Teuchos_SerialDenseSolver.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_SERIALDENSESOLVER_HPP_
#define _TEUCHOS_SERIALDENSESOLVER_HPP_

#include "Teuchos_CompObject.hpp"
#include "Teuchos_BLAS.hpp"
#include "Teuchos_LAPACK.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_ConfigDefs.hpp"
#include "Teuchos_SerialDenseMatrix.hpp"
#include "Teuchos_ScalarTraits.hpp"

#ifdef HAVE_TEUCHOSNUMERICS_EIGEN
#include "Eigen/Dense"
#endif

namespace Teuchos {

  template<typename OrdinalType, typename ScalarType>
  class SerialDenseSolver : public CompObject, public Object, public BLAS<OrdinalType, ScalarType>,
                            public LAPACK<OrdinalType, ScalarType>
  {

  public:

    typedef typename Teuchos::ScalarTraits<ScalarType>::magnitudeType MagnitudeType;
#ifdef HAVE_TEUCHOSNUMERICS_EIGEN
    typedef typename Eigen::Matrix<ScalarType,Eigen::Dynamic,Eigen::Dynamic,Eigen::ColMajor> EigenMatrix;
    typedef typename Eigen::Matrix<ScalarType,Eigen::Dynamic,1> EigenVector;
    typedef typename Eigen::InnerStride<Eigen::Dynamic> EigenInnerStride;
    typedef typename Eigen::OuterStride<Eigen::Dynamic> EigenOuterStride;
    typedef typename Eigen::Map<EigenVector,0,EigenInnerStride > EigenVectorMap;
    typedef typename Eigen::Map<const EigenVector,0,EigenInnerStride > EigenConstVectorMap;
    typedef typename Eigen::Map<EigenMatrix,0,EigenOuterStride > EigenMatrixMap;
    typedef typename Eigen::Map<const EigenMatrix,0,EigenOuterStride > EigenConstMatrixMap;
    typedef typename Eigen::PermutationMatrix<Eigen::Dynamic,Eigen::Dynamic,OrdinalType> EigenPermutationMatrix;
    typedef typename Eigen::Array<OrdinalType,Eigen::Dynamic,1> EigenOrdinalArray;
    typedef typename Eigen::Map<EigenOrdinalArray> EigenOrdinalArrayMap;
    typedef typename Eigen::Array<ScalarType,Eigen::Dynamic,1> EigenScalarArray;
    typedef typename Eigen::Map<EigenScalarArray> EigenScalarArrayMap;
#endif


    SerialDenseSolver();

    virtual ~SerialDenseSolver();



    int setMatrix(const RCP<SerialDenseMatrix<OrdinalType, ScalarType> >& A);


    int setVectors(const RCP<SerialDenseMatrix<OrdinalType, ScalarType> >& X,
                   const RCP<SerialDenseMatrix<OrdinalType, ScalarType> >& B);




    void factorWithEquilibration(bool flag) {equilibrate_ = flag; return;}


    void solveWithTranspose(bool flag) {transpose_ = flag; if (flag) TRANS_ = Teuchos::TRANS; else TRANS_ = Teuchos::NO_TRANS; return;}


    void solveWithTransposeFlag(Teuchos::ETransp trans) {TRANS_ = trans; transpose_ = (trans != Teuchos::NO_TRANS) ? true : false; }


    void solveToRefinedSolution(bool flag) {refineSolution_ = flag; return;}


    void estimateSolutionErrors(bool flag);




    int factor();


    int solve();


    int invert();


    int computeEquilibrateScaling();


    int equilibrateMatrix();


    int equilibrateRHS();


    int applyRefinement();


    int unequilibrateLHS();


     int reciprocalConditionEstimate(MagnitudeType & Value);



    bool transpose() {return(transpose_);}

    bool factored() {return(factored_);}

    bool equilibratedA() {return(equilibratedA_);}

    bool equilibratedB() {return(equilibratedB_);}

     bool shouldEquilibrate() {computeEquilibrateScaling(); return(shouldEquilibrate_);}

    bool solutionErrorsEstimated() {return(solutionErrorsEstimated_);}

    bool inverted() {return(inverted_);}

    bool reciprocalConditionEstimated() {return(reciprocalConditionEstimated_);}

    bool solved() {return(solved_);}

    bool solutionRefined() {return(solutionRefined_);}



    RCP<SerialDenseMatrix<OrdinalType, ScalarType> > getMatrix()  const {return(Matrix_);}

