COIN-OR::LEMON - Graph Library

source: lemon/lemon/lp_base.h @ 561:2eb5c8ca2c91

Last change on this file since 561:2eb5c8ca2c91 was 561:2eb5c8ca2c91, checked in by Janos Tapolcai <tapolcai@…>, 11 years ago

Dirty hacking for VS 2005 in lp_base.h (#209)

File size: 60.7 KB
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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/error.h>
29#include<lemon/assert.h>
30
31#include<lemon/core.h>
32#include<lemon/bits/solver_bits.h>
33
34///\file
35///\brief The interface of the LP solver interface.
36///\ingroup lp_group
37namespace lemon {
38
39  ///Common base class for LP and MIP solvers
40
41  ///Usually this class is not used directly, please use one of the concrete
42  ///implementations of the solver interface.
43  ///\ingroup lp_group
44  class LpBase {
45
46  protected:
47
48    _solver_bits::VarIndex rows;
49    _solver_bits::VarIndex cols;
50
51  public:
52
53    ///Possible outcomes of an LP solving procedure
54    enum SolveExitStatus {
55      ///This means that the problem has been successfully solved: either
56      ///an optimal solution has been found or infeasibility/unboundedness
57      ///has been proved.
58      SOLVED = 0,
59      ///Any other case (including the case when some user specified
60      ///limit has been exceeded)
61      UNSOLVED = 1
62    };
63
64    ///Direction of the optimization
65    enum Sense {
66      /// Minimization
67      MIN,
68      /// Maximization
69      MAX
70    };
71
72    ///The floating point type used by the solver
73    typedef double Value;
74    ///The infinity constant
75    static const Value INF;
76    ///The not a number constant
77    static const Value NaN;
78
79    friend class Col;
80    friend class ColIt;
81    friend class Row;
82    friend class RowIt;
83
84    ///Refer to a column of the LP.
85
86    ///This type is used to refer to a column of the LP.
87    ///
88    ///Its value remains valid and correct even after the addition or erase of
89    ///other columns.
90    ///
91    ///\note This class is similar to other Item types in LEMON, like
92    ///Node and Arc types in digraph.
93    class Col {
94      friend class LpBase;
95    protected:
96      int _id;
97      explicit Col(int id) : _id(id) {}
98    public:
99      typedef Value ExprValue;
100      typedef True LpCol;
101      /// Default constructor
102     
103      /// \warning The default constructor sets the Col to an
104      /// undefined value.
105      Col() {}
106      /// Invalid constructor \& conversion.
107     
108      /// This constructor initializes the Col to be invalid.
109      /// \sa Invalid for more details.     
110      Col(const Invalid&) : _id(-1) {}
111      /// Equality operator
112
113      /// Two \ref Col "Col"s are equal if and only if they point to
114      /// the same LP column or both are invalid.
115      bool operator==(Col c) const  {return _id == c._id;}
116      /// Inequality operator
117
118      /// \sa operator==(Col c)
119      ///
120      bool operator!=(Col c) const  {return _id != c._id;}
121      /// Artificial ordering operator.
122
123      /// To allow the use of this object in std::map or similar
124      /// associative container we require this.
125      ///
126      /// \note This operator only have to define some strict ordering of
127      /// the items; this order has nothing to do with the iteration
128      /// ordering of the items.
129      bool operator<(Col c) const  {return _id < c._id;}
130    };
131
132    ///Iterator for iterate over the columns of an LP problem
133
134    /// Its usage is quite simple, for example you can count the number
135    /// of columns in an LP \c lp:
136    ///\code
137    /// int count=0;
138    /// for (LpBase::ColIt c(lp); c!=INVALID; ++c) ++count;
139    ///\endcode
140    class ColIt : public Col {
141      const LpBase *_solver;
142    public:
143      /// Default constructor
144     
145      /// \warning The default constructor sets the iterator
146      /// to an undefined value.
147      ColIt() {}
148      /// Sets the iterator to the first Col
149     
150      /// Sets the iterator to the first Col.
151      ///
152      ColIt(const LpBase &solver) : _solver(&solver)
153      {
154        _solver->cols.firstItem(_id);
155      }
156      /// Invalid constructor \& conversion
157     
158      /// Initialize the iterator to be invalid.
159      /// \sa Invalid for more details.
160      ColIt(const Invalid&) : Col(INVALID) {}
161      /// Next column
162     
163      /// Assign the iterator to the next column.
164      ///
165      ColIt &operator++()
166      {
167        _solver->cols.nextItem(_id);
168        return *this;
169      }
170    };
171
172    /// \brief Returns the ID of the column.
173    static int id(const Col& col) { return col._id; }
174    /// \brief Returns the column with the given ID.
175    ///
176    /// \pre The argument should be a valid column ID in the LP problem.
177    static Col colFromId(int id) { return Col(id); }
178
179    ///Refer to a row of the LP.
180
181    ///This type is used to refer to a row of the LP.
182    ///
183    ///Its value remains valid and correct even after the addition or erase of
184    ///other rows.
185    ///
186    ///\note This class is similar to other Item types in LEMON, like
187    ///Node and Arc types in digraph.
188    class Row {
189      friend class LpBase;
190    protected:
191      int _id;
192      explicit Row(int id) : _id(id) {}
193    public:
194      typedef Value ExprValue;
195      typedef True LpRow;
196      /// Default constructor
197     
198      /// \warning The default constructor sets the Row to an
199      /// undefined value.
200      Row() {}
201      /// Invalid constructor \& conversion.
202     
203      /// This constructor initializes the Row to be invalid.
204      /// \sa Invalid for more details.     
205      Row(const Invalid&) : _id(-1) {}
206      /// Equality operator
207
208      /// Two \ref Row "Row"s are equal if and only if they point to
209      /// the same LP row or both are invalid.
210      bool operator==(Row r) const  {return _id == r._id;}
211      /// Inequality operator
212     
213      /// \sa operator==(Row r)
214      ///
215      bool operator!=(Row r) const  {return _id != r._id;}
216      /// Artificial ordering operator.
217
218      /// To allow the use of this object in std::map or similar
219      /// associative container we require this.
220      ///
221      /// \note This operator only have to define some strict ordering of
222      /// the items; this order has nothing to do with the iteration
223      /// ordering of the items.
224      bool operator<(Row r) const  {return _id < r._id;}
225    };
226
227    ///Iterator for iterate over the rows of an LP problem
228
229    /// Its usage is quite simple, for example you can count the number
230    /// of rows in an LP \c lp:
231    ///\code
232    /// int count=0;
233    /// for (LpBase::RowIt c(lp); c!=INVALID; ++c) ++count;
234    ///\endcode
235    class RowIt : public Row {
236      const LpBase *_solver;
237    public:
238      /// Default constructor
239     
240      /// \warning The default constructor sets the iterator
241      /// to an undefined value.
242      RowIt() {}
243      /// Sets the iterator to the first Row
244     
245      /// Sets the iterator to the first Row.
246      ///
247      RowIt(const LpBase &solver) : _solver(&solver)
248      {
249        _solver->rows.firstItem(_id);
250      }
251      /// Invalid constructor \& conversion
252     
253      /// Initialize the iterator to be invalid.
254      /// \sa Invalid for more details.
255      RowIt(const Invalid&) : Row(INVALID) {}
256      /// Next row
257     
258      /// Assign the iterator to the next row.
259      ///
260      RowIt &operator++()
261      {
262        _solver->rows.nextItem(_id);
263        return *this;
264      }
265    };
266
267    /// \brief Returns the ID of the row.
268    static int id(const Row& row) { return row._id; }
269    /// \brief Returns the row with the given ID.
270    ///
271    /// \pre The argument should be a valid row ID in the LP problem.
272    static Row rowFromId(int id) { return Row(id); }
273
274  public:
275
276    ///Linear expression of variables and a constant component
277
278    ///This data structure stores a linear expression of the variables
279    ///(\ref Col "Col"s) and also has a constant component.
280    ///
281    ///There are several ways to access and modify the contents of this
282    ///container.
283    ///\code
284    ///e[v]=5;
285    ///e[v]+=12;
286    ///e.erase(v);
287    ///\endcode
288    ///or you can also iterate through its elements.
289    ///\code
290    ///double s=0;
291    ///for(LpBase::Expr::ConstCoeffIt i(e);i!=INVALID;++i)
292    ///  s+=*i * primal(i);
293    ///\endcode
294    ///(This code computes the primal value of the expression).
