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Peter Boyle 2023-10-06 21:03:34 -04:00
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1107
Grid/algorithms/CoarsenedMatrix.h
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Grid/algorithms/GeneralCoarsenedMatrix.h
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/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./lib/algorithms/GeneralCoarsenedMatrix.h
Copyright (C) 2015
Author: Peter Boyle <pboyle@bnl.gov>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License along
with this program; if not, write to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
See the full license in the file "LICENSE" in the top level distribution directory
*************************************************************************************/
/* END LEGAL */
#pragma once
#include <Grid/qcd/QCD.h> // needed for Dagger(Yes|No), Inverse(Yes|No)
#include <Grid/lattice/PaddedCell.h>
#include <Grid/stencil/GeneralLocalStencil.h>
NAMESPACE_BEGIN(Grid);
// Fixme need coalesced read gpermute
template<class vobj> void gpermute(vobj & inout,int perm){
vobj tmp=inout;
if (perm & 0x1 ) { permute(inout,tmp,0); tmp=inout;}
if (perm & 0x2 ) { permute(inout,tmp,1); tmp=inout;}
if (perm & 0x4 ) { permute(inout,tmp,2); tmp=inout;}
if (perm & 0x8 ) { permute(inout,tmp,3); tmp=inout;}
}
/////////////////////////////////////////////////////////////////
// Reuse Aggregation class from CoarsenedMatrix for now
// Might think about *smoothed* Aggregation
// Equivalent of Geometry class in cartesian case
/////////////////////////////////////////////////////////////////
class NonLocalStencilGeometry {
public:
int depth;
int hops;
int npoint;
std::vector<Coordinate> shifts;
Coordinate stencil_size;
Coordinate stencil_lo;
Coordinate stencil_hi;
GridCartesian *grid;
GridCartesian *Grid() {return grid;};
int Depth(void){return 1;}; // Ghost zone depth
int Hops(void){return hops;}; // # of hops=> level of corner fill in in stencil
virtual int DimSkip(void) =0;
virtual ~NonLocalStencilGeometry() {};
int Reverse(int point)
{
int Nd = Grid()->Nd();
Coordinate shft = shifts[point];
Coordinate rev(Nd);
for(int mu=0;mu<Nd;mu++) rev[mu]= -shft[mu];
for(int p=0;p<npoint;p++){
if(rev==shifts[p]){
return p;
}
}
assert(0);
return -1;
}
void BuildShifts(void)
{
this->shifts.resize(0);
int Nd = this->grid->Nd();
int dd = this->DimSkip();
for(int s0=this->stencil_lo[dd+0];s0<=this->stencil_hi[dd+0];s0++){
for(int s1=this->stencil_lo[dd+1];s1<=this->stencil_hi[dd+1];s1++){
for(int s2=this->stencil_lo[dd+2];s2<=this->stencil_hi[dd+2];s2++){
for(int s3=this->stencil_lo[dd+3];s3<=this->stencil_hi[dd+3];s3++){
Coordinate sft(Nd,0);
sft[dd+0] = s0;
sft[dd+1] = s1;
sft[dd+2] = s2;
sft[dd+3] = s3;
int nhops = abs(s0)+abs(s1)+abs(s2)+abs(s3);
if(nhops<=this->hops) this->shifts.push_back(sft);
}}}}
this->npoint = this->shifts.size();
std::cout << GridLogMessage << "NonLocalStencilGeometry has "<< this->npoint << " terms in stencil "<<std::endl;
}
NonLocalStencilGeometry(GridCartesian *_coarse_grid,int _hops) : grid(_coarse_grid), hops(_hops)
{
Coordinate latt = grid->GlobalDimensions();
stencil_size.resize(grid->Nd());
stencil_lo.resize(grid->Nd());
stencil_hi.resize(grid->Nd());
for(int d=0;d<grid->Nd();d++){
if ( latt[d] == 1 ) {
stencil_lo[d] = 0;
stencil_hi[d] = 0;
stencil_size[d]= 1;
} else if ( latt[d] == 2 ) {
stencil_lo[d] = -1;
stencil_hi[d] = 0;
stencil_size[d]= 2;
} else if ( latt[d] > 2 ) {
stencil_lo[d] = -1;
stencil_hi[d] = 1;
stencil_size[d]= 3;
}
}
};
};
// Need to worry about red-black now
class NonLocalStencilGeometry4D : public NonLocalStencilGeometry {
public:
virtual int DimSkip(void) { return 0;};
