spxsolver.cpp

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/*                                                                           */
/*                  This file is part of the class library                   */
/*       SoPlex --- the Sequential object-oriented simPlex.                  */
/*                                                                           */
/*    Copyright (C) 1996-2018 Konrad-Zuse-Zentrum                            */
/*                            fuer Informationstechnik Berlin                */
/*                                                                           */
/*  SoPlex is distributed under the terms of the ZIB Academic Licence.       */
/*                                                                           */
/*  You should have received a copy of the ZIB Academic License              */
/*  along with SoPlex; see the file COPYING. If not email to soplex@zib.de.  */
/*                                                                           */
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

#include <assert.h>
#include <iostream>
#include <sstream>

#include "soplex/spxdefines.h"
#include "soplex.h"
#include "soplex/spxpricer.h"
#include "soplex/spxratiotester.h"
#include "soplex/spxstarter.h"
#include "soplex/spxout.h"
#include "soplex/timerfactory.h"

namespace soplex
{

bool SPxSolver::read(std::istream& in, NameSet* rowNames,
                  NameSet* colNames, DIdxSet* intVars)
{
   if( initialized )
   {
      clear();
      unInit();

      if (thepricer)
         thepricer->clear();

      if (theratiotester)
         theratiotester->clear();
   }

   unLoad();
   if (!SPxLP::read(in, rowNames, colNames, intVars))
      return false;

   theLP = this;

   return true;
}

void SPxSolver::reLoad()
{
   forceRecompNonbasicValue();
   unInit();
   unLoad();
   theLP = this;
   m_status = SPxSolver::UNKNOWN;
   if (thepricer)
      thepricer->clear();
   if (theratiotester)
      theratiotester->clear();
}

void SPxSolver::loadLP(const SPxLP& lp, bool initSlackBasis)
{
   clear();
   unInit();
   unLoad();
   resetClockStats();
   if (thepricer)
      thepricer->clear();
   if (theratiotester)
      theratiotester->clear();
   SPxLP::operator=(lp);
   reDim();
   SPxBasis::load(this, initSlackBasis);
}

void SPxSolver::setBasisSolver(SLinSolver* slu, const bool destroy)
{
   // we need to set the outstream before we load the solver to ensure that the basis
   // can be initialized with this pointer in loadSolver()
   assert(spxout != 0);
   slu->spxout = spxout;
   SPxBasis::loadBasisSolver(slu, destroy);
}

void SPxSolver::loadBasis(const SPxBasis::Desc& p_desc)
{
   unInit();
   if (SPxBasis::status() == SPxBasis::NO_PROBLEM)
   {
      SPxBasis::load(this, false);
   }
   setBasisStatus(SPxBasis::REGULAR);
   SPxBasis::loadDesc(p_desc);
}

void SPxSolver::setPricer(SPxPricer* x, const bool destroy)
{

   assert(!freePricer || thepricer != 0);

   if(freePricer)
   {
      delete thepricer;
      thepricer = 0;
   }

   if (x != 0 && x != thepricer)
   {
      setPricing(FULL);
      if (isInitialized())
         x->load(this);
      else
         x->clear();
   }

   if (thepricer && thepricer != x)
      thepricer->clear();
   thepricer = x;

   freePricer = destroy;
}

void SPxSolver::setTester(SPxRatioTester* x, const bool destroy)
{
   assert(!freeRatioTester || theratiotester != 0);

   if(freeRatioTester)
   {
      delete theratiotester;
      theratiotester = 0;
   }

   theratiotester = x;

   // set the solver pointer inside the ratiotester
   if( theratiotester != 0 )
   {
      if( isInitialized() )
         theratiotester->load(this);
      else
         theratiotester->clear();
   }

   freeRatioTester = destroy;
}

void SPxSolver::setStarter(SPxStarter* x, const bool destroy)
{

   assert(!freeStarter || thestarter != 0);

   if(freeStarter)
   {
      delete thestarter;
      thestarter = 0;
   }
   thestarter = x;

   freeStarter = destroy;
}

void SPxSolver::setType(Type tp)
{

   if (theType != tp)
   {
      theType = tp;

      forceRecompNonbasicValue();

      unInit();
      MSG_INFO3( (*spxout), (*spxout) << "Switching to "
                        << static_cast<const char*>((tp == LEAVE)
                           ? "leaving" : "entering")
                        << " algorithm" << std::endl; )
   }
}

void SPxSolver::initRep(Representation p_rep)
{

   Real tmpfeastol = feastol();
   Real tmpopttol = opttol();

   theRep = p_rep;

   if (theRep == COLUMN)
   {
      thevectors   = colSet();
      thecovectors = rowSet();
      theFrhs      = &primRhs;
      theFvec      = &primVec;
      theCoPrhs    = &dualRhs;
      theCoPvec    = &dualVec;
      thePvec      = &addVec;
      theRPvec     = theCoPvec;
      theCPvec     = thePvec;
      theUbound    = &theUCbound;
      theLbound    = &theLCbound;
      theCoUbound  = &theURbound;
      theCoLbound  = &theLRbound;
   }
   else
   {
      assert(theRep == ROW);

      thevectors   = rowSet();
      thecovectors = colSet();
      theFrhs      = &dualRhs;
      theFvec      = &dualVec;
      theCoPrhs    = &primRhs;
      theCoPvec    = &primVec;
      thePvec      = &addVec;
      theRPvec     = thePvec;
      theCPvec     = theCoPvec;
      theUbound    = &theURbound;
      theLbound    = &theLRbound;
      theCoUbound  = &theUCbound;
      theCoLbound  = &theLCbound;
   }
   unInit();
   reDim();

   forceRecompNonbasicValue();

   setFeastol(tmpfeastol);
   setOpttol(tmpopttol);

   SPxBasis::setRep();
   if (SPxBasis::status() > SPxBasis::NO_PROBLEM)
      SPxBasis::loadDesc(desc());

   if (thepricer && thepricer->solver() == this)
      thepricer->setRep(p_rep);
}

void SPxSolver::setRep(Representation p_rep)
{

   if (p_rep != theRep)
      initRep(p_rep);
}

// needed for strongbranching. use carefully
void SPxSolver::reinitializeVecs()
{

   initialized = true;

   if (type() == ENTER)
   {
      if (rep() == COLUMN)
         setPrimalBounds();
      else
         setDualRowBounds();

      setEnterBounds();
      computeEnterCoPrhs();
   }
   else
   {
      if (rep() == ROW)
         setPrimalBounds();
      else
         setDualColBounds();

      setLeaveBounds();
      computeLeaveCoPrhs();
   }

   SPxBasis::coSolve(*theCoPvec, *theCoPrhs);
   computePvec();
   computeFrhs();
   SPxBasis::solve(*theFvec, *theFrhs);

   theShift  = 0.0;
   lastShift = 0.0;

   if (type() == ENTER)
   {
      computeCoTest();
      computeTest();
   }
   else
   {
      computeFtest();
   }
   assert((testBounds(), 1));
}

void SPxSolver::resetClockStats()
{
   nClckSkipsLeft = 0;
   nCallsToTimelim = 0;
   theCumulativeTime = 0.0;
}

void SPxSolver::init()
{

   assert(thepricer      != 0);
   assert(theratiotester != 0);

   if (!initialized)
   {
      initialized = true;
      clearUpdateVecs();
      reDim();
      if (SPxBasis::status() <= SPxBasis::NO_PROBLEM || solver() != this)
         SPxBasis::load(this);
      initialized = false;
   }
   if (!matrixIsSetup)
      SPxBasis::loadDesc(desc());

   // Inna/Tobi: don't "upgrade" a singular basis to a regular one
   if( SPxBasis::status() == SPxBasis::SINGULAR )
      return;

   // catch pathological case for LPs with zero constraints
   if( dim() == 0 )
   {
      factorized = true;
   }

