source: trunk/Clp/src/ClpSimplexDual.cpp @ 909

// Copyright (C) 2002, International Business Machines
// Corporation and others.  All Rights Reserved.


/* Notes on implementation of dual simplex algorithm.

   When dual feasible:

   If primal feasible, we are optimal.  Otherwise choose an infeasible
   basic variable to leave basis (normally going to nearest bound) (B).  We
   now need to find an incoming variable which will leave problem
   dual feasible so we get the row of the tableau corresponding to
   the basic variable (with the correct sign depending if basic variable
   above or below feasibility region - as that affects whether reduced
   cost on outgoing variable has to be positive or negative).

   We now perform a ratio test to determine which incoming variable will
   preserve dual feasibility (C).  If no variable found then problem
   is infeasible (in primal sense).  If there is a variable, we then 
   perform pivot and repeat.  Trivial?

   -------------------------------------------

   A) How do we get dual feasible?  If all variables have bounds then
   it is trivial to get feasible by putting non-basic variables to
   correct bounds.  OSL did not have a phase 1/phase 2 approach but
   instead effectively put fake bounds on variables and this is the
   approach here, although I had hoped to make it cleaner.

   If there is a weight of X on getting dual feasible:
     Non-basic variables with negative reduced costs are put to
     lesser of their upper bound and their lower bound + X.
     Similarly, mutatis mutandis, for positive reduced costs.

   Free variables should normally be in basis, otherwise I have
   coding which may be able to come out (and may not be correct).

   In OSL, this weight was changed heuristically, here at present
   it is only increased if problem looks finished.  If problem is
   feasible I check for unboundedness.  If not unbounded we 
   could play with going into primal.  As long as weights increase
   any algorithm would be finite.
   
   B) Which outgoing variable to choose is a virtual base class.
   For difficult problems steepest edge is preferred while for
   very easy (large) problems we will need partial scan.

   C) Sounds easy, but this is hardest part of algorithm.
      1) Instead of stopping at first choice, we may be able
      to flip that variable to other bound and if objective
      still improving choose again.  These mini iterations can
      increase speed by orders of magnitude but we may need to
      go to more of a bucket choice of variable rather than looking
      at them one by one (for speed).
      2) Accuracy.  Reduced costs may be of wrong sign but less than
      tolerance.  Pivoting on these makes objective go backwards.
      OSL modified cost so a zero move was made, Gill et al
      (in primal analogue) modified so a strictly positive move was 
      made.  It is not quite as neat in dual but that is what we
      try and do.  The two problems are that re-factorizations can
      change reduced costs above and below tolerances and that when
      finished we need to reset costs and try again.
      3) Degeneracy.  Gill et al helps but may not be enough.  We
      may need more.  Also it can improve speed a lot if we perturb
      the costs significantly.  

  References:
     Forrest and Goldfarb, Steepest-edge simplex algorithms for
       linear programming - Mathematical Programming 1992
     Forrest and Tomlin, Implementing the simplex method for
       the Optimization Subroutine Library - IBM Systems Journal 1992
     Gill, Murray, Saunders, Wright A Practical Anti-Cycling
       Procedure for Linear and Nonlinear Programming SOL report 1988


  TODO:
 
  a) Better recovery procedures.  At present I never check on forward
     progress.  There is checkpoint/restart with reducing 
     re-factorization frequency, but this is only on singular 
     factorizations.
  b) Fast methods for large easy problems (and also the option for
     the code to automatically choose which method).
  c) We need to be able to stop in various ways for OSI - this
     is fairly easy.

 */


#include "CoinPragma.hpp"

#include <math.h>

#include "CoinHelperFunctions.hpp"
#include "ClpHelperFunctions.hpp"
#include "ClpSimplexDual.hpp"
#include "ClpEventHandler.hpp"
#include "ClpFactorization.hpp"
#include "CoinPackedMatrix.hpp"
#include "CoinIndexedVector.hpp"
#include "ClpDualRowDantzig.hpp"
#include "ClpMessage.hpp"
#include <cfloat>
#include <cassert>
#include <string>
#include <stdio.h>
#include <iostream>
//#define CLP_DEBUG 1
// To force to follow another run put logfile name here and define 
//#define FORCE_FOLLOW
#ifdef FORCE_FOLLOW
static FILE * fpFollow=NULL;
static char * forceFile="old.log";
static int force_in=-1;
static int force_out=-1;
static int force_iteration=0;
#endif
//#define VUB
#ifdef VUB
extern int * vub;
extern int * toVub;
extern int * nextDescendent;
#endif
// dual 

  /* *** Method
     This is a vanilla version of dual simplex.

     It tries to be a single phase approach with a weight of 1.0 being
     given to getting optimal and a weight of dualBound_ being
     given to getting dual feasible.  In this version I have used the
     idea that this weight can be thought of as a fake bound.  If the
     distance between the lower and upper bounds on a variable is less
     than the feasibility weight then we are always better off flipping
     to other bound to make dual feasible.  If the distance is greater
     then we make up a fake bound dualBound_ away from one bound.
     If we end up optimal or primal infeasible, we check to see if
     bounds okay.  If so we have finished, if not we increase dualBound_
     and continue (after checking if unbounded). I am undecided about
     free variables - there is coding but I am not sure about it.  At
     present I put them in basis anyway.

     The code is designed to take advantage of sparsity so arrays are
     seldom zeroed out from scratch or gone over in their entirety.
     The only exception is a full scan to find outgoing variable.  This
     will be changed to keep an updated list of infeasibilities (or squares
     if steepest edge).  Also on easy problems we don't need full scan - just
     pick first reasonable.

     One problem is how to tackle degeneracy and accuracy.  At present
     I am using the modification of costs which I put in OSL and which was
     extended by Gill et al.  I am still not sure of the exact details.

     The flow of dual is three while loops as follows:

     while (not finished) {

       while (not clean solution) {

          Factorize and/or clean up solution by flipping variables so
          dual feasible.  If looks finished check fake dual bounds.
          Repeat until status is iterating (-1) or finished (0,1,2)

       }

       while (status==-1) {

         Iterate until no pivot in or out or time to re-factorize.

         Flow is:

         choose pivot row (outgoing variable).  if none then
         we are primal feasible so looks as if done but we need to
         break and check bounds etc.

         Get pivot row in tableau

         Choose incoming column.  If we don't find one then we look
         primal infeasible so break and check bounds etc.  (Also the
         pivot tolerance is larger after any iterations so that may be
         reason)

         If we do find incoming column, we may have to adjust costs to
         keep going forwards (anti-degeneracy).  Check pivot will be stable
         and if unstable throw away iteration (we will need to implement
         flagging of basic variables sometime) and break to re-factorize.
         If minor error re-factorize after iteration.

         Update everything (this may involve flipping variables to stay
         dual feasible.

       }

     }

     At present we never check we are going forwards.  I overdid that in
     OSL so will try and make a last resort.

     Needs partial scan pivot out option.
     Needs dantzig, uninitialized and full steepest edge options (can still
     use partial scan)

     May need other anti-degeneracy measures, especially if we try and use
     loose tolerances as a way to solve in fewer iterations.

     I like idea of dynamic scaling.  This gives opportunity to decouple
     different implications of scaling for accuracy, iteration count and
     feasibility tolerance.

  */
#define CLEAN_FIXED 0
// Startup part of dual (may be extended to other algorithms)
int 
ClpSimplexDual::startupSolve(int ifValuesPass,double * saveDuals,int startFinishOptions)
{
  // If values pass then save given duals round check solution
  // sanity check
  // initialize - no values pass and algorithm_ is -1
  // put in standard form (and make row copy)
  // create modifiable copies of model rim and do optional scaling
  // If problem looks okay
  // Do initial factorization
  // If user asked for perturbation - do it
  if (!startup(0,startFinishOptions)) {
    // looks okay
    // Superbasic variables not allowed
    // If values pass then scale pi 
    if (ifValuesPass) {
      if (problemStatus_&&perturbation_<100) 
        perturb();
      int i;
      if (scalingFlag_>0) {
        for (i=0;i<numberRows_;i++) {
          dual_[i] = saveDuals[i]/rowScale_[i];
        }
      } else {
        CoinMemcpyN(saveDuals,numberRows_,dual_);
      }
      // now create my duals
      for (i=0;i<numberRows_;i++) {
        // slack
        double value = dual_[i];
        value += rowObjectiveWork_[i];
        saveDuals[i+numberColumns_]=value;
      }
      CoinMemcpyN(objectiveWork_,numberColumns_,saveDuals);
      transposeTimes(-1.0,dual_,saveDuals);
      // make reduced costs okay
      for (i=0;i<numberColumns_;i++) {
        if (getStatus(i)==atLowerBound) {
          if (saveDuals[i]<0.0) {
            //if (saveDuals[i]<-1.0e-3)
            //printf("bad dj at lb %d %g\n",i,saveDuals[i]);
            saveDuals[i]=0.0;
          }
        } else if (getStatus(i)==atUpperBound) {
          if (saveDuals[i]>0.0) {
            //if (saveDuals[i]>1.0e-3)
            //printf("bad dj at ub %d %g\n",i,saveDuals[i]);
            saveDuals[i]=0.0;
          }
        }
      }
      CoinMemcpyN(saveDuals,(numberColumns_+numberRows_),dj_);
      // set up possible ones
      for (i=0;i<numberRows_+numberColumns_;i++)
        clearPivoted(i);
      int iRow;
      for (iRow=0;iRow<numberRows_;iRow++) {
        int iPivot=pivotVariable_[iRow];
        if (fabs(saveDuals[iPivot])>dualTolerance_) {
          if (getStatus(iPivot)!=isFree) 
            setPivoted(iPivot);
        }
      }
    } else if ((specialOptions_&1024)!=0&&CLEAN_FIXED) {
      // set up possible ones
      for (int i=0;i<numberRows_+numberColumns_;i++)
        clearPivoted(i);
      int iRow;
      for (iRow=0;iRow<numberRows_;iRow++) {
        int iPivot=pivotVariable_[iRow];
        if (iPivot<numberColumns_&&lower_[iPivot]==upper_[iPivot]) {
          setPivoted(iPivot);
        }
      }
    } 

    double objectiveChange;
    numberFake_ =0; // Number of variables at fake bounds
    numberChanged_ =0; // Number of variables with changed costs
    changeBounds(true,NULL,objectiveChange);
    
    if (!ifValuesPass) {
      // Check optimal
      if (!numberDualInfeasibilities_&&!numberPrimalInfeasibilities_)
        problemStatus_=0;
    }
    if (problemStatus_<0&&perturbation_<100) {
      perturb();
      // Can't get here if values pass
      gutsOfSolution(NULL,NULL);
      if (handler_->logLevel()>2) {
        handler_->message(CLP_SIMPLEX_STATUS,messages_)
          <<numberIterations_<<objectiveValue();
        handler_->printing(sumPrimalInfeasibilities_>0.0)
          <<sumPrimalInfeasibilities_<<numberPrimalInfeasibilities_;
        handler_->printing(sumDualInfeasibilities_>0.0)
          <<sumDualInfeasibilities_<<numberDualInfeasibilities_;
        handler_->printing(numberDualInfeasibilitiesWithoutFree_
                           <numberDualInfeasibilities_)
                             <<numberDualInfeasibilitiesWithoutFree_;
        handler_->message()<<CoinMessageEol;
      }
    }
    return 0;
  } else {
    return 1;
  }
}
void 
ClpSimplexDual::finishSolve(int startFinishOptions)
{
  assert (problemStatus_||!sumPrimalInfeasibilities_);

  // clean up
  finish(startFinishOptions);
}
void 
ClpSimplexDual::gutsOfDual(int ifValuesPass,double * & saveDuals,int initialStatus,
                           ClpDataSave & data)
{
  int lastCleaned=0; // last time objective or bounds cleaned up
  
  // This says whether to restore things etc
  // startup will have factorized so can skip
  int factorType=0;
  // Start check for cycles
  progress_->startCheck();
  // Say change made on first iteration
  changeMade_=1;
  /*
    Status of problem:
    0 - optimal
    1 - infeasible
    2 - unbounded
    -1 - iterating
    -2 - factorization wanted
    -3 - redo checking without factorization
    -4 - looks infeasible
  */
  while (problemStatus_<0) {
    int iRow, iColumn;
    // clear
    for (iRow=0;iRow<4;iRow++) {
      rowArray_[iRow]->clear();
    }    
    
    for (iColumn=0;iColumn<2;iColumn++) {
      columnArray_[iColumn]->clear();
    }    
    
    // give matrix (and model costs and bounds a chance to be
    // refreshed (normally null)
    matrix_->refresh(this);
    // If getting nowhere - why not give it a kick
    // does not seem to work too well - do some more work
    if (perturbation_<101&&numberIterations_>2*(numberRows_+numberColumns_)
        &&initialStatus!=10) {
      perturb();
      // Can't get here if values pass
      gutsOfSolution(NULL,NULL);
      if (handler_->logLevel()>2) {
        handler_->message(CLP_SIMPLEX_STATUS,messages_)
          <<numberIterations_<<objectiveValue();
        handler_->printing(sumPrimalInfeasibilities_>0.0)
          <<sumPrimalInfeasibilities_<<numberPrimalInfeasibilities_;
        handler_->printing(sumDualInfeasibilities_>0.0)
          <<sumDualInfeasibilities_<<numberDualInfeasibilities_;
        handler_->printing(numberDualInfeasibilitiesWithoutFree_
                           <numberDualInfeasibilities_)
                             <<numberDualInfeasibilitiesWithoutFree_;
        handler_->message()<<CoinMessageEol;
      }
    }
    // may factorize, checks if problem finished
    statusOfProblemInDual(lastCleaned,factorType,saveDuals,data,
                          ifValuesPass);
    // If values pass then do easy ones on first time
    if (ifValuesPass&&
        progress_->lastIterationNumber(0)<0&&saveDuals) {
      doEasyOnesInValuesPass(saveDuals);
    }
    
    // Say good factorization
    factorType=1;
    if (data.sparseThreshold_) {
      // use default at present
      factorization_->sparseThreshold(0);
      factorization_->goSparse();
    }
    
    // exit if victory declared
    if (problemStatus_>=0)
      break;
    
    // test for maximum iterations
    if (hitMaximumIterations()||(ifValuesPass==2&&!saveDuals)) {
      problemStatus_=3;
      break;
    }
    if (ifValuesPass&&!saveDuals) {
      // end of values pass
      ifValuesPass=0;
      int status = eventHandler_->event(ClpEventHandler::endOfValuesPass);
      if (status>=0) {
        problemStatus_=5;
        secondaryStatus_=ClpEventHandler::endOfValuesPass;
        break;
      }
    }
    // Check event
    {
      int status = eventHandler_->event(ClpEventHandler::endOfFactorization);
      if (status>=0) {
        problemStatus_=5;
        secondaryStatus_=ClpEventHandler::endOfFactorization;
        break;
      }
    }
      // Do iterations
    whileIterating(saveDuals,ifValuesPass);
  }
}
int 
ClpSimplexDual::dual(int ifValuesPass,int startFinishOptions)
{
  algorithm_ = -1;
  
  // save data
  ClpDataSave data = saveData();
  double * saveDuals = NULL;
  if (ifValuesPass) {
    saveDuals = new double [numberRows_+numberColumns_];
    CoinMemcpyN(dual_,numberRows_,saveDuals);
  }
  int returnCode = startupSolve(ifValuesPass,saveDuals,startFinishOptions);
  // Save so can see if doing after primal
  int initialStatus=problemStatus_;
  
  if (!returnCode)
    gutsOfDual(ifValuesPass,saveDuals,initialStatus,data);
  if (problemStatus_==10)
    startFinishOptions |= 1;
  finishSolve(startFinishOptions);
  delete [] saveDuals;
  
  // Restore any saved stuff
  restoreData(data);
  return problemStatus_;
}
// old way
#if 0
int ClpSimplexDual::dual (int ifValuesPass , int startFinishOptions)
{
  algorithm_ = -1;

  // save data
  ClpDataSave data = saveData();
  // Save so can see if doing after primal
  int initialStatus=problemStatus_;

  // If values pass then save given duals round check solution
  double * saveDuals = NULL;
  if (ifValuesPass) {
    saveDuals = new double [numberRows_+numberColumns_];
    CoinMemcpyN(dual_,numberRows_,saveDuals);
  }
  // sanity check
  // initialize - no values pass and algorithm_ is -1
  // put in standard form (and make row copy)
  // create modifiable copies of model rim and do optional scaling
  // If problem looks okay
  // Do initial factorization
  // If user asked for perturbation - do it
  if (!startup(0,startFinishOptions)) {
    // looks okay
    // Superbasic variables not allowed
    // If values pass then scale pi 
    if (ifValuesPass) {
      if (problemStatus_&&perturbation_<100) 
        perturb();
      int i;
      if (scalingFlag_>0) {
        for (i=0;i<numberRows_;i++) {
          dual_[i] = saveDuals[i]/rowScale_[i];
        }
      } else {
        CoinMemcpyN(saveDuals,numberRows_,dual_);
      }
      // now create my duals
      for (i=0;i<numberRows_;i++) {
        // slack
        double value = dual_[i];
        value += rowObjectiveWork_[i];
        saveDuals[i+numberColumns_]=value;
      }
      CoinMemcpyN(objectiveWork_,numberColumns_,saveDuals);
      transposeTimes(-1.0,dual_,saveDuals);
      // make reduced costs okay
      for (i=0;i<numberColumns_;i++) {
        if (getStatus(i)==atLowerBound) {
          if (saveDuals[i]<0.0) {
            //if (saveDuals[i]<-1.0e-3)
            //printf("bad dj at lb %d %g\n",i,saveDuals[i]);
            saveDuals[i]=0.0;
          }
        } else if (getStatus(i)==atUpperBound) {
          if (saveDuals[i]>0.0) {
            //if (saveDuals[i]>1.0e-3)
            //printf("bad dj at ub %d %g\n",i,saveDuals[i]);
            saveDuals[i]=0.0;
          }
        }
      }
      CoinMemcpyN(saveDuals,numberColumns_+numberRows_,dj_);
      // set up possible ones
      for (i=0;i<numberRows_+numberColumns_;i++)
        clearPivoted(i);
      int iRow;
      for (iRow=0;iRow<numberRows_;iRow++) {
        int iPivot=pivotVariable_[iRow];
        if (fabs(saveDuals[iPivot])>dualTolerance_) {
          if (getStatus(iPivot)!=isFree) 
            setPivoted(iPivot);
        }
      }
    } else if ((specialOptions_&1024)!=0&&CLEAN_FIXED) {
      // set up possible ones
      for (int i=0;i<numberRows_+numberColumns_;i++)
        clearPivoted(i);
      int iRow;
      for (iRow=0;iRow<numberRows_;iRow++) {
        int iPivot=pivotVariable_[iRow];
        if (iPivot<numberColumns_&&lower_[iPivot]==upper_[iPivot]) {
          setPivoted(iPivot);
        }
      }
    } 

    double objectiveChange;
    numberFake_ =0; // Number of variables at fake bounds
    numberChanged_ =0; // Number of variables with changed costs
    changeBounds(true,NULL,objectiveChange);
    
    int lastCleaned=0; // last time objective or bounds cleaned up

    if (!ifValuesPass) {
      // Check optimal
      if (!numberDualInfeasibilities_&&!numberPrimalInfeasibilities_)
        problemStatus_=0;
    }
    if (problemStatus_<0&&perturbation_<100) {
      perturb();
      // Can't get here if values pass
      gutsOfSolution(NULL,NULL);
      if (handler_->logLevel()>2) {
        handler_->message(CLP_SIMPLEX_STATUS,messages_)
          <<numberIterations_<<objectiveValue();
        handler_->printing(sumPrimalInfeasibilities_>0.0)
          <<sumPrimalInfeasibilities_<<numberPrimalInfeasibilities_;
        handler_->printing(sumDualInfeasibilities_>0.0)
          <<sumDualInfeasibilities_<<numberDualInfeasibilities_;
        handler_->printing(numberDualInfeasibilitiesWithoutFree_
                           <numberDualInfeasibilities_)
                             <<numberDualInfeasibilitiesWithoutFree_;
        handler_->message()<<CoinMessageEol;
      }
    }
        
    // This says whether to restore things etc
    // startup will have factorized so can skip
    int factorType=0;
    // Start check for cycles
    progress_->startCheck();
    // Say change made on first iteration
    changeMade_=1;
    /*
      Status of problem:
      0 - optimal
      1 - infeasible
      2 - unbounded
      -1 - iterating
      -2 - factorization wanted
      -3 - redo checking without factorization
      -4 - looks infeasible
    */
    while (problemStatus_<0) {
      int iRow, iColumn;
      // clear
      for (iRow=0;iRow<4;iRow++) {
        rowArray_[iRow]->clear();
      }    
      
      for (iColumn=0;iColumn<2;iColumn++) {
        columnArray_[iColumn]->clear();
      }    
      
      // give matrix (and model costs and bounds a chance to be
      // refreshed (normally null)
      matrix_->refresh(this);
      // If getting nowhere - why not give it a kick
      // does not seem to work too well - do some more work
      if (perturbation_<101&&numberIterations_>2*(numberRows_+numberColumns_)
          &&initialStatus!=10) {
        perturb();
        // Can't get here if values pass
        gutsOfSolution(NULL,NULL);
        if (handler_->logLevel()>2) {
          handler_->message(CLP_SIMPLEX_STATUS,messages_)
            <<numberIterations_<<objectiveValue();
          handler_->printing(sumPrimalInfeasibilities_>0.0)
            <<sumPrimalInfeasibilities_<<numberPrimalInfeasibilities_;
          handler_->printing(sumDualInfeasibilities_>0.0)
            <<sumDualInfeasibilities_<<numberDualInfeasibilities_;
          handler_->printing(numberDualInfeasibilitiesWithoutFree_
                             <numberDualInfeasibilities_)
                               <<numberDualInfeasibilitiesWithoutFree_;
          handler_->message()<<CoinMessageEol;
        }
      }
      // may factorize, checks if problem finished
      statusOfProblemInDual(lastCleaned,factorType,saveDuals,data,
                            ifValuesPass);
      // If values pass then do easy ones on first time
      if (ifValuesPass&&
          progress_->lastIterationNumber(0)<0&&saveDuals) {
        doEasyOnesInValuesPass(saveDuals);
      }
      
      // Say good factorization
      factorType=1;
      if (data.sparseThreshold_) {
        // use default at present
        factorization_->sparseThreshold(0);
        factorization_->goSparse();
      }

      // exit if victory declared
      if (problemStatus_>=0)
        break;
      
      // test for maximum iterations
      if (hitMaximumIterations()||(ifValuesPass==2&&!saveDuals)) {
        problemStatus_=3;
        break;
      }
      if (ifValuesPass&&!saveDuals) {
        // end of values pass
        ifValuesPass=0;
        int status = eventHandler_->event(ClpEventHandler::endOfValuesPass);
        if (status>=0) {
          problemStatus_=5;
          secondaryStatus_=ClpEventHandler::endOfValuesPass;
          break;
        }
      }
      // Check event
      {
        int status = eventHandler_->event(ClpEventHandler::endOfFactorization);
        if (status>=0) {
          problemStatus_=5;
          secondaryStatus_=ClpEventHandler::endOfFactorization;
          break;
        }
      }
      // Do iterations
      whileIterating(saveDuals,ifValuesPass);
    }
  }

  assert (problemStatus_||!sumPrimalInfeasibilities_);

  // clean up
  finish(startFinishOptions);
  delete [] saveDuals;

  // Restore any saved stuff
  restoreData(data);
  return problemStatus_;
}
#endif
//#define CHECK_ACCURACY
#ifdef CHECK_ACCURACY
static double zzzzzz[100000];
#endif
/* Reasons to come out:
   -1 iterations etc
   -2 inaccuracy 
   -3 slight inaccuracy (and done iterations)
   +0 looks optimal (might be unbounded - but we will investigate)
   +1 looks infeasible
   +3 max iterations 
 */
int
ClpSimplexDual::whileIterating(double * & givenDuals,int ifValuesPass)
{
#if 0
  if (!numberIterations_&&auxiliaryModel_) {
    for (int i=0;i<numberColumns_;i++) {
      if (!columnLower_[i]==auxiliaryModel_->lowerRegion()[i+numberRows_+numberColumns_]) 
        {printf("%d a\n",i);break;}
      if (!columnUpper_[i]==auxiliaryModel_->upperRegion()[i+numberRows_+numberColumns_]) 
        {printf("%d b %g\n",i,auxiliaryModel_->upperRegion()[i+numberRows_+numberColumns_]);break;}
    }
    for (int i=0 ;i<numberRows_;i++) {
      if (!rowLower_[i]==auxiliaryModel_->lowerRegion()[i+numberRows_+2*numberColumns_]) 
        {printf("%d c\n",i);break;}
      if (!rowUpper_[i]==auxiliaryModel_->upperRegion()[i+numberRows_+2*numberColumns_]) 
        {printf("%d d\n",i);break;}
    }
  }
#endif
#ifdef CLP_DEBUG
  int debugIteration=-1;
#endif
  {
    int i;
    for (i=0;i<4;i++) {
      rowArray_[i]->clear();
    }    
    for (i=0;i<2;i++) {
      columnArray_[i]->clear();
    }    
  }      
  // if can't trust much and long way from optimal then relax
  if (largestPrimalError_>10.0)
    factorization_->relaxAccuracyCheck(CoinMin(1.0e2,largestPrimalError_/10.0));
  else
    factorization_->relaxAccuracyCheck(1.0);
  // status stays at -1 while iterating, >=0 finished, -2 to invert
  // status -3 to go to top without an invert
  int returnCode = -1;
  double saveSumDual = sumDualInfeasibilities_; // so we know to be careful

