COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/lp_base.h @ 2476:059dcdda37c5

Last change on this file since 2476:059dcdda37c5 was 2435:548f498fa059, checked in by Alpar Juttner, 13 years ago

Fix the bug

File size: 46.2 KB
Line 
1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2007
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<cmath>
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  ///Common base class for LP solvers
39 
40  ///\todo Much more docs
41  ///\ingroup lp_group
42  class LpSolverBase {
43
44  protected:
45
46    _lp_bits::LpId rows;
47    _lp_bits::LpId cols;
48   
49  public:
50   
51    ///Possible outcomes of an LP solving procedure
52    enum SolveExitStatus {
53      ///This means that the problem has been successfully solved: either
54      ///an optimal solution has been found or infeasibility/unboundedness
55      ///has been proved.
56      SOLVED = 0,
57      ///Any other case (including the case when some user specified
58      ///limit has been exceeded)
59      UNSOLVED = 1
60    };
61     
62      ///\e
63    enum SolutionStatus {
64      ///Feasible solution hasn't been found (but may exist).
65
66      ///\todo NOTFOUND might be a better name.
67      ///
68      UNDEFINED = 0,
69      ///The problem has no feasible solution
70      INFEASIBLE = 1,
71      ///Feasible solution found
72      FEASIBLE = 2,
73      ///Optimal solution exists and found
74      OPTIMAL = 3,
75      ///The cost function is unbounded
76
77      ///\todo Give a feasible solution and an infinite ray (and the
78      ///corresponding bases)
79      INFINITE = 4
80    };
81
82    ///\e The type of the investigated LP problem
83    enum ProblemTypes {
84      ///Primal-dual feasible
85      PRIMAL_DUAL_FEASIBLE = 0,
86      ///Primal feasible dual infeasible
87      PRIMAL_FEASIBLE_DUAL_INFEASIBLE = 1,
88      ///Primal infeasible dual feasible
89      PRIMAL_INFEASIBLE_DUAL_FEASIBLE = 2,
90      ///Primal-dual infeasible
91      PRIMAL_DUAL_INFEASIBLE = 3,
92      ///Could not determine so far
93      UNKNOWN = 4
94    };
95
96    ///The floating point type used by the solver
97    typedef double Value;
98    ///The infinity constant
99    static const Value INF;
100    ///The not a number constant
101    static const Value NaN;
102
103    static inline bool isNaN(const Value& v) { return v!=v; }
104   
105    friend class Col;
106    friend class ColIt;
107    friend class Row;
108   
109    ///Refer to a column of the LP.
110
111    ///This type is used to refer to a column of the LP.
112    ///
113    ///Its value remains valid and correct even after the addition or erase of
114    ///other columns.
115    ///
116    ///\todo Document what can one do with a Col (INVALID, comparing,
117    ///it is similar to Node/Edge)
118    class Col {
119    protected:
120      int id;
121      friend class LpSolverBase;
122      friend class MipSolverBase;
123      explicit Col(int _id) : id(_id) {}
124    public:
125      typedef Value ExprValue;
126      typedef True LpSolverCol;
127      Col() {}
128      Col(const Invalid&) : id(-1) {}
129      bool operator< (Col c) const  {return id< c.id;}
130      bool operator> (Col c) const  {return id> c.id;}
131      bool operator==(Col c) const  {return id==c.id;}
132      bool operator!=(Col c) const  {return id!=c.id;}
133    };
134
135    class ColIt : public Col {
136      const LpSolverBase *_lp;
137    public:
138      ColIt() {}
139      ColIt(const LpSolverBase &lp) : _lp(&lp)
140      {
141        _lp->cols.firstFix(id);
142      }
143      ColIt(const Invalid&) : Col(INVALID) {}
144      ColIt &operator++()
145      {
146        _lp->cols.nextFix(id);
147        return *this;
148      }
149    };
150
151    static int id(const Col& col) { return col.id; }
152 
153     
154    ///Refer to a row of the LP.
155
156    ///This type is used to refer to a row of the LP.
157    ///
158    ///Its value remains valid and correct even after the addition or erase of
159    ///other rows.
160    ///
161    ///\todo Document what can one do with a Row (INVALID, comparing,
162    ///it is similar to Node/Edge)
163    class Row {
164    protected:
165      int id;
166      friend class LpSolverBase;
167      explicit Row(int _id) : id(_id) {}
168    public:
169      typedef Value ExprValue;
170      typedef True LpSolverRow;
171      Row() {}
172      Row(const Invalid&) : id(-1) {}
173
174      bool operator< (Row c) const  {return id< c.id;}
175      bool operator> (Row c) const  {return id> c.id;}
176      bool operator==(Row c) const  {return id==c.id;}
177      bool operator!=(Row c) const  {return id!=c.id;}
178    };
179
180    class RowIt : public Row {
181      const LpSolverBase *_lp;
182    public:
183      RowIt() {}
184      RowIt(const LpSolverBase &lp) : _lp(&lp)
185      {
186        _lp->rows.firstFix(id);
187      }
188      RowIt(const Invalid&) : Row(INVALID) {}
189      RowIt &operator++()
190      {
191        _lp->rows.nextFix(id);
192        return *this;
193      }
194    };
195
196    static int id(const Row& row) { return row.id; }
197
198  protected:
199
200    int _lpId(const Col& c) const {
201      return cols.floatingId(id(c));
202    }
203
204    int _lpId(const Row& r) const {
205      return rows.floatingId(id(r));
206    }
207
208    Col _item(int i, Col) const {
209      return Col(cols.fixId(i));
210    }
211
212    Row _item(int i, Row) const {
213      return Row(rows.fixId(i));
214    }
215
216
217  public:
218   
219    ///Linear expression of variables and a constant component
220   
221    ///This data structure stores a linear expression of the variables
222    ///(\ref Col "Col"s) and also has a constant component.
223    ///
224    ///There are several ways to access and modify the contents of this
225    ///container.
226    ///- Its it fully compatible with \c std::map<Col,double>, so for expamle
227    ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can
228    ///read and modify the coefficients like
229    ///these.
230    ///\code
231    ///e[v]=5;
232    ///e[v]+=12;
233    ///e.erase(v);
234    ///\endcode
235    ///or you can also iterate through its elements.
236    ///\code
237    ///double s=0;
238    ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i)
239    ///  s+=i->second;
240    ///\endcode
241    ///(This code computes the sum of all coefficients).
