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81287133f3
Grid/extras/Hadrons/Modules/MContraction/A2APionField.hpp
Peter Boyle 81287133f3 New files
2018-08-28 11:32:41 +01:00

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#ifndef Hadrons_MContraction_A2APionField_hpp_
#define Hadrons_MContraction_A2APionField_hpp_
#include <Grid/Hadrons/Global.hpp>
#include <Grid/Hadrons/Module.hpp>
#include <Grid/Hadrons/ModuleFactory.hpp>
#include <Grid/Hadrons/AllToAllVectors.hpp>
#include <unsupported/Eigen/CXX11/Tensor>
BEGIN_HADRONS_NAMESPACE
/******************************************************************************
* A2APionField *
******************************************************************************/
BEGIN_MODULE_NAMESPACE(MContraction)
typedef std::pair<Gamma::Algebra, Gamma::Algebra> GammaPair;
class A2APionFieldPar : Serializable
{
public:
GRID_SERIALIZABLE_CLASS_MEMBERS(A2APionFieldPar,
int, cacheBlock,
int, schurBlock,
int, Nmom,
std::string, A2A_i,
std::string, A2A_j,
std::string, output);
};
template <typename FImpl>
class TA2APionField : public Module<A2APionFieldPar>
{
public:
FERM_TYPE_ALIASES(FImpl, );
SOLVER_TYPE_ALIASES(FImpl, );
typedef A2AModesSchurDiagTwo<typename FImpl::FermionField, FMat, Solver> A2ABase;
int d_unroll ;
public:
// constructor
TA2APionField(const std::string name);
// destructor
virtual ~TA2APionField(void){};
// dependency relation
virtual std::vector<std::string> getInput(void);
virtual std::vector<std::string> getOutput(void);
// setup
virtual void setup(void);
// execution
virtual void execute(void);
virtual void DeltaFeq2(int dt_min,int dt_max,
Eigen::Tensor<ComplexD,2> &dF2_fig8,
Eigen::Tensor<ComplexD,2> &dF2_trtr,
Eigen::Tensor<ComplexD,3> &WW_sd,
const LatticeFermion *vs,
const LatticeFermion *vd,
int orthogdim);
virtual void DeltaFeq2_alt(int dt_min,int dt_max,
Eigen::Tensor<ComplexD,2> &dF2_fig8,
Eigen::Tensor<ComplexD,2> &dF2_trtr,
Eigen::Tensor<ComplexD,1> &den0,
Eigen::Tensor<ComplexD,1> &den1,
Eigen::Tensor<ComplexD,3> &WW_sd,
const LatticeFermion *vs,
const LatticeFermion *vd,
int orthogdim);
///////////////////////////////////////
// Arithmetic help. Move to Grid??
///////////////////////////////////////
virtual void PionFieldXX(Eigen::Tensor<ComplexD,3> &mat,
const LatticeFermion *wi,
const LatticeFermion *vj,
int orthogdim,
int g5);
///////////////////////////
// Simple wrappers
///////////////////////////
virtual void PionFieldWVmom(Eigen::Tensor<ComplexD,4> &mat,
const LatticeFermion *wi,
const LatticeFermion *vj,
const std::vector<LatticeComplex > &mom,
int orthogdim);
virtual void PionFieldWV(Eigen::Tensor<ComplexD,3> &mat,
const LatticeFermion *wi,
const LatticeFermion *vj,
int orthogdim);
virtual void PionFieldVV(Eigen::Tensor<ComplexD,3> &mat,
const LatticeFermion *vi,
const LatticeFermion *vj,
int orthogdim);
virtual void PionFieldWW(Eigen::Tensor<ComplexD,3> &mat,
const LatticeFermion *wi,
const LatticeFermion *wj,
int orthogdim);
};
MODULE_REGISTER(A2APionField, ARG(TA2APionField<FIMPL>), MContraction);
MODULE_REGISTER(ZA2APionField, ARG(TA2APionField<ZFIMPL>), MContraction);
/******************************************************************************
* TA2APionField implementation *
******************************************************************************/
// constructor /////////////////////////////////////////////////////////////////
template <typename FImpl>
TA2APionField<FImpl>::TA2APionField(const std::string name)
: Module<A2APionFieldPar>(name)
{
}
// dependencies/products ///////////////////////////////////////////////////////
template <typename FImpl>
std::vector<std::string> TA2APionField<FImpl>::getInput(void)
{
std::vector<std::string> in;
in.push_back(par().A2A_i + "_class");
in.push_back(par().A2A_i + "_w_high_4d");
in.push_back(par().A2A_i + "_v_high_4d");
in.push_back(par().A2A_j + "_class");
in.push_back(par().A2A_j + "_w_high_4d");
in.push_back(par().A2A_j + "_v_high_4d");
return in;
}
template <typename FImpl>
std::vector<std::string> TA2APionField<FImpl>::getOutput(void)
{
std::vector<std::string> out = {};
return out;
}
// setup ///////////////////////////////////////////////////////////////////////
template <typename FImpl>
void TA2APionField<FImpl>::setup(void)
{
d_unroll = 32; // empirical default. Can be overridden if desired
// Four D fields
envTmp(std::vector<FermionField>, "wi", 1, par().schurBlock, FermionField(env().getGrid(1)));
envTmp(std::vector<FermionField>, "vi", 1, par().schurBlock, FermionField(env().getGrid(1)));
envTmp(std::vector<FermionField>, "wj", 1, par().schurBlock, FermionField(env().getGrid(1)));
envTmp(std::vector<FermionField>, "vj", 1, par().schurBlock, FermionField(env().getGrid(1)));
// 5D tmp
int Ls_i = env().getObjectLs(par().A2A_i + "_class");
envTmpLat(FermionField, "tmp_5d", Ls_i);
int Ls_j= env().getObjectLs(par().A2A_j + "_class");
assert ( Ls_i == Ls_j );
}
//////////////////////////////////////////////////////////////////////////////////
// Cache blocked arithmetic routine
// Could move to Grid ???
//////////////////////////////////////////////////////////////////////////////////
template <typename FImpl>
void TA2APionField<FImpl>::PionFieldWVmom(Eigen::Tensor<ComplexD,4> &mat,
const LatticeFermion *wi,
const LatticeFermion *vj,
const std::vector<LatticeComplex > &mom,
int orthogdim)
{
double t0,t1,t2,t3; t0=t1=t2=t3= 0.0;
typedef typename FImpl::SiteSpinor vobj;
typedef typename vobj::scalar_object sobj;
typedef typename vobj::scalar_type scalar_type;
typedef typename vobj::vector_type vector_type;
typedef iSpinMatrix<vector_type> SpinMatrix_v;
typedef iSpinMatrix<scalar_type> SpinMatrix_s;
int Lblock = mat.dimension(2);
int Rblock = mat.dimension(3);
GridBase *grid = wi[0]._grid;
const int nd = grid->_ndimension;
const int Nsimd = grid->Nsimd();
int Nt = grid->GlobalDimensions()[orthogdim];
int Nmom = mom.size();
int fd=grid->_fdimensions[orthogdim];
int ld=grid->_ldimensions[orthogdim];
int rd=grid->_rdimensions[orthogdim];
// will locally sum vectors first
// sum across these down to scalars
// splitting the SIMD
int MFrvol = rd*Lblock*Rblock*Nmom;
int MFlvol = ld*Lblock*Rblock*Nmom;
Vector<vector_type > lvSum(MFrvol);
parallel_for (int r = 0; r < MFrvol; r++){
lvSum[r] = zero;
}
Vector<scalar_type > lsSum(MFlvol);
parallel_for (int r = 0; r < MFlvol; r++){
lsSum[r]=scalar_type(0.0);
}
int e1= grid->_slice_nblock[orthogdim];
int e2= grid->_slice_block [orthogdim];
int stride=grid->_slice_stride[orthogdim];
t0-=usecond();
parallel_for(int r=0;r<rd;r++){
int so=r*grid->_ostride[orthogdim]; // base offset for start of plane
for(int n=0;n<e1;n++){
for(int b=0;b<e2;b++){
int ss= so+n*stride+b;
for(int i=0;i<Lblock;i++){
auto w = conjugate(wi[i]._odata[ss]);
for(int j=0;j<Rblock;j++){
auto v = vj[j]._odata[ss];
auto vv = w()(0)(0) * v()(0)(0)// Gamma5 Dirac basis explicitly written out
+ w()(0)(1) * v()(0)(1)
+ w()(0)(2) * v()(0)(2)
+ w()(1)(0) * v()(1)(0)
+ w()(1)(1) * v()(1)(1)
+ w()(1)(2) * v()(1)(2)
- w()(2)(0) * v()(2)(0)
- w()(2)(1) * v()(2)(1)
- w()(2)(2) * v()(2)(2)
- w()(3)(0) * v()(3)(0)
- w()(3)(1) * v()(3)(1)
- w()(3)(2) * v()(3)(2);
// After getting the sitewise product do the mom phase loop
int base = Nmom*i+Nmom*Lblock*j+Nmom*Lblock*Rblock*r;
for ( int m=0;m<Nmom;m++){
int idx = m+base;
auto phase = mom[m]._odata[ss];
mac(&lvSum[idx],&vv,&phase()()());
}
}
}
}
}
}
t0+=usecond();
// Sum across simd lanes in the plane, breaking out orthog dir.
