libtrilinos-teko-dev 12.4.2-2 / usr / include / trilinos / Teko_Utilities.hpp

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/** \file Teko_Utilities.hpp
  *
  * This file contains a number of useful functions and classes
  * used in Teko. They are distinct from the core functionality of
  * the preconditioner factory, however, the functions are critical
  * to construction of the preconditioners themselves.
  */

#ifndef __Teko_Utilities_hpp__
#define __Teko_Utilities_hpp__

#include "Epetra_CrsMatrix.h"

// Teuchos includes
#include "Teuchos_VerboseObject.hpp"

// Thyra includes
#include "Thyra_LinearOpBase.hpp"
#include "Thyra_PhysicallyBlockedLinearOpBase.hpp"
#include "Thyra_ProductVectorSpaceBase.hpp"
#include "Thyra_VectorSpaceBase.hpp"
#include "Thyra_ProductMultiVectorBase.hpp"
#include "Thyra_MultiVectorStdOps.hpp"
#include "Thyra_MultiVectorBase.hpp"
#include "Thyra_VectorBase.hpp"
#include "Thyra_VectorStdOps.hpp"
#include "Thyra_DefaultBlockedLinearOp.hpp"
#include "Thyra_DefaultMultipliedLinearOp.hpp"
#include "Thyra_DefaultScaledAdjointLinearOp.hpp"
#include "Thyra_DefaultAddedLinearOp.hpp"
#include "Thyra_DefaultIdentityLinearOp.hpp"
#include "Thyra_DefaultZeroLinearOp.hpp"

#ifdef _MSC_VER
#ifndef _MSC_EXTENSIONS
#define _MSC_EXTENSIONS
#define TEKO_DEFINED_MSC_EXTENSIONS
#endif
#include <iso646.h> // For C alternative tokens
#endif

// #define Teko_DEBUG_OFF
#define Teko_DEBUG_INT 5

namespace Teko {

using Thyra::multiply;
using Thyra::scale;
using Thyra::add;
using Thyra::identity;
using Thyra::zero; // make it to take one argument (square matrix)
using Thyra::block2x2;
using Thyra::block2x1;
using Thyra::block1x2;

/** \brief Build a graph Laplacian stenciled on a Epetra_CrsMatrix.
  *
  * This function builds a graph Laplacian given a (locally complete)
  * vector of coordinates and a stencil Epetra_CrsMatrix (could this be
  * a graph of Epetra_RowMatrix instead?). The resulting matrix will have
  * the negative of the inverse distance on off diagonals. And the sum
  * of the positive inverse distance of the off diagonals on the diagonal.
  * If there are no off diagonal entries in the stencil, the diagonal is
  * set to 0.
  *
  * \param[in]     dim     Number of physical dimensions (2D or 3D?).
  * \param[in]     coords  A vector containing the coordinates, with the <code>i</code>-th
  *                        coordinate beginning at <code>coords[i*dim]</code>.
  * \param[in]     stencil The stencil matrix used to describe the connectivity
  *                        of the graph Laplacian matrix.
  *
  * \returns The graph Laplacian matrix to be filled according to the <code>stencil</code> matrix.
  */
Teuchos::RCP<Epetra_CrsMatrix> buildGraphLaplacian(int dim,double * coords,const Epetra_CrsMatrix & stencil);

/** \brief Build a graph Laplacian stenciled on a Epetra_CrsMatrix.
  *
  * This function builds a graph Laplacian given a (locally complete)
  * vector of coordinates and a stencil Epetra_CrsMatrix (could this be
  * a graph of Epetra_RowMatrix instead?). The resulting matrix will have
  * the negative of the inverse distance on off diagonals. And the sum
  * of the positive inverse distance of the off diagonals on the diagonal.
  * If there are no off diagonal entries in the stencil, the diagonal is
  * set to 0.
  *
  * \param[in]     x       A vector containing the x-coordinates, with the <code>i</code>-th
  *                        coordinate beginning at <code>coords[i*stride]</code>.
  * \param[in]     y       A vector containing the y-coordinates, with the <code>i</code>-th
  *                        coordinate beginning at <code>coords[i*stride]</code>.
  * \param[in]     z       A vector containing the z-coordinates, with the <code>i</code>-th
  *                        coordinate beginning at <code>coords[i*stride]</code>.
  * \param[in]     stride  Stride between entries in the (x,y,z) coordinate array
  * \param[in]     stencil The stencil matrix used to describe the connectivity
  *                        of the graph Laplacian matrix.
  *
  * \returns The graph Laplacian matrix to be filled according to the <code>stencil</code> matrix.
  */
Teuchos::RCP<Epetra_CrsMatrix> buildGraphLaplacian(double * x,double * y,double * z,int stride,const Epetra_CrsMatrix & stencil);

