Teuchos_SerialDenseMatrix.hpp

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// @HEADER
// *****************************************************************************
//                    Teuchos: Common Tools Package
//
// Copyright 2004 NTESS and the Teuchos contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER
 
#ifndef _TEUCHOS_SERIALDENSEMATRIX_HPP_
#define _TEUCHOS_SERIALDENSEMATRIX_HPP_
#include "Teuchos_CompObject.hpp"
#include "Teuchos_BLAS.hpp"
#include "Teuchos_ScalarTraits.hpp"
#include "Teuchos_DataAccess.hpp"
#include "Teuchos_ConfigDefs.hpp"
#include "Teuchos_Assert.hpp"
#include "Teuchos_SerialSymDenseMatrix.hpp"
#include <cstddef>
#include <utility>
 
namespace Teuchos {
 
template<typename OrdinalType, typename ScalarType>
class SerialDenseMatrix : public CompObject, public BLAS<OrdinalType, ScalarType>
{
public:
 
  typedef OrdinalType ordinalType;
  typedef ScalarType scalarType;
 
 
 
 
  SerialDenseMatrix() = default;
 
 
  SerialDenseMatrix(OrdinalType numRows, OrdinalType numCols, bool zeroOut = true);
 
 
  SerialDenseMatrix(DataAccess CV, ScalarType* values, OrdinalType stride, OrdinalType numRows, OrdinalType numCols);
 
 
  SerialDenseMatrix(const SerialDenseMatrix<OrdinalType, ScalarType> &Source, ETransp trans = Teuchos::NO_TRANS);
 
 
  SerialDenseMatrix(DataAccess CV, const SerialDenseMatrix<OrdinalType, ScalarType> &Source);
 
 
  SerialDenseMatrix(DataAccess CV, const SerialDenseMatrix<OrdinalType, ScalarType> &Source, OrdinalType numRows, OrdinalType numCols, OrdinalType startRow=0, OrdinalType startCol=0);
 
  virtual ~SerialDenseMatrix();
 
 
 
  int shape(OrdinalType numRows, OrdinalType numCols);
 
  int shapeUninitialized(OrdinalType numRows, OrdinalType numCols);
 
 
  int reshape(OrdinalType numRows, OrdinalType numCols);
 
 
 
 
 
 
  SerialDenseMatrix<OrdinalType, ScalarType>& operator= (const SerialDenseMatrix<OrdinalType, ScalarType>& Source);
 
 
  SerialDenseMatrix<OrdinalType, ScalarType>& assign (const SerialDenseMatrix<OrdinalType, ScalarType>& Source);
 
 
  SerialDenseMatrix<OrdinalType, ScalarType>& operator= (const ScalarType value) { putScalar(value); return(*this); }
 
 
  int putScalar( const ScalarType value = Teuchos::ScalarTraits<ScalarType>::zero() );
 
 
  void swap (SerialDenseMatrix<OrdinalType, ScalarType> &B);
 
  int random();
 
 
 
 
 
  ScalarType& operator () (OrdinalType rowIndex, OrdinalType colIndex);
 
 
  const ScalarType& operator () (OrdinalType rowIndex, OrdinalType colIndex) const;
 
 
  ScalarType* operator [] (OrdinalType colIndex);
 
 
  const ScalarType* operator [] (OrdinalType colIndex) const;
 
 
  ScalarType* values() const { return values_; }
 
 
 
 
 
  SerialDenseMatrix<OrdinalType, ScalarType>& operator+= (const SerialDenseMatrix<OrdinalType, ScalarType>& Source);
 
 
  SerialDenseMatrix<OrdinalType, ScalarType>& operator-= (const SerialDenseMatrix<OrdinalType, ScalarType>& Source);
 
 
  SerialDenseMatrix<OrdinalType, ScalarType>& operator*= (const ScalarType alpha);
 
 
  int scale ( const ScalarType alpha );
 
 
  int scale ( const SerialDenseMatrix<OrdinalType, ScalarType>& A );
 
 
  int multiply (ETransp transa, ETransp transb, ScalarType alpha, const SerialDenseMatrix<OrdinalType, ScalarType> &A, const SerialDenseMatrix<OrdinalType, ScalarType> &B, ScalarType beta);
 
 
  int multiply (ESide sideA, ScalarType alpha, const SerialSymDenseMatrix<OrdinalType, ScalarType> &A, const SerialDenseMatrix<OrdinalType, ScalarType> &B, ScalarType beta);
 
