COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/lp_base.h @ 864:d3ea191c3412

Last change on this file since 864:d3ea191c3412 was 834:207ba6c0f2e4, checked in by Balazs Dezso <deba@…>, 10 years ago

Fix LpBase::addRow(Constr) (#334)

File size: 61.6 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/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      /// = 0. It 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      /// = 1. 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    ///Enum for \c messageLevel() parameter
73    enum MessageLevel {
74      /// No output (default value).
75      MESSAGE_NOTHING,
76      /// Error messages only.
77      MESSAGE_ERROR,
78      /// Warnings.
79      MESSAGE_WARNING,
80      /// Normal output.
81      MESSAGE_NORMAL,
82      /// Verbose output.
83      MESSAGE_VERBOSE
84    };
85   
86
87    ///The floating point type used by the solver
88    typedef double Value;
89    ///The infinity constant
90    static const Value INF;
91    ///The not a number constant
92    static const Value NaN;
93
94    friend class Col;
95    friend class ColIt;
96    friend class Row;
97    friend class RowIt;
98
99    ///Refer to a column of the LP.
100
101    ///This type is used to refer to a column of the LP.
102    ///
103    ///Its value remains valid and correct even after the addition or erase of
104    ///other columns.
105    ///
106    ///\note This class is similar to other Item types in LEMON, like
107    ///Node and Arc types in digraph.
108    class Col {
109      friend class LpBase;
110    protected:
111      int _id;
112      explicit Col(int id) : _id(id) {}
113    public:
114      typedef Value ExprValue;
115      typedef True LpCol;
116      /// Default constructor
117     
118      /// \warning The default constructor sets the Col to an
119      /// undefined value.
120      Col() {}
121      /// Invalid constructor \& conversion.
122     
123      /// This constructor initializes the Col to be invalid.
124      /// \sa Invalid for more details.     
125      Col(const Invalid&) : _id(-1) {}
126      /// Equality operator
127
128      /// Two \ref Col "Col"s are equal if and only if they point to
129      /// the same LP column or both are invalid.
130      bool operator==(Col c) const  {return _id == c._id;}
131      /// Inequality operator
132
133      /// \sa operator==(Col c)
134      ///
135      bool operator!=(Col c) const  {return _id != c._id;}
136      /// Artificial ordering operator.
137
138      /// To allow the use of this object in std::map or similar
139      /// associative container we require this.
140      ///
141      /// \note This operator only have to define some strict ordering of
142      /// the items; this order has nothing to do with the iteration
143      /// ordering of the items.
144      bool operator<(Col c) const  {return _id < c._id;}
145    };
146
147    ///Iterator for iterate over the columns of an LP problem
148
149    /// Its usage is quite simple, for example, you can count the number
150    /// of columns in an LP \c lp:
151    ///\code
152    /// int count=0;
153    /// for (LpBase::ColIt c(lp); c!=INVALID; ++c) ++count;
154    ///\endcode
155    class ColIt : public Col {
156      const LpBase *_solver;
157    public:
158      /// Default constructor
159     
160      /// \warning The default constructor sets the iterator
161      /// to an undefined value.
162      ColIt() {}
163      /// Sets the iterator to the first Col
164     
165      /// Sets the iterator to the first Col.
166      ///
167      ColIt(const LpBase &solver) : _solver(&solver)
168      {
169        _solver->cols.firstItem(_id);
170      }
171      /// Invalid constructor \& conversion
172     
173      /// Initialize the iterator to be invalid.
174      /// \sa Invalid for more details.
175      ColIt(const Invalid&) : Col(INVALID) {}
176      /// Next column
177     
178      /// Assign the iterator to the next column.
179      ///
180      ColIt &operator++()
181      {
182        _solver->cols.nextItem(_id);
183        return *this;
184      }
185    };
186
187    /// \brief Returns the ID of the column.
188    static int id(const Col& col) { return col._id; }
189    /// \brief Returns the column with the given ID.
190    ///
191    /// \pre The argument should be a valid column ID in the LP problem.
192    static Col colFromId(int id) { return Col(id); }
193
194    ///Refer to a row of the LP.
195
196    ///This type is used to refer to a row of the LP.
197    ///
198    ///Its value remains valid and correct even after the addition or erase of
199    ///other rows.
200    ///
201    ///\note This class is similar to other Item types in LEMON, like
202    ///Node and Arc types in digraph.
203    class Row {
204      friend class LpBase;
205    protected:
206      int _id;
207      explicit Row(int id) : _id(id) {}
208    public:
209      typedef Value ExprValue;
210      typedef True LpRow;
211      /// Default constructor
212     
213      /// \warning The default constructor sets the Row to an
214      /// undefined value.
215      Row() {}
216      /// Invalid constructor \& conversion.
217     
218      /// This constructor initializes the Row to be invalid.
219      /// \sa Invalid for more details.     
220      Row(const Invalid&) : _id(-1) {}
221      /// Equality operator
222
223      /// Two \ref Row "Row"s are equal if and only if they point to
224      /// the same LP row or both are invalid.
225      bool operator==(Row r) const  {return _id == r._id;}
226      /// Inequality operator
227     
228      /// \sa operator==(Row r)
229      ///
230      bool operator!=(Row r) const  {return _id != r._id;}
231      /// Artificial ordering operator.
232
233      /// To allow the use of this object in std::map or similar
234      /// associative container we require this.
235      ///
236      /// \note This operator only have to define some strict ordering of
237      /// the items; this order has nothing to do with the iteration
238      /// ordering of the items.
239      bool operator<(Row r) const  {return _id < r._id;}
240    };
241
242    ///Iterator for iterate over the rows of an LP problem
243
244    /// Its usage is quite simple, for example, you can count the number
245    /// of rows in an LP \c lp:
246    ///\code
247    /// int count=0;
248    /// for (LpBase::RowIt c(lp); c!=INVALID; ++c) ++count;
249    ///\endcode
250    class RowIt : public Row {
251      const LpBase *_solver;
252    public:
253      /// Default constructor
254     
255      /// \warning The default constructor sets the iterator
256      /// to an undefined value.
257      RowIt() {}
258      /// Sets the iterator to the first Row
259     
260      /// Sets the iterator to the first Row.
261      ///
262      RowIt(const LpBase &solver) : _solver(&solver)
263      {
264        _solver->rows.firstItem(_id);
265      }
266      /// Invalid constructor \& conversion
267     
268      /// Initialize the iterator to be invalid.
269      /// \sa Invalid for more details.
270      RowIt(const Invalid&) : Row(INVALID) {}
271      /// Next row
272     
273      /// Assign the iterator to the next row.
274      ///
275      RowIt &operator++()
276      {
277        _solver->rows.nextItem(_id);
278        return *this;
279      }
280    };
281
282    /// \brief Returns the ID of the row.
283    static int id(const Row& row) { return row._id; }
284    /// \brief Returns the row with the given ID.
285    ///
286    /// \pre The argument should be a valid row ID in the LP problem.
287    static Row rowFromId(int id) { return Row(id); }
288
289  public:
290
291    ///Linear expression of variables and a constant component
292
293    ///This data structure stores a linear expression of the variables
294    ///(\ref Col "Col"s) and also has a constant component.
295    ///
296    ///There are several ways to access and modify the contents of this
297    ///container.
298    ///\code
299    ///e[v]=5;
300    ///e[v]+=12;
301    ///e.erase(v);
302    ///\endcode
303    ///or you can also iterate through its elements.
304    ///\code
305    ///double s=0;
306    ///for(LpBase::Expr::ConstCoeffIt i(e);i!=INVALID;++i)
307    ///  s+=*i * primal(i);
308    ///\endcode
309    ///(This code computes the primal value of the expression).
310    ///- Numbers (<tt>double</tt>'s)
311    ///and variables (\ref Col "Col"s) directly convert to an
312    ///\ref Expr and the usual linear operations are defined, so
313    ///\code
314    ///v+w
315    ///2*v-3.12*(v-w/2)+2
316    ///v*2.1+(3*v+(v*12+w+6)*3)/2
317    ///\endcode
318    ///are valid expressions.
319    ///The usual assignment operations are also defined.
