PetscSolverGlobalMatrix.cc 21.5 KB
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//
// Software License for AMDiS
//
// Copyright (c) 2010 Dresden University of Technology 
// All rights reserved.
// Authors: Simon Vey, Thomas Witkowski et al.
//
// This file is part of AMDiS
//
// See also license.opensource.txt in the distribution.


#include "parallel/PetscSolverGlobalMatrix.h"
#include "parallel/StdMpi.h"
#include "parallel/MpiHelper.h"

namespace AMDiS {

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  void PetscSolverGlobalMatrix::fillPetscMatrix(Matrix<DOFMatrix*> *mat)
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  {
    FUNCNAME("PetscSolverGlobalMatrix::fillPetscMatrix()");

    TEST_EXIT_DBG(meshDistributor)("No mesh distributor object defined!\n");
    TEST_EXIT_DBG(mat)("No DOF matrix defined!\n");

    double wtime = MPI::Wtime();
    int nComponents = mat->getNumRows();
    int nRankRows = meshDistributor->getNumberRankDofs() * nComponents;
    int nOverallRows = meshDistributor->getNumberOverallDofs() * nComponents;

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    // === Create PETSc vector (solution and a temporary vector). ===
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    VecCreateMPI(PETSC_COMM_WORLD, nRankRows, nOverallRows, &petscSolVec);
    VecCreateMPI(PETSC_COMM_WORLD, nRankRows, nOverallRows, &petscTmpVec);
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    int recvAllValues = 0;
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    int sendValue = 
      static_cast<int>(meshDistributor->getLastMeshChangeIndex() != lastMeshNnz);
    meshDistributor->getMpiComm().Allreduce(&sendValue, &recvAllValues, 
					    1, MPI_INT, MPI_SUM);
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    recvAllValues = 1;

    if (!d_nnz || recvAllValues != 0 || alwaysCreateNnzStructure) {
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      if (d_nnz) {
	delete [] d_nnz;
	d_nnz = NULL;
	delete [] o_nnz;
	o_nnz = NULL;
      }

      createPetscNnzStructure(mat);
      lastMeshNnz = meshDistributor->getLastMeshChangeIndex();
    }


    // === Create PETSc matrix with the computed nnz data structure. ===

    MatCreateMPIAIJ(PETSC_COMM_WORLD, nRankRows, nRankRows, nOverallRows, nOverallRows,
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		     0, d_nnz, 0, o_nnz, &petscMatrix);

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#if (DEBUG != 0)
    MSG("Fill petsc matrix 1 needed %.5f seconds\n", MPI::Wtime() - wtime);
#endif

#if (DEBUG != 0)
    int a, b;
    MatGetOwnershipRange(petscMatrix, &a, &b);
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    TEST_EXIT(a == meshDistributor->getStartDofs() * nComponents)
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      ("Wrong matrix ownership range!\n");
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    TEST_EXIT(b == meshDistributor->getStartDofs() * nComponents + nRankRows)
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      ("Wrong matrix ownership range!\n");
#endif


    // === Transfer values from DOF matrices to the PETSc matrix. === 

    for (int i = 0; i < nComponents; i++)
      for (int j = 0; j < nComponents; j++)
	if ((*mat)[i][j])
	  setDofMatrix((*mat)[i][j], nComponents, i, j);

#if (DEBUG != 0)
    MSG("Fill petsc matrix 2 needed %.5f seconds\n", MPI::Wtime() - wtime);
#endif

    MatAssemblyBegin(petscMatrix, MAT_FINAL_ASSEMBLY);
    MatAssemblyEnd(petscMatrix, MAT_FINAL_ASSEMBLY);

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    // === Init PETSc solver. ===
    KSPCreate(PETSC_COMM_WORLD, &solver);
    KSPGetPC(solver, &pc);
    KSPSetOperators(solver, petscMatrix, petscMatrix, SAME_NONZERO_PATTERN); 
    KSPSetTolerances(solver, 0.0, 1e-8, PETSC_DEFAULT, PETSC_DEFAULT);
    KSPSetType(solver, KSPBCGS);
    KSPSetFromOptions(solver);
    PCSetFromOptions(pc);

    // Do not delete the solution vector, use it for the initial guess.
    if (!zeroStartVector)
      KSPSetInitialGuessNonzero(solver, PETSC_TRUE);

