COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/lp_base.h @ 2254:50cb2b90daa9

Last change on this file since 2254:50cb2b90daa9 was 2218:50f1a780a5ff, checked in by athos, 13 years ago

Interface to the cplex MIP solver: it is little, a bit sour but it is ours.

File size: 40.9 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    std::vector<int> index;
43    std::vector<int> cross;
44    int first_free;
45  public:
46    _FixId() : first_free(-1) {};
47    ///Convert a floating id to a fix one
48
49    ///\param n is a floating id
50    ///\return the corresponding fix id
51    int fixId(int n) const {return cross[n];}
52    ///Convert a fix id to a floating one
53
54    ///\param n is a fix id
55    ///\return the corresponding floating id
56    int floatingId(int n) const { return index[n];}
57    ///Add a new floating id.
58
59    ///\param n is a floating id
60    ///\return the fix id of the new value
61    ///\todo Multiple additions should also be handled.
62    int insert(int n)
63    {
64      if(n>=int(cross.size())) {
65        cross.resize(n+1);
66        if(first_free==-1) {
67          cross[n]=index.size();
68          index.push_back(n);
69        }
70        else {
71          cross[n]=first_free;
72          int next=index[first_free];
73          index[first_free]=n;
74          first_free=next;
75        }
76        return cross[n];
77      }
78      else {
79        ///\todo Create an own exception type.
80        throw LogicError(); //floatingId-s must form a continuous range;
81      }
82    }
83    ///Remove a fix id.
84
85    ///\param n is a fix id
86    ///
87    void erase(int n)
88    {
89      int fl=index[n];
90      index[n]=first_free;
91      first_free=n;
92      for(int i=fl+1;i<int(cross.size());++i) {
93        cross[i-1]=cross[i];
94        index[cross[i]]--;
95      }
96      cross.pop_back();
97    }
98    ///An upper bound on the largest fix id.
99
100    ///\todo Do we need this?
101    ///
102    std::size_t maxFixId() { return cross.size()-1; }
103 
104  };
105   
106  ///Common base class for LP solvers
107 
108  ///\todo Much more docs
109  ///\ingroup gen_opt_group
110  class LpSolverBase {
111
112  public:
113
114    ///Possible outcomes of an LP solving procedure
115    enum SolveExitStatus {
116      ///This means that the problem has been successfully solved: either
117      ///an optimal solution has been found or infeasibility/unboundedness
118      ///has been proved.
119      SOLVED = 0,
120      ///Any other case (including the case when some user specified limit has been exceeded)
121      UNSOLVED = 1
122    };
123     
124      ///\e
125    enum SolutionStatus {
126      ///Feasible solution hasn't been found (but may exist).
127
128      ///\todo NOTFOUND might be a better name.
129      ///
130      UNDEFINED = 0,
131      ///The problem has no feasible solution
132      INFEASIBLE = 1,
133      ///Feasible solution found
134      FEASIBLE = 2,
135      ///Optimal solution exists and found
136      OPTIMAL = 3,
137      ///The cost function is unbounded
138
139      ///\todo Give a feasible solution and an infinite ray (and the
140      ///corresponding bases)
141      INFINITE = 4
142    };
143
144    ///\e The type of the investigated LP problem
145    enum ProblemTypes {
146      ///Primal-dual feasible
147      PRIMAL_DUAL_FEASIBLE = 0,
148      ///Primal feasible dual infeasible
149      PRIMAL_FEASIBLE_DUAL_INFEASIBLE = 1,
150      ///Primal infeasible dual feasible
151      PRIMAL_INFEASIBLE_DUAL_FEASIBLE = 2,
152      ///Primal-dual infeasible
153      PRIMAL_DUAL_INFEASIBLE = 3,
154      ///Could not determine so far
155      UNKNOWN = 4
156    };
157
158    ///The floating point type used by the solver
159    typedef double Value;
160    ///The infinity constant
161    static const Value INF;
162    ///The not a number constant
163    static const Value NaN;
164
165    static inline bool isNaN(const Value& v) { return v!=v; }
166   
167    ///Refer to a column of the LP.
168
169    ///This type is used to refer to a column of the LP.
170    ///
171    ///Its value remains valid and correct even after the addition or erase of
172    ///other columns.
173    ///
174    ///\todo Document what can one do with a Col (INVALID, comparing,
175    ///it is similar to Node/Edge)
176    class Col {
177    protected:
178      int id;
179      friend class LpSolverBase;
180      friend class MipSolverBase;
181    public:
182      typedef Value ExprValue;
183      typedef True LpSolverCol;
184      Col() {}
185      Col(const Invalid&) : id(-1) {}
186      bool operator< (Col c) const  {return id< c.id;}
187      bool operator> (Col c) const  {return id> c.id;}
188      bool operator==(Col c) const  {return id==c.id;}
189      bool operator!=(Col c) const  {return id!=c.id;}
190    };
191
192    ///Refer to a row of the LP.
193
194    ///This type is used to refer to a row of the LP.
195    ///
196    ///Its value remains valid and correct even after the addition or erase of
197    ///other rows.
198    ///
199    ///\todo Document what can one do with a Row (INVALID, comparing,
200    ///it is similar to Node/Edge)
201    class Row {
202    protected:
203      int id;
204      friend class LpSolverBase;
205    public:
206      typedef Value ExprValue;
207      typedef True LpSolverRow;
208      Row() {}
209      Row(const Invalid&) : id(-1) {}
210
211      bool operator< (Row c) const  {return id< c.id;}
212      bool operator> (Row c) const  {return id> c.id;}
213      bool operator==(Row c) const  {return id==c.id;}
214      bool operator!=(Row c) const  {return id!=c.id;}
215   };
216   
217    ///Linear expression of variables and a constant component
218   
219    ///This data structure strores a linear expression of the variables
220    ///(\ref Col "Col"s) and also has a constant component.
