COIN-OR::LEMON - Graph Library

source: lemon/lemon/lp_base.h @ 481:7afc121e0689

Last change on this file since 481:7afc121e0689 was 481:7afc121e0689, checked in by Balazs Dezso <deba@…>, 10 years ago

Port LP and MIP solvers from SVN -r3509 (#44)

File size: 47.9 KB
Line 
1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2008
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_LP_BASE_H
20#define LEMON_LP_BASE_H
21
22#include<iostream>
23#include<vector>
24#include<map>
25#include<limits>
26#include<lemon/math.h>
27
28#include<lemon/core.h>
29#include<lemon/bits/lp_id.h>
30
31///\file
32///\brief The interface of the LP solver interface.
33///\ingroup lp_group
34namespace lemon {
35
36  /// Function to decide whether a floating point value is finite or not.
37
38  /// Retruns true if the argument is not infinity, minus infinity or NaN.
39  /// It does the same as the isfinite() function defined by C99.
40  template <typename T>
41  bool isFinite(T value)
42  {
43    typedef std::numeric_limits<T> Lim;
44    if ((Lim::has_infinity && (value == Lim::infinity() || value ==
45                               -Lim::infinity())) ||
46        ((Lim::has_quiet_NaN || Lim::has_signaling_NaN) && value != value))
47    {
48      return false;
49    }
50    return true;
51  }
52
53  ///Common base class for LP solvers
54
55  ///\todo Much more docs
56  ///\ingroup lp_group
57  class LpSolverBase {
58
59  protected:
60
61    _lp_bits::LpId rows;
62    _lp_bits::LpId cols;
63
64  public:
65
66    ///Possible outcomes of an LP solving procedure
67    enum SolveExitStatus {
68      ///This means that the problem has been successfully solved: either
69      ///an optimal solution has been found or infeasibility/unboundedness
70      ///has been proved.
71      SOLVED = 0,
72      ///Any other case (including the case when some user specified
73      ///limit has been exceeded)
74      UNSOLVED = 1
75    };
76
77      ///\e
78    enum SolutionStatus {
79      ///Feasible solution hasn't been found (but may exist).
80
81      ///\todo NOTFOUND might be a better name.
82      ///
83      UNDEFINED = 0,
84      ///The problem has no feasible solution
85      INFEASIBLE = 1,
86      ///Feasible solution found
87      FEASIBLE = 2,
88      ///Optimal solution exists and found
89      OPTIMAL = 3,
90      ///The cost function is unbounded
91
92      ///\todo Give a feasible solution and an infinite ray (and the
93      ///corresponding bases)
94      INFINITE = 4
95    };
96
97    ///\e The type of the investigated LP problem
98    enum ProblemTypes {
99      ///Primal-dual feasible
100      PRIMAL_DUAL_FEASIBLE = 0,
101      ///Primal feasible dual infeasible
102      PRIMAL_FEASIBLE_DUAL_INFEASIBLE = 1,
103      ///Primal infeasible dual feasible
104      PRIMAL_INFEASIBLE_DUAL_FEASIBLE = 2,
105      ///Primal-dual infeasible
106      PRIMAL_DUAL_INFEASIBLE = 3,
107      ///Could not determine so far
108      UNKNOWN = 4
109    };
110
111    ///The floating point type used by the solver
112    typedef double Value;
113    ///The infinity constant
114    static const Value INF;
115    ///The not a number constant
116    static const Value NaN;
117
118    static inline bool isNaN(const Value& v) { return v!=v; }
119
120    friend class Col;
121    friend class ColIt;
122    friend class Row;
123
124    ///Refer to a column of the LP.
125
126    ///This type is used to refer to a column of the LP.
127    ///
128    ///Its value remains valid and correct even after the addition or erase of
129    ///other columns.
130    ///
131    ///\todo Document what can one do with a Col (INVALID, comparing,
132    ///it is similar to Node/Edge)
133    class Col {
134    protected:
135      int id;
136      friend class LpSolverBase;
137      friend class MipSolverBase;
138      explicit Col(int _id) : id(_id) {}
139    public:
140      typedef Value ExprValue;
141      typedef True LpSolverCol;
142      Col() {}
143      Col(const Invalid&) : id(-1) {}
144      bool operator< (Col c) const  {return id< c.id;}
145      bool operator> (Col c) const  {return id> c.id;}
146      bool operator==(Col c) const  {return id==c.id;}
147      bool operator!=(Col c) const  {return id!=c.id;}
148    };
149
150    class ColIt : public Col {
151      const LpSolverBase *_lp;
152    public:
153      ColIt() {}
154      ColIt(const LpSolverBase &lp) : _lp(&lp)
155      {
156        _lp->cols.firstFix(id);
157      }
158      ColIt(const Invalid&) : Col(INVALID) {}
159      ColIt &operator++()
160      {
161        _lp->cols.nextFix(id);
162        return *this;
163      }
164    };
165
166    static int id(const Col& col) { return col.id; }
167
168
169    ///Refer to a row of the LP.
170
171    ///This type is used to refer to a row of the LP.
172    ///
173    ///Its value remains valid and correct even after the addition or erase of
174    ///other rows.
175    ///
176    ///\todo Document what can one do with a Row (INVALID, comparing,
177    ///it is similar to Node/Edge)
178    class Row {
179    protected:
180      int id;
181      friend class LpSolverBase;
182      explicit Row(int _id) : id(_id) {}
183    public:
184      typedef Value ExprValue;
185      typedef True LpSolverRow;
186      Row() {}
187      Row(const Invalid&) : id(-1) {}
188
189      bool operator< (Row c) const  {return id< c.id;}
190      bool operator> (Row c) const  {return id> c.id;}
191      bool operator==(Row c) const  {return id==c.id;}
192      bool operator!=(Row c) const  {return id!=c.id;}
193    };
194
195    class RowIt : public Row {
196      const LpSolverBase *_lp;
197    public:
198      RowIt() {}
199      RowIt(const LpSolverBase &lp) : _lp(&lp)
200      {
201        _lp->rows.firstFix(id);
202      }
203      RowIt(const Invalid&) : Row(INVALID) {}
204      RowIt &operator++()
205      {
206        _lp->rows.nextFix(id);
207        return *this;
208      }
209    };
210
211    static int id(const Row& row) { return row.id; }
212
213  protected:
214
215    int _lpId(const Col& c) const {
216      return cols.floatingId(id(c));
217    }
218
219    int _lpId(const Row& r) const {
220      return rows.floatingId(id(r));
221    }
222
223    Col _item(int i, Col) const {
224      return Col(cols.fixId(i));
225    }
226
227    Row _item(int i, Row) const {
228      return Row(rows.fixId(i));
229    }
230
231
232  public:
233
234    ///Linear expression of variables and a constant component
235
236    ///This data structure stores a linear expression of the variables
237    ///(\ref Col "Col"s) and also has a constant component.
