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HDCG but this is not complete and placeholder for later completion
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Peter Boyle
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lib/algorithms/iterative/AdefGeneric.h
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370
lib/algorithms/iterative/AdefGeneric.h
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#ifndef GRID_ALGORITHMS_ITERATIVE_GENERIC_PCG
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#define GRID_ALGORITHMS_ITERATIVE_GENERIC_PCG
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/*
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* Compared to Tang-2009: P=Pleft. P^T = PRight Q=MssInv.
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* Script A = SolverMatrix
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* Script P = Preconditioner
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*
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* Deflation methods considered
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* -- Solve P A x = P b [ like Luscher ]
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* DEF-1 M P A x = M P b [i.e. left precon]
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* DEF-2 P^T M A x = P^T M b
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* ADEF-1 Preconditioner = M P + Q [ Q + M + M A Q]
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* ADEF-2 Preconditioner = P^T M + Q
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* BNN Preconditioner = P^T M P + Q
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* BNN2 Preconditioner = M P + P^TM +Q - M P A M
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*
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* Implement ADEF-2
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*
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* Vstart = P^Tx + Qb
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* M1 = P^TM + Q
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* M2=M3=1
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* Vout = x
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*/
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// abstract base
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template<class Field, class CoarseField>
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class TwoLevelFlexiblePcg : public LinearFunction<Field>
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{
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public:
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int verbose;
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RealD Tolerance;
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Integer MaxIterations;
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const int mmax = 5;
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GridBase *grid;
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GridBase *coarsegrid;
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LinearOperatorBase<Field> *_Linop
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OperatorFunction<Field> *_Smoother,
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LinearFunction<CoarseField> *_CoarseSolver;
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// Need somthing that knows how to get from Coarse to fine and back again
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// more most opertor functions
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TwoLevelFlexiblePcg(RealD tol,
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Integer maxit,
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LinearOperatorBase<Field> *Linop,
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LinearOperatorBase<Field> *SmootherLinop,
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OperatorFunction<Field> *Smoother,
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OperatorFunction<CoarseField> CoarseLinop
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) :
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Tolerance(tol),
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MaxIterations(maxit),
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_Linop(Linop),
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_PreconditionerLinop(PrecLinop),
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_Preconditioner(Preconditioner)
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{
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verbose=0;
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};
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// The Pcg routine is common to all, but the various matrices differ from derived
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// implementation to derived implmentation
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void operator() (const Field &src, Field &psi){
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void operator() (const Field &src, Field &psi){
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psi.checkerboard = src.checkerboard;
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grid = src._grid;
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RealD f;
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RealD rtzp,rtz,a,d,b;
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RealD rptzp;
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RealD tn;
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RealD guess = norm2(psi);
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RealD ssq = norm2(src);
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RealD rsq = ssq*Tolerance*Tolerance;
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/////////////////////////////
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// Set up history vectors
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/////////////////////////////
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std::vector<Field> p (mmax,grid);
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std::vector<Field> mmp(mmax,grid);
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std::vector<RealD> pAp(mmax);
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Field x (grid); x = psi;
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Field z (grid);
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Field tmp(grid);
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Field r (grid);
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Field mu (grid);
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//////////////////////////
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// x0 = Vstart -- possibly modify guess
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//////////////////////////
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x=src;
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Vstart(x,src);
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// r0 = b -A x0
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HermOp(x,mmp); // Shouldn't this be something else?
