source: lemon-0.x/src/lemon/lp_base.h @ 1405:3626c7f10f14

/* -*- C++ -*-
 * src/lemon/lp_base.h - Part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
 *
 * Permission to use, modify and distribute this software is granted
 * provided that this copyright notice appears in all copies. For
 * precise terms see the accompanying LICENSE file.
 *
 * This software is provided "AS IS" with no warranty of any kind,
 * express or implied, and with no claim as to its suitability for any
 * purpose.
 *
 */

#ifndef LEMON_LP_BASE_H
#define LEMON_LP_BASE_H

#include<vector>
#include<map>
#include<limits>
#include<cmath>

#include<lemon/utility.h>
#include<lemon/error.h>
#include<lemon/invalid.h>

//#include"lin_expr.h"

///\file
///\brief The interface of the LP solver interface.
///\ingroup gen_opt_group
namespace lemon {
  
  ///Internal data structure to convert floating id's to fix one's
    
  ///\todo This might be implemented to be also usable in other places.
  class _FixId 
  {
    std::vector<int> index;
    std::vector<int> cross;
    int first_free;
  public:
    _FixId() : first_free(-1) {};
    ///Convert a floating id to a fix one

    ///\param n is a floating id
    ///\return the corresponding fix id
    int fixId(int n) {return cross[n];}
    ///Convert a fix id to a floating one

    ///\param n is a fix id
    ///\return the corresponding floating id
    int floatingId(int n) { return index[n];}
    ///Add a new floating id.

    ///\param n is a floating id
    ///\return the fix id of the new value
    ///\todo Multiple additions should also be handled.
    int insert(int n)
    {
      if(n>=int(cross.size())) {
        cross.resize(n+1);
        if(first_free==-1) {
          cross[n]=index.size();
          index.push_back(n);
        }
        else {
          cross[n]=first_free;
          int next=index[first_free];
          index[first_free]=n;
          first_free=next;
        }
        return cross[n];
      }
      ///\todo Create an own exception type.
      else throw LogicError(); //floatingId-s must form a continuous range;
    }
    ///Remove a fix id.

    ///\param n is a fix id
    ///
    void erase(int n) 
    {
      int fl=index[n];
      index[n]=first_free;
      first_free=n;
      for(int i=fl+1;i<int(cross.size());++i) {
        cross[i-1]=cross[i];
        index[cross[i]]--;
      }
      cross.pop_back();
    }
    ///An upper bound on the largest fix id.

    ///\todo Do we need this?
    ///
    std::size_t maxFixId() { return cross.size()-1; }
  
  };
    
  ///Common base class for LP solvers
  
  ///\todo Much more docs
  ///\ingroup gen_opt_group
  class LpSolverBase {

  public:

    ///\e
    enum SolveExitStatus {
      ///\e
      SOLVED = 0,
      ///\e
      UNSOLVED = 1
    };
      
    ///\e
    enum SolutionStatus {
      ///Feasible solution has'n been found (but may exist).

      ///\todo NOTFOUND might be a better name.
      ///
      UNDEFINED = 0,
      ///The problem has no feasible solution
      INFEASIBLE = 1,
      ///Feasible solution found
      FEASIBLE = 2,
      ///Optimal solution exists and found
      OPTIMAL = 3,
      ///The cost function is unbounded

      ///\todo Give a feasible solution and an infinite ray (and the
      ///corresponding bases)
      INFINITE = 4
    };
      
    ///The floating point type used by the solver
    typedef double Value;
    ///The infinity constant
    static const Value INF;
    ///The not a number constant
    static const Value NaN;
    
    ///Refer to a column of the LP.

    ///This type is used to refer to a column of the LP.
    ///
    ///Its value remains valid and correct even after the addition or erase of
    ///other columns.
    ///
    ///\todo Document what can one do with a Col (INVALID, comparing,
    ///it is similar to Node/Edge)
    class Col {
    protected:
      int id;
      friend class LpSolverBase;
    public:
      typedef Value ExprValue;
      typedef True LpSolverCol;
      Col() {}
      Col(const Invalid&) : id(-1) {}
      bool operator<(Col c) const  {return id<c.id;}
      bool operator==(Col c) const  {return id==c.id;}
      bool operator!=(Col c) const  {return id==c.id;}
    };

    ///Refer to a row of the LP.

