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+/* $Id: ClpSimplexDual.hpp 1761 2011-07-06 16:06:24Z forrest $ */
+// Copyright (C) 2002, International Business Machines
+// Corporation and others.  All Rights Reserved.
+// This code is licensed under the terms of the Eclipse Public License (EPL).
+/*
+   Authors
+
+   John Forrest
+
+ */
+#ifndef ClpSimplexDual_H
+#define ClpSimplexDual_H
+
+#include "ClpSimplex.hpp"
+
+/** This solves LPs using the dual simplex method
+
+    It inherits from ClpSimplex.  It has no data of its own and
+    is never created - only cast from a ClpSimplex object at algorithm time.
+
+*/
+
+class ClpSimplexDual : public ClpSimplex {
+
+public:
+
+     /**@name Description of algorithm */
+     //@{
+     /** Dual algorithm
+
+         Method
+
+        It tries to be a single phase approach with a weight of 1.0 being
+        given to getting optimal and a weight of updatedDualBound_ 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 updatedDualBound_ 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 updatedDualBound_
+        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 for
+        Dantzig row choice.  For steepest edge we keep an updated list
+        of infeasibilities (actually squares).
+        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 some
+        of what I think is the dual analog of 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 and break to re-factorize.
+        If minor error re-factorize after iteration.
+
+        Update everything (this may involve flipping variables to stay
+        dual feasible.
+
+          }
+
+        }
+
+        TODO's (or maybe not)
+
+        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.
+
+        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.
+
+        for use of exotic parameter startFinishoptions see Clpsimplex.hpp
+     */
+
+     int dual(int ifValuesPass, int startFinishOptions = 0);
+     /** 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))
+         Solutions are filled in as well - even down, odd up - also
+         status and number of iterations
+     */
+     int strongBranching(int numberVariables, const int * variables,
+                         double * newLower, double * newUpper,
+                         double ** outputSolution,
+                         int * outputStatus, int * outputIterations,
+                         bool stopOnFirstInfeasible = true,
+                         bool alwaysFinish = false,
+                         int startFinishOptions = 0);
+     /// This does first part of StrongBranching
+     ClpFactorization * setupForStrongBranching(char * arrays, int numberRows,
+               int numberColumns, bool solveLp = false);
+     /// This cleans up after strong branching
+     void cleanupAfterStrongBranching(ClpFactorization * factorization);
+     //@}
+
+     /**@name Functions used in dual */
+     //@{
+     /** This has the flow between re-factorizations
+         Broken out for clarity and will be used by strong branching
+
+         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
+
+         If givenPi not NULL then in values pass
+      */
+     int whileIterating(double * & givenPi, int ifValuesPass);
+     /** The duals are updated by the given arrays.
+         Returns number of infeasibilities.
+         After rowArray and columnArray will just have those which
+         have been flipped.
+         Variables may be flipped between bounds to stay dual feasible.
+         The output vector has movement of primal
+         solution (row length array) */
+     int updateDualsInDual(CoinIndexedVector * rowArray,
+                           CoinIndexedVector * columnArray,
+                           CoinIndexedVector * outputArray,
+                           double theta,
+                           double & objectiveChange,
+                           bool fullRecompute);
+     /** The duals are updated by the given arrays.
+         This is in values pass - so no changes to primal is made
+     */
+     void updateDualsInValuesPass(CoinIndexedVector * rowArray,
+                                  CoinIndexedVector * columnArray,
+                                  double theta);
+     /** While updateDualsInDual sees what effect is of flip
+         this does actual flipping.
+     */
+     void flipBounds(CoinIndexedVector * rowArray,
+                     CoinIndexedVector * columnArray);
+     /**
+         Row array has row part of pivot row
+         Column array has column part.
+         This chooses pivot column.
+         Spare arrays are used to save pivots which will go infeasible
+         We will check for basic so spare array will never overflow.
+         If necessary will modify costs
+         For speed, we may need to go to a bucket approach when many
+         variables are being flipped.
