Teko_Utilities.cpp

/*
// @HEADER
// 
// ***********************************************************************
// 
//      Teko: A package for block and physics based preconditioning
//                  Copyright 2010 Sandia Corporation 
//  
// Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
// the U.S. Government retains certain rights in this software.
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// 1. Redistributions of source code must retain the above copyright
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// 2. Redistributions in binary form must reproduce the above copyright
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// documentation and/or other materials provided with the distribution.
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// 3. Neither the name of the Corporation nor the names of the
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission. 
//  
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
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*/
 
#include "Teko_Config.h"
#include "Teko_Utilities.hpp"
 
// Thyra includes
#include "Thyra_MultiVectorStdOps.hpp"
#include "Thyra_ZeroLinearOpBase.hpp"
#include "Thyra_DefaultDiagonalLinearOp.hpp"
#include "Thyra_DefaultAddedLinearOp.hpp"
#include "Thyra_EpetraExtDiagScaledMatProdTransformer.hpp"
#include "Thyra_EpetraExtDiagScalingTransformer.hpp"
#include "Thyra_EpetraExtAddTransformer.hpp"
#include "Thyra_DefaultScaledAdjointLinearOp.hpp"
#include "Thyra_DefaultMultipliedLinearOp.hpp"
#include "Thyra_DefaultZeroLinearOp.hpp"
#include "Thyra_DefaultProductMultiVector.hpp"
#include "Thyra_DefaultProductVectorSpace.hpp"
#include "Thyra_MultiVectorStdOps.hpp"
#include "Thyra_VectorStdOps.hpp"
#include "Thyra_SpmdVectorBase.hpp"
#include "Thyra_get_Epetra_Operator.hpp"
#include "Thyra_EpetraThyraWrappers.hpp"
#include "Thyra_EpetraOperatorWrapper.hpp"
#include "Thyra_EpetraLinearOp.hpp"
 
// Teuchos includes
#include "Teuchos_Array.hpp"
 
// Epetra includes
#include "Epetra_Operator.h"
#include "Epetra_CrsGraph.h"
#include "Epetra_CrsMatrix.h"
#include "Epetra_Vector.h"
#include "Epetra_Map.h"
 
#include "EpetraExt_Transpose_RowMatrix.h"
#include "EpetraExt_MatrixMatrix.h"
 
// Anasazi includes
#include "AnasaziBasicEigenproblem.hpp"
#include "AnasaziThyraAdapter.hpp"
#include "AnasaziBlockKrylovSchurSolMgr.hpp"
#include "AnasaziBlockKrylovSchur.hpp"
#include "AnasaziStatusTestMaxIters.hpp"
 
// Isorropia includes
#ifdef Teko_ENABLE_Isorropia
#include "Isorropia_EpetraProber.hpp"
#endif
 
// Teko includes
#include "Teko_EpetraHelpers.hpp"
#include "Teko_EpetraOperatorWrapper.hpp"
#include "Teko_TpetraHelpers.hpp"
#include "Teko_TpetraOperatorWrapper.hpp"
 
// Tpetra
#include "Thyra_TpetraLinearOp.hpp"
#include "Tpetra_CrsMatrix.hpp"
#include "Tpetra_Vector.hpp"
#include "Thyra_TpetraThyraWrappers.hpp"
#include "TpetraExt_MatrixMatrix.hpp"
#include "Tpetra_RowMatrixTransposer.hpp"
 
#include <cmath>
 
namespace Teko {
 
using Teuchos::rcp;
using Teuchos::rcp_dynamic_cast;
using Teuchos::RCP;
#ifdef Teko_ENABLE_Isorropia
using Isorropia::Epetra::Prober;
#endif
 
const Teuchos::RCP<Teuchos::FancyOStream> getOutputStream()
{ 
   Teuchos::RCP<Teuchos::FancyOStream> os = 
         Teuchos::VerboseObjectBase::getDefaultOStream(); 
  
   //os->setShowProcRank(true);
   //os->setOutputToRootOnly(-1);
   return os;
}
 
// distance function...not parallel...entirely internal to this cpp file
inline double dist(int dim,double * coords,int row,int col)
{
   double value = 0.0;
   for(int i=0;i<dim;i++)
      value += std::pow(coords[dim*row+i]-coords[dim*col+i],2.0);
 
   // the distance between the two
   return std::sqrt(value);
}
 
// distance function...not parallel...entirely internal to this cpp file
inline double dist(double * x,double * y,double * z,int stride,int row,int col)
{
   double value = 0.0;
   if(x!=0) value += std::pow(x[stride*row]-x[stride*col],2.0);
   if(y!=0) value += std::pow(y[stride*row]-y[stride*col],2.0);
   if(z!=0) value += std::pow(z[stride*row]-z[stride*col],2.0);
 
   // the distance between the two
   return std::sqrt(value);
}
 
RCP<Epetra_CrsMatrix> buildGraphLaplacian(int dim,double * coords,const Epetra_CrsMatrix & stencil)
{
   // allocate a new matrix with storage for the laplacian...in case of diagonals add one extra storage
   RCP<Epetra_CrsMatrix> gl = rcp(new Epetra_CrsMatrix(Copy,stencil.RowMap(),stencil.ColMap(),
                                                       stencil.MaxNumEntries()+1),true);
 
   // allocate an additional value for the diagonal, if neccessary
   std::vector<double> rowData(stencil.GlobalMaxNumEntries()+1);
   std::vector<int> rowInd(stencil.GlobalMaxNumEntries()+1);
 
   // loop over all the rows
   for(int j=0;j<gl->NumMyRows();j++) {
      int row = gl->GRID(j);
      double diagValue = 0.0;
      int diagInd = -1;
      int rowSz = 0;
 
      // extract a copy of this row...put it in rowData, rowIndicies
      stencil.ExtractGlobalRowCopy(row,stencil.MaxNumEntries(),rowSz,&rowData[0],&rowInd[0]);
 
      // loop over elements of row
      for(int i=0;i<rowSz;i++) {
         int col = rowInd[i];
 
         // is this a 0 entry masquerading as some thing else?
         double value = rowData[i];
         if(value==0) continue;
 
         // for nondiagonal entries
         if(row!=col) {
            double d = dist(dim,coords,row,col);
            rowData[i] = -1.0/d;
            diagValue += rowData[i];
         }
         else 
            diagInd = i;
      }
    
      // handle diagonal entry
      if(diagInd<0) { // diagonal not in row
         rowData[rowSz] = -diagValue;
         rowInd[rowSz] = row;
         rowSz++;
      }
      else { // diagonal in row
         rowData[diagInd] = -diagValue;
         rowInd[diagInd] = row;
      }
 
      // insert row data into graph Laplacian matrix
      TEUCHOS_TEST_FOR_EXCEPT(gl->InsertGlobalValues(row,rowSz,&rowData[0],&rowInd[0]));
   }
 
   gl->FillComplete();
 
   return gl;
}
 
RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > buildGraphLaplacian(int dim,ST * coords,const Tpetra::CrsMatrix<ST,LO,GO,NT> & stencil)
{
   // allocate a new matrix with storage for the laplacian...in case of diagonals add one extra storage
   RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > gl = rcp(new Tpetra::CrsMatrix<ST,LO,GO,NT>(stencil.getRowMap(),stencil.getColMap(),
                                                       stencil.getGlobalMaxNumRowEntries()+1));
 
   // allocate an additional value for the diagonal, if neccessary
   auto rowInd = typename Tpetra::CrsMatrix<ST,LO,GO,NT>::nonconst_global_inds_host_view_type(Kokkos::ViewAllocateWithoutInitializing("rowIndices"),stencil.getGlobalMaxNumRowEntries()+1);
   auto rowData = typename Tpetra::CrsMatrix<ST,LO,GO,NT>::nonconst_values_host_view_type(Kokkos::ViewAllocateWithoutInitializing("rowIndices"),stencil.getGlobalMaxNumRowEntries()+1);
 
   // loop over all the rows
   for(LO j=0;j< (LO) gl->getNodeNumRows();j++) {
      GO row = gl->getRowMap()->getGlobalElement(j);
      ST diagValue = 0.0;
      GO diagInd = -1;
      size_t rowSz = 0;
 
      // extract a copy of this row...put it in rowData, rowIndicies
      stencil.getGlobalRowCopy(row,rowInd,rowData,rowSz);
 
      // loop over elements of row
      for(size_t i=0;i<rowSz;i++) {
        GO col = rowInd(i);
 
         // is this a 0 entry masquerading as some thing else?
         ST value = rowData[i];
         if(value==0) continue;
 
         // for nondiagonal entries
         if(row!=col) {
            ST d = dist(dim,coords,row,col);
            rowData[i] = -1.0/d;
            diagValue += rowData(i);
         }
         else 
            diagInd = i;
      }
    
      // handle diagonal entry
      if(diagInd<0) { // diagonal not in row
         rowData(rowSz) = -diagValue;
         rowInd(rowSz) = row;
         rowSz++;
      }
      else { // diagonal in row
         rowData(diagInd) = -diagValue;
         rowInd(diagInd) = row;
      }
 
      // insert row data into graph Laplacian matrix
      gl->replaceGlobalValues(row,rowInd,rowData);
   }
 
   gl->fillComplete();
 
   return gl;
}
 
RCP<Epetra_CrsMatrix> buildGraphLaplacian(double * x,double * y,double * z,int stride,const Epetra_CrsMatrix & stencil)
{
   // allocate a new matrix with storage for the laplacian...in case of diagonals add one extra storage
   RCP<Epetra_CrsMatrix> gl = rcp(new Epetra_CrsMatrix(Copy,stencil.RowMap(),stencil.ColMap(),
                                                       stencil.MaxNumEntries()+1),true);
 
   // allocate an additional value for the diagonal, if neccessary
   std::vector<double> rowData(stencil.GlobalMaxNumEntries()+1);
   std::vector<int> rowInd(stencil.GlobalMaxNumEntries()+1);
 
   // loop over all the rows
   for(int j=0;j<gl->NumMyRows();j++) {
      int row = gl->GRID(j);
      double diagValue = 0.0;
      int diagInd = -1;
      int rowSz = 0;
 
      // extract a copy of this row...put it in rowData, rowIndicies
      stencil.ExtractGlobalRowCopy(row,stencil.MaxNumEntries(),rowSz,&rowData[0],&rowInd[0]);
 
      // loop over elements of row
      for(int i=0;i<rowSz;i++) {
         int col = rowInd[i];
 
         // is this a 0 entry masquerading as some thing else?
         double value = rowData[i];
         if(value==0) continue;
 
         // for nondiagonal entries
         if(row!=col) {
            double d = dist(x,y,z,stride,row,col);
            rowData[i] = -1.0/d;
            diagValue += rowData[i];
         }
         else 
            diagInd = i;
      }
    
      // handle diagonal entry
      if(diagInd<0) { // diagonal not in row
         rowData[rowSz] = -diagValue;
         rowInd[rowSz] = row;
         rowSz++;
      }
      else { // diagonal in row
         rowData[diagInd] = -diagValue;
         rowInd[diagInd] = row;
      }
 
      // insert row data into graph Laplacian matrix
      TEUCHOS_TEST_FOR_EXCEPT(gl->InsertGlobalValues(row,rowSz,&rowData[0],&rowInd[0]));
   }
 
   gl->FillComplete();
 
   return gl;
}
 
RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > buildGraphLaplacian(ST * x,ST * y,ST * z,GO stride,const Tpetra::CrsMatrix<ST,LO,GO,NT> & stencil)
{
   // allocate a new matrix with storage for the laplacian...in case of diagonals add one extra storage
   RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > gl = rcp(new Tpetra::CrsMatrix<ST,LO,GO,NT>(stencil.getRowMap(),stencil.getColMap(),
                                                       stencil.getGlobalMaxNumRowEntries()+1),true);
 
   // allocate an additional value for the diagonal, if neccessary
   auto rowInd = typename Tpetra::CrsMatrix<ST,LO,GO,NT>::nonconst_global_inds_host_view_type(Kokkos::ViewAllocateWithoutInitializing("rowIndices"),stencil.getGlobalMaxNumRowEntries()+1);
   auto rowData = typename Tpetra::CrsMatrix<ST,LO,GO,NT>::nonconst_values_host_view_type(Kokkos::ViewAllocateWithoutInitializing("rowIndices"),stencil.getGlobalMaxNumRowEntries()+1);
 
   // loop over all the rows
   for(LO j=0;j<(LO) gl->getNodeNumRows();j++) {
      GO row = gl->getRowMap()->getGlobalElement(j);
      ST diagValue = 0.0;
      GO diagInd = -1;
      size_t rowSz = 0;
 
      // extract a copy of this row...put it in rowData, rowIndicies
      stencil.getGlobalRowCopy(row,rowInd,rowData,rowSz);
 
      // loop over elements of row
      for(size_t i=0;i<rowSz;i++) {
         GO col = rowInd(i);
 
         // is this a 0 entry masquerading as some thing else?
         ST value = rowData[i];
         if(value==0) continue;
 
         // for nondiagonal entries
         if(row!=col) {
            ST d = dist(x,y,z,stride,row,col);
            rowData[i] = -1.0/d;
            diagValue += rowData(i);
         }
         else 
            diagInd = i;
      }
    
      // handle diagonal entry
      if(diagInd<0) { // diagonal not in row
         rowData(rowSz) = -diagValue;
         rowInd(rowSz) = row;
         rowSz++;
      }
      else { // diagonal in row
         rowData(diagInd) = -diagValue;
         rowInd(diagInd) = row;
      }
 
