COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/lp_base.h @ 2609:c36f00f19f2b

Last change on this file since 2609:c36f00f19f2b was 2609:c36f00f19f2b, checked in by Balazs Dezso, 11 years ago

Fixing lp constraints (solving ticket #92)

File size: 47.0 KB
Line 
1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2008
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<iostream>
23#include<vector>
24#include<map>
25#include<limits>
26#include<lemon/math.h>
27
28#include<lemon/error.h>
29#include<lemon/bits/invalid.h>
30#include<lemon/bits/utility.h>
31#include<lemon/bits/lp_id.h>
32
33///\file
34///\brief The interface of the LP solver interface.
35///\ingroup lp_group
36namespace lemon {
37
38  /// Function to decide whether a floating point value is finite or not.
39
40  /// Retruns true if the argument is not infinity, minus infinity or NaN.
41  /// It does the same as the isfinite() function defined by C99.
42  template <typename T>
43  bool isFinite(T value)
44  {
45    typedef std::numeric_limits<T> Lim;
46    if (Lim::has_infinity && (value == Lim::infinity() || value ==
47          -Lim::infinity()) ||
48        (Lim::has_quiet_NaN || Lim::has_signaling_NaN) && value != value)
49    {
50      return false;
51    }
52    return true;
53  }
54
55  ///Common base class for LP solvers
56 
57  ///\todo Much more docs
58  ///\ingroup lp_group
59  class LpSolverBase {
60
61  protected:
62
63    _lp_bits::LpId rows;
64    _lp_bits::LpId cols;
65   
66  public:
67   
68    ///Possible outcomes of an LP solving procedure
69    enum SolveExitStatus {
70      ///This means that the problem has been successfully solved: either
71      ///an optimal solution has been found or infeasibility/unboundedness
72      ///has been proved.
73      SOLVED = 0,
74      ///Any other case (including the case when some user specified
75      ///limit has been exceeded)
76      UNSOLVED = 1
77    };
78     
79      ///\e
80    enum SolutionStatus {
81      ///Feasible solution hasn't been found (but may exist).
82
83      ///\todo NOTFOUND might be a better name.
84      ///
85      UNDEFINED = 0,
86      ///The problem has no feasible solution
87      INFEASIBLE = 1,
88      ///Feasible solution found
89      FEASIBLE = 2,
90      ///Optimal solution exists and found
91      OPTIMAL = 3,
92      ///The cost function is unbounded
93
94      ///\todo Give a feasible solution and an infinite ray (and the
95      ///corresponding bases)
96      INFINITE = 4
97    };
98
99    ///\e The type of the investigated LP problem
100    enum ProblemTypes {
101      ///Primal-dual feasible
102      PRIMAL_DUAL_FEASIBLE = 0,
103      ///Primal feasible dual infeasible
104      PRIMAL_FEASIBLE_DUAL_INFEASIBLE = 1,
105      ///Primal infeasible dual feasible
106      PRIMAL_INFEASIBLE_DUAL_FEASIBLE = 2,
107      ///Primal-dual infeasible
108      PRIMAL_DUAL_INFEASIBLE = 3,
109      ///Could not determine so far
110      UNKNOWN = 4
111    };
112
113    ///The floating point type used by the solver
114    typedef double Value;
115    ///The infinity constant
116    static const Value INF;
117    ///The not a number constant
118    static const Value NaN;
119
120    static inline bool isNaN(const Value& v) { return v!=v; }
121   
122    friend class Col;
123    friend class ColIt;
124    friend class Row;
125   
126    ///Refer to a column of the LP.
127
128    ///This type is used to refer to a column of the LP.
129    ///
130    ///Its value remains valid and correct even after the addition or erase of
131    ///other columns.
132    ///
133    ///\todo Document what can one do with a Col (INVALID, comparing,
134    ///it is similar to Node/Edge)
135    class Col {
136    protected:
137      int id;
138      friend class LpSolverBase;
139      friend class MipSolverBase;
140      explicit Col(int _id) : id(_id) {}
141    public:
142      typedef Value ExprValue;
143      typedef True LpSolverCol;
144      Col() {}
145      Col(const Invalid&) : id(-1) {}
146      bool operator< (Col c) const  {return id< c.id;}
147      bool operator> (Col c) const  {return id> c.id;}
148      bool operator==(Col c) const  {return id==c.id;}
149      bool operator!=(Col c) const  {return id!=c.id;}
150    };
151
152    class ColIt : public Col {
153      const LpSolverBase *_lp;
154    public:
155      ColIt() {}
156      ColIt(const LpSolverBase &lp) : _lp(&lp)
157      {
158        _lp->cols.firstFix(id);
159      }
160      ColIt(const Invalid&) : Col(INVALID) {}
161      ColIt &operator++()
162      {
163        _lp->cols.nextFix(id);
164        return *this;
165      }
166    };
167
168    static int id(const Col& col) { return col.id; }
169 
170     
171    ///Refer to a row of the LP.
172
173    ///This type is used to refer to a row of the LP.
174    ///
175    ///Its value remains valid and correct even after the addition or erase of
176    ///other rows.
177    ///
178    ///\todo Document what can one do with a Row (INVALID, comparing,
179    ///it is similar to Node/Edge)
180    class Row {
181    protected:
182      int id;
183      friend class LpSolverBase;
184      explicit Row(int _id) : id(_id) {}
185    public:
186      typedef Value ExprValue;
187      typedef True LpSolverRow;
188      Row() {}
189      Row(const Invalid&) : id(-1) {}
190
191      bool operator< (Row c) const  {return id< c.id;}
192      bool operator> (Row c) const  {return id> c.id;}
193      bool operator==(Row c) const  {return id==c.id;}
194      bool operator!=(Row c) const  {return id!=c.id;}
195    };
196
197    class RowIt : public Row {
198      const LpSolverBase *_lp;
199    public:
200      RowIt() {}
201      RowIt(const LpSolverBase &lp) : _lp(&lp)
202      {
203        _lp->rows.firstFix(id);
204      }
205      RowIt(const Invalid&) : Row(INVALID) {}
206      RowIt &operator++()
207      {
208        _lp->rows.nextFix(id);
209        return *this;
210      }
211    };
212
213    static int id(const Row& row) { return row.id; }
214
215  protected:
216
217    int _lpId(const Col& c) const {
218      return cols.floatingId(id(c));
219    }
220
221    int _lpId(const Row& r) const {
222      return rows.floatingId(id(r));
223    }
224
225    Col _item(int i, Col) const {
226      return Col(cols.fixId(i));
227    }
228
229    Row _item(int i, Row) const {
230      return Row(rows.fixId(i));
231    }
232
233
234  public:
235   
236    ///Linear expression of variables and a constant component
237   
238    ///This data structure stores a linear expression of the variables
239    ///(\ref Col "Col"s) and also has a constant component.
