RhodeCode

      public:

        /// Sets the iterator to the first term

        /// Sets the iterator to the first term of the expression.

        ///

        CoeffIt(Expr& e)

          : _it(e.comps.begin()), _end(e.comps.end()){}

        /// Convert the iterator to the column of the term

        operator Col() const {

          return colFromId(_it->first);

        }

        /// Returns the coefficient of the term

        Value& operator*() { return _it->second; }

        /// Returns the coefficient of the term

        const Value& operator*() const { return _it->second; }

        /// Next term

        /// Assign the iterator to the next term.

        ///

        CoeffIt& operator++() { ++_it; return *this; }

        /// Equality operator

        bool operator==(Invalid) const { return _it == _end; }

        /// Inequality operator

        bool operator!=(Invalid) const { return _it != _end; }

      };

      /// Const iterator over the expression

      ///The iterator iterates over the terms of the expression. 

      /// 

      ///\code

      ///double s=0;

      ///for(LpBase::Expr::ConstCoeffIt i(e);i!=INVALID;++i)

      ///  s+=*i * primal(i);

      ///\endcode

      class ConstCoeffIt {

      private:

        std::map<int, Value>::const_iterator _it, _end;

      public:

        /// Sets the iterator to the first term

        /// Sets the iterator to the first term of the expression.

        ///

        ConstCoeffIt(const Expr& e)

          : _it(e.comps.begin()), _end(e.comps.end()){}

        /// Convert the iterator to the column of the term

        operator Col() const {

          return colFromId(_it->first);

        }

        /// Returns the coefficient of the term

        const Value& operator*() const { return _it->second; }

        /// Next term

        /// Assign the iterator to the next term.

        ///

        ConstCoeffIt& operator++() { ++_it; return *this; }

        /// Equality operator

        bool operator==(Invalid) const { return _it == _end; }

        /// Inequality operator

        bool operator!=(Invalid) const { return _it != _end; }

      };

    };

    ///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

    ///  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 fail an assertion.

    class Constr

    {

    public:

      typedef LpBase::Expr Expr;

      typedef Expr::Key Key;

      typedef Expr::Value Value;

    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) {}

      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 "INF": the constraint is lower unbounded.

      ///- \ref NaN "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 "INF": the constraint is upper unbounded.

      ///- \ref NaN "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 {

        return _lb != -INF && !isNaN(_lb);

      }

      ///Is the constraint upper bounded?

      bool upperBounded() const {

        return _ub != INF && !isNaN(_ub);

      }

    };

    ///Linear expression of rows

    ///This data structure represents a column of the matrix,

    ///thas is it strores a linear expression of the dual variables

    ///(\ref Row "Row"s).

    ///

    ///There are several ways to access and modify the contents of this

    ///container.

    ///\code

    ///e[v]=5;

    ///e[v]+=12;

    ///e.erase(v);

    ///\endcode

    ///or you can also iterate through its elements.

    ///\code

    ///double s=0;

    ///for(LpBase::DualExpr::ConstCoeffIt i(e);i!=INVALID;++i)

    ///  s+=*i;

    ///\endcode

    ///(This code computes the sum of all coefficients).

    ///- Numbers (<tt>double</tt>'s)

    ///and variables (\ref Row "Row"s) directly convert to an

    ///\ref DualExpr and the usual linear operations are defined, so

    ///\code

    ///v+w

    ///2*v-3.12*(v-w/2)

    ///v*2.1+(3*v+(v*12+w)*3)/2

    ///\endcode

    ///are valid \ref DualExpr dual expressions.

    ///The usual assignment operations are also defined.

    ///\code

    ///e=v+w;

    ///e+=2*v-3.12*(v-w/2);

    ///e*=3.4;

    ///e/=5;

    ///\endcode

    ///

    ///\sa Expr

    class DualExpr {

      friend class LpBase;

    public:

      /// The key type of the expression

      typedef LpBase::Row Key;

      /// The value type of the expression

      typedef LpBase::Value Value;

    protected:

      std::map<int, Value> comps;

    public:

      typedef True SolverExpr;

      /// Default constructor

      /// Construct an empty expression, the coefficients are

      /// initialized to zero.