   // we better factorize explicitly before solving
   if( !factorized )
   {
      try
      {
         SPxBasis::factorize();
      }
      catch( const SPxException& )
      {
         // reload inital slack basis in case the factorization failed
         assert(SPxBasis::status() <= SPxBasis::SINGULAR);
         SPxBasis::restoreInitialBasis();
         SPxBasis::factorize();
         assert(factorized);
      }
   }

   m_numCycle = 0;

   if (type() == ENTER)
   {
      if (rep() == COLUMN)
      {
         setPrimalBounds();
         setBasisStatus(SPxBasis::PRIMAL);
      }
      else
      {
         setDualRowBounds();
         setBasisStatus(SPxBasis::DUAL);
      }
      setEnterBounds();
      computeEnterCoPrhs();
      // prepare support vectors for sparse pricing
      infeasibilities.setMax(dim());
      infeasibilitiesCo.setMax(coDim());
      isInfeasible.reSize(dim());
      isInfeasibleCo.reSize(coDim());
      theratiotester->setDelta(entertol());
   }
   else
   {
      if (rep() == ROW)
      {
         setPrimalBounds();
         setBasisStatus(SPxBasis::PRIMAL);
      }
      else
      {
         setDualColBounds();
         setBasisStatus(SPxBasis::DUAL);
      }
      setLeaveBounds();
      computeLeaveCoPrhs();
      // prepare support vectors for sparse pricing
      infeasibilities.setMax(dim());
      isInfeasible.reSize(dim());
      theratiotester->setDelta(leavetol());
   }

   SPxBasis::coSolve(*theCoPvec, *theCoPrhs);
   computePvec();
   computeFrhs();
   SPxBasis::solve(*theFvec, *theFrhs);

   theShift = 0.0;

   if (type() == ENTER)
   {
      shiftFvec();
      lastShift = theShift + entertol();

      computeCoTest();
      computeTest();
   }
   else
   {
      shiftPvec();
      lastShift = theShift + leavetol();

      computeFtest();
   }

   if (!initialized)
   {
      // if(thepricer->solver() != this)
      thepricer->load(this);
      // if(theratiotester->solver() != this)
      theratiotester->load(this);
      initialized = true;
   }
}

void SPxSolver::setPricing(Pricing pr)
{
   thePricing = pr;
   if (initialized && type() == ENTER)
   {
      computePvec();
      computeCoTest();
      computeTest();
   }
}

void SPxSolver::setDecompStatus(DecompStatus decomp_stat)
{
   if( decomp_stat == FINDSTARTBASIS )
      getStartingDecompBasis = true;
   else
      getStartingDecompBasis = false;
}

/*
    The following method resizes all vectors and arrays of |SoPlex|
    (excluding inherited vectors).
 */
void SPxSolver::reDim()
{

   int newsize = SPxLP::nCols() > SPxLP::nRows() ? SPxLP::nCols() : SPxLP::nRows();

   if (newsize > unitVecs.size())
   {
      unitVecs.reSize(newsize);

      while (newsize-- > 0)
         unitVecs[newsize] = UnitVector(newsize);
   }

   if (isInitialized())
   {
      theFrhs->reDim(dim());
      theFvec->reDim(dim());
      thePvec->reDim(coDim());

      theCoPrhs->reDim(dim());
      theCoPvec->reDim(dim());

      theTest.reDim(coDim());
      theCoTest.reDim(dim());

      theURbound.reDim(SPxLP::nRows());
      theLRbound.reDim(SPxLP::nRows());
      theUCbound.reDim(SPxLP::nCols());
      theLCbound.reDim(SPxLP::nCols());
      theUBbound.reDim(dim());
      theLBbound.reDim(dim());
   }
}

void SPxSolver::clear()
{
   unitVecs.reSize(0);

   dualRhs.clear();
   dualVec.clear();
   primRhs.clear();
   primVec.clear();
   addVec.clear();
   theURbound.clear();
   theLRbound.clear();
   theUCbound.clear();
   theLCbound.clear();
   theTest.clear();
   theCoTest.clear();

   forceRecompNonbasicValue();
   unInit();
   SPxLP::clear();
   setBasisStatus(SPxBasis::NO_PROBLEM);
   // clear the basis only when theLP is present, because LP data (nrows, ncols) is used in reDim()
   if( theLP != 0 )
      SPxBasis::reDim();

   infeasibilities.clear();
   infeasibilitiesCo.clear();
   isInfeasible.clear();
   isInfeasibleCo.clear();
}

void SPxSolver::unscaleLPandReloadBasis()
{
   SPxLPBase<Real>::unscaleLP();
   SPxBasis::invalidate();
   unInit();
   init();
}

void SPxSolver::clearUpdateVecs(void)
{
   theFvec->clearUpdate();
   thePvec->clearUpdate();
   theCoPvec->clearUpdate();
   solveVector2 = 0;
   solveVector3 = 0;
   coSolveVector2 = 0;
   coSolveVector3 = 0;
}

/*
    When the basis matrix factorization is recomputed from scratch,
    we also recompute the vectors.
 */
void SPxSolver::factorize()
{

   MSG_INFO3( (*spxout), (*spxout) << " --- refactorizing basis matrix" << std::endl; )

   try
   {
      SPxBasis::factorize();
   }
   catch( const SPxStatusException& )
   {
      assert(SPxBasis::status() == SPxBasis::SINGULAR);
      m_status = SINGULAR;
      std::stringstream s;
      s << "Basis is singular (numerical troubles, feastol = " << feastol() << ", opttol = " << opttol() << ")";
      throw SPxStatusException(s.str());
   }

   if( !initialized )
   {
      init();  // not sure if init() is neccessary here
      // we must not go on here because not all vectors (e.g. fVec) may be set up correctly
      return;
   }

   if (SPxBasis::status() >= SPxBasis::REGULAR)
   {
#ifndef NDEBUG
      DVector ftmp(fVec());
      DVector ptmp(pVec());
      DVector ctmp(coPvec());
#endif  // NDEBUG

      if (type() == LEAVE)
      {
         /* we have to recompute theFrhs, because roundoff errors can occur during updating, especially when
          * columns/rows with large bounds are present
          */
         computeFrhs();
         SPxBasis::solve (*theFvec, *theFrhs);
         SPxBasis::coSolve(*theCoPvec, *theCoPrhs);

#ifndef NDEBUG
         ftmp -= fVec();
         ptmp -= pVec();
         ctmp -= coPvec();
         if (ftmp.length() > DEFAULT_BND_VIOL)
         {
            MSG_DEBUG( std::cout << "DSOLVE21 fVec:   " << ftmp.length() << std::endl; )
            ftmp = fVec();
            multBaseWith(ftmp);
            ftmp -= fRhs();
            if (ftmp.length() > DEFAULT_BND_VIOL)
               MSG_INFO1( (*spxout), (*spxout) << "ESOLVE29 " << iteration() << ": fVec error = "
                                 << ftmp.length() << " exceeding DEFAULT_BND_VIOL = " << DEFAULT_BND_VIOL << std::endl; )
         }
         if (ctmp.length() > DEFAULT_BND_VIOL)
         {
            MSG_DEBUG( std::cout << "DSOLVE23 coPvec: " << ctmp.length() << std::endl; )
            ctmp = coPvec();
            multWithBase(ctmp);
            ctmp -= coPrhs();
            if (ctmp.length() > DEFAULT_BND_VIOL)
               MSG_INFO1( (*spxout), (*spxout) << "ESOLVE30 " << iteration() << ": coPvec error = "
                                 << ctmp.length() << " exceeding DEFAULT_BND_VIOL = " << DEFAULT_BND_VIOL << std::endl; )
         }
         if (ptmp.length() > DEFAULT_BND_VIOL)
         {
            MSG_DEBUG( std::cout << "DSOLVE24 pVec:   " << ptmp.length() << std::endl; )
         }
#endif  // NDEBUG

         computeFtest();
      }
      else
      {
         assert(type() == ENTER);

         SPxBasis::coSolve(*theCoPvec, *theCoPrhs);
         computeCoTest();

         if (pricing() == FULL)
         {
            /* to save time only recompute the row activities (in row rep) when we are already nearly optimal to
             * avoid missing any violations from previous updates */
            if( rep() == ROW && m_pricingViolCo < entertol() && m_pricingViol < entertol() )
               computePvec();

            /* was deactivated, but this leads to warnings in testVecs() */
            computeTest();
         }
      }
   }