295    ///- Numbers (<tt>double</tt>'s)
296    ///and variables (\ref Col "Col"s) directly convert to an
297    ///\ref Expr and the usual linear operations are defined, so
298    ///\code
299    ///v+w
300    ///2*v-3.12*(v-w/2)+2
301    ///v*2.1+(3*v+(v*12+w+6)*3)/2
302    ///\endcode
303    ///are valid expressions.
304    ///The usual assignment operations are also defined.
305    ///\code
306    ///e=v+w;
307    ///e+=2*v-3.12*(v-w/2)+2;
308    ///e*=3.4;
309    ///e/=5;
310    ///\endcode
311    ///- The constant member can be set and read by dereference
312    ///  operator (unary *)
313    ///
314    ///\code
315    ///*e=12;
316    ///double c=*e;
317    ///\endcode
318    ///
319    ///\sa Constr
320    class Expr {
321      friend class LpBase;
322    public:
323      /// The key type of the expression
324      typedef LpBase::Col Key;
325      /// The value type of the expression
326      typedef LpBase::Value Value;
327
328    protected:
329      Value const_comp;
330      std::map<int, Value> comps;
331
332    public:
333      typedef True SolverExpr;
334      /// Default constructor
335     
336      /// Construct an empty expression, the coefficients and
337      /// the constant component are initialized to zero.
338      Expr() : const_comp(0) {}
339      /// Construct an expression from a column
340
341      /// Construct an expression, which has a term with \c c variable
342      /// and 1.0 coefficient.
343      Expr(const Col &c) : const_comp(0) {
344        typedef std::map<int, Value>::value_type pair_type;
345        comps.insert(pair_type(id(c), 1));
346      }
347      /// Construct an expression from a constant
348
349      /// Construct an expression, which's constant component is \c v.
350      ///
351      Expr(const Value &v) : const_comp(v) {}
352      /// Returns the coefficient of the column
353      Value operator[](const Col& c) const {
354        std::map<int, Value>::const_iterator it=comps.find(id(c));
355        if (it != comps.end()) {
356          return it->second;
357        } else {
358          return 0;
359        }
360      }
361      /// Returns the coefficient of the column
362      Value& operator[](const Col& c) {
363        return comps[id(c)];
364      }
365      /// Sets the coefficient of the column
366      void set(const Col &c, const Value &v) {
367        if (v != 0.0) {
368          typedef std::map<int, Value>::value_type pair_type;
369          comps.insert(pair_type(id(c), v));
370        } else {
371          comps.erase(id(c));
372        }
373      }
374      /// Returns the constant component of the expression
375      Value& operator*() { return const_comp; }
376      /// Returns the constant component of the expression
377      const Value& operator*() const { return const_comp; }
378      /// \brief Removes the coefficients which's absolute value does
379      /// not exceed \c epsilon. It also sets to zero the constant
380      /// component, if it does not exceed epsilon in absolute value.
381      void simplify(Value epsilon = 0.0) {
382        std::map<int, Value>::iterator it=comps.begin();
383        while (it != comps.end()) {
384          std::map<int, Value>::iterator jt=it;
385          ++jt;
386          if (std::fabs((*it).second) <= epsilon) comps.erase(it);
387          it=jt;
388        }
389        if (std::fabs(const_comp) <= epsilon) const_comp = 0;
390      }
391
392      void simplify(Value epsilon = 0.0) const {
393        const_cast<Expr*>(this)->simplify(epsilon);
394      }
395
396      ///Sets all coefficients and the constant component to 0.
397      void clear() {
398        comps.clear();
399        const_comp=0;
400      }
401
402      ///Compound assignment
403      Expr &operator+=(const Expr &e) {
404        for (std::map<int, Value>::const_iterator it=e.comps.begin();
405             it!=e.comps.end(); ++it)
406          comps[it->first]+=it->second;
407        const_comp+=e.const_comp;
408        return *this;
409      }
410      ///Compound assignment
411      Expr &operator-=(const Expr &e) {
412        for (std::map<int, Value>::const_iterator it=e.comps.begin();
413             it!=e.comps.end(); ++it)
414          comps[it->first]-=it->second;
415        const_comp-=e.const_comp;
416        return *this;
417      }
418      ///Multiply with a constant
419      Expr &operator*=(const Value &v) {
420        for (std::map<int, Value>::iterator it=comps.begin();
421             it!=comps.end(); ++it)
422          it->second*=v;
423        const_comp*=v;
424        return *this;
425      }
426      ///Division with a constant
427      Expr &operator/=(const Value &c) {
428        for (std::map<int, Value>::iterator it=comps.begin();
429             it!=comps.end(); ++it)
430          it->second/=c;
431        const_comp/=c;
432        return *this;
433      }
434
435      ///Iterator over the expression
436     
437      ///The iterator iterates over the terms of the expression.
438      ///
439      ///\code
440      ///double s=0;
441      ///for(LpBase::Expr::CoeffIt i(e);i!=INVALID;++i)
442      ///  s+= *i * primal(i);
443      ///\endcode
444      class CoeffIt {
445      private:
446
447        std::map<int, Value>::iterator _it, _end;
448
449      public:
450
451        /// Sets the iterator to the first term
452       
453        /// Sets the iterator to the first term of the expression.
454        ///
455        CoeffIt(Expr& e)
456          : _it(e.comps.begin()), _end(e.comps.end()){}
457
458        /// Convert the iterator to the column of the term
459        operator Col() const {
460          return colFromId(_it->first);
461        }
462
463        /// Returns the coefficient of the term
464        Value& operator*() { return _it->second; }
465
466        /// Returns the coefficient of the term
467        const Value& operator*() const { return _it->second; }
468        /// Next term
469       
470        /// Assign the iterator to the next term.
471        ///
472        CoeffIt& operator++() { ++_it; return *this; }
473
474        /// Equality operator
475        bool operator==(Invalid) const { return _it == _end; }
476        /// Inequality operator
477        bool operator!=(Invalid) const { return _it != _end; }
478      };
479
480      /// Const iterator over the expression
481     
482      ///The iterator iterates over the terms of the expression.
483      ///
484      ///\code
485      ///double s=0;
486      ///for(LpBase::Expr::ConstCoeffIt i(e);i!=INVALID;++i)
487      ///  s+=*i * primal(i);
488      ///\endcode
489      class ConstCoeffIt {
490      private:
491
492        std::map<int, Value>::const_iterator _it, _end;
493
494      public:
495
496        /// Sets the iterator to the first term
497       
498        /// Sets the iterator to the first term of the expression.
499        ///
500        ConstCoeffIt(const Expr& e)
501          : _it(e.comps.begin()), _end(e.comps.end()){}
502
503        /// Convert the iterator to the column of the term
504        operator Col() const {
505          return colFromId(_it->first);
506        }
507
508        /// Returns the coefficient of the term
509        const Value& operator*() const { return _it->second; }
510
511        /// Next term
512       
513        /// Assign the iterator to the next term.
514        ///
515        ConstCoeffIt& operator++() { ++_it; return *this; }
516
517        /// Equality operator
518        bool operator==(Invalid) const { return _it == _end; }
519        /// Inequality operator
520        bool operator!=(Invalid) const { return _it != _end; }
521      };
522
523    };
524
525    ///Linear constraint
526
527    ///This data stucture represents a linear constraint in the LP.
528    ///Basically it is a linear expression with a lower or an upper bound
529    ///(or both). These parts of the constraint can be obtained by the member
530    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
531    ///respectively.
532    ///There are two ways to construct a constraint.
533    ///- You can set the linear expression and the bounds directly
534    ///  by the functions above.
535    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
536    ///  are defined between expressions, or even between constraints whenever
537    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
538    ///  \c s and \c t are numbers, then the followings are valid expressions
539    ///  and thus they can be used directly e.g. in \ref addRow() whenever
540    ///  it makes sense.
541    ///\code
542    ///  e<=s
543    ///  e<=f
544    ///  e==f
545    ///  s<=e<=t
546    ///  e>=t
547    ///\endcode
548    ///\warning The validity of a constraint is checked only at run
549    ///time, so e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will
550    ///compile, but will fail an assertion.
551    class Constr
552    {
553    public:
554      typedef LpBase::Expr Expr;
555      typedef Expr::Key Key;
556      typedef Expr::Value Value;
557
558    protected:
559      Expr _expr;
560      Value _lb,_ub;
561    public:
562      ///\e
563      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
564      ///\e
565      Constr(Value lb, const Expr &e, Value ub) :
566        _expr(e), _lb(lb), _ub(ub) {}
567      Constr(const Expr &e) :
568        _expr(e), _lb(NaN), _ub(NaN) {}
569      ///\e
570      void clear()
571      {
572        _expr.clear();
573        _lb=_ub=NaN;
574      }
575
576      ///Reference to the linear expression
577      Expr &expr() { return _expr; }
578      ///Cont reference to the linear expression
579      const Expr &expr() const { return _expr; }
580      ///Reference to the lower bound.