/** \brief Function used internally by Teko to find the output stream.
  * 
  * Function used internally by Teko to find the output stream.
  *
  * \returns An output stream to use for printing
  */
const Teuchos::RCP<Teuchos::FancyOStream> getOutputStream();
// inline const Teuchos::RCP<Teuchos::FancyOStream> getOutputStream();
// { return Teuchos::VerboseObjectBase::getDefaultOStream(); }

#ifndef Teko_DEBUG_OFF
   #define Teko_DEBUG_EXPR(str) str
   #define Teko_DEBUG_MSG(str,level) if(level<=Teko_DEBUG_INT) { \
      Teuchos::RCP<Teuchos::FancyOStream> out = Teko::getOutputStream(); \
      *out << "Teko: " << str << std::endl; }
   #define Teko_DEBUG_MSG_BEGIN(level) if(level<=Teko_DEBUG_INT) { \
      Teko::getOutputStream()->pushTab(3); \
      *Teko::getOutputStream() << "Teko: Begin debug MSG\n"; \
      std::ostream & DEBUG_STREAM = *Teko::getOutputStream(); \
      Teko::getOutputStream()->pushTab(3);
   #define Teko_DEBUG_MSG_END() Teko::getOutputStream()->popTab(); \
                             *Teko::getOutputStream() << "Teko: End debug MSG\n"; \
                              Teko::getOutputStream()->popTab(); }
   #define Teko_DEBUG_PUSHTAB() Teko::getOutputStream()->pushTab(3)
   #define Teko_DEBUG_POPTAB() Teko::getOutputStream()->popTab()

   struct __DebugScope__ {
      __DebugScope__(const std::string & str,int level)
         : str_(str), level_(level)
      { Teko_DEBUG_MSG("BEGIN "+str_,level_); Teko_DEBUG_PUSHTAB(); }      
      ~__DebugScope__()
      { Teko_DEBUG_POPTAB(); Teko_DEBUG_MSG("END "+str_,level_); } 
      std::string str_; int level_; };
   #define Teko_DEBUG_SCOPE(str,level) __DebugScope__ __dbgScope__(str,level);
#else 
   #define Teko_DEBUG_EXPR(str)
   #define Teko_DEBUG_MSG(str,level)
   #define Teko_DEBUG_MSG_BEGIN(level) if(false) { \
      std::ostream & DEBUG_STREAM = *Teko::getOutputStream();
   #define Teko_DEBUG_MSG_END() }
   #define Teko_DEBUG_PUSHTAB() 
   #define Teko_DEBUG_POPTAB() 
   #define Teko_DEBUG_SCOPE(str,level)
#endif

// typedefs for increased simplicity
typedef Teuchos::RCP<const Thyra::VectorSpaceBase<double> > VectorSpace;

// ----------------------------------------------------------------------------

//! @name MultiVector utilities
//@{

typedef Teuchos::RCP<Thyra::ProductMultiVectorBase<double> > BlockedMultiVector;
typedef Teuchos::RCP<Thyra::MultiVectorBase<double> > MultiVector;

//! Convert to a MultiVector from a BlockedMultiVector
inline MultiVector toMultiVector(BlockedMultiVector & bmv) { return bmv; }

//! Convert to a MultiVector from a BlockedMultiVector
inline const MultiVector toMultiVector(const BlockedMultiVector & bmv) { return bmv; }

//! Convert to a BlockedMultiVector from a MultiVector
inline const BlockedMultiVector toBlockedMultiVector(const MultiVector & bmv) 
{ return Teuchos::rcp_dynamic_cast<Thyra::ProductMultiVectorBase<double> >(bmv); }

//! Get the column count in a block linear operator
inline int blockCount(const BlockedMultiVector & bmv)
{ return bmv->productSpace()->numBlocks(); }