t1-=usecond();
parallel_for(int rt=0;rt<rd;rt++){
std::vector<int> icoor(nd);
iScalar<vector_type> temp;
std::vector<iScalar<scalar_type> > extracted(Nsimd);
// std::vector<scalar_type> extracted(Nsimd);
for(int i=0;i<Lblock;i++){
for(int j=0;j<Rblock;j++){
for(int m=0;m<Nmom;m++){
int ij_rdx = m+Nmom*i+Nmom*Lblock*j+Nmom*Lblock*Rblock*rt;
temp._internal = lvSum[ij_rdx];
extract(temp,extracted);
for(int idx=0;idx<Nsimd;idx++){
grid->iCoorFromIindex(icoor,idx);
int ldx = rt+icoor[orthogdim]*rd;
int ij_ldx = m+Nmom*i+Nmom*Lblock*j+Nmom*Lblock*Rblock*ldx;
lsSum[ij_ldx]=lsSum[ij_ldx]+extracted[idx]._internal;
}
}}}
}
t1+=usecond();
assert(mat.dimension(0) == Nmom);
assert(mat.dimension(1) == Nt);
t2-=usecond();
// ld loop and local only??
int pd = grid->_processors[orthogdim];
int pc = grid->_processor_coor[orthogdim];
parallel_for_nest2(int lt=0;lt<ld;lt++)
{
for(int pt=0;pt<pd;pt++){
int t = lt + pt*ld;
if (pt == pc){
for(int i=0;i<Lblock;i++){
for(int j=0;j<Rblock;j++){
for(int m=0;m<Nmom;m++){
int ij_dx = m+Nmom*i + Nmom*Lblock * j + Nmom*Lblock * Rblock * lt;
mat(m,t,i,j) = lsSum[ij_dx];
}
}
}
} else {
const scalar_type zz(0.0);
for(int i=0;i<Lblock;i++){
for(int j=0;j<Rblock;j++){
for(int m=0;m<Nmom;m++){
mat(m,t,i,j) =zz;
}
}
}
}
}
}
t2+=usecond();
t3-=usecond();
grid->GlobalSumVector(&mat(0,0,0,0),Nmom*Nt*Lblock*Rblock);
t3+=usecond();
}
///////////////////////////////////////////////////////////////////
//Meson
// Interested in
//
// sum_x,y Trace[ G S(x,tx,y,ty) G S(y,ty,x,tx) ]
//
// Conventional meson field:
//
// = sum_x,y Trace[ sum_j G |v_j(y,ty)> <w_j(x,tx)| G sum_i |v_i(x,tx) ><w_i(y,ty)| ]
// = sum_ij sum_x,y < w_j(x,tx)| G |v_i(x,tx) > <w_i(y,ty) (x)|G| v_j(y,ty) >
// = sum_ij PI_ji(tx) PI_ij(ty)
//
// G5-Hermiticity
//
// sum_x,y Trace[ G S(x,tx,y,ty) G S(y,ty,x,tx) ]
// = sum_x,y Trace[ G S(x,tx,y,ty) G g5 S^dag(x,tx,y,ty) g5 ]
// = sum_x,y Trace[ g5 G sum_j |v_j(y,ty)> <w_j(x,tx)| G g5 sum_i (|v_j(y,ty)> <w_i(x,tx)|)^dag ] -- (*)
//
// NB: Dag applies to internal indices spin,colour,complex
//
// = sum_ij sum_x,y Trace[ g5 G |v_j(y,ty)> <w_j(x,tx)| G g5 |w_i(x,tx)> <v_i(y,ty)| ]
// = sum_ij sum_x,y <v_i(y,ty)|g5 G |v_j(y,ty)> <w_j(x,tx)| G g5 |w_i(x,tx)>
// = sum_ij PionVV(ty) PionWW(tx)
//
// (*) is only correct estimator if w_i and w_j come from distinct noise sets to preserve the kronecker
// expectation value. Otherwise biased.
////////////////////////////////////////////////////////////////////
template <typename FImpl>
void TA2APionField<FImpl>::PionFieldXX(Eigen::Tensor<ComplexD,3> &mat,
const LatticeFermion *wi,
const LatticeFermion *vj,
int orthogdim,
int g5)
{
typedef typename FImpl::SiteSpinor vobj;
typedef typename vobj::scalar_object sobj;
typedef typename vobj::scalar_type scalar_type;
typedef typename vobj::vector_type vector_type;
typedef iSpinMatrix<vector_type> SpinMatrix_v;
typedef iSpinMatrix<scalar_type> SpinMatrix_s;
int Lblock = mat.dimension(1);
int Rblock = mat.dimension(2);
GridBase *grid = wi[0]._grid;
const int nd = grid->_ndimension;
const int Nsimd = grid->Nsimd();
int Nt = grid->GlobalDimensions()[orthogdim];
int fd=grid->_fdimensions[orthogdim];
int ld=grid->_ldimensions[orthogdim];
int rd=grid->_rdimensions[orthogdim];
// will locally sum vectors first
// sum across these down to scalars
// splitting the SIMD
int MFrvol = rd*Lblock*Rblock;
int MFlvol = ld*Lblock*Rblock;
Vector<vector_type > lvSum(MFrvol);
parallel_for (int r = 0; r < MFrvol; r++){
lvSum[r] = zero;
}
Vector<scalar_type > lsSum(MFlvol);
parallel_for (int r = 0; r < MFlvol; r++){
lsSum[r]=scalar_type(0.0);
}
int e1= grid->_slice_nblock[orthogdim];
int e2= grid->_slice_block [orthogdim];
int stride=grid->_slice_stride[orthogdim];
parallel_for(int r=0;r<rd;r++){
int so=r*grid->_ostride[orthogdim]; // base offset for start of plane
for(int n=0;n<e1;n++){
for(int b=0;b<e2;b++){
int ss= so+n*stride+b;
for(int i=0;i<Lblock;i++){
auto w = conjugate(wi[i]._odata[ss]);
for(int j=0;j<Rblock;j++){
auto v = vj[j]._odata[ss];
auto vv = v()(0)(0);
if (g5) {
vv = w()(0)(0) * v()(0)(0)// Gamma5 Dirac basis explicitly written out
+ w()(0)(1) * v()(0)(1)
+ w()(0)(2) * v()(0)(2)
+ w()(1)(0) * v()(1)(0)
+ w()(1)(1) * v()(1)(1)
+ w()(1)(2) * v()(1)(2)
- w()(2)(0) * v()(2)(0)
- w()(2)(1) * v()(2)(1)
- w()(2)(2) * v()(2)(2)
- w()(3)(0) * v()(3)(0)
- w()(3)(1) * v()(3)(1)
- w()(3)(2) * v()(3)(2);
} else {
vv = w()(0)(0) * v()(0)(0)// Gamma5 Dirac basis explicitly written out
+ w()(0)(1) * v()(0)(1)
+ w()(0)(2) * v()(0)(2)
+ w()(1)(0) * v()(1)(0)
+ w()(1)(1) * v()(1)(1)
+ w()(1)(2) * v()(1)(2)
+ w()(2)(0) * v()(2)(0)
+ w()(2)(1) * v()(2)(1)
+ w()(2)(2) * v()(2)(2)
+ w()(3)(0) * v()(3)(0)
+ w()(3)(1) * v()(3)(1)
+ w()(3)(2) * v()(3)(2);
}
int idx = i+Lblock*j+Lblock*Rblock*r;
lvSum[idx] = lvSum[idx]+vv;
}
}
}
}
}
// Sum across simd lanes in the plane, breaking out orthog dir.
parallel_for(int rt=0;rt<rd;rt++){
std::vector<int> icoor(nd);
iScalar<vector_type> temp;
std::vector<iScalar<scalar_type> > extracted(Nsimd);
for(int i=0;i<Lblock;i++){
for(int j=0;j<Rblock;j++){
int ij_rdx = i+Lblock*j+Lblock*Rblock*rt;
temp._internal =lvSum[ij_rdx];
extract(temp,extracted);
for(int idx=0;idx<Nsimd;idx++){
grid->iCoorFromIindex(icoor,idx);
int ldx = rt+icoor[orthogdim]*rd;
int ij_ldx =i+Lblock*j+Lblock*Rblock*ldx;
lsSum[ij_ldx]=lsSum[ij_ldx]+extracted[idx]._internal;
}
}}
}
assert(mat.dimension(0) == Nt);
// ld loop and local only??
