COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/lp_base.h @ 2366:bfbdded3763a

Last change on this file since 2366:bfbdded3763a was 2366:bfbdded3763a, checked in by Balazs Dezso, 13 years ago

Using const in lp interface
colByName functionality

File size: 46.0 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<iostream>
23
24
25#include<vector>
26#include<map>
27#include<limits>
28#include<cmath>
29
30#include<lemon/error.h>
31#include<lemon/bits/invalid.h>
32#include<lemon/bits/utility.h>
33#include<lemon/bits/lp_id.h>
34
35///\file
36///\brief The interface of the LP solver interface.
37///\ingroup gen_opt_group
38namespace lemon {
39
40  ///Common base class for LP solvers
41 
42  ///\todo Much more docs
43  ///\ingroup gen_opt_group
44  class LpSolverBase {
45
46  protected:
47
48    _lp_bits::LpId rows;
49    _lp_bits::LpId cols;
50   
51  public:
52   
53    ///Possible outcomes of an LP solving procedure
54    enum SolveExitStatus {
55      ///This means that the problem has been successfully solved: either
56      ///an optimal solution has been found or infeasibility/unboundedness
57      ///has been proved.
58      SOLVED = 0,
59      ///Any other case (including the case when some user specified
60      ///limit has been exceeded)
61      UNSOLVED = 1
62    };
63     
64      ///\e
65    enum SolutionStatus {
66      ///Feasible solution hasn't been found (but may exist).
67
68      ///\todo NOTFOUND might be a better name.
69      ///
70      UNDEFINED = 0,
71      ///The problem has no feasible solution
72      INFEASIBLE = 1,
73      ///Feasible solution found
74      FEASIBLE = 2,
75      ///Optimal solution exists and found
76      OPTIMAL = 3,
77      ///The cost function is unbounded
78
79      ///\todo Give a feasible solution and an infinite ray (and the
80      ///corresponding bases)
81      INFINITE = 4
82    };
83
84    ///\e The type of the investigated LP problem
85    enum ProblemTypes {
86      ///Primal-dual feasible
87      PRIMAL_DUAL_FEASIBLE = 0,
88      ///Primal feasible dual infeasible
89      PRIMAL_FEASIBLE_DUAL_INFEASIBLE = 1,
90      ///Primal infeasible dual feasible
91      PRIMAL_INFEASIBLE_DUAL_FEASIBLE = 2,
92      ///Primal-dual infeasible
93      PRIMAL_DUAL_INFEASIBLE = 3,
94      ///Could not determine so far
95      UNKNOWN = 4
96    };
97
98    ///The floating point type used by the solver
99    typedef double Value;
100    ///The infinity constant
101    static const Value INF;
102    ///The not a number constant
103    static const Value NaN;
104
105    static inline bool isNaN(const Value& v) { return v!=v; }
106   
107    friend class Col;
108    friend class ColIt;
109    friend class Row;
110   
111    ///Refer to a column of the LP.
112
113    ///This type is used to refer to a column of the LP.
114    ///
115    ///Its value remains valid and correct even after the addition or erase of
116    ///other columns.
117    ///
118    ///\todo Document what can one do with a Col (INVALID, comparing,
119    ///it is similar to Node/Edge)
120    class Col {
121    protected:
122      int id;
123      friend class LpSolverBase;
124      friend class MipSolverBase;
125      explicit Col(int _id) : id(_id) {}
126    public:
127      typedef Value ExprValue;
128      typedef True LpSolverCol;
129      Col() {}
130      Col(const Invalid&) : id(-1) {}
131      bool operator< (Col c) const  {return id< c.id;}
132      bool operator> (Col c) const  {return id> c.id;}
133      bool operator==(Col c) const  {return id==c.id;}
134      bool operator!=(Col c) const  {return id!=c.id;}
135    };
136
137    class ColIt : public Col {
138      const LpSolverBase *_lp;
139    public:
140      ColIt() {}
141      ColIt(const LpSolverBase &lp) : _lp(&lp)
142      {
143        _lp->cols.firstFix(id);
144      }
145      ColIt(const Invalid&) : Col(INVALID) {}
146      ColIt &operator++()
147      {
148        _lp->cols.nextFix(id);
149        return *this;
150      }
151    };
152
153    static int id(const Col& col) { return col.id; }
154 
155     
156    ///Refer to a row of the LP.
157
158    ///This type is used to refer to a row of the LP.
159    ///
160    ///Its value remains valid and correct even after the addition or erase of
161    ///other rows.
162    ///
163    ///\todo Document what can one do with a Row (INVALID, comparing,
164    ///it is similar to Node/Edge)
165    class Row {
166    protected:
167      int id;
168      friend class LpSolverBase;
169      explicit Row(int _id) : id(_id) {}
170    public:
171      typedef Value ExprValue;
172      typedef True LpSolverRow;
173      Row() {}
174      Row(const Invalid&) : id(-1) {}
175
176      bool operator< (Row c) const  {return id< c.id;}
177      bool operator> (Row c) const  {return id> c.id;}
178      bool operator==(Row c) const  {return id==c.id;}
179      bool operator!=(Row c) const  {return id!=c.id;}
180    };
181
182    class RowIt : public Row {
183      const LpSolverBase *_lp;
184    public:
185      RowIt() {}
186      RowIt(const LpSolverBase &lp) : _lp(&lp)
187      {
188        _lp->rows.firstFix(id);
189      }
190      RowIt(const Invalid&) : Row(INVALID) {}
191      RowIt &operator++()
192      {
193        _lp->rows.nextFix(id);
194        return *this;
195      }
196    };
197
198    static int id(const Row& row) { return row.id; }
199
200  protected:
201
202    int _lpId(const Col& col) const {
203      return cols.floatingId(id(col));
204    }
205
206    int _lpId(const Row& row) const {
207      return rows.floatingId(id(row));
208    }
209
210    Col _item(int id, Col) const {
211      return Col(cols.fixId(id));
212    }
213
214    Row _item(int id, Row) const {
215      return Row(rows.fixId(id));
216    }
217
218
219  public:
220   
221    ///Linear expression of variables and a constant component
222   
223    ///This data structure stores a linear expression of the variables
224    ///(\ref Col "Col"s) and also has a constant component.
225    ///
226    ///There are several ways to access and modify the contents of this
227    ///container.
228    ///- Its it fully compatible with \c std::map<Col,double>, so for expamle
229    ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can
230    ///read and modify the coefficients like
231    ///these.
232    ///\code
233    ///e[v]=5;
234    ///e[v]+=12;
235    ///e.erase(v);
236    ///\endcode
237    ///or you can also iterate through its elements.
