of a spin index free field via the StaggeredImpl::
|
||||
|
||||
typedef StaggeredImpl<vComplexF, FundamentalRepresentation > StaggeredImplF; // Float
|
||||
typedef StaggeredImpl<vComplexD, FundamentalRepresentation > StaggeredImplD; // Double
|
||||
|
||||
A number of alternate, non-fundamental Fermion representations are supported. Note that the Fermion
|
||||
action code is common to each of these, demonstrating the utility of the template Fimpl classes for separating
|
||||
the code that varies from the invariant sections::
|
||||
|
||||
typedef WilsonImpl<vComplexF, AdjointRepresentation, CoeffReal > WilsonAdjImplF; // Float
|
||||
typedef WilsonImpl<vComplexD, AdjointRepresentation, CoeffReal > WilsonAdjImplD; // Double
|
||||
|
||||
typedef WilsonImpl<vComplexF, TwoIndexSymmetricRepresentation, CoeffReal > WilsonTwoIndexSymmetricImplF; // Float
|
||||
typedef WilsonImpl<vComplexD, TwoIndexSymmetricRepresentation, CoeffReal > WilsonTwoIndexSymmetricImplD; // Double
|
||||
|
||||
typedef WilsonImpl<vComplexF, TwoIndexAntiSymmetricRepresentation, CoeffReal > WilsonTwoIndexAntiSymmetricImplF; // Float
|
||||
typedef WilsonImpl<vComplexD, TwoIndexAntiSymmetricRepresentation, CoeffReal > WilsonTwoIndexAntiSymmetricImplD; // Double
|
||||
|
||||
G-parity boundary conditions are supported, and an additional flavour index inserted on the Fermion field via the Gparity implementation::
|
||||
|
||||
typedef GparityWilsonImpl<vComplexF, FundamentalRepresentation,CoeffReal> GparityWilsonImplF; // Float
|
||||
typedef GparityWilsonImpl<vComplexD, FundamentalRepresentation,CoeffReal> GparityWilsonImplD; // Double
|
||||
|
||||
ZMobius Fermions use complex rather than real action coefficients and are supported via an alternate implementation::
|
||||
|
||||
typedef WilsonImpl<vComplexF, FundamentalRepresentation, CoeffComplex > ZWilsonImplF; // Float
|
||||
typedef WilsonImpl<vComplexD, FundamentalRepresentation, CoeffComplex > ZWilsonImplD; // Double
|
||||
|
||||
|
||||
Some example constructor calls are given below for Wilson and Clover fermions::
|
||||
|
||||
template <class Impl> class WilsonFermion;
|
||||
|
||||
With constructor::
|
||||
|
||||
WilsonFermion(GaugeField &_Umu, GridCartesian &Fgrid,
|
||||
GridRedBlackCartesian &Hgrid, RealD _mass,
|
||||
const ImplParams &p = ImplParams(),
|
||||
const WilsonAnisotropyCoefficients &anis = WilsonAnisotropyCoefficients() );
|
||||
|
||||
and::
|
||||
|
||||
template <class Impl> class WilsonCloverFermion : public WilsonFermion<Impl>;
|
||||
|
||||
with constructor::
|
||||
|
||||
WilsonCloverFermion(GaugeField &_Umu, GridCartesian &Fgrid,
|
||||
GridRedBlackCartesian &Hgrid,
|
||||
const RealD _mass,
|
||||
const RealD _csw_r = 0.0,
|
||||
const RealD _csw_t = 0.0,
|
||||
const WilsonAnisotropyCoefficients &clover_anisotropy = WilsonAnisotropyCoefficients(),
|
||||
const ImplParams &impl_p = ImplParams());
|
||||
|
||||
Additional paramters allow for anisotropic versions to be created, which take default values for
|
||||
the isotropic case.