221    ///
222    ///There are several ways to access and modify the contents of this
223    ///container.
224    ///- Its it fully compatible with \c std::map<Col,double>, so for expamle
225    ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can
226    ///read and modify the coefficients like
227    ///these.
228    ///\code
229    ///e[v]=5;
230    ///e[v]+=12;
231    ///e.erase(v);
232    ///\endcode
233    ///or you can also iterate through its elements.
234    ///\code
235    ///double s=0;
236    ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i)
237    ///  s+=i->second;
238    ///\endcode
239    ///(This code computes the sum of all coefficients).
240    ///- Numbers (<tt>double</tt>'s)
241    ///and variables (\ref Col "Col"s) directly convert to an
242    ///\ref Expr and the usual linear operations are defined, so 
243    ///\code
244    ///v+w
245    ///2*v-3.12*(v-w/2)+2
246    ///v*2.1+(3*v+(v*12+w+6)*3)/2
247    ///\endcode
248    ///are valid \ref Expr "Expr"essions.
249    ///The usual assignment operations are also defined.
250    ///\code
251    ///e=v+w;
252    ///e+=2*v-3.12*(v-w/2)+2;
253    ///e*=3.4;
254    ///e/=5;
255    ///\endcode
256    ///- The constant member can be set and read by \ref constComp()
257    ///\code
258    ///e.constComp()=12;
259    ///double c=e.constComp();
260    ///\endcode
261    ///
262    ///\note \ref clear() not only sets all coefficients to 0 but also
263    ///clears the constant components.
264    ///
265    ///\sa Constr
266    ///
267    class Expr : public std::map<Col,Value>
268    {
269    public:
270      typedef LpSolverBase::Col Key;
271      typedef LpSolverBase::Value Value;
272     
273    protected:
274      typedef std::map<Col,Value> Base;
275     
276      Value const_comp;
277  public:
278      typedef True IsLinExpression;
279      ///\e
280      Expr() : Base(), const_comp(0) { }
281      ///\e
282      Expr(const Key &v) : const_comp(0) {
283        Base::insert(std::make_pair(v, 1));
284      }
285      ///\e
286      Expr(const Value &v) : const_comp(v) {}
287      ///\e
288      void set(const Key &v,const Value &c) {
289        Base::insert(std::make_pair(v, c));
290      }
291      ///\e
292      Value &constComp() { return const_comp; }
293      ///\e
294      const Value &constComp() const { return const_comp; }
295     
296      ///Removes the components with zero coefficient.
297      void simplify() {
298        for (Base::iterator i=Base::begin(); i!=Base::end();) {
299          Base::iterator j=i;
300          ++j;
301          if ((*i).second==0) Base::erase(i);
302          i=j;
303        }
304      }
305
306      ///Removes the coefficients closer to zero than \c tolerance.
307      void simplify(double &tolerance) {
308        for (Base::iterator i=Base::begin(); i!=Base::end();) {
309          Base::iterator j=i;
310          ++j;
311          if (std::fabs((*i).second)<tolerance) Base::erase(i);
312          i=j;
313        }
314      }
315
316      ///Sets all coefficients and the constant component to 0.
317      void clear() {
318        Base::clear();
319        const_comp=0;
320      }
321
322      ///\e
323      Expr &operator+=(const Expr &e) {
324        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
325          (*this)[j->first]+=j->second;
326        const_comp+=e.const_comp;
327        return *this;
328      }
329      ///\e
330      Expr &operator-=(const Expr &e) {
331        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
332          (*this)[j->first]-=j->second;
333        const_comp-=e.const_comp;
334        return *this;
335      }
336      ///\e
337      Expr &operator*=(const Value &c) {
338        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
339          j->second*=c;
340        const_comp*=c;
341        return *this;
342      }
343      ///\e
344      Expr &operator/=(const Value &c) {
345        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
346          j->second/=c;
347        const_comp/=c;
348        return *this;
349      }
350    };
351   
352    ///Linear constraint
353
354    ///This data stucture represents a linear constraint in the LP.
355    ///Basically it is a linear expression with a lower or an upper bound
356    ///(or both). These parts of the constraint can be obtained by the member
357    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
358    ///respectively.
359    ///There are two ways to construct a constraint.
360    ///- You can set the linear expression and the bounds directly
361    ///  by the functions above.
362    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
363    ///  are defined between expressions, or even between constraints whenever
364    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
365    ///  \c s and \c t are numbers, then the followings are valid expressions
366    ///  and thus they can be used directly e.g. in \ref addRow() whenever
367    ///  it makes sense.
368    ///\code
369    ///  e<=s
370    ///  e<=f
371    ///  e==f
372    ///  s<=e<=t
373    ///  e>=t
374    ///\endcode
375    ///\warning The validity of a constraint is checked only at run time, so
376    ///e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will compile, but will throw a
377    ///\ref LogicError exception.
378    class Constr
379    {
380    public:
381      typedef LpSolverBase::Expr Expr;
382      typedef Expr::Key Key;
383      typedef Expr::Value Value;
384     
385//       static const Value INF;
386//       static const Value NaN;
387
388    protected:
389      Expr _expr;
390      Value _lb,_ub;
391    public:
392      ///\e
393      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
394      ///\e
395      Constr(Value lb,const Expr &e,Value ub) :
396        _expr(e), _lb(lb), _ub(ub) {}
397      ///\e
398      Constr(const Expr &e,Value ub) :
399        _expr(e), _lb(NaN), _ub(ub) {}
400      ///\e
401      Constr(Value lb,const Expr &e) :
402        _expr(e), _lb(lb), _ub(NaN) {}
403      ///\e
404      Constr(const Expr &e) :
405        _expr(e), _lb(NaN), _ub(NaN) {}
406      ///\e
407      void clear()
408      {
409        _expr.clear();
410        _lb=_ub=NaN;
411      }
412
413      ///Reference to the linear expression
414      Expr &expr() { return _expr; }
415      ///Cont reference to the linear expression
416      const Expr &expr() const { return _expr; }
417      ///Reference to the lower bound.