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    MSG("Fill petsc matrix needed %.5f seconds\n", MPI::Wtime() - wtime);
  }


  void PetscSolverGlobalMatrix::fillPetscRhs(SystemVector *vec)
  {
    FUNCNAME("PetscSolverGlobalMatrix::fillPetscRhs()");

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    TEST_EXIT_DBG(vec)("No DOF vector defined!\n");
    TEST_EXIT_DBG(meshDistributor)("No mesh distributor defined!\n");
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    int nComponents = vec->getSize();
    int nRankRows = meshDistributor->getNumberRankDofs() * nComponents;
    int nOverallRows = meshDistributor->getNumberOverallDofs() * nComponents;

    VecCreateMPI(PETSC_COMM_WORLD, nRankRows, nOverallRows, &petscRhsVec);
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    // === Transfer values from DOF vector to the PETSc vector. === 

    for (int i = 0; i < nComponents; i++)
      setDofVector(petscRhsVec, vec->getDOFVector(i), nComponents, i);

    VecAssemblyBegin(petscRhsVec);
    VecAssemblyEnd(petscRhsVec);
  }


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  void PetscSolverGlobalMatrix::solvePetscMatrix(SystemVector &vec, 
						 AdaptInfo *adaptInfo)
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  {
    FUNCNAME("PetscSolverGlobalMatrix::solvePetscMatrix()");

    int nComponents = vec.getSize();

    // === Set old solution to be initiual guess for PETSc solver. ===
    if (!zeroStartVector) {
      VecSet(petscSolVec, 0.0);
      
      for (int i = 0; i < nComponents; i++)
	setDofVector(petscSolVec, vec.getDOFVector(i), nComponents, i, true);
      
      VecAssemblyBegin(petscSolVec);
      VecAssemblyEnd(petscSolVec);
    }

    // PETSc.
    KSPSolve(solver, petscRhsVec, petscSolVec);

    // === Transfere values from PETSc's solution vectors to the DOF vectors. ===
    int nRankDofs = meshDistributor->getNumberRankDofs();
    PetscScalar *vecPointer;
    VecGetArray(petscSolVec, &vecPointer);

    for (int i = 0; i < nComponents; i++) {
      DOFVector<double> &dofvec = *(vec.getDOFVector(i));
      for (int j = 0; j < nRankDofs; j++)
	dofvec[meshDistributor->mapLocalToDofIndex(j)] = 
	  vecPointer[j * nComponents + i]; 
    }

    VecRestoreArray(petscSolVec, &vecPointer);


    // === Synchronize DOFs at common DOFs, i.e., DOFs that correspond to ===
    // === more than one partition.                                       ===
    meshDistributor->synchVector(vec);


    // Print iteration counter and residual norm of the solution.
    printSolutionInfo(adaptInfo);


    // === Destroy PETSc's variables. ===

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    VecDestroy(&petscRhsVec);
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  }


  void PetscSolverGlobalMatrix::destroyMatrixData()
  {
    FUNCNAME("PetscSolverGlobalMatrix::destroyMatrixData()");

    MatDestroy(&petscMatrix);
    KSPDestroy(&solver);
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    VecDestroy(&petscSolVec);
    VecDestroy(&petscTmpVec);
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  }


  void PetscSolverGlobalMatrix::setDofMatrix(DOFMatrix* mat, int dispMult, 
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					     int dispAddRow, int dispAddCol)
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  {
    FUNCNAME("PetscSolverGlobalMatrix::setDofMatrix()");

    TEST_EXIT(mat)("No DOFMatrix!\n");

    using mtl::tag::row; using mtl::tag::nz; using mtl::begin; using mtl::end;
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    namespace traits = mtl::traits;
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    typedef DOFMatrix::base_matrix_type Matrix;

    traits::col<Matrix>::type col(mat->getBaseMatrix());
    traits::const_value<Matrix>::type value(mat->getBaseMatrix());

    typedef traits::range_generator<row, Matrix>::type cursor_type;
    typedef traits::range_generator<nz, cursor_type>::type icursor_type;

    vector<int> cols;
    vector<double> values;
    cols.reserve(300);
    values.reserve(300);
    
    vector<int> globalCols;


    // === Traverse all rows of the dof matrix and insert row wise the values ===
    // === to the PETSc matrix.                                               ===

    for (cursor_type cursor = begin<row>(mat->getBaseMatrix()), 
	   cend = end<row>(mat->getBaseMatrix()); cursor != cend; ++cursor) {

