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Grid/extras/Hadrons/Modules/MContraction/A2Autils.hpp
Peter Boyle e307bb7528 Reorganise to abstract kernels that know about the lattice layout. 
Move these back into grid.
2018-09-04 12:30:00 +01:00

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#pragma once
#include <Grid/Hadrons/Global.hpp>
#include <unsupported/Eigen/CXX11/Tensor>
BEGIN_HADRONS_NAMESPACE
template <typename FImpl>
class A2Autils
{
public:
typedef typename FImpl::ComplexField ComplexField;
typedef typename FImpl::FermionField FermionField;
typedef typename FImpl::PropagatorField PropagatorField;
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;
typedef iSpinColourMatrix<vector_type> SpinColourMatrix_v;
static void MesonField(Eigen::Tensor<ComplexD,5> &mat,
const FermionField *lhs_wi,
const FermionField *rhs_vj,
std::vector<Gamma::Algebra> gammas,
const std::vector<ComplexField > &mom,
int orthogdim);
static void PionFieldWVmom(Eigen::Tensor<ComplexD,4> &mat,
const FermionField *wi,
const FermionField *vj,
const std::vector<ComplexField > &mom,
int orthogdim);
static void PionFieldXX(Eigen::Tensor<ComplexD,3> &mat,
const FermionField *wi,
const FermionField *vj,
int orthogdim,
int g5);
static void PionFieldWV(Eigen::Tensor<ComplexD,3> &mat,
const FermionField *wi,
const FermionField *vj,
int orthogdim);
static void PionFieldWW(Eigen::Tensor<ComplexD,3> &mat,
const FermionField *wi,
const FermionField *wj,
int orthogdim);
static void PionFieldVV(Eigen::Tensor<ComplexD,3> &mat,
const FermionField *vi,
const FermionField *vj,
int orthogdim);
static void ContractWWVV(std::vector<PropagatorField> &WWVV,
const Eigen::Tensor<ComplexD,3> &WW_sd,
const FermionField *vs,
const FermionField *vd);
static void DeltaFeq2(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 FermionField *vs,
const FermionField *vd,
int orthogdim);
};
template<class FImpl>
void A2Autils<FImpl>::MesonField(Eigen::Tensor<ComplexD,5> &mat,
const FermionField *lhs_wi,
const FermionField *rhs_vj,
std::vector<Gamma::Algebra> gammas,
const std::vector<ComplexField > &mom,
int orthogdim)
{
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(3);
int Rblock = mat.dimension(4);
GridBase *grid = lhs_wi[0]._grid;
const int Nd = grid->_ndimension;
const int Nsimd = grid->Nsimd();
int Nt = grid->GlobalDimensions()[orthogdim];
int Ngamma = gammas.size();
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<SpinMatrix_v > lvSum(MFrvol);
parallel_for (int r = 0; r < MFrvol; r++){
lvSum[r] = zero;
}
Vector<SpinMatrix_s > 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];
// potentially wasting cores here if local time extent too small
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 left = conjugate(lhs_wi[i]._odata[ss]);
for(int j=0;j<Rblock;j++){
SpinMatrix_v vv;
auto right = rhs_vj[j]._odata[ss];
for(int s1=0;s1<Ns;s1++){
for(int s2=0;s2<Ns;s2++){
vv()(s1,s2)() = left()(s2)(0) * right()(s1)(0)
+ left()(s2)(1) * right()(s1)(1)
+ left()(s2)(2) * right()(s1)(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);
}
}
}
}
}
}
// Sum across simd lanes in the plane, breaking out orthog dir.
