Teuchos_SerialBandDenseSolver.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_SERIALBANDDENSESOLVER_HPP_
#define _TEUCHOS_SERIALBANDDENSESOLVER_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_SerialBandDenseMatrix.hpp"
#include "Teuchos_SerialDenseSolver.hpp"
#include "Teuchos_ScalarTraits.hpp"
 
#ifdef HAVE_TEUCHOSNUMERICS_EIGEN
#include "Eigen/Dense"
#endif
 
namespace Teuchos {

 
  template<typename OrdinalType, typename ScalarType>
  class SerialBandDenseSolver : 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::internal::BandMatrix<ScalarType,Eigen::Dynamic,Eigen::Dynamic,Eigen::ColMajor> EigenBandMatrix;
    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



    SerialBandDenseSolver();

    virtual ~SerialBandDenseSolver();



    int setMatrix(const RCP<SerialBandDenseMatrix<OrdinalType, ScalarType> >& AB);


    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 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 reciprocalConditionEstimated() {return(reciprocalConditionEstimated_);}

    bool solved() {return(solved_);}

    bool solutionRefined() {return(solutionRefined_);}



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

    RCP<SerialBandDenseMatrix<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_);}

    OrdinalType numLower()  const {return(KL_);}

    OrdinalType numUpper()  const {return(KU_);}

    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_ = 3*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 reciprocalConditionEstimated_;
    bool refineSolution_;
    bool solutionRefined_;
 
    Teuchos::ETransp TRANS_;
 
    OrdinalType M_;
    OrdinalType N_;
    OrdinalType KL_;
    OrdinalType KU_;
    OrdinalType Min_MN_;
    OrdinalType LDA_;
    OrdinalType LDAF_;
    OrdinalType INFO_;
    OrdinalType LWORK_;
 
    std::vector<OrdinalType> IPIV_;
    std::vector<int> IWORK_;
 
    MagnitudeType ANORM_;
    MagnitudeType RCOND_;
    MagnitudeType ROWCND_;
    MagnitudeType COLCND_;
    MagnitudeType AMAX_;
 
    RCP<SerialBandDenseMatrix<OrdinalType, ScalarType> > Matrix_;
    RCP<SerialDenseMatrix<OrdinalType, ScalarType> > LHS_;
    RCP<SerialDenseMatrix<OrdinalType, ScalarType> > RHS_;
    RCP<SerialBandDenseMatrix<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:
 
    // SerialBandDenseSolver copy constructor (put here because we don't want user access)
    SerialBandDenseSolver(const SerialBandDenseSolver<OrdinalType, ScalarType>& Source);
    SerialBandDenseSolver & operator=(const SerialBandDenseSolver<OrdinalType, ScalarType>& Source);
 
  };
 
  // Helper traits to distinguish work arrays for real and complex-valued datatypes.
  using namespace details;
 
//=============================================================================
 
template<typename OrdinalType, typename ScalarType>
SerialBandDenseSolver<OrdinalType,ScalarType>::SerialBandDenseSolver()
  : CompObject(),
    equilibrate_(false),
    shouldEquilibrate_(false),
    equilibratedA_(false),
    equilibratedB_(false),
    transpose_(false),
    factored_(false),
    estimateSolutionErrors_(false),
    solutionErrorsEstimated_(false),
    solved_(false),
    reciprocalConditionEstimated_(false),
    refineSolution_(false),
    solutionRefined_(false),
    TRANS_(Teuchos::NO_TRANS),
    M_(0),
    N_(0),
    KL_(0),
    KU_(0),
    Min_MN_(0),
    LDA_(0),
    LDAF_(0),
    INFO_(0),
    LWORK_(0),
    ANORM_(0.0),
    RCOND_(ScalarTraits<MagnitudeType>::zero()),
    ROWCND_(ScalarTraits<MagnitudeType>::zero()),
    COLCND_(ScalarTraits<MagnitudeType>::zero()),
    AMAX_(ScalarTraits<MagnitudeType>::zero()),
    A_(NULL),
    AF_(NULL)
{
  resetMatrix();
}
//=============================================================================
 
template<typename OrdinalType, typename ScalarType>
SerialBandDenseSolver<OrdinalType,ScalarType>::~SerialBandDenseSolver()
{}
 
//=============================================================================
 
template<typename OrdinalType, typename ScalarType>
void SerialBandDenseSolver<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 SerialBandDenseSolver<OrdinalType,ScalarType>::resetMatrix()
{
  resetVectors();
  equilibratedA_ = false;
  factored_ = false;
  M_ = 0;
  N_ = 0;
  KL_ = 0;
  KU_ = 0;
  Min_MN_ = 0;
  LDA_ = 0;
  LDAF_ = 0;
  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 SerialBandDenseSolver<OrdinalType,ScalarType>::setMatrix(const RCP<SerialBandDenseMatrix<OrdinalType,ScalarType> >& AB)
{
 
