RhodeCode

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2008

 * 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_BITS_LP_SOLVER_ID_H

#define LEMON_BITS_LP_SOLVER_ID_H

namespace lemon {

  namespace _lp_bits {

    struct LpIdImpl {

      std::vector<int> index;

      std::vector<int> cross;

      int first_index;

      int first_free;

    };

    class LpId {

    public:

      class IdHandler {

      public:

        virtual ~IdHandler() {}

        virtual int addId(LpIdImpl&) = 0;

        virtual void eraseId(LpIdImpl&, int xn) = 0;

      };

      LpId(int min_index = 0) {

        id_handler = 0;

        impl.first_free = -1;

        impl.first_index = min_index;

        impl.cross.resize(impl.first_index);

      }

      LpId(const LpId& li) {

        id_handler = 0;

        impl = li.impl;

      }

      LpId& operator=(const LpId& li) {

        id_handler = 0;

        impl = li.impl;

        return *this;

      }

      void setIdHandler(IdHandler& ih) {

        id_handler = &ih;

      }

      int fixId(int fn) const {return impl.cross[fn];}

      int floatingId(int xn) const {return impl.index[xn];}

      int addId() {

        if (id_handler == 0) {

          int xn, fn = impl.cross.size();

          if (impl.first_free == -1) {

            xn = impl.index.size();

            impl.index.push_back(fn);

          } else {

            xn = impl.first_free;

            impl.first_free = impl.index[impl.first_free];

            impl.index[xn] = fn;

          }

          impl.cross.push_back(xn);

          return xn;

        } else {

          return id_handler->addId(impl);

        }

      }

      void eraseId(int xn) {

        if (id_handler == 0) {

          int fn = impl.index[xn];

          impl.index[xn] = impl.first_free;

          impl.first_free = xn;

          for(int i = fn + 1; i < int(impl.cross.size()); ++i) {

            impl.cross[i - 1] = impl.cross[i];

            impl.index[impl.cross[i]]--;

          }

          impl.cross.pop_back();

        } else {

          id_handler->eraseId(impl, xn);

        }

      }

      void firstFloating(int& fn) const {

        fn = impl.first_index;

        if (fn == int(impl.cross.size())) fn = -1;

      }

      void nextFloating(int& fn) const {

        ++fn;

        if (fn == int(impl.cross.size())) fn = -1;

      }

      void firstFix(int& xn) const {

        int fn;

        firstFloating(fn);

        xn = fn != -1 ? fixId(fn) : -1;

      }

      void nextFix(int& xn) const {

        int fn = floatingId(xn);

        nextFloating(fn);

        xn = fn != -1 ? fixId(fn) : -1;

      }

    protected:

      LpIdImpl impl;

      IdHandler *id_handler;

    };

    class RelocateIdHandler : public LpId::IdHandler {

    public:

      virtual int addId(LpIdImpl& impl) {

        int xn, fn = impl.cross.size();

        if (impl.first_free == -1) {

          xn = impl.index.size();

          impl.index.push_back(fn);

        } else {

          xn = impl.first_free;

          impl.first_free = impl.index[impl.first_free];

          impl.index[xn] = fn;

        }

        impl.cross.push_back(xn);

        return xn;

      }

      virtual void eraseId(LpIdImpl& impl, int xn) {

        int fn = impl.index[xn];

        impl.index[xn] = impl.first_free;

        impl.first_free = xn;

        impl.cross[fn] = impl.cross.back();

        impl.index[impl.cross.back()] = fn;

        impl.cross.pop_back();

      }

    };

  }

}

#endif

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2008

 * 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_H

#define LEMON_LP_H

#include<lemon/config.h>

#ifdef HAVE_GLPK

#include <lemon/lp_glpk.h>

#include <lemon/mip_glpk.h>

#elif HAVE_CPLEX

#include <lemon/lp_cplex.h>

#include <lemon/mip_cplex.h>

#elif HAVE_SOPLEX

#include <lemon/lp_soplex.h>

#endif

///\file

///\brief Defines a default LP solver

///\ingroup lp_group

namespace lemon {

#ifdef DOXYGEN

  ///The default LP solver identifier

  ///The default LP solver identifier.

  ///\ingroup lp_group

  ///

  ///Currently, the possible values are \c GLPK or \c CPLEX

#define DEFAULT_LP SOLVER

  ///The default LP solver

  ///The default LP solver.