    RCP<SerialDenseMatrix<OrdinalType, ScalarType> > getFactoredMatrix()  const {return(Factor_);}

    RCP<SerialDenseMatrix<OrdinalType, ScalarType> > getLHS() const {return(LHS_);}

    RCP<SerialDenseMatrix<OrdinalType, ScalarType> > getRHS() const {return(RHS_);}

    OrdinalType numRows()  const {return(M_);}

    OrdinalType numCols()  const {return(N_);}

    std::vector<OrdinalType> IPIV()  const {return(IPIV_);}

    MagnitudeType ANORM()  const {return(ANORM_);}

    MagnitudeType RCOND()  const {return(RCOND_);}


    MagnitudeType ROWCND()  const {return(ROWCND_);}


    MagnitudeType COLCND()  const {return(COLCND_);}

    MagnitudeType AMAX()  const {return(AMAX_);}

    std::vector<MagnitudeType> FERR()  const {return(FERR_);}

    std::vector<MagnitudeType> BERR()  const {return(BERR_);}

    std::vector<MagnitudeType> R()  const {return(R_);}

    std::vector<MagnitudeType> C()  const {return(C_);}


    void Print(std::ostream& os) const;
  protected:

    void allocateWORK() { LWORK_ = 4*N_; WORK_.resize( LWORK_ ); return;}
    void resetMatrix();
    void resetVectors();


    bool equilibrate_;
    bool shouldEquilibrate_;
    bool equilibratedA_;
    bool equilibratedB_;
    bool transpose_;
    bool factored_;
    bool estimateSolutionErrors_;
    bool solutionErrorsEstimated_;
    bool solved_;
    bool inverted_;
    bool reciprocalConditionEstimated_;
    bool refineSolution_;
    bool solutionRefined_;

    Teuchos::ETransp TRANS_;

    OrdinalType M_;
    OrdinalType N_;
    OrdinalType Min_MN_;
    OrdinalType LDA_;
    OrdinalType LDAF_;
    OrdinalType INFO_;
    OrdinalType LWORK_;

    std::vector<OrdinalType> IPIV_;

    MagnitudeType ANORM_;
    MagnitudeType RCOND_;
    MagnitudeType ROWCND_;
    MagnitudeType COLCND_;
    MagnitudeType AMAX_;

    RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Matrix_;
    RCP<SerialDenseMatrix<OrdinalType, ScalarType> > LHS_;
    RCP<SerialDenseMatrix<OrdinalType, ScalarType> > RHS_;
    RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Factor_;

    ScalarType * A_;
    ScalarType * AF_;
    std::vector<MagnitudeType> FERR_;
    std::vector<MagnitudeType> BERR_;
    std::vector<ScalarType> WORK_;
    std::vector<MagnitudeType> R_;
    std::vector<MagnitudeType> C_;
#ifdef HAVE_TEUCHOSNUMERICS_EIGEN
    Eigen::PartialPivLU<EigenMatrix> lu_;
#endif

  private:
    // SerialDenseSolver copy constructor (put here because we don't want user access)

    SerialDenseSolver(const SerialDenseSolver<OrdinalType, ScalarType>& Source);
    SerialDenseSolver & operator=(const SerialDenseSolver<OrdinalType, ScalarType>& Source);

  };

  namespace details {

    // Helper traits to distinguish work arrays for real and complex-valued datatypes.
    template<typename T>
    struct lapack_traits {
      typedef int iwork_type;
    };

    // Complex-valued specialization
    template<typename T>
    struct lapack_traits<std::complex<T> > {
      typedef typename ScalarTraits<T>::magnitudeType iwork_type;
    };

