MueLu_ParameterListInterpreter_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_PARAMETERLISTINTERPRETER_DEF_HPP
#define MUELU_PARAMETERLISTINTERPRETER_DEF_HPP

#include <Teuchos_XMLParameterListHelpers.hpp>

#include <Xpetra_Matrix.hpp>
#include <Xpetra_MatrixUtils.hpp>

#include "MueLu_ConfigDefs.hpp"

#include "MueLu_ParameterListInterpreter_decl.hpp"

#include "MueLu_MasterList.hpp"
#include "MueLu_Level.hpp"
#include "MueLu_Hierarchy.hpp"
#include "MueLu_FactoryManager.hpp"

#include "MueLu_AggregationExportFactory.hpp"
#include "MueLu_AggregateQualityEstimateFactory.hpp"
#include "MueLu_AmalgamationFactory.hpp"
#include "MueLu_BrickAggregationFactory.hpp"
#include "MueLu_ClassicalMapFactory.hpp"
#include "MueLu_ClassicalPFactory.hpp"
#include "MueLu_CoalesceDropFactory.hpp"
#include "MueLu_CoarseMapFactory.hpp"
#include "MueLu_ConstraintFactory.hpp"
#include "MueLu_CoordinatesTransferFactory.hpp"
#include "MueLu_DirectSolver.hpp"
#include "MueLu_EminPFactory.hpp"
#include "MueLu_Exceptions.hpp"
#include "MueLu_FacadeClassFactory.hpp"
#include "MueLu_FactoryFactory.hpp"
#include "MueLu_FilteredAFactory.hpp"
#include "MueLu_GenericRFactory.hpp"
#include "MueLu_InitialBlockNumberFactory.hpp"
#include "MueLu_LineDetectionFactory.hpp"
#include "MueLu_LocalOrdinalTransferFactory.hpp"
#include "MueLu_MatrixAnalysisFactory.hpp"
#include "MueLu_MultiVectorTransferFactory.hpp"
#include "MueLu_NotayAggregationFactory.hpp"
#include "MueLu_NullspaceFactory.hpp"
#include "MueLu_PatternFactory.hpp"
#include "MueLu_ReplicatePFactory.hpp"
#include "MueLu_CombinePFactory.hpp"
#include "MueLu_PgPFactory.hpp"
#include "MueLu_RAPFactory.hpp"
#include "MueLu_RAPShiftFactory.hpp"
#include "MueLu_RebalanceAcFactory.hpp"
#include "MueLu_RebalanceTransferFactory.hpp"
#include "MueLu_RepartitionFactory.hpp"
#include "MueLu_RepartitionHeuristicFactory.hpp"
#include "MueLu_ReitzingerPFactory.hpp"
#include "MueLu_SaPFactory.hpp"
#include "MueLu_ScaledNullspaceFactory.hpp"
#include "MueLu_SemiCoarsenPFactory.hpp"
#include "MueLu_SmootherFactory.hpp"
#include "MueLu_SmooVecCoalesceDropFactory.hpp"
#include "MueLu_TentativePFactory.hpp"
#include "MueLu_TogglePFactory.hpp"
#include "MueLu_ToggleCoordinatesTransferFactory.hpp"
#include "MueLu_TransPFactory.hpp"
#include "MueLu_UncoupledAggregationFactory.hpp"
#include "MueLu_ZoltanInterface.hpp"
#include "MueLu_Zoltan2Interface.hpp"
#include "MueLu_NodePartitionInterface.hpp"
#include "MueLu_LowPrecisionFactory.hpp"

#include "MueLu_CoalesceDropFactory_kokkos.hpp"
#include "MueLu_SemiCoarsenPFactory_kokkos.hpp"
#include "MueLu_TentativePFactory_kokkos.hpp"

#ifdef HAVE_MUELU_MATLAB
#include "../matlab/src/MueLu_MatlabSmoother_decl.hpp"
#include "../matlab/src/MueLu_MatlabSmoother_def.hpp"
#include "../matlab/src/MueLu_TwoLevelMatlabFactory_decl.hpp"
#include "../matlab/src/MueLu_TwoLevelMatlabFactory_def.hpp"
#include "../matlab/src/MueLu_SingleLevelMatlabFactory_decl.hpp"
#include "../matlab/src/MueLu_SingleLevelMatlabFactory_def.hpp"
#endif

#ifdef HAVE_MUELU_INTREPID2
#include "MueLu_IntrepidPCoarsenFactory.hpp"
#endif

#include <unordered_set>

namespace MueLu {

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::ParameterListInterpreter(ParameterList& paramList, Teuchos::RCP<const Teuchos::Comm<int> > comm, Teuchos::RCP<FactoryFactory> factFact, Teuchos::RCP<FacadeClassFactory> facadeFact)
  : factFact_(factFact) {
  RCP<Teuchos::TimeMonitor> tM = rcp(new Teuchos::TimeMonitor(*Teuchos::TimeMonitor::getNewTimer(std::string("MueLu: ParameterListInterpreter (ParameterList)"))));
  if (facadeFact == Teuchos::null)
    facadeFact_ = Teuchos::rcp(new FacadeClassFactory());
  else
    facadeFact_ = facadeFact;

  if (paramList.isParameter("xml parameter file")) {
    std::string filename = paramList.get("xml parameter file", "");
    if (filename.length() != 0) {
      TEUCHOS_TEST_FOR_EXCEPTION(comm.is_null(), Exceptions::RuntimeError, "xml parameter file requires a valid comm");

      ParameterList paramList2 = paramList;
      Teuchos::updateParametersFromXmlFileAndBroadcast(filename, Teuchos::Ptr<Teuchos::ParameterList>(&paramList2), *comm);
      SetParameterList(paramList2);

    } else {
      SetParameterList(paramList);
    }

  } else {
    SetParameterList(paramList);
  }
}

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::ParameterListInterpreter(const std::string& xmlFileName, const Teuchos::Comm<int>& comm, Teuchos::RCP<FactoryFactory> factFact, Teuchos::RCP<FacadeClassFactory> facadeFact)
  : factFact_(factFact) {
  RCP<Teuchos::TimeMonitor> tM = rcp(new Teuchos::TimeMonitor(*Teuchos::TimeMonitor::getNewTimer(std::string("MueLu: ParameterListInterpreter (XML)"))));
  if (facadeFact == Teuchos::null)
    facadeFact_ = Teuchos::rcp(new FacadeClassFactory());
  else
    facadeFact_ = facadeFact;

  ParameterList paramList;
  Teuchos::updateParametersFromXmlFileAndBroadcast(xmlFileName, Teuchos::Ptr<ParameterList>(&paramList), comm);
  SetParameterList(paramList);
}

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::~ParameterListInterpreter() = default;

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::SetParameterList(const ParameterList& paramList) {
  Cycle_            = Hierarchy::GetDefaultCycle();
  WCycleStartLevel_ = Hierarchy::GetDefaultCycleStartLevel();
  scalingFactor_    = Teuchos::ScalarTraits<double>::one();
  blockSize_        = 1;
  dofOffset_        = 0;

  if (paramList.isSublist("Hierarchy")) {
    SetFactoryParameterList(paramList);

  } else if (paramList.isParameter("MueLu preconditioner") == true) {
    this->GetOStream(Runtime0) << "Use facade class: " << paramList.get<std::string>("MueLu preconditioner") << std::endl;
    Teuchos::RCP<ParameterList> pp = facadeFact_->SetParameterList(paramList);
    SetFactoryParameterList(*pp);

  } else {
    // The validator doesn't work correctly for non-serializable data (Hint: template parameters), so strip it out
    ParameterList serialList, nonSerialList;

    ExtractNonSerializableData(paramList, serialList, nonSerialList);
    Validate(serialList);
    SetEasyParameterList(paramList);
  }
}

// =====================================================================================================
// ====================================== EASY interpreter =============================================
// =====================================================================================================
static inline bool areSame(const ParameterList& list1, const ParameterList& list2);

// Get value from one of the lists, or set it to default
// Use case: check for a parameter value in a level-specific sublist, then in a root level list;
// if it is absent from both, set it to default
#define MUELU_SET_VAR_2LIST(paramList, defaultList, paramName, paramType, varName) \
  paramType varName;                                                               \
  if (paramList.isParameter(paramName))                                            \
    varName = paramList.get<paramType>(paramName);                                 \
  else if (defaultList.isParameter(paramName))                                     \
    varName = defaultList.get<paramType>(paramName);                               \
  else                                                                             \
    varName = MasterList::getDefault<paramType>(paramName);

#define MUELU_TEST_AND_SET_VAR(paramList, paramName, paramType, varName) \
  (paramList.isParameter(paramName) ? varName = paramList.get<paramType>(paramName), true : false)

// Set parameter in a list if it is present in any of two lists
// User case: set factory specific parameter, first checking for a level-specific value, then cheking root level value
#define MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, paramName, paramType, listWrite)                                                     \
  try {                                                                                                                                             \
    if (paramList.isParameter(paramName))                                                                                                           \
      listWrite.set(paramName, paramList.get<paramType>(paramName));                                                                                \
    else if (defaultList.isParameter(paramName))                                                                                                    \
      listWrite.set(paramName, defaultList.get<paramType>(paramName));                                                                              \
  } catch (Teuchos::Exceptions::InvalidParameterType&) {                                                                                            \
    TEUCHOS_TEST_FOR_EXCEPTION_PURE_MSG(true, Teuchos::Exceptions::InvalidParameterType,                                                            \
                                        "Error: parameter \"" << paramName << "\" must be of type " << Teuchos::TypeNameTraits<paramType>::name()); \
  }

#define MUELU_TEST_PARAM_2LIST(paramList, defaultList, paramName, paramType, cmpValue) \
  (cmpValue == (paramList.isParameter(paramName) ? paramList.get<paramType>(paramName) : (defaultList.isParameter(paramName) ? defaultList.get<paramType>(paramName) : MasterList::getDefault<paramType>(paramName))))

#define MUELU_KOKKOS_FACTORY(varName, oldFactory, newFactory) \
  RCP<Factory> varName;                                       \
  if (!useKokkos_)                                            \
    varName = rcp(new oldFactory());                          \
  else                                                        \
    varName = rcp(new newFactory());
#define MUELU_KOKKOS_FACTORY_NO_DECL(varName, oldFactory, newFactory) \
  if (!useKokkos_)                                                    \
    varName = rcp(new oldFactory());                                  \
  else                                                                \
    varName = rcp(new newFactory());

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    SetEasyParameterList(const ParameterList& constParamList) {
  ParameterList paramList;

  MUELU_SET_VAR_2LIST(constParamList, constParamList, "problem: type", std::string, problemType);
  if (problemType != "unknown") {
    paramList = *MasterList::GetProblemSpecificList(problemType);
    paramList.setParameters(constParamList);
  } else {
    // Create a non const copy of the parameter list
    // Working with a modifiable list is much much easier than with original one
    paramList = constParamList;
  }

  // Check for Kokkos
  useKokkos_ = !Node::is_serial;
  (void)MUELU_TEST_AND_SET_VAR(paramList, "use kokkos refactor", bool, useKokkos_);

  // Check for timer synchronization
  MUELU_SET_VAR_2LIST(paramList, paramList, "synchronize factory timers", bool, syncTimers);
  if (syncTimers)
    Factory::EnableTimerSync();

  // Translate cycle type parameter
  if (paramList.isParameter("cycle type")) {
    std::map<std::string, CycleType> cycleMap;
    cycleMap["V"] = VCYCLE;
    cycleMap["W"] = WCYCLE;

    auto cycleType = paramList.get<std::string>("cycle type");
    TEUCHOS_TEST_FOR_EXCEPTION(cycleMap.count(cycleType) == 0, Exceptions::RuntimeError,
                               "Invalid cycle type: \"" << cycleType << "\"");
    Cycle_ = cycleMap[cycleType];
  }

  if (paramList.isParameter("W cycle start level")) {
    WCycleStartLevel_ = paramList.get<int>("W cycle start level");
  }

  if (paramList.isParameter("coarse grid correction scaling factor"))
    scalingFactor_ = paramList.get<double>("coarse grid correction scaling factor");

  this->maxCoarseSize_   = paramList.get<int>("coarse: max size", MasterList::getDefault<int>("coarse: max size"));
  this->numDesiredLevel_ = paramList.get<int>("max levels", MasterList::getDefault<int>("max levels"));
  blockSize_             = paramList.get<int>("number of equations", MasterList::getDefault<int>("number of equations"));

  (void)MUELU_TEST_AND_SET_VAR(paramList, "debug: graph level", int, this->graphOutputLevel_);

  // Generic data keeping (this keeps the data on all levels)
  if (paramList.isParameter("keep data"))
    this->dataToKeep_ = Teuchos::getArrayFromStringParameter<std::string>(paramList, "keep data");

  // Export level data
  if (paramList.isSublist("export data")) {
    ParameterList printList = paramList.sublist("export data");

    // Vectors, aggregates and other things that need special handling
    if (printList.isParameter("Nullspace"))
      this->nullspaceToPrint_ = Teuchos::getArrayFromStringParameter<int>(printList, "Nullspace");
    if (printList.isParameter("Coordinates"))
      this->coordinatesToPrint_ = Teuchos::getArrayFromStringParameter<int>(printList, "Coordinates");
    if (printList.isParameter("Material"))
      this->materialToPrint_ = Teuchos::getArrayFromStringParameter<int>(printList, "Material");
    if (printList.isParameter("Aggregates"))
      this->aggregatesToPrint_ = Teuchos::getArrayFromStringParameter<int>(printList, "Aggregates");
    if (printList.isParameter("pcoarsen: element to node map"))
      this->elementToNodeMapsToPrint_ = Teuchos::getArrayFromStringParameter<int>(printList, "pcoarsen: element to node map");

    // If we asked for an arbitrary matrix to be printed, we do that here
    for (auto iter = printList.begin(); iter != printList.end(); iter++) {
      const std::string& name = printList.name(iter);
      // Ignore the special cases
      if (name == "Nullspace" || name == "Coordinates" || name == "Material" || name == "Aggregates" || name == "pcoarsen: element to node map")
        continue;

      this->matricesToPrint_[name] = Teuchos::getArrayFromStringParameter<int>(printList, name);
    }
  }

  // Set verbosity parameter
  VerbLevel oldVerbLevel = VerboseObject::GetDefaultVerbLevel();
  {
    MUELU_SET_VAR_2LIST(paramList, paramList, "verbosity", std::string, verbosityLevel);
    this->verbosity_ = toVerbLevel(verbosityLevel);
    VerboseObject::SetDefaultVerbLevel(this->verbosity_);
  }

  MUELU_SET_VAR_2LIST(paramList, paramList, "output filename", std::string, outputFilename);
  if (outputFilename != "")
    VerboseObject::SetMueLuOFileStream(outputFilename);