581
582      ///\return
583      ///- \ref INF "INF": the constraint is lower unbounded.
584      ///- \ref NaN "NaN": lower bound has not been set.
585      ///- finite number: the lower bound
586      Value &lowerBound() { return _lb; }
587      ///The const version of \ref lowerBound()
588      const Value &lowerBound() const { return _lb; }
589      ///Reference to the upper bound.
590
591      ///\return
592      ///- \ref INF "INF": the constraint is upper unbounded.
593      ///- \ref NaN "NaN": upper bound has not been set.
594      ///- finite number: the upper bound
595      Value &upperBound() { return _ub; }
596      ///The const version of \ref upperBound()
597      const Value &upperBound() const { return _ub; }
598      ///Is the constraint lower bounded?
599      bool lowerBounded() const {
600        return _lb != -INF && !isNaN(_lb);
601      }
602      ///Is the constraint upper bounded?
603      bool upperBounded() const {
604        return _ub != INF && !isNaN(_ub);
605      }
606
607    };
608
609    ///Linear expression of rows
610
611    ///This data structure represents a column of the matrix,
612    ///thas is it strores a linear expression of the dual variables
613    ///(\ref Row "Row"s).
614    ///
615    ///There are several ways to access and modify the contents of this
616    ///container.
617    ///\code
618    ///e[v]=5;
619    ///e[v]+=12;
620    ///e.erase(v);
621    ///\endcode
622    ///or you can also iterate through its elements.
623    ///\code
624    ///double s=0;
625    ///for(LpBase::DualExpr::ConstCoeffIt i(e);i!=INVALID;++i)
626    ///  s+=*i;
627    ///\endcode
628    ///(This code computes the sum of all coefficients).
629    ///- Numbers (<tt>double</tt>'s)
630    ///and variables (\ref Row "Row"s) directly convert to an
631    ///\ref DualExpr and the usual linear operations are defined, so
632    ///\code
633    ///v+w
634    ///2*v-3.12*(v-w/2)
635    ///v*2.1+(3*v+(v*12+w)*3)/2
636    ///\endcode
637    ///are valid \ref DualExpr dual expressions.
638    ///The usual assignment operations are also defined.
639    ///\code
640    ///e=v+w;
641    ///e+=2*v-3.12*(v-w/2);
642    ///e*=3.4;
643    ///e/=5;
644    ///\endcode
645    ///
646    ///\sa Expr
647    class DualExpr {
648      friend class LpBase;
649    public:
650      /// The key type of the expression
651      typedef LpBase::Row Key;
652      /// The value type of the expression
653      typedef LpBase::Value Value;
654
655    protected:
656      std::map<int, Value> comps;
657
658    public:
659      typedef True SolverExpr;
660      /// Default constructor
661     
662      /// Construct an empty expression, the coefficients are
663      /// initialized to zero.
664      DualExpr() {}
665      /// Construct an expression from a row
666
667      /// Construct an expression, which has a term with \c r dual
668      /// variable and 1.0 coefficient.
669      DualExpr(const Row &r) {
670        typedef std::map<int, Value>::value_type pair_type;
671        comps.insert(pair_type(id(r), 1));
672      }
673      /// Returns the coefficient of the row
674      Value operator[](const Row& r) const {
675        std::map<int, Value>::const_iterator it = comps.find(id(r));
676        if (it != comps.end()) {
677          return it->second;
678        } else {
679          return 0;
680        }
681      }
682      /// Returns the coefficient of the row
683      Value& operator[](const Row& r) {
684        return comps[id(r)];
685      }
686      /// Sets the coefficient of the row
687      void set(const Row &r, const Value &v) {
688        if (v != 0.0) {
689          typedef std::map<int, Value>::value_type pair_type;
690          comps.insert(pair_type(id(r), v));
691        } else {
692          comps.erase(id(r));
693        }
694      }
695      /// \brief Removes the coefficients which's absolute value does
696      /// not exceed \c epsilon.
697      void simplify(Value epsilon = 0.0) {
698        std::map<int, Value>::iterator it=comps.begin();
699        while (it != comps.end()) {
700          std::map<int, Value>::iterator jt=it;
701          ++jt;
702          if (std::fabs((*it).second) <= epsilon) comps.erase(it);
703          it=jt;
704        }
705      }
706
707      void simplify(Value epsilon = 0.0) const {
708        const_cast<DualExpr*>(this)->simplify(epsilon);
709      }
710
711      ///Sets all coefficients to 0.
712      void clear() {
713        comps.clear();
714      }
715      ///Compound assignment
716      DualExpr &operator+=(const DualExpr &e) {
717        for (std::map<int, Value>::const_iterator it=e.comps.begin();
718             it!=e.comps.end(); ++it)
719          comps[it->first]+=it->second;
720        return *this;
721      }
722      ///Compound assignment
723      DualExpr &operator-=(const DualExpr &e) {
724        for (std::map<int, Value>::const_iterator it=e.comps.begin();
725             it!=e.comps.end(); ++it)
726          comps[it->first]-=it->second;
727        return *this;
728      }
729      ///Multiply with a constant
730      DualExpr &operator*=(const Value &v) {
731        for (std::map<int, Value>::iterator it=comps.begin();
732             it!=comps.end(); ++it)
733          it->second*=v;
734        return *this;
735      }
736      ///Division with a constant
737      DualExpr &operator/=(const Value &v) {
738        for (std::map<int, Value>::iterator it=comps.begin();
739             it!=comps.end(); ++it)
740          it->second/=v;
741        return *this;
742      }
743
744      ///Iterator over the expression
745     
746      ///The iterator iterates over the terms of the expression.
747      ///
748      ///\code
749      ///double s=0;
750      ///for(LpBase::DualExpr::CoeffIt i(e);i!=INVALID;++i)
751      ///  s+= *i * dual(i);
752      ///\endcode
753      class CoeffIt {
754      private:
755
756        std::map<int, Value>::iterator _it, _end;
757
758      public:
759
760        /// Sets the iterator to the first term
761       
762        /// Sets the iterator to the first term of the expression.
763        ///
764        CoeffIt(DualExpr& e)
765          : _it(e.comps.begin()), _end(e.comps.end()){}
766
767        /// Convert the iterator to the row of the term
768        operator Row() const {
769          return rowFromId(_it->first);
770        }
771
772        /// Returns the coefficient of the term
773        Value& operator*() { return _it->second; }
774
775        /// Returns the coefficient of the term
776        const Value& operator*() const { return _it->second; }
777
778        /// Next term
779       
780        /// Assign the iterator to the next term.
781        ///
782        CoeffIt& operator++() { ++_it; return *this; }
783
784        /// Equality operator
785        bool operator==(Invalid) const { return _it == _end; }
786        /// Inequality operator
787        bool operator!=(Invalid) const { return _it != _end; }
788      };
789
790      ///Iterator over the expression
791     
792      ///The iterator iterates over the terms of the expression.
793      ///
794      ///\code
795      ///double s=0;
796      ///for(LpBase::DualExpr::ConstCoeffIt i(e);i!=INVALID;++i)
797      ///  s+= *i * dual(i);
798      ///\endcode
799      class ConstCoeffIt {
800      private:
801
802        std::map<int, Value>::const_iterator _it, _end;
803
804      public:
805
806        /// Sets the iterator to the first term
807       
808        /// Sets the iterator to the first term of the expression.
809        ///
810        ConstCoeffIt(const DualExpr& e)
811          : _it(e.comps.begin()), _end(e.comps.end()){}
812
813        /// Convert the iterator to the row of the term
814        operator Row() const {
815          return rowFromId(_it->first);
816        }
817
818        /// Returns the coefficient of the term
819        const Value& operator*() const { return _it->second; }
820
821        /// Next term
822       
823        /// Assign the iterator to the next term.
