MueLu_TentativePFactory_kokkos_def.hpp

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// @HEADER
// *****************************************************************************
//        MueLu: A package for multigrid based preconditioning
//
// Copyright 2012 NTESS and the MueLu contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER
 
#ifndef MUELU_TENTATIVEPFACTORY_KOKKOS_DEF_HPP
#define MUELU_TENTATIVEPFACTORY_KOKKOS_DEF_HPP
 
#include "Kokkos_UnorderedMap.hpp"
#include "Xpetra_CrsGraphFactory.hpp"
 
#include "MueLu_TentativePFactory_kokkos_decl.hpp"
 
#include "MueLu_Aggregates.hpp"
#include "MueLu_AmalgamationInfo.hpp"
#include "MueLu_AmalgamationFactory.hpp"
 
#include "MueLu_MasterList.hpp"
#include "MueLu_PerfUtils.hpp"
#include "MueLu_Monitor.hpp"
 
#include "Xpetra_IO.hpp"
 
namespace MueLu {
 
namespace {  // anonymous
 
template <class LocalOrdinal, class View>
class ReduceMaxFunctor {
 public:
  ReduceMaxFunctor(View view)
    : view_(view) {}
 
  KOKKOS_INLINE_FUNCTION
  void operator()(const LocalOrdinal& i, LocalOrdinal& vmax) const {
    if (vmax < view_(i))
      vmax = view_(i);
  }
 
  KOKKOS_INLINE_FUNCTION
  void join(LocalOrdinal& dst, const LocalOrdinal& src) const {
    if (dst < src) {
      dst = src;
    }
  }
 
  KOKKOS_INLINE_FUNCTION
  void init(LocalOrdinal& dst) const {
    dst = 0;
  }
 
 private:
  View view_;
};
 
// local QR decomposition
template <class LOType, class GOType, class SCType, class DeviceType, class NspType, class aggRowsType, class maxAggDofSizeType, class agg2RowMapLOType, class statusType, class rowsType, class rowsAuxType, class colsAuxType, class valsAuxType>
class LocalQRDecompFunctor {
 private:
  typedef LOType LO;
  typedef GOType GO;
  typedef SCType SC;
 
  typedef typename DeviceType::execution_space execution_space;
  typedef typename KokkosKernels::ArithTraits<SC>::val_type impl_SC;
  typedef KokkosKernels::ArithTraits<impl_SC> impl_ATS;
  typedef typename impl_ATS::magnitudeType Magnitude;
 
 public:
  typedef Kokkos::View<impl_SC**, typename execution_space::scratch_memory_space, Kokkos::MemoryUnmanaged> shared_matrix;
  typedef Kokkos::View<impl_SC*, typename execution_space::scratch_memory_space, Kokkos::MemoryUnmanaged> shared_vector;
 
 private:
  NspType fineNS;
  NspType coarseNS;
  aggRowsType aggRows;
  maxAggDofSizeType maxAggDofSize;  //< maximum number of dofs in aggregate (max size of aggregate * numDofsPerNode)
  agg2RowMapLOType agg2RowMapLO;
  statusType statusAtomic;
  rowsType rows;
  rowsAuxType rowsAux;
  colsAuxType colsAux;
  valsAuxType valsAux;
  bool doQRStep;
 
 public:
  LocalQRDecompFunctor(NspType fineNS_, NspType coarseNS_, aggRowsType aggRows_, maxAggDofSizeType maxAggDofSize_, agg2RowMapLOType agg2RowMapLO_, statusType statusAtomic_, rowsType rows_, rowsAuxType rowsAux_, colsAuxType colsAux_, valsAuxType valsAux_, bool doQRStep_)
    : fineNS(fineNS_)
    , coarseNS(coarseNS_)
    , aggRows(aggRows_)
    , maxAggDofSize(maxAggDofSize_)
    , agg2RowMapLO(agg2RowMapLO_)
    , statusAtomic(statusAtomic_)
    , rows(rows_)
    , rowsAux(rowsAux_)
    , colsAux(colsAux_)
    , valsAux(valsAux_)
    , doQRStep(doQRStep_) {}
 
  KOKKOS_INLINE_FUNCTION
  void operator()(const typename Kokkos::TeamPolicy<execution_space>::member_type& thread, size_t& nnz) const {
    auto agg = thread.league_rank();
 
    // size of aggregate: number of DOFs in aggregate
    auto aggSize = aggRows(agg + 1) - aggRows(agg);
 
    const impl_SC one  = impl_ATS::one();
    const impl_SC two  = one + one;
    const impl_SC zero = impl_ATS::zero();
    const auto zeroM   = impl_ATS::magnitude(zero);
 
    int m = aggSize;
    int n = fineNS.extent(1);
 
    // calculate row offset for coarse nullspace
    Xpetra::global_size_t offset = agg * n;
 
    if (doQRStep) {
      // Extract the piece of the nullspace corresponding to the aggregate
      shared_matrix r(thread.team_shmem(), m, n);  // A (initially), R (at the end)
      for (int j = 0; j < n; j++)
        for (int k = 0; k < m; k++)
          r(k, j) = fineNS(agg2RowMapLO(aggRows(agg) + k), j);
#if 0
          printf("A\n");
          for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++)
              printf(" %5.3lf ", r(i,j));
            printf("\n");
          }
#endif
 
      // Calculate QR decomposition (standard)
      shared_matrix q(thread.team_shmem(), m, m);  // Q
      if (m >= n) {
        bool isSingular = false;
 
        // Initialize Q^T
        auto qt = q;
        for (int i = 0; i < m; i++) {
          for (int j = 0; j < m; j++)
            qt(i, j) = zero;
          qt(i, i) = one;
        }
 
        for (int k = 0; k < n; k++) {  // we ignore "n" instead of "n-1" to normalize
          // FIXME_KOKKOS: use team
          Magnitude s = zeroM, norm, norm_x;
          for (int i = k + 1; i < m; i++)
            s += pow(impl_ATS::magnitude(r(i, k)), 2);
          norm = sqrt(pow(impl_ATS::magnitude(r(k, k)), 2) + s);
 
          if (norm == zero) {
            isSingular = true;
            break;
          }
 
          r(k, k) -= norm * one;
 
          norm_x = sqrt(pow(impl_ATS::magnitude(r(k, k)), 2) + s);
          if (norm_x == zeroM) {
            // We have a single diagonal element in the column.
            // No reflections required. Just need to restor r(k,k).
            r(k, k) = norm * one;
            continue;
          }
 
          // FIXME_KOKKOS: use team
          for (int i = k; i < m; i++)
            r(i, k) /= norm_x;
 
          // Update R(k:m,k+1:n)
          for (int j = k + 1; j < n; j++) {
            // FIXME_KOKKOS: use team in the loops
            impl_SC si = zero;
            for (int i = k; i < m; i++)
              si += r(i, k) * r(i, j);
            for (int i = k; i < m; i++)
              r(i, j) -= two * si * r(i, k);
          }
 
          // Update Q^T (k:m,k:m)
          for (int j = k; j < m; j++) {
            // FIXME_KOKKOS: use team in the loops
            impl_SC si = zero;
            for (int i = k; i < m; i++)
              si += r(i, k) * qt(i, j);
            for (int i = k; i < m; i++)
              qt(i, j) -= two * si * r(i, k);
          }
 
          // Fix R(k:m,k)
          r(k, k) = norm * one;
          for (int i = k + 1; i < m; i++)
            r(i, k) = zero;
        }
 
#if 0
            // Q = (Q^T)^T
            for (int i = 0; i < m; i++)
              for (int j = 0; j < i; j++) {
                impl_SC tmp  = qt(i,j);
                qt(i,j) = qt(j,i);
                qt(j,i) = tmp;
              }
#endif
 
        // Build coarse nullspace using the upper triangular part of R
        for (int j = 0; j < n; j++)
          for (int k = 0; k <= j; k++)
            coarseNS(offset + k, j) = r(k, j);
 
        if (isSingular) {
          statusAtomic(1) = true;
          return;
        }
 
      } else {
        // Special handling for m < n (i.e. single node aggregates in structural mechanics)
 
        // The local QR decomposition is not possible in the "overconstrained"
        // case (i.e. number of columns in qr > number of rowsAux), which
        // corresponds to #DOFs in Aggregate < n. For usual problems this
        // is only possible for single node aggregates in structural mechanics.
        // (Similar problems may arise in discontinuous Galerkin problems...)
        // We bypass the QR decomposition and use an identity block in the
        // tentative prolongator for the single node aggregate and transfer the
        // corresponding fine level null space information 1-to-1 to the coarse
        // level null space part.
 
