RhodeCode

        return *this;

      }

      ///Compound assignment

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

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

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

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

        const_comp-=e.const_comp;

        return *this;

      }

      ///Multiply with a constant

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

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

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

          it->second*=v;

        const_comp*=v;

        return *this;

      }

      ///Division with a constant

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

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

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

          it->second/=c;

        const_comp/=c;

        return *this;

      }

      ///Iterator over the expression

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

      /// 

      ///\code

      ///double s=0;

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

      ///  s+= *i * primal(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(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 {

      }

      ///Is the constraint upper bounded?

      bool upperBounded() const {

      }

    };

    ///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)

    /// 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(); }

    ///@}

  };

  /// 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

  ///

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

    LpBase::Expr tmp(a);

    tmp-=b;

    return tmp;

  }

  ///Multiply with constant

  ///\relates LpBase::Expr

  ///

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

    LpBase::Expr tmp(a);

    tmp*=b;

    return tmp;

  }

  ///Multiply with constant

  ///\relates LpBase::Expr

  ///

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

    LpBase::Expr tmp(b);

    tmp*=a;

    return tmp;

  }

  ///Divide with constant

  ///\relates LpBase::Expr

  ///

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

    LpBase::Expr tmp(a);

    tmp/=b;

    return tmp;

  }

  ///Create constraint

  ///\relates LpBase::Constr

  ///

  inline LpBase::Constr operator<=(const LpBase::Expr &e,

                                   const LpBase::Expr &f) {

    return LpBase::Constr(0, f - e, LpBase::INF);

  }

  ///Create constraint

  ///\relates LpBase::Constr

  ///

  inline LpBase::Constr operator<=(const LpBase::Value &e,

                                   const LpBase::Expr &f) {

    return LpBase::Constr(e, f, LpBase::NaN);

  }

  ///Create constraint

  ///\relates LpBase::Constr

  ///

  inline LpBase::Constr operator<=(const LpBase::Expr &e,

                                   const LpBase::Value &f) {

    return LpBase::Constr(- LpBase::INF, e, f);

  }

  ///Create constraint

  ///\relates LpBase::Constr

  ///

  inline LpBase::Constr operator>=(const LpBase::Expr &e,

                                   const LpBase::Expr &f) {

    return LpBase::Constr(0, e - f, LpBase::INF);

  }

  ///Create constraint

  ///\relates LpBase::Constr

  ///

  inline LpBase::Constr operator>=(const LpBase::Value &e,

                                   const LpBase::Expr &f) {

    return LpBase::Constr(LpBase::NaN, f, e);

  }

  ///Create constraint

  ///\relates LpBase::Constr

  ///

  inline LpBase::Constr operator>=(const LpBase::Expr &e,

                                   const LpBase::Value &f) {

    return LpBase::Constr(f, e, LpBase::INF);

  }

  ///Create constraint

  ///\relates LpBase::Constr

  ///

  inline LpBase::Constr operator==(const LpBase::Expr &e,

                                   const LpBase::Value &f) {

    return LpBase::Constr(f, e, f);

  }

  ///Create constraint

  ///\relates LpBase::Constr

  ///

  inline LpBase::Constr operator==(const LpBase::Expr &e,

                                   const LpBase::Expr &f) {

    return LpBase::Constr(0, f - e, 0);

  }

  ///Create constraint

  ///\relates LpBase::Constr

  ///

  inline LpBase::Constr operator<=(const LpBase::Value &n,

                                   const LpBase::Constr &c) {

    LpBase::Constr tmp(c);

    tmp.lowerBound()=n;

    return tmp;

  }

  ///Create constraint

  ///\relates LpBase::Constr

  ///

  inline LpBase::Constr operator<=(const LpBase::Constr &c,

                                   const LpBase::Value &n)

  {

    LpBase::Constr tmp(c);

    tmp.upperBound()=n;

    return tmp;

  }

  ///Create constraint

  ///\relates LpBase::Constr

  ///

  inline LpBase::Constr operator>=(const LpBase::Value &n,

                                   const LpBase::Constr &c) {

    LpBase::Constr tmp(c);

    tmp.upperBound()=n;

    return tmp;

  }

  ///Create constraint

  ///\relates LpBase::Constr

  ///

  inline LpBase::Constr operator>=(const LpBase::Constr &c,

                                   const LpBase::Value &n)

  {

    LpBase::Constr tmp(c);

    tmp.lowerBound()=n;

    return tmp;

  }

  ///Addition

  ///\relates LpBase::DualExpr

  ///

  inline LpBase::DualExpr operator+(const LpBase::DualExpr &a,

                                    const LpBase::DualExpr &b) {

    LpBase::DualExpr tmp(a);

    tmp+=b;

    return tmp;

  }

  ///Substraction

  ///\relates LpBase::DualExpr

  ///

  inline LpBase::DualExpr operator-(const LpBase::DualExpr &a,

                                    const LpBase::DualExpr &b) {

    LpBase::DualExpr tmp(a);

    tmp-=b;

    return tmp;

  }

  ///Multiply with constant

  ///\relates LpBase::DualExpr

  ///

  inline LpBase::DualExpr operator*(const LpBase::DualExpr &a,

                                    const LpBase::Value &b) {

    LpBase::DualExpr tmp(a);

    tmp*=b;

    return tmp;

  }

  ///Multiply with constant

  ///\relates LpBase::DualExpr

  ///

  inline LpBase::DualExpr operator*(const LpBase::Value &a,

                                    const LpBase::DualExpr &b) {

    LpBase::DualExpr tmp(b);

    tmp*=a;

    return tmp;

