Tpetra_MultiVectorFiller.hpp

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#ifndef __Tpetra_MultiVectorFiller_hpp
#define __Tpetra_MultiVectorFiller_hpp

#include <Tpetra_MultiVector.hpp>
#include <Teuchos_CommHelpers.hpp>
#include <iterator>

namespace Tpetra {
namespace Details {
  // \fn sortAndMergeIn
  // \brief Sort and merge newEntries into allEntries, and make unique.
  //
  // \param allEntries [in/out]: Array in which current entries have
  //   already been stored, and in which the new entries are to be
  //   stored.  Passed by reference in case we need to resize it.
  //
  // \param currentEntries [in/out]: Current entries, which we assume
  //   have already been sorted and made unique.  Aliases the
  //   beginning of allEntries.
  //
  // \param newEntries [in/out] New entries, which have not yet been
  //   sorted or made unique.  This does <i>not</i> alias allEntries.
  //
  // Sort and make entries of newEntries unique.  Resize allEntries if
  // necessary to fit the unique entries of newEntries.  Merge
  // newEntries into allEntries and make the results unique.  (This is
  // cheaper than sorting the whole array.)
  //
  // \return A view of all the entries (current and new) in allEntries.
  template<class T>
  Teuchos::ArrayView<T>
  sortAndMergeIn (Teuchos::Array<T>& allEntries,
                  Teuchos::ArrayView<T> currentEntries,
                  Teuchos::ArrayView<T> newEntries)
  {
    using Teuchos::ArrayView;
    using Teuchos::as;
    typedef typename ArrayView<T>::iterator iter_type;
    typedef typename ArrayView<T>::size_type size_type;

    std::sort (newEntries.begin(), newEntries.end());
    iter_type it = std::unique (newEntries.begin(), newEntries.end());
    const size_type numNew = as<size_type> (it - newEntries.begin());
    // View of the sorted, made-unique new entries to merge in.
    ArrayView<T> newEntriesView = newEntries.view (0, numNew);

    const size_type numCur = currentEntries.size();
    if (allEntries.size() < numCur + numNew) {
      allEntries.resize (numCur + numNew);
    }
    ArrayView<T> allView = allEntries.view (0, numCur + numNew);
    ArrayView<T> newView = allEntries.view (numCur, numNew); // target of copy

    std::copy (newEntries.begin(), newEntries.end(), newView.begin());
    std::inplace_merge (allView.begin(), newView.begin(), allView.end());
    iter_type it2 = std::unique (allView.begin(), allView.end());
    const size_type numTotal = as<size_type> (it2 - allView.begin());

    return allEntries.view (0, numTotal);
  }

  template<class MV>
  class MultiVectorFillerData {
  public:
    typedef typename MV::scalar_type scalar_type;
    typedef typename MV::local_ordinal_type local_ordinal_type;
    typedef typename MV::global_ordinal_type global_ordinal_type;
    typedef typename MV::node_type node_type;

    typedef Tpetra::Map<local_ordinal_type, global_ordinal_type, node_type> map_type;

    MultiVectorFillerData (const Teuchos::RCP<const map_type>& map) :
      map_ (map),
      numCols_ (0)
    {}

    MultiVectorFillerData (const Teuchos::RCP<const map_type>& map,
                           const size_t numColumns) :
      map_ (map),
      numCols_ (numColumns),
      sourceIndices_ (numColumns),
      sourceValues_ (numColumns)
    {}

    void
    setNumColumns (const size_t newNumColumns)
    {
      const size_t oldNumColumns = getNumColumns();
      if (newNumColumns >= oldNumColumns) {
        for (size_t j = oldNumColumns; j < newNumColumns; ++j) {
          sourceIndices_.push_back (Teuchos::Array<global_ordinal_type> ());
          sourceValues_.push_back (Teuchos::Array<scalar_type> ());
        }
      }
      else {
        // This may not necessarily deallocate any data, but that's OK.
        sourceIndices_.resize (newNumColumns);
        sourceValues_.resize (newNumColumns);
      }
      numCols_ = oldNumColumns;
    }

    void
    sumIntoGlobalValues (Teuchos::ArrayView<const global_ordinal_type> rows,
                         size_t column,
                         Teuchos::ArrayView<const scalar_type> values)
    {
      if (column >= getNumColumns()) {
        for (size_t j = column; j < getNumColumns(); ++j) {
          sourceIndices_.push_back (Teuchos::Array<global_ordinal_type> ());
          sourceValues_.push_back (Teuchos::Array<scalar_type> ());
        }
      }
      std::copy (rows.begin(), rows.end(), std::back_inserter (sourceIndices_[column]));
      std::copy (values.begin(), values.end(), std::back_inserter (sourceValues_[column]));
    }

    void
    sumIntoGlobalValues (Teuchos::ArrayView<const global_ordinal_type> rows,
                         Teuchos::ArrayView<const scalar_type> values)
    {
      typedef global_ordinal_type GO;
      typedef scalar_type ST;
      typedef typename Teuchos::ArrayView<const GO>::const_iterator GoIter;
      typedef typename Teuchos::ArrayView<const ST>::const_iterator StIter;

      const size_t numColumns = getNumColumns();
      GoIter rowIter = rows.begin();
      StIter valIter = values.begin();
      for (size_t j = 0; j < numColumns; ++j) {
        GoIter rowIterNext = rowIter + numColumns;
        StIter valIterNext = valIter + numColumns;
        std::copy (rowIter, rowIterNext, std::back_inserter (sourceIndices_[j]));
        std::copy (valIter, valIterNext, std::back_inserter (sourceValues_[j]));
        rowIter = rowIterNext;
        valIter = valIterNext;
      }
    }

    template<class BinaryFunction>
    void
    locallyAssemble (MV& X, BinaryFunction& f)
    {
      using Teuchos::Array;
      using Teuchos::ArrayRCP;
      using Teuchos::ArrayView;
      using Teuchos::RCP;
      typedef local_ordinal_type LO;
      typedef global_ordinal_type GO;
      typedef scalar_type ST;
      typedef node_type NT;