  // Detect if we need to transfer coordinates to coarse levels. We do that iff
  //  - we use "distance laplacian" dropping on some level, or
  //  - we use a repartitioner on some level that needs coordinates
  //  - we use brick aggregation
  //  - we use Ifpack2 line partitioner
  // This is not ideal, as we may have "repartition: enable" turned on by default
  // and not present in the list, but it is better than nothing.
  useCoordinates_ = false;
  useBlockNumber_ = false;
  if (MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: drop scheme", std::string, "distance laplacian") ||
      MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: type", std::string, "brick") ||
      MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: export visualization data", bool, true)) {
    useCoordinates_ = true;
  } else if (MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: drop scheme", std::string, "block diagonal distance laplacian")) {
    useCoordinates_ = true;
    useBlockNumber_ = true;
  } else if (MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: drop scheme", std::string, "block diagonal") ||
             MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: drop scheme", std::string, "block diagonal classical") ||
             MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: drop scheme", std::string, "block diagonal signed classical") ||
             MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: drop scheme", std::string, "block diagonal colored signed classical") ||
             MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: drop scheme", std::string, "signed classical")) {
    useBlockNumber_ = true;
  } else if (paramList.isSublist("smoother: params")) {
    const auto smooParamList = paramList.sublist("smoother: params");
    if (smooParamList.isParameter("partitioner: type") &&
        (smooParamList.get<std::string>("partitioner: type") == "line")) {
      useCoordinates_ = true;
    }
  } else {
    for (int levelID = 0; levelID < this->numDesiredLevel_; levelID++) {
      std::string levelStr = "level " + toString(levelID);

      if (paramList.isSublist(levelStr)) {
        const ParameterList& levelList = paramList.sublist(levelStr);

        if (MUELU_TEST_PARAM_2LIST(levelList, paramList, "aggregation: drop scheme", std::string, "distance laplacian") ||
            MUELU_TEST_PARAM_2LIST(levelList, paramList, "aggregation: type", std::string, "brick") ||
            MUELU_TEST_PARAM_2LIST(levelList, paramList, "aggregation: export visualization data", bool, true)) {
          useCoordinates_ = true;
        } else if (MUELU_TEST_PARAM_2LIST(levelList, paramList, "aggregation: drop scheme", std::string, "block diagonal distance laplacian")) {
          useCoordinates_ = true;
          useBlockNumber_ = true;
        } else if (MUELU_TEST_PARAM_2LIST(levelList, paramList, "aggregation: drop scheme", std::string, "block diagonal") ||
                   MUELU_TEST_PARAM_2LIST(levelList, paramList, "aggregation: drop scheme", std::string, "block diagonal classical") ||
                   MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: drop scheme", std::string, "block diagonal signed classical") ||
                   MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: drop scheme", std::string, "block diagonal colored signed classical") ||
                   MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: drop scheme", std::string, "signed classical")) {
          useBlockNumber_ = true;
        }
      }
    }
  }

  useMaterial_ = false;
  if (MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: distance laplacian metric", std::string, "material")) {
    useMaterial_ = true;
  }

  if (MUELU_TEST_PARAM_2LIST(paramList, paramList, "repartition: enable", bool, true)) {
    // We don't need coordinates if we're doing the in-place restriction
    if (MUELU_TEST_PARAM_2LIST(paramList, paramList, "repartition: use subcommunicators", bool, true) &&
        MUELU_TEST_PARAM_2LIST(paramList, paramList, "repartition: use subcommunicators in place", bool, true)) {
      // do nothing --- these don't need coordinates
    } else if (!paramList.isSublist("repartition: params")) {
      useCoordinates_ = true;
    } else {
      const ParameterList& repParams = paramList.sublist("repartition: params");
      if (repParams.isType<std::string>("algorithm")) {
        const std::string algo = repParams.get<std::string>("algorithm");
        if (algo == "multijagged" || algo == "rcb") {
          useCoordinates_ = true;
        }
      } else {
        useCoordinates_ = true;
      }
    }
  }
  for (int levelID = 0; levelID < this->numDesiredLevel_; levelID++) {
    std::string levelStr = "level " + toString(levelID);

    if (paramList.isSublist(levelStr)) {
      const ParameterList& levelList = paramList.sublist(levelStr);

      if (MUELU_TEST_PARAM_2LIST(levelList, paramList, "repartition: enable", bool, true)) {
        if (!levelList.isSublist("repartition: params")) {
          useCoordinates_ = true;
          break;
        } else {
          const ParameterList& repParams = levelList.sublist("repartition: params");
          if (repParams.isType<std::string>("algorithm")) {
            const std::string algo = repParams.get<std::string>("algorithm");
            if (algo == "multijagged" || algo == "rcb") {
              useCoordinates_ = true;
              break;
            }
          } else {
            useCoordinates_ = true;
            break;
          }
        }
      }
    }
  }

  // Detect if we do implicit P and R rebalance
  changedPRrebalance_        = false;
  changedPRViaCopyrebalance_ = false;
  if (MUELU_TEST_PARAM_2LIST(paramList, paramList, "repartition: enable", bool, true)) {
    changedPRrebalance_        = MUELU_TEST_AND_SET_VAR(paramList, "repartition: rebalance P and R", bool, this->doPRrebalance_);
    changedPRViaCopyrebalance_ = MUELU_TEST_AND_SET_VAR(paramList, "repartition: explicit via new copy rebalance P and R", bool, this->doPRViaCopyrebalance_);
  }

  // Detect if we use implicit transpose
  changedImplicitTranspose_ = MUELU_TEST_AND_SET_VAR(paramList, "transpose: use implicit", bool, this->implicitTranspose_);

  // Detect if we use fuse prolongation and update
  (void)MUELU_TEST_AND_SET_VAR(paramList, "fuse prolongation and update", bool, this->fuseProlongationAndUpdate_);

  // Detect if we suppress the dimension check of the user-given nullspace
  (void)MUELU_TEST_AND_SET_VAR(paramList, "nullspace: suppress dimension check", bool, this->suppressNullspaceDimensionCheck_);

  if (paramList.isSublist("matvec params"))
    this->matvecParams_ = Teuchos::parameterList(paramList.sublist("matvec params"));

  // Create default manager
  // FIXME: should it be here, or higher up
  RCP<FactoryManager> defaultManager = rcp(new FactoryManager());
  defaultManager->SetVerbLevel(this->verbosity_);
  defaultManager->SetKokkosRefactor(useKokkos_);

  // We will ignore keeps0
  std::vector<keep_pair> keeps0;
  UpdateFactoryManager(paramList, ParameterList(), *defaultManager, 0 /*levelID*/, keeps0);

  //    std::cout<<"*** Default Manager ***"<<std::endl;
  //    defaultManager->Print();

  // Create level specific factory managers
  for (int levelID = 0; levelID < this->numDesiredLevel_; levelID++) {
    // Note, that originally if there were no level specific parameters, we
    // simply copied the defaultManager However, with the introduction of
    // levelID to UpdateFactoryManager (required for reuse), we can no longer
    // guarantee that the kept variables are the same for each level even if
    // dependency structure does not change.
    RCP<FactoryManager> levelManager = rcp(new FactoryManager(*defaultManager));
    levelManager->SetVerbLevel(defaultManager->GetVerbLevel());

    std::vector<keep_pair> keeps;
    if (paramList.isSublist("level " + toString(levelID))) {
      // We do this so the parameters on the level get flagged correctly as "used"
      ParameterList& levelList = paramList.sublist("level " + toString(levelID), true /*mustAlreadyExist*/);
      UpdateFactoryManager(levelList, paramList, *levelManager, levelID, keeps);

    } else {
      ParameterList levelList;
      UpdateFactoryManager(levelList, paramList, *levelManager, levelID, keeps);
    }

    this->keep_[levelID] = keeps;
    this->AddFactoryManager(levelID, 1, levelManager);

    //      std::cout<<"*** Level "<<levelID<<" Manager ***"<<std::endl;
    //      levelManager->Print();
  }

  // FIXME: parameters passed to packages, like Ifpack2, are not touched by us, resulting in "[unused]" flag
  // being displayed. On the other hand, we don't want to simply iterate through them touching. I don't know
  // what a good solution looks like
  if (MUELU_TEST_PARAM_2LIST(paramList, paramList, "print initial parameters", bool, true))
    this->GetOStream(static_cast<MsgType>(Runtime1), 0) << paramList << std::endl;

  if (MUELU_TEST_PARAM_2LIST(paramList, paramList, "print unused parameters", bool, true)) {
    // Check unused parameters
    ParameterList unusedParamList;

    // Check for unused parameters that aren't lists
    for (ParameterList::ConstIterator it = paramList.begin(); it != paramList.end(); it++) {
      const ParameterEntry& entry = paramList.entry(it);

      if (!entry.isList() && !entry.isUsed())
        unusedParamList.setEntry(paramList.name(it), entry);
    }

    // Check for unused parameters in level-specific sublists
    for (int levelID = 0; levelID < this->numDesiredLevel_; levelID++) {
      std::string levelStr = "level " + toString(levelID);

      if (paramList.isSublist(levelStr)) {
        const ParameterList& levelList = paramList.sublist(levelStr);

        for (ParameterList::ConstIterator itr = levelList.begin(); itr != levelList.end(); ++itr) {
          const ParameterEntry& entry = levelList.entry(itr);

          if (!entry.isList() && !entry.isUsed())
            unusedParamList.sublist(levelStr).setEntry(levelList.name(itr), entry);
        }
      }
    }

    if (unusedParamList.numParams() > 0) {
      std::ostringstream unusedParamsStream;
      int indent = 4;
      unusedParamList.print(unusedParamsStream, indent);

      this->GetOStream(Warnings1) << "The following parameters were not used:\n"
                                  << unusedParamsStream.str() << std::endl;
    }
  }

  VerboseObject::SetDefaultVerbLevel(oldVerbLevel);
}

// =====================================================================================================
// ==================================== UpdateFactoryManager ===========================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager(ParameterList& paramList, const ParameterList& defaultList, FactoryManager& manager,
                         int levelID, std::vector<keep_pair>& keeps) const {
  // NOTE: Factory::SetParameterList must be called prior to Factory::SetFactory, as
  // SetParameterList sets default values for non mentioned parameters, including factories

  using strings = std::unordered_set<std::string>;

  // shortcut
  if (paramList.numParams() == 0 && defaultList.numParams() > 0)
    paramList = ParameterList(defaultList);

  MUELU_SET_VAR_2LIST(paramList, defaultList, "reuse: type", std::string, reuseType);
  TEUCHOS_TEST_FOR_EXCEPTION(strings({"none", "tP", "RP", "emin", "RAP", "full", "S"}).count(reuseType) == 0,
                             Exceptions::RuntimeError, "Unknown \"reuse: type\" value: \"" << reuseType << "\". Please consult User's Guide.");

  MUELU_SET_VAR_2LIST(paramList, defaultList, "multigrid algorithm", std::string, multigridAlgo);
  TEUCHOS_TEST_FOR_EXCEPTION(strings({"unsmoothed", "sa", "pg", "emin", "matlab", "pcoarsen", "classical", "smoothed reitzinger", "unsmoothed reitzinger", "replicate", "combine"}).count(multigridAlgo) == 0,
                             Exceptions::RuntimeError, "Unknown \"multigrid algorithm\" value: \"" << multigridAlgo << "\". Please consult User's Guide.");
#ifndef HAVE_MUELU_MATLAB
  TEUCHOS_TEST_FOR_EXCEPTION(multigridAlgo == "matlab", Exceptions::RuntimeError,
                             "Cannot use matlab for multigrid algorithm - MueLu was not configured with MATLAB support.");
#endif
#ifndef HAVE_MUELU_INTREPID2
  TEUCHOS_TEST_FOR_EXCEPTION(multigridAlgo == "pcoarsen", Exceptions::RuntimeError,
                             "Cannot use IntrepidPCoarsen prolongator factory - MueLu was not configured with Intrepid support.");
#endif

  // Only some combinations of reuse and multigrid algorithms are tested, all
  // other are considered invalid at the moment
  if (reuseType == "none" || reuseType == "S" || reuseType == "RP" || reuseType == "RAP") {
    // This works for all kinds of multigrid algorithms

  } else if (reuseType == "tP" && (multigridAlgo != "sa" && multigridAlgo != "unsmoothed")) {
    reuseType = "none";
    this->GetOStream(Warnings0) << "Ignoring \"tP\" reuse option as it is only compatible with \"sa\", "
                                   "or \"unsmoothed\" multigrid algorithms"
                                << std::endl;

  } else if (reuseType == "emin" && multigridAlgo != "emin") {
    reuseType = "none";
    this->GetOStream(Warnings0) << "Ignoring \"emin\" reuse option it is only compatible with "
                                   "\"emin\" multigrid algorithm"
                                << std::endl;
  }

  // == Non-serializable data ===
  // Check both the parameter and the type
  bool have_userP = false;
  if (paramList.isParameter("P") && !paramList.get<RCP<Matrix> >("P").is_null())
    have_userP = true;

  // === Coarse solver ===
  UpdateFactoryManager_CoarseSolvers(paramList, defaultList, manager, levelID, keeps);

  // == Smoothers ==
  UpdateFactoryManager_Smoothers(paramList, defaultList, manager, levelID, keeps);

  // === BlockNumber ===
  if (levelID == 0)
    UpdateFactoryManager_BlockNumber(paramList, defaultList, manager, levelID, keeps);

  // === Aggregation ===
  if (multigridAlgo == "unsmoothed reitzinger" || multigridAlgo == "smoothed reitzinger")
    UpdateFactoryManager_Reitzinger(paramList, defaultList, manager, levelID, keeps);
  else
    UpdateFactoryManager_Aggregation_TentativeP(paramList, defaultList, manager, levelID, keeps);

  // === Nullspace ===
  RCP<Factory> nullSpaceFactory;  // Cache thcAN is guy for the combination of semi-coarsening & repartitioning
  UpdateFactoryManager_Nullspace(paramList, defaultList, manager, levelID, keeps, nullSpaceFactory);

  // === Prolongation ===
  // NOTE: None of the UpdateFactoryManager routines called here check the
  // multigridAlgo. This is intentional, to allow for reuse of components
  // underneath. Thus, the multigridAlgo was checked in the beginning of the
  // function.
  if (have_userP) {
    // User prolongator
    manager.SetFactory("P", NoFactory::getRCP());

  } else if (multigridAlgo == "unsmoothed" || multigridAlgo == "unsmoothed reitzinger") {
    // Unsmoothed aggregation
    manager.SetFactory("P", manager.GetFactory("Ptent"));

  } else if (multigridAlgo == "classical") {
    // Classical AMG
    manager.SetFactory("P", manager.GetFactory("Ptent"));

  } else if (multigridAlgo == "sa" || multigridAlgo == "smoothed reitzinger") {
    // Smoothed aggregation
    UpdateFactoryManager_SA(paramList, defaultList, manager, levelID, keeps);

  } else if (multigridAlgo == "emin") {
    // Energy minimization
    UpdateFactoryManager_Emin(paramList, defaultList, manager, levelID, keeps);

  } else if (multigridAlgo == "replicate") {
    UpdateFactoryManager_Replicate(paramList, defaultList, manager, levelID, keeps);

  } else if (multigridAlgo == "combine") {
    UpdateFactoryManager_Combine(paramList, defaultList, manager, levelID, keeps);

  } else if (multigridAlgo == "pg") {
    // Petrov-Galerkin
    UpdateFactoryManager_PG(paramList, defaultList, manager, levelID, keeps);

  } else if (multigridAlgo == "matlab") {
    // Matlab Coarsneing
    UpdateFactoryManager_Matlab(paramList, defaultList, manager, levelID, keeps);

  } else if (multigridAlgo == "pcoarsen") {
    // P-Coarsening
    UpdateFactoryManager_PCoarsen(paramList, defaultList, manager, levelID, keeps);
  }

  // === Semi-coarsening ===
  UpdateFactoryManager_SemiCoarsen(paramList, defaultList, manager, levelID, keeps);

  // === Restriction ===
  UpdateFactoryManager_Restriction(paramList, defaultList, manager, levelID, keeps);

  // === RAP ===
  UpdateFactoryManager_RAP(paramList, defaultList, manager, levelID, keeps);

  // == BlockNumber Transfer ==
  UpdateFactoryManager_LocalOrdinalTransfer("BlockNumber", multigridAlgo, paramList, defaultList, manager, levelID, keeps);

