COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/lp_base.h @ 2303:005b3f927287

Last change on this file since 2303:005b3f927287 was 2303:005b3f927287, checked in by Alpar Juttner, 13 years ago

ColIt? added. (Untested, but at least it compiles.)

File size: 41.6 KB
Line 
1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2006
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_LP_BASE_H
20#define LEMON_LP_BASE_H
21
22#include<vector>
23#include<map>
24#include<limits>
25#include<cmath>
26
27#include<lemon/bits/utility.h>
28#include<lemon/error.h>
29#include<lemon/bits/invalid.h>
30
31///\file
32///\brief The interface of the LP solver interface.
33///\ingroup gen_opt_group
34namespace lemon {
35 
36  ///Internal data structure to convert floating id's to fix one's
37   
38  ///\todo This might be implemented to be also usable in other places.
39  class _FixId
40  {
41  protected:
42    int _first_index;
43    int first_free;
44  public:
45    std::vector<int> index;
46    std::vector<int> cross;
47    _FixId() : _first_index(-1), first_free(-1) {};
48    ///Convert a floating id to a fix one
49
50    ///\param n is a floating id
51    ///\return the corresponding fix id
52    int fixId(int n) const {return cross[n];}
53    ///Convert a fix id to a floating one
54
55    ///\param n is a fix id
56    ///\return the corresponding floating id
57    int floatingId(int n) const { return index[n];}
58    ///Add a new floating id.
59
60    ///\param n is a floating id
61    ///\return the fix id of the new value
62    ///\todo Multiple additions should also be handled.
63    int insert(int n)
64    {
65      if(cross.empty()) _first_index=n;
66      if(n>=int(cross.size())) {
67        cross.resize(n+1);
68        if(first_free==-1) {
69          cross[n]=index.size();
70          index.push_back(n);
71        }
72        else {
73          cross[n]=first_free;
74          int next=index[first_free];
75          index[first_free]=n;
76          first_free=next;
77        }
78        return cross[n];
79      }
80      else {
81        ///\todo Create an own exception type.
82        throw LogicError(); //floatingId-s must form a continuous range;
83      }
84    }
85    ///Remove a fix id.
86
87    ///\param n is a fix id
88    ///
89    void erase(int n)
90    {
91      int fl=index[n];
92      index[n]=first_free;
93      first_free=n;
94      for(int i=fl+1;i<int(cross.size());++i) {
95        cross[i-1]=cross[i];
96        index[cross[i]]--;
97      }
98      cross.pop_back();
99    }
100    ///An upper bound on the largest fix id.
101
102    ///\todo Do we need this?
103    ///
104    std::size_t maxFixId() { return cross.size()-1; }
105 
106    ///Returns the first (smallest) inserted index
107
108    ///Returns the first (smallest) inserted index
109    ///or -1 if no index has been inserted before.
110    int firstIndex() {return _first_index;}
111  };
112   
113  ///Common base class for LP solvers
114 
115  ///\todo Much more docs
116  ///\ingroup gen_opt_group
117  class LpSolverBase {
118
119  protected:
120    _FixId rows;
121    _FixId cols;
122
123  public:
124
125    ///Possible outcomes of an LP solving procedure
126    enum SolveExitStatus {
127      ///This means that the problem has been successfully solved: either
128      ///an optimal solution has been found or infeasibility/unboundedness
129      ///has been proved.
130      SOLVED = 0,
131      ///Any other case (including the case when some user specified limit has been exceeded)
132      UNSOLVED = 1
133    };
134     
135      ///\e
136    enum SolutionStatus {
137      ///Feasible solution hasn't been found (but may exist).
138
139      ///\todo NOTFOUND might be a better name.
140      ///
141      UNDEFINED = 0,
142      ///The problem has no feasible solution
143      INFEASIBLE = 1,
144      ///Feasible solution found
145      FEASIBLE = 2,
146      ///Optimal solution exists and found
147      OPTIMAL = 3,
148      ///The cost function is unbounded
149
150      ///\todo Give a feasible solution and an infinite ray (and the
151      ///corresponding bases)
152      INFINITE = 4
153    };
154
155    ///\e The type of the investigated LP problem
156    enum ProblemTypes {
157      ///Primal-dual feasible
158      PRIMAL_DUAL_FEASIBLE = 0,
159      ///Primal feasible dual infeasible
160      PRIMAL_FEASIBLE_DUAL_INFEASIBLE = 1,
161      ///Primal infeasible dual feasible
162      PRIMAL_INFEASIBLE_DUAL_FEASIBLE = 2,
163      ///Primal-dual infeasible
164      PRIMAL_DUAL_INFEASIBLE = 3,
165      ///Could not determine so far
166      UNKNOWN = 4
167    };
168
169    ///The floating point type used by the solver
170    typedef double Value;
171    ///The infinity constant
172    static const Value INF;
173    ///The not a number constant
174    static const Value NaN;
175
176    static inline bool isNaN(const Value& v) { return v!=v; }
177   
178    friend class Col;
179    friend class ColIt;
180    friend class Row;
181   
182    ///Refer to a column of the LP.
183
184    ///This type is used to refer to a column of the LP.
185    ///
186    ///Its value remains valid and correct even after the addition or erase of
187    ///other columns.
188    ///
189    ///\todo Document what can one do with a Col (INVALID, comparing,
190    ///it is similar to Node/Edge)
191    class Col {
192    protected:
193      int id;
194      friend class LpSolverBase;
195      friend class MipSolverBase;
196    public:
197      typedef Value ExprValue;
198      typedef True LpSolverCol;
199      Col() {}
200      Col(const Invalid&) : id(-1) {}
201      bool operator< (Col c) const  {return id< c.id;}
202      bool operator> (Col c) const  {return id> c.id;}
203      bool operator==(Col c) const  {return id==c.id;}
204      bool operator!=(Col c) const  {return id!=c.id;}
205    };
206
207    class ColIt : public Col {
208      LpSolverBase *_lp;
209      ColIt() {}
210      ColIt(LpSolverBase &lp) : _lp(&lp)
211      {
212        id = _lp->cols.cross.empty()?-1:
213          _lp->cols.fixId(_lp->cols.firstIndex());
214      }
215      ColIt(const Invalid&) : Col(INVALID) {}
216      ColIt &operator++()
217      {
218        int fid = _lp->cols.floatingId(id)+1;
219        id = unsigned(fid)<_lp->cols.cross.size() ? _lp->cols.fixId(fid) : -1;
220        return *this;
221      }
222    };
223     
224    ///Refer to a row of the LP.
