/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/*                                                                           */
/*                  This file is part of the class library                   */
/*       SoPlex --- the Sequential object-oriented simPlex.                  */
/*                                                                           */
/*  Copyright (c) 1996-2026 Zuse Institute Berlin (ZIB)                      */
/*                                                                           */
/*  Licensed under the Apache License, Version 2.0 (the "License");          */
/*  you may not use this file except in compliance with the License.         */
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/*      http://www.apache.org/licenses/LICENSE-2.0                           */
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/*  limitations under the License.                                           */
/*                                                                           */
/*  You should have received a copy of the Apache-2.0 license                */
/*  along with SoPlex; see the file LICENSE. If not email to soplex@zib.de.  */
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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

/*      \SubSection{Updating the Basis for Entering Variables}
 */
#include <assert.h>

#include "soplex/spxdefines.h"
#include "soplex/spxratiotester.h"
#include "soplex/spxpricer.h"
#include "soplex/spxout.h"
#include "soplex/exceptions.h"

namespace soplex
{

/*
  In the entering simplex algorithms (i.e. iteratively a vector is selected to
  \em enter the simplex basis as in the dual rowwise and primal columnwise case)
  let $A$ denote the current basis, $x$ and entering vector and $f$ the
  feasibility vector. For a feasible basis $l \le f \le u$ holds.
  For the rowwise case $f$ is obtained by solving $f^T = c^T A^{-1}$,
  wherease in columnwisecase $f = A^{-1} b$.

  Let us further consider the rowwise case. Exchanging $x$ with the $i$-th
  vector of $A$ yields

  \begin{equation}\label{update.eq}
  A^{(i)} = E_i A \hbox{, with } E_i = I + e_i (x^T A^{-1} - e_i^T).
  \end{equation}

  With $E_i^{-1} = I + e_i \frac{e_i^T - \delta^T}{\delta}$,
  $\delta^T = x^T A^{-1}$ one gets the new feasibility vector

  \begin{eqnarray*}
  (f^{(i)})^T
  &=& c^T (A^{(i)})^{-1}      \\
  &=& c^T A^{-1} + c^T A^{-1} e_i \frac{e_i^T - \delta^T}{\delta_i} \\
  &=& f^T + \frac{f_i}{\delta_i} e_i^T - \frac{f_i}{\delta_i} \delta^T. \\
  \end{eqnarray*}

  The selection of the leaving vector $i^*$ for the basis must ensure, that for
  all $j \ne i^*$ $f^{(i^*)}_j$ remains within its bounds $l_j$ and $u_j$.
*/


/*
  Testing all values of |pVec| against its bounds. If $i$, say, is violated
  the violation is saved as negative value in |theTest[i]|.
*/

template <class R>
R SPxSolverBase<R>::test(int i, typename SPxBasisBase<R>::Desc::Status stat) const
{
   assert(type() == ENTER);
   assert(!isBasic(stat));

   R x;

   switch(stat)
   {
   case SPxBasisBase<R>::Desc::D_FREE:
   case SPxBasisBase<R>::Desc::D_ON_BOTH:
      assert(rep() == ROW);
      x = (*thePvec)[i] - this->lhs(i);

      if(x < 0)
         return x;

   // no break: next is else case
   //lint -fallthrough
   case SPxBasisBase<R>::Desc::D_ON_LOWER:
      assert(rep() == ROW);
      return this->rhs(i) - (*thePvec)[i];

   case SPxBasisBase<R>::Desc::D_ON_UPPER:
      assert(rep() == ROW);
      return (*thePvec)[i] - this->lhs(i);

   case SPxBasisBase<R>::Desc::P_ON_UPPER:
      assert(rep() == COLUMN);
      return this->maxObj(i) - (*thePvec)[i];

   case SPxBasisBase<R>::Desc::P_ON_LOWER:
      assert(rep() == COLUMN);
      return (*thePvec)[i] - this->maxObj(i);

   case SPxBasisBase<R>::Desc::P_FREE :
      x = this->maxObj(i) - (*thePvec)[i];
      return (x < 0) ? x : -x;

   default:
      return 0;
   }
}

template <class R>
void SPxSolverBase<R>::computeTest()
{

   const typename SPxBasisBase<R>::Desc& ds = this->desc();
   R pricingTol = leavetol();
   m_pricingViolCoUpToDate = true;
   m_pricingViolCo = 0;

   infeasibilitiesCo.clear();
   int sparsitythreshold = (int)(sparsePricingFactor * coDim());

   for(int i = 0; i < coDim(); ++i)
   {
      typename SPxBasisBase<R>::Desc::Status stat = ds.status(i);

      if(isBasic(stat))
      {
         theTest[i] = 0.0;

         if(remainingRoundsEnterCo == 0)
            isInfeasibleCo[i] = SPxPricer<R>::NOT_VIOLATED;
      }
      else
      {
         assert(!isBasic(stat));
         theTest[i] = test(i, stat);

         if(remainingRoundsEnterCo == 0)
         {
            if(theTest[i] < -pricingTol)
            {
               assert(infeasibilitiesCo.size() < infeasibilitiesCo.max());
               m_pricingViolCo -= theTest[i];
               infeasibilitiesCo.addIdx(i);
               isInfeasibleCo[i] = SPxPricer<R>::VIOLATED;
               ++m_numViol;
            }
            else
               isInfeasibleCo[i] = SPxPricer<R>::NOT_VIOLATED;

            if(infeasibilitiesCo.size() > sparsitythreshold)
            {
               SPX_MSG_INFO2((*this->spxout), (*this->spxout) << " --- using dense pricing"
                             << std::endl;)
               remainingRoundsEnterCo = SOPLEX_DENSEROUNDS;
               sparsePricingEnterCo = false;
               infeasibilitiesCo.clear();
            }
         }
         else if(theTest[i] < -pricingTol)
         {
            m_pricingViolCo -= theTest[i];
            ++m_numViol;
         }
      }
   }

   if(infeasibilitiesCo.size() == 0 && !sparsePricingEnterCo)
      --remainingRoundsEnterCo;
   else if(infeasibilitiesCo.size() <= sparsitythreshold && !sparsePricingEnterCo)
   {
      SPX_MSG_INFO2((*this->spxout),
                    std::streamsize prec = spxout->precision();

                    if(hyperPricingEnter)
                    (*this->spxout) << " --- using hypersparse pricing, ";
                    else
                       (*this->spxout) << " --- using sparse pricing, ";
                       (*this->spxout) << "sparsity: "
                       << std::setw(6) << std::fixed << std::setprecision(4)
                       << (R) infeasibilitiesCo.size() / coDim()
                       << std::scientific << std::setprecision(int(prec))
                       << std::endl;)
            sparsePricingEnterCo = true;
   }
}

template <class R>
R SPxSolverBase<R>::computePvec(int i)
{

   return (*thePvec)[i] = vector(i) * (*theCoPvec);
}

template <class R>
R SPxSolverBase<R>::computeTest(int i)
{
   typename SPxBasisBase<R>::Desc::Status stat = this->desc().status(i);

   if(isBasic(stat))
      return theTest[i] = 0;
   else
      return theTest[i] = test(i, stat);
}