NonLocalStencilGeometry4D(GridCartesian *Coarse,int _hops) : NonLocalStencilGeometry(Coarse,_hops) { };
virtual ~NonLocalStencilGeometry4D() {};
};
class NonLocalStencilGeometry5D : public NonLocalStencilGeometry {
public:
virtual int DimSkip(void) { return 1; };
NonLocalStencilGeometry5D(GridCartesian *Coarse,int _hops) : NonLocalStencilGeometry(Coarse,_hops) { };
virtual ~NonLocalStencilGeometry5D() {};
};
/*
* Bunch of different options classes
*/
class NextToNextToNextToNearestStencilGeometry4D : public NonLocalStencilGeometry4D {
public:
NextToNextToNextToNearestStencilGeometry4D(GridCartesian *Coarse) : NonLocalStencilGeometry4D(Coarse,4)
{
this->BuildShifts();
};
};
class NextToNextToNextToNearestStencilGeometry5D : public NonLocalStencilGeometry5D {
public:
NextToNextToNextToNearestStencilGeometry5D(GridCartesian *Coarse) : NonLocalStencilGeometry5D(Coarse,4)
{
this->BuildShifts();
};
};
class NextToNearestStencilGeometry4D : public NonLocalStencilGeometry4D {
public:
NextToNearestStencilGeometry4D(GridCartesian *Coarse) : NonLocalStencilGeometry4D(Coarse,2)
{
this->BuildShifts();
};
};
class NextToNearestStencilGeometry5D : public NonLocalStencilGeometry5D {
public:
NextToNearestStencilGeometry5D(GridCartesian *Coarse) : NonLocalStencilGeometry5D(Coarse,2)
{
this->BuildShifts();
};
};
class NearestStencilGeometry4D : public NonLocalStencilGeometry4D {
public:
NearestStencilGeometry4D(GridCartesian *Coarse) : NonLocalStencilGeometry4D(Coarse,1)
{
this->BuildShifts();
};
};
class NearestStencilGeometry5D : public NonLocalStencilGeometry5D {
public:
NearestStencilGeometry5D(GridCartesian *Coarse) : NonLocalStencilGeometry5D(Coarse,1)
{
this->BuildShifts();
};
};
// Fine Object == (per site) type of fine field
// nbasis == number of deflation vectors
template<class Fobj,class CComplex,int nbasis>
class GeneralCoarsenedMatrix : public SparseMatrixBase<Lattice<iVector<CComplex,nbasis > > > {
public:
typedef GeneralCoarsenedMatrix<Fobj,CComplex,nbasis> GeneralCoarseOp;
typedef iVector<CComplex,nbasis > siteVector;
typedef iMatrix<CComplex,nbasis > siteMatrix;
typedef Lattice<iScalar<CComplex> > CoarseComplexField;
typedef Lattice<siteVector> CoarseVector;
typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
typedef iMatrix<CComplex,nbasis > Cobj;
typedef Lattice< CComplex > CoarseScalar; // used for inner products on fine field
typedef Lattice<Fobj > FineField;
typedef CoarseVector Field;
////////////////////
// Data members
////////////////////
int hermitian;
GridBase * _FineGrid;
GridCartesian * _CoarseGrid;
NonLocalStencilGeometry &geom;
PaddedCell Cell;
GeneralLocalStencil Stencil;
std::vector<CoarseMatrix> _A;
std::vector<CoarseMatrix> _Adag;
///////////////////////
// Interface
///////////////////////
GridBase * Grid(void) { return _FineGrid; }; // this is all the linalg routines need to know
GridBase * FineGrid(void) { return _FineGrid; }; // this is all the linalg routines need to know
GridCartesian * CoarseGrid(void) { return _CoarseGrid; }; // this is all the linalg routines need to know
void ProjectNearestNeighbour(RealD shift, GeneralCoarseOp &CopyMe)
{
int nfound=0;
std::cout << " ProjectNearestNeighbour "<< CopyMe._A[0].Grid()<<std::endl;
for(int p=0;p<geom.npoint;p++){
for(int pp=0;pp<CopyMe.geom.npoint;pp++){
// Search for the same relative shift
// Avoids brutal handling of Grid pointers
if ( CopyMe.geom.shifts[pp]==geom.shifts[p] ) {
_A[p] = CopyMe.Cell.Extract(CopyMe._A[pp]);
_Adag[p] = CopyMe.Cell.Extract(CopyMe._Adag[pp]);
nfound++;
}
}
}
assert(nfound==geom.npoint);
ExchangeCoarseLinks();
}
GeneralCoarsenedMatrix(NonLocalStencilGeometry &_geom,GridBase *FineGrid, GridCartesian * CoarseGrid)
: geom(_geom),
_FineGrid(FineGrid),