225
226    ///This type is used to refer to a row of the LP.
227    ///
228    ///Its value remains valid and correct even after the addition or erase of
229    ///other rows.
230    ///
231    ///\todo Document what can one do with a Row (INVALID, comparing,
232    ///it is similar to Node/Edge)
233    class Row {
234    protected:
235      int id;
236      friend class LpSolverBase;
237    public:
238      typedef Value ExprValue;
239      typedef True LpSolverRow;
240      Row() {}
241      Row(const Invalid&) : id(-1) {}
242
243      bool operator< (Row c) const  {return id< c.id;}
244      bool operator> (Row c) const  {return id> c.id;}
245      bool operator==(Row c) const  {return id==c.id;}
246      bool operator!=(Row c) const  {return id!=c.id;}
247   };
248   
249    ///Linear expression of variables and a constant component
250   
251    ///This data structure strores a linear expression of the variables
252    ///(\ref Col "Col"s) and also has a constant component.
253    ///
254    ///There are several ways to access and modify the contents of this
255    ///container.
256    ///- Its it fully compatible with \c std::map<Col,double>, so for expamle
257    ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can
258    ///read and modify the coefficients like
259    ///these.
260    ///\code
261    ///e[v]=5;
262    ///e[v]+=12;
263    ///e.erase(v);
264    ///\endcode
265    ///or you can also iterate through its elements.
266    ///\code
267    ///double s=0;
268    ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i)
269    ///  s+=i->second;
270    ///\endcode
271    ///(This code computes the sum of all coefficients).
272    ///- Numbers (<tt>double</tt>'s)
273    ///and variables (\ref Col "Col"s) directly convert to an
274    ///\ref Expr and the usual linear operations are defined, so 
275    ///\code
276    ///v+w
277    ///2*v-3.12*(v-w/2)+2
278    ///v*2.1+(3*v+(v*12+w+6)*3)/2
279    ///\endcode
280    ///are valid \ref Expr "Expr"essions.
281    ///The usual assignment operations are also defined.
282    ///\code
283    ///e=v+w;
284    ///e+=2*v-3.12*(v-w/2)+2;
285    ///e*=3.4;
286    ///e/=5;
287    ///\endcode
288    ///- The constant member can be set and read by \ref constComp()
289    ///\code
290    ///e.constComp()=12;
291    ///double c=e.constComp();
292    ///\endcode
293    ///
294    ///\note \ref clear() not only sets all coefficients to 0 but also
295    ///clears the constant components.
296    ///
297    ///\sa Constr
298    ///
299    class Expr : public std::map<Col,Value>
300    {
301    public:
302      typedef LpSolverBase::Col Key;
303      typedef LpSolverBase::Value Value;
304     
305    protected:
306      typedef std::map<Col,Value> Base;
307     
308      Value const_comp;
309  public:
310      typedef True IsLinExpression;
311      ///\e
312      Expr() : Base(), const_comp(0) { }
313      ///\e
314      Expr(const Key &v) : const_comp(0) {
315        Base::insert(std::make_pair(v, 1));
316      }
317      ///\e
318      Expr(const Value &v) : const_comp(v) {}
319      ///\e
320      void set(const Key &v,const Value &c) {
321        Base::insert(std::make_pair(v, c));
322      }
323      ///\e
324      Value &constComp() { return const_comp; }
325      ///\e
326      const Value &constComp() const { return const_comp; }
327     
328      ///Removes the components with zero coefficient.
329      void simplify() {
330        for (Base::iterator i=Base::begin(); i!=Base::end();) {
331          Base::iterator j=i;
332          ++j;
333          if ((*i).second==0) Base::erase(i);
334          i=j;
335        }
336      }
337
338      ///Removes the coefficients closer to zero than \c tolerance.
339      void simplify(double &tolerance) {
340        for (Base::iterator i=Base::begin(); i!=Base::end();) {
341          Base::iterator j=i;
342          ++j;
343          if (std::fabs((*i).second)<tolerance) Base::erase(i);
344          i=j;
345        }
346      }
347
348      ///Sets all coefficients and the constant component to 0.
349      void clear() {
350        Base::clear();
351        const_comp=0;
352      }
353
354      ///\e
355      Expr &operator+=(const Expr &e) {
356        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
357          (*this)[j->first]+=j->second;
358        const_comp+=e.const_comp;
359        return *this;
360      }
361      ///\e
362      Expr &operator-=(const Expr &e) {
363        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
364          (*this)[j->first]-=j->second;
365        const_comp-=e.const_comp;
366        return *this;
367      }
368      ///\e
369      Expr &operator*=(const Value &c) {
370        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
371          j->second*=c;
372        const_comp*=c;
373        return *this;
374      }
375      ///\e
376      Expr &operator/=(const Value &c) {
377        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
378          j->second/=c;
379        const_comp/=c;
380        return *this;
381      }
382    };
383   
384    ///Linear constraint
385
386    ///This data stucture represents a linear constraint in the LP.
387    ///Basically it is a linear expression with a lower or an upper bound
388    ///(or both). These parts of the constraint can be obtained by the member
389    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
390    ///respectively.
391    ///There are two ways to construct a constraint.
392    ///- You can set the linear expression and the bounds directly
393    ///  by the functions above.
394    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
395    ///  are defined between expressions, or even between constraints whenever
396    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
397    ///  \c s and \c t are numbers, then the followings are valid expressions
398    ///  and thus they can be used directly e.g. in \ref addRow() whenever
399    ///  it makes sense.