 
 
 
 
  bool operator== (const SerialDenseMatrix<OrdinalType, ScalarType> &Operand) const;
 
 
  bool operator!= (const SerialDenseMatrix<OrdinalType, ScalarType> &Operand) const;
 
 
 
 
  OrdinalType numRows() const { return(numRows_); }
 
  OrdinalType numCols() const { return(numCols_); }
 
  OrdinalType stride() const { return(stride_); }
 
  bool empty() const { return(numRows_ == 0 || numCols_ == 0); }
 
 
 
  typename ScalarTraits<ScalarType>::magnitudeType normOne() const;
 
  typename ScalarTraits<ScalarType>::magnitudeType normInf() const;
 
  typename ScalarTraits<ScalarType>::magnitudeType normFrobenius() const;
 
 
 
  virtual std::ostream& print(std::ostream& os) const;
 
protected:
  void copyMat(ScalarType* inputMatrix, OrdinalType strideInput,
    OrdinalType numRows, OrdinalType numCols, ScalarType* outputMatrix,
    OrdinalType strideOutput, OrdinalType startRow, OrdinalType startCol,
    ScalarType alpha = ScalarTraits<ScalarType>::zero() );
  void deleteArrays();
  void checkIndex( OrdinalType rowIndex, OrdinalType colIndex = 0 ) const;
 
  static ScalarType*
  allocateValues(const OrdinalType numRows,
                 const OrdinalType numCols)
  {
    const size_t size = size_t(numRows) * size_t(numCols);
    if (size > 0)
      return new ScalarType[size];
    else
      return nullptr;
  }
 
  OrdinalType numRows_ = 0;
  OrdinalType numCols_ = 0;
  OrdinalType stride_ = 0;
  bool valuesCopied_ = false;
  ScalarType* values_ = nullptr;
}; // class Teuchos_SerialDenseMatrix
 
//----------------------------------------------------------------------------------------------------
//  Constructors and Destructor
//----------------------------------------------------------------------------------------------------
 
template<typename OrdinalType, typename ScalarType>
SerialDenseMatrix<OrdinalType, ScalarType>::SerialDenseMatrix(
  OrdinalType numRows_in, OrdinalType numCols_in, bool zeroOut
  )
  : numRows_(numRows_in),
    numCols_(numCols_in),
    stride_(numRows_in),
    valuesCopied_(true),
    values_(allocateValues(numRows_in, numCols_in))
{
  if (zeroOut) {
    putScalar();
  }
}
 
template<typename OrdinalType, typename ScalarType>
SerialDenseMatrix<OrdinalType, ScalarType>::SerialDenseMatrix(
  DataAccess CV, ScalarType* values_in, OrdinalType stride_in, OrdinalType numRows_in,
  OrdinalType numCols_in
  )
  : numRows_(numRows_in),
    numCols_(numCols_in),
    stride_(stride_in),
    valuesCopied_(false),
    values_(values_in)
{
  if(CV == Copy)
  {
    stride_ = numRows_;
    values_ = allocateValues(stride_, numCols_);
    copyMat(values_in, stride_in, numRows_, numCols_, values_, stride_, 0, 0);
    valuesCopied_ = true;
  }
}
 
template<typename OrdinalType, typename ScalarType>
SerialDenseMatrix<OrdinalType, ScalarType>::SerialDenseMatrix(const SerialDenseMatrix<OrdinalType, ScalarType> &Source, ETransp trans)
  : CompObject(Source),
    BLAS<OrdinalType, ScalarType>(Source),
    valuesCopied_(true)
{
  if ( trans == Teuchos::NO_TRANS )
  {
    numRows_ = Source.numRows_;
    numCols_ = Source.numCols_;
 