242    ///- Numbers (<tt>double</tt>'s)
243    ///and variables (\ref Col "Col"s) directly convert to an
244    ///\ref Expr and the usual linear operations are defined, so 
245    ///\code
246    ///v+w
247    ///2*v-3.12*(v-w/2)+2
248    ///v*2.1+(3*v+(v*12+w+6)*3)/2
249    ///\endcode
250    ///are valid \ref Expr "Expr"essions.
251    ///The usual assignment operations are also defined.
252    ///\code
253    ///e=v+w;
254    ///e+=2*v-3.12*(v-w/2)+2;
255    ///e*=3.4;
256    ///e/=5;
257    ///\endcode
258    ///- The constant member can be set and read by \ref constComp()
259    ///\code
260    ///e.constComp()=12;
261    ///double c=e.constComp();
262    ///\endcode
263    ///
264    ///\note \ref clear() not only sets all coefficients to 0 but also
265    ///clears the constant components.
266    ///
267    ///\sa Constr
268    ///
269    class Expr : public std::map<Col,Value>
270    {
271    public:
272      typedef LpSolverBase::Col Key;
273      typedef LpSolverBase::Value Value;
274     
275    protected:
276      typedef std::map<Col,Value> Base;
277     
278      Value const_comp;
279    public:
280      typedef True IsLinExpression;
281      ///\e
282      Expr() : Base(), const_comp(0) { }
283      ///\e
284      Expr(const Key &v) : const_comp(0) {
285        Base::insert(std::make_pair(v, 1));
286      }
287      ///\e
288      Expr(const Value &v) : const_comp(v) {}
289      ///\e
290      void set(const Key &v,const Value &c) {
291        Base::insert(std::make_pair(v, c));
292      }
293      ///\e
294      Value &constComp() { return const_comp; }
295      ///\e
296      const Value &constComp() const { return const_comp; }
297     
298      ///Removes the components with zero coefficient.
299      void simplify() {
300        for (Base::iterator i=Base::begin(); i!=Base::end();) {
301          Base::iterator j=i;
302          ++j;
303          if ((*i).second==0) Base::erase(i);
304          i=j;
305        }
306      }
307
308      void simplify() const {
309        const_cast<Expr*>(this)->simplify();
310      }
311
312      ///Removes the coefficients closer to zero than \c tolerance.
313      void simplify(double &tolerance) {
314        for (Base::iterator i=Base::begin(); i!=Base::end();) {
315          Base::iterator j=i;
316          ++j;
317          if (std::fabs((*i).second)<tolerance) Base::erase(i);
318          i=j;
319        }
320      }
321
322      ///Sets all coefficients and the constant component to 0.
323      void clear() {
324        Base::clear();
325        const_comp=0;
326      }
327
328      ///\e
329      Expr &operator+=(const Expr &e) {
330        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
331          (*this)[j->first]+=j->second;
332        const_comp+=e.const_comp;
333        return *this;
334      }
335      ///\e
336      Expr &operator-=(const Expr &e) {
337        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
338          (*this)[j->first]-=j->second;
339        const_comp-=e.const_comp;
340        return *this;
341      }
342      ///\e
343      Expr &operator*=(const Value &c) {
344        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
345          j->second*=c;
346        const_comp*=c;
347        return *this;
348      }
349      ///\e
350      Expr &operator/=(const Value &c) {
351        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
352          j->second/=c;
353        const_comp/=c;
354        return *this;
355      }
356
357      //std::ostream &
358      void prettyPrint(std::ostream &os) {
359        //std::fmtflags os.flags();
360        //os.setf(std::ios::showpos);
361        Base::iterator j=Base::begin();
362        if (j!=Base::end())
363          os<<j->second<<"*x["<<id(j->first)<<"]";
364        ++j;
365        for (; j!=Base::end(); ++j){
366          if (j->second>=0)
367            os<<"+";
368          os<<j->second<<"*x["<<id(j->first)<<"]";
369        }
370        //Nem valami korrekt, de nem talaltam meg, hogy kell
371        //os.unsetf(std::ios::showpos);
372
373        //return os;
374      }
375
376    };
377   
378    ///Linear constraint
379
380    ///This data stucture represents a linear constraint in the LP.
381    ///Basically it is a linear expression with a lower or an upper bound
382    ///(or both). These parts of the constraint can be obtained by the member
383    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
384    ///respectively.
385    ///There are two ways to construct a constraint.
386    ///- You can set the linear expression and the bounds directly
387    ///  by the functions above.
388    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
389    ///  are defined between expressions, or even between constraints whenever
390    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
391    ///  \c s and \c t are numbers, then the followings are valid expressions
392    ///  and thus they can be used directly e.g. in \ref addRow() whenever
393    ///  it makes sense.
394    ///\code
395    ///  e<=s
396    ///  e<=f
397    ///  e==f
398    ///  s<=e<=t
399    ///  e>=t
400    ///\endcode
401    ///\warning The validity of a constraint is checked only at run time, so
402    ///e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will compile, but will throw a
403    ///\ref LogicError exception.
404    class Constr
405    {
406    public:
407      typedef LpSolverBase::Expr Expr;
408      typedef Expr::Key Key;
409      typedef Expr::Value Value;
410     
411    protected:
412      Expr _expr;
413      Value _lb,_ub;
414    public:
415      ///\e
416      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
417      ///\e
418      Constr(Value lb,const Expr &e,Value ub) :
419        _expr(e), _lb(lb), _ub(ub) {}
420      ///\e
421      Constr(const Expr &e,Value ub) :
422        _expr(e), _lb(NaN), _ub(ub) {}
423      ///\e
424      Constr(Value lb,const Expr &e) :
425        _expr(e), _lb(lb), _ub(NaN) {}
426      ///\e
427      Constr(const Expr &e) :
428        _expr(e), _lb(NaN), _ub(NaN) {}
429      ///\e
430      void clear()
431      {
432        _expr.clear();
433        _lb=_ub=NaN;
434      }
435
436      ///Reference to the linear expression
437      Expr &expr() { return _expr; }
438      ///Cont reference to the linear expression
439      const Expr &expr() const { return _expr; }
440      ///Reference to the lower bound.
441
442      ///\return
443      ///- \ref INF "INF": the constraint is lower unbounded.
444      ///- \ref NaN "NaN": lower bound has not been set.
445      ///- finite number: the lower bound
446      Value &lowerBound() { return _lb; }
447      ///The const version of \ref lowerBound()
448      const Value &lowerBound() const { return _lb; }
449      ///Reference to the upper bound.
450
451      ///\return
452      ///- \ref INF "INF": the constraint is upper unbounded.
453      ///- \ref NaN "NaN": upper bound has not been set.
454      ///- finite number: the upper bound
455      Value &upperBound() { return _ub; }
456      ///The const version of \ref upperBound()
457      const Value &upperBound() const { return _ub; }
458      ///Is the constraint lower bounded?
