MueLu_SmooVecCoalesceDropFactory_def.hpp

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#include "MueLu_SmootherBase.hpp"
#ifndef MUELU_SMOOVECCOALESCEDROPFACTORY_DEF_HPP
#define MUELU_SMOOVECCOALESCEDROPFACTORY_DEF_HPP

#include <Xpetra_CrsGraphFactory.hpp>
#include <Xpetra_CrsGraph.hpp>
#include <Xpetra_ImportFactory.hpp>
#include <Xpetra_MapFactory.hpp>
#include <Xpetra_Map.hpp>
#include <Xpetra_Matrix.hpp>
#include <Xpetra_MultiVectorFactory.hpp>
#include <Xpetra_MultiVector.hpp>
#include <Xpetra_StridedMap.hpp>
#include <Xpetra_VectorFactory.hpp>
#include <Xpetra_Vector.hpp>

#include "MueLu_SmooVecCoalesceDropFactory_decl.hpp"

#include "MueLu_AmalgamationFactory.hpp"
#include "MueLu_AmalgamationInfo.hpp"
#include "MueLu_Exceptions.hpp"
#include "MueLu_GraphBase.hpp"
#include "MueLu_Graph.hpp"
#include "MueLu_Level.hpp"
#include "MueLu_LWGraph.hpp"
#include "MueLu_MasterList.hpp"
#include "MueLu_Monitor.hpp"
#include "MueLu_PreDropFunctionBaseClass.hpp"
#include "MueLu_PreDropFunctionConstVal.hpp"
#include "MueLu_Utilities.hpp"
#include "MueLu_TopSmootherFactory.hpp"
#include "MueLu_SmootherFactoryBase.hpp"
#include "MueLu_SmootherFactory.hpp"


#include <Xpetra_IO.hpp>

#include <algorithm>
#include <cstdlib>
#include <string>

// If defined, read environment variables.
// Should be removed once we are confident that this works.
// #define DJS_READ_ENV_VARIABLES

#include <stdio.h>
#include <stdlib.h>
#include <math.h>


#define poly0thOrderCoef   0
#define poly1stOrderCoef   1
#define poly2ndOrderCoef   2
#define poly3rdOrderCoef   3
#define poly4thOrderCoef   4

namespace MueLu {

  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  RCP<const ParameterList> SmooVecCoalesceDropFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::GetValidParameterList() const {
    RCP<ParameterList> validParamList = rcp(new ParameterList());

#define SET_VALID_ENTRY(name) validParamList->setEntry(name, MasterList::getEntry(name))
    SET_VALID_ENTRY("aggregation: drop scheme");
    {
      typedef Teuchos::StringToIntegralParameterEntryValidator<int> validatorType;
      validParamList->getEntry("aggregation: drop scheme").setValidator(
        rcp(new validatorType(Teuchos::tuple<std::string>("unsupported vector smoothing"), "aggregation: drop scheme")));
    }
    SET_VALID_ENTRY("aggregation: number of random vectors");
    SET_VALID_ENTRY("aggregation: number of times to pre or post smooth");
    SET_VALID_ENTRY("aggregation: penalty parameters");
#undef  SET_VALID_ENTRY

    validParamList->set< RCP<const FactoryBase> >("A",                  Teuchos::null, "Generating factory of the matrix A");
    validParamList->set< RCP<const FactoryBase> >("PreSmoother",        Teuchos::null, "Generating factory of the PreSmoother");
    validParamList->set< RCP<const FactoryBase> >("PostSmoother",       Teuchos::null, "Generating factory of the PostSmoother");

    return validParamList;
  }

  template <class Scalar,class LocalOrdinal, class GlobalOrdinal, class Node>
  SmooVecCoalesceDropFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::SmooVecCoalesceDropFactory() : predrop_(Teuchos::null) { }

  template <class Scalar,class LocalOrdinal, class GlobalOrdinal, class Node>
  void SmooVecCoalesceDropFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::DeclareInput(Level &currentLevel) const {
    Input(currentLevel, "A");
    if (currentLevel.IsAvailable("PreSmoother")) {    // rst: totally unsure that this is legal
      Input(currentLevel, "PreSmoother");             //      my guess is that this is not yet available
    }                                                 //      so this always comes out false. 
    else if (currentLevel.IsAvailable("PostSmoother")) {  // perhaps we can look on the param list?
      Input(currentLevel, "PostSmoother");
    }
  }

  template <class Scalar,class LocalOrdinal, class GlobalOrdinal, class Node>
  void SmooVecCoalesceDropFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Build(Level &currentLevel) const {