  OrdinalType m = AB->numRows();
  OrdinalType n = AB->numCols();
  OrdinalType kl = AB->lowerBandwidth();
  OrdinalType ku = AB->upperBandwidth();
 
  // Check that the new matrix is consistent.
  TEUCHOS_TEST_FOR_EXCEPTION(AB->values()==0, std::invalid_argument,
                     "SerialBandDenseSolver<T>::setMatrix: A is an empty SerialBandDenseMatrix<T>!");
 
  resetMatrix();
  Matrix_ = AB;
  Factor_ = AB;
  M_ = m;
  N_ = n;
  KL_ = kl;
  KU_ = ku-kl;
  Min_MN_ = TEUCHOS_MIN(M_,N_);
  LDA_ = AB->stride();
  LDAF_ = LDA_;
  A_ = AB->values();
  AF_ = AB->values();
 
  return(0);
}
//=============================================================================
 
template<typename OrdinalType, typename ScalarType>
int SerialBandDenseSolver<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,
                     "SerialBandDenseSolver<T>::setVectors: X and B are not the same size!");
  TEUCHOS_TEST_FOR_EXCEPTION(B->values()==0, std::invalid_argument,
                     "SerialBandDenseSolver<T>::setVectors: B is an empty SerialDenseMatrix<T>!");
  TEUCHOS_TEST_FOR_EXCEPTION(X->values()==0, std::invalid_argument,
                     "SerialBandDenseSolver<T>::setVectors: X is an empty SerialDenseMatrix<T>!");
  TEUCHOS_TEST_FOR_EXCEPTION(B->stride()<1, std::invalid_argument,
                     "SerialBandDenseSolver<T>::setVectors: B has an invalid stride!");
  TEUCHOS_TEST_FOR_EXCEPTION(X->stride()<1, std::invalid_argument,
                     "SerialBandDenseSolver<T>::setVectors: X has an invalid stride!");
 
  resetVectors();
  LHS_ = X;
  RHS_ = B;
  return(0);
}
//=============================================================================
 
template<typename OrdinalType, typename ScalarType>
void SerialBandDenseSolver<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 SerialBandDenseSolver<OrdinalType,ScalarType>::factor() {
 
  if (factored()) return(0); // Already factored
 
  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 SerialBandDenseMatrix<OrdinalType,ScalarType>(*Matrix_) );
      AF_ = Factor_->values();
      LDAF_ = Factor_->stride();
    }
 
  int ierr = 0;
  if (equilibrate_) ierr = equilibrateMatrix();
 
  if (ierr!=0) return(ierr);
 
  if (IPIV_.size()==0) IPIV_.resize( N_ ); // Allocated Pivot vector if not already done.
 
  INFO_ = 0;
 
#ifdef HAVE_TEUCHOSNUMERICS_EIGEN
  EigenMatrixMap aMap( AF_+KL_, KL_+KU_+1, N_, EigenOuterStride(LDAF_) );
  EigenMatrix fullMatrix(M_, N_);
  for (OrdinalType j=0; j<N_; j++) {
    for (OrdinalType i=TEUCHOS_MAX(0,j-KU_); i<=TEUCHOS_MIN(M_-1, j+KL_); i++) {
      fullMatrix(i,j) = aMap(KU_+i-j, j);
    }
  }
 
  EigenPermutationMatrix p;
  EigenOrdinalArray ind;
  EigenOrdinalArrayMap ipivMap( &IPIV_[0], Min_MN_ );
 
  lu_.compute(fullMatrix);
  p = lu_.permutationP();
  ind = p.indices();
 
  for (OrdinalType i=0; i<ipivMap.innerSize(); i++) {
    ipivMap(i) = ind(i);
  }
 
#else
  this->GBTRF(M_, N_, KL_, KU_, AF_, LDAF_, &IPIV_[0], &INFO_);
#endif
 
  factored_ = true;
 
  return(INFO_);
}
 
//=============================================================================
 
template<typename OrdinalType, typename ScalarType>
int SerialBandDenseSolver<OrdinalType,ScalarType>::solve() {
 
  // 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,
                     "SerialBandDenseSolver<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,
                     "SerialBandDenseSolver<T>::solve: No solution vector (LHS) has been set for the linear system!");
 
  if (!factored()) factor(); // Matrix must be factored
 
  TEUCHOS_TEST_FOR_EXCEPTION( (equilibratedA_ && !equilibratedB_) || (!equilibratedA_ && equilibratedB_) ,
                     std::logic_error, "SerialBandDenseSolver<T>::solve: Matrix and vectors must be similarly scaled!");
 
  if (shouldEquilibrate() && !equilibratedA_)
    std::cout << "WARNING!  SerialBandDenseSolver<T>::solve: System should be equilibrated!" << std::endl;
 