238    ///\code
239    ///double s=0;
240    ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i)
241    ///  s+=i->second;
242    ///\endcode
243    ///(This code computes the sum of all coefficients).
244    ///- Numbers (<tt>double</tt>'s)
245    ///and variables (\ref Col "Col"s) directly convert to an
246    ///\ref Expr and the usual linear operations are defined, so 
247    ///\code
248    ///v+w
249    ///2*v-3.12*(v-w/2)+2
250    ///v*2.1+(3*v+(v*12+w+6)*3)/2
251    ///\endcode
252    ///are valid \ref Expr "Expr"essions.
253    ///The usual assignment operations are also defined.
254    ///\code
255    ///e=v+w;
256    ///e+=2*v-3.12*(v-w/2)+2;
257    ///e*=3.4;
258    ///e/=5;
259    ///\endcode
260    ///- The constant member can be set and read by \ref constComp()
261    ///\code
262    ///e.constComp()=12;
263    ///double c=e.constComp();
264    ///\endcode
265    ///
266    ///\note \ref clear() not only sets all coefficients to 0 but also
267    ///clears the constant components.
268    ///
269    ///\sa Constr
270    ///
271    class Expr : public std::map<Col,Value>
272    {
273    public:
274      typedef LpSolverBase::Col Key;
275      typedef LpSolverBase::Value Value;
276     
277    protected:
278      typedef std::map<Col,Value> Base;
279     
280      Value const_comp;
281    public:
282      typedef True IsLinExpression;
283      ///\e
284      Expr() : Base(), const_comp(0) { }
285      ///\e
286      Expr(const Key &v) : const_comp(0) {
287        Base::insert(std::make_pair(v, 1));
288      }
289      ///\e
290      Expr(const Value &v) : const_comp(v) {}
291      ///\e
292      void set(const Key &v,const Value &c) {
293        Base::insert(std::make_pair(v, c));
294      }
295      ///\e
296      Value &constComp() { return const_comp; }
297      ///\e
298      const Value &constComp() const { return const_comp; }
299     
300      ///Removes the components with zero coefficient.
301      void simplify() {
302        for (Base::iterator i=Base::begin(); i!=Base::end();) {
303          Base::iterator j=i;
304          ++j;
305          if ((*i).second==0) Base::erase(i);
306          i=j;
307        }
308      }
309
310      void simplify() const {
311        const_cast<Expr*>(this)->simplify();
312      }
313
314      ///Removes the coefficients closer to zero than \c tolerance.
315      void simplify(double &tolerance) {
316        for (Base::iterator i=Base::begin(); i!=Base::end();) {
317          Base::iterator j=i;
318          ++j;
319          if (std::fabs((*i).second)<tolerance) Base::erase(i);
320          i=j;
321        }
322      }
323
324      ///Sets all coefficients and the constant component to 0.
325      void clear() {
326        Base::clear();
327        const_comp=0;
328      }
329
330      ///\e
331      Expr &operator+=(const Expr &e) {
332        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
333          (*this)[j->first]+=j->second;
334        const_comp+=e.const_comp;
335        return *this;
336      }
337      ///\e
338      Expr &operator-=(const Expr &e) {
339        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
340          (*this)[j->first]-=j->second;
341        const_comp-=e.const_comp;
342        return *this;
343      }
344      ///\e
345      Expr &operator*=(const Value &c) {
346        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
347          j->second*=c;
348        const_comp*=c;
349        return *this;
350      }
351      ///\e
352      Expr &operator/=(const Value &c) {
353        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
354          j->second/=c;
355        const_comp/=c;
356        return *this;
357      }
358
359      //std::ostream &
360      void prettyPrint(std::ostream &os) {
361        //std::fmtflags os.flags();
362        //os.setf(std::ios::showpos);
363        Base::iterator j=Base::begin();
364        if (j!=Base::end())
365          os<<j->second<<"*x["<<id(j->first)<<"]";
366        ++j;
367        for (; j!=Base::end(); ++j){
368          if (j->second>=0)
369            os<<"+";
370          os<<j->second<<"*x["<<id(j->first)<<"]";
371        }
372        //Nem valami korrekt, de nem talaltam meg, hogy kell
373        //os.unsetf(std::ios::showpos);
374
375        //return os;
376      }
377
378    };
379   
380    ///Linear constraint
381
382    ///This data stucture represents a linear constraint in the LP.
383    ///Basically it is a linear expression with a lower or an upper bound
384    ///(or both). These parts of the constraint can be obtained by the member
385    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
386    ///respectively.
387    ///There are two ways to construct a constraint.
388    ///- You can set the linear expression and the bounds directly
389    ///  by the functions above.
390    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
391    ///  are defined between expressions, or even between constraints whenever
392    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
393    ///  \c s and \c t are numbers, then the followings are valid expressions
394    ///  and thus they can be used directly e.g. in \ref addRow() whenever
395    ///  it makes sense.
396    ///\code
397    ///  e<=s
398    ///  e<=f
399    ///  e==f
400    ///  s<=e<=t
401    ///  e>=t
402    ///\endcode
403    ///\warning The validity of a constraint is checked only at run time, so
404    ///e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will compile, but will throw a
405    ///\ref LogicError exception.
406    class Constr
407    {
408    public:
409      typedef LpSolverBase::Expr Expr;
410      typedef Expr::Key Key;
411      typedef Expr::Value Value;
412     
413    protected:
414      Expr _expr;
415      Value _lb,_ub;
416    public:
417      ///\e
418      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
419      ///\e
420      Constr(Value lb,const Expr &e,Value ub) :
421        _expr(e), _lb(lb), _ub(ub) {}
422      ///\e
423      Constr(const Expr &e,Value ub) :
424        _expr(e), _lb(NaN), _ub(ub) {}
425      ///\e
426      Constr(Value lb,const Expr &e) :
427        _expr(e), _lb(lb), _ub(NaN) {}
428      ///\e
429      Constr(const Expr &e) :
430        _expr(e), _lb(NaN), _ub(NaN) {}
431      ///\e
432      void clear()
433      {
434        _expr.clear();
435        _lb=_ub=NaN;
436      }
437
438      ///Reference to the linear expression
439      Expr &expr() { return _expr; }
440      ///Cont reference to the linear expression
441      const Expr &expr() const { return _expr; }
442      ///Reference to the lower bound.
443
444      ///\return
445      ///- \ref INF "INF": the constraint is lower unbounded.
446      ///- \ref NaN "NaN": lower bound has not been set.
447      ///- finite number: the lower bound
448      Value &lowerBound() { return _lb; }
449      ///The const version of \ref lowerBound()
450      const Value &lowerBound() const { return _lb; }
451      ///Reference to the upper bound.