    FactoryMonitor m(*this, "Build", currentLevel);

    typedef Teuchos::ScalarTraits<SC> STS;

    if (predrop_ != Teuchos::null)
      GetOStream(Parameters0) << predrop_->description();

    RCP<Matrix> A = Get< RCP<Matrix> >(currentLevel, "A");

    const ParameterList  & pL = GetParameterList();

   LO nPDEs = A->GetFixedBlockSize();

   RCP< MultiVector > testVecs;
   RCP< MultiVector > nearNull;

#ifdef takeOut
   testVecs = Xpetra::IO<SC,LO,GO,Node>::ReadMultiVector("TpetraTVecs.mm", A->getRowMap());
#endif
   size_t numRandom= as<size_t>(pL.get<int>("aggregation: number of random vectors"));
   testVecs = MultiVectorFactory::Build(A->getRowMap(), numRandom, true);
   // use random test vectors but should be positive in order to not get 
   // crummy results ... so take abs() of randomize().
   testVecs->randomize();    
   for (size_t kk = 0; kk < testVecs->getNumVectors(); kk++ ) {
     Teuchos::ArrayRCP< Scalar > curVec = testVecs->getDataNonConst(kk);
     for (size_t ii = kk; ii < as<size_t>(A->getRowMap()->getNodeNumElements()); ii++ ) curVec[ii] = Teuchos::ScalarTraits<SC>::magnitude(curVec[ii]);
   }
   nearNull = MultiVectorFactory::Build(A->getRowMap(), nPDEs, true);

   // initialize null space to constants 
   for (size_t kk = 0; kk < nearNull->getNumVectors(); kk++ ) {
     Teuchos::ArrayRCP< Scalar > curVec = nearNull->getDataNonConst(kk);
     for (size_t ii = kk; ii < as<size_t>(A->getRowMap()->getNodeNumElements()); ii += nearNull->getNumVectors() ) curVec[ii] = Teuchos::ScalarTraits<Scalar>::one();
   }

   RCP< MultiVector > zeroVec_TVecs;
   RCP< MultiVector > zeroVec_Null;

   zeroVec_TVecs = MultiVectorFactory::Build(A->getRowMap(), testVecs->getNumVectors(), true);
   zeroVec_Null  = MultiVectorFactory::Build(A->getRowMap(), nPDEs, true);
   zeroVec_TVecs->putScalar(Teuchos::ScalarTraits<Scalar>::zero());
   zeroVec_Null->putScalar( Teuchos::ScalarTraits<Scalar>::zero());

   size_t nInvokeSmoother=as<size_t>(pL.get<int>("aggregation: number of times to pre or post smooth"));
   if (currentLevel.IsAvailable("PreSmoother")) {
     RCP<SmootherBase> preSmoo = currentLevel.Get< RCP<SmootherBase> >("PreSmoother");
     for (size_t ii = 0; ii < nInvokeSmoother; ii++) preSmoo->Apply(*testVecs,*zeroVec_TVecs,false);
     for (size_t ii = 0; ii < nInvokeSmoother; ii++) preSmoo->Apply(*nearNull,*zeroVec_Null,false);
   }
   else if (currentLevel.IsAvailable("PostSmoother")) {
     RCP<SmootherBase> postSmoo = currentLevel.Get< RCP<SmootherBase> >("PostSmoother");
     for (size_t ii = 0; ii < nInvokeSmoother; ii++) postSmoo->Apply(*testVecs,*zeroVec_TVecs,false);
     for (size_t ii = 0; ii < nInvokeSmoother; ii++) postSmoo->Apply(*nearNull, *zeroVec_Null,false);
   }
   else 
     TEUCHOS_TEST_FOR_EXCEPTION(true, Exceptions::RuntimeError, "Must set a smoother");