//! Get the <code>i</code>th block from a BlockedMultiVector object
inline MultiVector getBlock(int i,const BlockedMultiVector & bmv)
{ return Teuchos::rcp_const_cast<Thyra::MultiVectorBase<double> >(bmv->getMultiVectorBlock(i)); }

//! Perform a deep copy of the vector
inline MultiVector deepcopy(const MultiVector & v)
{ return v->clone_mv(); }

//! Perform a deep copy of the vector
inline MultiVector copyAndInit(const MultiVector & v,double scalar)
{ MultiVector mv = v->clone_mv(); Thyra::assign(mv.ptr(),scalar); return mv; }

//! Perform a deep copy of the blocked vector
inline BlockedMultiVector deepcopy(const BlockedMultiVector & v)
{ return toBlockedMultiVector(v->clone_mv()); }

/** \brief Copy the contents of a multivector to a destination vector.
  *
  * Copy the contents of a multivector to a new vector. If the destination
  * vector is null, a deep copy of the source multivector is made to a newly allocated
  * vector. Also, if the destination and the source do not match, a new destination
  * object is allocated and returned to the user.
  *
  * \param[in] src Source multivector to be copied.
  * \param[in] dst Destination multivector.  If null a new multivector will be allocated.
  *
  * \returns A copy of the source multivector. If dst is not null a pointer to this object
  *          is returned. Otherwise a new multivector is returned.
  */
inline MultiVector datacopy(const MultiVector & src,MultiVector & dst)
{ 
   if(dst==Teuchos::null)
      return deepcopy(src);

   bool rangeCompat = src->range()->isCompatible(*dst->range());
   bool domainCompat = src->domain()->isCompatible(*dst->domain());
 
   if(not (rangeCompat && domainCompat))
      return deepcopy(src);

   // perform data copy
   Thyra::assign<double>(dst.ptr(),*src);
   return dst;
}

/** \brief Copy the contents of a blocked multivector to a destination vector.
  *
  * Copy the contents of a blocked multivector to a new vector. If the destination
  * vector is null, a deep copy of the source multivector is made to a newly allocated
  * vector. Also, if the destination and the source do not match, a new destination
  * object is allocated and returned to the user.
  *
  * \param[in] src Source multivector to be copied.
  * \param[in] dst Destination multivector.  If null a new multivector will be allocated.
  *
  * \returns A copy of the source multivector. If dst is not null a pointer to this object
  *          is returned. Otherwise a new multivector is returned.
  */
inline BlockedMultiVector datacopy(const BlockedMultiVector & src,BlockedMultiVector & dst)
{ 
   if(dst==Teuchos::null)
      return deepcopy(src);

   bool rangeCompat = src->range()->isCompatible(*dst->range());
   bool domainCompat = src->domain()->isCompatible(*dst->domain());

   if(not (rangeCompat && domainCompat))
      return deepcopy(src);

   // perform data copy
   Thyra::assign<double>(dst.ptr(),*src);
   return dst;
}

//! build a BlockedMultiVector from a vector of MultiVectors
BlockedMultiVector buildBlockedMultiVector(const std::vector<MultiVector> & mvs);

/** Construct an indicator vector specified by a vector of indices to 
  * be set to ``on''.
  *
  * \param[in] indices Vector of indicies to turn on
  * \param[in] vs Vector space to construct the vector from
  * \param[in] onValue Value to set in the vector to on
  * \param[in] offValue Value to set in the vector to off
  *
  * \return Vector of on and off values.
  */
Teuchos::RCP<Thyra::VectorBase<double> > indicatorVector(
                                 const std::vector<int> & indices,
                                 const VectorSpace & vs,
                                 double onValue=1.0, double offValue=0.0);

//@}

// ----------------------------------------------------------------------------

//! @name LinearOp utilities
//@{
typedef Teuchos::RCP<Thyra::PhysicallyBlockedLinearOpBase<double> > BlockedLinearOp;
typedef Teuchos::RCP<const Thyra::LinearOpBase<double> > LinearOp;
typedef Teuchos::RCP<Thyra::LinearOpBase<double> > InverseLinearOp;
typedef Teuchos::RCP<Thyra::LinearOpBase<double> > ModifiableLinearOp;

//! Build a square zero operator from a single vector space
inline LinearOp zero(const VectorSpace & vs)
{ return Thyra::zero<double>(vs,vs); }