238    ///
239    ///There are several ways to access and modify the contents of this
240    ///container.
241    ///- Its it fully compatible with \c std::map<Col,double>, so for expamle
242    ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can
243    ///read and modify the coefficients like
244    ///these.
245    ///\code
246    ///e[v]=5;
247    ///e[v]+=12;
248    ///e.erase(v);
249    ///\endcode
250    ///or you can also iterate through its elements.
251    ///\code
252    ///double s=0;
253    ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i)
254    ///  s+=i->second;
255    ///\endcode
256    ///(This code computes the sum of all coefficients).
257    ///- Numbers (<tt>double</tt>'s)
258    ///and variables (\ref Col "Col"s) directly convert to an
259    ///\ref Expr and the usual linear operations are defined, so
260    ///\code
261    ///v+w
262    ///2*v-3.12*(v-w/2)+2
263    ///v*2.1+(3*v+(v*12+w+6)*3)/2
264    ///\endcode
265    ///are valid \ref Expr "Expr"essions.
266    ///The usual assignment operations are also defined.
267    ///\code
268    ///e=v+w;
269    ///e+=2*v-3.12*(v-w/2)+2;
270    ///e*=3.4;
271    ///e/=5;
272    ///\endcode
273    ///- The constant member can be set and read by \ref constComp()
274    ///\code
275    ///e.constComp()=12;
276    ///double c=e.constComp();
277    ///\endcode
278    ///
279    ///\note \ref clear() not only sets all coefficients to 0 but also
280    ///clears the constant components.
281    ///
282    ///\sa Constr
283    ///
284    class Expr : public std::map<Col,Value>
285    {
286    public:
287      typedef LpSolverBase::Col Key;
288      typedef LpSolverBase::Value Value;
289
290    protected:
291      typedef std::map<Col,Value> Base;
292
293      Value const_comp;
294    public:
295      typedef True IsLinExpression;
296      ///\e
297      Expr() : Base(), const_comp(0) { }
298      ///\e
299      Expr(const Key &v) : const_comp(0) {
300        Base::insert(std::make_pair(v, 1));
301      }
302      ///\e
303      Expr(const Value &v) : const_comp(v) {}
304      ///\e
305      void set(const Key &v,const Value &c) {
306        Base::insert(std::make_pair(v, c));
307      }
308      ///\e
309      Value &constComp() { return const_comp; }
310      ///\e
311      const Value &constComp() const { return const_comp; }
312
313      ///Removes the components with zero coefficient.
314      void simplify() {
315        for (Base::iterator i=Base::begin(); i!=Base::end();) {
316          Base::iterator j=i;
317          ++j;
318          if ((*i).second==0) Base::erase(i);
319          i=j;
320        }
321      }
322
323      void simplify() const {
324        const_cast<Expr*>(this)->simplify();
325      }
326
327      ///Removes the coefficients closer to zero than \c tolerance.
328      void simplify(double &tolerance) {
329        for (Base::iterator i=Base::begin(); i!=Base::end();) {
330          Base::iterator j=i;
331          ++j;
332          if (std::fabs((*i).second)<tolerance) Base::erase(i);
333          i=j;
334        }
335      }
336
337      ///Sets all coefficients and the constant component to 0.
338      void clear() {
339        Base::clear();
340        const_comp=0;
341      }
342
343      ///\e
344      Expr &operator+=(const Expr &e) {
345        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
346          (*this)[j->first]+=j->second;
347        const_comp+=e.const_comp;
348        return *this;
349      }
350      ///\e
351      Expr &operator-=(const Expr &e) {
352        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
353          (*this)[j->first]-=j->second;
354        const_comp-=e.const_comp;
355        return *this;
356      }
357      ///\e
358      Expr &operator*=(const Value &c) {
359        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
360          j->second*=c;
361        const_comp*=c;
362        return *this;
363      }
364      ///\e
365      Expr &operator/=(const Value &c) {
366        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
367          j->second/=c;
368        const_comp/=c;
369        return *this;
370      }
371
372    };
373
374    ///Linear constraint
375
376    ///This data stucture represents a linear constraint in the LP.
377    ///Basically it is a linear expression with a lower or an upper bound
378    ///(or both). These parts of the constraint can be obtained by the member
379    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
380    ///respectively.
381    ///There are two ways to construct a constraint.
382    ///- You can set the linear expression and the bounds directly
383    ///  by the functions above.
384    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
385    ///  are defined between expressions, or even between constraints whenever
386    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
387    ///  \c s and \c t are numbers, then the followings are valid expressions
388    ///  and thus they can be used directly e.g. in \ref addRow() whenever
389    ///  it makes sense.
390    ///\code
391    ///  e<=s
392    ///  e<=f
393    ///  e==f
394    ///  s<=e<=t
395    ///  e>=t
396    ///\endcode
397    ///\warning The validity of a constraint is checked only at run time, so
398    ///e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will compile, but will throw
399    ///an assertion.
400    class Constr
401    {
402    public:
403      typedef LpSolverBase::Expr Expr;
404      typedef Expr::Key Key;
405      typedef Expr::Value Value;
406
407    protected:
408      Expr _expr;
409      Value _lb,_ub;
410    public:
411      ///\e
412      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
413      ///\e
414      Constr(Value lb,const Expr &e,Value ub) :
415        _expr(e), _lb(lb), _ub(ub) {}
416      ///\e
417      Constr(const Expr &e,Value ub) :
418        _expr(e), _lb(NaN), _ub(ub) {}
419      ///\e
420      Constr(Value lb,const Expr &e) :
421        _expr(e), _lb(lb), _ub(NaN) {}
422      ///\e
423      Constr(const Expr &e) :
424        _expr(e), _lb(NaN), _ub(NaN) {}
425      ///\e
426      void clear()
427      {
428        _expr.clear();
429        _lb=_ub=NaN;
430      }
431
432      ///Reference to the linear expression
433      Expr &expr() { return _expr; }
434      ///Cont reference to the linear expression
435      const Expr &expr() const { return _expr; }
436      ///Reference to the lower bound.
437
438      ///\return
439      ///- \ref INF "INF": the constraint is lower unbounded.
440      ///- \ref NaN "NaN": lower bound has not been set.
441      ///- finite number: the lower bound
442      Value &lowerBound() { return _lb; }
443      ///The const version of \ref lowerBound()
444      const Value &lowerBound() const { return _lb; }
445      ///Reference to the upper bound.
446
447      ///\return
448      ///- \ref INF "INF": the constraint is upper unbounded.
449      ///- \ref NaN "NaN": upper bound has not been set.