    ///This type is used to refer to a row of the LP.
    ///
    ///Its value remains valid and correct even after the addition or erase of
    ///other rows.
    ///
    ///\todo Document what can one do with a Row (INVALID, comparing,
    ///it is similar to Node/Edge)
    class Row {
    protected:
      int id;
      friend class LpSolverBase;
    public:
      typedef Value ExprValue;
      typedef True LpSolverRow;
      Row() {}
      Row(const Invalid&) : id(-1) {}
      typedef True LpSolverRow;
      bool operator<(Row c) const  {return id<c.id;}
      bool operator==(Row c) const  {return id==c.id;}
      bool operator!=(Row c) const  {return id==c.id;} 
   };
    
    ///Linear expression of variables and a constant component
    
    ///This data structure strores a linear expression of the variables
    ///(\ref Col "Col"s) and also has a constant component.
    ///
    ///There are several ways to access and modify the contents of this
    ///container.
    ///- Its it fully compatible with \c std::map<Col,double>, so for expamle
    ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can
    ///read and modify the coefficients like
    ///these.
    ///\code
    ///e[v]=5;
    ///e[v]+=12;
    ///e.erase(v);
    ///\endcode
    ///or you can also iterate through its elements.
    ///\code
    ///double s=0;
    ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i)
    ///  s+=i->second;
    ///\endcode
    ///(This code computes the sum of all coefficients).
    ///- Numbers (<tt>double</tt>'s)
    ///and variables (\ref Col "Col"s) directly convert to an
    ///\ref Expr and the usual linear operations are defined so  
    ///\code
    ///v+w
    ///2*v-3.12*(v-w/2)+2
    ///v*2.1+(3*v+(v*12+w+6)*3)/2
    ///\endcode
    ///are valid \ref Expr "Expr"essions.
    ///The usual assignment operations are also defined.
    ///\code
    ///e=v+w;
    ///e+=2*v-3.12*(v-w/2)+2;
    ///e*=3.4;
    ///e/=5;
    ///\endcode
    ///- The constant member can be set and read by \ref constComp()
    ///\code
    ///e.constComp()=12;
    ///double c=e.constComp();
    ///\endcode
    ///
    ///\note \ref clear() not only sets all coefficients to 0 but also
    ///clears the constant components.
    ///
    ///\sa Constr
    ///
    class Expr : public std::map<Col,Value>
    {
    public:
      typedef LpSolverBase::Col Key; 
      typedef LpSolverBase::Value Value;
      
    protected:
      typedef std::map<Col,Value> Base;
      
      Value const_comp;
  public:
      typedef True IsLinExpression;
      ///\e
      Expr() : Base(), const_comp(0) { }
      ///\e
      Expr(const Key &v) : const_comp(0) {
        Base::insert(std::make_pair(v, 1));
      }
      ///\e
      Expr(const Value &v) : const_comp(v) {}
      ///\e
      void set(const Key &v,const Value &c) {
        Base::insert(std::make_pair(v, c));
      }
      ///\e
      Value &constComp() { return const_comp; }
      ///\e
      const Value &constComp() const { return const_comp; }
      
      ///Removes the components with zero coefficient.
      void simplify() {
        for (Base::iterator i=Base::begin(); i!=Base::end();) {
          Base::iterator j=i;
          ++j;
          if ((*i).second==0) Base::erase(i);
          j=i;
        }
      }

      ///Sets all coefficients and the constant component to 0.
      void clear() {
        Base::clear();
        const_comp=0;
      }

      ///\e
      Expr &operator+=(const Expr &e) {
        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
          (*this)[j->first]+=j->second;
        ///\todo it might be speeded up using "hints"
        const_comp+=e.const_comp;
        return *this;
      }
      ///\e
      Expr &operator-=(const Expr &e) {
        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
          (*this)[j->first]-=j->second;
        const_comp-=e.const_comp;
        return *this;
      }
      ///\e
      Expr &operator*=(const Value &c) {
        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
          j->second*=c;
        const_comp*=c;
        return *this;
      }
      ///\e
      Expr &operator/=(const Value &c) {
        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
          j->second/=c;
        const_comp/=c;
        return *this;
      }
    };
    