  ///\ingroup lp_group

  ///

  ///Currently, it is either \c LpGlpk or \c LpCplex

  typedef LpGlpk Lp;

  ///The default LP solver identifier string

  ///The default LP solver identifier string.

  ///\ingroup lp_group

  ///

  ///Currently, the possible values are "GLPK" or "CPLEX"

  const char default_solver_name[]="SOLVER";

  ///The default ILP solver.

  ///The default ILP solver.

  ///\ingroup lp_group

  ///

  ///Currently, it is either \c LpGlpk or \c LpCplex

  typedef MipGlpk Mip;

#else

#ifdef HAVE_GLPK

#define DEFAULT_LP GLPK

  typedef LpGlpk Lp;

  typedef MipGlpk Mip;

  const char default_solver_name[]="GLPK";

#elif HAVE_CPLEX

#define DEFAULT_LP CPLEX

  typedef LpCplex Lp;

  typedef MipCplex Mip;

  const char default_solver_name[]="CPLEX";

#elif HAVE_SOPLEX

#define DEFAULT_LP SOPLEX

  typedef LpSoplex Lp;

  const char default_solver_name[]="SOPLEX";

#endif

#endif

} //namespace lemon

#endif //LEMON_LP_H

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2008

 * 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.

 *

 */

///\file

///\brief The implementation of the LP solver interface.

#include <lemon/lp_base.h>

namespace lemon {

  const LpSolverBase::Value

  LpSolverBase::INF = std::numeric_limits<Value>::infinity();

  const LpSolverBase::Value

  LpSolverBase::NaN = std::numeric_limits<Value>::quiet_NaN();

//   const LpSolverBase::Constr::Value

//   LpSolverBase::Constr::INF = std::numeric_limits<Value>::infinity();

//   const LpSolverBase::Constr::Value

//   LpSolverBase::Constr::NaN = std::numeric_limits<Value>::quiet_NaN();

} //namespace lemon

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2008

 * 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<iostream>

#include<vector>

#include<map>

#include<limits>

#include<lemon/math.h>

#include<lemon/core.h>

#include<lemon/bits/lp_id.h>

///\file

///\brief The interface of the LP solver interface.

///\ingroup lp_group

namespace lemon {

  /// Function to decide whether a floating point value is finite or not.

  /// Retruns true if the argument is not infinity, minus infinity or NaN.

  /// It does the same as the isfinite() function defined by C99.

  template <typename T>

  bool isFinite(T value)

  {

    typedef std::numeric_limits<T> Lim;

    if ((Lim::has_infinity && (value == Lim::infinity() || value ==

                               -Lim::infinity())) ||

        ((Lim::has_quiet_NaN || Lim::has_signaling_NaN) && value != value))

    {

      return false;

    }

    return true;

  }

  ///Common base class for LP solvers

  ///\todo Much more docs

  ///\ingroup lp_group

  class LpSolverBase {

  protected:

    _lp_bits::LpId rows;

    _lp_bits::LpId cols;

  public:

    ///Possible outcomes of an LP solving procedure

    enum SolveExitStatus {

      ///This means that the problem has been successfully solved: either

      ///an optimal solution has been found or infeasibility/unboundedness

      ///has been proved.

      SOLVED = 0,

      ///Any other case (including the case when some user specified

      ///limit has been exceeded)

      UNSOLVED = 1

    };

      ///\e

    enum SolutionStatus {

      ///Feasible solution hasn't 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

    };

    ///\e The type of the investigated LP problem

    enum ProblemTypes {

      ///Primal-dual feasible

      PRIMAL_DUAL_FEASIBLE = 0,

      ///Primal feasible dual infeasible

      PRIMAL_FEASIBLE_DUAL_INFEASIBLE = 1,

      ///Primal infeasible dual feasible

      PRIMAL_INFEASIBLE_DUAL_FEASIBLE = 2,

      ///Primal-dual infeasible

      PRIMAL_DUAL_INFEASIBLE = 3,

      ///Could not determine so far

      UNKNOWN = 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;

    static inline bool isNaN(const Value& v) { return v!=v; }

    friend class Col;

    friend class ColIt;

    friend class Row;

