RhodeCode

/* -*- 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_GRAPH_TO_EPS_H

#define LEMON_GRAPH_TO_EPS_H

#include<iostream>

#include<fstream>

#include<sstream>

#include<algorithm>

#include<vector>

#ifndef WIN32

#include<sys/time.h>

#include<ctime>

#else

#define WIN32_LEAN_AND_MEAN

#define NOMINMAX

#include<windows.h>

#endif

#include<lemon/math.h>

#include<lemon/core.h>

#include<lemon/dim2.h>

#include<lemon/maps.h>

#include<lemon/color.h>

#include<lemon/bits/bezier.h>

#include<lemon/error.h>

///\ingroup eps_io

///\file

///\brief A well configurable tool for visualizing graphs

namespace lemon {

  namespace _graph_to_eps_bits {

    template<class MT>

    class _NegY {

    public:

      typedef typename MT::Key Key;

      typedef typename MT::Value Value;

      const MT ↦

      int yscale;

      _NegY(const MT &m,bool b) : map(m), yscale(1-b*2) {}

      Value operator[](Key n) { return Value(map[n].x,map[n].y*yscale);}

    };

  }

///Default traits class of GraphToEps

///Default traits class of \ref GraphToEps.

///

///\c G is the type of the underlying graph.

template<class G>

struct DefaultGraphToEpsTraits

{

  typedef G Graph;

  typedef typename Graph::Node Node;

  typedef typename Graph::NodeIt NodeIt;

  typedef typename Graph::Arc Arc;

  typedef typename Graph::ArcIt ArcIt;

  typedef typename Graph::InArcIt InArcIt;

  typedef typename Graph::OutArcIt OutArcIt;

  const Graph &g;

  std::ostream& os;

  typedef ConstMap<typename Graph::Node,dim2::Point<double> > CoordsMapType;

  CoordsMapType _coords;

  ConstMap<typename Graph::Node,double > _nodeSizes;

  ConstMap<typename Graph::Node,int > _nodeShapes;

  ConstMap<typename Graph::Node,Color > _nodeColors;

  ConstMap<typename Graph::Arc,Color > _arcColors;

  ConstMap<typename Graph::Arc,double > _arcWidths;

  double _arcWidthScale;

  double _nodeScale;

  double _xBorder, _yBorder;

  double _scale;

  double _nodeBorderQuotient;

  bool _drawArrows;

  double _arrowLength, _arrowWidth;

  bool _showNodes, _showArcs;

  bool _enableParallel;

  double _parArcDist;

  bool _showNodeText;

  ConstMap<typename Graph::Node,bool > _nodeTexts;

  double _nodeTextSize;

  bool _showNodePsText;

  ConstMap<typename Graph::Node,bool > _nodePsTexts;

  char *_nodePsTextsPreamble;

  bool _undirected;

  bool _pleaseRemoveOsStream;

  bool _scaleToA4;

  std::string _title;

  std::string _copyright;

  enum NodeTextColorType

    { DIST_COL=0, DIST_BW=1, CUST_COL=2, SAME_COL=3 } _nodeTextColorType;

  ConstMap<typename Graph::Node,Color > _nodeTextColors;

  bool _autoNodeScale;

  bool _autoArcWidthScale;

  bool _absoluteNodeSizes;

  bool _absoluteArcWidths;

  bool _negY;

  bool _preScale;

  ///Constructor

  ///Constructor

  ///\param _g  Reference to the graph to be printed.

  ///\param _os Reference to the output stream.

  ///\param _os Reference to the output stream.

  ///By default it is <tt>std::cout</tt>.

  ///\param _pros If it is \c true, then the \c ostream referenced by \c _os

  ///will be explicitly deallocated by the destructor.