  // === Coordinates ===
  UpdateFactoryManager_Coordinates(paramList, defaultList, manager, levelID, keeps);

  // === Material ===
  UpdateFactoryManager_Material(paramList, defaultList, manager, levelID, keeps);

  // === Pre-Repartition Keeps for Reuse ===
  if ((reuseType == "RP" || reuseType == "RAP" || reuseType == "full") && levelID)
    keeps.push_back(keep_pair("Nullspace", manager.GetFactory("Nullspace").get()));

  if (reuseType == "RP" && levelID) {
    keeps.push_back(keep_pair("P", manager.GetFactory("P").get()));
    if (!this->implicitTranspose_)
      keeps.push_back(keep_pair("R", manager.GetFactory("R").get()));
  }
  if ((reuseType == "tP" || reuseType == "RP" || reuseType == "emin") && useCoordinates_ && levelID)
    keeps.push_back(keep_pair("Coordinates", manager.GetFactory("Coordinates").get()));

  // === Repartitioning ===
  UpdateFactoryManager_Repartition(paramList, defaultList, manager, levelID, keeps, nullSpaceFactory);

  // === Lower precision transfers ===
  UpdateFactoryManager_LowPrecision(paramList, defaultList, manager, levelID, keeps);

  // === Final Keeps for Reuse ===
  if ((reuseType == "RAP" || reuseType == "full") && levelID) {
    keeps.push_back(keep_pair("P", manager.GetFactory("P").get()));
    if (!this->implicitTranspose_)
      keeps.push_back(keep_pair("R", manager.GetFactory("R").get()));
    keeps.push_back(keep_pair("A", manager.GetFactory("A").get()));
  }

  // In case you ever want to inspect the FactoryManager as it is generated for each level
  /*std::cout<<"*** Factory Manager on level "<<levelID<<" ***"<<std::endl;
    manager.Print(); */
}

// =====================================================================================================
// ========================================= Smoothers =================================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_Smoothers(ParameterList& paramList, const ParameterList& defaultList,
                                   FactoryManager& manager, int levelID, std::vector<keep_pair>& keeps) const {
  MUELU_SET_VAR_2LIST(paramList, defaultList, "multigrid algorithm", std::string, multigridAlgo);
  MUELU_SET_VAR_2LIST(paramList, defaultList, "reuse: type", std::string, reuseType);
  bool useMaxAbsDiagonalScaling = false;
  if (defaultList.isParameter("sa: use rowsumabs diagonal scaling"))
    useMaxAbsDiagonalScaling = defaultList.get<bool>("sa: use rowsumabs diagonal scaling");

  // === Smoothing ===
  // FIXME: should custom smoother check default list too?
  bool isCustomSmoother =
      paramList.isParameter("smoother: pre or post") ||
      paramList.isParameter("smoother: type") || paramList.isParameter("smoother: pre type") || paramList.isParameter("smoother: post type") ||
      paramList.isSublist("smoother: params") || paramList.isSublist("smoother: pre params") || paramList.isSublist("smoother: post params") ||
      paramList.isParameter("smoother: sweeps") || paramList.isParameter("smoother: pre sweeps") || paramList.isParameter("smoother: post sweeps") ||
      paramList.isParameter("smoother: overlap") || paramList.isParameter("smoother: pre overlap") || paramList.isParameter("smoother: post overlap");

  MUELU_SET_VAR_2LIST(paramList, defaultList, "smoother: pre or post", std::string, PreOrPost);
  if (PreOrPost == "none") {
    manager.SetFactory("Smoother", Teuchos::null);

  } else if (isCustomSmoother) {
    // FIXME: get default values from the factory
    // NOTE: none of the smoothers at the moment use parameter validation framework, so we
    // cannot get the default values from it.
#define TEST_MUTUALLY_EXCLUSIVE(arg1, arg2)                                                \
  TEUCHOS_TEST_FOR_EXCEPTION(paramList.isParameter(#arg1) && paramList.isParameter(#arg2), \
                             Exceptions::InvalidArgument, "You cannot specify both \"" #arg1 "\" and \"" #arg2 "\"");
#define TEST_MUTUALLY_EXCLUSIVE_S(arg1, arg2)                                          \
  TEUCHOS_TEST_FOR_EXCEPTION(paramList.isSublist(#arg1) && paramList.isSublist(#arg2), \
                             Exceptions::InvalidArgument, "You cannot specify both \"" #arg1 "\" and \"" #arg2 "\"");

    TEST_MUTUALLY_EXCLUSIVE("smoother: type", "smoother: pre type");
    TEST_MUTUALLY_EXCLUSIVE("smoother: type", "smoother: post type");
    TEST_MUTUALLY_EXCLUSIVE("smoother: sweeps", "smoother: pre sweeps");
    TEST_MUTUALLY_EXCLUSIVE("smoother: sweeps", "smoother: post sweeps");
    TEST_MUTUALLY_EXCLUSIVE("smoother: overlap", "smoother: pre overlap");
    TEST_MUTUALLY_EXCLUSIVE("smoother: overlap", "smoother: post overlap");
    TEST_MUTUALLY_EXCLUSIVE_S("smoother: params", "smoother: pre params");
    TEST_MUTUALLY_EXCLUSIVE_S("smoother: params", "smoother: post params");
    TEUCHOS_TEST_FOR_EXCEPTION(PreOrPost == "both" && (paramList.isParameter("smoother: pre type") != paramList.isParameter("smoother: post type")),
                               Exceptions::InvalidArgument, "You must specify both \"smoother: pre type\" and \"smoother: post type\"");

    // Default values
    int overlap = 0;
    ParameterList defaultSmootherParams;
    defaultSmootherParams.set("relaxation: type", "Symmetric Gauss-Seidel");
    defaultSmootherParams.set("relaxation: sweeps", Teuchos::OrdinalTraits<LO>::one());
    defaultSmootherParams.set("relaxation: damping factor", Teuchos::ScalarTraits<Scalar>::one());

    RCP<SmootherFactory> preSmoother = Teuchos::null, postSmoother = Teuchos::null;
    std::string preSmootherType, postSmootherType;
    ParameterList preSmootherParams, postSmootherParams;

    if (paramList.isParameter("smoother: overlap"))
      overlap = paramList.get<int>("smoother: overlap");

    if (PreOrPost == "pre" || PreOrPost == "both") {
      if (paramList.isParameter("smoother: pre type")) {
        preSmootherType = paramList.get<std::string>("smoother: pre type");
      } else {
        MUELU_SET_VAR_2LIST(paramList, defaultList, "smoother: type", std::string, preSmootherTypeTmp);
        preSmootherType = preSmootherTypeTmp;
      }
      if (paramList.isParameter("smoother: pre overlap"))
        overlap = paramList.get<int>("smoother: pre overlap");

      if (paramList.isSublist("smoother: pre params"))
        preSmootherParams = paramList.sublist("smoother: pre params");
      else if (paramList.isSublist("smoother: params"))
        preSmootherParams = paramList.sublist("smoother: params");
      else if (defaultList.isSublist("smoother: params"))
        preSmootherParams = defaultList.sublist("smoother: params");
      else if (preSmootherType == "RELAXATION")
        preSmootherParams = defaultSmootherParams;

      if (preSmootherType == "CHEBYSHEV" && useMaxAbsDiagonalScaling)
        preSmootherParams.set("chebyshev: use rowsumabs diagonal scaling", true);

#ifdef HAVE_MUELU_INTREPID2
      // Propagate P-coarsening for Topo smoothing
      if (multigridAlgo == "pcoarsen" && preSmootherType == "TOPOLOGICAL" &&
          defaultList.isParameter("pcoarsen: schedule") && defaultList.isParameter("pcoarsen: element")) {
        // P-Coarsening by schedule (new interface)
        // NOTE: levelID represents the *coarse* level in this case
        auto pcoarsen_schedule = Teuchos::getArrayFromStringParameter<int>(defaultList, "pcoarsen: schedule");
        auto pcoarsen_element  = defaultList.get<std::string>("pcoarsen: element");

        if (levelID < (int)pcoarsen_schedule.size()) {
          // Topo info for P-Coarsening
          auto lo = pcoarsen_element + std::to_string(pcoarsen_schedule[levelID]);
          preSmootherParams.set("pcoarsen: hi basis", lo);
        }
      }
#endif

#ifdef HAVE_MUELU_MATLAB
      if (preSmootherType == "matlab")
        preSmoother = rcp(new SmootherFactory(rcp(new MatlabSmoother(preSmootherParams))));
      else
#endif
        preSmoother = rcp(new SmootherFactory(rcp(new TrilinosSmoother(preSmootherType, preSmootherParams, overlap))));
    }

    if (PreOrPost == "post" || PreOrPost == "both") {
      if (paramList.isParameter("smoother: post type"))
        postSmootherType = paramList.get<std::string>("smoother: post type");
      else {
        MUELU_SET_VAR_2LIST(paramList, defaultList, "smoother: type", std::string, postSmootherTypeTmp);
        postSmootherType = postSmootherTypeTmp;
      }

      if (paramList.isSublist("smoother: post params"))
        postSmootherParams = paramList.sublist("smoother: post params");
      else if (paramList.isSublist("smoother: params"))
        postSmootherParams = paramList.sublist("smoother: params");
      else if (defaultList.isSublist("smoother: params"))
        postSmootherParams = defaultList.sublist("smoother: params");
      else if (postSmootherType == "RELAXATION")
        postSmootherParams = defaultSmootherParams;
      if (paramList.isParameter("smoother: post overlap"))
        overlap = paramList.get<int>("smoother: post overlap");

      if (postSmootherType == "CHEBYSHEV" && useMaxAbsDiagonalScaling)
        postSmootherParams.set("chebyshev: use rowsumabs diagonal scaling", true);

      if (postSmootherType == preSmootherType && areSame(preSmootherParams, postSmootherParams))
        postSmoother = preSmoother;
      else {
#ifdef HAVE_MUELU_INTREPID2
        // Propagate P-coarsening for Topo smoothing
        if (multigridAlgo == "pcoarsen" && preSmootherType == "TOPOLOGICAL" &&
            defaultList.isParameter("pcoarsen: schedule") && defaultList.isParameter("pcoarsen: element")) {
          // P-Coarsening by schedule (new interface)
          // NOTE: levelID represents the *coarse* level in this case
          auto pcoarsen_schedule = Teuchos::getArrayFromStringParameter<int>(defaultList, "pcoarsen: schedule");
          auto pcoarsen_element  = defaultList.get<std::string>("pcoarsen: element");

          if (levelID < (int)pcoarsen_schedule.size()) {
            // Topo info for P-Coarsening
            auto lo = pcoarsen_element + std::to_string(pcoarsen_schedule[levelID]);
            postSmootherParams.set("pcoarsen: hi basis", lo);
          }
        }
#endif

#ifdef HAVE_MUELU_MATLAB
        if (postSmootherType == "matlab")
          postSmoother = rcp(new SmootherFactory(rcp(new MatlabSmoother(postSmootherParams))));
        else
#endif
          postSmoother = rcp(new SmootherFactory(rcp(new TrilinosSmoother(postSmootherType, postSmootherParams, overlap))));
      }
    }

    if (preSmoother == postSmoother)
      manager.SetFactory("Smoother", preSmoother);
    else {
      manager.SetFactory("PreSmoother", preSmoother);
      manager.SetFactory("PostSmoother", postSmoother);
    }
  }

  // The first clause is not necessary, but it is here for clarity Smoothers
  // are reused if smoother explicitly said to reuse them, or if any other
  // reuse option is enabled
  bool reuseSmoothers = (reuseType == "S" || reuseType != "none");
  if (reuseSmoothers) {
    auto preSmootherFactory = rcp_const_cast<Factory>(rcp_dynamic_cast<const Factory>(manager.GetFactory("PreSmoother")));

    if (preSmootherFactory != Teuchos::null) {
      ParameterList postSmootherFactoryParams;
      postSmootherFactoryParams.set("keep smoother data", true);
      preSmootherFactory->SetParameterList(postSmootherFactoryParams);

      keeps.push_back(keep_pair("PreSmoother data", preSmootherFactory.get()));
    }

    auto postSmootherFactory = rcp_const_cast<Factory>(rcp_dynamic_cast<const Factory>(manager.GetFactory("PostSmoother")));
    if (postSmootherFactory != Teuchos::null) {
      ParameterList postSmootherFactoryParams;
      postSmootherFactoryParams.set("keep smoother data", true);
      postSmootherFactory->SetParameterList(postSmootherFactoryParams);

      keeps.push_back(keep_pair("PostSmoother data", postSmootherFactory.get()));
    }

    auto coarseFactory = rcp_const_cast<Factory>(rcp_dynamic_cast<const Factory>(manager.GetFactory("CoarseSolver")));
    if (coarseFactory != Teuchos::null) {
      ParameterList coarseFactoryParams;
      coarseFactoryParams.set("keep smoother data", true);
      coarseFactory->SetParameterList(coarseFactoryParams);

      keeps.push_back(keep_pair("PreSmoother data", coarseFactory.get()));
    }
  }

  if ((reuseType == "RAP" && levelID) || (reuseType == "full")) {
    // The difference between "RAP" and "full" is keeping smoothers. However,
    // as in both cases we keep coarse matrices, we do not need to update
    // coarse smoothers. On the other hand, if a user changes fine level
    // matrix, "RAP" would update the fine level smoother, while "full" would
    // not
    keeps.push_back(keep_pair("PreSmoother", manager.GetFactory("PreSmoother").get()));
    keeps.push_back(keep_pair("PostSmoother", manager.GetFactory("PostSmoother").get()));

    // We do keep_pair("PreSmoother", manager.GetFactory("CoarseSolver").get())
    // as the coarse solver factory is in fact a smoothing factory, so the
    // only pieces of data it generates are PreSmoother and PostSmoother
    keeps.push_back(keep_pair("PreSmoother", manager.GetFactory("CoarseSolver").get()));
  }
}

// =====================================================================================================
// ====================================== Coarse Solvers ===============================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_CoarseSolvers(ParameterList& paramList, const ParameterList& defaultList,
                                       FactoryManager& manager, int /* levelID */, std::vector<keep_pair>& /* keeps */) const {
  // FIXME: should custom coarse solver check default list too?
  bool isCustomCoarseSolver =
      paramList.isParameter("coarse: type") ||
      paramList.isParameter("coarse: params");
  if (MUELU_TEST_PARAM_2LIST(paramList, defaultList, "coarse: type", std::string, "none")) {
    manager.SetFactory("CoarseSolver", Teuchos::null);

  } else if (isCustomCoarseSolver) {
    // FIXME: get default values from the factory
    // NOTE: none of the smoothers at the moment use parameter validation framework, so we
    // cannot get the default values from it.
    MUELU_SET_VAR_2LIST(paramList, defaultList, "coarse: type", std::string, coarseType);

    int overlap = 0;
    if (paramList.isParameter("coarse: overlap"))
      overlap = paramList.get<int>("coarse: overlap");

    ParameterList coarseParams;
    if (paramList.isSublist("coarse: params"))
      coarseParams = paramList.sublist("coarse: params");
    else if (defaultList.isSublist("coarse: params"))
      coarseParams = defaultList.sublist("coarse: params");

    using strings = std::unordered_set<std::string>;