    if (!Source.valuesCopied_)
    {
      stride_ = Source.stride_;
      values_ = Source.values_;
      valuesCopied_ = false;
    }
    else
    {
      stride_ = numRows_;
      if(stride_ > 0 && numCols_ > 0) {
        values_ = allocateValues(stride_, numCols_);
        copyMat(Source.values_, Source.stride_, numRows_, numCols_, values_, stride_, 0, 0);
      }
      else {
        numRows_ = 0; numCols_ = 0; stride_ = 0;
        valuesCopied_ = false;
      }
    }
  }
  else if ( trans == Teuchos::CONJ_TRANS && ScalarTraits<ScalarType>::isComplex )
  {
    numRows_ = Source.numCols_;
    numCols_ = Source.numRows_;
    stride_ = numRows_;
    values_ = allocateValues(stride_, numCols_);
    for (OrdinalType j=0; j<numCols_; j++) {
      for (OrdinalType i=0; i<numRows_; i++) {
        values_[j*stride_ + i] = Teuchos::ScalarTraits<ScalarType>::conjugate(Source.values_[i*Source.stride_ + j]);
      }
    }
  }
  else
  {
    numRows_ = Source.numCols_;
    numCols_ = Source.numRows_;
    stride_ = numRows_;
    values_ = allocateValues(stride_, numCols_);
    for (OrdinalType j=0; j<numCols_; j++) {
      for (OrdinalType i=0; i<numRows_; i++) {
        values_[j*stride_ + i] = Source.values_[i*Source.stride_ + j];
      }
    }
  }
}
 
 
template<typename OrdinalType, typename ScalarType>
SerialDenseMatrix<OrdinalType, ScalarType>::SerialDenseMatrix(
  DataAccess CV, const SerialDenseMatrix<OrdinalType, ScalarType> &Source
  )
  : numRows_(Source.numRows_), numCols_(Source.numCols_), stride_(Source.stride_),
    valuesCopied_(false), values_(Source.values_)
{
  if(CV == Copy)
  {
    stride_ = numRows_;
    values_ = allocateValues(stride_, numCols_);
    copyMat(Source.values_, Source.stride_, numRows_, numCols_, values_, stride_, 0, 0);
    valuesCopied_ = true;
  }
}
 
 
template<typename OrdinalType, typename ScalarType>
SerialDenseMatrix<OrdinalType, ScalarType>::SerialDenseMatrix(
  DataAccess CV, const SerialDenseMatrix<OrdinalType, ScalarType> &Source,
  OrdinalType numRows_in, OrdinalType numCols_in, OrdinalType startRow,
  OrdinalType startCol
  )
  : CompObject(), numRows_(numRows_in), numCols_(numCols_in), stride_(Source.stride_),
    valuesCopied_(false), values_(Source.values_)
{
  if(CV == Copy)
  {
    stride_ = numRows_in;
    values_ = allocateValues(stride_, numCols_in);
    copyMat(Source.values_, Source.stride_, numRows_in, numCols_in, values_, stride_, startRow, startCol);
    valuesCopied_ = true;
  }
  else // CV == View
  {
    values_ = values_ + (stride_ * startCol) + startRow;
  }
}
 
template<typename OrdinalType, typename ScalarType>
SerialDenseMatrix<OrdinalType, ScalarType>::~SerialDenseMatrix()
{
  deleteArrays();
}
 
//----------------------------------------------------------------------------------------------------
//  Shape methods
//----------------------------------------------------------------------------------------------------
 
template<typename OrdinalType, typename ScalarType>
int SerialDenseMatrix<OrdinalType, ScalarType>::shape(
  OrdinalType numRows_in, OrdinalType numCols_in
  )
{
  deleteArrays(); // Get rid of anything that might be already allocated
  numRows_ = numRows_in;
  numCols_ = numCols_in;
  stride_ = numRows_;
  values_ = allocateValues(stride_, numCols_);
  putScalar();
  valuesCopied_ = true;
  return(0);
}
 
template<typename OrdinalType, typename ScalarType>
int SerialDenseMatrix<OrdinalType, ScalarType>::shapeUninitialized(
  OrdinalType numRows_in, OrdinalType numCols_in
  )
{
  deleteArrays(); // Get rid of anything that might be already allocated
  numRows_ = numRows_in;
  numCols_ = numCols_in;
  stride_ = numRows_;
  values_ = allocateValues(stride_, numCols_);
  valuesCopied_ = true;
  return(0);
}
 