  } // end namespace details

//=============================================================================

template<typename OrdinalType, typename ScalarType>
SerialDenseSolver<OrdinalType,ScalarType>::SerialDenseSolver()
  : CompObject(),
    equilibrate_(false),
    shouldEquilibrate_(false),
    equilibratedA_(false),
    equilibratedB_(false),
    transpose_(false),
    factored_(false),
    estimateSolutionErrors_(false),
    solutionErrorsEstimated_(false),
    solved_(false),
    inverted_(false),
    reciprocalConditionEstimated_(false),
    refineSolution_(false),
    solutionRefined_(false),
    TRANS_(Teuchos::NO_TRANS),
    M_(0),
    N_(0),
    Min_MN_(0),
    LDA_(0),
    LDAF_(0),
    INFO_(0),
    LWORK_(0),
    ANORM_(ScalarTraits<MagnitudeType>::zero()),
    RCOND_(ScalarTraits<MagnitudeType>::zero()),
    ROWCND_(ScalarTraits<MagnitudeType>::zero()),
    COLCND_(ScalarTraits<MagnitudeType>::zero()),
    AMAX_(ScalarTraits<MagnitudeType>::zero()),
    A_(0),
    AF_(0)
{
  resetMatrix();
}
//=============================================================================

template<typename OrdinalType, typename ScalarType>
SerialDenseSolver<OrdinalType,ScalarType>::~SerialDenseSolver()
{}

//=============================================================================

template<typename OrdinalType, typename ScalarType>
void SerialDenseSolver<OrdinalType,ScalarType>::resetVectors()
{
  LHS_ = Teuchos::null;
  RHS_ = Teuchos::null;
  reciprocalConditionEstimated_ = false;
  solutionRefined_ = false;
  solved_ = false;
  solutionErrorsEstimated_ = false;
  equilibratedB_ = false;
}
//=============================================================================

template<typename OrdinalType, typename ScalarType>
void SerialDenseSolver<OrdinalType,ScalarType>::resetMatrix()
{
  resetVectors();
  equilibratedA_ = false;
  factored_ = false;
  inverted_ = false;
  M_ = 0;
  N_ = 0;
  Min_MN_ = 0;
  LDA_ = 0;
  LDAF_ = 0;
  ANORM_ = -ScalarTraits<MagnitudeType>::one();
  RCOND_ = -ScalarTraits<MagnitudeType>::one();
  ROWCND_ = -ScalarTraits<MagnitudeType>::one();
  COLCND_ = -ScalarTraits<MagnitudeType>::one();
  AMAX_ = -ScalarTraits<MagnitudeType>::one();
  A_ = 0;
  AF_ = 0;
  INFO_ = 0;
  LWORK_ = 0;
  R_.resize(0);
  C_.resize(0);
}
//=============================================================================

template<typename OrdinalType, typename ScalarType>
int SerialDenseSolver<OrdinalType,ScalarType>::setMatrix(const RCP<SerialDenseMatrix<OrdinalType,ScalarType> >& A)
{
  resetMatrix();
  Matrix_ = A;
  Factor_ = A;
  M_ = A->numRows();
  N_ = A->numCols();
  Min_MN_ = TEUCHOS_MIN(M_,N_);
  LDA_ = A->stride();
  LDAF_ = LDA_;
  A_ = A->values();
  AF_ = A->values();
  return(0);
}
//=============================================================================

template<typename OrdinalType, typename ScalarType>
int SerialDenseSolver<OrdinalType,ScalarType>::setVectors(const RCP<SerialDenseMatrix<OrdinalType,ScalarType> >& X,
                                                           const RCP<SerialDenseMatrix<OrdinalType,ScalarType> >& B)
{
  // Check that these new vectors are consistent.
  TEUCHOS_TEST_FOR_EXCEPTION(B->numRows()!=X->numRows() || B->numCols() != X->numCols(), std::invalid_argument,
                     "SerialDenseSolver<T>::setVectors: X and B are not the same size!");
  TEUCHOS_TEST_FOR_EXCEPTION(B->values()==0, std::invalid_argument,
                     "SerialDenseSolver<T>::setVectors: B is an empty SerialDenseMatrix<T>!");
  TEUCHOS_TEST_FOR_EXCEPTION(X->values()==0, std::invalid_argument,
                     "SerialDenseSolver<T>::setVectors: X is an empty SerialDenseMatrix<T>!");
  TEUCHOS_TEST_FOR_EXCEPTION(B->stride()<1, std::invalid_argument,
                     "SerialDenseSolver<T>::setVectors: B has an invalid stride!");
  TEUCHOS_TEST_FOR_EXCEPTION(X->stride()<1, std::invalid_argument,
                     "SerialDenseSolver<T>::setVectors: X has an invalid stride!");