240    ///
241    ///There are several ways to access and modify the contents of this
242    ///container.
243    ///- Its it fully compatible with \c std::map<Col,double>, so for expamle
244    ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can
245    ///read and modify the coefficients like
246    ///these.
247    ///\code
248    ///e[v]=5;
249    ///e[v]+=12;
250    ///e.erase(v);
251    ///\endcode
252    ///or you can also iterate through its elements.
253    ///\code
254    ///double s=0;
255    ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i)
256    ///  s+=i->second;
257    ///\endcode
258    ///(This code computes the sum of all coefficients).
259    ///- Numbers (<tt>double</tt>'s)
260    ///and variables (\ref Col "Col"s) directly convert to an
261    ///\ref Expr and the usual linear operations are defined, so 
262    ///\code
263    ///v+w
264    ///2*v-3.12*(v-w/2)+2
265    ///v*2.1+(3*v+(v*12+w+6)*3)/2
266    ///\endcode
267    ///are valid \ref Expr "Expr"essions.
268    ///The usual assignment operations are also defined.
269    ///\code
270    ///e=v+w;
271    ///e+=2*v-3.12*(v-w/2)+2;
272    ///e*=3.4;
273    ///e/=5;
274    ///\endcode
275    ///- The constant member can be set and read by \ref constComp()
276    ///\code
277    ///e.constComp()=12;
278    ///double c=e.constComp();
279    ///\endcode
280    ///
281    ///\note \ref clear() not only sets all coefficients to 0 but also
282    ///clears the constant components.
283    ///
284    ///\sa Constr
285    ///
286    class Expr : public std::map<Col,Value>
287    {
288    public:
289      typedef LpSolverBase::Col Key;
290      typedef LpSolverBase::Value Value;
291     
292    protected:
293      typedef std::map<Col,Value> Base;
294     
295      Value const_comp;
296    public:
297      typedef True IsLinExpression;
298      ///\e
299      Expr() : Base(), const_comp(0) { }
300      ///\e
301      Expr(const Key &v) : const_comp(0) {
302        Base::insert(std::make_pair(v, 1));
303      }
304      ///\e
305      Expr(const Value &v) : const_comp(v) {}
306      ///\e
307      void set(const Key &v,const Value &c) {
308        Base::insert(std::make_pair(v, c));
309      }
310      ///\e
311      Value &constComp() { return const_comp; }
312      ///\e
313      const Value &constComp() const { return const_comp; }
314     
315      ///Removes the components with zero coefficient.
316      void simplify() {
317        for (Base::iterator i=Base::begin(); i!=Base::end();) {
318          Base::iterator j=i;
319          ++j;
320          if ((*i).second==0) Base::erase(i);
321          i=j;
322        }
323      }
324
325      void simplify() const {
326        const_cast<Expr*>(this)->simplify();
327      }
328
329      ///Removes the coefficients closer to zero than \c tolerance.
330      void simplify(double &tolerance) {
331        for (Base::iterator i=Base::begin(); i!=Base::end();) {
332          Base::iterator j=i;
333          ++j;
334          if (std::fabs((*i).second)<tolerance) Base::erase(i);
335          i=j;
336        }
337      }
338
339      ///Sets all coefficients and the constant component to 0.
340      void clear() {
341        Base::clear();
342        const_comp=0;
343      }
344
345      ///\e
346      Expr &operator+=(const Expr &e) {
347        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
348          (*this)[j->first]+=j->second;
349        const_comp+=e.const_comp;
350        return *this;
351      }
352      ///\e
353      Expr &operator-=(const Expr &e) {
354        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
355          (*this)[j->first]-=j->second;
356        const_comp-=e.const_comp;
357        return *this;
358      }
359      ///\e
360      Expr &operator*=(const Value &c) {
361        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
362          j->second*=c;
363        const_comp*=c;
364        return *this;
365      }
366      ///\e
367      Expr &operator/=(const Value &c) {
368        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
369          j->second/=c;
370        const_comp/=c;
371        return *this;
372      }
373
374    };
375   
376    ///Linear constraint
377
378    ///This data stucture represents a linear constraint in the LP.
379    ///Basically it is a linear expression with a lower or an upper bound
380    ///(or both). These parts of the constraint can be obtained by the member
381    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
382    ///respectively.
383    ///There are two ways to construct a constraint.
384    ///- You can set the linear expression and the bounds directly
385    ///  by the functions above.
386    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
387    ///  are defined between expressions, or even between constraints whenever
388    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
389    ///  \c s and \c t are numbers, then the followings are valid expressions
390    ///  and thus they can be used directly e.g. in \ref addRow() whenever
391    ///  it makes sense.
392    ///\code
393    ///  e<=s
394    ///  e<=f
395    ///  e==f
396    ///  s<=e<=t
397    ///  e>=t
398    ///\endcode
399    ///\warning The validity of a constraint is checked only at run time, so
400    ///e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will compile, but will throw a
401    ///\ref LogicError exception.
402    class Constr
403    {
404    public:
405      typedef LpSolverBase::Expr Expr;
406      typedef Expr::Key Key;
407      typedef Expr::Value Value;
408     
409    protected:
410      Expr _expr;
411      Value _lb,_ub;
412    public:
413      ///\e
414      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
415      ///\e
416      Constr(Value lb,const Expr &e,Value ub) :
417        _expr(e), _lb(lb), _ub(ub) {}
418      ///\e
419      Constr(const Expr &e,Value ub) :
420        _expr(e), _lb(NaN), _ub(ub) {}
421      ///\e
422      Constr(Value lb,const Expr &e) :
423        _expr(e), _lb(lb), _ub(NaN) {}
424      ///\e
425      Constr(const Expr &e) :
426        _expr(e), _lb(NaN), _ub(NaN) {}
427      ///\e
428      void clear()
429      {
430        _expr.clear();
431        _lb=_ub=NaN;
432      }
433
434      ///Reference to the linear expression
435      Expr &expr() { return _expr; }
436      ///Cont reference to the linear expression
437      const Expr &expr() const { return _expr; }
438      ///Reference to the lower bound.
439
440      ///\return
441      ///- \ref INF "INF": the constraint is lower unbounded.
442      ///- \ref NaN "NaN": lower bound has not been set.
443      ///- finite number: the lower bound
444      Value &lowerBound() { return _lb; }
445      ///The const version of \ref lowerBound()
446      const Value &lowerBound() const { return _lb; }
447      ///Reference to the upper bound.
448
449      ///\return
450      ///- \ref INF "INF": the constraint is upper unbounded.
451      ///- \ref NaN "NaN": upper bound has not been set.