      RCP<const Tpetra::Map<LO, GO, NT> > map = X.getMap();
      Array<LO> localIndices;
      const size_t numColumns = getNumColumns();
      for (size_t j = 0; j < numColumns; ++j) {
        const typename Array<const GO>::size_type numIndices = sourceIndices_[j].size();
        // Precompute all the local indices before saving to the
        // vector.  Hopefully this gives us a little bit of locality
        // in the global->local conversion, at the expense of a little
        // more storage.
        if (localIndices.size() < numIndices) {
          localIndices.resize (numIndices);
        }
        ArrayView<LO> localIndicesView = localIndices.view (0, numIndices);
        ArrayView<const GO> globalIndicesView = sourceIndices_[j].view (0, numIndices);
        for (typename ArrayView<const GO>::size_type i = 0; i < numIndices; ++i) {
          localIndices[i] = map->getLocalElement (globalIndicesView[i]);
        }

        ArrayRCP<ST> X_j = X.getDataNonConst (j);
        ArrayView<const ST> localValues = sourceValues_[j].view (0, numIndices);
        for (typename ArrayView<const GO>::size_type i = 0; i < numIndices; ++i) {
          const LO localInd = localIndices[i];
          X_j[localInd] = f (X_j[localInd], localValues[i]);
        }
      }
    }

    void
    locallyAssemble (MV& X)
    {
      std::plus<double> f;
      locallyAssemble<std::plus<scalar_type> > (X, f);
    }

    void clear() {
      Teuchos::Array<Teuchos::Array<global_ordinal_type> > newSourceIndices;
      Teuchos::Array<Teuchos::Array<scalar_type> > newSourceValues;
      // The standard STL idiom for clearing the contents of a vector completely.
      std::swap (sourceIndices_, newSourceIndices);
      std::swap (sourceValues_, newSourceValues);
    }

    Teuchos::Array<global_ordinal_type>
    getSourceIndices () const
    {
      using Teuchos::Array;
      using Teuchos::ArrayView;
      using Teuchos::as;
      typedef global_ordinal_type GO;
      typedef typename Array<GO>::size_type size_type;

      Array<GO> allInds (0); // will resize below
      const size_t numCols = getNumColumns();

      if (numCols == 1) {
        // Special case for 1 column avoids copying indices twice.
        // Pick the size of the array exactly the first time so there
        // are at most two allocations (the constructor may choose to
        // allocate).
        const size_type numNew = sourceIndices_[0].size();
        allInds.resize (allInds.size() + numNew);
        std::copy (sourceIndices_[0].begin(), sourceIndices_[0].end(),
                   allInds.begin());
        std::sort (allInds.begin(), allInds.end());
        typename Array<GO>::iterator it =
          std::unique (allInds.begin(), allInds.end());
        const size_type numFinal = as<size_type> (it - allInds.begin());
        allInds.resize (numFinal);
      }
      else {
        // Carefully collect all the row indices one column at a time.
        // This ensures that the total allocation size in this routine
        // is independent of the number of columns.  Also, only sort
        // the current column's indices.  Use merges to ensure sorted
        // order in the collected final result.
        ArrayView<GO> curIndsView = allInds.view (0, 0); // will grow
        Array<GO> newInds;
        for (size_t j = 0; j < numCols; ++j) {
          const size_type numNew = sourceIndices_[j].size();
          if (numNew > newInds.size()) {
            newInds.resize (numNew);
          }
          ArrayView<GO> newIndsView = newInds.view (0, numNew);
          std::copy (sourceIndices_[j].begin(), sourceIndices_[j].end(),
                     newIndsView.begin());
          curIndsView = sortAndMergeIn<GO> (allInds, curIndsView, newIndsView);
        }
      }
      return allInds;
    }

  private:
    Teuchos::RCP<const map_type> map_;
    size_t numCols_;
    Teuchos::Array<Teuchos::Array<global_ordinal_type> > sourceIndices_;
    Teuchos::Array<Teuchos::Array<scalar_type> > sourceValues_;

    size_t getNumColumns() const { return numCols_; }
  };

  template<class MV>
  class MultiVectorFillerData2 : public Teuchos::Describable {
  public:
    typedef typename MV::scalar_type scalar_type;
    typedef typename MV::local_ordinal_type local_ordinal_type;
    typedef typename MV::global_ordinal_type global_ordinal_type;
    typedef typename MV::node_type node_type;

    typedef Tpetra::Map<local_ordinal_type, global_ordinal_type, node_type> map_type;

    MultiVectorFillerData2 (const Teuchos::RCP<const map_type>& map,
                            const Teuchos::EVerbosityLevel verbLevel=Teuchos::VERB_DEFAULT,
                            const Teuchos::RCP<Teuchos::FancyOStream>& out=Teuchos::null) :
      map_ (map),
      numCols_ (0),
      verbLevel_ (verbLevel),
      out_ (out)
    {}