824        ///
825        ConstCoeffIt& operator++() { ++_it; return *this; }
826
827        /// Equality operator
828        bool operator==(Invalid) const { return _it == _end; }
829        /// Inequality operator
830        bool operator!=(Invalid) const { return _it != _end; }
831      };
832    };
833
834
835  protected:
836
837    class InsertIterator {
838    private:
839
840      std::map<int, Value>& _host;
841      const _solver_bits::VarIndex& _index;
842
843    public:
844
845      typedef std::output_iterator_tag iterator_category;
846      typedef void difference_type;
847      typedef void value_type;
848      typedef void reference;
849      typedef void pointer;
850
851      InsertIterator(std::map<int, Value>& host,
852                   const _solver_bits::VarIndex& index)
853        : _host(host), _index(index) {}
854
855      InsertIterator& operator=(const std::pair<int, Value>& value) {
856        typedef std::map<int, Value>::value_type pair_type;
857        _host.insert(pair_type(_index[value.first], value.second));
858        return *this;
859      }
860
861      InsertIterator& operator*() { return *this; }
862      InsertIterator& operator++() { return *this; }
863      InsertIterator operator++(int) { return *this; }
864
865    };
866
867    class ExprIterator {
868    private:
869      std::map<int, Value>::const_iterator _host_it;
870      const _solver_bits::VarIndex& _index;
871    public:
872
873      typedef std::bidirectional_iterator_tag iterator_category;
874      typedef std::ptrdiff_t difference_type;
875      typedef const std::pair<int, Value> value_type;
876      typedef value_type reference;
877
878      class pointer {
879      public:
880        pointer(value_type& _value) : value(_value) {}
881        value_type* operator->() { return &value; }
882      private:
883        value_type value;
884      };
885
886      ExprIterator(const std::map<int, Value>::const_iterator& host_it,
887                   const _solver_bits::VarIndex& index)
888        : _host_it(host_it), _index(index) {}
889
890      reference operator*() {
891        return std::make_pair(_index(_host_it->first), _host_it->second);
892      }
893
894      pointer operator->() {
895        return pointer(operator*());
896      }
897
898      ExprIterator& operator++() { ++_host_it; return *this; }
899      ExprIterator operator++(int) {
900        ExprIterator tmp(*this); ++_host_it; return tmp;
901      }
902
903      ExprIterator& operator--() { --_host_it; return *this; }
904      ExprIterator operator--(int) {
905        ExprIterator tmp(*this); --_host_it; return tmp;
906      }
907
908      bool operator==(const ExprIterator& it) const {
909        return _host_it == it._host_it;
910      }
911
912      bool operator!=(const ExprIterator& it) const {
913        return _host_it != it._host_it;
914      }
915
916    };
917
918  protected:
919
920    //Abstract virtual functions
921    virtual LpBase* _newSolver() const = 0;
922    virtual LpBase* _cloneSolver() const = 0;
923
924    virtual int _addColId(int col) { return cols.addIndex(col); }
925    virtual int _addRowId(int row) { return rows.addIndex(row); }
926
927    virtual void _eraseColId(int col) { cols.eraseIndex(col); }
928    virtual void _eraseRowId(int row) { rows.eraseIndex(row); }
929
930    virtual int _addCol() = 0;
931    virtual int _addRow() = 0;
932
933    virtual void _eraseCol(int col) = 0;
934    virtual void _eraseRow(int row) = 0;
935
936    virtual void _getColName(int col, std::string& name) const = 0;
937    virtual void _setColName(int col, const std::string& name) = 0;
938    virtual int _colByName(const std::string& name) const = 0;
939
940    virtual void _getRowName(int row, std::string& name) const = 0;
941    virtual void _setRowName(int row, const std::string& name) = 0;
942    virtual int _rowByName(const std::string& name) const = 0;
943
944    virtual void _setRowCoeffs(int i, ExprIterator b, ExprIterator e) = 0;
945    virtual void _getRowCoeffs(int i, InsertIterator b) const = 0;
946
947    virtual void _setColCoeffs(int i, ExprIterator b, ExprIterator e) = 0;
948    virtual void _getColCoeffs(int i, InsertIterator b) const = 0;
949
950    virtual void _setCoeff(int row, int col, Value value) = 0;
951    virtual Value _getCoeff(int row, int col) const = 0;
952
953    virtual void _setColLowerBound(int i, Value value) = 0;
954    virtual Value _getColLowerBound(int i) const = 0;
955
956    virtual void _setColUpperBound(int i, Value value) = 0;
957    virtual Value _getColUpperBound(int i) const = 0;
958
959    virtual void _setRowLowerBound(int i, Value value) = 0;
960    virtual Value _getRowLowerBound(int i) const = 0;
961
962    virtual void _setRowUpperBound(int i, Value value) = 0;
963    virtual Value _getRowUpperBound(int i) const = 0;
964
965    virtual void _setObjCoeffs(ExprIterator b, ExprIterator e) = 0;
966    virtual void _getObjCoeffs(InsertIterator b) const = 0;
967
968    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
969    virtual Value _getObjCoeff(int i) const = 0;
970
971    virtual void _setSense(Sense) = 0;
972    virtual Sense _getSense() const = 0;
973
974    virtual void _clear() = 0;
975
976    virtual const char* _solverName() const = 0;
977
978    //Own protected stuff
979
980    //Constant component of the objective function
981    Value obj_const_comp;
982
983    LpBase() : rows(), cols(), obj_const_comp(0) {}
984
985  public:
986
987    /// Virtual destructor
988    virtual ~LpBase() {}
989
990    ///Creates a new LP problem
991    LpBase* newSolver() {return _newSolver();}
992    ///Makes a copy of the LP problem
993    LpBase* cloneSolver() {return _cloneSolver();}
994
995    ///Gives back the name of the solver.
996    const char* solverName() const {return _solverName();}
997
998    ///\name Build up and modify the LP
999
1000    ///@{
1001
1002    ///Add a new empty column (i.e a new variable) to the LP
1003    Col addCol() { Col c; c._id = _addColId(_addCol()); return c;}
1004
1005    ///\brief Adds several new columns (i.e variables) at once
1006    ///
1007    ///This magic function takes a container as its argument and fills
1008    ///its elements with new columns (i.e. variables)
1009    ///\param t can be
1010    ///- a standard STL compatible iterable container with
1011    ///\ref Col as its \c values_type like
1012    ///\code
1013    ///std::vector<LpBase::Col>
1014    ///std::list<LpBase::Col>
1015    ///\endcode
1016    ///- a standard STL compatible iterable container with
1017    ///\ref Col as its \c mapped_type like
1018    ///\code
1019    ///std::map<AnyType,LpBase::Col>
1020    ///\endcode
1021    ///- an iterable lemon \ref concepts::WriteMap "write map" like
1022    ///\code
1023    ///ListGraph::NodeMap<LpBase::Col>
1024    ///ListGraph::ArcMap<LpBase::Col>
1025    ///\endcode
1026    ///\return The number of the created column.
1027#ifdef DOXYGEN
1028    template<class T>
1029    int addColSet(T &t) { return 0;}
1030#else
1031    template<class T>
1032    typename enable_if<typename T::value_type::LpCol,int>::type
1033    addColSet(T &t,dummy<0> = 0) {
1034      int s=0;
1035      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
1036      return s;
1037    }
1038    template<class T>
1039    typename enable_if<typename T::value_type::second_type::LpCol,
1040                       int>::type
1041    addColSet(T &t,dummy<1> = 1) {
1042      int s=0;
1043      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1044        i->second=addCol();
1045        s++;
1046      }
1047      return s;
1048    }
1049    template<class T>
1050    typename enable_if<typename T::MapIt::Value::LpCol,
1051                       int>::type
1052    addColSet(T &t,dummy<2> = 2) {
1053      int s=0;
1054      for(typename T::MapIt i(t); i!=INVALID; ++i)
1055        {
1056          i.set(addCol());
1057          s++;
1058        }
1059      return s;
1060    }
1061#endif
1062
1063    ///Set a column (i.e a dual constraint) of the LP
1064
1065    ///\param c is the column to be modified
1066    ///\param e is a dual linear expression (see \ref DualExpr)
1067    ///a better one.
1068    void col(Col c, const DualExpr &e) {
1069      e.simplify();
1070      _setColCoeffs(cols(id(c)), ExprIterator(e.comps.begin(), rows),
1071                    ExprIterator(e.comps.end(), rows));
1072    }
1073
1074    ///Get a column (i.e a dual constraint) of the LP
1075
1076    ///\param c is the column to get
1077    ///\return the dual expression associated to the column
1078    DualExpr col(Col c) const {
1079      DualExpr e;
1080      _getColCoeffs(cols(id(c)), InsertIterator(e.comps, rows));
1081      return e;
1082    }
1083
1084    ///Add a new column to the LP
1085
1086    ///\param e is a dual linear expression (see \ref DualExpr)
1087    ///\param o is the corresponding component of the objective
1088    ///function. It is 0 by default.
1089    ///\return The created column.
1090    Col addCol(const DualExpr &e, Value o = 0) {
1091      Col c=addCol();
1092      col(c,e);
1093      objCoeff(c,o);
1094      return c;
1095    }
1096
1097    ///Add a new empty row (i.e a new constraint) to the LP
1098
1099    ///This function adds a new empty row (i.e a new constraint) to the LP.