    ///Linear constraint

    ///This data stucture represents a linear constraint in the LP.
    ///Basically it is a linear expression with a lower or an upper bound
    ///(or both). These parts of the constraint can be obtained by the member
    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
    ///respectively.
    ///There are two ways to construct a constraint.
    ///- You can set the linear expression and the bounds directly
    ///  by the functions above.
    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
    ///  are defined between expressions, or even between constraints whenever
    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
    ///  \c s and \c t are numbers, then the followings are valid expressions
    ///  and thus they can be used directly e.g. in \ref addRow() whenever
    ///  it makes sense.
    ///  \code
    ///  e<=s
    ///  e<=f
    ///  s<=e<=t
    ///  e>=t
    ///  \endcode
    ///\warning The validity of a constraint is checked only at run time, so
    ///e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will compile, but will throw a
    ///\ref LogicError exception.
    class Constr
    {
    public:
      typedef LpSolverBase::Expr Expr;
      typedef Expr::Key Key;
      typedef Expr::Value Value;
      
//       static const Value INF;
//       static const Value NaN;

    protected:
      Expr _expr;
      Value _lb,_ub;
    public:
      ///\e
      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
      ///\e
      Constr(Value lb,const Expr &e,Value ub) :
        _expr(e), _lb(lb), _ub(ub) {}
      ///\e
      Constr(const Expr &e,Value ub) : 
        _expr(e), _lb(NaN), _ub(ub) {}
      ///\e
      Constr(Value lb,const Expr &e) :
        _expr(e), _lb(lb), _ub(NaN) {}
      ///\e
      Constr(const Expr &e) : 
        _expr(e), _lb(NaN), _ub(NaN) {}
      ///\e
      void clear() 
      {
        _expr.clear();
        _lb=_ub=NaN;
      }

      ///Reference to the linear expression 
      Expr &expr() { return _expr; }
      ///Cont reference to the linear expression 
      const Expr &expr() const { return _expr; }
      ///Reference to the lower bound.

      ///\return
      ///- -\ref INF: the constraint is lower unbounded.
      ///- -\ref NaN: lower bound has not been set.
      ///- finite number: the lower bound
      Value &lowerBound() { return _lb; }
      ///The const version of \ref lowerBound()
      const Value &lowerBound() const { return _lb; }
      ///Reference to the upper bound.

      ///\return
      ///- -\ref INF: the constraint is upper unbounded.
      ///- -\ref NaN: upper bound has not been set.
      ///- finite number: the upper bound
      Value &upperBound() { return _ub; }
      ///The const version of \ref upperBound()
      const Value &upperBound() const { return _ub; }
      ///Is the constraint lower bounded?
      bool lowerBounded() const { 
        using namespace std;
        return finite(_lb);
      }
      ///Is the constraint upper bounded?
      bool upperBounded() const {
        using namespace std;
        return finite(_ub);
      }
    };
    

  protected:
    _FixId rows;
    _FixId cols;

    //Abstract virtual functions
    virtual LpSolverBase &_newLp() = 0;
    virtual LpSolverBase &_copyLp() = 0;

    virtual int _addCol() = 0;
    virtual int _addRow() = 0;
    virtual void _setRowCoeffs(int i, 
                               int length,
                               int  const * indices, 
                               Value  const * values ) = 0;
    virtual void _setColCoeffs(int i, 
                               int length,
                               int  const * indices, 
                               Value  const * values ) = 0;
    virtual void _setColLowerBound(int i, Value value) = 0;
    virtual void _setColUpperBound(int i, Value value) = 0;
//     virtual void _setRowLowerBound(int i, Value value) = 0;
//     virtual void _setRowUpperBound(int i, Value value) = 0;
    virtual void _setRowBounds(int i, Value lower, Value upper) = 0;
    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
    virtual void _clearObj()=0;
//     virtual void _setObj(int length,
//                          int  const * indices, 
//                          Value  const * values ) = 0;
    virtual SolveExitStatus _solve() = 0;
    virtual Value _getPrimal(int i) = 0;
    virtual Value _getPrimalValue() = 0;
    virtual SolutionStatus _getPrimalStatus() = 0;
    virtual void _setMax() = 0;
    virtual void _setMin() = 0;
    
    //Own protected stuff
    
    //Constant component of the objective function
    Value obj_const_comp;
    


    
  public:

    ///\e
    LpSolverBase() : obj_const_comp(0) {}

    ///\e
    virtual ~LpSolverBase() {}

    ///Creates a new LP problem
    LpSolverBase &newLp() {return _newLp();}
    ///Makes a copy of the LP problem
    LpSolverBase &copyLp() {return _copyLp();}
    
