COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/lp_base.h @ 745:68792fb2870f

Last change on this file since 745:68792fb2870f was 584:33c6b6e755cd, checked in by Peter Kovacs <kpeter@…>, 11 years ago

Small doc improvements (#263)

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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      /// = 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 void _eraseCol(int col) = 0;
947    virtual void _eraseRow(int row) = 0;
948
949    virtual void _getColName(int col, std::string& name) const = 0;
950    virtual void _setColName(int col, const std::string& name) = 0;
951    virtual int _colByName(const std::string& name) const = 0;
952
953    virtual void _getRowName(int row, std::string& name) const = 0;
954    virtual void _setRowName(int row, const std::string& name) = 0;
955    virtual int _rowByName(const std::string& name) const = 0;
956
957    virtual void _setRowCoeffs(int i, ExprIterator b, ExprIterator e) = 0;
958    virtual void _getRowCoeffs(int i, InsertIterator b) const = 0;
959
960    virtual void _setColCoeffs(int i, ExprIterator b, ExprIterator e) = 0;
961    virtual void _getColCoeffs(int i, InsertIterator b) const = 0;
962
963    virtual void _setCoeff(int row, int col, Value value) = 0;
964    virtual Value _getCoeff(int row, int col) const = 0;
965
966    virtual void _setColLowerBound(int i, Value value) = 0;
967    virtual Value _getColLowerBound(int i) const = 0;
968
969    virtual void _setColUpperBound(int i, Value value) = 0;
970    virtual Value _getColUpperBound(int i) const = 0;
971
972    virtual void _setRowLowerBound(int i, Value value) = 0;
973    virtual Value _getRowLowerBound(int i) const = 0;
974
975    virtual void _setRowUpperBound(int i, Value value) = 0;
976    virtual Value _getRowUpperBound(int i) const = 0;
977
978    virtual void _setObjCoeffs(ExprIterator b, ExprIterator e) = 0;
979    virtual void _getObjCoeffs(InsertIterator b) const = 0;
980
981    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
982    virtual Value _getObjCoeff(int i) const = 0;
983
984    virtual void _setSense(Sense) = 0;
985    virtual Sense _getSense() const = 0;
986
987    virtual void _clear() = 0;
988
989    virtual const char* _solverName() const = 0;
990
991    virtual void _messageLevel(MessageLevel level) = 0;
992
993    //Own protected stuff
994
995    //Constant component of the objective function
996    Value obj_const_comp;
997
998    LpBase() : rows(), cols(), obj_const_comp(0) {}
999
1000  public:
1001
1002    /// Virtual destructor
1003    virtual ~LpBase() {}
1004
1005    ///Gives back the name of the solver.
1006    const char* solverName() const {return _solverName();}
1007
1008    ///\name Build Up and Modify the LP
1009
1010    ///@{
1011
1012    ///Add a new empty column (i.e a new variable) to the LP
1013    Col addCol() { Col c; c._id = _addColId(_addCol()); return c;}
1014
1015    ///\brief Adds several new columns (i.e variables) at once
1016    ///
1017    ///This magic function takes a container as its argument and fills
1018    ///its elements with new columns (i.e. variables)
1019    ///\param t can be
1020    ///- a standard STL compatible iterable container with
1021    ///\ref Col as its \c values_type like
1022    ///\code
1023    ///std::vector<LpBase::Col>
1024    ///std::list<LpBase::Col>
1025    ///\endcode
1026    ///- a standard STL compatible iterable container with
1027    ///\ref Col as its \c mapped_type like
1028    ///\code
1029    ///std::map<AnyType,LpBase::Col>
1030    ///\endcode
1031    ///- an iterable lemon \ref concepts::WriteMap "write map" like
1032    ///\code
1033    ///ListGraph::NodeMap<LpBase::Col>
1034    ///ListGraph::ArcMap<LpBase::Col>
1035    ///\endcode
1036    ///\return The number of the created column.