      // insert row data into graph Laplacian matrix
      gl->replaceGlobalValues(row,rowInd,rowData);
   }
 
   gl->fillComplete();
 
   return gl;
}
 
void applyOp(const LinearOp & A,const MultiVector & x,MultiVector & y,double alpha,double beta)
{
   Thyra::apply(*A,Thyra::NOTRANS,*x,y.ptr(),alpha,beta);
}
 
void applyTransposeOp(const LinearOp & A,const MultiVector & x,MultiVector & y,double alpha,double beta)
{
   Thyra::apply(*A,Thyra::TRANS,*x,y.ptr(),alpha,beta);
}
 
void update(double alpha,const MultiVector & x,double beta,MultiVector & y)
{
   Teuchos::Array<double> scale;
   Teuchos::Array<Teuchos::Ptr<const Thyra::MultiVectorBase<double> > >  vec;
 
   // build arrays needed for linear combo
   scale.push_back(alpha);
   vec.push_back(x.ptr());
 
   // compute linear combination
   Thyra::linear_combination<double>(scale,vec,beta,y.ptr());
}
 
BlockedLinearOp getUpperTriBlocks(const BlockedLinearOp & blo,bool callEndBlockFill)
{
   int rows = blockRowCount(blo);
 
   TEUCHOS_ASSERT(rows==blockColCount(blo));
 
   RCP<const Thyra::ProductVectorSpaceBase<double> > range = blo->productRange();
   RCP<const Thyra::ProductVectorSpaceBase<double> > domain = blo->productDomain();
 
   // allocate new operator
   BlockedLinearOp upper = createBlockedOp();
 
   // build new operator 
   upper->beginBlockFill(rows,rows);
 
   for(int i=0;i<rows;i++) {
      // put zero operators on the diagonal
      // this gurantees the vector space of
      // the new operator are fully defined
      RCP<const Thyra::LinearOpBase<double> > zed 
            = Thyra::zero<double>(range->getBlock(i),domain->getBlock(i));
      upper->setBlock(i,i,zed);
 
      for(int j=i+1;j<rows;j++) {
         // get block i,j
         LinearOp uij = blo->getBlock(i,j);
 
         // stuff it in U
         if(uij!=Teuchos::null)
            upper->setBlock(i,j,uij);
      }
   }
   if(callEndBlockFill)
      upper->endBlockFill();
 
   return upper;
}
 
BlockedLinearOp getLowerTriBlocks(const BlockedLinearOp & blo,bool callEndBlockFill)
{
   int rows = blockRowCount(blo);
 
   TEUCHOS_ASSERT(rows==blockColCount(blo));
 
   RCP<const Thyra::ProductVectorSpaceBase<double> > range = blo->productRange();
   RCP<const Thyra::ProductVectorSpaceBase<double> > domain = blo->productDomain();
 
   // allocate new operator
   BlockedLinearOp lower = createBlockedOp();
 
   // build new operator 
   lower->beginBlockFill(rows,rows);
 
   for(int i=0;i<rows;i++) {
      // put zero operators on the diagonal
      // this gurantees the vector space of
      // the new operator are fully defined
      RCP<const Thyra::LinearOpBase<double> > zed 
            = Thyra::zero<double>(range->getBlock(i),domain->getBlock(i));
      lower->setBlock(i,i,zed);
 
      for(int j=0;j<i;j++) {
         // get block i,j
         LinearOp uij = blo->getBlock(i,j);
 
         // stuff it in U
         if(uij!=Teuchos::null)
            lower->setBlock(i,j,uij);
      }
   }
   if(callEndBlockFill)
      lower->endBlockFill();
 
   return lower;
}
 
BlockedLinearOp zeroBlockedOp(const BlockedLinearOp & blo)
{
   int rows = blockRowCount(blo);
 
   TEUCHOS_ASSERT(rows==blockColCount(blo)); // assert that matrix is square
 
   RCP<const Thyra::ProductVectorSpaceBase<double> > range = blo->productRange();
   RCP<const Thyra::ProductVectorSpaceBase<double> > domain = blo->productDomain();
 
   // allocate new operator
   BlockedLinearOp zeroOp = createBlockedOp();
 
   // build new operator 
   zeroOp->beginBlockFill(rows,rows);
 
   for(int i=0;i<rows;i++) {
      // put zero operators on the diagonal
      // this gurantees the vector space of
      // the new operator are fully defined
      RCP<const Thyra::LinearOpBase<double> > zed 
            = Thyra::zero<double>(range->getBlock(i),domain->getBlock(i));
      zeroOp->setBlock(i,i,zed);
   }
 
   return zeroOp;
}
 
bool isZeroOp(const LinearOp op)
{
   // if operator is null...then its zero!
   if(op==Teuchos::null) return true;
 
   // try to cast it to a zero linear operator
   LinearOp test = rcp_dynamic_cast<const Thyra::ZeroLinearOpBase<double> >(op);
 
   // if it works...then its zero...otherwise its null
   if(test!=Teuchos::null) return true;
 
   // See if the operator is a wrapped zero op
   ST scalar = 0.0;
   Thyra::EOpTransp transp = Thyra::NOTRANS;
   RCP<const Thyra::LinearOpBase<ST> > wrapped_op;
   Thyra::unwrap(op, &scalar, &transp, &wrapped_op);
   test = rcp_dynamic_cast<const Thyra::ZeroLinearOpBase<double> >(wrapped_op);
   return test!=Teuchos::null;
}
 
ModifiableLinearOp getAbsRowSumMatrix(const LinearOp & op)
{
   bool isTpetra = false;
   RCP<const Epetra_CrsMatrix> eCrsOp;
   RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOp;
 
   try {
      // get Epetra or Tpetra Operator
      RCP<const Thyra::EpetraLinearOp > eOp = rcp_dynamic_cast<const Thyra::EpetraLinearOp >(op);
      RCP<const Thyra::TpetraLinearOp<ST,LO,GO,NT> > tOp = rcp_dynamic_cast<const Thyra::TpetraLinearOp<ST,LO,GO,NT> >(op);
 
      // cast it to a CrsMatrix
      RCP<Teuchos::FancyOStream> out = Teuchos::VerboseObjectBase::getDefaultOStream();
      if (!eOp.is_null()){
        eCrsOp = rcp_dynamic_cast<const Epetra_CrsMatrix>(eOp->epetra_op(),true);
      }   
      else if (!tOp.is_null()){
        tCrsOp = rcp_dynamic_cast<const Tpetra::CrsMatrix<ST,LO,GO,NT> >(tOp->getConstTpetraOperator(),true);
        isTpetra = true;
      }
      else
        throw std::logic_error("Neither Epetra nor Tpetra");
   }
   catch (std::exception & e) {
      RCP<Teuchos::FancyOStream> out = Teuchos::VerboseObjectBase::getDefaultOStream();
 
      *out << "Teko: getAbsRowSumMatrix requires an Epetra_CrsMatrix or a Tpetra::CrsMatrix\n";
      *out << "    Could not extract an Epetra_Operator or a Tpetra_Operator from a \"" << op->description() << std::endl;
      *out << "           OR\n";
      *out << "    Could not cast an Epetra_Operator to a Epetra_CrsMatrix or a Tpetra_Operator to a Tpetra::CrsMatrix\n";
      *out << std::endl;
      *out << "*** THROWN EXCEPTION ***\n";
      *out << e.what() << std::endl;
      *out << "************************\n";
      
      throw e;
   }
 
   if(!isTpetra){
     // extract diagonal
     const RCP<Epetra_Vector> ptrDiag = rcp(new Epetra_Vector(eCrsOp->RowMap()));
     Epetra_Vector & diag = *ptrDiag;
 
     // compute absolute value row sum
     diag.PutScalar(0.0);
     for(int i=0;i<eCrsOp->NumMyRows();i++) {
        double * values = 0;
        int numEntries;
        eCrsOp->ExtractMyRowView(i,numEntries,values);
 
        // build abs value row sum
        for(int j=0;j<numEntries;j++)
           diag[i] += std::abs(values[j]);
     }
 
     // build Thyra diagonal operator
     return Teko::Epetra::thyraDiagOp(ptrDiag,eCrsOp->RowMap(),"absRowSum( " + op->getObjectLabel() + " )");
   }
   else {
     // extract diagonal
     const RCP<Tpetra::Vector<ST,LO,GO,NT> > ptrDiag = Tpetra::createVector<ST,LO,GO,NT>(tCrsOp->getRowMap());
     Tpetra::Vector<ST,LO,GO,NT> & diag = *ptrDiag;
 
     // compute absolute value row sum
     diag.putScalar(0.0);
     for(LO i=0;i<(LO) tCrsOp->getNodeNumRows();i++) {
        LO numEntries = tCrsOp->getNumEntriesInLocalRow (i); 
        typename Tpetra::CrsMatrix<ST,LO,GO,NT>::local_inds_host_view_type indices;
        typename Tpetra::CrsMatrix<ST,LO,GO,NT>::values_host_view_type values;
        tCrsOp->getLocalRowView(i,indices,values);
 
        // build abs value row sum
        for(LO j=0;j<numEntries;j++)
           diag.sumIntoLocalValue(i,std::abs(values(j)));
     }
 
     // build Thyra diagonal operator
     return Teko::TpetraHelpers::thyraDiagOp(ptrDiag,*tCrsOp->getRowMap(),"absRowSum( " + op->getObjectLabel() + " ))");
 
   }
 
}
 
ModifiableLinearOp getAbsRowSumInvMatrix(const LinearOp & op)
{
   // if this is a blocked operator, extract diagonals block by block
   // FIXME: this does not add in values from off-diagonal blocks
   RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_op = rcp_dynamic_cast<const Thyra::PhysicallyBlockedLinearOpBase<double> >(op);
   if(blocked_op != Teuchos::null){
     int numRows = blocked_op->productRange()->numBlocks();
     TEUCHOS_ASSERT(blocked_op->productDomain()->numBlocks() == numRows);
     RCP<Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_diag = Thyra::defaultBlockedLinearOp<double>();
     blocked_diag->beginBlockFill(numRows,numRows);
     for(int r = 0; r < numRows; ++r){
       for(int c = 0; c < numRows; ++c){
         if(r==c)
           blocked_diag->setNonconstBlock(r,c,getAbsRowSumInvMatrix(blocked_op->getBlock(r,c)));
         else
           blocked_diag->setBlock(r,c,Thyra::zero<double>(blocked_op->getBlock(r,c)->range(),blocked_op->getBlock(r,c)->domain()));
       }
     }
     blocked_diag->endBlockFill();
     return blocked_diag;
   }
 
   if(Teko::TpetraHelpers::isTpetraLinearOp(op)) {
     ST scalar = 0.0;
     bool transp = false;
     RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOp = Teko::TpetraHelpers::getTpetraCrsMatrix(op, &scalar, &transp);
 
     // extract diagonal
     const RCP<Tpetra::Vector<ST,LO,GO,NT> > ptrDiag = Tpetra::createVector<ST,LO,GO,NT>(tCrsOp->getRowMap());
     Tpetra::Vector<ST,LO,GO,NT> & diag = *ptrDiag;
 
     // compute absolute value row sum
     diag.putScalar(0.0);
     for(LO i=0;i<(LO) tCrsOp->getNodeNumRows();i++) {
        LO numEntries = tCrsOp->getNumEntriesInLocalRow (i);
        typename Tpetra::CrsMatrix<ST,LO,GO,NT>::local_inds_host_view_type indices;
        typename Tpetra::CrsMatrix<ST,LO,GO,NT>::values_host_view_type values;
        tCrsOp->getLocalRowView(i,indices,values);
 
        // build abs value row sum
        for(LO j=0;j<numEntries;j++)
           diag.sumIntoLocalValue(i,std::abs(values(j)));
     }
     diag.scale(scalar);
     diag.reciprocal(diag); // invert entries
 
     // build Thyra diagonal operator
     return Teko::TpetraHelpers::thyraDiagOp(ptrDiag,*tCrsOp->getRowMap(),"absRowSum( " + op->getObjectLabel() + " ))");
 
   }
   else{
     RCP<const Thyra::EpetraLinearOp > eOp = rcp_dynamic_cast<const Thyra::EpetraLinearOp >(op,true);
     RCP<const Epetra_CrsMatrix> eCrsOp = rcp_dynamic_cast<const Epetra_CrsMatrix>(eOp->epetra_op(),true);
 
     // extract diagonal
     const RCP<Epetra_Vector> ptrDiag = rcp(new Epetra_Vector(eCrsOp->RowMap()));
     Epetra_Vector & diag = *ptrDiag;
 
     // compute absolute value row sum
     diag.PutScalar(0.0);
     for(int i=0;i<eCrsOp->NumMyRows();i++) {
        double * values = 0;
        int numEntries;
        eCrsOp->ExtractMyRowView(i,numEntries,values);
 
        // build abs value row sum
        for(int j=0;j<numEntries;j++)
           diag[i] += std::abs(values[j]);
     }
     diag.Reciprocal(diag); // invert entries
 
     // build Thyra diagonal operator
     return Teko::Epetra::thyraDiagOp(ptrDiag,eCrsOp->RowMap(),"absRowSum( " + op->getObjectLabel() + " )");
   }
 
}
 
ModifiableLinearOp getLumpedMatrix(const LinearOp & op)
{
   RCP<Thyra::VectorBase<ST> > ones = Thyra::createMember(op->domain());
   RCP<Thyra::VectorBase<ST> > diag = Thyra::createMember(op->range());
 
   // set to all ones
   Thyra::assign(ones.ptr(),1.0);
 
   // compute lumped diagonal
   // Thyra::apply(*op,Thyra::NONCONJ_ELE,*ones,&*diag);
   Thyra::apply(*op,Thyra::NOTRANS,*ones,diag.ptr());
 
   return rcp(new Thyra::DefaultDiagonalLinearOp<ST>(diag));
}
 
ModifiableLinearOp getInvLumpedMatrix(const LinearOp & op)
{
   RCP<Thyra::VectorBase<ST> > ones = Thyra::createMember(op->domain());
   RCP<Thyra::VectorBase<ST> > diag = Thyra::createMember(op->range());
 
