diff -r d8475431bbbb -r 8e85e6bbefdf lemon/lp_base.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/lp_base.h	Mon May 23 04:48:14 2005 +0000
@@ -0,0 +1,907 @@
+/* -*- C++ -*-
+ * 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 _setCoeff(int row, int col, Value value) = 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