1100    ///\return The created row
1101    Row addRow() { Row r; r._id = _addRowId(_addRow()); return r;}
1102
1103    ///\brief Add several new rows (i.e constraints) at once
1104    ///
1105    ///This magic function takes a container as its argument and fills
1106    ///its elements with new row (i.e. variables)
1107    ///\param t can be
1108    ///- a standard STL compatible iterable container with
1109    ///\ref Row as its \c values_type like
1110    ///\code
1111    ///std::vector<LpBase::Row>
1112    ///std::list<LpBase::Row>
1113    ///\endcode
1114    ///- a standard STL compatible iterable container with
1115    ///\ref Row as its \c mapped_type like
1116    ///\code
1117    ///std::map<AnyType,LpBase::Row>
1118    ///\endcode
1119    ///- an iterable lemon \ref concepts::WriteMap "write map" like
1120    ///\code
1121    ///ListGraph::NodeMap<LpBase::Row>
1122    ///ListGraph::ArcMap<LpBase::Row>
1123    ///\endcode
1124    ///\return The number of rows created.
1125#ifdef DOXYGEN
1126    template<class T>
1127    int addRowSet(T &t) { return 0;}
1128#else
1129    template<class T>
1130    typename enable_if<typename T::value_type::LpRow,int>::type
1131    addRowSet(T &t, dummy<0> = 0) {
1132      int s=0;
1133      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
1134      return s;
1135    }
1136    template<class T>
1137    typename enable_if<typename T::value_type::second_type::LpRow, int>::type
1138    addRowSet(T &t, dummy<1> = 1) {
1139      int s=0;
1140      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1141        i->second=addRow();
1142        s++;
1143      }
1144      return s;
1145    }
1146    template<class T>
1147    typename enable_if<typename T::MapIt::Value::LpRow, int>::type
1148    addRowSet(T &t, dummy<2> = 2) {
1149      int s=0;
1150      for(typename T::MapIt i(t); i!=INVALID; ++i)
1151        {
1152          i.set(addRow());
1153          s++;
1154        }
1155      return s;
1156    }
1157#endif
1158
1159    ///Set a row (i.e a constraint) of the LP
1160
1161    ///\param r is the row to be modified
1162    ///\param l is lower bound (-\ref INF means no bound)
1163    ///\param e is a linear expression (see \ref Expr)
1164    ///\param u is the upper bound (\ref INF means no bound)
1165    void row(Row r, Value l, const Expr &e, Value u) {
1166      e.simplify();
1167      _setRowCoeffs(rows(id(r)), ExprIterator(e.comps.begin(), cols),
1168                    ExprIterator(e.comps.end(), cols));
1169      _setRowLowerBound(rows(id(r)),l - *e);
1170      _setRowUpperBound(rows(id(r)),u - *e);
1171    }
1172
1173    ///Set a row (i.e a constraint) of the LP
1174
1175    ///\param r is the row to be modified
1176    ///\param c is a linear expression (see \ref Constr)
1177    void row(Row r, const Constr &c) {
1178      row(r, c.lowerBounded()?c.lowerBound():-INF,
1179          c.expr(), c.upperBounded()?c.upperBound():INF);
1180    }
1181
1182
1183    ///Get a row (i.e a constraint) of the LP
1184
1185    ///\param r is the row to get
1186    ///\return the expression associated to the row
1187    Expr row(Row r) const {
1188      Expr e;
1189      _getRowCoeffs(rows(id(r)), InsertIterator(e.comps, cols));
1190      return e;
1191    }
1192
1193    ///Add a new row (i.e a new constraint) to the LP
1194
1195    ///\param l is the lower bound (-\ref INF means no bound)
1196    ///\param e is a linear expression (see \ref Expr)
1197    ///\param u is the upper bound (\ref INF means no bound)
1198    ///\return The created row.
1199    Row addRow(Value l,const Expr &e, Value u) {
1200      Row r=addRow();
1201      row(r,l,e,u);
1202      return r;
1203    }
1204
1205    ///Add a new row (i.e a new constraint) to the LP
1206
1207    ///\param c is a linear expression (see \ref Constr)
1208    ///\return The created row.
1209    Row addRow(const Constr &c) {
1210      Row r=addRow();
1211      row(r,c);
1212      return r;
1213    }
1214    ///Erase a column (i.e a variable) from the LP
1215
1216    ///\param c is the column to be deleted
1217    void erase(Col c) {
1218      _eraseCol(cols(id(c)));
1219      _eraseColId(cols(id(c)));
1220    }
1221    ///Erase a row (i.e a constraint) from the LP
1222
1223    ///\param r is the row to be deleted
1224    void erase(Row r) {
1225      _eraseRow(rows(id(r)));
1226      _eraseRowId(rows(id(r)));
1227    }
1228
1229    /// Get the name of a column
1230
1231    ///\param c is the coresponding column
1232    ///\return The name of the colunm
1233    std::string colName(Col c) const {
1234      std::string name;
1235      _getColName(cols(id(c)), name);
1236      return name;
1237    }
1238
1239    /// Set the name of a column
1240
1241    ///\param c is the coresponding column
1242    ///\param name The name to be given
1243    void colName(Col c, const std::string& name) {
1244      _setColName(cols(id(c)), name);
1245    }
1246
1247    /// Get the column by its name
1248
1249    ///\param name The name of the column
1250    ///\return the proper column or \c INVALID
1251    Col colByName(const std::string& name) const {
1252      int k = _colByName(name);
1253      return k != -1 ? Col(cols[k]) : Col(INVALID);
1254    }
1255
1256    /// Get the name of a row
1257
1258    ///\param r is the coresponding row
1259    ///\return The name of the row
1260    std::string rowName(Row r) const {
1261      std::string name;
1262      _getRowName(rows(id(r)), name);
1263      return name;
1264    }
1265
1266    /// Set the name of a row
1267
1268    ///\param r is the coresponding row
1269    ///\param name The name to be given
1270    void rowName(Row r, const std::string& name) {
1271      _setRowName(rows(id(r)), name);
1272    }
1273
1274    /// Get the row by its name
1275
1276    ///\param name The name of the row
1277    ///\return the proper row or \c INVALID
1278    Row rowByName(const std::string& name) const {
1279      int k = _rowByName(name);
1280      return k != -1 ? Row(rows[k]) : Row(INVALID);
1281    }
1282
1283    /// Set an element of the coefficient matrix of the LP
1284
1285    ///\param r is the row of the element to be modified
1286    ///\param c is the column of the element to be modified
1287    ///\param val is the new value of the coefficient
1288    void coeff(Row r, Col c, Value val) {
1289      _setCoeff(rows(id(r)),cols(id(c)), val);
1290    }
1291
1292    /// Get an element of the coefficient matrix of the LP
1293
1294    ///\param r is the row of the element
1295    ///\param c is the column of the element
1296    ///\return the corresponding coefficient
1297    Value coeff(Row r, Col c) const {
1298      return _getCoeff(rows(id(r)),cols(id(c)));
1299    }
1300
1301    /// Set the lower bound of a column (i.e a variable)
1302
1303    /// The lower bound of a variable (column) has to be given by an
1304    /// extended number of type Value, i.e. a finite number of type
1305    /// Value or -\ref INF.
1306    void colLowerBound(Col c, Value value) {
1307      _setColLowerBound(cols(id(c)),value);
1308    }
1309
1310    /// Get the lower bound of a column (i.e a variable)
1311
1312    /// This function returns the lower bound for column (variable) \c c
1313    /// (this might be -\ref INF as well).
1314    ///\return The lower bound for column \c c
1315    Value colLowerBound(Col c) const {
1316      return _getColLowerBound(cols(id(c)));
1317    }
1318
1319    ///\brief Set the lower bound of  several columns
1320    ///(i.e variables) at once
1321    ///
1322    ///This magic function takes a container as its argument
1323    ///and applies the function on all of its elements.
1324    ///The lower bound of a variable (column) has to be given by an
1325    ///extended number of type Value, i.e. a finite number of type
1326    ///Value or -\ref INF.