459      bool lowerBounded() const {
460        using namespace std;
461        return finite(_lb);
462      }
463      ///Is the constraint upper bounded?
464      bool upperBounded() const {
465        using namespace std;
466        return finite(_ub);
467      }
468
469      void prettyPrint(std::ostream &os) {
470        if (_lb==-LpSolverBase::INF||isNaN(_lb))
471          os<<"-infty<=";
472        else
473          os<<_lb<<"<=";
474        _expr.prettyPrint(os);
475        if (_ub==LpSolverBase::INF)
476          os<<"<=infty";
477        else
478          os<<"<="<<_ub;
479        //return os;
480      }
481
482    };
483   
484    ///Linear expression of rows
485   
486    ///This data structure represents a column of the matrix,
487    ///thas is it strores a linear expression of the dual variables
488    ///(\ref Row "Row"s).
489    ///
490    ///There are several ways to access and modify the contents of this
491    ///container.
492    ///- Its it fully compatible with \c std::map<Row,double>, so for expamle
493    ///if \c e is an DualExpr and \c v
494    ///and \c w are of type \ref Row, then you can
495    ///read and modify the coefficients like
496    ///these.
497    ///\code
498    ///e[v]=5;
499    ///e[v]+=12;
500    ///e.erase(v);
501    ///\endcode
502    ///or you can also iterate through its elements.
503    ///\code
504    ///double s=0;
505    ///for(LpSolverBase::DualExpr::iterator i=e.begin();i!=e.end();++i)
506    ///  s+=i->second;
507    ///\endcode
508    ///(This code computes the sum of all coefficients).
509    ///- Numbers (<tt>double</tt>'s)
510    ///and variables (\ref Row "Row"s) directly convert to an
511    ///\ref DualExpr and the usual linear operations are defined, so
512    ///\code
513    ///v+w
514    ///2*v-3.12*(v-w/2)
515    ///v*2.1+(3*v+(v*12+w)*3)/2
516    ///\endcode
517    ///are valid \ref DualExpr "DualExpr"essions.
518    ///The usual assignment operations are also defined.
519    ///\code
520    ///e=v+w;
521    ///e+=2*v-3.12*(v-w/2);
522    ///e*=3.4;
523    ///e/=5;
524    ///\endcode
525    ///
526    ///\sa Expr
527    ///
528    class DualExpr : public std::map<Row,Value>
529    {
530    public:
531      typedef LpSolverBase::Row Key;
532      typedef LpSolverBase::Value Value;
533     
534    protected:
535      typedef std::map<Row,Value> Base;
536     
537    public:
538      typedef True IsLinExpression;
539      ///\e
540      DualExpr() : Base() { }
541      ///\e
542      DualExpr(const Key &v) {
543        Base::insert(std::make_pair(v, 1));
544      }
545      ///\e
546      void set(const Key &v,const Value &c) {
547        Base::insert(std::make_pair(v, c));
548      }
549     
550      ///Removes the components with zero coefficient.
551      void simplify() {
552        for (Base::iterator i=Base::begin(); i!=Base::end();) {
553          Base::iterator j=i;
554          ++j;
555          if ((*i).second==0) Base::erase(i);
556          i=j;
557        }
558      }
559
560      void simplify() const {
561        const_cast<DualExpr*>(this)->simplify();
562      }
563
564      ///Removes the coefficients closer to zero than \c tolerance.
565      void simplify(double &tolerance) {
566        for (Base::iterator i=Base::begin(); i!=Base::end();) {
567          Base::iterator j=i;
568          ++j;
569          if (std::fabs((*i).second)<tolerance) Base::erase(i);
570          i=j;
571        }
572      }
573
574      ///Sets all coefficients to 0.
575      void clear() {
576        Base::clear();
577      }
578
579      ///\e
580      DualExpr &operator+=(const DualExpr &e) {
581        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
582          (*this)[j->first]+=j->second;
583        return *this;
584      }
585      ///\e
586      DualExpr &operator-=(const DualExpr &e) {
587        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
588          (*this)[j->first]-=j->second;
589        return *this;
590      }
591      ///\e
592      DualExpr &operator*=(const Value &c) {
593        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
594          j->second*=c;
595        return *this;
596      }
597      ///\e
598      DualExpr &operator/=(const Value &c) {
599        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
600          j->second/=c;
601        return *this;
602      }
603    };
604   
605
606  private:
607
608    template <typename _Expr>
609    class MappedOutputIterator {
610    public:
611
612      typedef std::insert_iterator<_Expr> Base;
613
614      typedef std::output_iterator_tag iterator_category;
615      typedef void difference_type;
616      typedef void value_type;
617      typedef void reference;
618      typedef void pointer;
619     
620      MappedOutputIterator(const Base& _base, const LpSolverBase& _lp)
621        : base(_base), lp(_lp) {}
622
623      MappedOutputIterator& operator*() {
624        return *this;
625      }
626
627      MappedOutputIterator& operator=(const std::pair<int, Value>& value) {
628        *base = std::make_pair(lp._item(value.first, typename _Expr::Key()),
629                               value.second);
630        return *this;
631      }
632
633      MappedOutputIterator& operator++() {
634        ++base;
635        return *this;
636      }
637
638      MappedOutputIterator operator++(int) {
639        MappedOutputIterator tmp(*this);
640        ++base;
641        return tmp;
642      }
643
644      bool operator==(const MappedOutputIterator& it) const {
645        return base == it.base;
646      }
647
648      bool operator!=(const MappedOutputIterator& it) const {
649        return base != it.base;
650      }
651
652    private:
653      Base base;
654      const LpSolverBase& lp;
655    };
656
657    template <typename Expr>
658    class MappedInputIterator {
659    public:
660
661      typedef typename Expr::const_iterator Base;
662
663      typedef typename Base::iterator_category iterator_category;
664      typedef typename Base::difference_type difference_type;
665      typedef const std::pair<int, Value> value_type;
666      typedef value_type reference;
667      class pointer {
668      public:
669        pointer(value_type& _value) : value(_value) {}
670        value_type* operator->() { return &value; }
671      private:
672        value_type value;
673      };
674
675      MappedInputIterator(const Base& _base, const LpSolverBase& _lp)
676        : base(_base), lp(_lp) {}
677
678      reference operator*() {
679        return std::make_pair(lp._lpId(base->first), base->second);
680      }
681
682      pointer operator->() {
683        return pointer(operator*());
684      }
685
686      MappedInputIterator& operator++() {
687        ++base;
688        return *this;
689      }
690
691      MappedInputIterator operator++(int) {
692        MappedInputIterator tmp(*this);
693        ++base;
694        return tmp;
695      }
696
697      bool operator==(const MappedInputIterator& it) const {
698        return base == it.base;
699      }
700
701      bool operator!=(const MappedInputIterator& it) const {
702        return base != it.base;
703      }
704
705    private:
706      Base base;
707      const LpSolverBase& lp;
708    };
709
710  protected:
711
712    /// STL compatible iterator for lp col
713    typedef MappedInputIterator<Expr> ConstRowIterator;
714    /// STL compatible iterator for lp row
715    typedef MappedInputIterator<DualExpr> ConstColIterator;
716
717    /// STL compatible iterator for lp col
718    typedef MappedOutputIterator<Expr> RowIterator;
719    /// STL compatible iterator for lp row
720    typedef MappedOutputIterator<DualExpr> ColIterator;
721
722    //Abstract virtual functions
723    virtual LpSolverBase &_newLp() = 0;
724    virtual LpSolverBase &_copyLp(){
725      ///\todo This should be implemented here, too, when we have
726      ///problem retrieving routines. It can be overriden.