#ifdef ENABLE_ADDITIONAL_CHECKS
   /* moved this test after the computation of fTest and coTest below, since these vectors might not be set up at top, e.g. for an initial basis */
   if (SPxBasis::status() > SPxBasis::SINGULAR)
      testVecs();
#endif
}

/* We compute how much the current solution violates (primal or dual) feasibility. In the
   row/enter or column/leave algorithm the maximum violation of dual feasibility is
   computed. In the row/leave or column/enter algorithm the primal feasibility is checked.
   Additionally, the violation from pricing is taken into account. */
Real SPxSolver::maxInfeas() const
{
   Real inf = 0.0;

   if (type() == ENTER)
   {
      if( m_pricingViolUpToDate && m_pricingViolCoUpToDate )
         inf = m_pricingViol + m_pricingViolCo;

      for (int i = 0; i < dim(); i++)
      {
         if ((*theFvec)[i] > theUBbound[i])
            inf = MAXIMUM(inf, (*theFvec)[i] - theUBbound[i]);
         else if ((*theFvec)[i] < theLBbound[i])
            inf = MAXIMUM(inf, theLBbound[i] - (*theFvec)[i]);
      }
   }
   else
   {
      assert(type() == LEAVE);

      if( m_pricingViolUpToDate )
         inf = m_pricingViol;

      for (int i = 0; i < dim(); i++)
      {
         if ((*theCoPvec)[i] > (*theCoUbound)[i])
            inf = MAXIMUM(inf, (*theCoPvec)[i] - (*theCoUbound)[i]);
         else if ((*theCoPvec)[i] < (*theCoLbound)[i])
            inf = MAXIMUM(inf, (*theCoLbound)[i] - (*theCoPvec)[i]);
      }
      for (int i = 0; i < coDim(); i++)
      {
         if ((*thePvec)[i] > (*theUbound)[i])
            inf = MAXIMUM(inf, (*thePvec)[i] - (*theUbound)[i]);
         else if ((*thePvec)[i] < (*theLbound)[i])
            inf = MAXIMUM(inf, (*theLbound)[i] - (*thePvec)[i]);
      }
   }

   return inf;
}

/* check for (dual) violations above tol and immediately return false w/o checking the remaining values
   This method is useful for verifying whether an objective limit can be used as termination criterion */
bool SPxSolver::noViols(Real tol) const
{
   assert(tol >= 0.0);

   if( type() == ENTER )
   {
      for( int i = 0; i < dim(); i++ )
      {
         if( (*theFvec)[i] - theUBbound[i] > tol )
            return false;
         if( theLBbound[i] - (*theFvec)[i] > tol )
            return false;
      }
   }
   else
   {
      assert(type() == LEAVE);

      for( int i = 0; i < dim(); i++ )
      {
         if( (*theCoPvec)[i] - (*theCoUbound)[i] > tol )
            return false;
         if( (*theCoLbound)[i] - (*theCoPvec)[i] > tol )
            return false;
      }
      for (int i = 0; i < coDim(); i++)
      {
         if( (*thePvec)[i] - (*theUbound)[i] > tol )
            return false;
         if( (*theLbound)[i] - (*thePvec)[i] > tol )
            return false;
      }
   }
   return true;
}

Real SPxSolver::nonbasicValue()
{
   int i;
   Real val = 0;
   const SPxBasis::Desc& ds = desc();

#ifndef ENABLE_ADDITIONAL_CHECKS
   // if the value is available we don't need to recompute it
   if ( m_nonbasicValueUpToDate )
      return m_nonbasicValue;
#endif

   if (rep() == COLUMN)
   {
      if (type() == LEAVE)
      {
         for (i = nCols() - 1; i >= 0; --i)
         {
            switch (ds.colStatus(i))
            {
            case SPxBasis::Desc::P_ON_UPPER :
               val += theUCbound[i] * SPxLP::upper(i);
               //@ val += maxObj(i) * SPxLP::upper(i);
               break;
            case SPxBasis::Desc::P_ON_LOWER :
               val += theLCbound[i] * SPxLP::lower(i);
               //@ val += maxObj(i) * SPxLP::lower(i);
               break;
            case SPxBasis::Desc::P_FIXED :
               val += maxObj(i) * SPxLP::lower(i);
               break;
            default:
               break;
            }
         }
         for (i = nRows() - 1; i >= 0; --i)
         {
            switch (ds.rowStatus(i))
            {
            case SPxBasis::Desc::P_ON_UPPER :
               val += theLRbound[i] * SPxLP::rhs(i);
               break;
            case SPxBasis::Desc::P_ON_LOWER :
               val += theURbound[i] * SPxLP::lhs(i);
               break;
            case SPxBasis::Desc::P_FIXED :
               val += maxRowObj(i) * SPxLP::lhs(i);
               break;
            default:
               break;
            }
         }
      }
      else
      {
         assert(type() == ENTER);
         for (i = nCols() - 1; i >= 0; --i)
         {
            switch (ds.colStatus(i))
            {
            case SPxBasis::Desc::P_ON_UPPER :
               val += maxObj(i) * theUCbound[i];
               break;
            case SPxBasis::Desc::P_ON_LOWER :
               val += maxObj(i) * theLCbound[i];
               break;
            case SPxBasis::Desc::P_FIXED :
               assert(EQ(theLCbound[i], theUCbound[i]));
               val += maxObj(i) * theLCbound[i];
               break;
            default:
               break;
            }
         }
         for (i = nRows() - 1; i >= 0; --i)
         {
            switch (ds.rowStatus(i))
            {
            case SPxBasis::Desc::P_ON_UPPER :
               val += maxRowObj(i) * theLRbound[i];
               break;
            case SPxBasis::Desc::P_ON_LOWER :
               val += maxRowObj(i) * theURbound[i];
               break;
            case SPxBasis::Desc::P_FIXED :
               val += maxRowObj(i) * theURbound[i];
               break;
            default:
               break;
            }
         }
      }
   }
   else
   {
      assert(rep() == ROW);
      assert(type() == ENTER);
      for (i = nCols() - 1; i >= 0; --i)
      {
         switch (ds.colStatus(i))
         {
         case SPxBasis::Desc::D_ON_UPPER :
            val += theUCbound[i] * lower(i);
            break;
         case SPxBasis::Desc::D_ON_LOWER :
            val += theLCbound[i] * upper(i);
            break;
         case SPxBasis::Desc::D_ON_BOTH :
            val += theLCbound[i] * upper(i);
            val += theUCbound[i] * lower(i);
            break;
         default:
            break;
         }
      }
      for (i = nRows() - 1; i >= 0; --i)
      {
         switch (ds.rowStatus(i))
         {
         case SPxBasis::Desc::D_ON_UPPER :
            val += theURbound[i] * lhs(i);
            break;
         case SPxBasis::Desc::D_ON_LOWER :
            val += theLRbound[i] * rhs(i);
            break;
         case SPxBasis::Desc::D_ON_BOTH :
            val += theLRbound[i] * rhs(i);
            val += theURbound[i] * lhs(i);
            break;
         default:
            break;
         }
      }
   }

#ifdef ENABLE_ADDITIONAL_CHECKS
   if( m_nonbasicValueUpToDate && NE(m_nonbasicValue, val) )
   {
      MSG_ERROR( std::cerr << "stored nonbasic value: " << m_nonbasicValue
                 << ", correct nonbasic value: " << val
                 << ", violation: " << val - m_nonbasicValue << std::endl; )
      assert(EQrel(m_nonbasicValue, val, 1e-12));
   }
#endif

   if( !m_nonbasicValueUpToDate )
   {
      m_nonbasicValue = val;
      m_nonbasicValueUpToDate = true;
   }

   return val;
}

Real SPxSolver::value()
{
   assert(isInitialized());

   Real x;

   // calling value() without having a suitable status is an error.
   if (!isInitialized())
      return infinity;

   if (rep() == ROW)
   {
      if (type() == LEAVE)
         x = SPxLP::spxSense() * (coPvec() * fRhs()); // the contribution of maxRowObj() is missing
      else
         x = SPxLP::spxSense() * (nonbasicValue() + (coPvec() * fRhs()));
   }
   else
      x = SPxLP::spxSense() * (nonbasicValue() + fVec() * coPrhs());

   return x + objOffset();
}

bool SPxSolver::updateNonbasicValue(Real objChange)
{
   if( m_nonbasicValueUpToDate )
      m_nonbasicValue += objChange;