452
453      ///\return
454      ///- \ref INF "INF": the constraint is upper unbounded.
455      ///- \ref NaN "NaN": upper bound has not been set.
456      ///- finite number: the upper bound
457      Value &upperBound() { return _ub; }
458      ///The const version of \ref upperBound()
459      const Value &upperBound() const { return _ub; }
460      ///Is the constraint lower bounded?
461      bool lowerBounded() const {
462        using namespace std;
463        return finite(_lb);
464      }
465      ///Is the constraint upper bounded?
466      bool upperBounded() const {
467        using namespace std;
468        return finite(_ub);
469      }
470
471      void prettyPrint(std::ostream &os) {
472        if (_lb==-LpSolverBase::INF||isNaN(_lb))
473          os<<"-infty<=";
474        else
475          os<<_lb<<"<=";
476        _expr.prettyPrint(os);
477        if (_ub==LpSolverBase::INF)
478          os<<"<=infty";
479        else
480          os<<"<="<<_ub;
481        //return os;
482      }
483
484    };
485   
486    ///Linear expression of rows
487   
488    ///This data structure represents a column of the matrix,
489    ///thas is it strores a linear expression of the dual variables
490    ///(\ref Row "Row"s).
491    ///
492    ///There are several ways to access and modify the contents of this
493    ///container.
494    ///- Its it fully compatible with \c std::map<Row,double>, so for expamle
495    ///if \c e is an DualExpr and \c v
496    ///and \c w are of type \ref Row, then you can
497    ///read and modify the coefficients like
498    ///these.
499    ///\code
500    ///e[v]=5;
501    ///e[v]+=12;
502    ///e.erase(v);
503    ///\endcode
504    ///or you can also iterate through its elements.
505    ///\code
506    ///double s=0;
507    ///for(LpSolverBase::DualExpr::iterator i=e.begin();i!=e.end();++i)
508    ///  s+=i->second;
509    ///\endcode
510    ///(This code computes the sum of all coefficients).
511    ///- Numbers (<tt>double</tt>'s)
512    ///and variables (\ref Row "Row"s) directly convert to an
513    ///\ref DualExpr and the usual linear operations are defined, so
514    ///\code
515    ///v+w
516    ///2*v-3.12*(v-w/2)
517    ///v*2.1+(3*v+(v*12+w)*3)/2
518    ///\endcode
519    ///are valid \ref DualExpr "DualExpr"essions.
520    ///The usual assignment operations are also defined.
521    ///\code
522    ///e=v+w;
523    ///e+=2*v-3.12*(v-w/2);
524    ///e*=3.4;
525    ///e/=5;
526    ///\endcode
527    ///
528    ///\sa Expr
529    ///
530    class DualExpr : public std::map<Row,Value>
531    {
532    public:
533      typedef LpSolverBase::Row Key;
534      typedef LpSolverBase::Value Value;
535     
536    protected:
537      typedef std::map<Row,Value> Base;
538     
539    public:
540      typedef True IsLinExpression;
541      ///\e
542      DualExpr() : Base() { }
543      ///\e
544      DualExpr(const Key &v) {
545        Base::insert(std::make_pair(v, 1));
546      }
547      ///\e
548      void set(const Key &v,const Value &c) {
549        Base::insert(std::make_pair(v, c));
550      }
551     
552      ///Removes the components with zero coefficient.
553      void simplify() {
554        for (Base::iterator i=Base::begin(); i!=Base::end();) {
555          Base::iterator j=i;
556          ++j;
557          if ((*i).second==0) Base::erase(i);
558          i=j;
559        }
560      }
561
562      void simplify() const {
563        const_cast<DualExpr*>(this)->simplify();
564      }
565
566      ///Removes the coefficients closer to zero than \c tolerance.
567      void simplify(double &tolerance) {
568        for (Base::iterator i=Base::begin(); i!=Base::end();) {
569          Base::iterator j=i;
570          ++j;
571          if (std::fabs((*i).second)<tolerance) Base::erase(i);
572          i=j;
573        }
574      }
575
576      ///Sets all coefficients to 0.
577      void clear() {
578        Base::clear();
579      }
580
581      ///\e
582      DualExpr &operator+=(const DualExpr &e) {
583        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
584          (*this)[j->first]+=j->second;
585        return *this;
586      }
587      ///\e
588      DualExpr &operator-=(const DualExpr &e) {
589        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
590          (*this)[j->first]-=j->second;
591        return *this;
592      }
593      ///\e
594      DualExpr &operator*=(const Value &c) {
595        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
596          j->second*=c;
597        return *this;
598      }
599      ///\e
600      DualExpr &operator/=(const Value &c) {
601        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
602          j->second/=c;
603        return *this;
604      }
605    };
606   
607
608  private:
609
610    template <typename _Expr>
611    class MappedOutputIterator {
612    public:
613
614      typedef std::insert_iterator<_Expr> Base;
615
616      typedef std::output_iterator_tag iterator_category;
617      typedef void difference_type;
618      typedef void value_type;
619      typedef void reference;
620      typedef void pointer;
621     
622      MappedOutputIterator(const Base& _base, const LpSolverBase& _lp)
623        : base(_base), lp(_lp) {}
624
625      MappedOutputIterator& operator*() {
626        return *this;
627      }
628
629      MappedOutputIterator& operator=(const std::pair<int, Value>& value) {
630        *base = std::make_pair(lp._item(value.first, typename _Expr::Key()),
631                               value.second);
632        return *this;
633      }
634
635      MappedOutputIterator& operator++() {
636        ++base;
637        return *this;
638      }
639
640      MappedOutputIterator operator++(int) {
641        MappedOutputIterator tmp(*this);
642        ++base;
643        return tmp;
644      }
645
646      bool operator==(const MappedOutputIterator& it) const {
647        return base == it.base;
648      }
649
650      bool operator!=(const MappedOutputIterator& it) const {
651        return base != it.base;
652      }
653
654    private:
655      Base base;
656      const LpSolverBase& lp;
657    };
658
659    template <typename Expr>
660    class MappedInputIterator {
661    public:
662
663      typedef typename Expr::const_iterator Base;
664
665      typedef typename Base::iterator_category iterator_category;
666      typedef typename Base::difference_type difference_type;
667      typedef const std::pair<int, Value> value_type;
668      typedef value_type reference;
669      class pointer {
670      public:
671        pointer(value_type& _value) : value(_value) {}
672        value_type* operator->() { return &value; }
673      private:
674        value_type value;
675      };
676
677      MappedInputIterator(const Base& _base, const LpSolverBase& _lp)
678        : base(_base), lp(_lp) {}
679
680      reference operator*() {
681        return std::make_pair(lp._lpId(base->first), base->second);
682      }
683
684      pointer operator->() {
685        return pointer(operator*());
686      }
687
688      MappedInputIterator& operator++() {
689        ++base;
690        return *this;
691      }
692
693      MappedInputIterator operator++(int) {
694        MappedInputIterator tmp(*this);
695        ++base;
696        return tmp;
697      }
698
699      bool operator==(const MappedInputIterator& it) const {
700        return base == it.base;
701      }
702
703      bool operator!=(const MappedInputIterator& it) const {
704        return base != it.base;
705      }
706
707    private:
708      Base base;
709      const LpSolverBase& lp;
710    };
711
712  protected:
713
714    /// STL compatible iterator for lp col
715    typedef MappedInputIterator<Expr> ConstRowIterator;
716    /// STL compatible iterator for lp row
717    typedef MappedInputIterator<DualExpr> ConstColIterator;
718
719    /// STL compatible iterator for lp col
720    typedef MappedOutputIterator<Expr> RowIterator;
721    /// STL compatible iterator for lp row
722    typedef MappedOutputIterator<DualExpr> ColIterator;
723
724    //Abstract virtual functions
725    virtual LpSolverBase &_newLp() = 0;
726    virtual LpSolverBase &_copyLp(){
727      ///\todo This should be implemented here, too, when we have
728      ///problem retrieving routines. It can be overriden.