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axpy (r, -1.0,mmp[0], src); // Recomputes r=src-Ax0
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//////////////////////////////////
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// Compute z = M1 x
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//////////////////////////////////
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M1(r,z,tmp,mp,SmootherMirs);
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rtzp =real(innerProduct(r,z));
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///////////////////////////////////////
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// Solve for Mss mu = P A z and set p = z-mu
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// Def2: p = 1 - Q Az = Pright z
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// Other algos M2 is trivial
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///////////////////////////////////////
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M2(z,p[0]);
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for (int k=0;k<=MaxIterations;k++){
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int peri_k = k % mmax;
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int peri_kp = (k+1) % mmax;
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rtz=rtzp;
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d= M3(p[peri_k],mp,mmp[peri_k],tmp);
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a = rtz/d;
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// Memorise this
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pAp[peri_k] = d;
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axpy(x,a,p[peri_k],x);
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RealD rn = axpy_norm(r,-a,mmp[peri_k],r);
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// Compute z = M x
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M1(r,z,tmp,mp);
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rtzp =real(innerProduct(r,z));
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M2(z,mu); // ADEF-2 this is identity. Axpy possible to eliminate
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p[peri_kp]=p[peri_k];
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// Standard search direction p -> z + b p ; b =
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b = (rtzp)/rtz;
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int northog;
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// northog = (peri_kp==0)?1:peri_kp; // This is the fCG(mmax) algorithm
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northog = (k>mmax-1)?(mmax-1):k; // This is the fCG-Tr(mmax-1) algorithm
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for(int back=0; back < northog; back++){
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int peri_back = (k-back)%mmax;
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RealD pbApk= real(innerProduct(mmp[peri_back],p[peri_kp]));
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RealD beta = -pbApk/pAp[peri_back];
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axpy(p[peri_kp],beta,p[peri_back],p[peri_kp]);
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}
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RealD rrn=sqrt(rn/ssq);
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std::cout<<"TwoLevelfPcg: k= "<<k<<" residual = "<<rrn<<std::endl;
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// Stopping condition
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if ( rn <= rsq ) {
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HermOp(x,mmp); // Shouldn't this be something else?
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axpy(tmp,-1.0,src,mmp[0]);
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RealD psinorm = sqrt(norm2(x));
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RealD srcnorm = sqrt(norm2(src));
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RealD tmpnorm = sqrt(norm2(tmp));
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RealD true_residual = tmpnorm/srcnorm;
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std::cout<<"TwoLevelfPcg: true residual is "<<true_residual<<std::endl;
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std::cout<<"TwoLevelfPcg: target residual was"<<Tolerance<<std::endl;
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return k;
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}
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}
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// Non-convergence
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assert(0);
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}
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public:
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virtual void M(Field & in,Field & out,Field & tmp) {
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}
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virtual void M1(Field & in, Field & out) {// the smoother
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// [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
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Field tmp(grid);
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Field Min(grid);
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PcgM(in,Min); // Smoother call
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HermOp(Min,out);
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axpy(tmp,-1.0,out,in); // tmp = in - A Min
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ProjectToSubspace(tmp,PleftProj);
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ApplyInverse(PleftProj,PleftMss_proj); // Ass^{-1} [in - A Min]_s
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PromoteFromSubspace(PleftMss_proj,tmp);// tmp = Q[in - A Min]
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axpy(out,1.0,Min,tmp); // Min+tmp
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}
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virtual void M2(const Field & in, Field & out) {
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out=in;
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// Must override for Def2 only
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// case PcgDef2:
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// Pright(in,out);
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// break;
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}
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virtual RealD M3(const Field & p, Field & mmp){
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double d,dd;
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HermOpAndNorm(p,mmp,d,dd);
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return dd;
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// Must override for Def1 only
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// case PcgDef1:
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// d=linop_d->Mprec(p,mmp,tmp,0,1);// Dag no
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// linop_d->Mprec(mmp,mp,tmp,1);// Dag yes
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// Pleft(mp,mmp);
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// d=real(linop_d->inner(p,mmp));
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}
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virtual void VstartDef2(Field & xconst Field & src){
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//case PcgDef2:
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//case PcgAdef2:
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//case PcgAdef2f:
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//case PcgV11f:
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///////////////////////////////////
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// Choose x_0 such that
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// x_0 = guess + (A_ss^inv) r_s = guess + Ass_inv [src -Aguess]
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// = [1 - Ass_inv A] Guess + Assinv src
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// = P^T guess + Assinv src
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// = Vstart [Tang notation]
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// This gives:
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// W^T (src - A x_0) = src_s - A guess_s - r_s
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// = src_s - (A guess)_s - src_s + (A guess)_s
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// = 0
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///////////////////////////////////
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Field r(grid);
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Field mmp(grid);
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HermOp(x,mmp);
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axpy (r, -1.0, mmp, src); // r_{-1} = src - A x
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ProjectToSubspace(r,PleftProj);
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ApplyInverseCG(PleftProj,PleftMss_proj); // Ass^{-1} r_s
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PromoteFromSubspace(PleftMss_proj,mmp);
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x=x+mmp;
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}