    MultiVectorFillerData2 (const Teuchos::RCP<const map_type>& map,
                            const size_t numColumns,
                            const Teuchos::EVerbosityLevel verbLevel=Teuchos::VERB_DEFAULT,
                            const Teuchos::RCP<Teuchos::FancyOStream>& out=Teuchos::null) :
      map_ (map),
      numCols_ (numColumns),
      localVec_ (new MV (map, numColumns)),
      nonlocalIndices_ (numColumns),
      nonlocalValues_ (numColumns),
      verbLevel_ (verbLevel),
      out_ (out)
    {}

    std::string
    description() const
    {
      std::ostringstream oss;
      oss << "Tpetra::MultiVectorFillerData2<"
          << Teuchos::TypeNameTraits<MV>::name () << ">";
      return oss.str();
    }

    void
    describe (Teuchos::FancyOStream& out,
              const Teuchos::EVerbosityLevel verbLevel =
              Teuchos::Describable::verbLevel_default) const
    {
      using std::endl;
      using Teuchos::Array;
      using Teuchos::ArrayRCP;
      using Teuchos::ArrayView;
      using Teuchos::RCP;
      using Teuchos::VERB_DEFAULT;
      using Teuchos::VERB_NONE;
      using Teuchos::VERB_LOW;
      using Teuchos::VERB_MEDIUM;
      using Teuchos::VERB_HIGH;
      using Teuchos::VERB_EXTREME;

      // Set default verbosity if applicable.
      const Teuchos::EVerbosityLevel vl =
        (verbLevel == VERB_DEFAULT) ? VERB_LOW : verbLevel;

      RCP<const Teuchos::Comm<int> > comm = map_->getComm();
      const int myImageID = comm->getRank();
      const int numImages = comm->getSize();

      if (vl != VERB_NONE) {
        // Don't set the tab level unless we're printing something.
        Teuchos::OSTab tab (out);

        if (myImageID == 0) { // >= VERB_LOW prints description()
          out << this->description() << endl;
        }
        for (int imageCtr = 0; imageCtr < numImages; ++imageCtr) {
          if (myImageID == imageCtr) {
            if (vl != VERB_LOW) {
              // At verbosity > VERB_LOW, each process prints something.
              out << "Process " << myImageID << ":" << endl;

              Teuchos::OSTab procTab (out);
              // >= VERB_MEDIUM: print the local vector length.
              out << "local length=" << localVec_->getLocalLength();
              if (vl != VERB_MEDIUM) {
                // >= VERB_HIGH: print isConstantStride() and getStride()
                if (localVec_->isConstantStride()) {
                  out << ", constant stride=" << localVec_->getStride() << endl;
                }
                else {
                  out << ", not constant stride" << endl;
                }
                if (vl == VERB_EXTREME) {
                  // VERB_EXTREME: print all the values in the multivector.
                  out << "Local values:" << endl;
                  ArrayRCP<ArrayRCP<const scalar_type> > X = localVec_->get2dView();
                  for (size_t i = 0; i < localVec_->getLocalLength(); ++i) {
                    for (size_t j = 0; j < localVec_->getNumVectors(); ++j) {
                      out << X[j][i];
                      if (j < localVec_->getNumVectors() - 1) {
                        out << " ";
                      }
                    } // for each column
                    out << endl;
                  } // for each row

                  out << "Nonlocal indices and values:" << endl;
                  for (size_t j = 0; j < (size_t)nonlocalIndices_.size(); ++j) {
                    ArrayView<const global_ordinal_type> inds = nonlocalIndices_[j]();
                    ArrayView<const scalar_type> vals = nonlocalValues_[j]();

                    for (typename ArrayView<const global_ordinal_type>::size_type k = 0; k < inds.size(); ++k) {
                      out << "X(" << inds[k] << "," << j << ") = " << vals[k] << endl;
                    }
                  }
                } // if vl == VERB_EXTREME
              } // if (vl != VERB_MEDIUM)
              else { // vl == VERB_LOW
                out << endl;
              }
            } // if vl != VERB_LOW
          } // if it is my process' turn to print
        } // for each process in the communicator
      } // if vl != VERB_NONE
    }

    Teuchos::Array<global_ordinal_type>
    getSourceIndices () const
    {
      using Teuchos::Array;
      using Teuchos::ArrayView;
      using Teuchos::RCP;
      using Teuchos::rcp;
      using Tpetra::global_size_t;
      typedef global_ordinal_type GO;

      // Get the nonlocal row indices, sorted and made unique.
      // It's fair to assume that these are not contiguous.
      Array<GO> nonlocalIndices = getSortedUniqueNonlocalIndices();

      // Get the local row indices, not necessarily sorted or unique.
      ArrayView<const GO> localIndices = getLocalIndices ();

      // Copy the local indices into the full indices array, and sort
      // them there.  We'll merge in the nonlocal indices below.  This
      // can be more efficient than just sorting all the indices, if
      // there are a lot of nonlocal indices.
      Array<GO> indices (localIndices.size() + nonlocalIndices.size());
      ArrayView<GO> localIndView = indices.view (0, localIndices.size());
      std::copy (localIndices.begin(), localIndices.end(), localIndView.begin());
      std::sort (localIndView.begin(), localIndView.end());

      // Merge the local and nonlocal indices.
      if (nonlocalIndices.size() > 0) {
        typedef typename ArrayView<GO>::iterator iter_type;

        iter_type middle = localIndView.end();
        // We need a view, because std::inplace_merge needs all its
        // iterator inputs to have the same type.  Debug mode builds
        // are pickier than release mode builds, because the iterators
        // in a debug mode build are of a different type that does
        // run-time checking (they aren't just raw pointers).
        ArrayView<GO> indView = indices.view (0, indices.size());