int pd = grid->_processors[orthogdim];
int pc = grid->_processor_coor[orthogdim];
parallel_for_nest2(int lt=0;lt<ld;lt++)
{
for(int pt=0;pt<pd;pt++){
int t = lt + pt*ld;
if (pt == pc){
for(int i=0;i<Lblock;i++){
for(int j=0;j<Rblock;j++){
int ij_dx = i + Lblock * j + Lblock * Rblock * lt;
mat(t,i,j) = lsSum[ij_dx];
}
}
} else {
const scalar_type zz(0.0);
for(int i=0;i<Lblock;i++){
for(int j=0;j<Rblock;j++){
mat(t,i,j) =zz;
}
}
}
}
}
grid->GlobalSumVector(&mat(0,0,0),Nt*Lblock*Rblock);
}
template <typename FImpl>
void TA2APionField<FImpl>::PionFieldWV(Eigen::Tensor<ComplexD,3> &mat,
const LatticeFermion *wi,
const LatticeFermion *vj,
int orthogdim)
{
const int g5=1;
PionFieldXX(mat,wi,vj,orthogdim,g5);
}
template <typename FImpl>
void TA2APionField<FImpl>::PionFieldWW(Eigen::Tensor<ComplexD,3> &mat,
const LatticeFermion *wi,
const LatticeFermion *wj,
int orthogdim)
{
const int nog5=0;
PionFieldXX(mat,wi,wj,orthogdim,nog5);
}
template <typename FImpl>
void TA2APionField<FImpl>::PionFieldVV(Eigen::Tensor<ComplexD,3> &mat,
const LatticeFermion *vi,
const LatticeFermion *vj,
int orthogdim)
{
const int nog5=0;
PionFieldXX(mat,vi,vj,orthogdim,nog5);
}
/////////////////////////////////////////////////////////////////////////
// New dirac trace code needed for efficiency (I think).
// TODO: Ask Antonin to auto gen from Mathemetica
/////////////////////////////////////////////////////////////////////////
template<class vtype>
inline iScalar<vtype> traceGammaZ(const iMatrix<vtype, Ns> &rhs)
{
iScalar<vtype> ret;
ret() = timesI(rhs(2,0)) + timesMinusI(rhs(3,1)) + timesMinusI(rhs(0,2)) + timesI(rhs(1,3));
return ret;
};
template<class vtype>
inline iScalar<vtype> traceGammaZGamma5(const iMatrix<vtype, Ns> &rhs)
{
iScalar<vtype> ret;
ret() = timesMinusI(rhs(2,0)) + timesI(rhs(3,1)) + timesMinusI(rhs(0,2)) + timesI(rhs(1,3));
return ret;
};
template<class vtype>
inline iScalar<vtype> traceGammaY(const iMatrix<vtype, Ns> &rhs)
{
iScalar<vtype> ret;
ret() = -rhs(3,0) + rhs(2,1) + rhs(1,2) -rhs(0,3);
return ret;
};
template<class vtype>
inline iScalar<vtype> traceGammaYGamma5(const iMatrix<vtype, Ns> &rhs)
{
iScalar<vtype> ret;
ret() = rhs(3,0) - rhs(2,1) + rhs(1,2) -rhs(0,3);
return ret;
};
template<class vtype>
inline iScalar<vtype> traceGamma5(const iMatrix<vtype, Ns> &rhs)
{
iScalar<vtype> ret;
ret() = rhs(0, 0) + rhs(1, 1) - rhs(2, 2) - rhs(3,3);
return ret;
};
template<class vtype>
inline iScalar<vtype> traceGammaT(const iMatrix<vtype, Ns> &rhs)
{
iScalar<vtype> ret;
ret() = rhs(2, 0) + rhs(3, 1) + rhs(0, 2) + rhs(1,3);
return ret;
};
template<class vtype>
inline iScalar<vtype> traceGammaTGamma5(const iMatrix<vtype, Ns> &rhs)
{
iScalar<vtype> ret;
ret() = -rhs(2, 0) - rhs(3, 1) + rhs(0, 2) + rhs(1,3);
return ret;
};
template<class vtype>
inline iScalar<vtype> traceGammaX(const iMatrix<vtype, Ns> &rhs)
{
iScalar<vtype> ret;
ret() = timesMinusI(rhs(0, 3)) +timesMinusI(rhs(1, 2))
+ timesI(rhs(2, 1)) +timesI(rhs(3,0));
return ret;
};
template<class vtype>
inline iScalar<vtype> traceGammaXGamma5(const iMatrix<vtype, Ns> &rhs)
{
iScalar<vtype> ret;
ret() = timesMinusI(rhs(0, 3)) +timesMinusI(rhs(1, 2))
+ timesMinusI(rhs(2, 1)) +timesMinusI(rhs(3,0));
return ret;
};
////////////////////////////////////////////////////////////////////////
// DeltaF=2 contraction ; use exernal WW field for Kaon, anti Kaon sink
////////////////////////////////////////////////////////////////////////
//
// WW -- i vectors have adjoint, and j vectors not.
// -- Think of "i" as the strange quark, forward prop from 0
// -- Think of "j" as the anti-down quark.
//
// WW_sd are w^dag_s w_d
//
// Hence VV vectors correspondingly are v^dag_d, v_s from t=0
// and v^dag_d, v_s from t=dT
//
// There is an implicit g5 associated with each v^dag_d from use of g5 Hermiticity.
// The other gamma_5 lies in the WW external meson operator.
//
// From UKhadron wallbag.cc:
//
// LatticePropagator anti_d0 = adj( Gamma(G5) * Qd0 * Gamma(G5));
// LatticePropagator anti_d1 = adj( Gamma(G5) * Qd1 * Gamma(G5));
//
// PR1 = Qs0 * Gamma(G5) * anti_d0;
// PR2 = Qs1 * Gamma(G5) * anti_d1;
//
// TR1 = trace( PR1 * G1 );
// TR2 = trace( PR2 * G2 );
// Wick1 = TR1 * TR2;
//
// Wick2 = trace( PR1* G1 * PR2 * G2 );
// // was Wick2 = trace( Qs0 * Gamma(G5) * anti_d0 * G1 * Qs1 * Gamma(G5) * anti_d1 * G2 );
//
// TR TR(tx) = Wick1 = sum_x WW[t0]_sd < v^_d |g5 G| v_s> WW[t1]_s'd' < v^_d' |g5 G| v_s'> |_{x,tx)
// = sum_x [ Trace(WW[t0] VgV(t,x) ) x Trace( WW_[t1] VgV(t,x) ) ]
//
//
// Calc all Nt Trace(WW VV) products at once, take Nt^2 products of these.