400    ///\code
401    ///  e<=s
402    ///  e<=f
403    ///  e==f
404    ///  s<=e<=t
405    ///  e>=t
406    ///\endcode
407    ///\warning The validity of a constraint is checked only at run time, so
408    ///e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will compile, but will throw a
409    ///\ref LogicError exception.
410    class Constr
411    {
412    public:
413      typedef LpSolverBase::Expr Expr;
414      typedef Expr::Key Key;
415      typedef Expr::Value Value;
416     
417//       static const Value INF;
418//       static const Value NaN;
419
420    protected:
421      Expr _expr;
422      Value _lb,_ub;
423    public:
424      ///\e
425      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
426      ///\e
427      Constr(Value lb,const Expr &e,Value ub) :
428        _expr(e), _lb(lb), _ub(ub) {}
429      ///\e
430      Constr(const Expr &e,Value ub) :
431        _expr(e), _lb(NaN), _ub(ub) {}
432      ///\e
433      Constr(Value lb,const Expr &e) :
434        _expr(e), _lb(lb), _ub(NaN) {}
435      ///\e
436      Constr(const Expr &e) :
437        _expr(e), _lb(NaN), _ub(NaN) {}
438      ///\e
439      void clear()
440      {
441        _expr.clear();
442        _lb=_ub=NaN;
443      }
444
445      ///Reference to the linear expression
446      Expr &expr() { return _expr; }
447      ///Cont reference to the linear expression
448      const Expr &expr() const { return _expr; }
449      ///Reference to the lower bound.
450
451      ///\return
452      ///- \ref INF "INF": the constraint is lower unbounded.
453      ///- \ref NaN "NaN": lower bound has not been set.
454      ///- finite number: the lower bound
455      Value &lowerBound() { return _lb; }
456      ///The const version of \ref lowerBound()
457      const Value &lowerBound() const { return _lb; }
458      ///Reference to the upper bound.
459
460      ///\return
461      ///- \ref INF "INF": the constraint is upper unbounded.
462      ///- \ref NaN "NaN": upper bound has not been set.
463      ///- finite number: the upper bound
464      Value &upperBound() { return _ub; }
465      ///The const version of \ref upperBound()
466      const Value &upperBound() const { return _ub; }
467      ///Is the constraint lower bounded?
468      bool lowerBounded() const {
469        using namespace std;
470        return finite(_lb);
471      }
472      ///Is the constraint upper bounded?
473      bool upperBounded() const {
474        using namespace std;
475        return finite(_ub);
476      }
477    };
478   
479    ///Linear expression of rows
480   
481    ///This data structure represents a column of the matrix,
482    ///thas is it strores a linear expression of the dual variables
483    ///(\ref Row "Row"s).
484    ///
485    ///There are several ways to access and modify the contents of this
486    ///container.
487    ///- Its it fully compatible with \c std::map<Row,double>, so for expamle
488    ///if \c e is an DualExpr and \c v
489    ///and \c w are of type \ref Row, then you can
490    ///read and modify the coefficients like
491    ///these.
492    ///\code
493    ///e[v]=5;
494    ///e[v]+=12;
495    ///e.erase(v);
496    ///\endcode
497    ///or you can also iterate through its elements.
498    ///\code
499    ///double s=0;
500    ///for(LpSolverBase::DualExpr::iterator i=e.begin();i!=e.end();++i)
501    ///  s+=i->second;
502    ///\endcode
503    ///(This code computes the sum of all coefficients).
504    ///- Numbers (<tt>double</tt>'s)
505    ///and variables (\ref Row "Row"s) directly convert to an
506    ///\ref DualExpr and the usual linear operations are defined, so
507    ///\code
508    ///v+w
509    ///2*v-3.12*(v-w/2)
510    ///v*2.1+(3*v+(v*12+w)*3)/2
511    ///\endcode
512    ///are valid \ref DualExpr "DualExpr"essions.
513    ///The usual assignment operations are also defined.
514    ///\code
515    ///e=v+w;
516    ///e+=2*v-3.12*(v-w/2);
517    ///e*=3.4;
518    ///e/=5;
519    ///\endcode
520    ///
521    ///\sa Expr
522    ///
523    class DualExpr : public std::map<Row,Value>
524    {
525    public:
526      typedef LpSolverBase::Row Key;
527      typedef LpSolverBase::Value Value;
528     
529    protected:
530      typedef std::map<Row,Value> Base;
531     
532    public:
533      typedef True IsLinExpression;
534      ///\e
535      DualExpr() : Base() { }
536      ///\e
537      DualExpr(const Key &v) {
538        Base::insert(std::make_pair(v, 1));
539      }
540      ///\e
541      void set(const Key &v,const Value &c) {
542        Base::insert(std::make_pair(v, c));
543      }
544     
545      ///Removes the components with zero coefficient.
546      void simplify() {
547        for (Base::iterator i=Base::begin(); i!=Base::end();) {
548          Base::iterator j=i;
549          ++j;
550          if ((*i).second==0) Base::erase(i);
551          i=j;
552        }
553      }
554
555      ///Removes the coefficients closer to zero than \c tolerance.
556      void simplify(double &tolerance) {
557        for (Base::iterator i=Base::begin(); i!=Base::end();) {
558          Base::iterator j=i;
559          ++j;
560          if (std::fabs((*i).second)<tolerance) Base::erase(i);
561          i=j;
562        }
563      }
564
565
566      ///Sets all coefficients to 0.
567      void clear() {
568        Base::clear();
569      }
570
571      ///\e
572      DualExpr &operator+=(const DualExpr &e) {
573        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
574          (*this)[j->first]+=j->second;
575        return *this;
576      }
577      ///\e
578      DualExpr &operator-=(const DualExpr &e) {
579        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
580          (*this)[j->first]-=j->second;
581        return *this;
582      }
583      ///\e
584      DualExpr &operator*=(const Value &c) {
585        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
586          j->second*=c;
587        return *this;
588      }
589      ///\e
590      DualExpr &operator/=(const Value &c) {
591        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
592          j->second/=c;
593        return *this;
594      }
595    };
596   
597
598  protected:
599
600    //Abstract virtual functions
601    virtual LpSolverBase &_newLp() = 0;
602    virtual LpSolverBase &_copyLp(){
603      ///\todo This should be implemented here, too,  when we have problem retrieving routines. It can be overriden.