   // set to all ones
   Thyra::assign(ones.ptr(),1.0);
 
   // compute lumped diagonal
   Thyra::apply(*op,Thyra::NOTRANS,*ones,diag.ptr());
   Thyra::reciprocal(*diag,diag.ptr());
 
   return rcp(new Thyra::DefaultDiagonalLinearOp<ST>(diag));
}
 
const ModifiableLinearOp getDiagonalOp(const LinearOp & op)
{
   bool isTpetra = false;
   RCP<const Epetra_CrsMatrix> eCrsOp;
   RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOp;
 
   try {
      // get Epetra or Tpetra Operator
      RCP<const Thyra::EpetraLinearOp > eOp = rcp_dynamic_cast<const Thyra::EpetraLinearOp >(op);
      RCP<const Thyra::TpetraLinearOp<ST,LO,GO,NT> > tOp = rcp_dynamic_cast<const Thyra::TpetraLinearOp<ST,LO,GO,NT> >(op);
 
      // cast it to a CrsMatrix
      RCP<Teuchos::FancyOStream> out = Teuchos::VerboseObjectBase::getDefaultOStream();
      if (!eOp.is_null()){
        eCrsOp = rcp_dynamic_cast<const Epetra_CrsMatrix>(eOp->epetra_op(),true);
      }   
      else if (!tOp.is_null()){
        tCrsOp = rcp_dynamic_cast<const Tpetra::CrsMatrix<ST,LO,GO,NT> >(tOp->getConstTpetraOperator(),true);
        isTpetra = true;
      }
      else
        throw std::logic_error("Neither Epetra nor Tpetra");
   }
   catch (std::exception & e) {
      RCP<Teuchos::FancyOStream> out = Teuchos::VerboseObjectBase::getDefaultOStream();
 
      *out << "Teko: getDiagonalOp requires an Epetra_CrsMatrix or a Tpetra::CrsMatrix\n";
      *out << "    Could not extract an Epetra_Operator or a Tpetra_Operator from a \"" << op->description() << std::endl;
      *out << "           OR\n";
      *out << "    Could not cast an Epetra_Operator to a Epetra_CrsMatrix or a Tpetra_Operator to a Tpetra::CrsMatrix\n";
      *out << std::endl;
      *out << "*** THROWN EXCEPTION ***\n";
      *out << e.what() << std::endl;
      *out << "************************\n";
      
      throw e;
   }
 
   if(!isTpetra){
     // extract diagonal
     const RCP<Epetra_Vector> diag = rcp(new Epetra_Vector(eCrsOp->RowMap()));
     TEUCHOS_TEST_FOR_EXCEPT(eCrsOp->ExtractDiagonalCopy(*diag));
 
     // build Thyra diagonal operator
     return Teko::Epetra::thyraDiagOp(diag,eCrsOp->RowMap(),"inv(diag( " + op->getObjectLabel() + " ))");
   }
   else {
     // extract diagonal
     const RCP<Tpetra::Vector<ST,LO,GO,NT> > diag = Tpetra::createVector<ST,LO,GO,NT>(tCrsOp->getRowMap());
     tCrsOp->getLocalDiagCopy(*diag);
 
     // build Thyra diagonal operator
     return Teko::TpetraHelpers::thyraDiagOp(diag,*tCrsOp->getRowMap(),"inv(diag( " + op->getObjectLabel() + " ))");
 
   }
}
 
const MultiVector getDiagonal(const LinearOp & op)
{
   bool isTpetra = false;
   RCP<const Epetra_CrsMatrix> eCrsOp;
   RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOp;
 
   try {
      // get Epetra or Tpetra Operator
      RCP<const Thyra::EpetraLinearOp > eOp = rcp_dynamic_cast<const Thyra::EpetraLinearOp >(op);
      RCP<const Thyra::TpetraLinearOp<ST,LO,GO,NT> > tOp = rcp_dynamic_cast<const Thyra::TpetraLinearOp<ST,LO,GO,NT> >(op);
 
      // cast it to a CrsMatrix
      RCP<Teuchos::FancyOStream> out = Teuchos::VerboseObjectBase::getDefaultOStream();
      if (!eOp.is_null()){
        eCrsOp = rcp_dynamic_cast<const Epetra_CrsMatrix>(eOp->epetra_op(),true);
      }   
      else if (!tOp.is_null()){
        tCrsOp = rcp_dynamic_cast<const Tpetra::CrsMatrix<ST,LO,GO,NT> >(tOp->getConstTpetraOperator(),true);
        isTpetra = true;
      }
      else
        throw std::logic_error("Neither Epetra nor Tpetra");
   }
   catch (std::exception & e) {
      RCP<Teuchos::FancyOStream> out = Teuchos::VerboseObjectBase::getDefaultOStream();
  
      RCP<const Thyra::EpetraLinearOp > eOp = rcp_dynamic_cast<const Thyra::EpetraLinearOp >(op);
      RCP<const Thyra::TpetraLinearOp<ST,LO,GO,NT> > tOp = rcp_dynamic_cast<const Thyra::TpetraLinearOp<ST,LO,GO,NT> >(op);
      *out << eOp;
      *out << tOp;
 
      *out << "Teko: getDiagonal requires an Epetra_CrsMatrix or a Tpetra::CrsMatrix\n";
      *out << "    Could not extract an Epetra_Operator or a Tpetra_Operator from a \"" << op->description() << std::endl;
      *out << "           OR\n";
      *out << "    Could not cast an Epetra_Operator to a Epetra_CrsMatrix or a Tpetra_Operator to a Tpetra::CrsMatrix\n";
      *out << std::endl;
      *out << "*** THROWN EXCEPTION ***\n";
      *out << e.what() << std::endl;
      *out << "************************\n";
      
      throw e;
   }
 
   if(!isTpetra){
     // extract diagonal
     const RCP<Epetra_Vector> diag = rcp(new Epetra_Vector(eCrsOp->RowMap()));
     TEUCHOS_TEST_FOR_EXCEPT(eCrsOp->ExtractDiagonalCopy(*diag));
 
     return Thyra::create_Vector(diag,Thyra::create_VectorSpace(Teuchos::rcpFromRef(eCrsOp->RowMap())));
   }
   else {
     // extract diagonal
     const RCP<Tpetra::Vector<ST,LO,GO,NT> > diag = Tpetra::createVector<ST,LO,GO,NT>(tCrsOp->getRowMap());
     tCrsOp->getLocalDiagCopy(*diag);
 
     // build Thyra diagonal operator
     return Thyra::createVector<ST,LO,GO,NT>(diag,Thyra::createVectorSpace<ST,LO,GO,NT>(tCrsOp->getRowMap()));
 
   }
}
 
const MultiVector getDiagonal(const Teko::LinearOp & A,const DiagonalType & dt)
{
   LinearOp diagOp = Teko::getDiagonalOp(A,dt);
 
   Teuchos::RCP<const Thyra::MultiVectorBase<double> > v = 
         Teuchos::rcp_dynamic_cast<const Thyra::DiagonalLinearOpBase<double> >(diagOp)->getDiag(); 
   return Teuchos::rcp_const_cast<Thyra::MultiVectorBase<double> >(v);
}
 
const ModifiableLinearOp getInvDiagonalOp(const LinearOp & op)
{
   // if this is a diagonal linear op already, just take the reciprocal
   auto diagonal_op = rcp_dynamic_cast<const Thyra::DiagonalLinearOpBase<double>>(op);
   if(diagonal_op != Teuchos::null){
     auto diag = diagonal_op->getDiag();
     auto inv_diag = diag->clone_v();
     Thyra::reciprocal(*diag,inv_diag.ptr());
     return rcp(new Thyra::DefaultDiagonalLinearOp<double>(inv_diag));
   }
 
   // if this is a blocked operator, extract diagonals block by block
   RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_op = rcp_dynamic_cast<const Thyra::PhysicallyBlockedLinearOpBase<double> >(op);
   if(blocked_op != Teuchos::null){
     int numRows = blocked_op->productRange()->numBlocks();
     TEUCHOS_ASSERT(blocked_op->productDomain()->numBlocks() == numRows);
     RCP<Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_diag = Thyra::defaultBlockedLinearOp<double>();
     blocked_diag->beginBlockFill(numRows,numRows);
     for(int r = 0; r < numRows; ++r){
       for(int c = 0; c < numRows; ++c){
         if(r==c)
           blocked_diag->setNonconstBlock(r,c,getInvDiagonalOp(blocked_op->getBlock(r,c)));
         else
           blocked_diag->setBlock(r,c,Thyra::zero<double>(blocked_op->getBlock(r,c)->range(),blocked_op->getBlock(r,c)->domain()));
       }
     }
     blocked_diag->endBlockFill();
     return blocked_diag;
   }
 
   if (Teko::TpetraHelpers::isTpetraLinearOp(op)){
     ST scalar = 0.0;
     bool transp = false;
     RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOp = Teko::TpetraHelpers::getTpetraCrsMatrix(op, &scalar, &transp);
 
     // extract diagonal
     const RCP<Tpetra::Vector<ST,LO,GO,NT> > diag = Tpetra::createVector<ST,LO,GO,NT>(tCrsOp->getRowMap());
     diag->scale(scalar);
     tCrsOp->getLocalDiagCopy(*diag);
     diag->reciprocal(*diag);
 
     // build Thyra diagonal operator
     return Teko::TpetraHelpers::thyraDiagOp(diag,*tCrsOp->getRowMap(),"inv(diag( " + op->getObjectLabel() + " ))");
 
   }
   else {
     RCP<const Thyra::EpetraLinearOp > eOp = rcp_dynamic_cast<const Thyra::EpetraLinearOp >(op,true); 
     RCP<const Epetra_CrsMatrix> eCrsOp = rcp_dynamic_cast<const Epetra_CrsMatrix>(eOp->epetra_op(),true);
 
     // extract diagonal
     const RCP<Epetra_Vector> diag = rcp(new Epetra_Vector(eCrsOp->RowMap()));
     TEUCHOS_TEST_FOR_EXCEPT(eCrsOp->ExtractDiagonalCopy(*diag));
     diag->Reciprocal(*diag);
 
     // build Thyra diagonal operator
     return Teko::Epetra::thyraDiagOp(diag,eCrsOp->RowMap(),"inv(diag( " + op->getObjectLabel() + " ))");
   }
}
 
const LinearOp explicitMultiply(const LinearOp & opl,const LinearOp & opm,const LinearOp & opr)
{
   // if this is a blocked operator, multiply block by block
   // it is possible that not every factor in the product is blocked and these situations are handled separately
 
   bool isBlockedL = isPhysicallyBlockedLinearOp(opl);
   bool isBlockedM = isPhysicallyBlockedLinearOp(opm);
   bool isBlockedR = isPhysicallyBlockedLinearOp(opr);
 
   // all factors blocked
   if((isBlockedL && isBlockedM && isBlockedR)){
 
     double scalarl = 0.0;
     bool transpl = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opl = getPhysicallyBlockedLinearOp(opl,&scalarl,&transpl);
     double scalarm = 0.0;
     bool transpm = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opm = getPhysicallyBlockedLinearOp(opm,&scalarm,&transpm);
     double scalarr = 0.0;
     bool transpr = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opr = getPhysicallyBlockedLinearOp(opr,&scalarr,&transpr);
     double scalar = scalarl*scalarm*scalarr;
 
     int numRows = blocked_opl->productRange()->numBlocks();
     int numCols = blocked_opr->productDomain()->numBlocks();
     int numMiddle = blocked_opm->productRange()->numBlocks();
 
     // Assume that the middle block is block nxn and that it's diagonal. Otherwise use the two argument explicitMultiply twice
     TEUCHOS_ASSERT(blocked_opm->productDomain()->numBlocks() == numMiddle);
     TEUCHOS_ASSERT(blocked_opl->productDomain()->numBlocks() == numMiddle);
     TEUCHOS_ASSERT(blocked_opr->productRange()->numBlocks() == numMiddle);
 
     RCP<Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_product = Thyra::defaultBlockedLinearOp<double>();
     blocked_product->beginBlockFill(numRows,numCols);
     for(int r = 0; r < numRows; ++r){
       for(int c = 0; c < numCols; ++c){
         LinearOp product_rc = explicitMultiply(blocked_opl->getBlock(r,0),blocked_opm->getBlock(0,0),blocked_opr->getBlock(0,c));
         for(int m = 1; m < numMiddle; ++m){
           LinearOp product_m = explicitMultiply(blocked_opl->getBlock(r,m),blocked_opm->getBlock(m,m),blocked_opr->getBlock(m,c));
           product_rc = explicitAdd(product_rc,product_m);
         }
         blocked_product->setBlock(r,c,product_rc);
       }
     }
     blocked_product->endBlockFill();
     return Thyra::scale<double>(scalar,blocked_product.getConst());
   }
 
   // left and right factors blocked
   if(isBlockedL && !isBlockedM && isBlockedR){
     double scalarl = 0.0;
     bool transpl = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opl = getPhysicallyBlockedLinearOp(opl,&scalarl,&transpl);
     double scalarr = 0.0;
     bool transpr = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opr = getPhysicallyBlockedLinearOp(opr,&scalarr,&transpr);
     double scalar = scalarl*scalarr;
 
     int numRows = blocked_opl->productRange()->numBlocks();
     int numCols = blocked_opr->productDomain()->numBlocks();
     int numMiddle = 1;
 
     // Assume that the middle block is 1x1 diagonal. Left must be rx1, right 1xc
     TEUCHOS_ASSERT(blocked_opl->productDomain()->numBlocks() == numMiddle);
     TEUCHOS_ASSERT(blocked_opr->productRange()->numBlocks() == numMiddle);
 