   Teuchos::ArrayRCP<Scalar> penaltyPolyCoef(5);
   Teuchos::ArrayView<const double> inputPolyCoef;

   penaltyPolyCoef[poly0thOrderCoef] = 12.;
   penaltyPolyCoef[poly1stOrderCoef] = -.2;
   penaltyPolyCoef[poly2ndOrderCoef] = 0.0;
   penaltyPolyCoef[poly3rdOrderCoef] = 0.0;
   penaltyPolyCoef[poly4thOrderCoef] = 0.0;

   if(pL.isParameter("aggregation: penalty parameters") && pL.get<Teuchos::Array<double> >("aggregation: penalty parameters").size() > 0) {
      if (pL.get<Teuchos::Array<double> >("aggregation: penalty parameters").size() > penaltyPolyCoef.size()) 
         TEUCHOS_TEST_FOR_EXCEPTION(true, Exceptions::RuntimeError, "Number of penalty parameters must be " << penaltyPolyCoef.size() << " or less");
      inputPolyCoef = pL.get<Teuchos::Array<double> >("aggregation: penalty parameters")();
 
      for (size_t i =                                0; i < as<size_t>(inputPolyCoef.size())  ; i++) penaltyPolyCoef[i] = as<Scalar>(inputPolyCoef[i]);
      for (size_t i = as<size_t>(inputPolyCoef.size()); i < as<size_t>(penaltyPolyCoef.size()); i++) penaltyPolyCoef[i] = Teuchos::ScalarTraits<Scalar>::zero();
   }


   RCP<GraphBase>   filteredGraph;
   badGuysCoalesceDrop(*A, penaltyPolyCoef, nPDEs, *testVecs, *nearNull, filteredGraph);


#ifdef takeOut
   /* write out graph for serial debugging purposes only. */
 
   FILE* fp = fopen("codeOutput","w");
   fprintf(fp,"%d %d %d\n",(int) filteredGraph->GetNodeNumVertices(),(int) filteredGraph->GetNodeNumVertices(),
   (int) filteredGraph->GetNodeNumEdges());
   for (size_t i = 0; i < filteredGraph->GetNodeNumVertices(); i++) {
       ArrayView<const LO> inds = filteredGraph->getNeighborVertices(as<LO>(i));
       for (size_t j = 0; j < as<size_t>(inds.size()); j++) {
         fprintf(fp,"%d %d 1.00e+00\n",(int) i+1,(int) inds[j]+1);
       }
   }
   fclose(fp);
#endif

    SC threshold = .01;
    Set<bool>(currentLevel, "Filtering", (threshold != STS::zero()));
    Set(currentLevel, "Graph", filteredGraph);
    Set(currentLevel, "DofsPerNode", 1);

