void sLinsysRootAug::solveReduced( sData *prob, SimpleVector& b)
{
assert(locmz==0||gOuterSolve<3);
int myRank; MPI_Comm_rank(mpiComm, &myRank);
#ifdef TIMING
t_start=MPI_Wtime();
troot_total=tchild_total=tcomm_total=0.0;
#endif
assert(locnx+locmy+locmz==b.length());
SimpleVector& r = (*redRhs);
assert(r.length() <= b.length());
SparseGenMatrix& C = prob->getLocalD();
///////////////////////////////////////////////////////////////////////
// LOCAL SOLVE
///////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
// b=[b1;b2;b3] is a locnx+locmy+locmz vector
// the new rhs should be
// r = [b1-C^T*(zDiag)^{-1}*b3; b2]
///////////////////////////////////////////////////////////////////////
r.copyFromArray(b.elements()); //will copy only as many elems as r has
// aliases to parts (no mem allocations)
SimpleVector r3(&r[locnx+locmy], locmz); //r3 is used as a temp
//buffer for b3
SimpleVector r2(&r[locnx], locmy);
SimpleVector r1(&r[0], locnx);
///////////////////////////////////////////////////////////////////////
// compute r1 = b1 - C^T*(zDiag)^{-1}*b3
///////////////////////////////////////////////////////////////////////
if(locmz>0) {
assert(r3.length() == zDiag->length());
r3.componentDiv(*zDiag);//r3 is a copy of b3
C.transMult(1.0, r1, -1.0, r3);
}
///////////////////////////////////////////////////////////////////////
// r contains all the stuff -> solve for it
///////////////////////////////////////////////////////////////////////
if(gInnerSCsolve==0) {
// Option 1. - solve with the factors
solver->Dsolve(r);
} else if(gInnerSCsolve==1) {
// Option 2 - solve with the factors and perform iter. ref.
solveWithIterRef(prob, r);
} else {
assert(gInnerSCsolve==2);
// Option 3 - use the factors as preconditioner and apply BiCGStab
solveWithBiCGStab(prob, r);
}
///////////////////////////////////////////////////////////////////////
// r is the sln to the reduced system
// the sln to the aug system should be
// x = [r1; r2; (zDiag)^{-1} * (b3-C*r1);
///////////////////////////////////////////////////////////////////////
SimpleVector b1(&b[0], locnx);
SimpleVector b2(&b[locnx], locmy);
SimpleVector b3(&b[locnx+locmy], locmz);
b1.copyFrom(r1);
b2.copyFrom(r2);
if(locmz>0) {
C.mult(1.0, b3, -1.0, r1);
b3.componentDiv(*zDiag);
}
#ifdef TIMING
if(myRank==0 && gInnerSCsolve>=1)
cout << "Root - Refin times: child=" << tchild_total << " root=" << troot_total
<< " comm=" << tcomm_total << " total=" << MPI_Wtime()-t_start << endl;
#endif
}
/** rxy = beta*rxy + alpha * SC * x */
void sLinsysRootAug::SCmult( double beta, SimpleVector& rxy,
double alpha, SimpleVector& x,
sData* prob)
{
//if (iAmDistrib) {
//only one process substracts [ (Q+Dx0+C'*Dz0*C)*xx + A'*xy ] from r
// [ A*xx ]
int myRank; MPI_Comm_rank(mpiComm, &myRank);
if(myRank==0) {
//only this proc substracts from rxy
rxy.scalarMult(beta);
SparseSymMatrix& Q = prob->getLocalQ();
Q.mult(1.0,&rxy[0],1, alpha,&x[0],1);
if(locmz>0) {
SparseSymMatrix* CtDC_sp = dynamic_cast<SparseSymMatrix*>(CtDC);
CtDC_sp->mult(1.0,&rxy[0],1, alpha,&x[0],1);
}
SimpleVector& xDiagv = dynamic_cast<SimpleVector&>(*xDiag);
assert(xDiagv.length() == locnx);
for(int i=0; i<xDiagv.length(); i++)
rxy[i] += alpha*xDiagv[i]*x[i];
SparseGenMatrix& A=prob->getLocalB();
A.transMult(1.0,&rxy[0],1, alpha,&x[locnx],1);
A.mult(1.0,&rxy[locnx],1, alpha,&x[0],1);
} else {
//other processes set r to zero since they will get this portion from process 0
rxy.setToZero();
}
#ifdef TIMING
taux=MPI_Wtime();
#endif
// now children add [0 A^T C^T ]*inv(KKT)*[0;A;C] x
SimpleVector xx(locnx);
xx.copyFromArray(x.elements());
xx.scalarMult(-alpha);
for(size_t it=0; it<children.size(); it++) {
children[it]->addTermToSchurResidual(prob->children[it],rxy,xx);
}
#ifdef TIMING
tchild_total += (MPI_Wtime()-taux);
#endif
//~done computing residual
#ifdef TIMING
taux=MPI_Wtime();
#endif
//all-reduce residual
if(iAmDistrib) {
SimpleVector buf(rxy.length());
buf.setToZero(); //we use dx as the recv buffer
MPI_Allreduce(rxy.elements(), buf.elements(), locnx+locmy, MPI_DOUBLE, MPI_SUM, mpiComm);
rxy.copyFrom(buf);
}
#ifdef TIMING
tcomm_total += (MPI_Wtime()-taux);
#endif
}
