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+// Last edit: 04/03/10
+//
+// Name:     CglRedSplit2.hpp
+// Author:   Giacomo Nannicini
+//           Singapore University of Technology and Design
+//           Singapore
+//           email: nannicini@sutd.edu.sg
+//           based on CglRedSplit by Francois Margot
+// Date:     03/09/09
+//-----------------------------------------------------------------------------
+// Copyright (C) 2010, Giacomo Nannicini and others.  All Rights Reserved.
+
+#ifndef CglRedSplit2_H
+#define CglRedSplit2_H
+
+#include "CglCutGenerator.hpp"
+#include "CglRedSplit2Param.hpp"
+#include "CoinWarmStartBasis.hpp"
+#include "CoinHelperFunctions.hpp"
+#include "CoinTime.hpp"
+
+/** Reduce-and-Split Cut Generator Class; See method generateCuts().
+    Based on the papers "Practical strategies for generating rank-1
+    split cuts in mixed-integer linear programming" by G. Cornuejols
+    and G. Nannicini, published on Mathematical Programming
+    Computation, and "Combining Lift-and-Project and Reduce-and-Split"
+    by E. Balas, G. Cornuejols, T. Kis and G. Nannicini, published on
+    INFORMS Journal on Computing. Part of this code is based on
+    CglRedSplit by F. Margot. */
+
+class CglRedSplit2 : public CglCutGenerator {
+
+  friend void CglRedSplit2UnitTest(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.
+
+      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 a class of split cuts. We compute
+      linear combinations of the rows of the simplex tableau, trying
+      to reduce some of the coefficients on the nonbasic continuous
+      columns.  We have a large number of heuristics to choose which
+      coefficients should be reduced, and by using which rows. The
+      paper explains everything in detail.
+
+      Note that this generator can potentially generate a huge number
+      of cuts, depending on how it is parametered. Default parameters
+      should be good for most situations; if you want to go heavy on
+      split cuts, use more row selection strategies or a different
+      number of rows in the linear combinations. Again, look at the
+      paper for details. If you want to generate a small number of
+      cuts, default parameters are not the best choice.
+
+      A combination of Reduce-and-Split with Lift & Project is
+      described in the paper "Combining Lift-and-Project and
+      Reduce-and-Split". The Reduce-and-Split code for the
+      implementation used in that paper is included here.
+
+      This generator does not generate the same cuts as CglRedSplit,
+      therefore both generators can be used in conjunction.
+
+  */
+
+  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;
+
+  // Generate the row multipliers computed by Reduce-and-Split from the
+  // given OsiSolverInterface. The multipliers are written in lambda;
+  // lambda should be of size nrow*maxNumMultipliers. We generate at most
+  // maxNumMultipliers m-vectors of row multipliers, and return the number
+  // of m-vectors that were generated.
+  // If the caller wants to know which variables are basic in each row 
+  // (same order as lambda), basicVariables should be non-NULL (size nrow).
+  // This method can also generate the cuts corresponding to the multipliers
+  // returned; it suffices to pass non-NULL OsiCuts.
+  // This method is not needed by the typical user; however, it is useful
+  // in the context of generating Lift & Project cuts.
+  int generateMultipliers(const OsiSolverInterface& si, int* lambda,
+			  int maxNumMultipliers, int* basicVariables = NULL,
+			  OsiCuts* cs = NULL);
+
+  // Try to improve a Lift & Project cut, by employing the
+  // Reduce-and-Split procedure. We start from a row of a L&P tableau,
+  // and generate a cut trying to reduce the coefficients on the
+  // nonbasic variables.  Note that this L&P tableau will in general
+  // have nonbasic variables which are nonzero in the point that we
+  // want to cut off, so we should be careful.  Arguments:
+  // OsiSolverInterface which contains the simplex tableau, initial
+  // row from which the cut is derived, row rhs, row number of the
+  // source row (if it is in the simplex tableau; otherwise, a
+  // negative number; needed to avoid using duplicate rows), point
+  // that we want to cut off (note: this is NOT a basic solution for
+  // the OsiSolverInterace!), list of variables which are basic in
+  // xbar but are nonbasic in the OsiSolverInterface. The computed cut
+  // is written in OsiRowCut* cs. Finally, if a starting disjunction
+  // is provided in the vector lambda (of size ncols, i.e. a
+  // disjunction on the structural variables), the disjunction is
+  // modified according to the cut which is produced.
+  int tiltLandPcut(const OsiSolverInterface* si, double* row, 
+		   double rowRhs, int rownumber, const double* xbar, 
+		   const int* newnonbasics, OsiRowCut* cs, int* lambda = NULL);
+
+  //@}
+  
+  
+  /**@name Public Methods */
+  //@{
+
+  // Set the parameters to the values of the given CglRedSplit2Param object.
+  void setParam(const CglRedSplit2Param &source); 
+  // Return the CglRedSplit2Param object of the generator. 