     RCP<Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_product = Thyra::defaultBlockedLinearOp<double>();
     blocked_product->beginBlockFill(numRows,numCols);
     for(int r = 0; r < numRows; ++r){
       for(int c = 0; c < numCols; ++c){
         LinearOp product_rc = explicitMultiply(blocked_opl->getBlock(r,0),opm,blocked_opr->getBlock(0,c));
         blocked_product->setBlock(r,c,product_rc);
       }
     }
     blocked_product->endBlockFill();
     return Thyra::scale<double>(scalar,blocked_product.getConst());
   }
 
   // only right factor blocked
   if(!isBlockedL && !isBlockedM && isBlockedR){
     double scalarr = 0.0;
     bool transpr = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opr = getPhysicallyBlockedLinearOp(opr,&scalarr,&transpr);
     double scalar = scalarr;
 
     int numRows = 1;
     int numCols = blocked_opr->productDomain()->numBlocks();
     int numMiddle = 1;
 
     // Assume that the middle block is 1x1 diagonal, left is 1x1. Right must be 1xc
     TEUCHOS_ASSERT(blocked_opr->productRange()->numBlocks() == numMiddle);
 
     RCP<Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_product = Thyra::defaultBlockedLinearOp<double>();
     blocked_product->beginBlockFill(numRows,numCols);
     for(int c = 0; c < numCols; ++c){
       LinearOp product_c = explicitMultiply(opl,opm,blocked_opr->getBlock(0,c));
       blocked_product->setBlock(0,c,product_c);
     }
     blocked_product->endBlockFill();
     return Thyra::scale<double>(scalar,blocked_product.getConst());
   }
 
   //TODO: three more cases (only non-blocked - blocked - non-blocked not possible)
 
   bool isTpetral = Teko::TpetraHelpers::isTpetraLinearOp(opl);
   bool isTpetram = Teko::TpetraHelpers::isTpetraLinearOp(opm);
   bool isTpetrar = Teko::TpetraHelpers::isTpetraLinearOp(opr);
 
   if(isTpetral && isTpetram && isTpetrar){ // Both operators are Tpetra matrices so explicitly multiply them
 
      // Get left and right Tpetra crs operators
      ST scalarl = 0.0;
      bool transpl = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpl = Teko::TpetraHelpers::getTpetraCrsMatrix(opl, &scalarl, &transpl);
      ST scalarm = 0.0;
      bool transpm = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpm = Teko::TpetraHelpers::getTpetraCrsMatrix(opl, &scalarm, &transpm);
      ST scalarr = 0.0;
      bool transpr = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpr = Teko::TpetraHelpers::getTpetraCrsMatrix(opr, &scalarr, &transpr);
 
      // Build output operator
      RCP<Thyra::LinearOpBase<ST> > explicitOp = rcp(new Thyra::TpetraLinearOp<ST,LO,GO,NT>());
      RCP<Thyra::TpetraLinearOp<ST,LO,GO,NT> > tExplicitOp = rcp_dynamic_cast<Thyra::TpetraLinearOp<ST,LO,GO,NT> >(explicitOp);
 
      // Do explicit matrix-matrix multiply
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOplm = Tpetra::createCrsMatrix<ST,LO,GO,NT>(tCrsOpl->getRowMap());
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > explicitCrsOp = Tpetra::createCrsMatrix<ST,LO,GO,NT>(tCrsOpl->getRowMap());
      Tpetra::MatrixMatrix::Multiply<ST,LO,GO,NT>(*tCrsOpl,transpl,*tCrsOpm,transpm,*tCrsOplm); 
      Tpetra::MatrixMatrix::Multiply<ST,LO,GO,NT>(*tCrsOplm,false,*tCrsOpr,transpr,*explicitCrsOp); 
      explicitCrsOp->resumeFill();
      explicitCrsOp->scale(scalarl*scalarm*scalarr);
      explicitCrsOp->fillComplete(tCrsOpr->getDomainMap(),tCrsOpl->getRangeMap());
      tExplicitOp->initialize(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getDomainMap()),explicitCrsOp);  
      return tExplicitOp;
 
   } else if (isTpetral && !isTpetram && isTpetrar){ // Assume that the middle operator is diagonal
 
      // Get left and right Tpetra crs operators
      ST scalarl = 0.0;
      bool transpl = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpl = Teko::TpetraHelpers::getTpetraCrsMatrix(opl, &scalarl, &transpl);
      ST scalarr = 0.0;
      bool transpr = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpr = Teko::TpetraHelpers::getTpetraCrsMatrix(opr, &scalarr, &transpr);
      
      RCP<const Tpetra::Vector<ST,LO,GO,NT> > diagPtr;
 
      // Cast middle operator as DiagonalLinearOp and extract diagonal as Vector
      RCP<const Thyra::DiagonalLinearOpBase<ST> > dOpm = rcp_dynamic_cast<const Thyra::DiagonalLinearOpBase<ST> >(opm);
      if(dOpm != Teuchos::null){
        RCP<const Thyra::TpetraVector<ST,LO,GO,NT> > tPtr = rcp_dynamic_cast<const Thyra::TpetraVector<ST,LO,GO,NT> >(dOpm->getDiag(),true);
        diagPtr = rcp_dynamic_cast<const Tpetra::Vector<ST,LO,GO,NT> >(tPtr->getConstTpetraVector(),true);
      }
      // If it's not diagonal, maybe it's zero
      else if(rcp_dynamic_cast<const Thyra::ZeroLinearOpBase<ST> >(opm) != Teuchos::null){
        diagPtr = rcp(new Tpetra::Vector<ST,LO,GO,NT>(tCrsOpl->getDomainMap()));
      }
      else
        TEUCHOS_ASSERT(false);
      
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOplm = Tpetra::importAndFillCompleteCrsMatrix<Tpetra::CrsMatrix<ST,LO,GO,NT> >(tCrsOpl, Tpetra::Import<LO,GO,NT>(tCrsOpl->getRowMap(),tCrsOpl->getRowMap()));
 
      // Do the diagonal scaling
      tCrsOplm->rightScale(*diagPtr);
      
      // Build output operator
      RCP<Thyra::LinearOpBase<ST> > explicitOp = rcp(new Thyra::TpetraLinearOp<ST,LO,GO,NT>());
      RCP<Thyra::TpetraLinearOp<ST,LO,GO,NT> > tExplicitOp = rcp_dynamic_cast<Thyra::TpetraLinearOp<ST,LO,GO,NT> >(explicitOp);
 
      // Do explicit matrix-matrix multiply
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > explicitCrsOp = Tpetra::createCrsMatrix<ST,LO,GO,NT>(tCrsOpl->getRowMap());
      Tpetra::MatrixMatrix::Multiply<ST,LO,GO,NT>(*tCrsOplm,false,*tCrsOpr,transpr,*explicitCrsOp); 
      explicitCrsOp->resumeFill();
      explicitCrsOp->scale(scalarl*scalarr);
      explicitCrsOp->fillComplete(tCrsOpr->getDomainMap(),tCrsOpl->getRangeMap());
      tExplicitOp->initialize(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getDomainMap()),explicitCrsOp);  
      return tExplicitOp;
 
   } else { // Assume Epetra and we can use transformers
 
      // build implicit multiply
      const LinearOp implicitOp = Thyra::multiply(opl,opm,opr);
 
      // build transformer
      const RCP<Thyra::LinearOpTransformerBase<double> > prodTrans =
          Thyra::epetraExtDiagScaledMatProdTransformer();
 
      // build operator and multiply
      const RCP<Thyra::LinearOpBase<double> > explicitOp = prodTrans->createOutputOp();
      prodTrans->transform(*implicitOp,explicitOp.ptr());
      explicitOp->setObjectLabel("explicit( " + opl->getObjectLabel() +
                                        " * " + opm->getObjectLabel() +
                                        " * " + opr->getObjectLabel() + " )");
 
      return explicitOp;
 
   }
}
 
const ModifiableLinearOp explicitMultiply(const LinearOp & opl,const LinearOp & opm,const LinearOp & opr,
                                          const ModifiableLinearOp & destOp)
{
   bool isTpetral = Teko::TpetraHelpers::isTpetraLinearOp(opl);
   bool isTpetram = Teko::TpetraHelpers::isTpetraLinearOp(opm);
   bool isTpetrar = Teko::TpetraHelpers::isTpetraLinearOp(opr);
 
   if(isTpetral && isTpetram && isTpetrar){ // Both operators are Tpetra matrices so explicitly multiply them
 
      // Get left and right Tpetra crs operators
      ST scalarl = 0.0;
      bool transpl = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpl = Teko::TpetraHelpers::getTpetraCrsMatrix(opl, &scalarl, &transpl);
      ST scalarm = 0.0;
      bool transpm = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpm = Teko::TpetraHelpers::getTpetraCrsMatrix(opm, &scalarm, &transpm);
      ST scalarr = 0.0;
      bool transpr = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpr = Teko::TpetraHelpers::getTpetraCrsMatrix(opr, &scalarr, &transpr);
 
      // Build output operator
      auto tExplicitOp = rcp_dynamic_cast<Thyra::TpetraLinearOp<ST,LO,GO,NT> >(destOp);
      if(tExplicitOp.is_null())
        tExplicitOp = rcp(new Thyra::TpetraLinearOp<ST,LO,GO,NT>());
 
      // Do explicit matrix-matrix multiply
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOplm = Tpetra::createCrsMatrix<ST,LO,GO,NT>(tCrsOpl->getRowMap());
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > explicitCrsOp = Tpetra::createCrsMatrix<ST,LO,GO,NT>(tCrsOpl->getRowMap());
      Tpetra::MatrixMatrix::Multiply<ST,LO,GO,NT>(*tCrsOpl,transpl,*tCrsOpm,transpm,*tCrsOplm); 
      Tpetra::MatrixMatrix::Multiply<ST,LO,GO,NT>(*tCrsOplm,false,*tCrsOpr,transpr,*explicitCrsOp); 
      explicitCrsOp->resumeFill();
      explicitCrsOp->scale(scalarl*scalarm*scalarr);
      explicitCrsOp->fillComplete(tCrsOpr->getDomainMap(),tCrsOpl->getRangeMap());
      tExplicitOp->initialize(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getDomainMap()),explicitCrsOp);  
      return tExplicitOp;
 
   } else if (isTpetral && !isTpetram && isTpetrar){ // Assume that the middle operator is diagonal
 
      // Get left and right Tpetra crs operators
      ST scalarl = 0.0;
      bool transpl = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpl = Teko::TpetraHelpers::getTpetraCrsMatrix(opl, &scalarl, &transpl);
      ST scalarr = 0.0;
      bool transpr = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpr = Teko::TpetraHelpers::getTpetraCrsMatrix(opr, &scalarr, &transpr);
      
      // Cast middle operator as DiagonalLinearOp and extract diagonal as Vector
      RCP<const Thyra::DiagonalLinearOpBase<ST> > dOpm = rcp_dynamic_cast<const Thyra::DiagonalLinearOpBase<ST> >(opm,true);
      RCP<const Thyra::TpetraVector<ST,LO,GO,NT> > tPtr = rcp_dynamic_cast<const Thyra::TpetraVector<ST,LO,GO,NT> >(dOpm->getDiag(),true);
      RCP<const Tpetra::Vector<ST,LO,GO,NT> > diagPtr = rcp_dynamic_cast<const Tpetra::Vector<ST,LO,GO,NT> >(tPtr->getConstTpetraVector(),true);
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOplm = Tpetra::importAndFillCompleteCrsMatrix<Tpetra::CrsMatrix<ST,LO,GO,NT> >(tCrsOpl, Tpetra::Import<LO,GO,NT>(tCrsOpl->getRowMap(),tCrsOpl->getRowMap()));
 
      // Do the diagonal scaling
      tCrsOplm->rightScale(*diagPtr);
      
      // Build output operator
      RCP<Thyra::LinearOpBase<ST> > explicitOp = rcp(new Thyra::TpetraLinearOp<ST,LO,GO,NT>());
      RCP<Thyra::TpetraLinearOp<ST,LO,GO,NT> > tExplicitOp = rcp_dynamic_cast<Thyra::TpetraLinearOp<ST,LO,GO,NT> >(explicitOp);
 
      // Do explicit matrix-matrix multiply
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > explicitCrsOp = Tpetra::createCrsMatrix<ST,LO,GO,NT>(tCrsOpl->getRowMap());
      Tpetra::MatrixMatrix::Multiply<ST,LO,GO,NT>(*tCrsOplm,false,*tCrsOpr,transpr,*explicitCrsOp); 
      explicitCrsOp->resumeFill();
      explicitCrsOp->scale(scalarl*scalarr);
      explicitCrsOp->fillComplete(tCrsOpr->getDomainMap(),tCrsOpl->getRangeMap());
      tExplicitOp->initialize(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getDomainMap()),explicitCrsOp);  
      return tExplicitOp;
 
   } else { // Assume Epetra and we can use transformers
 
      // build implicit multiply
      const LinearOp implicitOp = Thyra::multiply(opl,opm,opr);
 
      // build transformer
      const RCP<Thyra::LinearOpTransformerBase<double> > prodTrans =
          Thyra::epetraExtDiagScaledMatProdTransformer();
 
      // build operator destination operator
      ModifiableLinearOp explicitOp; 
 
      // if neccessary build a operator to put the explicit multiply into
      if(destOp==Teuchos::null)
         explicitOp = prodTrans->createOutputOp();
      else
         explicitOp = destOp;
 
      // perform multiplication
      prodTrans->transform(*implicitOp,explicitOp.ptr());
 
      // label it
      explicitOp->setObjectLabel("explicit( " + opl->getObjectLabel() +
                                        " * " + opm->getObjectLabel() +
                                        " * " + opr->getObjectLabel() + " )");
 
      return explicitOp;
 