450      ///- finite number: the upper bound
451      Value &upperBound() { return _ub; }
452      ///The const version of \ref upperBound()
453      const Value &upperBound() const { return _ub; }
454      ///Is the constraint lower bounded?
455      bool lowerBounded() const {
456        return isFinite(_lb);
457      }
458      ///Is the constraint upper bounded?
459      bool upperBounded() const {
460        return isFinite(_ub);
461      }
462
463    };
464
465    ///Linear expression of rows
466
467    ///This data structure represents a column of the matrix,
468    ///thas is it strores a linear expression of the dual variables
469    ///(\ref Row "Row"s).
470    ///
471    ///There are several ways to access and modify the contents of this
472    ///container.
473    ///- Its it fully compatible with \c std::map<Row,double>, so for expamle
474    ///if \c e is an DualExpr and \c v
475    ///and \c w are of type \ref Row, then you can
476    ///read and modify the coefficients like
477    ///these.
478    ///\code
479    ///e[v]=5;
480    ///e[v]+=12;
481    ///e.erase(v);
482    ///\endcode
483    ///or you can also iterate through its elements.
484    ///\code
485    ///double s=0;
486    ///for(LpSolverBase::DualExpr::iterator i=e.begin();i!=e.end();++i)
487    ///  s+=i->second;
488    ///\endcode
489    ///(This code computes the sum of all coefficients).
490    ///- Numbers (<tt>double</tt>'s)
491    ///and variables (\ref Row "Row"s) directly convert to an
492    ///\ref DualExpr and the usual linear operations are defined, so
493    ///\code
494    ///v+w
495    ///2*v-3.12*(v-w/2)
496    ///v*2.1+(3*v+(v*12+w)*3)/2
497    ///\endcode
498    ///are valid \ref DualExpr "DualExpr"essions.
499    ///The usual assignment operations are also defined.
500    ///\code
501    ///e=v+w;
502    ///e+=2*v-3.12*(v-w/2);
503    ///e*=3.4;
504    ///e/=5;
505    ///\endcode
506    ///
507    ///\sa Expr
508    ///
509    class DualExpr : public std::map<Row,Value>
510    {
511    public:
512      typedef LpSolverBase::Row Key;
513      typedef LpSolverBase::Value Value;
514
515    protected:
516      typedef std::map<Row,Value> Base;
517
518    public:
519      typedef True IsLinExpression;
520      ///\e
521      DualExpr() : Base() { }
522      ///\e
523      DualExpr(const Key &v) {
524        Base::insert(std::make_pair(v, 1));
525      }
526      ///\e
527      void set(const Key &v,const Value &c) {
528        Base::insert(std::make_pair(v, c));
529      }
530
531      ///Removes the components with zero coefficient.
532      void simplify() {
533        for (Base::iterator i=Base::begin(); i!=Base::end();) {
534          Base::iterator j=i;
535          ++j;
536          if ((*i).second==0) Base::erase(i);
537          i=j;
538        }
539      }
540
541      void simplify() const {
542        const_cast<DualExpr*>(this)->simplify();
543      }
544
545      ///Removes the coefficients closer to zero than \c tolerance.
546      void simplify(double &tolerance) {
547        for (Base::iterator i=Base::begin(); i!=Base::end();) {
548          Base::iterator j=i;
549          ++j;
550          if (std::fabs((*i).second)<tolerance) Base::erase(i);
551          i=j;
552        }
553      }
554
555      ///Sets all coefficients to 0.
556      void clear() {
557        Base::clear();
558      }
559
560      ///\e
561      DualExpr &operator+=(const DualExpr &e) {
562        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
563          (*this)[j->first]+=j->second;
564        return *this;
565      }
566      ///\e
567      DualExpr &operator-=(const DualExpr &e) {
568        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
569          (*this)[j->first]-=j->second;
570        return *this;
571      }
572      ///\e
573      DualExpr &operator*=(const Value &c) {
574        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
575          j->second*=c;
576        return *this;
577      }
578      ///\e
579      DualExpr &operator/=(const Value &c) {
580        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
581          j->second/=c;
582        return *this;
583      }
584    };
585
586
587  private:
588
589    template <typename _Expr>
590    class MappedOutputIterator {
591    public:
592
593      typedef std::insert_iterator<_Expr> Base;
594
595      typedef std::output_iterator_tag iterator_category;
596      typedef void difference_type;
597      typedef void value_type;
598      typedef void reference;
599      typedef void pointer;
600
601      MappedOutputIterator(const Base& _base, const LpSolverBase& _lp)
602        : base(_base), lp(_lp) {}
603
604      MappedOutputIterator& operator*() {
605        return *this;
606      }
607
608      MappedOutputIterator& operator=(const std::pair<int, Value>& value) {
609        *base = std::make_pair(lp._item(value.first, typename _Expr::Key()),
610                               value.second);
611        return *this;
612      }
613
614      MappedOutputIterator& operator++() {
615        ++base;
616        return *this;
617      }
618
619      MappedOutputIterator operator++(int) {
620        MappedOutputIterator tmp(*this);
621        ++base;
622        return tmp;
623      }
624
625      bool operator==(const MappedOutputIterator& it) const {
626        return base == it.base;
627      }
628
629      bool operator!=(const MappedOutputIterator& it) const {
630        return base != it.base;
631      }
632
633    private:
634      Base base;
635      const LpSolverBase& lp;
636    };
637
638    template <typename Expr>
639    class MappedInputIterator {
640    public:
641
642      typedef typename Expr::const_iterator Base;
643
644      typedef typename Base::iterator_category iterator_category;
645      typedef typename Base::difference_type difference_type;
646      typedef const std::pair<int, Value> value_type;
647      typedef value_type reference;
648      class pointer {
649      public:
650        pointer(value_type& _value) : value(_value) {}
651        value_type* operator->() { return &value; }
652      private:
653        value_type value;
654      };
655
656      MappedInputIterator(const Base& _base, const LpSolverBase& _lp)
657        : base(_base), lp(_lp) {}
658
659      reference operator*() {
660        return std::make_pair(lp._lpId(base->first), base->second);
661      }
662
663      pointer operator->() {
664        return pointer(operator*());
665      }
666
667      MappedInputIterator& operator++() {
668        ++base;
669        return *this;
670      }
671
672      MappedInputIterator operator++(int) {