604
605      //Starting:
606      LpSolverBase & newlp(_newLp());
607      return newlp;
608      //return *(LpSolverBase*)0;
609    };
610
611    virtual int _addCol() = 0;
612    virtual int _addRow() = 0;
613    virtual void _eraseCol(int col) = 0;
614    virtual void _eraseRow(int row) = 0;
615    virtual void _getColName(int col,       std::string & name) = 0;
616    virtual void _setColName(int col, const std::string & name) = 0;
617    virtual void _setRowCoeffs(int i,
618                               int length,
619                               int  const * indices,
620                               Value  const * values ) = 0;
621    virtual void _setColCoeffs(int i,
622                               int length,
623                               int  const * indices,
624                               Value  const * values ) = 0;
625    virtual void _setCoeff(int row, int col, Value value) = 0;
626    virtual void _setColLowerBound(int i, Value value) = 0;
627    virtual void _setColUpperBound(int i, Value value) = 0;
628//     virtual void _setRowLowerBound(int i, Value value) = 0;
629//     virtual void _setRowUpperBound(int i, Value value) = 0;
630    virtual void _setRowBounds(int i, Value lower, Value upper) = 0;
631    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
632    virtual void _clearObj()=0;
633//     virtual void _setObj(int length,
634//                          int  const * indices,
635//                          Value  const * values ) = 0;
636    virtual SolveExitStatus _solve() = 0;
637    virtual Value _getPrimal(int i) = 0;
638    virtual Value _getDual(int i) = 0;
639    virtual Value _getPrimalValue() = 0;
640    virtual bool _isBasicCol(int i) = 0;
641    virtual SolutionStatus _getPrimalStatus() = 0;
642    virtual SolutionStatus _getDualStatus() = 0;
643    ///\todo This could be implemented here, too, using _getPrimalStatus() and
644    ///_getDualStatus()
645    virtual ProblemTypes _getProblemType() = 0;
646
647    virtual void _setMax() = 0;
648    virtual void _setMin() = 0;
649   
650    //Own protected stuff
651   
652    //Constant component of the objective function
653    Value obj_const_comp;
654   
655
656
657   
658  public:
659
660    ///\e
661    LpSolverBase() : obj_const_comp(0) {}
662
663    ///\e
664    virtual ~LpSolverBase() {}
665
666    ///Creates a new LP problem
667    LpSolverBase &newLp() {return _newLp();}
668    ///Makes a copy of the LP problem
669    LpSolverBase &copyLp() {return _copyLp();}
670   
671    ///\name Build up and modify the LP
672
673    ///@{
674
675    ///Add a new empty column (i.e a new variable) to the LP
676    Col addCol() { Col c; c.id=cols.insert(_addCol()); return c;}
677
678    ///\brief Adds several new columns
679    ///(i.e a variables) at once
680    ///
681    ///This magic function takes a container as its argument
682    ///and fills its elements
683    ///with new columns (i.e. variables)
684    ///\param t can be
685    ///- a standard STL compatible iterable container with
686    ///\ref Col as its \c values_type
687    ///like
688    ///\code
689    ///std::vector<LpSolverBase::Col>
690    ///std::list<LpSolverBase::Col>
691    ///\endcode
692    ///- a standard STL compatible iterable container with
693    ///\ref Col as its \c mapped_type
694    ///like
695    ///\code
696    ///std::map<AnyType,LpSolverBase::Col>
697    ///\endcode
698    ///- an iterable lemon \ref concepts::WriteMap "write map" like
699    ///\code
700    ///ListGraph::NodeMap<LpSolverBase::Col>
701    ///ListGraph::EdgeMap<LpSolverBase::Col>
702    ///\endcode
703    ///\return The number of the created column.
704#ifdef DOXYGEN
705    template<class T>
706    int addColSet(T &t) { return 0;}
707#else
708    template<class T>
709    typename enable_if<typename T::value_type::LpSolverCol,int>::type
710    addColSet(T &t,dummy<0> = 0) {
711      int s=0;
712      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
713      return s;
714    }
715    template<class T>
716    typename enable_if<typename T::value_type::second_type::LpSolverCol,
717                       int>::type
718    addColSet(T &t,dummy<1> = 1) {
719      int s=0;
720      for(typename T::iterator i=t.begin();i!=t.end();++i) {
721        i->second=addCol();
722        s++;
723      }
724      return s;
725    }
726    template<class T>
727    typename enable_if<typename T::MapIt::Value::LpSolverCol,
728                       int>::type
729    addColSet(T &t,dummy<2> = 2) {
730      int s=0;
731      for(typename T::MapIt i(t); i!=INVALID; ++i)
732        {
733          i.set(addCol());
734          s++;
735        }
736      return s;
737    }
738#endif
739
740    ///Set a column (i.e a dual constraint) of the LP
741
742    ///\param c is the column to be modified
743    ///\param e is a dual linear expression (see \ref DualExpr)
744    ///a better one.
745    void col(Col c,const DualExpr &e) {
746      std::vector<int> indices;
747      std::vector<Value> values;
748      indices.push_back(0);
749      values.push_back(0);
750      for(DualExpr::const_iterator i=e.begin(); i!=e.end(); ++i)
751        if((*i).second!=0) {
752          indices.push_back(rows.floatingId((*i).first.id));
753          values.push_back((*i).second);
754        }
755      _setColCoeffs(cols.floatingId(c.id),indices.size()-1,
756                    &indices[0],&values[0]);
757    }
758
759    ///Add a new column to the LP
760
761    ///\param e is a dual linear expression (see \ref DualExpr)
762    ///\param obj is the corresponding component of the objective
763    ///function. It is 0 by default.
764    ///\return The created column.