        //iter_type middle = &indices[nonlocalIndices.size()];
        std::copy (nonlocalIndices.begin(), nonlocalIndices.end(), middle);
        std::inplace_merge (indView.begin(), middle, indView.end());
      }
      return indices;
    }

    void
    setNumColumns (const size_t newNumColumns)
    {
      using Teuchos::Array;
      using Teuchos::Range1D;
      using Teuchos::RCP;

      const size_t oldNumColumns = numCols_;
      if (newNumColumns == oldNumColumns) {
        return; // No side effects if no change.
      }

      RCP<MV> newLocalVec;
      if (newNumColumns > oldNumColumns) {
        newLocalVec = rcp (new MV (map_, newNumColumns));
        // Assign the contents of the old local multivector to the
        // first oldNumColumns columns of the new local multivector,
        // then get rid of the old local multivector.
        RCP<MV> newLocalVecView =
          newLocalVec->subViewNonConst (Range1D (0, oldNumColumns-1));
        *newLocalVecView = *localVec_;
      }
      else {
        if (newNumColumns == 0) {
          // Tpetra::MultiVector doesn't let you construct a
          // multivector with zero columns.
          newLocalVec = Teuchos::null;
        }
        else {
          newLocalVec =
            localVec_->subViewNonConst (Range1D (0, newNumColumns-1));
        }
      }

      // Leave most side effects until the end, for exception safety.
      nonlocalIndices_.resize (newNumColumns);
      nonlocalValues_.resize (newNumColumns);
      localVec_ = newLocalVec;
      numCols_ = newNumColumns;
    }

    void
    sumIntoGlobalValues (Teuchos::ArrayView<const global_ordinal_type> rows,
                         size_t columnIndex,
                         Teuchos::ArrayView<const scalar_type> values)
    {
      using Teuchos::ArrayRCP;
      using Teuchos::ArrayView;
      typedef local_ordinal_type LO;
      typedef global_ordinal_type GO;
      typedef scalar_type ST;

      if (columnIndex >= getNumColumns()) {
        // Automatically expand the number of columns.  This
        // implicitly ensures that localVec_ is not null.
        setNumColumns (columnIndex + 1);
      }

      typename ArrayView<const GO>::const_iterator rowIter = rows.begin();
      typename ArrayView<const ST>::const_iterator valIter = values.begin();
      for ( ; rowIter != rows.end() && valIter != values.end(); ++rowIter, ++valIter) {
        const GO globalRowIndex = *rowIter;
        // Converting from global to local index could be logarithmic
        // in the number of global indices that this process owns,
        // depending on the Map implementation.  However, the lookup
        // allows us to store data in the local multivector, rather
        // than in a separate data structure.
        const LO localRowIndex = map_->getLocalElement (globalRowIndex);
        if (localRowIndex == Teuchos::OrdinalTraits<LO>::invalid()) {
          nonlocalIndices_[columnIndex].push_back (globalRowIndex);
          nonlocalValues_[columnIndex].push_back (*valIter);
        }
        else {
          // FIXME (mfh 27 Feb 2012) This will be very slow for GPU
          // Node types.  In that case, we should hold on to the view
          // of localVec_ as long as the number of columns doesn't
          // change, and make modifications to the view until
          // localAssemble() is called.
          ArrayRCP<ST> X_j = localVec_->getDataNonConst (columnIndex);
          // FIXME (mfh 27 Feb 2012) Allow different combine modes.
          // The current combine mode just adds to the current value
          // at that location.
          X_j[localRowIndex] += *valIter;
        }
      }
    }

    void
    sumIntoGlobalValues (Teuchos::ArrayView<const global_ordinal_type> rows,
                         Teuchos::ArrayView<const scalar_type> values)
    {
      using Teuchos::ArrayView;
      typedef typename ArrayView<const global_ordinal_type>::size_type size_type;

      const size_t numCols = getNumColumns();
      for (size_t j = 0; j < numCols; ++j) {
        const size_type offset = numCols*j;
        const size_type len = numCols;
        sumIntoGlobalValues (rows.view (offset, len), j, values.view (offset, len));
      }
    }

    template<class BinaryFunction>
    void
    locallyAssemble (MV& X, BinaryFunction& f)
    {
      using Teuchos::ArrayRCP;
      using Teuchos::ArrayView;
      using Teuchos::FancyOStream;
      using Teuchos::getFancyOStream;
      using Teuchos::oblackholestream;
      using Teuchos::RCP;
      using Teuchos::rcp;
      using std::endl;

      typedef local_ordinal_type LO;
      typedef global_ordinal_type GO;
      typedef scalar_type ST;

      // Default output stream prints nothing.
      RCP<FancyOStream> out = out_.is_null() ?
        getFancyOStream (rcp (new oblackholestream)) : out_;

      Teuchos::OSTab tab (out);
      *out << "locallyAssemble:" << endl;

      RCP<const map_type> srcMap = X.getMap();
      ArrayView<const GO> localIndices = map_->getNodeElementList ();

      for (size_t j = 0; j < X.getNumVectors(); ++j) {
        ArrayRCP<ST> X_j = X.getDataNonConst (j);

        // First add all the local data into X_j.
        ArrayRCP<const ST> local_j = localVec_->getDataNonConst (j);
        for (typename ArrayView<const GO>::const_iterator it = localIndices.begin();
             it != localIndices.end(); ++it) {
          const LO rowIndLocal = map_->getLocalElement (*it);
          const LO rowIndX = srcMap->getLocalElement (*it);

          TEUCHOS_TEST_FOR_EXCEPTION(rowIndX == Teuchos::OrdinalTraits<LO>::invalid(),
            std::invalid_argument, "locallyAssemble(): Input multivector X does "
            "not own the global index " << *it << ".  This probably means that "
            "X was not constructed with the right Map.");
          X_j[rowIndX] = f (X_j[rowIndX], local_j[rowIndLocal]);
        }