//
// Fig8(tx) = Wick2 = sum_x WW[t0]_sd WW[t1]_s'd' < v^_d |g5 G| v_s'> < v^_d' |g5 G| v_s> |_{x,tx}
//
// = sum_x Trace( WW[t0] VV[t,x] WW[t1] VV[t,x] )
//
// Might as well form Ns x Nj x Ngamma matrix
//
///////////////////////////////////////////////////////////////////////////////
template <typename FImpl>
void TA2APionField<FImpl>::DeltaFeq2(int dt_min,int dt_max,
Eigen::Tensor<ComplexD,2> &dF2_fig8,
Eigen::Tensor<ComplexD,2> &dF2_trtr,
Eigen::Tensor<ComplexD,3> &WW_sd,
const LatticeFermion *vs,
const LatticeFermion *vd,
int orthogdim)
{
LOG(Message) << "Computing A2A DeltaF=2 graph" << std::endl;
int dt = dt_min; // HACK ; should loop over dt
typedef typename FImpl::SiteSpinor vobj;
typedef typename vobj::scalar_object sobj;
typedef typename vobj::scalar_type scalar_type;
typedef typename vobj::vector_type vector_type;
typedef iSpinMatrix<vector_type> SpinMatrix_v;
typedef iSpinMatrix<scalar_type> SpinMatrix_s;
typedef iSinglet<vector_type> Scalar_v;
typedef iSinglet<scalar_type> Scalar_s;
int N_s = WW_sd.dimension(1);
int N_d = WW_sd.dimension(2);
GridBase *grid = vs[0]._grid;
const int nd = grid->_ndimension;
const int Nsimd = grid->Nsimd();
int Nt = grid->GlobalDimensions()[orthogdim];
dF2_trtr.resize(Nt,16);
dF2_fig8.resize(Nt,16);
for(int t=0;t<Nt;t++){
for(int g=0;g<dF2_trtr.dimension(1);g++) dF2_trtr(t,g)= ComplexD(0.0);
for(int g=0;g<dF2_fig8.dimension(1);g++) dF2_fig8(t,g)= ComplexD(0.0);
}
// std::vector<LatticePropagator> WWVV (Nt,grid)
int fd=grid->_fdimensions[orthogdim];
int ld=grid->_ldimensions[orthogdim];
int rd=grid->_rdimensions[orthogdim];
//////////////////////////////////////
// will locally sum vectors first
// sum across these down to scalars
// splitting the SIMD
//////////////////////////////////////
int MFrvol = rd*N_s*N_d;
int MFlvol = ld*N_s*N_d;
Vector<vector_type > lvSum(MFrvol);
parallel_for (int r = 0; r < MFrvol; r++){
lvSum[r] = zero;
}
Vector<scalar_type > lsSum(MFlvol);
parallel_for (int r = 0; r < MFlvol; r++){
lsSum[r]=scalar_type(0.0);
}
int e1= grid->_slice_nblock[orthogdim];
int e2= grid->_slice_block [orthogdim];
int stride=grid->_slice_stride[orthogdim];
Eigen::Tensor<Scalar_v,3> VgV_sd(N_s,N_d,16); // trace with dirac structure
Eigen::Tensor<Scalar_s,4> VgV_sd_l(N_s,N_d,16,Nsimd);
int Ng;
LOG(Message) << "Computing A2A DeltaF=2 graph entering site loop" << std::endl;
double t_tot =0;
double t_vv =0;
double t_extr =0;
double t_transp=0;
double t_WW =0;
double t_trtr =0;
double t_fig8 =0;
t_tot -=usecond();
for(int r=0;r<rd;r++){
LOG(Message) << "Computing A2A DeltaF=2 timeslice "<< r << "/"<<rd << std::endl;
int so=r*grid->_ostride[orthogdim]; // base offset for start of plane
for(int n=0;n<e1;n++){
for(int b=0;b<e2;b++){
int ss= so+n*stride+b;
///////////////////////////////////
// _ _
// O_VV+AA = s V_mu d s V_mu d
// _ _
// + s A_mu d s A_mu d
///////////////////////////////////
// assemble the v_s v_d spin outer, colour inner product matrix
// the #vecs will be large
t_vv -=usecond();
parallel_for(int d=0;d<N_d;d++){
auto _vd = conjugate(vd[d]._odata[ss]);
for(int s=0;s<N_s;s++){
SpinMatrix_v vv;
auto _vs = vs[s]._odata[ss];
for(int s1=0;s1<Ns;s1++){
for(int s2=0;s2<Ns;s2++){
vv()(s1,s2)() = _vd()(s2)(0) * _vs()(s1)(0)
+ _vd()(s2)(1) * _vs()(s1)(1)
+ _vd()(s2)(2) * _vs()(s1)(2);
}}
int g=0;
// VgV_sd(s,d,g++) = trace(vv); // S
// VgV_sd(s,d,g++)() = traceGamma5(vv());// P
VgV_sd(s,d,g++)() = traceGammaX(vv());// Vmu
VgV_sd(s,d,g++)() = traceGammaY(vv());
VgV_sd(s,d,g++)() = traceGammaZ(vv());
VgV_sd(s,d,g++)() = traceGammaT(vv());
VgV_sd(s,d,g++)() = traceGammaXGamma5(vv());// Amu
VgV_sd(s,d,g++)() = traceGammaYGamma5(vv());
VgV_sd(s,d,g++)() = traceGammaZGamma5(vv());
VgV_sd(s,d,g++)() = traceGammaTGamma5(vv());
/*
VgV_sd(s,d,g++)() = traceSigmaXY(vv);// Sigma_munu unimplemented
VgV_sd(s,d,g++)() = traceSigmaXZ(vv);
VgV_sd(s,d,g++)() = traceSigmaXT(vv);
VgV_sd(s,d,g++)() = traceSigmaYZ(vv);
VgV_sd(s,d,g++)() = traceSigmaYT(vv);
VgV_sd(s,d,g++)() = traceSigmaZT(vv);
*/
Ng = g;
}
}
t_vv +=usecond();
/////////////////////////////////////////////////////////////////////
// PLAN: Make use of the fact that the trace of the product of two
// matrices is a_ij b_ji = a_ij (b^T)_ij and write as a "ZDOT"
// with one of the matrices transposed.
//
// Further since we want to take the trace-product with nt
// other matrices can do these in a single pass and gain another 2x.
// Can do this data parallel on all SIMD lanes of VgV_sd, with a
// broadcast of WW[t0] and WW[t1].
//
//
// Strategies:
//
// Wick1: TR TR(tx) = sum_x [ Trace(WW[t0] VgV(t,x) ) x Trace( WW_[t1] VgV(t,x) ) ]
//
// Take Tr (WW[t'] . VgV^T) for all "t'", store in array.
//
// Accumulate (WW[t0].VgV). (WW[t1].VgV) for dt and (t-t0+nt) % nt.
//
// Wick2:
//
// Fig8(tx) = sum_x Trace( VV[t,x] WW[t0] VV[t,x] WW[t1] )
//
// for(t0)
// form (VV^T WW VV^T)^T = VV WW^T VV = M0
// for(t1)
// Accumulate Tr(M0 . WW[t1] in dt and (t-t0+nt)%nt
//
/////////////////////////////////////////////////////////////////////
// Loop over t0 accumulate the dT matrix elements.
for(int g=0;g<Ng;g++){
/////////////////////////////////////////////////
// break out into Nsimd sites worth of scalar code.
/////////////////////////////////////////////////
t_extr -=usecond();
parallel_for(int d=0;d<N_d;d++){
std::vector<Scalar_s> extracted(Nsimd);
Scalar_v temp;
for(int s=0;s<N_s;s++){
for(int l=0;l<Nsimd;l++){
temp = VgV_sd(s,d,g);
extract(temp,extracted);
for(int l=0;l<Nsimd;l++){
VgV_sd_l(s,d,g,l) = extracted[l]()()();
}
}// lane
}
}// s,d
t_extr +=usecond();
////////////////////////////////////////////
// Work on a series of scalar problems
////////////////////////////////////////////
for(int l=0;l<Nsimd;l++){
std::vector<int> icoor(nd);
grid->iCoorFromIindex(icoor,l);
int ttt = r+icoor[orthogdim]*rd;
Eigen::MatrixXcd VgV(N_d,N_s);
Eigen::MatrixXcd VgV_T(N_s,N_d);
Eigen::MatrixXcd WW0(N_s,N_d);
Eigen::MatrixXcd WW1(N_s,N_d);
/////////////////////////////////////////
// Single site VgV , scalar order
/////////////////////////////////////////
t_transp -=usecond();
parallel_for(int d=0;d<N_d;d++){ for(int s=0;s<N_s;s++){
// Note pre-transpose VgV in the copy out
VgV(d,s) = VgV_sd_l(s,d,g,l);
VgV_T(s,d) = VgV(d,s);
}}
t_transp +=usecond();
/////////////////////////////////////////
// loop over time planes of meson
/////////////////////////////////////////
for(int t0=0;t0<Nt;t0++){
int t1 = (t0+dt)%Nt; // Future loop over dT
int tt = (ttt-t0+Nt)%Nt; // Time of this site relative to t0
/////////////////////////////////////////////////////////////////
// Extract this pair of WW matrices infuture loop over dT
/////////////////////////////////////////////////////////////////
t_WW -=usecond();
parallel_for(int d=0;d<N_d;d++){ for(int s=0;s<N_s;s++){
WW0(s,d) = WW_sd(t0,s,d);
WW1(s,d) = WW_sd(t1,s,d);
}}
t_WW +=usecond();
/////////////////////////////////////////
// Wick1 -- transpose
/////////////////////////////////////////
// VgV_ds WW_sd
t_trtr -=usecond();
ComplexD trWW0VV = (VgV_T.array()*WW0.array()).sum();
ComplexD trWW1VV = (VgV_T.array()*WW1.array()).sum();
dF2_trtr(tt,g) += trWW0VV * trWW1VV;
t_trtr +=usecond();
/////////////////////////////////////////
// Wick2 -- transpose
/////////////////////////////////////////
// VgV_ds WW_sd VgV_d's'
//
// This is the time consuming loop.
t_fig8 -=usecond();
Eigen::MatrixXcd VVWW0VV = VgV * WW0 * VgV ;
Eigen::MatrixXcd VVWW0VV_T =VVWW0VV.transpose();
auto trVVWW0VVWW1 =(VVWW0VV_T.array()*WW1.array()).sum();
dF2_fig8(tt,g) += trVVWW0VVWW1;
t_fig8 +=usecond();
}// t0 loop
}// l loop
}// gamma
}// close loop over time plane and block stride loop within timeplane
}
}
grid->GlobalSumVector(&dF2_fig8(0),Nt*Ng);
grid->GlobalSumVector(&dF2_trtr(0),Nt*Ng);
t_tot +=usecond();
LOG(Message) << "Computing A2A DeltaF=2 graph t_tot " << t_tot << " us "<< std::endl;
LOG(Message) << "Computing A2A DeltaF=2 graph t_vv " << t_vv << " us "<< std::endl;
LOG(Message) << "Computing A2A DeltaF=2 graph t_extr " << t_extr << " us "<< std::endl;
LOG(Message) << "Computing A2A DeltaF=2 graph t_transp " << t_transp << " us "<< std::endl;
LOG(Message) << "Computing A2A DeltaF=2 graph t_WW " << t_WW << " us "<< std::endl;
LOG(Message) << "Computing A2A DeltaF=2 graph t_trtr " << t_trtr << " us "<< std::endl;
LOG(Message) << "Computing A2A DeltaF=2 graph t_fig8 " << t_fig8 << " us "<< std::endl;
}
// WW is w_s^dag (x) w_d (G5 implicitly absorbed)
//
// WWVV will have spin-col (x) spin-col tensor.