  } //Build

  template <class Scalar,class LocalOrdinal, class GlobalOrdinal, class Node>
  void SmooVecCoalesceDropFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::badGuysCoalesceDrop(const Matrix& Amat, Teuchos::ArrayRCP<Scalar> & penaltyPolyCoef , LO nPDEs, const MultiVector& testVecs, const MultiVector& nearNull, RCP<GraphBase>& filteredGraph) const {
  /* 
   * Compute coalesce/drop graph (in filteredGraph) for A. The basic idea is to 
   * balance trade-offs associated with 
   *
   *           (I - P inv(R P) R ) testVecs
   *
   * being worse for larger aggregates (less dropping) while MG cycle costs are  
   * cheaper with larger aggregates. MG costs are "penalties" in the 
   * optimization while (I - P inv(R P) R ) is the "fit" (how well a 
   * a fine grid function can be approximated on the coarse grid). 
   *
   * For MG costs, we don't actually approximate the cost. Instead, we
   * have just hardwired penalties below. Specifically, 
   *
   *     penalties[j] is the cost if aggregates are of size j+1, where right
   *                  now a linear function of the form const*(60-j) is used.
   *
   * (I - P inv(P^T P) P^T ) testVecs is estimated by just looking locally at
   * the vector portion corresponding to a possible aggregate defined by
   * all non-dropped connections in the ith row.  A tentative prolognator is
   * used for P. This prolongator corresponds to a null space vector given 
   * by 'nearNull', which is provided to dropper(). In initial testing, nearNull is 
   * first set as a vector of all 1's and then smoothed with a relaxation 
   * method applied to a nice matrix (with the same sparsity pattern as A). 
   * Originally, nearNull was used to handle Dir bcs where relaxation of the 
   * vector of 1's has a more pronounced effect. 
   *
   * For PDE systems, fit only considers the same dof at each node. That is,
   * it effectively assumes that we have a tentative prolongator with no
   * coupling between different dof types. When checking the fit for the kth
   * dof at a paritcular node, it only considers the kth dof of this node
   * and neighboring nodes. 
   *
   * Note: testVecs is supplied by the user, but normally is the result of
   * applying a relaxation scheme to Au = 0 where u is initial random.
   */
  
  GO     numMyNnz = Teuchos::as<GO>(Amat.getNodeNumEntries());
  size_t nLoc     = Amat.getRowMap()->getNodeNumElements();

  size_t nBlks    = nLoc/nPDEs;
  if (nBlks*nPDEs != nLoc ) 
     TEUCHOS_TEST_FOR_EXCEPTION(true, Exceptions::RuntimeError, "Number of local dofs not divisible by BlkSize");

  Teuchos::ArrayRCP<LO>   newRowPtr(nBlks+1); /* coalesce & drop matrix     */
  Teuchos::ArrayRCP<LO>   newCols(numMyNnz);  /* arrays                     */

  Teuchos::ArrayRCP<LO>   bcols(nBlks);       /* returned by dropfun(j,...) */
  Teuchos::ArrayRCP<bool> keepOrNot(nBlks);   /* gives cols for jth row and */
                                              /* whether or not entry is    */
                                              /* kept or dropped.           */

  LO   maxNzPerRow = 200;
  Teuchos::ArrayRCP<Scalar> penalties(maxNzPerRow); /* Penalty function */
                                                    /* described above. */ 
                                    
  Teuchos::ArrayRCP<bool> keepStatus(nBlks,true);  /* accumulated keepOrNot info */
  Teuchos::ArrayRCP<LO>   bColList(nBlks);         /* accumulated bcols info     */
                                                   /* for an entire block as     */
                                                   /* opposed to a single row    */
                                                   /* Additionally, keepOrNot[j] */
                                                   /* refers to status of jth    */
                                                   /* entry in a row while       */
                                                   /* keepStatus[j] refers to    */
                                                   /* whether the jth block is   */
                                                   /* kept within the block row. */

  Teuchos::ArrayRCP<bool> alreadyOnBColList(nBlks,false);  /* used to avoid recording the*/
                                                              /* same block column when     */
                                                              /* processing different pt    */
                                                              /* rows within a block.       */

  Teuchos::ArrayRCP<bool>   boundaryNodes(nBlks,false);


  for (LO i = 0; i <  maxNzPerRow; i++)
    penalties[i] = penaltyPolyCoef[poly0thOrderCoef] + 
                   penaltyPolyCoef[poly1stOrderCoef]*(as<Scalar>(i)) +
                   penaltyPolyCoef[poly2ndOrderCoef]*(as<Scalar>(i*i)) +
                  (penaltyPolyCoef[poly3rdOrderCoef]*(as<Scalar>(i*i))*(as<Scalar>(i)))  +  //perhaps avoids overflow?
                  (penaltyPolyCoef[poly4thOrderCoef]*(as<Scalar>(i*i))*(as<Scalar>(i*i)));