729
730      //Starting:
731      LpSolverBase & newlp(_newLp());
732      return newlp;
733      //return *(LpSolverBase*)0;
734    };
735
736    virtual int _addCol() = 0;
737    virtual int _addRow() = 0;
738
739    virtual void _eraseCol(int col) = 0;
740    virtual void _eraseRow(int row) = 0;
741
742    virtual void _getColName(int col, std::string & name) const = 0;
743    virtual void _setColName(int col, const std::string & name) = 0;
744    virtual int _colByName(const std::string& name) const = 0;
745
746    virtual void _setRowCoeffs(int i, ConstRowIterator b,
747                               ConstRowIterator e) = 0;
748    virtual void _getRowCoeffs(int i, RowIterator b) const = 0;
749    virtual void _setColCoeffs(int i, ConstColIterator b,
750                               ConstColIterator e) = 0;
751    virtual void _getColCoeffs(int i, ColIterator b) const = 0;
752    virtual void _setCoeff(int row, int col, Value value) = 0;
753    virtual Value _getCoeff(int row, int col) const = 0;
754    virtual void _setColLowerBound(int i, Value value) = 0;
755    virtual Value _getColLowerBound(int i) const = 0;
756    virtual void _setColUpperBound(int i, Value value) = 0;
757    virtual Value _getColUpperBound(int i) const = 0;
758    virtual void _setRowBounds(int i, Value lower, Value upper) = 0;
759    virtual void _getRowBounds(int i, Value &lower, Value &upper) const = 0;
760
761    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
762    virtual Value _getObjCoeff(int i) const = 0;
763    virtual void _clearObj()=0;
764
765    virtual SolveExitStatus _solve() = 0;
766    virtual Value _getPrimal(int i) const = 0;
767    virtual Value _getDual(int i) const = 0;
768    virtual Value _getPrimalValue() const = 0;
769    virtual bool _isBasicCol(int i) const = 0;
770    virtual SolutionStatus _getPrimalStatus() const = 0;
771    virtual SolutionStatus _getDualStatus() const = 0;
772    virtual ProblemTypes _getProblemType() const = 0;
773
774    virtual void _setMax() = 0;
775    virtual void _setMin() = 0;
776   
777
778    virtual bool _isMax() const = 0;
779
780    //Own protected stuff
781   
782    //Constant component of the objective function
783    Value obj_const_comp;
784       
785  public:
786
787    ///\e
788    LpSolverBase() : obj_const_comp(0) {}
789
790    ///\e
791    virtual ~LpSolverBase() {}
792
793    ///Creates a new LP problem
794    LpSolverBase &newLp() {return _newLp();}
795    ///Makes a copy of the LP problem
796    LpSolverBase &copyLp() {return _copyLp();}
797   
798    ///\name Build up and modify the LP
799
800    ///@{
801
802    ///Add a new empty column (i.e a new variable) to the LP
803    Col addCol() { Col c; _addCol(); c.id = cols.addId(); return c;}
804
805    ///\brief Adds several new columns
806    ///(i.e a variables) at once
807    ///
808    ///This magic function takes a container as its argument
809    ///and fills its elements
810    ///with new columns (i.e. variables)
811    ///\param t can be
812    ///- a standard STL compatible iterable container with
813    ///\ref Col as its \c values_type
814    ///like
815    ///\code
816    ///std::vector<LpSolverBase::Col>
817    ///std::list<LpSolverBase::Col>
818    ///\endcode
819    ///- a standard STL compatible iterable container with
820    ///\ref Col as its \c mapped_type
821    ///like
822    ///\code
823    ///std::map<AnyType,LpSolverBase::Col>
824    ///\endcode
825    ///- an iterable lemon \ref concepts::WriteMap "write map" like
826    ///\code
827    ///ListGraph::NodeMap<LpSolverBase::Col>
828    ///ListGraph::EdgeMap<LpSolverBase::Col>
829    ///\endcode
830    ///\return The number of the created column.
831#ifdef DOXYGEN
832    template<class T>
833    int addColSet(T &t) { return 0;}
834#else
835    template<class T>
836    typename enable_if<typename T::value_type::LpSolverCol,int>::type
837    addColSet(T &t,dummy<0> = 0) {
838      int s=0;
839      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
840      return s;
841    }
842    template<class T>
843    typename enable_if<typename T::value_type::second_type::LpSolverCol,
844                       int>::type
845    addColSet(T &t,dummy<1> = 1) {
846      int s=0;
847      for(typename T::iterator i=t.begin();i!=t.end();++i) {
848        i->second=addCol();
849        s++;
850      }
851      return s;
852    }
853    template<class T>
854    typename enable_if<typename T::MapIt::Value::LpSolverCol,
855                       int>::type
856    addColSet(T &t,dummy<2> = 2) {
857      int s=0;
858      for(typename T::MapIt i(t); i!=INVALID; ++i)
859        {
860          i.set(addCol());
861          s++;
862        }
863      return s;
864    }
865#endif
866
867    ///Set a column (i.e a dual constraint) of the LP
868
869    ///\param c is the column to be modified
870    ///\param e is a dual linear expression (see \ref DualExpr)
871    ///a better one.
