mirror of
https://github.com/paboyle/Grid.git
synced 2024-09-19 16:55:37 +01:00
Adef
This commit is contained in:
Peter Boyle
parent
d4dc5e0f43
commit
1fe4c205a3
@ -53,6 +53,7 @@ class TwoLevelCGmrhs
|
||||
// Fine operator, Smoother, CoarseSolver
|
||||
LinearOperatorBase<Field> &_FineLinop;
|
||||
LinearFunction<Field> &_Smoother;
|
||||
MultiRHSBlockCGLinalg<Field> _BlockCGLinalg;
|
||||
|
||||
GridStopWatch ProjectTimer;
|
||||
GridStopWatch PromoteTimer;
|
||||
@ -79,6 +80,301 @@ class TwoLevelCGmrhs
|
||||
|
||||
// Vector case
|
||||
virtual void operator() (std::vector<Field> &src, std::vector<Field> &x)
|
||||
{
|
||||
SolveSingleSystem(src,x);
|
||||
// SolvePrecBlockCG(src,x);
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
// Thin QR factorisation (google it)
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
//Dimensions
|
||||
// R_{ferm x Nblock} = Q_{ferm x Nblock} x C_{Nblock x Nblock} -> ferm x Nblock
|
||||
//
|
||||
// Rdag R = m_rr = Herm = L L^dag <-- Cholesky decomposition (LLT routine in Eigen)
|
||||
//
|
||||
// Q C = R => Q = R C^{-1}
|
||||
//
|
||||
// Want Ident = Q^dag Q = C^{-dag} R^dag R C^{-1} = C^{-dag} L L^dag C^{-1} = 1_{Nblock x Nblock}
|
||||
//
|
||||
// Set C = L^{dag}, and then Q^dag Q = ident
|
||||
//
|
||||
// Checks:
|
||||
// Cdag C = Rdag R ; passes.
|
||||
// QdagQ = 1 ; passes
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
void ThinQRfact (Eigen::MatrixXcd &m_zz,
|
||||
Eigen::MatrixXcd &C,
|
||||
Eigen::MatrixXcd &Cinv,
|
||||
std::vector<Field> & Q,
|
||||
std::vector<Field> & MQ,
|
||||
const std::vector<Field> & Z,
|
||||
const std::vector<Field> & MZ)
|
||||
{
|
||||
RealD t0=usecond();
|
||||
_BlockCGLinalg.InnerProductMatrix(m_zz,MZ,Z);
|
||||
RealD t1=usecond();
|
||||
|
||||
m_zz = 0.5*(m_zz+m_zz.adjoint());
|
||||
|
||||
Eigen::MatrixXcd L = m_zz.llt().matrixL();
|
||||
|
||||
C = L.adjoint();
|
||||
Cinv = C.inverse();
|
||||
|
||||
RealD t3=usecond();
|
||||
_BlockCGLinalg.MulMatrix( Q,Cinv,Z);
|
||||
_BlockCGLinalg.MulMatrix(MQ,Cinv,MZ);
|
||||
RealD t4=usecond();
|
||||
std::cout << " ThinQRfact IP :"<< t1-t0<<" us"<<std::endl;
|
||||
std::cout << " ThinQRfact Eigen :"<< t3-t1<<" us"<<std::endl;
|
||||
std::cout << " ThinQRfact MulMat:"<< t4-t3<<" us"<<std::endl;
|
||||
}
|
||||
|
||||
virtual void SolvePrecBlockCG (std::vector<Field> &src, std::vector<Field> &X)
|
||||
{
|
||||
std::cout << GridLogMessage<<"HDCG: mrhs fPrecBlockcg starting"<<std::endl;
|
||||
src[0].Grid()->Barrier();
|
||||
int nrhs = src.size();
|
||||
// std::vector<RealD> f(nrhs);
|
||||
// std::vector<RealD> rtzp(nrhs);
|
||||
// std::vector<RealD> rtz(nrhs);
|
||||
// std::vector<RealD> a(nrhs);
|
||||
// std::vector<RealD> d(nrhs);
|
||||
// std::vector<RealD> b(nrhs);
|
||||
// std::vector<RealD> rptzp(nrhs);
|
||||
|
||||
////////////////////////////////////////////
|
||||
//Initial residual computation & set up
|
||||
////////////////////////////////////////////
|
||||
std::vector<RealD> ssq(nrhs);
|
||||
for(int rhs=0;rhs<nrhs;rhs++){
|
||||
ssq[rhs]=norm2(src[rhs]); assert(ssq[rhs]!=0.0);
|
||||
}
|
||||
|
||||
///////////////////////////
|
||||
// Fields -- eliminate duplicates between fPcg and block cg
|
||||
///////////////////////////
|
||||
std::vector<Field> Mtmp(nrhs,grid);
|
||||
std::vector<Field> tmp(nrhs,grid);
|
||||
std::vector<Field> Z(nrhs,grid); // Rename Z to R
|
||||
std::vector<Field> MZ(nrhs,grid); // Rename MZ to Z
|
||||
std::vector<Field> Q(nrhs,grid); //
|
||||
std::vector<Field> MQ(nrhs,grid); // Rename to P
|
||||
std::vector<Field> D(nrhs,grid);
|
||||
std::vector<Field> AD(nrhs,grid);
|
||||
|
||||
/************************************************************************
|
||||
* Preconditioned Block conjugate gradient rQ
|
||||
* Generalise Sebastien Birk Thesis, after Dubrulle 2001.
