MueLu_LocalPermutationStrategy_def.hpp

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/*
 * MueLu_LocalPermutationStrategy_def.hpp
 *
 *  Created on: Feb 19, 2013
 *      Author: tobias
 */

#ifndef MUELU_LOCALPERMUTATIONSTRATEGY_DEF_HPP_
#define MUELU_LOCALPERMUTATIONSTRATEGY_DEF_HPP_

#include <algorithm>

#include <Xpetra_MultiVector.hpp>
#include <Xpetra_Matrix.hpp>
#include <Xpetra_MatrixMatrix.hpp>
#include <Xpetra_CrsGraph.hpp>
#include <Xpetra_Vector.hpp>
#include <Xpetra_VectorFactory.hpp>
#include <Xpetra_CrsMatrixWrap.hpp>

#include "MueLu_Utilities.hpp"
#include "MueLu_LocalPermutationStrategy_decl.hpp"

namespace MueLu {

  template<class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void LocalPermutationStrategy<Scalar, LocalOrdinal, GlobalOrdinal, Node>::BuildPermutations(size_t nDofsPerNode) const {

    permWidth_ = nDofsPerNode;

    result_permvecs_.clear();

    // build permutation string
    std::stringstream ss;
    for(size_t t = 0; t<nDofsPerNode; t++)
      ss << t;
    std::string cs = ss.str();
    //std::vector<std::string> result_perms;
    do {
      //result_perms.push_back(cs);

      std::vector<int> newPerm(cs.length(),-1);
      for(size_t len=0; len<cs.length(); len++) {
        newPerm[len] = Teuchos::as<int>(cs[len]-'0');
      }
      result_permvecs_.push_back(newPerm);

    } while (std::next_permutation(cs.begin(),cs.end()));
  }

  template<class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void LocalPermutationStrategy<Scalar, LocalOrdinal, GlobalOrdinal, Node>::BuildPermutation(const Teuchos::RCP<Matrix> & A, const Teuchos::RCP<const Map> /* permRowMap */, Level & currentLevel, const FactoryBase* genFactory) const {

    SC SC_ZERO = Teuchos::ScalarTraits<SC>::zero();

    size_t nDofsPerNode = 1;
    if (A->IsView("stridedMaps")) {
      Teuchos::RCP<const Map> permRowMapStrided = A->getRowMap("stridedMaps");
      nDofsPerNode = Teuchos::rcp_dynamic_cast<const StridedMap>(permRowMapStrided)->getFixedBlockSize();
    }

    RCP<const Teuchos::Comm<int> > comm = A->getRowMap()->getComm();

    std::vector<std::pair<GlobalOrdinal,GlobalOrdinal> > RowColPairs;

    // check whether we have to (re)build the permutation vector
    if(permWidth_ != nDofsPerNode)
      BuildPermutations(nDofsPerNode);

    // declare local variables used inside loop
    LocalOrdinal lonDofsPerNode = Teuchos::as<LocalOrdinal> (nDofsPerNode);
    Teuchos::ArrayView<const LocalOrdinal> indices;
    Teuchos::ArrayView<const Scalar> vals;
    Teuchos::SerialDenseMatrix<LocalOrdinal,Scalar> subBlockMatrix(nDofsPerNode, nDofsPerNode, true);
    std::vector<GlobalOrdinal> growIds(nDofsPerNode);

    // loop over local nodes
    // TODO what about nOffset?
    LocalOrdinal numLocalNodes = A->getRowMap()->getNodeNumElements()/nDofsPerNode;
    for (LocalOrdinal node = 0; node < numLocalNodes; ++node) {

      // zero out block matrix
      subBlockMatrix.putScalar();

      // loop over all DOFs in current node
      // Note: were assuming constant number of Dofs per node here!
      // TODO This is more complicated for variable dofs per node
      for (LocalOrdinal lrdof = 0; lrdof < lonDofsPerNode; ++lrdof) {
        GlobalOrdinal grow = getGlobalDofId(A, node, lrdof);
        growIds[lrdof] = grow;