#if 0
  // compute average infeasibility for backward test
  double averagePrimalInfeasibility = sumPrimalInfeasibilities_/
    ((double ) (numberPrimalInfeasibilities_+1));
#endif

  // Get dubious weights
  CoinBigIndex * dubiousWeights = NULL;
#ifdef DUBIOUS_WEIGHTS
  factorization_->getWeights(rowArray_[0]->getIndices());
  dubiousWeights = matrix_->dubiousWeights(this,rowArray_[0]->getIndices());
#endif
  // If values pass then get list of candidates
  int * candidateList = NULL;
  int numberCandidates = 0;
#ifdef CLP_DEBUG
  bool wasInValuesPass= (givenDuals!=NULL);
#endif
  int candidate=-1;
  if (givenDuals) {
    assert (ifValuesPass);
    ifValuesPass=1;
    candidateList = new int[numberRows_];
    // move reduced costs across
    CoinMemcpyN(givenDuals,numberRows_+numberColumns_,dj_);
    int iRow;
    for (iRow=0;iRow<numberRows_;iRow++) {
      int iPivot=pivotVariable_[iRow];
      if (flagged(iPivot))
        continue;
      if (fabs(dj_[iPivot])>dualTolerance_) {
        // for now safer to ignore free ones
        if (lower_[iPivot]>-1.0e50||upper_[iPivot]<1.0e50) 
          if (pivoted(iPivot)) 
            candidateList[numberCandidates++]=iRow;
      } else {
        clearPivoted(iPivot);
      }
    }
    // and set first candidate
    if (!numberCandidates) {
      delete [] candidateList;
      delete [] givenDuals;
      givenDuals=NULL;
      candidateList=NULL;
      int iRow;
      for (iRow=0;iRow<numberRows_;iRow++) {
        int iPivot=pivotVariable_[iRow];
        clearPivoted(iPivot);
      }
    }
  } else {
    assert (!ifValuesPass);
  }
#ifdef CHECK_ACCURACY
  {
    if (numberIterations_) {
      int il=-1;
      double largest=1.0e-1;
      int ilnb=-1;
      double largestnb=1.0e-8;
      for (int i=0;i<numberRows_+numberColumns_;i++) {
        double diff = fabs(solution_[i]-zzzzzz[i]);
        if (diff>largest) {
          largest=diff;
          il=i;
        }
        if (getColumnStatus(i)!=basic) {
          if (diff>largestnb) {
            largestnb=diff;
            ilnb=i;
          }
        } 
      }
      if (il>=0&&ilnb<0)
        printf("largest diff of %g at %d, nonbasic %g at %d\n",
               largest,il,largestnb,ilnb);
    }
  }
#endif
  while (problemStatus_==-1) {
#ifdef CLP_DEBUG
    if (givenDuals) {
      double value5=0.0;
      int i;
      for (i=0;i<numberRows_+numberColumns_;i++) {
        if (dj_[i]<-1.0e-6)
          if (upper_[i]<1.0e20)
            value5 += dj_[i]*upper_[i];
          else
            printf("bad dj %g on %d with large upper status %d\n",
                   dj_[i],i,status_[i]&7);
        else if (dj_[i] >1.0e-6)
          if (lower_[i]>-1.0e20)
            value5 += dj_[i]*lower_[i];
          else
            printf("bad dj %g on %d with large lower status %d\n",
                   dj_[i],i,status_[i]&7);
      }
      printf("Values objective Value %g\n",value5);
    }
    if ((handler_->logLevel()&32)&&wasInValuesPass) {
      double value5=0.0;
      int i;
      for (i=0;i<numberRows_+numberColumns_;i++) {
        if (dj_[i]<-1.0e-6)
          if (upper_[i]<1.0e20)
            value5 += dj_[i]*upper_[i];
        else if (dj_[i] >1.0e-6)
          if (lower_[i]>-1.0e20)
            value5 += dj_[i]*lower_[i];
      }
      printf("Values objective Value %g\n",value5);
      {
        int i;
        for (i=0;i<numberRows_+numberColumns_;i++) {
          int iSequence = i;
          double oldValue;
          
          switch(getStatus(iSequence)) {
            
          case basic:
          case ClpSimplex::isFixed:
            break;
          case isFree:
          case superBasic:
            abort();
            break;
          case atUpperBound:
            oldValue = dj_[iSequence];
            //assert (oldValue<=tolerance);
            assert (fabs(solution_[iSequence]-upper_[iSequence])<1.0e-7);
            break;
          case atLowerBound:
            oldValue = dj_[iSequence];
            //assert (oldValue>=-tolerance);
            assert (fabs(solution_[iSequence]-lower_[iSequence])<1.0e-7);
            break;
          }
        }
      }
    }
#endif
#ifdef CLP_DEBUG
    {
      int i;
      for (i=0;i<4;i++) {
        rowArray_[i]->checkClear();
      }    
      for (i=0;i<2;i++) {
        columnArray_[i]->checkClear();
      }    
    }      
#endif
#if CLP_DEBUG>2
    // very expensive
    if (numberIterations_>0&&numberIterations_<-801) {
      handler_->setLogLevel(63);
      double saveValue = objectiveValue_;
      double * saveRow1 = new double[numberRows_];
      double * saveRow2 = new double[numberRows_];
      memcpy(saveRow1,rowReducedCost_,numberRows_*sizeof(double));
      memcpy(saveRow2,rowActivityWork_,numberRows_*sizeof(double));
      double * saveColumn1 = new double[numberColumns_];
      double * saveColumn2 = new double[numberColumns_];
      memcpy(saveColumn1,reducedCostWork_,numberColumns_*sizeof(double));
      memcpy(saveColumn2,columnActivityWork_,numberColumns_*sizeof(double));
      gutsOfSolution(NULL,NULL);
      printf("xxx %d old obj %g, recomputed %g, sum dual inf %g\n",
             numberIterations_,
             saveValue,objectiveValue_,sumDualInfeasibilities_);
      if (saveValue>objectiveValue_+1.0e-2)
        printf("**bad**\n");
      memcpy(rowReducedCost_,saveRow1,numberRows_*sizeof(double));
      memcpy(rowActivityWork_,saveRow2,numberRows_*sizeof(double));
      memcpy(reducedCostWork_,saveColumn1,numberColumns_*sizeof(double));
      memcpy(columnActivityWork_,saveColumn2,numberColumns_*sizeof(double));
      delete [] saveRow1;
      delete [] saveRow2;
      delete [] saveColumn1;
      delete [] saveColumn2;
      objectiveValue_=saveValue;
    }
#endif
#if 0
    //    if (factorization_->pivots()){
    {
      int iPivot;
      double * array = rowArray_[3]->denseVector();
      int i;
      for (iPivot=0;iPivot<numberRows_;iPivot++) {
        int iSequence = pivotVariable_[iPivot];
        unpack(rowArray_[3],iSequence);
        factorization_->updateColumn(rowArray_[2],rowArray_[3]);
        assert (fabs(array[iPivot]-1.0)<1.0e-4);
        array[iPivot]=0.0;
        for (i=0;i<numberRows_;i++)
          assert (fabs(array[i])<1.0e-4);
        rowArray_[3]->clear();
      }
    }
#endif
#ifdef CLP_DEBUG
    {
      int iSequence, number=numberRows_+numberColumns_;
      for (iSequence=0;iSequence<number;iSequence++) {
        double lowerValue=lower_[iSequence];
        double upperValue=upper_[iSequence];
        double value=solution_[iSequence];
        if(getStatus(iSequence)!=basic&&getStatus(iSequence)!=isFree) {
          assert(lowerValue>-1.0e20);
          assert(upperValue<1.0e20);
        }
        switch(getStatus(iSequence)) {
          
        case basic:
          break;
        case isFree:
        case superBasic:
          break;
        case atUpperBound:
          assert (fabs(value-upperValue)<=primalTolerance_) ;
          break;
        case atLowerBound:
        case ClpSimplex::isFixed:
          assert (fabs(value-lowerValue)<=primalTolerance_) ;
          break;
        }
      }
    }
    if(numberIterations_==debugIteration) {
      printf("dodgy iteration coming up\n");
    }
#endif
    // choose row to go out
    // dualRow will go to virtual row pivot choice algorithm
    // make sure values pass off if it should be
    if (numberCandidates) 
      candidate = candidateList[--numberCandidates];
    else
      candidate=-1;
    dualRow(candidate);
    if (pivotRow_>=0) {
      // we found a pivot row
      if (handler_->detail(CLP_SIMPLEX_PIVOTROW,messages_)<100) {
        handler_->message(CLP_SIMPLEX_PIVOTROW,messages_)
          <<pivotRow_
          <<CoinMessageEol;
      }
      // check accuracy of weights
      dualRowPivot_->checkAccuracy();
      // Get good size for pivot
      // Allow first few iterations to take tiny
      double acceptablePivot=1.0e-1*acceptablePivot_;
      if (numberIterations_>100)
        acceptablePivot=acceptablePivot_;
      if (factorization_->pivots()>10||
          (factorization_->pivots()&&saveSumDual))
        acceptablePivot=1.0e+3*acceptablePivot_; // if we have iterated be more strict
      else if (factorization_->pivots()>5)
        acceptablePivot=1.0e+2*acceptablePivot_; // if we have iterated be slightly more strict
      else if (factorization_->pivots())
        acceptablePivot=acceptablePivot_; // relax
      double bestPossiblePivot=1.0;
      // get sign for finding row of tableau
      if (candidate<0) {
        // normal iteration
        // create as packed
        double direction=directionOut_;
        rowArray_[0]->createPacked(1,&pivotRow_,&direction);
        factorization_->updateColumnTranspose(rowArray_[1],rowArray_[0]);
        // Allow to do dualColumn0
        if (numberThreads_<-1)
          spareIntArray_[0]=1;
        spareDoubleArray_[0]=acceptablePivot;
        rowArray_[3]->clear();
        sequenceIn_=-1;
        // put row of tableau in rowArray[0] and columnArray[0]
        matrix_->transposeTimes(this,-1.0,
                              rowArray_[0],rowArray_[3],columnArray_[0]);
        // do ratio test for normal iteration
        bestPossiblePivot = dualColumn(rowArray_[0],columnArray_[0],rowArray_[3],
                 columnArray_[1],acceptablePivot,dubiousWeights);
      } else {
        // Make sure direction plausible
        CoinAssert (upperOut_<1.0e50||lowerOut_>-1.0e50);
        // If in integer cleanup do direction using duals
        // may be wrong way round
        if(ifValuesPass==2) {
          if (dual_[pivotRow_]>0.0) {
            // this will give a -1 in pivot row (as slacks are -1.0)
            directionOut_ = 1;
          } else {
            directionOut_ = -1;
          }
        }
        if (directionOut_<0&&fabs(valueOut_-upperOut_)>dualBound_+primalTolerance_) {
          if (fabs(valueOut_-upperOut_)>fabs(valueOut_-lowerOut_))
            directionOut_=1;
        } else if (directionOut_>0&&fabs(valueOut_-lowerOut_)>dualBound_+primalTolerance_) {
          if (fabs(valueOut_-upperOut_)<fabs(valueOut_-lowerOut_))
            directionOut_=-1;
        }
        double direction=directionOut_;
        rowArray_[0]->createPacked(1,&pivotRow_,&direction);
        factorization_->updateColumnTranspose(rowArray_[1],rowArray_[0]);
        // put row of tableau in rowArray[0] and columnArray[0]
        matrix_->transposeTimes(this,-1.0,
                              rowArray_[0],rowArray_[3],columnArray_[0]);
        acceptablePivot *= 10.0;
        // do ratio test
        if (ifValuesPass==1) {
          checkPossibleValuesMove(rowArray_[0],columnArray_[0],
                                  acceptablePivot);
        } else {
          checkPossibleCleanup(rowArray_[0],columnArray_[0],
                                  acceptablePivot);
          if (sequenceIn_<0) {
            rowArray_[0]->clear();
            columnArray_[0]->clear();
            continue; // can't do anything
          }
        }

        // recompute true dualOut_
        if (directionOut_<0) {
          dualOut_ = valueOut_ - upperOut_;
        } else {
          dualOut_ = lowerOut_ - valueOut_;
        }
        // check what happened if was values pass
        // may want to move part way i.e. movement
        bool normalIteration = (sequenceIn_!=sequenceOut_);

        clearPivoted(sequenceOut_);  // make sure won't be done again
        // see if end of values pass
        if (!numberCandidates) {
          int iRow;
          delete [] candidateList;
          delete [] givenDuals;
          candidate=-2; // -2 signals end 
          givenDuals=NULL;
          candidateList=NULL;
          ifValuesPass=1;
          for (iRow=0;iRow<numberRows_;iRow++) {
            int iPivot=pivotVariable_[iRow];
            //assert (fabs(dj_[iPivot]),1.0e-5);
            clearPivoted(iPivot);
          }
        }
        if (!normalIteration) {
          //rowArray_[0]->cleanAndPackSafe(1.0e-60);
          //columnArray_[0]->cleanAndPackSafe(1.0e-60);
          updateDualsInValuesPass(rowArray_[0],columnArray_[0],theta_);
          if (candidate==-2)
            problemStatus_=-2;
          continue; // skip rest of iteration
        } else {
          // recompute dualOut_
          if (directionOut_<0) {
            dualOut_ = valueOut_ - upperOut_;
          } else {
            dualOut_ = lowerOut_ - valueOut_;
          }
        }
      }
      if (sequenceIn_>=0) {
        // normal iteration
        // update the incoming column
        double btranAlpha = -alpha_*directionOut_; // for check
        unpackPacked(rowArray_[1]);
        factorization_->updateColumnFT(rowArray_[2],rowArray_[1]);
        // and update dual weights (can do in parallel - with extra array)
        alpha_ = dualRowPivot_->updateWeights(rowArray_[0],
                                              rowArray_[2],
                                              rowArray_[1]);
        // see if update stable
#ifdef CLP_DEBUG
        if ((handler_->logLevel()&32))
          printf("btran alpha %g, ftran alpha %g\n",btranAlpha,alpha_);
#endif
        double checkValue=1.0e-7;
        // if can't trust much and long way from optimal then relax
        if (largestPrimalError_>10.0)
          checkValue = CoinMin(1.0e-4,1.0e-8*largestPrimalError_);
        if (fabs(btranAlpha)<1.0e-12||fabs(alpha_)<1.0e-12||
            fabs(btranAlpha-alpha_)>checkValue*(1.0+fabs(alpha_))) {
          handler_->message(CLP_DUAL_CHECK,messages_)
            <<btranAlpha
            <<alpha_
            <<CoinMessageEol;
          if (factorization_->pivots()) {
            dualRowPivot_->unrollWeights();
            problemStatus_=-2; // factorize now
            rowArray_[0]->clear();
            rowArray_[1]->clear();
            columnArray_[0]->clear();
            returnCode=-2;
            break;
          } else {
            // take on more relaxed criterion
            double test;
            if (fabs(btranAlpha)<1.0e-8||fabs(alpha_)<1.0e-8)
              test = 1.0e-1*fabs(alpha_);
            else
              test = 1.0e-4*(1.0+fabs(alpha_));
            if (fabs(btranAlpha)<1.0e-12||fabs(alpha_)<1.0e-12||
                fabs(btranAlpha-alpha_)>test) {
              dualRowPivot_->unrollWeights();
              // need to reject something
              char x = isColumn(sequenceOut_) ? 'C' :'R';
              handler_->message(CLP_SIMPLEX_FLAG,messages_)
                <<x<<sequenceWithin(sequenceOut_)
                <<CoinMessageEol;
              setFlagged(sequenceOut_);
              progress_->clearBadTimes();
              lastBadIteration_ = numberIterations_; // say be more cautious
              rowArray_[0]->clear();
              rowArray_[1]->clear();
              columnArray_[0]->clear();
              if (fabs(alpha_)<1.0e-10&&fabs(btranAlpha)<1.0e-8&&numberIterations_>100) {
                //printf("I think should declare infeasible\n");
                problemStatus_=1;
                returnCode=1;
                break;
              }
              continue;
            }
          }
        }
        // update duals BEFORE replaceColumn so can do updateColumn
        double objectiveChange=0.0;
        // do duals first as variables may flip bounds
        // rowArray_[0] and columnArray_[0] may have flips
        // so use rowArray_[3] for work array from here on
        int nswapped = 0;
        //rowArray_[0]->cleanAndPackSafe(1.0e-60);
        //columnArray_[0]->cleanAndPackSafe(1.0e-60);
        if (candidate==-1) {
          // make sure incoming doesn't count
          Status saveStatus = getStatus(sequenceIn_);
          setStatus(sequenceIn_,basic);
          nswapped = updateDualsInDual(rowArray_[0],columnArray_[0],
                                       rowArray_[2],theta_,
                                       objectiveChange,false);
          setStatus(sequenceIn_,saveStatus);
        } else {
          updateDualsInValuesPass(rowArray_[0],columnArray_[0],theta_);
        }
        double oldDualOut = dualOut_;
        // which will change basic solution
        if (nswapped) {
          factorization_->updateColumn(rowArray_[3],rowArray_[2]);
          dualRowPivot_->updatePrimalSolution(rowArray_[2],
                                              1.0,objectiveChange);
          // recompute dualOut_
          valueOut_ = solution_[sequenceOut_];
          if (directionOut_<0) {
            dualOut_ = valueOut_ - upperOut_;
          } else {
            dualOut_ = lowerOut_ - valueOut_;
          }
#if 0
          if (dualOut_<0.0) {
#ifdef CLP_DEBUG
            if (handler_->logLevel()&32) {
              printf(" dualOut_ %g %g save %g\n",dualOut_,averagePrimalInfeasibility,saveDualOut);
              printf("values %g %g %g %g %g %g %g\n",lowerOut_,valueOut_,upperOut_,
                     objectiveChange,);
            }
#endif
            if (upperOut_==lowerOut_)
              dualOut_=0.0;
          }
          if(dualOut_<-CoinMax(1.0e-12*averagePrimalInfeasibility,1.0e-8)
             &&factorization_->pivots()>100&&
             getStatus(sequenceIn_)!=isFree) {
            // going backwards - factorize
            dualRowPivot_->unrollWeights();
            problemStatus_=-2; // factorize now
            returnCode=-2;
            break;
          }
#endif
        }
        // amount primal will move
        double movement = -dualOut_*directionOut_/alpha_;
        double movementOld = oldDualOut*directionOut_/alpha_;
        // so objective should increase by fabs(dj)*movement
        // but we already have objective change - so check will be good
        if (objectiveChange+fabs(movementOld*dualIn_)<-CoinMax(1.0e-5,1.0e-12*fabs(objectiveValue_))) {
#ifdef CLP_DEBUG
          if (handler_->logLevel()&32)
            printf("movement %g, swap change %g, rest %g  * %g\n",
                   objectiveChange+fabs(movement*dualIn_),
                   objectiveChange,movement,dualIn_);
#endif
          if(factorization_->pivots()) {
            // going backwards - factorize
            dualRowPivot_->unrollWeights();
            problemStatus_=-2; // factorize now
            returnCode=-2;
            break;
          }
        }
        CoinAssert(fabs(dualOut_)<1.0e50);
        // if stable replace in basis
        int updateStatus = factorization_->replaceColumn(this,
                                                         rowArray_[2],
                                                         rowArray_[1],
                                                         pivotRow_,
                                                         alpha_);
        // if no pivots, bad update but reasonable alpha - take and invert
        if (updateStatus==2&&
                   !factorization_->pivots()&&fabs(alpha_)>1.0e-5)
          updateStatus=4;
        if (updateStatus==1||updateStatus==4) {
          // slight error
          if (factorization_->pivots()>5||updateStatus==4) {
            problemStatus_=-2; // factorize now
            returnCode=-3;
          }
        } else if (updateStatus==2) {
          // major error
          dualRowPivot_->unrollWeights();
          // later we may need to unwind more e.g. fake bounds
          if (factorization_->pivots()) {
            problemStatus_=-2; // factorize now
            returnCode=-2;
            break;
          } else {
            // need to reject something
            char x = isColumn(sequenceOut_) ? 'C' :'R';
            handler_->message(CLP_SIMPLEX_FLAG,messages_)
              <<x<<sequenceWithin(sequenceOut_)
              <<CoinMessageEol;
            setFlagged(sequenceOut_);
            progress_->clearBadTimes();
            lastBadIteration_ = numberIterations_; // say be more cautious
            rowArray_[0]->clear();
            rowArray_[1]->clear();
            columnArray_[0]->clear();
            // make sure dual feasible
            // look at all rows and columns
            double objectiveChange=0.0;
            updateDualsInDual(rowArray_[0],columnArray_[0],rowArray_[1],
                              0.0,objectiveChange,true);
            continue;
          }
        } else if (updateStatus==3) {
          // out of memory
          // increase space if not many iterations
          if (factorization_->pivots()<
              0.5*factorization_->maximumPivots()&&
              factorization_->pivots()<200)
            factorization_->areaFactor(
                                       factorization_->areaFactor() * 1.1);
          problemStatus_=-2; // factorize now
        } else if (updateStatus==5) {
          problemStatus_=-2; // factorize now
        }
        // update primal solution
        if (theta_<0.0&&candidate==-1) {
#ifdef CLP_DEBUG
          if (handler_->logLevel()&32)
            printf("negative theta %g\n",theta_);
#endif
          theta_=0.0;
        }
        // do actual flips
        flipBounds(rowArray_[0],columnArray_[0],theta_);
        //rowArray_[1]->expand();
        dualRowPivot_->updatePrimalSolution(rowArray_[1],
                                            movement,
                                            objectiveChange);
#ifdef CLP_DEBUG
        double oldobj=objectiveValue_;
#endif
        // modify dualout
        dualOut_ /= alpha_;
        dualOut_ *= -directionOut_;
        //setStatus(sequenceIn_,basic);
        dj_[sequenceIn_]=0.0;
        double oldValue=valueIn_;
        if (directionIn_==-1) {
          // as if from upper bound
          valueIn_ = upperIn_+dualOut_;
        } else {
          // as if from lower bound
          valueIn_ = lowerIn_+dualOut_;
        }
        objectiveChange += cost_[sequenceIn_]*(valueIn_-oldValue);
        // outgoing
        // set dj to zero unless values pass
        if (directionOut_>0) {
          valueOut_ = lowerOut_;
          if (candidate==-1)
            dj_[sequenceOut_] = theta_;
        } else {
          valueOut_ = upperOut_;
          if (candidate==-1)
            dj_[sequenceOut_] = -theta_;
        }
        solution_[sequenceOut_]=valueOut_;
        int whatNext=housekeeping(objectiveChange);
#ifdef VUB
        {
          if ((sequenceIn_<numberColumns_&&vub[sequenceIn_]>=0)||toVub[sequenceIn_]>=0||
              (sequenceOut_<numberColumns_&&vub[sequenceOut_]>=0)||toVub[sequenceOut_]>=0) {
            int inSequence = sequenceIn_;
            int inVub = -1;
            if (sequenceIn_<numberColumns_)
              inVub = vub[sequenceIn_];
            int inBack = toVub[inSequence];
            int inSlack=-1;
            if (inSequence>=numberColumns_&&inBack>=0) {
              inSlack = inSequence-numberColumns_;
              inSequence = inBack;
              inBack = toVub[inSequence];
            }
            if (inVub>=0)
              printf("Vub %d in ",inSequence);
            if (inBack>=0&&inSlack<0)
              printf("%d (descendent of %d) in ",inSequence,inBack);
            if (inSlack>=0)
              printf("slack for row %d -> %d (descendent of %d) in ",inSlack,inSequence,inBack);
            int outSequence = sequenceOut_;
            int outVub = -1;
            if (sequenceOut_<numberColumns_)
              outVub = vub[sequenceOut_];
            int outBack = toVub[outSequence];
            int outSlack=-1;
            if (outSequence>=numberColumns_&&outBack>=0) {
              outSlack = outSequence-numberColumns_;
              outSequence = outBack;
              outBack = toVub[outSequence];
            }
            if (outVub>=0)
              printf("Vub %d out ",outSequence);
            if (outBack>=0&&outSlack<0)
              printf("%d (descendent of %d) out ",outSequence,outBack);
            if (outSlack>=0)
              printf("slack for row %d -> %d (descendent of %d) out ",outSlack,outSequence,outBack);
            printf("\n");
          }
        }
#endif
#if 0
        if (numberIterations_>206033)
          handler_->setLogLevel(63);
        if (numberIterations_>210567)
          exit(77);
#endif
        if (!givenDuals&&ifValuesPass&&ifValuesPass!=2) {
          handler_->message(CLP_END_VALUES_PASS,messages_)
            <<numberIterations_;
          whatNext=1;
        }
#ifdef CHECK_ACCURACY
        if (whatNext) {
          memcpy(zzzzzz,solution_,(numberRows_+numberColumns_)*sizeof(double));
        }
#endif
        //if (numberIterations_==1890)
        //whatNext=1;
        //if (numberIterations_>2000)
        //exit(77);
        // and set bounds correctly
        originalBound(sequenceIn_); 
        changeBound(sequenceOut_);
#ifdef CLP_DEBUG
        if (objectiveValue_<oldobj-1.0e-5&&(handler_->logLevel()&16))
          printf("obj backwards %g %g\n",objectiveValue_,oldobj);
#endif
        if (whatNext==1||candidate==-2) {
          problemStatus_ =-2; // refactorize
        } else if (whatNext==2) {
          // maximum iterations or equivalent
          problemStatus_= 3;
          returnCode=3;
          break;
        }
        // Check event
        {
          int status = eventHandler_->event(ClpEventHandler::endOfIteration);
          if (status>=0) {
            problemStatus_=5;
            secondaryStatus_=ClpEventHandler::endOfIteration;
            returnCode=4;
            break;
          }
        }
      } else {
        // no incoming column is valid
        pivotRow_=-1;
#ifdef CLP_DEBUG
        if (handler_->logLevel()&32)
          printf("** no column pivot\n");
#endif
        if (factorization_->pivots()<5&&acceptablePivot_<=1.0e-8) {
          // If not in branch and bound etc save ray
          if ((specialOptions_&(1024|4096))==0) {
            // create ray anyway
            delete [] ray_;
            ray_ = new double [ numberRows_];
            rowArray_[0]->expand(); // in case packed
            CoinMemcpyN(rowArray_[0]->denseVector(),numberRows_,ray_);
          }
          // If we have just factorized and infeasibility reasonable say infeas
          if (((specialOptions_&4096)!=0||bestPossiblePivot<1.0e-11)&&dualBound_>1.0e8) {
            if (valueOut_>upperOut_+1.0e-3||valueOut_<lowerOut_-1.0e-3
                || (specialOptions_&64)==0) {
              // say infeasible
              problemStatus_=1;
              // unless primal feasible!!!!
              //printf("%d %g %d %g\n",numberPrimalInfeasibilities_,sumPrimalInfeasibilities_,
              //     numberDualInfeasibilities_,sumDualInfeasibilities_);
              if (numberDualInfeasibilities_)
                problemStatus_=10;
              rowArray_[0]->clear();
              columnArray_[0]->clear();
              returnCode=1;
              break;
            }
          }
          // If special option set - put off as long as possible
          if ((specialOptions_&64)==0) {
            if (factorization_->pivots()==0)
              problemStatus_=-4; //say looks infeasible
          } else {
            // flag
            char x = isColumn(sequenceOut_) ? 'C' :'R';
            handler_->message(CLP_SIMPLEX_FLAG,messages_)
              <<x<<sequenceWithin(sequenceOut_)
              <<CoinMessageEol;
            setFlagged(sequenceOut_);
            if (!factorization_->pivots()) {
              rowArray_[0]->clear();
              columnArray_[0]->clear();
              continue;
            }
          }
        }
        if (factorization_->pivots()<5&&acceptablePivot_>1.0e-8) 
          acceptablePivot_=1.0e-8;
        rowArray_[0]->clear();
        columnArray_[0]->clear();
        returnCode=1;
        break;
      }
    } else {
      // no pivot row
#ifdef CLP_DEBUG
      if (handler_->logLevel()&32)
        printf("** no row pivot\n");
#endif
      // If in branch and bound try and get rid of fixed variables
      if ((specialOptions_&1024)!=0&&CLEAN_FIXED) {
        assert (!candidateList);
        candidateList = new int[numberRows_];
        int iRow;
        for (iRow=0;iRow<numberRows_;iRow++) {
          int iPivot=pivotVariable_[iRow];
          if (flagged(iPivot)||!pivoted(iPivot))
            continue;
          assert (iPivot<numberColumns_&&lower_[iPivot]==upper_[iPivot]);
          candidateList[numberCandidates++]=iRow;
        }
        // and set first candidate
        if (!numberCandidates) {
          delete [] candidateList;
          candidateList=NULL;
          int iRow;
          for (iRow=0;iRow<numberRows_;iRow++) {
            int iPivot=pivotVariable_[iRow];
            clearPivoted(iPivot);
          }
        } else {
          ifValuesPass=2;
          continue;
        }
      }
      int numberPivots = factorization_->pivots();
      bool specialCase;
      int useNumberFake;
      returnCode=0;
      if (numberPivots<20&&
          (specialOptions_&2048)!=0&&!numberChanged_&&perturbation_>=100
          &&dualBound_>1.0e8) {
        specialCase=true;
        // as dual bound high - should be okay
        useNumberFake=0;
      } else {
        specialCase=false;
        useNumberFake=numberFake_;
      }
      if (!numberPivots||specialCase) {
        // may have crept through - so may be optimal
        // check any flagged variables
        int iRow;
        for (iRow=0;iRow<numberRows_;iRow++) {
          int iPivot=pivotVariable_[iRow];
          if (flagged(iPivot))
            break;
        }
        if (iRow<numberRows_&&numberPivots) {
          // try factorization
          returnCode=-2;
        }
        