320    ///\code
321    ///e=v+w;
322    ///e+=2*v-3.12*(v-w/2)+2;
323    ///e*=3.4;
324    ///e/=5;
325    ///\endcode
326    ///- The constant member can be set and read by dereference
327    ///  operator (unary *)
328    ///
329    ///\code
330    ///*e=12;
331    ///double c=*e;
332    ///\endcode
333    ///
334    ///\sa Constr
335    class Expr {
336      friend class LpBase;
337    public:
338      /// The key type of the expression
339      typedef LpBase::Col Key;
340      /// The value type of the expression
341      typedef LpBase::Value Value;
342
343    protected:
344      Value const_comp;
345      std::map<int, Value> comps;
346
347    public:
348      typedef True SolverExpr;
349      /// Default constructor
350     
351      /// Construct an empty expression, the coefficients and
352      /// the constant component are initialized to zero.
353      Expr() : const_comp(0) {}
354      /// Construct an expression from a column
355
356      /// Construct an expression, which has a term with \c c variable
357      /// and 1.0 coefficient.
358      Expr(const Col &c) : const_comp(0) {
359        typedef std::map<int, Value>::value_type pair_type;
360        comps.insert(pair_type(id(c), 1));
361      }
362      /// Construct an expression from a constant
363
364      /// Construct an expression, which's constant component is \c v.
365      ///
366      Expr(const Value &v) : const_comp(v) {}
367      /// Returns the coefficient of the column
368      Value operator[](const Col& c) const {
369        std::map<int, Value>::const_iterator it=comps.find(id(c));
370        if (it != comps.end()) {
371          return it->second;
372        } else {
373          return 0;
374        }
375      }
376      /// Returns the coefficient of the column
377      Value& operator[](const Col& c) {
378        return comps[id(c)];
379      }
380      /// Sets the coefficient of the column
381      void set(const Col &c, const Value &v) {
382        if (v != 0.0) {
383          typedef std::map<int, Value>::value_type pair_type;
384          comps.insert(pair_type(id(c), v));
385        } else {
386          comps.erase(id(c));
387        }
388      }
389      /// Returns the constant component of the expression
390      Value& operator*() { return const_comp; }
391      /// Returns the constant component of the expression
392      const Value& operator*() const { return const_comp; }
393      /// \brief Removes the coefficients which's absolute value does
394      /// not exceed \c epsilon. It also sets to zero the constant
395      /// component, if it does not exceed epsilon in absolute value.
396      void simplify(Value epsilon = 0.0) {
397        std::map<int, Value>::iterator it=comps.begin();
398        while (it != comps.end()) {
399          std::map<int, Value>::iterator jt=it;
400          ++jt;
401          if (std::fabs((*it).second) <= epsilon) comps.erase(it);
402          it=jt;
403        }
404        if (std::fabs(const_comp) <= epsilon) const_comp = 0;
405      }
406
407      void simplify(Value epsilon = 0.0) const {
408        const_cast<Expr*>(this)->simplify(epsilon);
409      }
410
411      ///Sets all coefficients and the constant component to 0.
412      void clear() {
413        comps.clear();
414        const_comp=0;
415      }
416
417      ///Compound assignment
418      Expr &operator+=(const Expr &e) {
419        for (std::map<int, Value>::const_iterator it=e.comps.begin();
420             it!=e.comps.end(); ++it)
421          comps[it->first]+=it->second;
422        const_comp+=e.const_comp;
423        return *this;
424      }
425      ///Compound assignment
426      Expr &operator-=(const Expr &e) {
427        for (std::map<int, Value>::const_iterator it=e.comps.begin();
428             it!=e.comps.end(); ++it)
429          comps[it->first]-=it->second;
430        const_comp-=e.const_comp;
431        return *this;
432      }
433      ///Multiply with a constant
434      Expr &operator*=(const Value &v) {
435        for (std::map<int, Value>::iterator it=comps.begin();
436             it!=comps.end(); ++it)
437          it->second*=v;
438        const_comp*=v;
439        return *this;
440      }
441      ///Division with a constant
442      Expr &operator/=(const Value &c) {
443        for (std::map<int, Value>::iterator it=comps.begin();
444             it!=comps.end(); ++it)
445          it->second/=c;
446        const_comp/=c;
447        return *this;
448      }
449
450      ///Iterator over the expression
451     
452      ///The iterator iterates over the terms of the expression.
453      ///
454      ///\code
455      ///double s=0;
456      ///for(LpBase::Expr::CoeffIt i(e);i!=INVALID;++i)
457      ///  s+= *i * primal(i);
458      ///\endcode
459      class CoeffIt {
460      private:
461
462        std::map<int, Value>::iterator _it, _end;
463
464      public:
465
466        /// Sets the iterator to the first term
467       
468        /// Sets the iterator to the first term of the expression.
469        ///
470        CoeffIt(Expr& e)
471          : _it(e.comps.begin()), _end(e.comps.end()){}
472
473        /// Convert the iterator to the column of the term
474        operator Col() const {
475          return colFromId(_it->first);
476        }
477
478        /// Returns the coefficient of the term
479        Value& operator*() { return _it->second; }
480
481        /// Returns the coefficient of the term
482        const Value& operator*() const { return _it->second; }
483        /// Next term
484       
485        /// Assign the iterator to the next term.
486        ///
487        CoeffIt& operator++() { ++_it; return *this; }
488
489        /// Equality operator
490        bool operator==(Invalid) const { return _it == _end; }
491        /// Inequality operator
492        bool operator!=(Invalid) const { return _it != _end; }
493      };
494
495      /// Const iterator over the expression
496     
497      ///The iterator iterates over the terms of the expression.
498      ///
499      ///\code
500      ///double s=0;
501      ///for(LpBase::Expr::ConstCoeffIt i(e);i!=INVALID;++i)
502      ///  s+=*i * primal(i);
503      ///\endcode
504      class ConstCoeffIt {
505      private:
506
507        std::map<int, Value>::const_iterator _it, _end;
508
509      public:
510
511        /// Sets the iterator to the first term
512       
513        /// Sets the iterator to the first term of the expression.
514        ///
515        ConstCoeffIt(const Expr& e)
516          : _it(e.comps.begin()), _end(e.comps.end()){}
517
518        /// Convert the iterator to the column of the term
519        operator Col() const {
520          return colFromId(_it->first);
521        }
522
523        /// Returns the coefficient of the term
524        const Value& operator*() const { return _it->second; }
525
526        /// Next term
527       
528        /// Assign the iterator to the next term.
529        ///
530        ConstCoeffIt& operator++() { ++_it; return *this; }
531
532        /// Equality operator
533        bool operator==(Invalid) const { return _it == _end; }
534        /// Inequality operator
535        bool operator!=(Invalid) const { return _it != _end; }
536      };
537
538    };
539
540    ///Linear constraint
541
542    ///This data stucture represents a linear constraint in the LP.
543    ///Basically it is a linear expression with a lower or an upper bound
544    ///(or both). These parts of the constraint can be obtained by the member
545    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
546    ///respectively.
547    ///There are two ways to construct a constraint.
548    ///- You can set the linear expression and the bounds directly
549    ///  by the functions above.
550    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
551    ///  are defined between expressions, or even between constraints whenever
552    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
553    ///  \c s and \c t are numbers, then the followings are valid expressions
554    ///  and thus they can be used directly e.g. in \ref addRow() whenever
555    ///  it makes sense.
556    ///\code
557    ///  e<=s
558    ///  e<=f
559    ///  e==f
560    ///  s<=e<=t
561    ///  e>=t
562    ///\endcode
563    ///\warning The validity of a constraint is checked only at run
564    ///time, so e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will
565    ///compile, but will fail an assertion.
566    class Constr
567    {
568    public:
569      typedef LpBase::Expr Expr;
570      typedef Expr::Key Key;
571      typedef Expr::Value Value;
572
573    protected:
574      Expr _expr;
575      Value _lb,_ub;
576    public:
577      ///\e
578      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
579      ///\e
580      Constr(Value lb, const Expr &e, Value ub) :
581        _expr(e), _lb(lb), _ub(ub) {}
582      Constr(const Expr &e) :
583        _expr(e), _lb(NaN), _ub(NaN) {}
584      ///\e
585      void clear()
586      {
587        _expr.clear();
588        _lb=_ub=NaN;
589      }
590
591      ///Reference to the linear expression
592      Expr &expr() { return _expr; }
593      ///Cont reference to the linear expression
594      const Expr &expr() const { return _expr; }
595      ///Reference to the lower bound.
596
597      ///\return
598      ///- \ref INF "INF": the constraint is lower unbounded.
599      ///- \ref NaN "NaN": lower bound has not been set.
600      ///- finite number: the lower bound
601      Value &lowerBound() { return _lb; }
602      ///The const version of \ref lowerBound()
603      const Value &lowerBound() const { return _lb; }
604      ///Reference to the upper bound.
605
606      ///\return
607      ///- \ref INF "INF": the constraint is upper unbounded.
