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https://github.com/paboyle/Grid.git
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Much faster little dirac operator calculation
This commit is contained in:
Peter Boyle
parent
36a14e4ee3
commit
13713b2a76
@ -285,6 +285,7 @@ public:
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Aggregation<Fobj,CComplex,nbasis> & Subspace,
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GridBase *CoarseGrid)
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{
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#if 0
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std::cout << GridLogMessage<< "GeneralCoarsenMatrixMrhs "<< std::endl;
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GridBase *grid = Subspace.FineGrid;
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@ -362,7 +363,7 @@ public:
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blockZAXPY(phaF[p],pha[p],one,zz);
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}
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// Could save on storage here
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// Could save on temporary storage here
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std::vector<CoarseMatrix> _A;
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_A.resize(geom_srhs.npoint,CoarseGrid);
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@ -390,6 +391,7 @@ public:
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// Could do this with a block promote or similar BLAS call via the MultiRHSBlockProjector with a const matrix.
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for(int k=0;k<npoint;k++){
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FT = Zero();
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for(int l=0;l<npoint;l++){
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FT= FT+ invMkl(l,k)*ComputeProj[l];
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@ -412,7 +414,7 @@ public:
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// PopulateAdag();
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// }
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// Need to write something to populate Adag from A
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for(int p=0;p<geom_srhs.npoint;p++){
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GridtoBLAS(_A[p],BLAS_A[p]);
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}
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@ -426,7 +428,208 @@ Grid : Message : 11698.730568 s : CoarsenOperator inv 103948313 us
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Takes 600s to compute matrix elements, DOMINATED by the block project.
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Easy to speed up with the batched block project.
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Store npoint vectors, get npoint x Nbasis block projection, and 81 fold faster.
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// Block project below taks to 240s
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Grid : Message : 328.193418 s : CoarsenOperator phase 38338 us
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Grid : Message : 328.193434 s : CoarsenOperator phaseBZ 1711226 us
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Grid : Message : 328.193436 s : CoarsenOperator mat 122213270 us
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//Grid : Message : 328.193438 s : CoarsenOperator proj 1181154 us <-- this is mistimed
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//Grid : Message : 11698.730568 s : CoarsenOperator inv 103948313 us <-- Cut this ~10x if lucky by loop fusion
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*/
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#else
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RealD tproj=0.0;
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RealD tmat=0.0;
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RealD tphase=0.0;
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RealD tphaseBZ=0.0;
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RealD tinv=0.0;
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std::cout << GridLogMessage<< "GeneralCoarsenMatrixMrhs "<< std::endl;
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GridBase *grid = Subspace.FineGrid;
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/////////////////////////////////////////////////////////////
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// Orthogonalise the subblocks over the basis
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/////////////////////////////////////////////////////////////
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CoarseScalar InnerProd(CoarseGrid);
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blockOrthogonalise(InnerProd,Subspace.subspace);
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MultiRHSBlockProject<Lattice<Fobj> > Projector;
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Projector.Allocate(nbasis,grid,CoarseGrid);
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Projector.ImportBasis(Subspace.subspace);
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const int npoint = geom_srhs.npoint;
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Coordinate clatt = CoarseGrid->GlobalDimensions();
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int Nd = CoarseGrid->Nd();
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/*
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* Here, k,l index which possible momentum/shift within the N-points connected by MdagM.
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* Matrix index i is mapped to this shift via
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* geom.shifts[i]
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*
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* conj(pha[block]) proj[k (which mom)][j (basis vec cpt)][block]
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* = \sum_{l in ball} e^{i q_k . delta_l} < phi_{block,j} | MdagM | phi_{(block+delta_l),i} >
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* = \sum_{l in ball} e^{iqk.delta_l} A_ji^{b.b+l}
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* = M_{kl} A_ji^{b.b+l}
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*
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* Must assemble and invert matrix M_k,l = e^[i q_k . delta_l]
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*
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* Where q_k = delta_k . (2*M_PI/global_nb[mu])
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*
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* Then A{ji}^{b,b+l} = M^{-1}_{lm} ComputeProj_{m,b,i,j}
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*/
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Eigen::MatrixXcd Mkl = Eigen::MatrixXcd::Zero(npoint,npoint);
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Eigen::MatrixXcd invMkl = Eigen::MatrixXcd::Zero(npoint,npoint);
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ComplexD ci(0.0,1.0);
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for(int k=0;k<npoint;k++){ // Loop over momenta
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for(int l=0;l<npoint;l++){ // Loop over nbr relative
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ComplexD phase(0.0,0.0);
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for(int mu=0;mu<Nd;mu++){
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RealD TwoPiL = M_PI * 2.0/ clatt[mu];
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phase=phase+TwoPiL*geom_srhs.shifts[k][mu]*geom_srhs.shifts[l][mu];
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}
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phase=exp(phase*ci);
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Mkl(k,l) = phase;
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}
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}
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invMkl = Mkl.inverse();
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///////////////////////////////////////////////////////////////////////
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// Now compute the matrix elements of linop between the orthonormal
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// set of vectors.