1037#ifdef DOXYGEN
1038    template<class T>
1039    int addColSet(T &t) { return 0;}
1040#else
1041    template<class T>
1042    typename enable_if<typename T::value_type::LpCol,int>::type
1043    addColSet(T &t,dummy<0> = 0) {
1044      int s=0;
1045      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
1046      return s;
1047    }
1048    template<class T>
1049    typename enable_if<typename T::value_type::second_type::LpCol,
1050                       int>::type
1051    addColSet(T &t,dummy<1> = 1) {
1052      int s=0;
1053      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1054        i->second=addCol();
1055        s++;
1056      }
1057      return s;
1058    }
1059    template<class T>
1060    typename enable_if<typename T::MapIt::Value::LpCol,
1061                       int>::type
1062    addColSet(T &t,dummy<2> = 2) {
1063      int s=0;
1064      for(typename T::MapIt i(t); i!=INVALID; ++i)
1065        {
1066          i.set(addCol());
1067          s++;
1068        }
1069      return s;
1070    }
1071#endif
1072
1073    ///Set a column (i.e a dual constraint) of the LP
1074
1075    ///\param c is the column to be modified
1076    ///\param e is a dual linear expression (see \ref DualExpr)
1077    ///a better one.
1078    void col(Col c, const DualExpr &e) {
1079      e.simplify();
1080      _setColCoeffs(cols(id(c)), ExprIterator(e.comps.begin(), rows),
1081                    ExprIterator(e.comps.end(), rows));
1082    }
1083
1084    ///Get a column (i.e a dual constraint) of the LP
1085
1086    ///\param c is the column to get
1087    ///\return the dual expression associated to the column
1088    DualExpr col(Col c) const {
1089      DualExpr e;
1090      _getColCoeffs(cols(id(c)), InsertIterator(e.comps, rows));
1091      return e;
1092    }
1093
1094    ///Add a new column to the LP
1095
1096    ///\param e is a dual linear expression (see \ref DualExpr)
1097    ///\param o is the corresponding component of the objective
1098    ///function. It is 0 by default.
1099    ///\return The created column.
1100    Col addCol(const DualExpr &e, Value o = 0) {
1101      Col c=addCol();
1102      col(c,e);
1103      objCoeff(c,o);
1104      return c;
1105    }
1106
1107    ///Add a new empty row (i.e a new constraint) to the LP
1108
1109    ///This function adds a new empty row (i.e a new constraint) to the LP.
1110    ///\return The created row
1111    Row addRow() { Row r; r._id = _addRowId(_addRow()); return r;}
1112
1113    ///\brief Add several new rows (i.e constraints) at once
1114    ///
1115    ///This magic function takes a container as its argument and fills
1116    ///its elements with new row (i.e. variables)
1117    ///\param t can be
1118    ///- a standard STL compatible iterable container with
1119    ///\ref Row as its \c values_type like
1120    ///\code
1121    ///std::vector<LpBase::Row>
1122    ///std::list<LpBase::Row>
1123    ///\endcode
1124    ///- a standard STL compatible iterable container with
1125    ///\ref Row as its \c mapped_type like
1126    ///\code
1127    ///std::map<AnyType,LpBase::Row>
1128    ///\endcode
1129    ///- an iterable lemon \ref concepts::WriteMap "write map" like
1130    ///\code
1131    ///ListGraph::NodeMap<LpBase::Row>
1132    ///ListGraph::ArcMap<LpBase::Row>
1133    ///\endcode
1134    ///\return The number of rows created.