    RCP<SmootherPrototype> coarseSmoother;
    // TODO: this is not a proper place to check. If we consider direct solver to be a special
    // case of smoother, we would like to unify Amesos and Ifpack2 smoothers in src/Smoothers, and
    // have a single factory responsible for those. Then, this check would belong there.
    if (strings({"RELAXATION", "CHEBYSHEV", "ILUT", "ILU", "RILUK", "SCHWARZ", "Amesos",
                 "BLOCK RELAXATION", "BLOCK_RELAXATION", "BLOCKRELAXATION",
                 "SPARSE BLOCK RELAXATION", "SPARSE_BLOCK_RELAXATION", "SPARSEBLOCKRELAXATION",
                 "LINESMOOTHING_BANDEDRELAXATION", "LINESMOOTHING_BANDED_RELAXATION", "LINESMOOTHING_BANDED RELAXATION",
                 "LINESMOOTHING_TRIDIRELAXATION", "LINESMOOTHING_TRIDI_RELAXATION", "LINESMOOTHING_TRIDI RELAXATION",
                 "LINESMOOTHING_TRIDIAGONALRELAXATION", "LINESMOOTHING_TRIDIAGONAL_RELAXATION", "LINESMOOTHING_TRIDIAGONAL RELAXATION",
                 "TOPOLOGICAL", "FAST_ILU", "FAST_IC", "FAST_ILDL", "HIPTMAIR"})
            .count(coarseType)) {
      coarseSmoother = rcp(new TrilinosSmoother(coarseType, coarseParams, overlap));
    } else {
#ifdef HAVE_MUELU_MATLAB
      if (coarseType == "matlab")
        coarseSmoother = rcp(new MatlabSmoother(coarseParams));
      else
#endif
        coarseSmoother = rcp(new DirectSolver(coarseType, coarseParams));
    }

    manager.SetFactory("CoarseSolver", rcp(new SmootherFactory(coarseSmoother)));
  }
}

// =====================================================================================================
// ========================================= TentativeP=================================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_Reitzinger(ParameterList& paramList, const ParameterList& defaultList,
                                    FactoryManager& manager, int levelID, std::vector<keep_pair>& keeps) const {
  ParameterList rParams;
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: enable", bool, rParams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: use subcommunicators", bool, rParams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "tentative: constant column sums", bool, rParams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "tentative: calculate qr", bool, rParams);

  RCP<Factory> rFactory = rcp(new ReitzingerPFactory());
  rFactory->SetParameterList(rParams);

  // These are all going to be user provided, so NoFactory
  rFactory->SetFactory("Pnodal", NoFactory::getRCP());
  rFactory->SetFactory("NodeAggMatrix", NoFactory::getRCP());
  // rFactory->SetFactory("NodeMatrix", NoFactory::getRCP());

  if (levelID > 1)
    rFactory->SetFactory("D0", this->GetFactoryManager(levelID - 1)->GetFactory("D0"));
  else
    rFactory->SetFactory("D0", NoFactory::getRCP());

  manager.SetFactory("Ptent", rFactory);
  manager.SetFactory("D0", rFactory);
  manager.SetFactory("InPlaceMap", rFactory);
}

// =====================================================================================================
// ========================================= TentativeP=================================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_Aggregation_TentativeP(ParameterList& paramList, const ParameterList& defaultList,
                                                FactoryManager& manager, int levelID, std::vector<keep_pair>& keeps) const {
  using strings = std::unordered_set<std::string>;

  MUELU_SET_VAR_2LIST(paramList, defaultList, "reuse: type", std::string, reuseType);

  MUELU_SET_VAR_2LIST(paramList, defaultList, "aggregation: type", std::string, aggType);
  TEUCHOS_TEST_FOR_EXCEPTION(!strings({"uncoupled", "coupled", "brick", "matlab", "notay", "classical"}).count(aggType),
                             Exceptions::RuntimeError, "Unknown aggregation algorithm: \"" << aggType << "\". Please consult User's Guide.");

  // Only doing this for classical because otherwise, the gold tests get broken badly
  RCP<AmalgamationFactory> amalgFact;
  if (aggType == "classical") {
    amalgFact = rcp(new AmalgamationFactory());
    manager.SetFactory("UnAmalgamationInfo", amalgFact);
  }

  // Aggregation graph
  RCP<Factory> dropFactory;

  if (MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: drop scheme", std::string, "matlab")) {
#ifdef HAVE_MUELU_MATLAB
    dropFactory             = rcp(new SingleLevelMatlabFactory());
    ParameterList socParams = paramList.sublist("strength-of-connection: params");
    dropFactory->SetParameterList(socParams);
#else
    throw std::runtime_error("Cannot use MATLAB evolutionary strength-of-connection - MueLu was not configured with MATLAB support.");
#endif
  } else if (MUELU_TEST_PARAM_2LIST(paramList, paramList, "aggregation: drop scheme", std::string, "unsupported vector smoothing")) {
    dropFactory = rcp(new MueLu::SmooVecCoalesceDropFactory<SC, LO, GO, NO>());
    ParameterList dropParams;
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: drop scheme", std::string, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: block diagonal: interleaved blocksize", int, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: number of random vectors", int, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: number of times to pre or post smooth", int, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: penalty parameters", Teuchos::Array<double>, dropParams);
    dropFactory->SetParameterList(dropParams);
  } else {
    MUELU_KOKKOS_FACTORY_NO_DECL(dropFactory, CoalesceDropFactory, CoalesceDropFactory_kokkos);
    ParameterList dropParams;
    if (!rcp_dynamic_cast<CoalesceDropFactory>(dropFactory).is_null())
      dropParams.set("lightweight wrap", true);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: drop scheme", std::string, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: row sum drop tol", double, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: block diagonal: interleaved blocksize", int, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: drop tol", double, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: use ml scaling of drop tol", bool, dropParams);

    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: Dirichlet threshold", double, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: greedy Dirichlet", bool, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: distance laplacian algo", std::string, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: distance laplacian metric", std::string, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: classical algo", std::string, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: distance laplacian directional weights", Teuchos::Array<double>, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: coloring: localize color graph", bool, dropParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: dropping may create Dirichlet", bool, dropParams);
    if (useKokkos_) {
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: use lumping", bool, dropParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: reuse graph", bool, dropParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: reuse eigenvalue", bool, dropParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: use root stencil", bool, dropParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: Dirichlet threshold", double, dropParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: use spread lumping", bool, dropParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: spread lumping diag dom growth factor", double, dropParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: spread lumping diag dom cap", double, dropParams);
    }

    if (!amalgFact.is_null())
      dropFactory->SetFactory("UnAmalgamationInfo", manager.GetFactory("UnAmalgamationInfo"));

    if (dropParams.isParameter("aggregation: drop scheme")) {
      std::string drop_scheme = dropParams.get<std::string>("aggregation: drop scheme");
      if (drop_scheme == "block diagonal colored signed classical")
        manager.SetFactory("Coloring Graph", dropFactory);
      if (drop_scheme.find("block diagonal") != std::string::npos || drop_scheme == "signed classical") {
        if (levelID > 0)
          dropFactory->SetFactory("BlockNumber", this->GetFactoryManager(levelID - 1)->GetFactory("BlockNumber"));
        else
          dropFactory->SetFactory("BlockNumber", manager.GetFactory("BlockNumber"));
      }
    }

    dropFactory->SetParameterList(dropParams);
  }
  manager.SetFactory("Graph", dropFactory);

// Aggregation scheme
#ifndef HAVE_MUELU_MATLAB
  if (aggType == "matlab")
    throw std::runtime_error("Cannot use MATLAB aggregation - MueLu was not configured with MATLAB support.");
#endif
  RCP<Factory> aggFactory;
  if (aggType == "uncoupled") {
    aggFactory = rcp(new UncoupledAggregationFactory());
    ParameterList aggParams;
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: mode", std::string, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: ordering", std::string, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: min agg size", int, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: max agg size", int, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: max selected neighbors", int, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: backend", std::string, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: phase 1 algorithm", std::string, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: deterministic", bool, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: coloring algorithm", std::string, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: enable phase 1", bool, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: enable phase 2a", bool, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: enable phase 2b", bool, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: enable phase 3", bool, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: match ML phase1", bool, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: match ML phase2a", bool, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: match ML phase2b", bool, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: phase2a agg factor", double, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: preserve Dirichlet points", bool, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: error on nodes with no on-rank neighbors", bool, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: phase3 avoid singletons", bool, aggParams);
    aggFactory->SetParameterList(aggParams);
    // make sure that the aggregation factory has all necessary data
    aggFactory->SetFactory("DofsPerNode", manager.GetFactory("Graph"));
    aggFactory->SetFactory("Graph", manager.GetFactory("Graph"));
    //      aggFactory->SetFactory("UnAmalgamationInfo", manager.GetFactory("UnAmalgamationInfo"));

  } else if (aggType == "brick") {
    aggFactory = rcp(new BrickAggregationFactory());
    ParameterList aggParams;
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: brick x size", int, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: brick y size", int, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: brick z size", int, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: brick x Dirichlet", bool, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: brick y Dirichlet", bool, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: brick z Dirichlet", bool, aggParams);
    aggFactory->SetParameterList(aggParams);

    // Unlike other factories, BrickAggregationFactory makes the Graph/DofsPerNode itself
    manager.SetFactory("Graph", aggFactory);
    manager.SetFactory("DofsPerNode", aggFactory);
    manager.SetFactory("Filtering", aggFactory);
    if (levelID > 1) {
      // We check for levelID > 0, as in the interpreter aggFactory for
      // levelID really corresponds to level 0. Managers are clunky, as they
      // contain factories for two different levels
      aggFactory->SetFactory("Coordinates", this->GetFactoryManager(levelID - 1)->GetFactory("Coordinates"));
    }
  } else if (aggType == "classical") {
    // Map and coloring
    RCP<Factory> mapFact = rcp(new ClassicalMapFactory());
    ParameterList mapParams;
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: deterministic", bool, mapParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: coloring algorithm", std::string, mapParams);

    ParameterList tempParams;
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: drop scheme", std::string, tempParams);
    std::string drop_algo = tempParams.get<std::string>("aggregation: drop scheme");
    if (drop_algo == "block diagonal colored signed classical") {
      mapParams.set("aggregation: coloring: use color graph", true);
      mapFact->SetFactory("Coloring Graph", manager.GetFactory("Coloring Graph"));
    }
    mapFact->SetParameterList(mapParams);
    mapFact->SetFactory("Graph", manager.GetFactory("Graph"));
    mapFact->SetFactory("UnAmalgamationInfo", manager.GetFactory("UnAmalgamationInfo"));

    manager.SetFactory("FC Splitting", mapFact);
    manager.SetFactory("CoarseMap", mapFact);

    aggFactory = rcp(new ClassicalPFactory());
    ParameterList aggParams;
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: classical scheme", std::string, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: drop scheme", std::string, aggParams);
    aggFactory->SetParameterList(aggParams);
    aggFactory->SetFactory("FC Splitting", manager.GetFactory("FC Splitting"));
    aggFactory->SetFactory("CoarseMap", manager.GetFactory("CoarseMap"));
    aggFactory->SetFactory("DofsPerNode", manager.GetFactory("Graph"));
    aggFactory->SetFactory("Graph", manager.GetFactory("Graph"));

    if (drop_algo.find("block diagonal") != std::string::npos || drop_algo == "signed classical") {
      if (levelID > 0)
        aggFactory->SetFactory("BlockNumber", this->GetFactoryManager(levelID - 1)->GetFactory("BlockNumber"));
      else
        aggFactory->SetFactory("BlockNumber", manager.GetFactory("BlockNumber"));
    }

    // Now we short-circuit, because we neither need nor want TentativePFactory here
    manager.SetFactory("Ptent", aggFactory);
    manager.SetFactory("P Graph", aggFactory);

    if (reuseType == "tP" && levelID) {
      //        keeps.push_back(keep_pair("Nullspace", Ptent.get()));
      keeps.push_back(keep_pair("Ptent", aggFactory.get()));
    }
    return;
  } else if (aggType == "notay") {
    aggFactory = rcp(new NotayAggregationFactory());
    ParameterList aggParams;
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: pairwise: size", int, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: pairwise: tie threshold", double, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: Dirichlet threshold", double, aggParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: ordering", std::string, aggParams);
    aggFactory->SetParameterList(aggParams);
    aggFactory->SetFactory("DofsPerNode", manager.GetFactory("Graph"));
    aggFactory->SetFactory("Graph", manager.GetFactory("Graph"));
  }
#ifdef HAVE_MUELU_MATLAB
  else if (aggType == "matlab") {
    ParameterList aggParams = paramList.sublist("aggregation: params");
    aggFactory              = rcp(new SingleLevelMatlabFactory());
    aggFactory->SetParameterList(aggParams);
  }
#endif

  manager.SetFactory("Aggregates", aggFactory);

  // Coarse map
  RCP<Factory> coarseMap = rcp(new CoarseMapFactory());
  coarseMap->SetFactory("Aggregates", manager.GetFactory("Aggregates"));
  manager.SetFactory("CoarseMap", coarseMap);

  // Tentative P
  MUELU_KOKKOS_FACTORY(Ptent, TentativePFactory, TentativePFactory_kokkos);
  ParameterList ptentParams;
  if (paramList.isSublist("matrixmatrix: kernel params"))
    ptentParams.sublist("matrixmatrix: kernel params", false) = paramList.sublist("matrixmatrix: kernel params");
  if (defaultList.isSublist("matrixmatrix: kernel params"))
    ptentParams.sublist("matrixmatrix: kernel params", false) = defaultList.sublist("matrixmatrix: kernel params");
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "tentative: calculate qr", bool, ptentParams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "tentative: build coarse coordinates", bool, ptentParams);
  Ptent->SetParameterList(ptentParams);
  Ptent->SetFactory("Aggregates", manager.GetFactory("Aggregates"));
  Ptent->SetFactory("CoarseMap", manager.GetFactory("CoarseMap"));
  manager.SetFactory("Ptent", Ptent);

  if (reuseType == "tP" && levelID) {
    keeps.push_back(keep_pair("Nullspace", Ptent.get()));
    keeps.push_back(keep_pair("P", Ptent.get()));
  }
}

// =====================================================================================================
// ============================================ RAP ====================================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_RAP(ParameterList& paramList, const ParameterList& defaultList, FactoryManager& manager,
                             int levelID, std::vector<keep_pair>& keeps) const {
  if (paramList.isParameter("A") && !paramList.get<RCP<Matrix> >("A").is_null()) {
    // We have user matrix A
    manager.SetFactory("A", NoFactory::getRCP());
    return;
  }

  ParameterList RAPparams;

  RCP<RAPFactory> RAP;
  RCP<RAPShiftFactory> RAPs;
  // Allow for Galerkin or shifted RAP
  // FIXME: Should this not be some form of MUELU_SET_VAR_2LIST?
  std::string alg = paramList.get("rap: algorithm", "galerkin");
  if (alg == "shift" || alg == "non-galerkin") {
    RAPs = rcp(new RAPShiftFactory());
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "rap: shift", double, RAPparams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "rap: shift diagonal M", bool, RAPparams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "rap: shift low storage", bool, RAPparams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "rap: shift array", Teuchos::Array<double>, RAPparams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "rap: cfl array", Teuchos::Array<double>, RAPparams);

  } else {
    RAP = rcp(new RAPFactory());
  }

  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "rap: relative diagonal floor", Teuchos::Array<double>, RAPparams);

  if (paramList.isSublist("matrixmatrix: kernel params"))
    RAPparams.sublist("matrixmatrix: kernel params", false) = paramList.sublist("matrixmatrix: kernel params");
  if (defaultList.isSublist("matrixmatrix: kernel params"))
    RAPparams.sublist("matrixmatrix: kernel params", false) = defaultList.sublist("matrixmatrix: kernel params");
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "transpose: use implicit", bool, RAPparams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "rap: fix zero diagonals", bool, RAPparams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "rap: fix zero diagonals threshold", double, RAPparams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "rap: fix zero diagonals replacement", Scalar, RAPparams);