//! Replace nonzeros with a scalar value, used to zero out an operator
void putScalar(const ModifiableLinearOp & op,double scalar);

//! Get the range space of a linear operator
inline VectorSpace rangeSpace(const LinearOp & lo)
{ return lo->range(); }

//! Get the domain space of a linear operator
inline VectorSpace domainSpace(const LinearOp & lo)
{ return lo->domain(); }

//! Converts a LinearOp to a BlockedLinearOp
inline BlockedLinearOp toBlockedLinearOp(LinearOp & clo)
{
   Teuchos::RCP<Thyra::LinearOpBase<double> > lo = Teuchos::rcp_const_cast<Thyra::LinearOpBase<double> >(clo);
   return Teuchos::rcp_dynamic_cast<Thyra::PhysicallyBlockedLinearOpBase<double> > (lo);
}

//! Converts a LinearOp to a BlockedLinearOp
inline const BlockedLinearOp toBlockedLinearOp(const LinearOp & clo)
{
   Teuchos::RCP<Thyra::LinearOpBase<double> > lo = Teuchos::rcp_const_cast<Thyra::LinearOpBase<double> >(clo);
   return Teuchos::rcp_dynamic_cast<Thyra::PhysicallyBlockedLinearOpBase<double> > (lo);
}

//! Convert to a LinearOp from a BlockedLinearOp
inline LinearOp toLinearOp(BlockedLinearOp & blo) { return blo; }

//! Convert to a LinearOp from a BlockedLinearOp
inline const LinearOp toLinearOp(const BlockedLinearOp & blo) { return blo; }

//! Convert to a LinearOp from a BlockedLinearOp
inline LinearOp toLinearOp(ModifiableLinearOp & blo) { return blo; }

//! Convert to a LinearOp from a BlockedLinearOp
inline const LinearOp toLinearOp(const ModifiableLinearOp & blo) { return blo; }

//! Get the row count in a block linear operator
inline int blockRowCount(const BlockedLinearOp & blo)
{ return blo->productRange()->numBlocks(); }

//! Get the column count in a block linear operator
inline int blockColCount(const BlockedLinearOp & blo)
{ return blo->productDomain()->numBlocks(); }

//! Get the <code>i,j</code> block in a BlockedLinearOp object
inline LinearOp getBlock(int i,int j,const BlockedLinearOp & blo)
{ return blo->getBlock(i,j); }

//! Set the <code>i,j</code> block in a BlockedLinearOp object
inline void setBlock(int i,int j,BlockedLinearOp & blo, const LinearOp & lo)
{ return blo->setBlock(i,j,lo); }

//! Build a new blocked linear operator
inline BlockedLinearOp createBlockedOp()
{ return rcp(new Thyra::DefaultBlockedLinearOp<double>()); }

/** \brief Let the blocked operator know that you are going to 
  *        set the sub blocks.
  *
  * Let the blocked operator know that you are going to 
  * set the sub blocks. This is a simple wrapper around the
  * member function of the same name in Thyra.
  *
  * \param[in,out] blo Blocked operator to have its fill stage activated
  * \param[in]  rowCnt Number of block rows in this operator
  * \param[in]  colCnt Number of block columns in this operator
  */
inline void beginBlockFill(BlockedLinearOp & blo,int rowCnt,int colCnt)
{ blo->beginBlockFill(rowCnt,colCnt); }

/** \brief Let the blocked operator know that you are going to 
  *        set the sub blocks.
  *
  * Let the blocked operator know that you are going to 
  * set the sub blocks. This is a simple wrapper around the
  * member function of the same name in Thyra.
  *
  * \param[in,out] blo Blocked operator to have its fill stage activated
  */
inline void beginBlockFill(BlockedLinearOp & blo)
{ blo->beginBlockFill(); }

//! Notify the blocked operator that the fill stage is completed.
inline void endBlockFill(BlockedLinearOp & blo)
{ blo->endBlockFill(); }

//! Get the strictly upper triangular portion of the matrix
BlockedLinearOp getUpperTriBlocks(const BlockedLinearOp & blo,bool callEndBlockFill=true);

//! Get the strictly lower triangular portion of the matrix
BlockedLinearOp getLowerTriBlocks(const BlockedLinearOp & blo,bool callEndBlockFill=true);