   MSG_DEBUG( std::cout
      << "Iteration: " << iteration()
      << ": updated objValue: " << objChange
      << ", new value: " << m_nonbasicValue
      << ", correct value: " << nonbasicValue()
      << std::endl;
   )

   return m_nonbasicValueUpToDate;
}



void SPxSolver::setFeastol(Real d)
{

   if( d <= 0.0 )
      throw SPxInterfaceException("XSOLVE30 Cannot set feastol less than or equal to zero.");

   if( theRep == COLUMN )
      m_entertol = d;
   else
      m_leavetol = d;
}

void SPxSolver::setOpttol(Real d)
{

   if( d <= 0.0 )
      throw SPxInterfaceException("XSOLVE31 Cannot set opttol less than or equal to zero.");

   if( theRep == COLUMN )
      m_leavetol = d;
   else
      m_entertol = d;
}

void SPxSolver::setDelta(Real d)
{

   if( d <= 0.0 )
      throw SPxInterfaceException("XSOLVE32 Cannot set delta less than or equal to zero.");

   m_entertol = d;
   m_leavetol = d;
}

void SPxSolver::hyperPricing(bool h)
{
   hyperPricingEnter = h;
   hyperPricingLeave = h;
   if( h )
   {
      updateViols.setMax(dim());
      updateViolsCo.setMax(coDim());
   }
}

SPxSolver::SPxSolver(
   Type            p_type,
   Representation  p_rep,
   Timer::TYPE     ttype)
   : theType (p_type)
   , thePricing(FULL)
   , theRep(p_rep)
   , polishObj(POLISH_OFF)
   , theTime(0)
   , timerType(ttype)
   , theCumulativeTime(0.0)
   , maxIters (-1)
   , maxTime (infinity)
   , nClckSkipsLeft(0)
   , nCallsToTimelim(0)
   , objLimit(infinity)
   , m_status(UNKNOWN)
   , m_nonbasicValue(0.0)
   , m_nonbasicValueUpToDate(false)
   , m_pricingViol(0.0)
   , m_pricingViolUpToDate(false)
   , m_pricingViolCo(0.0)
   , m_pricingViolCoUpToDate(false)
   , theShift (0)
   , m_maxCycle(100)
   , m_numCycle(0)
   , initialized (false)
   , solveVector2 (0)
   , solveVector3 (0)
   , coSolveVector2(0)
   , coSolveVector3(0)
   , freePricer (false)
   , freeRatioTester (false)
   , freeStarter (false)
   , displayLine (0)
   , displayFreq (200)
   , sparsePricingFactor(SPARSITYFACTOR)
   , getStartingDecompBasis(false)
   , computeDegeneracy(false)
   , degenCompIterOffset(0)
   , fullPerturbation(false)
   , printCondition(0)
   , unitVecs (0)
   , primVec (0, Param::epsilon())
   , dualVec (0, Param::epsilon())
   , addVec (0, Param::epsilon())
   , thepricer (0)
   , theratiotester (0)
   , thestarter (0)
   , boundrange(0.0)
   , siderange(0.0)
   , objrange(0.0)
   , infeasibilities(0)
   , infeasibilitiesCo(0)
   , isInfeasible(0)
   , isInfeasibleCo(0)
   , sparsePricingLeave(false)
   , sparsePricingEnter(false)
   , sparsePricingEnterCo(false)
   , hyperPricingLeave(true)
   , hyperPricingEnter(true)
   , remainingRoundsLeave(0)
   , remainingRoundsEnter(0)
   , remainingRoundsEnterCo(0)
   , weights(0)
   , coWeights(0)
   , weightsAreSetup(false)
   , integerVariables(0)
{
   theTime = TimerFactory::createTimer(timerType);

   setDelta(DEFAULT_BND_VIOL);

   theLP = this;
   initRep(p_rep);

   // info: SPxBasis is not consistent in this moment.
   //assert(SPxSolver::isConsistent());
}

SPxSolver::~SPxSolver()
{
   assert(!freePricer || thepricer != 0);
   assert(!freeRatioTester || theratiotester != 0);
   assert(!freeStarter || thestarter != 0);

   if(freePricer)
   {
      delete thepricer;
      thepricer = 0;
   }

   if(freeRatioTester)
   {
      delete theratiotester;
      theratiotester = 0;
   }

   if(freeStarter)
   {
      delete thestarter;
      thestarter = 0;
   }

   // free timer
   assert(theTime);
   theTime->~Timer();
   spx_free(theTime);
}


SPxSolver& SPxSolver::operator=(const SPxSolver& base)
{
   if(this != &base)
   {
      SPxLP::operator=(base);
      SPxBasis::operator=(base);
      theType = base.theType;
      thePricing = base.thePricing;
      theRep = base.theRep;
      polishObj = base.polishObj;
      timerType = base.timerType;
      maxIters = base.maxIters;
      maxTime = base.maxTime;
      objLimit = base.objLimit;
      m_status = base.m_status;
      m_nonbasicValue = base.m_nonbasicValue;
      m_nonbasicValueUpToDate = base.m_nonbasicValueUpToDate;
      m_pricingViol = base.m_pricingViol;
      m_pricingViolUpToDate = base.m_pricingViolUpToDate;
      m_pricingViolCo = base.m_pricingViolCo;
      m_pricingViolCoUpToDate = base.m_pricingViolCoUpToDate;
      m_entertol = base.m_entertol;
      m_leavetol = base.m_leavetol;
      theShift = base.theShift;
      lastShift = base.lastShift;
      m_maxCycle = base.m_maxCycle;
      m_numCycle = base.m_numCycle;
      initialized = base.initialized;
      instableLeaveNum = base.instableLeaveNum;
      instableLeave = base.instableLeave;
      instableLeaveVal = base.instableLeaveVal;
      instableEnterId = base.instableEnterId;
      instableEnter = base.instableEnter;
      instableEnterVal = base.instableEnterVal;
      displayLine = base.displayLine;
      displayFreq = base.displayFreq;
      sparsePricingFactor = base.sparsePricingFactor;
      getStartingDecompBasis = base.getStartingDecompBasis;
      computeDegeneracy = base.computeDegeneracy;
      degenCompIterOffset = base.degenCompIterOffset;
      decompIterationLimit = base.decompIterationLimit;
      fullPerturbation = base.fullPerturbation;
      printCondition = base.printCondition;
      unitVecs = base.unitVecs;
      primRhs = base.primRhs;
      primVec = base.primVec;
      dualRhs = base.dualRhs;
      dualVec = base.dualVec;
      addVec = base.addVec;
      theURbound = base.theURbound;
      theLRbound = base.theLRbound;
      theUCbound = base.theUCbound;
      theLCbound = base.theLCbound;
      theUBbound = base.theUBbound;
      theLBbound = base.theLBbound;
      theCoTest = base.theCoTest;
      theTest = base.theTest;
      primalRay = base.primalRay;
      dualFarkas = base.dualFarkas;
      leaveCount = base.leaveCount;
      enterCount = base.enterCount;
      theCumulativeTime = base.theCumulativeTime;
      primalCount = base.primalCount;
      polishCount = base.polishCount;
      boundflips = base.boundflips;
      totalboundflips = base.totalboundflips;
      enterCycles = base.enterCycles;
      leaveCycles = base.leaveCycles;
      enterDegenCand = base.enterDegenCand;
      leaveDegenCand = base.leaveDegenCand;
      primalDegenSum = base.primalDegenSum;
      boundrange = base.boundrange;
      siderange = base.siderange;
      objrange = base.objrange;
      infeasibilities = base.infeasibilities;
      infeasibilitiesCo = base.infeasibilitiesCo;
      isInfeasible = base.isInfeasible;
      isInfeasibleCo = base.isInfeasibleCo;
      sparsePricingLeave = base.sparsePricingLeave;
      sparsePricingEnter = base.sparsePricingEnter;
      sparsePricingEnterCo = base.sparsePricingEnterCo;
      sparsePricingFactor = base.sparsePricingFactor;
      hyperPricingLeave = base.hyperPricingLeave;
      hyperPricingEnter = base.hyperPricingEnter;
      remainingRoundsLeave = base.remainingRoundsLeave;
      remainingRoundsEnter = base.remainingRoundsEnter;
      remainingRoundsEnterCo = base.remainingRoundsEnterCo;
      weights = base.weights;
      coWeights = base.coWeights;
      weightsAreSetup = base.weightsAreSetup;
      spxout = base.spxout;
      integerVariables = base.integerVariables;