  // if "rap: triple product" has not been set and algorithm is "unsmoothed" switch triple product on
  if (!paramList.isParameter("rap: triple product") &&
      paramList.isType<std::string>("multigrid algorithm") &&
      paramList.get<std::string>("multigrid algorithm") == "unsmoothed")
    paramList.set("rap: triple product", true);
  else
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "rap: triple product", bool, RAPparams);

  try {
    if (paramList.isParameter("aggregation: allow empty prolongator columns")) {
      RAPparams.set("CheckMainDiagonal", paramList.get<bool>("aggregation: allow empty prolongator columns"));
      RAPparams.set("RepairMainDiagonal", paramList.get<bool>("aggregation: allow empty prolongator columns"));
    } else if (defaultList.isParameter("aggregation: allow empty prolongator columns")) {
      RAPparams.set("CheckMainDiagonal", defaultList.get<bool>("aggregation: allow empty prolongator columns"));
      RAPparams.set("RepairMainDiagonal", defaultList.get<bool>("aggregation: allow empty prolongator columns"));
    }

  } catch (Teuchos::Exceptions::InvalidParameterType&) {
    TEUCHOS_TEST_FOR_EXCEPTION_PURE_MSG(true, Teuchos::Exceptions::InvalidParameterType,
                                        "Error: parameter \"aggregation: allow empty prolongator columns\" must be of type " << Teuchos::TypeNameTraits<bool>::name());
  }

  if (!RAP.is_null()) {
    RAP->SetParameterList(RAPparams);
    RAP->SetFactory("P", manager.GetFactory("P"));
  } else {
    RAPs->SetParameterList(RAPparams);
    RAPs->SetFactory("P", manager.GetFactory("P"));
  }

  if (!this->implicitTranspose_) {
    if (!RAP.is_null())
      RAP->SetFactory("R", manager.GetFactory("R"));
    else
      RAPs->SetFactory("R", manager.GetFactory("R"));
  }

  // Matrix analysis
  if (MUELU_TEST_PARAM_2LIST(paramList, defaultList, "matrix: compute analysis", bool, true)) {
    RCP<Factory> matrixAnalysisFact = rcp(new MatrixAnalysisFactory());

    if (!RAP.is_null())
      RAP->AddTransferFactory(matrixAnalysisFact);
    else
      RAPs->AddTransferFactory(matrixAnalysisFact);
  }

  // Aggregate qualities
  if (MUELU_TEST_PARAM_2LIST(paramList, defaultList, "aggregation: compute aggregate qualities", bool, true)) {
    RCP<Factory> aggQualityFact = rcp(new AggregateQualityEstimateFactory());
    ParameterList aggQualityParams;
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregate qualities: good aggregate threshold", double, aggQualityParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregate qualities: file output", bool, aggQualityParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregate qualities: file base", std::string, aggQualityParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregate qualities: check symmetry", bool, aggQualityParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregate qualities: algorithm", std::string, aggQualityParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregate qualities: zero threshold", double, aggQualityParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregate qualities: percentiles", Teuchos::Array<double>, aggQualityParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregate qualities: mode", std::string, aggQualityParams);
    aggQualityFact->SetParameterList(aggQualityParams);
    aggQualityFact->SetFactory("Aggregates", manager.GetFactory("Aggregates"));
    aggQualityFact->SetFactory("CoarseMap", manager.GetFactory("CoarseMap"));
    manager.SetFactory("AggregateQualities", aggQualityFact);

    if (!RAP.is_null())
      RAP->AddTransferFactory(aggQualityFact);
    else
      RAPs->AddTransferFactory(aggQualityFact);
  }

  if (MUELU_TEST_PARAM_2LIST(paramList, defaultList, "aggregation: export visualization data", bool, true)) {
    RCP<AggregationExportFactory> aggExport = rcp(new AggregationExportFactory());
    ParameterList aggExportParams;
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: output filename", std::string, aggExportParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: output file: agg style", std::string, aggExportParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: output file: iter", int, aggExportParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: output file: time step", int, aggExportParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: output file: fine graph edges", bool, aggExportParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: output file: coarse graph edges", bool, aggExportParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: output file: build colormap", bool, aggExportParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: output file: aggregate qualities", bool, aggExportParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: output file: material", bool, aggExportParams);
    aggExport->SetParameterList(aggExportParams);
    aggExport->SetFactory("AggregateQualities", manager.GetFactory("AggregateQualities"));
    aggExport->SetFactory("DofsPerNode", manager.GetFactory("DofsPerNode"));
    aggExport->SetFactory("Aggregates", manager.GetFactory("Aggregates"));
    aggExport->SetFactory("Graph", manager.GetFactory("Graph"));

    if (!RAP.is_null())
      RAP->AddTransferFactory(aggExport);
    else
      RAPs->AddTransferFactory(aggExport);
  }
  if (!RAP.is_null())
    manager.SetFactory("A", RAP);
  else
    manager.SetFactory("A", RAPs);

  MUELU_SET_VAR_2LIST(paramList, defaultList, "reuse: type", std::string, reuseType);
  MUELU_SET_VAR_2LIST(paramList, defaultList, "sa: use filtered matrix", bool, useFiltering);
  bool filteringChangesMatrix = useFiltering && !MUELU_TEST_PARAM_2LIST(paramList, defaultList, "aggregation: drop tol", double, 0);

  if (reuseType == "RP" || (reuseType == "tP" && !filteringChangesMatrix)) {
    if (!RAP.is_null()) {
      keeps.push_back(keep_pair("AP reuse data", RAP.get()));
      keeps.push_back(keep_pair("RAP reuse data", RAP.get()));

    } else {
      keeps.push_back(keep_pair("AP reuse data", RAPs.get()));
      keeps.push_back(keep_pair("RAP reuse data", RAPs.get()));
    }
  }
}

// =====================================================================================================
// ======================================= Coordinates =================================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_Coordinates(ParameterList& paramList, const ParameterList& /* defaultList */,
                                     FactoryManager& manager, int /* levelID */, std::vector<keep_pair>& /* keeps */) const {
  bool have_userCO = false;
  if (paramList.isParameter("Coordinates") && !paramList.get<RCP<MultiVector> >("Coordinates").is_null())
    have_userCO = true;

  if (useCoordinates_) {
    if (have_userCO) {
      manager.SetFactory("Coordinates", NoFactory::getRCP());

    } else {
      RCP<Factory> coords = rcp(new CoordinatesTransferFactory());
      coords->SetFactory("Aggregates", manager.GetFactory("Aggregates"));
      coords->SetFactory("CoarseMap", manager.GetFactory("CoarseMap"));
      manager.SetFactory("Coordinates", coords);

      auto RAP = rcp_const_cast<RAPFactory>(rcp_dynamic_cast<const RAPFactory>(manager.GetFactory("A")));
      if (!RAP.is_null()) {
        RAP->AddTransferFactory(manager.GetFactory("Coordinates"));
      } else {
        auto RAPs = rcp_const_cast<RAPShiftFactory>(rcp_dynamic_cast<const RAPShiftFactory>(manager.GetFactory("A")));
        RAPs->AddTransferFactory(manager.GetFactory("Coordinates"));
      }
    }
  }
}

// ======================================================================================================
// ========================================  Material ==================================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_Material(ParameterList& paramList, const ParameterList& /* defaultList */,
                                  FactoryManager& manager, int /* levelID */, std::vector<keep_pair>& /* keeps */) const {
  bool have_userMaterial = false;
  if (paramList.isParameter("Material") && !paramList.get<RCP<MultiVector> >("Material").is_null())
    have_userMaterial = true;

  if (useMaterial_) {
    if (have_userMaterial) {
      manager.SetFactory("Material", NoFactory::getRCP());
    } else {
      RCP<Factory> materialTransfer = rcp(new MultiVectorTransferFactory());
      ParameterList materialTransferParameters;
      materialTransferParameters.set("Vector name", "Material");
      materialTransferParameters.set("Transfer name", "P");
      materialTransferParameters.set("Normalize", true);
      materialTransfer->SetParameterList(materialTransferParameters);
      materialTransfer->SetFactory("Transfer factory", manager.GetFactory("Ptent"));
      manager.SetFactory("Material", materialTransfer);

      auto RAP = rcp_const_cast<RAPFactory>(rcp_dynamic_cast<const RAPFactory>(manager.GetFactory("A")));
      if (!RAP.is_null()) {
        RAP->AddTransferFactory(manager.GetFactory("Material"));
      } else {
        auto RAPs = rcp_const_cast<RAPShiftFactory>(rcp_dynamic_cast<const RAPShiftFactory>(manager.GetFactory("A")));
        RAPs->AddTransferFactory(manager.GetFactory("Material"));
      }
    }
  }
}

// =====================================================================================================
// =================================  LocalOrdinalTransfer =============================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_LocalOrdinalTransfer(const std::string& VarName, const std::string& multigridAlgo, ParameterList& paramList, const ParameterList& /* defaultList */,
                                              FactoryManager& manager, int levelID, std::vector<keep_pair>& /* keeps */) const {
  // NOTE: You would think this would be levelID > 0, but you'd be wrong, since the FactoryManager is basically
  // offset by a level from the things which actually do the work.
  if (useBlockNumber_ && (levelID > 0)) {
    auto RAP  = rcp_const_cast<RAPFactory>(rcp_dynamic_cast<const RAPFactory>(manager.GetFactory("A")));
    auto RAPs = rcp_const_cast<RAPShiftFactory>(rcp_dynamic_cast<const RAPShiftFactory>(manager.GetFactory("A")));
    if (!RAP.is_null() || !RAPs.is_null()) {
      RCP<Factory> fact = rcp(new LocalOrdinalTransferFactory(VarName, multigridAlgo));
      if (multigridAlgo == "classical")
        fact->SetFactory("P Graph", manager.GetFactory("P Graph"));
      else
        fact->SetFactory("Aggregates", manager.GetFactory("Aggregates"));
      fact->SetFactory("CoarseMap", manager.GetFactory("CoarseMap"));

      fact->SetFactory(VarName, this->GetFactoryManager(levelID - 1)->GetFactory(VarName));

      manager.SetFactory(VarName, fact);

      if (!RAP.is_null())
        RAP->AddTransferFactory(manager.GetFactory(VarName));
      else
        RAPs->AddTransferFactory(manager.GetFactory(VarName));
    }
  }
}

// ======================================================================================================
// ======================================  BlockNumber =================================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_BlockNumber(ParameterList& paramList, const ParameterList& defaultList,
                                     FactoryManager& manager, int levelID, std::vector<keep_pair>& keeps) const {
  if (useBlockNumber_) {
    ParameterList myParams;
    RCP<Factory> fact = rcp(new InitialBlockNumberFactory());
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: block diagonal: interleaved blocksize", int, myParams);
    fact->SetParameterList(myParams);
    manager.SetFactory("BlockNumber", fact);
  }
}

// =====================================================================================================
// =========================================== Restriction =============================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_Restriction(ParameterList& paramList, const ParameterList& defaultList, FactoryManager& manager,
                                     int levelID, std::vector<keep_pair>& /* keeps */) const {
  MUELU_SET_VAR_2LIST(paramList, defaultList, "multigrid algorithm", std::string, multigridAlgo);
  bool have_userR = false;
  if (paramList.isParameter("R") && !paramList.get<RCP<Matrix> >("R").is_null())
    have_userR = true;

  // === Restriction ===
  RCP<Factory> R;
  if (!this->implicitTranspose_) {
    MUELU_SET_VAR_2LIST(paramList, defaultList, "problem: symmetric", bool, isSymmetric);

    if (isSymmetric == false && (multigridAlgo == "unsmoothed" || multigridAlgo == "emin")) {
      this->GetOStream(Warnings0) << "Switching \"problem: symmetric\" parameter to symmetric as multigrid algorithm. " << multigridAlgo << " is primarily supposed to be used for symmetric problems.\n\n"
                                  << "Please note: if you are using \"unsmoothed\" transfer operators the \"problem: symmetric\" parameter "
                                  << "has no real mathematical meaning, i.e. you can use it for non-symmetric\n"
                                  << "problems, too. With \"problem: symmetric\"=\"symmetric\" you can use implicit transpose for building "
                                  << "the restriction operators which may drastically reduce the amount of consumed memory." << std::endl;
      isSymmetric = true;
    }
    TEUCHOS_TEST_FOR_EXCEPTION(multigridAlgo == "pg" && isSymmetric == true, Exceptions::RuntimeError,
                               "Petrov-Galerkin smoothed transfer operators are only allowed for non-symmetric problems: Set \"problem: symmetric\" to false!\n"
                               "While PG smoothed transfer operators generally would also work for symmetric problems this is an unusual use case. "
                               "You can use the factory-based xml interface though if you need PG-AMG for symmetric problems.");

    if (have_userR) {
      manager.SetFactory("R", NoFactory::getRCP());
    } else {
      if (isSymmetric)
        R = rcp(new TransPFactory());
      else
        R = rcp(new GenericRFactory());

      R->SetFactory("P", manager.GetFactory("P"));
      manager.SetFactory("R", R);
    }

  } else {
    manager.SetFactory("R", Teuchos::null);
  }

  // === Restriction: Nullspace Scaling ===
  if (paramList.isParameter("restriction: scale nullspace") && paramList.get<bool>("restriction: scale nullspace")) {
    RCP<TentativePFactory> tentPFactory = rcp(new TentativePFactory());
    Teuchos::ParameterList tentPlist;
    tentPlist.set("Nullspace name", "Scaled Nullspace");
    tentPFactory->SetParameterList(tentPlist);
    tentPFactory->SetFactory("Aggregates", manager.GetFactory("Aggregates"));
    tentPFactory->SetFactory("CoarseMap", manager.GetFactory("CoarseMap"));

    if (R.is_null()) R = rcp(new TransPFactory());
    R->SetFactory("P", tentPFactory);
  }
}

// =====================================================================================================
// ========================================= Repartition ===============================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_Repartition(ParameterList& paramList, const ParameterList& defaultList, FactoryManager& manager,
                                     int levelID, std::vector<keep_pair>& keeps, RCP<Factory>& nullSpaceFactory) const {
  // === Repartitioning ===
  MUELU_SET_VAR_2LIST(paramList, defaultList, "reuse: type", std::string, reuseType);
  MUELU_SET_VAR_2LIST(paramList, defaultList, "repartition: enable", bool, enableRepart);
  if (enableRepart) {
#if defined(HAVE_MPI) && (defined(HAVE_MUELU_ZOLTAN) || defined(HAVE_MUELU_ZOLTAN2))  // skip to the end, print warning, and turn off repartitioning if we don't have MPI and Zoltan/Zoltan2
    MUELU_SET_VAR_2LIST(paramList, defaultList, "repartition: use subcommunicators in place", bool, enableInPlace);
    // Short summary of the issue: RebalanceTransferFactory shares ownership
    // of "P" with SaPFactory, and therefore, changes the stored version.
    // That means that if SaPFactory generated P, and stored it on the level,
    // then after rebalancing the value in that storage changed. It goes
    // against the concept of factories (I think), that every factory is
    // responsible for its own objects, and they are immutable outside.
    //
    // In reuse, this is what happens: as we reuse Importer across setups,
    // the order of factories changes, and coupled with shared ownership
    // leads to problems.
    // *First setup*
    //    SaP               builds     P [and stores it]
    //    TransP            builds     R [and stores it]
    //    RAP               builds     A [and stores it]
    //    RebalanceTransfer rebalances P [and changes the P stored by SaP]   (*)
    //    RebalanceTransfer rebalances R
    //    RebalanceAc       rebalances A
    // *Second setup* ("RP" reuse)
    //    RebalanceTransfer rebalances P [which is incorrect due to (*)]
    //    RebalanceTransfer rebalances R
    //    RAP               builds     A [which is incorrect due to (*)]
    //    RebalanceAc       rebalances A [which throws due to map inconsistency]
    //    ...
    // *Second setup* ("tP" reuse)
    //    SaP               builds     P [and stores it]
    //    RebalanceTransfer rebalances P [and changes the P stored by SaP]   (**)
    //    TransP            builds     R [which is incorrect due to (**)]
    //    RebalanceTransfer rebalances R
    //    ...
    //
    // Couple solutions to this:
    //    1. [implemented] Requre "tP" and "PR" reuse to only be used with
    //       implicit rebalancing.
    //    2. Do deep copy of P, and changed domain map and importer there.
    //       Need to investigate how expensive this is.
    TEUCHOS_TEST_FOR_EXCEPTION(this->doPRrebalance_ && (reuseType == "tP" || reuseType == "RP"), Exceptions::InvalidArgument,
                               "Reuse types \"tP\" and \"PR\" require \"repartition: rebalance P and R\" set to \"false\"");

