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+// Last edit: 4/20/07
+//
+// Name:     CglRedSplit.hpp
+// Author:   Francois Margot
+//           Tepper School of Business
+//           Carnegie Mellon University, Pittsburgh, PA 15213
+//           email: fmargot@andrew.cmu.edu
+// Date:     2/6/05
+//
+// $Id: CglRedSplit.hpp 1119 2013-04-06 20:24:18Z stefan $
+//-----------------------------------------------------------------------------
+// Copyright (C) 2005, Francois Margot and others.  All Rights Reserved.
+// This code is licensed under the terms of the Eclipse Public License (EPL).
+
+#ifndef CglRedSplit_H
+#define CglRedSplit_H
+
+#include "CglCutGenerator.hpp"
+#include "CglRedSplitParam.hpp"
+
+/** Gomory Reduce-and-Split Cut Generator Class; See method generateCuts().
+    Based on the paper by K. Anderson, G. Cornuejols, Yanjun Li, 
+    "Reduce-and-Split Cuts: Improving the Performance of Mixed Integer 
+    Gomory Cuts", Management Science 51 (2005). */
+
+class CglRedSplit : public CglCutGenerator {
+
+  friend void CglRedSplitUnitTest(const OsiSolverInterface * siP,
+				  const std::string mpdDir);
+public:
+  /**@name generateCuts */
+  //@{
+  /** Generate Reduce-and-Split Mixed Integer Gomory cuts 
+      for the model of the solver interface si.
+
+      Insert the generated cuts into OsiCuts cs.
+
+      Warning: This generator currently works only with the Lp solvers Clp or 
+      Cplex9.0 or higher. It requires access to the optimal tableau and 
+      optimal basis inverse and makes assumptions on the way slack variables 
+      are added by the solver. The Osi implementations for Clp and Cplex 
+      verify these assumptions.
+
+      When calling the generator, the solver interface si 
+      must contain an optimized
+      problem and information related to the optimal basis must be available 
+      through the OsiSolverInterface methods (si->optimalBasisIsAvailable()
+      must return 'true'). It is also essential that the integrality of
+      structural variable i can be obtained using si->isInteger(i).
+
+      Reduce-and-Split cuts are variants of Gomory cuts: Starting from
+      the current optimal tableau, linear combinations of the rows of 
+      the current optimal simplex tableau are used for generating Gomory
+      cuts. The choice of the linear combinations is driven by the objective 
+      of reducing the coefficients of the non basic continuous variables
+      in the resulting row.
+      Note that this generator might not be able to generate cuts for some 
+      solutions violating integrality constraints. 
+
+  */
+  virtual void generateCuts(const OsiSolverInterface & si, OsiCuts & cs,
+			    const CglTreeInfo info = CglTreeInfo());
+
+  /// Return true if needs optimal basis to do cuts (will return true)
+  virtual bool needsOptimalBasis() const;
+  //@}
+  
+  
+  /**@name Public Methods */
+  //@{
+
+  // Set the parameters to the values of the given CglRedSplitParam object.
+  void setParam(const CglRedSplitParam &source); 
+  // Return the CglRedSplitParam object of the generator. 
+  inline CglRedSplitParam getParam() const {return param;}
+
+  // Compute entries of low_is_lub and up_is_lub.
+  void compute_is_lub();
+
+  // Compute entries of is_integer.
+  void compute_is_integer();
+
+  /// Set given_optsol to the given optimal solution given_sol.
+  /// If given_optsol is set using this method, 
+  /// the code will stop as soon as
+  /// a generated cut is violated by the given solution; exclusively 
+  /// for debugging purposes.