      if (base.theRep == COLUMN)
      {
         thevectors   = colSet();
         thecovectors = rowSet();
         theFrhs      = &primRhs;
         theFvec      = &primVec;
         theCoPrhs    = &dualRhs;
         theCoPvec    = &dualVec;
         thePvec      = &addVec;
         theRPvec     = theCoPvec;
         theCPvec     = thePvec;
         theUbound    = &theUCbound;
         theLbound    = &theLCbound;
         theCoUbound  = &theURbound;
         theCoLbound  = &theLRbound;
      }
      else
      {
         assert(base.theRep == ROW);

         thevectors   = rowSet();
         thecovectors = colSet();
         theFrhs      = &dualRhs;
         theFvec      = &dualVec;
         theCoPrhs    = &primRhs;
         theCoPvec    = &primVec;
         thePvec      = &addVec;
         theRPvec     = thePvec;
         theCPvec     = theCoPvec;
         theUbound    = &theURbound;
         theLbound    = &theLRbound;
         theCoUbound  = &theUCbound;
         theCoLbound  = &theLCbound;
      }

      SPxBasis::theLP = this;

      assert(!freePricer || thepricer != 0);
      assert(!freeRatioTester || theratiotester != 0);
      assert(!freeStarter || thestarter != 0);

      // thepricer
      if(freePricer)
      {
         delete thepricer;
         thepricer = 0;
      }
      if(base.thepricer == 0)
      {
         thepricer = 0;
         freePricer = false;
      }
      else
      {
         thepricer = base.thepricer->clone();
         freePricer = true;
         thepricer->load(this);
      }

      // theratiotester
      if(freeRatioTester)
      {
         delete theratiotester;
         theratiotester = 0;
      }
      if(base.theratiotester == 0)
      {
         theratiotester = 0;
         freeRatioTester = false;
      }
      else
      {
         theratiotester = base.theratiotester->clone();
         freeRatioTester = true;
         theratiotester->load(this);
      }

      // thestarter
      if(freeStarter)
      {
         delete thestarter;
         thestarter = 0;
      }
      if(base.thestarter == 0)
      {
         thestarter = 0;
         freeStarter = false;
      }
      else
      {
         thestarter = base.thestarter->clone();
         freeStarter = true;
      }

      assert(SPxSolver::isConsistent());
   }

   return *this;
}


SPxSolver::SPxSolver(const SPxSolver& base)
   : SPxLP (base)
   , SPxBasis(base)
   , theType(base.theType)
   , thePricing(base.thePricing)
   , theRep(base.theRep)
   , polishObj(base.polishObj)
   , timerType(base.timerType)
   , theCumulativeTime(base.theCumulativeTime)
   , maxIters(base.maxIters)
   , maxTime(base.maxTime)
   , nClckSkipsLeft(base.nClckSkipsLeft)
   , nCallsToTimelim(base.nCallsToTimelim)
   , objLimit(base.objLimit)
   , m_status(base.m_status)
   , m_nonbasicValue(base.m_nonbasicValue)
   , m_nonbasicValueUpToDate(base.m_nonbasicValueUpToDate)
   , m_pricingViol(base.m_pricingViol)
   , m_pricingViolUpToDate(base.m_pricingViolUpToDate)
   , m_pricingViolCo(base.m_pricingViolCo)
   , m_pricingViolCoUpToDate(base.m_pricingViolCoUpToDate)
   , m_entertol(base.m_entertol)
   , m_leavetol(base.m_leavetol)
   , theShift(base.theShift)
   , lastShift(base.lastShift)
   , m_maxCycle(base.m_maxCycle)
   , m_numCycle(base.m_numCycle)
   , initialized(base.initialized)
   , solveVector2 (0)
   , solveVector2rhs(base.solveVector2rhs)
   , solveVector3 (0)
   , solveVector3rhs(base.solveVector3rhs)
   , coSolveVector2(0)
   , coSolveVector2rhs(base.coSolveVector2rhs)
   , coSolveVector3(0)
   , coSolveVector3rhs(base.coSolveVector3rhs)
   , instableLeaveNum(base.instableLeaveNum)
   , instableLeave(base.instableLeave)
   , instableLeaveVal(base.instableLeaveVal)
   , instableEnterId(base.instableEnterId)
   , instableEnter(base.instableEnter)
   , instableEnterVal(base.instableEnterVal)
   , displayLine(base.displayLine)
   , displayFreq(base.displayFreq)
   , sparsePricingFactor(base.sparsePricingFactor)
   , getStartingDecompBasis(base.getStartingDecompBasis)
   , computeDegeneracy(base.computeDegeneracy)
   , degenCompIterOffset(base.degenCompIterOffset)
   , decompIterationLimit(base.decompIterationLimit)
   , fullPerturbation(base.fullPerturbation)
   , printCondition(base.printCondition)
   , unitVecs(base.unitVecs)
   , primRhs(base.primRhs)
   , primVec(base.primVec)
   , dualRhs(base.dualRhs)
   , dualVec(base.dualVec)
   , addVec(base.addVec)
   , theURbound(base.theURbound)
   , theLRbound(base.theLRbound)
   , theUCbound(base.theUCbound)
   , theLCbound(base.theLCbound)
   , theUBbound(base.theUBbound)
   , theLBbound(base.theLBbound)
   , theCoTest(base.theCoTest)
   , theTest(base.theTest)
   , primalRay(base.primalRay)
   , dualFarkas(base.dualFarkas)
   , leaveCount(base.leaveCount)
   , enterCount(base.enterCount)
   , primalCount(base.primalCount)
   , polishCount(base.polishCount)
   , boundflips(base.boundflips)
   , totalboundflips(base.totalboundflips)
   , enterCycles(base.enterCycles)
   , leaveCycles(base.leaveCycles)
   , enterDegenCand(base.enterDegenCand)
   , leaveDegenCand(base.leaveDegenCand)
   , primalDegenSum(base.primalDegenSum)
   , dualDegenSum(base.dualDegenSum)
   , boundrange(base.boundrange)
   , siderange(base.siderange)
   , objrange(base.objrange)
   , infeasibilities(base.infeasibilities)
   , infeasibilitiesCo(base.infeasibilitiesCo)
   , isInfeasible(base.isInfeasible)
   , isInfeasibleCo(base.isInfeasibleCo)
   , sparsePricingLeave(base.sparsePricingLeave)
   , sparsePricingEnter(base.sparsePricingEnter)
   , sparsePricingEnterCo(base.sparsePricingEnterCo)
   , hyperPricingLeave(base.hyperPricingLeave)
   , hyperPricingEnter(base.hyperPricingEnter)
   , remainingRoundsLeave(base.remainingRoundsLeave)
   , remainingRoundsEnter(base.remainingRoundsEnter)
   , remainingRoundsEnterCo(base.remainingRoundsEnterCo)
   , weights(base.weights)
   , coWeights(base.coWeights)
   , weightsAreSetup(base.weightsAreSetup)
   , spxout(base.spxout)
   , integerVariables(base.integerVariables)
{
   theTime = TimerFactory::createTimer(timerType);

   if (base.theRep == COLUMN)
   {
      thevectors   = colSet();
      thecovectors = rowSet();
      theFrhs      = &primRhs;
      theFvec      = &primVec;
      theCoPrhs    = &dualRhs;
      theCoPvec    = &dualVec;
      thePvec      = &addVec;
      theRPvec     = theCoPvec;
      theCPvec     = thePvec;
      theUbound    = &theUCbound;
      theLbound    = &theLCbound;
      theCoUbound  = &theURbound;
      theCoLbound  = &theLRbound;
   }
   else
   {
      assert(base.theRep == ROW);

      thevectors   = rowSet();
      thecovectors = colSet();
      theFrhs      = &dualRhs;
      theFvec      = &dualVec;
      theCoPrhs    = &primRhs;
      theCoPvec    = &primVec;
      thePvec      = &addVec;
      theRPvec     = thePvec;
      theCPvec     = theCoPvec;
      theUbound    = &theURbound;
      theLbound    = &theLRbound;
      theCoUbound  = &theUCbound;
      theCoLbound  = &theLCbound;
   }