765    Col addCol(const DualExpr &e, Value obj=0) {
766      Col c=addCol();
767      col(c,e);
768      objCoeff(c,obj);
769      return c;
770    }
771
772    ///Add a new empty row (i.e a new constraint) to the LP
773
774    ///This function adds a new empty row (i.e a new constraint) to the LP.
775    ///\return The created row
776    Row addRow() { Row r; r.id=rows.insert(_addRow()); return r;}
777
778    ///\brief Add several new rows
779    ///(i.e a constraints) at once
780    ///
781    ///This magic function takes a container as its argument
782    ///and fills its elements
783    ///with new row (i.e. variables)
784    ///\param t can be
785    ///- a standard STL compatible iterable container with
786    ///\ref Row as its \c values_type
787    ///like
788    ///\code
789    ///std::vector<LpSolverBase::Row>
790    ///std::list<LpSolverBase::Row>
791    ///\endcode
792    ///- a standard STL compatible iterable container with
793    ///\ref Row as its \c mapped_type
794    ///like
795    ///\code
796    ///std::map<AnyType,LpSolverBase::Row>
797    ///\endcode
798    ///- an iterable lemon \ref concepts::WriteMap "write map" like
799    ///\code
800    ///ListGraph::NodeMap<LpSolverBase::Row>
801    ///ListGraph::EdgeMap<LpSolverBase::Row>
802    ///\endcode
803    ///\return The number of rows created.
804#ifdef DOXYGEN
805    template<class T>
806    int addRowSet(T &t) { return 0;}
807#else
808    template<class T>
809    typename enable_if<typename T::value_type::LpSolverRow,int>::type
810    addRowSet(T &t,dummy<0> = 0) {
811      int s=0;
812      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
813      return s;
814    }
815    template<class T>
816    typename enable_if<typename T::value_type::second_type::LpSolverRow,
817                       int>::type
818    addRowSet(T &t,dummy<1> = 1) {
819      int s=0;
820      for(typename T::iterator i=t.begin();i!=t.end();++i) {
821        i->second=addRow();
822        s++;
823      }
824      return s;
825    }
826    template<class T>
827    typename enable_if<typename T::MapIt::Value::LpSolverRow,
828                       int>::type
829    addRowSet(T &t,dummy<2> = 2) {
830      int s=0;
831      for(typename T::MapIt i(t); i!=INVALID; ++i)
832        {
833          i.set(addRow());
834          s++;
835        }
836      return s;
837    }
838#endif
839
840    ///Set a row (i.e a constraint) of the LP
841
842    ///\param r is the row to be modified
843    ///\param l is lower bound (-\ref INF means no bound)
844    ///\param e is a linear expression (see \ref Expr)
845    ///\param u is the upper bound (\ref INF means no bound)
846    ///\bug This is a temportary function. The interface will change to
847    ///a better one.
848    ///\todo Option to control whether a constraint with a single variable is
849    ///added or not.
850    void row(Row r, Value l,const Expr &e, Value u) {
851      std::vector<int> indices;
852      std::vector<Value> values;
853      indices.push_back(0);
854      values.push_back(0);
855      for(Expr::const_iterator i=e.begin(); i!=e.end(); ++i)
856        if((*i).second!=0) { ///\bug EPSILON would be necessary here!!!
857          indices.push_back(cols.floatingId((*i).first.id));
858          values.push_back((*i).second);
859        }
860      _setRowCoeffs(rows.floatingId(r.id),indices.size()-1,
861                    &indices[0],&values[0]);
862//       _setRowLowerBound(rows.floatingId(r.id),l-e.constComp());
863//       _setRowUpperBound(rows.floatingId(r.id),u-e.constComp());
864       _setRowBounds(rows.floatingId(r.id),l-e.constComp(),u-e.constComp());
865    }
866
867    ///Set a row (i.e a constraint) of the LP
868
869    ///\param r is the row to be modified
870    ///\param c is a linear expression (see \ref Constr)
871    void row(Row r, const Constr &c) {
872      row(r,
873             c.lowerBounded()?c.lowerBound():-INF,
874             c.expr(),
875             c.upperBounded()?c.upperBound():INF);
876    }
877
878    ///Add a new row (i.e a new constraint) to the LP
879
880    ///\param l is the lower bound (-\ref INF means no bound)
881    ///\param e is a linear expression (see \ref Expr)
882    ///\param u is the upper bound (\ref INF means no bound)
883    ///\return The created row.
884    ///\bug This is a temportary function. The interface will change to
885    ///a better one.
886    Row addRow(Value l,const Expr &e, Value u) {
887      Row r=addRow();
888      row(r,l,e,u);
889      return r;
890    }
891
892    ///Add a new row (i.e a new constraint) to the LP
893
894    ///\param c is a linear expression (see \ref Constr)
895    ///\return The created row.
896    Row addRow(const Constr &c) {
897      Row r=addRow();
898      row(r,c);
899      return r;
900    }
901    ///Erase a coloumn (i.e a variable) from the LP
902
903    ///\param c is the coloumn to be deleted
904    ///\todo Please check this
905    void eraseCol(Col c) {
906      _eraseCol(cols.floatingId(c.id));
907      cols.erase(c.id);
908    }
909    ///Erase a  row (i.e a constraint) from the LP
910
911    ///\param r is the row to be deleted
912    ///\todo Please check this
913    void eraseRow(Row r) {
914      _eraseRow(rows.floatingId(r.id));
915      rows.erase(r.id);
916    }
917
918    /// Get the name of a column
919   
920    ///\param c is the coresponding coloumn
921    ///\return The name of the colunm
922    std::string colName(Col c){
923      std::string name;
924      _getColName(cols.floatingId(c.id), name);
925      return name;
926    }
927   
928    /// Set the name of a column
929   
930    ///\param c is the coresponding coloumn
931    ///\param name The name to be given
932    void colName(Col c, const std::string & name){
933      _setColName(cols.floatingId(c.id), name);
934    }
935   
936    /// Set an element of the coefficient matrix of the LP
937
938    ///\param r is the row of the element to be modified
939    ///\param c is the coloumn of the element to be modified
940    ///\param val is the new value of the coefficient
941
942    void coeff(Row r, Col c, Value val){
943      _setCoeff(rows.floatingId(r.id),cols.floatingId(c.id), val);
944    }
945
946    /// Set the lower bound of a column (i.e a variable)
947
948    /// The lower bound of a variable (column) has to be given by an
949    /// extended number of type Value, i.e. a finite number of type
950    /// Value or -\ref INF.