      DualExpr() {}

      /// Construct an expression from a row

      /// Construct an expression, which has a term with \c r dual

      /// variable and 1.0 coefficient.

      DualExpr(const Row &r) {

        typedef std::map<int, Value>::value_type pair_type;

        comps.insert(pair_type(id(r), 1));

      }

      /// Returns the coefficient of the row

      Value operator[](const Row& r) const {

        std::map<int, Value>::const_iterator it = comps.find(id(r));

        if (it != comps.end()) {

          return it->second;

        } else {

          return 0;

        }

      }

      /// Returns the coefficient of the row

      Value& operator[](const Row& r) {

        return comps[id(r)];

      }

      /// Sets the coefficient of the row

      void set(const Row &r, const Value &v) {

        if (v != 0.0) {

          typedef std::map<int, Value>::value_type pair_type;

          comps.insert(pair_type(id(r), v));

        } else {

          comps.erase(id(r));

        }

      }

      /// \brief Removes the coefficients which's absolute value does

      /// not exceed \c epsilon. 

      void simplify(Value epsilon = 0.0) {

        std::map<int, Value>::iterator it=comps.begin();

        while (it != comps.end()) {

          std::map<int, Value>::iterator jt=it;

          ++jt;

          if (std::fabs((*it).second) <= epsilon) comps.erase(it);

          it=jt;

        }

      }

      void simplify(Value epsilon = 0.0) const {

        const_cast<DualExpr*>(this)->simplify(epsilon);

      }

      ///Sets all coefficients to 0.

      void clear() {

        comps.clear();

      }

      ///Compound assignment

      DualExpr &operator+=(const DualExpr &e) {

        for (std::map<int, Value>::const_iterator it=e.comps.begin();

             it!=e.comps.end(); ++it)

          comps[it->first]+=it->second;

        return *this;

      }

      ///Compound assignment

      DualExpr &operator-=(const DualExpr &e) {

        for (std::map<int, Value>::const_iterator it=e.comps.begin();

             it!=e.comps.end(); ++it)

          comps[it->first]-=it->second;

        return *this;

      }

      ///Multiply with a constant

      DualExpr &operator*=(const Value &v) {

        for (std::map<int, Value>::iterator it=comps.begin();

             it!=comps.end(); ++it)

          it->second*=v;

        return *this;

      }

      ///Division with a constant

      DualExpr &operator/=(const Value &v) {

        for (std::map<int, Value>::iterator it=comps.begin();

             it!=comps.end(); ++it)

          it->second/=v;

        return *this;

      }

      ///Iterator over the expression

      ///The iterator iterates over the terms of the expression. 

      /// 

      ///\code

      ///double s=0;

      ///for(LpBase::DualExpr::CoeffIt i(e);i!=INVALID;++i)

      ///  s+= *i * dual(i);

      ///\endcode

      class CoeffIt {

      private:

        std::map<int, Value>::iterator _it, _end;

      public:

        /// Sets the iterator to the first term

        /// Sets the iterator to the first term of the expression.

        ///

        CoeffIt(DualExpr& e)

          : _it(e.comps.begin()), _end(e.comps.end()){}

        /// Convert the iterator to the row of the term

        operator Row() const {

          return rowFromId(_it->first);

        }

        /// Returns the coefficient of the term

        Value& operator*() { return _it->second; }

        /// Returns the coefficient of the term

        const Value& operator*() const { return _it->second; }

        /// Next term

        /// Assign the iterator to the next term.

        ///

        CoeffIt& operator++() { ++_it; return *this; }

        /// Equality operator

        bool operator==(Invalid) const { return _it == _end; }

        /// Inequality operator

        bool operator!=(Invalid) const { return _it != _end; }

      };

      ///Iterator over the expression

      ///The iterator iterates over the terms of the expression. 

      /// 

      ///\code

      ///double s=0;

      ///for(LpBase::DualExpr::ConstCoeffIt i(e);i!=INVALID;++i)

      ///  s+= *i * dual(i);

      ///\endcode

      class ConstCoeffIt {

      private:

        std::map<int, Value>::const_iterator _it, _end;

      public:

        /// Sets the iterator to the first term

        /// Sets the iterator to the first term of the expression.