   SPxBasis::theLP = this;

   if(base.thepricer == 0)
   {
      thepricer = 0;
      freePricer = false;
   }
   else
   {
      thepricer = base.thepricer->clone();
      freePricer = true;
      thepricer->clear();
      thepricer->load(this);
   }

   if(base.theratiotester == 0)
   {
      theratiotester = 0;
      freeRatioTester = false;
   }
   else
   {
      theratiotester = base.theratiotester->clone();
      freeRatioTester = true;
      theratiotester->clear();
      theratiotester->load(this);
   }

   if(base.thestarter == 0)
   {
      thestarter = 0;
      freeStarter = false;
   }
   else
   {
      thestarter = base.thestarter->clone();
      freeStarter = true;
   }

   assert(SPxSolver::isConsistent());
}

bool SPxSolver::isConsistent() const
{
#ifdef ENABLE_CONSISTENCY_CHECKS
   if (epsilon() < 0)
      return MSGinconsistent("SPxSolver");

   if (primVec.delta().getEpsilon() != dualVec.delta().getEpsilon())
      return MSGinconsistent("SPxSolver");

   if (dualVec.delta().getEpsilon() != addVec.delta().getEpsilon())
      return MSGinconsistent("SPxSolver");

   if (unitVecs.size() < SPxLP::nCols() || unitVecs.size() < SPxLP::nRows())
      return MSGinconsistent("SPxSolver");

   if (initialized)
   {
      if (theFrhs->dim() != dim())
         return MSGinconsistent("SPxSolver");
      if (theFvec->dim() != dim())
         return MSGinconsistent("SPxSolver");

      if (theCoPrhs->dim() != dim())
         return MSGinconsistent("SPxSolver");
      if (thePvec->dim() != coDim())
         return MSGinconsistent("SPxSolver");
      if (theCoPvec->dim() != dim())
         return MSGinconsistent("SPxSolver");

      if (theTest.dim() != coDim())
         return MSGinconsistent("SPxSolver");
      if (theCoTest.dim() != dim())
         return MSGinconsistent("SPxSolver");

      if (theURbound.dim() != SPxLP::nRows())
         return MSGinconsistent("SPxSolver");
      if (theLRbound.dim() != SPxLP::nRows())
         return MSGinconsistent("SPxSolver");
      if (theUCbound.dim() != SPxLP::nCols())
         return MSGinconsistent("SPxSolver");
      if (theLCbound.dim() != SPxLP::nCols())
         return MSGinconsistent("SPxSolver");
      if (theUBbound.dim() != dim())
         return MSGinconsistent("SPxSolver");
      if (theLBbound.dim() != dim())
         return MSGinconsistent("SPxSolver");
   }

   if (rep() == COLUMN)
   {
      if(thecovectors !=
         reinterpret_cast<const SVSet*>(static_cast<const LPRowSet*>(this))
         || thevectors !=
         reinterpret_cast<const SVSet*>(static_cast<const LPColSet*>(this))
         || theFrhs != &primRhs ||
         theFvec != &primVec ||
         theCoPrhs != &dualRhs ||
         theCoPvec != &dualVec ||
         thePvec != &addVec ||
         theRPvec != theCoPvec ||
         theCPvec != thePvec ||
         theUbound != &theUCbound ||
         theLbound != &theLCbound ||
         theCoUbound != &theURbound ||
         theCoLbound != &theLRbound)
         return MSGinconsistent("SPxSolver");
   }
   else
   {
      if (thecovectors
         != reinterpret_cast<const SVSet*>(static_cast<const LPColSet*>(this))
         || thevectors
         != reinterpret_cast<const SVSet*>(static_cast<const LPRowSet*>(this))
         || theFrhs != &dualRhs ||
         theFvec != &dualVec ||
         theCoPrhs != &primRhs ||
         theCoPvec != &primVec ||
         thePvec != &addVec ||
         theRPvec != thePvec ||
         theCPvec != theCoPvec ||
         theUbound != &theURbound ||
         theLbound != &theLRbound ||
         theCoUbound != &theUCbound ||
         theCoLbound != &theLCbound)
         return MSGinconsistent("SPxSolver");
   }

   return SPxLP::isConsistent()
          && primRhs.isConsistent()
          && primVec.isConsistent()
          && dualRhs.isConsistent()
          && dualVec.isConsistent()
          && addVec.isConsistent()
          && theTest.isConsistent()
          && theCoTest.isConsistent()
          && theURbound.isConsistent()
          && theLRbound.isConsistent()
          && theUCbound.isConsistent()
          && theLCbound.isConsistent()
          && SPxBasis::isConsistent()
         ;
#else
   return true;
#endif
}


void SPxSolver::setTerminationTime(Real p_time)
{
   if( p_time < 0.0 )
      p_time = 0.0;
   maxTime = p_time;
}

Real SPxSolver::terminationTime() const
{
   return maxTime;
}

void SPxSolver::setTerminationIter(int p_iteration)
{
   if( p_iteration < 0 )
      p_iteration = -1;
   maxIters = p_iteration;
}

int SPxSolver::terminationIter() const
{
   return maxIters;
}

// returns whether current time limit is reached; call to time() may be skipped unless \p forceCheck is true
bool SPxSolver::isTimeLimitReached(const bool forceCheck)
{
   // always update the number of calls, since the user might set a time limit later in the solving process
   ++nCallsToTimelim;

   // check if a time limit is actually set
   if( maxTime >= infinity )
      return false;

   // check if the expensive system call to update the time should be skipped again
   if( forceCheck || nCallsToTimelim < NINITCALLS ||  nClckSkipsLeft <= 0 )
   {
      Real currtime = time();

      if( currtime >= maxTime )
         return true;

      // determine the number of times the clock can be skipped again.
      int nClckSkips = MAXNCLCKSKIPS;
      Real avgtimeinterval = (currtime + cumulativeTime()) / (Real)(nCallsToTimelim);

      // it would not be safe to skip the clock so many times since we are approaching the time limit
      if( SAFETYFACTOR * (maxTime - currtime) / (avgtimeinterval + 1e-6) < nClckSkips )
         nClckSkips = 0;
      nClckSkipsLeft = nClckSkips;
   }
   else
      --nClckSkipsLeft;

   return false;
}


/**@todo A first version for the termination value is
 *       implemented. Currently we check if no bound violations (shifting)
 *       is present. It might be even possible to use this termination
 *       value in case of bound violations (shifting) but in this case it
 *       is quite difficult to determine if we already reached the limit.
 */
void SPxSolver::setTerminationValue(Real p_value)
{
   objLimit = p_value;
}

Real SPxSolver::terminationValue() const
{
   return objLimit;
}

SPxSolver::VarStatus
SPxSolver::basisStatusToVarStatus( SPxBasis::Desc::Status stat ) const
{
   VarStatus vstat;

   switch( stat )
   {
   case SPxBasis::Desc::P_ON_LOWER:
      vstat = ON_LOWER;
      break;
   case SPxBasis::Desc::P_ON_UPPER:
      vstat = ON_UPPER;
      break;
   case SPxBasis::Desc::P_FIXED:
      vstat = FIXED;
      break;
   case SPxBasis::Desc::P_FREE:
      vstat = ZERO;
      break;
   case SPxBasis::Desc::D_ON_UPPER:
   case SPxBasis::Desc::D_ON_LOWER:
   case SPxBasis::Desc::D_ON_BOTH:
   case SPxBasis::Desc::D_UNDEFINED:
   case SPxBasis::Desc::D_FREE:
      vstat = BASIC;
      break;
   default:
      MSG_ERROR( std::cerr << "ESOLVE26 ERROR: unknown basis status (" << stat << ")"
                        << std::endl; )
      throw SPxInternalCodeException("XSOLVE22 This should never happen.");
   }
   return vstat;
}