  DefaultGraphToEpsTraits(const G &_g,std::ostream& _os=std::cout,

                          bool _pros=false) :

    g(_g), os(_os),

    _coords(dim2::Point<double>(1,1)), _nodeSizes(1), _nodeShapes(0),

    _nodeColors(WHITE), _arcColors(BLACK),

    _arcWidths(1.0), _arcWidthScale(0.003),

    _nodeScale(.01), _xBorder(10), _yBorder(10), _scale(1.0),

    _nodeBorderQuotient(.1),

    _drawArrows(false), _arrowLength(1), _arrowWidth(0.3),

    _showNodes(true), _showArcs(true),

    _enableParallel(false), _parArcDist(1),

    _showNodeText(false), _nodeTexts(false), _nodeTextSize(1),

  ///Sets the width of the border around the picture

  GraphToEps<T> &border(double x, double y) {

    _xBorder=x;_yBorder=y;return *this;

  }

  ///Sets whether to draw arrows

  GraphToEps<T> &drawArrows(bool b=true) {_drawArrows=b;return *this;}

  ///Sets the length of the arrowheads

  GraphToEps<T> &arrowLength(double d=1.0) {_arrowLength*=d;return *this;}

  ///Sets the width of the arrowheads

  GraphToEps<T> &arrowWidth(double d=.3) {_arrowWidth*=d;return *this;}

  ///Scales the drawing to fit to A4 page

  GraphToEps<T> &scaleToA4() {_scaleToA4=true;return *this;}

  ///Enables parallel arcs

  GraphToEps<T> &enableParallel(bool b=true) {_enableParallel=b;return *this;}

  ///Sets the distance between parallel arcs

  GraphToEps<T> &parArcDist(double d) {_parArcDist*=d;return *this;}

  ///Hides the arcs

  GraphToEps<T> &hideArcs(bool b=true) {_showArcs=!b;return *this;}

  ///Hides the nodes

  GraphToEps<T> &hideNodes(bool b=true) {_showNodes=!b;return *this;}

  ///Sets the size of the node texts

  GraphToEps<T> &nodeTextSize(double d) {_nodeTextSize=d;return *this;}

  ///Sets the color of the node texts to be different from the node color

  ///Sets the color of the node texts to be as different from the node color

  ///as it is possible.

  GraphToEps<T> &distantColorNodeTexts()

  {_nodeTextColorType=DIST_COL;return *this;}

  ///Sets the color of the node texts to be black or white and always visible.

  ///Sets the color of the node texts to be black or white according to

  ///which is more different from the node color.

  GraphToEps<T> &distantBWNodeTexts()

  {_nodeTextColorType=DIST_BW;return *this;}

  ///Gives a preamble block for node Postscript block.

  ///Gives a preamble block for node Postscript block.

  ///

  ///\sa nodePsTexts()

  GraphToEps<T> & nodePsTextsPreamble(const char *str) {

    _nodePsTextsPreamble=str ;return *this;

  }

  ///Sets whether the graph is undirected

  ///Sets whether the graph is undirected.

  ///

  ///This setting is the default for undirected graphs.

  ///

  ///\sa directed()

   GraphToEps<T> &undirected(bool b=true) {_undirected=b;return *this;}

  ///Sets whether the graph is directed

  ///Sets whether the graph is directed.

  ///Use it to show the edges as a pair of directed ones.

  ///

  ///This setting is the default for digraphs.

  ///

  ///\sa undirected()

  GraphToEps<T> &directed(bool b=true) {_undirected=!b;return *this;}

  ///Sets the title.

  ///Sets the title of the generated image,

  ///namely it inserts a <tt>%%Title:</tt> DSC field to the header of

  ///the EPS file.

  GraphToEps<T> &title(const std::string &t) {_title=t;return *this;}

  ///Sets the copyright statement.

  ///Sets the copyright statement of the generated image,

  ///namely it inserts a <tt>%%Copyright:</tt> DSC field to the header of

  ///the EPS file.