1327#ifdef DOXYGEN
1328    template<class T>
1329    void colLowerBound(T &t, Value value) { return 0;}
1330#else
1331    template<class T>
1332    typename enable_if<typename T::value_type::LpCol,void>::type
1333    colLowerBound(T &t, Value value,dummy<0> = 0) {
1334      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1335        colLowerBound(*i, value);
1336      }
1337    }
1338    template<class T>
1339    typename enable_if<typename T::value_type::second_type::LpCol,
1340                       void>::type
1341    colLowerBound(T &t, Value value,dummy<1> = 1) {
1342      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1343        colLowerBound(i->second, value);
1344      }
1345    }
1346    template<class T>
1347    typename enable_if<typename T::MapIt::Value::LpCol,
1348                       void>::type
1349    colLowerBound(T &t, Value value,dummy<2> = 2) {
1350      for(typename T::MapIt i(t); i!=INVALID; ++i){
1351        colLowerBound(*i, value);
1352      }
1353    }
1354#endif
1355
1356    /// Set the upper bound of a column (i.e a variable)
1357
1358    /// The upper bound of a variable (column) has to be given by an
1359    /// extended number of type Value, i.e. a finite number of type
1360    /// Value or \ref INF.
1361    void colUpperBound(Col c, Value value) {
1362      _setColUpperBound(cols(id(c)),value);
1363    };
1364
1365    /// Get the upper bound of a column (i.e a variable)
1366
1367    /// This function returns the upper bound for column (variable) \c c
1368    /// (this might be \ref INF as well).
1369    /// \return The upper bound for column \c c
1370    Value colUpperBound(Col c) const {
1371      return _getColUpperBound(cols(id(c)));
1372    }
1373
1374    ///\brief Set the upper bound of  several columns
1375    ///(i.e variables) at once
1376    ///
1377    ///This magic function takes a container as its argument
1378    ///and applies the function on all of its elements.
1379    ///The upper bound of a variable (column) has to be given by an
1380    ///extended number of type Value, i.e. a finite number of type
1381    ///Value or \ref INF.
1382#ifdef DOXYGEN
1383    template<class T>
1384    void colUpperBound(T &t, Value value) { return 0;}
1385#else
1386    template<class T1>
1387    typename enable_if<typename T1::value_type::LpCol,void>::type
1388    colUpperBound(T1 &t, Value value,dummy<0> = 0) {
1389      for(typename T1::iterator i=t.begin();i!=t.end();++i) {
1390        colUpperBound(*i, value);
1391      }
1392    }
1393    template<class T1>
1394    typename enable_if<typename T1::value_type::second_type::LpCol,
1395                       void>::type
1396    colUpperBound(T1 &t, Value value,dummy<1> = 1) {
1397      for(typename T1::iterator i=t.begin();i!=t.end();++i) {
1398        colUpperBound(i->second, value);
1399      }
1400    }
1401    template<class T1>
1402    typename enable_if<typename T1::MapIt::Value::LpCol,
1403                       void>::type
1404    colUpperBound(T1 &t, Value value,dummy<2> = 2) {
1405      for(typename T1::MapIt i(t); i!=INVALID; ++i){
1406        colUpperBound(*i, value);
1407      }
1408    }
1409#endif
1410
1411    /// Set the lower and the upper bounds of a column (i.e a variable)
1412
1413    /// The lower and the upper bounds of
1414    /// a variable (column) have to be given by an
1415    /// extended number of type Value, i.e. a finite number of type
1416    /// Value, -\ref INF or \ref INF.
1417    void colBounds(Col c, Value lower, Value upper) {
1418      _setColLowerBound(cols(id(c)),lower);
1419      _setColUpperBound(cols(id(c)),upper);
1420    }
1421
1422    ///\brief Set the lower and the upper bound of several columns
1423    ///(i.e variables) at once
1424    ///
1425    ///This magic function takes a container as its argument
1426    ///and applies the function on all of its elements.
1427    /// The lower and the upper bounds of
1428    /// a variable (column) have to be given by an
1429    /// extended number of type Value, i.e. a finite number of type
1430    /// Value, -\ref INF or \ref INF.
1431#ifdef DOXYGEN
1432    template<class T>
1433    void colBounds(T &t, Value lower, Value upper) { return 0;}
1434#else
1435    template<class T2>
1436    typename enable_if<typename T2::value_type::LpCol,void>::type
1437    colBounds(T2 &t, Value lower, Value upper,dummy<0> = 0) {
1438      for(typename T2::iterator i=t.begin();i!=t.end();++i) {
1439        colBounds(*i, lower, upper);
1440      }
1441    }
1442    template<class T2>
1443    typename enable_if<typename T2::value_type::second_type::LpCol, void>::type
1444    colBounds(T2 &t, Value lower, Value upper,dummy<1> = 1) {
1445      for(typename T2::iterator i=t.begin();i!=t.end();++i) {
1446        colBounds(i->second, lower, upper);
1447      }
1448    }
1449    template<class T2>
1450    typename enable_if<typename T2::MapIt::Value::LpCol, void>::type
1451    colBounds(T2 &t, Value lower, Value upper,dummy<2> = 2) {
1452      for(typename T2::MapIt i(t); i!=INVALID; ++i){
1453        colBounds(*i, lower, upper);
1454      }
1455    }
1456#endif
1457
1458    /// Set the lower bound of a row (i.e a constraint)
1459
1460    /// The lower bound of a constraint (row) has to be given by an
1461    /// extended number of type Value, i.e. a finite number of type
1462    /// Value or -\ref INF.
1463    void rowLowerBound(Row r, Value value) {
1464      _setRowLowerBound(rows(id(r)),value);
1465    }
1466
1467    /// Get the lower bound of a row (i.e a constraint)
1468
1469    /// This function returns the lower bound for row (constraint) \c c
1470    /// (this might be -\ref INF as well).
1471    ///\return The lower bound for row \c r
1472    Value rowLowerBound(Row r) const {
1473      return _getRowLowerBound(rows(id(r)));
1474    }
1475
1476    /// Set the upper bound of a row (i.e a constraint)
1477
1478    /// The upper bound of a constraint (row) has to be given by an
1479    /// extended number of type Value, i.e. a finite number of type
1480    /// Value or -\ref INF.
1481    void rowUpperBound(Row r, Value value) {
1482      _setRowUpperBound(rows(id(r)),value);
1483    }
1484
1485    /// Get the upper bound of a row (i.e a constraint)
1486
1487    /// This function returns the upper bound for row (constraint) \c c
1488    /// (this might be -\ref INF as well).
1489    ///\return The upper bound for row \c r
1490    Value rowUpperBound(Row r) const {
1491      return _getRowUpperBound(rows(id(r)));
1492    }
1493
1494    ///Set an element of the objective function
1495    void objCoeff(Col c, Value v) {_setObjCoeff(cols(id(c)),v); };
1496
1497    ///Get an element of the objective function
1498    Value objCoeff(Col c) const { return _getObjCoeff(cols(id(c))); };
1499
1500    ///Set the objective function
1501
1502    ///\param e is a linear expression of type \ref Expr.
1503    ///
1504    void obj(const Expr& e) {
1505      _setObjCoeffs(ExprIterator(e.comps.begin(), cols),
1506                    ExprIterator(e.comps.end(), cols));
1507      obj_const_comp = *e;
1508    }
1509
1510    ///Get the objective function
1511
1512    ///\return the objective function as a linear expression of type
1513    ///Expr.