        // extract local row information from matrix
        A->getLocalRowView(A->getRowMap()->getLocalElement(grow), indices, vals);

        // find column entry with max absolute value
        typedef typename Teuchos::ScalarTraits<Scalar>::magnitudeType MT;
        MT maxVal = 0.0;
        for (size_t j = 0; j < Teuchos::as<size_t>(indices.size()); j++) {
          if(Teuchos::ScalarTraits<Scalar>::magnitude(vals[j]) > maxVal) {
            maxVal = Teuchos::ScalarTraits<Scalar>::magnitude(vals[j]);
          }
        }

        GlobalOrdinal grnodeid = globalDofId2globalNodeId(A,grow);

        for (size_t j = 0; j < Teuchos::as<size_t>(indices.size()); j++) {
          GlobalOrdinal gcol = A->getColMap()->getGlobalElement(indices[j]);
          GlobalOrdinal gcnodeid = globalDofId2globalNodeId(A,gcol); // -> global node id
          if (grnodeid == gcnodeid) {
            if(maxVal != Teuchos::ScalarTraits<MT>::zero ()) {
              subBlockMatrix(lrdof, gcol % nDofsPerNode) = vals[j]/maxVal;
            } else
            {
              subBlockMatrix(lrdof, gcol % nDofsPerNode) = vals[j]; // there is a problem
              std::cout << "maxVal never should be zero!!!!" << std::endl;
            }
          }
        }
      }

      // now we have the sub block matrix

      // build permutation string
      /*std::stringstream ss;
      for(size_t t = 0; t<nDofsPerNode; t++)
        ss << t;
      std::string cs = ss.str();
      std::vector<std::string> result_perms;
      do {
        result_perms.push_back(cs);
        //std::cout << result_perms.back() << std::endl;
      } while (std::next_permutation(cs.begin(),cs.end()));*/

      std::vector<Scalar> performance_vector = std::vector<Scalar>(result_permvecs_.size());
      for (size_t t = 0; t < result_permvecs_.size(); t++) {
        std::vector<int> vv = result_permvecs_[t];
        Scalar value = 1.0;
        for(size_t j=0; j<vv.size(); j++) {
          value = value * subBlockMatrix(j,vv[j]);
        }
        performance_vector[t] = value;
      }
      /*for(size_t t = 0; t < result_perms.size(); t++) {
        std::string s = result_perms[t];
        Scalar value = 1.0;
        for(size_t len=0; len<s.length(); len++) {
          int col = Teuchos::as<int>(s[len]-'0');
          value = value * subBlockMatrix(len,col);
        }
        performance_vector[t] = value;
      }*/

      // find permutation with maximum performance value
      typedef typename Teuchos::ScalarTraits<Scalar>::magnitudeType MT;
      MT maxVal = Teuchos::ScalarTraits<MT>::zero();
      size_t maxPerformancePermutationIdx = 0;
      for (size_t j = 0; j < Teuchos::as<size_t>(performance_vector.size()); j++) {
        if(Teuchos::ScalarTraits<Scalar>::magnitude(performance_vector[j]) > maxVal) {
          maxVal = Teuchos::ScalarTraits<Scalar>::magnitude(performance_vector[j]);
          maxPerformancePermutationIdx = j;
        }
      }

      // build RowColPairs for best permutation
      std::vector<int> bestPerformancePermutation = result_permvecs_[maxPerformancePermutationIdx];
      for(size_t t = 0; t<nDofsPerNode; t++) {
        RowColPairs.push_back(std::make_pair(growIds[t],growIds[bestPerformancePermutation[t]]));
      }

    } // end loop over local nodes


    // build Pperm and Qperm vectors
    Teuchos::RCP<Vector> Pperm = VectorFactory::Build(A->getRowMap());
    Teuchos::RCP<Vector> Qperm = VectorFactory::Build(A->getDomainMap());