452      ///- finite number: the upper bound
453      Value &upperBound() { return _ub; }
454      ///The const version of \ref upperBound()
455      const Value &upperBound() const { return _ub; }
456      ///Is the constraint lower bounded?
457      bool lowerBounded() const {
458        return isFinite(_lb);
459      }
460      ///Is the constraint upper bounded?
461      bool upperBounded() const {
462        return isFinite(_ub);
463      }
464
465    };
466   
467    ///Linear expression of rows
468   
469    ///This data structure represents a column of the matrix,
470    ///thas is it strores a linear expression of the dual variables
471    ///(\ref Row "Row"s).
472    ///
473    ///There are several ways to access and modify the contents of this
474    ///container.
475    ///- Its it fully compatible with \c std::map<Row,double>, so for expamle
476    ///if \c e is an DualExpr and \c v
477    ///and \c w are of type \ref Row, then you can
478    ///read and modify the coefficients like
479    ///these.
480    ///\code
481    ///e[v]=5;
482    ///e[v]+=12;
483    ///e.erase(v);
484    ///\endcode
485    ///or you can also iterate through its elements.
486    ///\code
487    ///double s=0;
488    ///for(LpSolverBase::DualExpr::iterator i=e.begin();i!=e.end();++i)
489    ///  s+=i->second;
490    ///\endcode
491    ///(This code computes the sum of all coefficients).
492    ///- Numbers (<tt>double</tt>'s)
493    ///and variables (\ref Row "Row"s) directly convert to an
494    ///\ref DualExpr and the usual linear operations are defined, so
495    ///\code
496    ///v+w
497    ///2*v-3.12*(v-w/2)
498    ///v*2.1+(3*v+(v*12+w)*3)/2
499    ///\endcode
500    ///are valid \ref DualExpr "DualExpr"essions.
501    ///The usual assignment operations are also defined.
502    ///\code
503    ///e=v+w;
504    ///e+=2*v-3.12*(v-w/2);
505    ///e*=3.4;
506    ///e/=5;
507    ///\endcode
508    ///
509    ///\sa Expr
510    ///
511    class DualExpr : public std::map<Row,Value>
512    {
513    public:
514      typedef LpSolverBase::Row Key;
515      typedef LpSolverBase::Value Value;
516     
517    protected:
518      typedef std::map<Row,Value> Base;
519     
520    public:
521      typedef True IsLinExpression;
522      ///\e
523      DualExpr() : Base() { }
524      ///\e
525      DualExpr(const Key &v) {
526        Base::insert(std::make_pair(v, 1));
527      }
528      ///\e
529      void set(const Key &v,const Value &c) {
530        Base::insert(std::make_pair(v, c));
531      }
532     
533      ///Removes the components with zero coefficient.
534      void simplify() {
535        for (Base::iterator i=Base::begin(); i!=Base::end();) {
536          Base::iterator j=i;
537          ++j;
538          if ((*i).second==0) Base::erase(i);
539          i=j;
540        }
541      }
542
543      void simplify() const {
544        const_cast<DualExpr*>(this)->simplify();
545      }
546
547      ///Removes the coefficients closer to zero than \c tolerance.
548      void simplify(double &tolerance) {
549        for (Base::iterator i=Base::begin(); i!=Base::end();) {
550          Base::iterator j=i;
551          ++j;
552          if (std::fabs((*i).second)<tolerance) Base::erase(i);
553          i=j;
554        }
555      }
556
557      ///Sets all coefficients to 0.
558      void clear() {
559        Base::clear();
560      }
561
562      ///\e
563      DualExpr &operator+=(const DualExpr &e) {
564        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
565          (*this)[j->first]+=j->second;
566        return *this;
567      }
568      ///\e
569      DualExpr &operator-=(const DualExpr &e) {
570        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
571          (*this)[j->first]-=j->second;
572        return *this;
573      }
574      ///\e
575      DualExpr &operator*=(const Value &c) {
576        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
577          j->second*=c;
578        return *this;
579      }
580      ///\e
581      DualExpr &operator/=(const Value &c) {
582        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
583          j->second/=c;
584        return *this;
585      }
586    };
587   
588
589  private:
590
591    template <typename _Expr>
592    class MappedOutputIterator {
593    public:
594
595      typedef std::insert_iterator<_Expr> Base;
596
597      typedef std::output_iterator_tag iterator_category;
598      typedef void difference_type;
599      typedef void value_type;
600      typedef void reference;
601      typedef void pointer;
602     
603      MappedOutputIterator(const Base& _base, const LpSolverBase& _lp)
604        : base(_base), lp(_lp) {}
605
606      MappedOutputIterator& operator*() {
607        return *this;
608      }
609
610      MappedOutputIterator& operator=(const std::pair<int, Value>& value) {
611        *base = std::make_pair(lp._item(value.first, typename _Expr::Key()),
612                               value.second);
613        return *this;
614      }
615
616      MappedOutputIterator& operator++() {
617        ++base;
618        return *this;
619      }
620
621      MappedOutputIterator operator++(int) {
622        MappedOutputIterator tmp(*this);
623        ++base;
624        return tmp;
625      }
626
627      bool operator==(const MappedOutputIterator& it) const {
628        return base == it.base;
629      }
630
631      bool operator!=(const MappedOutputIterator& it) const {
632        return base != it.base;
633      }
634
635    private:
636      Base base;
637      const LpSolverBase& lp;
638    };
639
640    template <typename Expr>
641    class MappedInputIterator {
642    public:
643
644      typedef typename Expr::const_iterator Base;
645
646      typedef typename Base::iterator_category iterator_category;
647      typedef typename Base::difference_type difference_type;
648      typedef const std::pair<int, Value> value_type;
649      typedef value_type reference;
650      class pointer {
651      public:
652        pointer(value_type& _value) : value(_value) {}
653        value_type* operator->() { return &value; }
654      private:
655        value_type value;
656      };
657
658      MappedInputIterator(const Base& _base, const LpSolverBase& _lp)
659        : base(_base), lp(_lp) {}
660
661      reference operator*() {
662        return std::make_pair(lp._lpId(base->first), base->second);
663      }
664
665      pointer operator->() {
666        return pointer(operator*());
667      }
668
669      MappedInputIterator& operator++() {
670        ++base;
671        return *this;
672      }
673
674      MappedInputIterator operator++(int) {