/** \brief Build a zero operator mimicing the block structure
  *        of the passed in matrix.
  *
  * Build a zero operator mimicing the block structure
  * of the passed in matrix. Currently this function assumes
  * that the operator is "block" square. Also, this function
  * calls <code>beginBlockFill</code> but does not call
  * <code>endBlockFill</code>.  This is so that the user
  * can fill the matrix as they wish once created.
  *
  * \param[in] blo Blocked operator with desired structure.
  *
  * \returns A zero operator with the same block structure as
  *          the argument <code>blo</code>.
  *
  * \note The caller is responsible for calling
  *       <code>endBlockFill</code> on the returned blocked
  *       operator.
  */
BlockedLinearOp zeroBlockedOp(const BlockedLinearOp & blo);

//! Figure out if this operator is the zero operator (or null!)
bool isZeroOp(const LinearOp op);

/** \brief Compute absolute row sum matrix.
  *
  * Compute the absolute row sum matrix. That is
  * a diagonal operator composed of the absolute value of the
  * row sum.
  *
  * \returns A diagonal operator.
  */
ModifiableLinearOp getAbsRowSumMatrix(const LinearOp & op);

/** \brief Compute inverse of the absolute row sum matrix.
  *
  * Compute the inverse of the absolute row sum matrix. That is
  * a diagonal operator composed of the inverse of the absolute value
  * of the row sum.
  *
  * \returns A diagonal operator.
  */
ModifiableLinearOp getAbsRowSumInvMatrix(const LinearOp & op);

/** \brief Compute the lumped version of this matrix.
  *
  * Compute the lumped version of this matrix. That is
  * a diagonal operator composed of the row sum.
  *
  * \returns A diagonal operator.
  */
ModifiableLinearOp getLumpedMatrix(const LinearOp & op);

/** \brief Compute the inverse of the lumped version of
  *        this matrix.
  *
  * Compute the inverse of the lumped version of this matrix.
  * That is a diagonal operator composed of the row sum.
  *
  * \returns A diagonal operator.
  */
ModifiableLinearOp getInvLumpedMatrix(const LinearOp & op);

//@}

//! @name Mathematical functions
//@{

/** \brief Apply a linear operator to a multivector (think of this as a matrix
  *        vector multiply).
  *
  * Apply a linear operator to a multivector. This also permits arbitrary scaling
  * and addition of the result. This function gives
  *     
  *    \f$ y = \alpha A x + \beta y \f$
  *
  * It is required that the range space of <code>A</code> is compatible with <code>y</code> and the domain space
  * of <code>A</code> is compatible with <code>x</code>.
  *
  * \param[in]     A
  * \param[in]     x
  * \param[in,out] y
  * \param[in]     alpha
  * \param[in]     beta
  *
  */
void applyOp(const LinearOp & A,const MultiVector & x,MultiVector & y,double alpha=1.0,double beta=0.0);

/** \brief Apply a linear operator to a blocked multivector (think of this as a matrix
  *        vector multiply).
  *
  * Apply a linear operator to a blocked multivector. This also permits arbitrary scaling
  * and addition of the result. This function gives
  *     
  *    \f$ y = \alpha A x + \beta y \f$
  *
  * It is required that the range space of <code>A</code> is compatible with <code>y</code> and the domain space
  * of <code>A</code> is compatible with <code>x</code>.
  *
  * \param[in]     A
  * \param[in]     x
  * \param[in,out] y
  * \param[in]     alpha
  * \param[in]     beta
  *
  */
inline void applyOp(const LinearOp & A,const BlockedMultiVector & x,BlockedMultiVector & y,double alpha=1.0,double beta=0.0)
{ const MultiVector x_mv = toMultiVector(x); MultiVector y_mv = toMultiVector(y);
  applyOp(A,x_mv,y_mv,alpha,beta); }

/** \brief Update the <code>y</code> vector so that \f$y = \alpha x+\beta y\f$
  *
  * Compute the linear combination \f$y=\alpha x + \beta y\f$. 
  *
  * \param[in]     alpha
  * \param[in]     x 
  * \param[in]     beta 
  * \param[in,out] y
  */
void update(double alpha,const MultiVector & x,double beta,MultiVector & y);

//! \brief Update for a BlockedMultiVector
inline void update(double alpha,const BlockedMultiVector & x,double beta,BlockedMultiVector & y)
{ MultiVector x_mv = toMultiVector(x); MultiVector y_mv = toMultiVector(y);
  update(alpha,x_mv,beta,y_mv); }