|
||||
|
||||
The constuctor signatures can be found in the header files in qcd/action/fermion/
|
||||
A complete list of the 4D ultralocal Fermion types is::
|
||||
|
||||
WilsonFermion<WilsonImplF> WilsonFermionF;
|
||||
WilsonFermion<WilsonAdjImplF> WilsonAdjFermionF;
|
||||
WilsonFermion<WilsonTwoIndexSymmetricImplF> WilsonTwoIndexSymmetricFermionF;
|
||||
WilsonFermion<WilsonTwoIndexAntiSymmetricImplF> WilsonTwoIndexAntiSymmetricFermionF;
|
||||
WilsonTMFermion<WilsonImplF> WilsonTMFermionF;
|
||||
WilsonCloverFermion<WilsonImplF> WilsonCloverFermionF;
|
||||
WilsonCloverFermion<WilsonAdjImplF> WilsonCloverAdjFermionF;
|
||||
WilsonCloverFermion<WilsonTwoIndexSymmetricImplF> WilsonCloverTwoIndexSymmetricFermionF;
|
||||
WilsonCloverFermion<WilsonTwoIndexAntiSymmetricImplF> WilsonCloverTwoIndexAntiSymmetricFermionF;
|
||||
ImprovedStaggeredFermion<StaggeredImplF> ImprovedStaggeredFermionF;
|
||||
|
||||
Cayley form chiral fermions (incl. domain wall)::
|
||||
|
||||
DomainWallFermion<WilsonImplF> DomainWallFermionF;
|
||||
DomainWallEOFAFermion<WilsonImplF> DomainWallEOFAFermionF;
|
||||
MobiusFermion<WilsonImplF> MobiusFermionF;
|
||||
MobiusEOFAFermion<WilsonImplF> MobiusEOFAFermionF;
|
||||
ZMobiusFermion<ZWilsonImplF> ZMobiusFermionF;
|
||||
ScaledShamirFermion<WilsonImplF> ScaledShamirFermionF;
|
||||
MobiusZolotarevFermion<WilsonImplF> MobiusZolotarevFermionF;
|
||||
ShamirZolotarevFermion<WilsonImplF> ShamirZolotarevFermionF;
|
||||
OverlapWilsonCayleyTanhFermion<WilsonImplF> OverlapWilsonCayleyTanhFermionF;
|
||||
OverlapWilsonCayleyZolotarevFermion<WilsonImplF> OverlapWilsonCayleyZolotarevFermionF;
|
||||
|
||||
Continued fraction overlap::
|
||||
|
||||
OverlapWilsonContFracTanhFermion<WilsonImplF> OverlapWilsonContFracTanhFermionF;
|
||||
OverlapWilsonContFracZolotarevFermion<WilsonImplF> OverlapWilsonContFracZolotarevFermionF;
|
||||
|
||||
Partial fraction overlap::
|
||||
|
||||
OverlapWilsonPartialFractionTanhFermion<WilsonImplF> OverlapWilsonPartialFractionTanhFermionF;
|
||||
OverlapWilsonPartialFractionZolotarevFermion<WilsonImplF> OverlapWilsonPartialFractionZolotarevFermionF;
|
||||
|
||||
Gparity cases; a partial list is defined until tested::
|
||||
|
||||
WilsonFermion<GparityWilsonImplF> GparityWilsonFermionF;
|
||||
DomainWallFermion<GparityWilsonImplF> GparityDomainWallFermionF;
|
||||
DomainWallEOFAFermion<GparityWilsonImplF> GparityDomainWallEOFAFermionF;
|
||||
|
||||
WilsonTMFermion<GparityWilsonImplF> GparityWilsonTMFermionF;
|
||||
MobiusFermion<GparityWilsonImplF> GparityMobiusFermionF;
|
||||
MobiusEOFAFermion<GparityWilsonImplF> GparityMobiusEOFAFermionF;
|
||||
|
||||
For each action, the suffix "F" can be replaced with "D" to obtain a double precision version. More generally,
|
||||
it is possible to perform communications with a different precision from computation.
|
||||
The number of combinations is rather large to list, but in the above listing the substitution is the
|
||||
obvious one.