    // TEUCHOS_TEST_FOR_EXCEPTION(aggType == "brick", Exceptions::InvalidArgument,
    //                            "Aggregation type \"brick\" requires \"repartition: enable\" set to \"false\"");

    MUELU_SET_VAR_2LIST(paramList, defaultList, "repartition: partitioner", std::string, partName);
    TEUCHOS_TEST_FOR_EXCEPTION(partName != "zoltan" && partName != "zoltan2", Exceptions::InvalidArgument,
                               "Invalid partitioner name: \"" << partName << "\". Valid options: \"zoltan\", \"zoltan2\"");

#ifndef HAVE_MUELU_ZOLTAN
    bool switched = false;
    if (partName == "zoltan") {
      this->GetOStream(Warnings0) << "Zoltan interface is not available, trying to switch to Zoltan2" << std::endl;
      partName = "zoltan2";
      switched = true;
    }
#else
#ifndef HAVE_MUELU_ZOLTAN2
    bool switched = false;
#endif  // HAVE_MUELU_ZOLTAN2
#endif  // HAVE_MUELU_ZOLTAN

#ifndef HAVE_MUELU_ZOLTAN2
    if (partName == "zoltan2" && !switched) {
      this->GetOStream(Warnings0) << "Zoltan2 interface is not available, trying to switch to Zoltan" << std::endl;
      partName = "zoltan";
    }
#endif  // HAVE_MUELU_ZOLTAN2

    MUELU_SET_VAR_2LIST(paramList, defaultList, "repartition: node repartition level", int, nodeRepartitionLevel);

    // RepartitionHeuristic
    auto repartheurFactory = rcp(new RepartitionHeuristicFactory());
    ParameterList repartheurParams;
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: node repartition level", int, repartheurParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: start level", int, repartheurParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: min rows per proc", int, repartheurParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: target rows per proc", int, repartheurParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: min rows per thread", int, repartheurParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: target rows per thread", int, repartheurParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: max imbalance", double, repartheurParams);
    repartheurFactory->SetParameterList(repartheurParams);
    repartheurFactory->SetFactory("A", manager.GetFactory("A"));
    manager.SetFactory("number of partitions", repartheurFactory);
    manager.SetFactory("repartition: heuristic target rows per process", repartheurFactory);

    // Partitioner
    RCP<Factory> partitioner;
    if (levelID == nodeRepartitionLevel) {
      //        partitioner = rcp(new NodePartitionInterface());
      partitioner = rcp(new MueLu::NodePartitionInterface<SC, LO, GO, NO>());
      ParameterList partParams;
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: node id", int, repartheurParams);
      partitioner->SetParameterList(partParams);
      partitioner->SetFactory("Node Comm", manager.GetFactory("Node Comm"));
    } else if (partName == "zoltan") {
#ifdef HAVE_MUELU_ZOLTAN
      partitioner = rcp(new ZoltanInterface());
      // NOTE: ZoltanInterface ("zoltan") does not support external parameters through ParameterList
#else
      throw Exceptions::RuntimeError("Zoltan interface is not available");
#endif  // HAVE_MUELU_ZOLTAN
    } else if (partName == "zoltan2") {
#ifdef HAVE_MUELU_ZOLTAN2
      partitioner = rcp(new Zoltan2Interface());
      ParameterList partParams;
      RCP<const ParameterList> partpartParams = rcp(new ParameterList(paramList.sublist("repartition: params", false)));
      partParams.set("ParameterList", partpartParams);
      partitioner->SetParameterList(partParams);
      partitioner->SetFactory("repartition: heuristic target rows per process",
                              manager.GetFactory("repartition: heuristic target rows per process"));
#else
      throw Exceptions::RuntimeError("Zoltan2 interface is not available");
#endif  // HAVE_MUELU_ZOLTAN2
    }

    partitioner->SetFactory("A", manager.GetFactory("A"));
    partitioner->SetFactory("number of partitions", manager.GetFactory("number of partitions"));
    if (useCoordinates_)
      partitioner->SetFactory("Coordinates", manager.GetFactory("Coordinates"));
    manager.SetFactory("Partition", partitioner);

    // Repartitioner
    auto repartFactory = rcp(new RepartitionFactory());
    ParameterList repartParams;
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: print partition distribution", bool, repartParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: remap parts", bool, repartParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: remap num values", int, repartParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: save importer", bool, repartParams);
    repartFactory->SetParameterList(repartParams);
    repartFactory->SetFactory("A", manager.GetFactory("A"));
    repartFactory->SetFactory("number of partitions", manager.GetFactory("number of partitions"));
    repartFactory->SetFactory("Partition", manager.GetFactory("Partition"));
    manager.SetFactory("Importer", repartFactory);
    if (reuseType != "none" && reuseType != "S" && levelID)
      keeps.push_back(keep_pair("Importer", manager.GetFactory("Importer").get()));

    if (enableInPlace) {
      // Rebalanced A (in place)
      // NOTE: This is for when we want to constrain repartitioning to match some other idea of what's going on.
      // The major application is the (1,1) hierarchy in the Maxwell1 preconditioner.
      auto newA = rcp(new RebalanceAcFactory());
      ParameterList rebAcParams;
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: use subcommunicators", bool, rebAcParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: use subcommunicators in place", bool, rebAcParams);
      newA->SetParameterList(rebAcParams);
      newA->SetFactory("A", manager.GetFactory("A"));
      newA->SetFactory("InPlaceMap", manager.GetFactory("InPlaceMap"));
      manager.SetFactory("A", newA);
    } else {
      // Rebalanced A
      auto newA = rcp(new RebalanceAcFactory());
      ParameterList rebAcParams;
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: use subcommunicators", bool, rebAcParams);
      newA->SetParameterList(rebAcParams);
      newA->SetFactory("A", manager.GetFactory("A"));
      newA->SetFactory("Importer", manager.GetFactory("Importer"));
      manager.SetFactory("A", newA);

      // Rebalanced P
      auto newP = rcp(new RebalanceTransferFactory());
      ParameterList newPparams;
      newPparams.set("type", "Interpolation");
      if (changedPRrebalance_)
        newPparams.set("repartition: rebalance P and R", this->doPRrebalance_);
      if (changedPRViaCopyrebalance_)
        newPparams.set("repartition: explicit via new copy rebalance P and R", true);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: use subcommunicators", bool, newPparams);
      newP->SetParameterList(newPparams);
      newP->SetFactory("Importer", manager.GetFactory("Importer"));
      newP->SetFactory("P", manager.GetFactory("P"));
      manager.SetFactory("P", newP);
      if (!paramList.isParameter("semicoarsen: number of levels"))
        newP->SetFactory("Nullspace", manager.GetFactory("Ptent"));
      else
        newP->SetFactory("Nullspace", manager.GetFactory("P"));  // TogglePFactory
      if (useCoordinates_) {
        newP->SetFactory("Coordinates", manager.GetFactory("Coordinates"));
        manager.SetFactory("Coordinates", newP);
      }
      if (useMaterial_) {
        newP->SetFactory("Material", manager.GetFactory("Material"));
        manager.SetFactory("Material", newP);
      }
      if (useBlockNumber_ && (levelID > 0)) {
        newP->SetFactory("BlockNumber", manager.GetFactory("BlockNumber"));
        manager.SetFactory("BlockNumber", newP);
      }

      // Rebalanced R
      auto newR = rcp(new RebalanceTransferFactory());
      ParameterList newRparams;
      newRparams.set("type", "Restriction");
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "repartition: use subcommunicators", bool, newRparams);
      if (changedPRrebalance_)
        newRparams.set("repartition: rebalance P and R", this->doPRrebalance_);
      if (changedPRViaCopyrebalance_)
        newPparams.set("repartition: explicit via new copy rebalance P and R", true);
      if (changedImplicitTranspose_)
        newRparams.set("transpose: use implicit", this->implicitTranspose_);
      newR->SetParameterList(newRparams);
      newR->SetFactory("Importer", manager.GetFactory("Importer"));
      if (!this->implicitTranspose_) {
        newR->SetFactory("R", manager.GetFactory("R"));
        manager.SetFactory("R", newR);
      }

      // NOTE: the role of NullspaceFactory is to provide nullspace on the finest
      // level if a user does not do that. For all other levels it simply passes
      // nullspace from a real factory to whoever needs it. If we don't use
      // repartitioning, that factory is "TentativePFactory"; if we do, it is
      // "RebalanceTransferFactory". But we still have to have NullspaceFactory as
      // the "Nullspace" of the manager
      // NOTE: This really needs to be set on the *NullSpaceFactory*, not manager.get("Nullspace").
      ParameterList newNullparams;
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "nullspace: calculate rotations", bool, newNullparams);
      nullSpaceFactory->SetFactory("Nullspace", newP);
      nullSpaceFactory->SetParameterList(newNullparams);
    }
#else
    paramList.set("repartition: enable", false);
#ifndef HAVE_MPI
    this->GetOStream(Warnings0) << "No repartitioning available for a serial run\n";
#else
    this->GetOStream(Warnings0) << "Zoltan/Zoltan2 are unavailable for repartitioning\n";
#endif  // HAVE_MPI
#endif  // defined(HAVE_MPI) && (defined(HAVE_MUELU_ZOLTAN) || defined(HAVE_MUELU_ZOLTAN2))
  }
}

// =====================================================================================================
// ========================================= Low precision transfers ===================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_LowPrecision(ParameterList& paramList, const ParameterList& defaultList, FactoryManager& manager,
                                      int levelID, std::vector<keep_pair>& keeps) const {
  MUELU_SET_VAR_2LIST(paramList, defaultList, "transfers: half precision", bool, enableLowPrecision);

  if (enableLowPrecision) {
    // Low precision P
    auto newP = rcp(new LowPrecisionFactory());
    ParameterList newPparams;
    newPparams.set("matrix key", "P");
    newP->SetParameterList(newPparams);
    newP->SetFactory("P", manager.GetFactory("P"));
    manager.SetFactory("P", newP);

    if (!this->implicitTranspose_) {
      // Low precision R
      auto newR = rcp(new LowPrecisionFactory());
      ParameterList newRparams;
      newRparams.set("matrix key", "R");
      newR->SetParameterList(newRparams);
      newR->SetFactory("R", manager.GetFactory("R"));
      manager.SetFactory("R", newR);
    }
  }
}

// =====================================================================================================
// =========================================== Nullspace ===============================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_Nullspace(ParameterList& paramList, const ParameterList& defaultList, FactoryManager& manager,
                                   int /* levelID */, std::vector<keep_pair>& /* keeps */, RCP<Factory>& nullSpaceFactory) const {
  // Nullspace
  RCP<Factory> nullSpace = rcp(new NullspaceFactory());

  bool have_userNS = false;
  if (paramList.isParameter("Nullspace") && !paramList.get<RCP<MultiVector> >("Nullspace").is_null())
    have_userNS = true;

  if (!have_userNS) {
    ParameterList newNullparams;
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "nullspace: calculate rotations", bool, newNullparams);
    nullSpace->SetParameterList(newNullparams);
    nullSpace->SetFactory("Nullspace", manager.GetFactory("Ptent"));
    manager.SetFactory("Nullspace", nullSpace);
  }
  nullSpaceFactory = nullSpace;

  if (paramList.isParameter("restriction: scale nullspace") && paramList.get<bool>("restriction: scale nullspace")) {
    RCP<ScaledNullspaceFactory> scaledNSfactory = rcp(new ScaledNullspaceFactory());
    scaledNSfactory->SetFactory("Nullspace", nullSpaceFactory);
    manager.SetFactory("Scaled Nullspace", scaledNSfactory);
  }
}

// =====================================================================================================
// ================================= Algorithm: SemiCoarsening =========================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_SemiCoarsen(ParameterList& paramList, const ParameterList& defaultList, FactoryManager& manager,
                                     int /* levelID */, std::vector<keep_pair>& /* keeps */) const {
  // === Semi-coarsening ===
  RCP<Factory> semicoarsenFactory = Teuchos::null;
  if (paramList.isParameter("semicoarsen: number of levels") &&
      paramList.get<int>("semicoarsen: number of levels") > 0) {
    ParameterList togglePParams;
    ParameterList semicoarsenPParams;
    ParameterList linedetectionParams;
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "semicoarsen: number of levels", int, togglePParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "semicoarsen: coarsen rate", int, semicoarsenPParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "semicoarsen: piecewise constant", bool, semicoarsenPParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "semicoarsen: piecewise linear", bool, semicoarsenPParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "semicoarsen: calculate nonsym restriction", bool, semicoarsenPParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "linedetection: orientation", std::string, linedetectionParams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "linedetection: num layers", int, linedetectionParams);

    MUELU_KOKKOS_FACTORY_NO_DECL(semicoarsenFactory, SemiCoarsenPFactory, SemiCoarsenPFactory_kokkos);
    RCP<LineDetectionFactory> linedetectionFactory = rcp(new LineDetectionFactory());
    RCP<TogglePFactory> togglePFactory             = rcp(new TogglePFactory());

    linedetectionFactory->SetParameterList(linedetectionParams);
    semicoarsenFactory->SetParameterList(semicoarsenPParams);
    togglePFactory->SetParameterList(togglePParams);

    togglePFactory->AddCoarseNullspaceFactory(semicoarsenFactory);
    togglePFactory->AddProlongatorFactory(semicoarsenFactory);
    togglePFactory->AddPtentFactory(semicoarsenFactory);
    togglePFactory->AddCoarseNullspaceFactory(manager.GetFactory("Ptent"));
    togglePFactory->AddProlongatorFactory(manager.GetFactory("P"));
    togglePFactory->AddPtentFactory(manager.GetFactory("Ptent"));

    manager.SetFactory("CoarseNumZLayers", linedetectionFactory);
    manager.SetFactory("LineDetection_Layers", linedetectionFactory);
    manager.SetFactory("LineDetection_VertLineIds", linedetectionFactory);

    manager.SetFactory("P", togglePFactory);
    manager.SetFactory("Ptent", togglePFactory);
    manager.SetFactory("Nullspace", togglePFactory);
  }

  if (paramList.isParameter("semicoarsen: number of levels")) {
    auto tf = rcp(new ToggleCoordinatesTransferFactory());
    tf->SetFactory("Chosen P", manager.GetFactory("P"));
    tf->AddCoordTransferFactory(semicoarsenFactory);