  GraphToEps<T> &copyright(const std::string &t) {_copyright=t;return *this;}

protected:

  bool isInsideNode(dim2::Point<double> p, double r,int t)

  {

    switch(t) {

    case CIRCLE:

    case MALE:

    case FEMALE:

      return p.normSquare()<=r*r;

    case SQUARE:

      return p.x<=r&&p.x>=-r&&p.y<=r&&p.y>=-r;

    case DIAMOND:

      return p.x+p.y<=r && p.x-p.y<=r && -p.x+p.y<=r && -p.x-p.y<=r;

    }

    return false;

  }

public:

  ~GraphToEps() { }

  ///Draws the graph.

  ///Like other functions using

  ///\ref named-templ-func-param "named template parameters",

  ///this function calls the algorithm itself, i.e. in this case

  ///it draws the graph.

  void run() {

    const double EPSILON=1e-9;

    if(dontPrint) return;

    _graph_to_eps_bits::_NegY<typename T::CoordsMapType>

      mycoords(_coords,_negY);

    os << "%!PS-Adobe-2.0 EPSF-2.0\n";

    if(_title.size()>0) os << "%%Title: " << _title << '\n';

     if(_copyright.size()>0) os << "%%Copyright: " << _copyright << '\n';

    os << "%%Creator: LEMON, graphToEps()\n";

    {

#ifndef WIN32

      timeval tv;

      gettimeofday(&tv, 0);

      char cbuf[26];

      ctime_r(&tv.tv_sec,cbuf);

      os << "%%CreationDate: " << cbuf;

#else

      SYSTEMTIME time;

      GetSystemTime(&time);

      if (GetDateFormat(LOCALE_USER_DEFAULT, 0, &time,

          GetTimeFormat(LOCALE_USER_DEFAULT, 0, &time,

          GetDateFormat(LOCALE_USER_DEFAULT, 0, &time,

        os << "%%CreationDate: " << buf1 << ' '

           << buf2 << ' ' << buf3 << std::endl;

      }

#endif

    }

    if (_autoArcWidthScale) {

      double max_w=0;

      for(ArcIt e(g);e!=INVALID;++e)

        max_w=std::max(double(_arcWidths[e]),max_w);

      if(max_w>EPSILON) {

        _arcWidthScale/=max_w;

      }

    }

    if (_autoNodeScale) {

      double max_s=0;

      for(NodeIt n(g);n!=INVALID;++n)

        max_s=std::max(double(_nodeSizes[n]),max_s);

      if(max_s>EPSILON) {

        _nodeScale/=max_s;

      }

    }

    double diag_len = 1;

    if(!(_absoluteNodeSizes&&_absoluteArcWidths)) {

      dim2::Box<double> bb;

      for(NodeIt n(g);n!=INVALID;++n) bb.add(mycoords[n]);

      if (bb.empty()) {

        bb = dim2::Box<double>(dim2::Point<double>(0,0));

      }

      diag_len = std::sqrt((bb.bottomLeft()-bb.topRight()).normSquare());

      if(diag_len<EPSILON) diag_len = 1;

      if(!_absoluteNodeSizes) _nodeScale*=diag_len;

      if(!_absoluteArcWidths) _arcWidthScale*=diag_len;

    }

    dim2::Box<double> bb;

    for(NodeIt n(g);n!=INVALID;++n) {

      double ns=_nodeSizes[n]*_nodeScale;

      dim2::Point<double> p(ns,ns);

      switch(_nodeShapes[n]) {

      case CIRCLE:

      case SQUARE:

      case DIAMOND:

        bb.add(p+mycoords[n]);

        bb.add(-p+mycoords[n]);

        break;

      case MALE:

        bb.add(-p+mycoords[n]);

        bb.add(dim2::Point<double>(1.5*ns,1.5*std::sqrt(3.0)*ns)+mycoords[n]);

        break;

      case FEMALE:

        bb.add(p+mycoords[n]);

        bb.add(dim2::Point<double>(-ns,-3.01*ns)+mycoords[n]);

        break;

      }

    }

    if (bb.empty()) {

      bb = dim2::Box<double>(dim2::Point<double>(0,0));

    }

    if(_scaleToA4)

      os <<"%%BoundingBox: 0 0 596 842\n%%DocumentPaperSizes: a4\n";

    else {

      if(_preScale) {

        //Rescale so that BoundingBox won't be neither to big nor too small.