_CoarseGrid(CoarseGrid),
hermitian(1),
Cell(_geom.Depth(),_CoarseGrid),
Stencil(Cell.grids.back(),geom.shifts)
{
{
int npoint = _geom.npoint;
autoView( Stencil_v , Stencil, AcceleratorRead);
int osites=Stencil.Grid()->oSites();
for(int ss=0;ss<osites;ss++){
for(int point=0;point<npoint;point++){
auto SE = Stencil_v.GetEntry(point,ss);
int o = SE->_offset;
assert( o< osites);
}
}
}
_A.resize(geom.npoint,CoarseGrid);
_Adag.resize(geom.npoint,CoarseGrid);
}
void M (const CoarseVector &in, CoarseVector &out)
{
Mult(_A,in,out);
}
void Mdag (const CoarseVector &in, CoarseVector &out)
{
if ( hermitian ) M(in,out);
else Mult(_Adag,in,out);
}
void Mult (std::vector<CoarseMatrix> &A,const CoarseVector &in, CoarseVector &out)
{
RealD tviews=0;
RealD ttot=0;
RealD tmult=0;
RealD texch=0;
RealD text=0;
ttot=-usecond();
conformable(CoarseGrid(),in.Grid());
conformable(in.Grid(),out.Grid());
out.Checkerboard() = in.Checkerboard();
CoarseVector tin=in;
texch-=usecond();
CoarseVector pin = Cell.Exchange(tin);
texch+=usecond();
CoarseVector pout(pin.Grid()); pout=Zero();
int npoint = geom.npoint;
typedef LatticeView<Cobj> Aview;
const int Nsimd = CComplex::Nsimd();
int osites=pin.Grid()->oSites();
// int gsites=pin.Grid()->gSites();
RealD flops = 1.0* npoint * nbasis * nbasis * 8 * osites;
RealD bytes = (1.0*osites*sizeof(siteMatrix)*npoint+2.0*osites*sizeof(siteVector))*npoint;
// for(int point=0;point<npoint;point++){
// conformable(A[point],pin);
// }
{
tviews-=usecond();
autoView( in_v , pin, AcceleratorRead);
autoView( out_v , pout, AcceleratorWrite);
autoView( Stencil_v , Stencil, AcceleratorRead);
tviews+=usecond();
for(int point=0;point<npoint;point++){
tviews-=usecond();
autoView( A_v, A[point],AcceleratorRead);
tviews+=usecond();
tmult-=usecond();
accelerator_for(sss, osites*nbasis, Nsimd, {
typedef decltype(coalescedRead(in_v[0])) calcVector;
int ss = sss/nbasis;
int b = sss%nbasis;
auto SE = Stencil_v.GetEntry(point,ss);
auto nbr = coalescedReadGeneralPermute(in_v[SE->_offset],SE->_permute,Nd);
auto res = out_v(ss)(b);
for(int bb=0;bb<nbasis;bb++) {
res = res + coalescedRead(A_v[ss](b,bb))*nbr(bb);
}
coalescedWrite(out_v[ss](b),res);
});
tmult+=usecond();
}
}
text-=usecond();
out = Cell.Extract(pout);
text+=usecond();
ttot+=usecond();
std::cout << GridLogPerformance<<"Coarse Mult Aviews "<<tviews<<" us"<<std::endl;
std::cout << GridLogPerformance<<"Coarse Mult exch "<<texch<<" us"<<std::endl;
std::cout << GridLogPerformance<<"Coarse Mult mult "<<tmult<<" us"<<std::endl;
std::cout << GridLogPerformance<<"Coarse Mult ext "<<text<<" us"<<std::endl;
std::cout << GridLogPerformance<<"Coarse Mult tot "<<ttot<<" us"<<std::endl;
std::cout << GridLogPerformance<<"Coarse Kernel "<< flops/tmult<<" mflop/s"<<std::endl;
std::cout << GridLogPerformance<<"Coarse Kernel "<< bytes/tmult<<" MB/s"<<std::endl;
std::cout << GridLogPerformance<<"Coarse flops/s "<< flops/ttot<<" mflop/s"<<std::endl;
std::cout << GridLogPerformance<<"Coarse bytes "<< bytes/1e6<<" MB"<<std::endl;
};
void PopulateAdag(void)
{
for(int64_t bidx=0;bidx<CoarseGrid()->gSites() ;bidx++){
Coordinate bcoor;
CoarseGrid()->GlobalIndexToGlobalCoor(bidx,bcoor);
for(int p=0;p<geom.npoint;p++){
Coordinate scoor = bcoor;
for(int mu=0;mu<bcoor.size();mu++){
int L = CoarseGrid()->GlobalDimensions()[mu];
scoor[mu] = (bcoor[mu] - geom.shifts[p][mu] + L) % L; // Modulo arithmetic
}
// Flip to poke/peekLocalSite and not too bad
auto link = peekSite(_A[p],scoor);
int pp = geom.Reverse(p);
pokeSite(adj(link),_Adag[pp],bcoor);
}
}
}
/////////////////////////////////////////////////////////////
//
// A) Only reduced flops option is to use a padded cell of depth 4
// and apply MpcDagMpc in the padded cell.