/*
  Testing all values of #coPvec# against its bounds. If $i$, say, is violated
  the violation is saved as negative value in |theCoTest[i]|.
*/
template <class R>
R SPxSolverBase<R>::coTest(int i, typename SPxBasisBase<R>::Desc::Status stat) const
{
   assert(type() == ENTER);
   assert(!isBasic(stat));

   R x;

   switch(stat)
   {
   case SPxBasisBase<R>::Desc::D_FREE:
   case SPxBasisBase<R>::Desc::D_ON_BOTH :
      assert(rep() == ROW);
      x = (*theCoPvec)[i] - SPxLPBase<R>::lower(i);

      if(x < 0)
         return x;

   // no break: next is else case
   //lint -fallthrough
   case SPxBasisBase<R>::Desc::D_ON_LOWER:
      assert(rep() == ROW);
      return SPxLPBase<R>::upper(i) - (*theCoPvec)[i];

   case SPxBasisBase<R>::Desc::D_ON_UPPER:
      assert(rep() == ROW);
      return (*theCoPvec)[i] - SPxLPBase<R>::lower(i);

   case SPxBasisBase<R>::Desc::P_ON_UPPER:
      assert(rep() == COLUMN);
      return (*theCoPvec)[i] - this->maxRowObj(i);             // slacks !

   case SPxBasisBase<R>::Desc::P_ON_LOWER:
      assert(rep() == COLUMN);
      return this->maxRowObj(i) - (*theCoPvec)[i];             // slacks !

   default:
      return 0;
   }
}

template <class R>
void SPxSolverBase<R>::computeCoTest()
{
   int i;
   R pricingTol = leavetol();
   m_pricingViolUpToDate = true;
   m_pricingViol = 0;
   m_numViol = 0;
   infeasibilities.clear();
   int sparsitythreshold = (int)(sparsePricingFactor * dim());
   const typename SPxBasisBase<R>::Desc& ds = this->desc();

   for(i = dim() - 1; i >= 0; --i)
   {
      typename SPxBasisBase<R>::Desc::Status stat = ds.coStatus(i);

      if(isBasic(stat))
      {
         theCoTest[i] = 0;

         if(remainingRoundsEnter == 0)
            isInfeasible[i] = SPxPricer<R>::NOT_VIOLATED;
      }
      else
      {
         theCoTest[i] = coTest(i, stat);

         if(remainingRoundsEnter == 0)
         {
            if(theCoTest[i] < -pricingTol)
            {
               assert(infeasibilities.size() < infeasibilities.max());
               m_pricingViol -= theCoTest[i];
               infeasibilities.addIdx(i);
               isInfeasible[i] = SPxPricer<R>::VIOLATED;
               ++m_numViol;
            }
            else
               isInfeasible[i] = SPxPricer<R>::NOT_VIOLATED;

            if(infeasibilities.size() > sparsitythreshold)
            {
               SPX_MSG_INFO2((*this->spxout), (*this->spxout) << " --- using dense pricing"
                             << std::endl;)
               remainingRoundsEnter = SOPLEX_DENSEROUNDS;
               sparsePricingEnter = false;
               infeasibilities.clear();
            }
         }
         else if(theCoTest[i] < -pricingTol)
         {
            m_pricingViol -= theCoTest[i];
            ++m_numViol;
         }
      }
   }

   if(infeasibilities.size() == 0 && !sparsePricingEnter)
      --remainingRoundsEnter;
   else if(infeasibilities.size() <= sparsitythreshold && !sparsePricingEnter)
   {
      SPX_MSG_INFO2((*this->spxout),
                    std::streamsize prec = spxout->precision();

                    if(hyperPricingEnter)
                    (*this->spxout) << " --- using hypersparse pricing, ";
                    else
                       (*this->spxout) << " --- using sparse pricing, ";
                       (*this->spxout) << "sparsity: "
                       << std::setw(6) << std::fixed << std::setprecision(4)
                       << (R) infeasibilities.size() / dim()
                       << std::scientific << std::setprecision(int(prec))
                       << std::endl;)
            sparsePricingEnter = true;
   }
}

/*
  The following methods require propersy initialized vectors |fVec| and
  #coPvec#.
*/
template <class R>
void SPxSolverBase<R>::updateTest()
{
   thePvec->delta().setup();

   const IdxSet& idx = thePvec->idx();
   const typename SPxBasisBase<R>::Desc& ds = this->desc();
   R pricingTol = leavetol();

   int i;
   updateViolsCo.clear();

   for(i = idx.size() - 1; i >= 0; --i)
   {
      int j = idx.index(i);
      typename SPxBasisBase<R>::Desc::Status stat = ds.status(j);

      if(!isBasic(stat))
      {
         if(m_pricingViolCoUpToDate && theTest[j] < -pricingTol)
            m_pricingViolCo += theTest[j];

         theTest[j] = test(j, stat);

         if(sparsePricingEnterCo)
         {
            if(theTest[j] < -pricingTol)
            {
               assert(remainingRoundsEnterCo == 0);
               m_pricingViolCo -= theTest[j];

               if(isInfeasibleCo[j] == SPxPricer<R>::NOT_VIOLATED)
               {
                  infeasibilitiesCo.addIdx(j);
                  isInfeasibleCo[j] = SPxPricer<R>::VIOLATED;
               }

               if(hyperPricingEnter)
                  updateViolsCo.addIdx(j);
            }
            else
            {
               isInfeasibleCo[j] = SPxPricer<R>::NOT_VIOLATED;
            }
         }
         else if(theTest[j] < -pricingTol)
            m_pricingViolCo -= theTest[j];
      }
      else
      {
         isInfeasibleCo[j] = SPxPricer<R>::NOT_VIOLATED;
         theTest[j] = 0;
      }
   }
}

template <class R>
void SPxSolverBase<R>::updateCoTest()
{
   theCoPvec->delta().setup();

   const IdxSet& idx = theCoPvec->idx();
   const typename SPxBasisBase<R>::Desc& ds = this->desc();
   R pricingTol = leavetol();

   int i;
   updateViols.clear();

   for(i = idx.size() - 1; i >= 0; --i)
   {
      int j = idx.index(i);
      typename SPxBasisBase<R>::Desc::Status stat = ds.coStatus(j);

      if(!isBasic(stat))
      {
         if(m_pricingViolUpToDate && theCoTest[j] < -pricingTol)
            m_pricingViol += theCoTest[j];

         theCoTest[j] = coTest(j, stat);

         if(sparsePricingEnter)
         {
            if(theCoTest[j] < -pricingTol)
            {
               assert(remainingRoundsEnter == 0);
               m_pricingViol -= theCoTest[j];

               if(isInfeasible[j] == SPxPricer<R>::NOT_VIOLATED)
               {
                  //                if( !hyperPricingEnter )
                  infeasibilities.addIdx(j);
                  isInfeasible[j] = SPxPricer<R>::VIOLATED;
               }

               if(hyperPricingEnter)
                  updateViols.addIdx(j);
            }
            else
            {
               // @todo do we need to remove index j from infeasibilitiesCo?
               isInfeasible[j] = SPxPricer<R>::NOT_VIOLATED;
            }
         }
         else if(theCoTest[j] < -pricingTol)
            m_pricingViol -= theCoTest[j];
      }
      else
      {
         isInfeasible[j] = SPxPricer<R>::NOT_VIOLATED;
         theCoTest[j] = 0;
      }
   }
}