727
728      //Starting:
729      LpSolverBase & newlp(_newLp());
730      return newlp;
731      //return *(LpSolverBase*)0;
732    };
733
734    virtual int _addCol() = 0;
735    virtual int _addRow() = 0;
736
737    virtual void _eraseCol(int col) = 0;
738    virtual void _eraseRow(int row) = 0;
739
740    virtual void _getColName(int col, std::string & name) const = 0;
741    virtual void _setColName(int col, const std::string & name) = 0;
742    virtual int _colByName(const std::string& name) const = 0;
743
744    virtual void _setRowCoeffs(int i, ConstRowIterator b,
745                               ConstRowIterator e) = 0;
746    virtual void _getRowCoeffs(int i, RowIterator b) const = 0;
747    virtual void _setColCoeffs(int i, ConstColIterator b,
748                               ConstColIterator e) = 0;
749    virtual void _getColCoeffs(int i, ColIterator b) const = 0;
750    virtual void _setCoeff(int row, int col, Value value) = 0;
751    virtual Value _getCoeff(int row, int col) const = 0;
752    virtual void _setColLowerBound(int i, Value value) = 0;
753    virtual Value _getColLowerBound(int i) const = 0;
754    virtual void _setColUpperBound(int i, Value value) = 0;
755    virtual Value _getColUpperBound(int i) const = 0;
756    virtual void _setRowBounds(int i, Value lower, Value upper) = 0;
757    virtual void _getRowBounds(int i, Value &lower, Value &upper) const = 0;
758
759    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
760    virtual Value _getObjCoeff(int i) const = 0;
761    virtual void _clearObj()=0;
762
763    virtual SolveExitStatus _solve() = 0;
764    virtual Value _getPrimal(int i) const = 0;
765    virtual Value _getDual(int i) const = 0;
766    virtual Value _getPrimalValue() const = 0;
767    virtual bool _isBasicCol(int i) const = 0;
768    virtual SolutionStatus _getPrimalStatus() const = 0;
769    virtual SolutionStatus _getDualStatus() const = 0;
770    virtual ProblemTypes _getProblemType() const = 0;
771
772    virtual void _setMax() = 0;
773    virtual void _setMin() = 0;
774   
775
776    virtual bool _isMax() const = 0;
777
778    //Own protected stuff
779   
780    //Constant component of the objective function
781    Value obj_const_comp;
782       
783  public:
784
785    ///\e
786    LpSolverBase() : obj_const_comp(0) {}
787
788    ///\e
789    virtual ~LpSolverBase() {}
790
791    ///Creates a new LP problem
792    LpSolverBase &newLp() {return _newLp();}
793    ///Makes a copy of the LP problem
794    LpSolverBase &copyLp() {return _copyLp();}
795   
796    ///\name Build up and modify the LP
797
798    ///@{
799
800    ///Add a new empty column (i.e a new variable) to the LP
801    Col addCol() { Col c; _addCol(); c.id = cols.addId(); return c;}
802
803    ///\brief Adds several new columns
804    ///(i.e a variables) at once
805    ///
806    ///This magic function takes a container as its argument
807    ///and fills its elements
808    ///with new columns (i.e. variables)
809    ///\param t can be
810    ///- a standard STL compatible iterable container with
811    ///\ref Col as its \c values_type
812    ///like
813    ///\code
814    ///std::vector<LpSolverBase::Col>
815    ///std::list<LpSolverBase::Col>
816    ///\endcode
817    ///- a standard STL compatible iterable container with
818    ///\ref Col as its \c mapped_type
819    ///like
820    ///\code
821    ///std::map<AnyType,LpSolverBase::Col>
822    ///\endcode
823    ///- an iterable lemon \ref concepts::WriteMap "write map" like
824    ///\code
825    ///ListGraph::NodeMap<LpSolverBase::Col>
826    ///ListGraph::EdgeMap<LpSolverBase::Col>
827    ///\endcode
828    ///\return The number of the created column.
829#ifdef DOXYGEN
830    template<class T>
831    int addColSet(T &t) { return 0;}
832#else
833    template<class T>
834    typename enable_if<typename T::value_type::LpSolverCol,int>::type
835    addColSet(T &t,dummy<0> = 0) {
836      int s=0;
837      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
838      return s;
839    }
840    template<class T>
841    typename enable_if<typename T::value_type::second_type::LpSolverCol,
842                       int>::type
843    addColSet(T &t,dummy<1> = 1) {
844      int s=0;
845      for(typename T::iterator i=t.begin();i!=t.end();++i) {
846        i->second=addCol();
847        s++;
848      }
849      return s;
850    }
851    template<class T>
852    typename enable_if<typename T::MapIt::Value::LpSolverCol,
853                       int>::type
854    addColSet(T &t,dummy<2> = 2) {
855      int s=0;
856      for(typename T::MapIt i(t); i!=INVALID; ++i)
857        {
858          i.set(addCol());
859          s++;
860        }
861      return s;
862    }
863#endif
864
865    ///Set a column (i.e a dual constraint) of the LP
866
867    ///\param c is the column to be modified
868    ///\param e is a dual linear expression (see \ref DualExpr)
869    ///a better one.
