MueLu_ParameterListInterpreter_def.hpp

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//
// ***********************************************************************
//
//        MueLu: A package for multigrid based preconditioning
//                  Copyright 2012 Sandia Corporation
//
// Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
// the U.S. Government retains certain rights in this software.
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// modification, are permitted provided that the following conditions are
// met:
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// 1. Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
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// 2. Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
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// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
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// Questions? Contact
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// @HEADER
#ifndef MUELU_PARAMETERLISTINTERPRETER_DEF_HPP
#define MUELU_PARAMETERLISTINTERPRETER_DEF_HPP

#include <Teuchos_XMLParameterListHelpers.hpp>

#include <Xpetra_Matrix.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_BrickAggregationFactory.hpp"
#include "MueLu_CoalesceDropFactory.hpp"
#include "MueLu_CoarseMapFactory.hpp"
#include "MueLu_ConstraintFactory.hpp"
#include "MueLu_CoordinatesTransferFactory.hpp"
#include "MueLu_CoupledAggregationFactory.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_LineDetectionFactory.hpp"
#include "MueLu_MasterList.hpp"
#include "MueLu_NullspaceFactory.hpp"
#include "MueLu_PatternFactory.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_SaPFactory.hpp"
#include "MueLu_SemiCoarsenPFactory.hpp"
#include "MueLu_SmootherFactory.hpp"
#include "MueLu_TentativePFactory.hpp"
#include "MueLu_TogglePFactory.hpp"
#include "MueLu_ToggleCoordinatesTransferFactory.hpp"
#include "MueLu_TransPFactory.hpp"
#include "MueLu_UncoupledAggregationFactory.hpp"
#include "MueLu_HybridAggregationFactory.hpp"
#include "MueLu_ZoltanInterface.hpp"
#include "MueLu_Zoltan2Interface.hpp"
#include "MueLu_NodePartitionInterface.hpp"

#ifdef HAVE_MUELU_KOKKOS_REFACTOR
#include "MueLu_CoalesceDropFactory_kokkos.hpp"
#include "MueLu_CoarseMapFactory_kokkos.hpp"
#include "MueLu_CoordinatesTransferFactory_kokkos.hpp"
#include "MueLu_NullspaceFactory_kokkos.hpp"
#include "MueLu_SaPFactory_kokkos.hpp"
#include "MueLu_TentativePFactory_kokkos.hpp"
#include "MueLu_UncoupledAggregationFactory_kokkos.hpp"
#endif

#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>
  void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::SetParameterList(const ParameterList& paramList) {
    Cycle_     = Hierarchy::GetDefaultCycle();
    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) ) ) )

#ifndef HAVE_MUELU_KOKKOS_REFACTOR
#define MUELU_KOKKOS_FACTORY(varName, oldFactory, newFactory) \
  RCP<Factory> varName = rcp(new oldFactory());
#define MUELU_KOKKOS_FACTORY_NO_DECL(varName, oldFactory, newFactory) \
  varName = rcp(new oldFactory());
#else
#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());
#endif

  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
#if !defined(HAVE_MUELU_KOKKOS_REFACTOR)
    useKokkos_ = false;
#elif defined(HAVE_MUELU_KOKKOS_REFACTOR_USE_BY_DEFAULT)
    ParameterList tempList("tempList");
    tempList.set("use kokkos refactor",true);
    MUELU_SET_VAR_2LIST(paramList, tempList, "use kokkos refactor", bool, useKokkos);
    useKokkos_ = useKokkos;
#else
    MUELU_SET_VAR_2LIST(paramList, paramList, "use kokkos refactor", bool, useKokkos);
    useKokkos_ = useKokkos;
#endif

    // 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("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_);

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

      if (printList.isParameter("A"))
        this->matricesToPrint_     = Teuchos::getArrayFromStringParameter<int>(printList, "A");
      if (printList.isParameter("P"))
        this->prolongatorsToPrint_ = Teuchos::getArrayFromStringParameter<int>(printList, "P");
      if (printList.isParameter("R"))
        this->restrictorsToPrint_  = Teuchos::getArrayFromStringParameter<int>(printList, "R");
      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("pcoarsen: element to node map"))
        this->elementToNodeMapsToPrint_  = Teuchos::getArrayFromStringParameter<int>(printList, "pcoarsen: element to node map");
    }