872    void col(Col c,const DualExpr &e) {
873      e.simplify();
874      _setColCoeffs(_lpId(c), ConstColIterator(e.begin(), *this),
875                    ConstColIterator(e.end(), *this));
876    }
877
878    ///Get a column (i.e a dual constraint) of the LP
879
880    ///\param r is the column to get
881    ///\return the dual expression associated to the column
882    DualExpr col(Col c) const {
883      DualExpr e;
884      _getColCoeffs(_lpId(c), ColIterator(std::inserter(e, e.end()), *this));
885      return e;
886    }
887
888    ///Add a new column to the LP
889
890    ///\param e is a dual linear expression (see \ref DualExpr)
891    ///\param obj is the corresponding component of the objective
892    ///function. It is 0 by default.
893    ///\return The created column.
894    Col addCol(const DualExpr &e, Value obj=0) {
895      Col c=addCol();
896      col(c,e);
897      objCoeff(c,obj);
898      return c;
899    }
900
901    ///Add a new empty row (i.e a new constraint) to the LP
902
903    ///This function adds a new empty row (i.e a new constraint) to the LP.
904    ///\return The created row
905    Row addRow() { Row r; _addRow(); r.id = rows.addId(); return r;}
906
907    ///\brief Add several new rows
908    ///(i.e a constraints) at once
909    ///
910    ///This magic function takes a container as its argument
911    ///and fills its elements
912    ///with new row (i.e. variables)
913    ///\param t can be
914    ///- a standard STL compatible iterable container with
915    ///\ref Row as its \c values_type
916    ///like
917    ///\code
918    ///std::vector<LpSolverBase::Row>
919    ///std::list<LpSolverBase::Row>
920    ///\endcode
921    ///- a standard STL compatible iterable container with
922    ///\ref Row as its \c mapped_type
923    ///like
924    ///\code
925    ///std::map<AnyType,LpSolverBase::Row>
926    ///\endcode
927    ///- an iterable lemon \ref concepts::WriteMap "write map" like
928    ///\code
929    ///ListGraph::NodeMap<LpSolverBase::Row>
930    ///ListGraph::EdgeMap<LpSolverBase::Row>
931    ///\endcode
932    ///\return The number of rows created.
933#ifdef DOXYGEN
934    template<class T>
935    int addRowSet(T &t) { return 0;}
936#else
937    template<class T>
938    typename enable_if<typename T::value_type::LpSolverRow,int>::type
939    addRowSet(T &t,dummy<0> = 0) {
940      int s=0;
941      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
942      return s;
943    }
944    template<class T>
945    typename enable_if<typename T::value_type::second_type::LpSolverRow,
946                       int>::type
947    addRowSet(T &t,dummy<1> = 1) {
948      int s=0;
949      for(typename T::iterator i=t.begin();i!=t.end();++i) {
950        i->second=addRow();
951        s++;
952      }
953      return s;
954    }
955    template<class T>
956    typename enable_if<typename T::MapIt::Value::LpSolverRow,
957                       int>::type
958    addRowSet(T &t,dummy<2> = 2) {
959      int s=0;
960      for(typename T::MapIt i(t); i!=INVALID; ++i)
961        {
962          i.set(addRow());
963          s++;
964        }
965      return s;
966    }
967#endif
968
969    ///Set a row (i.e a constraint) of the LP
970
971    ///\param r is the row to be modified
972    ///\param l is lower bound (-\ref INF means no bound)
973    ///\param e is a linear expression (see \ref Expr)
974    ///\param u is the upper bound (\ref INF means no bound)
975    ///\bug This is a temportary function. The interface will change to
976    ///a better one.
977    ///\todo Option to control whether a constraint with a single variable is
978    ///added or not.
979    void row(Row r, Value l, const Expr &e, Value u) {
980      e.simplify();
981      _setRowCoeffs(_lpId(r), ConstRowIterator(e.begin(), *this),
982                    ConstRowIterator(e.end(), *this));
983      _setRowBounds(_lpId(r),l-e.constComp(),u-e.constComp());
984    }
985
986    ///Set a row (i.e a constraint) of the LP
987
988    ///\param r is the row to be modified
989    ///\param c is a linear expression (see \ref Constr)
990    void row(Row r, const Constr &c) {
991      row(r, c.lowerBounded()?c.lowerBound():-INF,
992          c.expr(), c.upperBounded()?c.upperBound():INF);
993    }
994
995   
996    ///Get a row (i.e a constraint) of the LP
997
998    ///\param r is the row to get
999    ///\return the expression associated to the row
1000    Expr row(Row r) const {
1001      Expr e;
1002      _getRowCoeffs(_lpId(r), RowIterator(std::inserter(e, e.end()), *this));
1003      return e;
1004    }
1005
1006    ///Add a new row (i.e a new constraint) to the LP
1007
1008    ///\param l is the lower bound (-\ref INF means no bound)
1009    ///\param e is a linear expression (see \ref Expr)
1010    ///\param u is the upper bound (\ref INF means no bound)
1011    ///\return The created row.
1012    ///\bug This is a temportary function. The interface will change to
1013    ///a better one.
1014    Row addRow(Value l,const Expr &e, Value u) {
1015      Row r=addRow();
1016      row(r,l,e,u);
1017      return r;
1018    }
1019
1020    ///Add a new row (i.e a new constraint) to the LP
1021
1022    ///\param c is a linear expression (see \ref Constr)
1023    ///\return The created row.
1024    Row addRow(const Constr &c) {
1025      Row r=addRow();
1026      row(r,c);
1027      return r;
1028    }
1029    ///Erase a coloumn (i.e a variable) from the LP
1030
1031    ///\param c is the coloumn to be deleted
1032    ///\todo Please check this
1033    void eraseCol(Col c) {
1034      _eraseCol(_lpId(c));
1035      cols.eraseId(c.id);
1036    }
1037    ///Erase a  row (i.e a constraint) from the LP
1038
1039    ///\param r is the row to be deleted
1040    ///\todo Please check this
1041    void eraseRow(Row r) {
1042      _eraseRow(_lpId(r));
1043      rows.eraseId(r.id);
1044    }
1045
1046    /// Get the name of a column
1047   
1048    ///\param c is the coresponding coloumn
1049    ///\return The name of the colunm
1050    std::string colName(Col c) const {
1051      std::string name;
1052      _getColName(_lpId(c), name);
1053      return name;
1054    }
1055   
1056    /// Set the name of a column
1057   
1058    ///\param c is the coresponding coloumn
1059    ///\param name The name to be given
1060    void colName(Col c, const std::string& name) {
1061      _setColName(_lpId(c), name);
1062    }
1063   
1064    /// Set an element of the coefficient matrix of the LP
1065
1066    ///\param r is the row of the element to be modified
1067    ///\param c is the coloumn of the element to be modified
1068    ///\param val is the new value of the coefficient
1069
1070    void coeff(Row r, Col c, Value val) {
1071      _setCoeff(_lpId(r),_lpId(c), val);
1072    }
1073
1074    /// Get an element of the coefficient matrix of the LP
1075
1076    ///\param r is the row of the element in question
1077    ///\param c is the coloumn of the element in question
1078    ///\return the corresponding coefficient
1079
1080    Value coeff(Row r, Col c) const {
1081      return _getCoeff(_lpId(r),_lpId(c));
1082    }
1083
1084    /// Set the lower bound of a column (i.e a variable)
1085
1086    /// The lower bound of a variable (column) has to be given by an
1087    /// extended number of type Value, i.e. a finite number of type
1088    /// Value or -\ref INF.