        // NOTE: The resulting tentative prolongation operator has
        // (m*DofsPerNode-n) zero columns leading to a singular
        // coarse level operator A.  To deal with that one has the following
        // options:
        // - Use the "RepairMainDiagonal" flag in the RAPFactory (default:
        //   false) to add some identity block to the diagonal of the zero rowsAux
        //   in the coarse level operator A, such that standard level smoothers
        //   can be used again.
        // - Use special (projection-based) level smoothers, which can deal
        //   with singular matrices (very application specific)
        // - Adapt the code below to avoid zero columns. However, we do not
        //   support a variable number of DOFs per node in MueLu/Xpetra which
        //   makes the implementation really hard.
        //
        // FIXME: do we need to check for singularity here somehow? Zero
        // columns would be easy but linear dependency would require proper QR.
 
        // R = extended (by adding identity rowsAux) qr
        for (int j = 0; j < n; j++)
          for (int k = 0; k < n; k++)
            if (k < m)
              coarseNS(offset + k, j) = r(k, j);
            else
              coarseNS(offset + k, j) = (k == j ? one : zero);
 
        // Q = I (rectangular)
        for (int i = 0; i < m; i++)
          for (int j = 0; j < n; j++)
            q(i, j) = (j == i ? one : zero);
      }
 
      // Process each row in the local Q factor and fill helper arrays to assemble P
      for (int j = 0; j < m; j++) {
        LO localRow     = agg2RowMapLO(aggRows(agg) + j);
        size_t rowStart = rowsAux(localRow);
        size_t lnnz     = 0;
        for (int k = 0; k < n; k++) {
          // skip zeros
          if (q(j, k) != zero) {
            colsAux(rowStart + lnnz) = offset + k;
            valsAux(rowStart + lnnz) = q(j, k);
            lnnz++;
          }
        }
        rows(localRow + 1) = lnnz;
        nnz += lnnz;
      }
 
#if 0
          printf("R\n");
          for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++)
              printf(" %5.3lf ", coarseNS(i,j));
            printf("\n");
          }
 
          printf("Q\n");
          for (int i = 0; i < aggSize; i++) {
            for (int j = 0; j < aggSize; j++)
              printf(" %5.3lf ", q(i,j));
            printf("\n");
          }
#endif
    } else {
      //      "no-QR" option     //
      // Local Q factor is just the fine nullspace support over the current aggregate.
      // Local R factor is the identity.
      // TODO I have not implemented any special handling for aggregates that are too
      // TODO small to locally support the nullspace, as is done in the standard QR
      // TODO case above.
 
      for (int j = 0; j < m; j++) {
        LO localRow     = agg2RowMapLO(aggRows(agg) + j);
        size_t rowStart = rowsAux(localRow);
        size_t lnnz     = 0;
        for (int k = 0; k < n; k++) {
          const impl_SC qr_jk = fineNS(localRow, k);
          // skip zeros
          if (qr_jk != zero) {
            colsAux(rowStart + lnnz) = offset + k;
            valsAux(rowStart + lnnz) = qr_jk;
            lnnz++;
          }
        }
        rows(localRow + 1) = lnnz;
        nnz += lnnz;
      }
 
      for (int j = 0; j < n; j++)
        coarseNS(offset + j, j) = one;
    }
  }
};
 
}  // namespace
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
RCP<const ParameterList> TentativePFactory_kokkos<Scalar, LocalOrdinal, GlobalOrdinal, Node>::GetValidParameterList() const {
  RCP<ParameterList> validParamList = rcp(new ParameterList());
 
#define SET_VALID_ENTRY(name) validParamList->setEntry(name, MasterList::getEntry(name))
  SET_VALID_ENTRY("tentative: calculate qr");
  SET_VALID_ENTRY("tentative: build coarse coordinates");
#undef SET_VALID_ENTRY
 
  validParamList->set<RCP<const FactoryBase>>("A", Teuchos::null, "Generating factory of the matrix A");
  validParamList->set<RCP<const FactoryBase>>("Aggregates", Teuchos::null, "Generating factory of the aggregates");
  validParamList->set<RCP<const FactoryBase>>("Nullspace", Teuchos::null, "Generating factory of the nullspace");
  validParamList->set<RCP<const FactoryBase>>("Scaled Nullspace", Teuchos::null, "Generating factory of the scaled nullspace");
  validParamList->set<RCP<const FactoryBase>>("UnAmalgamationInfo", Teuchos::null, "Generating factory of UnAmalgamationInfo");
  validParamList->set<RCP<const FactoryBase>>("CoarseMap", Teuchos::null, "Generating factory of the coarse map");
  validParamList->set<RCP<const FactoryBase>>("Coordinates", Teuchos::null, "Generating factory of the coordinates");
  validParamList->set<RCP<const FactoryBase>>("Node Comm", Teuchos::null, "Generating factory of the node level communicator");
 
  // Make sure we don't recursively validate options for the matrixmatrix kernels
  ParameterList norecurse;
  norecurse.disableRecursiveValidation();
  validParamList->set<ParameterList>("matrixmatrix: kernel params", norecurse, "MatrixMatrix kernel parameters");
 
  return validParamList;
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void TentativePFactory_kokkos<Scalar, LocalOrdinal, GlobalOrdinal, Node>::DeclareInput(Level& fineLevel, Level& /* coarseLevel */) const {
  const ParameterList& pL = GetParameterList();
  // NOTE: This guy can only either be 'Nullspace' or 'Scaled Nullspace' or else the validator above will cause issues
  std::string nspName = "Nullspace";
  if (pL.isParameter("Nullspace name")) nspName = pL.get<std::string>("Nullspace name");
 