951    void colLowerBound(Col c, Value value) {
952      _setColLowerBound(cols.floatingId(c.id),value);
953    }
954   
955    ///\brief Set the lower bound of  several columns
956    ///(i.e a variables) at once
957    ///
958    ///This magic function takes a container as its argument
959    ///and applies the function on all of its elements.
960    /// The lower bound of a variable (column) has to be given by an
961    /// extended number of type Value, i.e. a finite number of type
962    /// Value or -\ref INF.
963#ifdef DOXYGEN
964    template<class T>
965    void colLowerBound(T &t, Value value) { return 0;}
966#else
967    template<class T>
968    typename enable_if<typename T::value_type::LpSolverCol,void>::type
969    colLowerBound(T &t, Value value,dummy<0> = 0) {
970      for(typename T::iterator i=t.begin();i!=t.end();++i) {
971        colLowerBound(*i, value);
972      }
973    }
974    template<class T>
975    typename enable_if<typename T::value_type::second_type::LpSolverCol,
976                       void>::type
977    colLowerBound(T &t, Value value,dummy<1> = 1) {
978      for(typename T::iterator i=t.begin();i!=t.end();++i) {
979        colLowerBound(i->second, value);
980      }
981    }
982    template<class T>
983    typename enable_if<typename T::MapIt::Value::LpSolverCol,
984                       void>::type
985    colLowerBound(T &t, Value value,dummy<2> = 2) {
986      for(typename T::MapIt i(t); i!=INVALID; ++i){
987        colLowerBound(*i, value);
988      }
989    }
990#endif
991   
992    /// Set the upper bound of a column (i.e a variable)
993
994    /// The upper bound of a variable (column) has to be given by an
995    /// extended number of type Value, i.e. a finite number of type
996    /// Value or \ref INF.
997    void colUpperBound(Col c, Value value) {
998      _setColUpperBound(cols.floatingId(c.id),value);
999    };
1000
1001    ///\brief Set the lower bound of  several columns
1002    ///(i.e a variables) at once
1003    ///
1004    ///This magic function takes a container as its argument
1005    ///and applies the function on all of its elements.
1006    /// The upper bound of a variable (column) has to be given by an
1007    /// extended number of type Value, i.e. a finite number of type
1008    /// Value or \ref INF.
1009#ifdef DOXYGEN
1010    template<class T>
1011    void colUpperBound(T &t, Value value) { return 0;}
1012#else
1013    template<class T>
1014    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1015    colUpperBound(T &t, Value value,dummy<0> = 0) {
1016      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1017        colUpperBound(*i, value);
1018      }
1019    }
1020    template<class T>
1021    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1022                       void>::type
1023    colUpperBound(T &t, Value value,dummy<1> = 1) {
1024      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1025        colUpperBound(i->second, value);
1026      }
1027    }
1028    template<class T>
1029    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1030                       void>::type
1031    colUpperBound(T &t, Value value,dummy<2> = 2) {
1032      for(typename T::MapIt i(t); i!=INVALID; ++i){
1033        colUpperBound(*i, value);
1034      }
1035    }
1036#endif
1037
1038    /// Set the lower and the upper bounds of a column (i.e a variable)
1039
1040    /// The lower and the upper bounds of
1041    /// a variable (column) have to be given by an
1042    /// extended number of type Value, i.e. a finite number of type
1043    /// Value, -\ref INF or \ref INF.
1044    void colBounds(Col c, Value lower, Value upper) {
1045      _setColLowerBound(cols.floatingId(c.id),lower);
1046      _setColUpperBound(cols.floatingId(c.id),upper);
1047    }
1048   
1049    ///\brief Set the lower and the upper bound of several columns
1050    ///(i.e a variables) at once
1051    ///
1052    ///This magic function takes a container as its argument
1053    ///and applies the function on all of its elements.
1054    /// The lower and the upper bounds of
1055    /// a variable (column) have to be given by an
1056    /// extended number of type Value, i.e. a finite number of type
1057    /// Value, -\ref INF or \ref INF.
1058#ifdef DOXYGEN
1059    template<class T>
1060    void colBounds(T &t, Value lower, Value upper) { return 0;}
1061#else
1062    template<class T>
1063    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1064    colBounds(T &t, Value lower, Value upper,dummy<0> = 0) {
1065      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1066        colBounds(*i, lower, upper);
1067      }
1068    }
1069    template<class T>
1070    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1071                       void>::type
1072    colBounds(T &t, Value lower, Value upper,dummy<1> = 1) {
1073      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1074        colBounds(i->second, lower, upper);
1075      }
1076    }
1077    template<class T>
1078    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1079                       void>::type
1080    colBounds(T &t, Value lower, Value upper,dummy<2> = 2) {
1081      for(typename T::MapIt i(t); i!=INVALID; ++i){
1082        colBounds(*i, lower, upper);
1083      }
1084    }
1085#endif
1086   
1087//     /// Set the lower bound of a row (i.e a constraint)
1088
1089//     /// The lower bound of a linear expression (row) has to be given by an
1090//     /// extended number of type Value, i.e. a finite number of type
1091//     /// Value or -\ref INF.
1092//     void rowLowerBound(Row r, Value value) {
1093//       _setRowLowerBound(rows.floatingId(r.id),value);
1094//     };
1095//     /// Set the upper bound of a row (i.e a constraint)
1096
1097//     /// The upper bound of a linear expression (row) has to be given by an
1098//     /// extended number of type Value, i.e. a finite number of type
1099//     /// Value or \ref INF.