template<typename OrdinalType, typename ScalarType>
int SerialDenseMatrix<OrdinalType, ScalarType>::reshape(
  OrdinalType numRows_in, OrdinalType numCols_in
  )
{
  // Allocate space for new matrix
  ScalarType* values_tmp = allocateValues(numRows_in, numCols_in);
  ScalarType zero = ScalarTraits<ScalarType>::zero();
  for(OrdinalType k = 0; k < numRows_in * numCols_in; k++)
  {
    values_tmp[k] = zero;
  }
  OrdinalType numRows_tmp = TEUCHOS_MIN(numRows_, numRows_in);
  OrdinalType numCols_tmp = TEUCHOS_MIN(numCols_, numCols_in);
  if(values_ != 0)
  {
    copyMat(values_, stride_, numRows_tmp, numCols_tmp, values_tmp,
      numRows_in, 0, 0); // Copy principal submatrix of A to new A
  }
  deleteArrays(); // Get rid of anything that might be already allocated
  numRows_ = numRows_in;
  numCols_ = numCols_in;
  stride_ = numRows_;
  values_ = values_tmp; // Set pointer to new A
  valuesCopied_ = true;
  return(0);
}
 
//----------------------------------------------------------------------------------------------------
//   Set methods
//----------------------------------------------------------------------------------------------------
 
template<typename OrdinalType, typename ScalarType>
int SerialDenseMatrix<OrdinalType, ScalarType>::putScalar( const ScalarType value_in )
{
  // Set each value of the dense matrix to "value".
  for(OrdinalType j = 0; j < numCols_; j++)
  {
    for(OrdinalType i = 0; i < numRows_; i++)
          {
            values_[i + j*stride_] = value_in;
          }
  }
  return 0;
}
 
template<typename OrdinalType, typename ScalarType> void
SerialDenseMatrix<OrdinalType, ScalarType>::swap(
  SerialDenseMatrix<OrdinalType, ScalarType> &B)
{
  // Notes:
  // > DefaultBLASImpl::SWAP() uses a deep copy. This fn uses a pointer swap.
  // > this fn covers both Vector and Matrix, such that some care must be
  //   employed to not swap across types (creating a Vector with non-unitary
  //   numCols_)
  // > Inherited data that is not currently swapped (since inactive/deprecated):
  //   >> Teuchos::CompObject:
  //        Flops *flopCounter_ [Note: all SerialDenseMatrix ctors initialize a
  //        NULL flop-counter using CompObject(), such that any flop increments
  //        that are computed are not accumulated.]
  //   >> Teuchos::Object: (now removed from inheritance list)
  //        static int tracebackMode (no swap for statics)
  //        std::string label_ (has been reported as a cause of memory overhead)
 
  std::swap(values_ ,      B.values_);
  std::swap(numRows_,      B.numRows_);
  std::swap(numCols_,      B.numCols_);
  std::swap(stride_,       B.stride_);
  std::swap(valuesCopied_, B.valuesCopied_);
}
 
template<typename OrdinalType, typename ScalarType>
int SerialDenseMatrix<OrdinalType, ScalarType>::random()
{
  // Set each value of the dense matrix to a random value.
  for(OrdinalType j = 0; j < numCols_; j++)
  {
    for(OrdinalType i = 0; i < numRows_; i++)
          {
            values_[i + j*stride_] = ScalarTraits<ScalarType>::random();
          }
  }
  return 0;
}
 
template<typename OrdinalType, typename ScalarType>
SerialDenseMatrix<OrdinalType,ScalarType>&
SerialDenseMatrix<OrdinalType, ScalarType>::operator=(
  const SerialDenseMatrix<OrdinalType,ScalarType>& Source
  )
{
  if(this == &Source)
    return(*this); // Special case of source same as target
  if((!valuesCopied_) && (!Source.valuesCopied_) && (values_ == Source.values_))
    return(*this); // Special case of both are views to same data.
 
  // If the source is a view then we will return a view, else we will return a copy.
  if (!Source.valuesCopied_) {
    if(valuesCopied_)       {
      // Clean up stored data if this was previously a copy.
      deleteArrays();
    }
    numRows_ = Source.numRows_;
    numCols_ = Source.numCols_;
    stride_ = Source.stride_;
    values_ = Source.values_;
  }
  else {
    // If we were a view, we will now be a copy.
    if(!valuesCopied_) {
      numRows_ = Source.numRows_;
      numCols_ = Source.numCols_;
      stride_ = Source.numRows_;
      if(stride_ > 0 && numCols_ > 0) {
        values_ = allocateValues(stride_, numCols_);
        valuesCopied_ = true;
      }
      else {
        values_ = 0;
      }
    }
    // If we were a copy, we will stay a copy.
    else {
      if((Source.numRows_ <= stride_) && (Source.numCols_ == numCols_)) { // we don't need to reallocate
        numRows_ = Source.numRows_;
        numCols_ = Source.numCols_;
      }
      else { // we need to allocate more space (or less space)
        deleteArrays();
        numRows_ = Source.numRows_;
        numCols_ = Source.numCols_;
        stride_ = Source.numRows_;
        if(stride_ > 0 && numCols_ > 0) {
          values_ = allocateValues(stride_, numCols_);
          valuesCopied_ = true;
        }
      }
    }
    copyMat(Source.values_, Source.stride_, numRows_, numCols_, values_, stride_, 0, 0);
  }
  return(*this);
}
 