//! Scale a multivector by a constant
inline void scale(const double alpha,MultiVector & x) { Thyra::scale<double>(alpha,x.ptr()); }

//! Scale a multivector by a constant
inline void scale(const double alpha,BlockedMultiVector & x) 
{  MultiVector x_mv = toMultiVector(x); scale(alpha,x_mv); }

//! Scale a modifiable linear op by a constant
inline LinearOp scale(const double alpha,ModifiableLinearOp & a) 
{  return Thyra::nonconstScale(alpha,a); }

//! Construct an implicit adjoint of the linear operators
inline LinearOp adjoint(ModifiableLinearOp & a) 
{  return Thyra::nonconstAdjoint(a); }

//@}

//! \name Epetra_Operator specific functions
//@{

/** \brief Get the diaonal of a linear operator
  *
  * Get the diagonal of a linear operator. Currently
  * it is assumed that the underlying operator is
  * an Epetra_RowMatrix.
  *
  * \param[in] op The operator whose diagonal is to be
  *               extracted.
  *
  * \returns An diagonal operator.
  */
const ModifiableLinearOp getDiagonalOp(const LinearOp & op);

/** \brief Get the diagonal of a linear operator
  *
  * Get the diagonal of a linear operator, putting it
  * in the first column of a multivector.
  */
const MultiVector getDiagonal(const LinearOp & op);

/** \brief Get the diaonal of a linear operator
  *
  * Get the inverse of the diagonal of a linear operator.
  * Currently it is assumed that the underlying operator is
  * an Epetra_RowMatrix.
  *
  * \param[in] op The operator whose diagonal is to be
  *               extracted and inverted
  *
  * \returns An diagonal operator.
  */
const ModifiableLinearOp getInvDiagonalOp(const LinearOp & op);

/** \brief Multiply three linear operators. 
  *
  * Multiply three linear operators. This currently assumes
  * that the underlying implementation uses Epetra_CrsMatrix.
  * The exception is that opm is allowed to be an diagonal matrix.
  *
  * \param[in] opl Left operator (assumed to be a Epetra_CrsMatrix)
  * \param[in] opm Middle operator (assumed to be a Epetra_CrsMatrix or a diagonal matrix)
  * \param[in] opr Right operator (assumed to be a Epetra_CrsMatrix)
  *
  * \returns Matrix product with a Epetra_CrsMatrix implementation
  */
const LinearOp explicitMultiply(const LinearOp & opl,const LinearOp & opm,const LinearOp & opr);

/** \brief Multiply three linear operators. 
  *
  * Multiply three linear operators. This currently assumes
  * that the underlying implementation uses Epetra_CrsMatrix.
  * The exception is that opm is allowed to be an diagonal matrix.
  *
  * \param[in] opl Left operator (assumed to be a Epetra_CrsMatrix)
  * \param[in] opm Middle operator (assumed to be a Epetra_CrsMatrix or a diagonal matrix)
  * \param[in] opr Right operator (assumed to be a Epetra_CrsMatrix)
  * \param[in,out] destOp The operator to be used as the destination operator,
  *                       if this is null this function creates a new operator
  *
  * \returns Matrix product with a Epetra_CrsMatrix implementation
  */
const ModifiableLinearOp explicitMultiply(const LinearOp & opl,const LinearOp & opm,const LinearOp & opr,
                                          const ModifiableLinearOp & destOp);

/** \brief Multiply two linear operators. 
  *
  * Multiply two linear operators. This currently assumes
  * that the underlying implementation uses Epetra_CrsMatrix.
  *
  * \param[in] opl Left operator (assumed to be a Epetra_CrsMatrix)
  * \param[in] opr Right operator (assumed to be a Epetra_CrsMatrix)
  *
  * \returns Matrix product with a Epetra_CrsMatrix implementation
  */
const LinearOp explicitMultiply(const LinearOp & opl,const LinearOp & opr);