    RCP<Factory> coords = rcp(new CoordinatesTransferFactory());
    coords->SetFactory("Aggregates", manager.GetFactory("Aggregates"));
    coords->SetFactory("CoarseMap", manager.GetFactory("CoarseMap"));
    tf->AddCoordTransferFactory(coords);
    manager.SetFactory("Coordinates", tf);
  }
}

// =====================================================================================================
// ================================== Algorithm: P-Coarsening ==========================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_PCoarsen(ParameterList& paramList, const ParameterList& defaultList, FactoryManager& manager,
                                  int levelID, std::vector<keep_pair>& keeps) const {
#ifdef HAVE_MUELU_INTREPID2
  // This only makes sense to invoke from the default list.
  if (defaultList.isParameter("pcoarsen: schedule") && defaultList.isParameter("pcoarsen: element")) {
    // P-Coarsening by schedule (new interface)
    // NOTE: levelID represents the *coarse* level in this case
    auto pcoarsen_schedule = Teuchos::getArrayFromStringParameter<int>(defaultList, "pcoarsen: schedule");
    auto pcoarsen_element  = defaultList.get<std::string>("pcoarsen: element");

    if (levelID >= (int)pcoarsen_schedule.size()) {
      // Past the p-coarsening levels, we do Smoothed Aggregation
      // NOTE: We should probably consider allowing other options past p-coarsening
      UpdateFactoryManager_SA(paramList, defaultList, manager, levelID, keeps);

    } else {
      // P-Coarsening
      ParameterList Pparams;
      auto P         = rcp(new IntrepidPCoarsenFactory());
      std::string lo = pcoarsen_element + std::to_string(pcoarsen_schedule[levelID]);
      std::string hi = (levelID ? pcoarsen_element + std::to_string(pcoarsen_schedule[levelID - 1]) : lo);
      Pparams.set("pcoarsen: hi basis", hi);
      Pparams.set("pcoarsen: lo basis", lo);
      P->SetParameterList(Pparams);
      manager.SetFactory("P", P);

      // Add special nullspace handling
      rcp_dynamic_cast<Factory>(manager.GetFactoryNonConst("Nullspace"))->SetFactory("Nullspace", manager.GetFactory("P"));
    }

  } else {
    // P-Coarsening by manual specification (old interface)
    ParameterList Pparams;
    auto P = rcp(new IntrepidPCoarsenFactory());
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "pcoarsen: hi basis", std::string, Pparams);
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "pcoarsen: lo basis", std::string, Pparams);
    P->SetParameterList(Pparams);
    manager.SetFactory("P", P);

    // Add special nullspace handling
    rcp_dynamic_cast<Factory>(manager.GetFactoryNonConst("Nullspace"))->SetFactory("Nullspace", manager.GetFactory("P"));
  }

#endif
}

// =====================================================================================================
// ============================== Algorithm: Smoothed Aggregation ======================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_SA(ParameterList& paramList, const ParameterList& defaultList, FactoryManager& manager, int /* levelID */, std::vector<keep_pair>& keeps) const {
  // Smoothed aggregation
  RCP<Factory> P = rcp(new SaPFactory());
  ParameterList Pparams;
  if (paramList.isSublist("matrixmatrix: kernel params"))
    Pparams.sublist("matrixmatrix: kernel params", false) = paramList.sublist("matrixmatrix: kernel params");
  if (defaultList.isSublist("matrixmatrix: kernel params"))
    Pparams.sublist("matrixmatrix: kernel params", false) = defaultList.sublist("matrixmatrix: kernel params");
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "sa: damping factor", double, Pparams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "sa: calculate eigenvalue estimate", bool, Pparams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "sa: max eigenvalue", double, Pparams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "sa: eigenvalue estimate num iterations", int, Pparams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "sa: use rowsumabs diagonal scaling", bool, Pparams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "sa: rowsumabs diagonal replacement tolerance", double, Pparams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "sa: rowsumabs diagonal replacement value", double, Pparams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "sa: rowsumabs use automatic diagonal tolerance", bool, Pparams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "sa: enforce constraints", bool, Pparams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "sa: eigen-analysis type", std::string, Pparams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "tentative: calculate qr", bool, Pparams);

  P->SetParameterList(Pparams);

  // Filtering
  MUELU_SET_VAR_2LIST(paramList, defaultList, "sa: use filtered matrix", bool, useFiltering);
  if (useFiltering) {
    // NOTE: Here, non-Kokkos and Kokkos versions diverge in the way the
    // dependency tree is setup. The Kokkos version has merged the the
    // FilteredAFactory into the CoalesceDropFactory.
    if (!useKokkos_) {
      RCP<Factory> filterFactory = rcp(new FilteredAFactory());

      ParameterList fParams;
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: use lumping", bool, fParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: reuse graph", bool, fParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: reuse eigenvalue", bool, fParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: use root stencil", bool, fParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: Dirichlet threshold", double, fParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: use spread lumping", bool, fParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: spread lumping diag dom growth factor", double, fParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: spread lumping diag dom cap", double, fParams);
      filterFactory->SetParameterList(fParams);
      filterFactory->SetFactory("Graph", manager.GetFactory("Graph"));
      filterFactory->SetFactory("Aggregates", manager.GetFactory("Aggregates"));
      filterFactory->SetFactory("UnAmalgamationInfo", manager.GetFactory("UnAmalgamationInfo"));
      // I'm not sure why we need this line. See comments for DofsPerNode for UncoupledAggregation above
      filterFactory->SetFactory("Filtering", manager.GetFactory("Graph"));

      P->SetFactory("A", filterFactory);

    } else {
      P->SetFactory("A", manager.GetFactory("Graph"));
    }
  }

  P->SetFactory("P", manager.GetFactory("Ptent"));
  manager.SetFactory("P", P);

  bool filteringChangesMatrix = useFiltering && !MUELU_TEST_PARAM_2LIST(paramList, defaultList, "aggregation: drop tol", double, 0);
  MUELU_SET_VAR_2LIST(paramList, defaultList, "reuse: type", std::string, reuseType);
  if (reuseType == "tP" && !filteringChangesMatrix)
    keeps.push_back(keep_pair("AP reuse data", P.get()));
}

// =====================================================================================================
// =============================== Algorithm: Energy Minimization ======================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_Emin(ParameterList& paramList, const ParameterList& defaultList, FactoryManager& manager,
                              int /* levelID */, std::vector<keep_pair>& /* keeps */) const {
  MUELU_SET_VAR_2LIST(paramList, defaultList, "emin: pattern", std::string, patternType);
  MUELU_SET_VAR_2LIST(paramList, defaultList, "reuse: type", std::string, reuseType);
  TEUCHOS_TEST_FOR_EXCEPTION(patternType != "AkPtent", Exceptions::InvalidArgument,
                             "Invalid pattern name: \"" << patternType << "\". Valid options: \"AkPtent\"");
  // Pattern
  auto patternFactory = rcp(new PatternFactory());
  ParameterList patternParams;
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "emin: pattern order", int, patternParams);
  patternFactory->SetParameterList(patternParams);
  patternFactory->SetFactory("P", manager.GetFactory("Ptent"));

  // Filtering
  MUELU_SET_VAR_2LIST(paramList, defaultList, "emin: use filtered matrix", bool, useFiltering);
  if (useFiltering) {
    // NOTE: Here, non-Kokkos and Kokkos versions diverge in the way the
    // dependency tree is setup. The Kokkos version has merged the the
    // FilteredAFactory into the CoalesceDropFactory.
    if (!useKokkos_) {
      RCP<Factory> filterFactory = rcp(new FilteredAFactory());

      ParameterList fParams;
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: use lumping", bool, fParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: reuse graph", bool, fParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: reuse eigenvalue", bool, fParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: use root stencil", bool, fParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: Dirichlet threshold", double, fParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: use spread lumping", bool, fParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: spread lumping diag dom growth factor", double, fParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: spread lumping diag dom cap", double, fParams);
      filterFactory->SetParameterList(fParams);
      filterFactory->SetFactory("Graph", manager.GetFactory("Graph"));
      filterFactory->SetFactory("Aggregates", manager.GetFactory("Aggregates"));
      filterFactory->SetFactory("UnAmalgamationInfo", manager.GetFactory("UnAmalgamationInfo"));
      // I'm not sure why we need this line. See comments for DofsPerNode for UncoupledAggregation above
      filterFactory->SetFactory("Filtering", manager.GetFactory("Graph"));

      patternFactory->SetFactory("A", filterFactory);

    } else {
      patternFactory->SetFactory("A", manager.GetFactory("Graph"));
    }
  }

  manager.SetFactory("Ppattern", patternFactory);

  // Constraint
  auto constraintFactory = rcp(new ConstraintFactory());
  constraintFactory->SetFactory("Ppattern", manager.GetFactory("Ppattern"));
  constraintFactory->SetFactory("CoarseNullspace", manager.GetFactory("Ptent"));
  manager.SetFactory("Constraint", constraintFactory);

  // Energy minimization
  ParameterList Pparams;
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "emin: num iterations", int, Pparams);
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "emin: iterative method", std::string, Pparams);
  if (reuseType == "emin") {
    MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "emin: num reuse iterations", int, Pparams);
    Pparams.set("Keep P0", true);
    Pparams.set("Keep Constraint0", true);
  }

  // Emin Factory
  auto P = rcp(new EminPFactory());
  P->SetParameterList(Pparams);
  P->SetFactory("P", manager.GetFactory("Ptent"));
  P->SetFactory("Constraint", manager.GetFactory("Constraint"));
  manager.SetFactory("P", P);
}

// =====================================================================================================
// ================================= Algorithm: Petrov-Galerkin ========================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_PG(ParameterList& /* paramList */, const ParameterList& /* defaultList */, FactoryManager& manager,
                            int /* levelID */, std::vector<keep_pair>& /* keeps */) const {
  TEUCHOS_TEST_FOR_EXCEPTION(this->implicitTranspose_, Exceptions::RuntimeError,
                             "Implicit transpose not supported with Petrov-Galerkin smoothed transfer operators: Set \"transpose: use implicit\" to false!\n"
                             "Petrov-Galerkin transfer operator smoothing for non-symmetric problems requires a separate handling of the restriction operator which "
                             "does not allow the usage of implicit transpose easily.");

  // Petrov-Galerkin
  auto P = rcp(new PgPFactory());
  P->SetFactory("P", manager.GetFactory("Ptent"));
  manager.SetFactory("P", P);
}

// =====================================================================================================
// ================================= Algorithm: Replicate       ========================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_Replicate(ParameterList& paramList, const ParameterList& defaultList, FactoryManager& manager, int /* levelID */, std::vector<keep_pair>& keeps) const {
  auto P = rcp(new MueLu::ReplicatePFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>());

  ParameterList Pparams;
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "replicate: npdes", int, Pparams);

  P->SetParameterList(Pparams);
  manager.SetFactory("P", P);
}

// =====================================================================================================
// ====================================== Algorithm: Combine ============================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_Combine(ParameterList& paramList, const ParameterList& defaultList, FactoryManager& manager, int /* levelID */, std::vector<keep_pair>& keeps) const {
  auto P = rcp(new MueLu::CombinePFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>());

  ParameterList Pparams;
  MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "combine: numBlks", int, Pparams);

  P->SetParameterList(Pparams);
  manager.SetFactory("P", P);
}

// =====================================================================================================
// ====================================== Algorithm: Matlab ============================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    UpdateFactoryManager_Matlab(ParameterList& paramList, const ParameterList& /* defaultList */, FactoryManager& manager,
                                int /* levelID */, std::vector<keep_pair>& /* keeps */) const {
#ifdef HAVE_MUELU_MATLAB
  ParameterList Pparams = paramList.sublist("transfer: params");
  auto P                = rcp(new TwoLevelMatlabFactory());
  P->SetParameterList(Pparams);
  P->SetFactory("P", manager.GetFactory("Ptent"));
  manager.SetFactory("P", P);
#else
  (void)paramList;
  (void)manager;
#endif
}

#undef MUELU_SET_VAR_2LIST
#undef MUELU_TEST_AND_SET_VAR
#undef MUELU_TEST_AND_SET_PARAM_2LIST
#undef MUELU_TEST_PARAM_2LIST
#undef MUELU_KOKKOS_FACTORY

size_t LevenshteinDistance(const char* s, size_t len_s, const char* t, size_t len_t);

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Validate(const ParameterList& constParamList) const {
  ParameterList paramList        = constParamList;
  const ParameterList& validList = *MasterList::List();
  // Validate up to maxLevels level specific parameter sublists
  const int maxLevels = 100;

  // Extract level specific list
  std::vector<ParameterList> paramLists;
  for (int levelID = 0; levelID < maxLevels; levelID++) {
    std::string sublistName = "level " + toString(levelID);
    if (paramList.isSublist(sublistName)) {
      paramLists.push_back(paramList.sublist(sublistName));
      // paramLists.back().setName(sublistName);
      paramList.remove(sublistName);
    }
  }
  paramLists.push_back(paramList);
  // paramLists.back().setName("main");
#ifdef HAVE_MUELU_MATLAB
  // If Muemex is supported, hide custom level variables from validator by removing them from paramList's sublists
  for (size_t i = 0; i < paramLists.size(); i++) {
    std::vector<std::string> customVars;  // list of names (keys) to be removed from list

    for (Teuchos::ParameterList::ConstIterator it = paramLists[i].begin(); it != paramLists[i].end(); it++) {
      std::string paramName = paramLists[i].name(it);

      if (IsParamMuemexVariable(paramName))
        customVars.push_back(paramName);
    }

    // Remove the keys
    for (size_t j = 0; j < customVars.size(); j++)
      paramLists[i].remove(customVars[j], false);
  }
#endif

  const int maxDepth = 0;
  for (size_t i = 0; i < paramLists.size(); i++) {
    // validate every sublist
    try {
      paramLists[i].validateParameters(validList, maxDepth);

    } catch (const Teuchos::Exceptions::InvalidParameterName& e) {
      std::string eString = e.what();

      // Parse name from: <Error, the parameter {name="smoothe: type",...>
      size_t nameStart = eString.find_first_of('"') + 1;
      size_t nameEnd   = eString.find_first_of('"', nameStart);
      std::string name = eString.substr(nameStart, nameEnd - nameStart);

      size_t bestScore     = 100;
      std::string bestName = "";
      for (ParameterList::ConstIterator it = validList.begin(); it != validList.end(); it++) {
        const std::string& pName = validList.name(it);
        this->GetOStream(Runtime1) << "| " << pName;
        size_t score = LevenshteinDistance(name.c_str(), name.length(), pName.c_str(), pName.length());
        this->GetOStream(Runtime1) << " -> " << score << std::endl;
        if (score < bestScore) {
          bestScore = score;
          bestName  = pName;
        }
      }
      if (bestScore < 10 && bestName != "") {
        TEUCHOS_TEST_FOR_EXCEPTION(true, Teuchos::Exceptions::InvalidParameterName,
                                   eString << "The parameter name \"" + name + "\" is not valid. Did you mean \"" + bestName << "\"?\n");

      } else {
        TEUCHOS_TEST_FOR_EXCEPTION(true, Teuchos::Exceptions::InvalidParameterName,
                                   eString << "The parameter name \"" + name + "\" is not valid.\n");
      }
    }
  }
}

// =====================================================================================================
// ==================================== FACTORY interpreter ============================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    SetFactoryParameterList(const ParameterList& constParamList) {
  // Create a non const copy of the parameter list
  // Working with a modifiable list is much much easier than with original one
  ParameterList paramList = constParamList;