+  void set_given_optsol(const double *given_sol, const int card_sol);
+
+  /// Print some of the data members  
+  void print() const;
+
+  /// Print the current simplex tableau  
+  void printOptTab(OsiSolverInterface *solver) const;
+  
+  //@}
+
+ /**@name Public Methods (soon to be obsolete)*/
+  //@{
+  //************************************************************
+  // TO BE REMOVED
+  /** Set limit, the maximum number of non zero coefficients in generated cut;
+      Default: 50 */
+  void setLimit(int limit);
+  /** Get value of limit */
+  int getLimit() const;
+
+  /** Set away, the minimum distance from being integer used for selecting 
+      rows for cut generation;  all rows whose pivot variable should be 
+      integer but is more than away from integrality will be selected; 
+      Default: 0.05 */
+  void setAway(double value);
+  /// Get value of away
+  double getAway() const;
+ /** Set the value of LUB, value considered large for the absolute value of
+      a lower or upper bound on a variable;
+      Default: 1000 */
+  void setLUB(double value);
+  /** Get the value of LUB */
+  double getLUB() const;
+
+  /** Set the value of EPS, epsilon for double computations;
+      Default: 1e-7 */
+  void setEPS(double value);
+  /** Get the value of EPS */
+  double getEPS() const;
+
+  /** Set the value of EPS_COEFF, epsilon for values of coefficients;
+      Default: 1e-8 */
+  void setEPS_COEFF(double value);
+  /** Get the value of EPS_COEFF */
+  double getEPS_COEFF() const;
+
+  /** Set the value of EPS_COEFF_LUB, epsilon for values of coefficients for 
+      variables with absolute value of lower or upper bound larger than LUB;
+      Default: 1e-13 */
+  void setEPS_COEFF_LUB(double value);
+  /** Get the value of EPS_COEFF_LUB */
+  double getEPS_COEFF_LUB() const;
+
+  /** Set the value of EPS_RELAX, value used for relaxing the right hand side
+      of each generated cut;
+      Default: 1e-8 */
+  void setEPS_RELAX(double value);
+  /** Get the value of EPS_RELAX */
+  double getEPS_RELAX() const;
+
+  /** Set the value of normIsZero, the threshold for considering a norm to be 
+      0; Default: 1e-5 */
+  void setNormIsZero(double value);
+  /** Get the value of normIsZero */
+  double getNormIsZero() const;
+
+  /** Set the value of minReduc, threshold for relative norm improvement for
+   performing  a reduction; Default: 0.05 */
+  void setMinReduc(double value);
+  /// Get the value of minReduc
+  double getMinReduc() const;
+
+  /** Set the maximum allowed value for (mTab * mTab * CoinMax(mTab, nTab)) where 
+      mTab is the number of rows used in the combinations and nTab is the 
+      number of continuous non basic variables. The work of the generator is 
+      proportional to (mTab * mTab * CoinMax(mTab, nTab)). Reducing the value of 
+      maxTab makes the generator faster, but weaker. Default: 1e7. */
+  void setMaxTab(double value);
+  /// Get the value of maxTab
+  double getMaxTab() const;
+  // END TO BE REMOVED
+  //************************************************************
+
+  //@}
+
+  /**@name Constructors and destructors */
+  //@{
+  /// Default constructor 
+  CglRedSplit();
+
+  /// Constructor with specified parameters 
+  CglRedSplit(const CglRedSplitParam &RS_param);
+ 
+  /// Copy constructor 
+  CglRedSplit (const CglRedSplit &);
+
+  /// Clone
+  virtual CglCutGenerator * clone() const;
+
+  /// Assignment operator 
+  CglRedSplit &
+    operator=(
+    const CglRedSplit& rhs);
+  
+  /// Destructor 
+  virtual
+    ~CglRedSplit ();
+  /// Create C++ lines to get to current state
+  virtual std::string generateCpp( FILE * fp);
+  //@}
+    
+private:
+  
+  // Private member methods
+
+/**@name Private member methods */
+
+  //@{
+
+  // Method generating the cuts after all CglRedSplit members are properly set.
+  void generateCuts(OsiCuts & cs);
+
+  /// Compute the fractional part of value, allowing for small error.
+  inline double rs_above_integer(double value); 
+
+  /// Perform row r1 of pi := row r1 of pi - step * row r2 of pi.
+  void update_pi_mat(int r1, int r2, int step);
+
+  /// Perform row r1 of tab := row r1 of tab - step * row r2 of tab.