//
// Want this to look like a strange fwd prop, anti-d prop.
//
// Take WW_sd v^dag_d (x) v_s
//
//
template <typename FImpl>
void TA2APionField<FImpl>::DeltaFeq2_alt(int dt_min,int dt_max,
Eigen::Tensor<ComplexD,2> &dF2_fig8,
Eigen::Tensor<ComplexD,2> &dF2_trtr,
Eigen::Tensor<ComplexD,1> &den0,
Eigen::Tensor<ComplexD,1> &den1,
Eigen::Tensor<ComplexD,3> &WW_sd,
const LatticeFermion *vs,
const LatticeFermion *vd,
int orthogdim)
{
LOG(Message) << "Computing A2A DeltaF=2 graph" << std::endl;
int dt = dt_min; // HACK ; should loop over dt
auto G5 = Gamma(Gamma::Algebra::Gamma5);
typedef typename FImpl::SiteSpinor vobj;
typedef typename vobj::scalar_object sobj;
typedef typename vobj::scalar_type scalar_type;
typedef typename vobj::vector_type vector_type;
typedef iSpinMatrix<vector_type> SpinMatrix_v;
typedef iSpinMatrix<scalar_type> SpinMatrix_s;
typedef iSinglet<vector_type> Scalar_v;
typedef iSinglet<scalar_type> Scalar_s;
int N_s = WW_sd.dimension(1);
int N_d = WW_sd.dimension(2);
GridBase *grid = vs[0]._grid;
const int nd = grid->_ndimension;
const int Nsimd = grid->Nsimd();
int N_t = grid->GlobalDimensions()[orthogdim];
double vol = 1.0;
for(int dim=0;dim<nd;dim++){
vol = vol * grid->GlobalDimensions()[dim];
}
double nodes = grid->NodeCount();
dF2_trtr.resize(N_t,16);
dF2_fig8.resize(N_t,16);
den0.resize(N_t);
den1.resize(N_t);
for(int t=0;t<N_t;t++){
for(int g=0;g<dF2_trtr.dimension(1);g++) dF2_trtr(t,g)= ComplexD(0.0);
for(int g=0;g<dF2_fig8.dimension(1);g++) dF2_fig8(t,g)= ComplexD(0.0);
den0(t) =ComplexD(0.0);
den1(t) =ComplexD(0.0);
}
LatticeComplex D0(grid); // <P|A0> correlator from each wall
LatticeComplex D1(grid);
LatticeComplex O1_trtr(grid);
LatticeComplex O2_trtr(grid);
LatticeComplex O3_trtr(grid);
LatticeComplex O4_trtr(grid);
LatticeComplex O5_trtr(grid);
LatticeComplex O1_fig8(grid);
LatticeComplex O2_fig8(grid);
LatticeComplex O3_fig8(grid);
LatticeComplex O4_fig8(grid);
LatticeComplex O5_fig8(grid);
O1_trtr = zero;
O2_trtr = zero;
O3_trtr = zero;
O4_trtr = zero;
O5_trtr = zero;
O1_fig8 = zero;
O2_fig8 = zero;
O3_fig8 = zero;
O4_fig8 = zero;
O5_fig8 = zero;
D0 = zero;
D1 = zero;
double t_tot = -usecond();
std::vector<LatticePropagator> WWVV (N_t,grid);
for(int t=0;t<N_t;t++){
WWVV[t] = zero;
}
//////////////////////////////////////////////////////////
// Easily cache blocked and unrolled.
//////////////////////////////////////////////////////////
//
// Ways to speed up?? 20 min in 8^3 x 16 local volume with 400 modes.
//
// Flops are (cmul=6 + 1 (add))* 12*12 * N_s * N_d
// Bytes are read Nc x Ns x 2 + read/write Nc^2 x Ns^2 complex
//
double t_outer= -usecond();
double t_outer_0 =0.0;
double t_outer_1 =0.0;
#undef METHOD_1
#define METHOD_5
#ifdef METHOD_1
LOG(Message) << "METHOD_1" << std::endl;
// Method-1
// i) calculate flop rate and data rate. 17 GF/s and 80 GB/s
// Dominated by accumulating the N_t summands
parallel_for(int ss=0;ss<grid->oSites();ss++){
for(int s=0;s<N_s;s++){
for(int d=0;d<N_d;d++){
double t0=-usecond();
// RHS is conjugated
auto tmp = outerProduct(vs[s]._odata[ss],vd[d]._odata[ss]);
t0+=usecond();
double t1=-usecond();
for(int t=0;t<N_t;t++) {
WWVV[t]._odata[ss] += WW_sd(t,s,d) * tmp;
}
t1+=usecond();
#pragma omp critical
{ t_outer_0+=t0; t_outer_1+=t1;}
}
}
}
#endif
double b_outer = (12+12+2*12*12 ) * N_s * N_d * vol * sizeof(Complex);
double f_outer = 8 * 12*12 * N_s * N_d * vol;
#ifdef METHOD_5
LOG(Message) << "METHOD_5" << std::endl;
// Method-5
parallel_for(int ss=0;ss<grid->oSites();ss++){
for(int d_o=0;d_o<N_d;d_o+=d_unroll){
for(int t=0;t<N_t;t++){
for(int s=0;s<N_s;s++){
auto tmp1 = vs[s]._odata[ss];
vobj tmp2 = zero;
// Surprisingly slow
for(int d=d_o;d<MIN(d_o+d_unroll,N_d);d++){
Scalar_v coeff = WW_sd(t,s,d);
mac(&tmp2 ,& coeff, & vd[d]._odata[ss]);
}
// Outer product of tmp1 with a sum of terms suppressed by d_unroll
tmp2 = conjugate(tmp2);
for(int s1=0;s1<Ns;s1++){
for(int s2=0;s2<Ns;s2++){
WWVV[t]._odata[ss]()(s1,s2)(0,0) += tmp1()(s1)(0)*tmp2()(s2)(0);
WWVV[t]._odata[ss]()(s1,s2)(0,1) += tmp1()(s1)(0)*tmp2()(s2)(1);
WWVV[t]._odata[ss]()(s1,s2)(0,2) += tmp1()(s1)(0)*tmp2()(s2)(2);
WWVV[t]._odata[ss]()(s1,s2)(1,0) += tmp1()(s1)(1)*tmp2()(s2)(0);
WWVV[t]._odata[ss]()(s1,s2)(1,1) += tmp1()(s1)(1)*tmp2()(s2)(1);
WWVV[t]._odata[ss]()(s1,s2)(1,2) += tmp1()(s1)(1)*tmp2()(s2)(2);
WWVV[t]._odata[ss]()(s1,s2)(2,0) += tmp1()(s1)(2)*tmp2()(s2)(0);
WWVV[t]._odata[ss]()(s1,s2)(2,1) += tmp1()(s1)(2)*tmp2()(s2)(1);
WWVV[t]._odata[ss]()(s1,s2)(2,2) += tmp1()(s1)(2)*tmp2()(s2)(2);
}}
}}
}
}
#endif
t_outer+=usecond();
//////////////////////////////
// Implicit gamma-5
//////////////////////////////
for(int t=0;t<N_t;t++){
WWVV[t] = WWVV[t]* G5 ;
}
//////////////////////////////////////////////////
// Used to store appropriate correlation funcs
//////////////////////////////////////////////////
std::vector<TComplex> C1;
std::vector<TComplex> C2;
std::vector<TComplex> C3;
std::vector<TComplex> C4;
std::vector<TComplex> C5;
//////////////////////////////////////////////////////////
// Could do AA, VV, SS, PP, TT and form linear combinations later.
// Almost 2x. but for many modes, the above loop dominates.