418
419      ///\return
420      ///- \ref INF "INF": the constraint is lower unbounded.
421      ///- \ref NaN "NaN": lower bound has not been set.
422      ///- finite number: the lower bound
423      Value &lowerBound() { return _lb; }
424      ///The const version of \ref lowerBound()
425      const Value &lowerBound() const { return _lb; }
426      ///Reference to the upper bound.
427
428      ///\return
429      ///- \ref INF "INF": the constraint is upper unbounded.
430      ///- \ref NaN "NaN": upper bound has not been set.
431      ///- finite number: the upper bound
432      Value &upperBound() { return _ub; }
433      ///The const version of \ref upperBound()
434      const Value &upperBound() const { return _ub; }
435      ///Is the constraint lower bounded?
436      bool lowerBounded() const {
437        using namespace std;
438        return finite(_lb);
439      }
440      ///Is the constraint upper bounded?
441      bool upperBounded() const {
442        using namespace std;
443        return finite(_ub);
444      }
445    };
446   
447    ///Linear expression of rows
448   
449    ///This data structure represents a column of the matrix,
450    ///thas is it strores a linear expression of the dual variables
451    ///(\ref Row "Row"s).
452    ///
453    ///There are several ways to access and modify the contents of this
454    ///container.
455    ///- Its it fully compatible with \c std::map<Row,double>, so for expamle
456    ///if \c e is an DualExpr and \c v
457    ///and \c w are of type \ref Row, then you can
458    ///read and modify the coefficients like
459    ///these.
460    ///\code
461    ///e[v]=5;
462    ///e[v]+=12;
463    ///e.erase(v);
464    ///\endcode
465    ///or you can also iterate through its elements.
466    ///\code
467    ///double s=0;
468    ///for(LpSolverBase::DualExpr::iterator i=e.begin();i!=e.end();++i)
469    ///  s+=i->second;
470    ///\endcode
471    ///(This code computes the sum of all coefficients).
472    ///- Numbers (<tt>double</tt>'s)
473    ///and variables (\ref Row "Row"s) directly convert to an
474    ///\ref DualExpr and the usual linear operations are defined, so
475    ///\code
476    ///v+w
477    ///2*v-3.12*(v-w/2)
478    ///v*2.1+(3*v+(v*12+w)*3)/2
479    ///\endcode
480    ///are valid \ref DualExpr "DualExpr"essions.
481    ///The usual assignment operations are also defined.
482    ///\code
483    ///e=v+w;
484    ///e+=2*v-3.12*(v-w/2);
485    ///e*=3.4;
486    ///e/=5;
487    ///\endcode
488    ///
489    ///\sa Expr
490    ///
491    class DualExpr : public std::map<Row,Value>
492    {
493    public:
494      typedef LpSolverBase::Row Key;
495      typedef LpSolverBase::Value Value;
496     
497    protected:
498      typedef std::map<Row,Value> Base;
499     
500    public:
501      typedef True IsLinExpression;
502      ///\e
503      DualExpr() : Base() { }
504      ///\e
505      DualExpr(const Key &v) {
506        Base::insert(std::make_pair(v, 1));
507      }
508      ///\e
509      void set(const Key &v,const Value &c) {
510        Base::insert(std::make_pair(v, c));
511      }
512     
513      ///Removes the components with zero coefficient.
514      void simplify() {
515        for (Base::iterator i=Base::begin(); i!=Base::end();) {
516          Base::iterator j=i;
517          ++j;
518          if ((*i).second==0) Base::erase(i);
519          i=j;
520        }
521      }
522
523      ///Removes the coefficients closer to zero than \c tolerance.
524      void simplify(double &tolerance) {
525        for (Base::iterator i=Base::begin(); i!=Base::end();) {
526          Base::iterator j=i;
527          ++j;
528          if (std::fabs((*i).second)<tolerance) Base::erase(i);
529          i=j;
530        }
531      }
532
533
534      ///Sets all coefficients to 0.
535      void clear() {
536        Base::clear();
537      }
538
539      ///\e
540      DualExpr &operator+=(const DualExpr &e) {
541        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
542          (*this)[j->first]+=j->second;
543        return *this;
544      }
545      ///\e
546      DualExpr &operator-=(const DualExpr &e) {
547        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
548          (*this)[j->first]-=j->second;
549        return *this;
550      }
551      ///\e
552      DualExpr &operator*=(const Value &c) {
553        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
554          j->second*=c;
555        return *this;
556      }
557      ///\e
558      DualExpr &operator/=(const Value &c) {
559        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
560          j->second/=c;
561        return *this;
562      }
563    };
564   
565
566  protected:
567    _FixId rows;
568    _FixId cols;
569
570    //Abstract virtual functions
571    virtual LpSolverBase &_newLp() = 0;
572    virtual LpSolverBase &_copyLp(){
573      ///\todo This should be implemented here, too,  when we have problem retrieving routines. It can be overriden.