675        MappedInputIterator tmp(*this);
676        ++base;
677        return tmp;
678      }
679
680      bool operator==(const MappedInputIterator& it) const {
681        return base == it.base;
682      }
683
684      bool operator!=(const MappedInputIterator& it) const {
685        return base != it.base;
686      }
687
688    private:
689      Base base;
690      const LpSolverBase& lp;
691    };
692
693  protected:
694
695    /// STL compatible iterator for lp col
696    typedef MappedInputIterator<Expr> ConstRowIterator;
697    /// STL compatible iterator for lp row
698    typedef MappedInputIterator<DualExpr> ConstColIterator;
699
700    /// STL compatible iterator for lp col
701    typedef MappedOutputIterator<Expr> RowIterator;
702    /// STL compatible iterator for lp row
703    typedef MappedOutputIterator<DualExpr> ColIterator;
704
705    //Abstract virtual functions
706    virtual LpSolverBase* _newLp() = 0;
707    virtual LpSolverBase* _copyLp(){
708      LpSolverBase* newlp = _newLp();
709
710      std::map<Col, Col> ref;
711      for (LpSolverBase::ColIt it(*this); it != INVALID; ++it) {
712        Col ccol = newlp->addCol();
713        ref[it] = ccol;
714        newlp->colName(ccol, colName(it));
715        newlp->colLowerBound(ccol, colLowerBound(it));
716        newlp->colUpperBound(ccol, colUpperBound(it));
717      }
718
719      for (LpSolverBase::RowIt it(*this); it != INVALID; ++it) {
720        Expr e = row(it), ce;
721        for (Expr::iterator jt = e.begin(); jt != e.end(); ++jt) {
722          ce[ref[jt->first]] = jt->second;
723        }
724        ce += e.constComp();
725        Row r = newlp->addRow(ce);
726
727        double lower, upper;
728        getRowBounds(it, lower, upper);
729        newlp->rowBounds(r, lower, upper);
730      }
731
732      return newlp;
733    };
734
735    virtual int _addCol() = 0;
736    virtual int _addRow() = 0;
737
738    virtual void _eraseCol(int col) = 0;
739    virtual void _eraseRow(int row) = 0;
740
741    virtual void _getColName(int col, std::string & name) const = 0;
742    virtual void _setColName(int col, const std::string & name) = 0;
743    virtual int _colByName(const std::string& name) const = 0;
744
745    virtual void _setRowCoeffs(int i, ConstRowIterator b,
746                               ConstRowIterator e) = 0;
747    virtual void _getRowCoeffs(int i, RowIterator b) const = 0;
748    virtual void _setColCoeffs(int i, ConstColIterator b,
749                               ConstColIterator e) = 0;
750    virtual void _getColCoeffs(int i, ColIterator b) const = 0;
751    virtual void _setCoeff(int row, int col, Value value) = 0;
752    virtual Value _getCoeff(int row, int col) const = 0;
753    virtual void _setColLowerBound(int i, Value value) = 0;
754    virtual Value _getColLowerBound(int i) const = 0;
755    virtual void _setColUpperBound(int i, Value value) = 0;
756    virtual Value _getColUpperBound(int i) const = 0;
757    virtual void _setRowBounds(int i, Value lower, Value upper) = 0;
758    virtual void _getRowBounds(int i, Value &lower, Value &upper) const = 0;
759
760    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
761    virtual Value _getObjCoeff(int i) const = 0;
762    virtual void _clearObj()=0;
763
764    virtual SolveExitStatus _solve() = 0;
765    virtual Value _getPrimal(int i) const = 0;
766    virtual Value _getDual(int i) const = 0;
767    virtual Value _getPrimalValue() const = 0;
768    virtual bool _isBasicCol(int i) const = 0;
769    virtual SolutionStatus _getPrimalStatus() const = 0;
770    virtual SolutionStatus _getDualStatus() const = 0;
771    virtual ProblemTypes _getProblemType() const = 0;
772
773    virtual void _setMax() = 0;
774    virtual void _setMin() = 0;
775   
776
777    virtual bool _isMax() const = 0;
778
779    //Own protected stuff
780   
781    //Constant component of the objective function
782    Value obj_const_comp;
783       
784  public:
785
786    ///\e
787    LpSolverBase() : obj_const_comp(0) {}
788
789    ///\e
790    virtual ~LpSolverBase() {}
791
792    ///Creates a new LP problem
793    LpSolverBase* newLp() {return _newLp();}
794    ///Makes a copy of the LP problem
795    LpSolverBase* copyLp() {return _copyLp();}
796   
797    ///\name Build up and modify the LP
798
799    ///@{
800
801    ///Add a new empty column (i.e a new variable) to the LP
802    Col addCol() { Col c; _addCol(); c.id = cols.addId(); return c;}
803
804    ///\brief Adds several new columns
805    ///(i.e a variables) at once
806    ///
807    ///This magic function takes a container as its argument
808    ///and fills its elements
809    ///with new columns (i.e. variables)
810    ///\param t can be
811    ///- a standard STL compatible iterable container with
812    ///\ref Col as its \c values_type
813    ///like
814    ///\code
815    ///std::vector<LpSolverBase::Col>
816    ///std::list<LpSolverBase::Col>
817    ///\endcode
818    ///- a standard STL compatible iterable container with
819    ///\ref Col as its \c mapped_type
820    ///like
821    ///\code
822    ///std::map<AnyType,LpSolverBase::Col>
823    ///\endcode
824    ///- an iterable lemon \ref concepts::WriteMap "write map" like
825    ///\code
826    ///ListGraph::NodeMap<LpSolverBase::Col>
827    ///ListGraph::EdgeMap<LpSolverBase::Col>
828    ///\endcode
829    ///\return The number of the created column.
830#ifdef DOXYGEN
831    template<class T>
832    int addColSet(T &t) { return 0;}
833#else
834    template<class T>
835    typename enable_if<typename T::value_type::LpSolverCol,int>::type
836    addColSet(T &t,dummy<0> = 0) {
837      int s=0;
838      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
839      return s;
840    }
841    template<class T>
842    typename enable_if<typename T::value_type::second_type::LpSolverCol,
843                       int>::type
844    addColSet(T &t,dummy<1> = 1) {
845      int s=0;
846      for(typename T::iterator i=t.begin();i!=t.end();++i) {
847        i->second=addCol();
848        s++;
849      }
850      return s;
851    }
852    template<class T>
853    typename enable_if<typename T::MapIt::Value::LpSolverCol,
854                       int>::type
855    addColSet(T &t,dummy<2> = 2) {
856      int s=0;
857      for(typename T::MapIt i(t); i!=INVALID; ++i)
858        {
859          i.set(addCol());
860          s++;
861        }
862      return s;
863    }
864#endif
865
866    ///Set a column (i.e a dual constraint) of the LP
867
868    ///\param c is the column to be modified
869    ///\param e is a dual linear expression (see \ref DualExpr)
870    ///a better one.