  Input(fineLevel, "A");
  Input(fineLevel, "Aggregates");
  Input(fineLevel, nspName);
  Input(fineLevel, "UnAmalgamationInfo");
  Input(fineLevel, "CoarseMap");
  if (fineLevel.GetLevelID() == 0 &&
      fineLevel.IsAvailable("Coordinates", NoFactory::get()) &&  // we have coordinates (provided by user app)
      pL.get<bool>("tentative: build coarse coordinates")) {     // and we want coordinates on other levels
    bTransferCoordinates_ = true;                                // then set the transfer coordinates flag to true
    Input(fineLevel, "Coordinates");
  } else if (bTransferCoordinates_) {
    Input(fineLevel, "Coordinates");
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void TentativePFactory_kokkos<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Build(Level& fineLevel, Level& coarseLevel) const {
  return BuildP(fineLevel, coarseLevel);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void TentativePFactory_kokkos<Scalar, LocalOrdinal, GlobalOrdinal, Node>::BuildP(Level& fineLevel, Level& coarseLevel) const {
  FactoryMonitor m(*this, "Build", coarseLevel);
 
  typedef typename Teuchos::ScalarTraits<Scalar>::coordinateType coordinate_type;
  typedef Xpetra::MultiVectorFactory<coordinate_type, LO, GO, NO> RealValuedMultiVectorFactory;
  const ParameterList& pL = GetParameterList();
  std::string nspName     = "Nullspace";
  if (pL.isParameter("Nullspace name")) nspName = pL.get<std::string>("Nullspace name");
 
  auto A             = Get<RCP<Matrix>>(fineLevel, "A");
  auto aggregates    = Get<RCP<Aggregates>>(fineLevel, "Aggregates");
  auto amalgInfo     = Get<RCP<AmalgamationInfo>>(fineLevel, "UnAmalgamationInfo");
  auto fineNullspace = Get<RCP<MultiVector>>(fineLevel, nspName);
  auto coarseMap     = Get<RCP<const Map>>(fineLevel, "CoarseMap");
  RCP<RealValuedMultiVector> fineCoords;
  if (bTransferCoordinates_) {
    fineCoords = Get<RCP<RealValuedMultiVector>>(fineLevel, "Coordinates");
  }
 
  RCP<Matrix> Ptentative;
  // No coarse DoFs so we need to bail by setting Ptentattive to null and returning
  // This level will ultimately be removed in MueLu_Hierarchy_defs.h via a resize()
  if (aggregates->GetNumGlobalAggregatesComputeIfNeeded() == 0) {
    Ptentative = Teuchos::null;
    Set(coarseLevel, "P", Ptentative);
    return;
  }
  RCP<MultiVector> coarseNullspace;
  RCP<RealValuedMultiVector> coarseCoords;
 
  if (bTransferCoordinates_) {
    RCP<const Map> coarseCoordMap;
 
    LO blkSize = 1;
    if (rcp_dynamic_cast<const StridedMap>(coarseMap) != Teuchos::null)
      blkSize = rcp_dynamic_cast<const StridedMap>(coarseMap)->getFixedBlockSize();
 
    if (blkSize == 1) {
      // Scalar system
      // No amalgamation required, we can use the coarseMap
      coarseCoordMap = coarseMap;
    } else {
      // Vector system
      AmalgamationFactory<SC, LO, GO, NO>::AmalgamateMap(rcp_dynamic_cast<const StridedMap>(coarseMap), coarseCoordMap);
    }
 
    coarseCoords = RealValuedMultiVectorFactory::Build(coarseCoordMap, fineCoords->getNumVectors(), false);
 
    // Create overlapped fine coordinates to reduce global communication
    auto uniqueMap                           = fineCoords->getMap();
    RCP<RealValuedMultiVector> ghostedCoords = fineCoords;
    if (aggregates->AggregatesCrossProcessors()) {
      auto nonUniqueMap = aggregates->GetMap();
      auto importer     = ImportFactory::Build(uniqueMap, nonUniqueMap);
 
      ghostedCoords = RealValuedMultiVectorFactory::Build(nonUniqueMap, fineCoords->getNumVectors(), false);
      ghostedCoords->doImport(*fineCoords, *importer, Xpetra::INSERT);
    }
 
    // The good new is that his graph has already been constructed for the
    // TentativePFactory and was cached in Aggregates. So this is a no-op.
    auto aggGraph = aggregates->GetGraph();
    auto numAggs  = aggGraph.numRows();
 
    auto fineCoordsView   = fineCoords->getLocalViewDevice(Tpetra::Access::ReadOnly);
    auto coarseCoordsView = coarseCoords->getLocalViewDevice(Tpetra::Access::OverwriteAll);
 
    // Fill in coarse coordinates
    {
      SubFactoryMonitor m2(*this, "AverageCoords", coarseLevel);
 
      const auto dim = fineCoords->getNumVectors();
 
      typename AppendTrait<decltype(fineCoordsView), Kokkos::RandomAccess>::type fineCoordsRandomView = fineCoordsView;
      for (size_t j = 0; j < dim; j++) {
        Kokkos::parallel_for(
            "MueLu::TentativeP::BuildCoords", Kokkos::RangePolicy<local_ordinal_type, execution_space>(0, numAggs),
            KOKKOS_LAMBDA(const LO i) {
              // A row in this graph represents all node ids in the aggregate
              // Therefore, averaging is very easy
 
              auto aggregate = aggGraph.rowConst(i);
 
              coordinate_type sum = 0.0;  // do not use Scalar here (Stokhos)
              for (size_t colID = 0; colID < static_cast<size_t>(aggregate.length); colID++)
                sum += fineCoordsRandomView(aggregate(colID), j);
 
              coarseCoordsView(i, j) = sum / aggregate.length;
            });
      }
    }
  }
 
  if (!aggregates->AggregatesCrossProcessors()) {
    if (Xpetra::Helpers<SC, LO, GO, NO>::isTpetraBlockCrs(A)) {
      BuildPuncoupledBlockCrs(coarseLevel, A, aggregates, amalgInfo, fineNullspace, coarseMap, Ptentative, coarseNullspace,
                              coarseLevel.GetLevelID());
    } else {
      BuildPuncoupled(coarseLevel, A, aggregates, amalgInfo, fineNullspace, coarseMap, Ptentative, coarseNullspace, coarseLevel.GetLevelID());
    }
  } else
    BuildPcoupled(A, aggregates, amalgInfo, fineNullspace, coarseMap, Ptentative, coarseNullspace);
 
  // If available, use striding information of fine level matrix A for range
  // map and coarseMap as domain map; otherwise use plain range map of
  // Ptent = plain range map of A for range map and coarseMap as domain map.
  // NOTE:
  // The latter is not really safe, since there is no striding information
  // for the range map. This is not really a problem, since striding
  // information is always available on the intermedium levels and the
  // coarsest levels.
  if (A->IsView("stridedMaps") == true)
    Ptentative->CreateView("stridedMaps", A->getRowMap("stridedMaps"), coarseMap);
  else
    Ptentative->CreateView("stridedMaps", Ptentative->getRangeMap(), coarseMap);
 
  if (bTransferCoordinates_) {
    Set(coarseLevel, "Coordinates", coarseCoords);
  }
 
  // FIXME: We should remove the NodeComm on levels past the threshold
  if (fineLevel.IsAvailable("Node Comm")) {
    RCP<const Teuchos::Comm<int>> nodeComm = Get<RCP<const Teuchos::Comm<int>>>(fineLevel, "Node Comm");
    Set<RCP<const Teuchos::Comm<int>>>(coarseLevel, "Node Comm", nodeComm);
  }
 