      // Global index of the current row DOF.
      int globalRowDof = meshDistributor->mapLocalToGlobal(*cursor);
      // Test if the current row DOF is a periodic DOF.
      bool periodicRow = meshDistributor->isPeriodicDof(globalRowDof);

      if (!periodicRow) {
	// === Row DOF index is not periodic. ===

	// Calculate PETSc row index.

	int rowIndex = globalRowDof * dispMult + dispAddRow;

	cols.clear();
	values.clear();

	for (icursor_type icursor = begin<nz>(cursor), icend = end<nz>(cursor); 
	     icursor != icend; ++icursor) {

	  // Global index of the current column index.
	  int globalColDof = meshDistributor->mapLocalToGlobal(col(*icursor));
	  // Test if the current col dof is a periodic dof.
	  bool periodicCol = meshDistributor->isPeriodicDof(globalColDof);
	  // Calculate PETSc col index.
	  int colIndex = globalColDof * dispMult + dispAddCol;

	  // Ignore all zero entries, expect it is a diagonal entry.
 	  if (value(*icursor) == 0.0 && rowIndex != colIndex)
 	    continue;

	  if (!periodicCol) {
	    // Calculate the exact position of the column index in the PETSc matrix.
	    cols.push_back(colIndex);
	    values.push_back(value(*icursor));
	  } else {
	    // === Row index is not periodic, but column index is. ===

	    // Create set of all periodic associations of the column index.
	    std::set<int> perAsc;
	    std::set<int>& perColAsc = 
	      meshDistributor->getPerDofAssociations(globalColDof);
	    for (std::set<int>::iterator it = perColAsc.begin(); 
		 it != perColAsc.end(); ++it)
	      if (*it >= -3)
		perAsc.insert(*it);
    
	    // Scale value to the number of periodic associations of the column index.
	    double scaledValue = 
	      value(*icursor) * pow(0.5, static_cast<double>(perAsc.size()));

	    
	    // === Create set of all matrix column indices due to the periodic ===
	    // === associations of the column DOF index.                       ===

	    vector<int> newCols;

	    // First, add the original matrix index.
	    newCols.push_back(globalColDof);
	    
	    // And add all periodic matrix indices.
	    for (std::set<int>::iterator it = perAsc.begin(); 
		 it != perAsc.end(); ++it) {
	      int nCols = static_cast<int>(newCols.size());

	      for (int i = 0; i < nCols; i++) {
 		TEST_EXIT_DBG(meshDistributor->isPeriodicDof(newCols[i], *it))
 		  ("Wrong periodic DOF associations at boundary %d with DOF %d!\n",
		   *it, newCols[i]);

		newCols.push_back(meshDistributor->getPeriodicMapping(newCols[i], *it));
	      }
	    }

	    for (unsigned int i = 0; i < newCols.size(); i++) {
	      cols.push_back(newCols[i] * dispMult + dispAddCol);
	      values.push_back(scaledValue);	      
	    }
	  }
	}

	MatSetValues(petscMatrix, 1, &rowIndex, cols.size(), 
		     &(cols[0]), &(values[0]), ADD_VALUES);	
      } else {
	// === Row DOF index is periodic. ===

	// Because this row is periodic, we will have to add the entries of this 
	// matrix row to multiple rows. The following maps store to each row an
	// array of column indices and values of the entries that must be added to
	// the PETSc matrix.
	map<int, vector<int> > colsMap;
	map<int, vector<double> > valsMap;

	// Traverse all column entries.
	for (icursor_type icursor = begin<nz>(cursor), icend = end<nz>(cursor); 
	     icursor != icend; ++icursor) {

	  // Global index of the current column index.
	  int globalColDof = meshDistributor->mapLocalToGlobal(col(*icursor));

	  // Ignore all zero entries, expect it is a diagonal entry.
 	  if (value(*icursor) == 0.0 && globalRowDof != globalColDof)
 	    continue;