/*  \Section{Compute statistics on entering variable}
    Here is a list of variables relevant when including |Id| to the basis.
    They are computed by |computeEnterStats()|.
*/
template <class R>
void SPxSolverBase<R>::getEnterVals
(
   SPxId enterId,
   R& enterTest,
   R& enterUB,
   R& enterLB,
   R& enterVal,
   R& enterMax,
   R& enterPric,
   typename SPxBasisBase<R>::Desc::Status& enterStat,
   R& enterRO,
   StableSum<R>& objChange
)
{
   int enterIdx;
   typename SPxBasisBase<R>::Desc& ds = this->desc();

   if(enterId.isSPxColId())
   {
      enterIdx = this->number(SPxColId(enterId));
      enterStat = ds.colStatus(enterIdx);
      assert(!isBasic(enterStat));

      /*      For an #Id# to enter the basis we better recompute the Test value.
       */
      if(rep() == COLUMN)
      {
         computePvec(enterIdx);
         enterTest = computeTest(enterIdx);
         theTest[enterIdx] = 0;
      }
      else
      {
         enterTest = coTest()[enterIdx];
         theCoTest[enterIdx] = 0;
      }

      switch(enterStat)
      {
      // primal/columnwise cases:
      case SPxBasisBase<R>::Desc::P_ON_UPPER :
         assert(rep() == COLUMN);
         enterUB = theUCbound[enterIdx];
         enterLB = theLCbound[enterIdx];
         enterVal = enterUB;
         enterMax = enterLB - enterUB;
         enterPric = (*thePvec)[enterIdx];
         enterRO = this->maxObj(enterIdx);
         objChange -= enterVal * enterRO;

         if(enterLB <= R(-infinity))
            ds.colStatus(enterIdx) = SPxBasisBase<R>::Desc::D_ON_LOWER;
         else if(EQ(enterLB, enterUB, this->epsilon()))
            ds.colStatus(enterIdx) = SPxBasisBase<R>::Desc::D_FREE;
         else
            ds.colStatus(enterIdx) = SPxBasisBase<R>::Desc::D_ON_BOTH;

         break;

      case SPxBasisBase<R>::Desc::P_ON_LOWER :
         assert(rep() == COLUMN);
         enterUB = theUCbound[enterIdx];
         enterLB = theLCbound[enterIdx];
         enterVal = enterLB;
         enterMax = enterUB - enterLB;
         enterPric = (*thePvec)[enterIdx];
         enterRO = this->maxObj(enterIdx);
         objChange -= enterVal * enterRO;

         if(enterUB >= R(infinity))
            ds.colStatus(enterIdx) = SPxBasisBase<R>::Desc::D_ON_UPPER;
         else if(EQ(enterLB, enterUB, this->epsilon()))
            ds.colStatus(enterIdx) = SPxBasisBase<R>::Desc::D_FREE;
         else
            ds.colStatus(enterIdx) = SPxBasisBase<R>::Desc::D_ON_BOTH;

         break;

      case SPxBasisBase<R>::Desc::P_FREE :
         assert(rep() == COLUMN);
         enterUB = theUCbound[enterIdx];
         enterLB = theLCbound[enterIdx];
         enterVal = 0;
         enterPric = (*thePvec)[enterIdx];
         enterRO = this->maxObj(enterIdx);
         ds.colStatus(enterIdx) = SPxBasisBase<R>::Desc::D_UNDEFINED;
         enterMax = (enterRO - enterPric > 0) ? R(infinity) : R(-infinity);
         break;

      // dual/rowwise cases:
      case SPxBasisBase<R>::Desc::D_ON_UPPER :
         assert(rep() == ROW);
         assert(theUCbound[enterIdx] < R(infinity));
         enterUB = theUCbound[enterIdx];
         enterLB = R(-infinity);
         enterMax = R(-infinity);
         enterVal = enterUB;
         enterPric = (*theCoPvec)[enterIdx];
         enterRO = SPxLPBase<R>::lower(enterIdx);
         objChange -= enterRO * enterVal;
         ds.colStatus(enterIdx) = SPxBasisBase<R>::Desc::P_ON_LOWER;
         break;

      case SPxBasisBase<R>::Desc::D_ON_LOWER :
         assert(rep() == ROW);
         assert(theLCbound[enterIdx] > R(-infinity));
         enterLB = theLCbound[enterIdx];
         enterUB = R(infinity);
         enterMax = R(infinity);
         enterVal = enterLB;
         enterPric = (*theCoPvec)[enterIdx];
         enterRO = SPxLPBase<R>::upper(enterIdx);
         objChange -= enterRO * enterVal;
         ds.colStatus(enterIdx) = SPxBasisBase<R>::Desc::P_ON_UPPER;
         break;

      case SPxBasisBase<R>::Desc::D_FREE:
         assert(rep() == ROW);
         assert(SPxLPBase<R>::lower(enterIdx) == SPxLPBase<R>::upper(enterIdx));
         enterUB = R(infinity);
         enterLB = R(-infinity);
         enterVal = 0;
         enterRO = SPxLPBase<R>::upper(enterIdx);
         enterPric = (*theCoPvec)[enterIdx];

         if(enterPric > enterRO)
            enterMax = R(infinity);
         else
            enterMax = R(-infinity);

         ds.colStatus(enterIdx) = SPxBasisBase<R>::Desc::P_FIXED;
         break;

      case SPxBasisBase<R>::Desc::D_ON_BOTH :
         assert(rep() == ROW);
         enterPric = (*theCoPvec)[enterIdx];

         if(enterPric > SPxLPBase<R>::upper(enterIdx))
         {
            enterLB = theLCbound[enterIdx];
            enterUB = R(infinity);
            enterMax = R(infinity);
            enterVal = enterLB;
            enterRO = SPxLPBase<R>::upper(enterIdx);
            ds.colStatus(enterIdx) = SPxBasisBase<R>::Desc::P_ON_UPPER;
         }
         else
         {
            enterUB = theUCbound[enterIdx];
            enterVal = enterUB;
            enterRO = SPxLPBase<R>::lower(enterIdx);
            enterLB = R(-infinity);
            enterMax = R(-infinity);
            ds.colStatus(enterIdx) = SPxBasisBase<R>::Desc::P_ON_LOWER;
         }

         objChange -= theLCbound[enterIdx] * SPxLPBase<R>::upper(enterIdx);
         objChange -= theUCbound[enterIdx] * SPxLPBase<R>::lower(enterIdx);
         break;

      default:
         throw SPxInternalCodeException("XENTER01 This should never happen.");
      }