        if (useNumberFake||numberDualInfeasibilities_) {
          // may be dual infeasible
          problemStatus_=-5;
        } else {
          if (iRow<numberRows_) {
#ifdef CLP_DEBUG
            std::cerr<<"Flagged variables at end - infeasible?"<<std::endl;
            //printf("Probably infeasible - pivot was %g\n",alpha_);
#endif
            //if (fabs(alpha_)<1.0e-4) {
            //problemStatus_=1;
            //} else {
#ifdef CLP_DEBUG
            abort();
#endif
            //}
            problemStatus_=-5;
          } else {
            if (numberPivots) {
              // objective may be wrong
              objectiveValue_ = innerProduct(cost_,numberColumns_+numberRows_,solution_);
              objectiveValue_ += objective_->nonlinearOffset();
              objectiveValue_ /= (objectiveScale_*rhsScale_);
              if ((specialOptions_&16384)==0) {
                // and dual_ may be wrong (i.e. for fixed or basic)
                CoinIndexedVector * arrayVector = rowArray_[1];
                arrayVector->clear();
                int iRow;
                double * array = arrayVector->denseVector();
                /* Use dual_ instead of array
                   Even though dual_ is only numberRows_ long this is
                   okay as gets permuted to longer rowArray_[2]
                */
                arrayVector->setDenseVector(dual_);
                int * index = arrayVector->getIndices();
                int number=0;
                for (iRow=0;iRow<numberRows_;iRow++) {
                  int iPivot=pivotVariable_[iRow];
                  double value = cost_[iPivot];
                  dual_[iRow]=value;
                  if (value) {
                    index[number++]=iRow;
                  }
                }
                arrayVector->setNumElements(number);
                // Extended duals before "updateTranspose"
                matrix_->dualExpanded(this,arrayVector,NULL,0);
                // Btran basic costs
                rowArray_[2]->clear();
                factorization_->updateColumnTranspose(rowArray_[2],arrayVector);
                // and return vector
                arrayVector->setDenseVector(array);
              }
            }
            problemStatus_=0;
            sumPrimalInfeasibilities_=0.0;
            if ((specialOptions_&(1024+16384))!=0) {
              CoinIndexedVector * arrayVector = rowArray_[1];
              arrayVector->clear();
              double * rhs = arrayVector->denseVector();
              times(1.0,solution_,rhs);
#ifdef CHECK_ACCURACY
              bool bad=false;
#endif
              bool bad2=false;
              int i;
              for ( i=0;i<numberRows_;i++) {
                if (rhs[i]<rowLowerWork_[i]-primalTolerance_||
                    rhs[i]>rowUpperWork_[i]+primalTolerance_) {
                  bad2=true;
#ifdef CHECK_ACCURACY
                  printf("row %d out of bounds %g, %g correct %g bad %g\n",i,
                         rowLowerWork_[i],rowUpperWork_[i],
                         rhs[i],rowActivityWork_[i]);
#endif
                } else if (fabs(rhs[i]-rowActivityWork_[i])>1.0e-3) {
#ifdef CHECK_ACCURACY
                  bad=true;
                  printf("row %d correct %g bad %g\n",i,rhs[i],rowActivityWork_[i]);
#endif
                }
                rhs[i]=0.0;
              }
              for ( i=0;i<numberColumns_;i++) {
                if (solution_[i]<columnLowerWork_[i]-primalTolerance_||
                    solution_[i]>columnUpperWork_[i]+primalTolerance_) {
                  bad2=true;
#ifdef CHECK_ACCURACY
                  printf("column %d out of bounds %g, %g correct %g bad %g\n",i,
                         columnLowerWork_[i],columnUpperWork_[i],
                         solution_[i],columnActivityWork_[i]);
#endif
                }
              }
              if (bad2) {
                problemStatus_=-3;
                returnCode=-2;
                // Force to re-factorize early next time
                int numberPivots = factorization_->pivots();
                forceFactorization_=CoinMin(forceFactorization_,(numberPivots+1)>>1);
              }
            }
          }
        }
      } else {
        problemStatus_=-3;
        returnCode=-2;
        // Force to re-factorize early next time
        int numberPivots = factorization_->pivots();
        forceFactorization_=CoinMin(forceFactorization_,(numberPivots+1)>>1);
      }
      break;
    }
  }
  if (givenDuals) {
    CoinMemcpyN(dj_,numberRows_+numberColumns_,givenDuals);
    // get rid of any values pass array
    delete [] candidateList;
  }
  delete [] dubiousWeights;
  return returnCode;
}
/* The duals are updated by the given arrays.
   Returns number of infeasibilities.
   rowArray and columnarray will have flipped
   The output vector has movement (row length array) */
int
ClpSimplexDual::updateDualsInDual(CoinIndexedVector * rowArray,
                                  CoinIndexedVector * columnArray,
                                  CoinIndexedVector * outputArray,
                                  double theta,
                                  double & objectiveChange,
                                  bool fullRecompute)
{
  
  outputArray->clear();
  
  
  int numberInfeasibilities=0;
  int numberRowInfeasibilities=0;
  
  // get a tolerance
  double tolerance = dualTolerance_;
  // we can't really trust infeasibilities if there is dual error
  double error = CoinMin(1.0e-2,largestDualError_);
  // allow tolerance at least slightly bigger than standard
  tolerance = tolerance +  error;
  
  double changeObj=0.0;

  // Coding is very similar but we can save a bit by splitting
  // Do rows
  if (!fullRecompute) {
    int i;
    double * reducedCost = djRegion(0);
    const double * lower = lowerRegion(0);
    const double * upper = upperRegion(0);
    const double * cost = costRegion(0);
    double * work;
    int number;
    int * which;
    assert(rowArray->packedMode());
    work = rowArray->denseVector();
    number = rowArray->getNumElements();
    which = rowArray->getIndices();
    for (i=0;i<number;i++) {
      int iSequence = which[i];
      double alphaI = work[i];
      work[i]=0.0;
      
      Status status = getStatus(iSequence+numberColumns_);
      // more likely to be at upper bound ?
      if (status==atUpperBound) {

        double value = reducedCost[iSequence]-theta*alphaI;
        reducedCost[iSequence]=value;

        if (value>tolerance) {
          // to lower bound (if swap)
          which[numberInfeasibilities++]=iSequence;
          double movement = lower[iSequence]-upper[iSequence];
          assert (fabs(movement)<1.0e30);
#ifdef CLP_DEBUG
          if ((handler_->logLevel()&32))
            printf("%d %d, new dj %g, alpha %g, movement %g\n",
                   0,iSequence,value,alphaI,movement);
#endif
          changeObj += movement*cost[iSequence];
          outputArray->quickAdd(iSequence,-movement);
        }
      } else if (status==atLowerBound) {

        double value = reducedCost[iSequence]-theta*alphaI;
        reducedCost[iSequence]=value;

        if (value<-tolerance) {
          // to upper bound 
          which[numberInfeasibilities++]=iSequence;
          double movement = upper[iSequence] - lower[iSequence];
          assert (fabs(movement)<1.0e30);
#ifdef CLP_DEBUG
          if ((handler_->logLevel()&32))
            printf("%d %d, new dj %g, alpha %g, movement %g\n",
                   0,iSequence,value,alphaI,movement);
#endif
          changeObj += movement*cost[iSequence];
          outputArray->quickAdd(iSequence,-movement);
        }
      }
    }
  } else  {
    double * solution = solutionRegion(0);
    double * reducedCost = djRegion(0);
    const double * lower = lowerRegion(0);
    const double * upper = upperRegion(0);
    const double * cost = costRegion(0);
    int * which;
    which = rowArray->getIndices();
    int iSequence;
    for (iSequence=0;iSequence<numberRows_;iSequence++) {
      double value = reducedCost[iSequence];
      
      Status status = getStatus(iSequence+numberColumns_);
      // more likely to be at upper bound ?
      if (status==atUpperBound) {
        double movement=0.0;

        if (value>tolerance) {
          // to lower bound (if swap)
          // put back alpha
          which[numberInfeasibilities++]=iSequence;
          movement = lower[iSequence]-upper[iSequence];
          changeObj += movement*cost[iSequence];
          outputArray->quickAdd(iSequence,-movement);
          assert (fabs(movement)<1.0e30);
        } else if (value>-tolerance) {
          // at correct bound but may swap
          FakeBound bound = getFakeBound(iSequence+numberColumns_);
          if (bound==ClpSimplexDual::upperFake) {
            movement = lower[iSequence]-upper[iSequence];
            assert (fabs(movement)<1.0e30);
            setStatus(iSequence+numberColumns_,atLowerBound);
            solution[iSequence] = lower[iSequence];
            changeObj += movement*cost[iSequence];
            numberFake_--;
            setFakeBound(iSequence+numberColumns_,noFake);
          }
        }
      } else if (status==atLowerBound) {
        double movement=0.0;

        if (value<-tolerance) {
          // to upper bound 
          // put back alpha
          which[numberInfeasibilities++]=iSequence;
          movement = upper[iSequence] - lower[iSequence];
          assert (fabs(movement)<1.0e30);
          changeObj += movement*cost[iSequence];
          outputArray->quickAdd(iSequence,-movement);
        } else if (value<tolerance) {
          // at correct bound but may swap
          FakeBound bound = getFakeBound(iSequence+numberColumns_);
          if (bound==ClpSimplexDual::lowerFake) {
            movement = upper[iSequence]-lower[iSequence];
            assert (fabs(movement)<1.0e30);
            setStatus(iSequence+numberColumns_,atUpperBound);
            solution[iSequence] = upper[iSequence];
            changeObj += movement*cost[iSequence];
            numberFake_--;
            setFakeBound(iSequence+numberColumns_,noFake);
          }
        }
      }
    }
  }

  // Do columns
  if (!fullRecompute) {
    int i;
    double * reducedCost = djRegion(1);
    const double * lower = lowerRegion(1);
    const double * upper = upperRegion(1);
    const double * cost = costRegion(1);
    double * work;
    int number;
    int * which;
    // set number of infeasibilities in row array
    numberRowInfeasibilities=numberInfeasibilities;
    rowArray->setNumElements(numberInfeasibilities);
    numberInfeasibilities=0;
    work = columnArray->denseVector();
    number = columnArray->getNumElements();
    which = columnArray->getIndices();
    
    for (i=0;i<number;i++) {
      int iSequence = which[i];
      double alphaI = work[i];
      work[i]=0.0;
      
      Status status = getStatus(iSequence);
      if (status==atLowerBound) {
        double value = reducedCost[iSequence]-theta*alphaI;
        reducedCost[iSequence]=value;
        double movement=0.0;

        if (value<-tolerance) {
          // to upper bound 
          which[numberInfeasibilities++]=iSequence;
          movement = upper[iSequence] - lower[iSequence];
          assert (fabs(movement)<1.0e30);
#ifdef CLP_DEBUG
          if ((handler_->logLevel()&32))
            printf("%d %d, new dj %g, alpha %g, movement %g\n",
                   1,iSequence,value,alphaI,movement);
#endif
          changeObj += movement*cost[iSequence];
          matrix_->add(this,outputArray,iSequence,movement);
        }
      } else if (status==atUpperBound) {
        double value = reducedCost[iSequence]-theta*alphaI;
        reducedCost[iSequence]=value;
        double movement=0.0;

        if (value>tolerance) {
          // to lower bound (if swap)
          which[numberInfeasibilities++]=iSequence;
          movement = lower[iSequence]-upper[iSequence];
          assert (fabs(movement)<1.0e30);
#ifdef CLP_DEBUG
          if ((handler_->logLevel()&32))
            printf("%d %d, new dj %g, alpha %g, movement %g\n",
                   1,iSequence,value,alphaI,movement);
#endif
          changeObj += movement*cost[iSequence];
          matrix_->add(this,outputArray,iSequence,movement);
        }
      } else if (status==isFree) {
        double value = reducedCost[iSequence]-theta*alphaI;
        reducedCost[iSequence]=value;
      }
    }
  } else {
    double * solution = solutionRegion(1);
    double * reducedCost = djRegion(1);
    const double * lower = lowerRegion(1);
    const double * upper = upperRegion(1);
    const double * cost = costRegion(1);
    int * which;
    // set number of infeasibilities in row array
    numberRowInfeasibilities=numberInfeasibilities;
    rowArray->setNumElements(numberInfeasibilities);
    numberInfeasibilities=0;
    which = columnArray->getIndices();
    int iSequence;
    for (iSequence=0;iSequence<numberColumns_;iSequence++) {
      double value = reducedCost[iSequence];
      
      Status status = getStatus(iSequence);
      if (status==atLowerBound) {
        double movement=0.0;

        if (value<-tolerance) {
          // to upper bound 
          // put back alpha
          which[numberInfeasibilities++]=iSequence;
          movement = upper[iSequence] - lower[iSequence];
          assert (fabs(movement)<1.0e30);
          changeObj += movement*cost[iSequence];
          matrix_->add(this,outputArray,iSequence,movement);
        } else if (value<tolerance) {
          // at correct bound but may swap
          FakeBound bound = getFakeBound(iSequence);
          if (bound==ClpSimplexDual::lowerFake) {
            movement = upper[iSequence]-lower[iSequence];
            assert (fabs(movement)<1.0e30);
            setStatus(iSequence,atUpperBound);
            solution[iSequence] = upper[iSequence];
            changeObj += movement*cost[iSequence];
            numberFake_--;
            setFakeBound(iSequence,noFake);
          }
        }
      } else if (status==atUpperBound) {
        double movement=0.0;

        if (value>tolerance) {
          // to lower bound (if swap)
          // put back alpha
          which[numberInfeasibilities++]=iSequence;
          movement = lower[iSequence]-upper[iSequence];
          assert (fabs(movement)<1.0e30);
          changeObj += movement*cost[iSequence];
          matrix_->add(this,outputArray,iSequence,movement);
        } else if (value>-tolerance) {
          // at correct bound but may swap
          FakeBound bound = getFakeBound(iSequence);
          if (bound==ClpSimplexDual::upperFake) {
            movement = lower[iSequence]-upper[iSequence];
            assert (fabs(movement)<1.0e30);
            setStatus(iSequence,atLowerBound);
            solution[iSequence] = lower[iSequence];
            changeObj += movement*cost[iSequence];
            numberFake_--;
            setFakeBound(iSequence,noFake);
          }
        }
      }
    }
  }
#ifdef CLP_DEBUG
  if (fullRecompute&&numberFake_&&(handler_->logLevel()&16)!=0) 
    printf("%d fake after full update\n",numberFake_);
#endif
  // set number of infeasibilities
  columnArray->setNumElements(numberInfeasibilities);
  numberInfeasibilities += numberRowInfeasibilities;
  if (fullRecompute) {
    // do actual flips
    flipBounds(rowArray,columnArray,0.0);
  }
  objectiveChange += changeObj;
  return numberInfeasibilities;
}
void
ClpSimplexDual::updateDualsInValuesPass(CoinIndexedVector * rowArray,
                                  CoinIndexedVector * columnArray,
                                        double theta)
{
  
  // use a tighter tolerance except for all being okay
  double tolerance = dualTolerance_;
  
  // Coding is very similar but we can save a bit by splitting
  // Do rows
  {
    int i;
    double * reducedCost = djRegion(0);
    double * work;
    int number;
    int * which;
    work = rowArray->denseVector();
    number = rowArray->getNumElements();
    which = rowArray->getIndices();
    for (i=0;i<number;i++) {
      int iSequence = which[i];
      double alphaI = work[i];
      double value = reducedCost[iSequence]-theta*alphaI;
      work[i]=0.0;
      reducedCost[iSequence]=value;
      
      Status status = getStatus(iSequence+numberColumns_);
      // more likely to be at upper bound ?
      if (status==atUpperBound) {

        if (value>tolerance) 
          reducedCost[iSequence]=0.0;
      } else if (status==atLowerBound) {

        if (value<-tolerance) {
          reducedCost[iSequence]=0.0;
        }
      }
    }
  }
  rowArray->setNumElements(0);

  // Do columns
  {
    int i;
    double * reducedCost = djRegion(1);
    double * work;
    int number;
    int * which;
    work = columnArray->denseVector();
    number = columnArray->getNumElements();
    which = columnArray->getIndices();
    
    for (i=0;i<number;i++) {
      int iSequence = which[i];
      double alphaI = work[i];
      double value = reducedCost[iSequence]-theta*alphaI;
      work[i]=0.0;
      reducedCost[iSequence]=value;
      