   }
}
 
const LinearOp explicitMultiply(const LinearOp & opl,const LinearOp & opr)
{
   // if this is a blocked operator, multiply block by block
   // it is possible that not every factor in the product is blocked and these situations are handled separately
 
   bool isBlockedL = isPhysicallyBlockedLinearOp(opl);
   bool isBlockedR = isPhysicallyBlockedLinearOp(opr);
 
   // both factors blocked
   if((isBlockedL && isBlockedR)){
     double scalarl = 0.0;
     bool transpl = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opl = getPhysicallyBlockedLinearOp(opl,&scalarl,&transpl);
     double scalarr = 0.0;
     bool transpr = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opr = getPhysicallyBlockedLinearOp(opr,&scalarr,&transpr);
     double scalar = scalarl*scalarr;
 
     int numRows = blocked_opl->productRange()->numBlocks();
     int numCols = blocked_opr->productDomain()->numBlocks();
     int numMiddle = blocked_opl->productDomain()->numBlocks();
 
     TEUCHOS_ASSERT(blocked_opr->productRange()->numBlocks() == numMiddle);
 
     RCP<Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_product = Thyra::defaultBlockedLinearOp<double>();
     blocked_product->beginBlockFill(numRows,numCols);
     for(int r = 0; r < numRows; ++r){
       for(int c = 0; c < numCols; ++c){
         LinearOp product_rc = explicitMultiply(blocked_opl->getBlock(r,0),blocked_opr->getBlock(0,c));
         for(int m = 1; m < numMiddle; ++m){
           LinearOp product_m = explicitMultiply(blocked_opl->getBlock(r,m),blocked_opr->getBlock(m,c));
           product_rc = explicitAdd(product_rc,product_m);
         }
         blocked_product->setBlock(r,c,Thyra::scale(scalar,product_rc));
       }
     }
     blocked_product->endBlockFill();
     return blocked_product;
   }
 
   // only left factor blocked
   if((isBlockedL && !isBlockedR)){
     double scalarl = 0.0;
     bool transpl = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opl = getPhysicallyBlockedLinearOp(opl,&scalarl,&transpl);
     double scalar = scalarl;
 
     int numRows = blocked_opl->productRange()->numBlocks();
     int numCols = 1;
     int numMiddle = 1;
 
     TEUCHOS_ASSERT(blocked_opl->productDomain()->numBlocks() == numMiddle);
 
     RCP<Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_product = Thyra::defaultBlockedLinearOp<double>();
     blocked_product->beginBlockFill(numRows,numCols);
     for(int r = 0; r < numRows; ++r){
       LinearOp product_r = explicitMultiply(blocked_opl->getBlock(r,0),opr);
       blocked_product->setBlock(r,0,Thyra::scale(scalar,product_r));
     }
     blocked_product->endBlockFill();
     return blocked_product;
   }
 
   // only right factor blocked
   if((!isBlockedL && isBlockedR)){
     double scalarr = 0.0;
     bool transpr = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opr = getPhysicallyBlockedLinearOp(opr,&scalarr,&transpr);
     double scalar = scalarr;
 
     int numRows = 1;
     int numCols = blocked_opr->productDomain()->numBlocks();
     int numMiddle = 1;
 
     TEUCHOS_ASSERT(blocked_opr->productRange()->numBlocks() == numMiddle);
 
     RCP<Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_product = Thyra::defaultBlockedLinearOp<double>();
     blocked_product->beginBlockFill(numRows,numCols);
     for(int c = 0; c < numCols; ++c){
       LinearOp product_c = explicitMultiply(opl,blocked_opr->getBlock(0,c));
       blocked_product->setBlock(0,c,Thyra::scale(scalar,product_c));
     }
     blocked_product->endBlockFill();
     return blocked_product;
   }
 
   bool isTpetral = Teko::TpetraHelpers::isTpetraLinearOp(opl);
   bool isTpetrar = Teko::TpetraHelpers::isTpetraLinearOp(opr);
 
   if(isTpetral && isTpetrar){ // Both operators are Tpetra matrices so explicitly multiply them
      // Get left and right Tpetra crs operators
      ST scalarl = 0.0;
      bool transpl = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpl = Teko::TpetraHelpers::getTpetraCrsMatrix(opl, &scalarl, &transpl);
      ST scalarr = 0.0;
      bool transpr = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpr = Teko::TpetraHelpers::getTpetraCrsMatrix(opr, &scalarr, &transpr);
 
      // Build output operator
      RCP<Thyra::LinearOpBase<ST> > explicitOp = rcp(new Thyra::TpetraLinearOp<ST,LO,GO,NT>());
      RCP<Thyra::TpetraLinearOp<ST,LO,GO,NT> > tExplicitOp = rcp_dynamic_cast<Thyra::TpetraLinearOp<ST,LO,GO,NT> >(explicitOp);
 
      // Do explicit matrix-matrix multiply
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > explicitCrsOp = Tpetra::createCrsMatrix<ST,LO,GO,NT>(tCrsOpl->getRowMap());
      Tpetra::MatrixMatrix::Multiply<ST,LO,GO,NT>(*tCrsOpl,transpl,*tCrsOpr,transpr,*explicitCrsOp);
      explicitCrsOp->resumeFill();
      explicitCrsOp->scale(scalarl*scalarr);
      explicitCrsOp->fillComplete(tCrsOpr->getDomainMap(),tCrsOpl->getRangeMap());
      tExplicitOp->initialize(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getDomainMap()),explicitCrsOp);  
      return tExplicitOp;
 
   } else if (isTpetral && !isTpetrar){ // Assume that the right operator is diagonal
 
      // Get left Tpetra crs operator
      ST scalarl = 0.0;
      bool transpl = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpl = Teko::TpetraHelpers::getTpetraCrsMatrix(opl, &scalarl, &transpl);
      
      // Cast right operator as DiagonalLinearOp and extract diagonal as Vector
      RCP<const Thyra::DiagonalLinearOpBase<ST> > dOpr = rcp_dynamic_cast<const Thyra::DiagonalLinearOpBase<ST> >(opr,true);
      RCP<const Thyra::TpetraVector<ST,LO,GO,NT> > tPtr = rcp_dynamic_cast<const Thyra::TpetraVector<ST,LO,GO,NT> >(dOpr->getDiag(),true);
      RCP<const Tpetra::Vector<ST,LO,GO,NT> > diagPtr = rcp_dynamic_cast<const Tpetra::Vector<ST,LO,GO,NT> >(tPtr->getConstTpetraVector(),true);
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > explicitCrsOp = Tpetra::importAndFillCompleteCrsMatrix<Tpetra::CrsMatrix<ST,LO,GO,NT> >(tCrsOpl, Tpetra::Import<LO,GO,NT>(tCrsOpl->getRowMap(),tCrsOpl->getRowMap()));
      
      explicitCrsOp->rightScale(*diagPtr);
      explicitCrsOp->resumeFill();
      explicitCrsOp->scale(scalarl);
      explicitCrsOp->fillComplete(tCrsOpl->getDomainMap(),tCrsOpl->getRangeMap());
      
      return Thyra::constTpetraLinearOp<ST,LO,GO,NT>(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getDomainMap()),explicitCrsOp);
 
   } else if (!isTpetral && isTpetrar){ // Assume that the left operator is diagonal
 
      // Get right Tpetra crs operator
      ST scalarr = 0.0;
      bool transpr = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpr = Teko::TpetraHelpers::getTpetraCrsMatrix(opr, &scalarr, &transpr);
      
      RCP<const Tpetra::Vector<ST,LO,GO,NT> > diagPtr;
 
      // Cast left operator as DiagonalLinearOp and extract diagonal as Vector
      RCP<const Thyra::DiagonalLinearOpBase<ST> > dOpl = rcp_dynamic_cast<const Thyra::DiagonalLinearOpBase<ST> >(opl);
      if(dOpl != Teuchos::null){
        RCP<const Thyra::TpetraVector<ST,LO,GO,NT> > tPtr = rcp_dynamic_cast<const Thyra::TpetraVector<ST,LO,GO,NT> >(dOpl->getDiag(),true);
        diagPtr = rcp_dynamic_cast<const Tpetra::Vector<ST,LO,GO,NT> >(tPtr->getConstTpetraVector(),true);
      }
      // If it's not diagonal, maybe it's zero
      else if(rcp_dynamic_cast<const Thyra::ZeroLinearOpBase<ST> >(opl) != Teuchos::null){
        diagPtr = rcp(new Tpetra::Vector<ST,LO,GO,NT>(tCrsOpr->getRangeMap()));
      }
      else
        TEUCHOS_ASSERT(false);
      
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > explicitCrsOp = Tpetra::importAndFillCompleteCrsMatrix<Tpetra::CrsMatrix<ST,LO,GO,NT> >(tCrsOpr, Tpetra::Import<LO,GO,NT>(tCrsOpr->getRowMap(),tCrsOpr->getRowMap()));
      
      explicitCrsOp->leftScale(*diagPtr);
      explicitCrsOp->resumeFill();
      explicitCrsOp->scale(scalarr);
      explicitCrsOp->fillComplete(tCrsOpr->getDomainMap(),tCrsOpr->getRangeMap());
      
      return Thyra::constTpetraLinearOp<ST,LO,GO,NT>(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getDomainMap()),explicitCrsOp);
 
   } else { // Assume Epetra and we can use transformers
 
     // build implicit multiply
     const LinearOp implicitOp = Thyra::multiply(opl,opr);
 
     // build a scaling transformer
     RCP<Thyra::LinearOpTransformerBase<double> > prodTrans  
           = Thyra::epetraExtDiagScalingTransformer();
 
     // check to see if a scaling transformer works: if not use the 
     // DiagScaledMatrixProduct transformer
     if(not prodTrans->isCompatible(*implicitOp))
         prodTrans = Thyra::epetraExtDiagScaledMatProdTransformer();
 
     // build operator and multiply
     const RCP<Thyra::LinearOpBase<double> > explicitOp = prodTrans->createOutputOp();
     prodTrans->transform(*implicitOp,explicitOp.ptr());
     explicitOp->setObjectLabel("explicit( " + opl->getObjectLabel() +
                                       " * " + opr->getObjectLabel() + " )");
 
     return explicitOp;
   }
}
 
const ModifiableLinearOp explicitMultiply(const LinearOp & opl,const LinearOp & opr,
                                          const ModifiableLinearOp & destOp)
{
   // if this is a blocked operator, multiply block by block
   // it is possible that not every factor in the product is blocked and these situations are handled separately
 
   bool isBlockedL = isPhysicallyBlockedLinearOp(opl);
   bool isBlockedR = isPhysicallyBlockedLinearOp(opr);
 
   // both factors blocked
   if((isBlockedL && isBlockedR)){
     double scalarl = 0.0;
     bool transpl = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opl = getPhysicallyBlockedLinearOp(opl,&scalarl,&transpl);
     double scalarr = 0.0;
     bool transpr = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opr = getPhysicallyBlockedLinearOp(opr,&scalarr,&transpr);
     double scalar = scalarl*scalarr;
 
     int numRows = blocked_opl->productRange()->numBlocks();
     int numCols = blocked_opr->productDomain()->numBlocks();
     int numMiddle = blocked_opl->productDomain()->numBlocks();
 
     TEUCHOS_ASSERT(blocked_opr->productRange()->numBlocks() == numMiddle);
 
     RCP<Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_product = Thyra::defaultBlockedLinearOp<double>();
     blocked_product->beginBlockFill(numRows,numCols);
     for(int r = 0; r < numRows; ++r){
       for(int c = 0; c < numCols; ++c){
 
         LinearOp product_rc = explicitMultiply(blocked_opl->getBlock(r,0),blocked_opr->getBlock(0,c));
         for(int m = 1; m < numMiddle; ++m){
           LinearOp product_m = explicitMultiply(blocked_opl->getBlock(r,m),blocked_opr->getBlock(m,c));
           product_rc = explicitAdd(product_rc,product_m);
         }
         blocked_product->setBlock(r,c,Thyra::scale(scalar,product_rc));
       }
     }
     blocked_product->endBlockFill();
     return blocked_product;
   }
 
   // only left factor blocked
   if((isBlockedL && !isBlockedR)){
     double scalarl = 0.0;
     bool transpl = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opl = getPhysicallyBlockedLinearOp(opl,&scalarl,&transpl);
     double scalar = scalarl;
 
     int numRows = blocked_opl->productRange()->numBlocks();
     int numCols = 1;
     int numMiddle = 1;
 
     TEUCHOS_ASSERT(blocked_opl->productDomain()->numBlocks() == numMiddle);
 
     RCP<Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_product = Thyra::defaultBlockedLinearOp<double>();
     blocked_product->beginBlockFill(numRows,numCols);
     for(int r = 0; r < numRows; ++r){
       LinearOp product_r = explicitMultiply(blocked_opl->getBlock(r,0),opr);
       blocked_product->setBlock(r,0,Thyra::scale(scalar,product_r));
     }
     blocked_product->endBlockFill();
     return blocked_product;
   }
 
   // only right factor blocked
   if((!isBlockedL && isBlockedR)){
     double scalarr = 0.0;
     bool transpr = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opr = getPhysicallyBlockedLinearOp(opr,&scalarr,&transpr);
     double scalar = scalarr;
 
     int numRows = 1;
     int numCols = blocked_opr->productDomain()->numBlocks();
     int numMiddle = 1;
 
     TEUCHOS_ASSERT(blocked_opr->productRange()->numBlocks() == numMiddle);
 