608      ///- \ref NaN "NaN": upper bound has not been set.
609      ///- finite number: the upper bound
610      Value &upperBound() { return _ub; }
611      ///The const version of \ref upperBound()
612      const Value &upperBound() const { return _ub; }
613      ///Is the constraint lower bounded?
614      bool lowerBounded() const {
615        return _lb != -INF && !isNaN(_lb);
616      }
617      ///Is the constraint upper bounded?
618      bool upperBounded() const {
619        return _ub != INF && !isNaN(_ub);
620      }
621
622    };
623
624    ///Linear expression of rows
625
626    ///This data structure represents a column of the matrix,
627    ///thas is it strores a linear expression of the dual variables
628    ///(\ref Row "Row"s).
629    ///
630    ///There are several ways to access and modify the contents of this
631    ///container.
632    ///\code
633    ///e[v]=5;
634    ///e[v]+=12;
635    ///e.erase(v);
636    ///\endcode
637    ///or you can also iterate through its elements.
638    ///\code
639    ///double s=0;
640    ///for(LpBase::DualExpr::ConstCoeffIt i(e);i!=INVALID;++i)
641    ///  s+=*i;
642    ///\endcode
643    ///(This code computes the sum of all coefficients).
644    ///- Numbers (<tt>double</tt>'s)
645    ///and variables (\ref Row "Row"s) directly convert to an
646    ///\ref DualExpr and the usual linear operations are defined, so
647    ///\code
648    ///v+w
649    ///2*v-3.12*(v-w/2)
650    ///v*2.1+(3*v+(v*12+w)*3)/2
651    ///\endcode
652    ///are valid \ref DualExpr dual expressions.
653    ///The usual assignment operations are also defined.
654    ///\code
655    ///e=v+w;
656    ///e+=2*v-3.12*(v-w/2);
657    ///e*=3.4;
658    ///e/=5;
659    ///\endcode
660    ///
661    ///\sa Expr
662    class DualExpr {
663      friend class LpBase;
664    public:
665      /// The key type of the expression
666      typedef LpBase::Row Key;
667      /// The value type of the expression
668      typedef LpBase::Value Value;
669
670    protected:
671      std::map<int, Value> comps;
672
673    public:
674      typedef True SolverExpr;
675      /// Default constructor
676     
677      /// Construct an empty expression, the coefficients are
678      /// initialized to zero.
679      DualExpr() {}
680      /// Construct an expression from a row
681
682      /// Construct an expression, which has a term with \c r dual
683      /// variable and 1.0 coefficient.
684      DualExpr(const Row &r) {
685        typedef std::map<int, Value>::value_type pair_type;
686        comps.insert(pair_type(id(r), 1));
687      }
688      /// Returns the coefficient of the row
689      Value operator[](const Row& r) const {
690        std::map<int, Value>::const_iterator it = comps.find(id(r));
691        if (it != comps.end()) {
692          return it->second;
693        } else {
694          return 0;
695        }
696      }
697      /// Returns the coefficient of the row
698      Value& operator[](const Row& r) {
699        return comps[id(r)];
700      }
701      /// Sets the coefficient of the row
702      void set(const Row &r, const Value &v) {
703        if (v != 0.0) {
704          typedef std::map<int, Value>::value_type pair_type;
705          comps.insert(pair_type(id(r), v));
706        } else {
707          comps.erase(id(r));
708        }
709      }
710      /// \brief Removes the coefficients which's absolute value does
711      /// not exceed \c epsilon.
712      void simplify(Value epsilon = 0.0) {
713        std::map<int, Value>::iterator it=comps.begin();
714        while (it != comps.end()) {
715          std::map<int, Value>::iterator jt=it;
716          ++jt;
717          if (std::fabs((*it).second) <= epsilon) comps.erase(it);
718          it=jt;
719        }
720      }
721
722      void simplify(Value epsilon = 0.0) const {
723        const_cast<DualExpr*>(this)->simplify(epsilon);
724      }
725
726      ///Sets all coefficients to 0.
727      void clear() {
728        comps.clear();
729      }
730      ///Compound assignment
731      DualExpr &operator+=(const DualExpr &e) {
732        for (std::map<int, Value>::const_iterator it=e.comps.begin();
733             it!=e.comps.end(); ++it)
734          comps[it->first]+=it->second;
735        return *this;
736      }
737      ///Compound assignment
738      DualExpr &operator-=(const DualExpr &e) {
739        for (std::map<int, Value>::const_iterator it=e.comps.begin();
740             it!=e.comps.end(); ++it)
741          comps[it->first]-=it->second;
742        return *this;
743      }
744      ///Multiply with a constant
745      DualExpr &operator*=(const Value &v) {
746        for (std::map<int, Value>::iterator it=comps.begin();
747             it!=comps.end(); ++it)
748          it->second*=v;
749        return *this;
750      }
751      ///Division with a constant
752      DualExpr &operator/=(const Value &v) {
753        for (std::map<int, Value>::iterator it=comps.begin();
754             it!=comps.end(); ++it)
755          it->second/=v;
756        return *this;
757      }
758
759      ///Iterator over the expression
760     
761      ///The iterator iterates over the terms of the expression.
762      ///
763      ///\code
764      ///double s=0;
765      ///for(LpBase::DualExpr::CoeffIt i(e);i!=INVALID;++i)
766      ///  s+= *i * dual(i);
767      ///\endcode
768      class CoeffIt {
769      private:
770
771        std::map<int, Value>::iterator _it, _end;
772
773      public:
774
775        /// Sets the iterator to the first term
776       
777        /// Sets the iterator to the first term of the expression.
778        ///
779        CoeffIt(DualExpr& e)
780          : _it(e.comps.begin()), _end(e.comps.end()){}
781
782        /// Convert the iterator to the row of the term
783        operator Row() const {
784          return rowFromId(_it->first);
785        }
786
787        /// Returns the coefficient of the term
788        Value& operator*() { return _it->second; }
789
790        /// Returns the coefficient of the term
791        const Value& operator*() const { return _it->second; }
792
793        /// Next term
794       
795        /// Assign the iterator to the next term.
796        ///
797        CoeffIt& operator++() { ++_it; return *this; }
798
799        /// Equality operator
800        bool operator==(Invalid) const { return _it == _end; }
801        /// Inequality operator
802        bool operator!=(Invalid) const { return _it != _end; }
803      };
804
805      ///Iterator over the expression
806     
807      ///The iterator iterates over the terms of the expression.
808      ///
809      ///\code
810      ///double s=0;
811      ///for(LpBase::DualExpr::ConstCoeffIt i(e);i!=INVALID;++i)
812      ///  s+= *i * dual(i);
813      ///\endcode
814      class ConstCoeffIt {
815      private:
816
817        std::map<int, Value>::const_iterator _it, _end;
818
819      public:
820
821        /// Sets the iterator to the first term
822       
823        /// Sets the iterator to the first term of the expression.
824        ///
825        ConstCoeffIt(const DualExpr& e)
826          : _it(e.comps.begin()), _end(e.comps.end()){}
827
828        /// Convert the iterator to the row of the term
829        operator Row() const {
830          return rowFromId(_it->first);
831        }
832
833        /// Returns the coefficient of the term
834        const Value& operator*() const { return _it->second; }
835
836        /// Next term
837       
838        /// Assign the iterator to the next term.