      Status status = getStatus(iSequence);
      if (status==atLowerBound) {
        if (value<-tolerance) 
          reducedCost[iSequence]=0.0;
      } else if (status==atUpperBound) {
        if (value>tolerance) 
          reducedCost[iSequence]=0.0;
      }
    }
  }
  columnArray->setNumElements(0);
}
/* 
   Chooses dual pivot row
   Would be faster with separate region to scan
   and will have this (with square of infeasibility) when steepest
   For easy problems we can just choose one of the first rows we look at
*/
void
ClpSimplexDual::dualRow(int alreadyChosen)
{
  // get pivot row using whichever method it is
  int chosenRow=-1;
#ifdef FORCE_FOLLOW
  bool forceThis=false;
  if (!fpFollow&&strlen(forceFile)) {
    fpFollow = fopen(forceFile,"r");
    assert (fpFollow);
  }
  if (fpFollow) {
    if (numberIterations_<=force_iteration) {
      // read to next Clp0102
      char temp[300];
      while (fgets(temp,250,fpFollow)) {
        if (strncmp(temp,"Clp0102",7))
          continue;
        char cin,cout;
        sscanf(temp+9,"%d%*f%*s%*c%c%d%*s%*c%c%d",
               &force_iteration,&cin,&force_in,&cout,&force_out);
        if (cin=='R')
          force_in += numberColumns_;
        if (cout=='R')
          force_out += numberColumns_;
        forceThis=true;
        assert (numberIterations_==force_iteration-1);
        printf("Iteration %d will force %d out and %d in\n",
               force_iteration,force_out,force_in);
        alreadyChosen=force_out;
        break;
      }
    } else {
      // use old
      forceThis=true;
    }
    if (!forceThis) {
      fclose(fpFollow);
      fpFollow=NULL;
      forceFile="";
    }
  }
#endif
  double freeAlpha=0.0;
  if (alreadyChosen<0) {
    // first see if any free variables and put them in basis
    int nextFree = nextSuperBasic();
    //nextFree=-1; //off
    if (nextFree>=0) {
      // unpack vector and find a good pivot
      unpack(rowArray_[1],nextFree);
      factorization_->updateColumn(rowArray_[2],rowArray_[1]);
      
      double * work=rowArray_[1]->denseVector();
      int number=rowArray_[1]->getNumElements();
      int * which=rowArray_[1]->getIndices();
      double bestFeasibleAlpha=0.0;
      int bestFeasibleRow=-1;
      double bestInfeasibleAlpha=0.0;
      int bestInfeasibleRow=-1;
      int i;
      
      for (i=0;i<number;i++) {
        int iRow = which[i];
        double alpha = fabs(work[iRow]);
        if (alpha>1.0e-3) {
          int iSequence=pivotVariable_[iRow];
          double value = solution_[iSequence];
          double lower = lower_[iSequence];
          double upper = upper_[iSequence];
          double infeasibility=0.0;
          if (value>upper)
            infeasibility = value-upper;
          else if (value<lower)
            infeasibility = lower-value;
          if (infeasibility*alpha>bestInfeasibleAlpha&&alpha>1.0e-1) {
            if (!flagged(iSequence)) {
              bestInfeasibleAlpha = infeasibility*alpha;
              bestInfeasibleRow=iRow;
            }
          }
          if (alpha>bestFeasibleAlpha&&(lower>-1.0e20||upper<1.0e20)) {
            bestFeasibleAlpha = alpha;
            bestFeasibleRow=iRow;
          }
        }
      }
      if (bestInfeasibleRow>=0) 
        chosenRow = bestInfeasibleRow;
      else if (bestFeasibleAlpha>1.0e-2)
        chosenRow = bestFeasibleRow;
      if (chosenRow>=0) {
        pivotRow_=chosenRow;
        freeAlpha=work[chosenRow];
      }
      rowArray_[1]->clear();
    } 
  } else {
    // in values pass
    chosenRow=alreadyChosen;
#ifdef FORCE_FOLLOW
    if(forceThis) {
      alreadyChosen=-1;
      chosenRow=-1;
      for (int i=0;i<numberRows_;i++) {
        if (pivotVariable_[i]==force_out) {
          chosenRow=i;
          break;
        }
      }
      assert (chosenRow>=0);
    }
#endif
    pivotRow_=chosenRow;
  }
  if (chosenRow<0) 
    pivotRow_=dualRowPivot_->pivotRow();

  if (pivotRow_>=0) {
    sequenceOut_ = pivotVariable_[pivotRow_];
    valueOut_ = solution_[sequenceOut_];
    lowerOut_ = lower_[sequenceOut_];
    upperOut_ = upper_[sequenceOut_];
    if (alreadyChosen<0) {
      // if we have problems we could try other way and hope we get a 
      // zero pivot?
      if (valueOut_>upperOut_) {
        directionOut_ = -1;
        dualOut_ = valueOut_ - upperOut_;
      } else if (valueOut_<lowerOut_) {
        directionOut_ = 1;
        dualOut_ = lowerOut_ - valueOut_;
      } else {
#if 1
        // odd (could be free) - it's feasible - go to nearest
        if (valueOut_-lowerOut_<upperOut_-valueOut_) {
          directionOut_ = 1;
          dualOut_ = lowerOut_ - valueOut_;
        } else {
          directionOut_ = -1;
          dualOut_ = valueOut_ - upperOut_;
        }
#else
        // odd (could be free) - it's feasible - improve obj
        printf("direction from alpha of %g is %d\n",
               freeAlpha,freeAlpha>0.0 ? 1 : -1);
        if (valueOut_-lowerOut_>1.0e20)
          freeAlpha=1.0;
        else if(upperOut_-valueOut_>1.0e20) 
          freeAlpha=-1.0;
        //if (valueOut_-lowerOut_<upperOut_-valueOut_) {
        if (freeAlpha<0.0) {
          directionOut_ = 1;
          dualOut_ = lowerOut_ - valueOut_;
        } else {
          directionOut_ = -1;
          dualOut_ = valueOut_ - upperOut_;
        }
        printf("direction taken %d - bounds %g %g %g\n",
               directionOut_,lowerOut_,valueOut_,upperOut_);
#endif
      }
#ifdef CLP_DEBUG
      assert(dualOut_>=0.0);
#endif
    } else {
      // in values pass so just use sign of dj
      // We don't want to go through any barriers so set dualOut low
      // free variables will never be here
      dualOut_ = 1.0e-6;
      if (dj_[sequenceOut_]>0.0) {
        // this will give a -1 in pivot row (as slacks are -1.0)
        directionOut_ = 1;
      } else {
        directionOut_ = -1;
      }
    }
  }
  return ;
}
// Checks if any fake bounds active - if so returns number and modifies
// dualBound_ and everything.
// Free variables will be left as free
// Returns number of bounds changed if >=0
// Returns -1 if not initialize and no effect
// Fills in changeVector which can be used to see if unbounded
// and cost of change vector
int
ClpSimplexDual::changeBounds(bool initialize,
                                 CoinIndexedVector * outputArray,
                                 double & changeCost)
{ 
  numberFake_ = 0;
  if (!initialize) {
    int numberInfeasibilities;
    double newBound;
    newBound = 5.0*dualBound_;
    numberInfeasibilities=0;
    changeCost=0.0;
    // put back original bounds and then check
    createRim(1);
    int iSequence;
    // bounds will get bigger - just look at ones at bounds
    for (iSequence=0;iSequence<numberRows_+numberColumns_;iSequence++) {
      double lowerValue=lower_[iSequence];
      double upperValue=upper_[iSequence];
      double value=solution_[iSequence];
      setFakeBound(iSequence,ClpSimplexDual::noFake);
      switch(getStatus(iSequence)) {

      case basic:
      case ClpSimplex::isFixed:
        break;
      case isFree:
      case superBasic:
        break;
      case atUpperBound:
        if (fabs(value-upperValue)>primalTolerance_) 
          numberInfeasibilities++;
        break;
      case atLowerBound:
        if (fabs(value-lowerValue)>primalTolerance_) 
          numberInfeasibilities++;
        break;
      }
    }
    // If dual infeasible then carry on
    if (numberInfeasibilities) {
      handler_->message(CLP_DUAL_CHECKB,messages_)
        <<newBound
        <<CoinMessageEol;
      int iSequence;
      for (iSequence=0;iSequence<numberRows_+numberColumns_;iSequence++) {
        double lowerValue=lower_[iSequence];
        double upperValue=upper_[iSequence];
        double newLowerValue;
        double newUpperValue;
        Status status = getStatus(iSequence);
        if (status==atUpperBound||
            status==atLowerBound) {
          double value = solution_[iSequence];
          if (value-lowerValue<=upperValue-value) {
            newLowerValue = CoinMax(lowerValue,value-0.666667*newBound);
            newUpperValue = CoinMin(upperValue,newLowerValue+newBound);
          } else {
            newUpperValue = CoinMin(upperValue,value+0.666667*newBound);
            newLowerValue = CoinMax(lowerValue,newUpperValue-newBound);
          }
          lower_[iSequence]=newLowerValue;
          upper_[iSequence]=newUpperValue;
          if (newLowerValue > lowerValue) {
            if (newUpperValue < upperValue) {
              setFakeBound(iSequence,ClpSimplexDual::bothFake);
              numberFake_++;
            } else {
              setFakeBound(iSequence,ClpSimplexDual::lowerFake);
              numberFake_++;
            }
          } else {
            if (newUpperValue < upperValue) {
              setFakeBound(iSequence,ClpSimplexDual::upperFake);
              numberFake_++;
            }
          }
          if (status==atUpperBound)
            solution_[iSequence] = newUpperValue;
          else
            solution_[iSequence] = newLowerValue;
          double movement = solution_[iSequence] - value;
          if (movement&&outputArray) {
            if (iSequence>=numberColumns_) {
              outputArray->quickAdd(iSequence,-movement);
              changeCost += movement*cost_[iSequence];
            } else {
              matrix_->add(this,outputArray,iSequence,movement);
              changeCost += movement*cost_[iSequence];
            }
          }
        }
      }
      dualBound_ = newBound;
    } else {
      numberInfeasibilities=-1;
    }
    return numberInfeasibilities;
  } else {
    int iSequence;
      
    for (iSequence=0;iSequence<numberRows_+numberColumns_;iSequence++) {
      Status status = getStatus(iSequence);
      if (status==atUpperBound||
          status==atLowerBound) {
        double lowerValue=lower_[iSequence];
        double upperValue=upper_[iSequence];
        double value = solution_[iSequence];
        if (lowerValue>-largeValue_||upperValue<largeValue_) {
          if (lowerValue-value>-0.5*dualBound_||
              upperValue-value<0.5*dualBound_) {
            if (fabs(lowerValue-value)<=fabs(upperValue-value)) {
              if (upperValue > lowerValue + dualBound_) {
                upper_[iSequence]=lowerValue+dualBound_;
                setFakeBound(iSequence,ClpSimplexDual::upperFake);
                numberFake_++;
              }
            } else {
              if (lowerValue < upperValue - dualBound_) {
                lower_[iSequence]=upperValue-dualBound_;
                setFakeBound(iSequence,ClpSimplexDual::lowerFake);
                numberFake_++;
              }
            }
          } else {
            lower_[iSequence]=-0.5*dualBound_;
            upper_[iSequence]= 0.5*dualBound_;
            setFakeBound(iSequence,ClpSimplexDual::bothFake);
            numberFake_++;
          }
          if (status==atUpperBound)
            solution_[iSequence]=upper_[iSequence];
          else
            solution_[iSequence]=lower_[iSequence];
        } else {
          // set non basic free variables to fake bounds
          // I don't think we should ever get here
          CoinAssert(!("should not be here"));
          lower_[iSequence]=-0.5*dualBound_;
          upper_[iSequence]= 0.5*dualBound_;
          setFakeBound(iSequence,ClpSimplexDual::bothFake);
          numberFake_++;
          setStatus(iSequence,atUpperBound);
          solution_[iSequence]=0.5*dualBound_;
        }
      }
    }

    return 1;
  }
}
int
ClpSimplexDual::dualColumn0(const CoinIndexedVector * rowArray,
                           const CoinIndexedVector * columnArray,
                           CoinIndexedVector * spareArray,
                           double acceptablePivot,
                           double & upperReturn, double &bestReturn,double & badFree)
{
  // do first pass to get possibles 
  double * spare = spareArray->denseVector();
  int * index = spareArray->getIndices();
  const double * work;
  int number;
  const int * which;
  const double * reducedCost;
  // We can also see if infeasible or pivoting on free
  double tentativeTheta = 1.0e25;
  double upperTheta = 1.0e31;
  double freePivot = acceptablePivot;
  double bestPossible=0.0;
  int numberRemaining=0;
  int i;
  badFree=0.0;
  for (int iSection=0;iSection<2;iSection++) {

    int addSequence;

    if (!iSection) {
      work = rowArray->denseVector();
      number = rowArray->getNumElements();
      which = rowArray->getIndices();
      reducedCost = rowReducedCost_;
      addSequence = numberColumns_;
    } else {
      work = columnArray->denseVector();
      number = columnArray->getNumElements();
      which = columnArray->getIndices();
      reducedCost = reducedCostWork_;
      addSequence = 0;
    }
    
    for (i=0;i<number;i++) {
      int iSequence = which[i];
      double alpha;
      double oldValue;
      double value;
      bool keep;

      switch(getStatus(iSequence+addSequence)) {
          
      case basic:
      case ClpSimplex::isFixed:
        break;
      case isFree:
      case superBasic:
        alpha = work[i];
        bestPossible = CoinMax(bestPossible,fabs(alpha));
        oldValue = reducedCost[iSequence];
        // If free has to be very large - should come in via dualRow
        //if (getStatus(iSequence+addSequence)==isFree&&fabs(alpha)<1.0e-3)
        //break;
        if (oldValue>dualTolerance_) {
          keep = true;
        } else if (oldValue<-dualTolerance_) {
          keep = true;
        } else {
          if (fabs(alpha)>CoinMax(10.0*acceptablePivot,1.0e-5)) {
            keep = true;
          } else {
            keep=false;
            badFree=CoinMax(badFree,fabs(alpha));
          }
        }
        if (keep) {
          // free - choose largest
          if (fabs(alpha)>freePivot) {
            freePivot=fabs(alpha);
            sequenceIn_ = iSequence + addSequence;
            theta_=oldValue/alpha;
            alpha_=alpha;
          }
        }
        break;
      case atUpperBound:
        alpha = work[i];
        oldValue = reducedCost[iSequence];
        value = oldValue-tentativeTheta*alpha;
        //assert (oldValue<=dualTolerance_*1.0001);
        if (value>dualTolerance_) {
          bestPossible = CoinMax(bestPossible,-alpha);
          value = oldValue-upperTheta*alpha;
          if (value>dualTolerance_ && -alpha>=acceptablePivot) 
            upperTheta = (oldValue-dualTolerance_)/alpha;
          // add to list
          spare[numberRemaining]=alpha;
          index[numberRemaining++]=iSequence+addSequence;
        }
        break;
      case atLowerBound:
        alpha = work[i];
        oldValue = reducedCost[iSequence];
        value = oldValue-tentativeTheta*alpha;
        //assert (oldValue>=-dualTolerance_*1.0001);
        if (value<-dualTolerance_) {
          bestPossible = CoinMax(bestPossible,alpha);
          value = oldValue-upperTheta*alpha;
          if (value<-dualTolerance_ && alpha>=acceptablePivot) 
            upperTheta = (oldValue+dualTolerance_)/alpha;
          // add to list
          spare[numberRemaining]=alpha;
          index[numberRemaining++]=iSequence+addSequence;
        }
        break;
      }
    }
  }
  upperReturn = upperTheta;
  bestReturn = bestPossible;
  return numberRemaining;
}
/* 
   Row array has row part of pivot row (as duals so sign may be switched)
   Column array has column part.
   This chooses pivot column.
   Spare array will be needed when we start getting clever.
   We will check for basic so spare array will never overflow.
   If necessary will modify costs
*/
double
ClpSimplexDual::dualColumn(CoinIndexedVector * rowArray,
                           CoinIndexedVector * columnArray,
                           CoinIndexedVector * spareArray,
                           CoinIndexedVector * spareArray2,
                           double acceptablePivot,
                           CoinBigIndex * dubiousWeights)
{
  int numberPossiblySwapped=0;
  int numberRemaining=0;
  
  double totalThru=0.0; // for when variables flip
  //double saveAcceptable=acceptablePivot;
  //acceptablePivot=1.0e-9;

  double bestEverPivot=acceptablePivot;
  int lastSequence = -1;
  double lastPivot=0.0;
  double upperTheta;
  double newTolerance = dualTolerance_;
  //newTolerance = dualTolerance_+1.0e-6*dblParam_[ClpDualTolerance];
  // will we need to increase tolerance
  bool thisIncrease=false;
  // If we think we need to modify costs (not if something from broad sweep)
  bool modifyCosts=false;
  // Increase in objective due to swapping bounds (may be negative)
  double increaseInObjective=0.0;

  // use spareArrays to put ones looked at in
  // we are going to flip flop between
  int iFlip = 0;
  // Possible list of pivots
  int interesting[2];
  // where possible swapped ones are
  int swapped[2];
  // for zeroing out arrays after
  int marker[2][2];
  // pivot elements
  double * array[2], * spare, * spare2;
  // indices
  int * indices[2], * index, * index2;
  spareArray2->clear();
  array[0] = spareArray->denseVector();
  indices[0] = spareArray->getIndices();
  spare = array[0];
  index = indices[0];
  array[1] = spareArray2->denseVector();
  indices[1] = spareArray2->getIndices();
  int i;

  // initialize lists
  for (i=0;i<2;i++) {
    interesting[i]=0;
    swapped[i]=numberColumns_;
    marker[i][0]=0;
    marker[i][1]=numberColumns_;
  }
  /*
    First we get a list of possible pivots.  We can also see if the
    problem looks infeasible or whether we want to pivot in free variable.
    This may make objective go backwards but can only happen a finite
    number of times and I do want free variables basic.

    Then we flip back and forth.  At the start of each iteration
    interesting[iFlip] should have possible candidates and swapped[iFlip]
    will have pivots if we decide to take a previous pivot.
    At end of each iteration interesting[1-iFlip] should have
    candidates if we go through this theta and swapped[1-iFlip]
    pivots if we don't go through.

    At first we increase theta and see what happens.  We start
    theta at a reasonable guess.  If in right area then we do bit by bit.

   */

  // do first pass to get possibles 
  upperTheta = 1.0e31;
  double bestPossible=0.0;
  double badFree=0.0;
  if (spareIntArray_[0]!=-1) {
    numberRemaining = dualColumn0(rowArray,columnArray,spareArray,
                                  acceptablePivot,upperTheta,bestPossible,badFree);
  } else {
    // already done
    numberRemaining = spareArray->getNumElements();
    spareArray->setNumElements(0);
    upperTheta = spareDoubleArray_[0];
    bestPossible = spareDoubleArray_[1];
    theta_ = spareDoubleArray_[2];
    alpha_ = spareDoubleArray_[3];
    sequenceIn_ = spareIntArray_[1];
  }
  // switch off
  spareIntArray_[0]=0;
  // We can also see if infeasible or pivoting on free
  double tentativeTheta = 1.0e25;
  interesting[0]=numberRemaining;
  marker[0][0] = numberRemaining;

  if (!numberRemaining&&sequenceIn_<0)
    return 0.0; // Looks infeasible

  // If sum of bad small pivots too much
#define MORE_CAREFUL
#ifdef MORE_CAREFUL
  bool badSumPivots=false;
#endif
  if (sequenceIn_>=0) {
    // free variable - always choose
  } else {

    theta_=1.0e50;
    // now flip flop between spare arrays until reasonable theta
    tentativeTheta = CoinMax(10.0*upperTheta,1.0e-7);
    
    // loops increasing tentative theta until can't go through
    
    while (tentativeTheta < 1.0e22) {
      double thruThis = 0.0;
      
      double bestPivot=acceptablePivot;
      int bestSequence=-1;
      
      numberPossiblySwapped = numberColumns_;
      numberRemaining = 0;

      upperTheta = 1.0e50;

      spare = array[iFlip];
      index = indices[iFlip];
      spare2 = array[1-iFlip];
      index2 = indices[1-iFlip];

      // try 3 different ways
      // 1 bias increase by ones with slightly wrong djs
      // 2 bias by all
      // 3 bias by all - tolerance 
#define TRYBIAS 3


      double increaseInThis=0.0; //objective increase in this loop
      
      for (i=0;i<interesting[iFlip];i++) {
        int iSequence = index[i];
        double alpha = spare[i];
        double oldValue = dj_[iSequence];
        double value = oldValue-tentativeTheta*alpha;

        if (alpha < 0.0) {
          //at upper bound
          if (value>newTolerance) {
            double range = upper_[iSequence] - lower_[iSequence];
            thruThis -= range*alpha;
#if TRYBIAS==1
            if (oldValue>0.0)
              increaseInThis -= oldValue*range;
#elif TRYBIAS==2
            increaseInThis -= oldValue*range;
#else
            increaseInThis -= (oldValue+dualTolerance_)*range;
#endif
            // goes on swapped list (also means candidates if too many)
            spare2[--numberPossiblySwapped]=alpha;
            index2[numberPossiblySwapped]=iSequence;
            if (fabs(alpha)>bestPivot) {
              bestPivot=fabs(alpha);
              bestSequence=numberPossiblySwapped;
            }
          } else {
            value = oldValue-upperTheta*alpha;
            if (value>newTolerance && -alpha>=acceptablePivot) 
              upperTheta = (oldValue-newTolerance)/alpha;
            spare2[numberRemaining]=alpha;
            index2[numberRemaining++]=iSequence;
          }
        } else {
          // at lower bound
          if (value<-newTolerance) {
            double range = upper_[iSequence] - lower_[iSequence];
            thruThis += range*alpha;
            //?? is this correct - and should we look at good ones
#if TRYBIAS==1
            if (oldValue<0.0)
              increaseInThis += oldValue*range;
#elif TRYBIAS==2
            increaseInThis += oldValue*range;
#else
            increaseInThis += (oldValue-dualTolerance_)*range;
#endif
            // goes on swapped list (also means candidates if too many)
            spare2[--numberPossiblySwapped]=alpha;
            index2[numberPossiblySwapped]=iSequence;
            if (fabs(alpha)>bestPivot) {
              bestPivot=fabs(alpha);
              bestSequence=numberPossiblySwapped;
            }
          } else {
            value = oldValue-upperTheta*alpha;
            if (value<-newTolerance && alpha>=acceptablePivot) 
              upperTheta = (oldValue+newTolerance)/alpha;
            spare2[numberRemaining]=alpha;
            index2[numberRemaining++]=iSequence;
          }
        }
      }
      swapped[1-iFlip]=numberPossiblySwapped;
      interesting[1-iFlip]=numberRemaining;
      marker[1-iFlip][0]= CoinMax(marker[1-iFlip][0],numberRemaining);
      marker[1-iFlip][1]= CoinMin(marker[1-iFlip][1],numberPossiblySwapped);
      
      if (totalThru+thruThis>=fabs(dualOut_)||
          increaseInObjective+increaseInThis<0.0) {
        // We should be pivoting in this batch
        // so compress down to this lot
        numberRemaining=0;
        for (i=numberColumns_-1;i>=swapped[1-iFlip];i--) {
          spare[numberRemaining]=spare2[i];
          index[numberRemaining++]=index2[i];
        }
        interesting[iFlip]=numberRemaining;
        int iTry;
#define MAXTRY 100
        // first get ratio with tolerance
        for (iTry=0;iTry<MAXTRY;iTry++) {
          
          upperTheta=1.0e50;
          numberPossiblySwapped = numberColumns_;
          numberRemaining = 0;

          increaseInThis=0.0; //objective increase in this loop

          thruThis=0.0;

          spare = array[iFlip];
          index = indices[iFlip];
          spare2 = array[1-iFlip];
          index2 = indices[1-iFlip];
          for (i=0;i<interesting[iFlip];i++) {
            int iSequence=index[i];
            double alpha=spare[i];
            double oldValue = dj_[iSequence];
            double value = oldValue-upperTheta*alpha;
            
            if (alpha < 0.0) {
              //at upper bound
              if (value>newTolerance) {
                if (-alpha>=acceptablePivot) {
                  upperTheta = (oldValue-newTolerance)/alpha;
                }
              }
            } else {
              // at lower bound
              if (value<-newTolerance) {
                if (alpha>=acceptablePivot) {
                  upperTheta = (oldValue+newTolerance)/alpha;
                }
              }
            }
          }
          bestPivot=acceptablePivot;
          sequenceIn_=-1;
#ifdef DUBIOUS_WEIGHTS
          double bestWeight=COIN_DBL_MAX;
#endif
          double largestPivot=acceptablePivot;
          // now choose largest and sum all ones which will go through
          //printf("XX it %d number %d\n",numberIterations_,interesting[iFlip]);
  // Sum of bad small pivots
#ifdef MORE_CAREFUL
          double sumBadPivots=0.0;
          badSumPivots=false;
#endif
          // Make sure upperTheta will work (-O2 and above gives problems)
          upperTheta *= 1.0000000001;
          for (i=0;i<interesting[iFlip];i++) {
            int iSequence=index[i];
            double alpha=spare[i];
            double value = dj_[iSequence]-upperTheta*alpha;
            double badDj=0.0;
            
            bool addToSwapped=false;
            