   LO nzTotal = 0, numBCols = 0, row = -1, Nbcols, bcol;
   newRowPtr[0] = 0;

   /* proceed block by block */
   for (LO i = 0; i < as<LO>(nBlks); i++) {
     newRowPtr[i+1] = newRowPtr[i];
     for (LO j = 0; j < nPDEs; j++) {
       row = row + 1;

       Teuchos::ArrayView<const LocalOrdinal> indices;
       Teuchos::ArrayView<const Scalar> vals;

       Amat.getLocalRowView(row, indices, vals);
 
       if (indices.size() > maxNzPerRow) {
          LO oldSize = maxNzPerRow;
          maxNzPerRow = indices.size() + 100;
          penalties.resize(as<size_t>(maxNzPerRow),0.0);
          for (LO k = oldSize; k < maxNzPerRow; k++)
            penalties[k] = penaltyPolyCoef[poly0thOrderCoef] + 
                   penaltyPolyCoef[poly1stOrderCoef]*(as<Scalar>(i)) +
                   penaltyPolyCoef[poly2ndOrderCoef]*(as<Scalar>(i*i)) +
                  (penaltyPolyCoef[poly3rdOrderCoef]*(as<Scalar>(i*i))*(as<Scalar>(i)))  + 
                  (penaltyPolyCoef[poly4thOrderCoef]*(as<Scalar>(i*i))*(as<Scalar>(i*i)));
       }
       badGuysDropfunc(row, indices, vals, testVecs, nPDEs, penalties, nearNull, bcols,keepOrNot,Nbcols,nLoc);
       for (LO k=0; k < Nbcols; k++) { 
         bcol = bcols[k];

         /* add to bColList if not already on it */

         if  (alreadyOnBColList[bcol] == false) {/* for PDE systems only record */
           bColList[numBCols++]  = bcol;     /* neighboring block one time  */
           alreadyOnBColList[bcol] = true;
         }
         /* drop if any pt row within block indicates entry should be dropped */

         if (keepOrNot[k] == false) keepStatus[bcol] = false; 

       }  /* for (k=0; k < Nbcols; k++)   */
     } /* for (j = 0; i < nPDEs; j++)  */

     /* finished with block row. Now record block entries that we keep */
     /* and reset keepStatus, bColList, and alreadyOnBColList.      */

     if ( numBCols < 2) boundaryNodes[i] = true;
     for (LO j=0; j < numBCols; j++) {
       bcol = bColList[j];
       if (keepStatus[bcol] == true) { 
         newCols[nzTotal] = bColList[j]; 
         newRowPtr[i+1]++;
         nzTotal = nzTotal + 1;
       }
       keepStatus[bcol] = true;
       alreadyOnBColList[bcol] = false;
       bColList[j] = 0;
     }
     numBCols = 0;
   } /* for (i = 0; i < nBlks; i++)  */

   /* create array of the correct size and copy over newCols to it */

   Teuchos::ArrayRCP<LO> finalCols(nzTotal);   
   for (LO i = 0; i < nzTotal; i++) finalCols[i] = newCols[i];

   // Not using column map because we do not allow for any off-proc stuff. 
   // Not sure if this is okay.  FIXME

   RCP<const Map> rowMap = Amat.getRowMap(); // , colMap = Amat.getColMap();

   LO nAmalgNodesOnProc = rowMap->getNodeNumElements()/nPDEs;
   Teuchos::Array<GO> nodalGIDs(nAmalgNodesOnProc);
   typename Teuchos::ScalarTraits<Scalar>::coordinateType temp;
   for (size_t i = 0; i < as<size_t>(nAmalgNodesOnProc); i++ ) {
     GO gid = rowMap->getGlobalElement(i*nPDEs);
     temp =  ((typename Teuchos::ScalarTraits<Scalar>::coordinateType) (gid))/((typename Teuchos::ScalarTraits<Scalar>::coordinateType) (nPDEs));
     nodalGIDs[i] = as<GO>(floor(temp));
   }
   GO nAmalgNodesGlobal = rowMap->getGlobalNumElements();
   GO nBlkGlobal       = nAmalgNodesGlobal/nPDEs;
   if (nBlkGlobal*nPDEs != nAmalgNodesGlobal) 
     TEUCHOS_TEST_FOR_EXCEPTION(true, Exceptions::RuntimeError, "Number of global dofs not divisible by BlkSize");