1100//     void rowUpperBound(Row r, Value value) {
1101//       _setRowUpperBound(rows.floatingId(r.id),value);
1102//     };
1103
1104    /// Set the lower and the upper bounds of a row (i.e a constraint)
1105
1106    /// The lower and the upper bounds of
1107    /// a constraint (row) have to be given by an
1108    /// extended number of type Value, i.e. a finite number of type
1109    /// Value, -\ref INF or \ref INF.
1110    void rowBounds(Row c, Value lower, Value upper) {
1111      _setRowBounds(rows.floatingId(c.id),lower, upper);
1112      // _setRowUpperBound(rows.floatingId(c.id),upper);
1113    }
1114   
1115    ///Set an element of the objective function
1116    void objCoeff(Col c, Value v) {_setObjCoeff(cols.floatingId(c.id),v); };
1117    ///Set the objective function
1118   
1119    ///\param e is a linear expression of type \ref Expr.
1120    ///\bug Is should be called obj()
1121    void setObj(Expr e) {
1122      _clearObj();
1123      for (Expr::iterator i=e.begin(); i!=e.end(); ++i)
1124        objCoeff((*i).first,(*i).second);
1125      obj_const_comp=e.constComp();
1126    }
1127
1128    ///Maximize
1129    void max() { _setMax(); }
1130    ///Minimize
1131    void min() { _setMin(); }
1132
1133   
1134    ///@}
1135
1136
1137    ///\name Solve the LP
1138
1139    ///@{
1140
1141    ///\e Solve the LP problem at hand
1142    ///
1143    ///\return The result of the optimization procedure. Possible
1144    ///values and their meanings can be found in the documentation of
1145    ///\ref SolveExitStatus.
1146    ///
1147    ///\todo Which method is used to solve the problem
1148    SolveExitStatus solve() { return _solve(); }
1149   
1150    ///@}
1151   
1152    ///\name Obtain the solution
1153
1154    ///@{
1155
1156    /// The status of the primal problem (the original LP problem)
1157    SolutionStatus primalStatus() {
1158      return _getPrimalStatus();
1159    }
1160
1161    /// The status of the dual (of the original LP) problem
1162    SolutionStatus dualStatus() {
1163      return _getDualStatus();
1164    }
1165
1166    ///The type of the original LP problem
1167    ProblemTypes problemType() {
1168      return _getProblemType();
1169    }
1170
1171    ///\e
1172    Value primal(Col c) { return _getPrimal(cols.floatingId(c.id)); }
1173
1174    ///\e
1175    Value dual(Row r) { return _getDual(rows.floatingId(r.id)); }
1176
1177    ///\e
1178    bool isBasicCol(Col c) { return _isBasicCol(cols.floatingId(c.id)); }
1179
1180    ///\e
1181
1182    ///\return
1183    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
1184    /// of the primal problem, depending on whether we minimize or maximize.
1185    ///- \ref NaN if no primal solution is found.
1186    ///- The (finite) objective value if an optimal solution is found.
1187    Value primalValue() { return _getPrimalValue()+obj_const_comp;}
1188    ///@}
1189   
1190  }; 
1191
1192
1193  ///Common base class for MIP solvers
1194  ///\todo Much more docs
1195  ///\ingroup gen_opt_group
1196  class MipSolverBase : virtual public LpSolverBase{
1197  public:
1198
1199    ///Possible variable (coloumn) types (e.g. real, integer, binary etc.)
1200    enum ColTypes {
1201      ///Continuous variable
1202      REAL = 0,
1203      ///Integer variable
1204
1205      ///Unfortunately, cplex 7.5 somewhere writes something like
1206      ///#define INTEGER 'I'
1207      INT = 1
1208      ///\todo No support for other types yet.
1209    };
1210
1211    ///Sets the type of the given coloumn to the given type
1212    ///
1213    ///Sets the type of the given coloumn to the given type.
1214    void colType(Col c, ColTypes col_type) {
1215      _colType(cols.floatingId(c.id),col_type);
1216    }
1217
1218    ///Gives back the type of the column.
1219    ///
1220    ///Gives back the type of the column.
1221    ColTypes colType(Col c){
1222      return _colType(cols.floatingId(c.id));
1223    }
1224
1225    ///Sets the type of the given Col to integer or remove that property.
1226    ///
1227    ///Sets the type of the given Col to integer or remove that property.
1228    void integer(Col c, bool enable) {
1229      if (enable)
1230        colType(c,INT);
1231      else
1232        colType(c,REAL);
1233    }
1234
1235    ///Gives back whether the type of the column is integer or not.
1236    ///
1237    ///Gives back the type of the column.
1238    ///\return true if the column has integer type and false if not.