871    void col(Col c,const DualExpr &e) {
872      e.simplify();
873      _setColCoeffs(_lpId(c), ConstColIterator(e.begin(), *this),
874                    ConstColIterator(e.end(), *this));
875    }
876
877    ///Get a column (i.e a dual constraint) of the LP
878
879    ///\param r is the column to get
880    ///\return the dual expression associated to the column
881    DualExpr col(Col c) const {
882      DualExpr e;
883      _getColCoeffs(_lpId(c), ColIterator(std::inserter(e, e.end()), *this));
884      return e;
885    }
886
887    ///Add a new column to the LP
888
889    ///\param e is a dual linear expression (see \ref DualExpr)
890    ///\param obj is the corresponding component of the objective
891    ///function. It is 0 by default.
892    ///\return The created column.
893    Col addCol(const DualExpr &e, Value o = 0) {
894      Col c=addCol();
895      col(c,e);
896      objCoeff(c,o);
897      return c;
898    }
899
900    ///Add a new empty row (i.e a new constraint) to the LP
901
902    ///This function adds a new empty row (i.e a new constraint) to the LP.
903    ///\return The created row
904    Row addRow() { Row r; _addRow(); r.id = rows.addId(); return r;}
905
906    ///\brief Add several new rows
907    ///(i.e a constraints) at once
908    ///
909    ///This magic function takes a container as its argument
910    ///and fills its elements
911    ///with new row (i.e. variables)
912    ///\param t can be
913    ///- a standard STL compatible iterable container with
914    ///\ref Row as its \c values_type
915    ///like
916    ///\code
917    ///std::vector<LpSolverBase::Row>
918    ///std::list<LpSolverBase::Row>
919    ///\endcode
920    ///- a standard STL compatible iterable container with
921    ///\ref Row as its \c mapped_type
922    ///like
923    ///\code
924    ///std::map<AnyType,LpSolverBase::Row>
925    ///\endcode
926    ///- an iterable lemon \ref concepts::WriteMap "write map" like
927    ///\code
928    ///ListGraph::NodeMap<LpSolverBase::Row>
929    ///ListGraph::EdgeMap<LpSolverBase::Row>
930    ///\endcode
931    ///\return The number of rows created.
932#ifdef DOXYGEN
933    template<class T>
934    int addRowSet(T &t) { return 0;}
935#else
936    template<class T>
937    typename enable_if<typename T::value_type::LpSolverRow,int>::type
938    addRowSet(T &t,dummy<0> = 0) {
939      int s=0;
940      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
941      return s;
942    }
943    template<class T>
944    typename enable_if<typename T::value_type::second_type::LpSolverRow,
945                       int>::type
946    addRowSet(T &t,dummy<1> = 1) {
947      int s=0;
948      for(typename T::iterator i=t.begin();i!=t.end();++i) {
949        i->second=addRow();
950        s++;
951      }
952      return s;
953    }
954    template<class T>
955    typename enable_if<typename T::MapIt::Value::LpSolverRow,
956                       int>::type
957    addRowSet(T &t,dummy<2> = 2) {
958      int s=0;
959      for(typename T::MapIt i(t); i!=INVALID; ++i)
960        {
961          i.set(addRow());
962          s++;
963        }
964      return s;
965    }
966#endif
967
968    ///Set a row (i.e a constraint) of the LP
969
970    ///\param r is the row to be modified
971    ///\param l is lower bound (-\ref INF means no bound)
972    ///\param e is a linear expression (see \ref Expr)
973    ///\param u is the upper bound (\ref INF means no bound)
974    ///\bug This is a temporary function. The interface will change to
975    ///a better one.
976    ///\todo Option to control whether a constraint with a single variable is
977    ///added or not.
978    void row(Row r, Value l, const Expr &e, Value u) {
979      e.simplify();
980      _setRowCoeffs(_lpId(r), ConstRowIterator(e.begin(), *this),
981                    ConstRowIterator(e.end(), *this));
982      _setRowBounds(_lpId(r),l-e.constComp(),u-e.constComp());
983    }
984
985    ///Set a row (i.e a constraint) of the LP
986
987    ///\param r is the row to be modified
988    ///\param c is a linear expression (see \ref Constr)
989    void row(Row r, const Constr &c) {
990      row(r, c.lowerBounded()?c.lowerBound():-INF,
991          c.expr(), c.upperBounded()?c.upperBound():INF);
992    }
993
994   
995    ///Get a row (i.e a constraint) of the LP
996
997    ///\param r is the row to get
998    ///\return the expression associated to the row
999    Expr row(Row r) const {
1000      Expr e;
1001      _getRowCoeffs(_lpId(r), RowIterator(std::inserter(e, e.end()), *this));
1002      return e;
1003    }
1004
1005    ///Add a new row (i.e a new constraint) to the LP
1006
1007    ///\param l is the lower bound (-\ref INF means no bound)
1008    ///\param e is a linear expression (see \ref Expr)
1009    ///\param u is the upper bound (\ref INF means no bound)
1010    ///\return The created row.
1011    ///\bug This is a temporary function. The interface will change to
1012    ///a better one.
1013    Row addRow(Value l,const Expr &e, Value u) {
1014      Row r=addRow();
1015      row(r,l,e,u);
1016      return r;
1017    }
1018
1019    ///Add a new row (i.e a new constraint) to the LP
1020
1021    ///\param c is a linear expression (see \ref Constr)
1022    ///\return The created row.
1023    Row addRow(const Constr &c) {
1024      Row r=addRow();
1025      row(r,c);
1026      return r;
1027    }
1028    ///Erase a coloumn (i.e a variable) from the LP
1029
1030    ///\param c is the coloumn to be deleted
1031    ///\todo Please check this
1032    void eraseCol(Col c) {
1033      _eraseCol(_lpId(c));
1034      cols.eraseId(c.id);
1035    }
1036    ///Erase a  row (i.e a constraint) from the LP
1037
1038    ///\param r is the row to be deleted
1039    ///\todo Please check this
1040    void eraseRow(Row r) {
1041      _eraseRow(_lpId(r));
1042      rows.eraseId(r.id);
1043    }
1044
1045    /// Get the name of a column
1046   
1047    ///\param c is the coresponding coloumn
1048    ///\return The name of the colunm
1049    std::string colName(Col c) const {
1050      std::string name;
1051      _getColName(_lpId(c), name);
1052      return name;
1053    }
1054   
1055    /// Set the name of a column
1056   
1057    ///\param c is the coresponding coloumn
1058    ///\param name The name to be given
1059    void colName(Col c, const std::string& name) {
1060      _setColName(_lpId(c), name);
1061    }
1062
1063    /// Get the column by its name
1064   
1065    ///\param name The name of the column
1066    ///\return the proper column or \c INVALID
1067    Col colByName(const std::string& name) const {
1068      int k = _colByName(name);
1069      return k != -1 ? Col(cols.fixId(k)) : Col(INVALID);
1070    }
1071   
1072    /// Set an element of the coefficient matrix of the LP
1073
1074    ///\param r is the row of the element to be modified
1075    ///\param c is the coloumn of the element to be modified
1076    ///\param val is the new value of the coefficient
1077
1078    void coeff(Row r, Col c, Value val) {
1079      _setCoeff(_lpId(r),_lpId(c), val);
1080    }
1081
1082    /// Get an element of the coefficient matrix of the LP
1083
1084    ///\param r is the row of the element in question
1085    ///\param c is the coloumn of the element in question
1086    ///\return the corresponding coefficient
1087
1088    Value coeff(Row r, Col c) const {
1089      return _getCoeff(_lpId(r),_lpId(c));
1090    }
1091
1092    /// Set the lower bound of a column (i.e a variable)
1093
1094    /// The lower bound of a variable (column) has to be given by an
1095    /// extended number of type Value, i.e. a finite number of type
1096    /// Value or -\ref INF.