1135#ifdef DOXYGEN
1136    template<class T>
1137    int addRowSet(T &t) { return 0;}
1138#else
1139    template<class T>
1140    typename enable_if<typename T::value_type::LpRow,int>::type
1141    addRowSet(T &t, dummy<0> = 0) {
1142      int s=0;
1143      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
1144      return s;
1145    }
1146    template<class T>
1147    typename enable_if<typename T::value_type::second_type::LpRow, int>::type
1148    addRowSet(T &t, dummy<1> = 1) {
1149      int s=0;
1150      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1151        i->second=addRow();
1152        s++;
1153      }
1154      return s;
1155    }
1156    template<class T>
1157    typename enable_if<typename T::MapIt::Value::LpRow, int>::type
1158    addRowSet(T &t, dummy<2> = 2) {
1159      int s=0;
1160      for(typename T::MapIt i(t); i!=INVALID; ++i)
1161        {
1162          i.set(addRow());
1163          s++;
1164        }
1165      return s;
1166    }
1167#endif
1168
1169    ///Set a row (i.e a constraint) of the LP
1170
1171    ///\param r is the row to be modified
1172    ///\param l is lower bound (-\ref INF means no bound)
1173    ///\param e is a linear expression (see \ref Expr)
1174    ///\param u is the upper bound (\ref INF means no bound)
1175    void row(Row r, Value l, const Expr &e, Value u) {
1176      e.simplify();
1177      _setRowCoeffs(rows(id(r)), ExprIterator(e.comps.begin(), cols),
1178                    ExprIterator(e.comps.end(), cols));
1179      _setRowLowerBound(rows(id(r)),l - *e);
1180      _setRowUpperBound(rows(id(r)),u - *e);
1181    }
1182
1183    ///Set a row (i.e a constraint) of the LP
1184
1185    ///\param r is the row to be modified
1186    ///\param c is a linear expression (see \ref Constr)
1187    void row(Row r, const Constr &c) {
1188      row(r, c.lowerBounded()?c.lowerBound():-INF,
1189          c.expr(), c.upperBounded()?c.upperBound():INF);
1190    }
1191
1192
1193    ///Get a row (i.e a constraint) of the LP
1194
1195    ///\param r is the row to get
1196    ///\return the expression associated to the row
1197    Expr row(Row r) const {
1198      Expr e;
1199      _getRowCoeffs(rows(id(r)), InsertIterator(e.comps, cols));
1200      return e;
1201    }
1202
1203    ///Add a new row (i.e a new constraint) to the LP
1204
1205    ///\param l is the lower bound (-\ref INF means no bound)
1206    ///\param e is a linear expression (see \ref Expr)
1207    ///\param u is the upper bound (\ref INF means no bound)
1208    ///\return The created row.
1209    Row addRow(Value l,const Expr &e, Value u) {
1210      Row r=addRow();
1211      row(r,l,e,u);
1212      return r;
1213    }
1214
1215    ///Add a new row (i.e a new constraint) to the LP
1216
1217    ///\param c is a linear expression (see \ref Constr)
1218    ///\return The created row.
1219    Row addRow(const Constr &c) {
1220      Row r=addRow();
1221      row(r,c);
1222      return r;
1223    }
1224    ///Erase a column (i.e a variable) from the LP
1225
1226    ///\param c is the column to be deleted
1227    void erase(Col c) {
1228      _eraseCol(cols(id(c)));
1229      _eraseColId(cols(id(c)));
1230    }
1231    ///Erase a row (i.e a constraint) from the LP
1232
1233    ///\param r is the row to be deleted
1234    void erase(Row r) {
1235      _eraseRow(rows(id(r)));
1236      _eraseRowId(rows(id(r)));
1237    }
1238
1239    /// Get the name of a column
1240
1241    ///\param c is the coresponding column
1242    ///\return The name of the colunm
1243    std::string colName(Col c) const {
1244      std::string name;
1245      _getColName(cols(id(c)), name);
1246      return name;
1247    }
1248
1249    /// Set the name of a column
1250
1251    ///\param c is the coresponding column
1252    ///\param name The name to be given
1253    void colName(Col c, const std::string& name) {
1254      _setColName(cols(id(c)), name);
1255    }
1256
1257    /// Get the column by its name
1258
1259    ///\param name The name of the column
1260    ///\return the proper column or \c INVALID
1261    Col colByName(const std::string& name) const {
1262      int k = _colByName(name);
1263      return k != -1 ? Col(cols[k]) : Col(INVALID);
1264    }
1265
1266    /// Get the name of a row
1267
1268    ///\param r is the coresponding row
1269    ///\return The name of the row
1270    std::string rowName(Row r) const {
1271      std::string name;
1272      _getRowName(rows(id(r)), name);
1273      return name;
1274    }
1275
1276    /// Set the name of a row
1277
1278    ///\param r is the coresponding row
1279    ///\param name The name to be given
1280    void rowName(Row r, const std::string& name) {
1281      _setRowName(rows(id(r)), name);
1282    }
1283
1284    /// Get the row by its name
1285
1286    ///\param name The name of the row
1287    ///\return the proper row or \c INVALID
1288    Row rowByName(const std::string& name) const {
1289      int k = _rowByName(name);
1290      return k != -1 ? Row(rows[k]) : Row(INVALID);
1291    }
1292
1293    /// Set an element of the coefficient matrix of the LP
1294
1295    ///\param r is the row of the element to be modified
1296    ///\param c is the column of the element to be modified
1297    ///\param val is the new value of the coefficient
1298    void coeff(Row r, Col c, Value val) {
1299      _setCoeff(rows(id(r)),cols(id(c)), val);
1300    }
1301
1302    /// Get an element of the coefficient matrix of the LP
1303
1304    ///\param r is the row of the element
1305    ///\param c is the column of the element
1306    ///\return the corresponding coefficient
1307    Value coeff(Row r, Col c) const {
1308      return _getCoeff(rows(id(r)),cols(id(c)));
1309    }
1310
1311    /// Set the lower bound of a column (i.e a variable)
1312
1313    /// The lower bound of a variable (column) has to be given by an
1314    /// extended number of type Value, i.e. a finite number of type
1315    /// Value or -\ref INF.