    // Set verbosity parameter
    VerbLevel oldVerbLevel = VerboseObject::GetDefaultVerbLevel();
    {
      std::map<std::string, MsgType> verbMap;
      verbMap["none"]    = None;
      verbMap["low"]     = Low;
      verbMap["medium"]  = Medium;
      verbMap["high"]    = High;
      verbMap["extreme"] = Extreme;
      verbMap["test"]    = Test;

      MUELU_SET_VAR_2LIST(paramList, paramList, "verbosity", std::string, verbosityLevel);

      TEUCHOS_TEST_FOR_EXCEPTION(verbMap.count(verbosityLevel) == 0, Exceptions::RuntimeError,
                                 "Invalid verbosity level: \"" << verbosityLevel << "\"");
      this->verbosity_ = verbMap[verbosityLevel];
      VerboseObject::SetDefaultVerbLevel(this->verbosity_);
    }

    // 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;
    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(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;
            break;
          }
        }
      }
    }

    if(MUELU_TEST_PARAM_2LIST(paramList, paramList, "repartition: enable",      bool,        true)) {
      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;
    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_);

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

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

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

    // 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);
    }

    // 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"}).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;

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

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

    // === Aggregation ===
    UpdateFactoryManager_Aggregation_TentativeP(paramList, defaultList, manager, levelID, keeps);

    // === Nullspace ===
    RCP<Factory> nullSpaceFactory; // Cache this 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") {
      // Unsmoothed aggregation
      manager.SetFactory("P", manager.GetFactory("Ptent"));

    } else if (multigridAlgo == "sa") {
      // 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 == "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);

    // === Coordinates ===
    UpdateFactoryManager_Coordinates(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);

    // === 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()));
    }
  }

  // =====================================================================================================
  // ========================================= 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);

    // === 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;

#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 == 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")) {
      this->GetOStream(Warnings0) << "No coarse grid solver" << std::endl;
      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"}).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)));
    }
  }

  // =====================================================================================================
  // ========================================= Smoothers =================================================
  // =====================================================================================================
  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);

    // 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 {
      MUELU_KOKKOS_FACTORY_NO_DECL(dropFactory, CoalesceDropFactory, CoalesceDropFactory_kokkos);
      ParameterList dropParams;
      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: drop tol",             double, dropParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: Dirichlet threshold",  double, 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);
      }
      dropFactory->SetParameterList(dropParams);
    }
    manager.SetFactory("Graph", dropFactory);

    // Aggregation scheme
    MUELU_SET_VAR_2LIST(paramList, defaultList, "aggregation: type", std::string, aggType);
    TEUCHOS_TEST_FOR_EXCEPTION(!strings({"uncoupled", "coupled", "brick", "matlab"}).count(aggType),
        Exceptions::RuntimeError, "Unknown aggregation algorithm: \"" << aggType << "\". Please consult User's Guide.");
    #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") {
      MUELU_KOKKOS_FACTORY_NO_DECL(aggFactory, UncoupledAggregationFactory, UncoupledAggregationFactory_kokkos);
      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);
      if(useKokkos_) {
        //if not using kokkos refactor Uncoupled, there is no algorithm option (always Serial)
        MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "aggregation: phase 1 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: 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"));

    } else if (aggType == "coupled") {
      aggFactory = rcp(new CoupledAggregationFactory());
      aggFactory->SetFactory("Graph", manager.GetFactory("Graph"));

    } 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);
      aggFactory->SetParameterList(aggParams);

      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"));
      }
    }
#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
    MUELU_KOKKOS_FACTORY(coarseMap, CoarseMapFactory, CoarseMapFactory_kokkos);
    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());
    }

    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: 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"));
    }

    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);
      aggExport->SetParameterList(aggExportParams);
      aggExport->SetFactory("DofsPerNode", manager.GetFactory("DofsPerNode"));

      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()));
      }
    }
  }

  // =====================================================================================================
  // ======================================= Restriction =================================================
  // =====================================================================================================
  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 {
        MUELU_KOKKOS_FACTORY(coords, CoordinatesTransferFactory, CoordinatesTransferFactory_kokkos);
        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"));
        }
      }
    }
  }

  // =====================================================================================================
  // ======================================= 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 ===
    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 {
          RCP<Factory> R;
          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);
      }
  }

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

    if (enableRepart) {
#ifdef HAVE_MPI
      // 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\"");