673        MappedInputIterator tmp(*this);
674        ++base;
675        return tmp;
676      }
677
678      bool operator==(const MappedInputIterator& it) const {
679        return base == it.base;
680      }
681
682      bool operator!=(const MappedInputIterator& it) const {
683        return base != it.base;
684      }
685
686    private:
687      Base base;
688      const LpSolverBase& lp;
689    };
690
691  protected:
692
693    /// STL compatible iterator for lp col
694    typedef MappedInputIterator<Expr> ConstRowIterator;
695    /// STL compatible iterator for lp row
696    typedef MappedInputIterator<DualExpr> ConstColIterator;
697
698    /// STL compatible iterator for lp col
699    typedef MappedOutputIterator<Expr> RowIterator;
700    /// STL compatible iterator for lp row
701    typedef MappedOutputIterator<DualExpr> ColIterator;
702
703    //Abstract virtual functions
704    virtual LpSolverBase* _newLp() = 0;
705    virtual LpSolverBase* _copyLp(){
706      LpSolverBase* newlp = _newLp();
707
708      std::map<Col, Col> ref;
709      for (LpSolverBase::ColIt it(*this); it != INVALID; ++it) {
710        Col ccol = newlp->addCol();
711        ref[it] = ccol;
712        newlp->colName(ccol, colName(it));
713        newlp->colLowerBound(ccol, colLowerBound(it));
714        newlp->colUpperBound(ccol, colUpperBound(it));
715      }
716
717      for (LpSolverBase::RowIt it(*this); it != INVALID; ++it) {
718        Expr e = row(it), ce;
719        for (Expr::iterator jt = e.begin(); jt != e.end(); ++jt) {
720          ce[ref[jt->first]] = jt->second;
721        }
722        ce += e.constComp();
723        Row r = newlp->addRow(ce);
724
725        double lower, upper;
726        getRowBounds(it, lower, upper);
727        newlp->rowBounds(r, lower, upper);
728      }
729
730      return newlp;
731    };
732
733    virtual int _addCol() = 0;
734    virtual int _addRow() = 0;
735
736    virtual void _eraseCol(int col) = 0;
737    virtual void _eraseRow(int row) = 0;
738
739    virtual void _getColName(int col, std::string & name) const = 0;
740    virtual void _setColName(int col, const std::string & name) = 0;
741    virtual int _colByName(const std::string& name) const = 0;
742
743    virtual void _setRowCoeffs(int i, ConstRowIterator b,
744                               ConstRowIterator e) = 0;
745    virtual void _getRowCoeffs(int i, RowIterator b) const = 0;
746    virtual void _setColCoeffs(int i, ConstColIterator b,
747                               ConstColIterator e) = 0;
748    virtual void _getColCoeffs(int i, ColIterator b) const = 0;
749    virtual void _setCoeff(int row, int col, Value value) = 0;
750    virtual Value _getCoeff(int row, int col) const = 0;
751    virtual void _setColLowerBound(int i, Value value) = 0;
752    virtual Value _getColLowerBound(int i) const = 0;
753    virtual void _setColUpperBound(int i, Value value) = 0;
754    virtual Value _getColUpperBound(int i) const = 0;
755    virtual void _setRowBounds(int i, Value lower, Value upper) = 0;
756    virtual void _getRowBounds(int i, Value &lower, Value &upper) const = 0;
757
758    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
759    virtual Value _getObjCoeff(int i) const = 0;
760    virtual void _clearObj()=0;
761
762    virtual SolveExitStatus _solve() = 0;
763    virtual Value _getPrimal(int i) const = 0;
764    virtual Value _getDual(int i) const = 0;
765    virtual Value _getPrimalValue() const = 0;
766    virtual bool _isBasicCol(int i) const = 0;
767    virtual SolutionStatus _getPrimalStatus() const = 0;
768    virtual SolutionStatus _getDualStatus() const = 0;
769    virtual ProblemTypes _getProblemType() const = 0;
770
771    virtual void _setMax() = 0;
772    virtual void _setMin() = 0;
773
774
775    virtual bool _isMax() const = 0;
776
777    //Own protected stuff
778
779    //Constant component of the objective function
780    Value obj_const_comp;
781
782  public:
783
784    ///\e
785    LpSolverBase() : obj_const_comp(0) {}
786
787    ///\e
788    virtual ~LpSolverBase() {}
789
790    ///Creates a new LP problem
791    LpSolverBase* newLp() {return _newLp();}
792    ///Makes a copy of the LP problem
793    LpSolverBase* copyLp() {return _copyLp();}
794
795    ///\name Build up and modify the LP
796
797    ///@{
798
799    ///Add a new empty column (i.e a new variable) to the LP
800    Col addCol() { Col c; _addCol(); c.id = cols.addId(); return c;}
801
802    ///\brief Adds several new columns
803    ///(i.e a variables) at once
804    ///
805    ///This magic function takes a container as its argument
806    ///and fills its elements
807    ///with new columns (i.e. variables)
808    ///\param t can be
809    ///- a standard STL compatible iterable container with
810    ///\ref Col as its \c values_type
811    ///like
812    ///\code
813    ///std::vector<LpSolverBase::Col>
814    ///std::list<LpSolverBase::Col>
815    ///\endcode
816    ///- a standard STL compatible iterable container with
817    ///\ref Col as its \c mapped_type
818    ///like
819    ///\code
820    ///std::map<AnyType,LpSolverBase::Col>
821    ///\endcode
822    ///- an iterable lemon \ref concepts::WriteMap "write map" like
823    ///\code
824    ///ListGraph::NodeMap<LpSolverBase::Col>
825    ///ListGraph::EdgeMap<LpSolverBase::Col>
826    ///\endcode
827    ///\return The number of the created column.
828#ifdef DOXYGEN
829    template<class T>
830    int addColSet(T &t) { return 0;}
831#else
832    template<class T>
833    typename enable_if<typename T::value_type::LpSolverCol,int>::type
834    addColSet(T &t,dummy<0> = 0) {
835      int s=0;
836      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
837      return s;
838    }
839    template<class T>
840    typename enable_if<typename T::value_type::second_type::LpSolverCol,
841                       int>::type
842    addColSet(T &t,dummy<1> = 1) {
843      int s=0;
844      for(typename T::iterator i=t.begin();i!=t.end();++i) {
845        i->second=addCol();
846        s++;
847      }
848      return s;
849    }
850    template<class T>
851    typename enable_if<typename T::MapIt::Value::LpSolverCol,
852                       int>::type
853    addColSet(T &t,dummy<2> = 2) {
854      int s=0;
855      for(typename T::MapIt i(t); i!=INVALID; ++i)
856        {
857          i.set(addCol());
858          s++;
859        }
860      return s;
861    }
862#endif
863
864    ///Set a column (i.e a dual constraint) of the LP
865
866    ///\param c is the column to be modified
867    ///\param e is a dual linear expression (see \ref DualExpr)
868    ///a better one.