1316    void colLowerBound(Col c, Value value) {
1317      _setColLowerBound(cols(id(c)),value);
1318    }
1319
1320    /// Get the lower bound of a column (i.e a variable)
1321
1322    /// This function returns the lower bound for column (variable) \c c
1323    /// (this might be -\ref INF as well).
1324    ///\return The lower bound for column \c c
1325    Value colLowerBound(Col c) const {
1326      return _getColLowerBound(cols(id(c)));
1327    }
1328
1329    ///\brief Set the lower bound of  several columns
1330    ///(i.e variables) at once
1331    ///
1332    ///This magic function takes a container as its argument
1333    ///and applies the function on all of its elements.
1334    ///The lower bound of a variable (column) has to be given by an
1335    ///extended number of type Value, i.e. a finite number of type
1336    ///Value or -\ref INF.
1337#ifdef DOXYGEN
1338    template<class T>
1339    void colLowerBound(T &t, Value value) { return 0;}
1340#else
1341    template<class T>
1342    typename enable_if<typename T::value_type::LpCol,void>::type
1343    colLowerBound(T &t, Value value,dummy<0> = 0) {
1344      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1345        colLowerBound(*i, value);
1346      }
1347    }
1348    template<class T>
1349    typename enable_if<typename T::value_type::second_type::LpCol,
1350                       void>::type
1351    colLowerBound(T &t, Value value,dummy<1> = 1) {
1352      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1353        colLowerBound(i->second, value);
1354      }
1355    }
1356    template<class T>
1357    typename enable_if<typename T::MapIt::Value::LpCol,
1358                       void>::type
1359    colLowerBound(T &t, Value value,dummy<2> = 2) {
1360      for(typename T::MapIt i(t); i!=INVALID; ++i){
1361        colLowerBound(*i, value);
1362      }
1363    }
1364#endif
1365
1366    /// Set the upper bound of a column (i.e a variable)
1367
1368    /// The upper bound of a variable (column) has to be given by an
1369    /// extended number of type Value, i.e. a finite number of type
1370    /// Value or \ref INF.
1371    void colUpperBound(Col c, Value value) {
1372      _setColUpperBound(cols(id(c)),value);
1373    };
1374
1375    /// Get the upper bound of a column (i.e a variable)
1376
1377    /// This function returns the upper bound for column (variable) \c c
1378    /// (this might be \ref INF as well).
1379    /// \return The upper bound for column \c c
1380    Value colUpperBound(Col c) const {
1381      return _getColUpperBound(cols(id(c)));
1382    }
1383
1384    ///\brief Set the upper bound of  several columns
1385    ///(i.e variables) at once
1386    ///
1387    ///This magic function takes a container as its argument
1388    ///and applies the function on all of its elements.
1389    ///The upper bound of a variable (column) has to be given by an
1390    ///extended number of type Value, i.e. a finite number of type
1391    ///Value or \ref INF.
1392#ifdef DOXYGEN
1393    template<class T>
1394    void colUpperBound(T &t, Value value) { return 0;}
1395#else
1396    template<class T1>
1397    typename enable_if<typename T1::value_type::LpCol,void>::type
1398    colUpperBound(T1 &t, Value value,dummy<0> = 0) {
1399      for(typename T1::iterator i=t.begin();i!=t.end();++i) {
1400        colUpperBound(*i, value);
1401      }
1402    }
1403    template<class T1>
1404    typename enable_if<typename T1::value_type::second_type::LpCol,
1405                       void>::type
1406    colUpperBound(T1 &t, Value value,dummy<1> = 1) {
1407      for(typename T1::iterator i=t.begin();i!=t.end();++i) {
1408        colUpperBound(i->second, value);
1409      }
1410    }
1411    template<class T1>
1412    typename enable_if<typename T1::MapIt::Value::LpCol,
1413                       void>::type
1414    colUpperBound(T1 &t, Value value,dummy<2> = 2) {
1415      for(typename T1::MapIt i(t); i!=INVALID; ++i){
1416        colUpperBound(*i, value);
1417      }
1418    }
1419#endif
1420
1421    /// Set the lower and the upper bounds of a column (i.e a variable)
1422
1423    /// The lower and the upper bounds of
1424    /// a variable (column) have to be given by an
1425    /// extended number of type Value, i.e. a finite number of type
1426    /// Value, -\ref INF or \ref INF.