839        ///
840        ConstCoeffIt& operator++() { ++_it; return *this; }
841
842        /// Equality operator
843        bool operator==(Invalid) const { return _it == _end; }
844        /// Inequality operator
845        bool operator!=(Invalid) const { return _it != _end; }
846      };
847    };
848
849
850  protected:
851
852    class InsertIterator {
853    private:
854
855      std::map<int, Value>& _host;
856      const _solver_bits::VarIndex& _index;
857
858    public:
859
860      typedef std::output_iterator_tag iterator_category;
861      typedef void difference_type;
862      typedef void value_type;
863      typedef void reference;
864      typedef void pointer;
865
866      InsertIterator(std::map<int, Value>& host,
867                   const _solver_bits::VarIndex& index)
868        : _host(host), _index(index) {}
869
870      InsertIterator& operator=(const std::pair<int, Value>& value) {
871        typedef std::map<int, Value>::value_type pair_type;
872        _host.insert(pair_type(_index[value.first], value.second));
873        return *this;
874      }
875
876      InsertIterator& operator*() { return *this; }
877      InsertIterator& operator++() { return *this; }
878      InsertIterator operator++(int) { return *this; }
879
880    };
881
882    class ExprIterator {
883    private:
884      std::map<int, Value>::const_iterator _host_it;
885      const _solver_bits::VarIndex& _index;
886    public:
887
888      typedef std::bidirectional_iterator_tag iterator_category;
889      typedef std::ptrdiff_t difference_type;
890      typedef const std::pair<int, Value> value_type;
891      typedef value_type reference;
892
893      class pointer {
894      public:
895        pointer(value_type& _value) : value(_value) {}
896        value_type* operator->() { return &value; }
897      private:
898        value_type value;
899      };
900
901      ExprIterator(const std::map<int, Value>::const_iterator& host_it,
902                   const _solver_bits::VarIndex& index)
903        : _host_it(host_it), _index(index) {}
904
905      reference operator*() {
906        return std::make_pair(_index(_host_it->first), _host_it->second);
907      }
908
909      pointer operator->() {
910        return pointer(operator*());
911      }
912
913      ExprIterator& operator++() { ++_host_it; return *this; }
914      ExprIterator operator++(int) {
915        ExprIterator tmp(*this); ++_host_it; return tmp;
916      }
917
918      ExprIterator& operator--() { --_host_it; return *this; }
919      ExprIterator operator--(int) {
920        ExprIterator tmp(*this); --_host_it; return tmp;
921      }
922
923      bool operator==(const ExprIterator& it) const {
924        return _host_it == it._host_it;
925      }
926
927      bool operator!=(const ExprIterator& it) const {
928        return _host_it != it._host_it;
929      }
930
931    };
932
933  protected:
934
935    //Abstract virtual functions
936
937    virtual int _addColId(int col) { return cols.addIndex(col); }
938    virtual int _addRowId(int row) { return rows.addIndex(row); }
939
940    virtual void _eraseColId(int col) { cols.eraseIndex(col); }
941    virtual void _eraseRowId(int row) { rows.eraseIndex(row); }
942
943    virtual int _addCol() = 0;
944    virtual int _addRow() = 0;
945
946    virtual int _addRow(Value l, ExprIterator b, ExprIterator e, Value u) {
947      int row = _addRow();
948      _setRowCoeffs(row, b, e);
949      _setRowLowerBound(row, l);
950      _setRowUpperBound(row, u);
951      return row;
952    }
953
954    virtual void _eraseCol(int col) = 0;
955    virtual void _eraseRow(int row) = 0;
956
957    virtual void _getColName(int col, std::string& name) const = 0;
958    virtual void _setColName(int col, const std::string& name) = 0;
959    virtual int _colByName(const std::string& name) const = 0;
960
961    virtual void _getRowName(int row, std::string& name) const = 0;
962    virtual void _setRowName(int row, const std::string& name) = 0;
963    virtual int _rowByName(const std::string& name) const = 0;
964
965    virtual void _setRowCoeffs(int i, ExprIterator b, ExprIterator e) = 0;
966    virtual void _getRowCoeffs(int i, InsertIterator b) const = 0;
967
968    virtual void _setColCoeffs(int i, ExprIterator b, ExprIterator e) = 0;
969    virtual void _getColCoeffs(int i, InsertIterator b) const = 0;
970
971    virtual void _setCoeff(int row, int col, Value value) = 0;
972    virtual Value _getCoeff(int row, int col) const = 0;
973
974    virtual void _setColLowerBound(int i, Value value) = 0;
975    virtual Value _getColLowerBound(int i) const = 0;
976
977    virtual void _setColUpperBound(int i, Value value) = 0;
978    virtual Value _getColUpperBound(int i) const = 0;
979
980    virtual void _setRowLowerBound(int i, Value value) = 0;
981    virtual Value _getRowLowerBound(int i) const = 0;
982
983    virtual void _setRowUpperBound(int i, Value value) = 0;
984    virtual Value _getRowUpperBound(int i) const = 0;
985
986    virtual void _setObjCoeffs(ExprIterator b, ExprIterator e) = 0;
987    virtual void _getObjCoeffs(InsertIterator b) const = 0;
988
989    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
990    virtual Value _getObjCoeff(int i) const = 0;
991
992    virtual void _setSense(Sense) = 0;
993    virtual Sense _getSense() const = 0;
994
995    virtual void _clear() = 0;
996
997    virtual const char* _solverName() const = 0;
998
999    virtual void _messageLevel(MessageLevel level) = 0;
1000
1001    //Own protected stuff
1002
1003    //Constant component of the objective function
1004    Value obj_const_comp;
1005
1006    LpBase() : rows(), cols(), obj_const_comp(0) {}
1007
1008  public:
1009
1010    /// Virtual destructor
1011    virtual ~LpBase() {}
1012
1013    ///Gives back the name of the solver.
1014    const char* solverName() const {return _solverName();}
1015
1016    ///\name Build Up and Modify the LP
1017
1018    ///@{
1019
1020    ///Add a new empty column (i.e a new variable) to the LP
1021    Col addCol() { Col c; c._id = _addColId(_addCol()); return c;}
1022
1023    ///\brief Adds several new columns (i.e variables) at once
1024    ///
1025    ///This magic function takes a container as its argument and fills
1026    ///its elements with new columns (i.e. variables)
1027    ///\param t can be
1028    ///- a standard STL compatible iterable container with
1029    ///\ref Col as its \c values_type like
1030    ///\code
1031    ///std::vector<LpBase::Col>
1032    ///std::list<LpBase::Col>
1033    ///\endcode
1034    ///- a standard STL compatible iterable container with
1035    ///\ref Col as its \c mapped_type like
1036    ///\code
1037    ///std::map<AnyType,LpBase::Col>
1038    ///\endcode
1039    ///- an iterable lemon \ref concepts::WriteMap "write map" like
1040    ///\code
1041    ///ListGraph::NodeMap<LpBase::Col>
1042    ///ListGraph::ArcMap<LpBase::Col>
1043    ///\endcode
1044    ///\return The number of the created column.
1045#ifdef DOXYGEN
1046    template<class T>
1047    int addColSet(T &t) { return 0;}
1048#else
1049    template<class T>
1050    typename enable_if<typename T::value_type::LpCol,int>::type
1051    addColSet(T &t,dummy<0> = 0) {
1052      int s=0;
1053      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
1054      return s;
1055    }
1056    template<class T>
1057    typename enable_if<typename T::value_type::second_type::LpCol,
1058                       int>::type
1059    addColSet(T &t,dummy<1> = 1) {
1060      int s=0;
1061      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1062        i->second=addCol();
1063        s++;
1064      }
1065      return s;
1066    }
1067    template<class T>
1068    typename enable_if<typename T::MapIt::Value::LpCol,
1069                       int>::type
1070    addColSet(T &t,dummy<2> = 2) {
1071      int s=0;
1072      for(typename T::MapIt i(t); i!=INVALID; ++i)
1073        {
1074          i.set(addCol());
1075          s++;
1076        }
1077      return s;
1078    }
1079#endif
1080
1081    ///Set a column (i.e a dual constraint) of the LP
1082
1083    ///\param c is the column to be modified
1084    ///\param e is a dual linear expression (see \ref DualExpr)
1085    ///a better one.
1086    void col(Col c, const DualExpr &e) {
1087      e.simplify();
1088      _setColCoeffs(cols(id(c)), ExprIterator(e.comps.begin(), rows),
1089                    ExprIterator(e.comps.end(), rows));
1090    }
1091
1092    ///Get a column (i.e a dual constraint) of the LP
1093
1094    ///\param c is the column to get
1095    ///\return the dual expression associated to the column
1096    DualExpr col(Col c) const {
1097      DualExpr e;
1098      _getColCoeffs(cols(id(c)), InsertIterator(e.comps, rows));
1099      return e;
1100    }
1101
1102    ///Add a new column to the LP
1103
1104    ///\param e is a dual linear expression (see \ref DualExpr)
1105    ///\param o is the corresponding component of the objective
1106    ///function. It is 0 by default.
1107    ///\return The created column.
1108    Col addCol(const DualExpr &e, Value o = 0) {
1109      Col c=addCol();
1110      col(c,e);
1111      objCoeff(c,o);
1112      return c;
1113    }
1114
1115    ///Add a new empty row (i.e a new constraint) to the LP
1116
1117    ///This function adds a new empty row (i.e a new constraint) to the LP.