869    void col(Col c,const DualExpr &e) {
870      e.simplify();
871      _setColCoeffs(_lpId(c), ConstColIterator(e.begin(), *this),
872                    ConstColIterator(e.end(), *this));
873    }
874
875    ///Get a column (i.e a dual constraint) of the LP
876
877    ///\param r is the column to get
878    ///\return the dual expression associated to the column
879    DualExpr col(Col c) const {
880      DualExpr e;
881      _getColCoeffs(_lpId(c), ColIterator(std::inserter(e, e.end()), *this));
882      return e;
883    }
884
885    ///Add a new column to the LP
886
887    ///\param e is a dual linear expression (see \ref DualExpr)
888    ///\param obj is the corresponding component of the objective
889    ///function. It is 0 by default.
890    ///\return The created column.
891    Col addCol(const DualExpr &e, Value o = 0) {
892      Col c=addCol();
893      col(c,e);
894      objCoeff(c,o);
895      return c;
896    }
897
898    ///Add a new empty row (i.e a new constraint) to the LP
899
900    ///This function adds a new empty row (i.e a new constraint) to the LP.
901    ///\return The created row
902    Row addRow() { Row r; _addRow(); r.id = rows.addId(); return r;}
903
904    ///\brief Add several new rows
905    ///(i.e a constraints) at once
906    ///
907    ///This magic function takes a container as its argument
908    ///and fills its elements
909    ///with new row (i.e. variables)
910    ///\param t can be
911    ///- a standard STL compatible iterable container with
912    ///\ref Row as its \c values_type
913    ///like
914    ///\code
915    ///std::vector<LpSolverBase::Row>
916    ///std::list<LpSolverBase::Row>
917    ///\endcode
918    ///- a standard STL compatible iterable container with
919    ///\ref Row as its \c mapped_type
920    ///like
921    ///\code
922    ///std::map<AnyType,LpSolverBase::Row>
923    ///\endcode
924    ///- an iterable lemon \ref concepts::WriteMap "write map" like
925    ///\code
926    ///ListGraph::NodeMap<LpSolverBase::Row>
927    ///ListGraph::EdgeMap<LpSolverBase::Row>
928    ///\endcode
929    ///\return The number of rows created.
930#ifdef DOXYGEN
931    template<class T>
932    int addRowSet(T &t) { return 0;}
933#else
934    template<class T>
935    typename enable_if<typename T::value_type::LpSolverRow,int>::type
936    addRowSet(T &t,dummy<0> = 0) {
937      int s=0;
938      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
939      return s;
940    }
941    template<class T>
942    typename enable_if<typename T::value_type::second_type::LpSolverRow,
943                       int>::type
944    addRowSet(T &t,dummy<1> = 1) {
945      int s=0;
946      for(typename T::iterator i=t.begin();i!=t.end();++i) {
947        i->second=addRow();
948        s++;
949      }
950      return s;
951    }
952    template<class T>
953    typename enable_if<typename T::MapIt::Value::LpSolverRow,
954                       int>::type
955    addRowSet(T &t,dummy<2> = 2) {
956      int s=0;
957      for(typename T::MapIt i(t); i!=INVALID; ++i)
958        {
959          i.set(addRow());
960          s++;
961        }
962      return s;
963    }
964#endif
965
966    ///Set a row (i.e a constraint) of the LP
967
968    ///\param r is the row to be modified
969    ///\param l is lower bound (-\ref INF means no bound)
970    ///\param e is a linear expression (see \ref Expr)
971    ///\param u is the upper bound (\ref INF means no bound)
972    ///\bug This is a temporary function. The interface will change to
973    ///a better one.
974    ///\todo Option to control whether a constraint with a single variable is
975    ///added or not.
976    void row(Row r, Value l, const Expr &e, Value u) {
977      e.simplify();
978      _setRowCoeffs(_lpId(r), ConstRowIterator(e.begin(), *this),
979                    ConstRowIterator(e.end(), *this));
980      _setRowBounds(_lpId(r),l-e.constComp(),u-e.constComp());
981    }
982
983    ///Set a row (i.e a constraint) of the LP
984
985    ///\param r is the row to be modified
986    ///\param c is a linear expression (see \ref Constr)
987    void row(Row r, const Constr &c) {
988      row(r, c.lowerBounded()?c.lowerBound():-INF,
989          c.expr(), c.upperBounded()?c.upperBound():INF);
990    }
991
992
993    ///Get a row (i.e a constraint) of the LP
994
995    ///\param r is the row to get
996    ///\return the expression associated to the row
997    Expr row(Row r) const {
998      Expr e;
999      _getRowCoeffs(_lpId(r), RowIterator(std::inserter(e, e.end()), *this));
1000      return e;
1001    }
1002
1003    ///Add a new row (i.e a new constraint) to the LP
1004
1005    ///\param l is the lower bound (-\ref INF means no bound)
1006    ///\param e is a linear expression (see \ref Expr)
1007    ///\param u is the upper bound (\ref INF means no bound)
1008    ///\return The created row.
1009    ///\bug This is a temporary function. The interface will change to
1010    ///a better one.
1011    Row addRow(Value l,const Expr &e, Value u) {
1012      Row r=addRow();
1013      row(r,l,e,u);
1014      return r;
1015    }
1016
1017    ///Add a new row (i.e a new constraint) to the LP
1018
1019    ///\param c is a linear expression (see \ref Constr)
1020    ///\return The created row.
1021    Row addRow(const Constr &c) {
1022      Row r=addRow();
1023      row(r,c);
1024      return r;
1025    }
1026    ///Erase a coloumn (i.e a variable) from the LP
1027
1028    ///\param c is the coloumn to be deleted
1029    ///\todo Please check this
1030    void eraseCol(Col c) {
1031      _eraseCol(_lpId(c));
1032      cols.eraseId(c.id);
1033    }
1034    ///Erase a  row (i.e a constraint) from the LP
1035
1036    ///\param r is the row to be deleted
1037    ///\todo Please check this
1038    void eraseRow(Row r) {
1039      _eraseRow(_lpId(r));
1040      rows.eraseId(r.id);
1041    }
1042
1043    /// Get the name of a column
1044
1045    ///\param c is the coresponding coloumn
1046    ///\return The name of the colunm
1047    std::string colName(Col c) const {
1048      std::string name;
1049      _getColName(_lpId(c), name);
1050      return name;
1051    }
1052
1053    /// Set the name of a column
1054
1055    ///\param c is the coresponding coloumn
1056    ///\param name The name to be given
1057    void colName(Col c, const std::string& name) {
1058      _setColName(_lpId(c), name);
1059    }
1060
1061    /// Get the column by its name
1062
1063    ///\param name The name of the column
1064    ///\return the proper column or \c INVALID
1065    Col colByName(const std::string& name) const {
1066      int k = _colByName(name);
1067      return k != -1 ? Col(cols.fixId(k)) : Col(INVALID);
1068    }
1069
1070    /// Set an element of the coefficient matrix of the LP
1071
1072    ///\param r is the row of the element to be modified
1073    ///\param c is the coloumn of the element to be modified
1074    ///\param val is the new value of the coefficient
1075
1076    void coeff(Row r, Col c, Value val) {
1077      _setCoeff(_lpId(r),_lpId(c), val);
1078    }
1079
1080    /// Get an element of the coefficient matrix of the LP
1081
1082    ///\param r is the row of the element in question
1083    ///\param c is the coloumn of the element in question
1084    ///\return the corresponding coefficient
1085
1086    Value coeff(Row r, Col c) const {
1087      return _getCoeff(_lpId(r),_lpId(c));
1088    }
1089
1090    /// Set the lower bound of a column (i.e a variable)
1091
1092    /// The lower bound of a variable (column) has to be given by an
1093    /// extended number of type Value, i.e. a finite number of type
1094    /// Value or -\ref INF.