+  inline CglRedSplit2Param& getParam() {return param;}
+
+  /// Print some of the data members; used for debugging
+  void print() const;
+
+  /// Print the current simplex tableau  
+  void printOptTab(OsiSolverInterface *solver) const;
+  
+  //@}
+
+  /**@name Constructors and destructors */
+  //@{
+  /// Default constructor 
+  CglRedSplit2();
+
+  /// Constructor with specified parameters 
+  CglRedSplit2(const CglRedSplit2Param &RS_param);
+ 
+  /// Copy constructor 
+  CglRedSplit2(const CglRedSplit2 &);
+
+  /// Clone
+  virtual CglCutGenerator * clone() const;
+
+  /// Assignment operator 
+  CglRedSplit2 & operator=(const CglRedSplit2& rhs);
+  
+  /// Destructor 
+  virtual ~CglRedSplit2 ();
+
+  //@}
+
+private:
+  
+  // Private member methods
+
+/**@name Private member methods */
+
+  //@{
+
+  // Method generating the cuts after all CglRedSplit2 members are 
+  // properly set. This does the actual work. Returns the number of
+  // generated cuts (or multipliers).
+  // Will generate cuts if cs != NULL, and will generate multipliers
+  // if lambda != NULL. 
+  int generateCuts(OsiCuts* cs, int maxNumCuts, int* lambda = NULL);
+
+  /// Compute the fractional part of value, allowing for small error.
+  inline double rs_above_integer(const double value) const; 
+
+  /// Fill workNonBasicTab, depending on the column selection strategy.
+  /// Accepts a list of variables indices that should be ignored; by
+  /// default, this list is empty (it is only used by Lift & Project).
+  /// The list ignore_list contains -1 as the last element.
+  /// Note that the implementation of the ignore_list is not very efficient
+  /// if the list is long, so it should be used only if its short.
+  void fill_workNonBasicTab(CglRedSplit2Param::ColumnSelectionStrategy 
+			    strategy, const int* ignore_list = NULL);
+
+  /// Fill workNonBasicTab, alternate version for Lift & Project: also
+  /// reduces columns which are now nonbasic but are basic in xbar.
+  /// This function should be called only when CglRedSplit2 is used in
+  /// conjunction with CglLandP to generate L&P+RS cuts.
+  void fill_workNonBasicTab(const int* newnonbasics, const double* xbar,
+			    CglRedSplit2Param::ColumnScalingStrategy scaling);
+
+  /// Reduce rows of workNonBasicTab, i.e. compute integral linear
+  /// combinations of the rows in order to reduce row coefficients on
+  /// workNonBasicTab
+  void reduce_workNonBasicTab(int numRows, 
+			      CglRedSplit2Param::RowSelectionStrategy 
+			      rowSelectionStrategy,
+			      int maxIterations);
+
+  /// Generate a linear combination of the rows of the current LP
+  /// tableau, using the row multipliers stored in the matrix pi_mat
+  /// on the row of index index_row
+  void generate_row(int index_row, double *row);
+
+  /// Generate a mixed integer Gomory cut, when all non basic 
+  /// variables are non negative and at their lower bound.
+  int generate_cgcut(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);
+
+  /// Returns 1 if the row has acceptable max/min coeff ratio.
+  /// Compute max_coeff: maximum absolute value of the coefficients.
+  /// Compute min_coeff: minimum absolute value of the coefficients
+  /// larger than EPS_COEFF.
+  /// Return 0 if max_coeff/min_coeff > MAXDYN.
+  int check_dynamism(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);
+
+  // Compute entries of is_integer.
+  void compute_is_integer();
+
+  // Check that two vectors are different.
+  bool rs_are_different_vectors(const int *vect1, 
+				const int *vect2,
+				const int dim);
+
+  // allocate matrix of integers
+  void rs_allocmatINT(int ***v, int m, int n);
+  // deallocate matrix of integers
+  void rs_deallocmatINT(int ***v, int m);
+  // allocate matrix of doubles
+  void rs_allocmatDBL(double ***v, int m, int n);
+  // deallocate matrix of doubles
+  void rs_deallocmatDBL(double ***v, int m);
+  // print a vector of integers
+  void rs_printvecINT(const char *vecstr, const int *x, int n) const;
+  // print a vector of doubles
+  void rs_printvecDBL(const char *vecstr, const double *x, int n) const;
+  // print a matrix of integers
+  void rs_printmatINT(const char *vecstr, const int * const *x, int m, int n) const;
+  // print a matrix of doubles
+  void rs_printmatDBL(const char *vecstr, const double * const *x, int m, int n) const;
+  // dot product
+  double rs_dotProd(const double *u, const double *v, int dim) const;
+  double rs_dotProd(const int *u, const double *v, int dim) const;
+  // From Numerical Recipes in C: LU decomposition
+  int ludcmp(double **a, int n, int *indx, double *d, double* vv) const;
+  // from Numerical Recipes in C: backward substitution
+  void lubksb(double **a, int n, int *indx, double *b) const;
+
+  // Check if the linear combination given by listOfRows with given multipliers
+  // improves the norm of row #rowindex; note: multipliers are rounded!