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///////////////////////////////////////////////////////////////////////
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FineField phaV(grid); // Phased block basis vector
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FineField MphaV(grid);// Matrix applied
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std::vector<FineComplexField> phaF(npoint,grid);
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std::vector<CoarseComplexField> pha(npoint,CoarseGrid);
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CoarseVector coarseInner(CoarseGrid);
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tphase=-usecond();
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typedef typename CComplex::scalar_type SComplex;
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FineComplexField one(grid); one=SComplex(1.0);
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FineComplexField zz(grid); zz = Zero();
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for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
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/////////////////////////////////////////////////////
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// Stick a phase on every block
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/////////////////////////////////////////////////////
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CoarseComplexField coor(CoarseGrid);
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pha[p]=Zero();
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for(int mu=0;mu<Nd;mu++){
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LatticeCoordinate(coor,mu);
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RealD TwoPiL = M_PI * 2.0/ clatt[mu];
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pha[p] = pha[p] + (TwoPiL * geom_srhs.shifts[p][mu]) * coor;
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}
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pha[p] =exp(pha[p]*ci);
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blockZAXPY(phaF[p],pha[p],one,zz);
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}
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tphase+=usecond();
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// Could save on temporary storage here
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std::vector<CoarseMatrix> _A;
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_A.resize(geom_srhs.npoint,CoarseGrid);
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// Count use small chunks than npoint == 81 and save memory
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std::vector<FineField> _MphaV;
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_MphaV.resize(npoint,grid);
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std::vector<CoarseVector> ComputeProj(npoint,CoarseGrid);
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CoarseVector FT(CoarseGrid);
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for(int i=0;i<nbasis;i++){// Loop over basis vectors
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std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<"/"<<nbasis<< std::endl;
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std::cout << GridLogMessage << " phasing the fine vector "<<std::endl;
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for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
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tphaseBZ-=usecond();
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phaV = phaF[p]*Subspace.subspace[i];
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tphaseBZ+=usecond();
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/////////////////////////////////////////////////////////////////////
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// Multiple phased subspace vector by matrix and project to subspace
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// Remove local bulk phase to leave relative phases
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/////////////////////////////////////////////////////////////////////
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tmat-=usecond();
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linop.Op(phaV,MphaV);
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_MphaV[p] = MphaV;
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tmat+=usecond();
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}
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std::cout << GridLogMessage << " Calling block project "<<std::endl;
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tproj-=usecond();
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Projector.blockProject(_MphaV,ComputeProj);
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tproj+=usecond();
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std::cout << GridLogMessage << " conj phasing the coarse vectors "<<std::endl;
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for(int p=0;p<npoint;p++){
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ComputeProj[p] = conjugate(pha[p])*ComputeProj[p];
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}
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// Could do this with a block promote or similar BLAS call via the MultiRHSBlockProjector with a const matrix.
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std::cout << GridLogMessage << " Starting FT inv "<<std::endl;
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tinv-=usecond();
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for(int k=0;k<npoint;k++){
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FT = Zero();
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// 81 kernel calls as many ComputeProj vectors
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// Could fuse with a vector of views, but ugly
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// Could unroll the expression and run fewer kernels -- much more attractive
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// Could also do non blocking.
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#if 0
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for(int l=0;l<npoint;l++){
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FT= FT+ invMkl(l,k)*ComputeProj[l];
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}
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#else
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const int radix = 9;
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int ll;
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for(ll=0;ll+radix-1<npoint;ll+=radix){
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// When ll = npoint-radix, ll+radix-1 = npoint-1, and we do it all.