  resetVectors();
  LHS_ = X;
  RHS_ = B;
  return(0);
}
//=============================================================================

template<typename OrdinalType, typename ScalarType>
void SerialDenseSolver<OrdinalType,ScalarType>::estimateSolutionErrors(bool flag)
{
  estimateSolutionErrors_ = flag;

  // If the errors are estimated, this implies that the solution must be refined
  refineSolution_ = refineSolution_ || flag;
}
//=============================================================================

template<typename OrdinalType, typename ScalarType>
int SerialDenseSolver<OrdinalType,ScalarType>::factor() {

  if (factored()) return(0); // Already factored

  TEUCHOS_TEST_FOR_EXCEPTION(inverted(), std::logic_error,
                     "SerialDenseSolver<T>::factor: Cannot factor an inverted matrix!");

  ANORM_ = Matrix_->normOne(); // Compute 1-Norm of A


  // If we want to refine the solution, then the factor must
  // be stored separatedly from the original matrix

  if (A_ == AF_)
    if (refineSolution_ ) {
      Factor_ = rcp( new SerialDenseMatrix<OrdinalType,ScalarType>(Teuchos::Copy, *Matrix_) );
      AF_ = Factor_->values();
      LDAF_ = Factor_->stride();
    }

  int ierr = 0;
  if (equilibrate_) ierr = equilibrateMatrix();

  if (ierr!=0) return(ierr);

  if ((int)IPIV_.size()!=Min_MN_) IPIV_.resize( Min_MN_ ); // Allocated Pivot vector if not already done.

  INFO_ = 0;

#ifdef HAVE_TEUCHOSNUMERICS_EIGEN
  EigenMatrixMap aMap( AF_, M_, N_, EigenOuterStride(LDAF_) );
  EigenPermutationMatrix p;
  EigenOrdinalArray ind;
  EigenOrdinalArrayMap ipivMap( &IPIV_[0], Min_MN_ );

  lu_.compute(aMap);
  p = lu_.permutationP();
  ind = p.indices();

  EigenMatrix luMat = lu_.matrixLU();
  for (OrdinalType j=0; j<aMap.outerSize(); j++) {
    for (OrdinalType i=0; i<aMap.innerSize(); i++) {
      aMap(i,j) = luMat(i,j);
    }
  }
  for (OrdinalType i=0; i<ipivMap.innerSize(); i++) {
    ipivMap(i) = ind(i);
  }
#else
  this->GETRF(M_, N_, AF_, LDAF_, &IPIV_[0], &INFO_);
#endif

  factored_ = true;

  return(INFO_);
}

//=============================================================================

template<typename OrdinalType, typename ScalarType>
int SerialDenseSolver<OrdinalType,ScalarType>::solve() {

  // We will call one of four routines depending on what services the user wants and
  // whether or not the matrix has been inverted or factored already.
  //
  // If the matrix has been inverted, use DGEMM to compute solution.
  // Otherwise, if the user want the matrix to be equilibrated or wants a refined solution, we will
  // call the X interface.
  // Otherwise, if the matrix is already factored we will call the TRS interface.
  // Otherwise, if the matrix is unfactored we will call the SV interface.

  int ierr = 0;
  if (equilibrate_) {
    ierr = equilibrateRHS();
  }
  if (ierr != 0) return(ierr);  // Can't equilibrate B, so return.