1089    void colLowerBound(Col c, Value value) {
1090      _setColLowerBound(_lpId(c),value);
1091    }
1092
1093    /// Get the lower bound of a column (i.e a variable)
1094
1095    /// This function returns the lower bound for column (variable) \t c
1096    /// (this might be -\ref INF as well). 
1097    ///\return The lower bound for coloumn \t c
1098    Value colLowerBound(Col c) const {
1099      return _getColLowerBound(_lpId(c));
1100    }
1101   
1102    ///\brief Set the lower bound of  several columns
1103    ///(i.e a variables) at once
1104    ///
1105    ///This magic function takes a container as its argument
1106    ///and applies the function on all of its elements.
1107    /// The lower bound of a variable (column) has to be given by an
1108    /// extended number of type Value, i.e. a finite number of type
1109    /// Value or -\ref INF.
1110#ifdef DOXYGEN
1111    template<class T>
1112    void colLowerBound(T &t, Value value) { return 0;}
1113#else
1114    template<class T>
1115    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1116    colLowerBound(T &t, Value value,dummy<0> = 0) {
1117      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1118        colLowerBound(*i, value);
1119      }
1120    }
1121    template<class T>
1122    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1123                       void>::type
1124    colLowerBound(T &t, Value value,dummy<1> = 1) {
1125      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1126        colLowerBound(i->second, value);
1127      }
1128    }
1129    template<class T>
1130    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1131                       void>::type
1132    colLowerBound(T &t, Value value,dummy<2> = 2) {
1133      for(typename T::MapIt i(t); i!=INVALID; ++i){
1134        colLowerBound(*i, value);
1135      }
1136    }
1137#endif
1138   
1139    /// Set the upper bound of a column (i.e a variable)
1140
1141    /// The upper bound of a variable (column) has to be given by an
1142    /// extended number of type Value, i.e. a finite number of type
1143    /// Value or \ref INF.
1144    void colUpperBound(Col c, Value value) {
1145      _setColUpperBound(_lpId(c),value);
1146    };
1147
1148    /// Get the upper bound of a column (i.e a variable)
1149
1150    /// This function returns the upper bound for column (variable) \t c
1151    /// (this might be \ref INF as well). 
1152    ///\return The upper bound for coloumn \t c
1153    Value colUpperBound(Col c) const {
1154      return _getColUpperBound(_lpId(c));
1155    }
1156
1157    ///\brief Set the upper bound of  several columns
1158    ///(i.e a variables) at once
1159    ///
1160    ///This magic function takes a container as its argument
1161    ///and applies the function on all of its elements.
1162    /// The upper bound of a variable (column) has to be given by an
1163    /// extended number of type Value, i.e. a finite number of type
1164    /// Value or \ref INF.
1165#ifdef DOXYGEN
1166    template<class T>
1167    void colUpperBound(T &t, Value value) { return 0;}
1168#else
1169    template<class T>
1170    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1171    colUpperBound(T &t, Value value,dummy<0> = 0) {
1172      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1173        colUpperBound(*i, value);
1174      }
1175    }
1176    template<class T>
1177    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1178                       void>::type
1179    colUpperBound(T &t, Value value,dummy<1> = 1) {
1180      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1181        colUpperBound(i->second, value);
1182      }
1183    }
1184    template<class T>
1185    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1186                       void>::type
1187    colUpperBound(T &t, Value value,dummy<2> = 2) {
1188      for(typename T::MapIt i(t); i!=INVALID; ++i){
1189        colUpperBound(*i, value);
1190      }
1191    }
1192#endif
1193
1194    /// Set the lower and the upper bounds of a column (i.e a variable)
1195
1196    /// The lower and the upper bounds of
1197    /// a variable (column) have to be given by an
1198    /// extended number of type Value, i.e. a finite number of type
1199    /// Value, -\ref INF or \ref INF.
1200    void colBounds(Col c, Value lower, Value upper) {
1201      _setColLowerBound(_lpId(c),lower);
1202      _setColUpperBound(_lpId(c),upper);
1203    }
1204   
1205    ///\brief Set the lower and the upper bound of several columns
1206    ///(i.e a variables) at once
1207    ///
1208    ///This magic function takes a container as its argument
1209    ///and applies the function on all of its elements.
1210    /// The lower and the upper bounds of
1211    /// a variable (column) have to be given by an
1212    /// extended number of type Value, i.e. a finite number of type
1213    /// Value, -\ref INF or \ref INF.
1214#ifdef DOXYGEN
1215    template<class T>
1216    void colBounds(T &t, Value lower, Value upper) { return 0;}
1217#else
1218    template<class T>
1219    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1220    colBounds(T &t, Value lower, Value upper,dummy<0> = 0) {
1221      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1222        colBounds(*i, lower, upper);
1223      }
1224    }
1225    template<class T>
1226    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1227                       void>::type
1228    colBounds(T &t, Value lower, Value upper,dummy<1> = 1) {
1229      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1230        colBounds(i->second, lower, upper);
1231      }
1232    }
1233    template<class T>
1234    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1235                       void>::type
1236    colBounds(T &t, Value lower, Value upper,dummy<2> = 2) {
1237      for(typename T::MapIt i(t); i!=INVALID; ++i){
1238        colBounds(*i, lower, upper);
1239      }
1240    }
1241#endif
1242   
1243
1244    /// Set the lower and the upper bounds of a row (i.e a constraint)
1245
1246    /// The lower and the upper bound of a constraint (row) have to be
1247    /// given by an extended number of type Value, i.e. a finite
1248    /// number of type Value, -\ref INF or \ref INF. There is no
1249    /// separate function for the lower and the upper bound because
1250    /// that would have been hard to implement for CPLEX.
