void SteepestDescentSolver<Scalar, LocalOrdinal, GlobalOrdinal, Node, LocalMatOps>::Iterate(const Matrix& Aref, const Constraint& C, const Matrix& P0, RCP<Matrix>& P) const {
RCP<const Matrix> A = rcpFromRef(Aref);
RCP<Matrix> AP, G;
Teuchos::FancyOStream& mmfancy = this->GetOStream(Statistics2, 0);
Teuchos::ArrayRCP<const SC> D = Utils::GetMatrixDiagonal(*A);
RCP<CrsMatrix> Ptmp_ = CrsMatrixFactory::Build(C.GetPattern());
Ptmp_->fillComplete(P0.getDomainMap(), P0.getRangeMap());
RCP<Matrix> Ptmp = rcp(new CrsMatrixWrap(Ptmp_));
// Initial P0 would only be used for multiplication
P = rcp_const_cast<Matrix>(rcpFromRef(P0));
for (size_t k = 0; k < nIts_; k++) {
AP = Utils::Multiply(*A, false, *P, false, mmfancy, true, false);
#if 0
// gradient = -2 A^T * A * P
SC stepLength = 2*stepLength_;
G = Utils::Multiply(*A, true, *AP, false, true, true);
C.Apply(*G, *Ptmp);
#else
// gradient = - A * P
SC stepLength = stepLength_;
Utils::MyOldScaleMatrix(*AP, D, true, false, false);
C.Apply(*AP, *Ptmp);
#endif
RCP<Matrix> newP;
Utils2::TwoMatrixAdd(*Ptmp, false, -stepLength, *P, false, Teuchos::ScalarTraits<Scalar>::one(), newP, mmfancy);
newP->fillComplete(P->getDomainMap(), P->getRangeMap() );
P = newP;
}
}
void CGSolver<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Iterate(const Matrix& Aref, const Constraint& C, const Matrix& P0, RCP<Matrix>& finalP) const {
// Note: this function matrix notations follow Saad's "Iterative methods", ed. 2, pg. 246
// So, X is the unknown prolongator, P's are conjugate directions, Z's are preconditioned P's
PrintMonitor m(*this, "CG iterations");
if (nIts_ == 0) {
finalP = MatrixFactory2::BuildCopy(rcpFromRef(P0));
return;
}
RCP<const Matrix> A = rcpFromRef(Aref);
ArrayRCP<const SC> D = Utilities::GetMatrixDiagonal(*A);
bool useTpetra = (A->getRowMap()->lib() == Xpetra::UseTpetra);
Teuchos::FancyOStream& mmfancy = this->GetOStream(Statistics2);
SC one = Teuchos::ScalarTraits<SC>::one();
RCP<Matrix> X, P, R, Z, AP;
RCP<Matrix> newX, tmpAP;
#ifndef TWO_ARG_MATRIX_ADD
RCP<Matrix> newR, newP;
#endif
SC oldRZ, newRZ, alpha, beta, app;
// T is used only for projecting onto
RCP<CrsMatrix> T_ = CrsMatrixFactory::Build(C.GetPattern());
T_->fillComplete(P0.getDomainMap(), P0.getRangeMap());
RCP<Matrix> T = rcp(new CrsMatrixWrap(T_));
// Initial P0 would only be used for multiplication
X = rcp_const_cast<Matrix>(rcpFromRef(P0));
tmpAP = MatrixMatrix::Multiply(*A, false, *X, false, mmfancy, true/*doFillComplete*/, true/*optimizeStorage*/);
C.Apply(*tmpAP, *T);
// R_0 = -A*X_0
R = Xpetra::MatrixFactory2<Scalar, LocalOrdinal, GlobalOrdinal, Node>::BuildCopy(T);
R->resumeFill();
R->scale(-one);
R->fillComplete(R->getDomainMap(), R->getRangeMap());
// Z_0 = M^{-1}R_0
Z = Xpetra::MatrixFactory2<Scalar, LocalOrdinal, GlobalOrdinal, Node>::BuildCopy(R);
Utilities::MyOldScaleMatrix(*Z, D, true, true, false);
// P_0 = Z_0
P = Xpetra::MatrixFactory2<Scalar, LocalOrdinal, GlobalOrdinal, Node>::BuildCopy(Z);
oldRZ = Utilities::Frobenius(*R, *Z);
for (size_t i = 0; i < nIts_; i++) {
// AP = constrain(A*P)
if (i == 0 || useTpetra) {
// Construct the MxM pattern from scratch
// This is done by default for Tpetra as the three argument version requires tmpAP
// to *not* be locally indexed which defeats the purpose
// TODO: need a three argument Tpetra version which allows reuse of already fill-completed matrix
tmpAP = MatrixMatrix::Multiply(*A, false, *P, false, mmfancy, true/*doFillComplete*/, true/*optimizeStorage*/);
} else {
// Reuse the MxM pattern
tmpAP = MatrixMatrix::Multiply(*A, false, *P, false, tmpAP, mmfancy, true/*doFillComplete*/, true/*optimizeStorage*/);
}
C.Apply(*tmpAP, *T);
AP = T;
app = Utilities::Frobenius(*AP, *P);
if (Teuchos::ScalarTraits<SC>::magnitude(app) < Teuchos::ScalarTraits<SC>::sfmin()) {
// It happens, for instance, if P = 0
// For example, if we use TentativePFactory for both nonzero pattern and initial guess
// I think it might also happen because of numerical breakdown, but we don't test for that yet
if (i == 0)
X = MatrixFactory2::BuildCopy(rcpFromRef(P0));
break;
}
// alpha = (R_i, Z_i)/(A*P_i, P_i)
alpha = oldRZ / app;
this->GetOStream(Runtime1,1) << "alpha = " << alpha << std::endl;
// X_{i+1} = X_i + alpha*P_i
#ifndef TWO_ARG_MATRIX_ADD
newX = Teuchos::null;
MatrixMatrix::TwoMatrixAdd(*P, false, alpha, *X, false, one, newX, mmfancy);
newX->fillComplete(P0.getDomainMap(), P0.getRangeMap());
X.swap(newX);
#else
MatrixMatrix::TwoMatrixAdd(*P, false, alpha, *X, one);
#endif
if (i == nIts_ - 1)
break;
// R_{i+1} = R_i - alpha*A*P_i
#ifndef TWO_ARG_MATRIX_ADD
newR = Teuchos::null;
MatrixMatrix::TwoMatrixAdd(*AP, false, -alpha, *R, false, one, newR, mmfancy);
newR->fillComplete(P0.getDomainMap(), P0.getRangeMap());
R.swap(newR);
#else
MatrixMatrix::TwoMatrixAdd(*AP, false, -alpha, *R, one);
#endif
// Z_{i+1} = M^{-1} R_{i+1}
Z = MatrixFactory2::BuildCopy(R);
Utilities::MyOldScaleMatrix(*Z, D, true, true, false);
// beta = (R_{i+1}, Z_{i+1})/(R_i, Z_i)
newRZ = Utilities::Frobenius(*R, *Z);
beta = newRZ / oldRZ;
// P_{i+1} = Z_{i+1} + beta*P_i
#ifndef TWO_ARG_MATRIX_ADD
newP = Teuchos::null;
MatrixMatrix::TwoMatrixAdd(*P, false, beta, *Z, false, one, newP, mmfancy);
newP->fillComplete(P0.getDomainMap(), P0.getRangeMap());
P.swap(newP);
#else
MatrixMatrix::TwoMatrixAdd(*Z, false, one, *P, beta);
#endif
oldRZ = newRZ;
}
finalP = X;
}