+  void update_redTab(int r1, int r2, int step);
+
+  /// Find optimal integer step for changing row r1 by adding to it a 
+  /// multiple of another row r2.
+  void find_step(int r1, int r2, int *step, 
+		 double *reduc, double *norm);
+
+  /// Test if an ordered pair of rows yields a reduction. Perform the
+  /// reduction if it is acceptable.
+  int test_pair(int r1, int r2, double *norm);
+
+  /// Reduce rows of contNonBasicTab.
+  void reduce_contNonBasicTab();
+
+  /// Generate a row of the current LP tableau.
+  void generate_row(int index_row, double *row);
+
+  /// Generate a mixed integer Chvatal-Gomory cut, when all non basic 
+  /// variables are non negative and at their lower bound.
+  int generate_cgcut(double *row, double *rhs);
+
+  /// Generate a mixed integer Chvatal-Gomory cut, when all non basic 
+  /// variables are non negative and at their lower bound (different formula)
+  int generate_cgcut_2(int basic_ind, double *row, double *rhs);
+
+  /// Use multiples of the initial inequalities to cancel out the coefficients
+  /// of the slack variables.
+  void eliminate_slacks(double *row, 
+			const double *elements, 
+			const int *start,
+			const int *indices,
+			const int *rowLength,
+			const double *rhs, double *rowrhs);
+
+  /// Change the sign of the coefficients of the continuous non basic
+  /// variables at their upper bound.
+  void flip(double *row);
+
+  /// Change the sign of the coefficients of the continuous non basic
+  /// variables at their upper bound and do the translations restoring
+  /// the original bounds. Modify the right hand side
+  /// accordingly.
+  void unflip(double *row, double *rowrhs, double *slack_val);
+
+  /// Return the scale factor for the row. 
+  /// Compute max_coeff: maximum absolute value of the coefficients.
+  /// Compute min_coeff: minimum absolute value of the coefficients
+  /// larger than EPS_COEFF.
+  /// Return -1 if max_coeff < EPS_COEFF or if max_coeff/min_coeff > MAXDYN
+  /// or MAXDYN_LUB (depending if the row has a non zero coeff. for a variable
+  /// with large lower/upper bound) */.
+  double row_scale_factor(double *row);
+
+  /// Generate the packed cut from the row representation.
+  int generate_packed_row(const double *xlp, double *row,
+			  int *rowind, double *rowelem, 
+			  int *card_row, double & rhs);
+
+  /// Check that the generated cuts do not cut a given optimal solution.
+  void check_optsol(const int calling_place,
+		    const double *xlp, const double *slack_val,
+		    const int do_flip);
+
+  /// Check that the generated cuts do not cut a given optimal solution.
+  void check_optsol(const int calling_place,
+		    const double *xlp, const double *slack_val,
+		    const double *ck_row, const double ck_rhs, 
+		    const int cut_number, const int do_flip);
+
+  // Check that two vectors are different.
+  bool rs_are_different_vectors(const int *vect1, 
+				const int *vect2,
+				const int dim);
+
+  // Check that two vectors are different.
+  bool rs_are_different_vectors(const double *vect1, 
+				const double *vect2,
+				const int dim);
+
+  // Check that two matrices are different.
+  bool rs_are_different_matrices(const CoinPackedMatrix *mat1, 
+				 const CoinPackedMatrix *mat2,
+				 const int nmaj,
+				 const int nmin);
+  //@}
+
+  
+  // Private member data
+
+/**@name Private member data */
+
+  //@{
+
+  /// Object with CglRedSplitParam members. 
+  CglRedSplitParam param;
+
+  /// Number of rows ( = number of slack variables) in the current LP.
+  int nrow; 
+
+  /// Number of structural variables in the current LP.
+  int ncol;
+
+  /// Lower bounds for structural variables
+  const double *colLower;
+
+  /// Upper bounds for structural variables
+  const double *colUpper;
+  
+  /// Lower bounds for constraints
+  const double *rowLower;
+
+  /// Upper bounds for constraints
+  const double *rowUpper;
+
+  /// Righ hand side for constraints (upper bound for ranged constraints).