//////////////////////////////////////////////////////////
double t_contr= -usecond();
for(int t0=0;t0<N_t;t0++){
// No loop over t1
// Cost is trivial to add given cost of outer product
{
int t1 = (t0+dt)%N_t;
parallel_for(int ss=0;ss<grid->oSites();ss++){
auto VV0= WWVV[t0]._odata[ss];
auto VV1= WWVV[t1]._odata[ss];
// Tr Tr Wick contraction
auto VX = Gamma(Gamma::Algebra::GammaX);
auto VY = Gamma(Gamma::Algebra::GammaY);
auto VZ = Gamma(Gamma::Algebra::GammaZ);
auto VT = Gamma(Gamma::Algebra::GammaT);
auto AX = Gamma(Gamma::Algebra::GammaXGamma5);
auto AY = Gamma(Gamma::Algebra::GammaYGamma5);
auto AZ = Gamma(Gamma::Algebra::GammaZGamma5);
auto AT = Gamma(Gamma::Algebra::GammaTGamma5);
auto S = Gamma(Gamma::Algebra::Identity);
auto P = Gamma(Gamma::Algebra::Gamma5);
auto T0 = Gamma(Gamma::Algebra::SigmaXY);
auto T1 = Gamma(Gamma::Algebra::SigmaXZ);
auto T2 = Gamma(Gamma::Algebra::SigmaXT);
auto T3 = Gamma(Gamma::Algebra::SigmaYZ);
auto T4 = Gamma(Gamma::Algebra::SigmaYT);
auto T5 = Gamma(Gamma::Algebra::SigmaZT);
O1_trtr._odata[ss] = trace(VX*VV0) * trace(VX*VV1)
+ trace(VY*VV0) * trace(VY*VV1)
+ trace(VZ*VV0) * trace(VZ*VV1)
+ trace(VT*VV0) * trace(VT*VV1)
+ trace(AX*VV0) * trace(AX*VV1)
+ trace(AY*VV0) * trace(AY*VV1)
+ trace(AZ*VV0) * trace(AZ*VV1)
+ trace(AT*VV0) * trace(AT*VV1);
O2_trtr._odata[ss] = trace(VX*VV0) * trace(VX*VV1)
+ trace(VY*VV0) * trace(VY*VV1)
+ trace(VZ*VV0) * trace(VZ*VV1)
+ trace(VT*VV0) * trace(VT*VV1)
- trace(AX*VV0) * trace(AX*VV1)
- trace(AY*VV0) * trace(AY*VV1)
- trace(AZ*VV0) * trace(AZ*VV1)
- trace(AT*VV0) * trace(AT*VV1);
O3_trtr._odata[ss] = trace(S*VV0) * trace(S*VV1)
+ trace(P*VV0) * trace(P*VV1);
O4_trtr._odata[ss] = trace(S*VV0) * trace(S*VV1)
- trace(P*VV0) * trace(P*VV1);
O5_trtr._odata[ss] = trace(T0*VV0) * trace(T0*VV1)
+ trace(T1*VV0) * trace(T1*VV1)
+ trace(T2*VV0) * trace(T2*VV1)
+ trace(T3*VV0) * trace(T3*VV1)
+ trace(T4*VV0) * trace(T4*VV1)
+ trace(T5*VV0) * trace(T5*VV1);
////////////////////////////////////
// Fig8 Wick contraction
////////////////////////////////////
// was (UKhadron) Wick2 = trace( Qs0 * Gamma(G5) * anti_d0 * G * Qs1 * Gamma(G5) * anti_d1 * G );
//
// = trace( [ Vs WW_sd'[t0] Vd'^dag ] G [ Vs' WW_s'd[t1] Vd^dag ] G )
// = trace( WWVV * G * WWVV * G )
//
// Can do VV and AA seperately and then add/sub later cheaper
O1_fig8._odata[ss] = trace (VV0 * VX * VV1 * VX)
+ trace (VV0 * VY * VV1 * VY)
+ trace (VV0 * VZ * VV1 * VZ)
+ trace (VV0 * VT * VV1 * VT)
+ trace (VV0 * AX * VV1 * AX)
+ trace (VV0 * AY * VV1 * AY)
+ trace (VV0 * AZ * VV1 * AZ)
+ trace (VV0 * AT * VV1 * AT);
O2_fig8._odata[ss] = trace (VV0 * VX * VV1 * VX)
+ trace (VV0 * VY * VV1 * VY)
+ trace (VV0 * VZ * VV1 * VZ)
+ trace (VV0 * VT * VV1 * VT)
- trace (VV0 * AX * VV1 * AX)
- trace (VV0 * AY * VV1 * AY)
- trace (VV0 * AZ * VV1 * AZ)
- trace (VV0 * AT * VV1 * AT);
O3_fig8._odata[ss] = trace (VV0 * S * VV1 * S)
+ trace (VV0 * P * VV1 * P);
O4_fig8._odata[ss] = trace (VV0 * S * VV1 * S)
- trace (VV0 * P * VV1 * P);
O5_fig8._odata[ss] = trace (VV0 * T0 * VV1 * T0)
+ trace (VV0 * T1 * VV1 * T1)
+ trace (VV0 * T2 * VV1 * T2)
+ trace (VV0 * T3 * VV1 * T3)
+ trace (VV0 * T4 * VV1 * T4)
+ trace (VV0 * T5 * VV1 * T5);
// Hack force PP correlator
// D0._odata[ss] = trace(P*VV0); // These match signed off
// D1._odata[ss] = trace(P*VV1);
D0._odata[ss] = trace(AT*VV0);
D1._odata[ss] = trace(AT*VV1);
}
sliceSum(O1_trtr,C1, orthogdim);
sliceSum(O2_trtr,C2, orthogdim);
sliceSum(O3_trtr,C3, orthogdim);
sliceSum(O4_trtr,C4, orthogdim);
sliceSum(O5_trtr,C5, orthogdim);
for(int t=0;t<N_t;t++){// 2x from Wick contraction reordering
dF2_trtr(t,0)+= 2.0*C1[(t+t0)%N_t]()()()/vol;
dF2_trtr(t,1)+= 2.0*C2[(t+t0)%N_t]()()()/vol;
dF2_trtr(t,2)+= 2.0*C3[(t+t0)%N_t]()()()/vol;
dF2_trtr(t,3)+= 2.0*C4[(t+t0)%N_t]()()()/vol;
dF2_trtr(t,4)+= 2.0*C5[(t+t0)%N_t]()()()/vol;
}
sliceSum(O1_fig8,C1, orthogdim);
sliceSum(O2_fig8,C2, orthogdim);
sliceSum(O3_fig8,C3, orthogdim);
sliceSum(O4_fig8,C4, orthogdim);
sliceSum(O5_fig8,C5, orthogdim);
for(int t=0;t<N_t;t++){
dF2_fig8(t,0)= 2.0*C1[(t+t0)%N_t]()()()/vol;
dF2_fig8(t,1)= 2.0*C2[(t+t0)%N_t]()()()/vol;
dF2_fig8(t,2)= 2.0*C3[(t+t0)%N_t]()()()/vol;
dF2_fig8(t,3)= 2.0*C4[(t+t0)%N_t]()()()/vol;
dF2_fig8(t,4)= 2.0*C5[(t+t0)%N_t]()()()/vol;
}
sliceSum(D0,C1, orthogdim);
sliceSum(D1,C2, orthogdim);
for(int t=0;t<N_t;t++){
den0(t)+=C1[(t+t0)%N_t]()()()/vol;
den1(t)+=C2[(t+t0)%N_t]()()()/vol;
}
}
}
t_contr +=usecond();
t_tot+=usecond();
double million=1.0e6;
LOG(Message) << "Computing A2A DeltaF=2 graph t_tot " << t_tot /million << " s "<< std::endl;
LOG(Message) << "Computing A2A DeltaF=2 graph t_outer " << t_outer /million << " s "<< std::endl;
LOG(Message) << "Computing A2A DeltaF=2 graph t_outer_0 " << t_outer_0 /million << " s "<< std::endl;
LOG(Message) << "Computing A2A DeltaF=2 graph t_outer_1 " << t_outer_1 /million << " s "<< std::endl;
LOG(Message) << "Computing A2A DeltaF=2 graph t_contr " << t_contr /million << " s "<< std::endl;
LOG(Message) << "Computing A2A DeltaF=2 graph mflops/s outer " << f_outer/t_outer << " MF/s "<< std::endl;
LOG(Message) << "Computing A2A DeltaF=2 graph MB/s outer " << b_outer/t_outer << " MB/s "<< std::endl;
LOG(Message) << "Computing A2A DeltaF=2 graph mflops/s outer/node " << f_outer/t_outer/nodes << " MF/s "<< std::endl;
LOG(Message) << "Computing A2A DeltaF=2 graph MB/s outer/node " << b_outer/t_outer/nodes << " MB/s "<< std::endl;
}
// execution ///////////////////////////////////////////////////////////////////
template <typename FImpl>
void TA2APionField<FImpl>::execute(void)
{
LOG(Message) << "Computing A2A Pion fields" << std::endl;
auto &a2a_i = envGet(A2ABase, par().A2A_i + "_class");
auto &a2a_j = envGet(A2ABase, par().A2A_j + "_class");
///////////////////////////////////////////////
// Square assumption for now Nl = Nr = N
///////////////////////////////////////////////
int nt = env().getDim(Tp);
int nx = env().getDim(Xp);
int ny = env().getDim(Yp);
int nz = env().getDim(Zp);
// int N_i = a2a_i.par().N;
// int N_j = a2a_j.par().N;
int N_i = a2a_i.getN();
int N_j = a2a_j.getN();
int nmom=par().Nmom;
int schurBlock = par().schurBlock;
int cacheBlock = par().cacheBlock;
///////////////////////////////////////////////
// Momentum setup
///////////////////////////////////////////////
GridBase *grid = env().getGrid(1);
std::vector<LatticeComplex> phases(nmom,grid);
for(int m=0;m<nmom;m++){
phases[m] = Complex(1.0); // All zero momentum for now
}
///////////////////////////////////////////////////////////////////////
// i and j represent different flavours, hits, with different ranks.