   Teuchos::RCP<Map> AmalgRowMap = MapFactory::Build(rowMap->lib(), nBlkGlobal,
                                                    nodalGIDs(),0,rowMap->getComm());

   filteredGraph = rcp(new LWGraph(newRowPtr, finalCols, AmalgRowMap, AmalgRowMap, "thresholded graph of A"));
   filteredGraph->SetBoundaryNodeMap(boundaryNodes);

  }

  template <class Scalar,class LocalOrdinal, class GlobalOrdinal, class Node>
  void SmooVecCoalesceDropFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::badGuysDropfunc(LO row, const Teuchos::ArrayView<const LocalOrdinal>& cols, const Teuchos::ArrayView<const Scalar>& vals, const MultiVector&  testVecs, LO nPDEs, Teuchos::ArrayRCP<Scalar> & penalties, const MultiVector& nearNull, Teuchos::ArrayRCP<LO>& Bcols, Teuchos::ArrayRCP<bool>& keepOrNot, LO &Nbcols, LO nLoc) const {

  LO nLeng  = cols.size();
  typename Teuchos::ScalarTraits<Scalar>::coordinateType temp;
  temp =  ((typename Teuchos::ScalarTraits<Scalar>::coordinateType) (row))/((typename Teuchos::ScalarTraits<Scalar>::coordinateType) (nPDEs));
  LO blkRow = as<LO>(floor(temp));
  Teuchos::ArrayRCP<Scalar> badGuy( nLeng, 0.0);
  Teuchos::ArrayRCP<Scalar> subNull(nLeng, 0.0);  /* subset of nearNull       */
                                                  /* associated with current  */
                                                  /* dof within node.         */
  
  /* Only consider testVecs associated with same dof & on processor. Further   */
  /* collapse testVecs to a single badGuy vector by basically taking the worst */
  /* (least smooth) values for each of the off diags. In particular, we look at*/
  /* the ratio of each off-diag test value / diag test value and compare this  */
  /* with the nearNull vector ratio. The further the testVec ratio is from the */
  /* nearNull ratio, the harder is will be to accurately interpolate is these  */
  /* two guys are aggregated. So, the biggest ratio mismatch is used to choose */
  /* the testVec entry associated with each off-diagonal entry.                */


  for (LO i = 0; i < nLeng; i++) keepOrNot[i] = false;   

  LO diagInd = -1;
  Nbcols     = 0; 
  LO rowDof  =  row  -  blkRow*nPDEs;
  Teuchos::ArrayRCP< const Scalar > oneNull = nearNull.getData( as<size_t>(rowDof));

  for (LO i = 0; i < nLeng; i++) {
    if ((cols[i] < nLoc ) && (vals[i] != 0.0)) {   /* on processor */
      temp =  ((typename Teuchos::ScalarTraits<Scalar>::coordinateType) (cols[i]))/((typename Teuchos::ScalarTraits<Scalar>::coordinateType) (nPDEs));
      LO colDof = cols[i] - (as<LO>(floor( temp    )))*nPDEs;
      if (colDof == rowDof) { /* same dof within node as row */
        Bcols[  Nbcols] = (cols[i] - colDof)/nPDEs;
        subNull[Nbcols] = oneNull[cols[i]];