574
575      //Starting:
576      LpSolverBase & newlp(_newLp());
577      return newlp;
578      //return *(LpSolverBase*)0;
579    };
580
581    virtual int _addCol() = 0;
582    virtual int _addRow() = 0;
583    virtual void _eraseCol(int col) = 0;
584    virtual void _eraseRow(int row) = 0;
585    virtual void _getColName(int col,       std::string & name) = 0;
586    virtual void _setColName(int col, const std::string & name) = 0;
587    virtual void _setRowCoeffs(int i,
588                               int length,
589                               int  const * indices,
590                               Value  const * values ) = 0;
591    virtual void _setColCoeffs(int i,
592                               int length,
593                               int  const * indices,
594                               Value  const * values ) = 0;
595    virtual void _setCoeff(int row, int col, Value value) = 0;
596    virtual void _setColLowerBound(int i, Value value) = 0;
597    virtual void _setColUpperBound(int i, Value value) = 0;
598//     virtual void _setRowLowerBound(int i, Value value) = 0;
599//     virtual void _setRowUpperBound(int i, Value value) = 0;
600    virtual void _setRowBounds(int i, Value lower, Value upper) = 0;
601    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
602    virtual void _clearObj()=0;
603//     virtual void _setObj(int length,
604//                          int  const * indices,
605//                          Value  const * values ) = 0;
606    virtual SolveExitStatus _solve() = 0;
607    virtual Value _getPrimal(int i) = 0;
608    virtual Value _getDual(int i) = 0;
609    virtual Value _getPrimalValue() = 0;
610    virtual bool _isBasicCol(int i) = 0;
611    virtual SolutionStatus _getPrimalStatus() = 0;
612    virtual SolutionStatus _getDualStatus() = 0;
613    ///\todo This could be implemented here, too, using _getPrimalStatus() and
614    ///_getDualStatus()
615    virtual ProblemTypes _getProblemType() = 0;
616
617    virtual void _setMax() = 0;
618    virtual void _setMin() = 0;
619   
620    //Own protected stuff
621   
622    //Constant component of the objective function
623    Value obj_const_comp;
624   
625
626
627   
628  public:
629
630    ///\e
631    LpSolverBase() : obj_const_comp(0) {}
632
633    ///\e
634    virtual ~LpSolverBase() {}
635
636    ///Creates a new LP problem
637    LpSolverBase &newLp() {return _newLp();}
638    ///Makes a copy of the LP problem
639    LpSolverBase &copyLp() {return _copyLp();}
640   
641    ///\name Build up and modify the LP
642
643    ///@{
644
645    ///Add a new empty column (i.e a new variable) to the LP
646    Col addCol() { Col c; c.id=cols.insert(_addCol()); return c;}
647
648    ///\brief Adds several new columns
649    ///(i.e a variables) at once
650    ///
651    ///This magic function takes a container as its argument
652    ///and fills its elements
653    ///with new columns (i.e. variables)
654    ///\param t can be
655    ///- a standard STL compatible iterable container with
656    ///\ref Col as its \c values_type
657    ///like
658    ///\code
659    ///std::vector<LpSolverBase::Col>
660    ///std::list<LpSolverBase::Col>
661    ///\endcode
662    ///- a standard STL compatible iterable container with
663    ///\ref Col as its \c mapped_type
664    ///like
665    ///\code
666    ///std::map<AnyType,LpSolverBase::Col>
667    ///\endcode
668    ///- an iterable lemon \ref concept::WriteMap "write map" like
669    ///\code
670    ///ListGraph::NodeMap<LpSolverBase::Col>
671    ///ListGraph::EdgeMap<LpSolverBase::Col>
672    ///\endcode
673    ///\return The number of the created column.
674#ifdef DOXYGEN
675    template<class T>
676    int addColSet(T &t) { return 0;}
677#else
678    template<class T>
679    typename enable_if<typename T::value_type::LpSolverCol,int>::type
680    addColSet(T &t,dummy<0> = 0) {
681      int s=0;
682      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
683      return s;
684    }
685    template<class T>
686    typename enable_if<typename T::value_type::second_type::LpSolverCol,
687                       int>::type
688    addColSet(T &t,dummy<1> = 1) {
689      int s=0;
690      for(typename T::iterator i=t.begin();i!=t.end();++i) {
691        i->second=addCol();
692        s++;
693      }
694      return s;
695    }
696    template<class T>
697    typename enable_if<typename T::MapIt::Value::LpSolverCol,
698                       int>::type
699    addColSet(T &t,dummy<2> = 2) {
700      int s=0;
701      for(typename T::MapIt i(t); i!=INVALID; ++i)
702        {
703          i.set(addCol());
704          s++;
705        }
706      return s;
707    }
708#endif
709
710    ///Set a column (i.e a dual constraint) of the LP
711
712    ///\param c is the column to be modified
713    ///\param e is a dual linear expression (see \ref DualExpr)
714    ///a better one.
715    void col(Col c,const DualExpr &e) {
716      std::vector<int> indices;
717      std::vector<Value> values;
718      indices.push_back(0);
719      values.push_back(0);
720      for(DualExpr::const_iterator i=e.begin(); i!=e.end(); ++i)
721        if((*i).second!=0) {
722          indices.push_back(rows.floatingId((*i).first.id));
723          values.push_back((*i).second);
724        }
725      _setColCoeffs(cols.floatingId(c.id),indices.size()-1,
726                    &indices[0],&values[0]);
727    }
728
729    ///Add a new column to the LP
730
731    ///\param e is a dual linear expression (see \ref DualExpr)
732    ///\param obj is the corresponding component of the objective
733    ///function. It is 0 by default.
734    ///\return The created column.
735    Col addCol(const DualExpr &e, Value obj=0) {
736      Col c=addCol();
737      col(c,e);
738      objCoeff(c,obj);
739      return c;
740    }
741
742    ///Add a new empty row (i.e a new constraint) to the LP
743
744    ///This function adds a new empty row (i.e a new constraint) to the LP.