|
||||
* Introduce preconditioning following Saad Ch9
|
||||
************************************************************************
|
||||
* Dimensions:
|
||||
*
|
||||
* X,B etc... ==(Nferm x nrhs)
|
||||
* Matrix A==(Nferm x Nferm)
|
||||
*
|
||||
* Nferm = Nspin x Ncolour x Ncomplex x Nlattice_site
|
||||
* QC => Thin QR factorisation (google it)
|
||||
*
|
||||
* R = B-AX
|
||||
* Z = Mi R
|
||||
* QC = Z
|
||||
* D = Q
|
||||
* for k:
|
||||
* R = AD
|
||||
* Z = Mi R
|
||||
* M = [D^dag R]^{-1}
|
||||
* X = X + D M C
|
||||
* QS = Q - Z.M
|
||||
* D = Q + D S^dag
|
||||
* C = S C
|
||||
*/
|
||||
Eigen::MatrixXcd m_DZ = Eigen::MatrixXcd::Identity(nrhs,nrhs);
|
||||
Eigen::MatrixXcd m_M = Eigen::MatrixXcd::Identity(nrhs,nrhs);
|
||||
Eigen::MatrixXcd m_zz = Eigen::MatrixXcd::Zero(nrhs,nrhs);
|
||||
Eigen::MatrixXcd m_rr = Eigen::MatrixXcd::Zero(nrhs,nrhs);
|
||||
|
||||
Eigen::MatrixXcd m_C = Eigen::MatrixXcd::Zero(nrhs,nrhs);
|
||||
Eigen::MatrixXcd m_Cinv = Eigen::MatrixXcd::Zero(nrhs,nrhs);
|
||||
Eigen::MatrixXcd m_S = Eigen::MatrixXcd::Zero(nrhs,nrhs);
|
||||
Eigen::MatrixXcd m_Sinv = Eigen::MatrixXcd::Zero(nrhs,nrhs);
|
||||
|
||||
Eigen::MatrixXcd m_tmp = Eigen::MatrixXcd::Identity(nrhs,nrhs);
|
||||
Eigen::MatrixXcd m_tmp1 = Eigen::MatrixXcd::Identity(nrhs,nrhs);
|
||||
|
||||
GridStopWatch HDCGTimer;
|
||||
|
||||
//////////////////////////
|
||||
// x0 = Vstart -- possibly modify guess
|
||||
//////////////////////////
|
||||
Vstart(X,src);
|
||||
|
||||
//////////////////////////
|
||||
// R = B-AX
|
||||
//////////////////////////
|
||||
for(int rhs=0;rhs<nrhs;rhs++){
|
||||
// r0 = b -A x0
|
||||
_FineLinop.HermOp(X[rhs],tmp[rhs]);
|
||||
axpy (Z[rhs], -1.0,tmp[rhs], src[rhs]); // Computes R=Z=src - A X0
|
||||
}
|
||||
|
||||
//////////////////////////////////
|
||||
// Compute MZ = M1 Z = M1 B - M1 A x0
|
||||
//////////////////////////////////
|
||||
PcgM1(Z,MZ);
|
||||
|
||||
//////////////////////////////////
|
||||
// QC = Z
|
||||
//////////////////////////////////
|
||||
ThinQRfact (m_zz, m_C, m_Cinv, Q, MQ, Z, MZ);
|
||||
|
||||
//////////////////////////////////
|
||||
// D=MQ
|
||||
//////////////////////////////////
|
||||
for(int b=0;b<nrhs;b++) D[b]=MQ[b]; // LLT rotation of the MZ basis of search dirs
|
||||
|
||||
std::cout << GridLogMessage<<"PrecBlockCGrQ vec computed initial residual and QR fact " <<std::endl;
|
||||
|
||||
ProjectTimer.Reset();
|
||||
PromoteTimer.Reset();
|
||||
DeflateTimer.Reset();
|
||||
CoarseTimer.Reset();
|
||||
SmoothTimer.Reset();
|
||||
FineTimer.Reset();
|
||||
InsertTimer.Reset();
|
||||
|
||||
GridStopWatch M1Timer;
|
||||
GridStopWatch M2Timer;
|
||||
GridStopWatch M3Timer;
|
||||
GridStopWatch LinalgTimer;
|
||||
GridStopWatch InnerProdTimer;
|
||||
|
||||
HDCGTimer.Start();
|
||||
|
||||
std::vector<RealD> rn(nrhs);