1118    ///\return The created row
1119    Row addRow() { Row r; r._id = _addRowId(_addRow()); return r;}
1120
1121    ///\brief Add several new rows (i.e constraints) at once
1122    ///
1123    ///This magic function takes a container as its argument and fills
1124    ///its elements with new row (i.e. variables)
1125    ///\param t can be
1126    ///- a standard STL compatible iterable container with
1127    ///\ref Row as its \c values_type like
1128    ///\code
1129    ///std::vector<LpBase::Row>
1130    ///std::list<LpBase::Row>
1131    ///\endcode
1132    ///- a standard STL compatible iterable container with
1133    ///\ref Row as its \c mapped_type like
1134    ///\code
1135    ///std::map<AnyType,LpBase::Row>
1136    ///\endcode
1137    ///- an iterable lemon \ref concepts::WriteMap "write map" like
1138    ///\code
1139    ///ListGraph::NodeMap<LpBase::Row>
1140    ///ListGraph::ArcMap<LpBase::Row>
1141    ///\endcode
1142    ///\return The number of rows created.
1143#ifdef DOXYGEN
1144    template<class T>
1145    int addRowSet(T &t) { return 0;}
1146#else
1147    template<class T>
1148    typename enable_if<typename T::value_type::LpRow,int>::type
1149    addRowSet(T &t, dummy<0> = 0) {
1150      int s=0;
1151      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
1152      return s;
1153    }
1154    template<class T>
1155    typename enable_if<typename T::value_type::second_type::LpRow, int>::type
1156    addRowSet(T &t, dummy<1> = 1) {
1157      int s=0;
1158      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1159        i->second=addRow();
1160        s++;
1161      }
1162      return s;
1163    }
1164    template<class T>
1165    typename enable_if<typename T::MapIt::Value::LpRow, int>::type
1166    addRowSet(T &t, dummy<2> = 2) {
1167      int s=0;
1168      for(typename T::MapIt i(t); i!=INVALID; ++i)
1169        {
1170          i.set(addRow());
1171          s++;
1172        }
1173      return s;
1174    }
1175#endif
1176
1177    ///Set a row (i.e a constraint) of the LP
1178
1179    ///\param r is the row to be modified
1180    ///\param l is lower bound (-\ref INF means no bound)
1181    ///\param e is a linear expression (see \ref Expr)
1182    ///\param u is the upper bound (\ref INF means no bound)
1183    void row(Row r, Value l, const Expr &e, Value u) {
1184      e.simplify();
1185      _setRowCoeffs(rows(id(r)), ExprIterator(e.comps.begin(), cols),
1186                    ExprIterator(e.comps.end(), cols));
1187      _setRowLowerBound(rows(id(r)),l - *e);
1188      _setRowUpperBound(rows(id(r)),u - *e);
1189    }
1190
1191    ///Set a row (i.e a constraint) of the LP
1192
1193    ///\param r is the row to be modified
1194    ///\param c is a linear expression (see \ref Constr)
1195    void row(Row r, const Constr &c) {
1196      row(r, c.lowerBounded()?c.lowerBound():-INF,
1197          c.expr(), c.upperBounded()?c.upperBound():INF);
1198    }
1199
1200
1201    ///Get a row (i.e a constraint) of the LP
1202
1203    ///\param r is the row to get
1204    ///\return the expression associated to the row
1205    Expr row(Row r) const {
1206      Expr e;
1207      _getRowCoeffs(rows(id(r)), InsertIterator(e.comps, cols));
1208      return e;
1209    }
1210
1211    ///Add a new row (i.e a new constraint) to the LP
1212
1213    ///\param l is the lower bound (-\ref INF means no bound)
1214    ///\param e is a linear expression (see \ref Expr)
1215    ///\param u is the upper bound (\ref INF means no bound)
1216    ///\return The created row.
1217    Row addRow(Value l,const Expr &e, Value u) {
1218      Row r;
1219      e.simplify();
1220      r._id = _addRowId(_addRow(l - *e, ExprIterator(e.comps.begin(), cols),
1221                                ExprIterator(e.comps.end(), cols), u - *e));
1222      return r;
1223    }
1224
1225    ///Add a new row (i.e a new constraint) to the LP
1226
1227    ///\param c is a linear expression (see \ref Constr)
1228    ///\return The created row.
1229    Row addRow(const Constr &c) {
1230      Row r;
1231      c.expr().simplify();
1232      r._id = _addRowId(_addRow(c.lowerBounded()?c.lowerBound()-*c.expr():-INF,
1233                                ExprIterator(c.expr().comps.begin(), cols),
1234                                ExprIterator(c.expr().comps.end(), cols),
1235                                c.upperBounded()?c.upperBound()-*c.expr():INF));
1236      return r;
1237    }
1238    ///Erase a column (i.e a variable) from the LP
1239
1240    ///\param c is the column to be deleted
1241    void erase(Col c) {
1242      _eraseCol(cols(id(c)));
1243      _eraseColId(cols(id(c)));
1244    }
1245    ///Erase a row (i.e a constraint) from the LP
1246
1247    ///\param r is the row to be deleted
1248    void erase(Row r) {
1249      _eraseRow(rows(id(r)));
1250      _eraseRowId(rows(id(r)));
1251    }
1252
1253    /// Get the name of a column
1254
1255    ///\param c is the coresponding column
1256    ///\return The name of the colunm
1257    std::string colName(Col c) const {
1258      std::string name;
1259      _getColName(cols(id(c)), name);
1260      return name;
1261    }
1262
1263    /// Set the name of a column
1264
1265    ///\param c is the coresponding column
1266    ///\param name The name to be given
1267    void colName(Col c, const std::string& name) {
1268      _setColName(cols(id(c)), name);
1269    }
1270
1271    /// Get the column by its name
1272
1273    ///\param name The name of the column
1274    ///\return the proper column or \c INVALID
1275    Col colByName(const std::string& name) const {
1276      int k = _colByName(name);
1277      return k != -1 ? Col(cols[k]) : Col(INVALID);
1278    }
1279
1280    /// Get the name of a row
1281
1282    ///\param r is the coresponding row
1283    ///\return The name of the row
1284    std::string rowName(Row r) const {
1285      std::string name;
1286      _getRowName(rows(id(r)), name);
1287      return name;
1288    }
1289
1290    /// Set the name of a row
1291
1292    ///\param r is the coresponding row
1293    ///\param name The name to be given
1294    void rowName(Row r, const std::string& name) {
1295      _setRowName(rows(id(r)), name);
1296    }
1297
1298    /// Get the row by its name
1299
1300    ///\param name The name of the row
1301    ///\return the proper row or \c INVALID
1302    Row rowByName(const std::string& name) const {
1303      int k = _rowByName(name);
1304      return k != -1 ? Row(rows[k]) : Row(INVALID);
1305    }
1306
1307    /// Set an element of the coefficient matrix of the LP
1308
1309    ///\param r is the row of the element to be modified
1310    ///\param c is the column of the element to be modified
1311    ///\param val is the new value of the coefficient
1312    void coeff(Row r, Col c, Value val) {
1313      _setCoeff(rows(id(r)),cols(id(c)), val);
1314    }
1315
1316    /// Get an element of the coefficient matrix of the LP
1317
1318    ///\param r is the row of the element
1319    ///\param c is the column of the element
1320    ///\return the corresponding coefficient
1321    Value coeff(Row r, Col c) const {
1322      return _getCoeff(rows(id(r)),cols(id(c)));
1323    }
1324
1325    /// Set the lower bound of a column (i.e a variable)
1326
1327    /// The lower bound of a variable (column) has to be given by an
1328    /// extended number of type Value, i.e. a finite number of type
1329    /// Value or -\ref INF.
1330    void colLowerBound(Col c, Value value) {
1331      _setColLowerBound(cols(id(c)),value);
1332    }
1333
1334    /// Get the lower bound of a column (i.e a variable)
1335
1336    /// This function returns the lower bound for column (variable) \c c
1337    /// (this might be -\ref INF as well).
1338    ///\return The lower bound for column \c c
1339    Value colLowerBound(Col c) const {
1340      return _getColLowerBound(cols(id(c)));
1341    }
1342
1343    ///\brief Set the lower bound of  several columns
1344    ///(i.e variables) at once
1345    ///
1346    ///This magic function takes a container as its argument
1347    ///and applies the function on all of its elements.
1348    ///The lower bound of a variable (column) has to be given by an
1349    ///extended number of type Value, i.e. a finite number of type
1350    ///Value or -\ref INF.