        ///

        ConstCoeffIt(const DualExpr& e)

          : _it(e.comps.begin()), _end(e.comps.end()){}

        /// Convert the iterator to the row of the term

        operator Row() const {

          return rowFromId(_it->first);

        }

        /// Returns the coefficient of the term

        const Value& operator*() const { return _it->second; }

        /// Next term

        /// Assign the iterator to the next term.

        ///

        ConstCoeffIt& operator++() { ++_it; return *this; }

        /// Equality operator

        bool operator==(Invalid) const { return _it == _end; }

        /// Inequality operator

        bool operator!=(Invalid) const { return _it != _end; }

      };

    };

  protected:

    class InsertIterator {

    private:

      std::map<int, Value>& _host;

      const _solver_bits::VarIndex& _index;

    public:

      typedef std::output_iterator_tag iterator_category;

      typedef void difference_type;

      typedef void value_type;

      typedef void reference;

      typedef void pointer;

      InsertIterator(std::map<int, Value>& host,

                   const _solver_bits::VarIndex& index)

        : _host(host), _index(index) {}

      InsertIterator& operator=(const std::pair<int, Value>& value) {

        typedef std::map<int, Value>::value_type pair_type;

        _host.insert(pair_type(_index[value.first], value.second));

        return *this;

      }

      InsertIterator& operator*() { return *this; }

      InsertIterator& operator++() { return *this; }

      InsertIterator operator++(int) { return *this; }

    };

    class ExprIterator {

    private:

      std::map<int, Value>::const_iterator _host_it;

      const _solver_bits::VarIndex& _index;

    public:

      typedef std::bidirectional_iterator_tag iterator_category;

      typedef std::ptrdiff_t difference_type;

      typedef const std::pair<int, Value> value_type;

      typedef value_type reference;

      class pointer {

      public:

        pointer(value_type& _value) : value(_value) {}

        value_type* operator->() { return &value; }

      private:

        value_type value;

      };

      ExprIterator(const std::map<int, Value>::const_iterator& host_it,

                   const _solver_bits::VarIndex& index)

        : _host_it(host_it), _index(index) {}

      reference operator*() {

        return std::make_pair(_index(_host_it->first), _host_it->second);

      }

      pointer operator->() {

        return pointer(operator*());

      }

      ExprIterator& operator++() { ++_host_it; return *this; }

      ExprIterator operator++(int) {

        ExprIterator tmp(*this); ++_host_it; return tmp;

      }

      ExprIterator& operator--() { --_host_it; return *this; }

      ExprIterator operator--(int) {

        ExprIterator tmp(*this); --_host_it; return tmp;

      }

      bool operator==(const ExprIterator& it) const {

        return _host_it == it._host_it;

      }

      bool operator!=(const ExprIterator& it) const {

        return _host_it != it._host_it;

      }

    };

  protected:

    //Abstract virtual functions

    virtual int _addColId(int col) { return cols.addIndex(col); }

    virtual int _addRowId(int row) { return rows.addIndex(row); }

    virtual void _eraseColId(int col) { cols.eraseIndex(col); }

    virtual void _eraseRowId(int row) { rows.eraseIndex(row); }

    virtual int _addCol() = 0;

    virtual int _addRow() = 0;

    virtual int _addRow(Value l, ExprIterator b, ExprIterator e, Value u) {

      int row = _addRow();

      _setRowCoeffs(row, b, e);

      _setRowLowerBound(row, l);

      _setRowUpperBound(row, u);

      return row;