870    void col(Col c,const DualExpr &e) {
871      e.simplify();
872      _setColCoeffs(_lpId(c), ConstColIterator(e.begin(), *this),
873                    ConstColIterator(e.end(), *this));
874    }
875
876    ///Get a column (i.e a dual constraint) of the LP
877
878    ///\param r is the column to get
879    ///\return the dual expression associated to the column
880    DualExpr col(Col c) const {
881      DualExpr e;
882      _getColCoeffs(_lpId(c), ColIterator(std::inserter(e, e.end()), *this));
883      return e;
884    }
885
886    ///Add a new column to the LP
887
888    ///\param e is a dual linear expression (see \ref DualExpr)
889    ///\param obj is the corresponding component of the objective
890    ///function. It is 0 by default.
891    ///\return The created column.
892    Col addCol(const DualExpr &e, Value o = 0) {
893      Col c=addCol();
894      col(c,e);
895      objCoeff(c,o);
896      return c;
897    }
898
899    ///Add a new empty row (i.e a new constraint) to the LP
900
901    ///This function adds a new empty row (i.e a new constraint) to the LP.
902    ///\return The created row
903    Row addRow() { Row r; _addRow(); r.id = rows.addId(); return r;}
904
905    ///\brief Add several new rows
906    ///(i.e a constraints) at once
907    ///
908    ///This magic function takes a container as its argument
909    ///and fills its elements
910    ///with new row (i.e. variables)
911    ///\param t can be
912    ///- a standard STL compatible iterable container with
913    ///\ref Row as its \c values_type
914    ///like
915    ///\code
916    ///std::vector<LpSolverBase::Row>
917    ///std::list<LpSolverBase::Row>
918    ///\endcode
919    ///- a standard STL compatible iterable container with
920    ///\ref Row as its \c mapped_type
921    ///like
922    ///\code
923    ///std::map<AnyType,LpSolverBase::Row>
924    ///\endcode
925    ///- an iterable lemon \ref concepts::WriteMap "write map" like
926    ///\code
927    ///ListGraph::NodeMap<LpSolverBase::Row>
928    ///ListGraph::EdgeMap<LpSolverBase::Row>
929    ///\endcode
930    ///\return The number of rows created.
931#ifdef DOXYGEN
932    template<class T>
933    int addRowSet(T &t) { return 0;}
934#else
935    template<class T>
936    typename enable_if<typename T::value_type::LpSolverRow,int>::type
937    addRowSet(T &t,dummy<0> = 0) {
938      int s=0;
939      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
940      return s;
941    }
942    template<class T>
943    typename enable_if<typename T::value_type::second_type::LpSolverRow,
944                       int>::type
945    addRowSet(T &t,dummy<1> = 1) {
946      int s=0;
947      for(typename T::iterator i=t.begin();i!=t.end();++i) {
948        i->second=addRow();
949        s++;
950      }
951      return s;
952    }
953    template<class T>
954    typename enable_if<typename T::MapIt::Value::LpSolverRow,
955                       int>::type
956    addRowSet(T &t,dummy<2> = 2) {
957      int s=0;
958      for(typename T::MapIt i(t); i!=INVALID; ++i)
959        {
960          i.set(addRow());
961          s++;
962        }
963      return s;
964    }
965#endif
966
967    ///Set a row (i.e a constraint) of the LP
968
969    ///\param r is the row to be modified
970    ///\param l is lower bound (-\ref INF means no bound)
971    ///\param e is a linear expression (see \ref Expr)
972    ///\param u is the upper bound (\ref INF means no bound)
973    ///\bug This is a temporary function. The interface will change to
974    ///a better one.
975    ///\todo Option to control whether a constraint with a single variable is
976    ///added or not.
977    void row(Row r, Value l, const Expr &e, Value u) {
978      e.simplify();
979      _setRowCoeffs(_lpId(r), ConstRowIterator(e.begin(), *this),
980                    ConstRowIterator(e.end(), *this));
981      _setRowBounds(_lpId(r),l-e.constComp(),u-e.constComp());
982    }
983
984    ///Set a row (i.e a constraint) of the LP
985
986    ///\param r is the row to be modified
987    ///\param c is a linear expression (see \ref Constr)
988    void row(Row r, const Constr &c) {
989      row(r, c.lowerBounded()?c.lowerBound():-INF,
990          c.expr(), c.upperBounded()?c.upperBound():INF);
991    }
992
993   
994    ///Get a row (i.e a constraint) of the LP
995
996    ///\param r is the row to get
997    ///\return the expression associated to the row
998    Expr row(Row r) const {
999      Expr e;
1000      _getRowCoeffs(_lpId(r), RowIterator(std::inserter(e, e.end()), *this));
1001      return e;
1002    }
1003
1004    ///Add a new row (i.e a new constraint) to the LP
1005
1006    ///\param l is the lower bound (-\ref INF means no bound)
1007    ///\param e is a linear expression (see \ref Expr)
1008    ///\param u is the upper bound (\ref INF means no bound)
1009    ///\return The created row.
1010    ///\bug This is a temporary function. The interface will change to
1011    ///a better one.
1012    Row addRow(Value l,const Expr &e, Value u) {
1013      Row r=addRow();
1014      row(r,l,e,u);
1015      return r;
1016    }
1017
1018    ///Add a new row (i.e a new constraint) to the LP
1019
1020    ///\param c is a linear expression (see \ref Constr)
1021    ///\return The created row.
1022    Row addRow(const Constr &c) {
1023      Row r=addRow();
1024      row(r,c);
1025      return r;
1026    }
1027    ///Erase a coloumn (i.e a variable) from the LP
1028
1029    ///\param c is the coloumn to be deleted
1030    ///\todo Please check this
1031    void eraseCol(Col c) {
1032      _eraseCol(_lpId(c));
1033      cols.eraseId(c.id);
1034    }
1035    ///Erase a  row (i.e a constraint) from the LP
1036
1037    ///\param r is the row to be deleted
1038    ///\todo Please check this
1039    void eraseRow(Row r) {
1040      _eraseRow(_lpId(r));
1041      rows.eraseId(r.id);
1042    }
1043
1044    /// Get the name of a column
1045   
1046    ///\param c is the coresponding coloumn
1047    ///\return The name of the colunm
1048    std::string colName(Col c) const {
1049      std::string name;
1050      _getColName(_lpId(c), name);
1051      return name;
1052    }
1053   
1054    /// Set the name of a column
1055   
1056    ///\param c is the coresponding coloumn
1057    ///\param name The name to be given
1058    void colName(Col c, const std::string& name) {
1059      _setColName(_lpId(c), name);
1060    }
1061
1062    /// Get the column by its name
1063   
1064    ///\param name The name of the column
1065    ///\return the proper column or \c INVALID
1066    Col colByName(const std::string& name) const {
1067      int k = _colByName(name);
1068      return k != -1 ? Col(cols.fixId(k)) : Col(INVALID);
1069    }
1070   
1071    /// Set an element of the coefficient matrix of the LP
1072
1073    ///\param r is the row of the element to be modified
1074    ///\param c is the coloumn of the element to be modified
1075    ///\param val is the new value of the coefficient
1076
1077    void coeff(Row r, Col c, Value val) {
1078      _setCoeff(_lpId(r),_lpId(c), val);
1079    }
1080
1081    /// Get an element of the coefficient matrix of the LP
1082
1083    ///\param r is the row of the element in question
1084    ///\param c is the coloumn of the element in question
1085    ///\return the corresponding coefficient
1086
1087    Value coeff(Row r, Col c) const {
1088      return _getCoeff(_lpId(r),_lpId(c));
1089    }
1090
1091    /// Set the lower bound of a column (i.e a variable)
1092
1093    /// The lower bound of a variable (column) has to be given by an
1094    /// extended number of type Value, i.e. a finite number of type
1095    /// Value or -\ref INF.