  // Parameter List Parsing:
  // ---------
  //   <ParameterList name="MueLu">
  //     <ParameterList name="Matrix">
  //   </ParameterList>
  if (paramList.isSublist("Matrix")) {
    blockSize_ = paramList.sublist("Matrix").get<int>("PDE equations", MasterList::getDefault<int>("number of equations"));
    dofOffset_ = paramList.sublist("Matrix").get<GlobalOrdinal>("DOF offset", 0);  // undocumented parameter allowing to define a DOF offset of the global dofs of an operator (defaul = 0)
  }

  // create new FactoryFactory object if necessary
  if (factFact_ == Teuchos::null)
    factFact_ = Teuchos::rcp(new FactoryFactory());

  // Parameter List Parsing:
  // ---------
  //   <ParameterList name="MueLu">
  //     <ParameterList name="Factories"> <== call BuildFactoryMap() on this parameter list
  //     ...
  //     </ParameterList>
  //   </ParameterList>
  FactoryMap factoryMap;
  FactoryManagerMap factoryManagers;
  if (paramList.isSublist("Factories"))
    this->BuildFactoryMap(paramList.sublist("Factories"), factoryMap, factoryMap, factoryManagers);

  // Parameter List Parsing:
  // ---------
  //   <ParameterList name="MueLu">
  //     <ParameterList name="Hierarchy">
  //       <Parameter name="verbose"  type="string" value="Warnings"/> <== get
  //       <Parameter name="numDesiredLevel" type="int" value="10"/>   <== get
  //
  //       <ParameterList name="firstLevel">                           <== parse first args and call BuildFactoryMap() on the rest of this parameter list
  //         ...
  //       </ParameterList>
  //     </ParameterList>
  //   </ParameterList>
  if (paramList.isSublist("Hierarchy")) {
    ParameterList hieraList = paramList.sublist("Hierarchy");  // copy because list temporally modified (remove 'id')

    // Get hierarchy options
    if (hieraList.isParameter("max levels")) {
      this->numDesiredLevel_ = hieraList.get<int>("max levels");
      hieraList.remove("max levels");
    }

    if (hieraList.isParameter("coarse: max size")) {
      this->maxCoarseSize_ = hieraList.get<int>("coarse: max size");
      hieraList.remove("coarse: max size");
    }

    if (hieraList.isParameter("repartition: rebalance P and R")) {
      this->doPRrebalance_ = hieraList.get<bool>("repartition: rebalance P and R");
      hieraList.remove("repartition: rebalance P and R");
    }

    if (hieraList.isParameter("transpose: use implicit")) {
      this->implicitTranspose_ = hieraList.get<bool>("transpose: use implicit");
      hieraList.remove("transpose: use implicit");
    }

    if (hieraList.isParameter("fuse prolongation and update")) {
      this->fuseProlongationAndUpdate_ = hieraList.get<bool>("fuse prolongation and update");
      hieraList.remove("fuse prolongation and update");
    }

    if (hieraList.isParameter("nullspace: suppress dimension check")) {
      this->suppressNullspaceDimensionCheck_ = hieraList.get<bool>("nullspace: suppress dimension check");
      hieraList.remove("nullspace: suppress dimension check");
    }

    if (hieraList.isParameter("number of vectors")) {
      this->sizeOfMultiVectors_ = hieraList.get<int>("number of vectors");
      hieraList.remove("number of vectors");
    }

    if (hieraList.isSublist("matvec params"))
      this->matvecParams_ = Teuchos::parameterList(hieraList.sublist("matvec params"));

    if (hieraList.isParameter("coarse grid correction scaling factor")) {
      this->scalingFactor_ = hieraList.get<double>("coarse grid correction scaling factor");
      hieraList.remove("coarse grid correction scaling factor");
    }

    // Translate cycle type parameter
    if (hieraList.isParameter("cycle type")) {
      std::map<std::string, CycleType> cycleMap;
      cycleMap["V"] = VCYCLE;
      cycleMap["W"] = WCYCLE;

      std::string cycleType = hieraList.get<std::string>("cycle type");
      TEUCHOS_TEST_FOR_EXCEPTION(cycleMap.count(cycleType) == 0, Exceptions::RuntimeError, "Invalid cycle type: \"" << cycleType << "\"");
      this->Cycle_ = cycleMap[cycleType];
    }

    if (hieraList.isParameter("W cycle start level")) {
      this->WCycleStartLevel_ = hieraList.get<int>("W cycle start level");
    }

    if (hieraList.isParameter("verbosity")) {
      std::string vl = hieraList.get<std::string>("verbosity");
      hieraList.remove("verbosity");
      this->verbosity_ = toVerbLevel(vl);
    }

    if (hieraList.isParameter("output filename"))
      VerboseObject::SetMueLuOFileStream(hieraList.get<std::string>("output filename"));

    if (hieraList.isParameter("dependencyOutputLevel"))
      this->graphOutputLevel_ = hieraList.get<int>("dependencyOutputLevel");

    // Check for the reuse case
    if (hieraList.isParameter("reuse"))
      Factory::DisableMultipleCheckGlobally();

    if (hieraList.isSublist("DataToWrite")) {
      // TODO We should be able to specify any data.  If it exists, write it.
      // TODO This would requires something like std::set<dataName, Array<int> >
      ParameterList foo    = hieraList.sublist("DataToWrite");
      std::string dataName = "Matrices";
      if (foo.isParameter(dataName))
        this->matricesToPrint_["A"] = Teuchos::getArrayFromStringParameter<int>(foo, dataName);
      dataName = "Prolongators";
      if (foo.isParameter(dataName))
        this->matricesToPrint_["P"] = Teuchos::getArrayFromStringParameter<int>(foo, dataName);
      dataName = "Restrictors";
      if (foo.isParameter(dataName))
        this->matricesToPrint_["R"] = Teuchos::getArrayFromStringParameter<int>(foo, dataName);
      dataName = "D0";
      if (foo.isParameter(dataName))
        this->matricesToPrint_["D0"] = Teuchos::getArrayFromStringParameter<int>(foo, dataName);
    }

    // Get level configuration
    for (ParameterList::ConstIterator param = hieraList.begin(); param != hieraList.end(); ++param) {
      const std::string& paramName = hieraList.name(param);

      if (paramName != "DataToWrite" && hieraList.isSublist(paramName)) {
        ParameterList levelList = hieraList.sublist(paramName);  // copy because list temporally modified (remove 'id')

        int startLevel = 0;
        if (levelList.isParameter("startLevel")) {
          startLevel = levelList.get<int>("startLevel");
          levelList.remove("startLevel");
        }
        int numDesiredLevel = 1;
        if (levelList.isParameter("numDesiredLevel")) {
          numDesiredLevel = levelList.get<int>("numDesiredLevel");
          levelList.remove("numDesiredLevel");
        }

        // Parameter List Parsing:
        // ---------
        //   <ParameterList name="firstLevel">
        //      <Parameter name="startLevel"       type="int" value="0"/>
        //      <Parameter name="numDesiredLevel"  type="int" value="1"/>
        //      <Parameter name="verbose"          type="string" value="Warnings"/>
        //
        //      [] <== call BuildFactoryMap() on the rest of the parameter list
        //
        //  </ParameterList>
        FactoryMap levelFactoryMap;
        BuildFactoryMap(levelList, factoryMap, levelFactoryMap, factoryManagers);

        RCP<FactoryManager> m = rcp(new FactoryManager(levelFactoryMap));
        if (hieraList.isParameter("use kokkos refactor"))
          m->SetKokkosRefactor(hieraList.get<bool>("use kokkos refactor"));

        if (startLevel >= 0)
          this->AddFactoryManager(startLevel, numDesiredLevel, m);
        else
          TEUCHOS_TEST_FOR_EXCEPTION(true, Exceptions::RuntimeError, "MueLu::ParameterListInterpreter():: invalid level id");
      } /* TODO: else { } */
    }
  }
}

// TODO: static?


template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    BuildFactoryMap(const ParameterList& paramList, const FactoryMap& factoryMapIn, FactoryMap& factoryMapOut, FactoryManagerMap& factoryManagers) const {
  for (ParameterList::ConstIterator param = paramList.begin(); param != paramList.end(); ++param) {
    const std::string& paramName              = paramList.name(param);   //< paramName contains the user chosen factory name (e.g., "smootherFact1")
    const Teuchos::ParameterEntry& paramValue = paramList.entry(param);  //< for factories, paramValue should be either a list or just a MueLu Factory (e.g., TrilinosSmoother)

    // TODO: do not allow name of existing MueLu classes (can be tested using FactoryFactory)

    if (paramValue.isList()) {
      ParameterList paramList1 = Teuchos::getValue<ParameterList>(paramValue);
      if (paramList1.isParameter("factory")) {  // default: just a factory definition
        // New Factory is a sublist with internal parameters and/or data dependencies
        TEUCHOS_TEST_FOR_EXCEPTION(paramList1.isParameter("dependency for") == true, Exceptions::RuntimeError,
                                   "MueLu::ParameterListInterpreter(): It seems that in the parameter lists for defining " << paramName << " there is both a 'factory' and 'dependency for' parameter. This is not allowed. Please remove the 'dependency for' parameter.");

        factoryMapOut[paramName] = factFact_->BuildFactory(paramValue, factoryMapIn, factoryManagers);

      } else if (paramList1.isParameter("dependency for")) {  // add more data dependencies to existing factory
        TEUCHOS_TEST_FOR_EXCEPTION(paramList1.isParameter("factory") == true, Exceptions::RuntimeError,
                                   "MueLu::ParameterListInterpreter(): It seems that in the parameter lists for defining " << paramName << " there is both a 'factory' and 'dependency for' parameter. This is not allowed.");

        std::string factoryName = paramList1.get<std::string>("dependency for");

        RCP<const FactoryBase> factbase = factoryMapIn.find(factoryName /*paramName*/)->second;  // access previously defined factory
        TEUCHOS_TEST_FOR_EXCEPTION(factbase.is_null() == true, Exceptions::RuntimeError,
                                   "MueLu::ParameterListInterpreter(): could not find factory " + factoryName + " in factory map. Did you define it before?");

        RCP<const Factory> factoryconst = Teuchos::rcp_dynamic_cast<const Factory>(factbase);
        RCP<Factory> factory            = Teuchos::rcp_const_cast<Factory>(factoryconst);

        // Read the RCP<Factory> parameters of the class T
        RCP<const ParameterList> validParamList = factory->GetValidParameterList();
        for (ParameterList::ConstIterator vparam = validParamList->begin(); vparam != validParamList->end(); ++vparam) {
          const std::string& pName = validParamList->name(vparam);

          if (!paramList1.isParameter(pName)) {
            // Ignore unknown parameters
            continue;
          }

          if (validParamList->isType<RCP<const FactoryBase> >(pName)) {
            // Generate or get factory described by pName and set dependency
            RCP<const FactoryBase> generatingFact = factFact_->BuildFactory(paramList1.getEntry(pName), factoryMapIn, factoryManagers);
            factory->SetFactory(pName, generatingFact.create_weak());

          } else if (validParamList->isType<RCP<const ParameterList> >(pName)) {
            if (pName == "ParameterList") {
              // NOTE: we cannot use
              //     subList = sublist(rcpFromRef(paramList), pName)
              // here as that would result in sublist also being a reference to a temporary object.
              // The resulting dereferencing in the corresponding factory would then segfault
              RCP<const ParameterList> subList = Teuchos::sublist(rcp(new ParameterList(paramList1)), pName);
              factory->SetParameter(pName, ParameterEntry(subList));
            }
          } else {
            factory->SetParameter(pName, paramList1.getEntry(pName));
          }
        }

      } else if (paramList1.isParameter("group")) {  // definitiion of a factory group (for a factory manager)
        // Define a new (sub) FactoryManager
        std::string groupType = paramList1.get<std::string>("group");
        TEUCHOS_TEST_FOR_EXCEPTION(groupType != "FactoryManager", Exceptions::RuntimeError,
                                   "group must be of type \"FactoryManager\".");

        ParameterList groupList = paramList1;  // copy because list temporally modified (remove 'id')
        groupList.remove("group");

        bool setKokkosRefactor = false;
        bool kokkosRefactor    = useKokkos_;
        if (groupList.isParameter("use kokkos refactor")) {
          kokkosRefactor = groupList.get<bool>("use kokkos refactor");
          groupList.remove("use kokkos refactor");
          setKokkosRefactor = true;
        }

        FactoryMap groupFactoryMap;
        BuildFactoryMap(groupList, factoryMapIn, groupFactoryMap, factoryManagers);

        // do not store groupFactoryMap in factoryMapOut
        // Create a factory manager object from groupFactoryMap
        RCP<FactoryManager> m = rcp(new FactoryManager(groupFactoryMap));
        if (setKokkosRefactor)
          m->SetKokkosRefactor(kokkosRefactor);
        factoryManagers[paramName] = m;

      } else {
        this->GetOStream(Warnings0) << "Could not interpret parameter list " << paramList1 << std::endl;
        TEUCHOS_TEST_FOR_EXCEPTION(false, Exceptions::RuntimeError,
                                   "XML Parameter list must either be of type \"factory\" or of type \"group\".");
      }
    } else {
      // default: just a factory (no parameter list)
      factoryMapOut[paramName] = factFact_->BuildFactory(paramValue, factoryMapIn, factoryManagers);
    }
  }
}

// =====================================================================================================
// ======================================= MISC functions ==============================================
// =====================================================================================================
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::SetupOperator(Operator& Op) const {
  try {
    Matrix& A = dynamic_cast<Matrix&>(Op);
    if (A.IsFixedBlockSizeSet() && (A.GetFixedBlockSize() != blockSize_))
      this->GetOStream(Warnings0) << "Setting matrix block size to " << blockSize_ << " (value of the parameter in the list) "
                                  << "instead of " << A.GetFixedBlockSize() << " (provided matrix)." << std::endl
                                  << "You may want to check \"number of equations\" (or \"PDE equations\" for factory style list) parameter." << std::endl;

    A.SetFixedBlockSize(blockSize_, dofOffset_);

#ifdef HAVE_MUELU_DEBUG
    MatrixUtils::checkLocalRowMapMatchesColMap(A);
#endif  // HAVE_MUELU_DEBUG

  } catch (std::bad_cast&) {
    this->GetOStream(Warnings0) << "Skipping setting block size as the operator is not a matrix" << std::endl;
  }
}

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::SetupHierarchy(Hierarchy& H) const {
  H.SetCycle(Cycle_);
  H.SetCycleStartLevel(WCycleStartLevel_);
  H.SetProlongatorScalingFactor(scalingFactor_);
  HierarchyManager::SetupHierarchy(H);
}

static bool compare(const ParameterList& list1, const ParameterList& list2) {
  // First loop through and validate the parameters at this level.
  // In addition, we generate a list of sublists that we will search next
  for (ParameterList::ConstIterator it = list1.begin(); it != list1.end(); it++) {
    const std::string& name               = it->first;
    const Teuchos::ParameterEntry& entry1 = it->second;

    const Teuchos::ParameterEntry* entry2 = list2.getEntryPtr(name);
    if (!entry2)  // entry is not present in the second list
      return false;
    if (entry1.isList() && entry2->isList()) {  // sublist check
      compare(Teuchos::getValue<ParameterList>(entry1), Teuchos::getValue<ParameterList>(*entry2));
      continue;
    }
    if (entry1.getAny(false) != entry2->getAny(false))  // entries have different types or different values
      return false;
  }

  return true;
}

static inline bool areSame(const ParameterList& list1, const ParameterList& list2) {
  return compare(list1, list2) && compare(list2, list1);
}

}  // namespace MueLu

#define MUELU_PARAMETERLISTINTERPRETER_SHORT
#endif /* MUELU_PARAMETERLISTINTERPRETER_DEF_HPP */