745    ///\return The created row
746    Row addRow() { Row r; r.id=rows.insert(_addRow()); return r;}
747
748    ///\brief Add several new rows
749    ///(i.e a constraints) at once
750    ///
751    ///This magic function takes a container as its argument
752    ///and fills its elements
753    ///with new row (i.e. variables)
754    ///\param t can be
755    ///- a standard STL compatible iterable container with
756    ///\ref Row as its \c values_type
757    ///like
758    ///\code
759    ///std::vector<LpSolverBase::Row>
760    ///std::list<LpSolverBase::Row>
761    ///\endcode
762    ///- a standard STL compatible iterable container with
763    ///\ref Row as its \c mapped_type
764    ///like
765    ///\code
766    ///std::map<AnyType,LpSolverBase::Row>
767    ///\endcode
768    ///- an iterable lemon \ref concept::WriteMap "write map" like
769    ///\code
770    ///ListGraph::NodeMap<LpSolverBase::Row>
771    ///ListGraph::EdgeMap<LpSolverBase::Row>
772    ///\endcode
773    ///\return The number of rows created.
774#ifdef DOXYGEN
775    template<class T>
776    int addRowSet(T &t) { return 0;}
777#else
778    template<class T>
779    typename enable_if<typename T::value_type::LpSolverRow,int>::type
780    addRowSet(T &t,dummy<0> = 0) {
781      int s=0;
782      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
783      return s;
784    }
785    template<class T>
786    typename enable_if<typename T::value_type::second_type::LpSolverRow,
787                       int>::type
788    addRowSet(T &t,dummy<1> = 1) {
789      int s=0;
790      for(typename T::iterator i=t.begin();i!=t.end();++i) {
791        i->second=addRow();
792        s++;
793      }
794      return s;
795    }
796    template<class T>
797    typename enable_if<typename T::MapIt::Value::LpSolverRow,
798                       int>::type
799    addRowSet(T &t,dummy<2> = 2) {
800      int s=0;
801      for(typename T::MapIt i(t); i!=INVALID; ++i)
802        {
803          i.set(addRow());
804          s++;
805        }
806      return s;
807    }
808#endif
809
810    ///Set a row (i.e a constraint) of the LP
811
812    ///\param r is the row to be modified
813    ///\param l is lower bound (-\ref INF means no bound)
814    ///\param e is a linear expression (see \ref Expr)
815    ///\param u is the upper bound (\ref INF means no bound)
816    ///\bug This is a temportary function. The interface will change to
817    ///a better one.
818    ///\todo Option to control whether a constraint with a single variable is
819    ///added or not.
820    void row(Row r, Value l,const Expr &e, Value u) {
821      std::vector<int> indices;
822      std::vector<Value> values;
823      indices.push_back(0);
824      values.push_back(0);
825      for(Expr::const_iterator i=e.begin(); i!=e.end(); ++i)
826        if((*i).second!=0) { ///\bug EPSILON would be necessary here!!!
827          indices.push_back(cols.floatingId((*i).first.id));
828          values.push_back((*i).second);
829        }
830      _setRowCoeffs(rows.floatingId(r.id),indices.size()-1,
831                    &indices[0],&values[0]);
832//       _setRowLowerBound(rows.floatingId(r.id),l-e.constComp());
833//       _setRowUpperBound(rows.floatingId(r.id),u-e.constComp());
834       _setRowBounds(rows.floatingId(r.id),l-e.constComp(),u-e.constComp());
835    }
836
837    ///Set a row (i.e a constraint) of the LP
838
839    ///\param r is the row to be modified
840    ///\param c is a linear expression (see \ref Constr)
841    void row(Row r, const Constr &c) {
842      row(r,
843             c.lowerBounded()?c.lowerBound():-INF,
844             c.expr(),
845             c.upperBounded()?c.upperBound():INF);
846    }
847
848    ///Add a new row (i.e a new constraint) to the LP
849
850    ///\param l is the lower bound (-\ref INF means no bound)
851    ///\param e is a linear expression (see \ref Expr)
852    ///\param u is the upper bound (\ref INF means no bound)
853    ///\return The created row.
854    ///\bug This is a temportary function. The interface will change to
855    ///a better one.
856    Row addRow(Value l,const Expr &e, Value u) {
857      Row r=addRow();
858      row(r,l,e,u);
859      return r;
860    }
861
862    ///Add a new row (i.e a new constraint) to the LP
863
864    ///\param c is a linear expression (see \ref Constr)
865    ///\return The created row.
866    Row addRow(const Constr &c) {
867      Row r=addRow();
868      row(r,c);
869      return r;
870    }
871    ///Erase a coloumn (i.e a variable) from the LP
872
873    ///\param c is the coloumn to be deleted
874    ///\todo Please check this
875    void eraseCol(Col c) {
876      _eraseCol(cols.floatingId(c.id));
877      cols.erase(c.id);
878    }
879    ///Erase a  row (i.e a constraint) from the LP
880
881    ///\param r is the row to be deleted
882    ///\todo Please check this
883    void eraseRow(Row r) {
884      _eraseRow(rows.floatingId(r.id));
885      rows.erase(r.id);
886    }
887
888    /// Get the name of a column
889   
890    ///\param c is the coresponding coloumn
891    ///\return The name of the colunm
892    std::string ColName(Col c){
893      std::string name;
894      _getColName(cols.floatingId(c.id), name);
895      return name;
896    }
897   
898    /// Set the name of a column
899   
900    ///\param c is the coresponding coloumn
901    ///\param name The name to be given
902    void ColName(Col c, const std::string & name){
903      _setColName(cols.floatingId(c.id), name);
904    }
905   
906    /// Set an element of the coefficient matrix of the LP
907
908    ///\param r is the row of the element to be modified
909    ///\param c is the coloumn of the element to be modified
910    ///\param val is the new value of the coefficient
911
912    void Coeff(Row r, Col c, Value val){
913      _setCoeff(rows.floatingId(r.id),cols.floatingId(c.id), val);
914    }
915
916    /// Set the lower bound of a column (i.e a variable)
917
918    /// The lower bound of a variable (column) has to be given by an
919    /// extended number of type Value, i.e. a finite number of type
920    /// Value or -\ref INF.
921    void colLowerBound(Col c, Value value) {
922      _setColLowerBound(cols.floatingId(c.id),value);
923    }
924   
925    ///\brief Set the lower bound of  several columns
926    ///(i.e a variables) at once
927    ///
928    ///This magic function takes a container as its argument
929    ///and applies the function on all of its elements.