  Set(coarseLevel, "Nullspace", coarseNullspace);
  Set(coarseLevel, "P", Ptentative);
 
  if (IsPrint(Statistics2)) {
    RCP<ParameterList> params = rcp(new ParameterList());
    params->set("printLoadBalancingInfo", true);
    GetOStream(Statistics2) << PerfUtils::PrintMatrixInfo(*Ptentative, "Ptent", params);
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void TentativePFactory_kokkos<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    BuildPuncoupled(Level& coarseLevel, RCP<Matrix> A, RCP<Aggregates> aggregates,
                    RCP<AmalgamationInfo> amalgInfo, RCP<MultiVector> fineNullspace,
                    RCP<const Map> coarseMap, RCP<Matrix>& Ptentative,
                    RCP<MultiVector>& coarseNullspace, const int levelID) const {
  auto rowMap = A->getRowMap();
  auto colMap = A->getColMap();
 
  const size_t numRows = rowMap->getLocalNumElements();
  const size_t NSDim   = fineNullspace->getNumVectors();
 
  typedef KokkosKernels::ArithTraits<SC> ATS;
  using impl_SC      = typename ATS::val_type;
  using impl_ATS     = KokkosKernels::ArithTraits<impl_SC>;
  const impl_SC zero = impl_ATS::zero(), one = impl_ATS::one();
 
  const LO INVALID = Teuchos::OrdinalTraits<LO>::invalid();
 
  typename Aggregates::local_graph_type aggGraph;
  {
    SubFactoryMonitor m2(*this, "Get Aggregates graph", coarseLevel);
    aggGraph = aggregates->GetGraph();
  }
  auto aggRows = aggGraph.row_map;
  auto aggCols = aggGraph.entries;
 
  // Aggregates map is based on the amalgamated column map
  // We can skip global-to-local conversion if LIDs in row map are
  // same as LIDs in column map
  bool goodMap;
  {
    SubFactoryMonitor m2(*this, "Check good map", coarseLevel);
    goodMap = isGoodMap(*rowMap, *colMap);
  }
  // FIXME_KOKKOS: need to proofread later code for bad maps
  TEUCHOS_TEST_FOR_EXCEPTION(!goodMap, Exceptions::RuntimeError,
                             "MueLu: TentativePFactory_kokkos: for now works only with good maps "
                             "(i.e. \"matching\" row and column maps)");
 
  // STEP 1: do unamalgamation
  // The non-kokkos version uses member functions from the AmalgamationInfo
  // container class to unamalgamate the data. In contrast, the kokkos
  // version of TentativePFactory does the unamalgamation here and only uses
  // the data of the AmalgamationInfo container class
 
  // Extract information for unamalgamation
  LO fullBlockSize, blockID, stridingOffset, stridedBlockSize;
  GO indexBase;
  amalgInfo->GetStridingInformation(fullBlockSize, blockID, stridingOffset, stridedBlockSize, indexBase);
  GO globalOffset = amalgInfo->GlobalOffset();
 
  // Extract aggregation info (already in Kokkos host views)
  auto procWinner            = aggregates->GetProcWinner()->getLocalViewDevice(Tpetra::Access::ReadOnly);
  auto vertex2AggId          = aggregates->GetVertex2AggId()->getLocalViewDevice(Tpetra::Access::ReadOnly);
  const size_t numAggregates = aggregates->GetNumAggregates();
 
  int myPID = aggregates->GetMap()->getComm()->getRank();
 
  // Create Kokkos::View (on the device) to store the aggreate dof sizes
  // Later used to get aggregate dof offsets
  // NOTE: This zeros itself on construction
  typedef typename Aggregates::aggregates_sizes_type::non_const_type AggSizeType;
  AggSizeType aggDofSizes;
 
  if (stridedBlockSize == 1) {
    SubFactoryMonitor m2(*this, "Calc AggSizes", coarseLevel);
 
    // FIXME_KOKKOS: use ViewAllocateWithoutInitializing + set a single value
    aggDofSizes = AggSizeType("agg_dof_sizes", numAggregates + 1);
 
    auto sizesConst = aggregates->ComputeAggregateSizes();
    Kokkos::deep_copy(Kokkos::subview(aggDofSizes, Kokkos::make_pair(static_cast<size_t>(1), numAggregates + 1)), sizesConst);
 
  } else {
    SubFactoryMonitor m2(*this, "Calc AggSizes", coarseLevel);
 
    // FIXME_KOKKOS: use ViewAllocateWithoutInitializing + set a single value
    aggDofSizes = AggSizeType("agg_dof_sizes", numAggregates + 1);
 
    auto nodeMap = aggregates->GetMap()->getLocalMap();
    auto dofMap  = colMap->getLocalMap();
 
    Kokkos::parallel_for(
        "MueLu:TentativePF:Build:compute_agg_sizes", range_type(0, numAggregates),
        KOKKOS_LAMBDA(const LO agg) {
          auto aggRowView = aggGraph.rowConst(agg);
 
          size_t size = 0;
          for (LO colID = 0; colID < aggRowView.length; colID++) {
            GO nodeGID = nodeMap.getGlobalElement(aggRowView(colID));
 
            for (LO k = 0; k < stridedBlockSize; k++) {
              GO dofGID = (nodeGID - indexBase) * fullBlockSize + k + indexBase + globalOffset + stridingOffset;
 
              if (dofMap.getLocalElement(dofGID) != INVALID)
                size++;
            }
          }
          aggDofSizes(agg + 1) = size;
        });
  }
 
  // Find maximum dof size for aggregates
  // Later used to reserve enough scratch space for local QR decompositions
  LO maxAggSize = 0;
  ReduceMaxFunctor<LO, decltype(aggDofSizes)> reduceMax(aggDofSizes);
  Kokkos::parallel_reduce("MueLu:TentativePF:Build:max_agg_size", range_type(0, aggDofSizes.extent(0)), reduceMax, maxAggSize);
 
  // parallel_scan (exclusive)
  // The aggDofSizes View then contains the aggregate dof offsets
  Kokkos::parallel_scan(
      "MueLu:TentativePF:Build:aggregate_sizes:stage1_scan", range_type(0, numAggregates + 1),
      KOKKOS_LAMBDA(const LO i, LO& update, const bool& final_pass) {
        update += aggDofSizes(i);
        if (final_pass)
          aggDofSizes(i) = update;
      });
 
  // Create Kokkos::View on the device to store mapping
  // between (local) aggregate id and row map ids (LIDs)
  Kokkos::View<LO*, DeviceType> agg2RowMapLO(Kokkos::ViewAllocateWithoutInitializing("agg2row_map_LO"), numRows);
  {
    SubFactoryMonitor m2(*this, "Create Agg2RowMap", coarseLevel);
 
    AggSizeType aggOffsets(Kokkos::ViewAllocateWithoutInitializing("aggOffsets"), numAggregates);
    Kokkos::deep_copy(aggOffsets, Kokkos::subview(aggDofSizes, Kokkos::make_pair(static_cast<size_t>(0), numAggregates)));
 
    Kokkos::parallel_for(
        "MueLu:TentativePF:Build:createAgg2RowMap", range_type(0, vertex2AggId.extent(0)),
        KOKKOS_LAMBDA(const LO lnode) {
          if (procWinner(lnode, 0) == myPID) {
            // No need for atomics, it's one-to-one
            auto aggID = vertex2AggId(lnode, 0);
 
            auto offset = Kokkos::atomic_fetch_add(&aggOffsets(aggID), stridedBlockSize);
            // FIXME: I think this may be wrong
            // We unconditionally add the whole block here. When we calculated
            // aggDofSizes, we did the isLocalElement check. Something's fishy.
            for (LO k = 0; k < stridedBlockSize; k++)
              agg2RowMapLO(offset + k) = lnode * stridedBlockSize + k;
          }
        });
  }
 
  // STEP 2: prepare local QR decomposition
  // Reserve memory for tentative prolongation operator
  coarseNullspace = MultiVectorFactory::Build(coarseMap, NSDim, true);
 