        if (cols[i] != row) { /* not diagonal  */
          Scalar worstRatio = -1.0;
          Scalar targetRatio = subNull[Nbcols]/oneNull[row];
          Scalar actualRatio;
          for (size_t kk = 0; kk < testVecs.getNumVectors(); kk++ ) {
            Teuchos::ArrayRCP< const Scalar > curVec = testVecs.getData(kk);
            actualRatio = curVec[cols[i]]/curVec[row];
            if (Teuchos::ScalarTraits<SC>::magnitude(actualRatio - targetRatio) > Teuchos::ScalarTraits<SC>::magnitude(worstRatio)) {
               badGuy[Nbcols] = actualRatio;
               worstRatio = Teuchos::ScalarTraits<SC>::magnitude(actualRatio - targetRatio);
            }
          }
        }
        else {
          badGuy[   Nbcols] = 1.; 
          keepOrNot[Nbcols] = true; 
          diagInd            = Nbcols;
        }
        (Nbcols)++;
      }
    }
  }

  /* Make sure that diagonal entry is in block col list */

  if (diagInd == -1) {
    Bcols[    Nbcols] = (row - rowDof)/nPDEs;
    subNull[  Nbcols] = 1.;
    badGuy[   Nbcols] = 1.; 
    keepOrNot[Nbcols] = true; 
    diagInd            = Nbcols;
    (Nbcols)++;
  }

  Scalar currentRP          = oneNull[row]*oneNull[row];
  Scalar currentRTimesBadGuy= oneNull[row]*badGuy[diagInd];
  Scalar currentScore       = penalties[0]; /* (I - P inv(R*P)*R )=0 for size */
                                     /* size 1 agg, so fit is perfect  */

  /* starting from a set that only includes the diagonal entry consider adding */
  /* one off-diagonal at a time until the fitValue exceeds the penalty term.   */
  /* Here, the fit value is  (I - P inv(R P) R ) and we always consider the    */
  /* lowest fitValue that is not currently in the set. R and P correspond to   */
  /* a simple tentaive grid transfer associated with an aggregate that         */
  /* includes the diagonal, all already determined neighbors, and the potential*/
  /* new neighbor                                                              */

  LO nKeep = 1, flag  = 1, minId;
  Scalar minFit, minFitRP = 0., minFitRTimesBadGuy = 0.;
  Scalar newRP, newRTimesBadGuy; 

  while (flag == 1) {
    /* compute a fit for each possible off-diagonal neighbor */
    /* that has not already been added as a neighbor         */

    minFit = 1000000.;
    minId  = -1;

    for (LO i=0; i < Nbcols; i++) {
      if (keepOrNot[i] == false) { 
        keepOrNot[i] = true;  /* temporarily view i as non-dropped neighbor */
        newRP          = currentRP           + subNull[i]*subNull[i];
        newRTimesBadGuy= currentRTimesBadGuy + subNull[i]*badGuy[i];
        Scalar ratio = newRTimesBadGuy/newRP;

        Scalar newFit = 0.0;
        for (LO k=0; k < Nbcols; k++) { 
          if (keepOrNot[k] == true) {
             Scalar diff = badGuy[k] - ratio*subNull[k];
             newFit = newFit + diff*diff;
          }
        }
        if (Teuchos::ScalarTraits<SC>::magnitude(newFit) < Teuchos::ScalarTraits<SC>::magnitude(minFit)) {
          minId     = i;
          minFit    = newFit;
          minFitRP  = newRP;
          minFitRTimesBadGuy= newRTimesBadGuy;
        }
        keepOrNot[i] = false;
      }
    }
    if (minId == -1) flag = 0; 
    else {
      minFit = sqrt(minFit);
      Scalar newScore = penalties[nKeep] + minFit;
      if (Teuchos::ScalarTraits<SC>::magnitude(newScore) < Teuchos::ScalarTraits<SC>::magnitude(currentScore)) {
        nKeep           = nKeep + 1;
        keepOrNot[minId]= true;
        currentScore    = newScore;
        currentRP       = minFitRP;
        currentRTimesBadGuy= minFitRTimesBadGuy;
      }
      else flag = 0;
    }
  }
  }

} //namespace MueLu

#endif // MUELU_SMOOVECCOALESCEDROPFACTORY_DEF_HPP