	  // === Add all periodic associations of both, the row and the column ===
	  // === indices to the set perAsc.                                    ===

	  std::set<int> perAsc;

	  if (meshDistributor->isPeriodicDof(globalColDof)) {
	    std::set<int>& perColAsc = 
	      meshDistributor->getPerDofAssociations(globalColDof);
	    for (std::set<int>::iterator it = perColAsc.begin(); 
		 it != perColAsc.end(); ++it)
	      if (*it >= -3)
		perAsc.insert(*it);
	  }

	  std::set<int>& perRowAsc = 
	    meshDistributor->getPerDofAssociations(globalRowDof);
	  for (std::set<int>::iterator it = perRowAsc.begin(); 
	       it != perRowAsc.end(); ++it)
	    if (*it >= -3)
	      perAsc.insert(*it);

	  // Scale the value with respect to the number of periodic associations.
	  double scaledValue = 
	    value(*icursor) * pow(0.5, static_cast<double>(perAsc.size()));


	  // === Create all matrix entries with respect to the periodic  ===
	  // === associations of the row and column indices.             ===

	  vector<pair<int, int> > entry;
	  
	  // First, add the original entry.
	  entry.push_back(make_pair(globalRowDof, globalColDof));

	  // Then, traverse the periodic associations of the row and column indices
	  // and create the corresponding entries.
	  for (std::set<int>::iterator it = perAsc.begin(); it != perAsc.end(); ++it) {
	    int nEntry = static_cast<int>(entry.size());
	    for (int i = 0; i < nEntry; i++) {
	      int perRowDof = 0;
	      if (meshDistributor->getPeriodicMapping()[*it].count(entry[i].first))
		perRowDof = meshDistributor->getPeriodicMapping(entry[i].first, *it);
	      else
		perRowDof = entry[i].first;

	      int perColDof;
	      if (meshDistributor->getPeriodicMapping()[*it].count(entry[i].second))
		perColDof = meshDistributor->getPeriodicMapping(entry[i].second, *it);
	      else
		perColDof = entry[i].second;	      	      
	      

	      entry.push_back(make_pair(perRowDof, perColDof));
	    }
	  }


	  // === Translate the matrix entries to PETSc's matrix.

	  for (vector<pair<int, int> >::iterator eIt = entry.begin(); 
	       eIt != entry.end(); ++eIt) {
	    // Calculate row and column indices of the PETSc matrix.
	    int rowIndex = eIt->first * dispMult + dispAddRow;
	    int colIndex = eIt->second * dispMult + dispAddCol;

	    colsMap[rowIndex].push_back(colIndex);
	    valsMap[rowIndex].push_back(scaledValue);
	  }
	}


	// === Finally, add all periodic rows to the PETSc matrix. ===

	for (map<int, vector<int> >::iterator rowIt = colsMap.begin();
	     rowIt != colsMap.end(); ++rowIt) {
	  TEST_EXIT_DBG(rowIt->second.size() == valsMap[rowIt->first].size())
	    ("Should not happen!\n");

	  int rowIndex = rowIt->first;
	  MatSetValues(petscMatrix, 1, &rowIndex, rowIt->second.size(),
		       &(rowIt->second[0]), &(valsMap[rowIt->first][0]), ADD_VALUES);
	}
      }
    }
  }


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  void PetscSolverGlobalMatrix::setDofVector(Vec& petscVec, 
					     DOFVector<double>* vec, 
					     int dispMult, 
					     int dispAdd, 
					     bool rankOnly)
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  {
    FUNCNAME("PetscSolverGlobalMatrix::setDofVector()");

    // Traverse all used DOFs in the dof vector.
    DOFVector<double>::Iterator dofIt(vec, USED_DOFS);
    for (dofIt.reset(); !dofIt.end(); ++dofIt) {
      if (rankOnly && !meshDistributor->getIsRankDof(dofIt.getDOFIndex()))
	continue;

      // Calculate global row index of the DOF.
      DegreeOfFreedom globalRowDof = 
	meshDistributor->mapLocalToGlobal(dofIt.getDOFIndex());
      // Calculate PETSc index of the row DOF.
      int index = globalRowDof * dispMult + dispAdd;

      if (meshDistributor->isPeriodicDof(globalRowDof)) {
	std::set<int>& perAsc = meshDistributor->getPerDofAssociations(globalRowDof);
	double value = *dofIt / (perAsc.size() + 1.0);
	VecSetValues(petscVec, 1, &index, &value, ADD_VALUES);

	for (std::set<int>::iterator perIt = perAsc.begin(); perIt != perAsc.end(); ++perIt) {
	  int mappedDof = meshDistributor->getPeriodicMapping(globalRowDof, *perIt);
	  int mappedIndex = mappedDof * dispMult + dispAdd;
	  VecSetValues(petscVec, 1, &mappedIndex, &value, ADD_VALUES);
	}
      } else {
	// The DOF index is not periodic.
	double value = *dofIt;
	VecSetValues(petscVec, 1, &index, &value, ADD_VALUES);
      }
    }
  }


  void PetscSolverGlobalMatrix::createPetscNnzStructure(Matrix<DOFMatrix*> *mat)
  {
    FUNCNAME("PetscSolverGlobalMatrix::createPetscNnzStructure()");