1514    Expr obj() const {
1515      Expr e;
1516      _getObjCoeffs(InsertIterator(e.comps, cols));
1517      *e = obj_const_comp;
1518      return e;
1519    }
1520
1521
1522    ///Set the direction of optimization
1523    void sense(Sense sense) { _setSense(sense); }
1524
1525    ///Query the direction of the optimization
1526    Sense sense() const {return _getSense(); }
1527
1528    ///Set the sense to maximization
1529    void max() { _setSense(MAX); }
1530
1531    ///Set the sense to maximization
1532    void min() { _setSense(MIN); }
1533
1534    ///Clears the problem
1535    void clear() { _clear(); }
1536
1537    ///@}
1538
1539  };
1540
1541  /// Addition
1542
1543  ///\relates LpBase::Expr
1544  ///
1545  inline LpBase::Expr operator+(const LpBase::Expr &a, const LpBase::Expr &b) {
1546    LpBase::Expr tmp(a);
1547    tmp+=b;
1548    return tmp;
1549  }
1550  ///Substraction
1551
1552  ///\relates LpBase::Expr
1553  ///
1554  inline LpBase::Expr operator-(const LpBase::Expr &a, const LpBase::Expr &b) {
1555    LpBase::Expr tmp(a);
1556    tmp-=b;
1557    return tmp;
1558  }
1559  ///Multiply with constant
1560
1561  ///\relates LpBase::Expr
1562  ///
1563  inline LpBase::Expr operator*(const LpBase::Expr &a, const LpBase::Value &b) {
1564    LpBase::Expr tmp(a);
1565    tmp*=b;
1566    return tmp;
1567  }
1568
1569  ///Multiply with constant
1570
1571  ///\relates LpBase::Expr
1572  ///
1573  inline LpBase::Expr operator*(const LpBase::Value &a, const LpBase::Expr &b) {
1574    LpBase::Expr tmp(b);
1575    tmp*=a;
1576    return tmp;
1577  }
1578  ///Divide with constant
1579
1580  ///\relates LpBase::Expr
1581  ///
1582  inline LpBase::Expr operator/(const LpBase::Expr &a, const LpBase::Value &b) {
1583    LpBase::Expr tmp(a);
1584    tmp/=b;
1585    return tmp;
1586  }
1587
1588  ///Create constraint
1589
1590  ///\relates LpBase::Constr
1591  ///
1592  inline LpBase::Constr operator<=(const LpBase::Expr &e,
1593                                   const LpBase::Expr &f) {
1594    return LpBase::Constr(0, f - e, LpBase::INF);
1595  }
1596
1597  ///Create constraint
1598
1599  ///\relates LpBase::Constr
1600  ///
1601  inline LpBase::Constr operator<=(const LpBase::Value &e,
1602                                   const LpBase::Expr &f) {
1603    return LpBase::Constr(e, f, LpBase::NaN);
1604  }
1605
1606  ///Create constraint
1607
1608  ///\relates LpBase::Constr
1609  ///
1610  inline LpBase::Constr operator<=(const LpBase::Expr &e,
1611                                   const LpBase::Value &f) {
1612    return LpBase::Constr(- LpBase::INF, e, f);
1613  }
1614
1615  ///Create constraint
1616
1617  ///\relates LpBase::Constr
1618  ///
1619  inline LpBase::Constr operator>=(const LpBase::Expr &e,
1620                                   const LpBase::Expr &f) {
1621    return LpBase::Constr(0, e - f, LpBase::INF);
1622  }
1623
1624
1625  ///Create constraint
1626
1627  ///\relates LpBase::Constr
1628  ///
1629  inline LpBase::Constr operator>=(const LpBase::Value &e,
1630                                   const LpBase::Expr &f) {
1631    return LpBase::Constr(LpBase::NaN, f, e);
1632  }
1633
1634
1635  ///Create constraint
1636
1637  ///\relates LpBase::Constr
1638  ///
1639  inline LpBase::Constr operator>=(const LpBase::Expr &e,
1640                                   const LpBase::Value &f) {
1641    return LpBase::Constr(f, e, LpBase::INF);
1642  }
1643
1644  ///Create constraint
1645
1646  ///\relates LpBase::Constr
1647  ///
1648  inline LpBase::Constr operator==(const LpBase::Expr &e,
1649                                   const LpBase::Value &f) {
1650    return LpBase::Constr(f, e, f);
1651  }
1652
1653  ///Create constraint
1654
1655  ///\relates LpBase::Constr
1656  ///
1657  inline LpBase::Constr operator==(const LpBase::Expr &e,
1658                                   const LpBase::Expr &f) {
1659    return LpBase::Constr(0, f - e, 0);
1660  }
1661
1662  ///Create constraint
1663
1664  ///\relates LpBase::Constr
1665  ///
1666  inline LpBase::Constr operator<=(const LpBase::Value &n,
1667                                   const LpBase::Constr &c) {
1668    LpBase::Constr tmp(c);
1669    LEMON_ASSERT(isNaN(tmp.lowerBound()), "Wrong LP constraint");
1670    tmp.lowerBound()=n;
1671    return tmp;
1672  }
1673  ///Create constraint
1674
1675  ///\relates LpBase::Constr
1676  ///
1677  inline LpBase::Constr operator<=(const LpBase::Constr &c,
1678                                   const LpBase::Value &n)
1679  {
1680    LpBase::Constr tmp(c);
1681    LEMON_ASSERT(isNaN(tmp.upperBound()), "Wrong LP constraint");
1682    tmp.upperBound()=n;
1683    return tmp;
1684  }
1685
1686  ///Create constraint
1687
1688  ///\relates LpBase::Constr
1689  ///
1690  inline LpBase::Constr operator>=(const LpBase::Value &n,
1691                                   const LpBase::Constr &c) {
1692    LpBase::Constr tmp(c);
1693    LEMON_ASSERT(isNaN(tmp.upperBound()), "Wrong LP constraint");
1694    tmp.upperBound()=n;
1695    return tmp;
1696  }
1697  ///Create constraint
1698
1699  ///\relates LpBase::Constr
1700  ///
1701  inline LpBase::Constr operator>=(const LpBase::Constr &c,
1702                                   const LpBase::Value &n)
1703  {
1704    LpBase::Constr tmp(c);
1705    LEMON_ASSERT(isNaN(tmp.lowerBound()), "Wrong LP constraint");
1706    tmp.lowerBound()=n;
1707    return tmp;
1708  }
1709
1710  ///Addition
1711
1712  ///\relates LpBase::DualExpr
1713  ///
1714  inline LpBase::DualExpr operator+(const LpBase::DualExpr &a,
1715                                    const LpBase::DualExpr &b) {
1716    LpBase::DualExpr tmp(a);
1717    tmp+=b;
1718    return tmp;
1719  }
1720  ///Substraction
1721
1722  ///\relates LpBase::DualExpr
1723  ///
1724  inline LpBase::DualExpr operator-(const LpBase::DualExpr &a,
1725                                    const LpBase::DualExpr &b) {
1726    LpBase::DualExpr tmp(a);
1727    tmp-=b;
1728    return tmp;
1729  }
1730  ///Multiply with constant
1731
1732  ///\relates LpBase::DualExpr
1733  ///
1734  inline LpBase::DualExpr operator*(const LpBase::DualExpr &a,
1735                                    const LpBase::Value &b) {
1736    LpBase::DualExpr tmp(a);
1737    tmp*=b;
1738    return tmp;
1739  }
1740
1741  ///Multiply with constant
1742
1743  ///\relates LpBase::DualExpr
1744  ///
1745  inline LpBase::DualExpr operator*(const LpBase::Value &a,
1746                                    const LpBase::DualExpr &b) {
1747    LpBase::DualExpr tmp(b);
1748    tmp*=a;
1749    return tmp;
1750  }
1751  ///Divide with constant
1752
1753  ///\relates LpBase::DualExpr
1754  ///
1755  inline LpBase::DualExpr operator/(const LpBase::DualExpr &a,
1756                                    const LpBase::Value &b) {
1757    LpBase::DualExpr tmp(a);
1758    tmp/=b;
1759    return tmp;
1760  }
1761
1762  /// \ingroup lp_group
1763  ///
1764  /// \brief Common base class for LP solvers
1765  ///
1766  /// This class is an abstract base class for LP solvers. This class
1767  /// provides a full interface for set and modify an LP problem,
1768  /// solve it and retrieve the solution. You can use one of the
1769  /// descendants as a concrete implementation, or the \c Lp
1770  /// default LP solver. However, if you would like to handle LP
1771  /// solvers as reference or pointer in a generic way, you can use
1772  /// this class directly.
1773  class LpSolver : virtual public LpBase {
1774  public:
1775
1776    /// The problem types for primal and dual problems
1777    enum ProblemType {
1778      ///Feasible solution hasn't been found (but may exist).
1779      UNDEFINED = 0,
1780      ///The problem has no feasible solution
1781      INFEASIBLE = 1,
1782      ///Feasible solution found
1783      FEASIBLE = 2,
1784      ///Optimal solution exists and found
1785      OPTIMAL = 3,
1786      ///The cost function is unbounded
1787      UNBOUNDED = 4
1788    };
1789
1790    ///The basis status of variables
1791    enum VarStatus {
1792      /// The variable is in the basis
1793      BASIC,
1794      /// The variable is free, but not basic
1795      FREE,
1796      /// The variable has active lower bound
1797      LOWER,
1798      /// The variable has active upper bound
1799      UPPER,
1800      /// The variable is non-basic and fixed
1801      FIXED
1802    };
1803
1804  protected:
1805
1806    virtual SolveExitStatus _solve() = 0;
1807
1808    virtual Value _getPrimal(int i) const = 0;
1809    virtual Value _getDual(int i) const = 0;
1810
1811    virtual Value _getPrimalRay(int i) const = 0;
1812    virtual Value _getDualRay(int i) const = 0;
1813
1814    virtual Value _getPrimalValue() const = 0;
1815
1816    virtual VarStatus _getColStatus(int i) const = 0;
1817    virtual VarStatus _getRowStatus(int i) const = 0;
1818
1819    virtual ProblemType _getPrimalType() const = 0;
1820    virtual ProblemType _getDualType() const = 0;
1821
1822  public:
1823
1824    ///\name Solve the LP
1825
1826    ///@{
1827
1828    ///\e Solve the LP problem at hand
1829    ///
1830    ///\return The result of the optimization procedure. Possible
1831    ///values and their meanings can be found in the documentation of
1832    ///\ref SolveExitStatus.