1351#ifdef DOXYGEN
1352    template<class T>
1353    void colLowerBound(T &t, Value value) { return 0;}
1354#else
1355    template<class T>
1356    typename enable_if<typename T::value_type::LpCol,void>::type
1357    colLowerBound(T &t, Value value,dummy<0> = 0) {
1358      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1359        colLowerBound(*i, value);
1360      }
1361    }
1362    template<class T>
1363    typename enable_if<typename T::value_type::second_type::LpCol,
1364                       void>::type
1365    colLowerBound(T &t, Value value,dummy<1> = 1) {
1366      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1367        colLowerBound(i->second, value);
1368      }
1369    }
1370    template<class T>
1371    typename enable_if<typename T::MapIt::Value::LpCol,
1372                       void>::type
1373    colLowerBound(T &t, Value value,dummy<2> = 2) {
1374      for(typename T::MapIt i(t); i!=INVALID; ++i){
1375        colLowerBound(*i, value);
1376      }
1377    }
1378#endif
1379
1380    /// Set the upper bound of a column (i.e a variable)
1381
1382    /// The upper bound of a variable (column) has to be given by an
1383    /// extended number of type Value, i.e. a finite number of type
1384    /// Value or \ref INF.
1385    void colUpperBound(Col c, Value value) {
1386      _setColUpperBound(cols(id(c)),value);
1387    };
1388
1389    /// Get the upper bound of a column (i.e a variable)
1390
1391    /// This function returns the upper bound for column (variable) \c c
1392    /// (this might be \ref INF as well).
1393    /// \return The upper bound for column \c c
1394    Value colUpperBound(Col c) const {
1395      return _getColUpperBound(cols(id(c)));
1396    }
1397
1398    ///\brief Set the upper bound of  several columns
1399    ///(i.e variables) at once
1400    ///
1401    ///This magic function takes a container as its argument
1402    ///and applies the function on all of its elements.
1403    ///The upper bound of a variable (column) has to be given by an
1404    ///extended number of type Value, i.e. a finite number of type
1405    ///Value or \ref INF.
1406#ifdef DOXYGEN
1407    template<class T>
1408    void colUpperBound(T &t, Value value) { return 0;}
1409#else
1410    template<class T1>
1411    typename enable_if<typename T1::value_type::LpCol,void>::type
1412    colUpperBound(T1 &t, Value value,dummy<0> = 0) {
1413      for(typename T1::iterator i=t.begin();i!=t.end();++i) {
1414        colUpperBound(*i, value);
1415      }
1416    }
1417    template<class T1>
1418    typename enable_if<typename T1::value_type::second_type::LpCol,
1419                       void>::type
1420    colUpperBound(T1 &t, Value value,dummy<1> = 1) {
1421      for(typename T1::iterator i=t.begin();i!=t.end();++i) {
1422        colUpperBound(i->second, value);
1423      }
1424    }
1425    template<class T1>
1426    typename enable_if<typename T1::MapIt::Value::LpCol,
1427                       void>::type
1428    colUpperBound(T1 &t, Value value,dummy<2> = 2) {
1429      for(typename T1::MapIt i(t); i!=INVALID; ++i){
1430        colUpperBound(*i, value);
1431      }
1432    }
1433#endif
1434
1435    /// Set the lower and the upper bounds of a column (i.e a variable)
1436
1437    /// The lower and the upper bounds of
1438    /// a variable (column) have to be given by an
1439    /// extended number of type Value, i.e. a finite number of type
1440    /// Value, -\ref INF or \ref INF.
1441    void colBounds(Col c, Value lower, Value upper) {
1442      _setColLowerBound(cols(id(c)),lower);
1443      _setColUpperBound(cols(id(c)),upper);
1444    }
1445
1446    ///\brief Set the lower and the upper bound of several columns
1447    ///(i.e variables) at once
1448    ///
1449    ///This magic function takes a container as its argument
1450    ///and applies the function on all of its elements.
1451    /// The lower and the upper bounds of
1452    /// a variable (column) have to be given by an
1453    /// extended number of type Value, i.e. a finite number of type
1454    /// Value, -\ref INF or \ref INF.
1455#ifdef DOXYGEN
1456    template<class T>
1457    void colBounds(T &t, Value lower, Value upper) { return 0;}
1458#else
1459    template<class T2>
1460    typename enable_if<typename T2::value_type::LpCol,void>::type
1461    colBounds(T2 &t, Value lower, Value upper,dummy<0> = 0) {
1462      for(typename T2::iterator i=t.begin();i!=t.end();++i) {
1463        colBounds(*i, lower, upper);
1464      }
1465    }
1466    template<class T2>
1467    typename enable_if<typename T2::value_type::second_type::LpCol, void>::type
1468    colBounds(T2 &t, Value lower, Value upper,dummy<1> = 1) {
1469      for(typename T2::iterator i=t.begin();i!=t.end();++i) {
1470        colBounds(i->second, lower, upper);
1471      }
1472    }
1473    template<class T2>
1474    typename enable_if<typename T2::MapIt::Value::LpCol, void>::type
1475    colBounds(T2 &t, Value lower, Value upper,dummy<2> = 2) {
1476      for(typename T2::MapIt i(t); i!=INVALID; ++i){
1477        colBounds(*i, lower, upper);
1478      }
1479    }
1480#endif
1481
1482    /// Set the lower bound of a row (i.e a constraint)
1483
1484    /// The lower bound of a constraint (row) has to be given by an
1485    /// extended number of type Value, i.e. a finite number of type
1486    /// Value or -\ref INF.
1487    void rowLowerBound(Row r, Value value) {
1488      _setRowLowerBound(rows(id(r)),value);
1489    }
1490
1491    /// Get the lower bound of a row (i.e a constraint)
1492
1493    /// This function returns the lower bound for row (constraint) \c c
1494    /// (this might be -\ref INF as well).
1495    ///\return The lower bound for row \c r
1496    Value rowLowerBound(Row r) const {
1497      return _getRowLowerBound(rows(id(r)));
1498    }
1499
1500    /// Set the upper bound of a row (i.e a constraint)
1501
1502    /// The upper bound of a constraint (row) has to be given by an
1503    /// extended number of type Value, i.e. a finite number of type
1504    /// Value or -\ref INF.
1505    void rowUpperBound(Row r, Value value) {
1506      _setRowUpperBound(rows(id(r)),value);
1507    }
1508
1509    /// Get the upper bound of a row (i.e a constraint)
1510
1511    /// This function returns the upper bound for row (constraint) \c c
1512    /// (this might be -\ref INF as well).
1513    ///\return The upper bound for row \c r
1514    Value rowUpperBound(Row r) const {
1515      return _getRowUpperBound(rows(id(r)));
1516    }
1517
1518    ///Set an element of the objective function
1519    void objCoeff(Col c, Value v) {_setObjCoeff(cols(id(c)),v); };
1520
1521    ///Get an element of the objective function
1522    Value objCoeff(Col c) const { return _getObjCoeff(cols(id(c))); };
1523
1524    ///Set the objective function
1525
1526    ///\param e is a linear expression of type \ref Expr.
1527    ///
1528    void obj(const Expr& e) {
1529      _setObjCoeffs(ExprIterator(e.comps.begin(), cols),
1530                    ExprIterator(e.comps.end(), cols));
1531      obj_const_comp = *e;
1532    }
1533
1534    ///Get the objective function
1535
1536    ///\return the objective function as a linear expression of type
1537    ///Expr.