        // Now add the nonlocal data into X_j.
        ArrayView<const GO> nonlocalIndices = nonlocalIndices_[j]();
        typename ArrayView<const GO>::const_iterator indexIter = nonlocalIndices.begin();
        ArrayView<const ST> nonlocalValues = nonlocalValues_[j]();
        typename ArrayView<const ST>::const_iterator valueIter = nonlocalValues.begin();
        for ( ; indexIter != nonlocalIndices.end() && valueIter != nonlocalValues.end();
              ++indexIter, ++valueIter) {
          const LO rowIndX = srcMap->getLocalElement (*indexIter);
          X_j[rowIndX] = f (X_j[rowIndX], *valueIter);
        }
      }

      *out << "Locally assembled vector:" << endl;
      X.describe (*out, Teuchos::VERB_EXTREME);
    }

    void
    locallyAssemble (MV& X)
    {
      std::plus<double> f;
      locallyAssemble<std::plus<scalar_type> > (X, f);
    }

    void clear() {
      Teuchos::Array<Teuchos::Array<global_ordinal_type> > newNonlocalIndices;
      Teuchos::Array<Teuchos::Array<scalar_type> > newNonlocalValues;
      // The standard STL idiom for clearing the contents of a vector
      // completely.  Setting the size to zero may not necessarily
      // deallocate data.
      std::swap (nonlocalIndices_, newNonlocalIndices);
      std::swap (nonlocalValues_, newNonlocalValues);

      // Don't actually deallocate the multivector of local entries.
      // Just fill it with zero.  This is because the caller hasn't
      // reset the number of columns.
      if (! localVec_.is_null()) {
        localVec_->putScalar (Teuchos::ScalarTraits<scalar_type>::zero());
      }
    }

  private:
    Teuchos::RCP<const map_type> map_;

    size_t numCols_;

    Teuchos::RCP<MV> localVec_;

    Teuchos::Array<Teuchos::Array<global_ordinal_type> > nonlocalIndices_;

    Teuchos::Array<Teuchos::Array<scalar_type> > nonlocalValues_;

    Teuchos::EVerbosityLevel verbLevel_;

    Teuchos::RCP<Teuchos::FancyOStream> out_;

    size_t getNumColumns() const { return numCols_; }

    Teuchos::ArrayView<const global_ordinal_type>
    getLocalIndices() const
    {
      return map_->getNodeElementList ();
    }

    Teuchos::Array<global_ordinal_type>
    getSortedUniqueNonlocalIndices() const
    {
      using Teuchos::Array;
      using Teuchos::ArrayView;
      using Teuchos::as;
      typedef global_ordinal_type GO;
      typedef typename Array<GO>::size_type size_type;

      Array<GO> allNonlocals (0); // will resize below
      const size_t numCols = getNumColumns();

      if (numCols == 1) {
        // Special case for 1 column avoids copying indices twice.
        // Pick the size of the array exactly the first time so there
        // are at most two allocations (the constructor may choose to
        // allocate).
        const size_type numNew = nonlocalIndices_[0].size();
        allNonlocals.resize (allNonlocals.size() + numNew);
        std::copy (nonlocalIndices_[0].begin(), nonlocalIndices_[0].end(),
                   allNonlocals.begin());
        std::sort (allNonlocals.begin(), allNonlocals.end());
        typename Array<GO>::iterator it =
          std::unique (allNonlocals.begin(), allNonlocals.end());
        const size_type numFinal = as<size_type> (it - allNonlocals.begin());
        allNonlocals.resize (numFinal);
      }
      else {
        // Carefully collect all the row indices one column at a time.
        // This ensures that the total allocation size in this routine
        // is independent of the number of columns.  Also, only sort
        // the current column's indices.  Use merges to ensure sorted
        // order in the collected final result.
        ArrayView<GO> curNonlocalsView = allNonlocals.view (0, 0); // will grow
        Array<GO> newNonlocals;
        for (size_t j = 0; j < numCols; ++j) {
          const size_type numNew = nonlocalIndices_[j].size();
          if (numNew > newNonlocals.size()) {
            newNonlocals.resize (numNew);
          }
          ArrayView<GO> newNonlocalsView = newNonlocals.view (0, numNew);
          std::copy (nonlocalIndices_[j].begin(), nonlocalIndices_[j].end(),
                     newNonlocalsView.begin());
          curNonlocalsView = sortAndMergeIn<GO> (allNonlocals, curNonlocalsView,
                                                 newNonlocalsView);
        }
      }
      return allNonlocals;
    }
  };
} // namespace Details
} // namespace Tpetra

namespace Tpetra {

  template<class MV>
  class MultiVectorFiller {
  public:
    typedef typename MV::scalar_type scalar_type;
    typedef typename MV::local_ordinal_type local_ordinal_type;
    typedef typename MV::global_ordinal_type global_ordinal_type;
    typedef typename MV::node_type node_type;
    typedef Tpetra::Map<local_ordinal_type, global_ordinal_type, node_type> map_type;

    MultiVectorFiller (const Teuchos::RCP<const map_type>& map,
                       const size_t numCols);

    void globalAssemble (MV& X_out, const bool forceReuseMap = false);

    void
    describe (Teuchos::FancyOStream& out,
              const Teuchos::EVerbosityLevel verbLevel=Teuchos::Describable::verbLevel_default) const
    {
      data_.describe (out, verbLevel);
    }

    void
    sumIntoGlobalValues (Teuchos::ArrayView<const global_ordinal_type> rows,
                         size_t column,
                         Teuchos::ArrayView<const scalar_type> values)
    {
      data_.sumIntoGlobalValues (rows, column, values);
    }

    void
    sumIntoGlobalValues (Teuchos::ArrayView<const global_ordinal_type> rows,
                         Teuchos::ArrayView<const scalar_type> values)
    {
      data_.sumIntoGlobalValues (rows, values);
    }

  private:
    Teuchos::RCP<const map_type> ctorMap_;