            if (alpha < 0.0) {
              //at upper bound
              if (value>=0.0) { 
                addToSwapped=true;
#if TRYBIAS==1
                badDj = -CoinMax(dj_[iSequence],0.0);
#elif TRYBIAS==2
                badDj = -dj_[iSequence];
#else
                badDj = -dj_[iSequence]-dualTolerance_;
#endif
              }
            } else {
              // at lower bound
              if (value<=0.0) {
                addToSwapped=true;
#if TRYBIAS==1
                badDj = CoinMin(dj_[iSequence],0.0);
#elif TRYBIAS==2
                badDj = dj_[iSequence];
#else
                badDj = dj_[iSequence]-dualTolerance_;
#endif
              }
            }
            if (!addToSwapped) {
              // add to list of remaining
              spare2[numberRemaining]=alpha;
              index2[numberRemaining++]=iSequence;
            } else {
              // add to list of swapped
              spare2[--numberPossiblySwapped]=alpha;
              index2[numberPossiblySwapped]=iSequence;
              // select if largest pivot
              bool take=false;
              double absAlpha = fabs(alpha);
#ifdef DUBIOUS_WEIGHTS
              // User could do anything to break ties here
              double weight;
              if (dubiousWeights)
                weight=dubiousWeights[iSequence];
              else
                weight=1.0;
              weight += CoinDrand48()*1.0e-2;
              if (absAlpha>2.0*bestPivot) {
                take=true;
              } else if (absAlpha>largestPivot) {
                // could multiply absAlpha and weight
                if (weight*bestPivot<bestWeight*absAlpha)
                  take=true;
              }
#else
              if (absAlpha>bestPivot) 
                take=true;
#endif
#ifdef MORE_CAREFUL
              if (absAlpha<acceptablePivot&&upperTheta<1.0e20) {
                if (alpha < 0.0) {
                  //at upper bound
                  if (value>dualTolerance_) {
                    double gap=upper_[iSequence]-lower_[iSequence];
                    if (gap<1.0e20)
                      sumBadPivots += value*gap; 
                    else
                      sumBadPivots += 1.0e20;
                    //printf("bad %d alpha %g dj at upper %g\n",
                    //     iSequence,alpha,value);
                  }
                } else {
                  //at lower bound
                  if (value<-dualTolerance_) {
                    double gap=upper_[iSequence]-lower_[iSequence];
                    if (gap<1.0e20)
                      sumBadPivots -= value*gap; 
                    else
                      sumBadPivots += 1.0e20;
                    //printf("bad %d alpha %g dj at lower %g\n",
                    //     iSequence,alpha,value);
                  }
                }
              }
#endif
#ifdef FORCE_FOLLOW
              if (iSequence==force_in) {
                printf("taking %d - alpha %g best %g\n",force_in,absAlpha,largestPivot);
                take=true;
              }
#endif
              if (take) {
                sequenceIn_ = numberPossiblySwapped;
                bestPivot =  absAlpha;
                theta_ = dj_[iSequence]/alpha;
                largestPivot = CoinMax(largestPivot,0.5*bestPivot);
#ifdef DUBIOUS_WEIGHTS
                bestWeight = weight;
#endif
                //printf(" taken seq %d alpha %g weight %d\n",
                //   iSequence,absAlpha,dubiousWeights[iSequence]);
              } else {
                //printf(" not taken seq %d alpha %g weight %d\n",
                //   iSequence,absAlpha,dubiousWeights[iSequence]);
              }
              double range = upper_[iSequence] - lower_[iSequence];
              thruThis += range*fabs(alpha);
              increaseInThis += badDj*range;
            }
          }
#ifdef MORE_CAREFUL
          // If we have done pivots and things look bad set alpha_ 0.0 to force factorization
          if (sumBadPivots>1.0e4) {
            if (handler_->logLevel()>1)
            printf("maybe forcing re-factorization - sum %g  %d pivots\n",sumBadPivots,
                   factorization_->pivots());
            badSumPivots=true;
          }
#endif
          swapped[1-iFlip]=numberPossiblySwapped;
          interesting[1-iFlip]=numberRemaining;
          marker[1-iFlip][0]= CoinMax(marker[1-iFlip][0],numberRemaining);
          marker[1-iFlip][1]= CoinMin(marker[1-iFlip][1],numberPossiblySwapped);
          // If we stop now this will be increase in objective (I think)
          double increase = (fabs(dualOut_)-totalThru)*theta_;
          increase += increaseInObjective;
          if (theta_<0.0)
            thruThis += fabs(dualOut_); // force using this one
          if (increaseInObjective<0.0&&increase<0.0&&lastSequence>=0) {
            // back
            // We may need to be more careful - we could do by
            // switch so we always do fine grained?
            bestPivot=0.0;
          } else {
            // add in
            totalThru += thruThis;
            increaseInObjective += increaseInThis;
          }
          if (bestPivot<0.1*bestEverPivot&&
              bestEverPivot>1.0e-6&&
              (bestPivot<1.0e-3||totalThru*2.0>fabs(dualOut_))) {
            // back to previous one
            sequenceIn_=lastSequence;
            // swap regions
            iFlip = 1-iFlip;
            break;
          } else if (sequenceIn_==-1&&upperTheta>largeValue_) {
            if (lastPivot>acceptablePivot) {
              // back to previous one
              sequenceIn_=lastSequence;
              // swap regions
              iFlip = 1-iFlip;
            } else {
              // can only get here if all pivots too small
            }
            break;
          } else if (totalThru>=fabs(dualOut_)) {
            modifyCosts=true; // fine grain - we can modify costs
            break; // no point trying another loop
          } else {
            lastSequence=sequenceIn_;
            if (bestPivot>bestEverPivot)
              bestEverPivot=bestPivot;
            iFlip = 1 -iFlip;
            modifyCosts=true; // fine grain - we can modify costs
          }
        }
        if (iTry==MAXTRY)
          iFlip = 1-iFlip; // flip back
        break;
      } else {
        // skip this lot
        if (bestPivot>1.0e-3||bestPivot>bestEverPivot) {
          bestEverPivot=bestPivot;
          lastSequence=bestSequence;
        } else {
          // keep old swapped
          CoinMemcpyN(array[iFlip]+swapped[iFlip],
                 numberColumns_-swapped[iFlip],array[1-iFlip]+swapped[iFlip]);
          CoinMemcpyN(indices[iFlip]+swapped[iFlip],
                 numberColumns_-swapped[iFlip],indices[1-iFlip]+swapped[iFlip]);
          marker[1-iFlip][1] = CoinMin(marker[1-iFlip][1],swapped[iFlip]);
          swapped[1-iFlip]=swapped[iFlip];
        }
        increaseInObjective += increaseInThis;
        iFlip = 1 - iFlip; // swap regions
        tentativeTheta = 2.0*upperTheta;
        totalThru += thruThis;
      }
    }
    
    // can get here without sequenceIn_ set but with lastSequence
    if (sequenceIn_<0&&lastSequence>=0) {
      // back to previous one
      sequenceIn_=lastSequence;
      // swap regions
      iFlip = 1-iFlip;
    }
    
#define MINIMUMTHETA 1.0e-18
    // Movement should be minimum for anti-degeneracy - unless
    // fixed variable out
    double minimumTheta;
    if (upperOut_>lowerOut_)
      minimumTheta=MINIMUMTHETA;
    else
      minimumTheta=0.0;
    if (sequenceIn_>=0) {
      // at this stage sequenceIn_ is just pointer into index array
      // flip just so we can use iFlip
      iFlip = 1 -iFlip;
      spare = array[iFlip];
      index = indices[iFlip];
      double oldValue;
      alpha_ = spare[sequenceIn_];
      sequenceIn_ = indices[iFlip][sequenceIn_];
      oldValue = dj_[sequenceIn_];
      theta_ = CoinMax(oldValue/alpha_,0.0);
      if (theta_<minimumTheta&&fabs(alpha_)<1.0e5&&1) {
        // can't pivot to zero
#if 0
        if (oldValue-minimumTheta*alpha_>=-dualTolerance_) {
          theta_=minimumTheta;
        } else if (oldValue-minimumTheta*alpha_>=-newTolerance) {
          theta_=minimumTheta;
          thisIncrease=true;
        } else {
          theta_=CoinMax((oldValue+newTolerance)/alpha_,0.0);
          thisIncrease=true;
        }
#else
        theta_=minimumTheta;
#endif 
      }
      // may need to adjust costs so all dual feasible AND pivoted is exactly 0
      //int costOffset = numberRows_+numberColumns_;
      if (modifyCosts) {
        int i;
        for (i=numberColumns_-1;i>=swapped[iFlip];i--) {
          int iSequence=index[i];
          double alpha=spare[i];
          double value = dj_[iSequence]-theta_*alpha;
            
          // can't be free here
          
          if (alpha < 0.0) {
            //at upper bound
            if (value>dualTolerance_) {
              thisIncrease=true;
#define MODIFYCOST 2
#if MODIFYCOST
              // modify cost to hit new tolerance
              double modification = alpha*theta_-dj_[iSequence]
                +newTolerance;
              if ((specialOptions_&(2048+4096+16384))!=0) {
                if ((specialOptions_&16384)!=0) {
                  if (fabs(modification)<1.0e-8)
                    modification=0.0;
                } else if ((specialOptions_&2048)!=0) {
                  if (fabs(modification)<1.0e-10)
                    modification=0.0;
                } else {
                  if (fabs(modification)<1.0e-12)
                    modification=0.0;
                }
              }
              dj_[iSequence] += modification;
              cost_[iSequence] +=  modification;
              if (modification)
                numberChanged_ ++; // Say changed costs
              //cost_[iSequence+costOffset] += modification; // save change
#endif
            }
          } else {
            // at lower bound
            if (-value>dualTolerance_) {
              thisIncrease=true;
#if MODIFYCOST
              // modify cost to hit new tolerance
              double modification = alpha*theta_-dj_[iSequence]
                -newTolerance;
              //modification = CoinMax(modification,-dualTolerance_);
              //assert (fabs(modification)<1.0e-7);
              if ((specialOptions_&(2048+4096))!=0) {
                if ((specialOptions_&2048)!=0) {
                  if (fabs(modification)<1.0e-10)
                    modification=0.0;
                } else {
                  if (fabs(modification)<1.0e-12)
                    modification=0.0;
                }
              }
              dj_[iSequence] += modification;
              cost_[iSequence] +=  modification;
              if (modification)
                numberChanged_ ++; // Say changed costs
              //cost_[iSequence+costOffset] += modification; // save change
#endif
            }
          }
        }
      }
    }
  }

  if (sequenceIn_>=0) {
#ifdef MORE_CAREFUL
    // If we have done pivots and things look bad set alpha_ 0.0 to force factorization
    if (badSumPivots&&factorization_->pivots()) {
      if (handler_->logLevel()>1)
        printf("forcing re-factorization\n");
      alpha_=0.0;
    }
    if (fabs(theta_*badFree)>10.0*dualTolerance_&&factorization_->pivots()) {
      if (handler_->logLevel()>1)
        printf("forcing re-factorizationon free\n");
      alpha_=0.0;
    }
#endif
    lowerIn_ = lower_[sequenceIn_];
    upperIn_ = upper_[sequenceIn_];
    valueIn_ = solution_[sequenceIn_];
    dualIn_ = dj_[sequenceIn_];

    if (numberTimesOptimal_) {
      // can we adjust cost back closer to original
      //*** add coding
    }
#if MODIFYCOST>1    
    // modify cost to hit zero exactly
    // so (dualIn_+modification)==theta_*alpha_
    double modification = theta_*alpha_-dualIn_;
    if ((specialOptions_&(2048+4096))!=0) {
      if ((specialOptions_&16384)!=0) {
        // in fast dual
        if (fabs(modification)<1.0e-7)
          modification=0.0;
      } else if ((specialOptions_&2048)!=0) {
        if (fabs(modification)<1.0e-10)
          modification=0.0;
      } else {
        if (fabs(modification)<1.0e-12)
          modification=0.0;
      }
    }
    dualIn_ += modification;
    dj_[sequenceIn_]=dualIn_;
    cost_[sequenceIn_] += modification;
    if (modification)
      numberChanged_ ++; // Say changed costs
    //int costOffset = numberRows_+numberColumns_;
    //cost_[sequenceIn_+costOffset] += modification; // save change
    //assert (fabs(modification)<1.0e-6);
#ifdef CLP_DEBUG
    if ((handler_->logLevel()&32)&&fabs(modification)>1.0e-15)
      printf("exact %d new cost %g, change %g\n",sequenceIn_,
             cost_[sequenceIn_],modification);
#endif
#endif
    
    if (alpha_<0.0) {
      // as if from upper bound
      directionIn_=-1;
      upperIn_=valueIn_;
    } else {
      // as if from lower bound
      directionIn_=1;
      lowerIn_=valueIn_;
    }
  }
  //if (thisIncrease) 
  //dualTolerance_+= 1.0e-6*dblParam_[ClpDualTolerance];

  // clear arrays

  for (i=0;i<2;i++) {
    CoinZeroN(array[i],marker[i][0]);
    CoinZeroN(array[i]+marker[i][1],numberColumns_-marker[i][1]);
  }
  return bestPossible;
}
#ifdef CLP_ALL_ONE_FILE
#undef MAXTRY
#endif
/* Checks if tentative optimal actually means unbounded
   Returns -3 if not, 2 if is unbounded */
int 
ClpSimplexDual::checkUnbounded(CoinIndexedVector * ray,
                                   CoinIndexedVector * spare,
                                   double changeCost)
{
  int status=2; // say unbounded
  factorization_->updateColumn(spare,ray);
  // get reduced cost
  int i;
  int number=ray->getNumElements();
  int * index = ray->getIndices();
  double * array = ray->denseVector();
  for (i=0;i<number;i++) {
    int iRow=index[i];
    int iPivot=pivotVariable_[iRow];
    changeCost -= cost(iPivot)*array[iRow];
  }
  double way;
  if (changeCost>0.0) {
    //try going down
    way=1.0;
  } else if (changeCost<0.0) {
    //try going up
    way=-1.0;
  } else {
#ifdef CLP_DEBUG
    printf("can't decide on up or down\n");
#endif
    way=0.0;
    status=-3;
  }
  double movement=1.0e10*way; // some largish number
  double zeroTolerance = 1.0e-14*dualBound_;
  for (i=0;i<number;i++) {
    int iRow=index[i];
    int iPivot=pivotVariable_[iRow];
    double arrayValue = array[iRow];
    if (fabs(arrayValue)<zeroTolerance)
      arrayValue=0.0;
    double newValue=solution(iPivot)+movement*arrayValue;
    if (newValue>upper(iPivot)+primalTolerance_||
        newValue<lower(iPivot)-primalTolerance_)
      status=-3; // not unbounded
  }
  if (status==2) {
    // create ray
    delete [] ray_;
    ray_ = new double [numberColumns_];
    CoinZeroN(ray_,numberColumns_);
    for (i=0;i<number;i++) {
      int iRow=index[i];
      int iPivot=pivotVariable_[iRow];
      double arrayValue = array[iRow];
      if (iPivot<numberColumns_&&fabs(arrayValue)>=zeroTolerance)
        ray_[iPivot] = way* array[iRow];
    }
  }
  ray->clear();
  return status;
}
/* Checks if finished.  Updates status */
void 
ClpSimplexDual::statusOfProblemInDual(int & lastCleaned,int type,
                                      double * givenDuals, ClpDataSave & saveData,
                                      int ifValuesPass)
{
  // If lots of iterations then adjust costs if large ones
  if (numberIterations_>4*(numberRows_+numberColumns_)&&objectiveScale_==1.0) {
    double largest=0.0;
    for (int i=0;i<numberRows_;i++) {
      int iColumn = pivotVariable_[i];
      largest = CoinMax(largest,fabs(cost_[iColumn]));
    }
    if (largest>1.0e6) {
      objectiveScale_ = 1.0e6/largest;
      for (int i=0;i<numberRows_+numberColumns_;i++)
        cost_[i] *= objectiveScale_;
    }
  }
  bool normalType=true;
  int numberPivots = factorization_->pivots();
  double realDualInfeasibilities=0.0;
  if (type==2) {
    // trouble - restore solution
    CoinMemcpyN(saveStatus_,numberColumns_+numberRows_,status_);
    CoinMemcpyN(savedSolution_+numberColumns_ ,
           numberRows_,rowActivityWork_);
    CoinMemcpyN(savedSolution_ ,
           numberColumns_,columnActivityWork_);
    // restore extra stuff
    int dummy;
    matrix_->generalExpanded(this,6,dummy);
    forceFactorization_=1; // a bit drastic but ..
    changeMade_++; // say something changed
  }
  int tentativeStatus = problemStatus_;
  double changeCost;
  bool unflagVariables = true;
  if (problemStatus_>-3||factorization_->pivots()) {
    // factorize
    // later on we will need to recover from singularities
    // also we could skip if first time
    // save dual weights
    dualRowPivot_->saveWeights(this,1);
    if (type) {
      // is factorization okay?
      if (internalFactorize(1)) {
        // no - restore previous basis
        unflagVariables = false;
        assert (type==1);
        changeMade_++; // say something changed
        // Keep any flagged variables
        int i;
        for (i=0;i<numberRows_+numberColumns_;i++) {
          if (flagged(i))
            saveStatus_[i] |= 64; //say flagged
        }
        CoinMemcpyN(saveStatus_,numberColumns_+numberRows_,status_);
        CoinMemcpyN(savedSolution_+numberColumns_ ,
               numberRows_,rowActivityWork_);
        CoinMemcpyN(savedSolution_ ,
               numberColumns_,columnActivityWork_);
        // restore extra stuff
        int dummy;
        matrix_->generalExpanded(this,6,dummy);
        // get correct bounds on all variables
        double dummyChangeCost=0.0;
        changeBounds(true,rowArray_[2],dummyChangeCost);
        // throw away change
        for (i=0;i<4;i++) 
          rowArray_[i]->clear();
        // need to reject something
        char x = isColumn(sequenceOut_) ? 'C' :'R';
        handler_->message(CLP_SIMPLEX_FLAG,messages_)
          <<x<<sequenceWithin(sequenceOut_)
          <<CoinMessageEol;
        setFlagged(sequenceOut_);
        progress_->clearBadTimes();
        
        // Go to safe 
        factorization_->pivotTolerance(0.99);
        forceFactorization_=1; // a bit drastic but ..
        type = 2;
        //assert (internalFactorize(1)==0);
        if (internalFactorize(1)) {
          CoinMemcpyN(saveStatus_,numberColumns_+numberRows_,status_);
          CoinMemcpyN(savedSolution_+numberColumns_ ,
                 numberRows_,rowActivityWork_);
          CoinMemcpyN(savedSolution_ ,
                 numberColumns_,columnActivityWork_);
          // restore extra stuff
          int dummy;
          matrix_->generalExpanded(this,6,dummy);
          // debug
          int returnCode = internalFactorize(1);
          while (returnCode) {
            // ouch 
            // switch off dense
            int saveDense = factorization_->denseThreshold();
            factorization_->setDenseThreshold(0);
            // Go to safe
            factorization_->pivotTolerance(0.99);
            // make sure will do safe factorization
            pivotVariable_[0]=-1;
            returnCode=internalFactorize(2);
            factorization_->setDenseThreshold(saveDense);
          }
        }
      }
    }
    if (problemStatus_!=-4||factorization_->pivots()>10)
      problemStatus_=-3;
  }
  // at this stage status is -3 or -4 if looks infeasible
  // get primal and dual solutions
  gutsOfSolution(givenDuals,NULL);
  // If bad accuracy treat as singular
  if ((largestPrimalError_>1.0e15||largestDualError_>1.0e15)&&numberIterations_) {
    // restore previous basis
    unflagVariables = false;
    changeMade_++; // say something changed
    // Keep any flagged variables
    int i;
    for (i=0;i<numberRows_+numberColumns_;i++) {
      if (flagged(i))
        saveStatus_[i] |= 64; //say flagged
    }
    CoinMemcpyN(saveStatus_,numberColumns_+numberRows_,status_);
    CoinMemcpyN(savedSolution_+numberColumns_ ,
           numberRows_,rowActivityWork_);
    CoinMemcpyN(savedSolution_ ,
           numberColumns_,columnActivityWork_);
    // restore extra stuff
    int dummy;
    matrix_->generalExpanded(this,6,dummy);
    // get correct bounds on all variables
    //double dummyChangeCost=0.0;
    //changeBounds(true,rowArray_[2],dummyChangeCost);
    // throw away change
    for (i=0;i<4;i++) 
      rowArray_[i]->clear();
    // need to reject something
    char x = isColumn(sequenceOut_) ? 'C' :'R';
    handler_->message(CLP_SIMPLEX_FLAG,messages_)
      <<x<<sequenceWithin(sequenceOut_)
      <<CoinMessageEol;
    setFlagged(sequenceOut_);
    progress_->clearBadTimes();
    