/** \brief Multiply two linear operators. 
  *
  * Multiply two linear operators. This currently assumes
  * that the underlying implementation uses Epetra_CrsMatrix.
  * The exception is that opm is allowed to be an diagonal matrix.
  *
  * \param[in] opl Left operator (assumed to be a Epetra_CrsMatrix)
  * \param[in] opr Right operator (assumed to be a Epetra_CrsMatrix)
  * \param[in,out] destOp The operator to be used as the destination operator,
  *                       if this is null this function creates a new operator
  *
  * \returns Matrix product with a Epetra_CrsMatrix implementation
  */
const ModifiableLinearOp explicitMultiply(const LinearOp & opl,const LinearOp & opr,
                                          const ModifiableLinearOp & destOp);

/** \brief Add two linear operators. 
  *
  * Add two linear operators. This currently assumes
  * that the underlying implementation uses Epetra_CrsMatrix.
  *
  * \param[in] opl Left operator (assumed to be a Epetra_CrsMatrix)
  * \param[in] opr Right operator (assumed to be a Epetra_CrsMatrix)
  *
  * \returns Matrix sum with a Epetra_CrsMatrix implementation
  */
const LinearOp explicitAdd(const LinearOp & opl,const LinearOp & opr);

/** \brief Add two linear operators. 
  *
  * Add two linear operators. This currently assumes
  * that the underlying implementation uses Epetra_CrsMatrix.
  *
  * \param[in] opl Left operator (assumed to be a Epetra_CrsMatrix)
  * \param[in] opr Right operator (assumed to be a Epetra_CrsMatrix)
  * \param[in,out] destOp The operator to be used as the destination operator,
  *                       if this is null this function creates a new operator
  *
  * \returns Matrix sum with a Epetra_CrsMatrix implementation
  */
const ModifiableLinearOp explicitAdd(const LinearOp & opl,const LinearOp & opr,
                                     const ModifiableLinearOp & destOp);

/** Sum into the modifiable linear op.
  */
const ModifiableLinearOp explicitSum(const LinearOp & opl,
                                     const ModifiableLinearOp & destOp);

/** Build an explicit transpose of a linear operator. (Concrete data
  * underneath.
  */
const LinearOp explicitTranspose(const LinearOp & op);

/** \brief Take the first column of a multivector and build a
  *        diagonal linear operator
  */
const LinearOp buildDiagonal(const MultiVector & v,const std::string & lbl="ANYM");

/** \brief Using the first column of a multivector, take the elementwise build a
  *        inverse and build the inverse diagonal operator.
  */
const LinearOp buildInvDiagonal(const MultiVector & v,const std::string & lbl="ANYM");

//@}

/** \brief Compute the spectral radius of a matrix
  *
  * Compute the spectral radius of matrix A.  This utilizes the 
  * Trilinos-Anasazi BlockKrylovShcur method for computing eigenvalues.
  * It attempts to compute the largest (in magnitude) eigenvalue to a given
  * level of tolerance.
  *
  * \param[in] A   matrix whose spectral radius is needed
  * \param[in] tol The <em>most</em> accuracy needed (the algorithm will run until
  *            it reaches this level of accuracy and then it will quit).
  *            If this level is not reached it will return something to indicate
  *            it has not converged.
  * \param[in] isHermitian Is the matrix Hermitian
  * \param[in] numBlocks The size of the orthogonal basis built (like in GMRES) before
  *                  restarting.  Increase the memory usage by O(restart*n). At least
  *                  restart=3 is required.
  * \param[in] restart How many restarts are permitted
  * \param[in] verbosity See the Anasazi documentation
  *
  * \return The spectral radius of the matrix.  If the algorithm didn't converge the
  *         number is the negative of the ritz-values. If a <code>NaN</code> is returned
  *         there was a problem constructing the Anasazi problem
  */
double computeSpectralRad(const Teuchos::RCP<const Thyra::LinearOpBase<double> > & A,double tol,
                          bool isHermitian=false,int numBlocks=5,int restart=0,int verbosity=0);