1251    void rowBounds(Row c, Value lower, Value upper) {
1252      _setRowBounds(_lpId(c),lower, upper);
1253    }
1254   
1255    /// Get the lower and the upper bounds of a row (i.e a constraint)
1256
1257    /// The lower and the upper bound of
1258    /// a constraint (row) are 
1259    /// extended numbers of type Value, i.e.  finite numbers of type
1260    /// Value, -\ref INF or \ref INF.
1261    /// \todo There is no separate function for the
1262    /// lower and the upper bound because we had problems with the
1263    /// implementation of the setting functions for CPLEX: 
1264    /// check out whether this can be done for these functions.
1265    void getRowBounds(Row c, Value &lower, Value &upper) const {
1266      _getRowBounds(_lpId(c),lower, upper);
1267    }
1268
1269    ///Set an element of the objective function
1270    void objCoeff(Col c, Value v) {_setObjCoeff(_lpId(c),v); };
1271
1272    ///Get an element of the objective function
1273    Value objCoeff(Col c) const { return _getObjCoeff(_lpId(c)); };
1274
1275    ///Set the objective function
1276
1277    ///\param e is a linear expression of type \ref Expr.
1278    ///\bug Is should be called obj()
1279    void setObj(Expr e) {
1280      _clearObj();
1281      for (Expr::iterator i=e.begin(); i!=e.end(); ++i)
1282        objCoeff((*i).first,(*i).second);
1283      obj_const_comp=e.constComp();
1284    }
1285
1286    ///Get the objective function
1287
1288    ///\return the objective function as a linear expression of type \ref Expr.
1289    Expr obj() const {
1290      Expr e;
1291      for (ColIt it(*this); it != INVALID; ++it) {
1292        double c = objCoeff(it);
1293        if (c != 0.0) {
1294          e.insert(std::make_pair(it, c));
1295        }
1296      }
1297      return e;
1298    }
1299   
1300
1301    ///Maximize
1302    void max() { _setMax(); }
1303    ///Minimize
1304    void min() { _setMin(); }
1305
1306    ///Query function: is this a maximization problem?
1307    bool is_max() const {return _isMax(); }
1308
1309    ///Query function: is this a minimization problem?
1310    bool is_min() const {return !is_max(); }
1311   
1312    ///@}
1313
1314
1315    ///\name Solve the LP
1316
1317    ///@{
1318
1319    ///\e Solve the LP problem at hand
1320    ///
1321    ///\return The result of the optimization procedure. Possible
1322    ///values and their meanings can be found in the documentation of
1323    ///\ref SolveExitStatus.
1324    ///
1325    ///\todo Which method is used to solve the problem
1326    SolveExitStatus solve() { return _solve(); }
1327   
1328    ///@}
1329   
1330    ///\name Obtain the solution
1331
1332    ///@{
1333
1334    /// The status of the primal problem (the original LP problem)
1335    SolutionStatus primalStatus() const {
1336      return _getPrimalStatus();
1337    }
1338
1339    /// The status of the dual (of the original LP) problem
1340    SolutionStatus dualStatus() const {
1341      return _getDualStatus();
1342    }
1343
1344    ///The type of the original LP problem
1345    ProblemTypes problemType() const {
1346      return _getProblemType();
1347    }
1348
1349    ///\e
1350    Value primal(Col c) const { return _getPrimal(_lpId(c)); }
1351
1352    ///\e
1353    Value dual(Row r) const { return _getDual(_lpId(r)); }
1354
1355    ///\e
1356    bool isBasicCol(Col c) const { return _isBasicCol(_lpId(c)); }
1357
1358    ///\e
1359
1360    ///\return
1361    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
1362    /// of the primal problem, depending on whether we minimize or maximize.
1363    ///- \ref NaN if no primal solution is found.
1364    ///- The (finite) objective value if an optimal solution is found.
1365    Value primalValue() const { return _getPrimalValue()+obj_const_comp;}
1366    ///@}
1367   
1368  }; 
1369
1370
1371  ///Common base class for MIP solvers
1372  ///\todo Much more docs
1373  ///\ingroup gen_opt_group
1374  class MipSolverBase : virtual public LpSolverBase{
1375  public:
1376
1377    ///Possible variable (coloumn) types (e.g. real, integer, binary etc.)
1378    enum ColTypes {
1379      ///Continuous variable
1380      REAL = 0,
1381      ///Integer variable
1382
1383      ///Unfortunately, cplex 7.5 somewhere writes something like
1384      ///#define INTEGER 'I'
1385      INT = 1
1386      ///\todo No support for other types yet.
1387    };
1388
1389    ///Sets the type of the given coloumn to the given type
1390    ///
1391    ///Sets the type of the given coloumn to the given type.
1392    void colType(Col c, ColTypes col_type) {
1393      _colType(_lpId(c),col_type);
1394    }
1395
1396    ///Gives back the type of the column.
1397    ///
1398    ///Gives back the type of the column.
1399    ColTypes colType(Col c) const {
1400      return _colType(_lpId(c));
1401    }
1402
1403    ///Sets the type of the given Col to integer or remove that property.
1404    ///
1405    ///Sets the type of the given Col to integer or remove that property.
1406    void integer(Col c, bool enable) {
1407      if (enable)
1408        colType(c,INT);
1409      else
1410        colType(c,REAL);
1411    }
1412
1413    ///Gives back whether the type of the column is integer or not.
1414    ///
1415    ///Gives back the type of the column.
1416    ///\return true if the column has integer type and false if not.