SPxBasis::Desc::Status
SPxSolver::varStatusToBasisStatusRow( int row, SPxSolver::VarStatus stat ) const
{
   SPxBasis::Desc::Status rstat;

   switch( stat )
   {
   case FIXED :
      assert(EQ(rhs(row), lhs(row), feastol()));
      rstat = SPxBasis::Desc::P_FIXED;
      break;
   case ON_UPPER :
      assert(rhs(row) < infinity);
      rstat = lhs(row) < rhs(row)
         ? SPxBasis::Desc::P_ON_UPPER
         : SPxBasis::Desc::P_FIXED;
      break;
   case ON_LOWER :
      assert(lhs(row) > -infinity);
      rstat = lhs(row) < rhs(row)
         ? SPxBasis::Desc::P_ON_LOWER
         : SPxBasis::Desc::P_FIXED;
      break;
   case ZERO :
      /* A 'free' row (i.e., infinite lower & upper bounds) does not really make sense. The user
       * might (think to) know better, e.g., when temporarily turning off a row. We therefore apply
       * the same adjustment as in the column case in varStatusToBasisStatusCol(). */
      if (lhs(row) <= -infinity && rhs(row) >= infinity)
         rstat = SPxBasis::Desc::P_FREE;
      else
      {
         if ( lhs(row) == rhs(row) )
         {
            assert( rhs(row) < infinity );
            rstat = SPxBasis::Desc::P_FIXED;
         }
         else
         {
            if ( lhs(row) > -infinity )
               rstat = SPxBasis::Desc::P_ON_LOWER;
            else
            {
               assert( rhs(row) < infinity );
               rstat = SPxBasis::Desc::P_ON_UPPER;
            }
         }
      }
      break;
   case BASIC :
      rstat = dualRowStatus(row);
      break;
   default:
      MSG_ERROR( std::cerr << "ESOLVE27 ERROR: unknown VarStatus (" << int(stat) << ")"
                        << std::endl; )
      throw SPxInternalCodeException("XSOLVE23 This should never happen.");
   }
   return rstat;
}

SPxBasis::Desc::Status
SPxSolver::varStatusToBasisStatusCol( int col, SPxSolver::VarStatus stat ) const
{
   SPxBasis::Desc::Status cstat;

   switch( stat )
   {
   case FIXED :
      if (upper(col) == lower(col))
         cstat = SPxBasis::Desc::P_FIXED;
      else if (maxObj(col) > 0.0)
         cstat = SPxBasis::Desc::P_ON_UPPER;
      else
         cstat = SPxBasis::Desc::P_ON_LOWER;
      break;
   case ON_UPPER :
      assert(upper(col) < infinity);
      cstat = lower(col) < upper(col)
         ? SPxBasis::Desc::P_ON_UPPER
         : SPxBasis::Desc::P_FIXED;
      break;
   case ON_LOWER :
      assert(lower(col) > -infinity);
      cstat = lower(col) < upper(col)
         ? SPxBasis::Desc::P_ON_LOWER
         : SPxBasis::Desc::P_FIXED;
      break;
   case ZERO :
      /* In this case the upper and lower bounds on the variable should be infinite. The bounds
       * might, however, have changed and we try to recover from this by changing the status to
       * 'resonable' settings. A solve has to find the correct values afterwards. Note that the
       * approach below is consistent with changesoplex.cpp (e.g., changeUpperStatus() and
       * changeLowerStatus() ). */
      if (lower(col) <= -infinity && upper(col) >= infinity)
         cstat = SPxBasis::Desc::P_FREE;
      else
      {
         if ( lower(col) == upper(col) )
         {
            assert( upper(col) < infinity );
            cstat = SPxBasis::Desc::P_FIXED;
         }
         else
         {
            if ( lower(col) > -infinity )
               cstat = SPxBasis::Desc::P_ON_LOWER;
            else
            {
               assert( upper(col) < infinity );
               cstat = SPxBasis::Desc::P_ON_UPPER;
            }
         }
      }
      break;
   case BASIC :
      cstat = dualColStatus(col);
      break;
   default:
      MSG_ERROR( std::cerr << "ESOLVE28 ERROR: unknown VarStatus (" << int(stat) << ")"
                        << std::endl; )
      throw SPxInternalCodeException("XSOLVE24 This should never happen.");
   }
   return cstat;
}

SPxSolver::VarStatus SPxSolver::getBasisRowStatus( int row ) const
{
   assert( 0 <= row && row < nRows() );
   return basisStatusToVarStatus( desc().rowStatus( row ) );
}

SPxSolver::VarStatus SPxSolver::getBasisColStatus( int col ) const
{
   assert( 0 <= col && col < nCols() );
   return basisStatusToVarStatus( desc().colStatus( col ) );
}

SPxSolver::Status SPxSolver::getBasis(VarStatus row[], VarStatus col[], const int rowsSize, const int colsSize) const
{
   const SPxBasis::Desc& d = desc();
   int i;

   assert(rowsSize < 0 || rowsSize >= nRows());
   assert(colsSize < 0 || colsSize >= nCols());

   if (col)
      for (i = nCols() - 1; i >= 0; --i)
         col[i] = basisStatusToVarStatus( d.colStatus(i) );

   if (row)
      for (i = nRows() - 1; i >= 0; --i)
         row[i] = basisStatusToVarStatus( d.rowStatus(i) );

   return status();
}

bool SPxSolver::isBasisValid(DataArray<VarStatus> p_rows, DataArray<VarStatus> p_cols)
{

   int basisdim;

   if ( p_rows.size() != nRows() || p_cols.size() != nCols() )
      return false;

   basisdim = 0;
   for ( int row = nRows()-1; row >= 0; --row )
   {
      if ( p_rows[row] == UNDEFINED )
            return false;
      // row is basic
      else if ( p_rows[row] == BASIC )
      {
         basisdim++;
      }
      // row is nonbasic
      else
      {
         if ( (p_rows[row] == FIXED && lhs(row) != rhs(row))
              || (p_rows[row] == ON_UPPER && rhs(row) >= infinity)
              || (p_rows[row] == ON_LOWER && lhs(row) <= -infinity) )
            return false;
      }
   }

   for ( int col = nCols()-1; col >= 0; --col )
   {
      if ( p_cols[col] == UNDEFINED )
            return false;
      // col is basic
      else if ( p_cols[col] == BASIC )
      {
         basisdim++;
      }
      // col is nonbasic
      else
      {
         if ( (p_cols[col] == FIXED && lower(col) != upper(col))
              || (p_cols[col] == ON_UPPER && upper(col) >= infinity)
              || (p_cols[col] == ON_LOWER && lower(col) <= -infinity) )
            return false;
      }
   }

   if ( basisdim != dim() )
      return false;

   // basis valid
   return true;
}

void SPxSolver::setBasis(const VarStatus p_rows[], const VarStatus p_cols[])
{
   if (SPxBasis::status() == SPxBasis::NO_PROBLEM)
      SPxBasis::load(this, false);

   SPxBasis::Desc ds = desc();
   int i;

   for(i = 0; i < nRows(); i++)
      ds.rowStatus(i) = varStatusToBasisStatusRow( i, p_rows[i] );

   for(i = 0; i < nCols(); i++)
      ds.colStatus(i) = varStatusToBasisStatusCol( i, p_cols[i] );

   loadBasis(ds);
   forceRecompNonbasicValue();
}

// NOTE: This only works for the row representation. Need to update to account for column representation.
// The degenvec differs relative to the algorithm being used.
// For the primal simplex, degenvec is the primal solution values.
// For the dual simplex, the degenvec is the feasvec (ROW) and pVec (COLUMN).
Real SPxSolver::getDegeneracyLevel(Vector degenvec)
{
   int numDegenerate = 0;
   Real degeneracyLevel = 0;