930    /// The lower bound of a variable (column) has to be given by an
931    /// extended number of type Value, i.e. a finite number of type
932    /// Value or -\ref INF.
933#ifdef DOXYGEN
934    template<class T>
935    void colLowerBound(T &t, Value value) { return 0;}
936#else
937    template<class T>
938    typename enable_if<typename T::value_type::LpSolverCol,void>::type
939    colLowerBound(T &t, Value value,dummy<0> = 0) {
940      for(typename T::iterator i=t.begin();i!=t.end();++i) {
941        colLowerBound(*i, value);
942      }
943    }
944    template<class T>
945    typename enable_if<typename T::value_type::second_type::LpSolverCol,
946                       void>::type
947    colLowerBound(T &t, Value value,dummy<1> = 1) {
948      for(typename T::iterator i=t.begin();i!=t.end();++i) {
949        colLowerBound(i->second, value);
950      }
951    }
952    template<class T>
953    typename enable_if<typename T::MapIt::Value::LpSolverCol,
954                       void>::type
955    colLowerBound(T &t, Value value,dummy<2> = 2) {
956      for(typename T::MapIt i(t); i!=INVALID; ++i){
957        colLowerBound(*i, value);
958      }
959    }
960#endif
961   
962    /// Set the upper bound of a column (i.e a variable)
963
964    /// The upper bound of a variable (column) has to be given by an
965    /// extended number of type Value, i.e. a finite number of type
966    /// Value or \ref INF.
967    void colUpperBound(Col c, Value value) {
968      _setColUpperBound(cols.floatingId(c.id),value);
969    };
970
971    ///\brief Set the lower bound of  several columns
972    ///(i.e a variables) at once
973    ///
974    ///This magic function takes a container as its argument
975    ///and applies the function on all of its elements.
976    /// The upper bound of a variable (column) has to be given by an
977    /// extended number of type Value, i.e. a finite number of type
978    /// Value or \ref INF.
979#ifdef DOXYGEN
980    template<class T>
981    void colUpperBound(T &t, Value value) { return 0;}
982#else
983    template<class T>
984    typename enable_if<typename T::value_type::LpSolverCol,void>::type
985    colUpperBound(T &t, Value value,dummy<0> = 0) {
986      for(typename T::iterator i=t.begin();i!=t.end();++i) {
987        colUpperBound(*i, value);
988      }
989    }
990    template<class T>
991    typename enable_if<typename T::value_type::second_type::LpSolverCol,
992                       void>::type
993    colUpperBound(T &t, Value value,dummy<1> = 1) {
994      for(typename T::iterator i=t.begin();i!=t.end();++i) {
995        colUpperBound(i->second, value);
996      }
997    }
998    template<class T>
999    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1000                       void>::type
1001    colUpperBound(T &t, Value value,dummy<2> = 2) {
1002      for(typename T::MapIt i(t); i!=INVALID; ++i){
1003        colUpperBound(*i, value);
1004      }
1005    }
1006#endif
1007
1008    /// Set the lower and the upper bounds of a column (i.e a variable)
1009
1010    /// The lower and the upper bounds of
1011    /// a variable (column) have to be given by an
1012    /// extended number of type Value, i.e. a finite number of type
1013    /// Value, -\ref INF or \ref INF.
1014    void colBounds(Col c, Value lower, Value upper) {
1015      _setColLowerBound(cols.floatingId(c.id),lower);
1016      _setColUpperBound(cols.floatingId(c.id),upper);
1017    }
1018   
1019    ///\brief Set the lower and the upper bound of several columns
1020    ///(i.e a variables) at once
1021    ///
1022    ///This magic function takes a container as its argument
1023    ///and applies the function on all of its elements.
1024    /// The lower and the upper bounds of
1025    /// a variable (column) have to be given by an
1026    /// extended number of type Value, i.e. a finite number of type
1027    /// Value, -\ref INF or \ref INF.
1028#ifdef DOXYGEN
1029    template<class T>
1030    void colBounds(T &t, Value lower, Value upper) { return 0;}
1031#else
1032    template<class T>
1033    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1034    colBounds(T &t, Value lower, Value upper,dummy<0> = 0) {
1035      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1036        colBounds(*i, lower, upper);
1037      }
1038    }
1039    template<class T>
1040    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1041                       void>::type
1042    colBounds(T &t, Value lower, Value upper,dummy<1> = 1) {
1043      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1044        colBounds(i->second, lower, upper);
1045      }
1046    }
1047    template<class T>
1048    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1049                       void>::type
1050    colBounds(T &t, Value lower, Value upper,dummy<2> = 2) {
1051      for(typename T::MapIt i(t); i!=INVALID; ++i){
1052        colBounds(*i, lower, upper);
1053      }
1054    }
1055#endif
1056   
1057//     /// Set the lower bound of a row (i.e a constraint)
1058
1059//     /// The lower bound of a linear expression (row) has to be given by an
1060//     /// extended number of type Value, i.e. a finite number of type
1061//     /// Value or -\ref INF.
1062//     void rowLowerBound(Row r, Value value) {
1063//       _setRowLowerBound(rows.floatingId(r.id),value);
1064//     };
1065//     /// Set the upper bound of a row (i.e a constraint)
1066
1067//     /// The upper bound of a linear expression (row) has to be given by an
1068//     /// extended number of type Value, i.e. a finite number of type
1069//     /// Value or \ref INF.
1070//     void rowUpperBound(Row r, Value value) {
1071//       _setRowUpperBound(rows.floatingId(r.id),value);
1072//     };
1073
1074    /// Set the lower and the upper bounds of a row (i.e a constraint)
1075
1076    /// The lower and the upper bounds of
1077    /// a constraint (row) have to be given by an
1078    /// extended number of type Value, i.e. a finite number of type
1079    /// Value, -\ref INF or \ref INF.