//
// Makes for ONE application of MpcDagMpc per vector instead of 30 or 80.
// With the effective cell size around (B+8)^4 perhaps 12^4/4^4 ratio
// Cost is 81x more, same as stencil size.
//
// But: can eliminate comms and do as local dirichlet.
//
// Local exchange gauge field once.
// Apply to all vectors, local only computation.
// Must exchange ghost subcells in reverse process of PaddedCell to take inner products
//
// B) Can reduce cost: pad by 1, apply Deo (4^4+6^4+8^4+8^4 )/ (4x 4^4)
// pad by 2, apply Doe
// pad by 3, apply Deo
// then break out 8x directions; cost is ~10x MpcDagMpc per vector
//
// => almost factor of 10 in setup cost, excluding data rearrangement
//
// Intermediates -- ignore the corner terms, leave approximate and force Hermitian
// Intermediates -- pad by 2 and apply 1+8+24 = 33 times.
/////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////
// BFM HDCG style approach: Solve a system of equations to get Aij
//////////////////////////////////////////////////////////
/*
* Here, k,l index which possible shift within the 3^Nd "ball" connected by MdagM.
*
* conj(phases[block]) proj[k][ block*Nvec+j ] = \sum_ball e^{i q_k . delta} < phi_{block,j} | MdagM | phi_{(block+delta),i} >
* = \sum_ball e^{iqk.delta} A_ji
*
* Must invert matrix M_k,l = e^[i q_k . delta_l]
*
* Where q_k = delta_k . (2*M_PI/global_nb[mu])
*/
void CoarsenOperator(LinearOperatorBase<Lattice<Fobj> > &linop,
Aggregation<Fobj,CComplex,nbasis> & Subspace)
{
std::cout << GridLogMessage<< "GeneralCoarsenMatrix "<< std::endl;
GridBase *grid = FineGrid();
RealD tproj=0.0;
RealD teigen=0.0;
RealD tmat=0.0;
RealD tphase=0.0;
RealD tinv=0.0;
/////////////////////////////////////////////////////////////
// Orthogonalise the subblocks over the basis
/////////////////////////////////////////////////////////////
CoarseScalar InnerProd(CoarseGrid());
blockOrthogonalise(InnerProd,Subspace.subspace);
const int npoint = geom.npoint;
Coordinate clatt = CoarseGrid()->GlobalDimensions();
int Nd = CoarseGrid()->Nd();
/*
* Here, k,l index which possible momentum/shift within the N-points connected by MdagM.
* Matrix index i is mapped to this shift via
* geom.shifts[i]
*
* conj(pha[block]) proj[k (which mom)][j (basis vec cpt)][block]
* = \sum_{l in ball} e^{i q_k . delta_l} < phi_{block,j} | MdagM | phi_{(block+delta_l),i} >
* = \sum_{l in ball} e^{iqk.delta_l} A_ji^{b.b+l}
* = M_{kl} A_ji^{b.b+l}
*
* Must assemble and invert matrix M_k,l = e^[i q_k . delta_l]
*
* Where q_k = delta_k . (2*M_PI/global_nb[mu])
*
* Then A{ji}^{b,b+l} = M^{-1}_{lm} ComputeProj_{m,b,i,j}
*/
teigen-=usecond();
Eigen::MatrixXcd Mkl = Eigen::MatrixXcd::Zero(npoint,npoint);
Eigen::MatrixXcd invMkl = Eigen::MatrixXcd::Zero(npoint,npoint);
ComplexD ci(0.0,1.0);
for(int k=0;k<npoint;k++){ // Loop over momenta
for(int l=0;l<npoint;l++){ // Loop over nbr relative
ComplexD phase(0.0,0.0);
for(int mu=0;mu<Nd;mu++){
RealD TwoPiL = M_PI * 2.0/ clatt[mu];
phase=phase+TwoPiL*geom.shifts[k][mu]*geom.shifts[l][mu];
}
phase=exp(phase*ci);
Mkl(k,l) = phase;
}
}
invMkl = Mkl.inverse();
teigen+=usecond();
///////////////////////////////////////////////////////////////////////
// Now compute the matrix elements of linop between the orthonormal
// set of vectors.