      SPxOut::debug(this, "DENTER03 SPxSolverBase::getEnterVals() : col {}: {} -> {} objChange: {}\n",
                    enterIdx, enterStat, ds.colStatus(enterIdx), objChange);
   }

   else
   {
      assert(enterId.isSPxRowId());
      enterIdx = this->number(SPxRowId(enterId));
      enterStat = ds.rowStatus(enterIdx);
      assert(!isBasic(enterStat));

      /*      For an #Id# to enter the basis we better recompute the Test value.
       */
      if(rep() == ROW)
      {
         computePvec(enterIdx);
         enterTest = computeTest(enterIdx);
         theTest[enterIdx] = 0;
      }
      else
      {
         enterTest = coTest()[enterIdx];
         theCoTest[enterIdx] = 0;
      }

      switch(enterStat)
      {
      // primal/columnwise cases:
      case SPxBasisBase<R>::Desc::P_ON_UPPER :
         assert(rep() == COLUMN);
         enterUB = theURbound[enterIdx];
         enterLB = theLRbound[enterIdx];
         enterVal = enterLB;
         enterMax = enterUB - enterLB;
         enterPric = (*theCoPvec)[enterIdx];
         enterRO = this->maxRowObj(enterIdx);
         objChange -= enterRO * enterVal;

         if(enterUB >= R(infinity))
            ds.rowStatus(enterIdx) = SPxBasisBase<R>::Desc::D_ON_LOWER;
         else if(EQ(enterLB, enterUB, this->epsilon()))
            ds.rowStatus(enterIdx) = SPxBasisBase<R>::Desc::D_FREE;
         else
            ds.rowStatus(enterIdx) = SPxBasisBase<R>::Desc::D_ON_BOTH;

         break;

      case SPxBasisBase<R>::Desc::P_ON_LOWER :
         assert(rep() == COLUMN);
         enterUB = theURbound[enterIdx];
         enterLB = theLRbound[enterIdx];
         enterVal = enterUB;
         enterMax = enterLB - enterUB;
         enterPric = (*theCoPvec)[enterIdx];
         enterRO = this->maxRowObj(enterIdx);
         objChange -= enterRO * enterVal;

         if(enterLB <= R(-infinity))
            ds.rowStatus(enterIdx) = SPxBasisBase<R>::Desc::D_ON_UPPER;
         else if(EQ(enterLB, enterUB, this->epsilon()))
            ds.rowStatus(enterIdx) = SPxBasisBase<R>::Desc::D_FREE;
         else
            ds.rowStatus(enterIdx) = SPxBasisBase<R>::Desc::D_ON_BOTH;

         break;

      case SPxBasisBase<R>::Desc::P_FREE :
         assert(rep() == COLUMN);
#if 1
         throw SPxInternalCodeException("XENTER02 This should never happen.");
#else
         SPX_MSG_ERROR(r_cerr() << "EENTER99 ERROR: not yet debugged!" << std::endl;)
         enterPric = (*theCoPvec)[enterIdx];
         enterRO = this->maxRowObj(enterIdx);
         ds.rowStatus(enterIdx) = SPxBasisBase<R>::Desc::D_UNDEFINED;
#endif
         break;

      // dual/rowwise cases:
      case SPxBasisBase<R>::Desc::D_ON_UPPER :
         assert(rep() == ROW);
         assert(theURbound[enterIdx] < R(infinity));
         enterUB = theURbound[enterIdx];
         enterLB = R(-infinity);
         enterVal = enterUB;
         enterMax = R(-infinity);
         enterPric = (*thePvec)[enterIdx];
         enterRO = this->lhs(enterIdx);
         objChange -= enterRO * enterVal;
         ds.rowStatus(enterIdx) = SPxBasisBase<R>::Desc::P_ON_LOWER;
         break;

      case SPxBasisBase<R>::Desc::D_ON_LOWER :
         assert(rep() == ROW);
         assert(theLRbound[enterIdx] > R(-infinity));
         enterLB = theLRbound[enterIdx];
         enterUB = R(infinity);
         enterVal = enterLB;
         enterMax = R(infinity);
         enterPric = (*thePvec)[enterIdx];
         enterRO = this->rhs(enterIdx);
         objChange -= enterRO * enterVal;
         ds.rowStatus(enterIdx) = SPxBasisBase<R>::Desc::P_ON_UPPER;
         break;

      case SPxBasisBase<R>::Desc::D_FREE:
         assert(rep() == ROW);
         assert(this->rhs(enterIdx) == this->lhs(enterIdx));
         enterUB = R(infinity);
         enterLB = R(-infinity);
         enterVal = 0;
         enterPric = (*thePvec)[enterIdx];
         enterRO = this->rhs(enterIdx);
         enterMax = (enterPric > enterRO) ? R(infinity) : R(-infinity);
         ds.rowStatus(enterIdx) = SPxBasisBase<R>::Desc::P_FIXED;
         break;

      case SPxBasisBase<R>::Desc::D_ON_BOTH :
         assert(rep() == ROW);
         enterPric = (*thePvec)[enterIdx];

         if(enterPric > this->rhs(enterIdx))
         {
            enterLB = theLRbound[enterIdx];
            enterVal = enterLB;
            enterUB = R(infinity);
            enterMax = R(infinity);
            enterRO = this->rhs(enterIdx);
            ds.rowStatus(enterIdx) = SPxBasisBase<R>::Desc::P_ON_UPPER;
         }
         else
         {
            enterUB = theURbound[enterIdx];
            enterVal = enterUB;
            enterLB = R(-infinity);
            enterMax = R(-infinity);
            enterRO = this->lhs(enterIdx);
            ds.rowStatus(enterIdx) = SPxBasisBase<R>::Desc::P_ON_LOWER;
         }

         objChange -= theLRbound[enterIdx] * this->rhs(enterIdx);
         objChange -= theURbound[enterIdx] * this->lhs(enterIdx);
         break;

      default:
         throw SPxInternalCodeException("XENTER03 This should never happen.");
      }

      SPxOut::debug(this, "DENTER05 SPxSolverBase::getEnterVals() : row {}: {} -> {} objChange: {}\n",
                    enterIdx, enterStat, ds.rowStatus(enterIdx), objChange);
   }
}