1095    void colLowerBound(Col c, Value value) {
1096      _setColLowerBound(_lpId(c),value);
1097    }
1098
1099    /// Get the lower bound of a column (i.e a variable)
1100
1101    /// This function returns the lower bound for column (variable) \t c
1102    /// (this might be -\ref INF as well).
1103    ///\return The lower bound for coloumn \t c
1104    Value colLowerBound(Col c) const {
1105      return _getColLowerBound(_lpId(c));
1106    }
1107
1108    ///\brief Set the lower bound of  several columns
1109    ///(i.e a variables) at once
1110    ///
1111    ///This magic function takes a container as its argument
1112    ///and applies the function on all of its elements.
1113    /// The lower bound of a variable (column) has to be given by an
1114    /// extended number of type Value, i.e. a finite number of type
1115    /// Value or -\ref INF.
1116#ifdef DOXYGEN
1117    template<class T>
1118    void colLowerBound(T &t, Value value) { return 0;}
1119#else
1120    template<class T>
1121    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1122    colLowerBound(T &t, Value value,dummy<0> = 0) {
1123      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1124        colLowerBound(*i, value);
1125      }
1126    }
1127    template<class T>
1128    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1129                       void>::type
1130    colLowerBound(T &t, Value value,dummy<1> = 1) {
1131      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1132        colLowerBound(i->second, value);
1133      }
1134    }
1135    template<class T>
1136    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1137                       void>::type
1138    colLowerBound(T &t, Value value,dummy<2> = 2) {
1139      for(typename T::MapIt i(t); i!=INVALID; ++i){
1140        colLowerBound(*i, value);
1141      }
1142    }
1143#endif
1144
1145    /// Set the upper bound of a column (i.e a variable)
1146
1147    /// The upper bound of a variable (column) has to be given by an
1148    /// extended number of type Value, i.e. a finite number of type
1149    /// Value or \ref INF.
1150    void colUpperBound(Col c, Value value) {
1151      _setColUpperBound(_lpId(c),value);
1152    };
1153
1154    /// Get the upper bound of a column (i.e a variable)
1155
1156    /// This function returns the upper bound for column (variable) \t c
1157    /// (this might be \ref INF as well).
1158    ///\return The upper bound for coloumn \t c
1159    Value colUpperBound(Col c) const {
1160      return _getColUpperBound(_lpId(c));
1161    }
1162
1163    ///\brief Set the upper bound of  several columns
1164    ///(i.e a variables) at once
1165    ///
1166    ///This magic function takes a container as its argument
1167    ///and applies the function on all of its elements.
1168    /// The upper bound of a variable (column) has to be given by an
1169    /// extended number of type Value, i.e. a finite number of type
1170    /// Value or \ref INF.
1171#ifdef DOXYGEN
1172    template<class T>
1173    void colUpperBound(T &t, Value value) { return 0;}
1174#else
1175    template<class T>
1176    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1177    colUpperBound(T &t, Value value,dummy<0> = 0) {
1178      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1179        colUpperBound(*i, value);
1180      }
1181    }
1182    template<class T>
1183    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1184                       void>::type
1185    colUpperBound(T &t, Value value,dummy<1> = 1) {
1186      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1187        colUpperBound(i->second, value);
1188      }
1189    }
1190    template<class T>
1191    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1192                       void>::type
1193    colUpperBound(T &t, Value value,dummy<2> = 2) {
1194      for(typename T::MapIt i(t); i!=INVALID; ++i){
1195        colUpperBound(*i, value);
1196      }
1197    }
1198#endif
1199
1200    /// Set the lower and the upper bounds of a column (i.e a variable)
1201
1202    /// The lower and the upper bounds of
1203    /// a variable (column) have to be given by an
1204    /// extended number of type Value, i.e. a finite number of type
1205    /// Value, -\ref INF or \ref INF.
1206    void colBounds(Col c, Value lower, Value upper) {
1207      _setColLowerBound(_lpId(c),lower);
1208      _setColUpperBound(_lpId(c),upper);
1209    }
1210
1211    ///\brief Set the lower and the upper bound of several columns
1212    ///(i.e a variables) at once
1213    ///
1214    ///This magic function takes a container as its argument
1215    ///and applies the function on all of its elements.
1216    /// The lower and the upper bounds of
1217    /// a variable (column) have to be given by an
1218    /// extended number of type Value, i.e. a finite number of type
1219    /// Value, -\ref INF or \ref INF.
1220#ifdef DOXYGEN
1221    template<class T>
1222    void colBounds(T &t, Value lower, Value upper) { return 0;}
1223#else
1224    template<class T>
1225    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1226    colBounds(T &t, Value lower, Value upper,dummy<0> = 0) {
1227      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1228        colBounds(*i, lower, upper);
1229      }
1230    }
1231    template<class T>
1232    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1233                       void>::type
1234    colBounds(T &t, Value lower, Value upper,dummy<1> = 1) {
1235      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1236        colBounds(i->second, lower, upper);
1237      }
1238    }
1239    template<class T>
1240    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1241                       void>::type
1242    colBounds(T &t, Value lower, Value upper,dummy<2> = 2) {
1243      for(typename T::MapIt i(t); i!=INVALID; ++i){
1244        colBounds(*i, lower, upper);
1245      }
1246    }
1247#endif
1248
1249
1250    /// Set the lower and the upper bounds of a row (i.e a constraint)
1251
1252    /// The lower and the upper bound of a constraint (row) have to be
1253    /// given by an extended number of type Value, i.e. a finite
1254    /// number of type Value, -\ref INF or \ref INF. There is no
1255    /// separate function for the lower and the upper bound because
1256    /// that would have been hard to implement for CPLEX.
1257    void rowBounds(Row c, Value lower, Value upper) {
1258      _setRowBounds(_lpId(c),lower, upper);
1259    }
1260
1261    /// Get the lower and the upper bounds of a row (i.e a constraint)
1262
1263    /// The lower and the upper bound of
1264    /// a constraint (row) are
1265    /// extended numbers of type Value, i.e.  finite numbers of type
1266    /// Value, -\ref INF or \ref INF.