+         Returns best possible pivot value
+     */
+     double dualColumn(CoinIndexedVector * rowArray,
+                       CoinIndexedVector * columnArray,
+                       CoinIndexedVector * spareArray,
+                       CoinIndexedVector * spareArray2,
+                       double accpetablePivot,
+                       CoinBigIndex * dubiousWeights);
+     /// Does first bit of dualColumn
+     int dualColumn0(const CoinIndexedVector * rowArray,
+                     const CoinIndexedVector * columnArray,
+                     CoinIndexedVector * spareArray,
+                     double acceptablePivot,
+                     double & upperReturn, double &bestReturn, double & badFree);
+     /**
+         Row array has row part of pivot row
+         Column array has column part.
+         This sees what is best thing to do in dual values pass
+         if sequenceIn==sequenceOut can change dual on chosen row and leave variable in basis
+     */
+     void checkPossibleValuesMove(CoinIndexedVector * rowArray,
+                                  CoinIndexedVector * columnArray,
+                                  double acceptablePivot);
+     /**
+         Row array has row part of pivot row
+         Column array has column part.
+         This sees what is best thing to do in branch and bound cleanup
+         If sequenceIn_ < 0 then can't do anything
+     */
+     void checkPossibleCleanup(CoinIndexedVector * rowArray,
+                               CoinIndexedVector * columnArray,
+                               double acceptablePivot);
+     /**
+         This sees if we can move duals in dual values pass.
+         This is done before any pivoting
+     */
+     void doEasyOnesInValuesPass(double * givenReducedCosts);
+     /**
+         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
+
+         If alreadyChosen >=0 then in values pass and that row has been
+         selected
+     */
+     void dualRow(int alreadyChosen);
+     /** Checks if any fake bounds active - if so returns number and modifies
+         updatedDualBound_ 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
+         If 2 sets to original (just changed)
+     */
+     int changeBounds(int initialize, CoinIndexedVector * outputArray,
+                      double & changeCost);
+     /** As changeBounds but just changes new bounds for a single variable.
+         Returns true if change */
+     bool changeBound( int iSequence);
+     /// Restores bound to original bound
+     void originalBound(int iSequence);
+     /** Checks if tentative optimal actually means unbounded in dual
+         Returns -3 if not, 2 if is unbounded */
+     int checkUnbounded(CoinIndexedVector * ray, CoinIndexedVector * spare,
+                        double changeCost);
+     /**  Refactorizes if necessary
+          Checks if finished.  Updates status.
+          lastCleaned refers to iteration at which some objective/feasibility
+          cleaning too place.
+
+          type - 0 initial so set up save arrays etc
+               - 1 normal -if good update save
+           - 2 restoring from saved
+     */
+     void statusOfProblemInDual(int & lastCleaned, int type,
+                                double * givenDjs, ClpDataSave & saveData,
+                                int ifValuesPass);
+     /** Perturbs problem (method depends on perturbation())
+         returns nonzero if should go to dual */
+     int perturb();
+     /** Fast iterations.  Misses out a lot of initialization.
+         Normally stops on maximum iterations, first re-factorization
+         or tentative optimum.  If looks interesting then continues as
+         normal.  Returns 0 if finished properly, 1 otherwise.
+     */
+     int fastDual(bool alwaysFinish = false);
+     /** Checks number of variables at fake bounds.  This is used by fastDual
+         so can exit gracefully before end */
+     int numberAtFakeBound();
+
+     /** Pivot in a variable and choose an outgoing one.  Assumes dual
+         feasible - will not go through a reduced cost.  Returns step length in theta
+         Return codes as before but -1 means no acceptable pivot
+     */
+     int pivotResultPart1();
+     /** Get next free , -1 if none */
+     int nextSuperBasic();
+     /** Startup part of dual (may be extended to other algorithms)
+         returns 0 if good, 1 if bad */
+     int startupSolve(int ifValuesPass, double * saveDuals, int startFinishOptions);
+     void finishSolve(int startFinishOptions);
+     void gutsOfDual(int ifValuesPass, double * & saveDuals, int initialStatus,
+                     ClpDataSave & saveData);
+     //int dual2(int ifValuesPass,int startFinishOptions=0);
+     void resetFakeBounds(int type);
+
+     //@}
+};
+#endif