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