// in general non-square case.
///////////////////////////////////////////////////////////////////////
Eigen::Tensor<ComplexD,4> pionFieldWVmom_ij (nmom,nt,N_i,N_j);
Eigen::Tensor<ComplexD,3> pionFieldWV_ij (nt,N_i,N_j);
Eigen::Tensor<ComplexD,4> pionFieldWVmom_ji (nmom,nt,N_j,N_i);
Eigen::Tensor<ComplexD,3> pionFieldWV_ji (nt,N_j,N_i);
LOG(Message) << "Rank for A2A PionField is " << N_i << " x "<<N_j << std::endl;
envGetTmp(std::vector<FermionField>, wi);
envGetTmp(std::vector<FermionField>, vi);
envGetTmp(std::vector<FermionField>, wj);
envGetTmp(std::vector<FermionField>, vj);
envGetTmp(FermionField, tmp_5d);
LOG(Message) << "Finding v and w vectors " << std::endl;
//////////////////////////////////////////////////////////////////////////
// i,j is first loop over SchurBlock factors reusing 5D matrices
// ii,jj is second loop over cacheBlock factors for high perf contractoin
// iii,jjj are loops within cacheBlock
// Total index is sum of these i+ii+iii etc...
//////////////////////////////////////////////////////////////////////////
double flops = 0.0;
double bytes = 0.0;
double vol = nx*ny*nz*nt;
double vol3 = nx*ny*nz;
double t_schur=0;
double t_contr_vwm=0;
double t_contr_vw=0;
double t_contr_ww=0;
double t_contr_vv=0;
double tt0 = usecond();
for(int i=0;i<N_i;i+=schurBlock){ //loop over SchurBlocking to suppress 5D matrix overhead
for(int j=0;j<N_j;j+=schurBlock){
///////////////////////////////////////////////////////////////
// Get the W and V vectors for this schurBlock^2 set of terms
///////////////////////////////////////////////////////////////
int N_ii = MIN(N_i-i,schurBlock);
int N_jj = MIN(N_j-j,schurBlock);
t_schur-=usecond();
for(int ii =0;ii < N_ii;ii++) a2a_i.return_w(i+ii, tmp_5d, wi[ii]);
for(int jj =0;jj < N_jj;jj++) a2a_j.return_w(j+jj, tmp_5d, wj[jj]);
for(int ii =0;ii < N_ii;ii++) a2a_i.return_v(i+ii, tmp_5d, vi[ii]);
for(int jj =0;jj < N_jj;jj++) a2a_j.return_v(j+jj, tmp_5d, vj[jj]);
t_schur+=usecond();
LOG(Message) << "Found i w&v vectors " << i <<" .. " << i+N_ii-1 << std::endl;
LOG(Message) << "Found j w&v vectors " << j <<" .. " << j+N_jj-1 << std::endl;
///////////////////////////////////////////////////////////////
// Series of cache blocked chunks of the contractions within this SchurBlock
///////////////////////////////////////////////////////////////
for(int ii=0;ii<N_ii;ii+=cacheBlock){
for(int jj=0;jj<N_jj;jj+=cacheBlock){
int N_iii = MIN(N_ii-ii,cacheBlock);
int N_jjj = MIN(N_jj-jj,cacheBlock);
Eigen::Tensor<ComplexD,4> pionFieldWVmomB_ij(nmom,nt,N_iii,N_jjj);
Eigen::Tensor<ComplexD,4> pionFieldWVmomB_ji(nmom,nt,N_jjj,N_iii);
Eigen::Tensor<ComplexD,3> pionFieldWVB_ij(nt,N_iii,N_jjj);
Eigen::Tensor<ComplexD,3> pionFieldWVB_ji(nt,N_jjj,N_iii);
t_contr_vwm-=usecond();
PionFieldWVmom(pionFieldWVmomB_ij, &wi[ii], &vj[jj], phases,Tp);
PionFieldWVmom(pionFieldWVmomB_ji, &wj[jj], &vi[ii], phases,Tp);
t_contr_vwm+=usecond();
t_contr_vw-=usecond();
PionFieldWV(pionFieldWVB_ij, &wi[ii], &vj[jj],Tp);
PionFieldWV(pionFieldWVB_ji, &wj[jj], &vi[ii],Tp);
t_contr_vw+=usecond();
flops += vol * ( 2 * 8.0 + 6.0 + 8.0*nmom) * N_iii*N_jjj;
bytes += vol * (12.0 * sizeof(Complex) ) * N_iii*N_jjj
+ vol * ( 2.0 * sizeof(Complex) *nmom ) * N_iii*N_jjj;
///////////////////////////////////////////////////////////////
// Copy back to full meson field tensor
///////////////////////////////////////////////////////////////
parallel_for_nest2(int iii=0;iii< N_iii;iii++) {
for(int jjj=0;jjj< N_jjj;jjj++) {
for(int m =0;m< nmom;m++) {
for(int t =0;t< nt;t++) {
pionFieldWVmom_ij(m,t,i+ii+iii,j+jj+jjj) = pionFieldWVmomB_ij(m,t,iii,jjj);
pionFieldWVmom_ji(m,t,j+jj+jjj,i+ii+iii) = pionFieldWVmomB_ji(m,t,jjj,iii);
}}
for(int t =0;t< nt;t++) {
pionFieldWV_ij(t,i+ii+iii,j+jj+jjj) = pionFieldWVB_ij(t,iii,jjj);
pionFieldWV_ji(t,j+jj+jjj,i+ii+iii) = pionFieldWVB_ji(t,jjj,iii);
}
}}
}}
}}
double nodes=grid->NodeCount();
double tt1 = usecond();
LOG(Message) << " Contraction of PionFields took "<<(tt1-tt0)/1.0e6<< " seconds " << std::endl;
LOG(Message) << " Schur "<<(t_schur)/1.0e6<< " seconds " << std::endl;
LOG(Message) << " Contr WVmom "<<(t_contr_vwm)/1.0e6<< " seconds " << std::endl;
LOG(Message) << " Contr WV "<<(t_contr_vw)/1.0e6<< " seconds " << std::endl;
double t_kernel = t_contr_vwm;
LOG(Message) << " Arith "<<flops/(t_kernel)/1.0e3/nodes<< " Gflop/s / node " << std::endl;
LOG(Message) << " Arith "<<bytes/(t_kernel)/1.0e3/nodes<< " GB/s /node " << std::endl;
/////////////////////////////////////////////////////////////////////////
// Test: Build the pion correlator (two end)
// < PI_ij(t0) PI_ji (t0+t) >
/////////////////////////////////////////////////////////////////////////
std::vector<ComplexD> corrMom(nt,ComplexD(0.0));
for(int i=0;i<N_i;i++){
for(int j=0;j<N_j;j++){
int m=0; // first momentum
for(int t0=0;t0<nt;t0++){
for(int t=0;t<nt;t++){
int tt = (t0+t)%nt;
corrMom[t] += pionFieldWVmom_ij(m,t0,i,j)* pionFieldWVmom_ji(m,tt,j,i);
}}
}}
for(int t=0;t<nt;t++) corrMom[t] = corrMom[t]/ (double)nt;
for(int t=0;t<nt;t++) LOG(Message) << " C_vwm " << t << " " << corrMom[t]<<std::endl;
/////////////////////////////////////////////////////////////////////////
// Test: Build the pion correlator (two end) from zero mom contraction
// < PI_ij(t0) PI_ji (t0+t) >
/////////////////////////////////////////////////////////////////////////
std::vector<ComplexD> corr(nt,ComplexD(0.0));
for(int i=0;i<N_i;i++){
for(int j=0;j<N_j;j++){
for(int t0=0;t0<nt;t0++){
for(int t=0;t<nt;t++){
int tt = (t0+t)%nt;
corr[t] += pionFieldWV_ij(t0,i,j)* pionFieldWV_ji(tt,j,i);
}}
}}
for(int t=0;t<nt;t++) corr[t] = corr[t]/ (double)nt;
for(int t=0;t<nt;t++) LOG(Message) << " C_vw " << t << " " << corr[t]<<std::endl;
/////////////////////////////////////////////////////////////////////////
// Test: Build the pion correlator from zero mom contraction with revers
// charge flow
/////////////////////////////////////////////////////////////////////////
std::vector<ComplexD> corr_wwvv(nt,ComplexD(0.0));
wi.resize(N_i,grid);
vi.resize(N_i,grid);
wj.resize(N_j,grid);
vj.resize(N_j,grid);
for(int i =0;i < N_i;i++) a2a_i.return_v(i, tmp_5d, vi[i]);
for(int i =0;i < N_i;i++) a2a_i.return_w(i, tmp_5d, wi[i]);
for(int j =0;j < N_j;j++) a2a_j.return_v(j, tmp_5d, vj[j]);
for(int j =0;j < N_j;j++) a2a_j.return_w(j, tmp_5d, wj[j]);
Eigen::Tensor<ComplexD,3> pionFieldWW_ij (nt,N_i,N_j);
Eigen::Tensor<ComplexD,3> pionFieldVV_ji (nt,N_j,N_i);
Eigen::Tensor<ComplexD,3> pionFieldWW_ji (nt,N_j,N_i);
Eigen::Tensor<ComplexD,3> pionFieldVV_ij (nt,N_i,N_j);
PionFieldWW(pionFieldWW_ij, &wi[0], &wj[0],Tp);
PionFieldVV(pionFieldVV_ji, &vj[0], &vi[0],Tp);
PionFieldWW(pionFieldWW_ji, &wj[0], &wi[0],Tp);
PionFieldVV(pionFieldVV_ij, &vi[0], &vj[0],Tp);
for(int i=0;i<N_i;i++){
for(int j=0;j<N_j;j++){
for(int t0=0;t0<nt;t0++){
for(int t=0;t<nt;t++){
int tt = (t0+t)%nt;
corr_wwvv[t] += pionFieldWW_ij(t0,i,j)* pionFieldVV_ji(tt,j,i);
corr_wwvv[t] += pionFieldWW_ji(t0,j,i)* pionFieldVV_ij(tt,i,j);
}}
}}
for(int t=0;t<nt;t++) corr_wwvv[t] = corr_wwvv[t] / vol /2.0 ; // (ij+ji noise contribs if i!=j ).