    ///\name Build up and modify of the LP

    ///@{

    ///Add a new empty column (i.e a new variable) to the LP
    Col addCol() { Col c; c.id=cols.insert(_addCol()); return c;}

    ///\brief Adds several new columns
    ///(i.e a variables) at once
    ///
    ///This magic function takes a container as its argument
    ///and fills its elements
    ///with new columns (i.e. variables)
    ///\param t can be
    ///- a standard STL compatible iterable container with
    ///\ref Col as its \c values_type
    ///like
    ///\code
    ///std::vector<LpSolverBase::Col>
    ///std::list<LpSolverBase::Col>
    ///\endcode
    ///- a standard STL compatible iterable container with
    ///\ref Col as its \c mapped_type
    ///like
    ///\code
    ///std::map<AnyType,LpSolverBase::Col>
    ///\endcode
    ///- an iterable lemon \ref concept::WriteMap "write map" like 
    ///\code
    ///ListGraph::NodeMap<LpSolverBase::Col>
    ///ListGraph::EdgeMap<LpSolverBase::Col>
    ///\endcode
    ///\return The number of the created column.
#ifdef DOXYGEN
    template<class T>
    int addColSet(T &t) { return 0;} 
#else
    template<class T>
    typename enable_if<typename T::value_type::LpSolverCol,int>::type
    addColSet(T &t,dummy<0> = 0) {
      int s=0;
      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
      return s;
    }
    template<class T>
    typename enable_if<typename T::value_type::second_type::LpSolverCol,
                       int>::type
    addColSet(T &t,dummy<1> = 1) { 
      int s=0;
      for(typename T::iterator i=t.begin();i!=t.end();++i) {
        i->second=addCol();
        s++;
      }
      return s;
    }
    template<class T>
    typename enable_if<typename T::ValueSet::value_type::LpSolverCol,
                       int>::type
    addColSet(T &t,dummy<2> = 2) { 
      ///\bug <tt>return addColSet(t.valueSet());</tt> should also work.
      int s=0;
      for(typename T::ValueSet::iterator i=t.valueSet().begin();
          i!=t.valueSet().end();
          ++i)
        {
          *i=addCol();
          s++;
        }
      return s;
    }
#endif

    ///Add a new empty row (i.e a new constaint) to the LP

    ///This function adds a new empty row (i.e a new constaint) to the LP.
    ///\return The created row
    Row addRow() { Row r; r.id=rows.insert(_addRow()); return r;}

    ///Set a row (i.e a constaint) of the LP

    ///\param r is the row to be modified
    ///\param l is lower bound (-\ref INF means no bound)
    ///\param e is a linear expression (see \ref Expr)
    ///\param u is the upper bound (\ref INF means no bound)
    ///\bug This is a temportary function. The interface will change to
    ///a better one.
    ///\todo Option to control whether a constraint with a single variable is
    ///added or not.
    void setRow(Row r, Value l,const Expr &e, Value u) {
      std::vector<int> indices;
      std::vector<Value> values;
      indices.push_back(0);
      values.push_back(0);
      for(Expr::const_iterator i=e.begin(); i!=e.end(); ++i)
        if((*i).second!=0) { ///\bug EPSILON would be necessary here!!!
          indices.push_back(cols.floatingId((*i).first.id));
          values.push_back((*i).second);
        }
      _setRowCoeffs(rows.floatingId(r.id),indices.size()-1,
                    &indices[0],&values[0]);
//       _setRowLowerBound(rows.floatingId(r.id),l-e.constComp());
//       _setRowUpperBound(rows.floatingId(r.id),u-e.constComp());
       _setRowBounds(rows.floatingId(r.id),l-e.constComp(),u-e.constComp());
    }

    ///Set a row (i.e a constaint) of the LP

    ///\param r is the row to be modified
    ///\param c is a linear expression (see \ref Constr)
    void setRow(Row r, const Constr &c) {
      setRow(r,
             c.lowerBounded()?c.lowerBound():-INF,
             c.expr(),
             c.upperBounded()?c.upperBound():INF);
    }