1538    Expr obj() const {
1539      Expr e;
1540      _getObjCoeffs(InsertIterator(e.comps, cols));
1541      *e = obj_const_comp;
1542      return e;
1543    }
1544
1545
1546    ///Set the direction of optimization
1547    void sense(Sense sense) { _setSense(sense); }
1548
1549    ///Query the direction of the optimization
1550    Sense sense() const {return _getSense(); }
1551
1552    ///Set the sense to maximization
1553    void max() { _setSense(MAX); }
1554
1555    ///Set the sense to maximization
1556    void min() { _setSense(MIN); }
1557
1558    ///Clears the problem
1559    void clear() { _clear(); }
1560
1561    /// Sets the message level of the solver
1562    void messageLevel(MessageLevel level) { _messageLevel(level); }
1563
1564    ///@}
1565
1566  };
1567
1568  /// Addition
1569
1570  ///\relates LpBase::Expr
1571  ///
1572  inline LpBase::Expr operator+(const LpBase::Expr &a, const LpBase::Expr &b) {
1573    LpBase::Expr tmp(a);
1574    tmp+=b;
1575    return tmp;
1576  }
1577  ///Substraction
1578
1579  ///\relates LpBase::Expr
1580  ///
1581  inline LpBase::Expr operator-(const LpBase::Expr &a, const LpBase::Expr &b) {
1582    LpBase::Expr tmp(a);
1583    tmp-=b;
1584    return tmp;
1585  }
1586  ///Multiply with constant
1587
1588  ///\relates LpBase::Expr
1589  ///
1590  inline LpBase::Expr operator*(const LpBase::Expr &a, const LpBase::Value &b) {
1591    LpBase::Expr tmp(a);
1592    tmp*=b;
1593    return tmp;
1594  }
1595
1596  ///Multiply with constant
1597
1598  ///\relates LpBase::Expr
1599  ///
1600  inline LpBase::Expr operator*(const LpBase::Value &a, const LpBase::Expr &b) {
1601    LpBase::Expr tmp(b);
1602    tmp*=a;
1603    return tmp;
1604  }
1605  ///Divide with constant
1606
1607  ///\relates LpBase::Expr
1608  ///
1609  inline LpBase::Expr operator/(const LpBase::Expr &a, const LpBase::Value &b) {
1610    LpBase::Expr tmp(a);
1611    tmp/=b;
1612    return tmp;
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, f - e, LpBase::INF);
1622  }
1623
1624  ///Create constraint
1625
1626  ///\relates LpBase::Constr
1627  ///
1628  inline LpBase::Constr operator<=(const LpBase::Value &e,
1629                                   const LpBase::Expr &f) {
1630    return LpBase::Constr(e, f, LpBase::NaN);
1631  }
1632
1633  ///Create constraint
1634
1635  ///\relates LpBase::Constr
1636  ///
1637  inline LpBase::Constr operator<=(const LpBase::Expr &e,
1638                                   const LpBase::Value &f) {
1639    return LpBase::Constr(- LpBase::INF, e, f);
1640  }
1641
1642  ///Create constraint
1643
1644  ///\relates LpBase::Constr
1645  ///
1646  inline LpBase::Constr operator>=(const LpBase::Expr &e,
1647                                   const LpBase::Expr &f) {
1648    return LpBase::Constr(0, e - f, LpBase::INF);
1649  }
1650
1651
1652  ///Create constraint
1653
1654  ///\relates LpBase::Constr
1655  ///
1656  inline LpBase::Constr operator>=(const LpBase::Value &e,
1657                                   const LpBase::Expr &f) {
1658    return LpBase::Constr(LpBase::NaN, f, e);
1659  }
1660
1661
1662  ///Create constraint
1663
1664  ///\relates LpBase::Constr
1665  ///
1666  inline LpBase::Constr operator>=(const LpBase::Expr &e,
1667                                   const LpBase::Value &f) {
1668    return LpBase::Constr(f, e, LpBase::INF);
1669  }
1670
1671  ///Create constraint
1672
1673  ///\relates LpBase::Constr
1674  ///
1675  inline LpBase::Constr operator==(const LpBase::Expr &e,
1676                                   const LpBase::Value &f) {
1677    return LpBase::Constr(f, e, f);
1678  }
1679
1680  ///Create constraint
1681
1682  ///\relates LpBase::Constr
1683  ///
1684  inline LpBase::Constr operator==(const LpBase::Expr &e,
1685                                   const LpBase::Expr &f) {
1686    return LpBase::Constr(0, f - e, 0);
1687  }
1688
1689  ///Create constraint
1690
1691  ///\relates LpBase::Constr
1692  ///
1693  inline LpBase::Constr operator<=(const LpBase::Value &n,
1694                                   const LpBase::Constr &c) {
1695    LpBase::Constr tmp(c);
1696    LEMON_ASSERT(isNaN(tmp.lowerBound()), "Wrong LP constraint");
1697    tmp.lowerBound()=n;
1698    return tmp;
1699  }
1700  ///Create constraint
1701
1702  ///\relates LpBase::Constr
1703  ///
1704  inline LpBase::Constr operator<=(const LpBase::Constr &c,
1705                                   const LpBase::Value &n)
1706  {
1707    LpBase::Constr tmp(c);
1708    LEMON_ASSERT(isNaN(tmp.upperBound()), "Wrong LP constraint");
1709    tmp.upperBound()=n;
1710    return tmp;
1711  }
1712
1713  ///Create constraint
1714
1715  ///\relates LpBase::Constr
1716  ///
1717  inline LpBase::Constr operator>=(const LpBase::Value &n,
1718                                   const LpBase::Constr &c) {
1719    LpBase::Constr tmp(c);
1720    LEMON_ASSERT(isNaN(tmp.upperBound()), "Wrong LP constraint");
1721    tmp.upperBound()=n;
1722    return tmp;
1723  }
1724  ///Create constraint
1725
1726  ///\relates LpBase::Constr
1727  ///
1728  inline LpBase::Constr operator>=(const LpBase::Constr &c,
1729                                   const LpBase::Value &n)
1730  {
1731    LpBase::Constr tmp(c);
1732    LEMON_ASSERT(isNaN(tmp.lowerBound()), "Wrong LP constraint");
1733    tmp.lowerBound()=n;
1734    return tmp;
1735  }
1736
1737  ///Addition
1738
1739  ///\relates LpBase::DualExpr
1740  ///
1741  inline LpBase::DualExpr operator+(const LpBase::DualExpr &a,
1742                                    const LpBase::DualExpr &b) {
1743    LpBase::DualExpr tmp(a);
1744    tmp+=b;
1745    return tmp;
1746  }
1747  ///Substraction
1748
1749  ///\relates LpBase::DualExpr
1750  ///
1751  inline LpBase::DualExpr operator-(const LpBase::DualExpr &a,
1752                                    const LpBase::DualExpr &b) {
1753    LpBase::DualExpr tmp(a);
1754    tmp-=b;
1755    return tmp;
1756  }
1757  ///Multiply with constant
1758
1759  ///\relates LpBase::DualExpr
1760  ///
1761  inline LpBase::DualExpr operator*(const LpBase::DualExpr &a,
1762                                    const LpBase::Value &b) {
1763    LpBase::DualExpr tmp(a);
1764    tmp*=b;
1765    return tmp;
1766  }
1767
1768  ///Multiply with constant
1769
1770  ///\relates LpBase::DualExpr
1771  ///
1772  inline LpBase::DualExpr operator*(const LpBase::Value &a,
1773                                    const LpBase::DualExpr &b) {
1774    LpBase::DualExpr tmp(b);
1775    tmp*=a;
1776    return tmp;
1777  }
1778  ///Divide with constant
1779
1780  ///\relates LpBase::DualExpr
1781  ///
1782  inline LpBase::DualExpr operator/(const LpBase::DualExpr &a,
1783                                    const LpBase::Value &b) {
1784    LpBase::DualExpr tmp(a);
1785    tmp/=b;
1786    return tmp;
1787  }
1788
1789  /// \ingroup lp_group
1790  ///
1791  /// \brief Common base class for LP solvers
1792  ///
1793  /// This class is an abstract base class for LP solvers. This class
1794  /// provides a full interface for set and modify an LP problem,
1795  /// solve it and retrieve the solution. You can use one of the
1796  /// descendants as a concrete implementation, or the \c Lp
1797  /// default LP solver. However, if you would like to handle LP
1798  /// solvers as reference or pointer in a generic way, you can use
1799  /// this class directly.
1800  class LpSolver : virtual public LpBase {
1801  public:
1802
1803    /// The problem types for primal and dual problems
1804    enum ProblemType {
1805      /// = 0. Feasible solution hasn't been found (but may exist).
1806      UNDEFINED = 0,
1807      /// = 1. The problem has no feasible solution.
1808      INFEASIBLE = 1,
1809      /// = 2. Feasible solution found.
1810      FEASIBLE = 2,
1811      /// = 3. Optimal solution exists and found.
1812      OPTIMAL = 3,
1813      /// = 4. The cost function is unbounded.
1814      UNBOUNDED = 4
1815    };
1816
1817    ///The basis status of variables
1818    enum VarStatus {
1819      /// The variable is in the basis
1820      BASIC,
1821      /// The variable is free, but not basic
1822      FREE,
1823      /// The variable has active lower bound
1824      LOWER,
1825      /// The variable has active upper bound
1826      UPPER,
1827      /// The variable is non-basic and fixed
1828      FIXED
1829    };
1830
1831  protected:
1832
1833    virtual SolveExitStatus _solve() = 0;
1834
1835    virtual Value _getPrimal(int i) const = 0;
1836    virtual Value _getDual(int i) const = 0;
1837
1838    virtual Value _getPrimalRay(int i) const = 0;
1839    virtual Value _getDualRay(int i) const = 0;
1840
1841    virtual Value _getPrimalValue() const = 0;
1842
1843    virtual VarStatus _getColStatus(int i) const = 0;
1844    virtual VarStatus _getRowStatus(int i) const = 0;
1845
1846    virtual ProblemType _getPrimalType() const = 0;
1847    virtual ProblemType _getDualType() const = 0;
1848
1849  public:
1850
1851    ///Allocate a new LP problem instance
1852    virtual LpSolver* newSolver() const = 0;
1853    ///Make a copy of the LP problem
1854    virtual LpSolver* cloneSolver() const = 0;
1855
1856    ///\name Solve the LP
1857
1858    ///@{
1859
1860    ///\e Solve the LP problem at hand
1861    ///
1862    ///\return The result of the optimization procedure. Possible
1863    ///values and their meanings can be found in the documentation of
1864    ///\ref SolveExitStatus.