template<typename OrdinalType, typename ScalarType>
SerialDenseMatrix<OrdinalType, ScalarType>& SerialDenseMatrix<OrdinalType, ScalarType>::operator+= (const SerialDenseMatrix<OrdinalType,ScalarType>& Source )
{
  // Check for compatible dimensions
  if ((numRows_ != Source.numRows_) || (numCols_ != Source.numCols_))
  {
    TEUCHOS_CHK_REF(*this); // Return *this without altering it.
  }
  copyMat(Source.values_, Source.stride_, numRows_, numCols_, values_, stride_, 0, 0, ScalarTraits<ScalarType>::one());
  return(*this);
}
 
template<typename OrdinalType, typename ScalarType>
SerialDenseMatrix<OrdinalType, ScalarType>& SerialDenseMatrix<OrdinalType, ScalarType>::operator-= (const SerialDenseMatrix<OrdinalType,ScalarType>& Source )
{
  // Check for compatible dimensions
  if ((numRows_ != Source.numRows_) || (numCols_ != Source.numCols_))
  {
    TEUCHOS_CHK_REF(*this); // Return *this without altering it.
  }
  copyMat(Source.values_, Source.stride_, numRows_, numCols_, values_, stride_, 0, 0, -ScalarTraits<ScalarType>::one());
  return(*this);
}
 
template<typename OrdinalType, typename ScalarType>
SerialDenseMatrix<OrdinalType,ScalarType>& SerialDenseMatrix<OrdinalType, ScalarType>::assign (const SerialDenseMatrix<OrdinalType,ScalarType>& Source) {
  if(this == &Source)
    return(*this); // Special case of source same as target
  if((!valuesCopied_) && (!Source.valuesCopied_) && (values_ == Source.values_))
    return(*this); // Special case of both are views to same data.
 
  // Check for compatible dimensions
  if ((numRows_ != Source.numRows_) || (numCols_ != Source.numCols_))
  {
    TEUCHOS_CHK_REF(*this); // Return *this without altering it.
  }
  copyMat(Source.values_, Source.stride_, numRows_, numCols_, values_, stride_, 0, 0);
  return(*this);
}
 
//----------------------------------------------------------------------------------------------------
//   Accessor methods
//----------------------------------------------------------------------------------------------------
 
template<typename OrdinalType, typename ScalarType>
inline ScalarType& SerialDenseMatrix<OrdinalType, ScalarType>::operator () (OrdinalType rowIndex, OrdinalType colIndex)
{
#ifdef HAVE_TEUCHOS_ARRAY_BOUNDSCHECK
  checkIndex( rowIndex, colIndex );
#endif
  return(values_[colIndex * stride_ + rowIndex]);
}
 
template<typename OrdinalType, typename ScalarType>
inline const ScalarType& SerialDenseMatrix<OrdinalType, ScalarType>::operator () (OrdinalType rowIndex, OrdinalType colIndex) const
{
#ifdef HAVE_TEUCHOS_ARRAY_BOUNDSCHECK
  checkIndex( rowIndex, colIndex );
#endif
  return(values_[colIndex * stride_ + rowIndex]);
}
 
template<typename OrdinalType, typename ScalarType>
inline const ScalarType* SerialDenseMatrix<OrdinalType, ScalarType>::operator [] (OrdinalType colIndex) const
{
#ifdef HAVE_TEUCHOS_ARRAY_BOUNDSCHECK
  checkIndex( 0, colIndex );
#endif
  return(values_ + colIndex * stride_);
}
 
template<typename OrdinalType, typename ScalarType>
inline ScalarType* SerialDenseMatrix<OrdinalType, ScalarType>::operator [] (OrdinalType colIndex)
{
#ifdef HAVE_TEUCHOS_ARRAY_BOUNDSCHECK
  checkIndex( 0, colIndex );
#endif
  return(values_ + colIndex * stride_);
}
 