1080    void rowBounds(Row c, Value lower, Value upper) {
1081      _setRowBounds(rows.floatingId(c.id),lower, upper);
1082      // _setRowUpperBound(rows.floatingId(c.id),upper);
1083    }
1084   
1085    ///Set an element of the objective function
1086    void objCoeff(Col c, Value v) {_setObjCoeff(cols.floatingId(c.id),v); };
1087    ///Set the objective function
1088   
1089    ///\param e is a linear expression of type \ref Expr.
1090    ///\bug Is should be called obj()
1091    void setObj(Expr e) {
1092      _clearObj();
1093      for (Expr::iterator i=e.begin(); i!=e.end(); ++i)
1094        objCoeff((*i).first,(*i).second);
1095      obj_const_comp=e.constComp();
1096    }
1097
1098    ///Maximize
1099    void max() { _setMax(); }
1100    ///Minimize
1101    void min() { _setMin(); }
1102
1103   
1104    ///@}
1105
1106
1107    ///\name Solve the LP
1108
1109    ///@{
1110
1111    ///\e Solve the LP problem at hand
1112    ///
1113    ///\return The result of the optimization procedure. Possible
1114    ///values and their meanings can be found in the documentation of
1115    ///\ref SolveExitStatus.
1116    ///
1117    ///\todo Which method is used to solve the problem
1118    SolveExitStatus solve() { return _solve(); }
1119   
1120    ///@}
1121   
1122    ///\name Obtain the solution
1123
1124    ///@{
1125
1126    /// The status of the primal problem (the original LP problem)
1127    SolutionStatus primalStatus() {
1128      return _getPrimalStatus();
1129    }
1130
1131    /// The status of the dual (of the original LP) problem
1132    SolutionStatus dualStatus() {
1133      return _getDualStatus();
1134    }
1135
1136    ///The type of the original LP problem
1137    ProblemTypes problemType() {
1138      return _getProblemType();
1139    }
1140
1141    ///\e
1142    Value primal(Col c) { return _getPrimal(cols.floatingId(c.id)); }
1143
1144    ///\e
1145    Value dual(Row r) { return _getDual(rows.floatingId(r.id)); }
1146
1147    ///\e
1148    bool isBasicCol(Col c) { return _isBasicCol(cols.floatingId(c.id)); }
1149
1150    ///\e
1151
1152    ///\return
1153    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
1154    /// of the primal problem, depending on whether we minimize or maximize.
1155    ///- \ref NaN if no primal solution is found.
1156    ///- The (finite) objective value if an optimal solution is found.
1157    Value primalValue() { return _getPrimalValue()+obj_const_comp;}
1158    ///@}
1159   
1160  }; 
1161
1162
1163  ///Common base class for MIP solvers
1164  ///\todo Much more docs
1165  ///\ingroup gen_opt_group
1166  class MipSolverBase : virtual public LpSolverBase{
1167  public:
1168
1169    ///Possible variable (coloumn) types (e.g. real, integer, binary etc.)
1170    enum ColTypes {
1171      ///Continuous variable
1172      REAL = 0,
1173      ///Integer variable
1174
1175      ///Unfortunately, cplex 7.5 somewhere writes something like
1176      ///#define INTEGER 'I'
1177      LEMON_INTEGER = 1
1178      ///\todo No support for other types yet.
1179    };
1180
1181    ///Sets the type of the given coloumn to the given type
1182    ///
1183    ///Sets the type of the given coloumn to the given type.
1184    void colType(Col c, ColTypes col_type) {
1185      _colType(cols.floatingId(c.id),col_type);
1186    }
1187
1188    ///Gives back the type of the column.
1189    ///
1190    ///Gives back the type of the column.
1191    ColTypes colType(Col c){
1192      return _colType(cols.floatingId(c.id));
1193    }
1194
1195    ///Sets the type of the given Col to integer or remove that property.
1196    ///
1197    ///Sets the type of the given Col to integer or remove that property.
1198    void integer(Col c, bool enable) {
1199      if (enable)
1200        colType(c,LEMON_INTEGER);
1201      else
1202        colType(c,REAL);
1203    }
1204
1205    ///Gives back whether the type of the column is integer or not.
1206    ///
1207    ///Gives back the type of the column.
1208    ///\return true if the column has integer type and false if not.