  // Pull out the nullspace vectors so that we can have random access (on the device)
  auto fineNS   = fineNullspace->getLocalViewDevice(Tpetra::Access::ReadWrite);
  auto coarseNS = coarseNullspace->getLocalViewDevice(Tpetra::Access::ReadWrite);
 
  size_t nnz = 0;  // actual number of nnz
 
  typedef typename Xpetra::Matrix<SC, LO, GO, NO>::local_matrix_device_type local_matrix_type;
  typedef typename local_matrix_type::row_map_type::non_const_type rows_type;
  typedef typename local_matrix_type::index_type::non_const_type cols_type;
  typedef typename local_matrix_type::values_type::non_const_type vals_type;
 
  // Device View for status (error messages...)
  typedef Kokkos::View<int[10], DeviceType> status_type;
  status_type status("status");
 
  typename AppendTrait<decltype(fineNS), Kokkos::RandomAccess>::type fineNSRandom = fineNS;
  typename AppendTrait<status_type, Kokkos::Atomic>::type statusAtomic            = status;
 
  const ParameterList& pL = GetParameterList();
  const bool& doQRStep    = pL.get<bool>("tentative: calculate qr");
  if (!doQRStep) {
    GetOStream(Runtime1) << "TentativePFactory : bypassing local QR phase" << std::endl;
    if (NSDim > 1)
      GetOStream(Warnings0) << "TentativePFactor : for nontrivial nullspace, this may degrade performance" << std::endl;
  }
 
  size_t nnzEstimate = numRows * NSDim;
  rows_type rowsAux(Kokkos::ViewAllocateWithoutInitializing("Ptent_aux_rows"), numRows + 1);
  cols_type colsAux(Kokkos::ViewAllocateWithoutInitializing("Ptent_aux_cols"), nnzEstimate);
  vals_type valsAux("Ptent_aux_vals", nnzEstimate);
  rows_type rows("Ptent_rows", numRows + 1);
  {
    // Stage 0: fill in views.
    SubFactoryMonitor m2(*this, "Stage 0 (InitViews)", coarseLevel);
 
    // The main thing to notice is initialization of vals with INVALID. These
    // values will later be used to compress the arrays
    Kokkos::parallel_for(
        "MueLu:TentativePF:BuildPuncoupled:for1", range_type(0, numRows + 1),
        KOKKOS_LAMBDA(const LO row) {
          rowsAux(row) = row * NSDim;
        });
    Kokkos::parallel_for(
        "MueLu:TentativePF:BuildUncoupled:for2", range_type(0, nnzEstimate),
        KOKKOS_LAMBDA(const LO j) {
          colsAux(j) = INVALID;
        });
  }
 
  if (NSDim == 1) {
    // 1D is special, as it is the easiest. We don't even need to the QR,
    // just normalize an array. Plus, no worries abot small aggregates.  In
    // addition, we do not worry about compression. It is unlikely that
    // nullspace will have zeros. If it does, a prolongator row would be
    // zero and we'll get singularity anyway.
    SubFactoryMonitor m2(*this, "Stage 1 (LocalQR)", coarseLevel);
 
    // Set up team policy with numAggregates teams and one thread per team.
    // Each team handles a slice of the data associated with one aggregate
    // and performs a local QR decomposition (in this case real QR is
    // unnecessary).
    const Kokkos::TeamPolicy<execution_space> policy(numAggregates, 1);
 
    if (doQRStep) {
      Kokkos::parallel_for(
          "MueLu:TentativePF:BuildUncoupled:main_loop", policy,
          KOKKOS_LAMBDA(const typename Kokkos::TeamPolicy<execution_space>::member_type& thread) {
            auto agg = thread.league_rank();
 
            // size of the aggregate (number of DOFs in aggregate)
            LO aggSize = aggRows(agg + 1) - aggRows(agg);
 
            // Extract the piece of the nullspace corresponding to the aggregate, and
            // put it in the flat array, "localQR" (in column major format) for the
            // QR routine. Trivial in 1D.
            auto norm = impl_ATS::magnitude(zero);
 
            // Calculate QR by hand
            // FIXME: shouldn't there be stridedblock here?
            // FIXME_KOKKOS: shouldn't there be stridedblock here?
            for (decltype(aggSize) k = 0; k < aggSize; k++) {
              auto dnorm = impl_ATS::magnitude(fineNSRandom(agg2RowMapLO(aggRows(agg) + k), 0));
              norm += dnorm * dnorm;
            }
            norm = sqrt(norm);
 
            if (norm == zero) {
              // zero column; terminate the execution
              statusAtomic(1) = true;
              return;
            }
 
            // R = norm
            coarseNS(agg, 0) = norm;
 
            // Q = localQR(:,0)/norm
            for (decltype(aggSize) k = 0; k < aggSize; k++) {
              LO localRow      = agg2RowMapLO(aggRows(agg) + k);
              impl_SC localVal = fineNSRandom(agg2RowMapLO(aggRows(agg) + k), 0) / norm;
 
              rows(localRow + 1) = 1;
              colsAux(localRow)  = agg;
              valsAux(localRow)  = localVal;
            }
          });
 
      typename status_type::host_mirror_type statusHost = Kokkos::create_mirror_view(status);
      Kokkos::deep_copy(statusHost, status);
      for (decltype(statusHost.size()) i = 0; i < statusHost.size(); i++)
        if (statusHost(i)) {
          std::ostringstream oss;
          oss << "MueLu::TentativePFactory::MakeTentative: ";
          switch (i) {
            case 0: oss << "!goodMap is not implemented"; break;
            case 1: oss << "fine level NS part has a zero column"; break;
          }
          throw Exceptions::RuntimeError(oss.str());
        }
 
    } else {
      Kokkos::parallel_for(
          "MueLu:TentativePF:BuildUncoupled:main_loop_noqr", policy,
          KOKKOS_LAMBDA(const typename Kokkos::TeamPolicy<execution_space>::member_type& thread) {
            auto agg = thread.league_rank();
 
            // size of the aggregate (number of DOFs in aggregate)
            LO aggSize = aggRows(agg + 1) - aggRows(agg);
 
            // R = norm
            coarseNS(agg, 0) = one;
 
            // Q = localQR(:,0)/norm
            for (decltype(aggSize) k = 0; k < aggSize; k++) {
              LO localRow      = agg2RowMapLO(aggRows(agg) + k);
              impl_SC localVal = fineNSRandom(agg2RowMapLO(aggRows(agg) + k), 0);
 
              rows(localRow + 1) = 1;
              colsAux(localRow)  = agg;
              valsAux(localRow)  = localVal;
            }
          });
    }
 
    Kokkos::parallel_reduce(
        "MueLu:TentativeP:CountNNZ", range_type(0, numRows + 1),
        KOKKOS_LAMBDA(const LO i, size_t& nnz_count) {
          nnz_count += rows(i);
        },
        nnz);
 
  } else {  // NSdim > 1
    // FIXME_KOKKOS: This code branch is completely unoptimized.
    // Work to do:
    //   - Optimize QR decomposition
    //   - Remove INVALID usage similarly to CoalesceDropFactory_kokkos by
    //     packing new values in the beginning of each row
    // We do use auxilary view in this case, so keep a second rows view for
    // counting nonzeros in rows
 