  }

  ///Divide with constant

  ///\relates LpBase::DualExpr

  ///

  inline LpBase::DualExpr operator/(const LpBase::DualExpr &a,

                                    const LpBase::Value &b) {

    LpBase::DualExpr tmp(a);

    tmp/=b;

    return tmp;

  }

  /// \ingroup lp_group

  ///

  /// \brief Common base class for LP solvers

  ///

  /// This class is an abstract base class for LP solvers. This class

  /// provides a full interface for set and modify an LP problem,

  /// solve it and retrieve the solution. You can use one of the

  /// descendants as a concrete implementation, or the \c Lp

  /// default LP solver. However, if you would like to handle LP

  /// solvers as reference or pointer in a generic way, you can use

  /// this class directly.

  class LpSolver : virtual public LpBase {

  public:

    /// The problem types for primal and dual problems

    enum ProblemType {

      ///Feasible solution hasn't been found (but may exist).

      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

      UNBOUNDED = 4

    };

    ///The basis status of variables

    enum VarStatus {

      /// The variable is in the basis

      BASIC, 

      /// The variable is free, but not basic

      FREE,

      /// The variable has active lower bound 

      LOWER,

      /// The variable has active upper bound

      UPPER,

      /// The variable is non-basic and fixed

      FIXED

    };

  protected:

    virtual SolveExitStatus _solve() = 0;

    virtual Value _getPrimal(int i) const = 0;

    virtual Value _getDual(int i) const = 0;

    virtual Value _getPrimalRay(int i) const = 0;

    virtual Value _getDualRay(int i) const = 0;

    virtual Value _getPrimalValue() const = 0;

    virtual VarStatus _getColStatus(int i) const = 0;

    virtual VarStatus _getRowStatus(int i) const = 0;

    virtual ProblemType _getPrimalType() const = 0;

    virtual ProblemType _getDualType() const = 0;

  public:

    ///\name Solve the LP

    ///@{

    ///\e Solve the LP problem at hand

    ///

    ///\return The result of the optimization procedure. Possible

    ///values and their meanings can be found in the documentation of

    ///\ref SolveExitStatus.

    SolveExitStatus solve() { return _solve(); }

    ///@}

    ///\name Obtain the solution

    ///@{

    /// The type of the primal problem

    ProblemType primalType() const {

      return _getPrimalType();

    }

    /// The type of the dual problem

    ProblemType dualType() const {

      return _getDualType();

    }

    /// Return the primal value of the column

    /// Return the primal value of the column.

    /// \pre The problem is solved.

    Value primal(Col c) const { return _getPrimal(cols(id(c))); }

    /// Return the primal value of the expression

    /// Return the primal value of the expression, i.e. the dot

    /// product of the primal solution and the expression.

    /// \pre The problem is solved.

    Value primal(const Expr& e) const {

      double res = *e;

      for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {

        res += *c * primal(c);

      }

      return res;

    }

    /// Returns a component of the primal ray

    /// The primal ray is solution of the modified primal problem,

    /// where we change each finite bound to 0, and we looking for a

    /// negative objective value in case of minimization, and positive

    /// objective value for maximization. If there is such solution,

    /// that proofs the unsolvability of the dual problem, and if a

    /// feasible primal solution exists, then the unboundness of

    /// primal problem.

    ///

    /// \pre The problem is solved and the dual problem is infeasible.

    /// \note Some solvers does not provide primal ray calculation

    /// functions.

    Value primalRay(Col c) const { return _getPrimalRay(cols(id(c))); }

    /// Return the dual value of the row

    /// Return the dual value of the row.

    /// \pre The problem is solved.

    Value dual(Row r) const { return _getDual(rows(id(r))); }

    /// Return the dual value of the dual expression

    /// Return the dual value of the dual expression, i.e. the dot

    /// product of the dual solution and the dual expression.

    /// \pre The problem is solved.

    Value dual(const DualExpr& e) const {

      double res = 0.0;

      for (DualExpr::ConstCoeffIt r(e); r != INVALID; ++r) {

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

 *

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

 *

 * Copyright (C) 2003-2009

 * 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_MATH_H

#define LEMON_MATH_H

///\ingroup misc

///\file

///\brief Some extensions to the standard \c cmath library.

///

///Some extensions to the standard \c cmath library.

///

///This file includes the standard math library (cmath).

#include<cmath>

namespace lemon {

  /// \addtogroup misc

  /// @{

  /// The Euler constant

  const long double E       = 2.7182818284590452353602874713526625L;

  /// log_2(e)

  const long double LOG2E   = 1.4426950408889634073599246810018921L;

  /// log_10(e)

  const long double LOG10E  = 0.4342944819032518276511289189166051L;

  /// ln(2)

  const long double LN2     = 0.6931471805599453094172321214581766L;

  /// ln(10)

  const long double LN10    = 2.3025850929940456840179914546843642L;

  /// pi

  const long double PI      = 3.1415926535897932384626433832795029L;

  /// pi/2

  const long double PI_2    = 1.5707963267948966192313216916397514L;

  /// pi/4

  const long double PI_4    = 0.7853981633974483096156608458198757L;

  /// sqrt(2)

  const long double SQRT2   = 1.4142135623730950488016887242096981L;

  /// 1/sqrt(2)

  const long double SQRT1_2 = 0.7071067811865475244008443621048490L;

  ///Check whether the parameter is NaN or not

  ///This function checks whether the parameter is NaN or not.

  ///Is should be equivalent with std::isnan(), but it is not

  ///provided by all compilers.

    {

      return v!=v;

    }

  /// @}

} //namespace lemon

#endif //LEMON_TOLERANCE_H