    Teuchos::RCP<const map_type> sourceMap_;

    Teuchos::RCP<const map_type> targetMap_;

    Teuchos::RCP<MV> sourceVec_;

    Tpetra::Details::MultiVectorFillerData2<MV> data_;

    typedef Tpetra::Export<local_ordinal_type, global_ordinal_type, node_type> export_type;
    Teuchos::RCP<export_type> exporter_;

    void locallyAssemble (MV& X_in) {
      data_.locallyAssemble (X_in);
    }

    Teuchos::Array<global_ordinal_type> getSourceIndices () const {
      return data_.getSourceIndices();
    }

    Teuchos::RCP<const map_type>
    computeSourceMap (const global_ordinal_type indexBase,
                      const Teuchos::RCP<const Teuchos::Comm<int> >& comm,
                      const Teuchos::RCP<node_type>& node);
  };

  template<class MV>
  MultiVectorFiller<MV>::MultiVectorFiller (const Teuchos::RCP<const typename MultiVectorFiller<MV>::map_type>& map, const size_t numCols)
    : ctorMap_ (map),
      sourceMap_ (Teuchos::null),
      targetMap_ (Teuchos::null),
      data_ (map, numCols),
      exporter_ (Teuchos::null)
  {}

  template<class MV>
  Teuchos::RCP<const typename MultiVectorFiller<MV>::map_type>
  MultiVectorFiller<MV>::
  computeSourceMap (const global_ordinal_type indexBase,
                    const Teuchos::RCP<const Teuchos::Comm<int> >& comm,
                    const Teuchos::RCP<node_type>& node)
  {
    using Teuchos::Array;
    using Teuchos::ArrayView;
    using Teuchos::rcp;
    typedef global_ordinal_type GO;

    Array<GO> indices = getSourceIndices ();

    // Passing "invalid" for the numGlobalElements argument of the Map
    // constructor tells the Map to compute the global number of
    // elements itself.
    const Tpetra::global_size_t invalid =
      Teuchos::OrdinalTraits<Tpetra::global_size_t>::invalid();
    return rcp (new map_type (invalid, indices, indexBase, comm, node));
  }

  template<class MV>
  void
  MultiVectorFiller<MV>::globalAssemble (MV& X_out, const bool forceReuseMap)
  {
    using Teuchos::ArrayView;
    using Teuchos::Array;
    using Teuchos::Range1D;
    using Teuchos::RCP;
    using Teuchos::rcp;

    const size_t numVecs = X_out.getNumVectors();

    if (numVecs == 0) {
      // Nothing to do!  Of course, this does not check for whether
      // X_out has the right number of rows.  That's OK, though.
      // Compare to the definition of the BLAS' _AXPY for an input
      // vector containing NaNs, but multiplied by alpha=0.
      return;
    }
    //
    // Get the target Map of the Export.  If X_out's Map is the same
    // as the target Map from last time, then we may be able to
    // recycle the Export from last time, if the source Map is also
    // the same.
    //
    RCP<const map_type> targetMap;
    bool assumeSameTargetMap = false;
    if (targetMap_.is_null()) {
      targetMap_ = X_out.getMap();
      targetMap = targetMap_;
      assumeSameTargetMap = false;
    }
    else {
      if (forceReuseMap) {
        targetMap = targetMap_;
        assumeSameTargetMap = true;
      }
      else  {
        // If X_out's Map is the same as targetMap_, we may be able to
        // reuse the Export.  Constructing the Export may be more
        // expensive than calling isSameAs() (which requires just a
        // few reductions and reading through the lists of owned
        // global indices), so it's worth checking.
        if (targetMap_->isSameAs (*(X_out.getMap()))) {
          assumeSameTargetMap = true;
          targetMap = targetMap_;
        }
      }
    }
    //
    // Get the source Map of the Export.  If the source Map of the
    // Export is the same as last time, then we may be able to recycle
    // the Export from last time, if the target Map is also the same.
    //
    RCP<const map_type> sourceMap;
    bool computedSourceMap = false;
    {
      if (forceReuseMap && ! sourceMap_.is_null()) {
        sourceMap = sourceMap_;
      }
      else {
        sourceMap = computeSourceMap (ctorMap_->getIndexBase(),
                                      ctorMap_->getComm(),
                                      ctorMap_->getNode());
        computedSourceMap = true;
      }
    }
    if (computedSourceMap) {
      sourceMap_ = sourceMap;
    }
    //
    // Now that we have the source and target Maps of the Export, we
    // can check whether we can recycle the Export from last time.
    //
    const bool mustComputeExport =
      (exporter_.is_null() || (assumeSameTargetMap && ! computedSourceMap));
    if (mustComputeExport) {
      exporter_ = rcp (new export_type (sourceMap_, targetMap_));
    }

    // Source multivector for the Export.
    RCP<MV> X_in;
    const bool mustReallocateVec = sourceVec_.is_null() ||
      sourceVec_->getNumVectors() < numVecs || ! assumeSameTargetMap;

    if (mustReallocateVec) {
      // Reallocating nonlocalVec_ ensures that it has the right Map.
      sourceVec_ = rcp (new MV (sourceMap_, numVecs));
      X_in = sourceVec_;
    } else {
      if (sourceVec_->getNumVectors() == numVecs) {
        X_in = sourceVec_;
      } else { // sourceVec_ has more vectors than needed.
        X_in = sourceVec_->subViewNonConst (Range1D (0, numVecs-1));
      }
    }