  TEUCHOS_TEST_FOR_EXCEPTION( RHS_==Teuchos::null, std::invalid_argument,
                     "SerialDenseSolver<T>::solve: No right-hand side vector (RHS) has been set for the linear system!");
  TEUCHOS_TEST_FOR_EXCEPTION( LHS_==Teuchos::null, std::invalid_argument,
                     "SerialDenseSolver<T>::solve: No solution vector (LHS) has been set for the linear system!");

  if (inverted()) {

    TEUCHOS_TEST_FOR_EXCEPTION( RHS_->values() == LHS_->values(), std::invalid_argument,
                        "SerialDenseSolver<T>::solve: X and B must be different vectors if matrix is inverted.");
    TEUCHOS_TEST_FOR_EXCEPTION( (equilibratedA_ && !equilibratedB_) || (!equilibratedA_ && equilibratedB_) ,
                                 std::logic_error, "SerialDenseSolver<T>::solve: Matrix and vectors must be similarly scaled!");

    INFO_ = 0;
    this->GEMM(TRANS_, Teuchos::NO_TRANS, N_, RHS_->numCols(), N_, 1.0, AF_, LDAF_,
               RHS_->values(), RHS_->stride(), 0.0, LHS_->values(), LHS_->stride());
    if (INFO_!=0) return(INFO_);
    solved_ = true;
  }
  else {

    if (!factored()) factor(); // Matrix must be factored
  
    TEUCHOS_TEST_FOR_EXCEPTION( (equilibratedA_ && !equilibratedB_) || (!equilibratedA_ && equilibratedB_) ,
                                 std::logic_error, "SerialDenseSolver<T>::solve: Matrix and vectors must be similarly scaled!");

    if (RHS_->values()!=LHS_->values()) {
       (*LHS_) = (*RHS_); // Copy B to X if needed
    }
    INFO_ = 0;

#ifdef HAVE_TEUCHOSNUMERICS_EIGEN
    EigenMatrixMap rhsMap( RHS_->values(), RHS_->numRows(), RHS_->numCols(), EigenOuterStride(RHS_->stride()) );
    EigenMatrixMap lhsMap( LHS_->values(), LHS_->numRows(), LHS_->numCols(), EigenOuterStride(LHS_->stride()) );
    if ( TRANS_ == Teuchos::NO_TRANS ) {
      lhsMap = lu_.solve(rhsMap);
    } else if ( TRANS_ == Teuchos::TRANS ) {
      lu_.matrixLU().template triangularView<Eigen::Upper>().transpose().solveInPlace(lhsMap);
      lu_.matrixLU().template triangularView<Eigen::UnitLower>().transpose().solveInPlace(lhsMap);
      EigenMatrix x = lu_.permutationP().transpose() * lhsMap;
      lhsMap = x;
    } else {
      lu_.matrixLU().template triangularView<Eigen::Upper>().adjoint().solveInPlace(lhsMap);
      lu_.matrixLU().template triangularView<Eigen::UnitLower>().adjoint().solveInPlace(lhsMap);
      EigenMatrix x = lu_.permutationP().transpose() * lhsMap;
      lhsMap = x;
    }
#else
    this->GETRS(ETranspChar[TRANS_], N_, RHS_->numCols(), AF_, LDAF_, &IPIV_[0], LHS_->values(), LHS_->stride(), &INFO_);
#endif

    if (INFO_!=0) return(INFO_);
    solved_ = true;

  }

  // Warn the user that the matrix should be equilibrated, if it isn't being done already.
  if (shouldEquilibrate() && !equilibratedA_)
    std::cout << "WARNING!  SerialDenseSolver<T>::solve: System should be equilibrated!" << std::endl;

  int ierr1=0;
  if (refineSolution_ && !inverted()) ierr1 = applyRefinement();
  if (ierr1!=0)
    return(ierr1);

  if (equilibrate_) ierr1 = unequilibrateLHS();
  return(ierr1);
}
//=============================================================================

template<typename OrdinalType, typename ScalarType>
int SerialDenseSolver<OrdinalType,ScalarType>::applyRefinement()
{
  TEUCHOS_TEST_FOR_EXCEPTION(!solved(), std::logic_error,
                     "SerialDenseSolver<T>::applyRefinement: Must have an existing solution!");
  TEUCHOS_TEST_FOR_EXCEPTION(A_==AF_, std::logic_error,
                     "SerialDenseSolver<T>::applyRefinement: Cannot apply refinement if no original copy of A!");

#ifdef HAVE_TEUCHOSNUMERICS_EIGEN
  // Implement templated GERFS or use Eigen.
  return (-1);
#else