    {
      SubFactoryMonitor m2 = SubFactoryMonitor(*this, doQRStep ? "Stage 1 (LocalQR)" : "Stage 1 (Fill coarse nullspace and tentative P)", coarseLevel);
      // Set up team policy with numAggregates teams and one thread per team.
      // Each team handles a slice of the data associated with one aggregate
      // and performs a local QR decomposition
      Kokkos::TeamPolicy<execution_space> policy(numAggregates, 1);  // numAggregates teams a 1 thread
      LocalQRDecompFunctor<LocalOrdinal, GlobalOrdinal, Scalar, DeviceType, decltype(fineNSRandom),
                           decltype(aggDofSizes /*aggregate sizes in dofs*/), decltype(maxAggSize), decltype(agg2RowMapLO),
                           decltype(statusAtomic), decltype(rows), decltype(rowsAux), decltype(colsAux),
                           decltype(valsAux)>
          localQRFunctor(fineNSRandom, coarseNS, aggDofSizes, maxAggSize, agg2RowMapLO, statusAtomic,
                         rows, rowsAux, colsAux, valsAux, doQRStep);
      if (doQRStep) {
        using shared_matrix = typename decltype(localQRFunctor)::shared_matrix;
        int m               = maxAggSize;
        int n               = fineNSRandom.extent(1);
        int size            = shared_matrix::shmem_size(m, n) +  // r
                   shared_matrix::shmem_size(m, m);              // q
 
        if (size < policy.scratch_size_max(/*level=*/(int)0))
          policy.set_scratch_size(/*level=*/(int)0, Kokkos::PerTeam(size));
        else if (size < policy.scratch_size_max(/*level=*/(int)1))
          policy.set_scratch_size(/*level=*/(int)1, Kokkos::PerTeam(size));
        else
          throw Exceptions::RuntimeError("Neither L0 scratch memory (max size " + std::to_string(policy.scratch_size_max((int)0)) +
                                         "), nor L1 scratch memory (max size " + std::to_string(policy.scratch_size_max((int)1)) +
                                         ") is large enough for requested allocation of size " + std::to_string(size));
      }
      Kokkos::parallel_reduce("MueLu:TentativePF:BuildUncoupled:main_qr_loop", policy, localQRFunctor, nnz);
    }
 
    typename status_type::host_mirror_type statusHost = Kokkos::create_mirror_view(status);
    Kokkos::deep_copy(statusHost, status);
    for (decltype(statusHost.size()) i = 0; i < statusHost.size(); i++)
      if (statusHost(i)) {
        std::ostringstream oss;
        oss << "MueLu::TentativePFactory::MakeTentative: ";
        switch (i) {
          case 0: oss << "!goodMap is not implemented"; break;
          case 1: oss << "fine level NS part has a zero column"; break;
        }
        throw Exceptions::RuntimeError(oss.str());
      }
  }
 
  // Compress the cols and vals by ignoring INVALID column entries that correspond
  // to 0 in QR.
 
  // The real cols and vals are constructed using calculated (not estimated) nnz
  cols_type cols;
  vals_type vals;
 
  if (nnz != nnzEstimate) {
    {
      // Stage 2: compress the arrays
      SubFactoryMonitor m2(*this, "Stage 2 (CompressRows)", coarseLevel);
 
      Kokkos::parallel_scan(
          "MueLu:TentativePF:Build:compress_rows", range_type(0, numRows + 1),
          KOKKOS_LAMBDA(const LO i, LO& upd, const bool& final) {
            upd += rows(i);
            if (final)
              rows(i) = upd;
          });
    }
 
    {
      SubFactoryMonitor m2(*this, "Stage 2 (CompressCols)", coarseLevel);
 
      cols = cols_type("Ptent_cols", nnz);
      vals = vals_type("Ptent_vals", nnz);
 
      // FIXME_KOKKOS: this can be spedup by moving correct cols and vals values
      // to the beginning of rows. See CoalesceDropFactory_kokkos for
      // example.
      Kokkos::parallel_for(
          "MueLu:TentativePF:Build:compress_cols_vals", range_type(0, numRows),
          KOKKOS_LAMBDA(const LO i) {
            LO rowStart = rows(i);
 
            size_t lnnz = 0;
            for (auto j = rowsAux(i); j < rowsAux(i + 1); j++)
              if (colsAux(j) != INVALID) {
                cols(rowStart + lnnz) = colsAux(j);
                vals(rowStart + lnnz) = valsAux(j);
                lnnz++;
              }
          });
    }
 
  } else {
    rows = rowsAux;
    cols = colsAux;
    vals = valsAux;
  }
 
  GetOStream(Runtime1) << "TentativePFactory : aggregates do not cross process boundaries" << std::endl;
 
  {
    // Stage 3: construct Xpetra::Matrix
    SubFactoryMonitor m2(*this, "Stage 3 (LocalMatrix+FillComplete)", coarseLevel);
 
    local_matrix_type lclMatrix = local_matrix_type("A", numRows, coarseMap->getLocalNumElements(), nnz, vals, rows, cols);
 
    // Managing labels & constants for ESFC
    RCP<ParameterList> FCparams;
    if (pL.isSublist("matrixmatrix: kernel params"))
      FCparams = rcp(new ParameterList(pL.sublist("matrixmatrix: kernel params")));
    else
      FCparams = rcp(new ParameterList);
 
    // By default, we don't need global constants for TentativeP
    FCparams->set("compute global constants", FCparams->get("compute global constants", false));
    FCparams->set("Timer Label", std::string("MueLu::TentativeP-") + toString(levelID));
 
    auto PtentCrs = CrsMatrixFactory::Build(lclMatrix, rowMap, coarseMap, coarseMap, A->getDomainMap());
    Ptentative    = rcp(new CrsMatrixWrap(PtentCrs));
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void TentativePFactory_kokkos<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    BuildPuncoupledBlockCrs(Level& coarseLevel, RCP<Matrix> A, RCP<Aggregates> aggregates,
                            RCP<AmalgamationInfo> amalgInfo, RCP<MultiVector> fineNullspace,
                            RCP<const Map> coarsePointMap, RCP<Matrix>& Ptentative,
                            RCP<MultiVector>& coarseNullspace, const int levelID) const {
  /* This routine generates a BlockCrs P for a BlockCrs A.  There are a few assumptions here, which meet the use cases we care about, but could
       be generalized later, if we ever need to do so:
       1) Null space dimension === block size of matrix:  So no elasticity right now
       2) QR is not supported:  Under assumption #1, this shouldn't cause problems.
       3) Maps are "good": Aka the first chunk of the ColMap is the RowMap.
 
       These assumptions keep our code way simpler and still support the use cases we actually care about.
     */
 
  RCP<const Map> rowMap   = A->getRowMap();
  RCP<const Map> rangeMap = A->getRangeMap();
  RCP<const Map> colMap   = A->getColMap();
  //    const size_t numFinePointRows = rangeMap->getLocalNumElements();
  const size_t numFineBlockRows = rowMap->getLocalNumElements();
 
  // typedef Teuchos::ScalarTraits<SC> STS;
  // typedef typename STS::magnitudeType Magnitude;
  const LO INVALID = Teuchos::OrdinalTraits<LO>::invalid();
 
  typedef KokkosKernels::ArithTraits<SC> ATS;
  using impl_SC     = typename ATS::val_type;
  using impl_ATS    = KokkosKernels::ArithTraits<impl_SC>;
  const impl_SC one = impl_ATS::one();
 
  //    const GO     numAggs   = aggregates->GetNumAggregates();
  const size_t NSDim = fineNullspace->getNumVectors();
  auto aggSizes      = aggregates->ComputeAggregateSizes();
 
  typename Aggregates::local_graph_type aggGraph;
  {
    SubFactoryMonitor m2(*this, "Get Aggregates graph", coarseLevel);
    aggGraph = aggregates->GetGraph();
  }
  auto aggRows = aggGraph.row_map;
  auto aggCols = aggGraph.entries;
 