|
||||
for (int k=0;k<=MaxIterations;k++){
|
||||
|
||||
////////////////////
|
||||
// Z = AD
|
||||
////////////////////
|
||||
M3Timer.Start();
|
||||
for(int b=0;b<nrhs;b++) _FineLinop.HermOp(D[b], Z[b]);
|
||||
M3Timer.Stop();
|
||||
|
||||
////////////////////
|
||||
// MZ = M1 Z <==== the Multigrid preconditioner
|
||||
////////////////////
|
||||
M1Timer.Start();
|
||||
PcgM1(Z,MZ);
|
||||
M1Timer.Stop();
|
||||
|
||||
FineTimer.Start();
|
||||
////////////////////
|
||||
// M = [D^dag Z]^{-1} = (<Ddag MZ>_M)^{-1} inner prod, generalising Saad derivation of Precon CG
|
||||
////////////////////
|
||||
InnerProdTimer.Start();
|
||||
_BlockCGLinalg.InnerProductMatrix(m_DZ,D,Z);
|
||||
InnerProdTimer.Stop();
|
||||
m_M = m_DZ.inverse();
|
||||
|
||||
///////////////////////////
|
||||
// X = X + D MC
|
||||
///////////////////////////
|
||||
m_tmp = m_M * m_C;
|
||||
LinalgTimer.Start();
|
||||
_BlockCGLinalg.MaddMatrix(X,m_tmp, D,X); // D are the search directions and X takes the updates
|
||||
LinalgTimer.Stop();
|
||||
|
||||
///////////////////////////
|
||||
// QS = Q - M Z
|
||||
// (MQ) S = MQ - M (M1Z)
|
||||
///////////////////////////
|
||||
LinalgTimer.Start();
|
||||
_BlockCGLinalg.MaddMatrix(tmp ,m_M, Z, Q,-1.0);
|
||||
_BlockCGLinalg.MaddMatrix(Mtmp,m_M,MZ,MQ,-1.0);
|
||||
ThinQRfact (m_zz, m_S, m_Sinv, Q, MQ, tmp, Mtmp);
|
||||
LinalgTimer.Stop();
|
||||
|
||||
////////////////////////////
|
||||
// D = MQ + D S^dag
|
||||
////////////////////////////
|
||||
m_tmp = m_S.adjoint();
|
||||
LinalgTimer.Start();
|
||||
_BlockCGLinalg.MaddMatrix(D,m_tmp,D,MQ);
|
||||
LinalgTimer.Stop();
|
||||
|
||||
////////////////////////////
|
||||
// C = S C
|
||||
////////////////////////////
|
||||
m_C = m_S*m_C;
|
||||
|
||||
////////////////////////////
|
||||
// convergence monitor
|
||||
////////////////////////////
|
||||
m_rr = m_C.adjoint() * m_C;
|
||||
|
||||
FineTimer.Stop();
|
||||
|
||||
RealD max_resid=0;
|
||||
RealD rrsum=0;
|
||||
RealD sssum=0;
|
||||
RealD rr;
|
||||
|
||||
for(int b=0;b<nrhs;b++) {
|
||||
rrsum+=real(m_rr(b,b));
|
||||
sssum+=ssq[b];
|
||||
rr = real(m_rr(b,b))/ssq[b];
|
||||
if ( rr > max_resid ) max_resid = rr;
|
||||
}
|
||||
std::cout << GridLogMessage <<
|
||||
"\t Prec BlockCGrQ Iteration "<<k<<" ave resid "<< std::sqrt(rrsum/sssum) << " max "<< std::sqrt(max_resid) <<std::endl;
|
||||
|
||||
|
||||
if ( max_resid < Tolerance*Tolerance ) {
|
||||
|
||||
HDCGTimer.Stop();
|
||||
std::cout<<GridLogMessage<<"HDCG: mrhs PrecBlockCGrQ converged in "<<k<<" iterations and "<<HDCGTimer.Elapsed()<<std::endl;;
|
||||
std::cout<<GridLogMessage<<"HDCG: mrhs PrecBlockCGrQ : Linalg "<<LinalgTimer.Elapsed()<<std::endl;;
|
||||
std::cout<<GridLogMessage<<"HDCG: mrhs PrecBlockCGrQ : fine H "<<M3Timer.Elapsed()<<std::endl;;
|
||||