  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->GBTRS(ETranspChar[TRANS_], N_, KL_, KU_, RHS_->numCols(), AF_, LDAF_, &IPIV_[0], LHS_->values(), LHS_->stride(), &INFO_);
#endif
 
  if (INFO_!=0) return(INFO_);
  solved_ = true;
 
  int ierr1=0;
  if (refineSolution_) ierr1 = applyRefinement();
  if (ierr1!=0)
    return(ierr1);
 
  if (equilibrate_) ierr1 = unequilibrateLHS();
 
  return(ierr1);
}
//=============================================================================
 
template<typename OrdinalType, typename ScalarType>
int SerialBandDenseSolver<OrdinalType,ScalarType>::applyRefinement()
{
  TEUCHOS_TEST_FOR_EXCEPTION(!solved(), std::logic_error,
                     "SerialBandDenseSolver<T>::applyRefinement: Must have an existing solution!");
  TEUCHOS_TEST_FOR_EXCEPTION(A_==AF_, std::logic_error,
                     "SerialBandDenseSolver<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> GBRFS_WORK( N_ );
  this->GBRFS(ETranspChar[TRANS_], N_, KL_, KU_, NRHS, A_+KL_, LDA_, AF_, LDAF_, &IPIV_[0],
              RHS_->values(), RHS_->stride(), LHS_->values(), LHS_->stride(),
              &FERR_[0], &BERR_[0], &WORK_[0], &GBRFS_WORK[0], &INFO_);
 
  solutionErrorsEstimated_ = true;
  reciprocalConditionEstimated_ = true;
  solutionRefined_ = true;
 
  return(INFO_);
#endif
}
 
//=============================================================================
 
template<typename OrdinalType, typename ScalarType>
int SerialBandDenseSolver<OrdinalType,ScalarType>::computeEquilibrateScaling()
{
  if (R_.size()!=0) return(0); // Already computed
 
  R_.resize( M_ );
  C_.resize( N_ );
 
  INFO_ = 0;
  this->GBEQU (M_, N_, KL_, KU_, AF_+KL_, 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 SerialBandDenseSolver<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_ + KL_ + j*LDA_ + TEUCHOS_MAX(KU_-j, 0);
      ScalarType s1 = C_[j];
      for (i=TEUCHOS_MAX(0,j-KU_); i<=TEUCHOS_MIN(M_-1,j+KL_); i++) {
        *ptr = *ptr*s1*R_[i];
        ptr++;
      }
    }
  } else {
 
    ScalarType * ptr;
    ScalarType * ptrL;
    ScalarType * ptrU;
    for (j=0; j<N_; j++) {
      ptr = A_ + KL_ + j*LDA_ + TEUCHOS_MAX(KU_-j, 0);
      ScalarType s1 = C_[j];
      for (i=TEUCHOS_MAX(0,j-KU_); i<=TEUCHOS_MIN(M_-1,j+KL_); i++) {
        *ptr = *ptr*s1*R_[i];
        ptr++;
      }
    }
    for (j=0; j<N_; j++) {
      ptrU = AF_ + j*LDAF_ + TEUCHOS_MAX(KL_+KU_-j, 0);
      ptrL = AF_ + KL_ + KU_ + 1 + j*LDAF_;
      ScalarType s1 = C_[j];
      for (i=TEUCHOS_MAX(0,j-(KL_+KU_)); i<=TEUCHOS_MIN(M_-1,j); i++) {
        *ptrU = *ptrU*s1*R_[i];
        ptrU++;
      }
      for (i=TEUCHOS_MAX(0,j); i<=TEUCHOS_MIN(M_-1,j+KL_); i++) {
        *ptrL = *ptrL*s1*R_[i];
        ptrL++;
      }
    }
  }
 
  equilibratedA_ = true;
 
  return(0);
}
 
//=============================================================================
 
template<typename OrdinalType, typename ScalarType>
int SerialBandDenseSolver<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 SerialBandDenseSolver<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 SerialBandDenseSolver<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> GBCON_WORK( N_ );
  this->GBCON( '1', N_, KL_, KU_, AF_, LDAF_, &IPIV_[0], ANORM_, &RCOND_, &WORK_[0], &GBCON_WORK[0], &INFO_);
  reciprocalConditionEstimated_ = true;
  Value = RCOND_;
 
  return(INFO_);
#endif
}
//=============================================================================
 
template<typename OrdinalType, typename ScalarType>
void SerialBandDenseSolver<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_SERIALBANDDENSESOLVER_HPP_ */