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FT = FT
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+ invMkl(ll+0,k)*ComputeProj[ll+0]
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+ invMkl(ll+1,k)*ComputeProj[ll+1]
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+ invMkl(ll+2,k)*ComputeProj[ll+2]
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+ invMkl(ll+3,k)*ComputeProj[ll+3]
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+ invMkl(ll+4,k)*ComputeProj[ll+4]
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+ invMkl(ll+5,k)*ComputeProj[ll+5]
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+ invMkl(ll+6,k)*ComputeProj[ll+6]
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+ invMkl(ll+7,k)*ComputeProj[ll+7]
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+ invMkl(ll+8,k)*ComputeProj[ll+8];
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}
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for(int l=ll;l<npoint;l++){
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FT= FT+ invMkl(l,k)*ComputeProj[l];
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}
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#endif
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// 1 kernel call -- must be cheaper
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int osites=CoarseGrid->oSites();
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autoView( A_v , _A[k], AcceleratorWrite);
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autoView( FT_v , FT, AcceleratorRead);
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accelerator_for(sss, osites, 1, {
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for(int j=0;j<nbasis;j++){
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A_v[sss](i,j) = FT_v[sss](j);
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}
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});
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}
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tinv+=usecond();
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}
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// Only needed if nonhermitian
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// if ( ! hermitian ) {
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// std::cout << GridLogMessage<<"PopulateAdag "<<std::endl;
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// PopulateAdag();
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// }
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// Need to write something to populate Adag from A
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std::cout << GridLogMessage << " Calling GridtoBLAS "<<std::endl;
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for(int p=0;p<geom_srhs.npoint;p++){
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GridtoBLAS(_A[p],BLAS_A[p]);
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}
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std::cout << GridLogMessage<<"CoarsenOperator phase "<<tphase<<" us"<<std::endl;
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std::cout << GridLogMessage<<"CoarsenOperator phaseBZ "<<tphaseBZ<<" us"<<std::endl;
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std::cout << GridLogMessage<<"CoarsenOperator mat "<<tmat <<" us"<<std::endl;
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std::cout << GridLogMessage<<"CoarsenOperator proj "<<tproj<<" us"<<std::endl;
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std::cout << GridLogMessage<<"CoarsenOperator inv "<<tinv<<" us"<<std::endl;
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#endif
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}
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void Mdag(const CoarseVector &in, CoarseVector &out)
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{
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@ -497,17 +700,19 @@ Store npoint vectors, get npoint x Nbasis block projection, and 81 fold faster.
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BLAStoGrid(out,BLAS_C);
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t_BtoG+=usecond();
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t_tot+=usecond();
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/*
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std::cout << GridLogMessage << "New Mrhs coarse DONE "<<std::endl;
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std::cout << GridLogMessage<<"Coarse Mult exch "<<t_exch<<" us"<<std::endl;
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std::cout << GridLogMessage<<"Coarse Mult mult "<<t_mult<<" us"<<std::endl;
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std::cout << GridLogMessage<<"Coarse Mult GtoB "<<t_GtoB<<" us"<<std::endl;
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std::cout << GridLogMessage<<"Coarse Mult BtoG "<<t_BtoG<<" us"<<std::endl;
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std::cout << GridLogMessage<<"Coarse Mult tot "<<t_tot<<" us"<<std::endl;
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std::cout << GridLogMessage<<std::endl;
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*/
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// std::cout << GridLogMessage<<std::endl;
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// std::cout << GridLogMessage<<"Coarse Kernel flops "<< flops<<std::endl;
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std::cout << GridLogMessage<<"Coarse Kernel flop/s "<< flops/t_mult<<" mflop/s"<<std::endl;
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// std::cout << GridLogMessage<<"Coarse Kernel flop/s "<< flops/t_mult<<" mflop/s"<<std::endl;
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// std::cout << GridLogMessage<<"Coarse Kernel bytes/s "<< bytes/t_mult/1000<<" GB/s"<<std::endl;
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std::cout << GridLogMessage<<"Coarse overall flops/s "<< flops/t_tot<<" mflop/s"<<std::endl;
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// std::cout << GridLogMessage<<"Coarse overall flops/s "<< flops/t_tot<<" mflop/s"<<std::endl;
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// std::cout << GridLogMessage<<"Coarse total bytes "<< bytes/1e6<<" MB"<<std::endl;
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};
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virtual void Mdiag (const Field &in, Field &out){ assert(0);};
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