1427    void colBounds(Col c, Value lower, Value upper) {
1428      _setColLowerBound(cols(id(c)),lower);
1429      _setColUpperBound(cols(id(c)),upper);
1430    }
1431
1432    ///\brief Set the lower and the upper bound of several columns
1433    ///(i.e variables) at once
1434    ///
1435    ///This magic function takes a container as its argument
1436    ///and applies the function on all of its elements.
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#ifdef DOXYGEN
1442    template<class T>
1443    void colBounds(T &t, Value lower, Value upper) { return 0;}
1444#else
1445    template<class T2>
1446    typename enable_if<typename T2::value_type::LpCol,void>::type
1447    colBounds(T2 &t, Value lower, Value upper,dummy<0> = 0) {
1448      for(typename T2::iterator i=t.begin();i!=t.end();++i) {
1449        colBounds(*i, lower, upper);
1450      }
1451    }
1452    template<class T2>
1453    typename enable_if<typename T2::value_type::second_type::LpCol, void>::type
1454    colBounds(T2 &t, Value lower, Value upper,dummy<1> = 1) {
1455      for(typename T2::iterator i=t.begin();i!=t.end();++i) {
1456        colBounds(i->second, lower, upper);
1457      }
1458    }
1459    template<class T2>
1460    typename enable_if<typename T2::MapIt::Value::LpCol, void>::type
1461    colBounds(T2 &t, Value lower, Value upper,dummy<2> = 2) {
1462      for(typename T2::MapIt i(t); i!=INVALID; ++i){
1463        colBounds(*i, lower, upper);
1464      }
1465    }
1466#endif
1467
1468    /// Set the lower bound of a row (i.e a constraint)
1469
1470    /// The lower bound of a constraint (row) has to be given by an
1471    /// extended number of type Value, i.e. a finite number of type
1472    /// Value or -\ref INF.
1473    void rowLowerBound(Row r, Value value) {
1474      _setRowLowerBound(rows(id(r)),value);
1475    }
1476
1477    /// Get the lower bound of a row (i.e a constraint)
1478
1479    /// This function returns the lower bound for row (constraint) \c c
1480    /// (this might be -\ref INF as well).
1481    ///\return The lower bound for row \c r
1482    Value rowLowerBound(Row r) const {
1483      return _getRowLowerBound(rows(id(r)));
1484    }
1485
1486    /// Set the upper bound of a row (i.e a constraint)
1487
1488    /// The upper bound of a constraint (row) has to be given by an
1489    /// extended number of type Value, i.e. a finite number of type
1490    /// Value or -\ref INF.
1491    void rowUpperBound(Row r, Value value) {
1492      _setRowUpperBound(rows(id(r)),value);
1493    }
1494
1495    /// Get the upper bound of a row (i.e a constraint)
1496
1497    /// This function returns the upper bound for row (constraint) \c c
1498    /// (this might be -\ref INF as well).
1499    ///\return The upper bound for row \c r
1500    Value rowUpperBound(Row r) const {
1501      return _getRowUpperBound(rows(id(r)));
1502    }
1503
1504    ///Set an element of the objective function
1505    void objCoeff(Col c, Value v) {_setObjCoeff(cols(id(c)),v); };
1506
1507    ///Get an element of the objective function
1508    Value objCoeff(Col c) const { return _getObjCoeff(cols(id(c))); };
1509
1510    ///Set the objective function
1511
1512    ///\param e is a linear expression of type \ref Expr.
1513    ///
1514    void obj(const Expr& e) {
1515      _setObjCoeffs(ExprIterator(e.comps.begin(), cols),
1516                    ExprIterator(e.comps.end(), cols));
1517      obj_const_comp = *e;
1518    }
1519
1520    ///Get the objective function
1521
1522    ///\return the objective function as a linear expression of type
1523    ///Expr.