1097    void colLowerBound(Col c, Value value) {
1098      _setColLowerBound(_lpId(c),value);
1099    }
1100
1101    /// Get the lower bound of a column (i.e a variable)
1102
1103    /// This function returns the lower bound for column (variable) \t c
1104    /// (this might be -\ref INF as well). 
1105    ///\return The lower bound for coloumn \t c
1106    Value colLowerBound(Col c) const {
1107      return _getColLowerBound(_lpId(c));
1108    }
1109   
1110    ///\brief Set the lower bound of  several columns
1111    ///(i.e a variables) at once
1112    ///
1113    ///This magic function takes a container as its argument
1114    ///and applies the function on all of its elements.
1115    /// The lower bound of a variable (column) has to be given by an
1116    /// extended number of type Value, i.e. a finite number of type
1117    /// Value or -\ref INF.
1118#ifdef DOXYGEN
1119    template<class T>
1120    void colLowerBound(T &t, Value value) { return 0;}
1121#else
1122    template<class T>
1123    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1124    colLowerBound(T &t, Value value,dummy<0> = 0) {
1125      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1126        colLowerBound(*i, value);
1127      }
1128    }
1129    template<class T>
1130    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1131                       void>::type
1132    colLowerBound(T &t, Value value,dummy<1> = 1) {
1133      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1134        colLowerBound(i->second, value);
1135      }
1136    }
1137    template<class T>
1138    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1139                       void>::type
1140    colLowerBound(T &t, Value value,dummy<2> = 2) {
1141      for(typename T::MapIt i(t); i!=INVALID; ++i){
1142        colLowerBound(*i, value);
1143      }
1144    }
1145#endif
1146   
1147    /// Set the upper bound of a column (i.e a variable)
1148
1149    /// The upper bound of a variable (column) has to be given by an
1150    /// extended number of type Value, i.e. a finite number of type
1151    /// Value or \ref INF.
1152    void colUpperBound(Col c, Value value) {
1153      _setColUpperBound(_lpId(c),value);
1154    };
1155
1156    /// Get the upper bound of a column (i.e a variable)
1157
1158    /// This function returns the upper bound for column (variable) \t c
1159    /// (this might be \ref INF as well). 
1160    ///\return The upper bound for coloumn \t c
1161    Value colUpperBound(Col c) const {
1162      return _getColUpperBound(_lpId(c));
1163    }
1164
1165    ///\brief Set the upper bound of  several columns
1166    ///(i.e a variables) at once
1167    ///
1168    ///This magic function takes a container as its argument
1169    ///and applies the function on all of its elements.
1170    /// The upper bound of a variable (column) has to be given by an
1171    /// extended number of type Value, i.e. a finite number of type
1172    /// Value or \ref INF.
1173#ifdef DOXYGEN
1174    template<class T>
1175    void colUpperBound(T &t, Value value) { return 0;}
1176#else
1177    template<class T>
1178    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1179    colUpperBound(T &t, Value value,dummy<0> = 0) {
1180      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1181        colUpperBound(*i, value);
1182      }
1183    }
1184    template<class T>
1185    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1186                       void>::type
1187    colUpperBound(T &t, Value value,dummy<1> = 1) {
1188      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1189        colUpperBound(i->second, value);
1190      }
1191    }
1192    template<class T>
1193    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1194                       void>::type
1195    colUpperBound(T &t, Value value,dummy<2> = 2) {
1196      for(typename T::MapIt i(t); i!=INVALID; ++i){
1197        colUpperBound(*i, value);
1198      }
1199    }
1200#endif
1201
1202    /// Set the lower and the upper bounds of a column (i.e a variable)
1203
1204    /// The lower and the upper bounds of
1205    /// a variable (column) have to be given by an
1206    /// extended number of type Value, i.e. a finite number of type
1207    /// Value, -\ref INF or \ref INF.
1208    void colBounds(Col c, Value lower, Value upper) {
1209      _setColLowerBound(_lpId(c),lower);
1210      _setColUpperBound(_lpId(c),upper);
1211    }
1212   
1213    ///\brief Set the lower and the upper bound of several columns
1214    ///(i.e a variables) at once
1215    ///
1216    ///This magic function takes a container as its argument
1217    ///and applies the function on all of its elements.
1218    /// The lower and the upper bounds of
1219    /// a variable (column) have to be given by an
1220    /// extended number of type Value, i.e. a finite number of type
1221    /// Value, -\ref INF or \ref INF.
1222#ifdef DOXYGEN
1223    template<class T>
1224    void colBounds(T &t, Value lower, Value upper) { return 0;}
1225#else
1226    template<class T>
1227    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1228    colBounds(T &t, Value lower, Value upper,dummy<0> = 0) {
1229      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1230        colBounds(*i, lower, upper);
1231      }
1232    }
1233    template<class T>
1234    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1235                       void>::type
1236    colBounds(T &t, Value lower, Value upper,dummy<1> = 1) {
1237      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1238        colBounds(i->second, lower, upper);
1239      }
1240    }
1241    template<class T>
1242    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1243                       void>::type
1244    colBounds(T &t, Value lower, Value upper,dummy<2> = 2) {
1245      for(typename T::MapIt i(t); i!=INVALID; ++i){
1246        colBounds(*i, lower, upper);
1247      }
1248    }
1249#endif
1250   
1251
1252    /// Set the lower and the upper bounds of a row (i.e a constraint)
1253
1254    /// The lower and the upper bound of a constraint (row) have to be
1255    /// given by an extended number of type Value, i.e. a finite
1256    /// number of type Value, -\ref INF or \ref INF. There is no
1257    /// separate function for the lower and the upper bound because
1258    /// that would have been hard to implement for CPLEX.
1259    void rowBounds(Row c, Value lower, Value upper) {
1260      _setRowBounds(_lpId(c),lower, upper);
1261    }
1262   
1263    /// Get the lower and the upper bounds of a row (i.e a constraint)
1264
1265    /// The lower and the upper bound of
1266    /// a constraint (row) are 
1267    /// extended numbers of type Value, i.e.  finite numbers of type
1268    /// Value, -\ref INF or \ref INF.