    }

    virtual void _eraseCol(int col) = 0;

    virtual void _eraseRow(int row) = 0;

    virtual void _getColName(int col, std::string& name) const = 0;

    virtual void _setColName(int col, const std::string& name) = 0;

    virtual int _colByName(const std::string& name) const = 0;

    virtual void _getRowName(int row, std::string& name) const = 0;

    virtual void _setRowName(int row, const std::string& name) = 0;

    virtual int _rowByName(const std::string& name) const = 0;

    virtual void _setRowCoeffs(int i, ExprIterator b, ExprIterator e) = 0;

    virtual void _getRowCoeffs(int i, InsertIterator b) const = 0;

    virtual void _setColCoeffs(int i, ExprIterator b, ExprIterator e) = 0;

    virtual void _getColCoeffs(int i, InsertIterator b) const = 0;

    virtual void _setCoeff(int row, int col, Value value) = 0;

    virtual Value _getCoeff(int row, int col) const = 0;

    virtual void _setColLowerBound(int i, Value value) = 0;

    virtual Value _getColLowerBound(int i) const = 0;

    virtual void _setColUpperBound(int i, Value value) = 0;

    virtual Value _getColUpperBound(int i) const = 0;

    virtual void _setRowLowerBound(int i, Value value) = 0;

    virtual Value _getRowLowerBound(int i) const = 0;

    virtual void _setRowUpperBound(int i, Value value) = 0;

    virtual Value _getRowUpperBound(int i) const = 0;

    virtual void _setObjCoeffs(ExprIterator b, ExprIterator e) = 0;

    virtual void _getObjCoeffs(InsertIterator b) const = 0;

    virtual void _setObjCoeff(int i, Value obj_coef) = 0;

    virtual Value _getObjCoeff(int i) const = 0;

    virtual void _setSense(Sense) = 0;

    virtual Sense _getSense() const = 0;

    virtual void _clear() = 0;

    virtual const char* _solverName() const = 0;

    virtual void _messageLevel(MessageLevel level) = 0;

    //Own protected stuff

    //Constant component of the objective function

    Value obj_const_comp;

    LpBase() : rows(), cols(), obj_const_comp(0) {}

  public:

    /// Virtual destructor

    virtual ~LpBase() {}

    ///Gives back the name of the solver.

    const char* solverName() const {return _solverName();}

    ///\name Build Up and Modify the LP

    ///@{

    ///Add a new empty column (i.e a new variable) to the LP

    Col addCol() { Col c; c._id = _addColId(_addCol()); return c;}

    ///\brief Adds several new columns (i.e 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<LpBase::Col>

    ///std::list<LpBase::Col>

    ///\endcode

    ///- a standard STL compatible iterable container with

    ///\ref Col as its \c mapped_type like

    ///\code

    ///std::map<AnyType,LpBase::Col>

    ///\endcode

    ///- an iterable lemon \ref concepts::WriteMap "write map" like

    ///\code

    ///ListGraph::NodeMap<LpBase::Col>

    ///ListGraph::ArcMap<LpBase::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::LpCol,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::LpCol,

                       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::MapIt::Value::LpCol,

                       int>::type

    addColSet(T &t,dummy<2> = 2) {

      int s=0;

      for(typename T::MapIt i(t); i!=INVALID; ++i)

        {

          i.set(addCol());

          s++;

        }

      return s;

    }

#endif

    ///Set a column (i.e a dual constraint) of the LP

    ///\param c is the column to be modified

    ///\param e is a dual linear expression (see \ref DualExpr)

    ///a better one.

    void col(Col c, const DualExpr &e) {

      e.simplify();

      _setColCoeffs(cols(id(c)), ExprIterator(e.comps.begin(), rows),

                    ExprIterator(e.comps.end(), rows));

    }

    ///Get a column (i.e a dual constraint) of the LP

    ///\param c is the column to get

    ///\return the dual expression associated to the column

    DualExpr col(Col c) const {

      DualExpr e;

      _getColCoeffs(cols(id(c)), InsertIterator(e.comps, rows));

      return e;

    }

    ///Add a new column to the LP

    ///\param e is a dual linear expression (see \ref DualExpr)

    ///\param o is the corresponding component of the objective

    ///function. It is 0 by default.

    ///\return The created column.

    Col addCol(const DualExpr &e, Value o = 0) {

      Col c=addCol();

      col(c,e);

      objCoeff(c,o);

      return c;

    }

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

    ///This function adds a new empty row (i.e a new constraint) to the LP.