/*      process leaving variable
 */
template <class R>
void SPxSolverBase<R>::getEnterVals2
(
   int leaveIdx,
   R enterMax,
   R& leavebound,
   StableSum<R>& objChange
)
{
   int idx;
   typename SPxBasisBase<R>::Desc& ds = this->desc();
   SPxId leftId = this->baseId(leaveIdx);

   if(leftId.isSPxRowId())
   {
      idx = this->number(SPxRowId(leftId));
      typename SPxBasisBase<R>::Desc::Status leaveStat = ds.rowStatus(idx);

      // coverity[switch_selector_expr_is_constant]
      switch(leaveStat)
      {
      case SPxBasisBase<R>::Desc::P_FIXED :
         assert(rep() == ROW);
         throw SPxInternalCodeException("XENTER04 This should never happen.");
         break;

      case SPxBasisBase<R>::Desc::P_ON_UPPER :
         assert(rep() == ROW);
         leavebound = theLBbound[leaveIdx];
         theLRbound[idx] = leavebound;
         ds.rowStatus(idx) = this->dualRowStatus(idx);

         switch(ds.rowStatus(idx))
         {
         case SPxBasisBase<R>::Desc::D_ON_UPPER :
            objChange += theURbound[idx] * this->lhs(idx);
            break;

         case SPxBasisBase<R>::Desc::D_ON_LOWER :
            objChange += theLRbound[idx] * this->rhs(idx);
            break;

         case SPxBasisBase<R>::Desc::D_ON_BOTH :
            objChange += theURbound[idx] * this->lhs(idx);
            objChange += theLRbound[idx] * this->rhs(idx);
            break;

         default:
            break;
         }

         break;

      case SPxBasisBase<R>::Desc::P_ON_LOWER :
         assert(rep() == ROW);
         leavebound = theUBbound[leaveIdx];
         theURbound[idx] = leavebound;
         ds.rowStatus(idx) = this->dualRowStatus(idx);

         switch(ds.rowStatus(idx))
         {
         case SPxBasisBase<R>::Desc::D_ON_UPPER :
            objChange += theURbound[idx] * this->lhs(idx);
            break;

         case SPxBasisBase<R>::Desc::D_ON_LOWER :
            objChange += theLRbound[idx] * this->rhs(idx);
            break;

         case SPxBasisBase<R>::Desc::D_ON_BOTH :
            objChange += theURbound[idx] * this->lhs(idx);
            objChange += theLRbound[idx] * this->rhs(idx);
            break;

         default:
            break;
         }

         break;

      case SPxBasisBase<R>::Desc::P_FREE :
         assert(rep() == ROW);
#if 1
         throw SPxInternalCodeException("XENTER05 This should never happen.");
#else
         SPX_MSG_ERROR(r_cerr() << "EENTER98 ERROR: not yet debugged!" << std::endl;)

         if((*theCoPvec)[leaveIdx] - theLBbound[leaveIdx] <
               theUBbound[leaveIdx] - (*theCoPvec)[leaveIdx])
         {
            leavebound = theLBbound[leaveIdx];
            theLRbound[idx] = leavebound;
         }
         else
         {
            leavebound = theUBbound[leaveIdx];
            theURbound[idx] = leavebound;
         }

         ds.rowStatus(idx) = SPxBasisBase<R>::Desc::D_UNDEFINED;
#endif
         break;

      // primal/columnwise cases:
      case SPxBasisBase<R>::Desc::D_UNDEFINED :
         assert(rep() == COLUMN);
         throw SPxInternalCodeException("XENTER06 This should never happen.");
         break;

      case SPxBasisBase<R>::Desc::D_FREE :
         assert(rep() == COLUMN);

         if(theFvec->delta()[leaveIdx] * enterMax < 0)
            leavebound = theUBbound[leaveIdx];
         else
            leavebound = theLBbound[leaveIdx];

         theLRbound[idx] = leavebound;
         theURbound[idx] = leavebound;
         objChange += leavebound * this->maxRowObj(leaveIdx);
         ds.rowStatus(idx) = SPxBasisBase<R>::Desc::P_FIXED;
         break;

      case SPxBasisBase<R>::Desc::D_ON_UPPER :
         assert(rep() == COLUMN);
         leavebound = theUBbound[leaveIdx];
         theURbound[idx] = leavebound;
         objChange += leavebound * this->maxRowObj(leaveIdx);
         ds.rowStatus(idx) = SPxBasisBase<R>::Desc::P_ON_LOWER;
         break;

      case SPxBasisBase<R>::Desc::D_ON_LOWER :
         assert(rep() == COLUMN);
         leavebound = theLBbound[leaveIdx];
         theLRbound[idx] = leavebound;
         objChange += leavebound * this->maxRowObj(leaveIdx);
         ds.rowStatus(idx) = SPxBasisBase<R>::Desc::P_ON_UPPER;
         break;

      case SPxBasisBase<R>::Desc::D_ON_BOTH :
         assert(rep() == COLUMN);

         if(enterMax * theFvec->delta()[leaveIdx] < 0)
         {
            leavebound = theUBbound[leaveIdx];
            theURbound[idx] = leavebound;
            objChange += leavebound * this->maxRowObj(leaveIdx);
            ds.rowStatus(idx) = SPxBasisBase<R>::Desc::P_ON_LOWER;
         }
         else
         {
            leavebound = theLBbound[leaveIdx];
            theLRbound[idx] = leavebound;
            objChange += leavebound * this->maxRowObj(leaveIdx);
            ds.rowStatus(idx) = SPxBasisBase<R>::Desc::P_ON_UPPER;
         }

         break;

      default:
         throw SPxInternalCodeException("XENTER07 This should never happen.");
      }

      SPxOut::debug(this, "DENTER06 SPxSolverBase::getEnterVals2(): row {}: {} -> {} objChange: {}\n",
                    idx, leaveStat, ds.rowStatus(idx), objChange);
   }

   else
   {
      assert(leftId.isSPxColId());
      idx = this->number(SPxColId(leftId));
      typename SPxBasisBase<R>::Desc::Status leaveStat = ds.colStatus(idx);

      // coverity[switch_selector_expr_is_constant]
      switch(leaveStat)
      {
      case SPxBasisBase<R>::Desc::P_ON_UPPER :
         assert(rep() == ROW);
         leavebound = theLBbound[leaveIdx];
         theLCbound[idx] = leavebound;
         ds.colStatus(idx) = this->dualColStatus(idx);

         switch(ds.colStatus(idx))
         {
         case SPxBasisBase<R>::Desc::D_ON_UPPER :
            objChange += theUCbound[idx] * this->lower(idx);
            break;

         case SPxBasisBase<R>::Desc::D_ON_LOWER :
            objChange += theLCbound[idx] * this->upper(idx);
            break;

         case SPxBasisBase<R>::Desc::D_ON_BOTH :
            objChange += theLCbound[idx] * this->upper(idx);
            objChange += theUCbound[idx] * this->lower(idx);
            break;

         default:
            break;
         }

         break;

      case SPxBasisBase<R>::Desc::P_ON_LOWER :
         assert(rep() == ROW);
         leavebound = theUBbound[leaveIdx];
         theUCbound[idx] = leavebound;
         ds.colStatus(idx) = this->dualColStatus(idx);