//----------------------------------------------------------------------------------------------------
//   Norm methods
//----------------------------------------------------------------------------------------------------
 
template<typename OrdinalType, typename ScalarType>
typename ScalarTraits<ScalarType>::magnitudeType SerialDenseMatrix<OrdinalType, ScalarType>::normOne() const
{
  OrdinalType i, j;
  typename ScalarTraits<ScalarType>::magnitudeType anorm = ScalarTraits<ScalarType>::magnitude(ScalarTraits<ScalarType>::zero());
  typename ScalarTraits<ScalarType>::magnitudeType absSum = ScalarTraits<ScalarType>::magnitude(ScalarTraits<ScalarType>::zero());
  ScalarType* ptr;
  for(j = 0; j < numCols_; j++)
  {
    ScalarType sum = 0;
    ptr = values_ + j * stride_;
    for(i = 0; i < numRows_; i++)
          {
            sum += ScalarTraits<ScalarType>::magnitude(*ptr++);
          }
    absSum = ScalarTraits<ScalarType>::magnitude(sum);
    if(absSum > anorm)
          {
            anorm = absSum;
          }
  }
  // don't compute flop increment unless there is an accumulator
  if (flopCounter_!=0) updateFlops(numRows_ * numCols_);
  return(anorm);
}
 
template<typename OrdinalType, typename ScalarType>
typename ScalarTraits<ScalarType>::magnitudeType SerialDenseMatrix<OrdinalType, ScalarType>::normInf() const
{
  OrdinalType i, j;
  typename ScalarTraits<ScalarType>::magnitudeType sum, anorm = ScalarTraits<ScalarType>::magnitude(ScalarTraits<ScalarType>::zero());
 
  for (i = 0; i < numRows_; i++) {
    sum = ScalarTraits<ScalarType>::magnitude(ScalarTraits<ScalarType>::zero());
    for (j=0; j< numCols_; j++) {
      sum += ScalarTraits<ScalarType>::magnitude(*(values_+i+j*stride_));
    }
    anorm = TEUCHOS_MAX( anorm, sum );
  }
  // don't compute flop increment unless there is an accumulator
  if (flopCounter_!=0) updateFlops(numRows_ * numCols_);
  return(anorm);
}
 
template<typename OrdinalType, typename ScalarType>
typename ScalarTraits<ScalarType>::magnitudeType SerialDenseMatrix<OrdinalType, ScalarType>::normFrobenius() const
{
  OrdinalType i, j;
  typename ScalarTraits<ScalarType>::magnitudeType anorm = ScalarTraits<ScalarType>::magnitude(ScalarTraits<ScalarType>::zero());
  for (j = 0; j < numCols_; j++) {
    for (i = 0; i < numRows_; i++) {
      anorm += ScalarTraits<ScalarType>::magnitude(values_[i+j*stride_]*values_[i+j*stride_]);
    }
  }
  anorm = ScalarTraits<ScalarType>::magnitude(ScalarTraits<ScalarType>::squareroot(anorm));
  // don't compute flop increment unless there is an accumulator
  if (flopCounter_!=0) updateFlops(numRows_ * numCols_);
  return(anorm);
}
 
//----------------------------------------------------------------------------------------------------
//   Comparison methods
//----------------------------------------------------------------------------------------------------
 
template<typename OrdinalType, typename ScalarType>
bool SerialDenseMatrix<OrdinalType, ScalarType>::operator== (const SerialDenseMatrix<OrdinalType, ScalarType> &Operand) const
{
  bool result = 1;
  if((numRows_ != Operand.numRows_) || (numCols_ != Operand.numCols_))
  {
    result = 0;
  }
  else
  {
    OrdinalType i, j;
    for(i = 0; i < numRows_; i++)
          {
            for(j = 0; j < numCols_; j++)
      {
        if((*this)(i, j) != Operand(i, j))
        {
          return 0;
        }
      }
          }
  }
  return result;
}
 
template<typename OrdinalType, typename ScalarType>
bool SerialDenseMatrix<OrdinalType, ScalarType>::operator!= (const SerialDenseMatrix<OrdinalType, ScalarType> &Operand) const
{
  return !((*this) == Operand);
}
 