  OrdinalType NRHS = RHS_->numCols();
  FERR_.resize( NRHS );
  BERR_.resize( NRHS );
  allocateWORK();

  INFO_ = 0;
  std::vector<typename details::lapack_traits<ScalarType>::iwork_type> GERFS_WORK( N_ );
  this->GERFS(ETranspChar[TRANS_], N_, NRHS, A_, LDA_, AF_, LDAF_, &IPIV_[0],
              RHS_->values(), RHS_->stride(), LHS_->values(), LHS_->stride(),
              &FERR_[0], &BERR_[0], &WORK_[0], &GERFS_WORK[0], &INFO_);

  solutionErrorsEstimated_ = true;
  reciprocalConditionEstimated_ = true;
  solutionRefined_ = true;

  return(INFO_);
#endif
}

//=============================================================================

template<typename OrdinalType, typename ScalarType>
int SerialDenseSolver<OrdinalType,ScalarType>::computeEquilibrateScaling()
{
  if (R_.size()!=0) return(0); // Already computed

  R_.resize( M_ );
  C_.resize( N_ );

  INFO_ = 0;
  this->GEEQU (M_, N_, AF_, LDAF_, &R_[0], &C_[0], &ROWCND_, &COLCND_, &AMAX_, &INFO_);

  if (COLCND_<0.1*ScalarTraits<MagnitudeType>::one() ||
      ROWCND_<0.1*ScalarTraits<MagnitudeType>::one() ||
      AMAX_ < ScalarTraits<ScalarType>::rmin() || AMAX_ > ScalarTraits<ScalarType>::rmax() )
    shouldEquilibrate_ = true;

  return(INFO_);
}

//=============================================================================

template<typename OrdinalType, typename ScalarType>
int SerialDenseSolver<OrdinalType,ScalarType>::equilibrateMatrix()
{
  OrdinalType i, j;
  int ierr = 0;

  if (equilibratedA_) return(0); // Already done.
  if (R_.size()==0) ierr = computeEquilibrateScaling(); // Compute R and C if needed.
  if (ierr!=0) return(ierr);     // If return value is not zero, then can't equilibrate.
  if (A_==AF_) {
    ScalarType * ptr;
    for (j=0; j<N_; j++) {
      ptr = A_ + j*LDA_;
      ScalarType s1 = C_[j];
      for (i=0; i<M_; i++) {
        *ptr = *ptr*s1*R_[i];
        ptr++;
      }
    }
  }
  else {
    ScalarType * ptr;
    ScalarType * ptr1;
    for (j=0; j<N_; j++) {
      ptr = A_ + j*LDA_;
      ptr1 = AF_ + j*LDAF_;
      ScalarType s1 = C_[j];
      for (i=0; i<M_; i++) {
        *ptr = *ptr*s1*R_[i];
        ptr++;
        *ptr1 = *ptr1*s1*R_[i];
        ptr1++;
      }
    }
  }

  equilibratedA_ = true;

  return(0);
}

//=============================================================================

template<typename OrdinalType, typename ScalarType>
int SerialDenseSolver<OrdinalType,ScalarType>::equilibrateRHS()
{
  OrdinalType i, j;
  int ierr = 0;

  if (equilibratedB_) return(0); // Already done.
  if (R_.size()==0) ierr = computeEquilibrateScaling(); // Compute R and C if needed.
  if (ierr!=0) return(ierr);     // Can't count on R and C being computed.

  MagnitudeType * R_tmp = &R_[0];
  if (transpose_) R_tmp = &C_[0];

  OrdinalType LDB = RHS_->stride(), NRHS = RHS_->numCols();
  ScalarType * B = RHS_->values();
  ScalarType * ptr;
  for (j=0; j<NRHS; j++) {
    ptr = B + j*LDB;
    for (i=0; i<M_; i++) {
      *ptr = *ptr*R_tmp[i];
      ptr++;
    }
  }

  equilibratedB_ = true;

  return(0);
}

//=============================================================================

template<typename OrdinalType, typename ScalarType>
int SerialDenseSolver<OrdinalType,ScalarType>::unequilibrateLHS()
{
  OrdinalType i, j;

  if (!equilibratedB_) return(0); // Nothing to do

  MagnitudeType * C_tmp = &C_[0];
  if (transpose_) C_tmp = &R_[0];