    TEST_EXIT_DBG(!d_nnz)("There is something wrong!\n");
    TEST_EXIT_DBG(!o_nnz)("There is something wrong!\n");

    int nComponents = mat->getNumRows();
    int nRankRows = meshDistributor->getNumberRankDofs() * nComponents;
    d_nnz = new int[nRankRows];
    o_nnz = new int[nRankRows];
    for (int i = 0; i < nRankRows; i++) {
      d_nnz[i] = 0;
      o_nnz[i] = 0;
    }

    using mtl::tag::row; using mtl::tag::nz; using mtl::begin; using mtl::end;
    namespace traits = mtl::traits;
    typedef DOFMatrix::base_matrix_type Matrix;
    typedef vector<pair<int, int> > MatrixNnzEntry;
    typedef map<int, DofContainer> RankToDofContainer;

    // Stores to each rank a list of nnz entries (i.e. pairs of row and column index)
    // that this rank will send to. These nnz entries will be assembled on this rank,
    // but because the row DOFs are not DOFs of this rank they will be send to the
    // owner of the row DOFs.
    map<int, MatrixNnzEntry> sendMatrixEntry;

    // Maps to each DOF that must be send to another rank the rank number of the
    // receiving rank.
    map<DegreeOfFreedom, int> sendDofToRank;


    // First, create for all ranks we send data to MatrixNnzEntry object with 0 entries.
    for (RankToDofContainer::iterator it = meshDistributor->getRecvDofs().begin();
	 it != meshDistributor->getRecvDofs().end(); ++it) {
      sendMatrixEntry[it->first].resize(0);

      for (DofContainer::iterator dofIt = it->second.begin();
	   dofIt != it->second.end(); ++dofIt)
	sendDofToRank[**dofIt] = it->first;
    }


    std::set<int> recvFromRank;
    for (RankToDofContainer::iterator it = meshDistributor->getSendDofs().begin();
	 it != meshDistributor->getSendDofs().end(); ++it)
      recvFromRank.insert(it->first);


    for (int i = 0; i < nComponents; i++) {
      for (int j = 0; j < nComponents; j++) {
 	if (!(*mat)[i][j])
	  continue;

	Matrix bmat = (*mat)[i][j]->getBaseMatrix();

	traits::col<Matrix>::type col(bmat);
	traits::const_value<Matrix>::type value(bmat);
	  
	typedef traits::range_generator<row, Matrix>::type cursor_type;
	typedef traits::range_generator<nz, cursor_type>::type icursor_type;
	
	for (cursor_type cursor = begin<row>(bmat), 
	       cend = end<row>(bmat); cursor != cend; ++cursor) {
	  
	  int globalRowDof = meshDistributor->mapLocalToGlobal(*cursor);

	  vector<int> rows;
	  rows.push_back(globalRowDof);
	  vector<int> rowRank;
	  if (meshDistributor->getIsRankDof(*cursor)) {
	    rowRank.push_back(meshDistributor->getMpiRank());
	  } else {
	    // Find out who is the member of this DOF.
	    TEST_EXIT_DBG(sendDofToRank.count(*cursor))("DOF %d has no receiver!\n", *cursor);
	    
	    rowRank.push_back(sendDofToRank[*cursor]);
	  }

	  // Map the local row number to the global DOF index and create from it
	  // the global PETSc row index of this DOF.
	  
	  int petscRowIdx = globalRowDof * nComponents + i;
	  
	  if (meshDistributor->getIsRankDof(*cursor)) {
	    	    
	    // === The current row DOF is a rank dof, so create the corresponding ===
	    // === nnz values directly on rank's nnz data.                        ===
	    