    ///\return The created row

    Row addRow() { Row r; r._id = _addRowId(_addRow()); return r;}

    ///\brief Add several new rows (i.e constraints) at once

    ///

    ///This magic function takes a container as its argument and fills

    ///its elements with new row (i.e. variables)

    ///\param t can be

    ///- a standard STL compatible iterable container with

    ///\ref Row as its \c values_type like

    ///\code

    ///std::vector<LpBase::Row>

    ///std::list<LpBase::Row>

    ///\endcode

    ///- a standard STL compatible iterable container with

    ///\ref Row as its \c mapped_type like

    ///\code

    ///std::map<AnyType,LpBase::Row>

    ///\endcode

    ///- an iterable lemon \ref concepts::WriteMap "write map" like

    ///\code

    ///ListGraph::NodeMap<LpBase::Row>

    ///ListGraph::ArcMap<LpBase::Row>

    ///\endcode

    ///\return The number of rows created.

#ifdef DOXYGEN

    template<class T>

    int addRowSet(T &t) { return 0;}

#else

    template<class T>

    typename enable_if<typename T::value_type::LpRow,int>::type

    addRowSet(T &t, dummy<0> = 0) {

      int s=0;

      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}

      return s;

    }

    template<class T>

    typename enable_if<typename T::value_type::second_type::LpRow, int>::type

    addRowSet(T &t, dummy<1> = 1) {

      int s=0;

      for(typename T::iterator i=t.begin();i!=t.end();++i) {

        i->second=addRow();

        s++;

      }

      return s;

    }

    template<class T>

    typename enable_if<typename T::MapIt::Value::LpRow, int>::type

    addRowSet(T &t, dummy<2> = 2) {

      int s=0;

      for(typename T::MapIt i(t); i!=INVALID; ++i)

        {

          i.set(addRow());

          s++;

        }

      return s;

    }

#endif

    ///Set a row (i.e a constraint) 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)

    void row(Row r, Value l, const Expr &e, Value u) {

      e.simplify();

      _setRowCoeffs(rows(id(r)), ExprIterator(e.comps.begin(), cols),

                    ExprIterator(e.comps.end(), cols));

      _setRowLowerBound(rows(id(r)),l - *e);

      _setRowUpperBound(rows(id(r)),u - *e);

    }

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

    ///\param r is the row to be modified

    ///\param c is a linear expression (see \ref Constr)

    void row(Row r, const Constr &c) {

      row(r, c.lowerBounded()?c.lowerBound():-INF,

          c.expr(), c.upperBounded()?c.upperBound():INF);

    }

    ///Get a row (i.e a constraint) of the LP

    ///\param r is the row to get

    ///\return the expression associated to the row

    Expr row(Row r) const {

      Expr e;

      _getRowCoeffs(rows(id(r)), InsertIterator(e.comps, cols));

      return e;

    }

    ///Add a new row (i.e a new constraint) 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.

    Row addRow(Value l,const Expr &e, Value u) {

      Row r;

      e.simplify();

      r._id = _addRowId(_addRow(l - *e, ExprIterator(e.comps.begin(), cols),

                                ExprIterator(e.comps.end(), cols), u - *e));

      return r;

    }

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

    ///\param c is a linear expression (see \ref Constr)

    ///\return The created row.

    Row addRow(const Constr &c) {

      Row r;

      c.expr().simplify();

                                ExprIterator(c.expr().comps.begin(), cols),

                                ExprIterator(c.expr().comps.end(), cols),

      return r;

    }

    ///Erase a column (i.e a variable) from the LP

    ///\param c is the column to be deleted

    void erase(Col c) {

      _eraseCol(cols(id(c)));

      _eraseColId(cols(id(c)));

    }

    ///Erase a row (i.e a constraint) from the LP

    ///\param r is the row to be deleted

    void erase(Row r) {

      _eraseRow(rows(id(r)));

      _eraseRowId(rows(id(r)));

    }

    /// Get the name of a column

    ///\param c is the coresponding column

    ///\return The name of the colunm

    std::string colName(Col c) const {

      std::string name;

      _getColName(cols(id(c)), name);

      return name;

    }

    /// Set the name of a column

    ///\param c is the coresponding column

    ///\param name The name to be given

    void colName(Col c, const std::string& name) {

      _setColName(cols(id(c)), name);