std::cout<<GridLogMessage<<"HDCG: mrhs PrecBlockCGrQ : prec M1 "<<M1Timer.Elapsed()<<std::endl;;
|
||||
std::cout<<GridLogMessage<<"**** M1 breakdown:"<<std::endl;
|
||||
std::cout<<GridLogMessage<<"HDCG: mrhs PrecBlockCGrQ : Project "<<ProjectTimer.Elapsed()<<std::endl;;
|
||||
std::cout<<GridLogMessage<<"HDCG: mrhs PrecBlockCGrQ : Promote "<<PromoteTimer.Elapsed()<<std::endl;;
|
||||
std::cout<<GridLogMessage<<"HDCG: mrhs PrecBlockCGrQ : Deflate "<<DeflateTimer.Elapsed()<<std::endl;;
|
||||
std::cout<<GridLogMessage<<"HDCG: mrhs PrecBlockCGrQ : Coarse "<<CoarseTimer.Elapsed()<<std::endl;;
|
||||
std::cout<<GridLogMessage<<"HDCG: mrhs PrecBlockCGrQ : Fine "<<FineTimer.Elapsed()<<std::endl;;
|
||||
std::cout<<GridLogMessage<<"HDCG: mrhs PrecBlockCGrQ : Smooth "<<SmoothTimer.Elapsed()<<std::endl;;
|
||||
std::cout<<GridLogMessage<<"HDCG: mrhs PrecBlockCGrQ : Insert "<<InsertTimer.Elapsed()<<std::endl;;
|
||||
|
||||
for(int rhs=0;rhs<nrhs;rhs++){
|
||||
|
||||
_FineLinop.HermOp(X[rhs],tmp[rhs]);
|
||||
|
||||
Field mytmp(grid);
|
||||
axpy(mytmp,-1.0,src[rhs],tmp[rhs]);
|
||||
|
||||
RealD xnorm = sqrt(norm2(X[rhs]));
|
||||
RealD srcnorm = sqrt(norm2(src[rhs]));
|
||||
RealD tmpnorm = sqrt(norm2(mytmp));
|
||||
RealD true_residual = tmpnorm/srcnorm;
|
||||
std::cout<<GridLogMessage
|
||||
<<"HDCG: true residual ["<<rhs<<"] is "<<true_residual
|
||||
<<" solution "<<xnorm
|
||||
<<" source "<<srcnorm
|
||||
<<std::endl;
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
}
|
||||
HDCGTimer.Stop();
|
||||
std::cout<<GridLogMessage<<"HDCG: PrecBlockCGrQ not converged "<<HDCGTimer.Elapsed()<<std::endl;
|
||||
assert(0);
|
||||
}
|
||||
|
||||
virtual void SolveSingleSystem (std::vector<Field> &src, std::vector<Field> &x)
|
||||
{
|
||||
std::cout << GridLogMessage<<"HDCG: mrhs fPcg starting"<<std::endl;
|
||||
src[0].Grid()->Barrier();
|
||||
@ -361,15 +657,23 @@ public:
|
||||
CoarseField PleftProjMrhs(this->coarsegridmrhs);
|
||||
CoarseField PleftMss_projMrhs(this->coarsegridmrhs);
|
||||
|
||||
#undef SMOOTHER_BLOCK_SOLVE
|
||||
#if SMOOTHER_BLOCK_SOLVE
|
||||
this->SmoothTimer.Start();
|
||||
this->_Smoother(in,Min);
|
||||
this->SmoothTimer.Stop();
|
||||
#else
|
||||
for(int rhs=0;rhs<nrhs;rhs++) {
|
||||
|
||||
this->SmoothTimer.Start();
|
||||
this->_Smoother(in[rhs],Min[rhs]);
|
||||
this->SmoothTimer.Stop();
|
||||
|
||||
}
|
||||
#endif
|
||||
|
||||
for(int rhs=0;rhs<nrhs;rhs++) {
|
||||
|
||||
this->FineTimer.Start();
|
||||
this->_FineLinop.HermOp(Min[rhs],out[rhs]);
|
||||
|
||||
axpy(tmp[rhs],-1.0,out[rhs],in[rhs]); // resid = in - A Min
|
||||
this->FineTimer.Stop();
|
||||
|
||||
@ -407,7 +711,7 @@ public:
|
||||
this->FineTimer.Stop();
|
||||
}
|
||||
};
|
||||
|
||||
|
||||
|
||||
NAMESPACE_END(Grid);
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user