    ///Add a new row (i.e a new constaint) to the LP

    ///\param l is the lower bound (-\ref INF means no bound)
    ///\param e is a linear expression (see \ref Expr)
    ///\param u is the upper bound (\ref INF means no bound)
    ///\return The created row.
    ///\bug This is a temportary function. The interface will change to
    ///a better one.
    Row addRow(Value l,const Expr &e, Value u) {
      Row r=addRow();
      setRow(r,l,e,u);
      return r;
    }

    ///Add a new row (i.e a new constaint) to the LP

    ///\param c is a linear expression (see \ref Constr)
    ///\return The created row.
    Row addRow(const Constr &c) {
      Row r=addRow();
      setRow(r,c);
      return r;
    }

    /// Set the lower bound of a column (i.e a variable)

    /// The upper bound of a variable (column) has to be given by an 
    /// extended number of type Value, i.e. a finite number of type 
    /// Value or -\ref INF.
    void colLowerBound(Col c, Value value) {
      _setColLowerBound(cols.floatingId(c.id),value);
    }
    /// Set the upper bound of a column (i.e a variable)

    /// The upper bound of a variable (column) has to be given by an 
    /// extended number of type Value, i.e. a finite number of type 
    /// Value or \ref INF.
    void colUpperBound(Col c, Value value) {
      _setColUpperBound(cols.floatingId(c.id),value);
    };
    /// Set the lower and the upper bounds of a column (i.e a variable)

    /// The lower and the upper bounds of
    /// a variable (column) have to be given by an 
    /// extended number of type Value, i.e. a finite number of type 
    /// Value, -\ref INF or \ref INF.
    void colBounds(Col c, Value lower, Value upper) {
      _setColLowerBound(cols.floatingId(c.id),lower);
      _setColUpperBound(cols.floatingId(c.id),upper);
    }
    
//     /// Set the lower bound of a row (i.e a constraint)

//     /// The lower bound of a linear expression (row) has to be given by an 
//     /// extended number of type Value, i.e. a finite number of type 
//     /// Value or -\ref INF.
//     void rowLowerBound(Row r, Value value) {
//       _setRowLowerBound(rows.floatingId(r.id),value);
//     };
//     /// Set the upper bound of a row (i.e a constraint)

//     /// The upper bound of a linear expression (row) has to be given by an 
//     /// extended number of type Value, i.e. a finite number of type 
//     /// Value or \ref INF.
//     void rowUpperBound(Row r, Value value) {
//       _setRowUpperBound(rows.floatingId(r.id),value);
//     };

    /// Set the lower and the upper bounds of a row (i.e a constraint)

    /// The lower and the upper bounds of
    /// a constraint (row) have to be given by an 
    /// extended number of type Value, i.e. a finite number of type 
    /// Value, -\ref INF or \ref INF.
    void rowBounds(Row c, Value lower, Value upper) {
      _setRowBounds(rows.floatingId(c.id),lower, upper);
      // _setRowUpperBound(rows.floatingId(c.id),upper);
    }
    
    ///Set an element of the objective function
    void objCoeff(Col c, Value v) {_setObjCoeff(cols.floatingId(c.id),v); };
    ///Set the objective function
    
    ///\param e is a linear expression of type \ref Expr.
    ///\bug The previous objective function is not cleared!
    void setObj(Expr e) {
      _clearObj();
      for (Expr::iterator i=e.begin(); i!=e.end(); ++i)
        objCoeff((*i).first,(*i).second);
      obj_const_comp=e.constComp();
    }

    ///Maximize
    void max() { _setMax(); }
    ///Minimize
    void min() { _setMin(); }

    
    ///@}


    ///\name Solve the LP

    ///@{

    ///\e
    SolveExitStatus solve() { return _solve(); }
    
    ///@}
    
    ///\name Obtain the solution

    ///@{

    ///\e
    SolutionStatus primalStatus() {
      return _getPrimalStatus();
    }

    ///\e
    Value primal(Col c) { return _getPrimal(cols.floatingId(c.id)); }

    ///\e

    ///\return
    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
    /// of the primal problem, depending on whether we minimize or maximize.
    ///- \ref NaN if no primal solution is found.
    ///- The (finite) objective value if an optimal solution is found.
    Value primalValue() { return _getPrimalValue()+obj_const_comp;}
    ///@}
    
  };  