    ///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;

      friend class MipSolverBase;

      explicit Col(int _id) : id(_id) {}

    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;}

      bool operator!=(Col c) const  {return id!=c.id;}

    };

    class ColIt : public Col {

      const LpSolverBase *_lp;

    public:

      ColIt() {}

      ColIt(const LpSolverBase &lp) : _lp(&lp)

      {

        _lp->cols.firstFix(id);

      }

      ColIt(const Invalid&) : Col(INVALID) {}

      ColIt &operator++()

      {

        _lp->cols.nextFix(id);

        return *this;

      }

    };

    static int id(const Col& col) { return col.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;

      explicit Row(int _id) : id(_id) {}

    public:

      typedef Value ExprValue;

      typedef True LpSolverRow;

      Row() {}

      Row(const Invalid&) : id(-1) {}

      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;}

      bool operator!=(Row c) const  {return id!=c.id;}

    };

    class RowIt : public Row {

      const LpSolverBase *_lp;

    public:

      RowIt() {}

      RowIt(const LpSolverBase &lp) : _lp(&lp)

      {

        _lp->rows.firstFix(id);

      }

      RowIt(const Invalid&) : Row(INVALID) {}

      RowIt &operator++()

      {

        _lp->rows.nextFix(id);

        return *this;

      }

    };

    static int id(const Row& row) { return row.id; }

  protected:

    int _lpId(const Col& c) const {

      return cols.floatingId(id(c));

    }

    int _lpId(const Row& r) const {

      return rows.floatingId(id(r));

    }

    Col _item(int i, Col) const {

      return Col(cols.fixId(i));

    }

    Row _item(int i, Row) const {

      return Row(rows.fixId(i));

    }

  public:

    ///Linear expression of variables and a constant component

    ///This data structure stores 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);

          i=j;

        }

      }

      void simplify() const {

        const_cast<Expr*>(this)->simplify();

      }

      ///Removes the coefficients closer to zero than \c tolerance.

      void simplify(double &tolerance) {

        for (Base::iterator i=Base::begin(); i!=Base::end();) {

          Base::iterator j=i;

          ++j;

          if (std::fabs((*i).second)<tolerance) Base::erase(i);

          i=j;

        }

      }

      ///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;

        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

    ///  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 

    ///an assertion.

    class Constr

    {

    public:

      typedef LpSolverBase::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) {}

      ///\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 "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 isFinite(_lb);

      }

      ///Is the constraint upper bounded?

      bool upperBounded() const {

        return isFinite(_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.

    ///- Its it fully compatible with \c std::map<Row,double>, so for expamle

    ///if \c e is an DualExpr and \c v

    ///and \c w are of type \ref Row, 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::DualExpr::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 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 "DualExpr"essions.

    ///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 : public std::map<Row,Value>

    {

    public:

      typedef LpSolverBase::Row Key;

      typedef LpSolverBase::Value Value;

    protected:

      typedef std::map<Row,Value> Base;

    public:

      typedef True IsLinExpression;

      ///\e

      DualExpr() : Base() { }

      ///\e

      DualExpr(const Key &v) {

        Base::insert(std::make_pair(v, 1));

      }

      ///\e

      void set(const Key &v,const Value &c) {

        Base::insert(std::make_pair(v, c));

      }

      ///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);

          i=j;

        }

      }

      void simplify() const {

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

      }

      ///Removes the coefficients closer to zero than \c tolerance.

      void simplify(double &tolerance) {

        for (Base::iterator i=Base::begin(); i!=Base::end();) {

          Base::iterator j=i;

          ++j;

          if (std::fabs((*i).second)<tolerance) Base::erase(i);

          i=j;

        }

      }

      ///Sets all coefficients to 0.

      void clear() {

        Base::clear();

      }

      ///\e

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

        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)

          (*this)[j->first]+=j->second;

        return *this;

      }

      ///\e

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

        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)

          (*this)[j->first]-=j->second;

        return *this;

      }

      ///\e

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

        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)

          j->second*=c;

        return *this;

      }

      ///\e

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

        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)

          j->second/=c;

        return *this;

      }

    };

  private:

    template <typename _Expr>

    class MappedOutputIterator {

    public:

      typedef std::insert_iterator<_Expr> Base;

      typedef std::output_iterator_tag iterator_category;

      typedef void difference_type;

      typedef void value_type;

      typedef void reference;

      typedef void pointer;

      MappedOutputIterator(const Base& _base, const LpSolverBase& _lp)