    // Go to safer 
    double newTolerance = CoinMin(1.1*factorization_->pivotTolerance(),0.99);
    factorization_->pivotTolerance(newTolerance);
    forceFactorization_=1; // a bit drastic but ..
    type = 2;
    //assert (internalFactorize(1)==0);
    if (internalFactorize(1)) {
      CoinMemcpyN(saveStatus_,numberColumns_+numberRows_,status_);
      CoinMemcpyN(savedSolution_+numberColumns_ ,
              numberRows_,rowActivityWork_);
      CoinMemcpyN(savedSolution_ ,
           numberColumns_,columnActivityWork_);
      // restore extra stuff
      int dummy;
      matrix_->generalExpanded(this,6,dummy);
      // debug
      int returnCode = internalFactorize(1);
      while (returnCode) {
        // ouch 
        // switch off dense
        int saveDense = factorization_->denseThreshold();
        factorization_->setDenseThreshold(0);
        // Go to safe
        factorization_->pivotTolerance(0.99);
        // make sure will do safe factorization
        pivotVariable_[0]=-1;
        returnCode=internalFactorize(2);
        factorization_->setDenseThreshold(saveDense);
      }
    }
    // get primal and dual solutions
    gutsOfSolution(givenDuals,NULL);
  } else if (largestPrimalError_<1.0e-7&&largestDualError_<1.0e-7) {
    // Can reduce tolerance
    double newTolerance = CoinMax(0.99*factorization_->pivotTolerance(),saveData.pivotTolerance_);
    factorization_->pivotTolerance(newTolerance);
  } 
  // Double check infeasibility if no action
  if (progress_->lastIterationNumber(0)==numberIterations_) {
    if (dualRowPivot_->looksOptimal()) {
      numberPrimalInfeasibilities_ = 0;
      sumPrimalInfeasibilities_ = 0.0;
    }
#if 1
  } else {
    double thisObj = objectiveValue_;
    double lastObj = progress_->lastObjective(0);
    if (lastObj>thisObj+1.0e-3*CoinMax(fabs(thisObj),fabs(lastObj))+1.0
        &&!ifValuesPass&&firstFree_<0) {
      int maxFactor = factorization_->maximumPivots();
      if (maxFactor>10&&numberPivots>1) {
        //printf("lastobj %g thisobj %g\n",lastObj,thisObj);
        //if (forceFactorization_<0)
        //forceFactorization_= maxFactor;
        //forceFactorization_ = CoinMax(1,(forceFactorization_>>1));
        forceFactorization_=1;
        //printf("Reducing factorization frequency - bad backwards\n");
        unflagVariables = false;
        changeMade_++; // say something changed
        CoinMemcpyN(saveStatus_,numberColumns_+numberRows_,status_);
        CoinMemcpyN(savedSolution_+numberColumns_ ,
                numberRows_,rowActivityWork_);
        CoinMemcpyN(savedSolution_ ,
                numberColumns_,columnActivityWork_);
        // restore extra stuff
        int dummy;
        matrix_->generalExpanded(this,6,dummy);
        // get correct bounds on all variables
        double dummyChangeCost=0.0;
        changeBounds(true,rowArray_[2],dummyChangeCost);
        // throw away change
        for (int i=0;i<4;i++) 
          rowArray_[i]->clear();
        if(factorization_->pivotTolerance()<0.2)
          factorization_->pivotTolerance(0.2);
        if (internalFactorize(1)) {
          CoinMemcpyN(saveStatus_,numberColumns_+numberRows_,status_);
          CoinMemcpyN(savedSolution_+numberColumns_ ,
                  numberRows_,rowActivityWork_);
          CoinMemcpyN(savedSolution_ ,
                  numberColumns_,columnActivityWork_);
          // restore extra stuff
          int dummy;
          matrix_->generalExpanded(this,6,dummy);
          // debug
          int returnCode = internalFactorize(1);
          while (returnCode) {
            // ouch 
            // switch off dense
            int saveDense = factorization_->denseThreshold();
            factorization_->setDenseThreshold(0);
            // Go to safe
            factorization_->pivotTolerance(0.99);
            // make sure will do safe factorization
            pivotVariable_[0]=-1;
            returnCode=internalFactorize(2);
            factorization_->setDenseThreshold(saveDense);
          }
        }
        type = 2; // so will restore weights
        // get primal and dual solutions
        gutsOfSolution(givenDuals,NULL);
      } 
    }
#endif
  }
  // Up tolerance if looks a bit odd
  if (numberIterations_>CoinMax(1000,numberRows_>>4)&&(specialOptions_&64)!=0) {
    if (sumPrimalInfeasibilities_&&sumPrimalInfeasibilities_<1.0e5) {
      int backIteration = progress_->lastIterationNumber(CLP_PROGRESS-1);
      if (backIteration>0&&numberIterations_-backIteration<9*CLP_PROGRESS) {
        if (factorization_->pivotTolerance()<0.9) {
          // up tolerance
          factorization_->pivotTolerance(CoinMin(factorization_->pivotTolerance()*1.05+0.02,0.91));
          //printf("tol now %g\n",factorization_->pivotTolerance());
          progress_->clearIterationNumbers();
        }
      }
    }
  }
  // Check if looping
  int loop;
  if (!givenDuals&&type!=2) 
    loop = progress_->looping();
  else
    loop=-1;
  int situationChanged=0;
  if (loop>=0) {
    problemStatus_ = loop; //exit if in loop
    if (!problemStatus_) {
      // declaring victory
      numberPrimalInfeasibilities_ = 0;
      sumPrimalInfeasibilities_ = 0.0;
    } else {
      problemStatus_ = 10; // instead - try other algorithm
    }
    return;
  } else if (loop<-1) {
    // something may have changed
    gutsOfSolution(NULL,NULL);
    situationChanged=1;
  }
  // really for free variables in
  if((progressFlag_&2)!=0) {
    situationChanged=2;
  }
  progressFlag_ = 0; //reset progress flag
  if (handler_->detail(CLP_SIMPLEX_STATUS,messages_)<100) {
    handler_->message(CLP_SIMPLEX_STATUS,messages_)
      <<numberIterations_<<objectiveValue();
    handler_->printing(sumPrimalInfeasibilities_>0.0)
      <<sumPrimalInfeasibilities_<<numberPrimalInfeasibilities_;
    handler_->printing(sumDualInfeasibilities_>0.0)
      <<sumDualInfeasibilities_<<numberDualInfeasibilities_;
    handler_->printing(numberDualInfeasibilitiesWithoutFree_
                       <numberDualInfeasibilities_)
                         <<numberDualInfeasibilitiesWithoutFree_;
    handler_->message()<<CoinMessageEol;
  }
  realDualInfeasibilities=sumDualInfeasibilities_;
  double saveTolerance =dualTolerance_;
  // If we need to carry on cleaning variables
  if (!numberPrimalInfeasibilities_&&(specialOptions_&1024)!=0&&CLEAN_FIXED) {
    for (int iRow=0;iRow<numberRows_;iRow++) {
      int iPivot=pivotVariable_[iRow];
      if (!flagged(iPivot)&&pivoted(iPivot)) {
        // carry on
        numberPrimalInfeasibilities_=-1;
        sumOfRelaxedPrimalInfeasibilities_ = 1.0;
        sumPrimalInfeasibilities_ = 1.0;
        break;
      }
    }
  }
  /* If we are primal feasible and any dual infeasibilities are on
     free variables then it is better to go to primal */
  if (!numberPrimalInfeasibilities_&&!numberDualInfeasibilitiesWithoutFree_&&
      numberDualInfeasibilities_)
    problemStatus_=10;
  // dual bound coming in
  //double saveDualBound = dualBound_;
  while (problemStatus_<=-3) {
    int cleanDuals=0;
    if (situationChanged!=0)
      cleanDuals=1;
    int numberChangedBounds=0;
    int doOriginalTolerance=0;
    if ( lastCleaned==numberIterations_)
      doOriginalTolerance=1;
    // check optimal
    // give code benefit of doubt
    if (sumOfRelaxedDualInfeasibilities_ == 0.0&&
        sumOfRelaxedPrimalInfeasibilities_ == 0.0) {
      // say optimal (with these bounds etc)
      numberDualInfeasibilities_ = 0;
      sumDualInfeasibilities_ = 0.0;
      numberPrimalInfeasibilities_ = 0;
      sumPrimalInfeasibilities_ = 0.0;
    }
    //if (dualFeasible()||problemStatus_==-4||(primalFeasible()&&!numberDualInfeasibilitiesWithoutFree_)) {
    if (dualFeasible()||problemStatus_==-4) {
      progress_->modifyObjective(objectiveValue_
                               -sumDualInfeasibilities_*dualBound_);
      if (primalFeasible()&&!givenDuals) {
        normalType=false;
        // may be optimal - or may be bounds are wrong
        handler_->message(CLP_DUAL_BOUNDS,messages_)
          <<dualBound_
          <<CoinMessageEol;
        // save solution in case unbounded
        CoinMemcpyN(columnActivityWork_,numberColumns_,
                          columnArray_[0]->denseVector());
        CoinMemcpyN(rowActivityWork_,numberRows_,
                          rowArray_[2]->denseVector());
        numberChangedBounds=changeBounds(false,rowArray_[3],changeCost);
        if (numberChangedBounds<=0&&!numberDualInfeasibilities_) {
          //looks optimal - do we need to reset tolerance
          if (perturbation_==101) {
            perturbation_=102; // stop any perturbations
            cleanDuals=1;
            // make sure fake bounds are back
            //computeObjectiveValue();
            changeBounds(true,NULL,changeCost);
            //computeObjectiveValue();
            createRim(4);
            // make sure duals are current
            computeDuals(givenDuals);
            checkDualSolution();
            //if (numberDualInfeasibilities_)
              numberChanged_=1; // force something to happen
            //else
            //computeObjectiveValue();
          }
          if (lastCleaned<numberIterations_&&numberTimesOptimal_<4&&
              (numberChanged_||(specialOptions_&4096)==0)) {
            doOriginalTolerance=2;
            numberTimesOptimal_++;
            changeMade_++; // say something changed
            if (numberTimesOptimal_==1) {
              dualTolerance_ = dblParam_[ClpDualTolerance];
              // better to have small tolerance even if slower
              factorization_->zeroTolerance(1.0e-15);
            } else {
              dualTolerance_ = dblParam_[ClpDualTolerance];
              dualTolerance_ *= pow(2.0,numberTimesOptimal_-1);
            }
            cleanDuals=2; // If nothing changed optimal else primal
          } else {
            problemStatus_=0; // optimal
            if (lastCleaned<numberIterations_&&numberChanged_) {
              handler_->message(CLP_SIMPLEX_GIVINGUP,messages_)
                <<CoinMessageEol;
            }
          }
        } else {
          cleanDuals=1;
          if (doOriginalTolerance==1) {
            // check unbounded
            // find a variable with bad dj
            int iSequence;
            int iChosen=-1;
            double largest = 100.0*primalTolerance_;
            for (iSequence=0;iSequence<numberRows_+numberColumns_;
                 iSequence++) {
              double djValue = dj_[iSequence];
              double originalLo = originalLower(iSequence);
              double originalUp = originalUpper(iSequence);
              if (fabs(djValue)>fabs(largest)) {
                if (getStatus(iSequence)!=basic) {
                  if (djValue>0&&originalLo<-1.0e20) {
                    if (djValue>fabs(largest)) {
                      largest=djValue;
                      iChosen=iSequence;
                    }
                  } else if (djValue<0&&originalUp>1.0e20) {
                    if (-djValue>fabs(largest)) {
                      largest=djValue;
                      iChosen=iSequence;
                    }
                  } 
                }
              }
            }
            if (iChosen>=0) {
              int iSave=sequenceIn_;
              sequenceIn_=iChosen;
              unpack(rowArray_[1]);
              sequenceIn_ = iSave;
              // if dual infeasibilities then must be free vector so add in dual
              if (numberDualInfeasibilities_) {
                if (fabs(changeCost)>1.0e-5)
                  printf("Odd free/unbounded combo\n");
                changeCost += cost_[iChosen];
              }
              problemStatus_ = checkUnbounded(rowArray_[1],rowArray_[0],
                                              changeCost);
              rowArray_[1]->clear();
            } else {
              problemStatus_=-3;
            }
            if (problemStatus_==2&&perturbation_==101) {
              perturbation_=102; // stop any perturbations
              cleanDuals=1;
              createRim(4);
              problemStatus_=-1;
            }
            if (problemStatus_==2) {
              // it is unbounded - restore solution
              // but first add in changes to non-basic
              int iColumn;
              double * original = columnArray_[0]->denseVector();
              for (iColumn=0;iColumn<numberColumns_;iColumn++) {
                if(getColumnStatus(iColumn)!= basic)
                  ray_[iColumn] += 
                    columnActivityWork_[iColumn]-original[iColumn];
                columnActivityWork_[iColumn] = original[iColumn];
              }
              CoinMemcpyN(rowArray_[2]->denseVector(),numberRows_,
                                rowActivityWork_);
            }
          } else {
            doOriginalTolerance=2;
            rowArray_[0]->clear();
          }
        }
        CoinZeroN(columnArray_[0]->denseVector(),numberColumns_);
        CoinZeroN(rowArray_[2]->denseVector(),numberRows_);
      } 
      if (problemStatus_==-4||problemStatus_==-5) {
        // may be infeasible - or may be bounds are wrong
        numberChangedBounds=changeBounds(false,NULL,changeCost);
        /* Should this be here as makes no difference to being feasible.
           But seems to make a difference to run times. */
        if (perturbation_==101&&0) {
          perturbation_=102; // stop any perturbations
          cleanDuals=1;
          numberChangedBounds=1;
          // make sure fake bounds are back
          changeBounds(true,NULL,changeCost);
          createRim(4);
        }
        if (numberChangedBounds<=0||dualBound_>1.0e20||
            (largestPrimalError_>1.0&&dualBound_>1.0e17)) {
          problemStatus_=1; // infeasible
          if (perturbation_==101) {
            perturbation_=102; // stop any perturbations
            //cleanDuals=1;
            //numberChangedBounds=1;
            //createRim(4);
          }
        } else {
          normalType=false;
          problemStatus_=-1; //iterate
          cleanDuals=1;
          if (numberChangedBounds<=0)
            doOriginalTolerance=2;
          // and delete ray which has been created
          delete [] ray_;
          ray_ = NULL;
        }

      }
    } else {
      cleanDuals=1;
    }
    if (problemStatus_<0) {
      if (doOriginalTolerance==2) {
        // put back original tolerance
        lastCleaned=numberIterations_;
        numberChanged_ =0; // Number of variables with changed costs
        handler_->message(CLP_DUAL_ORIGINAL,messages_)
          <<CoinMessageEol;
        perturbation_=102; // stop any perturbations
#if 0
        double * xcost = new double[numberRows_+numberColumns_];
        double * xlower = new double[numberRows_+numberColumns_];
        double * xupper = new double[numberRows_+numberColumns_];
        double * xdj = new double[numberRows_+numberColumns_];
        double * xsolution = new double[numberRows_+numberColumns_];
        memcpy(xcost,cost_,(numberRows_+numberColumns_)*sizeof(double));
        memcpy(xlower,lower_,(numberRows_+numberColumns_)*sizeof(double));
        memcpy(xupper,upper_,(numberRows_+numberColumns_)*sizeof(double));
        memcpy(xdj,dj_,(numberRows_+numberColumns_)*sizeof(double));
        memcpy(xsolution,solution_,(numberRows_+numberColumns_)*sizeof(double));
#endif
        createRim(4);
        // make sure duals are current
        computeDuals(givenDuals);
        checkDualSolution();
#if 0
        int i;
        for (i=0;i<numberRows_+numberColumns_;i++) {
          if (cost_[i]!=xcost[i])
            printf("** %d old cost %g new %g sol %g\n",
                   i,xcost[i],cost_[i],solution_[i]);
          if (lower_[i]!=xlower[i])
            printf("** %d old lower %g new %g sol %g\n",
                   i,xlower[i],lower_[i],solution_[i]);
          if (upper_[i]!=xupper[i])
            printf("** %d old upper %g new %g sol %g\n",
                   i,xupper[i],upper_[i],solution_[i]);
          if (dj_[i]!=xdj[i])
            printf("** %d old dj %g new %g sol %g\n",
                   i,xdj[i],dj_[i],solution_[i]);
          if (solution_[i]!=xsolution[i])
            printf("** %d old solution %g new %g sol %g\n",
                   i,xsolution[i],solution_[i],solution_[i]);
        }
        //delete [] xcost;
        //delete [] xupper;
        //delete [] xlower;
        //delete [] xdj;
        //delete [] xsolution;
#endif
        // put back bounds as they were if was optimal
        if (doOriginalTolerance==2&&cleanDuals!=2) {
          changeMade_++; // say something changed
          /* We may have already changed some bounds in this function
             so save numberFake_ and add in.

             Worst that can happen is that we waste a bit of time  - but it must be finite.
          */
          int saveNumberFake = numberFake_;
          changeBounds(true,NULL,changeCost);
          numberFake_ += saveNumberFake;
          cleanDuals=2;
          //cleanDuals=1;
        }
#if 0
        //int i;
        for (i=0;i<numberRows_+numberColumns_;i++) {
          if (cost_[i]!=xcost[i])
            printf("** %d old cost %g new %g sol %g\n",
                   i,xcost[i],cost_[i],solution_[i]);
          if (lower_[i]!=xlower[i])
            printf("** %d old lower %g new %g sol %g\n",
                   i,xlower[i],lower_[i],solution_[i]);
          if (upper_[i]!=xupper[i])
            printf("** %d old upper %g new %g sol %g\n",
                   i,xupper[i],upper_[i],solution_[i]);
          if (dj_[i]!=xdj[i])
            printf("** %d old dj %g new %g sol %g\n",
                   i,xdj[i],dj_[i],solution_[i]);
          if (solution_[i]!=xsolution[i])
            printf("** %d old solution %g new %g sol %g\n",
                   i,xsolution[i],solution_[i],solution_[i]);
        }
        delete [] xcost;
        delete [] xupper;
        delete [] xlower;
        delete [] xdj;
        delete [] xsolution;
#endif
      }
      if (cleanDuals==1||(cleanDuals==2&&!numberDualInfeasibilities_)) {
        // make sure dual feasible
        // look at all rows and columns
        rowArray_[0]->clear();
        columnArray_[0]->clear();
        double objectiveChange=0.0;
#if 0
        double * xcost = new double[numberRows_+numberColumns_];
        double * xlower = new double[numberRows_+numberColumns_];
        double * xupper = new double[numberRows_+numberColumns_];
        double * xdj = new double[numberRows_+numberColumns_];
        double * xsolution = new double[numberRows_+numberColumns_];
        memcpy(xcost,cost_,(numberRows_+numberColumns_)*sizeof(double));
        memcpy(xlower,lower_,(numberRows_+numberColumns_)*sizeof(double));
        memcpy(xupper,upper_,(numberRows_+numberColumns_)*sizeof(double));
        memcpy(xdj,dj_,(numberRows_+numberColumns_)*sizeof(double));
        memcpy(xsolution,solution_,(numberRows_+numberColumns_)*sizeof(double));
#endif
        if (givenDuals)
          dualTolerance_=1.0e50;
        updateDualsInDual(rowArray_[0],columnArray_[0],rowArray_[1],
          0.0,objectiveChange,true);
        dualTolerance_=saveTolerance;
#if 0
        int i;
        for (i=0;i<numberRows_+numberColumns_;i++) {
          if (cost_[i]!=xcost[i])
            printf("** %d old cost %g new %g sol %g\n",
                   i,xcost[i],cost_[i],solution_[i]);
          if (lower_[i]!=xlower[i])
            printf("** %d old lower %g new %g sol %g\n",
                   i,xlower[i],lower_[i],solution_[i]);
          if (upper_[i]!=xupper[i])
            printf("** %d old upper %g new %g sol %g\n",
                   i,xupper[i],upper_[i],solution_[i]);
          if (dj_[i]!=xdj[i])
            printf("** %d old dj %g new %g sol %g\n",
                   i,xdj[i],dj_[i],solution_[i]);
          if (solution_[i]!=xsolution[i])
            printf("** %d old solution %g new %g sol %g\n",
                   i,xsolution[i],solution_[i],solution_[i]);
        }
        delete [] xcost;
        delete [] xupper;
        delete [] xlower;
        delete [] xdj;
        delete [] xsolution;
#endif
        // for now - recompute all
        gutsOfSolution(NULL,NULL);
        if (givenDuals)
          dualTolerance_=1.0e50;
        updateDualsInDual(rowArray_[0],columnArray_[0],rowArray_[1],
          0.0,objectiveChange,true);
        dualTolerance_=saveTolerance;
        //assert(numberDualInfeasibilitiesWithoutFree_==0);

        if (numberDualInfeasibilities_||situationChanged==2) 
          problemStatus_=-1; // carry on as normal
        situationChanged=0;
      } else {
        // iterate
        if (cleanDuals!=2) 
          problemStatus_=-1;
        else 
          problemStatus_ = 10; // try primal
      }
    }
  }
  if (type==0||type==1) {
    if (!type) {
      // create save arrays
      delete [] saveStatus_;
      delete [] savedSolution_;
      saveStatus_ = new unsigned char [numberRows_+numberColumns_];
      savedSolution_ = new double [numberRows_+numberColumns_];
    }
    // save arrays
    CoinMemcpyN(status_,numberColumns_+numberRows_,saveStatus_);
    CoinMemcpyN(rowActivityWork_,
           numberRows_,savedSolution_+numberColumns_);
    CoinMemcpyN(columnActivityWork_,numberColumns_,savedSolution_);
    // save extra stuff
    int dummy;
    matrix_->generalExpanded(this,5,dummy);
  }

  // restore weights (if saved) - also recompute infeasibility list
  if (tentativeStatus>-3) 
    dualRowPivot_->saveWeights(this,(type <2) ? 2 : 4);
  else
    dualRowPivot_->saveWeights(this,3);
  // unflag all variables (we may want to wait a bit?)
  if ((tentativeStatus!=-2&&tentativeStatus!=-1)&&unflagVariables) {
    int iRow;
    int numberFlagged=0;
    for (iRow=0;iRow<numberRows_;iRow++) {
      int iPivot=pivotVariable_[iRow];
      if (flagged(iPivot)) {
        numberFlagged++;
        clearFlagged(iPivot);
      }
    }
#if 0
    if (numberFlagged) {
      printf("unflagging %d variables - status %d ninf %d nopt %d\n",numberFlagged,tentativeStatus,
             numberPrimalInfeasibilities_,
             numberTimesOptimal_);
    }
#endif
    unflagVariables = numberFlagged>0;
    if (numberFlagged&&!numberPivots) {
      /* looks like trouble as we have not done any iterations.
         Try changing pivot tolerance then give it a few goes and give up */
      if (factorization_->pivotTolerance()<0.9) {
        factorization_->pivotTolerance(0.99);
      } else if (numberTimesOptimal_<10) {
        numberTimesOptimal_++;
      } else {
        unflagVariables=false;
        changeMade_=false;
        secondaryStatus_ = 1; // and say probably infeasible
      }
    }
  }
  // see if cutoff reached
  double limit = 0.0;
  getDblParam(ClpDualObjectiveLimit, limit);
  if(fabs(limit)<1.0e30&&objectiveValue()*optimizationDirection_>
           limit&&
           !numberAtFakeBound()&&!numberDualInfeasibilities_) {
    //printf("lim %g obj %g %g\n",limit,objectiveValue_,objectiveValue());
    // Even if not perturbed internal costs may have changed
    if (true||perturbation_==101) {
      // be careful
      if (numberIterations_) {
        computeObjectiveValue(true); // value without perturbation
        if(objectiveValue()*optimizationDirection_>limit) {
          problemStatus_=1;
          secondaryStatus_ = 1; // and say was on cutoff
        }
      }
    } else {
      problemStatus_=1;
      secondaryStatus_ = 1; // and say was on cutoff
    }
  }
  // If we are in trouble and in branch and bound give up
  if ((specialOptions_&1024)!=0) {
    int looksBad=0;
    if (largestPrimalError_*largestDualError_>1.0e2) {
      looksBad=1;
    } else if (largestPrimalError_>1.0e-2
        &&objectiveValue_>CoinMin(1.0e15,1.0e3*limit)) {
      looksBad=2;
    }
    if (looksBad) {
      if (factorization_->pivotTolerance()<0.9) {
        // up tolerance
        factorization_->pivotTolerance(CoinMin(factorization_->pivotTolerance()*1.05+0.02,0.91));
      } else if (numberIterations_>10000) {
        if (handler_->logLevel()>0)
          printf("bad dual - saying infeasible %d\n",looksBad);
        problemStatus_=1;
        secondaryStatus_ = 1; // and say was on cutoff
      } else if (largestPrimalError_>1.0e5) {
        allSlackBasis();
        problemStatus_=10;
        //if (handler_->logLevel()>0)
          printf("bad dual - going to primal %d %g\n",looksBad,largestPrimalError_);
      }
    }
  }
  if (problemStatus_<0&&!changeMade_) {
    problemStatus_=4; // unknown
  }
  lastGoodIteration_ = numberIterations_;
  if (problemStatus_<0) {
    sumDualInfeasibilities_=realDualInfeasibilities; // back to say be careful
    if (sumDualInfeasibilities_)
      numberDualInfeasibilities_=1;
  }
#if 1
  double thisObj = progress_->lastObjective(0);
  double lastObj = progress_->lastObjective(1);
  if (lastObj>thisObj+1.0e-4*CoinMax(fabs(thisObj),fabs(lastObj))+1.0e-4
      &&givenDuals==NULL&&firstFree_<0) {
    int maxFactor = factorization_->maximumPivots();
    if (maxFactor>10) {
      if (forceFactorization_<0)
        forceFactorization_= maxFactor;
      forceFactorization_ = CoinMax(1,(forceFactorization_>>1));
      //printf("Reducing factorization frequency\n");
    } 
  }
#endif
}
/* While updateDualsInDual sees what effect is of flip
   this does actual flipping.
   If change >0.0 then value in array >0.0 => from lower to upper
*/
void 
ClpSimplexDual::flipBounds(CoinIndexedVector * rowArray,
                  CoinIndexedVector * columnArray,
                  double change)
{
  int number;
  int * which;
  
  int iSection;

  for (iSection=0;iSection<2;iSection++) {
    int i;
    double * solution = solutionRegion(iSection);
    double * lower = lowerRegion(iSection);
    double * upper = upperRegion(iSection);
    int addSequence;
    if (!iSection) {
      number = rowArray->getNumElements();
      which = rowArray->getIndices();
      addSequence = numberColumns_;
    } else {
      number = columnArray->getNumElements();
      which = columnArray->getIndices();
      addSequence = 0;
    }
    
    for (i=0;i<number;i++) {
      int iSequence = which[i];
      Status status = getStatus(iSequence+addSequence);