1269    /// \todo There is no separate function for the
1270    /// lower and the upper bound because we had problems with the
1271    /// implementation of the setting functions for CPLEX: 
1272    /// check out whether this can be done for these functions.
1273    void getRowBounds(Row c, Value &lower, Value &upper) const {
1274      _getRowBounds(_lpId(c),lower, upper);
1275    }
1276
1277    ///Set an element of the objective function
1278    void objCoeff(Col c, Value v) {_setObjCoeff(_lpId(c),v); };
1279
1280    ///Get an element of the objective function
1281    Value objCoeff(Col c) const { return _getObjCoeff(_lpId(c)); };
1282
1283    ///Set the objective function
1284
1285    ///\param e is a linear expression of type \ref Expr.
1286    void obj(Expr e) {
1287      _clearObj();
1288      for (Expr::iterator i=e.begin(); i!=e.end(); ++i)
1289        objCoeff((*i).first,(*i).second);
1290      obj_const_comp=e.constComp();
1291    }
1292
1293    ///Get the objective function
1294
1295    ///\return the objective function as a linear expression of type \ref Expr.
1296    Expr obj() const {
1297      Expr e;
1298      for (ColIt it(*this); it != INVALID; ++it) {
1299        double c = objCoeff(it);
1300        if (c != 0.0) {
1301          e.insert(std::make_pair(it, c));
1302        }
1303      }
1304      return e;
1305    }
1306   
1307
1308    ///Maximize
1309    void max() { _setMax(); }
1310    ///Minimize
1311    void min() { _setMin(); }
1312
1313    ///Query function: is this a maximization problem?
1314    bool isMax() const {return _isMax(); }
1315
1316    ///Query function: is this a minimization problem?
1317    bool isMin() const {return !isMax(); }
1318   
1319    ///@}
1320
1321
1322    ///\name Solve the LP
1323
1324    ///@{
1325
1326    ///\e Solve the LP problem at hand
1327    ///
1328    ///\return The result of the optimization procedure. Possible
1329    ///values and their meanings can be found in the documentation of
1330    ///\ref SolveExitStatus.
1331    ///
1332    ///\todo Which method is used to solve the problem
1333    SolveExitStatus solve() { return _solve(); }
1334   
1335    ///@}
1336   
1337    ///\name Obtain the solution
1338
1339    ///@{
1340
1341    /// The status of the primal problem (the original LP problem)
1342    SolutionStatus primalStatus() const {
1343      return _getPrimalStatus();
1344    }
1345
1346    /// The status of the dual (of the original LP) problem
1347    SolutionStatus dualStatus() const {
1348      return _getDualStatus();
1349    }
1350
1351    ///The type of the original LP problem
1352    ProblemTypes problemType() const {
1353      return _getProblemType();
1354    }
1355
1356    ///\e
1357    Value primal(Col c) const { return _getPrimal(_lpId(c)); }
1358    ///\e
1359    Value primal(const Expr& e) const {
1360      double res = e.constComp();
1361      for (std::map<Col, double>::const_iterator it = e.begin();
1362           it != e.end(); ++it) {
1363        res += _getPrimal(_lpId(it->first)) * it->second;
1364      }
1365      return res;
1366    }
1367
1368    ///\e
1369    Value dual(Row r) const { return _getDual(_lpId(r)); }
1370    ///\e
1371    Value dual(const DualExpr& e) const {
1372      double res = 0.0;
1373      for (std::map<Row, double>::const_iterator it = e.begin();
1374           it != e.end(); ++it) {
1375        res += _getPrimal(_lpId(it->first)) * it->second;
1376      }
1377      return res;
1378    }
1379
1380    ///\e
1381    bool isBasicCol(Col c) const { return _isBasicCol(_lpId(c)); }
1382
1383    ///\e
1384
1385    ///\return
1386    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
1387    /// of the primal problem, depending on whether we minimize or maximize.
1388    ///- \ref NaN if no primal solution is found.
1389    ///- The (finite) objective value if an optimal solution is found.
1390    Value primalValue() const { return _getPrimalValue()+obj_const_comp;}
1391    ///@}
1392   
1393  }; 
1394
1395
1396  /// \ingroup lp_group
1397  ///
1398  /// \brief Common base class for MIP solvers
1399  /// \todo Much more docs
1400  class MipSolverBase : virtual public LpSolverBase{
1401  public:
1402
1403    ///Possible variable (coloumn) types (e.g. real, integer, binary etc.)
1404    enum ColTypes {
1405      ///Continuous variable
1406      REAL = 0,
1407      ///Integer variable
1408
1409      ///Unfortunately, cplex 7.5 somewhere writes something like
1410      ///#define INTEGER 'I'
1411      INT = 1
1412      ///\todo No support for other types yet.
1413    };
1414
1415    ///Sets the type of the given coloumn to the given type
1416    ///
1417    ///Sets the type of the given coloumn to the given type.
1418    void colType(Col c, ColTypes col_type) {
1419      _colType(_lpId(c),col_type);
1420    }
1421
1422    ///Gives back the type of the column.
1423    ///
1424    ///Gives back the type of the column.
1425    ColTypes colType(Col c) const {
1426      return _colType(_lpId(c));
1427    }
1428
1429    ///Sets the type of the given Col to integer or remove that property.
1430    ///
1431    ///Sets the type of the given Col to integer or remove that property.
1432    void integer(Col c, bool enable) {
1433      if (enable)
1434        colType(c,INT);
1435      else
1436        colType(c,REAL);
1437    }
1438
1439    ///Gives back whether the type of the column is integer or not.
1440    ///
1441    ///Gives back the type of the column.
1442    ///\return true if the column has integer type and false if not.