1239    bool integer(Col c){
1240      return (colType(c)==INT);
1241    }
1242
1243    /// The status of the MIP problem
1244    SolutionStatus mipStatus() {
1245      return _getMipStatus();
1246    }
1247
1248  protected:
1249
1250    virtual ColTypes _colType(int col) = 0;
1251    virtual void _colType(int col, ColTypes col_type) = 0;
1252    virtual SolutionStatus _getMipStatus()=0;
1253
1254  };
1255 
1256  ///\relates LpSolverBase::Expr
1257  ///
1258  inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a,
1259                                      const LpSolverBase::Expr &b)
1260  {
1261    LpSolverBase::Expr tmp(a);
1262    tmp+=b;
1263    return tmp;
1264  }
1265  ///\e
1266 
1267  ///\relates LpSolverBase::Expr
1268  ///
1269  inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a,
1270                                      const LpSolverBase::Expr &b)
1271  {
1272    LpSolverBase::Expr tmp(a);
1273    tmp-=b;
1274    return tmp;
1275  }
1276  ///\e
1277 
1278  ///\relates LpSolverBase::Expr
1279  ///
1280  inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a,
1281                                      const LpSolverBase::Value &b)
1282  {
1283    LpSolverBase::Expr tmp(a);
1284    tmp*=b;
1285    return tmp;
1286  }
1287 
1288  ///\e
1289 
1290  ///\relates LpSolverBase::Expr
1291  ///
1292  inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a,
1293                                      const LpSolverBase::Expr &b)
1294  {
1295    LpSolverBase::Expr tmp(b);
1296    tmp*=a;
1297    return tmp;
1298  }
1299  ///\e
1300 
1301  ///\relates LpSolverBase::Expr
1302  ///
1303  inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a,
1304                                      const LpSolverBase::Value &b)
1305  {
1306    LpSolverBase::Expr tmp(a);
1307    tmp/=b;
1308    return tmp;
1309  }
1310 
1311  ///\e
1312 
1313  ///\relates LpSolverBase::Constr
1314  ///
1315  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1316                                         const LpSolverBase::Expr &f)
1317  {
1318    return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0);
1319  }
1320
1321  ///\e
1322 
1323  ///\relates LpSolverBase::Constr
1324  ///
1325  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e,
1326                                         const LpSolverBase::Expr &f)
1327  {
1328    return LpSolverBase::Constr(e,f);
1329  }
1330
1331  ///\e
1332 
1333  ///\relates LpSolverBase::Constr
1334  ///
1335  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1336                                         const LpSolverBase::Value &f)
1337  {
1338    return LpSolverBase::Constr(e,f);
1339  }
1340
1341  ///\e
1342 
1343  ///\relates LpSolverBase::Constr
1344  ///
1345  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1346                                         const LpSolverBase::Expr &f)
1347  {
1348    return LpSolverBase::Constr(-LpSolverBase::INF,f-e,0);
1349  }
1350
1351
1352  ///\e
1353 
1354  ///\relates LpSolverBase::Constr
1355  ///
1356  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e,
1357                                         const LpSolverBase::Expr &f)
1358  {
1359    return LpSolverBase::Constr(f,e);
1360  }
1361
1362
1363  ///\e
1364 
1365  ///\relates LpSolverBase::Constr
1366  ///
1367  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1368                                         const LpSolverBase::Value &f)
1369  {
1370    return LpSolverBase::Constr(f,e);
1371  }
1372
1373  ///\e
1374 
1375  ///\relates LpSolverBase::Constr
1376  ///
1377  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
1378                                         const LpSolverBase::Expr &f)
1379  {
1380    return LpSolverBase::Constr(0,e-f,0);
1381  }
1382
1383  ///\e
1384 
1385  ///\relates LpSolverBase::Constr
1386  ///
1387  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n,
1388                                         const LpSolverBase::Constr&c)
1389  {
1390    LpSolverBase::Constr tmp(c);
1391    ///\todo Create an own exception type.
1392    if(!LpSolverBase::isNaN(tmp.lowerBound())) throw LogicError();
1393    else tmp.lowerBound()=n;
1394    return tmp;
1395  }
1396  ///\e
1397 
1398  ///\relates LpSolverBase::Constr
1399  ///
1400  inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c,
1401                                         const LpSolverBase::Value &n)
1402  {
1403    LpSolverBase::Constr tmp(c);
1404    ///\todo Create an own exception type.
1405    if(!LpSolverBase::isNaN(tmp.upperBound())) throw LogicError();
1406    else tmp.upperBound()=n;
1407    return tmp;
1408  }
1409
1410  ///\e
1411 
1412  ///\relates LpSolverBase::Constr
1413  ///
1414  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n,
1415                                         const LpSolverBase::Constr&c)
1416  {
1417    LpSolverBase::Constr tmp(c);
1418    ///\todo Create an own exception type.
1419    if(!LpSolverBase::isNaN(tmp.upperBound())) throw LogicError();
1420    else tmp.upperBound()=n;
1421    return tmp;
1422  }
1423  ///\e
1424 
1425  ///\relates LpSolverBase::Constr
1426  ///
1427  inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c,
1428                                         const LpSolverBase::Value &n)
1429  {
1430    LpSolverBase::Constr tmp(c);
1431    ///\todo Create an own exception type.
1432    if(!LpSolverBase::isNaN(tmp.lowerBound())) throw LogicError();
1433    else tmp.lowerBound()=n;
1434    return tmp;
1435  }
1436
1437  ///\e
1438 
1439  ///\relates LpSolverBase::DualExpr
1440  ///
1441  inline LpSolverBase::DualExpr operator+(const LpSolverBase::DualExpr &a,
1442                                      const LpSolverBase::DualExpr &b)
1443  {
1444    LpSolverBase::DualExpr tmp(a);
1445    tmp+=b;
1446    return tmp;
1447  }
1448  ///\e
1449 
1450  ///\relates LpSolverBase::DualExpr
1451  ///
1452  inline LpSolverBase::DualExpr operator-(const LpSolverBase::DualExpr &a,
1453                                      const LpSolverBase::DualExpr &b)
1454  {
1455    LpSolverBase::DualExpr tmp(a);
1456    tmp-=b;
1457    return tmp;
1458  }
1459  ///\e
1460 
1461  ///\relates LpSolverBase::DualExpr
1462  ///
1463  inline LpSolverBase::DualExpr operator*(const LpSolverBase::DualExpr &a,
1464                                      const LpSolverBase::Value &b)
1465  {
1466    LpSolverBase::DualExpr tmp(a);
1467    tmp*=b;
1468    return tmp;
1469  }
1470 
1471  ///\e
1472 
1473  ///\relates LpSolverBase::DualExpr
1474  ///
1475  inline LpSolverBase::DualExpr operator*(const LpSolverBase::Value &a,
1476                                      const LpSolverBase::DualExpr &b)
1477  {
1478    LpSolverBase::DualExpr tmp(b);
1479    tmp*=a;
1480    return tmp;
1481  }
1482  ///\e
1483 
1484  ///\relates LpSolverBase::DualExpr
1485  ///
1486  inline LpSolverBase::DualExpr operator/(const LpSolverBase::DualExpr &a,
1487                                      const LpSolverBase::Value &b)
1488  {
1489    LpSolverBase::DualExpr tmp(a);
1490    tmp/=b;
1491    return tmp;
1492  }
1493 
1494
1495} //namespace lemon
1496
1497#endif //LEMON_LP_BASE_H
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