     RCP<Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_product = Thyra::defaultBlockedLinearOp<double>();
     blocked_product->beginBlockFill(numRows,numCols);
     for(int c = 0; c < numCols; ++c){
       LinearOp product_c = explicitMultiply(opl,blocked_opr->getBlock(0,c));
       blocked_product->setBlock(0,c,Thyra::scale(scalar,product_c));
     }
     blocked_product->endBlockFill();
     return blocked_product;
   }
 
   bool isTpetral = Teko::TpetraHelpers::isTpetraLinearOp(opl);
   bool isTpetrar = Teko::TpetraHelpers::isTpetraLinearOp(opr);
 
   if(isTpetral && isTpetrar){ // Both operators are Tpetra matrices so use the explicit Tpetra matrix-matrix multiply
 
      // Get left and right Tpetra crs operators
      ST scalarl = 0.0;
      bool transpl = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpl = Teko::TpetraHelpers::getTpetraCrsMatrix(opl, &scalarl, &transpl);
      ST scalarr = 0.0;
      bool transpr = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpr = Teko::TpetraHelpers::getTpetraCrsMatrix(opr, &scalarr, &transpr);
 
      // Build output operator
      RCP<Thyra::LinearOpBase<ST> > explicitOp;
      if(destOp!=Teuchos::null)
         explicitOp = destOp;
      else
         explicitOp = rcp(new Thyra::TpetraLinearOp<ST,LO,GO,NT>());
      RCP<Thyra::TpetraLinearOp<ST,LO,GO,NT> > tExplicitOp = rcp_dynamic_cast<Thyra::TpetraLinearOp<ST,LO,GO,NT> >(explicitOp);
 
      // Do explicit matrix-matrix multiply
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > explicitCrsOp = Tpetra::createCrsMatrix<ST,LO,GO,NT>(tCrsOpl->getRowMap());
      Tpetra::MatrixMatrix::Multiply<ST,LO,GO,NT>(*tCrsOpl,transpl,*tCrsOpr,transpr,*explicitCrsOp); 
      explicitCrsOp->resumeFill();
      explicitCrsOp->scale(scalarl*scalarr);
      explicitCrsOp->fillComplete(tCrsOpr->getDomainMap(),tCrsOpl->getRangeMap());
      tExplicitOp->initialize(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getDomainMap()),explicitCrsOp);  
      return tExplicitOp;
 
   } else if (isTpetral && !isTpetrar){ // Assume that the right operator is diagonal
 
      // Get left Tpetra crs operator
      ST scalarl = 0.0;
      bool transpl = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpl = Teko::TpetraHelpers::getTpetraCrsMatrix(opl, &scalarl, &transpl);
      
      // Cast right operator as DiagonalLinearOp and extract diagonal as Vector
      RCP<const Thyra::DiagonalLinearOpBase<ST> > dOpr = rcp_dynamic_cast<const Thyra::DiagonalLinearOpBase<ST> >(opr);
      RCP<const Thyra::TpetraVector<ST,LO,GO,NT> > tPtr = rcp_dynamic_cast<const Thyra::TpetraVector<ST,LO,GO,NT> >(dOpr->getDiag(),true);
      RCP<const Tpetra::Vector<ST,LO,GO,NT> > diagPtr = rcp_dynamic_cast<const Tpetra::Vector<ST,LO,GO,NT> >(tPtr->getConstTpetraVector(),true);
 
      // Scale by the diagonal operator
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > explicitCrsOp = Tpetra::importAndFillCompleteCrsMatrix<Tpetra::CrsMatrix<ST,LO,GO,NT> >(tCrsOpl, Tpetra::Import<LO,GO,NT>(tCrsOpl->getRowMap(),tCrsOpl->getRowMap()));
      explicitCrsOp->rightScale(*diagPtr);      
      explicitCrsOp->resumeFill();
      explicitCrsOp->scale(scalarl);
      explicitCrsOp->fillComplete(tCrsOpl->getDomainMap(),tCrsOpl->getRangeMap());
      return Thyra::tpetraLinearOp<ST,LO,GO,NT>(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getDomainMap()),explicitCrsOp);
 
   } else if (!isTpetral && isTpetrar){ // Assume that the left operator is diagonal
 
      // Get right Tpetra crs operator
      ST scalarr = 0.0;
      bool transpr = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpr = Teko::TpetraHelpers::getTpetraCrsMatrix(opr, &scalarr, &transpr);
      
      // Cast leftt operator as DiagonalLinearOp and extract diagonal as Vector
      RCP<const Thyra::DiagonalLinearOpBase<ST> > dOpl = rcp_dynamic_cast<const Thyra::DiagonalLinearOpBase<ST> >(opl,true);
      RCP<const Thyra::TpetraVector<ST,LO,GO,NT> > tPtr = rcp_dynamic_cast<const Thyra::TpetraVector<ST,LO,GO,NT> >(dOpl->getDiag(),true);
      RCP<const Tpetra::Vector<ST,LO,GO,NT> > diagPtr = rcp_dynamic_cast<const Tpetra::Vector<ST,LO,GO,NT> >(tPtr->getConstTpetraVector(),true);
 
      // Scale by the diagonal operator
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > explicitCrsOp = Tpetra::importAndFillCompleteCrsMatrix<Tpetra::CrsMatrix<ST,LO,GO,NT> >(tCrsOpr, Tpetra::Import<LO,GO,NT>(tCrsOpr->getRowMap(),tCrsOpr->getRowMap()));
      explicitCrsOp->leftScale(*diagPtr);
      explicitCrsOp->resumeFill();
      explicitCrsOp->scale(scalarr);
      explicitCrsOp->fillComplete(tCrsOpr->getDomainMap(),tCrsOpr->getRangeMap());
      return Thyra::tpetraLinearOp<ST,LO,GO,NT>(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getDomainMap()),explicitCrsOp);
 
   } else { // Assume Epetra and we can use transformers
 
     // build implicit multiply
     const LinearOp implicitOp = Thyra::multiply(opl,opr);
 
      // build a scaling transformer
   
      RCP<Thyra::LinearOpTransformerBase<double> > prodTrans  
            = Thyra::epetraExtDiagScalingTransformer();
 
      // check to see if a scaling transformer works: if not use the 
      // DiagScaledMatrixProduct transformer
      if(not prodTrans->isCompatible(*implicitOp))
          prodTrans = Thyra::epetraExtDiagScaledMatProdTransformer();
 
      // build operator destination operator
      ModifiableLinearOp explicitOp; 
 
      // if neccessary build a operator to put the explicit multiply into
      if(destOp==Teuchos::null)
         explicitOp = prodTrans->createOutputOp();
      else
         explicitOp = destOp;
 
      // perform multiplication
      prodTrans->transform(*implicitOp,explicitOp.ptr());
 
      // label it
      explicitOp->setObjectLabel("explicit( " + opl->getObjectLabel() +
                                     " * " + opr->getObjectLabel() + " )");
 
      return explicitOp;
   }
}
 
const LinearOp explicitAdd(const LinearOp & opl_in,const LinearOp & opr_in)
{
   // if both blocked, add block by block
   if(isPhysicallyBlockedLinearOp(opl_in) && isPhysicallyBlockedLinearOp(opr_in)){
     double scalarl = 0.0;
     bool transpl = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opl = getPhysicallyBlockedLinearOp(opl_in, &scalarl, &transpl);
 
     double scalarr = 0.0;
     bool transpr = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opr = getPhysicallyBlockedLinearOp(opr_in, &scalarr, &transpr);
 
     int numRows = blocked_opl->productRange()->numBlocks();
     int numCols = blocked_opl->productDomain()->numBlocks();
     TEUCHOS_ASSERT(blocked_opr->productRange()->numBlocks() == numRows);
     TEUCHOS_ASSERT(blocked_opr->productDomain()->numBlocks() == numCols);
 
     RCP<Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_sum = Thyra::defaultBlockedLinearOp<double>();
     blocked_sum->beginBlockFill(numRows,numCols);
     for(int r = 0; r < numRows; ++r)
       for(int c = 0; c < numCols; ++c)
         blocked_sum->setBlock(r,c,explicitAdd(Thyra::scale(scalarl,blocked_opl->getBlock(r,c)),Thyra::scale(scalarr,blocked_opr->getBlock(r,c))));
     blocked_sum->endBlockFill();
     return blocked_sum;
   }
  
   // if only one is blocked, it must be 1x1
   LinearOp opl = opl_in;
   LinearOp opr = opr_in;
   if(isPhysicallyBlockedLinearOp(opl_in)){
     double scalarl = 0.0;
     bool transpl = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opl = getPhysicallyBlockedLinearOp(opl_in, &scalarl, &transpl);
     TEUCHOS_ASSERT(blocked_opl->productRange()->numBlocks() == 1);
     TEUCHOS_ASSERT(blocked_opl->productDomain()->numBlocks() == 1);
     opl = Thyra::scale(scalarl,blocked_opl->getBlock(0,0));
   }
   if(isPhysicallyBlockedLinearOp(opr_in)){
     double scalarr = 0.0;
     bool transpr = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opr = getPhysicallyBlockedLinearOp(opr_in, &scalarr, &transpr);
     TEUCHOS_ASSERT(blocked_opr->productRange()->numBlocks() == 1);
     TEUCHOS_ASSERT(blocked_opr->productDomain()->numBlocks() == 1);
     opr = Thyra::scale(scalarr,blocked_opr->getBlock(0,0));
   }
 
   bool isTpetral = Teko::TpetraHelpers::isTpetraLinearOp(opl);
   bool isTpetrar = Teko::TpetraHelpers::isTpetraLinearOp(opr);
 
   // if one of the operators in the sum is a thyra zero op
   if(isZeroOp(opl)){
     if(isZeroOp(opr))
       return opr; // return a zero op if both are zero
     if(isTpetrar){ // if other op is tpetra, replace this with a zero crs matrix
       ST scalar = 0.0;
       bool transp = false;
       auto crs_op = Teko::TpetraHelpers::getTpetraCrsMatrix(opr, &scalar, &transp);
       auto zero_crs = Tpetra::createCrsMatrix<ST,LO,GO,NT>(crs_op->getRowMap());
       zero_crs->fillComplete();
       opl = Thyra::constTpetraLinearOp<ST,LO,GO,NT>(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(crs_op->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(crs_op->getDomainMap()),zero_crs);
       isTpetral = true;
     } else
       return opr->clone();
   }
   if(isZeroOp(opr)){
     if(isTpetral){ // if other op is tpetra, replace this with a zero crs matrix
       ST scalar = 0.0;
       bool transp = false;
       auto crs_op = Teko::TpetraHelpers::getTpetraCrsMatrix(opr, &scalar, &transp);
       auto zero_crs = Tpetra::createCrsMatrix<ST,LO,GO,NT>(crs_op->getRowMap());
       zero_crs->fillComplete();
       opr = Thyra::constTpetraLinearOp<ST,LO,GO,NT>(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(crs_op->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(crs_op->getDomainMap()),zero_crs);
       isTpetrar = true;
     } else
       return opl->clone();
   }
 
   if(isTpetral && isTpetrar){ // Both operators are Tpetra matrices so use the explicit Tpetra matrix-matrix add
 
      // Get left and right Tpetra crs operators
      ST scalarl = 0.0;
      bool transpl = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpl = Teko::TpetraHelpers::getTpetraCrsMatrix(opl, &scalarl, &transpl);
      ST scalarr = 0.0;
      bool transpr = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpr = Teko::TpetraHelpers::getTpetraCrsMatrix(opr, &scalarr, &transpr);
 
      // Build output operator
      RCP<Thyra::LinearOpBase<ST> > explicitOp = rcp(new Thyra::TpetraLinearOp<ST,LO,GO,NT>());
      RCP<Thyra::TpetraLinearOp<ST,LO,GO,NT> > tExplicitOp = rcp_dynamic_cast<Thyra::TpetraLinearOp<ST,LO,GO,NT> >(explicitOp);
 
      // Do explicit matrix-matrix add
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > explicitCrsOp = Tpetra::MatrixMatrix::add<ST,LO,GO,NT>(scalarl,transpl,*tCrsOpl,scalarr,transpr,*tCrsOpr); 
      tExplicitOp->initialize(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getDomainMap()),explicitCrsOp);  
      return tExplicitOp;
 
   }else{//Assume Epetra
     // build implicit add
     const LinearOp implicitOp = Thyra::add(opl,opr);
 
     // build transformer
     const RCP<Thyra::LinearOpTransformerBase<double> > prodTrans =
         Thyra::epetraExtAddTransformer();
 
     // build operator and add
     const RCP<Thyra::LinearOpBase<double> > explicitOp = prodTrans->createOutputOp();
     prodTrans->transform(*implicitOp,explicitOp.ptr());
     explicitOp->setObjectLabel("explicit( " + opl->getObjectLabel() +
                                     " + " + opr->getObjectLabel() + " )");
 
     return explicitOp;
   }
}
 
const ModifiableLinearOp explicitAdd(const LinearOp & opl,const LinearOp & opr,
                                     const ModifiableLinearOp & destOp)
{
   // if blocked, add block by block
   if(isPhysicallyBlockedLinearOp(opl)){
     TEUCHOS_ASSERT(isPhysicallyBlockedLinearOp(opr));
 
     double scalarl = 0.0;
     bool transpl = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opl = getPhysicallyBlockedLinearOp(opl, &scalarl, &transpl);
 
     double scalarr = 0.0;
     bool transpr = false;
     RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_opr = getPhysicallyBlockedLinearOp(opr, &scalarr, &transpr);
 
     int numRows = blocked_opl->productRange()->numBlocks();
     int numCols = blocked_opl->productDomain()->numBlocks();
     TEUCHOS_ASSERT(blocked_opr->productRange()->numBlocks() == numRows);
     TEUCHOS_ASSERT(blocked_opr->productDomain()->numBlocks() == numCols);
 