1443    bool integer(Col c) const {
1444      return (colType(c)==INT);
1445    }
1446
1447    /// The status of the MIP problem
1448    SolutionStatus mipStatus() const {
1449      return _getMipStatus();
1450    }
1451
1452  protected:
1453
1454    virtual ColTypes _colType(int col) const = 0;
1455    virtual void _colType(int col, ColTypes col_type) = 0;
1456    virtual SolutionStatus _getMipStatus() const = 0;
1457
1458  };
1459 
1460  ///\relates LpSolverBase::Expr
1461  ///
1462  inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a,
1463                                      const LpSolverBase::Expr &b)
1464  {
1465    LpSolverBase::Expr tmp(a);
1466    tmp+=b;
1467    return tmp;
1468  }
1469  ///\e
1470 
1471  ///\relates LpSolverBase::Expr
1472  ///
1473  inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a,
1474                                      const LpSolverBase::Expr &b)
1475  {
1476    LpSolverBase::Expr tmp(a);
1477    tmp-=b;
1478    return tmp;
1479  }
1480  ///\e
1481 
1482  ///\relates LpSolverBase::Expr
1483  ///
1484  inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a,
1485                                      const LpSolverBase::Value &b)
1486  {
1487    LpSolverBase::Expr tmp(a);
1488    tmp*=b;
1489    return tmp;
1490  }
1491 
1492  ///\e
1493 
1494  ///\relates LpSolverBase::Expr
1495  ///
1496  inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a,
1497                                      const LpSolverBase::Expr &b)
1498  {
1499    LpSolverBase::Expr tmp(b);
1500    tmp*=a;
1501    return tmp;
1502  }
1503  ///\e
1504 
1505  ///\relates LpSolverBase::Expr
1506  ///
1507  inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a,
1508                                      const LpSolverBase::Value &b)
1509  {
1510    LpSolverBase::Expr tmp(a);
1511    tmp/=b;
1512    return tmp;
1513  }
1514 
1515  ///\e
1516 
1517  ///\relates LpSolverBase::Constr
1518  ///
1519  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1520                                         const LpSolverBase::Expr &f)
1521  {
1522    return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0);
1523  }
1524
1525  ///\e
1526 
1527  ///\relates LpSolverBase::Constr
1528  ///
1529  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e,
1530                                         const LpSolverBase::Expr &f)
1531  {
1532    return LpSolverBase::Constr(e,f);
1533  }
1534
1535  ///\e
1536 
1537  ///\relates LpSolverBase::Constr
1538  ///
1539  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1540                                         const LpSolverBase::Value &f)
1541  {
1542    return LpSolverBase::Constr(-LpSolverBase::INF,e,f);
1543  }
1544
1545  ///\e
1546 
1547  ///\relates LpSolverBase::Constr
1548  ///
1549  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1550                                         const LpSolverBase::Expr &f)
1551  {
1552    return LpSolverBase::Constr(-LpSolverBase::INF,f-e,0);
1553  }
1554
1555
1556  ///\e
1557 
1558  ///\relates LpSolverBase::Constr
1559  ///
1560  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e,
1561                                         const LpSolverBase::Expr &f)
1562  {
1563    return LpSolverBase::Constr(f,e);
1564  }
1565
1566
1567  ///\e
1568 
1569  ///\relates LpSolverBase::Constr
1570  ///
1571  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1572                                         const LpSolverBase::Value &f)
1573  {
1574    return LpSolverBase::Constr(f,e,LpSolverBase::INF);
1575  }
1576
1577  ///\e
1578
1579  ///\relates LpSolverBase::Constr
1580  ///
1581  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
1582                                         const LpSolverBase::Value &f)
1583  {
1584    return LpSolverBase::Constr(f,e,f);
1585  }
1586
1587  ///\e
1588 
1589  ///\relates LpSolverBase::Constr
1590  ///
1591  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
1592                                         const LpSolverBase::Expr &f)
1593  {
1594    return LpSolverBase::Constr(0,e-f,0);
1595  }
1596
1597  ///\e
1598 
1599  ///\relates LpSolverBase::Constr
1600  ///
1601  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n,
1602                                         const LpSolverBase::Constr&c)
1603  {
1604    LpSolverBase::Constr tmp(c);
1605    ///\todo Create an own exception type.
1606    if(!LpSolverBase::isNaN(tmp.lowerBound())) throw LogicError();
1607    else tmp.lowerBound()=n;
1608    return tmp;
1609  }
1610  ///\e
1611 
1612  ///\relates LpSolverBase::Constr
1613  ///
1614  inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c,
1615                                         const LpSolverBase::Value &n)
1616  {
1617    LpSolverBase::Constr tmp(c);
1618    ///\todo Create an own exception type.
1619    if(!LpSolverBase::isNaN(tmp.upperBound())) throw LogicError();
1620    else tmp.upperBound()=n;
1621    return tmp;
1622  }
1623
1624  ///\e
1625 
1626  ///\relates LpSolverBase::Constr
1627  ///
1628  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n,
1629                                         const LpSolverBase::Constr&c)
1630  {
1631    LpSolverBase::Constr tmp(c);
1632    ///\todo Create an own exception type.
1633    if(!LpSolverBase::isNaN(tmp.upperBound())) throw LogicError();
1634    else tmp.upperBound()=n;
1635    return tmp;
1636  }
1637  ///\e
1638 
1639  ///\relates LpSolverBase::Constr
1640  ///
1641  inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c,
1642                                         const LpSolverBase::Value &n)
1643  {
1644    LpSolverBase::Constr tmp(c);
1645    ///\todo Create an own exception type.
1646    if(!LpSolverBase::isNaN(tmp.lowerBound())) throw LogicError();
1647    else tmp.lowerBound()=n;
1648    return tmp;
1649  }
1650
1651  ///\e
1652 
1653  ///\relates LpSolverBase::DualExpr
1654  ///
1655  inline LpSolverBase::DualExpr operator+(const LpSolverBase::DualExpr &a,
1656                                          const LpSolverBase::DualExpr &b)
1657  {
1658    LpSolverBase::DualExpr tmp(a);
1659    tmp+=b;
1660    return tmp;
1661  }
1662  ///\e
1663 
1664  ///\relates LpSolverBase::DualExpr
1665  ///
1666  inline LpSolverBase::DualExpr operator-(const LpSolverBase::DualExpr &a,
1667                                          const LpSolverBase::DualExpr &b)
1668  {
1669    LpSolverBase::DualExpr tmp(a);
1670    tmp-=b;
1671    return tmp;
1672  }
1673  ///\e
1674 
1675  ///\relates LpSolverBase::DualExpr
1676  ///
1677  inline LpSolverBase::DualExpr operator*(const LpSolverBase::DualExpr &a,
1678                                          const LpSolverBase::Value &b)
1679  {
1680    LpSolverBase::DualExpr tmp(a);
1681    tmp*=b;
1682    return tmp;
1683  }
1684 
1685  ///\e
1686 
1687  ///\relates LpSolverBase::DualExpr
1688  ///
1689  inline LpSolverBase::DualExpr operator*(const LpSolverBase::Value &a,
1690                                          const LpSolverBase::DualExpr &b)
1691  {
1692    LpSolverBase::DualExpr tmp(b);
1693    tmp*=a;
1694    return tmp;
1695  }
1696  ///\e
1697 
1698  ///\relates LpSolverBase::DualExpr
1699  ///
1700  inline LpSolverBase::DualExpr operator/(const LpSolverBase::DualExpr &a,
1701                                          const LpSolverBase::Value &b)
1702  {
1703    LpSolverBase::DualExpr tmp(a);
1704    tmp/=b;
1705    return tmp;
1706  }
1707 
1708
1709} //namespace lemon
1710
1711#endif //LEMON_LP_BASE_H
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