    // "Locally assemble" the data into X_in by summing together
    // entries with the same indices.
    locallyAssemble (*X_in);

    // Do the Export.
    const Tpetra::CombineMode combineMode = Tpetra::ADD;
    X_out.doExport (*X_in, *exporter_, combineMode);
  }

  namespace Test {

    template<class MV>
    class MultiVectorFillerTester {
    public:
      typedef typename MV::scalar_type scalar_type;
      typedef typename MV::local_ordinal_type local_ordinal_type;
      typedef typename MV::global_ordinal_type global_ordinal_type;
      typedef typename MV::node_type node_type;
      typedef Tpetra::Map<local_ordinal_type, global_ordinal_type, node_type> map_type;

      static void
      testSameMap (const Teuchos::RCP<const map_type>& targetMap,
                   const global_ordinal_type eltSize, // Must be odd
                   const size_t numCols,
                   const Teuchos::RCP<Teuchos::FancyOStream>& outStream=Teuchos::null,
                   const Teuchos::EVerbosityLevel verbosityLevel=Teuchos::VERB_DEFAULT)
      {
        using Teuchos::Array;
        using Teuchos::ArrayRCP;
        using Teuchos::ArrayView;
        using Teuchos::as;
        using Teuchos::Comm;
        using Teuchos::FancyOStream;
        using Teuchos::getFancyOStream;
        using Teuchos::oblackholestream;
        using Teuchos::ptr;
        using Teuchos::RCP;
        using Teuchos::rcp;
        using Teuchos::rcpFromRef;
        using Teuchos::REDUCE_SUM;
        using Teuchos::reduceAll;
        using std::cerr;
        using std::endl;

        typedef local_ordinal_type LO;
        typedef global_ordinal_type GO;
        typedef scalar_type ST;
        typedef Teuchos::ScalarTraits<ST> STS;

        TEUCHOS_TEST_FOR_EXCEPTION(eltSize % 2 == 0, std::invalid_argument,
          "Element size (eltSize) argument must be odd.");
        TEUCHOS_TEST_FOR_EXCEPTION(numCols == 0, std::invalid_argument,
          "Number of columns (numCols) argument must be nonzero.");
        // Default behavior is to print nothing out.
        RCP<FancyOStream> out = outStream.is_null() ?
          getFancyOStream (rcp (new oblackholestream)) : outStream;
        const Teuchos::EVerbosityLevel verbLevel =
          (verbosityLevel == Teuchos::VERB_DEFAULT) ?
          Teuchos::VERB_NONE : verbosityLevel;

        //RCP<MV> X = rcp (new MV (targetMap, numCols));

        const GO indexBase = targetMap->getIndexBase();
        Array<GO> rows (eltSize);
        Array<ST> values (eltSize);
        std::fill (values.begin(), values.end(), STS::one());

        // Make this a pointer so we can free its contents, in case
        // those contents depend on the input to globalAssemble().
        RCP<MultiVectorFiller<MV> > filler =
          rcp (new MultiVectorFiller<MV> (targetMap, numCols));

        TEUCHOS_TEST_FOR_EXCEPTION(! targetMap->isContiguous(),
          std::invalid_argument, "MultiVectorFiller test currently only works "
          "for contiguous Maps.");

        const GO minGlobalIndex = targetMap->getMinGlobalIndex();
        const GO maxGlobalIndex = targetMap->getMaxGlobalIndex();
        const GO minAllGlobalIndex = targetMap->getMinAllGlobalIndex();
        const GO maxAllGlobalIndex = targetMap->getMaxAllGlobalIndex();
        for (size_t j = 0; j < numCols; ++j) {
          for (GO i = minGlobalIndex; i <= maxGlobalIndex; ++i) {
            // Overlap over processes, without running out of bounds.
            const GO start = std::max (i - eltSize/2, minAllGlobalIndex);
            const GO end = std::min (i + eltSize/2, maxAllGlobalIndex);
            const GO len = end - start + 1;

            TEUCHOS_TEST_FOR_EXCEPTION(len > eltSize, std::logic_error,
              "At start,end = " << start << "," << end << ", len = " << len
              << " > eltSize = " << eltSize << ".");

            for (GO k = 0; k < len; ++k) {
              rows[k] = start + k;
            }
            if (verbLevel == Teuchos::VERB_EXTREME) {
              *out << "Inserting: "
                   << Teuchos::toString (rows.view(0,len)) << ", "
                   << Teuchos::toString (values.view(0, len)) << std::endl;
            }
            filler->sumIntoGlobalValues (rows.view(0, len), j, values.view(0, len));
          }
        }

        if (verbLevel == Teuchos::VERB_EXTREME) {
          *out << "Filler:" << std::endl;
          filler->describe (*out, verbLevel);
          *out << std::endl;
        }

        MV X_out (targetMap, numCols);
        filler->globalAssemble (X_out);
        filler = Teuchos::null;

        if (verbLevel == Teuchos::VERB_EXTREME) {
          *out << "X_out:" << std::endl;
          X_out.describe (*out, verbLevel);
          *out << std::endl;
        }

        // Create multivector for comparison.
        MV X_expected (targetMap, numCols);
        const scalar_type two = STS::one() + STS::one();
        for (size_t j = 0; j < numCols; ++j) {
          ArrayRCP<ST> X_j = X_expected.getDataNonConst (j);