1524    Expr obj() const {
1525      Expr e;
1526      _getObjCoeffs(InsertIterator(e.comps, cols));
1527      *e = obj_const_comp;
1528      return e;
1529    }
1530
1531
1532    ///Set the direction of optimization
1533    void sense(Sense sense) { _setSense(sense); }
1534
1535    ///Query the direction of the optimization
1536    Sense sense() const {return _getSense(); }
1537
1538    ///Set the sense to maximization
1539    void max() { _setSense(MAX); }
1540
1541    ///Set the sense to maximization
1542    void min() { _setSense(MIN); }
1543
1544    ///Clears the problem
1545    void clear() { _clear(); }
1546
1547    /// Sets the message level of the solver
1548    void messageLevel(MessageLevel level) { _messageLevel(level); }
1549
1550    ///@}
1551
1552  };
1553
1554  /// Addition
1555
1556  ///\relates LpBase::Expr
1557  ///
1558  inline LpBase::Expr operator+(const LpBase::Expr &a, const LpBase::Expr &b) {
1559    LpBase::Expr tmp(a);
1560    tmp+=b;
1561    return tmp;
1562  }
1563  ///Substraction
1564
1565  ///\relates LpBase::Expr
1566  ///
1567  inline LpBase::Expr operator-(const LpBase::Expr &a, const LpBase::Expr &b) {
1568    LpBase::Expr tmp(a);
1569    tmp-=b;
1570    return tmp;
1571  }
1572  ///Multiply with constant
1573
1574  ///\relates LpBase::Expr
1575  ///
1576  inline LpBase::Expr operator*(const LpBase::Expr &a, const LpBase::Value &b) {
1577    LpBase::Expr tmp(a);
1578    tmp*=b;
1579    return tmp;
1580  }
1581
1582  ///Multiply with constant
1583
1584  ///\relates LpBase::Expr
1585  ///
1586  inline LpBase::Expr operator*(const LpBase::Value &a, const LpBase::Expr &b) {
1587    LpBase::Expr tmp(b);
1588    tmp*=a;
1589    return tmp;
1590  }
1591  ///Divide with constant
1592
1593  ///\relates LpBase::Expr
1594  ///
1595  inline LpBase::Expr operator/(const LpBase::Expr &a, const LpBase::Value &b) {
1596    LpBase::Expr tmp(a);
1597    tmp/=b;
1598    return tmp;
1599  }
1600
1601  ///Create constraint
1602
1603  ///\relates LpBase::Constr
1604  ///
1605  inline LpBase::Constr operator<=(const LpBase::Expr &e,
1606                                   const LpBase::Expr &f) {
1607    return LpBase::Constr(0, f - e, LpBase::INF);
1608  }
1609
1610  ///Create constraint
1611
1612  ///\relates LpBase::Constr
1613  ///
1614  inline LpBase::Constr operator<=(const LpBase::Value &e,
1615                                   const LpBase::Expr &f) {
1616    return LpBase::Constr(e, f, LpBase::NaN);
1617  }
1618
1619  ///Create constraint
1620
1621  ///\relates LpBase::Constr
1622  ///
1623  inline LpBase::Constr operator<=(const LpBase::Expr &e,
1624                                   const LpBase::Value &f) {
1625    return LpBase::Constr(- LpBase::INF, e, f);
1626  }
1627
1628  ///Create constraint
1629
1630  ///\relates LpBase::Constr
1631  ///
1632  inline LpBase::Constr operator>=(const LpBase::Expr &e,
1633                                   const LpBase::Expr &f) {
1634    return LpBase::Constr(0, e - f, LpBase::INF);
1635  }
1636
1637
1638  ///Create constraint
1639
1640  ///\relates LpBase::Constr
1641  ///
1642  inline LpBase::Constr operator>=(const LpBase::Value &e,
1643                                   const LpBase::Expr &f) {
1644    return LpBase::Constr(LpBase::NaN, f, e);
1645  }
1646
1647
1648  ///Create constraint
1649
1650  ///\relates LpBase::Constr
1651  ///
1652  inline LpBase::Constr operator>=(const LpBase::Expr &e,
1653                                   const LpBase::Value &f) {
1654    return LpBase::Constr(f, e, LpBase::INF);
1655  }
1656
1657  ///Create constraint
1658
1659  ///\relates LpBase::Constr
1660  ///
1661  inline LpBase::Constr operator==(const LpBase::Expr &e,
1662                                   const LpBase::Value &f) {