///////////////////////////////////////////////////////////////////////
FineField phaV(grid); // Phased block basis vector
FineField MphaV(grid);// Matrix applied
CoarseVector coarseInner(CoarseGrid());
std::vector<CoarseVector> ComputeProj(npoint,CoarseGrid());
std::vector<CoarseVector> FT(npoint,CoarseGrid());
for(int i=0;i<nbasis;i++){// Loop over basis vectors
std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<"/"<<nbasis<< std::endl;
for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
/////////////////////////////////////////////////////
// Stick a phase on every block
/////////////////////////////////////////////////////
tphase-=usecond();
CoarseComplexField coor(CoarseGrid());
CoarseComplexField pha(CoarseGrid()); pha=Zero();
for(int mu=0;mu<Nd;mu++){
LatticeCoordinate(coor,mu);
RealD TwoPiL = M_PI * 2.0/ clatt[mu];
pha = pha + (TwoPiL * geom.shifts[p][mu]) * coor;
}
pha =exp(pha*ci);
phaV=Zero();
blockZAXPY(phaV,pha,Subspace.subspace[i],phaV);
tphase+=usecond();
/////////////////////////////////////////////////////////////////////
// Multiple phased subspace vector by matrix and project to subspace
// Remove local bulk phase to leave relative phases
/////////////////////////////////////////////////////////////////////
tmat-=usecond();
linop.Op(phaV,MphaV);
tmat+=usecond();
tproj-=usecond();
blockProject(coarseInner,MphaV,Subspace.subspace);
coarseInner = conjugate(pha) * coarseInner;
ComputeProj[p] = coarseInner;
tproj+=usecond();
}
tinv-=usecond();
for(int k=0;k<npoint;k++){
FT[k] = Zero();
for(int l=0;l<npoint;l++){
FT[k]= FT[k]+ invMkl(l,k)*ComputeProj[l];
}
int osites=CoarseGrid()->oSites();
autoView( A_v , _A[k], AcceleratorWrite);
autoView( FT_v , FT[k], AcceleratorRead);
accelerator_for(sss, osites, 1, {
for(int j=0;j<nbasis;j++){
A_v[sss](j,i) = FT_v[sss](j);
}
});
}
tinv+=usecond();
}
for(int p=0;p<geom.npoint;p++){
Coordinate coor({0,0,0,0,0});
auto sval = peekSite(_A[p],coor);
}
// Only needed if nonhermitian
if ( ! hermitian ) {
std::cout << GridLogMessage<<"PopulateAdag "<<std::endl;
PopulateAdag();
}
// Need to write something to populate Adag from A
std::cout << GridLogMessage<<"ExchangeCoarseLinks "<<std::endl;
ExchangeCoarseLinks();
std::cout << GridLogMessage<<"CoarsenOperator eigen "<<teigen<<" us"<<std::endl;
std::cout << GridLogMessage<<"CoarsenOperator phase "<<tphase<<" us"<<std::endl;
std::cout << GridLogMessage<<"CoarsenOperator mat "<<tmat <<" us"<<std::endl;
std::cout << GridLogMessage<<"CoarsenOperator proj "<<tproj<<" us"<<std::endl;
std::cout << GridLogMessage<<"CoarsenOperator inv "<<tinv<<" us"<<std::endl;
}
void ExchangeCoarseLinks(void){
for(int p=0;p<geom.npoint;p++){
std::cout << "Exchange "<<p<<std::endl;
_A[p] = Cell.Exchange(_A[p]);
_Adag[p]= Cell.Exchange(_Adag[p]);
}
}
virtual void Mdiag (const Field &in, Field &out){ assert(0);};
virtual void Mdir (const Field &in, Field &out,int dir, int disp){assert(0);};
virtual void MdirAll (const Field &in, std::vector<Field> &out){assert(0);};
};
NAMESPACE_END(Grid);

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Grid/algorithms/multigrid/Multigrid.h → Grid/algorithms/multigrid/MultiGrid.h
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