1096    void colLowerBound(Col c, Value value) {
1097      _setColLowerBound(_lpId(c),value);
1098    }
1099
1100    /// Get the lower bound of a column (i.e a variable)
1101
1102    /// This function returns the lower bound for column (variable) \t c
1103    /// (this might be -\ref INF as well). 
1104    ///\return The lower bound for coloumn \t c
1105    Value colLowerBound(Col c) const {
1106      return _getColLowerBound(_lpId(c));
1107    }
1108   
1109    ///\brief Set the lower bound of  several columns
1110    ///(i.e a variables) at once
1111    ///
1112    ///This magic function takes a container as its argument
1113    ///and applies the function on all of its elements.
1114    /// The lower bound of a variable (column) has to be given by an
1115    /// extended number of type Value, i.e. a finite number of type
1116    /// Value or -\ref INF.
1117#ifdef DOXYGEN
1118    template<class T>
1119    void colLowerBound(T &t, Value value) { return 0;}
1120#else
1121    template<class T>
1122    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1123    colLowerBound(T &t, Value value,dummy<0> = 0) {
1124      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1125        colLowerBound(*i, value);
1126      }
1127    }
1128    template<class T>
1129    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1130                       void>::type
1131    colLowerBound(T &t, Value value,dummy<1> = 1) {
1132      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1133        colLowerBound(i->second, value);
1134      }
1135    }
1136    template<class T>
1137    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1138                       void>::type
1139    colLowerBound(T &t, Value value,dummy<2> = 2) {
1140      for(typename T::MapIt i(t); i!=INVALID; ++i){
1141        colLowerBound(*i, value);
1142      }
1143    }
1144#endif
1145   
1146    /// Set the upper bound of a column (i.e a variable)
1147
1148    /// The upper bound of a variable (column) has to be given by an
1149    /// extended number of type Value, i.e. a finite number of type
1150    /// Value or \ref INF.
1151    void colUpperBound(Col c, Value value) {
1152      _setColUpperBound(_lpId(c),value);
1153    };
1154
1155    /// Get the upper bound of a column (i.e a variable)
1156
1157    /// This function returns the upper bound for column (variable) \t c
1158    /// (this might be \ref INF as well). 
1159    ///\return The upper bound for coloumn \t c
1160    Value colUpperBound(Col c) const {
1161      return _getColUpperBound(_lpId(c));
1162    }
1163
1164    ///\brief Set the upper bound of  several columns
1165    ///(i.e a variables) at once
1166    ///
1167    ///This magic function takes a container as its argument
1168    ///and applies the function on all of its elements.
1169    /// The upper bound of a variable (column) has to be given by an
1170    /// extended number of type Value, i.e. a finite number of type
1171    /// Value or \ref INF.
1172#ifdef DOXYGEN
1173    template<class T>
1174    void colUpperBound(T &t, Value value) { return 0;}
1175#else
1176    template<class T>
1177    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1178    colUpperBound(T &t, Value value,dummy<0> = 0) {
1179      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1180        colUpperBound(*i, value);
1181      }
1182    }
1183    template<class T>
1184    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1185                       void>::type
1186    colUpperBound(T &t, Value value,dummy<1> = 1) {
1187      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1188        colUpperBound(i->second, value);
1189      }
1190    }
1191    template<class T>
1192    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1193                       void>::type
1194    colUpperBound(T &t, Value value,dummy<2> = 2) {
1195      for(typename T::MapIt i(t); i!=INVALID; ++i){
1196        colUpperBound(*i, value);
1197      }
1198    }
1199#endif
1200
1201    /// Set the lower and the upper bounds of a column (i.e a variable)
1202
1203    /// The lower and the upper bounds of
1204    /// a variable (column) have to be given by an
1205    /// extended number of type Value, i.e. a finite number of type
1206    /// Value, -\ref INF or \ref INF.
1207    void colBounds(Col c, Value lower, Value upper) {
1208      _setColLowerBound(_lpId(c),lower);
1209      _setColUpperBound(_lpId(c),upper);
1210    }
1211   
1212    ///\brief Set the lower and the upper bound of several columns
1213    ///(i.e a variables) at once
1214    ///
1215    ///This magic function takes a container as its argument
1216    ///and applies the function on all of its elements.
1217    /// The lower and the upper bounds of
1218    /// a variable (column) have to be given by an
1219    /// extended number of type Value, i.e. a finite number of type
1220    /// Value, -\ref INF or \ref INF.
1221#ifdef DOXYGEN
1222    template<class T>
1223    void colBounds(T &t, Value lower, Value upper) { return 0;}
1224#else
1225    template<class T>
1226    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1227    colBounds(T &t, Value lower, Value upper,dummy<0> = 0) {
1228      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1229        colBounds(*i, lower, upper);
1230      }
1231    }
1232    template<class T>
1233    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1234                       void>::type
1235    colBounds(T &t, Value lower, Value upper,dummy<1> = 1) {
1236      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1237        colBounds(i->second, lower, upper);
1238      }
1239    }
1240    template<class T>
1241    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1242                       void>::type
1243    colBounds(T &t, Value lower, Value upper,dummy<2> = 2) {
1244      for(typename T::MapIt i(t); i!=INVALID; ++i){
1245        colBounds(*i, lower, upper);
1246      }
1247    }
1248#endif
1249   
1250
1251    /// Set the lower and the upper bounds of a row (i.e a constraint)
1252
1253    /// The lower and the upper bound of a constraint (row) have to be
1254    /// given by an extended number of type Value, i.e. a finite
1255    /// number of type Value, -\ref INF or \ref INF. There is no
1256    /// separate function for the lower and the upper bound because
1257    /// that would have been hard to implement for CPLEX.