/** \brief Compute the smallest eigenvalue of an operator
  *
  * Compute the smallest eigenvalue of matrix A.  This utilizes the 
  * Trilinos-Anasazi BlockKrylovShcur method for computing eigenvalues.
  * It attempts to compute the smallest (in magnitude) eigenvalue to a given
  * level of tolerance.
  *
  * \param[in] A   matrix whose spectral radius is needed
  * \param[in] tol The <em>most</em> accuracy needed (the algorithm will run until
  *            it reaches this level of accuracy and then it will quit).
  *            If this level is not reached it will return something to indicate
  *            it has not converged.
  * \param[in] isHermitian Is the matrix Hermitian
  * \param[in] numBlocks The size of the orthogonal basis built (like in GMRES) before
  *                  restarting.  Increase the memory usage by O(restart*n). At least
  *                  restart=3 is required.
  * \param[in] restart How many restarts are permitted
  * \param[in] verbosity See the Anasazi documentation
  *
  * \return The smallest magnitude eigenvalue of the matrix.  If the algorithm didn't converge the
  *         number is the negative of the ritz-values. If a <code>NaN</code> is returned
  *         there was a problem constructing the Anasazi problem
  */
double computeSmallestMagEig(const Teuchos::RCP<const Thyra::LinearOpBase<double> > & A, double tol,
                          bool isHermitian=false,int numBlocks=5,int restart=0,int verbosity=0);

//! Type describing the type of diagonal to construct. 
typedef enum {  Diagonal     //! Specifies that just the diagonal is used
              , Lumped       //! Specifies that row sum is used to form a diagonal
              , AbsRowSum    //! Specifies that the \f$i^{th}\f$ diagonal entry is \f$\sum_j |A_{ij}|\f$
	      , BlkDiag      //! Specifies that a block diagonal approximation is to be used
              , NotDiag      //! For user convenience, if Teko recieves this value, exceptions will be thrown	      
              } DiagonalType;

/** Get a diagonal operator from a matrix. The mechanism for computing
  * the diagonal is specified by a <code>DiagonalType</code> arugment.
  *
  * \param[in] A <code>Epetra_CrsMatrix</code> to extract the diagonal from.
  * \param[in] dt Specifies the type of diagonal that is desired.
  *
  * \returns A diagonal operator.
  */
ModifiableLinearOp getDiagonalOp(const Teko::LinearOp & A,const DiagonalType & dt);

/** Get the inverse of a diagonal operator from a matrix. The mechanism for computing
  * the diagonal is specified by a <code>DiagonalType</code> arugment.
  *
  * \param[in] A <code>Epetra_CrsMatrix</code> to extract the diagonal from.
  * \param[in] dt Specifies the type of diagonal that is desired.
  *
  * \returns A inverse of a diagonal operator.
  */
ModifiableLinearOp getInvDiagonalOp(const Teko::LinearOp & A,const DiagonalType & dt);

/** \brief Get the diagonal of a sparse linear operator
  *
  * \param[in] Op Sparse linear operator to get diagonal of
  * \param[in] dt Type of diagonal operator required.
  */
const MultiVector getDiagonal(const LinearOp & op,const DiagonalType & dt);

/** Get a string corresponding to the type of digaonal specified.
  *
  * \param[in] dt The type of diagonal.
  *
  * \returns A string name representing this diagonal type.
  */
std::string getDiagonalName(const DiagonalType & dt);

/** Get a type corresponding to the name of a diagonal specified.
  *
  * \param[in] name String representing the diagonal type
  *
  * \returns The type representation of the string, if the
  *          string is not recognized this function returns
  *          a <code>NotDiag</code>
  */
DiagonalType getDiagonalType(std::string name);

LinearOp probe(Teuchos::RCP<const Epetra_CrsGraph> &G, const LinearOp & Op);

/** Get the one norm of the vector
  */
double norm_1(const MultiVector & v,std::size_t col);

/** Get the two norm of the vector
  */
double norm_2(const MultiVector & v,std::size_t col);

/** This replaces entries of a vector falling below a particular
  * bound. Thus a an entry will be greater than or equal to \code{lowerBound}.
  */
void clipLower(MultiVector & v,double lowerBound);

/** This replaces entries of a vector above a particular
  * bound. Thus a an entry will be less than or equal to \code{upperBound}.
  */
void clipUpper(MultiVector & v,double upperBound);

/** This replaces entries of a vector equal to a particular value
  * with a new value.
  */
void replaceValue(MultiVector & v,double currentValue,double newValue);

/** Compute the averages of each column of the multivector.
  */
void columnAverages(const MultiVector & v,std::vector<double> & averages);

/** Compute the average of the solution.
  */
double average(const MultiVector & v);

} // end namespace Teko

#ifdef _MSC_VER
#ifdef TEKO_DEFINED_MSC_EXTENSIONS
#undef _MSC_EXTENSIONS
#endif
#endif

#endif