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Grid/lib/algorithms/iterative/AdefGeneric.h

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