         switch(ds.colStatus(idx))
         {
         case SPxBasisBase<R>::Desc::D_ON_UPPER :
            objChange += theUCbound[idx] * this->lower(idx);
            break;

         case SPxBasisBase<R>::Desc::D_ON_LOWER :
            objChange += theLCbound[idx] * this->upper(idx);
            break;

         case SPxBasisBase<R>::Desc::D_ON_BOTH :
            objChange += theLCbound[idx] * this->upper(idx);
            objChange += theUCbound[idx] * this->lower(idx);
            break;

         default:
            break;
         }

         break;

      case SPxBasisBase<R>::Desc::P_FREE :
         assert(rep() == ROW);

         if(theFvec->delta()[leaveIdx] * enterMax > 0)
         {
            leavebound = theLBbound[leaveIdx];
            theLCbound[idx] = leavebound;
         }
         else
         {
            leavebound = theUBbound[leaveIdx];
            theUCbound[idx] = leavebound;
         }

         ds.colStatus(idx) = SPxBasisBase<R>::Desc::D_UNDEFINED;
         break;

      case SPxBasisBase<R>::Desc::P_FIXED:
         assert(rep() == ROW);
         throw SPxInternalCodeException("XENTER08 This should never happen.");
         break;

      // primal/columnwise cases:
      case SPxBasisBase<R>::Desc::D_FREE :
         assert(rep() == COLUMN);

         if(theFvec->delta()[leaveIdx] * enterMax > 0)
            leavebound = theLBbound[leaveIdx];
         else
            leavebound = theUBbound[leaveIdx];

         theUCbound[idx] =
            theLCbound[idx] = leavebound;
         objChange += this->maxObj(idx) * leavebound;
         ds.colStatus(idx) = SPxBasisBase<R>::Desc::P_FIXED;
         break;

      case SPxBasisBase<R>::Desc::D_ON_UPPER :
         assert(rep() == COLUMN);
         leavebound = theLBbound[leaveIdx];
         theLCbound[idx] = leavebound;
         objChange += this->maxObj(idx) * leavebound;
         ds.colStatus(idx) = SPxBasisBase<R>::Desc::P_ON_LOWER;
         break;

      case SPxBasisBase<R>::Desc::D_ON_LOWER :
         assert(rep() == COLUMN);
         leavebound = theUBbound[leaveIdx];
         theUCbound[idx] = leavebound;
         objChange += this->maxObj(idx) * leavebound;
         ds.colStatus(idx) = SPxBasisBase<R>::Desc::P_ON_UPPER;
         break;

      case SPxBasisBase<R>::Desc::D_ON_BOTH :
      case SPxBasisBase<R>::Desc::D_UNDEFINED :
         assert(rep() == COLUMN);

         if(enterMax * theFvec->delta()[leaveIdx] < 0)
         {
            leavebound = theUBbound[leaveIdx];
            theUCbound[idx] = leavebound;
            objChange += this->maxObj(idx) * leavebound;
            ds.colStatus(idx) = SPxBasisBase<R>::Desc::P_ON_UPPER;
         }
         else
         {
            leavebound = theLBbound[leaveIdx];
            theLCbound[idx] = leavebound;
            objChange += this->maxObj(idx) * leavebound;
            ds.colStatus(idx) = SPxBasisBase<R>::Desc::P_ON_LOWER;
         }

         break;

      default:
         throw SPxInternalCodeException("XENTER09 This should never happen.");
      }

      SPxOut::debug(this, "DENTER07 SPxSolverBase::getEnterVals2(): col {}: {} -> {} objChange: {}\n",
                    idx, leaveStat, ds.colStatus(idx), objChange);
   }
}

template <class R>
void
SPxSolverBase<R>::ungetEnterVal(
   SPxId enterId,
   typename SPxBasisBase<R>::Desc::Status enterStat,
   R leaveVal,
   const SVectorBase<R>& vec,
   StableSum<R>& objChange
)
{
   assert(rep() == COLUMN);
   int enterIdx;
   typename SPxBasisBase<R>::Desc& ds = this->desc();

   if(enterId.isSPxColId())
   {
      enterIdx = this->number(SPxColId(enterId));

      if(enterStat == SPxBasisBase<R>::Desc::P_ON_UPPER)
      {
         ds.colStatus(enterIdx) = SPxBasisBase<R>::Desc::P_ON_LOWER;
         objChange += theLCbound[enterIdx] * this->maxObj(enterIdx);
      }
      else
      {
         ds.colStatus(enterIdx) = SPxBasisBase<R>::Desc::P_ON_UPPER;
         objChange += theUCbound[enterIdx] * this->maxObj(enterIdx);
      }

      theFrhs->multAdd(leaveVal, vec);
   }
   else
   {
      enterIdx = this->number(SPxRowId(enterId));
      assert(enterId.isSPxRowId());

      if(enterStat == SPxBasisBase<R>::Desc::P_ON_UPPER)
      {
         ds.rowStatus(enterIdx) = SPxBasisBase<R>::Desc::P_ON_LOWER;
         objChange += (theURbound[enterIdx]) * this->maxRowObj(enterIdx);
      }
      else
      {
         ds.rowStatus(enterIdx) = SPxBasisBase<R>::Desc::P_ON_UPPER;
         objChange += (theLRbound[enterIdx]) * this->maxRowObj(enterIdx);
      }

      (*theFrhs)[enterIdx] += leaveVal;
   }

   if(isId(enterId))
   {
      theTest[enterIdx] = 0;
      isInfeasibleCo[enterIdx] = SPxPricer<R>::NOT_VIOLATED;
   }
   else
   {
      theCoTest[enterIdx] = 0;
      isInfeasible[enterIdx] = SPxPricer<R>::NOT_VIOLATED;
   }
}

template <class R>
void SPxSolverBase<R>::rejectEnter(
   SPxId enterId,
   R enterTest,
   typename SPxBasisBase<R>::Desc::Status enterStat
)
{
   int enterIdx = this->number(enterId);

   if(isId(enterId))
   {
      theTest[enterIdx] = enterTest;
      this->desc().status(enterIdx) = enterStat;
   }
   else
   {
      theCoTest[enterIdx] = enterTest;
      this->desc().coStatus(enterIdx) = enterStat;
   }
}

template <class R>
void SPxSolverBase<R>::computePrimalray4Col(R direction, SPxId enterId)
{
   R sign = (direction > 0 ? 1.0 : -1.0);

   primalRay.clear();
   primalRay.setMax(fVec().delta().size() + 1);

   for(int j = 0; j < fVec().delta().size(); ++j)
   {
      SPxId i = this->baseId(fVec().idx().index(j));

      if(i.isSPxColId())
         primalRay.add(this->number(SPxColId(i)), sign * fVec().delta().value(j));
   }

   if(enterId.isSPxColId())
      primalRay.add(this->number(SPxColId(enterId)), -sign);
}

template <class R>
void SPxSolverBase<R>::computeDualfarkas4Row(R direction, SPxId enterId)
{
   R sign = (direction > 0 ? -1.0 : 1.0);

   dualFarkas.clear();
   dualFarkas.setMax(fVec().delta().size() + 1);

   for(int j = 0; j < fVec().delta().size(); ++j)
   {
      SPxId spxid = this->baseId(fVec().idx().index(j));

      if(spxid.isSPxRowId())
         dualFarkas.add(this->number(SPxRowId(spxid)), sign * fVec().delta().value(j));
   }

   if(enterId.isSPxRowId())
      dualFarkas.add(this->number(SPxRowId(enterId)), -sign);
}

template <class R>
bool SPxSolverBase<R>::enter(SPxId& enterId, bool polish)
{
   assert(enterId.isValid());
   assert(type() == ENTER);
   assert(initialized);