    }

    /// Get the column by its name

    ///\param name The name of the column

    ///\return the proper column or \c INVALID

    Col colByName(const std::string& name) const {

      int k = _colByName(name);

      return k != -1 ? Col(cols[k]) : Col(INVALID);

    }

    /// Get the name of a row

    ///\param r is the coresponding row

    ///\return The name of the row

    std::string rowName(Row r) const {

      std::string name;

      _getRowName(rows(id(r)), name);

      return name;

    }

    /// Set the name of a row

    ///\param r is the coresponding row

    ///\param name The name to be given

    void rowName(Row r, const std::string& name) {

      _setRowName(rows(id(r)), name);

    }

    /// Get the row by its name

    ///\param name The name of the row

    ///\return the proper row or \c INVALID

    Row rowByName(const std::string& name) const {

      int k = _rowByName(name);

      return k != -1 ? Row(rows[k]) : Row(INVALID);

    }

    /// Set an element of the coefficient matrix of the LP

    ///\param r is the row of the element to be modified

    ///\param c is the column of the element to be modified

    ///\param val is the new value of the coefficient

    void coeff(Row r, Col c, Value val) {

      _setCoeff(rows(id(r)),cols(id(c)), val);

    }

    /// Get an element of the coefficient matrix of the LP

    ///\param r is the row of the element

    ///\param c is the column of the element

    ///\return the corresponding coefficient

    Value coeff(Row r, Col c) const {

      return _getCoeff(rows(id(r)),cols(id(c)));

    }

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

    /// The lower 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(id(c)),value);

    }

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

    /// This function returns the lower bound for column (variable) \c c

    /// (this might be -\ref INF as well).

    ///\return The lower bound for column \c c

    Value colLowerBound(Col c) const {

      return _getColLowerBound(cols(id(c)));

    }

    ///\brief Set the lower bound of  several columns

    ///(i.e variables) at once

    ///

    ///This magic function takes a container as its argument

    ///and applies the function on all of its elements.

    ///The lower 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.

#ifdef DOXYGEN

    template<class T>

    void colLowerBound(T &t, Value value) { return 0;}

#else

    template<class T>

    typename enable_if<typename T::value_type::LpCol,void>::type

    colLowerBound(T &t, Value value,dummy<0> = 0) {

      for(typename T::iterator i=t.begin();i!=t.end();++i) {

        colLowerBound(*i, value);

      }

    }

    template<class T>

    typename enable_if<typename T::value_type::second_type::LpCol,

                       void>::type

    colLowerBound(T &t, Value value,dummy<1> = 1) {

      for(typename T::iterator i=t.begin();i!=t.end();++i) {

        colLowerBound(i->second, value);

      }

    }

    template<class T>

    typename enable_if<typename T::MapIt::Value::LpCol,

                       void>::type

    colLowerBound(T &t, Value value,dummy<2> = 2) {

      for(typename T::MapIt i(t); i!=INVALID; ++i){

        colLowerBound(*i, value);

      }

    }

#endif

    /// 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(id(c)),value);

    };

    /// Get the upper bound of a column (i.e a variable)

    /// This function returns the upper bound for column (variable) \c c

    /// (this might be \ref INF as well).

    /// \return The upper bound for column \c c

    Value colUpperBound(Col c) const {

      return _getColUpperBound(cols(id(c)));

    }

    ///\brief Set the upper bound of  several columns

    ///(i.e variables) at once

    ///

    ///This magic function takes a container as its argument

    ///and applies the function on all of its elements.

    ///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.

#ifdef DOXYGEN

    template<class T>

    void colUpperBound(T &t, Value value) { return 0;}

#else

    template<class T1>

    typename enable_if<typename T1::value_type::LpCol,void>::type

    colUpperBound(T1 &t, Value value,dummy<0> = 0) {

      for(typename T1::iterator i=t.begin();i!=t.end();++i) {

        colUpperBound(*i, value);

      }

    }

    template<class T1>

    typename enable_if<typename T1::value_type::second_type::LpCol,

                       void>::type

    colUpperBound(T1 &t, Value value,dummy<1> = 1) {

      for(typename T1::iterator i=t.begin();i!=t.end();++i) {

        colUpperBound(i->second, value);

      }

    }

    template<class T1>

    typename enable_if<typename T1::MapIt::Value::LpCol,

                       void>::type

    colUpperBound(T1 &t, Value value,dummy<2> = 2) {

      for(typename T1::MapIt i(t); i!=INVALID; ++i){

        colUpperBound(*i, value);

      }

    }

#endif

    /// 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(id(c)),lower);

      _setColUpperBound(cols(id(c)),upper);

    }

    ///\brief Set the lower and the upper bound of several columns

    ///(i.e variables) at once

    ///

    ///This magic function takes a container as its argument

    ///and applies the function on all of its elements.

