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),

    _showNodePsText(false), _nodePsTexts(false), _nodePsTextsPreamble(0),

    _undirected(lemon::UndirectedTagIndicator<G>::value),

    _pleaseRemoveOsStream(_pros), _scaleToA4(false),

    _nodeTextColorType(SAME_COL), _nodeTextColors(BLACK),

    _autoNodeScale(false),

    _autoArcWidthScale(false),

    _absoluteNodeSizes(false),

    _absoluteArcWidths(false),

    _negY(false),

    _preScale(true)

  {}

};

///Auxiliary class to implement the named parameters of \ref graphToEps()

///Auxiliary class to implement the named parameters of \ref graphToEps().

///

///For detailed examples see the \ref graph_to_eps_demo.cc demo file.

template<class T> class GraphToEps : public T

{

  // Can't believe it is required by the C++ standard

  using T::g;

  using T::os;

  using T::_coords;

  using T::_nodeSizes;

  using T::_nodeShapes;

  using T::_nodeColors;

  using T::_arcColors;

  using T::_arcWidths;

  using T::_arcWidthScale;

  using T::_nodeScale;

  using T::_xBorder;

  using T::_yBorder;

  using T::_scale;

  using T::_nodeBorderQuotient;

  using T::_drawArrows;

  using T::_arrowLength;

  using T::_arrowWidth;

  using T::_showNodes;

  using T::_showArcs;

  using T::_enableParallel;

  using T::_parArcDist;

  using T::_showNodeText;

  using T::_nodeTexts;

  using T::_nodeTextSize;

  using T::_showNodePsText;

  using T::_nodePsTexts;

  using T::_nodePsTextsPreamble;

  using T::_undirected;

  using T::_pleaseRemoveOsStream;

  using T::_scaleToA4;

  using T::_title;

  using T::_copyright;

  GraphToEps<T> &autoNodeScale(bool b=true) {

    _autoNodeScale=b;return *this;

  }

  ///Turns on/off the absolutematic node size scaling.

  ///Turns on/off the absolutematic node size scaling.

  ///

  ///\sa nodeScale()

  ///

  GraphToEps<T> &absoluteNodeSizes(bool b=true) {

    _absoluteNodeSizes=b;return *this;

  }

  ///Negates the Y coordinates.

  GraphToEps<T> &negateY(bool b=true) {

    _negY=b;return *this;

  }

  ///Turn on/off pre-scaling

  ///By default graphToEps() rescales the whole image in order to avoid

  ///very big or very small bounding boxes.

  ///

  ///This (p)rescaling can be turned off with this function.

  ///

  GraphToEps<T> &preScale(bool b=true) {

    _preScale=b;return *this;

  }

  ///Sets a global scale factor for arc widths

  /// Sets a global scale factor for arc widths.

  ///

  /// If arcWidths() is not given, this function simply sets the arc

  /// widths to \c d.  If arcWidths() is given, but

  /// autoArcWidthScale() is not, then the arc withs given by

  /// arcWidths() will be multiplied by the value \c d.

  /// If both arcWidths() and autoArcWidthScale() are used, then the

  /// arc withs will be scaled in such a way that the greatest width will be

  /// equal to \c d.

  GraphToEps<T> &arcWidthScale(double d=.003) {_arcWidthScale=d;return *this;}

  ///Turns on/off the automatic arc width scaling.

  ///Turns on/off the automatic arc width scaling.

  ///

  ///\sa arcWidthScale()

  ///

  GraphToEps<T> &autoArcWidthScale(bool b=true) {

    _autoArcWidthScale=b;return *this;

  }

  ///Turns on/off the absolutematic arc width scaling.

  ///Turns on/off the absolutematic arc width scaling.

  ///

  ///\sa arcWidthScale()

  ///

  GraphToEps<T> &absoluteArcWidths(bool b=true) {

    _absoluteArcWidths=b;return *this;

  }

  ///Sets a global scale factor for the whole picture

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

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

  GraphToEps<T> &border(double b=10) {_xBorder=_yBorder=b;return *this;}

  ///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"

       << "  1 index 1 index lineto\n"

       << "  exch 5 index 3 sqrt .5 mul mul sub exch 5 index .5 mul sub"

       << " lineto\n"

       << "  stroke\n"

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

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

       << "  } bind def\n";

    os << "/arrl " << _arrowLength << " def\n";

    os << "/arrw " << _arrowWidth << " def\n";

    // l dx_norm dy_norm

    os << "/lrl { 2 index mul exch 2 index mul exch rlineto pop} bind def\n";

    //len w dx_norm dy_norm x1 y1 cr cg cb

    os << "/arr { setrgbcolor /y1 exch def /x1 exch def /dy exch def /dx "

       << "exch def\n"

       << "       /w exch def /len exch def\n"

      //<< "0.1 setlinewidth x1 y1 moveto dx len mul dy len mul rlineto stroke"

       << "       newpath x1 dy w 2 div mul add y1 dx w 2 div mul sub moveto\n"

       << "       len w sub arrl sub dx dy lrl\n"

       << "       arrw dy dx neg lrl\n"

       << "       dx arrl w add mul dy w 2 div arrw add mul sub\n"

       << "       dy arrl w add mul dx w 2 div arrw add mul add rlineto\n"

       << "       dx arrl w add mul neg dy w 2 div arrw add mul sub\n"

       << "       dy arrl w add mul neg dx w 2 div arrw add mul add rlineto\n"

       << "       arrw dy dx neg lrl\n"

       << "       len w sub arrl sub neg dx dy lrl\n"

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

    os << "/cshow { 2 index 2 index moveto dup stringwidth pop\n"

       << "         neg 2 div fosi .35 mul neg rmoveto show pop pop} def\n";

    os << "\ngsave\n";

    if(_scaleToA4)

      if(bb.height()>bb.width()) {

        double sc= std::min((A4HEIGHT-2*A4BORDER)/bb.height(),

                  (A4WIDTH-2*A4BORDER)/bb.width());

        os << ((A4WIDTH -2*A4BORDER)-sc*bb.width())/2 + A4BORDER << ' '

           << ((A4HEIGHT-2*A4BORDER)-sc*bb.height())/2 + A4BORDER

           << " translate\n"

           << sc << " dup scale\n"

           << -bb.left() << ' ' << -bb.bottom() << " translate\n";

      }

      else {

        double sc= std::min((A4HEIGHT-2*A4BORDER)/bb.width(),

                  (A4WIDTH-2*A4BORDER)/bb.height());

        os << ((A4WIDTH -2*A4BORDER)-sc*bb.height())/2 + A4BORDER << ' '

           << ((A4HEIGHT-2*A4BORDER)-sc*bb.width())/2 + A4BORDER

           << " translate\n"

           << sc << " dup scale\n90 rotate\n"

           << -bb.left() << ' ' << -bb.top() << " translate\n";

        }

    else if(_scale!=1.0) os << _scale << " dup scale\n";

    if(_showArcs) {

      os << "%Arcs:\ngsave\n";

      if(_enableParallel) {

        std::vector<Arc> el;

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

          if((!_undirected||g.source(e)<g.target(e))&&_arcWidths[e]>0

             &&g.source(e)!=g.target(e))

            el.push_back(e);

        std::sort(el.begin(),el.end(),arcLess(g));

        typename std::vector<Arc>::iterator j;

/* -*- 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

        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;