+  // Returns the difference with respect to the old norm (if negative there is
+  // an improvement, if positive norm increases)
+  double compute_norm_change(double oldnorm, const int* listOfRows,
+			     int numElemList, const double* multipliers) const;
+
+  // Compute the list of rows that should be used to reduce row #rowIndex
+  int get_list_rows_reduction(int rowIndex, int numRowsReduction, 
+			      int* list, const double* norm, 
+			      CglRedSplit2Param::RowSelectionStrategy 
+			      rowSelectionStrategy) const;
+
+  // Sorts the rows by increasing number of nonzeroes with respect to a given
+  // row (rowIndex), on the nonbasic variables (whichTab == 0 means only
+  // integer, whichTab == 1 means only workTab, whichTab == 2 means both).
+  // The array for sorting must be allocated (and deleted) by caller.
+  // Corresponds to BRS1 in the paper.
+  int sort_rows_by_nonzeroes(struct sortElement* array, int rowIndex, 
+			     int maxRows, int whichTab) const;
+
+  // Greedy variant of the previous function; slower but typically
+  // more effective. Corresponds to BRS2 in the paper.
+  int sort_rows_by_nonzeroes_greedy(struct sortElement* array, int rowIndex, 
+				    int maxRows, int whichTab) const;
+
+  // Sorts the rows by decreasing absolute value of the cosine of the
+  // angle with respect to a given row (rowIndex), on the nonbasic
+  // variables (whichTab == 0 means only integer, whichTab == 1 means
+  // only workTab, whichTab == 2 means both).  The array for sorting
+  // must be allocated (and deleted) by caller. Very effective
+  // strategy in practice. Corresponds to BRS3 in the paper.
+  int sort_rows_by_cosine(struct sortElement* array, int rowIndex, 
+			  int maxRows, int whichTab) const;
+
+  // Did we hit the time limit?
+  inline bool checkTime() const{
+    if ((CoinCpuTime() - startTime) < param.getTimeLimit()){
+      return true;
+    }
+    return false;
+  }
+
+  //@}
+
+  
+  // Private member data
+
+  /**@name Private member data */
+  
+  //@{
+
+  /// Object with CglRedSplit2Param members. 
+  CglRedSplit2Param param;
+
+  /// Number of rows ( = number of slack variables) in the current LP.
+  int nrow; 
+
+  /// Number of structural variables in the current LP.
+  int ncol;
+
+  /// Number of rows which have been reduced
+  int numRedRows;
+
+  /// 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;
+
+  /// Reduced costs for columns
+  const double *reducedCost;
+
+  /// Row price
+  const double *rowPrice;
+
+  /// Objective coefficients
+  const double* objective;
+
+  /// Number of integer basic structural variables 
+  int card_intBasicVar;
+
+  /// 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 continuous non basic variables (structural or slack) in the
+  /// current working set for coefficient reduction
+  int card_workNonBasicVar;
+
+  /// 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
+  int *cv_intBasicVar;  
+
+  /// Characteristic vector for integer basic structural variables
+  /// with non integer value in the current lp solution.
+  int *cv_intBasicVar_frac;  
+
+  /// Characteristic vector for rows of the tableau selected for reduction
+  /// with non integer value in the current lp solution
+  int *cv_fracRowsTab;  
+
+  /// List of integer structural basic variables 
+  /// (in order of pivot in selected rows for cut generation).
+  int *intBasicVar;
+
+  /// List of integer structural basic variables with fractional value
+  /// (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).
+  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;
+
+  /// Simplex tableau for continuous non basic variables (structural or slack).
+  /// Only rows used for generation.
+  /// Dimensions: mTab by card_contNonBasicVar.
+  double **contNonBasicTab;
+
+  /// Current tableau for continuous non basic variables (structural or slack).
+  /// Only columns used for coefficient reduction.
+  /// Dimensions: mTab by card_workNonBasicVar.
+  double **workNonBasicTab;
+
+  /// Simplex 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;
+
+  /// Norm of rows in workNonBasicTab; needed for faster computations
+  double *norm;
+
+  /// Characteristic vectors of structural integer variables or continuous
+  /// variables currently fixed to integer values. 
+  int *is_integer;
+
+  /// 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 matrix of coefficient ordered by rows. 
+  /// Reset by each call to generateCuts().
+  const CoinPackedMatrix *byRow;
+
+  /// Time at which cut computations began.
+  /// Reset by each call to generateCuts().
+  double startTime;
+
+  //@}
+};
+
+//#############################################################################
+/** A function that tests some of the methods in the CglRedSplit2
+    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 CglRedSplit2UnitTest(const OsiSolverInterface * siP,
+			 const std::string mpdDir );
+
+
+#endif