  // Need to generate the coarse block map
  // NOTE: We assume NSDim == block size here
  // NOTE: We also assume that coarseMap has contiguous GIDs
  // const size_t numCoarsePointRows = coarsePointMap->getLocalNumElements();
  const size_t numCoarseBlockRows = coarsePointMap->getLocalNumElements() / NSDim;
  RCP<const Map> coarseBlockMap   = MapFactory::Build(coarsePointMap->lib(),
                                                      Teuchos::OrdinalTraits<Xpetra::global_size_t>::invalid(),
                                                      numCoarseBlockRows,
                                                      coarsePointMap->getIndexBase(),
                                                      coarsePointMap->getComm());
  // Sanity checking
  const ParameterList& pL = GetParameterList();
  //    const bool &doQRStep = pL.get<bool>("tentative: calculate qr");
 
  // The aggregates use the amalgamated column map, which in this case is what we want
 
  // Aggregates map is based on the amalgamated column map
  // We can skip global-to-local conversion if LIDs in row map are
  // same as LIDs in column map
  bool goodMap = MueLu::Utilities<SC, LO, GO, NO>::MapsAreNested(*rowMap, *colMap);
  TEUCHOS_TEST_FOR_EXCEPTION(!goodMap, Exceptions::RuntimeError,
                             "MueLu: TentativePFactory_kokkos: for now works only with good maps "
                             "(i.e. \"matching\" row and column maps)");
 
  // STEP 1: do unamalgamation
  // The non-kokkos version uses member functions from the AmalgamationInfo
  // container class to unamalgamate the data. In contrast, the kokkos
  // version of TentativePFactory does the unamalgamation here and only uses
  // the data of the AmalgamationInfo container class
 
  // Extract information for unamalgamation
  LO fullBlockSize, blockID, stridingOffset, stridedBlockSize;
  GO indexBase;
  amalgInfo->GetStridingInformation(fullBlockSize, blockID, stridingOffset, stridedBlockSize, indexBase);
  // GO globalOffset = amalgInfo->GlobalOffset();
 
  // Extract aggregation info (already in Kokkos host views)
  auto procWinner            = aggregates->GetProcWinner()->getLocalViewDevice(Tpetra::Access::ReadOnly);
  auto vertex2AggId          = aggregates->GetVertex2AggId()->getLocalViewDevice(Tpetra::Access::ReadOnly);
  const size_t numAggregates = aggregates->GetNumAggregates();
 
  int myPID = aggregates->GetMap()->getComm()->getRank();
 
  // Create Kokkos::View (on the device) to store the aggreate dof sizes
  // Later used to get aggregate dof offsets
  // NOTE: This zeros itself on construction
  typedef typename Aggregates::aggregates_sizes_type::non_const_type AggSizeType;
  AggSizeType aggDofSizes;  // This turns into "starts" after the parallel_scan
 
  {
    SubFactoryMonitor m2(*this, "Calc AggSizes", coarseLevel);
 
    // FIXME_KOKKOS: use ViewAllocateWithoutInitializing + set a single value
    aggDofSizes = AggSizeType("agg_dof_sizes", numAggregates + 1);
 
    Kokkos::deep_copy(Kokkos::subview(aggDofSizes, Kokkos::make_pair(static_cast<size_t>(1), numAggregates + 1)), aggSizes);
  }
 
  // Find maximum dof size for aggregates
  // Later used to reserve enough scratch space for local QR decompositions
  LO maxAggSize = 0;
  ReduceMaxFunctor<LO, decltype(aggDofSizes)> reduceMax(aggDofSizes);
  Kokkos::parallel_reduce("MueLu:TentativePF:Build:max_agg_size", range_type(0, aggDofSizes.extent(0)), reduceMax, maxAggSize);
 
  // parallel_scan (exclusive)
  // The aggDofSizes View then contains the aggregate dof offsets
  Kokkos::parallel_scan(
      "MueLu:TentativePF:Build:aggregate_sizes:stage1_scan", range_type(0, numAggregates + 1),
      KOKKOS_LAMBDA(const LO i, LO& update, const bool& final_pass) {
        update += aggDofSizes(i);
        if (final_pass)
          aggDofSizes(i) = update;
      });
 
  // Create Kokkos::View on the device to store mapping
  // between (local) aggregate id and row map ids (LIDs)
  Kokkos::View<LO*, DeviceType> aggToRowMapLO(Kokkos::ViewAllocateWithoutInitializing("aggtorow_map_LO"), numFineBlockRows);
  {
    SubFactoryMonitor m2(*this, "Create AggToRowMap", coarseLevel);
 
    AggSizeType aggOffsets(Kokkos::ViewAllocateWithoutInitializing("aggOffsets"), numAggregates);
    Kokkos::deep_copy(aggOffsets, Kokkos::subview(aggDofSizes, Kokkos::make_pair(static_cast<size_t>(0), numAggregates)));
 
    Kokkos::parallel_for(
        "MueLu:TentativePF:Build:createAgg2RowMap", range_type(0, vertex2AggId.extent(0)),
        KOKKOS_LAMBDA(const LO lnode) {
          if (procWinner(lnode, 0) == myPID) {
            // No need for atomics, it's one-to-one
            auto aggID = vertex2AggId(lnode, 0);
 
            auto offset = Kokkos::atomic_fetch_add(&aggOffsets(aggID), stridedBlockSize);
            // FIXME: I think this may be wrong
            // We unconditionally add the whole block here. When we calculated
            // aggDofSizes, we did the isLocalElement check. Something's fishy.
            for (LO k = 0; k < stridedBlockSize; k++)
              aggToRowMapLO(offset + k) = lnode * stridedBlockSize + k;
          }
        });
  }
 
  // STEP 2: prepare local QR decomposition
  // Reserve memory for tentative prolongation operator
  coarseNullspace = MultiVectorFactory::Build(coarsePointMap, NSDim, true);
 
  // Pull out the nullspace vectors so that we can have random access (on the device)
  auto fineNS   = fineNullspace->getLocalViewDevice(Tpetra::Access::ReadWrite);
  auto coarseNS = coarseNullspace->getLocalViewDevice(Tpetra::Access::ReadWrite);
 
  typedef typename Xpetra::Matrix<SC, LO, GO, NO>::local_matrix_device_type local_matrix_type;
  typedef typename local_matrix_type::row_map_type::non_const_type rows_type;
  typedef typename local_matrix_type::index_type::non_const_type cols_type;
  // typedef typename local_matrix_type::values_type::non_const_type    vals_type;
 
  // Device View for status (error messages...)
  typedef Kokkos::View<int[10], DeviceType> status_type;
  status_type status("status");
 
  typename AppendTrait<decltype(fineNS), Kokkos::RandomAccess>::type fineNSRandom = fineNS;
  typename AppendTrait<status_type, Kokkos::Atomic>::type statusAtomic            = status;
 
  // We're going to bypass QR in the BlockCrs version of the code regardless of what the user asks for
  GetOStream(Runtime1) << "TentativePFactory : bypassing local QR phase" << std::endl;
 
  // BlockCrs requires that we build the (block) graph first, so let's do that...
 