1663    return LpBase::Constr(f, e, f);
1664  }
1665
1666  ///Create constraint
1667
1668  ///\relates LpBase::Constr
1669  ///
1670  inline LpBase::Constr operator==(const LpBase::Expr &e,
1671                                   const LpBase::Expr &f) {
1672    return LpBase::Constr(0, f - e, 0);
1673  }
1674
1675  ///Create constraint
1676
1677  ///\relates LpBase::Constr
1678  ///
1679  inline LpBase::Constr operator<=(const LpBase::Value &n,
1680                                   const LpBase::Constr &c) {
1681    LpBase::Constr tmp(c);
1682    LEMON_ASSERT(isNaN(tmp.lowerBound()), "Wrong LP constraint");
1683    tmp.lowerBound()=n;
1684    return tmp;
1685  }
1686  ///Create constraint
1687
1688  ///\relates LpBase::Constr
1689  ///
1690  inline LpBase::Constr operator<=(const LpBase::Constr &c,
1691                                   const LpBase::Value &n)
1692  {
1693    LpBase::Constr tmp(c);
1694    LEMON_ASSERT(isNaN(tmp.upperBound()), "Wrong LP constraint");
1695    tmp.upperBound()=n;
1696    return tmp;
1697  }
1698
1699  ///Create constraint
1700
1701  ///\relates LpBase::Constr
1702  ///
1703  inline LpBase::Constr operator>=(const LpBase::Value &n,
1704                                   const LpBase::Constr &c) {
1705    LpBase::Constr tmp(c);
1706    LEMON_ASSERT(isNaN(tmp.upperBound()), "Wrong LP constraint");
1707    tmp.upperBound()=n;
1708    return tmp;
1709  }
1710  ///Create constraint
1711
1712  ///\relates LpBase::Constr
1713  ///
1714  inline LpBase::Constr operator>=(const LpBase::Constr &c,
1715                                   const LpBase::Value &n)
1716  {
1717    LpBase::Constr tmp(c);
1718    LEMON_ASSERT(isNaN(tmp.lowerBound()), "Wrong LP constraint");
1719    tmp.lowerBound()=n;
1720    return tmp;
1721  }
1722
1723  ///Addition
1724
1725  ///\relates LpBase::DualExpr
1726  ///
1727  inline LpBase::DualExpr operator+(const LpBase::DualExpr &a,
1728                                    const LpBase::DualExpr &b) {
1729    LpBase::DualExpr tmp(a);
1730    tmp+=b;
1731    return tmp;
1732  }
1733  ///Substraction
1734
1735  ///\relates LpBase::DualExpr
1736  ///
1737  inline LpBase::DualExpr operator-(const LpBase::DualExpr &a,
1738                                    const LpBase::DualExpr &b) {
1739    LpBase::DualExpr tmp(a);
1740    tmp-=b;
1741    return tmp;
1742  }
1743  ///Multiply with constant
1744
1745  ///\relates LpBase::DualExpr
1746  ///
1747  inline LpBase::DualExpr operator*(const LpBase::DualExpr &a,
1748                                    const LpBase::Value &b) {
1749    LpBase::DualExpr tmp(a);
1750    tmp*=b;
1751    return tmp;
1752  }
1753
1754  ///Multiply with constant
1755
1756  ///\relates LpBase::DualExpr
1757  ///
1758  inline LpBase::DualExpr operator*(const LpBase::Value &a,
1759                                    const LpBase::DualExpr &b) {
1760    LpBase::DualExpr tmp(b);
1761    tmp*=a;
1762    return tmp;
1763  }
1764  ///Divide with constant
1765
1766  ///\relates LpBase::DualExpr
1767  ///
1768  inline LpBase::DualExpr operator/(const LpBase::DualExpr &a,
1769                                    const LpBase::Value &b) {
1770    LpBase::DualExpr tmp(a);
1771    tmp/=b;
1772    return tmp;
1773  }
1774
1775  /// \ingroup lp_group
1776  ///
1777  /// \brief Common base class for LP solvers
1778  ///
1779  /// This class is an abstract base class for LP solvers. This class
1780  /// provides a full interface for set and modify an LP problem,
1781  /// solve it and retrieve the solution. You can use one of the
1782  /// descendants as a concrete implementation, or the \c Lp
1783  /// default LP solver. However, if you would like to handle LP
1784  /// solvers as reference or pointer in a generic way, you can use
1785  /// this class directly.