1833    SolveExitStatus solve() { return _solve(); }
1834
1835    ///@}
1836
1837    ///\name Obtain the solution
1838
1839    ///@{
1840
1841    /// The type of the primal problem
1842    ProblemType primalType() const {
1843      return _getPrimalType();
1844    }
1845
1846    /// The type of the dual problem
1847    ProblemType dualType() const {
1848      return _getDualType();
1849    }
1850
1851    /// Return the primal value of the column
1852
1853    /// Return the primal value of the column.
1854    /// \pre The problem is solved.
1855    Value primal(Col c) const { return _getPrimal(cols(id(c))); }
1856
1857    /// Return the primal value of the expression
1858
1859    /// Return the primal value of the expression, i.e. the dot
1860    /// product of the primal solution and the expression.
1861    /// \pre The problem is solved.
1862    Value primal(const Expr& e) const {
1863      double res = *e;
1864      for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {
1865        res += *c * primal(c);
1866      }
1867      return res;
1868    }
1869    /// Returns a component of the primal ray
1870   
1871    /// The primal ray is solution of the modified primal problem,
1872    /// where we change each finite bound to 0, and we looking for a
1873    /// negative objective value in case of minimization, and positive
1874    /// objective value for maximization. If there is such solution,
1875    /// that proofs the unsolvability of the dual problem, and if a
1876    /// feasible primal solution exists, then the unboundness of
1877    /// primal problem.
1878    ///
1879    /// \pre The problem is solved and the dual problem is infeasible.
1880    /// \note Some solvers does not provide primal ray calculation
1881    /// functions.
1882    Value primalRay(Col c) const { return _getPrimalRay(cols(id(c))); }
1883
1884    /// Return the dual value of the row
1885
1886    /// Return the dual value of the row.
1887    /// \pre The problem is solved.
1888    Value dual(Row r) const { return _getDual(rows(id(r))); }
1889
1890    /// Return the dual value of the dual expression
1891
1892    /// Return the dual value of the dual expression, i.e. the dot
1893    /// product of the dual solution and the dual expression.
1894    /// \pre The problem is solved.
1895    Value dual(const DualExpr& e) const {
1896      double res = 0.0;
1897      for (DualExpr::ConstCoeffIt r(e); r != INVALID; ++r) {
1898        res += *r * dual(r);
1899      }
1900      return res;
1901    }
1902
1903    /// Returns a component of the dual ray
1904   
1905    /// The dual ray is solution of the modified primal problem, where
1906    /// we change each finite bound to 0 (i.e. the objective function
1907    /// coefficients in the primal problem), and we looking for a
1908    /// ositive objective value. If there is such solution, that
1909    /// proofs the unsolvability of the primal problem, and if a
1910    /// feasible dual solution exists, then the unboundness of
1911    /// dual problem.
1912    ///
1913    /// \pre The problem is solved and the primal problem is infeasible.
1914    /// \note Some solvers does not provide dual ray calculation
1915    /// functions.
1916    Value dualRay(Row r) const { return _getDualRay(rows(id(r))); }
1917
1918    /// Return the basis status of the column
1919
1920    /// \see VarStatus
1921    VarStatus colStatus(Col c) const { return _getColStatus(cols(id(c))); }
1922
1923    /// Return the basis status of the row
1924
1925    /// \see VarStatus
1926    VarStatus rowStatus(Row r) const { return _getRowStatus(rows(id(r))); }
1927
1928    ///The value of the objective function
1929
1930    ///\return
1931    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
1932    /// of the primal problem, depending on whether we minimize or maximize.
1933    ///- \ref NaN if no primal solution is found.
1934    ///- The (finite) objective value if an optimal solution is found.
1935    Value primal() const { return _getPrimalValue()+obj_const_comp;}
1936    ///@}
1937
1938    LpSolver* newSolver() {return _newSolver();}
1939    LpSolver* cloneSolver() {return _cloneSolver();}
1940
1941  protected:
1942
1943    virtual LpSolver* _newSolver() const = 0;
1944    virtual LpSolver* _cloneSolver() const = 0;
1945  };
1946
1947
1948  /// \ingroup lp_group
1949  ///
1950  /// \brief Common base class for MIP solvers
1951  ///
1952  /// This class is an abstract base class for MIP solvers. This class
1953  /// provides a full interface for set and modify an MIP problem,
1954  /// solve it and retrieve the solution. You can use one of the
1955  /// descendants as a concrete implementation, or the \c Lp
1956  /// default MIP solver. However, if you would like to handle MIP
1957  /// solvers as reference or pointer in a generic way, you can use
1958  /// this class directly.
1959  class MipSolver : virtual public LpBase {
1960  public:
1961
1962    /// The problem types for MIP problems
1963    enum ProblemType {
1964      ///Feasible solution hasn't been found (but may exist).
1965      UNDEFINED = 0,
1966      ///The problem has no feasible solution
1967      INFEASIBLE = 1,
1968      ///Feasible solution found
1969      FEASIBLE = 2,
1970      ///Optimal solution exists and found
1971      OPTIMAL = 3,
1972      ///The cost function is unbounded
1973      ///
1974      ///The Mip or at least the relaxed problem is unbounded
1975      UNBOUNDED = 4
1976    };
1977
1978    ///\name Solve the MIP
1979
1980    ///@{
1981
1982    /// Solve the MIP problem at hand
1983    ///
1984    ///\return The result of the optimization procedure. Possible
1985    ///values and their meanings can be found in the documentation of
1986    ///\ref SolveExitStatus.
1987    SolveExitStatus solve() { return _solve(); }
1988
1989    ///@}
1990
1991    ///\name Setting column type
1992    ///@{
1993
1994    ///Possible variable (column) types (e.g. real, integer, binary etc.)
1995    enum ColTypes {
1996      ///Continuous variable (default)
1997      REAL = 0,
1998      ///Integer variable
1999      INTEGER = 1
2000    };
2001
2002    ///Sets the type of the given column to the given type
2003
2004    ///Sets the type of the given column to the given type.
2005    ///
2006    void colType(Col c, ColTypes col_type) {
2007      _setColType(cols(id(c)),col_type);
2008    }
2009
2010    ///Gives back the type of the column.
2011
2012    ///Gives back the type of the column.
2013    ///
2014    ColTypes colType(Col c) const {
2015      return _getColType(cols(id(c)));
2016    }
2017    ///@}
2018
2019    ///\name Obtain the solution
2020
2021    ///@{
2022
2023    /// The type of the MIP problem
2024    ProblemType type() const {
2025      return _getType();
2026    }
2027
2028    /// Return the value of the row in the solution
2029
2030    ///  Return the value of the row in the solution.
2031    /// \pre The problem is solved.
2032    Value sol(Col c) const { return _getSol(cols(id(c))); }
2033
2034    /// Return the value of the expression in the solution
2035
2036    /// Return the value of the expression in the solution, i.e. the
2037    /// dot product of the solution and the expression.
2038    /// \pre The problem is solved.
2039    Value sol(const Expr& e) const {
2040      double res = *e;
2041      for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {
2042        res += *c * sol(c);
2043      }
2044      return res;
2045    }
2046    ///The value of the objective function
2047   
2048    ///\return
2049    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
2050    /// of the problem, depending on whether we minimize or maximize.
2051    ///- \ref NaN if no primal solution is found.
2052    ///- The (finite) objective value if an optimal solution is found.
2053    Value solValue() const { return _getSolValue()+obj_const_comp;}
2054    ///@}
2055
2056  protected:
2057
2058    virtual SolveExitStatus _solve() = 0;
2059    virtual ColTypes _getColType(int col) const = 0;
2060    virtual void _setColType(int col, ColTypes col_type) = 0;
2061    virtual ProblemType _getType() const = 0;
2062    virtual Value _getSol(int i) const = 0;
2063    virtual Value _getSolValue() const = 0;
2064
2065  public:
2066
2067    MipSolver* newSolver() {return _newSolver();}
2068    MipSolver* cloneSolver() {return _cloneSolver();}
2069
2070  protected:
2071
2072    virtual MipSolver* _newSolver() const = 0;
2073    virtual MipSolver* _cloneSolver() const = 0;
2074  };
2075
2076
2077
2078} //namespace lemon
2079
2080#endif //LEMON_LP_BASE_H
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