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

      // 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: 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) {
#ifdef HAVE_MPI
        //        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
        throw Exceptions::RuntimeError("MPI is not available");
#endif
      }
      else if (partName == "zoltan") {
#ifdef HAVE_MUELU_ZOLTAN
        partitioner = rcp(new ZoltanInterface());
        // NOTE: ZoltanInteface ("zoltan") does not support external parameters through ParameterList
#else
        throw Exceptions::RuntimeError("Zoltan interface is not available");
#endif
      } 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
      }
     
      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);
      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()));

      // 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_);
      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"));
      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("P",           newP);
      if (useCoordinates_)
        manager.SetFactory("Coordinates", 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 (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").
      nullSpaceFactory->SetFactory("Nullspace", newP);
#else
      throw Exceptions::RuntimeError("No repartitioning available for a serial run");
#endif
    }
  }

  // =====================================================================================================
  // =========================================== 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
    MUELU_KOKKOS_FACTORY(nullSpace, NullspaceFactory, NullspaceFactory_kokkos);

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

    if (!have_userNS) {
      nullSpace->SetFactory("Nullspace", manager.GetFactory("Ptent"));
      manager.SetFactory("Nullspace", nullSpace);
    }
    nullSpaceFactory = nullSpace;
  }

  // =====================================================================================================
  // ================================= 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<SemiCoarsenPFactory>  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, "linedetection: orientation",    std::string, linedetectionParams);
      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "linedetection: num layers",     int,         linedetectionParams);

      semicoarsenFactory                             = rcp(new SemiCoarsenPFactory());
      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);

      MUELU_KOKKOS_FACTORY(coords, CoordinatesTransferFactory, CoordinatesTransferFactory_kokkos);
      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
    MUELU_KOKKOS_FACTORY(P, SaPFactory, SaPFactory_kokkos);
    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);
    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);
        filterFactory->SetParameterList(fParams);
        filterFactory->SetFactory("Graph",      manager.GetFactory("Graph"));
        // 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"));
    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
    auto P = rcp(new EminPFactory());
    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);
    }
    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: 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("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];
      }

      //TODO Move this its own class or MueLu::Utils?
      std::map<std::string, MsgType> verbMap;
      //for developers
      verbMap["Errors"]         = Errors;
      verbMap["Warnings0"]      = Warnings0;
      verbMap["Warnings00"]     = Warnings00;
      verbMap["Warnings1"]      = Warnings1;
      verbMap["PerfWarnings"]   = PerfWarnings;
      verbMap["Runtime0"]       = Runtime0;
      verbMap["Runtime1"]       = Runtime1;
      verbMap["RuntimeTimings"] = RuntimeTimings;
      verbMap["NoTimeReport"]   = NoTimeReport;
      verbMap["Parameters0"]    = Parameters0;
      verbMap["Parameters1"]    = Parameters1;
      verbMap["Statistics0"]    = Statistics0;
      verbMap["Statistics1"]    = Statistics1;
      verbMap["Timings0"]       = Timings0;
      verbMap["Timings1"]       = Timings1;
      verbMap["TimingsByLevel"] = TimingsByLevel;
      verbMap["External"]       = External;
      verbMap["Debug"]          = Debug;
      verbMap["Test"]           = Test;
      //for users and developers
      verbMap["None"]           = None;
      verbMap["Low"]            = Low;
      verbMap["Medium"]         = Medium;
      verbMap["High"]           = High;
      verbMap["Extreme"]        = Extreme;
      if (hieraList.isParameter("verbosity")) {
        std::string vl = hieraList.get<std::string>("verbosity");
        hieraList.remove("verbosity");
        //TODO Move this to its own class or MueLu::Utils?
        if (verbMap.find(vl) != verbMap.end())
          this->verbosity_ = verbMap[vl];
        else
          TEUCHOS_TEST_FOR_EXCEPTION(true, Exceptions::RuntimeError, "MueLu::ParameterListInterpreter():: invalid verbosity level");
      }

      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_ = Teuchos::getArrayFromStringParameter<int>(foo, dataName);
        dataName = "Prolongators";
        if (foo.isParameter(dataName))
          this->prolongatorsToPrint_ = Teuchos::getArrayFromStringParameter<int>(foo, dataName);
        dataName = "Restrictors";
        if (foo.isParameter(dataName))
          this->restrictorsToPrint_ = 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");

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

          // do not store groupFactoryMap in factoryMapOut
          // Create a factory manager object from groupFactoryMap
          RCP<FactoryManagerBase> m = rcp(new FactoryManager(groupFactoryMap));

          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.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_);

    } catch (std::bad_cast& e) {
      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.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 */