for(int t=0;t<nt;t++) LOG(Message) << " C_wwvv " << t << " " << corr_wwvv[t]<<std::endl;
/////////////////////////////////////////////////////////////////////////
// This is only correct if there are NO low modes
// Use the "ii" case to construct possible Z wall source one end trick
/////////////////////////////////////////////////////////////////////////
std::vector<ComplexD> corr_z2(nt,ComplexD(0.0));
Eigen::Tensor<ComplexD,3> pionFieldWW (nt,N_i,N_i);
Eigen::Tensor<ComplexD,3> pionFieldVV (nt,N_i,N_i);
PionFieldWW(pionFieldWW, &wi[0], &wi[0],Tp);
PionFieldVV(pionFieldVV, &vi[0], &vi[0],Tp);
for(int i=0;i<N_i;i++){
for(int t0=0;t0<nt;t0++){
for(int t=0;t<nt;t++){
int tt = (t0+t)%nt;
corr_z2[t] += pionFieldWW(t0,i,i) * pionFieldVV(tt,i,i) /vol ;
}}
}
LOG(Message) << " C_z2 WARNING only correct if Nl == 0 "<<std::endl;
for(int t=0;t<nt;t++) LOG(Message) << " C_z2 " << t << " " << corr_z2[t]<<std::endl;
/////////////////////////////////////////////////////////////////////////
// Test: Build a bag contraction
/////////////////////////////////////////////////////////////////////////
Eigen::Tensor<ComplexD,2> DeltaF2_fig8 (nt,16);
Eigen::Tensor<ComplexD,2> DeltaF2_trtr (nt,16);
Eigen::Tensor<ComplexD,1> denom0 (nt);
Eigen::Tensor<ComplexD,1> denom1 (nt);
const int dT=16;
DeltaFeq2_alt (dT,dT,DeltaF2_fig8,DeltaF2_trtr,
denom0,denom1,
pionFieldWW_ij,&vi[0],&vj[0],Tp);
for(int t=0;t<nt;t++) LOG(Message) << " denom0 [" << t << "] " << denom0(t)<<std::endl;
for(int t=0;t<nt;t++) LOG(Message) << " denom1 [" << t << "] " << denom1(t)<<std::endl;
for(int g=0;g<4;g++){
for(int t=0;t<nt;t++) LOG(Message) << " DeltaF2_fig8 [" << t << ","<<g<<"] " << DeltaF2_fig8(t,g)<<std::endl;
for(int t=0;t<nt;t++) LOG(Message) << " DeltaF2_trtr [" << t << ","<<g<<"] " << DeltaF2_trtr(t,g)<<std::endl;
}
for(int g=0;g<4;g++){
for(int t=0;t<nt;t++)
LOG(Message) << " Bag [" << t << ","<<g<<"] "
<< (DeltaF2_fig8(t,g)+DeltaF2_trtr(t,g))
/ ( 8.0/3.0 * denom0[t]*denom1[t])
<<std::endl;
}
/////////////////////////////////////////////////////////////////////////
// Test: Build a bag contraction the Z2 way
// Build a wall bag comparison assuming no low modes
/////////////////////////////////////////////////////////////////////////
LOG(Message) << " Bag_z2 WARNING only correct if Nl == 0 "<<std::endl;
int t0=0;
int t1=dT;
int Nl=0;
LatticePropagator Qd0(grid);
LatticePropagator Qd1(grid);
LatticePropagator Qs0(grid);
LatticePropagator Qs1(grid);
for(int s=0;s<4;s++){
for(int c=0;c<3;c++){
int idx0 = Nl+t0*12+s*3+c;
int idx1 = Nl+t1*12+s*3+c;
FermToProp<FImpl>(Qd0, vi[idx0], s, c);
FermToProp<FImpl>(Qd1, vi[idx1], s, c);
FermToProp<FImpl>(Qs0, vj[idx0], s, c);
FermToProp<FImpl>(Qs1, vj[idx1], s, c);
}
}
std::vector<Gamma::Algebra> gammas ( {
Gamma::Algebra::GammaX,
Gamma::Algebra::GammaY,
Gamma::Algebra::GammaZ,
Gamma::Algebra::GammaT,
Gamma::Algebra::GammaXGamma5,
Gamma::Algebra::GammaYGamma5,
Gamma::Algebra::GammaZGamma5,
Gamma::Algebra::GammaTGamma5,
Gamma::Algebra::Identity,
Gamma::Algebra::Gamma5,
Gamma::Algebra::SigmaXY,
Gamma::Algebra::SigmaXZ,
Gamma::Algebra::SigmaXT,
Gamma::Algebra::SigmaYZ,
Gamma::Algebra::SigmaYT,
Gamma::Algebra::SigmaZT
});
auto G5 = Gamma::Algebra::Gamma5;
LatticePropagator anti_d0 = adj( Gamma(G5) * Qd0 * Gamma(G5));
LatticePropagator anti_d1 = adj( Gamma(G5) * Qd1 * Gamma(G5));
LatticeComplex TR1(grid);
LatticeComplex TR2(grid);
LatticeComplex Wick1(grid);
LatticeComplex Wick2(grid);
LatticePropagator PR1(grid);
LatticePropagator PR2(grid);
PR1 = Qs0 * Gamma(G5) * anti_d0;
PR2 = Qs1 * Gamma(G5) * anti_d1;
for(int g=0;g<Nd*Nd;g++){
auto g1 = gammas[g];
Gamma G1 (g1);
TR1 = trace( PR1 * G1 );
TR2 = trace( PR2 * G1 );
Wick1 = TR1*TR2;
Wick2 = trace( PR1* G1 * PR2 * G1 );
std::vector<TComplex> C1;
std::vector<TComplex> C2;
std::vector<TComplex> C3;
sliceSum(Wick1,C1, Tp);
sliceSum(Wick2,C2, Tp);
sliceSum(TR1 ,C3, Tp);
if(g<5){
for(int t=0;t<C1.size();t++){
LOG(Message) << " Wick1["<<g<<","<<t<< "] "<< C1[t]<<std::endl;
}
for(int t=0;t<C2.size();t++){
LOG(Message) << " Wick2["<<g<<","<<t<< "] "<< C2[t]<<std::endl;
}
}
if( (g==9) || (g==7) ){
for(int t=0;t<C3.size();t++){
LOG(Message) << " <G|P>["<<g<<","<<t<< "] "<< C3[t]<<std::endl;
}
}
}
}
END_MODULE_NAMESPACE
END_HADRONS_NAMESPACE
#endif // Hadrons_MContraction_A2APionField_hpp_
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