parallel_for(int rt=0;rt<rd;rt++){
std::vector<int> icoor(Nd);
std::vector<SpinMatrix_s> 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;
extract(lvSum[ij_rdx],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];
}
}}}
}
assert(mat.dimension(0) == Nmom);
assert(mat.dimension(1) == Ngamma);
assert(mat.dimension(2) == 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++){
for(int m=0;m<Nmom;m++){
int ij_dx = m+Nmom*i + Nmom*Lblock * j + Nmom*Lblock * Rblock * lt;
for(int mu=0;mu<Ngamma;mu++){
// this is a bit slow
mat(m,mu,t,i,j) = trace(lsSum[ij_dx]*Gamma(gammas[mu]));
}
}
}
}
} else {
const scalar_type zz(0.0);
for(int i=0;i<Lblock;i++){
for(int j=0;j<Rblock;j++){
for(int mu=0;mu<Ngamma;mu++){
for(int m=0;m<Nmom;m++){
mat(m,mu,t,i,j) =zz;
}
}
}
}
}
}
}
////////////////////////////////////////////////////////////////////
// This global sum is taking as much as 50% of time on 16 nodes
// Vector size is 7 x 16 x 32 x 16 x 16 x sizeof(complex) = 2MB - 60MB depending on volume
// Healthy size that should suffice
////////////////////////////////////////////////////////////////////
grid->GlobalSumVector(&mat(0,0,0,0,0),Nmom*Ngamma*Nt*Lblock*Rblock);
}
///////////////////////////////////////////////////////////////////
//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<class FImpl>
void A2Autils<FImpl>::PionFieldXX(Eigen::Tensor<ComplexD,3> &mat,
const FermionField *wi,
const FermionField *vj,
int orthogdim,
int g5)
{
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]);
if (g5) {
w()(2)(0) = - w()(2)(0);
w()(2)(1) = - w()(2)(1);
w()(2)(2) = - w()(2)(2);
w()(3)(0) = - w()(3)(0);
w()(3)(1) = - w()(3)(1);
w()(3)(2) = - w()(3)(2);
}
for(int j=0;j<Rblock;j++){
auto v = vj[j]._odata[ss];
auto vv = v()(0)(0);
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<class FImpl>
void A2Autils<FImpl>::PionFieldWVmom(Eigen::Tensor<ComplexD,4> &mat,
const FermionField *wi,
const FermionField *vj,
const std::vector<ComplexField > &mom,
int orthogdim)
{
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];
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()()());
}
}
}
}
}
}
// 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);
// 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;
}
}}}
}
assert(mat.dimension(0) == Nmom);
assert(mat.dimension(1) == 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++){
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;
}
}
}
}
}
}
grid->GlobalSumVector(&mat(0,0,0,0),Nmom*Nt*Lblock*Rblock);
}
template<class FImpl>
void A2Autils<FImpl>::PionFieldWV(Eigen::Tensor<ComplexD,3> &mat,
const FermionField *wi,
const FermionField *vj,
int orthogdim)
{
const int g5=1;
PionFieldXX(mat,wi,vj,orthogdim,g5);
}
template<class FImpl>
void A2Autils<FImpl>::PionFieldWW(Eigen::Tensor<ComplexD,3> &mat,
const FermionField *wi,
const FermionField *wj,
int orthogdim)
{
const int nog5=0;
PionFieldXX(mat,wi,wj,orthogdim,nog5);
}
template<class FImpl>
void A2Autils<FImpl>::PionFieldVV(Eigen::Tensor<ComplexD,3> &mat,
const FermionField *vi,
const FermionField *vj,
int orthogdim)
{
const int nog5=0;
PionFieldXX(mat,vi,vj,orthogdim,nog5);
}
////////////////////////////////////////////
// Schematic thoughts about more generalised four quark insertion
//
// -- Pupil or fig8 type topology (depending on flavour structure) done below
// -- Have Bag style -- WWVV VVWW
// _ _
// / \/ \
// \_/\_/
//
// - Kpipi style (two pion insertions)
// K
// *********
// Type 1
// *********
// x
// ___ _____ pi(b)
// K / \/____/
// \ \
// \____\pi(a)
//
//
// W^W_sd V_s(x) V^_d(xa) Wa(xa) Va^(x) WW_bb' Vb Vb'(x)
//
// (Kww.PIvw) VV ; pi_ww.VV
//
// But Norman and Chris say g5 hermiticity not used, except on K
//
// Kww PIvw PIvw
//
// (W^W_sd PIa_dd') PIb_uu' (v_s v_d' w_u v_u')(x)
//
// - Can form (Nmode^3)
//
// (Kww . PIvw)_sd and then V_sV_d tensor product contracting this
//
// - Can form
//
// (PIvw)_uu' W_uV_u' tensor product.
//
// Both are lattice propagators.
//
// Contract with the same four quark type contraction as BK.
//
// *********
// Type 2
// *********
// _ _____ pi
// K / \/ |
// \_/\_____|pi
//
// Norman/Chris would say
//
// (Kww VV)(x) . (PIwv Piwv) VW(x)
//
// Full four quark via g5 hermiticity
//
// (Kww VV)(x) . (PIww Pivw) VV(x)
//
// *********
// Type 3
// *********
// ___ _____ pi
// K / \/ |
// \ /\ |
// \ \/ |
// \________|pi
//
//
// (V(x) . Kww . pi_vw . pivw . V(x)). WV(x)
//
// No difference possible to Norman, Chris, Diaqian
//
// *********
// Type 4
// *********
// ___ pi
// K / \/\ |\
// \___/\/ |/
// pi
//
// (Kww VV ) WV x Tr(PIwv PIwv)
//
// Could use alternate PI_ww PIvv for disco loop interesting comparison
//
// *********
// Primitives / Utilities for assembly
// *********
//
// i) Basic type for meson field - mode indexed object, whether WW, VW, VV etc..
