MueLu_CGSolver_def.hpp

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#ifndef MUELU_CGSOLVER_DEF_HPP
#define MUELU_CGSOLVER_DEF_HPP

#include <Xpetra_MatrixFactory.hpp>
#include <Xpetra_MatrixMatrix.hpp>

#include "MueLu_Utilities.hpp"
#include "MueLu_Constraint.hpp"
#include "MueLu_Monitor.hpp"


#include "MueLu_CGSolver.hpp"



namespace MueLu {

  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  CGSolver<Scalar, LocalOrdinal, GlobalOrdinal, Node>::CGSolver(size_t Its)
  : nIts_(Its)
  { }

  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  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;
  }

} // namespace MueLu

#endif //ifndef MUELU_CGSOLVER_DECL_HPP