1258    void rowBounds(Row c, Value lower, Value upper) {
1259      _setRowBounds(_lpId(c),lower, upper);
1260    }
1261   
1262    /// Get the lower and the upper bounds of a row (i.e a constraint)
1263
1264    /// The lower and the upper bound of
1265    /// a constraint (row) are 
1266    /// extended numbers of type Value, i.e.  finite numbers of type
1267    /// Value, -\ref INF or \ref INF.
1268    /// \todo There is no separate function for the
1269    /// lower and the upper bound because we had problems with the
1270    /// implementation of the setting functions for CPLEX: 
1271    /// check out whether this can be done for these functions.
1272    void getRowBounds(Row c, Value &lower, Value &upper) const {
1273      _getRowBounds(_lpId(c),lower, upper);
1274    }
1275
1276    ///Set an element of the objective function
1277    void objCoeff(Col c, Value v) {_setObjCoeff(_lpId(c),v); };
1278
1279    ///Get an element of the objective function
1280    Value objCoeff(Col c) const { return _getObjCoeff(_lpId(c)); };
1281
1282    ///Set the objective function
1283
1284    ///\param e is a linear expression of type \ref Expr.
1285    void obj(Expr e) {
1286      _clearObj();
1287      for (Expr::iterator i=e.begin(); i!=e.end(); ++i)
1288        objCoeff((*i).first,(*i).second);
1289      obj_const_comp=e.constComp();
1290    }
1291
1292    ///Get the objective function
1293
1294    ///\return the objective function as a linear expression of type \ref Expr.
1295    Expr obj() const {
1296      Expr e;
1297      for (ColIt it(*this); it != INVALID; ++it) {
1298        double c = objCoeff(it);
1299        if (c != 0.0) {
1300          e.insert(std::make_pair(it, c));
1301        }
1302      }
1303      return e;
1304    }
1305   
1306
1307    ///Maximize
1308    void max() { _setMax(); }
1309    ///Minimize
1310    void min() { _setMin(); }
1311
1312    ///Query function: is this a maximization problem?
1313    bool isMax() const {return _isMax(); }
1314
1315    ///Query function: is this a minimization problem?
1316    bool isMin() const {return !isMax(); }
1317   
1318    ///@}
1319
1320
1321    ///\name Solve the LP
1322
1323    ///@{
1324
1325    ///\e Solve the LP problem at hand
1326    ///
1327    ///\return The result of the optimization procedure. Possible
1328    ///values and their meanings can be found in the documentation of
1329    ///\ref SolveExitStatus.
1330    ///
1331    ///\todo Which method is used to solve the problem
1332    SolveExitStatus solve() { return _solve(); }
1333   
1334    ///@}
1335   
1336    ///\name Obtain the solution
1337
1338    ///@{
1339
1340    /// The status of the primal problem (the original LP problem)
1341    SolutionStatus primalStatus() const {
1342      return _getPrimalStatus();
1343    }
1344
1345    /// The status of the dual (of the original LP) problem
1346    SolutionStatus dualStatus() const {
1347      return _getDualStatus();
1348    }
1349
1350    ///The type of the original LP problem
1351    ProblemTypes problemType() const {
1352      return _getProblemType();
1353    }
1354
1355    ///\e
1356    Value primal(Col c) const { return _getPrimal(_lpId(c)); }
1357
1358    ///\e
1359    Value dual(Row r) const { return _getDual(_lpId(r)); }
1360
1361    ///\e
1362    bool isBasicCol(Col c) const { return _isBasicCol(_lpId(c)); }
1363
1364    ///\e
1365
1366    ///\return
1367    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
1368    /// of the primal problem, depending on whether we minimize or maximize.
1369    ///- \ref NaN if no primal solution is found.
1370    ///- The (finite) objective value if an optimal solution is found.
1371    Value primalValue() const { return _getPrimalValue()+obj_const_comp;}
1372    ///@}
1373   
1374  }; 
1375
1376
1377  /// \ingroup lp_group
1378  ///
1379  /// \brief Common base class for MIP solvers
1380  /// \todo Much more docs
1381  class MipSolverBase : virtual public LpSolverBase{
1382  public:
1383
1384    ///Possible variable (coloumn) types (e.g. real, integer, binary etc.)
1385    enum ColTypes {
1386      ///Continuous variable
1387      REAL = 0,
1388      ///Integer variable
1389
1390      ///Unfortunately, cplex 7.5 somewhere writes something like
1391      ///#define INTEGER 'I'
1392      INT = 1
1393      ///\todo No support for other types yet.
1394    };
1395
1396    ///Sets the type of the given coloumn to the given type
1397    ///
1398    ///Sets the type of the given coloumn to the given type.
1399    void colType(Col c, ColTypes col_type) {
1400      _colType(_lpId(c),col_type);
1401    }
1402
1403    ///Gives back the type of the column.
1404    ///
1405    ///Gives back the type of the column.
1406    ColTypes colType(Col c) const {
1407      return _colType(_lpId(c));
1408    }
1409
1410    ///Sets the type of the given Col to integer or remove that property.
1411    ///
1412    ///Sets the type of the given Col to integer or remove that property.
1413    void integer(Col c, bool enable) {
1414      if (enable)
1415        colType(c,INT);
1416      else
1417        colType(c,REAL);
1418    }
1419
1420    ///Gives back whether the type of the column is integer or not.
1421    ///
1422    ///Gives back the type of the column.
1423    ///\return true if the column has integer type and false if not.