    Pperm->putScalar(SC_ZERO);
    Qperm->putScalar(SC_ZERO);

    Teuchos::ArrayRCP<Scalar> PpermData = Pperm->getDataNonConst(0);
    Teuchos::ArrayRCP<Scalar> QpermData = Qperm->getDataNonConst(0);

    typename std::vector<std::pair<GlobalOrdinal, GlobalOrdinal> >::iterator p = RowColPairs.begin();
    while(p != RowColPairs.end() ) {
      GlobalOrdinal ik = (*p).first;
      GlobalOrdinal jk = (*p).second;

      LocalOrdinal lik = A->getRowMap()->getLocalElement(ik);
      LocalOrdinal ljk = A->getDomainMap()->getLocalElement(jk);

      Pperm->replaceLocalValue(lik,ik);
      Qperm->replaceLocalValue(ljk,ik);

      p = RowColPairs.erase(p);
    }

    if(RowColPairs.size()>0) GetOStream(Warnings0) << "MueLu::LocalPermutationStrategy: There are Row/col pairs left!" << std::endl;

    // Qperm should be fine
    // build matrices

    // create new empty Matrix
    Teuchos::RCP<CrsMatrixWrap> permPTmatrix = Teuchos::rcp(new CrsMatrixWrap(A->getRowMap(),1,Xpetra::StaticProfile));
    Teuchos::RCP<CrsMatrixWrap> permQTmatrix = Teuchos::rcp(new CrsMatrixWrap(A->getRowMap(),1,Xpetra::StaticProfile));

    for(size_t row=0; row<A->getNodeNumRows(); row++) {
      Teuchos::ArrayRCP<GlobalOrdinal> indoutP(1,Teuchos::as<GO>(Teuchos::ScalarTraits<Scalar>::real(PpermData[row]))); // column idx for Perm^T
      Teuchos::ArrayRCP<GlobalOrdinal> indoutQ(1,Teuchos::as<GO>(Teuchos::ScalarTraits<Scalar>::real(QpermData[row]))); // column idx for Qperm
      Teuchos::ArrayRCP<Scalar> valout(1,Teuchos::ScalarTraits<Scalar>::one());
      permPTmatrix->insertGlobalValues(A->getRowMap()->getGlobalElement(row), indoutP.view(0,indoutP.size()), valout.view(0,valout.size()));
      permQTmatrix->insertGlobalValues (A->getRowMap()->getGlobalElement(row), indoutQ.view(0,indoutQ.size()), valout.view(0,valout.size()));
    }

    permPTmatrix->fillComplete();
    permQTmatrix->fillComplete();

    Teuchos::RCP<Matrix> permPmatrix = Utilities::Transpose(*permPTmatrix,true);

    /*for(size_t row=0; row<permPTmatrix->getNodeNumRows(); row++) {
      if(permPTmatrix->getNumEntriesInLocalRow(row) != 1)
        GetOStream(Warnings0) <<"#entries in row " << row << " of permPTmatrix is " << permPTmatrix->getNumEntriesInLocalRow(row) << std::endl;
      if(permPmatrix->getNumEntriesInLocalRow(row) != 1)
        GetOStream(Warnings0) <<"#entries in row " << row << " of permPmatrix is " << permPmatrix->getNumEntriesInLocalRow(row) << std::endl;
      if(permQTmatrix->getNumEntriesInLocalRow(row) != 1)
        GetOStream(Warnings0) <<"#entries in row " << row << " of permQmatrix is " << permQTmatrix->getNumEntriesInLocalRow(row) << std::endl;
    }*/

    // build permP * A * permQT
    Teuchos::RCP<Matrix> ApermQt = Xpetra::MatrixMatrix<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Multiply(*A, false, *permQTmatrix, false, GetOStream(Statistics2),true,true);
    Teuchos::RCP<Matrix> permPApermQt = Xpetra::MatrixMatrix<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Multiply(*permPmatrix, false, *ApermQt, false, GetOStream(Statistics2),true,true);