        while(bb.height()*_scale>1000||bb.width()*_scale>1000) _scale/=10;

        while(bb.height()*_scale<100||bb.width()*_scale<100) _scale*=10;

      }

      os << "%%BoundingBox: "

         << int(floor(bb.left()   * _scale - _xBorder)) << ' '

         << int(floor(bb.bottom() * _scale - _yBorder)) << ' '

         << int(ceil(bb.right()  * _scale + _xBorder)) << ' '

         << int(ceil(bb.top()    * _scale + _yBorder)) << '\n';

    }

    os << "%%EndComments\n";

    //x1 y1 x2 y2 x3 y3 cr cg cb w

    os << "/lb { setlinewidth setrgbcolor newpath moveto\n"

       << "      4 2 roll 1 index 1 index curveto stroke } bind def\n";

    os << "/l { setlinewidth setrgbcolor newpath moveto lineto stroke }"

       << " bind def\n";

    //x y r

    os << "/c { newpath dup 3 index add 2 index moveto 0 360 arc closepath }"

       << " bind def\n";

    //x y r

    os << "/sq { newpath 2 index 1 index add 2 index 2 index add moveto\n"

       << "      2 index 1 index sub 2 index 2 index add lineto\n"

       << "      2 index 1 index sub 2 index 2 index sub lineto\n"

       << "      2 index 1 index add 2 index 2 index sub lineto\n"

       << "      closepath pop pop pop} bind def\n";

    //x y r

    os << "/di { newpath 2 index 1 index add 2 index moveto\n"

       << "      2 index             2 index 2 index add lineto\n"

       << "      2 index 1 index sub 2 index             lineto\n"

       << "      2 index             2 index 2 index sub lineto\n"

       << "      closepath pop pop pop} bind def\n";

    // x y r cr cg cb

    os << "/nc { 0 0 0 setrgbcolor 5 index 5 index 5 index c fill\n"

       << "     setrgbcolor " << 1+_nodeBorderQuotient << " div c fill\n"

       << "   } bind def\n";

    os << "/nsq { 0 0 0 setrgbcolor 5 index 5 index 5 index sq fill\n"

       << "     setrgbcolor " << 1+_nodeBorderQuotient << " div sq fill\n"

       << "   } bind def\n";

    os << "/ndi { 0 0 0 setrgbcolor 5 index 5 index 5 index di fill\n"

       << "     setrgbcolor " << 1+_nodeBorderQuotient << " div di fill\n"

       << "   } bind def\n";

    os << "/nfemale { 0 0 0 setrgbcolor 3 index "

       << _nodeBorderQuotient/(1+_nodeBorderQuotient)

       << " 1.5 mul mul setlinewidth\n"

       << "  newpath 5 index 5 index moveto "

       << "5 index 5 index 5 index 3.01 mul sub\n"

       << "  lineto 5 index 4 index .7 mul sub 5 index 5 index 2.2 mul sub"

       << " moveto\n"

       << "  5 index 4 index .7 mul add 5 index 5 index 2.2 mul sub lineto "

       << "stroke\n"

       << "  5 index 5 index 5 index c fill\n"

       << "  setrgbcolor " << 1+_nodeBorderQuotient << " div c fill\n"

       << "  } bind def\n";

    os << "/nmale {\n"

       << "  0 0 0 setrgbcolor 3 index "

       << _nodeBorderQuotient/(1+_nodeBorderQuotient)

       <<" 1.5 mul mul setlinewidth\n"

       << "  newpath 5 index 5 index moveto\n"

       << "  5 index 4 index 1 mul 1.5 mul add\n"

       << "  5 index 5 index 3 sqrt 1.5 mul mul add\n"

       << "  1 index 1 index lineto\n"

       << "  1 index 1 index 7 index sub moveto\n"

/* -*- 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 {

} //namespace lemon

        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)

  /// 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(); }

/* -*- 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;