  OrdinalType LDX = LHS_->stride(), NLHS = LHS_->numCols();
  ScalarType * X = LHS_->values();
  ScalarType * ptr;
  for (j=0; j<NLHS; j++) {
    ptr = X + j*LDX;
    for (i=0; i<N_; i++) {
      *ptr = *ptr*C_tmp[i];
      ptr++;
    }
  }

  return(0);
}

//=============================================================================

template<typename OrdinalType, typename ScalarType>
int SerialDenseSolver<OrdinalType,ScalarType>::invert()
{

  if (!factored()) factor(); // Need matrix factored.

#ifdef HAVE_TEUCHOSNUMERICS_EIGEN
  EigenMatrixMap invMap( AF_, M_, N_, EigenOuterStride(LDAF_) );
  EigenMatrix invMat = lu_.inverse();
  for (OrdinalType j=0; j<invMap.outerSize(); j++) {
    for (OrdinalType i=0; i<invMap.innerSize(); i++) {
      invMap(i,j) = invMat(i,j);
    }
  }
#else

  /* This section work with LAPACK Version 3.0 only
  // Setting LWORK = -1 and calling GETRI will return optimal work space size in WORK_TMP
  OrdinalType LWORK_TMP = -1;
  ScalarType WORK_TMP;
  GETRI( N_, AF_, LDAF_, &IPIV_[0], &WORK_TMP, &LWORK_TMP, &INFO_);
  LWORK_TMP = WORK_TMP; // Convert to integer
  if (LWORK_TMP>LWORK_) {
  LWORK_ = LWORK_TMP;
  WORK_.resize( LWORK_ );
  }
  */
  // This section will work with any version of LAPACK
  allocateWORK();

  INFO_ = 0;
  this->GETRI( N_, AF_, LDAF_, &IPIV_[0], &WORK_[0], LWORK_, &INFO_);
#endif

  inverted_ = true;
  factored_ = false;

  return(INFO_);

}

//=============================================================================

template<typename OrdinalType, typename ScalarType>
int SerialDenseSolver<OrdinalType,ScalarType>::reciprocalConditionEstimate(MagnitudeType & Value)
{
#ifdef HAVE_TEUCHOSNUMERICS_EIGEN
  // Implement templated GECON or use Eigen. Eigen currently doesn't have a condition estimation function.
  return (-1);
#else
  if (reciprocalConditionEstimated()) {
    Value = RCOND_;
    return(0); // Already computed, just return it.
  }

  if ( ANORM_<ScalarTraits<MagnitudeType>::zero() ) ANORM_ = Matrix_->normOne();

  int ierr = 0;
  if (!factored()) ierr = factor(); // Need matrix factored.
  if (ierr!=0) return(ierr);

  allocateWORK();

  // We will assume a one-norm condition number
  INFO_ = 0;
  std::vector<typename details::lapack_traits<ScalarType>::iwork_type> GECON_WORK( 2*N_ );
  this->GECON( '1', N_, AF_, LDAF_, ANORM_, &RCOND_, &WORK_[0], &GECON_WORK[0], &INFO_);

  reciprocalConditionEstimated_ = true;
  Value = RCOND_;

  return(INFO_);
#endif
}
//=============================================================================

template<typename OrdinalType, typename ScalarType>
void SerialDenseSolver<OrdinalType,ScalarType>::Print(std::ostream& os) const {

  if (Matrix_!=Teuchos::null) os << "Solver Matrix"          << std::endl << *Matrix_ << std::endl;
  if (Factor_!=Teuchos::null) os << "Solver Factored Matrix" << std::endl << *Factor_ << std::endl;
  if (LHS_   !=Teuchos::null) os << "Solver LHS"             << std::endl << *LHS_    << std::endl;
  if (RHS_   !=Teuchos::null) os << "Solver RHS"             << std::endl << *RHS_    << std::endl;

}

} // namespace Teuchos

#endif /* _TEUCHOS_SERIALDENSESOLVER_HPP_ */