     RCP<Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_sum = Teuchos::rcp_dynamic_cast<Thyra::DefaultBlockedLinearOp<double>>(destOp);
     if(blocked_sum.is_null()) {
       // take care of the null case, this means we must alllocate memory
       blocked_sum = Thyra::defaultBlockedLinearOp<double>();
 
       blocked_sum->beginBlockFill(numRows,numCols);
       for(int r = 0; r < numRows; ++r) {
         for(int c = 0; c < numCols; ++c) {
           auto block = explicitAdd(Thyra::scale(scalarl,blocked_opl->getBlock(r,c)),Thyra::scale(scalarr,blocked_opr->getBlock(r,c)),Teuchos::null);
           blocked_sum->setNonconstBlock(r,c,block);
         }
       }
       blocked_sum->endBlockFill();
 
     }
     else {
       // in this case memory can be reused
       for(int r = 0; r < numRows; ++r)
         for(int c = 0; c < numCols; ++c)
           explicitAdd(Thyra::scale(scalarl,blocked_opl->getBlock(r,c)),Thyra::scale(scalarr,blocked_opr->getBlock(r,c)),blocked_sum->getNonconstBlock(r,c));
     }
 
     return blocked_sum;
   }
 
   bool isTpetral = Teko::TpetraHelpers::isTpetraLinearOp(opl);
   bool isTpetrar = Teko::TpetraHelpers::isTpetraLinearOp(opr);
 
   if(isTpetral && isTpetrar){ // Both operators are Tpetra matrices so use the explicit Tpetra matrix-matrix add
 
      // Get left and right Tpetra crs operators
      ST scalarl = 0.0;
      bool transpl = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpl = Teko::TpetraHelpers::getTpetraCrsMatrix(opl, &scalarl, &transpl);
      ST scalarr = 0.0;
      bool transpr = false;
      RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOpr = Teko::TpetraHelpers::getTpetraCrsMatrix(opr, &scalarr, &transpr);
 
      // Build output operator
      RCP<Thyra::LinearOpBase<ST> > explicitOp;
      if(destOp!=Teuchos::null)
         explicitOp = destOp;
      else
         explicitOp = rcp(new Thyra::TpetraLinearOp<ST,LO,GO,NT>());
      RCP<Thyra::TpetraLinearOp<ST,LO,GO,NT> > tExplicitOp = rcp_dynamic_cast<Thyra::TpetraLinearOp<ST,LO,GO,NT> >(explicitOp);
 
      // Do explicit matrix-matrix add
      RCP<Tpetra::CrsMatrix<ST,LO,GO,NT> > explicitCrsOp = Tpetra::MatrixMatrix::add<ST,LO,GO,NT>(scalarl,transpl,*tCrsOpl,scalarr,transpr,*tCrsOpr); 
      tExplicitOp->initialize(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(explicitCrsOp->getDomainMap()),explicitCrsOp);  
      return tExplicitOp;
 
   }else{ // Assume Epetra
 
     // build implicit add
     const LinearOp implicitOp = Thyra::add(opl,opr);
 
     // build transformer
     const RCP<Thyra::LinearOpTransformerBase<double> > prodTrans =
         Thyra::epetraExtAddTransformer();
 
     // build or reuse destination operator
     RCP<Thyra::LinearOpBase<double> > explicitOp;
     if(destOp!=Teuchos::null)
        explicitOp = destOp;
     else
        explicitOp = prodTrans->createOutputOp();
 
     // perform add
     prodTrans->transform(*implicitOp,explicitOp.ptr());
     explicitOp->setObjectLabel("explicit( " + opl->getObjectLabel() +
                                     " + " + opr->getObjectLabel() + " )");
 
     return explicitOp;
   }
}
 
const ModifiableLinearOp explicitSum(const LinearOp & op,
                                     const ModifiableLinearOp & destOp)
{
   // convert operators to Epetra_CrsMatrix
   const RCP<const Epetra_CrsMatrix> epetraOp =
         rcp_dynamic_cast<const Epetra_CrsMatrix>(get_Epetra_Operator(*op), true);
 
   if(destOp==Teuchos::null) {
      Teuchos::RCP<Epetra_Operator> epetraDest = Teuchos::rcp(new Epetra_CrsMatrix(*epetraOp));
 
      return Thyra::nonconstEpetraLinearOp(epetraDest);
   }
 
   const RCP<Epetra_CrsMatrix> epetraDest =
         rcp_dynamic_cast<Epetra_CrsMatrix>(get_Epetra_Operator(*destOp), true);
 
   EpetraExt::MatrixMatrix::Add(*epetraOp,false,1.0,*epetraDest,1.0);
 
   return destOp;
}
 
const LinearOp explicitTranspose(const LinearOp & op)
{
   if(Teko::TpetraHelpers::isTpetraLinearOp(op)){
 
     RCP<const Thyra::TpetraLinearOp<ST,LO,GO,NT> > tOp = rcp_dynamic_cast<const Thyra::TpetraLinearOp<ST,LO,GO,NT> >(op,true);
     RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOp = rcp_dynamic_cast<const Tpetra::CrsMatrix<ST,LO,GO,NT> >(tOp->getConstTpetraOperator(),true);
 
     Tpetra::RowMatrixTransposer<ST,LO,GO,NT> transposer(tCrsOp);
     RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > transOp = transposer.createTranspose();
 
     return Thyra::constTpetraLinearOp<ST,LO,GO,NT>(Thyra::tpetraVectorSpace<ST,LO,GO,NT>(transOp->getRangeMap()),Thyra::tpetraVectorSpace<ST,LO,GO,NT>(transOp->getDomainMap()),transOp);
 
   } else {
 
     RCP<const Epetra_Operator> eOp = Thyra::get_Epetra_Operator(*op);
     TEUCHOS_TEST_FOR_EXCEPTION(eOp==Teuchos::null,std::logic_error,
                               "Teko::explicitTranspose Not an Epetra_Operator");
     RCP<const Epetra_RowMatrix> eRowMatrixOp 
           = Teuchos::rcp_dynamic_cast<const Epetra_RowMatrix>(eOp);
     TEUCHOS_TEST_FOR_EXCEPTION(eRowMatrixOp==Teuchos::null,std::logic_error,
                               "Teko::explicitTranspose Not an Epetra_RowMatrix");
 
     // we now have a delete transpose operator
     EpetraExt::RowMatrix_Transpose tranposeOp;
     Epetra_RowMatrix & eMat = tranposeOp(const_cast<Epetra_RowMatrix &>(*eRowMatrixOp));
 
     // this copy is because of a poor implementation of the EpetraExt::Transform 
     // implementation
     Teuchos::RCP<Epetra_CrsMatrix> crsMat 
           = Teuchos::rcp(new Epetra_CrsMatrix(dynamic_cast<Epetra_CrsMatrix &>(eMat)));
 
     return Thyra::epetraLinearOp(crsMat);
   }
}
 
double frobeniusNorm(const LinearOp & op_in)
{
  LinearOp op;
  double scalar = 1.0;
 
  // if blocked, must be 1x1
  if(isPhysicallyBlockedLinearOp(op_in)){
    bool transp = false;
    RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > blocked_op = getPhysicallyBlockedLinearOp(op_in,&scalar,&transp);
    TEUCHOS_ASSERT(blocked_op->productRange()->numBlocks() == 1);
    TEUCHOS_ASSERT(blocked_op->productDomain()->numBlocks() == 1);
    op = blocked_op->getBlock(0,0);
  } else
    op = op_in;
 
  if(Teko::TpetraHelpers::isTpetraLinearOp(op)){
    const RCP<const Thyra::TpetraLinearOp<ST,LO,GO,NT> > tOp = rcp_dynamic_cast<const Thyra::TpetraLinearOp<ST,LO,GO,NT> >(op);
    const RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > crsOp = rcp_dynamic_cast<const Tpetra::CrsMatrix<ST,LO,GO,NT> >(tOp->getConstTpetraOperator(),true);
    return crsOp->getFrobeniusNorm();
  } else {
    const RCP<const Epetra_Operator> epOp = Thyra::get_Epetra_Operator(*op);
    const RCP<const Epetra_CrsMatrix> crsOp = rcp_dynamic_cast<const Epetra_CrsMatrix>(epOp,true);
    return crsOp->NormFrobenius();
  }
}
 
double oneNorm(const LinearOp & op)
{
  if(Teko::TpetraHelpers::isTpetraLinearOp(op)){
    TEUCHOS_TEST_FOR_EXCEPTION(true,std::logic_error,"One norm not currently implemented for Tpetra matrices");
    
  } else {
    const RCP<const Epetra_Operator> epOp = Thyra::get_Epetra_Operator(*op);
    const RCP<const Epetra_CrsMatrix> crsOp = rcp_dynamic_cast<const Epetra_CrsMatrix>(epOp,true);
    return crsOp->NormOne();
  }
}
 
double infNorm(const LinearOp & op)
{
  if(Teko::TpetraHelpers::isTpetraLinearOp(op)){
    ST scalar = 0.0;
    bool transp = false;
    RCP<const Tpetra::CrsMatrix<ST,LO,GO,NT> > tCrsOp = Teko::TpetraHelpers::getTpetraCrsMatrix(op, &scalar, &transp);
 
    // extract diagonal
    const RCP<Tpetra::Vector<ST,LO,GO,NT> > ptrDiag = Tpetra::createVector<ST,LO,GO,NT>(tCrsOp->getRowMap());
    Tpetra::Vector<ST,LO,GO,NT> & diag = *ptrDiag;
 
    // compute absolute value row sum
    diag.putScalar(0.0);
    for(LO i=0;i<(LO) tCrsOp->getNodeNumRows();i++) {
       LO numEntries = tCrsOp->getNumEntriesInLocalRow (i);
       typename Tpetra::CrsMatrix<ST,LO,GO,NT>::local_inds_host_view_type indices;
       typename Tpetra::CrsMatrix<ST,LO,GO,NT>::values_host_view_type values;
       tCrsOp->getLocalRowView(i,indices,values);
 
       // build abs value row sum
       for(LO j=0;j<numEntries;j++)
          diag.sumIntoLocalValue(i,std::abs(values(j)));
    }
    return diag.normInf()*scalar;    
 
  } else {
    const RCP<const Epetra_Operator> epOp = Thyra::get_Epetra_Operator(*op);
    const RCP<const Epetra_CrsMatrix> crsOp = rcp_dynamic_cast<const Epetra_CrsMatrix>(epOp,true);
    return crsOp->NormInf();
  }
}
 
const LinearOp buildDiagonal(const MultiVector & src,const std::string & lbl)
{
   RCP<Thyra::VectorBase<double> > dst = Thyra::createMember(src->range()); 
   Thyra::copy(*src->col(0),dst.ptr());
   
   return Thyra::diagonal<double>(dst,lbl);
}
 
const LinearOp buildInvDiagonal(const MultiVector & src,const std::string & lbl)
{
   const RCP<const Thyra::VectorBase<double> > srcV = src->col(0);
   RCP<Thyra::VectorBase<double> > dst = Thyra::createMember(srcV->range()); 
   Thyra::reciprocal<double>(*srcV,dst.ptr());
 
   return Thyra::diagonal<double>(dst,lbl);
}
 
BlockedMultiVector buildBlockedMultiVector(const std::vector<MultiVector> & mvv)
{
   Teuchos::Array<MultiVector> mvA;
   Teuchos::Array<VectorSpace> vsA;
 
   // build arrays of multi vectors and vector spaces
   std::vector<MultiVector>::const_iterator itr;
   for(itr=mvv.begin();itr!=mvv.end();++itr) {
      mvA.push_back(*itr);
      vsA.push_back((*itr)->range());
   }
 
   // construct the product vector space
   const RCP<const Thyra::DefaultProductVectorSpace<double> > vs
         = Thyra::productVectorSpace<double>(vsA);
 
   return Thyra::defaultProductMultiVector<double>(vs,mvA);
}
 
Teuchos::RCP<Thyra::VectorBase<double> > indicatorVector(
                                 const std::vector<int> & indices,
                                 const VectorSpace & vs,
                                 double onValue, double offValue)
 
{
   using Teuchos::RCP;
 
   // create a new vector
   RCP<Thyra::VectorBase<double> > v = Thyra::createMember<double>(vs);
   Thyra::put_scalar<double>(offValue,v.ptr()); // fill it with "off" values
 
   // set on values
   for(std::size_t i=0;i<indices.size();i++) 
      Thyra::set_ele<double>(indices[i],onValue,v.ptr());
 
   return v;
}
 
double computeSpectralRad(const RCP<const Thyra::LinearOpBase<double> > & A, double tol,
                          bool isHermitian,int numBlocks,int restart,int verbosity)
{
   typedef Thyra::LinearOpBase<double> OP;
   typedef Thyra::MultiVectorBase<double> MV;
 
   int startVectors = 1;
 
   // construct an initial guess
   const RCP<MV> ivec = Thyra::createMember(A->domain());
   Thyra::randomize(-1.0,1.0,ivec.ptr());
   
   RCP<Anasazi::BasicEigenproblem<double,MV,OP> > eigProb
         = rcp(new Anasazi::BasicEigenproblem<double,MV,OP>(A,ivec));
   eigProb->setNEV(1);
   eigProb->setHermitian(isHermitian);
 
   // set the problem up
   if(not eigProb->setProblem()) {
      // big time failure!
      return Teuchos::ScalarTraits<double>::nan();
   }
 
   // we want largert magnitude eigenvalue
   std::string which("LM"); // largest magnitude
 
   // Create the parameter list for the eigensolver
   // verbosity+=Anasazi::TimingDetails;
   Teuchos::ParameterList MyPL;
   MyPL.set( "Verbosity", verbosity );
   MyPL.set( "Which", which );
   MyPL.set( "Block Size", startVectors );
   MyPL.set( "Num Blocks", numBlocks );
   MyPL.set( "Maximum Restarts", restart ); 
   MyPL.set( "Convergence Tolerance", tol );
 