  // NOTE: Because we're assuming that the NSDim == BlockSize, we only have one
  // block non-zero per row in the matrix;
  rows_type ia(Kokkos::ViewAllocateWithoutInitializing("BlockGraph_rowptr"), numFineBlockRows + 1);
  cols_type ja(Kokkos::ViewAllocateWithoutInitializing("BlockGraph_colind"), numFineBlockRows);
 
  Kokkos::parallel_for(
      "MueLu:TentativePF:BlockCrs:graph_init", range_type(0, numFineBlockRows),
      KOKKOS_LAMBDA(const LO j) {
        ia[j] = j;
        ja[j] = INVALID;
 
        if (j == (LO)numFineBlockRows - 1)
          ia[numFineBlockRows] = numFineBlockRows;
      });
 
  // Fill Graph
  const Kokkos::TeamPolicy<execution_space> policy(numAggregates, 1);
  Kokkos::parallel_for(
      "MueLu:TentativePF:BlockCrs:fillGraph", policy,
      KOKKOS_LAMBDA(const typename Kokkos::TeamPolicy<execution_space>::member_type& thread) {
        auto agg                     = thread.league_rank();
        Xpetra::global_size_t offset = agg;
 
        // size of the aggregate (number of DOFs in aggregate)
        LO aggSize = aggRows(agg + 1) - aggRows(agg);
 
        for (LO j = 0; j < aggSize; j++) {
          // FIXME: Allow for bad maps
          const LO localRow     = aggToRowMapLO[aggDofSizes[agg] + j];
          const size_t rowStart = ia[localRow];
          ja[rowStart]          = offset;
        }
      });
 
  // Compress storage (remove all INVALID, which happen when we skip zeros)
  // We do that in-place
  {
    // Stage 2: compress the arrays
    SubFactoryMonitor m2(*this, "Stage 2 (CompressData)", coarseLevel);
    // Fill i_temp with the correct row starts
    rows_type i_temp(Kokkos::ViewAllocateWithoutInitializing("BlockGraph_rowptr"), numFineBlockRows + 1);
    LO nnz = 0;
    Kokkos::parallel_scan(
        "MueLu:TentativePF:BlockCrs:compress_rows", range_type(0, numFineBlockRows),
        KOKKOS_LAMBDA(const LO i, LO& upd, const bool& final) {
          if (final)
            i_temp[i] = upd;
          for (auto j = ia[i]; j < ia[i + 1]; j++)
            if (ja[j] != INVALID)
              upd++;
          if (final && i == (LO)numFineBlockRows - 1)
            i_temp[numFineBlockRows] = upd;
        },
        nnz);
 
    cols_type j_temp(Kokkos::ViewAllocateWithoutInitializing("BlockGraph_colind"), nnz);
 
    Kokkos::parallel_for(
        "MueLu:TentativePF:BlockCrs:compress_cols", range_type(0, numFineBlockRows),
        KOKKOS_LAMBDA(const LO i) {
          size_t rowStart = i_temp[i];
          size_t lnnz     = 0;
          for (auto j = ia[i]; j < ia[i + 1]; j++)
            if (ja[j] != INVALID) {
              j_temp[rowStart + lnnz] = ja[j];
              lnnz++;
            }
        });
 
    ia = i_temp;
    ja = j_temp;
  }
 
  RCP<CrsGraph> BlockGraph = CrsGraphFactory::Build(rowMap, coarseBlockMap, ia, ja);
 
  // Managing labels & constants for ESFC
  {
    RCP<ParameterList> FCparams;
    if (pL.isSublist("matrixmatrix: kernel params"))
      FCparams = rcp(new ParameterList(pL.sublist("matrixmatrix: kernel params")));
    else
      FCparams = rcp(new ParameterList);
    // By default, we don't need global constants for TentativeP
    FCparams->set("compute global constants", FCparams->get("compute global constants", false));
    std::string levelIDs = toString(levelID);
    FCparams->set("Timer Label", std::string("MueLu::TentativeP-") + levelIDs);
    RCP<const Export> dummy_e;
    RCP<const Import> dummy_i;
    BlockGraph->expertStaticFillComplete(coarseBlockMap, rowMap, dummy_i, dummy_e, FCparams);
  }
 
  // We can't leave the ia/ja pointers floating around, because of host/device view counting, so
  // we clear them here
  ia = rows_type();
  ja = cols_type();
 
  // Now let's make a BlockCrs Matrix
  // NOTE: Assumes block size== NSDim
  RCP<Xpetra::CrsMatrix<SC, LO, GO, NO>> P_xpetra            = Xpetra::CrsMatrixFactory<SC, LO, GO, NO>::BuildBlock(BlockGraph, coarsePointMap, rangeMap, NSDim);
  RCP<Xpetra::TpetraBlockCrsMatrix<SC, LO, GO, NO>> P_tpetra = rcp_dynamic_cast<Xpetra::TpetraBlockCrsMatrix<SC, LO, GO, NO>>(P_xpetra);
  if (P_tpetra.is_null()) throw std::runtime_error("BuildPUncoupled: Matrix factory did not return a Tpetra::BlockCrsMatrix");
  RCP<CrsMatrixWrap> P_wrap = rcp(new CrsMatrixWrap(P_xpetra));
 
  auto values     = P_tpetra->getTpetra_BlockCrsMatrix()->getValuesDeviceNonConst();
  const LO stride = NSDim * NSDim;
 
  Kokkos::parallel_for(
      "MueLu:TentativePF:BlockCrs:main_loop_noqr", policy,
      KOKKOS_LAMBDA(const typename Kokkos::TeamPolicy<execution_space>::member_type& thread) {
        auto agg = thread.league_rank();
 
        // size of the aggregate (number of DOFs in aggregate)
        LO aggSize                   = aggRows(agg + 1) - aggRows(agg);
        Xpetra::global_size_t offset = agg * NSDim;
 
        // Q = localQR(:,0)/norm
        for (LO j = 0; j < aggSize; j++) {
          LO localBlockRow = aggToRowMapLO(aggRows(agg) + j);
          LO rowStart      = localBlockRow * stride;
          for (LO r = 0; r < (LO)NSDim; r++) {
            LO localPointRow = localBlockRow * NSDim + r;
            for (LO c = 0; c < (LO)NSDim; c++) {
              values[rowStart + r * NSDim + c] = fineNSRandom(localPointRow, c);
            }
          }
        }
 
        // R = norm
        for (LO j = 0; j < (LO)NSDim; j++)
          coarseNS(offset + j, j) = one;
      });
 
  Ptentative = P_wrap;
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void TentativePFactory_kokkos<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    BuildPcoupled(RCP<Matrix> /* A */, RCP<Aggregates> /* aggregates */,
                  RCP<AmalgamationInfo> /* amalgInfo */, RCP<MultiVector> /* fineNullspace */,
                  RCP<const Map> /* coarseMap */, RCP<Matrix>& /* Ptentative */,
                  RCP<MultiVector>& /* coarseNullspace */) const {
  throw Exceptions::RuntimeError("MueLu: Construction of coupled tentative P is not implemented");
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
bool TentativePFactory_kokkos<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    isGoodMap(const Map& rowMap, const Map& colMap) const {
  auto rowLocalMap = rowMap.getLocalMap();
  auto colLocalMap = colMap.getLocalMap();
 
  const size_t numRows = rowLocalMap.getLocalNumElements();
  const size_t numCols = colLocalMap.getLocalNumElements();
 
  if (numCols < numRows)
    return false;
 
  size_t numDiff = 0;
  Kokkos::parallel_reduce(
      "MueLu:TentativePF:isGoodMap", range_type(0, numRows),
      KOKKOS_LAMBDA(const LO i, size_t& diff) {
        diff += (rowLocalMap.getGlobalElement(i) != colLocalMap.getGlobalElement(i));
      },
      numDiff);
 
  return (numDiff == 0);
}
 
}  // namespace MueLu
 
#define MUELU_TENTATIVEPFACTORY_KOKKOS_SHORT
#endif  // MUELU_TENTATIVEPFACTORY_KOKKOS_DEF_HPP