1267    /// \todo There is no separate function for the
1268    /// lower and the upper bound because we had problems with the
1269    /// implementation of the setting functions for CPLEX:
1270    /// check out whether this can be done for these functions.
1271    void getRowBounds(Row c, Value &lower, Value &upper) const {
1272      _getRowBounds(_lpId(c),lower, upper);
1273    }
1274
1275    ///Set an element of the objective function
1276    void objCoeff(Col c, Value v) {_setObjCoeff(_lpId(c),v); };
1277
1278    ///Get an element of the objective function
1279    Value objCoeff(Col c) const { return _getObjCoeff(_lpId(c)); };
1280
1281    ///Set the objective function
1282
1283    ///\param e is a linear expression of type \ref Expr.
1284    void obj(Expr e) {
1285      _clearObj();
1286      for (Expr::iterator i=e.begin(); i!=e.end(); ++i)
1287        objCoeff((*i).first,(*i).second);
1288      obj_const_comp=e.constComp();
1289    }
1290
1291    ///Get the objective function
1292
1293    ///\return the objective function as a linear expression of type \ref Expr.
1294    Expr obj() const {
1295      Expr e;
1296      for (ColIt it(*this); it != INVALID; ++it) {
1297        double c = objCoeff(it);
1298        if (c != 0.0) {
1299          e.insert(std::make_pair(it, c));
1300        }
1301      }
1302      return e;
1303    }
1304
1305
1306    ///Maximize
1307    void max() { _setMax(); }
1308    ///Minimize
1309    void min() { _setMin(); }
1310
1311    ///Query function: is this a maximization problem?
1312    bool isMax() const {return _isMax(); }
1313
1314    ///Query function: is this a minimization problem?
1315    bool isMin() const {return !isMax(); }
1316
1317    ///@}
1318
1319
1320    ///\name Solve the LP
1321
1322    ///@{
1323
1324    ///\e Solve the LP problem at hand
1325    ///
1326    ///\return The result of the optimization procedure. Possible
1327    ///values and their meanings can be found in the documentation of
1328    ///\ref SolveExitStatus.
1329    ///
1330    ///\todo Which method is used to solve the problem
1331    SolveExitStatus solve() { return _solve(); }
1332
1333    ///@}
1334
1335    ///\name Obtain the solution
1336
1337    ///@{
1338
1339    /// The status of the primal problem (the original LP problem)
1340    SolutionStatus primalStatus() const {
1341      return _getPrimalStatus();
1342    }
1343
1344    /// The status of the dual (of the original LP) problem
1345    SolutionStatus dualStatus() const {
1346      return _getDualStatus();
1347    }
1348
1349    ///The type of the original LP problem
1350    ProblemTypes problemType() const {
1351      return _getProblemType();
1352    }
1353
1354    ///\e
1355    Value primal(Col c) const { return _getPrimal(_lpId(c)); }
1356    ///\e
1357    Value primal(const Expr& e) const {
1358      double res = e.constComp();
1359      for (std::map<Col, double>::const_iterator it = e.begin();
1360           it != e.end(); ++it) {
1361        res += _getPrimal(_lpId(it->first)) * it->second;
1362      }
1363      return res;
1364    }
1365
1366    ///\e
1367    Value dual(Row r) const { return _getDual(_lpId(r)); }
1368    ///\e
1369    Value dual(const DualExpr& e) const {
1370      double res = 0.0;
1371      for (std::map<Row, double>::const_iterator it = e.begin();
1372           it != e.end(); ++it) {
1373        res += _getPrimal(_lpId(it->first)) * it->second;
1374      }
1375      return res;
1376    }
1377
1378    ///\e
1379    bool isBasicCol(Col c) const { return _isBasicCol(_lpId(c)); }
1380
1381    ///\e
1382
1383    ///\return
1384    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
1385    /// of the primal problem, depending on whether we minimize or maximize.
1386    ///- \ref NaN if no primal solution is found.
1387    ///- The (finite) objective value if an optimal solution is found.
1388    Value primalValue() const { return _getPrimalValue()+obj_const_comp;}
1389    ///@}
1390
1391  };
1392
1393
1394  /// \ingroup lp_group
1395  ///
1396  /// \brief Common base class for MIP solvers
1397  /// \todo Much more docs
1398  class MipSolverBase : virtual public LpSolverBase{
1399  public:
1400
1401    ///Possible variable (coloumn) types (e.g. real, integer, binary etc.)
1402    enum ColTypes {
1403      ///Continuous variable
1404      REAL = 0,
1405      ///Integer variable
1406
1407      ///Unfortunately, cplex 7.5 somewhere writes something like
1408      ///#define INTEGER 'I'
1409      INT = 1
1410      ///\todo No support for other types yet.
1411    };
1412
1413    ///Sets the type of the given coloumn to the given type
1414    ///
1415    ///Sets the type of the given coloumn to the given type.
1416    void colType(Col c, ColTypes col_type) {
1417      _colType(_lpId(c),col_type);
1418    }
1419
1420    ///Gives back the type of the column.
1421    ///
1422    ///Gives back the type of the column.
1423    ColTypes colType(Col c) const {
1424      return _colType(_lpId(c));
1425    }
1426
1427    ///Sets the type of the given Col to integer or remove that property.
1428    ///
1429    ///Sets the type of the given Col to integer or remove that property.
1430    void integer(Col c, bool enable) {
1431      if (enable)
1432        colType(c,INT);
1433      else
1434        colType(c,REAL);
1435    }
1436
1437    ///Gives back whether the type of the column is integer or not.
1438    ///
1439    ///Gives back the type of the column.
1440    ///\return true if the column has integer type and false if not.