   // build status test manager
   // RCP<Anasazi::StatusTestMaxIters<double,MV,OP> > statTest
   //       = rcp(new Anasazi::StatusTestMaxIters<double,MV,OP>(numBlocks*(restart+1)));
 
   // Create the Block Krylov Schur solver
   // This takes as inputs the eigenvalue problem and the solver parameters
   Anasazi::BlockKrylovSchurSolMgr<double,MV,OP> MyBlockKrylovSchur(eigProb, MyPL );
 
   // Solve the eigenvalue problem, and save the return code
   Anasazi::ReturnType solverreturn = MyBlockKrylovSchur.solve();
 
   if(solverreturn==Anasazi::Unconverged) {
      double real = MyBlockKrylovSchur.getRitzValues().begin()->realpart;
      double comp = MyBlockKrylovSchur.getRitzValues().begin()->imagpart;
 
      return -std::abs(std::sqrt(real*real+comp*comp));
 
      // cout << "Anasazi::BlockKrylovSchur::solve() did not converge!" << std::endl; 
      // return -std::abs(MyBlockKrylovSchur.getRitzValues().begin()->realpart);
   }
   else { // solverreturn==Anasazi::Converged
      double real = eigProb->getSolution().Evals.begin()->realpart;
      double comp = eigProb->getSolution().Evals.begin()->imagpart;
 
      return std::abs(std::sqrt(real*real+comp*comp));
 
      // cout << "Anasazi::BlockKrylovSchur::solve() converged!" << endl;
      // return std::abs(eigProb->getSolution().Evals.begin()->realpart);
   }
}
 
double computeSmallestMagEig(const RCP<const Thyra::LinearOpBase<double> > & A, double tol,
                             bool isHermitian,int numBlocks,int restart,int verbosity)
{
   typedef Thyra::LinearOpBase<double> OP;
   typedef Thyra::MultiVectorBase<double> MV;
 
   int startVectors = 1;
 
   // construct an initial guess
   const RCP<MV> ivec = Thyra::createMember(A->domain());
   Thyra::randomize(-1.0,1.0,ivec.ptr());
   
   RCP<Anasazi::BasicEigenproblem<double,MV,OP> > eigProb
         = rcp(new Anasazi::BasicEigenproblem<double,MV,OP>(A,ivec));
   eigProb->setNEV(1);
   eigProb->setHermitian(isHermitian);
 
   // set the problem up
   if(not eigProb->setProblem()) {
      // big time failure!
      return Teuchos::ScalarTraits<double>::nan();
   }
 
   // we want largert magnitude eigenvalue
   std::string which("SM"); // smallest magnitude
 
   // Create the parameter list for the eigensolver
   Teuchos::ParameterList MyPL;
   MyPL.set( "Verbosity", verbosity );
   MyPL.set( "Which", which );
   MyPL.set( "Block Size", startVectors );
   MyPL.set( "Num Blocks", numBlocks );
   MyPL.set( "Maximum Restarts", restart ); 
   MyPL.set( "Convergence Tolerance", tol );
 
   // build status test manager
   // RCP<Anasazi::StatusTestMaxIters<double,MV,OP> > statTest
   //       = rcp(new Anasazi::StatusTestMaxIters<double,MV,OP>(10));
 
   // Create the Block Krylov Schur solver
   // This takes as inputs the eigenvalue problem and the solver parameters
   Anasazi::BlockKrylovSchurSolMgr<double,MV,OP> MyBlockKrylovSchur(eigProb, MyPL );
 
   // Solve the eigenvalue problem, and save the return code
   Anasazi::ReturnType solverreturn = MyBlockKrylovSchur.solve();
 
   if(solverreturn==Anasazi::Unconverged) {
      // cout << "Anasazi::BlockKrylovSchur::solve() did not converge! " << std::endl;
      return -std::abs(MyBlockKrylovSchur.getRitzValues().begin()->realpart);
   }
   else { // solverreturn==Anasazi::Converged
      // cout << "Anasazi::BlockKrylovSchur::solve() converged!" << endl;
      return std::abs(eigProb->getSolution().Evals.begin()->realpart);
   }
}
 
ModifiableLinearOp getDiagonalOp(const Teko::LinearOp & A,const DiagonalType & dt)
{
   switch(dt) {
   case Diagonal:
      return getDiagonalOp(A);  
   case Lumped:
      return getLumpedMatrix(A);  
   case AbsRowSum:
      return getAbsRowSumMatrix(A);  
   case NotDiag:
   default:
      TEUCHOS_TEST_FOR_EXCEPT(true);
   };
 
   return Teuchos::null;
}
 
ModifiableLinearOp getInvDiagonalOp(const Teko::LinearOp & A,const Teko::DiagonalType & dt)
{
   switch(dt) {
   case Diagonal:
      return getInvDiagonalOp(A);  
   case Lumped:
      return getInvLumpedMatrix(A);  
   case AbsRowSum:
      return getAbsRowSumInvMatrix(A);  
   case NotDiag:
   default:
      TEUCHOS_TEST_FOR_EXCEPT(true);
   };
 
   return Teuchos::null;
}
 
std::string getDiagonalName(const DiagonalType & dt)
{
   switch(dt) {
   case Diagonal:
      return "Diagonal";
   case Lumped:
      return "Lumped";
   case AbsRowSum:
      return "AbsRowSum";
   case NotDiag:
      return "NotDiag";
   case BlkDiag:
      return "BlkDiag";
   };
 
   return "<error>";
}
 
DiagonalType getDiagonalType(std::string name)
{
   if(name=="Diagonal")
      return Diagonal;
   if(name=="Lumped")
     return Lumped;
   if(name=="AbsRowSum")
      return AbsRowSum;
   if(name=="BlkDiag")
      return BlkDiag;
 
   return NotDiag;
}
 
LinearOp probe(Teuchos::RCP<const Epetra_CrsGraph> &G,const LinearOp & Op){
#ifdef Teko_ENABLE_Isorropia
  Teuchos::ParameterList probeList;
  Prober prober(G,probeList,true);
  Teuchos::RCP<Epetra_CrsMatrix> Mat=rcp(new Epetra_CrsMatrix(Copy,*G));
  Teko::Epetra::EpetraOperatorWrapper Mwrap(Op);
  prober.probe(Mwrap,*Mat);
  return Thyra::epetraLinearOp(Mat);    
#else
  (void)G;
  (void)Op;
  TEUCHOS_TEST_FOR_EXCEPTION(true,std::runtime_error,"Probe requires Isorropia");
#endif
}
 
double norm_1(const MultiVector & v,std::size_t col)
{
   Teuchos::Array<double> n(v->domain()->dim());
   Thyra::norms_1<double>(*v,n);
 
   return n[col];
}
 
double norm_2(const MultiVector & v,std::size_t col)
{
   Teuchos::Array<double> n(v->domain()->dim());
   Thyra::norms_2<double>(*v,n);
 
   return n[col];
}
 
void putScalar(const ModifiableLinearOp & op,double scalar) 
{
   try {
      // get Epetra_Operator
      RCP<Epetra_Operator> eOp = Thyra::get_Epetra_Operator(*op);
 
      // cast it to a CrsMatrix
      RCP<Epetra_CrsMatrix> eCrsOp = rcp_dynamic_cast<Epetra_CrsMatrix>(eOp,true);
 
     eCrsOp->PutScalar(scalar);
   }
   catch (std::exception & e) {
      RCP<Teuchos::FancyOStream> out = Teuchos::VerboseObjectBase::getDefaultOStream();
 
      *out << "Teko: putScalar requires an Epetra_CrsMatrix\n";
      *out << "    Could not extract an Epetra_Operator from a \"" << op->description() << std::endl;
      *out << "           OR\n";
      *out << "    Could not cast an Epetra_Operator to a Epetra_CrsMatrix\n";
      *out << std::endl;
      *out << "*** THROWN EXCEPTION ***\n";
      *out << e.what() << std::endl;
      *out << "************************\n";
      
      throw e;
   }
}
 
void clipLower(MultiVector & v,double lowerBound)
{
   using Teuchos::RCP;
   using Teuchos::rcp_dynamic_cast;
 
   // cast so entries are accessible
   // RCP<Thyra::SpmdMultiVectorBase<double> > spmdMVec  
   //    = rcp_dynamic_cast<Thyra::DefaultSpmdMultiVector<double> >(v);
   
   for(Thyra::Ordinal i=0;i<v->domain()->dim();i++) {
      RCP<Thyra::SpmdVectorBase<double> > spmdVec  
         = rcp_dynamic_cast<Thyra::SpmdVectorBase<double> >(v->col(i),true);
   
      Teuchos::ArrayRCP<double> values;
      // spmdMVec->getNonconstLocalData(Teuchos::ptrFromRef(values),Teuchos::ptrFromRef(i));
      spmdVec->getNonconstLocalData(Teuchos::ptrFromRef(values));
      for(Teuchos::ArrayRCP<double>::size_type j=0;j<values.size();j++) {
         if(values[j]<lowerBound)
            values[j] = lowerBound;
      }
   }
}
 
void clipUpper(MultiVector & v,double upperBound)
{
   using Teuchos::RCP;
   using Teuchos::rcp_dynamic_cast;
 
   // cast so entries are accessible
   // RCP<Thyra::SpmdMultiVectorBase<double> > spmdMVec  
   //   = rcp_dynamic_cast<Thyra::DefaultSpmdMultiVector<double> >(v);
   for(Thyra::Ordinal i=0;i<v->domain()->dim();i++) {
      RCP<Thyra::SpmdVectorBase<double> > spmdVec  
         = rcp_dynamic_cast<Thyra::SpmdVectorBase<double> >(v->col(i),true);
   
      Teuchos::ArrayRCP<double> values;
      // spmdMVec->getNonconstLocalData(Teuchos::ptrFromRef(values),Teuchos::ptrFromRef(i));
      spmdVec->getNonconstLocalData(Teuchos::ptrFromRef(values));
      for(Teuchos::ArrayRCP<double>::size_type j=0;j<values.size();j++) {
         if(values[j]>upperBound)
            values[j] = upperBound;
      }
   }
}
 
void replaceValue(MultiVector & v,double currentValue,double newValue)
{
   using Teuchos::RCP;
   using Teuchos::rcp_dynamic_cast;
 
   // cast so entries are accessible
   // RCP<Thyra::SpmdMultiVectorBase<double> > spmdMVec  
   //    = rcp_dynamic_cast<Thyra::SpmdMultiVectorBase<double> >(v,true);
   for(Thyra::Ordinal i=0;i<v->domain()->dim();i++) {
      RCP<Thyra::SpmdVectorBase<double> > spmdVec  
         = rcp_dynamic_cast<Thyra::SpmdVectorBase<double> >(v->col(i),true);
   
      Teuchos::ArrayRCP<double> values;
      // spmdMVec->getNonconstLocalData(Teuchos::ptrFromRef(values),Teuchos::ptrFromRef(i));
      spmdVec->getNonconstLocalData(Teuchos::ptrFromRef(values));
      for(Teuchos::ArrayRCP<double>::size_type j=0;j<values.size();j++) {
         if(values[j]==currentValue)
            values[j] = newValue;
      }
   }
}
 
void columnAverages(const MultiVector & v,std::vector<double> & averages)
{
   averages.resize(v->domain()->dim());
 
   // sum over each column
   Thyra::sums<double>(*v,averages);
 
   // build averages
   Thyra::Ordinal rows = v->range()->dim();
   for(std::size_t i=0;i<averages.size();i++)
      averages[i] = averages[i]/rows;
}
 
double average(const MultiVector & v)
{
   Thyra::Ordinal rows = v->range()->dim();
   Thyra::Ordinal cols = v->domain()->dim();
 
   std::vector<double> averages;
   columnAverages(v,averages);
 
   double sum = 0.0;
   for(std::size_t i=0;i<averages.size();i++)
      sum += averages[i] * rows;
 
   return sum/(rows*cols);
}
 
bool isPhysicallyBlockedLinearOp(const LinearOp & op)
{
   // See if the operator is a PBLO
   RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > pblo = rcp_dynamic_cast<const Thyra::PhysicallyBlockedLinearOpBase<double> >(op);
   if (!pblo.is_null())
     return true;
 
   // See if the operator is a wrapped PBLO
   ST scalar = 0.0;
   Thyra::EOpTransp transp = Thyra::NOTRANS;
   RCP<const Thyra::LinearOpBase<ST> > wrapped_op;
   Thyra::unwrap(op, &scalar, &transp, &wrapped_op);
   pblo = rcp_dynamic_cast<const Thyra::PhysicallyBlockedLinearOpBase<double> >(wrapped_op);
   if (!pblo.is_null())
     return true;
 
   return false;
}
 
RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > getPhysicallyBlockedLinearOp(const LinearOp & op, ST *scalar, bool *transp)
{
    // If the operator is a TpetraLinearOp
    RCP<const Thyra::PhysicallyBlockedLinearOpBase<double> > pblo = rcp_dynamic_cast<const Thyra::PhysicallyBlockedLinearOpBase<double> >(op);
    if(!pblo.is_null()){
      *scalar = 1.0;
      *transp = false;
      return pblo;
    }
 
    // If the operator is a wrapped TpetraLinearOp
    RCP<const Thyra::LinearOpBase<ST> > wrapped_op;
    Thyra::EOpTransp eTransp = Thyra::NOTRANS;
    Thyra::unwrap(op, scalar, &eTransp, &wrapped_op);
    pblo = rcp_dynamic_cast<const Thyra::PhysicallyBlockedLinearOpBase<double> >(wrapped_op,true);
    if(!pblo.is_null()){
      *transp = true;
      if(eTransp == Thyra::NOTRANS)
        *transp = false;
      return pblo;
    }
 
    return Teuchos::null;
}
 
 
}