   SPxId none;          // invalid id used when enter fails
   R enterTest;      // correct test value of entering var
   R enterUB;        // upper bound of entering variable
   R enterLB;        // lower bound of entering variable
   R enterVal;       // current value of entering variable
   R enterMax;       // maximum value for entering shift
   R enterPric;      // priced value of entering variable
   typename SPxBasisBase<R>::Desc::Status enterStat;      // status of entering variable
   R enterRO;        // rhs/obj of entering variable
   StableSum<R> objChange;
   const SVectorBase<R>* enterVec = enterVector(enterId);

   bool instable = instableEnter;
   assert(!instable || instableEnterId.isValid());

   getEnterVals(enterId, enterTest, enterUB, enterLB,
                enterVal, enterMax, enterPric, enterStat, enterRO, objChange);

   if(!polish && enterTest > -epsilon())
   {
      rejectEnter(enterId, enterTest, enterStat);
      this->change(-1, none, nullptr);

      SPxOut::debug(this, "DENTER08 rejecting false enter pivot\n");

      return false;
   }

   /*  Before performing the actual basis update, we must determine, how this
       is to be accomplished.
   */
   // BH 2005-11-15: Obviously solve4update() is only called if theFvec.delta()
   // is setup (i.e. the indices of the NZEs are stored within it) and there are
   // 0 NZEs (???).
   // In that case theFvec->delta() is set such that
   //   Base * theFvec->delta() = enterVec
   if(theFvec->delta().isSetup() && theFvec->delta().size() == 0)
      SPxBasisBase<R>::solve4update(theFvec->delta(), *enterVec);

#ifdef ENABLE_ADDITIONAL_CHECKS
   else
   {
      // BH 2005-11-29: This code block seems to check the assertion
      //   || Base * theFvec->delta() - enterVec ||_2 <= entertol()
      VectorBase<R> tmp(dim());
      // BH 2005-11-15: This cast is necessary since SSVectorBase<R>  inherits protected from VectorBase<R>.
      tmp = reinterpret_cast<VectorBase<R>&>(theFvec->delta());
      this->multBaseWith(tmp);
      tmp -= *enterVec;

      if(tmp.length() > entertol())
      {
         // This happens frequently and does usually not hurt, so print these
         // warnings only with verbose level INFO2 and higher.
         SPX_MSG_INFO2((*this->spxout), (*this->spxout) << "WENTER09 fVec updated error = "
                       << tmp.length() << std::endl;)
      }
   }

#endif  // ENABLE_ADDITIONAL_CHECKS

   if(!polish && m_numCycle > m_maxCycle)
   {
      if(-enterMax > 0)
         perturbMaxEnter();
      else
         perturbMinEnter();
   }

   R leaveVal = -enterMax;

   boundflips = 0;
   int leaveIdx = theratiotester->selectLeave(leaveVal, enterTest, polish);

   /* in row representation, fixed columns and rows should not leave the basis */
   assert(leaveIdx < 0 || !this->baseId(leaveIdx).isSPxColId()
          || this->desc().colStatus(this->number(SPxColId(this->baseId(leaveIdx)))) !=
          SPxBasisBase<R>::Desc::P_FIXED);
   assert(leaveIdx < 0 || !this->baseId(leaveIdx).isSPxRowId()
          || this->desc().rowStatus(this->number(SPxRowId(this->baseId(leaveIdx)))) !=
          SPxBasisBase<R>::Desc::P_FIXED);

   instableEnterVal = 0;
   instableEnterId = SPxId();
   instableEnter = false;

   /*
     We now tried to find a variable to leave the basis. If one has been
     found, a regular basis update is to be performed.
   */
   if(leaveIdx >= 0)
   {
      if(spxAbs(leaveVal) < entertol())
      {
         if(NE(theUBbound[leaveIdx], theLBbound[leaveIdx], this->tolerances()->epsilon())
               && enterStat != SPxBasisBase<R>::Desc::P_FREE && enterStat != SPxBasisBase<R>::Desc::D_FREE)
         {
            m_numCycle++;
            enterCycles++;
         }
      }
      else
         m_numCycle /= 2;

      // setup for updating the copricing vector
      if(coSolveVector3 && coSolveVector2)
      {
         assert(coSolveVector2->isConsistent());
         assert(coSolveVector2rhs->isSetup());
         assert(coSolveVector3->isConsistent());
         assert(coSolveVector3rhs->isSetup());
         assert(boundflips > 0);
         SPxBasisBase<R>::coSolve(theCoPvec->delta(), *coSolveVector2, *coSolveVector3
                                  , unitVecs[leaveIdx], *coSolveVector2rhs, *coSolveVector3rhs);
         (*theCoPvec) -= (*coSolveVector3);
      }
      else if(coSolveVector3)
      {
         assert(coSolveVector3->isConsistent());
         assert(coSolveVector3rhs->isSetup());
         assert(boundflips > 0);
         SPxBasisBase<R>::coSolve(theCoPvec->delta(), *coSolveVector3, unitVecs[leaveIdx],
                                  *coSolveVector3rhs);
         (*theCoPvec) -= (*coSolveVector3);
      }
      else if(coSolveVector2)
         SPxBasisBase<R>::coSolve(theCoPvec->delta(), *coSolveVector2, unitVecs[leaveIdx],
                                  *coSolveVector2rhs);
      else
         SPxBasisBase<R>::coSolve(theCoPvec->delta(), unitVecs[leaveIdx]);

      if(boundflips > 0)
      {
         for(int i = coSolveVector3->dim() - 1; i >= 0; --i)
         {
            if(spxAbs((*coSolveVector3)[i]) > epsilon())
               (*thePvec).multAdd(-(*coSolveVector3)[i], (*thecovectors)[i]);
         }

         // we need to update enterPric in case it was changed by bound flips
         if(enterId.isSPxColId())
            enterPric = (*theCoPvec)[this->number(SPxColId(enterId))];
         else
            enterPric = (*thePvec)[this->number(SPxRowId(enterId))];