    /// 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.

#ifdef DOXYGEN

    template<class T>

    void colBounds(T &t, Value lower, Value upper) { return 0;}

#else

    template<class T2>

    typename enable_if<typename T2::value_type::LpCol,void>::type

    colBounds(T2 &t, Value lower, Value upper,dummy<0> = 0) {

      for(typename T2::iterator i=t.begin();i!=t.end();++i) {

        colBounds(*i, lower, upper);

      }

    }

    template<class T2>

    typename enable_if<typename T2::value_type::second_type::LpCol, void>::type

    colBounds(T2 &t, Value lower, Value upper,dummy<1> = 1) {

      for(typename T2::iterator i=t.begin();i!=t.end();++i) {

        colBounds(i->second, lower, upper);

      }

    }

    template<class T2>

    typename enable_if<typename T2::MapIt::Value::LpCol, void>::type

    colBounds(T2 &t, Value lower, Value upper,dummy<2> = 2) {

      for(typename T2::MapIt i(t); i!=INVALID; ++i){

        colBounds(*i, lower, upper);

      }

    }

#endif

    /// Set the lower bound of a row (i.e a constraint)

    /// The lower bound of a constraint (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(id(r)),value);

    }

    /// Get the lower bound of a row (i.e a constraint)

    /// This function returns the lower bound for row (constraint) \c c

    /// (this might be -\ref INF as well).

    ///\return The lower bound for row \c r

    Value rowLowerBound(Row r) const {

      return _getRowLowerBound(rows(id(r)));

    }

    /// Set the upper bound of a row (i.e a constraint)

    /// The upper bound of a constraint (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(id(r)),value);

    }

    /// Get the upper bound of a row (i.e a constraint)

    /// This function returns the upper bound for row (constraint) \c c

    /// (this might be -\ref INF as well).

    ///\return The upper bound for row \c r

    Value rowUpperBound(Row r) const {

      return _getRowUpperBound(rows(id(r)));

    }

    ///Set an element of the objective function

    void objCoeff(Col c, Value v) {_setObjCoeff(cols(id(c)),v); };

    ///Get an element of the objective function

    Value objCoeff(Col c) const { return _getObjCoeff(cols(id(c))); };

    ///Set the objective function

    ///\param e is a linear expression of type \ref Expr.

    ///

    void obj(const Expr& e) {

      _setObjCoeffs(ExprIterator(e.comps.begin(), cols),

                    ExprIterator(e.comps.end(), cols));

      obj_const_comp = *e;

    }

    ///Get the objective function

    ///\return the objective function as a linear expression of type

    ///Expr.

    Expr obj() const {

      Expr e;

      _getObjCoeffs(InsertIterator(e.comps, cols));

      *e = obj_const_comp;

      return e;

    }

    ///Set the direction of optimization

    void sense(Sense sense) { _setSense(sense); }

    ///Query the direction of the optimization

    Sense sense() const {return _getSense(); }

    ///Set the sense to maximization

    void max() { _setSense(MAX); }

    ///Set the sense to maximization

    void min() { _setSense(MIN); }

    ///Clears the problem

    void clear() { _clear(); }

    /// Sets the message level of the solver

    void messageLevel(MessageLevel level) { _messageLevel(level); }

    ///@}

  };

  /// Addition

  ///\relates LpBase::Expr

  ///

  inline LpBase::Expr operator+(const LpBase::Expr &a, const LpBase::Expr &b) {

    LpBase::Expr tmp(a);

    tmp+=b;

    return tmp;

  }

  ///Substraction

  ///\relates LpBase::Expr