1865    SolveExitStatus solve() { return _solve(); }
1866
1867    ///@}
1868
1869    ///\name Obtain the Solution
1870
1871    ///@{
1872
1873    /// The type of the primal problem
1874    ProblemType primalType() const {
1875      return _getPrimalType();
1876    }
1877
1878    /// The type of the dual problem
1879    ProblemType dualType() const {
1880      return _getDualType();
1881    }
1882
1883    /// Return the primal value of the column
1884
1885    /// Return the primal value of the column.
1886    /// \pre The problem is solved.
1887    Value primal(Col c) const { return _getPrimal(cols(id(c))); }
1888
1889    /// Return the primal value of the expression
1890
1891    /// Return the primal value of the expression, i.e. the dot
1892    /// product of the primal solution and the expression.
1893    /// \pre The problem is solved.
1894    Value primal(const Expr& e) const {
1895      double res = *e;
1896      for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {
1897        res += *c * primal(c);
1898      }
1899      return res;
1900    }
1901    /// Returns a component of the primal ray
1902   
1903    /// The primal ray is solution of the modified primal problem,
1904    /// where we change each finite bound to 0, and we looking for a
1905    /// negative objective value in case of minimization, and positive
1906    /// objective value for maximization. If there is such solution,
1907    /// that proofs the unsolvability of the dual problem, and if a
1908    /// feasible primal solution exists, then the unboundness of
1909    /// primal problem.
1910    ///
1911    /// \pre The problem is solved and the dual problem is infeasible.
1912    /// \note Some solvers does not provide primal ray calculation
1913    /// functions.
1914    Value primalRay(Col c) const { return _getPrimalRay(cols(id(c))); }
1915
1916    /// Return the dual value of the row
1917
1918    /// Return the dual value of the row.
1919    /// \pre The problem is solved.
1920    Value dual(Row r) const { return _getDual(rows(id(r))); }
1921
1922    /// Return the dual value of the dual expression
1923
1924    /// Return the dual value of the dual expression, i.e. the dot
1925    /// product of the dual solution and the dual expression.
1926    /// \pre The problem is solved.
1927    Value dual(const DualExpr& e) const {
1928      double res = 0.0;
1929      for (DualExpr::ConstCoeffIt r(e); r != INVALID; ++r) {
1930        res += *r * dual(r);
1931      }
1932      return res;
1933    }
1934
1935    /// Returns a component of the dual ray
1936   
1937    /// The dual ray is solution of the modified primal problem, where
1938    /// we change each finite bound to 0 (i.e. the objective function
1939    /// coefficients in the primal problem), and we looking for a
1940    /// ositive objective value. If there is such solution, that
1941    /// proofs the unsolvability of the primal problem, and if a
1942    /// feasible dual solution exists, then the unboundness of
1943    /// dual problem.
1944    ///
1945    /// \pre The problem is solved and the primal problem is infeasible.
1946    /// \note Some solvers does not provide dual ray calculation
1947    /// functions.
1948    Value dualRay(Row r) const { return _getDualRay(rows(id(r))); }
1949
1950    /// Return the basis status of the column
1951
1952    /// \see VarStatus
1953    VarStatus colStatus(Col c) const { return _getColStatus(cols(id(c))); }
1954
1955    /// Return the basis status of the row
1956
1957    /// \see VarStatus
1958    VarStatus rowStatus(Row r) const { return _getRowStatus(rows(id(r))); }
1959
1960    ///The value of the objective function
1961
1962    ///\return
1963    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
1964    /// of the primal problem, depending on whether we minimize or maximize.
1965    ///- \ref NaN if no primal solution is found.
1966    ///- The (finite) objective value if an optimal solution is found.
1967    Value primal() const { return _getPrimalValue()+obj_const_comp;}
1968    ///@}
1969
1970  protected:
1971
1972  };
1973
1974
1975  /// \ingroup lp_group
1976  ///
1977  /// \brief Common base class for MIP solvers
1978  ///
1979  /// This class is an abstract base class for MIP solvers. This class
1980  /// provides a full interface for set and modify an MIP problem,
1981  /// solve it and retrieve the solution. You can use one of the
1982  /// descendants as a concrete implementation, or the \c Lp
1983  /// default MIP solver. However, if you would like to handle MIP
1984  /// solvers as reference or pointer in a generic way, you can use
1985  /// this class directly.
1986  class MipSolver : virtual public LpBase {
1987  public:
1988
1989    /// The problem types for MIP problems
1990    enum ProblemType {
1991      /// = 0. Feasible solution hasn't been found (but may exist).
1992      UNDEFINED = 0,
1993      /// = 1. The problem has no feasible solution.
1994      INFEASIBLE = 1,
1995      /// = 2. Feasible solution found.
1996      FEASIBLE = 2,
1997      /// = 3. Optimal solution exists and found.
1998      OPTIMAL = 3,
1999      /// = 4. The cost function is unbounded.
2000      ///The Mip or at least the relaxed problem is unbounded.
2001      UNBOUNDED = 4
2002    };
2003
2004    ///Allocate a new MIP problem instance
2005    virtual MipSolver* newSolver() const = 0;
2006    ///Make a copy of the MIP problem
2007    virtual MipSolver* cloneSolver() const = 0;
2008
2009    ///\name Solve the MIP
2010
2011    ///@{
2012
2013    /// Solve the MIP problem at hand
2014    ///
2015    ///\return The result of the optimization procedure. Possible
2016    ///values and their meanings can be found in the documentation of
2017    ///\ref SolveExitStatus.
2018    SolveExitStatus solve() { return _solve(); }
2019
2020    ///@}
2021
2022    ///\name Set Column Type
2023    ///@{
2024
2025    ///Possible variable (column) types (e.g. real, integer, binary etc.)
2026    enum ColTypes {
2027      /// = 0. Continuous variable (default).
2028      REAL = 0,
2029      /// = 1. Integer variable.
2030      INTEGER = 1
2031    };
2032
2033    ///Sets the type of the given column to the given type
2034
2035    ///Sets the type of the given column to the given type.
2036    ///
2037    void colType(Col c, ColTypes col_type) {
2038      _setColType(cols(id(c)),col_type);
2039    }
2040
2041    ///Gives back the type of the column.
2042
2043    ///Gives back the type of the column.
2044    ///
2045    ColTypes colType(Col c) const {
2046      return _getColType(cols(id(c)));
2047    }
2048    ///@}
2049
2050    ///\name Obtain the Solution
2051
2052    ///@{
2053
2054    /// The type of the MIP problem
2055    ProblemType type() const {
2056      return _getType();
2057    }
2058
2059    /// Return the value of the row in the solution
2060
2061    ///  Return the value of the row in the solution.
2062    /// \pre The problem is solved.
2063    Value sol(Col c) const { return _getSol(cols(id(c))); }
2064
2065    /// Return the value of the expression in the solution
2066
2067    /// Return the value of the expression in the solution, i.e. the
2068    /// dot product of the solution and the expression.
2069    /// \pre The problem is solved.
2070    Value sol(const Expr& e) const {
2071      double res = *e;
2072      for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {
2073        res += *c * sol(c);
2074      }
2075      return res;
2076    }
2077    ///The value of the objective function
2078   
2079    ///\return
2080    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
2081    /// of the problem, depending on whether we minimize or maximize.
2082    ///- \ref NaN if no primal solution is found.
2083    ///- The (finite) objective value if an optimal solution is found.
2084    Value solValue() const { return _getSolValue()+obj_const_comp;}
2085    ///@}
2086
2087  protected:
2088
2089    virtual SolveExitStatus _solve() = 0;
2090    virtual ColTypes _getColType(int col) const = 0;
2091    virtual void _setColType(int col, ColTypes col_type) = 0;
2092    virtual ProblemType _getType() const = 0;
2093    virtual Value _getSol(int i) const = 0;
2094    virtual Value _getSolValue() const = 0;
2095
2096  };
2097
2098
2099
2100} //namespace lemon
2101
2102#endif //LEMON_LP_BASE_H
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