   // iterating over all columns in the basis matrix
   // this identifies the basis indices and those that have a zero dual multiplier (rows) or zero reduced cost (cols).
   if( rep() == ROW )
   {
      for( int i = 0; i < nCols(); ++i ) // @todo Check the use of numColsReal for the reduced problem.
      {
         // degeneracy in the dual simplex exists if there are rows with a zero dual multiplier or columns with a zero
         // reduced costs. This requirement is regardless of the objective sense.
         if( isZero(degenvec[i], feastol()) )
            numDegenerate++;
      }

      if( type() == ENTER )   // dual simplex
         degeneracyLevel = Real(numDegenerate)/nCols();
      else                    // primal simplex
      {
         assert(type() == LEAVE);
         Real degenVars = (numDegenerate > (nCols() - nRows())) ? Real(numDegenerate - (nCols() - nRows())) : 0.0;
         degeneracyLevel = degenVars/nRows();
      }
   }
   else
   {
      assert(rep() == COLUMN);

      for( int i = 0; i < nCols(); i++ )
      {
         if( type() == LEAVE )   // dual simplex
         {
            if( isZero(maxObj()[i] - degenvec[i], feastol()) )
               numDegenerate++;
         }
         else                    // primal simplex
         {
            assert( type() == ENTER );
            if( isZero(degenvec[i], feastol()) )
               numDegenerate++;
         }
      }


      if( type() == LEAVE )   // dual simplex
      {
         Real degenVars = nRows() > numDegenerate ? Real(nRows() - numDegenerate) : 0.0;
         degeneracyLevel = degenVars/nCols();
      }
      else                    // primal simplex
      {
         assert(type() == ENTER);
         Real degenVars = (numDegenerate > (nCols() - nRows())) ? Real(numDegenerate - (nCols() - nRows())) : 0.0;
         degeneracyLevel = degenVars/nRows();
      }
   }

   return degeneracyLevel;
}

void SPxSolver::getNdualNorms(int& nnormsRow, int& nnormsCol) const
{
   nnormsRow = 0;
   nnormsCol = 0;

   if( weightsAreSetup )
   {
      if( type() == SPxSolver::LEAVE && rep() == SPxSolver::COLUMN )
      {
         nnormsRow = coWeights.dim();
         nnormsCol = 0;

         assert(nnormsRow == dim());
      }
      else if( type() == SPxSolver::ENTER && rep() == SPxSolver::ROW )
      {
         nnormsRow = weights.dim();
         nnormsCol = coWeights.dim();

         assert(nnormsRow == coDim());
         assert(nnormsCol == dim());
      }
   }
}

bool SPxSolver::getDualNorms(int& nnormsRow, int& nnormsCol, Real* norms) const
{
   nnormsRow = 0;
   nnormsCol = 0;

   if( !weightsAreSetup )
      return false;

   if( type() == SPxSolver::LEAVE && rep() == SPxSolver::COLUMN )
   {
      nnormsCol = 0;
      nnormsRow = coWeights.dim();

      assert(nnormsRow == dim());

      for( int i = 0; i < nnormsRow; ++i)
         norms[i] = coWeights[i];
   }
   else if( type() == SPxSolver::ENTER && rep() == SPxSolver::ROW )
   {
      nnormsRow = weights.dim();
      nnormsCol = coWeights.dim();

      assert(nnormsCol == dim());
      assert(nnormsRow == coDim());

      for( int i = 0; i < nnormsRow; ++i )
         norms[i] = weights[i];

      for( int i = 0; i < nnormsCol; ++i )
         norms[nnormsRow + i] = coWeights[i];
   }
   else
      return false;

   return true;
}

bool SPxSolver::setDualNorms(int nnormsRow, int nnormsCol, Real* norms)
{
   weightsAreSetup = false;

   if( type() == SPxSolver::LEAVE && rep() == SPxSolver::COLUMN)
   {
      coWeights.reDim(dim(), false);
      assert(coWeights.dim() >= nnormsRow);
      for( int i = 0; i < nnormsRow; ++i )
         coWeights[i] = norms[i];
      weightsAreSetup = true;
   }
   else if( type() == SPxSolver::ENTER && rep() == SPxSolver::ROW)
   {
      weights.reDim(coDim(), false);
      coWeights.reDim(dim(), false);
      assert(weights.dim() >= nnormsRow);
      assert(coWeights.dim() >= nnormsCol);
      for( int i = 0; i < nnormsRow; ++i )
         weights[i] = norms[i];
      for( int i = 0; i < nnormsCol; ++i )
         coWeights[i] = norms[nnormsRow + i];
      weightsAreSetup = true;
   }
   else
      return false;
   return true;
}

void SPxSolver::setIntegralityInformation(int ncols, int* intInfo)
{
   assert(ncols == nCols() || (ncols == 0 && intInfo == NULL));

   integerVariables.reSize(ncols);
   for( int i = 0; i < ncols; ++i )
   {
      integerVariables[i] = intInfo[i];
   }
}



//
// Auxiliary functions.
//

// Pretty-printing of variable status.
std::ostream& operator<<( std::ostream& os,
                          const SPxSolver::VarStatus& status )
{
   switch( status )
      {
      case SPxSolver::BASIC:
         os << "BASIC";
         break;
      case SPxSolver::FIXED:
         os << "FIXED";
         break;
      case SPxSolver::ON_LOWER:
         os << "ON_LOWER";
         break;
      case SPxSolver::ON_UPPER:
         os << "ON_UPPER";
         break;
      case SPxSolver::ZERO:
         os << "ZERO";
         break;
      case SPxSolver::UNDEFINED:
         os << "UNDEFINED";
         break;
      default:
         os << "?invalid?";
         break;
      }
   return os;
}

// Pretty-printing of solver status.
std::ostream& operator<<( std::ostream& os,
                          const SPxSolver::Status& status )
{
   switch ( status )
      {
      case SPxSolver::ERROR:
         os << "ERROR";
         break;
      case SPxSolver::NO_RATIOTESTER:
         os << "NO_RATIOTESTER";
         break;
      case SPxSolver::NO_PRICER:
         os << "NO_PRICER";
         break;
      case SPxSolver::NO_SOLVER:
         os << "NO_SOLVER";
         break;
      case SPxSolver::NOT_INIT:
         os << "NOT_INIT";
         break;
      case SPxSolver::ABORT_CYCLING:
         os << "ABORT_CYCLING";
         break;
      case SPxSolver::ABORT_TIME:
         os << "ABORT_TIME";
         break;
      case SPxSolver::ABORT_ITER:
         os << "ABORT_ITER";
         break;
      case SPxSolver::ABORT_VALUE:
         os << "ABORT_VALUE";
         break;
      case SPxSolver::SINGULAR:
         os << "SINGULAR";
         break;
      case SPxSolver::NO_PROBLEM:
         os << "NO_PROBLEM";
         break;
      case SPxSolver::REGULAR:
         os << "REGULAR";
         break;
      case SPxSolver::RUNNING:
         os << "RUNNING";
         break;
      case SPxSolver::UNKNOWN:
         os << "UNKNOWN";
         break;
      case SPxSolver::OPTIMAL:
         os << "OPTIMAL";
         break;
      case SPxSolver::UNBOUNDED:
         os << "UNBOUNDED";
         break;
      case SPxSolver::INFEASIBLE:
         os << "INFEASIBLE";
         break;
      default:
         os << "?other?";
         break;
      }
   return os;
}

// Pretty-printing of algorithm.
std::ostream& operator<<( std::ostream& os,
                          const SPxSolver::Type& status )
{
   switch ( status )
      {
      case SPxSolver::ENTER:
         os << "ENTER";
         break;
      case SPxSolver::LEAVE:
         os << "LEAVE";
         break;
      default:
         os << "?other?";
         break;
      }
   return os;
}

// Pretty-printing of representation.
std::ostream& operator<<( std::ostream& os,
                          const SPxSolver::Representation& status )
{
   switch ( status )
      {
      case SPxSolver::ROW:
         os << "ROW";
         break;
      case SPxSolver::COLUMN:
         os << "COLUMN";
         break;
      default:
         os << "?other?";
         break;
      }
   return os;
}


} // namespace soplex