         SPxOut::debug(this, "IEBFRT02 breakpoints passed / bounds flipped = {}\n", boundflips);
         totalboundflips += boundflips;
      }

      (*theCoPrhs)[leaveIdx] = enterRO;
      theCoPvec->value() = (enterRO - enterPric) / theFvec->delta()[leaveIdx];

      if(theCoPvec->value() > epsilon() || theCoPvec->value() < -epsilon())
      {
         if(pricing() == FULL)
         {
            thePvec->value() = theCoPvec->value();
            setupPupdate();
         }

         doPupdate();
      }

      assert(thePvec->isConsistent());
      assert(theCoPvec->isConsistent());

      assert(!this->baseId(leaveIdx).isSPxRowId()
             || this->desc().rowStatus(this->number(SPxRowId(this->baseId(leaveIdx)))) !=
             SPxBasisBase<R>::Desc::P_FIXED);
      assert(!this->baseId(leaveIdx).isSPxColId()
             || this->desc().colStatus(this->number(SPxColId(this->baseId(leaveIdx)))) !=
             SPxBasisBase<R>::Desc::P_FIXED);

      R leavebound;             // bound on which leaving variable moves

      try
      {
         getEnterVals2(leaveIdx, enterMax, leavebound, objChange);
      }
      catch(const SPxException& F)
      {
         rejectEnter(enterId, enterTest, enterStat);
         this->change(-1, none, nullptr);
         throw F;
      }

      //  process entering variable
      theUBbound[leaveIdx] = enterUB;
      theLBbound[leaveIdx] = enterLB;

      //  compute tests:
      updateCoTest();

      if(pricing() == FULL)
         updateTest();

      // update feasibility vectors
      theFvec->value() = leaveVal;
      theFvec->update();
      (*theFvec)[leaveIdx] = enterVal - leaveVal;

      if(leavebound > epsilon() || leavebound < -epsilon())
         theFrhs->multAdd(-leavebound, this->baseVec(leaveIdx));

      if(enterVal > epsilon() || enterVal < -epsilon())
         theFrhs->multAdd(enterVal, *enterVec);

      // update objective funtion value
      updateNonbasicValue(objChange);

      //  change basis matrix
      this->change(leaveIdx, enterId, enterVec, &(theFvec->delta()));

      return true;
   }
   /*  No leaving vector could be found that would yield a stable pivot step.
    */
   else if(NE(leaveVal, -enterMax, this->tolerances()->epsilon()))
   {
      /* In the ENTER algorithm, when for a selected entering variable we find only
         an instable leaving variable, then the basis change is not conducted.
         Instead, we save the entering variable's id in instableEnterId and set
         the test value to zero, hoping to find a different leaving
         variable with a stable leavingvariable.
         If this fails, however, and no more entering variable is found, we have to
         perform the instable basis change using instableEnterId. In this (and only
         in this) case, the flag instableEnter is set to true.

         leaveVal != enterMax is the case that selectLeave has found only an instable leaving
         variable. We store this leaving variable for later if we are not already in the
         instable case */

      if(!instable)
      {
         instableEnterId = enterId;
         instableEnterVal = enterTest;

         SPxOut::debug(this, "DENTER09 rejecting enter pivot and looking for others\n");

         rejectEnter(enterId, enterTest / 10.0, enterStat);
         this->change(-1, none, nullptr);
      }
      else
      {
         SPxOut::debug(this, "DENTER10 rejecting enter pivot in instable state, resetting values\n");
         rejectEnter(enterId, enterTest, enterStat);
         this->change(-1, none, nullptr);
      }

      return false;
   }
   /*  No leaving vector has been selected from the basis. However, if the
       shift amount for |fVec| is bounded, we are in the case, that the
       entering variable is moved from one bound to its other, before any of
       the basis feasibility variables reaches their bound. This may only
       happen in primal/columnwise case with upper and lower bounds on
       variables.
   */
   else if(!polish && leaveVal < R(infinity) && leaveVal > R(-infinity))
   {
      assert(rep() == COLUMN);
      assert(EQ(leaveVal, -enterMax, this->epsilon()));

      this->change(-1, enterId, enterVec);

      theFvec->value() = leaveVal;
      theFvec->update();

      ungetEnterVal(enterId, enterStat, leaveVal, *enterVec, objChange);

      // update objective funtion value
      updateNonbasicValue(objChange);

      SPxOut::debug(this, "DENTER11 moving entering variable from one bound to the other\n");

      return false;
   }
   /*  No variable could be selected to leave the basis and even the entering
       variable is unbounded --- this is a failure.
   */
   else
   {
      /* The following line originally was in the "lastUpdate() > 1" case;
         we need it in the INFEASIBLE/UNBOUNDED case, too, to have the
         basis descriptor at the correct size.
      */
      rejectEnter(enterId, enterTest, enterStat);
      this->change(-1, none, nullptr);

      if(polish)
         return false;

      else if(this->lastUpdate() > 1)
      {
         SPX_MSG_INFO3((*this->spxout), (*this->spxout) << "IENTER01 factorization triggered in "
                       << "enter() for feasibility test" << std::endl;)

         try
         {
            factorize();
         }
         catch(const SPxStatusException& E)
         {
            // don't exit immediately but handle the singularity correctly
            assert(SPxBasisBase<R>::status() == SPxBasisBase<R>::SINGULAR);
            SPX_MSG_INFO3((*this->spxout),
                          (*this->spxout) << "Caught exception in factorization: " << E.what() <<
                          std::endl;)
         }

         /* after a factorization, the entering column/row might not be infeasible or suboptimal anymore, hence we do
          * not try to call leave(leaveIdx), but rather return to the main solving loop and call the pricer again
          */
         return false;
      }

      /* do not exit with status infeasible or unbounded if there is only a very small violation
       * ROW: recompute the primal variables and activities for another, more precise, round of pricing
       */
      else if(spxAbs(enterTest) < entertol())
      {
         SPX_MSG_INFO3((*this->spxout),
                       (*this->spxout) << "IENTER11 clean up step to reduce numerical errors" <<
                       std::endl;)

         SPxBasisBase<R>::coSolve(*theCoPvec, *theCoPrhs);
         computePvec();
         computeCoTest();
         computeTest();

         return false;
      }

      SPX_MSG_INFO3((*this->spxout), (*this->spxout) << "IENTER02 unboundedness/infeasibility found in "
                    << "enter()" << std::endl;)

      if(rep() == ROW)
      {
         computeDualfarkas4Row(leaveVal, enterId);
         setBasisStatus(SPxBasisBase<R>::INFEASIBLE);
      }
      /**@todo if shift() is not zero, we must not conclude primal unboundedness */
      else
      {
         computePrimalray4Col(leaveVal, enterId);
         setBasisStatus(SPxBasisBase<R>::UNBOUNDED);
      }

      return false;
   }
}
} // namespace soplex
