/* $Id$
 *
 * Name:    exprMul.hpp
 * Author:  Pietro Belotti
 * Purpose: definition of multiplications
 *
 * (C) Carnegie-Mellon University, 2006-10.
 * This file is licensed under the Eclipse Public License (EPL)
 */

#ifndef COUENNE_EXPRMUL_H
#define COUENNE_EXPRMUL_H

#include <vector>

#include "CouenneExprOp.hpp"

namespace Couenne {

class CouenneCutGenerator;

/// class for multiplications, \f$ \prod_{i=1}^n f_i(x) \f$

class COUENNELIB_EXPORT exprMul: public exprOp {

 public:

  /// Constructor
  exprMul (expression **, int);

  /// Constructor with two arguments
  exprMul (expression *, expression *);

  /// Cloning method
  virtual expression *clone (Domain *d = NULL) const
  {return new exprMul (clonearglist (d), nargs_);}

  /// Print operator
  std::string printOp () const
  {return "*";}

  /// Method to evaluate the expression
  inline CouNumber operator () ();

  /// return l-2 norm of gradient at given point
  virtual CouNumber gradientNorm (const double *x);

  /// differentiation
  expression *differentiate (int index); 

  /// simplification
  expression *simplify ();

  /// get a measure of "how linear" the expression is:
  virtual int Linearity ();

  /// Get lower and upper bound of an expression (if any)
  virtual void getBounds (expression *&, expression *&);

  /// Get value of lower and upper bound of an expression (if any)
  virtual void getBounds (CouNumber &lb, CouNumber &ub);

  /// reduce expression in standard form, creating additional aux
  /// variables (and constraints)
  virtual exprAux *standardize (CouenneProblem *p, bool addAux = true);

  /// generate equality between *this and *w
  virtual void generateCuts (expression *w, //const OsiSolverInterface &si, 
			     OsiCuts &cs, const CouenneCutGenerator *cg, 
			     t_chg_bounds * = NULL, int = -1, 
			     CouNumber = -COUENNE_INFINITY, 
			     CouNumber =  COUENNE_INFINITY);

  /// code for comparison
  virtual enum expr_type code () 
  {return COU_EXPRMUL;}

  /// implied bound processing
  virtual bool impliedBound (int, CouNumber *, CouNumber *, t_chg_bounds *, 
			     enum Couenne::expression::auxSign = Couenne::expression::AUX_EQ);

  /// set up branching object by evaluating many branching points for
  /// each expression's arguments
  virtual CouNumber selectBranch (const CouenneObject *obj, 
				  const OsiBranchingInformation *info,
				  expression * &var, 
				  double * &brpts, 
 				  double * &brDist, // distance of current LP
					  	    // point to new convexifications
				  int &way);

  /// compute \f$y^{lv}\f$ and \f$y^{uv}\f$ for Violation Transfer algorithm
  virtual void closestFeasible (expression *varind,
				expression *vardep,
				CouNumber &left,
				CouNumber &right) const;
protected:

  /// inferring bounds on factors of a product
  int impliedBoundMul (CouNumber wl, 
		       CouNumber wu, 
		       std::vector <CouNumber> &xl,
		       std::vector <CouNumber> &xu,
		       std::vector <std::pair <int, CouNumber> > &nl,
		       std::vector <std::pair <int, CouNumber> > &nu);

  /// balanced strategy for branching point selection in products
  CouNumber balancedMul (const OsiBranchingInformation *info, int index, int wind);

  /// can this expression be further linearized or are we on its
  /// concave ("bad") side
  virtual bool isCuttable (CouenneProblem *problem, int index) const
  {return false;} // concave on both sides, as for products
};


/// compute multiplication
inline CouNumber exprMul:: operator () () {

  CouNumber ret = 1.;
  expression **al = arglist_;

  for (int n = nargs_; n--;)
    ret *= (**al++) ();

  return ret;
}


/// unified convexification of products and divisions
COUENNELIB_EXPORT
void unifiedProdCuts (const CouenneCutGenerator *, OsiCuts &, 
		      int, CouNumber, CouNumber, CouNumber,
		      int, CouNumber, CouNumber, CouNumber,
		      int, CouNumber, CouNumber, CouNumber,
		      t_chg_bounds *, enum expression::auxSign);


/// better cuts than those from unifiedProdCuts
COUENNELIB_EXPORT
void upperEnvHull (const CouenneCutGenerator *cg, OsiCuts &cs, 
		   int xi, CouNumber x0, CouNumber xl, CouNumber xu,
		   int yi, CouNumber y0, CouNumber yl, CouNumber yu,
		   int wi, CouNumber w0, CouNumber wl, CouNumber wu);


/// compute distance from future convexifications in set \f$\{(x,y,w):
/// w = xy\}\f$ with x,y,w bounded. Unified with exprDiv
COUENNELIB_EXPORT
double *computeMulBrDist (const OsiBranchingInformation *info,
			  int xi, int yi, int wi, int brind, double *brpt, int nPts = 1);

}

#endif