    /*
    MueLu::Utils<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Write("A.mat", *A);
    MueLu::Utils<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Write("permP.mat", *permPmatrix);
    MueLu::Utils<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Write("permQt.mat", *permQTmatrix);
    MueLu::Utils<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Write("permPApermQt.mat", *permPApermQt);
    */
    // build scaling matrix
    Teuchos::RCP<Vector> diagVec = VectorFactory::Build(permPApermQt->getRowMap(),true);
    Teuchos::RCP<Vector> invDiagVec = VectorFactory::Build(permPApermQt->getRowMap(),true);
    Teuchos::ArrayRCP< const Scalar > diagVecData = diagVec->getData(0);
    Teuchos::ArrayRCP< Scalar > invDiagVecData = invDiagVec->getDataNonConst(0);

    LO lCntZeroDiagonals = 0;
    permPApermQt->getLocalDiagCopy(*diagVec);
    for(size_t i = 0; i<diagVec->getMap()->getNodeNumElements(); ++i) {
      if(diagVecData[i] != SC_ZERO)
        invDiagVecData[i] = Teuchos::ScalarTraits<Scalar>::one()/diagVecData[i];
      else {
        invDiagVecData[i] = Teuchos::ScalarTraits<Scalar>::one();
        lCntZeroDiagonals++;
        //GetOStream(Statistics0) << "MueLu::LocalPermutationStrategy: found zero on diagonal in row " << i << std::endl;
      }
    }

#if 0
    GO gCntZeroDiagonals  = 0;
    GO glCntZeroDiagonals = Teuchos::as<GlobalOrdinal>(lCntZeroDiagonals);  /* LO->GO conversion */
    MueLu_sumAll(comm,glCntZeroDiagonals,gCntZeroDiagonals);
    GetOStream(Statistics0) << "MueLu::LocalPermutationStrategy: found " << gCntZeroDiagonals << " zeros on diagonal" << std::endl;
#endif

    Teuchos::RCP<CrsMatrixWrap> diagScalingOp = Teuchos::rcp(new CrsMatrixWrap(permPApermQt->getRowMap(),1,Xpetra::StaticProfile));

    for(size_t row=0; row<A->getNodeNumRows(); row++) {
      Teuchos::ArrayRCP<GlobalOrdinal> indout(1,permPApermQt->getRowMap()->getGlobalElement(row)); // column idx for Perm^T
      Teuchos::ArrayRCP<Scalar> valout(1,invDiagVecData[row]);
      diagScalingOp->insertGlobalValues(A->getRowMap()->getGlobalElement(row), indout.view(0,indout.size()), valout.view(0,valout.size()));
    }
    diagScalingOp->fillComplete();

    Teuchos::RCP<Matrix> scaledA = Xpetra::MatrixMatrix<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Multiply(*diagScalingOp, false, *permPApermQt, false, GetOStream(Statistics2), true, true);
    currentLevel.Set("A", Teuchos::rcp_dynamic_cast<Matrix>(scaledA), genFactory);

    currentLevel.Set("permA", Teuchos::rcp_dynamic_cast<Matrix>(permPApermQt), genFactory);
    currentLevel.Set("permP", Teuchos::rcp_dynamic_cast<Matrix>(permPmatrix), genFactory);
    currentLevel.Set("permQT", Teuchos::rcp_dynamic_cast<Matrix>(permQTmatrix), genFactory);
    currentLevel.Set("permScaling", Teuchos::rcp_dynamic_cast<Matrix>(diagScalingOp), genFactory);