	    // This is the local row index of the local PETSc matrix.
	    int localPetscRowIdx = 
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	      petscRowIdx - meshDistributor->getStartDofs() * nComponents;
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	    TEST_EXIT_DBG(localPetscRowIdx >= 0 && localPetscRowIdx < nRankRows)
	      ("Should not happen! \n Debug info: localRowIdx = %d   globalRowIndx = %d   petscRowIdx = %d   localPetscRowIdx = %d   rStart = %d   nCompontens = %d   nRankRows = %d\n",
	       *cursor, 
	       meshDistributor->mapLocalToGlobal(*cursor), 
	       petscRowIdx, 
	       localPetscRowIdx, 
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	       meshDistributor->getStartDofs(), 
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	       nComponents, 
	       nRankRows);
	    
	    
	    // Traverse all non zero entries in this row.
	    for (icursor_type icursor = begin<nz>(cursor), 
		   icend = end<nz>(cursor); icursor != icend; ++icursor) {
	      int petscColIdx = 
		meshDistributor->mapLocalToGlobal(col(*icursor)) * nComponents + j;
	      
	      if (value(*icursor) != 0.0 || petscRowIdx == petscColIdx) {
		// The row DOF is a rank DOF, if also the column is a rank DOF, 
		// increment the d_nnz values for this row, otherwise the o_nnz value.
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		if (petscColIdx >= meshDistributor->getStartDofs() * nComponents && 
		    petscColIdx < meshDistributor->getStartDofs() * nComponents + nRankRows)
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		  d_nnz[localPetscRowIdx]++;
		else
		  o_nnz[localPetscRowIdx]++;
	      }    
	    }
	  } else {
	    // === The current row DOF is not a rank dof, i.e., it will be created ===
	    // === on this rank, but after this it will be send to another rank    ===
	    // === matrix. So we need to send also the corresponding nnz structure ===
	    // === of this row to the corresponding rank.                          ===
	    
	    // Send all non zero entries to the member of the row DOF.
	    int sendToRank = sendDofToRank[*cursor];
	    
	    for (icursor_type icursor = begin<nz>(cursor), 
		   icend = end<nz>(cursor); icursor != icend; ++icursor) {
	      if (value(*icursor) != 0.0) {
		int petscColIdx = 
		  meshDistributor->mapLocalToGlobal(col(*icursor)) * nComponents + j;
		
		sendMatrixEntry[sendToRank].
		  push_back(make_pair(petscRowIdx, petscColIdx));
	      }
	    }
	    
	  } // if (isRankDof[*cursor]) ... else ...
	} // for each row in mat[i][j]
      } 
    }

    // === Send and recv the nnz row structure to/from other ranks. ===

    StdMpi<MatrixNnzEntry> stdMpi(meshDistributor->getMpiComm(), true);
    stdMpi.send(sendMatrixEntry);
    for (std::set<int>::iterator it = recvFromRank.begin(); 
	 it != recvFromRank.end(); ++it)
      stdMpi.recv(*it);
    stdMpi.startCommunication();


    // === Evaluate the nnz structure this rank got from other ranks and add it to ===
    // === the PETSc nnz data structure.                                           ===

    for (map<int, MatrixNnzEntry>::iterator it = stdMpi.getRecvData().begin();
	 it != stdMpi.getRecvData().end(); ++it) {
      if (it->second.size() > 0) {
	for (unsigned int i = 0; i < it->second.size(); i++) {
	  int r = it->second[i].first;
	  int c = it->second[i].second;

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	  int localRowIdx = r - meshDistributor->getStartDofs() * nComponents;
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	  TEST_EXIT_DBG(localRowIdx >= 0 && localRowIdx < nRankRows)
	    ("Got row index %d/%d (nRankRows = %d) from rank %d. Should not happen!\n",
	     r, localRowIdx, nRankRows, it->first);
	  
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	  if (c < meshDistributor->getStartDofs() * nComponents || 
	      c >= meshDistributor->getStartDofs() * nComponents + nRankRows)
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	    o_nnz[localRowIdx]++;
	  else
	    d_nnz[localRowIdx]++;
	}
      }
    }

    // The above algorithm for calculating the number of nnz per row over-
    // approximates the value, i.e., the number is always equal or larger to 
    // the real number of nnz values in the global parallel matrix. For small
    // matrices, the problem may arise, that the result is larger than the
    // number of elements in a row. This is fixed in the following.

    if (nRankRows < 100) 
      for (int i = 0; i < nRankRows; i++)
	d_nnz[i] = std::min(d_nnz[i], nRankRows);
  }

}