//----------------------------------------------------------------------------------------------------
//   Multiplication method
//----------------------------------------------------------------------------------------------------
 
template<typename OrdinalType, typename ScalarType>
SerialDenseMatrix<OrdinalType, ScalarType>& SerialDenseMatrix<OrdinalType, ScalarType>::operator*= (const ScalarType alpha )
{
  this->scale( alpha );
  return(*this);
}
 
template<typename OrdinalType, typename ScalarType>
int SerialDenseMatrix<OrdinalType, ScalarType>::scale( const ScalarType alpha )
{
  OrdinalType i, j;
  ScalarType* ptr;
 
  for (j=0; j<numCols_; j++) {
    ptr = values_ + j*stride_;
    for (i=0; i<numRows_; i++) { *ptr = alpha * (*ptr); ptr++; }
  }
  // don't compute flop increment unless there is an accumulator
  if (flopCounter_!=0) updateFlops( numRows_*numCols_ );
  return(0);
}
 
template<typename OrdinalType, typename ScalarType>
int SerialDenseMatrix<OrdinalType, ScalarType>::scale( const SerialDenseMatrix<OrdinalType,ScalarType>& A )
{
  OrdinalType i, j;
  ScalarType* ptr;
 
  // Check for compatible dimensions
  if ((numRows_ != A.numRows_) || (numCols_ != A.numCols_))
  {
    TEUCHOS_CHK_ERR(-1); // Return error
  }
  for (j=0; j<numCols_; j++) {
    ptr = values_ + j*stride_;
    for (i=0; i<numRows_; i++) { *ptr = A(i,j) * (*ptr); ptr++; }
  }
  // don't compute flop increment unless there is an accumulator
  if (flopCounter_!=0) updateFlops( numRows_*numCols_ );
  return(0);
}
 
template<typename OrdinalType, typename ScalarType>
int  SerialDenseMatrix<OrdinalType, ScalarType>::multiply(ETransp transa, ETransp transb, ScalarType alpha, const SerialDenseMatrix<OrdinalType, ScalarType> &A, const SerialDenseMatrix<OrdinalType, ScalarType> &B, ScalarType beta)
{
  // Check for compatible dimensions
  OrdinalType A_nrows = (ETranspChar[transa]!='N') ? A.numCols() : A.numRows();
  OrdinalType A_ncols = (ETranspChar[transa]!='N') ? A.numRows() : A.numCols();
  OrdinalType B_nrows = (ETranspChar[transb]!='N') ? B.numCols() : B.numRows();
  OrdinalType B_ncols = (ETranspChar[transb]!='N') ? B.numRows() : B.numCols();
  if ((numRows_ != A_nrows) || (A_ncols != B_nrows) || (numCols_ != B_ncols))
  {
    TEUCHOS_CHK_ERR(-1); // Return error
  }
  // Call GEMM function
  this->GEMM(transa, transb, numRows_, numCols_, A_ncols, alpha, A.values(), A.stride(), B.values(), B.stride(), beta, values_, stride_);
 
  // don't compute flop increment unless there is an accumulator
  if (flopCounter_!=0) {
    double nflops = 2 * numRows_;
    nflops *= numCols_;
    nflops *= A_ncols;
    updateFlops(nflops);
  }
  return(0);
}
 
template<typename OrdinalType, typename ScalarType>
int SerialDenseMatrix<OrdinalType, ScalarType>::multiply (ESide sideA, ScalarType alpha, const SerialSymDenseMatrix<OrdinalType, ScalarType> &A, const SerialDenseMatrix<OrdinalType, ScalarType> &B, ScalarType beta)
{
  // Check for compatible dimensions
  OrdinalType A_nrows = A.numRows(), A_ncols = A.numCols();
  OrdinalType B_nrows = B.numRows(), B_ncols = B.numCols();
 
  if (ESideChar[sideA]=='L') {
    if ((numRows_ != A_nrows) || (A_ncols != B_nrows) || (numCols_ != B_ncols)) {
      TEUCHOS_CHK_ERR(-1); // Return error
    }
  } else {
    if ((numRows_ != B_nrows) || (B_ncols != A_nrows) || (numCols_ != A_ncols)) {
      TEUCHOS_CHK_ERR(-1); // Return error
    }
  }
 
  // Call SYMM function
  EUplo uplo = (A.upper() ? Teuchos::UPPER_TRI : Teuchos::LOWER_TRI);
  this->SYMM(sideA, uplo, numRows_, numCols_, alpha, A.values(), A.stride(), B.values(), B.stride(), beta, values_, stride_);
 