    // count zeros on diagonal in P -> number of row permutations
    Teuchos::RCP<Vector> diagPVec = VectorFactory::Build(permPmatrix->getRowMap(),true);
    permPmatrix->getLocalDiagCopy(*diagPVec);
    Teuchos::ArrayRCP< const Scalar > diagPVecData = diagPVec->getData(0);
    GlobalOrdinal lNumRowPermutations = 0;
    GlobalOrdinal gNumRowPermutations = 0;
    for(size_t i = 0; i<diagPVec->getMap()->getNodeNumElements(); ++i) {
      if(diagPVecData[i] == SC_ZERO) {
        lNumRowPermutations++;
      }
    }

    // sum up all entries in multipleColRequests over all processors
    MueLu_sumAll(diagPVec->getMap()->getComm(), lNumRowPermutations, gNumRowPermutations);

    // count zeros on diagonal in Q^T -> number of column permutations
    Teuchos::RCP<Vector> diagQTVec = VectorFactory::Build(permQTmatrix->getRowMap(),true);
    permQTmatrix->getLocalDiagCopy(*diagQTVec);
    Teuchos::ArrayRCP< const Scalar > diagQTVecData = diagQTVec->getData(0);
    GlobalOrdinal lNumColPermutations = 0;
    GlobalOrdinal gNumColPermutations = 0;
    for(size_t i = 0; i<diagQTVec->getMap()->getNodeNumElements(); ++i) {
      if(diagQTVecData[i] == SC_ZERO) {
        lNumColPermutations++;
      }
    }

    // sum up all entries in multipleColRequests over all processors
    MueLu_sumAll(diagQTVec->getMap()->getComm(), lNumColPermutations, gNumColPermutations);

    currentLevel.Set("#RowPermutations", gNumRowPermutations, genFactory/*this*/);
    currentLevel.Set("#ColPermutations", gNumColPermutations, genFactory/*this*/);
    currentLevel.Set("#WideRangeRowPermutations", 0, genFactory/*this*/);
    currentLevel.Set("#WideRangeColPermutations", 0, genFactory/*this*/);

    GetOStream(Statistics0) << "#Row    permutations/max possible permutations: " << gNumRowPermutations << "/" << diagPVec->getMap()->getGlobalNumElements() << std::endl;
    GetOStream(Statistics0) << "#Column permutations/max possible permutations: " << gNumColPermutations << "/" << diagQTVec->getMap()->getGlobalNumElements() << std::endl;
  }

  template<class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  GlobalOrdinal LocalPermutationStrategy<Scalar, LocalOrdinal, GlobalOrdinal, Node>::getGlobalDofId(const Teuchos::RCP<Matrix> & A, LocalOrdinal localNodeId, LocalOrdinal localDof) const {
    size_t nDofsPerNode = 1;
    if (A->IsView("stridedMaps")) {
      Teuchos::RCP<const Map> permRowMapStrided = A->getRowMap("stridedMaps");
      nDofsPerNode = Teuchos::rcp_dynamic_cast<const StridedMap>(permRowMapStrided)->getFixedBlockSize();
    }

    LocalOrdinal localDofId = localNodeId * nDofsPerNode + localDof;

    return A->getRowMap()->getGlobalElement(localDofId);
  }

  template<class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  GlobalOrdinal LocalPermutationStrategy<Scalar, LocalOrdinal, GlobalOrdinal, Node>::globalDofId2globalNodeId( const Teuchos::RCP<Matrix> & A, GlobalOrdinal grid ) const {
    size_t nDofsPerNode = 1;
    if (A->IsView("stridedMaps")) {
      Teuchos::RCP<const Map> permRowMapStrided = A->getRowMap("stridedMaps");
      nDofsPerNode = Teuchos::rcp_dynamic_cast<const StridedMap>(permRowMapStrided)->getFixedBlockSize();
    }

    return (GlobalOrdinal) grid / (GlobalOrdinal)nDofsPerNode; // TODO what about nOffset???
  }

} // namespace MueLu


#endif /* MUELU_LOCALPERMUTATIONSTRATEGY_DEF_HPP_ */