  ///\e
  
  ///\relates LpSolverBase::Expr
  ///
  inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a,
                                      const LpSolverBase::Expr &b) 
  {
    LpSolverBase::Expr tmp(a);
    tmp+=b; ///\todo Doesn't STL have some special 'merge' algorithm?
    return tmp;
  }
  ///\e
  
  ///\relates LpSolverBase::Expr
  ///
  inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a,
                                      const LpSolverBase::Expr &b) 
  {
    LpSolverBase::Expr tmp(a);
    tmp-=b; ///\todo Doesn't STL have some special 'merge' algorithm?
    return tmp;
  }
  ///\e
  
  ///\relates LpSolverBase::Expr
  ///
  inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a,
                                      const LpSolverBase::Value &b) 
  {
    LpSolverBase::Expr tmp(a);
    tmp*=b; ///\todo Doesn't STL have some special 'merge' algorithm?
    return tmp;
  }
  
  ///\e
  
  ///\relates LpSolverBase::Expr
  ///
  inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a,
                                      const LpSolverBase::Expr &b) 
  {
    LpSolverBase::Expr tmp(b);
    tmp*=a; ///\todo Doesn't STL have some special 'merge' algorithm?
    return tmp;
  }
  ///\e
  
  ///\relates LpSolverBase::Expr
  ///
  inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a,
                                      const LpSolverBase::Value &b) 
  {
    LpSolverBase::Expr tmp(a);
    tmp/=b; ///\todo Doesn't STL have some special 'merge' algorithm?
    return tmp;
  }
  
  ///\e
  
  ///\relates LpSolverBase::Constr
  ///
  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
                                         const LpSolverBase::Expr &f) 
  {
    return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0);
  }

  ///\e
  
  ///\relates LpSolverBase::Constr
  ///
  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e,
                                         const LpSolverBase::Expr &f) 
  {
    return LpSolverBase::Constr(e,f);
  }

  ///\e
  
  ///\relates LpSolverBase::Constr
  ///
  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
                                         const LpSolverBase::Value &f) 
  {
    return LpSolverBase::Constr(e,f);
  }

  ///\e
  
  ///\relates LpSolverBase::Constr
  ///
  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
                                         const LpSolverBase::Expr &f) 
  {
    return LpSolverBase::Constr(-LpSolverBase::INF,f-e,0);
  }


  ///\e
  
  ///\relates LpSolverBase::Constr
  ///
  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e,
                                         const LpSolverBase::Expr &f) 
  {
    return LpSolverBase::Constr(f,e);
  }


  ///\e
  
  ///\relates LpSolverBase::Constr
  ///
  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
                                         const LpSolverBase::Value &f) 
  {
    return LpSolverBase::Constr(f,e);
  }

  ///\e
  
  ///\relates LpSolverBase::Constr
  ///
  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
                                         const LpSolverBase::Expr &f) 
  {
    return LpSolverBase::Constr(0,e-f,0);
  }

  ///\e
  
  ///\relates LpSolverBase::Constr
  ///
  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n,
                                         const LpSolverBase::Constr&c) 
  {
    LpSolverBase::Constr tmp(c);
    ///\todo Create an own exception type.
    if(!isnan(tmp.lowerBound())) throw LogicError();
    else tmp.lowerBound()=n;
    return tmp;
  }
  ///\e
  
  ///\relates LpSolverBase::Constr
  ///
  inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c,
                                         const LpSolverBase::Value &n)
  {
    LpSolverBase::Constr tmp(c);
    ///\todo Create an own exception type.
    if(!isnan(tmp.upperBound())) throw LogicError();
    else tmp.upperBound()=n;
    return tmp;
  }

  ///\e
  
  ///\relates LpSolverBase::Constr
  ///
  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n,
                                         const LpSolverBase::Constr&c) 
  {
    LpSolverBase::Constr tmp(c);
    ///\todo Create an own exception type.
    if(!isnan(tmp.upperBound())) throw LogicError();
    else tmp.upperBound()=n;
    return tmp;
  }
  ///\e
  
  ///\relates LpSolverBase::Constr
  ///
  inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c,
                                         const LpSolverBase::Value &n)
  {
    LpSolverBase::Constr tmp(c);
    ///\todo Create an own exception type.
    if(!isnan(tmp.lowerBound())) throw LogicError();
    else tmp.lowerBound()=n;
    return tmp;
  }


} //namespace lemon

#endif //LEMON_LP_BASE_H