+  const double *rowRhs;
+
+  /// Number of integer basic structural variables that are fractional in the
+  /// current lp solution (at least param.away_ from being integer).  
+  int card_intBasicVar_frac;
+
+  /// Number of integer non basic structural variables in the
+  /// current lp solution.  
+  int card_intNonBasicVar; 
+
+  /// Number of continuous non basic variables (structural or slack) in the
+  /// current lp solution.  
+  int card_contNonBasicVar;
+
+  /// Number of non basic variables (structural or slack) at their
+  /// upper bound in the current lp solution.
+  int card_nonBasicAtUpper; 
+
+  /// Number of non basic variables (structural or slack) at their
+  /// lower bound in the current lp solution.
+  int card_nonBasicAtLower;
+
+  /// Characteristic vector for integer basic structural variables
+  /// with non integer value in the current lp solution.
+  int *cv_intBasicVar_frac;  
+
+  /// List of integer structural basic variables 
+  /// (in order of pivot in selected rows for cut generation).
+  int *intBasicVar_frac;
+
+  /// List of integer structural non basic variables.
+  int *intNonBasicVar; 
+
+  /// List of continuous non basic variables (structural or slack). 
+  // slacks are considered continuous (no harm if this is not the case).
+  int *contNonBasicVar;
+
+  /// List of non basic variables (structural or slack) at their 
+  /// upper bound. 
+  int *nonBasicAtUpper;
+
+  /// List of non basic variables (structural or slack) at their lower
+  /// bound.
+  int *nonBasicAtLower;
+
+  /// Number of rows in the reduced tableau (= card_intBasicVar_frac).
+  int mTab;
+
+  /// Number of columns in the reduced tableau (= card_contNonBasicVar)
+  int nTab;
+
+  /// Tableau of multipliers used to alter the rows used in generation.
+  /// Dimensions: mTab by mTab. Initially, pi_mat is the identity matrix.
+  int **pi_mat;
+
+  /// Current tableau for continuous non basic variables (structural or slack).
+  /// Only rows used for generation.
+  /// Dimensions: mTab by nTab.
+  double **contNonBasicTab;
+
+  /// Current tableau for integer non basic structural variables.
+  /// Only rows used for generation.
+  // Dimensions: mTab by card_intNonBasicVar.
+  double **intNonBasicTab;
+
+  /// Right hand side of the tableau.
+  /// Only rows used for generation.
+  double *rhsTab ;
+
+  /// Given optimal solution that should not be cut; only for debug. 
+  const double *given_optsol;
+
+  /// Number of entries in given_optsol.
+  int card_given_optsol;
+
+  /// Characteristic vectors of structural integer variables or continuous
+  /// variables currently fixed to integer values. 
+  int *is_integer;
+
+  /// Characteristic vector of the structural variables whose lower bound 
+  /// in absolute value is larger than LUB. 
+  int *low_is_lub;
+
+  /// Characteristic vector of the structural variables whose upper bound 
+  /// in absolute value is larger than LUB. 
+  int *up_is_lub;
+
+  /// Pointer on solver. Reset by each call to generateCuts().
+  OsiSolverInterface *solver;
+
+  /// Pointer on point to separate. Reset by each call to generateCuts().
+  const double *xlp;
+
+  /// Pointer on row activity. Reset by each call to generateCuts().
+  const double *rowActivity;
+
+  /// Pointer on column type. Reset by each call to generateCuts().
+  const char *colType;
+
+  /// Pointer on matrix of coefficient ordered by rows. 
+  /// Reset by each call to generateCuts().
+  const CoinPackedMatrix *byRow;
+
+  //@}
+};
+
+//#############################################################################
+/** A function that tests the methods in the CglRedSplit class. The
+    only reason for it not to be a member method is that this way it doesn't
+    have to be compiled into the library. And that's a gain, because the
+    library should be compiled with optimization on, but this method should be
+    compiled with debugging. */
+void CglRedSplitUnitTest(const OsiSolverInterface * siP,
+			 const std::string mpdDir );
+
+
+#endif