1209    bool integer(Col c){
1210      return (colType(c)==LEMON_INTEGER);
1211    }
1212
1213    /// The status of the MIP problem
1214    SolutionStatus mipStatus() {
1215      return _getMipStatus();
1216    }
1217
1218  protected:
1219
1220    virtual ColTypes _colType(int col) = 0;
1221    virtual void _colType(int col, ColTypes col_type) = 0;
1222    virtual SolutionStatus _getMipStatus()=0;
1223
1224  };
1225 
1226  ///\relates LpSolverBase::Expr
1227  ///
1228  inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a,
1229                                      const LpSolverBase::Expr &b)
1230  {
1231    LpSolverBase::Expr tmp(a);
1232    tmp+=b;
1233    return tmp;
1234  }
1235  ///\e
1236 
1237  ///\relates LpSolverBase::Expr
1238  ///
1239  inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a,
1240                                      const LpSolverBase::Expr &b)
1241  {
1242    LpSolverBase::Expr tmp(a);
1243    tmp-=b;
1244    return tmp;
1245  }
1246  ///\e
1247 
1248  ///\relates LpSolverBase::Expr
1249  ///
1250  inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a,
1251                                      const LpSolverBase::Value &b)
1252  {
1253    LpSolverBase::Expr tmp(a);
1254    tmp*=b;
1255    return tmp;
1256  }
1257 
1258  ///\e
1259 
1260  ///\relates LpSolverBase::Expr
1261  ///
1262  inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a,
1263                                      const LpSolverBase::Expr &b)
1264  {
1265    LpSolverBase::Expr tmp(b);
1266    tmp*=a;
1267    return tmp;
1268  }
1269  ///\e
1270 
1271  ///\relates LpSolverBase::Expr
1272  ///
1273  inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a,
1274                                      const LpSolverBase::Value &b)
1275  {
1276    LpSolverBase::Expr tmp(a);
1277    tmp/=b;
1278    return tmp;
1279  }
1280 
1281  ///\e
1282 
1283  ///\relates LpSolverBase::Constr
1284  ///
1285  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1286                                         const LpSolverBase::Expr &f)
1287  {
1288    return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0);
1289  }
1290
1291  ///\e
1292 
1293  ///\relates LpSolverBase::Constr
1294  ///
1295  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e,
1296                                         const LpSolverBase::Expr &f)
1297  {
1298    return LpSolverBase::Constr(e,f);
1299  }
1300
1301  ///\e
1302 
1303  ///\relates LpSolverBase::Constr
1304  ///
1305  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1306                                         const LpSolverBase::Value &f)
1307  {
1308    return LpSolverBase::Constr(e,f);
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,f-e,0);
1319  }
1320
1321
1322  ///\e
1323 
1324  ///\relates LpSolverBase::Constr
1325  ///
1326  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e,
1327                                         const LpSolverBase::Expr &f)
1328  {
1329    return LpSolverBase::Constr(f,e);
1330  }
1331
1332
1333  ///\e
1334 
1335  ///\relates LpSolverBase::Constr
1336  ///
1337  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1338                                         const LpSolverBase::Value &f)
1339  {
1340    return LpSolverBase::Constr(f,e);
1341  }
1342
1343  ///\e
1344 
1345  ///\relates LpSolverBase::Constr
1346  ///
1347  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
1348                                         const LpSolverBase::Expr &f)
1349  {
1350    return LpSolverBase::Constr(0,e-f,0);
1351  }
1352
1353  ///\e
1354 
1355  ///\relates LpSolverBase::Constr
1356  ///
1357  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n,
1358                                         const LpSolverBase::Constr&c)
1359  {
1360    LpSolverBase::Constr tmp(c);
1361    ///\todo Create an own exception type.
1362    if(!LpSolverBase::isNaN(tmp.lowerBound())) throw LogicError();
1363    else tmp.lowerBound()=n;
1364    return tmp;
1365  }
1366  ///\e
1367 
1368  ///\relates LpSolverBase::Constr
1369  ///
1370  inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c,
1371                                         const LpSolverBase::Value &n)
1372  {
1373    LpSolverBase::Constr tmp(c);
1374    ///\todo Create an own exception type.
1375    if(!LpSolverBase::isNaN(tmp.upperBound())) throw LogicError();
1376    else tmp.upperBound()=n;
1377    return tmp;
1378  }
1379
1380  ///\e
1381 
1382  ///\relates LpSolverBase::Constr
1383  ///
1384  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n,
1385                                         const LpSolverBase::Constr&c)
1386  {
1387    LpSolverBase::Constr tmp(c);
1388    ///\todo Create an own exception type.
1389    if(!LpSolverBase::isNaN(tmp.upperBound())) throw LogicError();
1390    else tmp.upperBound()=n;
1391    return tmp;
1392  }
1393  ///\e
1394 
1395  ///\relates LpSolverBase::Constr
1396  ///
1397  inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c,
1398                                         const LpSolverBase::Value &n)
1399  {
1400    LpSolverBase::Constr tmp(c);
1401    ///\todo Create an own exception type.
1402    if(!LpSolverBase::isNaN(tmp.lowerBound())) throw LogicError();
1403    else tmp.lowerBound()=n;
1404    return tmp;
1405  }
1406
1407  ///\e
1408 
1409  ///\relates LpSolverBase::DualExpr
1410  ///
1411  inline LpSolverBase::DualExpr operator+(const LpSolverBase::DualExpr &a,
1412                                      const LpSolverBase::DualExpr &b)
1413  {
1414    LpSolverBase::DualExpr tmp(a);
1415    tmp+=b;
1416    return tmp;
1417  }
1418  ///\e
1419 
1420  ///\relates LpSolverBase::DualExpr
1421  ///
1422  inline LpSolverBase::DualExpr operator-(const LpSolverBase::DualExpr &a,
1423                                      const LpSolverBase::DualExpr &b)
1424  {
1425    LpSolverBase::DualExpr tmp(a);
1426    tmp-=b;
1427    return tmp;
1428  }
1429  ///\e
1430 
1431  ///\relates LpSolverBase::DualExpr
1432  ///
1433  inline LpSolverBase::DualExpr operator*(const LpSolverBase::DualExpr &a,
1434                                      const LpSolverBase::Value &b)
1435  {
1436    LpSolverBase::DualExpr tmp(a);
1437    tmp*=b;
1438    return tmp;
1439  }
1440 
1441  ///\e
1442 
1443  ///\relates LpSolverBase::DualExpr
1444  ///
1445  inline LpSolverBase::DualExpr operator*(const LpSolverBase::Value &a,
1446                                      const LpSolverBase::DualExpr &b)
1447  {
1448    LpSolverBase::DualExpr tmp(b);
1449    tmp*=a;
1450    return tmp;
1451  }
1452  ///\e
1453 
1454  ///\relates LpSolverBase::DualExpr
1455  ///
1456  inline LpSolverBase::DualExpr operator/(const LpSolverBase::DualExpr &a,
1457                                      const LpSolverBase::Value &b)
1458  {
1459    LpSolverBase::DualExpr tmp(a);
1460    tmp/=b;
1461    return tmp;
1462  }
1463 
1464
1465} //namespace lemon
1466
1467#endif //LEMON_LP_BASE_H
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