1441    bool integer(Col c) const {
1442      return (colType(c)==INT);
1443    }
1444
1445    /// The status of the MIP problem
1446    SolutionStatus mipStatus() const {
1447      return _getMipStatus();
1448    }
1449
1450  protected:
1451
1452    virtual ColTypes _colType(int col) const = 0;
1453    virtual void _colType(int col, ColTypes col_type) = 0;
1454    virtual SolutionStatus _getMipStatus() const = 0;
1455
1456  };
1457
1458  ///\relates LpSolverBase::Expr
1459  ///
1460  inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a,
1461                                      const LpSolverBase::Expr &b)
1462  {
1463    LpSolverBase::Expr tmp(a);
1464    tmp+=b;
1465    return tmp;
1466  }
1467  ///\e
1468
1469  ///\relates LpSolverBase::Expr
1470  ///
1471  inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a,
1472                                      const LpSolverBase::Expr &b)
1473  {
1474    LpSolverBase::Expr tmp(a);
1475    tmp-=b;
1476    return tmp;
1477  }
1478  ///\e
1479
1480  ///\relates LpSolverBase::Expr
1481  ///
1482  inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a,
1483                                      const LpSolverBase::Value &b)
1484  {
1485    LpSolverBase::Expr tmp(a);
1486    tmp*=b;
1487    return tmp;
1488  }
1489
1490  ///\e
1491
1492  ///\relates LpSolverBase::Expr
1493  ///
1494  inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a,
1495                                      const LpSolverBase::Expr &b)
1496  {
1497    LpSolverBase::Expr tmp(b);
1498    tmp*=a;
1499    return tmp;
1500  }
1501  ///\e
1502
1503  ///\relates LpSolverBase::Expr
1504  ///
1505  inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a,
1506                                      const LpSolverBase::Value &b)
1507  {
1508    LpSolverBase::Expr tmp(a);
1509    tmp/=b;
1510    return tmp;
1511  }
1512
1513  ///\e
1514
1515  ///\relates LpSolverBase::Constr
1516  ///
1517  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1518                                         const LpSolverBase::Expr &f)
1519  {
1520    return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0);
1521  }
1522
1523  ///\e
1524
1525  ///\relates LpSolverBase::Constr
1526  ///
1527  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e,
1528                                         const LpSolverBase::Expr &f)
1529  {
1530    return LpSolverBase::Constr(e,f);
1531  }
1532
1533  ///\e
1534
1535  ///\relates LpSolverBase::Constr
1536  ///
1537  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1538                                         const LpSolverBase::Value &f)
1539  {
1540    return LpSolverBase::Constr(-LpSolverBase::INF,e,f);
1541  }
1542
1543  ///\e
1544
1545  ///\relates LpSolverBase::Constr
1546  ///
1547  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1548                                         const LpSolverBase::Expr &f)
1549  {
1550    return LpSolverBase::Constr(-LpSolverBase::INF,f-e,0);
1551  }
1552
1553
1554  ///\e
1555
1556  ///\relates LpSolverBase::Constr
1557  ///
1558  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e,
1559                                         const LpSolverBase::Expr &f)
1560  {
1561    return LpSolverBase::Constr(f,e);
1562  }
1563
1564
1565  ///\e
1566
1567  ///\relates LpSolverBase::Constr
1568  ///
1569  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1570                                         const LpSolverBase::Value &f)
1571  {
1572    return LpSolverBase::Constr(f,e,LpSolverBase::INF);
1573  }
1574
1575  ///\e
1576
1577  ///\relates LpSolverBase::Constr
1578  ///
1579  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
1580                                         const LpSolverBase::Value &f)
1581  {
1582    return LpSolverBase::Constr(f,e,f);
1583  }
1584
1585  ///\e
1586
1587  ///\relates LpSolverBase::Constr
1588  ///
1589  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
1590                                         const LpSolverBase::Expr &f)
1591  {
1592    return LpSolverBase::Constr(0,e-f,0);
1593  }
1594
1595  ///\e
1596
1597  ///\relates LpSolverBase::Constr
1598  ///
1599  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n,
1600                                         const LpSolverBase::Constr&c)
1601  {
1602    LpSolverBase::Constr tmp(c);
1603    LEMON_ASSERT(LpSolverBase::isNaN(tmp.lowerBound()), "Wrong LP constraint");
1604    tmp.lowerBound()=n;
1605    return tmp;
1606  }
1607  ///\e
1608
1609  ///\relates LpSolverBase::Constr
1610  ///
1611  inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c,
1612                                         const LpSolverBase::Value &n)
1613  {
1614    LpSolverBase::Constr tmp(c);
1615    LEMON_ASSERT(LpSolverBase::isNaN(tmp.upperBound()), "Wrong LP constraint");
1616    tmp.upperBound()=n;
1617    return tmp;
1618  }
1619
1620  ///\e
1621
1622  ///\relates LpSolverBase::Constr
1623  ///
1624  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n,
1625                                         const LpSolverBase::Constr&c)
1626  {
1627    LpSolverBase::Constr tmp(c);
1628    LEMON_ASSERT(LpSolverBase::isNaN(tmp.upperBound()), "Wrong LP constraint");
1629    tmp.upperBound()=n;
1630    return tmp;
1631  }
1632  ///\e
1633
1634  ///\relates LpSolverBase::Constr
1635  ///
1636  inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c,
1637                                         const LpSolverBase::Value &n)
1638  {
1639    LpSolverBase::Constr tmp(c);
1640    LEMON_ASSERT(LpSolverBase::isNaN(tmp.lowerBound()), "Wrong LP constraint");
1641    tmp.lowerBound()=n;
1642    return tmp;
1643  }
1644
1645  ///\e
1646
1647  ///\relates LpSolverBase::DualExpr
1648  ///
1649  inline LpSolverBase::DualExpr operator+(const LpSolverBase::DualExpr &a,
1650                                          const LpSolverBase::DualExpr &b)
1651  {
1652    LpSolverBase::DualExpr tmp(a);
1653    tmp+=b;
1654    return tmp;
1655  }
1656  ///\e
1657
1658  ///\relates LpSolverBase::DualExpr
1659  ///
1660  inline LpSolverBase::DualExpr operator-(const LpSolverBase::DualExpr &a,
1661                                          const LpSolverBase::DualExpr &b)
1662  {
1663    LpSolverBase::DualExpr tmp(a);
1664    tmp-=b;
1665    return tmp;
1666  }
1667  ///\e
1668
1669  ///\relates LpSolverBase::DualExpr
1670  ///
1671  inline LpSolverBase::DualExpr operator*(const LpSolverBase::DualExpr &a,
1672                                          const LpSolverBase::Value &b)
1673  {
1674    LpSolverBase::DualExpr tmp(a);
1675    tmp*=b;
1676    return tmp;
1677  }
1678
1679  ///\e
1680
1681  ///\relates LpSolverBase::DualExpr
1682  ///
1683  inline LpSolverBase::DualExpr operator*(const LpSolverBase::Value &a,
1684                                          const LpSolverBase::DualExpr &b)
1685  {
1686    LpSolverBase::DualExpr tmp(b);
1687    tmp*=a;
1688    return tmp;
1689  }
1690  ///\e
1691
1692  ///\relates LpSolverBase::DualExpr
1693  ///
1694  inline LpSolverBase::DualExpr operator/(const LpSolverBase::DualExpr &a,
1695                                          const LpSolverBase::Value &b)
1696  {
1697    LpSolverBase::DualExpr tmp(a);
1698    tmp/=b;
1699    return tmp;
1700  }
1701
1702
1703} //namespace lemon
1704
1705#endif //LEMON_LP_BASE_H
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