        : base(_base), lp(_lp) {}

      MappedOutputIterator& operator*() {

        return *this;

      }

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

        *base = std::make_pair(lp._item(value.first, typename _Expr::Key()),

                               value.second);

        return *this;

      }

      MappedOutputIterator& operator++() {

        ++base;

        return *this;

      }

      MappedOutputIterator operator++(int) {

        MappedOutputIterator tmp(*this);

        ++base;

        return tmp;

      }

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

        return base == it.base;

      }

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

        return base != it.base;

      }

    private:

      Base base;

      const LpSolverBase& lp;

    };

    template <typename Expr>

    class MappedInputIterator {

    public:

      typedef typename Expr::const_iterator Base;

      typedef typename Base::iterator_category iterator_category;

      typedef typename Base::difference_type 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;

      };

      MappedInputIterator(const Base& _base, const LpSolverBase& _lp)

        : base(_base), lp(_lp) {}

      reference operator*() {

        return std::make_pair(lp._lpId(base->first), base->second);

      }

      pointer operator->() {

        return pointer(operator*());

      }

      MappedInputIterator& operator++() {

        ++base;

        return *this;

      }

      MappedInputIterator operator++(int) {

        MappedInputIterator tmp(*this);

        ++base;

        return tmp;

      }

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

        return base == it.base;

      }

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

        return base != it.base;

      }

    private:

      Base base;

      const LpSolverBase& lp;

    };

  protected:

    /// STL compatible iterator for lp col

    typedef MappedInputIterator<Expr> ConstRowIterator;

    /// STL compatible iterator for lp row

    typedef MappedInputIterator<DualExpr> ConstColIterator;

    /// STL compatible iterator for lp col

    typedef MappedOutputIterator<Expr> RowIterator;

    /// STL compatible iterator for lp row

    typedef MappedOutputIterator<DualExpr> ColIterator;

    //Abstract virtual functions

    virtual LpSolverBase* _newLp() = 0;

    virtual LpSolverBase* _copyLp(){

      LpSolverBase* newlp = _newLp();

      std::map<Col, Col> ref;

      for (LpSolverBase::ColIt it(*this); it != INVALID; ++it) {

        Col ccol = newlp->addCol();

        ref[it] = ccol;

        newlp->colName(ccol, colName(it));

        newlp->colLowerBound(ccol, colLowerBound(it));

        newlp->colUpperBound(ccol, colUpperBound(it));

      }

      for (LpSolverBase::RowIt it(*this); it != INVALID; ++it) {

        Expr e = row(it), ce;

        for (Expr::iterator jt = e.begin(); jt != e.end(); ++jt) {

          ce[ref[jt->first]] = jt->second;

        }

        ce += e.constComp();

        Row r = newlp->addRow(ce);

        double lower, upper;

        getRowBounds(it, lower, upper);

        newlp->rowBounds(r, lower, upper);

      }

      return newlp;

    };

    virtual int _addCol() = 0;

    virtual int _addRow() = 0;

    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 _setRowCoeffs(int i, ConstRowIterator b,

                               ConstRowIterator e) = 0;

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

    virtual void _setColCoeffs(int i, ConstColIterator b,

                               ConstColIterator e) = 0;

    virtual void _getColCoeffs(int i, ColIterator 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 _setRowBounds(int i, Value lower, Value upper) = 0;

    virtual void _getRowBounds(int i, Value &lower, Value &upper) const = 0;

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

    virtual Value _getObjCoeff(int i) const = 0;

    virtual void _clearObj()=0;

    virtual SolveExitStatus _solve() = 0;

    virtual Value _getPrimal(int i) const = 0;

    virtual Value _getDual(int i) const = 0;

    virtual Value _getPrimalValue() const = 0;

    virtual bool _isBasicCol(int i) const = 0;

    virtual SolutionStatus _getPrimalStatus() const = 0;

    virtual SolutionStatus _getDualStatus() const = 0;

    virtual ProblemTypes _getProblemType() const = 0;

    virtual void _setMax() = 0;

    virtual void _setMin() = 0;

    virtual bool _isMax() const = 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 the LP

    ///@{

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

    Col addCol() { Col c; _addCol(); c.id = cols.addId(); return c;}

    ///\brief Adds several new columns

    ///(i.e a variables) at once

    ///