  // don't compute flop increment unless there is an accumulator
  if (flopCounter_!=0) {
    double nflops = 2 * numRows_;
    nflops *= numCols_;
    nflops *= A_ncols;
    updateFlops(nflops);
  }
  return(0);
}
 
template<typename OrdinalType, typename ScalarType>
std::ostream& SerialDenseMatrix<OrdinalType, ScalarType>::print(std::ostream& os) const
{
  os << std::endl;
  if(valuesCopied_)
    os << "Values_copied : yes" << std::endl;
  else
    os << "Values_copied : no" << std::endl;
  os << "Rows : " << numRows_ << std::endl;
  os << "Columns : " << numCols_ << std::endl;
  os << "LDA : " << stride_ << std::endl;
  if(numRows_ == 0 || numCols_ == 0) {
    os << "(matrix is empty, no values to display)" << std::endl;
  } else {
    for(OrdinalType i = 0; i < numRows_; i++) {
      for(OrdinalType j = 0; j < numCols_; j++){
        os << (*this)(i,j) << " ";
      }
      os << std::endl;
    }
  }
  return os;
}
 
//----------------------------------------------------------------------------------------------------
//   Protected methods
//----------------------------------------------------------------------------------------------------
 
template<typename OrdinalType, typename ScalarType>
inline void SerialDenseMatrix<OrdinalType, ScalarType>::checkIndex( OrdinalType rowIndex, OrdinalType colIndex ) const {
  TEUCHOS_TEST_FOR_EXCEPTION(rowIndex < 0 || rowIndex >= numRows_, std::out_of_range,
    "SerialDenseMatrix<T>::checkIndex: "
    "Row index " << rowIndex << " out of range [0, "<< numRows_ << ")");
  TEUCHOS_TEST_FOR_EXCEPTION(colIndex < 0 || colIndex >= numCols_, std::out_of_range,
    "SerialDenseMatrix<T>::checkIndex: "
    "Col index " << colIndex << " out of range [0, "<< numCols_ << ")");
}
 
template<typename OrdinalType, typename ScalarType>
void SerialDenseMatrix<OrdinalType, ScalarType>::deleteArrays(void)
{
  if (valuesCopied_)
  {
    delete [] values_;
    values_ = 0;
    valuesCopied_ = false;
  }
}
 
template<typename OrdinalType, typename ScalarType>
void SerialDenseMatrix<OrdinalType, ScalarType>::copyMat(
  ScalarType* inputMatrix, OrdinalType strideInput, OrdinalType numRows_in,
  OrdinalType numCols_in, ScalarType* outputMatrix, OrdinalType strideOutput,
  OrdinalType startRow, OrdinalType startCol, ScalarType alpha
  )
{
  OrdinalType i, j;
  ScalarType* ptr1 = 0;
  ScalarType* ptr2 = 0;
  for(j = 0; j < numCols_in; j++) {
    ptr1 = outputMatrix + (j * strideOutput);
    ptr2 = inputMatrix + (j + startCol) * strideInput + startRow;
    if (alpha != Teuchos::ScalarTraits<ScalarType>::zero() ) {
      for(i = 0; i < numRows_in; i++)
            {
              *ptr1++ += alpha*(*ptr2++);
            }
    } else {
      for(i = 0; i < numRows_in; i++)
            {
              *ptr1++ = *ptr2++;
            }
    }
  }
}
 
template<typename OrdinalType, typename ScalarType>
struct SerialDenseMatrixPrinter {
public:
  const SerialDenseMatrix<OrdinalType,ScalarType> &obj;
  SerialDenseMatrixPrinter(
        const SerialDenseMatrix<OrdinalType,ScalarType> &obj_in)
      : obj(obj_in) {}
};
 
template<typename OrdinalType, typename ScalarType>
std::ostream&
operator<<(std::ostream &out,
           const SerialDenseMatrixPrinter<OrdinalType,ScalarType> printer)
{
  printer.obj.print(out);
  return out;
}
 
template<typename OrdinalType, typename ScalarType>
SerialDenseMatrixPrinter<OrdinalType,ScalarType>
printMat(const SerialDenseMatrix<OrdinalType,ScalarType> &obj)
{
  return SerialDenseMatrixPrinter<OrdinalType,ScalarType>(obj);
}
 
 
} // namespace Teuchos
 
 
#endif /* _TEUCHOS_SERIALDENSEMATRIX_HPP_ */