          // Each entry of the column should have the value eltSize,
          // except for the first and last few entries in the whole
          // column (globally, not locally).
          for (GO i = minGlobalIndex; i <= maxGlobalIndex; ++i) {
            const LO localIndex = targetMap->getLocalElement (i);
            TEUCHOS_TEST_FOR_EXCEPTION(i == Teuchos::OrdinalTraits<LO>::invalid(),
              std::logic_error, "Global index " << i << " is not in the "
              "multivector's Map.");

            if (i <= minAllGlobalIndex + eltSize/2) {
              X_j[localIndex] = two + as<ST>(i) - as<ST>(indexBase);
            }
            else if (i >= maxAllGlobalIndex - eltSize/2) {
              X_j[localIndex] = two + as<ST>(maxAllGlobalIndex) - as<ST>(i);
            }
            else {
              X_j[localIndex] = as<ST>(eltSize);
            }
          } // for each global index which my process owns
        } // for each column of the multivector

        if (verbLevel == Teuchos::VERB_EXTREME) {
          *out << "X_expected:" << std::endl;
          X_expected.describe (*out, verbLevel);
          *out << std::endl;
        }

        Array<GO> errorLocations;
        for (size_t j = 0; j < numCols; ++j) {
          ArrayRCP<const ST> X_out_j = X_out.getData (j);
          ArrayRCP<const ST> X_expected_j = X_expected.getData (j);

          // Each entry of the column should have the value eltSize,
          // except for the first and last few entries in the whole
          // column (globally, not locally).
          for (GO i = minGlobalIndex; i <= maxGlobalIndex; ++i) {
            const LO localIndex = targetMap->getLocalElement (i);
            TEUCHOS_TEST_FOR_EXCEPTION(i == Teuchos::OrdinalTraits<LO>::invalid(),
              std::logic_error, "Global index " << i << " is not in the "
              "multivector's Map.");

            // The floating-point additions should be exact in this
            // case, except for very large values of eltSize.
            if (X_out_j[localIndex] != X_expected_j[localIndex]) {
              errorLocations.push_back (i);
            }
          } // for each global index which my process owns

          const typename Array<GO>::size_type localNumErrors = errorLocations.size();
          typename Array<GO>::size_type globalNumErrors = 0;
          RCP<const Comm<int> > comm = targetMap->getComm();
          reduceAll (*comm, REDUCE_SUM, localNumErrors, ptr (&globalNumErrors));

          if (globalNumErrors != 0) {
            std::ostringstream os;
            os << "Proc " << comm->getRank() << ": " << localNumErrors
               << " incorrect value" << (localNumErrors != 1 ? "s" : "")
               << ".  Error locations: [ ";
            std::copy (errorLocations.begin(), errorLocations.end(),
                       std::ostream_iterator<GO> (os, " "));
            os << "].";
            // Iterate through all processes in the communicator,
            // printing out each process' local errors.
            for (int p = 0; p < comm->getSize(); ++p) {
              if (p == comm->getRank()) {
                cerr << os.str() << endl;
              }
              // Barriers to let output finish.
              comm->barrier();
              comm->barrier();
              comm->barrier();
            }
            TEUCHOS_TEST_FOR_EXCEPTION(globalNumErrors != 0, std::logic_error,
              "Over all procs: " << globalNumErrors << " total error"
              << (globalNumErrors != 1 ? "s" : "") << ".");
          } // if there were any errors in column j
        } // for each column j
      }
    };

    template<class ScalarType,
             class LocalOrdinalType,
             class GlobalOrdinalType,
             class NodeType>
    void
    testMultiVectorFiller (const Teuchos::RCP<const Teuchos::Comm<int> >& comm,
                           const Teuchos::RCP<NodeType>& node,
                           const size_t unknownsPerNode,
                           const GlobalOrdinalType unknownsPerElt,
                           const size_t numCols,
                           const Teuchos::RCP<Teuchos::FancyOStream>& outStream,
                           const Teuchos::EVerbosityLevel verbLevel)
    {
      using Tpetra::createContigMapWithNode;
      using Teuchos::FancyOStream;
      using Teuchos::getFancyOStream;
      using Teuchos::oblackholestream;
      using Teuchos::ParameterList;
      using Teuchos::RCP;
      using Teuchos::rcp;
      using std::cerr;
      using std::endl;

      typedef ScalarType ST;
      typedef LocalOrdinalType LO;
      typedef GlobalOrdinalType GO;
      typedef NodeType NT;
      typedef Tpetra::Map<LO, GO, NT> MT;
      typedef Tpetra::MultiVector<ST, LO, GO, NT> MV;

      RCP<FancyOStream> out = outStream.is_null() ?
        getFancyOStream (rcp (new oblackholestream)) : outStream;
      const Tpetra::global_size_t invalid =
        Teuchos::OrdinalTraits<Tpetra::global_size_t>::invalid();
      RCP<const MT> targetMap =
        createContigMapWithNode<LO, GO, NT> (invalid, unknownsPerNode, comm, node);

      std::ostringstream os;
      try {
        MultiVectorFillerTester<MV>::testSameMap (targetMap, unknownsPerElt, numCols, out, verbLevel);
      } catch (std::exception& e) {
        os << e.what();
      }

      for (int p = 0; p < comm->getSize(); ++p) {
        if (p == comm->getRank()) {
          *out << "On process " << comm->getRank() << ": " << os.str() << endl;
        }
        comm->barrier();
        comm->barrier();
        comm->barrier();
      }
    }

    void
    testSortAndMergeIn ();

  } // namespace Test
} // namespace Tpetra


#endif // __Tpetra_MultiVectorFiller_hpp