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virtual void Vstart(Field & x,const Field & src){
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return;
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}
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/////////////////////////////////////////////////////////////////////
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// Only Def1 has non-trivial Vout. Override in Def1
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/////////////////////////////////////////////////////////////////////
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virtual void Vout (Field & in, Field & out,Field & src){
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out = in;
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//case PcgDef1:
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// //Qb + PT x
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// ProjectToSubspace(src,PleftProj);
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// ApplyInverse(PleftProj,PleftMss_proj); // Ass^{-1} r_s
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// PromoteFromSubspace(PleftMss_proj,tmp);
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//
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// Pright(in,out);
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//
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// linop_d->axpy(out,tmp,out,1.0);
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// break;
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}
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////////////////////////////////////////////////////////////////////////////////////////////////
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// Pright and Pleft are common to all implementations
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////////////////////////////////////////////////////////////////////////////////////////////////
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virtual void Pright(Field & in,Field & out){
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// P_R = [ 1 0 ]
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// [ -Mss^-1 Msb 0 ]
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Field in_sbar(grid);
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ProjectToSubspace(in,PleftProj);
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PromoteFromSubspace(PleftProj,out);
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axpy(in_sbar,-1.0,out,in); // in_sbar = in - in_s
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HermOp(in_sbar,out);
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ProjectToSubspace(out,PleftProj); // Mssbar in_sbar (project)
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ApplyInverse (PleftProj,PleftMss_proj); // Mss^{-1} Mssbar
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PromoteFromSubspace(PleftMss_proj,out); //
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axpy(out,-1.0,out,in_sbar); // in_sbar - Mss^{-1} Mssbar in_sbar
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}
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virtual void Pleft (Field & in,Field & out){
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// P_L = [ 1 -Mbs Mss^-1]
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// [ 0 0 ]
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Field in_sbar(grid);
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Field tmp2(grid);
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Field Mtmp(grid);
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ProjectToSubspace(in,PleftProj);
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PromoteFromSubspace(PleftProj,out);
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axpy(in_sbar,-1.0,out,in); // in_sbar = in - in_s
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ApplyInverse(PleftProj,PleftMss_proj); // Mss^{-1} in_s
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PromoteFromSubspace(PleftMss_proj,out);
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HermOp(out,Mtmp);
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ProjectToSubspace(Mtmp,PleftProj); // Msbar s Mss^{-1}
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PromoteFromSubspace(PleftProj,tmp2);
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axpy(out,-1.0,tmp2,Mtmp);
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axpy(out,-1.0,out,in_sbar); // in_sbar - Msbars Mss^{-1} in_s
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}
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}
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template<class Field>
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class TwoLevelFlexiblePcgADef2 : public TwoLevelFlexiblePcg<Field> {
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public:
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virtual void M(Field & in,Field & out,Field & tmp){
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}
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virtual void M1(Field & in, Field & out,Field & tmp,Field & mp){
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}
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virtual void M2(Field & in, Field & out){
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}
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virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp){
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}
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virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp){
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}
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}
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/*
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template<class Field>
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class TwoLevelFlexiblePcgAD : public TwoLevelFlexiblePcg<Field> {
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public:
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virtual void M(Field & in,Field & out,Field & tmp);
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virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
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virtual void M2(Field & in, Field & out);
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virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
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virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
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}
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template<class Field>
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class TwoLevelFlexiblePcgDef1 : public TwoLevelFlexiblePcg<Field> {
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public:
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virtual void M(Field & in,Field & out,Field & tmp);
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virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
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virtual void M2(Field & in, Field & out);
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virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
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virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
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virtual void Vout (Field & in, Field & out,Field & src,Field & tmp);
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}
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template<class Field>
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class TwoLevelFlexiblePcgDef2 : public TwoLevelFlexiblePcg<Field> {
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public:
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virtual void M(Field & in,Field & out,Field & tmp);
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virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
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virtual void M2(Field & in, Field & out);
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virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
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virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
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}
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template<class Field>
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class TwoLevelFlexiblePcgV11: public TwoLevelFlexiblePcg<Field> {
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public:
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virtual void M(Field & in,Field & out,Field & tmp);
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virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
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virtual void M2(Field & in, Field & out);
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virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
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virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
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}
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*/
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#endif
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