1417    bool integer(Col c) const {
1418      return (colType(c)==INT);
1419    }
1420
1421    /// The status of the MIP problem
1422    SolutionStatus mipStatus() const {
1423      return _getMipStatus();
1424    }
1425
1426  protected:
1427
1428    virtual ColTypes _colType(int col) const = 0;
1429    virtual void _colType(int col, ColTypes col_type) = 0;
1430    virtual SolutionStatus _getMipStatus() const = 0;
1431
1432  };
1433 
1434  ///\relates LpSolverBase::Expr
1435  ///
1436  inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a,
1437                                      const LpSolverBase::Expr &b)
1438  {
1439    LpSolverBase::Expr tmp(a);
1440    tmp+=b;
1441    return tmp;
1442  }
1443  ///\e
1444 
1445  ///\relates LpSolverBase::Expr
1446  ///
1447  inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a,
1448                                      const LpSolverBase::Expr &b)
1449  {
1450    LpSolverBase::Expr tmp(a);
1451    tmp-=b;
1452    return tmp;
1453  }
1454  ///\e
1455 
1456  ///\relates LpSolverBase::Expr
1457  ///
1458  inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a,
1459                                      const LpSolverBase::Value &b)
1460  {
1461    LpSolverBase::Expr tmp(a);
1462    tmp*=b;
1463    return tmp;
1464  }
1465 
1466  ///\e
1467 
1468  ///\relates LpSolverBase::Expr
1469  ///
1470  inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a,
1471                                      const LpSolverBase::Expr &b)
1472  {
1473    LpSolverBase::Expr tmp(b);
1474    tmp*=a;
1475    return tmp;
1476  }
1477  ///\e
1478 
1479  ///\relates LpSolverBase::Expr
1480  ///
1481  inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a,
1482                                      const LpSolverBase::Value &b)
1483  {
1484    LpSolverBase::Expr tmp(a);
1485    tmp/=b;
1486    return tmp;
1487  }
1488 
1489  ///\e
1490 
1491  ///\relates LpSolverBase::Constr
1492  ///
1493  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1494                                         const LpSolverBase::Expr &f)
1495  {
1496    return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0);
1497  }
1498
1499  ///\e
1500 
1501  ///\relates LpSolverBase::Constr
1502  ///
1503  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e,
1504                                         const LpSolverBase::Expr &f)
1505  {
1506    return LpSolverBase::Constr(e,f);
1507  }
1508
1509  ///\e
1510 
1511  ///\relates LpSolverBase::Constr
1512  ///
1513  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1514                                         const LpSolverBase::Value &f)
1515  {
1516    return LpSolverBase::Constr(e,f);
1517  }
1518
1519  ///\e
1520 
1521  ///\relates LpSolverBase::Constr
1522  ///
1523  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1524                                         const LpSolverBase::Expr &f)
1525  {
1526    return LpSolverBase::Constr(-LpSolverBase::INF,f-e,0);
1527  }
1528
1529
1530  ///\e
1531 
1532  ///\relates LpSolverBase::Constr
1533  ///
1534  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e,
1535                                         const LpSolverBase::Expr &f)
1536  {
1537    return LpSolverBase::Constr(f,e);
1538  }
1539
1540
1541  ///\e
1542 
1543  ///\relates LpSolverBase::Constr
1544  ///
1545  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1546                                         const LpSolverBase::Value &f)
1547  {
1548    return LpSolverBase::Constr(f,e);
1549  }
1550
1551  ///\e
1552
1553  ///\relates LpSolverBase::Constr
1554  ///
1555  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
1556                                         const LpSolverBase::Value &f)
1557  {
1558    return LpSolverBase::Constr(f,e,f);
1559  }
1560
1561  ///\e
1562 
1563  ///\relates LpSolverBase::Constr
1564  ///
1565  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
1566                                         const LpSolverBase::Expr &f)
1567  {
1568    return LpSolverBase::Constr(0,e-f,0);
1569  }
1570
1571  ///\e
1572 
1573  ///\relates LpSolverBase::Constr
1574  ///
1575  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n,
1576                                         const LpSolverBase::Constr&c)
1577  {
1578    LpSolverBase::Constr tmp(c);
1579    ///\todo Create an own exception type.
1580    if(!LpSolverBase::isNaN(tmp.lowerBound())) throw LogicError();
1581    else tmp.lowerBound()=n;
1582    return tmp;
1583  }
1584  ///\e
1585 
1586  ///\relates LpSolverBase::Constr
1587  ///
1588  inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c,
1589                                         const LpSolverBase::Value &n)
1590  {
1591    LpSolverBase::Constr tmp(c);
1592    ///\todo Create an own exception type.
1593    if(!LpSolverBase::isNaN(tmp.upperBound())) throw LogicError();
1594    else tmp.upperBound()=n;
1595    return tmp;
1596  }
1597
1598  ///\e
1599 
1600  ///\relates LpSolverBase::Constr
1601  ///
1602  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n,
1603                                         const LpSolverBase::Constr&c)
1604  {
1605    LpSolverBase::Constr tmp(c);
1606    ///\todo Create an own exception type.
1607    if(!LpSolverBase::isNaN(tmp.upperBound())) throw LogicError();
1608    else tmp.upperBound()=n;
1609    return tmp;
1610  }
1611  ///\e
1612 
1613  ///\relates LpSolverBase::Constr
1614  ///
1615  inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c,
1616                                         const LpSolverBase::Value &n)
1617  {
1618    LpSolverBase::Constr tmp(c);
1619    ///\todo Create an own exception type.
1620    if(!LpSolverBase::isNaN(tmp.lowerBound())) throw LogicError();
1621    else tmp.lowerBound()=n;
1622    return tmp;
1623  }
1624
1625  ///\e
1626 
1627  ///\relates LpSolverBase::DualExpr
1628  ///
1629  inline LpSolverBase::DualExpr operator+(const LpSolverBase::DualExpr &a,
1630                                          const LpSolverBase::DualExpr &b)
1631  {
1632    LpSolverBase::DualExpr tmp(a);
1633    tmp+=b;
1634    return tmp;
1635  }
1636  ///\e
1637 
1638  ///\relates LpSolverBase::DualExpr
1639  ///
1640  inline LpSolverBase::DualExpr operator-(const LpSolverBase::DualExpr &a,
1641                                          const LpSolverBase::DualExpr &b)
1642  {
1643    LpSolverBase::DualExpr tmp(a);
1644    tmp-=b;
1645    return tmp;
1646  }
1647  ///\e
1648 
1649  ///\relates LpSolverBase::DualExpr
1650  ///
1651  inline LpSolverBase::DualExpr operator*(const LpSolverBase::DualExpr &a,
1652                                          const LpSolverBase::Value &b)
1653  {
1654    LpSolverBase::DualExpr tmp(a);
1655    tmp*=b;
1656    return tmp;
1657  }
1658 
1659  ///\e
1660 
1661  ///\relates LpSolverBase::DualExpr
1662  ///
1663  inline LpSolverBase::DualExpr operator*(const LpSolverBase::Value &a,
1664                                          const LpSolverBase::DualExpr &b)
1665  {
1666    LpSolverBase::DualExpr tmp(b);
1667    tmp*=a;
1668    return tmp;
1669  }
1670  ///\e
1671 
1672  ///\relates LpSolverBase::DualExpr
1673  ///
1674  inline LpSolverBase::DualExpr operator/(const LpSolverBase::DualExpr &a,
1675                                          const LpSolverBase::Value &b)
1676  {
1677    LpSolverBase::DualExpr tmp(a);
1678    tmp/=b;
1679    return tmp;
1680  }
1681 
1682
1683} //namespace lemon
1684
1685#endif //LEMON_LP_BASE_H
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