|
||||
|
||||
========== ================ ==================
|
||||
Suffix Computation Communication
|
||||
========== ================ ==================
|
||||
F fp32 fp32
|
||||
D fp64 fp64
|
||||
R default default
|
||||
FH fp32 fp16
|
||||
DF fp64 fp32
|
||||
RL default lower
|
||||
========== ================ ==================
|
||||
|
||||
|
||||
Pseudofermion
|
||||
---------------
|
||||
|
||||
Pseudofermion actions are defined in qcd/action/pseudofermion/ .
|
||||
These action terms are built from template classes::
|
||||
|
||||
// Base even odd HMC on the normal Mee based 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 )
|
||||
//
|
||||
// Determinant is det of middle factor. This assumes Mee is indept of U.
|
||||
template<class Impl> class SchurDifferentiableOperator ;
|
||||
|
||||
// S = phi^dag (Mdag M)^-1 phi
|
||||
template <class Impl> class TwoFlavourPseudoFermionAction ;
|
||||
|
||||
// S = phi^dag V (Mdag M)^-1 Vdag phi
|
||||
template<class Impl> class TwoFlavourRatioPseudoFermionAction ;
|
||||
|
||||
// S = phi^dag (Mdag M)^-1 phi (odd)
|
||||
// + phi^dag (Mdag M)^-1 phi (even)
|
||||
template <class Impl> class TwoFlavourEvenOddPseudoFermionAction;
|
||||
|
||||
// S = phi^dag V (Mdag M)^-1 Vdag phi
|
||||
template <class Impl> class TwoFlavourEvenOddRatioPseudoFermionAction ;
|
||||
|
||||
|
||||
Rational HMC pseudofermion terms::
|
||||
|
||||
// S_f = chi^dag * N(M^dag*M)/D(M^dag*M) * chi
|
||||
//
|
||||
// Here, M is some operator
|
||||
// N and D makeup the rat. poly
|
||||
template<class Impl> class OneFlavourRationalPseudoFermionAction;
|
||||
|
||||
// S_f = chi^dag* P(V^dag*V)/Q(V^dag*V)* N(M^dag*M)/D(M^dag*M)* P(V^dag*V)/Q(V^dag*V)* chi
|
||||
//
|
||||
// Here P/Q \sim R_{1/4} ~ (V^dagV)^{1/4}
|
||||
// Here N/D \sim R_{-1/2} ~ (M^dagM)^{-1/2}
|
||||
template<class Impl> class OneFlavourRatioRationalPseudoFermionAction;
|
||||
|
||||
|
||||
// S = phi^dag (Mdag M)^-1/2 phi
|
||||
template <class Impl> class OneFlavourEvenOddRationalPseudoFermionAction;
|
||||
|
||||
// S_f = chi^dag* P(V^dag*V)/Q(V^dag*V)* N(M^dag*M)/D(M^dag*M)* P(V^dag*V)/Q(V^dag*V)* chi
|
||||
//
|
||||
// Here P/Q \sim R_{1/4} ~ (V^dagV)^{1/4}
|
||||
// Here N/D \sim R_{-1/2} ~ (M^dagM)^{-1/2}
|
||||
template<class Impl> class OneFlavourEvenOddRatioRationalPseudoFermionAction;
|
||||
|
||||
The relevant Fermion operators are constructed externally,
|
||||
and references are passed in to these object constructors. Thus, they work for any Fermion operator and the code
|
||||
can be shared. For example, one of the constructors is given as::
|
||||
|
||||
TwoFlavourEvenOddRatioPseudoFermionAction(FermionOperator<Impl> &_NumOp,
|
||||
FermionOperator<Impl> &_DenOp,
|
||||
OperatorFunction<FermionField> & DS,
|
||||
OperatorFunction<FermionField> & AS) :
|
||||
|
||||
|
||||
The exact one flavour algorithm for Domain Wall Fermions is present but is not documented here::
|
||||
|
||||
#include <Grid/qcd/action/pseudofermion/ExactOneFlavourRatio.h>
|
||||
|
||||
HMC
|
||||
=========================================
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user