// ii) Multiply two meson fields (modes^3) ; use BLAS MKL via Eigen
// iii) Multiply and trace two meson fields ; use BLAS MKL via Eigen. The element wise product trick
// iv) Contract a meson field (whether WW,VW, VV WV) with W and V fields to form LatticePropagator
// v) L^3 sum a four quark contaction with two LatticePropagators.
//
// Use lambda functions to enable flexibility in v)
// Use lambda functions to unify the pion field / meson field contraction codes.
////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
// 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] )
//
///////////////////////////////////////////////////////////////////////////////
//
// 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<class FImpl>
void A2Autils<FImpl>::ContractWWVV(std::vector<PropagatorField> &WWVV,
const Eigen::Tensor<ComplexD,3> &WW_sd,
const FermionField *vs,
const FermionField *vd)
{
GridBase *grid = vs[0]._grid;
int nd = grid->_ndimension;
int Nsimd = grid->Nsimd();
int N_t = WW_sd.dimension(0);
int N_s = WW_sd.dimension(1);
int N_d = WW_sd.dimension(2);
int d_unroll = 32;// Empirical optimisation
for(int t=0;t<N_t;t++){
WWVV[t] = zero;
}
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;
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]);
}
//////////////////////////
// Fast 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);
}}
}}
}
}
}
template<class FImpl>
void A2Autils<FImpl>::DeltaFeq2(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 FermionField *vs,
const FermionField *vd,
int orthogdim)
{
GridBase *grid = vs[0]._grid;
LOG(Message) << "Computing A2A DeltaF=2 graph" << std::endl;
auto G5 = Gamma(Gamma::Algebra::Gamma5);
double nodes = grid->NodeCount();
int nd = grid->_ndimension;
int Nsimd = grid->Nsimd();
int N_t = WW_sd.dimension(0);
int N_s = WW_sd.dimension(1);
int N_d = WW_sd.dimension(2);
assert(grid->GlobalDimensions()[orthogdim] == N_t);
double vol = 1.0;
for(int dim=0;dim<nd;dim++){
vol = vol * grid->GlobalDimensions()[dim];
}
double t_tot = -usecond();
std::vector<PropagatorField> WWVV (N_t,grid);
double t_outer= -usecond();
ContractWWVV(WWVV,WW_sd,&vs[0],&vd[0]);
t_outer+=usecond();
//////////////////////////////
// Implicit gamma-5
//////////////////////////////
for(int t=0;t<N_t;t++){
WWVV[t] = WWVV[t]* G5 ;
}
////////////////////////////////////////////////////////
// Contraction
////////////////////////////////////////////////////////
dF2_trtr.resize(N_t,5);
dF2_fig8.resize(N_t,5);
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);
}
ComplexField D0(grid); D0 = zero; // <P|A0> correlator from each wall
ComplexField D1(grid); D1 = zero;
ComplexField O1_trtr(grid); O1_trtr = zero;
ComplexField O2_trtr(grid); O2_trtr = zero;
ComplexField O3_trtr(grid); O3_trtr = zero;
ComplexField O4_trtr(grid); O4_trtr = zero;
ComplexField O5_trtr(grid); O5_trtr = zero;
ComplexField O1_fig8(grid); O1_fig8 = zero;
ComplexField O2_fig8(grid); O2_fig8 = zero;
ComplexField O3_fig8(grid); O3_fig8 = zero;
ComplexField O4_fig8(grid); O4_fig8 = zero;
ComplexField O5_fig8(grid); O5_fig8 = zero;
//////////////////////////////////////////////////
// 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();
// 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);
std::cout <<GridLogMessage << " dt " <<dt_min<<"..." <<dt_max<<std::endl;
for(int t0=0;t0<N_t;t0++){
std::cout <<GridLogMessage << " t0 " <<t0<<std::endl;
// for(int dt=dt_min;dt<dt_max;dt++){
{
int dt = dt_min;
int t1 = (t0+dt)%N_t;
std::cout <<GridLogMessage << " t1 " <<t1<<std::endl;
parallel_for(int ss=0;ss<grid->oSites();ss++){
auto VV0= WWVV[t0]._odata[ss];
auto VV1= WWVV[t1]._odata[ss];
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
////////////////////////////////////
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);
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_contr " << t_contr /million << " s "<< std::endl;
}
END_HADRONS_NAMESPACE
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