      switch(status) {

      case basic:
      case isFree:
      case superBasic:
      case ClpSimplex::isFixed:
        break;
      case atUpperBound:
        // to lower bound
        setStatus(iSequence+addSequence,atLowerBound);
        solution[iSequence] = lower[iSequence];
        break;
      case atLowerBound:
        // to upper bound 
        setStatus(iSequence+addSequence,atUpperBound);
        solution[iSequence] = upper[iSequence];
        break;
      }
    }
  }
  rowArray->setNumElements(0);
  columnArray->setNumElements(0);
}
// Restores bound to original bound
void 
ClpSimplexDual::originalBound( int iSequence)
{
  if (getFakeBound(iSequence)!=noFake)
    numberFake_--;;
  if (auxiliaryModel_) {
    // just copy back
    lower_[iSequence]=auxiliaryModel_->lowerRegion()[iSequence+numberRows_+numberColumns_];
    upper_[iSequence]=auxiliaryModel_->upperRegion()[iSequence+numberRows_+numberColumns_];
    return;
  }
  if (iSequence>=numberColumns_) {
    // rows
    int iRow = iSequence-numberColumns_;
    rowLowerWork_[iRow]=rowLower_[iRow];
    rowUpperWork_[iRow]=rowUpper_[iRow];
    if (rowScale_) {
      if (rowLowerWork_[iRow]>-1.0e50)
        rowLowerWork_[iRow] *= rowScale_[iRow]*rhsScale_;
      if (rowUpperWork_[iRow]<1.0e50)
        rowUpperWork_[iRow] *= rowScale_[iRow]*rhsScale_;
    } else if (rhsScale_!=1.0) {
      if (rowLowerWork_[iRow]>-1.0e50)
        rowLowerWork_[iRow] *= rhsScale_;
      if (rowUpperWork_[iRow]<1.0e50)
        rowUpperWork_[iRow] *= rhsScale_;
    }
  } else {
    // columns
    columnLowerWork_[iSequence]=columnLower_[iSequence];
    columnUpperWork_[iSequence]=columnUpper_[iSequence];
    if (rowScale_) {
      double multiplier = 1.0/columnScale_[iSequence];
      if (columnLowerWork_[iSequence]>-1.0e50)
        columnLowerWork_[iSequence] *= multiplier*rhsScale_;
      if (columnUpperWork_[iSequence]<1.0e50)
        columnUpperWork_[iSequence] *= multiplier*rhsScale_;
    } else if (rhsScale_!=1.0) {
      if (columnLowerWork_[iSequence]>-1.0e50)
        columnLowerWork_[iSequence] *= rhsScale_;
      if (columnUpperWork_[iSequence]<1.0e50)
        columnUpperWork_[iSequence] *= rhsScale_;
    }
  }
  setFakeBound(iSequence,noFake);
}
/* As changeBounds but just changes new bounds for a single variable.
   Returns true if change */
bool 
ClpSimplexDual::changeBound( int iSequence)
{
  // old values 
  double oldLower=lower_[iSequence];
  double oldUpper=upper_[iSequence];
  double value=solution_[iSequence];
  bool modified=false;
  originalBound(iSequence);
  // original values
  double lowerValue=lower_[iSequence];
  double upperValue=upper_[iSequence];
  // back to altered values
  lower_[iSequence] = oldLower;
  upper_[iSequence] = oldUpper;
  if (getFakeBound(iSequence)!=noFake)
    numberFake_--;;
  if (value==oldLower) {
    if (upperValue > oldLower + dualBound_) {
      upper_[iSequence]=oldLower+dualBound_;
      setFakeBound(iSequence,upperFake);
      modified=true;
      numberFake_++;
    }
  } else if (value==oldUpper) {
    if (lowerValue < oldUpper - dualBound_) {
      lower_[iSequence]=oldUpper-dualBound_;
      setFakeBound(iSequence,lowerFake);
      modified=true;
      numberFake_++;
    }
  } else {
    assert(value==oldLower||value==oldUpper);
  }
  return modified;
}
// Perturbs problem
void 
ClpSimplexDual::perturb()
{
  if (perturbation_>100)
    return; //perturbed already
  if (perturbation_==100)
    perturbation_=50; // treat as normal
  int savePerturbation = perturbation_;
  bool modifyRowCosts=false;
  // dual perturbation
  double perturbation=1.0e-20;
  // maximum fraction of cost to perturb
  double maximumFraction = 1.0e-5;
  double constantPerturbation = 100.0*dualTolerance_;
  int maxLength=0;
  int minLength=numberRows_;
  double averageCost = 0.0;
  // look at element range
  double smallestNegative;
  double largestNegative;
  double smallestPositive;
  double largestPositive;
  matrix_->rangeOfElements(smallestNegative, largestNegative,
                           smallestPositive, largestPositive);
  smallestPositive = CoinMin(fabs(smallestNegative),smallestPositive);
  largestPositive = CoinMax(fabs(largestNegative),largestPositive);
  double elementRatio = largestPositive/smallestPositive;
  int numberNonZero=0;
  if (!numberIterations_&&perturbation_==50) {
    // See if we need to perturb
    double * sort = new double[numberColumns_];
    // Use objective BEFORE scaling
    const double * obj = objective();
    int i;
    for (i=0;i<numberColumns_;i++) {
      double value = fabs(obj[i]);
      sort[i]=value;
      averageCost += value;
      if (value)
        numberNonZero++;
    }
    if (numberNonZero)
      averageCost /= (double) numberNonZero;
    else
      averageCost = 1.0;
    std::sort(sort,sort+numberColumns_);
    int number=1;
    double last = sort[0];
    for (i=1;i<numberColumns_;i++) {
      if (last!=sort[i])
        number++;
      last=sort[i];
    }
    delete [] sort;
#if 0
    printf("nnz %d percent %d",number,(number*100)/numberColumns_);
    if (number*4>numberColumns_)
      printf(" - Would not perturb\n");
    else
      printf(" - Would perturb\n");
    //exit(0);
#endif
    //printf("ratio number diff costs %g, element ratio %g\n",((double)number)/((double) numberColumns_),
    //                                                                elementRatio);
    //number=0;
    if (number*4>numberColumns_||elementRatio>1.0e12) {
      perturbation_=100;
      return; // good enough
    }
  }
  int iColumn;
  for (iColumn=0;iColumn<numberColumns_;iColumn++) {
    if (columnLowerWork_[iColumn]<columnUpperWork_[iColumn]) {
      int length = matrix_->getVectorLength(iColumn);
      if (length>2) {
        maxLength = CoinMax(maxLength,length);
        minLength = CoinMin(minLength,length);
      }
    }
  }
  // If > 70 then do rows
  if (perturbation_>=70) {
    modifyRowCosts=true;
    perturbation_ -= 20;
    printf("Row costs modified, ");
  }
  bool uniformChange=false;
  if (perturbation_>50) {
    // Experiment
    // maximumFraction could be 1.0e-10 to 1.0 
    double m[]={1.0e-10,1.0e-9,1.0e-8,1.0e-7,1.0e-6,1.0e-5,1.0e-4,1.0e-3,1.0e-2,1.0e-1,1.0};
    maximumFraction = m[CoinMin(perturbation_-51,10)];
  }
  int iRow;
  double smallestNonZero=1.0e100;
  numberNonZero=0;
  if (perturbation_>=50) {
    perturbation = 1.0e-8;
    bool allSame=true;
    double lastValue=0.0;
    for (iRow=0;iRow<numberRows_;iRow++) {
      double lo = rowLowerWork_[iRow];
      double up = rowUpperWork_[iRow];
      if (lo<up) {
        double value = fabs(rowObjectiveWork_[iRow]);
        perturbation = CoinMax(perturbation,value);
        if (value) {
          modifyRowCosts=true;
          smallestNonZero = CoinMin(smallestNonZero,value);
        }
      } 
      if (lo&&lo>-1.0e10) {
        numberNonZero++;
        lo=fabs(lo);
        if (!lastValue) 
          lastValue=lo;
        else if (fabs(lo-lastValue)>1.0e-7)
          allSame=false;
      }
      if (up&&up<1.0e10) {
        numberNonZero++;
        up=fabs(up);
        if (!lastValue) 
          lastValue=up;
        else if (fabs(up-lastValue)>1.0e-7)
          allSame=false;
      }
    }
    double lastValue2=0.0;
    for (iColumn=0;iColumn<numberColumns_;iColumn++) { 
      double lo = columnLowerWork_[iColumn];
      double up = columnUpperWork_[iColumn];
      if (lo<up) {
        double value = 
          fabs(objectiveWork_[iColumn]);
        perturbation = CoinMax(perturbation,value);
        if (value) {
          smallestNonZero = CoinMin(smallestNonZero,value);
        }
      }
      if (lo&&lo>-1.0e10) {
        //numberNonZero++;
        lo=fabs(lo);
        if (!lastValue2) 
          lastValue2=lo;
        else if (fabs(lo-lastValue2)>1.0e-7)
          allSame=false;
      }
      if (up&&up<1.0e10) {
        //numberNonZero++;
        up=fabs(up);
        if (!lastValue2) 
          lastValue2=up;
        else if (fabs(up-lastValue2)>1.0e-7)
          allSame=false;
      }
    }
    if (allSame) {
      // Check elements
      double smallestNegative;
      double largestNegative;
      double smallestPositive;
      double largestPositive;
      matrix_->rangeOfElements(smallestNegative,largestNegative,
                               smallestPositive,largestPositive);
      if (smallestNegative==largestNegative&&
          smallestPositive==largestPositive) {
        // Really hit perturbation
        double adjust = CoinMin(100.0*maximumFraction,1.0e-3*CoinMax(lastValue,lastValue2));
        maximumFraction = CoinMax(adjust,maximumFraction);
      }
    }
    perturbation = CoinMin(perturbation,smallestNonZero/maximumFraction);
  } else {
    // user is in charge
    maximumFraction = 1.0e-1;
    // but some experiments
    if (perturbation_<=-900) {
      modifyRowCosts=true;
      perturbation_ += 1000;
      printf("Row costs modified, ");
    }
    if (perturbation_<=-10) {
      perturbation_ += 10; 
      maximumFraction = 1.0;
      if ((-perturbation_)%100>=10) {
        uniformChange=true;
        perturbation_+=20;
      }
      while (perturbation_<-10) {
        perturbation_ += 100;
        maximumFraction *= 1.0e-1;
      }
    }
    perturbation = pow(10.0,perturbation_);
  }
  double largestZero=0.0;
  double largest=0.0;
  double largestPerCent=0.0;
  // modify costs
  bool printOut=(handler_->logLevel()==63);
  printOut=false;
  if (modifyRowCosts) {
    for (iRow=0;iRow<numberRows_;iRow++) {
      if (rowLowerWork_[iRow]<rowUpperWork_[iRow]) {
        double value = perturbation;
        double currentValue = rowObjectiveWork_[iRow];
        value = CoinMin(value,maximumFraction*(fabs(currentValue)+1.0e-1*perturbation+1.0e-3));
        if (rowLowerWork_[iRow]>-largeValue_) {
          if (fabs(rowLowerWork_[iRow])<fabs(rowUpperWork_[iRow])) 
            value *= CoinDrand48();
          else
            value *= -CoinDrand48();
        } else if (rowUpperWork_[iRow]<largeValue_) {
          value *= -CoinDrand48();
        } else {
          value=0.0;
        }
        if (currentValue) {
          largest = CoinMax(largest,fabs(value));
          if (fabs(value)>fabs(currentValue)*largestPerCent)
            largestPerCent=fabs(value/currentValue);
        } else {
          largestZero=CoinMax(largestZero,fabs(value));
        }
        if (printOut)
          printf("row %d cost %g change %g\n",iRow,rowObjectiveWork_[iRow],value);
        rowObjectiveWork_[iRow] += value;
      }
    }
  }
  // more its but faster double weight[]={1.0e-4,1.0e-2,1.0e-1,1.0,2.0,10.0,100.0,200.0,400.0,600.0,1000.0};
  // good its double weight[]={1.0e-4,1.0e-2,5.0e-1,1.0,2.0,5.0,10.0,20.0,30.0,40.0,100.0};
  double weight[]={1.0e-4,1.0e-2,5.0e-1,1.0,2.0,5.0,10.0,20.0,30.0,40.0,100.0};
  //double weight[]={1.0e-4,1.0e-2,5.0e-1,1.0,20.0,50.0,100.0,120.0,130.0,140.0,200.0};
  double extraWeight=10.0;
  // Scale back if wanted
  double weight2[]={1.0e-4,1.0e-2,5.0e-1,1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0};
  if (constantPerturbation<99.0*dualTolerance_) {
    perturbation *= 0.1;
    extraWeight=0.5;
    memcpy(weight,weight2,sizeof(weight2));
  }
  // adjust weights if all columns long
  double factor=1.0;
  if (maxLength) {
    factor = 3.0/(double) minLength;
  }
  // Make variables with more elements more expensive
  const double m1 = 0.5;
  double smallestAllowed = CoinMin(1.0e-2*dualTolerance_,maximumFraction);
  //double largestAllowed = CoinMax(1.0e3*dualTolerance_,maximumFraction*10.0*averageCost);
  double largestAllowed = CoinMax(1.0e3*dualTolerance_,maximumFraction*averageCost);
  for (iColumn=0;iColumn<numberColumns_;iColumn++) {
    if (columnLowerWork_[iColumn]<columnUpperWork_[iColumn]&&getStatus(iColumn)!=basic) {
      double value = perturbation;
      double currentValue = objectiveWork_[iColumn];
      value = CoinMin(value,constantPerturbation+maximumFraction*(fabs(currentValue)+1.0e-1*perturbation+1.0e-8));
      //value = CoinMin(value,constantPerturbation;+maximumFraction*fabs(currentValue));
      double value2 = constantPerturbation+1.0e-1*smallestNonZero;
      if (uniformChange) {
        value = maximumFraction;
        value2=maximumFraction;
      }
      if (columnLowerWork_[iColumn]>-largeValue_) {
        if (fabs(columnLowerWork_[iColumn])<
            fabs(columnUpperWork_[iColumn])) {
          value *= (1.0-m1 +m1*CoinDrand48());
          value2 *= (1.0-m1 +m1*CoinDrand48());
        } else {
          value *= -(1.0-m1+m1*CoinDrand48());
          value2 *= -(1.0-m1+m1*CoinDrand48());
        }
      } else if (columnUpperWork_[iColumn]<largeValue_) {
        value *= -(1.0-m1+m1*CoinDrand48());
        value2 *= -(1.0-m1+m1*CoinDrand48());
      } else {
        value=0.0;
      }
      if (value) {
        int length = matrix_->getVectorLength(iColumn);
        if (length>3) {
          length = (int) ((double) length * factor);
          length = CoinMax(3,length);
        }
        double multiplier;
#if 1
        if (length<10)
          multiplier=weight[length];
        else
          multiplier = weight[10];
#else
        if (length<10)
          multiplier=weight[length];
        else
          multiplier = weight[10]+extraWeight*(length-10);
        multiplier *= 0.5;
#endif
        value *= multiplier;
        value = CoinMin(value,value2);
        if (savePerturbation<50||savePerturbation>60) {
          if (fabs(value)<=dualTolerance_)
            value=0.0;
        } else if (value) {
          // get in range 
          if (fabs(value)<=smallestAllowed) {
            value *= 10.0;
            while (fabs(value)<=smallestAllowed) 
              value *= 10.0;
          } else if (fabs(value)>largestAllowed) {
            value *= 0.1;
            while (fabs(value)>largestAllowed) 
              value *= 0.1;
          }
        }
        if (currentValue) {
          largest = CoinMax(largest,fabs(value));
          if (fabs(value)>fabs(currentValue)*largestPerCent)
            largestPerCent=fabs(value/currentValue);
        } else {
          largestZero=CoinMax(largestZero,fabs(value));
        }
        // but negative if at ub
        if (getStatus(iColumn)==atUpperBound)
          value = -value;
        if (printOut)
          printf("col %d cost %g change %g\n",iColumn,objectiveWork_[iColumn],value);
        objectiveWork_[iColumn] += value;
      }
    }
  }
  handler_->message(CLP_SIMPLEX_PERTURB,messages_)
    <<100.0*maximumFraction<<perturbation<<largest<<100.0*largestPerCent<<largestZero
    <<CoinMessageEol;
  // and zero changes
  //int nTotal = numberRows_+numberColumns_;
  //CoinZeroN(cost_+nTotal,nTotal);
  // say perturbed
  perturbation_=101;

}
/* For strong branching.  On input lower and upper are new bounds
   while on output they are change in objective function values 
   (>1.0e50 infeasible).
   Return code is 0 if nothing interesting, -1 if infeasible both
   ways and +1 if infeasible one way (check values to see which one(s))
   Returns -2 if bad factorization
*/
int ClpSimplexDual::strongBranching(int numberVariables,const int * variables,
                                    double * newLower, double * newUpper,
                                    double ** outputSolution,
                                    int * outputStatus, int * outputIterations,
                                    bool stopOnFirstInfeasible,
                                    bool alwaysFinish,
                                    int startFinishOptions)
{
  int i;
  int returnCode=0;
  double saveObjectiveValue = objectiveValue_;
  algorithm_ = -1;

  //scaling(false);

  // put in standard form (and make row copy)
  // create modifiable copies of model rim and do optional scaling
  createRim(7+8+16+32,true,startFinishOptions);

  // change newLower and newUpper if scaled

  // Do initial factorization
  // and set certain stuff
  // We can either set increasing rows so ...IsBasic gives pivot row
  // or we can just increment iBasic one by one
  // for now let ...iBasic give pivot row
  int useFactorization=false;
  if ((startFinishOptions&2)!=0&&(whatsChanged_&(2+512))==2+512)
    useFactorization=true; // Keep factorization if possible
  // switch off factorization if bad
  if (pivotVariable_[0]<0)
    useFactorization=false;
  if (!useFactorization||factorization_->numberRows()!=numberRows_) {
    useFactorization = false;
    factorization_->increasingRows(2);
    // row activities have negative sign
    factorization_->slackValue(-1.0);
    factorization_->zeroTolerance(1.0e-13);

    int factorizationStatus = internalFactorize(0);
    if (factorizationStatus<0) {
      // some error
      // we should either debug or ignore 
#ifndef NDEBUG
      printf("***** ClpDual strong branching factorization error - debug\n");
#endif
      return -2;
    } else if (factorizationStatus&&factorizationStatus<=numberRows_) {
      handler_->message(CLP_SINGULARITIES,messages_)
        <<factorizationStatus
        <<CoinMessageEol;
    }
  }
  // save stuff
  ClpFactorization saveFactorization(*factorization_);
  // save basis and solution 
  double * saveSolution = new double[numberRows_+numberColumns_];
  CoinMemcpyN(solution_,
         numberRows_+numberColumns_,saveSolution);
  unsigned char * saveStatus = 
    new unsigned char [numberRows_+numberColumns_];
  CoinMemcpyN(status_,numberColumns_+numberRows_,saveStatus);
  // save bounds as createRim makes clean copies
  double * saveLower = new double[numberRows_+numberColumns_];
  CoinMemcpyN(lower_,
         numberRows_+numberColumns_,saveLower);
  double * saveUpper = new double[numberRows_+numberColumns_];
  CoinMemcpyN(upper_,
         numberRows_+numberColumns_,saveUpper);
  double * saveObjective = new double[numberRows_+numberColumns_];
  CoinMemcpyN(cost_,
         numberRows_+numberColumns_,saveObjective);
  int * savePivot = new int [numberRows_];
  CoinMemcpyN(pivotVariable_, numberRows_,savePivot);
  // need to save/restore weights.

  int iSolution = 0;
  for (i=0;i<numberVariables;i++) {
    int iColumn = variables[i];
    double objectiveChange;
    double saveBound;
    
    // try down
    
    saveBound = columnUpper_[iColumn];
    // external view - in case really getting optimal 
    columnUpper_[iColumn] = newUpper[i];
    if (scalingFlag_<=0) 
      upper_[iColumn] = newUpper[i]*rhsScale_;
    else 
      upper_[iColumn] = (newUpper[i]/columnScale_[iColumn])*rhsScale_; // scale
    // Start of fast iterations
    int status = fastDual(alwaysFinish);
    CoinAssert (problemStatus_||objectiveValue_<1.0e50);
    // make sure plausible
    double obj = CoinMax(objectiveValue_,saveObjectiveValue);
    if (status&&problemStatus_!=3) {
      // not finished - might be optimal
      checkPrimalSolution(rowActivityWork_,columnActivityWork_);
      double limit = 0.0;
      getDblParam(ClpDualObjectiveLimit, limit);
      if (!numberPrimalInfeasibilities_&&obj<limit) { 
        problemStatus_=0;
      } 
      status=problemStatus_;
    }
    if (status||(problemStatus_==0&&!isDualObjectiveLimitReached())) {
      objectiveChange = obj-saveObjectiveValue;
    } else {
      objectiveChange = 1.0e100;
      status=1;
    }
    if (problemStatus_==3)
      status=2;

    if (scalingFlag_<=0) {
      CoinMemcpyN(solution_,numberColumns_,outputSolution[iSolution]);
    } else {
      int j;
      double * sol = outputSolution[iSolution];
      for (j=0;j<numberColumns_;j++) 
        sol[j] = solution_[j]*columnScale_[j];
    }
    outputStatus[iSolution]=status;
    outputIterations[iSolution]=numberIterations_;
    iSolution++;
    // restore
    CoinMemcpyN(saveSolution,
            numberRows_+numberColumns_,solution_);
    CoinMemcpyN(saveStatus,numberColumns_+numberRows_,status_);
    CoinMemcpyN(saveLower,
            numberRows_+numberColumns_,lower_);
    CoinMemcpyN(saveUpper,
            numberRows_+numberColumns_,upper_);
    CoinMemcpyN(saveObjective,
            numberRows_+numberColumns_,cost_);
    columnUpper_[iColumn] = saveBound;
    CoinMemcpyN(savePivot, numberRows_,pivotVariable_);
    delete factorization_;
    factorization_ = new ClpFactorization(saveFactorization);

    newUpper[i]=objectiveChange;
#ifdef CLP_DEBUG
    printf("down on %d costs %g\n",iColumn,objectiveChange);
#endif
          
    // try up
    
    saveBound = columnLower_[iColumn];
    // external view - in case really getting optimal 
    columnLower_[iColumn] = newLower[i];
    if (scalingFlag_<=0) 
      lower_[iColumn] = newLower[i]*rhsScale_;
    else 
      lower_[iColumn] = (newLower[i]/columnScale_[iColumn])*rhsScale_; // scale
    // Start of fast iterations
    status = fastDual(alwaysFinish);
    // make sure plausible
    obj = CoinMax(objectiveValue_,saveObjectiveValue);
    if (status&&problemStatus_!=3) {
      // not finished - might be optimal
      checkPrimalSolution(rowActivityWork_,columnActivityWork_);
      double limit = 0.0;
      getDblParam(ClpDualObjectiveLimit, limit);
      if (!numberPrimalInfeasibilities_&&obj< limit) { 
        problemStatus_=0;
      } 
      status=problemStatus_;
    }
    if (status||(problemStatus_==0&&!isDualObjectiveLimitReached())) {
      objectiveChange = obj-saveObjectiveValue;
    } else {
      objectiveChange = 1.0e100;
      status=1;
    }
    if (problemStatus_==3)
      status=2;
    if (scalingFlag_<=0) {
      CoinMemcpyN(solution_,numberColumns_,outputSolution[iSolution]);
    } else {
      int j;
      double * sol = outputSolution[iSolution];
      for (j=0;j<numberColumns_;j++) 
        sol[j] = solution_[j]*columnScale_[j];
    }
    outputStatus[iSolution]=status;
    outputIterations[iSolution]=numberIterations_;
    iSolution++;

    // restore
    CoinMemcpyN(saveSolution,
            numberRows_+numberColumns_,solution_);
    CoinMemcpyN(saveStatus,numberColumns_+numberRows_,status_);
    CoinMemcpyN(saveLower,
            numberRows_+numberColumns_,lower_);
    CoinMemcpyN(saveUpper,
            numberRows_+numberColumns_,upper_);
    CoinMemcpyN(saveObjective,
            numberRows_+numberColumns_,cost_);
    columnLower_[iColumn] = saveBound;
    CoinMemcpyN(savePivot, numberRows_,pivotVariable_);
    delete factorization_;
    factorization_ = new ClpFactorization(saveFactorization);

    newLower[i]=objectiveChange;
#ifdef CLP_DEBUG
    printf("up on %d costs %g\n",iColumn,objectiveChange);
#endif
          
    /* Possibilities are:
       Both sides feasible - store
       Neither side feasible - set objective high and exit if desired
       One side feasible - change bounds and resolve
    */
    if (newUpper[i]<1.0e100) {
      if(newLower[i]<1.0e100) {
        // feasible - no action
      } else {
        // up feasible, down infeasible
        returnCode=1;
        if (stopOnFirstInfeasible)
          break;
      }
    } else {
      if(newLower[i]<1.0e100) {
        // down feasible, up infeasible
        returnCode=1;
        if (stopOnFirstInfeasible)
          break;
      } else {
        // neither side feasible
        returnCode=-1;
        break;
      }
    }
  }
  delete [] saveSolution;
  delete [] saveLower;
  delete [] saveUpper;
  delete [] saveObjective;
  delete [] saveStatus;
  delete [] savePivot;
  if ((startFinishOptions&1)==0) {
    deleteRim(1);
    whatsChanged_=0;
  } else {
    // Original factorization will have been put back by last loop
    //delete factorization_;
    //factorization_ = new ClpFactorization(saveFactorization);
    deleteRim(0);
    // mark all as current
    whatsChanged_ = 0xffff;
  }
  objectiveValue_ = saveObjectiveValue;
  return returnCode;
}
// treat no pivot as finished (unless interesting)
int ClpSimplexDual::fastDual(bool alwaysFinish)
{
  algorithm_ = -1;
  secondaryStatus_=0;
  // Say in fast dual
  specialOptions_ |= 16384;
  //handler_->setLogLevel(63);
  // save data
  ClpDataSave data = saveData();
  dualTolerance_=dblParam_[ClpDualTolerance];
  primalTolerance_=dblParam_[ClpPrimalTolerance];

  // save dual bound
  double saveDualBound = dualBound_;

  double objectiveChange;
  // for dual we will change bounds using dualBound_
  // for this we need clean basis so it is after factorize
  gutsOfSolution(NULL,NULL);
  numberFake_ =0; // Number of variables at fake bounds
  numberChanged_ =0; // Number of variables with changed costs
  changeBounds(true,NULL,objectiveChange);

  problemStatus_ = -1;
  numberIterations_=0;
  factorization_->sparseThreshold(0);
  factorization_->goSparse();

  int lastCleaned=0; // last time objective or bounds cleaned up

  // number of times we have declared optimality
  numberTimesOptimal_=0;

  // This says whether to restore things etc
  int factorType=0;
  /*
    Status of problem:
    0 - optimal
    1 - infeasible
    2 - unbounded
    -1 - iterating
    -2 - factorization wanted
    -3 - redo checking without factorization
    -4 - looks infeasible

    BUT also from whileIterating return code is:

   -1 iterations etc
   -2 inaccuracy 
   -3 slight inaccuracy (and done iterations)
   +0 looks optimal (might be unbounded - but we will investigate)
   +1 looks infeasible
   +3 max iterations 

  */

  int returnCode = 0;

  int iRow,iColumn;
  while (problemStatus_<0) {
    // clear
    for (iRow=0;iRow<4;iRow++) {
      rowArray_[iRow]->clear();
    }    
    
    for (iColumn=0;iColumn<2;iColumn++) {
      columnArray_[iColumn]->clear();
    }    

    // give matrix (and model costs and bounds a chance to be
    // refreshed (normally null)
    matrix_->refresh(this);
    // may factorize, checks if problem finished
    // should be able to speed this up on first time
    statusOfProblemInDual(lastCleaned,factorType,NULL,data,0);

    // Say good factorization
    factorType=1;

    // Do iterations
    if (problemStatus_<0) {
      double * givenPi=NULL;
      returnCode = whileIterating(givenPi,0);
      if ((!alwaysFinish&&returnCode<0)||returnCode==3) {
        if (returnCode!=3)
          assert (problemStatus_<0);
        returnCode=1;
        problemStatus_ = 3; 
        // can't say anything interesting - might as well return
#ifdef CLP_DEBUG
        printf("returning from fastDual after %d iterations with code %d\n",
               numberIterations_,returnCode);
#endif
        break;
      }
      returnCode=0;
    }
  }

  // clear
  for (iRow=0;iRow<4;iRow++) {
    rowArray_[iRow]->clear();
  }    
  
  for (iColumn=0;iColumn<2;iColumn++) {
    columnArray_[iColumn]->clear();
  }    
  // Say not in fast dual
  specialOptions_ &= ~16384;
  assert(!numberFake_||((specialOptions_&(2048|4096))!=0&&dualBound_>1.0e8)
         ||returnCode||problemStatus_); // all bounds should be okay
  // Restore any saved stuff
  restoreData(data);
  dualBound_ = saveDualBound;
  return returnCode;
}
// This does first part of StrongBranching
ClpFactorization * 
ClpSimplexDual::setupForStrongBranching(char * arrays, int numberRows, int numberColumns)
{
  algorithm_ = -1;
  // put in standard form (and make row copy)
  // create modifiable copies of model rim and do optional scaling
  int startFinishOptions;
  /*  COIN_CLP_VETTED
      Looks safe for Cbc
  */
  bool safeOption = ((specialOptions_&COIN_CBC_USING_CLP)!=0);
  if((specialOptions_&4096)==0||(auxiliaryModel_&&!safeOption)) {
    startFinishOptions=0;
  } else {
    startFinishOptions=1+2+4;
  }
  createRim(7+8+16+32,true,startFinishOptions);
  // Do initial factorization
  // and set certain stuff
  // We can either set increasing rows so ...IsBasic gives pivot row
  // or we can just increment iBasic one by one
  // for now let ...iBasic give pivot row
  bool useFactorization=false;
  if ((startFinishOptions&2)!=0&&(whatsChanged_&(2+512))==2+512) {
    useFactorization=true; // Keep factorization if possible
    // switch off factorization if bad
    if (pivotVariable_[0]<0||factorization_->numberRows()!=numberRows_) 
      useFactorization=false;
  }
  if (!useFactorization) {
    factorization_->increasingRows(2);
    // row activities have negative sign
    factorization_->slackValue(-1.0);
    factorization_->zeroTolerance(1.0e-13);

    int factorizationStatus = internalFactorize(0);
    if (factorizationStatus<0) {
      // some error
      // we should either debug or ignore 
#ifndef NDEBUG
      printf("***** ClpDual strong branching factorization error - debug\n");
#endif
    } else if (factorizationStatus&&factorizationStatus<=numberRows_) {
      handler_->message(CLP_SINGULARITIES,messages_)
        <<factorizationStatus
        <<CoinMessageEol;
    }
  }
  double * arrayD = (double *) arrays;
  arrayD[0]=objectiveValue()*optimizationDirection_;
  double * saveSolution = arrayD+1;
  double * saveLower = saveSolution + (numberRows+numberColumns);
  double * saveUpper = saveLower + (numberRows+numberColumns);
  double * saveObjective = saveUpper + (numberRows+numberColumns);
  double * saveLowerOriginal = saveObjective + (numberRows+numberColumns);
  double * saveUpperOriginal = saveLowerOriginal + numberColumns;
  arrayD = saveUpperOriginal + numberColumns;
  int * savePivot = (int *) arrayD;
  int * whichRow = savePivot+numberRows;
  int * whichColumn = whichRow + 3*numberRows;
  int * arrayI = whichColumn + 2*numberColumns;
  unsigned char * saveStatus = (unsigned char *) (arrayI+1);
  // save stuff
  // save basis and solution 
  CoinMemcpyN(solution_,
          numberRows_+numberColumns_,saveSolution);
  CoinMemcpyN(status_,numberColumns_+numberRows_,saveStatus);
  CoinMemcpyN(lower_,
          numberRows_+numberColumns_,saveLower);
  CoinMemcpyN(upper_,
          numberRows_+numberColumns_,saveUpper);
  CoinMemcpyN(cost_,
          numberRows_+numberColumns_,saveObjective);
  CoinMemcpyN(pivotVariable_, numberRows_,savePivot);
  return new ClpFactorization(*factorization_);
}
// This cleans up after strong branching
void 
ClpSimplexDual::cleanupAfterStrongBranching()
{
  int startFinishOptions;
  /*  COIN_CLP_VETTED
      Looks safe for Cbc
  */
  bool safeOption = ((specialOptions_&COIN_CBC_USING_CLP)!=0);
  if((specialOptions_&4096)==0||(auxiliaryModel_&&!safeOption)) {
    startFinishOptions=0;
  } else {
    startFinishOptions=1+2+4;
  }
  if ((startFinishOptions&1)==0) {
    deleteRim(1);
    whatsChanged_=0;
  } else {
    // Original factorization will have been put back by last loop
    //delete factorization_;
    //factorization_ = new ClpFactorization(saveFactorization);
    deleteRim(0);
    // mark all as current
    whatsChanged_ = 0xffff;
  }
}
/* Checks number of variables at fake bounds.  This is used by fastDual
   so can exit gracefully before end */
int 
ClpSimplexDual::numberAtFakeBound()
{
  int iSequence;
  int numberFake=0;
  
  for (iSequence=0;iSequence<numberRows_+numberColumns_;iSequence++) {
    FakeBound bound = getFakeBound(iSequence);
    switch(getStatus(iSequence)) {

    case basic:
      break;
    case isFree:
    case superBasic:
    case ClpSimplex::isFixed:
      assert (bound==noFake);
      break;
    case atUpperBound:
      if (bound==upperFake||bound==bothFake)
        numberFake++;
      break;
    case atLowerBound:
      if (bound==lowerFake||bound==bothFake)
        numberFake++;
      break;
    }
  }
  numberFake_ = numberFake;
  return numberFake;
}
/* Pivot out a variable and choose an incoing one.  Assumes dual
   feasible - will not go through a reduced cost.  
   Returns step length in theta
   Returns ray in ray_ (or NULL if no pivot)
   Return codes as before but -1 means no acceptable pivot
*/
int 
ClpSimplexDual::pivotResult()
{
  abort();
  return 0;
}
/* 
   Row array has row part of pivot row
   Column array has column part.
   This is used in dual values pass
*/
void
ClpSimplexDual::checkPossibleValuesMove(CoinIndexedVector * rowArray,
                                        CoinIndexedVector * columnArray,
                                        double acceptablePivot)
{
  double * work;
  int number;
  int * which;
  int iSection;

  double tolerance = dualTolerance_*1.001;

  double thetaDown = 1.0e31;
  double changeDown ;
  double thetaUp = 1.0e31;
  double bestAlphaDown = acceptablePivot*0.99999;
  double bestAlphaUp = acceptablePivot*0.99999;
  int sequenceDown =-1;
  int sequenceUp = sequenceOut_;

  double djBasic = dj_[sequenceOut_];
  if (djBasic>0.0) {
    // basic at lower bound so directionOut_ 1 and -1 in pivot row
    // dj will go to zero on other way
    thetaUp = djBasic;
    changeDown = -lower_[sequenceOut_];
  } else {
    // basic at upper bound so directionOut_ -1 and 1 in pivot row
    // dj will go to zero on other way
    thetaUp = -djBasic;
    changeDown = upper_[sequenceOut_];
  }
  bestAlphaUp = 1.0;
  int addSequence;

  double alphaUp=0.0;
  double alphaDown=0.0;

  for (iSection=0;iSection<2;iSection++) {

    int i;
    if (!iSection) {
      work = rowArray->denseVector();
      number = rowArray->getNumElements();
      which = rowArray->getIndices();
      addSequence = numberColumns_;
    } else {
      work = columnArray->denseVector();
      number = columnArray->getNumElements();
      which = columnArray->getIndices();
      addSequence = 0;
    }
    
    for (i=0;i<number;i++) {
      int iSequence = which[i];
      int iSequence2 = iSequence + addSequence;
      double alpha;
      double oldValue;
      double value;

      switch(getStatus(iSequence2)) {
          
      case basic: 
        break;
      case ClpSimplex::isFixed:
        alpha = work[i];
        changeDown += alpha*upper_[iSequence2];
        break;
      case isFree:
      case superBasic:
        alpha = work[i];
        // dj must be effectively zero as dual feasible
        if (fabs(alpha)>bestAlphaUp) {
          thetaDown = 0.0;
          thetaUp = 0.0;
          bestAlphaDown = fabs(alpha);
          bestAlphaUp = bestAlphaUp;
          sequenceDown =iSequence2;
          sequenceUp = sequenceDown;
          alphaUp = alpha;
          alphaDown = alpha;
        }
        break;
      case atUpperBound:
        alpha = work[i];
        oldValue = dj_[iSequence2];
        changeDown += alpha*upper_[iSequence2];
        if (alpha>=acceptablePivot) {
          // might do other way
          value = oldValue+thetaUp*alpha;
          if (value>-tolerance) {
            if (value>tolerance||fabs(alpha)>bestAlphaUp) {
              thetaUp = -oldValue/alpha;
              bestAlphaUp = fabs(alpha);
              sequenceUp = iSequence2;
              alphaUp = alpha;
            }
          }
        } else if (alpha<=-acceptablePivot) {
          // might do this way
          value = oldValue-thetaDown*alpha;
          if (value>-tolerance) {
            if (value>tolerance||fabs(alpha)>bestAlphaDown) {
              thetaDown = oldValue/alpha;
              bestAlphaDown = fabs(alpha);
              sequenceDown = iSequence2;
              alphaDown = alpha;
            }
          }
        }
        break;
      case atLowerBound:
        alpha = work[i];
        oldValue = dj_[iSequence2];
        changeDown += alpha*lower_[iSequence2];
        if (alpha<=-acceptablePivot) {
          // might do other way
          value = oldValue+thetaUp*alpha;
          if (value<tolerance) {
            if (value<-tolerance||fabs(alpha)>bestAlphaUp) {
              thetaUp = -oldValue/alpha;
              bestAlphaUp = fabs(alpha);
              sequenceUp = iSequence2;
              alphaUp = alpha;
            }
          }
        } else if (alpha>=acceptablePivot) {
          // might do this way
          value = oldValue-thetaDown*alpha;
          if (value<tolerance) {
            if (value<-tolerance||fabs(alpha)>bestAlphaDown) {
              thetaDown = oldValue/alpha;
              bestAlphaDown = fabs(alpha);
              sequenceDown = iSequence2;
              alphaDown = alpha;
            }
          }
        }
        break;
      }
    }
  }
  thetaUp *= -1.0;
  double changeUp = -thetaUp * changeDown;
  changeDown = -thetaDown*changeDown;
  if (CoinMax(fabs(thetaDown),fabs(thetaUp))<1.0e-8) {
    // largest
    if (fabs(alphaDown)<fabs(alphaUp)) {
      sequenceDown =-1;
    }
  }
  // choose
  sequenceIn_=-1;
  if (changeDown>changeUp&&sequenceDown>=0) {
    theta_ = thetaDown;
    if (fabs(changeDown)<1.0e30)
      sequenceIn_ = sequenceDown;
    alpha_ = alphaDown;
#ifdef CLP_DEBUG
    if ((handler_->logLevel()&32))
      printf("predicted way - dirout %d, change %g,%g theta %g\n",
             directionOut_,changeDown,changeUp,theta_);
#endif
  } else {
    theta_ = thetaUp;
    if (fabs(changeUp)<1.0e30)
      sequenceIn_ = sequenceUp;
    alpha_ = alphaUp;
    if (sequenceIn_!=sequenceOut_) {
#ifdef CLP_DEBUG
      if ((handler_->logLevel()&32))
        printf("opposite way - dirout %d, change %g,%g theta %g\n",
               directionOut_,changeDown,changeUp,theta_);
#endif
    } else {
#ifdef CLP_DEBUG
      if ((handler_->logLevel()&32))
        printf("opposite way to zero dj - dirout %d, change %g,%g theta %g\n",
               directionOut_,changeDown,changeUp,theta_);
#endif
    }
  }
  if (sequenceIn_>=0) {
    lowerIn_ = lower_[sequenceIn_];
    upperIn_ = upper_[sequenceIn_];
    valueIn_ = solution_[sequenceIn_];
    dualIn_ = dj_[sequenceIn_];

    if (alpha_<0.0) {
      // as if from upper bound
      directionIn_=-1;
      upperIn_=valueIn_;
    } else {
      // as if from lower bound
      directionIn_=1;
      lowerIn_=valueIn_;
    }
  }
}
/* 
   Row array has row part of pivot row
   Column array has column part.
   This is used in cleanup
*/
void
ClpSimplexDual::checkPossibleCleanup(CoinIndexedVector * rowArray,
                                        CoinIndexedVector * columnArray,
                                        double acceptablePivot)
{
  double * work;
  int number;
  int * which;
  int iSection;

  double tolerance = dualTolerance_*1.001;

  double thetaDown = 1.0e31;
  double thetaUp = 1.0e31;
  double bestAlphaDown = acceptablePivot*10.0;
  double bestAlphaUp = acceptablePivot*10.0;
  int sequenceDown =-1;
  int sequenceUp = -1;

  double djSlack = dj_[pivotRow_];
  if (getRowStatus(pivotRow_)==basic)
    djSlack=COIN_DBL_MAX;
  if (fabs(djSlack)<tolerance)
    djSlack=0.0;
  int addSequence;

  double alphaUp=0.0;
  double alphaDown=0.0;
  for (iSection=0;iSection<2;iSection++) {

    int i;
    if (!iSection) {
      work = rowArray->denseVector();
      number = rowArray->getNumElements();
      which = rowArray->getIndices();
      addSequence = numberColumns_;
    } else {
      work = columnArray->denseVector();
      number = columnArray->getNumElements();
      which = columnArray->getIndices();
      addSequence = 0;
    }
    
    for (i=0;i<number;i++) {
      int iSequence = which[i];
      int iSequence2 = iSequence + addSequence;
      double alpha;
      double oldValue;
      double value;

      switch(getStatus(iSequence2)) {
          
      case basic: 
        break;
      case ClpSimplex::isFixed:
        alpha = work[i];
        if (addSequence) {
          printf("possible - pivot row %d this %d\n",pivotRow_,iSequence);
          oldValue = dj_[iSequence2];
          if (alpha<=-acceptablePivot) {
            // might do other way
            value = oldValue+thetaUp*alpha;
            if (value<tolerance) {
              if (value<-tolerance||fabs(alpha)>bestAlphaUp) {
                thetaUp = -oldValue/alpha;
                bestAlphaUp = fabs(alpha);
                sequenceUp = iSequence2;
                alphaUp = alpha;
              }
            }
          } else if (alpha>=acceptablePivot) {
            // might do this way
            value = oldValue-thetaDown*alpha;
            if (value<tolerance) {
              if (value<-tolerance||fabs(alpha)>bestAlphaDown) {
                thetaDown = oldValue/alpha;
                bestAlphaDown = fabs(alpha);
                sequenceDown = iSequence2;
                alphaDown = alpha;
              }
            }
          }
        }
        break;
      case isFree:
      case superBasic:
        alpha = work[i];
        // dj must be effectively zero as dual feasible
        if (fabs(alpha)>bestAlphaUp) {
          thetaDown = 0.0;
          thetaUp = 0.0;
          bestAlphaDown = fabs(alpha);
          bestAlphaUp = bestAlphaUp;
          sequenceDown =iSequence2;
          sequenceUp = sequenceDown;
          alphaUp = alpha;
          alphaDown = alpha;
        }
        break;
      case atUpperBound:
        alpha = work[i];
        oldValue = dj_[iSequence2];
        if (alpha>=acceptablePivot) {
          // might do other way
          value = oldValue+thetaUp*alpha;
          if (value>-tolerance) {
            if (value>tolerance||fabs(alpha)>bestAlphaUp) {
              thetaUp = -oldValue/alpha;
              bestAlphaUp = fabs(alpha);
              sequenceUp = iSequence2;
              alphaUp = alpha;
            }
          }
        } else if (alpha<=-acceptablePivot) {
          // might do this way
          value = oldValue-thetaDown*alpha;
          if (value>-tolerance) {
            if (value>tolerance||fabs(alpha)>bestAlphaDown) {
              thetaDown = oldValue/alpha;
              bestAlphaDown = fabs(alpha);
              sequenceDown = iSequence2;
              alphaDown = alpha;
            }
          }
        }
        break;
      case atLowerBound:
        alpha = work[i];
        oldValue = dj_[iSequence2];
        if (alpha<=-acceptablePivot) {
          // might do other way
          value = oldValue+thetaUp*alpha;
          if (value<tolerance) {
            if (value<-tolerance||fabs(alpha)>bestAlphaUp) {
              thetaUp = -oldValue/alpha;
              bestAlphaUp = fabs(alpha);
              sequenceUp = iSequence2;
              alphaUp = alpha;
            }
          }
        } else if (alpha>=acceptablePivot) {
          // might do this way
          value = oldValue-thetaDown*alpha;
          if (value<tolerance) {
            if (value<-tolerance||fabs(alpha)>bestAlphaDown) {
              thetaDown = oldValue/alpha;
              bestAlphaDown = fabs(alpha);
              sequenceDown = iSequence2;
              alphaDown = alpha;
            }
          }
        }
        break;
      }
    }
  }
  thetaUp *= -1.0;
  // largest
  if (bestAlphaDown<bestAlphaUp) 
    sequenceDown =-1;
  else
    sequenceUp=-1;

  sequenceIn_=-1;
  
  if (sequenceDown>=0) {
    theta_ = thetaDown;
    sequenceIn_ = sequenceDown;
    alpha_ = alphaDown;
#ifdef CLP_DEBUG
    if ((handler_->logLevel()&32))
      printf("predicted way - dirout %d, theta %g\n",
             directionOut_,theta_);
#endif
  } else if (sequenceUp>=0) {
    theta_ = thetaUp;
    sequenceIn_ = sequenceUp;
    alpha_ = alphaUp;
#ifdef CLP_DEBUG
    if ((handler_->logLevel()&32))
      printf("opposite way - dirout %d,theta %g\n",
             directionOut_,theta_);
#endif
  }
  if (sequenceIn_>=0) {
    lowerIn_ = lower_[sequenceIn_];
    upperIn_ = upper_[sequenceIn_];
    valueIn_ = solution_[sequenceIn_];
    dualIn_ = dj_[sequenceIn_];

    if (alpha_<0.0) {
      // as if from upper bound
      directionIn_=-1;
      upperIn_=valueIn_;
    } else {
      // as if from lower bound
      directionIn_=1;
      lowerIn_=valueIn_;
    }
  }
}
/* 
   This sees if we can move duals in dual values pass.
   This is done before any pivoting
*/
void ClpSimplexDual::doEasyOnesInValuesPass(double * dj)
{
  // Get column copy
  CoinPackedMatrix * columnCopy = matrix();
  // Get a row copy in standard format
  CoinPackedMatrix copy;
  copy.reverseOrderedCopyOf(*columnCopy);
  // get matrix data pointers
  const int * column = copy.getIndices();
  const CoinBigIndex * rowStart = copy.getVectorStarts();
  const int * rowLength = copy.getVectorLengths(); 
  const double * elementByRow = copy.getElements();
  double tolerance = dualTolerance_*1.001;

  int iRow;
#ifdef CLP_DEBUG
  {
    double value5=0.0;
    int i;
    for (i=0;i<numberRows_+numberColumns_;i++) {
      if (dj[i]<-1.0e-6)
        value5 += dj[i]*upper_[i];
      else if (dj[i] >1.0e-6)
        value5 += dj[i]*lower_[i];
    }
    printf("Values objective Value before %g\n",value5);
  }
#endif
  // for scaled row
  double * scaled=NULL;
  if (rowScale_)
    scaled = new double[numberColumns_];
  for (iRow=0;iRow<numberRows_;iRow++) {

    int iSequence = iRow + numberColumns_;
    double djBasic = dj[iSequence];
    if (getRowStatus(iRow)==basic&&fabs(djBasic)>tolerance) {

      double changeUp ;
      // always -1 in pivot row
      if (djBasic>0.0) {
        // basic at lower bound
        changeUp = -lower_[iSequence];
      } else {
        // basic at upper bound
        changeUp = upper_[iSequence];
      }
      bool canMove=true;
      int i;
      const double * thisElements = elementByRow + rowStart[iRow]; 
      const int * thisIndices = column+rowStart[iRow];
      if (rowScale_) {
        assert (!auxiliaryModel_);
        // scale row
        double scale = rowScale_[iRow];
        for (i = 0;i<rowLength[iRow];i++) {
          int iColumn = thisIndices[i];
          double alpha = thisElements[i];
          scaled[i] = scale*alpha*columnScale_[iColumn];
        }
        thisElements = scaled;
      }
      for (i = 0;i<rowLength[iRow];i++) {
        int iColumn = thisIndices[i];
        double alpha = thisElements[i];
        double oldValue = dj[iColumn];;
        double value;

        switch(getStatus(iColumn)) {
          
        case basic:
          if (dj[iColumn]<-tolerance&&
              fabs(solution_[iColumn]-upper_[iColumn])<1.0e-8) {
            // at ub
            changeUp += alpha*upper_[iColumn];
            // might do other way
            value = oldValue+djBasic*alpha;
            if (value>tolerance) 
              canMove=false;
          } else if (dj[iColumn]>tolerance&&
              fabs(solution_[iColumn]-lower_[iColumn])<1.0e-8) {
            changeUp += alpha*lower_[iColumn];
            // might do other way
            value = oldValue+djBasic*alpha;
            if (value<-tolerance)
              canMove=false;
          } else {
            canMove=false;
          }
          break;
        case ClpSimplex::isFixed:
          changeUp += alpha*upper_[iColumn];
          break;
        case isFree:
        case superBasic:
          canMove=false;
        break;
      case atUpperBound:
        changeUp += alpha*upper_[iColumn];
        // might do other way
        value = oldValue+djBasic*alpha;
        if (value>tolerance) 
          canMove=false;
        break;
      case atLowerBound:
        changeUp += alpha*lower_[iColumn];
        // might do other way
        value = oldValue+djBasic*alpha;
        if (value<-tolerance)
          canMove=false;
        break;
        }
      }
      if (canMove) {
        if (changeUp*djBasic>1.0e-12||fabs(changeUp)<1.0e-8) {
          // move 
          for (i = 0;i<rowLength[iRow];i++) {
            int iColumn = thisIndices[i];
            double alpha = thisElements[i];
            dj[iColumn] += djBasic * alpha;
          }
          dj[iSequence]=0.0;
#ifdef CLP_DEBUG
          {
            double value5=0.0;
            int i;
            for (i=0;i<numberRows_+numberColumns_;i++) {
              if (dj[i]<-1.0e-6)
                value5 += dj[i]*upper_[i];
              else if (dj[i] >1.0e-6)
                value5 += dj[i]*lower_[i];
            }
            printf("Values objective Value after row %d old dj %g %g\n",
                   iRow,djBasic,value5);
          }
#endif
        }
      }
    }      
  }
  delete [] scaled;
}
int
ClpSimplexDual::nextSuperBasic()
{
  if (firstFree_>=0) {
    int returnValue=firstFree_;
    int iColumn=firstFree_+1;
    for (;iColumn<numberRows_+numberColumns_;iColumn++) {
      if (getStatus(iColumn)==isFree) 
        if (fabs(dj_[iColumn])>1.0e2*dualTolerance_) 
          break;
    }
    firstFree_ = iColumn;
    if (firstFree_==numberRows_+numberColumns_)
      firstFree_=-1;
    return returnValue;
  } else {
    return -1;
  }
}