1424    bool integer(Col c) const {
1425      return (colType(c)==INT);
1426    }
1427
1428    /// The status of the MIP problem
1429    SolutionStatus mipStatus() const {
1430      return _getMipStatus();
1431    }
1432
1433  protected:
1434
1435    virtual ColTypes _colType(int col) const = 0;
1436    virtual void _colType(int col, ColTypes col_type) = 0;
1437    virtual SolutionStatus _getMipStatus() const = 0;
1438
1439  };
1440 
1441  ///\relates LpSolverBase::Expr
1442  ///
1443  inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a,
1444                                      const LpSolverBase::Expr &b)
1445  {
1446    LpSolverBase::Expr tmp(a);
1447    tmp+=b;
1448    return tmp;
1449  }
1450  ///\e
1451 
1452  ///\relates LpSolverBase::Expr
1453  ///
1454  inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a,
1455                                      const LpSolverBase::Expr &b)
1456  {
1457    LpSolverBase::Expr tmp(a);
1458    tmp-=b;
1459    return tmp;
1460  }
1461  ///\e
1462 
1463  ///\relates LpSolverBase::Expr
1464  ///
1465  inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a,
1466                                      const LpSolverBase::Value &b)
1467  {
1468    LpSolverBase::Expr tmp(a);
1469    tmp*=b;
1470    return tmp;
1471  }
1472 
1473  ///\e
1474 
1475  ///\relates LpSolverBase::Expr
1476  ///
1477  inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a,
1478                                      const LpSolverBase::Expr &b)
1479  {
1480    LpSolverBase::Expr tmp(b);
1481    tmp*=a;
1482    return tmp;
1483  }
1484  ///\e
1485 
1486  ///\relates LpSolverBase::Expr
1487  ///
1488  inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a,
1489                                      const LpSolverBase::Value &b)
1490  {
1491    LpSolverBase::Expr tmp(a);
1492    tmp/=b;
1493    return tmp;
1494  }
1495 
1496  ///\e
1497 
1498  ///\relates LpSolverBase::Constr
1499  ///
1500  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1501                                         const LpSolverBase::Expr &f)
1502  {
1503    return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0);
1504  }
1505
1506  ///\e
1507 
1508  ///\relates LpSolverBase::Constr
1509  ///
1510  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e,
1511                                         const LpSolverBase::Expr &f)
1512  {
1513    return LpSolverBase::Constr(e,f);
1514  }
1515
1516  ///\e
1517 
1518  ///\relates LpSolverBase::Constr
1519  ///
1520  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1521                                         const LpSolverBase::Value &f)
1522  {
1523    return LpSolverBase::Constr(e,f);
1524  }
1525
1526  ///\e
1527 
1528  ///\relates LpSolverBase::Constr
1529  ///
1530  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1531                                         const LpSolverBase::Expr &f)
1532  {
1533    return LpSolverBase::Constr(-LpSolverBase::INF,f-e,0);
1534  }
1535
1536
1537  ///\e
1538 
1539  ///\relates LpSolverBase::Constr
1540  ///
1541  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e,
1542                                         const LpSolverBase::Expr &f)
1543  {
1544    return LpSolverBase::Constr(f,e);
1545  }
1546
1547
1548  ///\e
1549 
1550  ///\relates LpSolverBase::Constr
1551  ///
1552  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1553                                         const LpSolverBase::Value &f)
1554  {
1555    return LpSolverBase::Constr(f,e);
1556  }
1557
1558  ///\e
1559
1560  ///\relates LpSolverBase::Constr
1561  ///
1562  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
1563                                         const LpSolverBase::Value &f)
1564  {
1565    return LpSolverBase::Constr(f,e,f);
1566  }
1567
1568  ///\e
1569 
1570  ///\relates LpSolverBase::Constr
1571  ///
1572  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
1573                                         const LpSolverBase::Expr &f)
1574  {
1575    return LpSolverBase::Constr(0,e-f,0);
1576  }
1577
1578  ///\e
1579 
1580  ///\relates LpSolverBase::Constr
1581  ///
1582  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n,
1583                                         const LpSolverBase::Constr&c)
1584  {
1585    LpSolverBase::Constr tmp(c);
1586    ///\todo Create an own exception type.
1587    if(!LpSolverBase::isNaN(tmp.lowerBound())) throw LogicError();
1588    else tmp.lowerBound()=n;
1589    return tmp;
1590  }
1591  ///\e
1592 
1593  ///\relates LpSolverBase::Constr
1594  ///
1595  inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c,
1596                                         const LpSolverBase::Value &n)
1597  {
1598    LpSolverBase::Constr tmp(c);
1599    ///\todo Create an own exception type.
1600    if(!LpSolverBase::isNaN(tmp.upperBound())) throw LogicError();
1601    else tmp.upperBound()=n;
1602    return tmp;
1603  }
1604
1605  ///\e
1606 
1607  ///\relates LpSolverBase::Constr
1608  ///
1609  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n,
1610                                         const LpSolverBase::Constr&c)
1611  {
1612    LpSolverBase::Constr tmp(c);
1613    ///\todo Create an own exception type.
1614    if(!LpSolverBase::isNaN(tmp.upperBound())) throw LogicError();
1615    else tmp.upperBound()=n;
1616    return tmp;
1617  }
1618  ///\e
1619 
1620  ///\relates LpSolverBase::Constr
1621  ///
1622  inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c,
1623                                         const LpSolverBase::Value &n)
1624  {
1625    LpSolverBase::Constr tmp(c);
1626    ///\todo Create an own exception type.
1627    if(!LpSolverBase::isNaN(tmp.lowerBound())) throw LogicError();
1628    else tmp.lowerBound()=n;
1629    return tmp;
1630  }
1631
1632  ///\e
1633 
1634  ///\relates LpSolverBase::DualExpr
1635  ///
1636  inline LpSolverBase::DualExpr operator+(const LpSolverBase::DualExpr &a,
1637                                          const LpSolverBase::DualExpr &b)
1638  {
1639    LpSolverBase::DualExpr tmp(a);
1640    tmp+=b;
1641    return tmp;
1642  }
1643  ///\e
1644 
1645  ///\relates LpSolverBase::DualExpr
1646  ///
1647  inline LpSolverBase::DualExpr operator-(const LpSolverBase::DualExpr &a,
1648                                          const LpSolverBase::DualExpr &b)
1649  {
1650    LpSolverBase::DualExpr tmp(a);
1651    tmp-=b;
1652    return tmp;
1653  }
1654  ///\e
1655 
1656  ///\relates LpSolverBase::DualExpr
1657  ///
1658  inline LpSolverBase::DualExpr operator*(const LpSolverBase::DualExpr &a,
1659                                          const LpSolverBase::Value &b)
1660  {
1661    LpSolverBase::DualExpr tmp(a);
1662    tmp*=b;
1663    return tmp;
1664  }
1665 
1666  ///\e
1667 
1668  ///\relates LpSolverBase::DualExpr
1669  ///
1670  inline LpSolverBase::DualExpr operator*(const LpSolverBase::Value &a,
1671                                          const LpSolverBase::DualExpr &b)
1672  {
1673    LpSolverBase::DualExpr tmp(b);
1674    tmp*=a;
1675    return tmp;
1676  }
1677  ///\e
1678 
1679  ///\relates LpSolverBase::DualExpr
1680  ///
1681  inline LpSolverBase::DualExpr operator/(const LpSolverBase::DualExpr &a,
1682                                          const LpSolverBase::Value &b)
1683  {
1684    LpSolverBase::DualExpr tmp(a);
1685    tmp/=b;
1686    return tmp;
1687  }
1688 
1689
1690} //namespace lemon
1691
1692#endif //LEMON_LP_BASE_H
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