1786  class LpSolver : virtual public LpBase {
1787  public:
1788
1789    /// The problem types for primal and dual problems
1790    enum ProblemType {
1791      /// = 0. Feasible solution hasn't been found (but may exist).
1792      UNDEFINED = 0,
1793      /// = 1. The problem has no feasible solution.
1794      INFEASIBLE = 1,
1795      /// = 2. Feasible solution found.
1796      FEASIBLE = 2,
1797      /// = 3. Optimal solution exists and found.
1798      OPTIMAL = 3,
1799      /// = 4. The cost function is unbounded.
1800      UNBOUNDED = 4
1801    };
1802
1803    ///The basis status of variables
1804    enum VarStatus {
1805      /// The variable is in the basis
1806      BASIC,
1807      /// The variable is free, but not basic
1808      FREE,
1809      /// The variable has active lower bound
1810      LOWER,
1811      /// The variable has active upper bound
1812      UPPER,
1813      /// The variable is non-basic and fixed
1814      FIXED
1815    };
1816
1817  protected:
1818
1819    virtual SolveExitStatus _solve() = 0;
1820
1821    virtual Value _getPrimal(int i) const = 0;
1822    virtual Value _getDual(int i) const = 0;
1823
1824    virtual Value _getPrimalRay(int i) const = 0;
1825    virtual Value _getDualRay(int i) const = 0;
1826
1827    virtual Value _getPrimalValue() const = 0;
1828
1829    virtual VarStatus _getColStatus(int i) const = 0;
1830    virtual VarStatus _getRowStatus(int i) const = 0;
1831
1832    virtual ProblemType _getPrimalType() const = 0;
1833    virtual ProblemType _getDualType() const = 0;
1834
1835  public:
1836
1837    ///Allocate a new LP problem instance
1838    virtual LpSolver* newSolver() const = 0;
1839    ///Make a copy of the LP problem
1840    virtual LpSolver* cloneSolver() const = 0;
1841
1842    ///\name Solve the LP
1843
1844    ///@{
1845
1846    ///\e Solve the LP problem at hand
1847    ///
1848    ///\return The result of the optimization procedure. Possible
1849    ///values and their meanings can be found in the documentation of
1850    ///\ref SolveExitStatus.
1851    SolveExitStatus solve() { return _solve(); }
1852
1853    ///@}
1854
1855    ///\name Obtain the Solution
1856
1857    ///@{
1858
1859    /// The type of the primal problem
1860    ProblemType primalType() const {
1861      return _getPrimalType();
1862    }
1863
1864    /// The type of the dual problem
1865    ProblemType dualType() const {
1866      return _getDualType();
1867    }
1868
1869    /// Return the primal value of the column
1870
1871    /// Return the primal value of the column.
1872    /// \pre The problem is solved.
1873    Value primal(Col c) const { return _getPrimal(cols(id(c))); }
1874
1875    /// Return the primal value of the expression
1876
1877    /// Return the primal value of the expression, i.e. the dot
1878    /// product of the primal solution and the expression.
1879    /// \pre The problem is solved.
1880    Value primal(const Expr& e) const {
1881      double res = *e;
1882      for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {
1883        res += *c * primal(c);
1884      }
1885      return res;
1886    }
1887    /// Returns a component of the primal ray
1888   
1889    /// The primal ray is solution of the modified primal problem,
1890    /// where we change each finite bound to 0, and we looking for a
1891    /// negative objective value in case of minimization, and positive
1892    /// objective value for maximization. If there is such solution,
1893    /// that proofs the unsolvability of the dual problem, and if a
1894    /// feasible primal solution exists, then the unboundness of
1895    /// primal problem.
1896    ///
1897    /// \pre The problem is solved and the dual problem is infeasible.
1898    /// \note Some solvers does not provide primal ray calculation
1899    /// functions.
1900    Value primalRay(Col c) const { return _getPrimalRay(cols(id(c))); }
1901
1902    /// Return the dual value of the row
1903
1904    /// Return the dual value of the row.
1905    /// \pre The problem is solved.
1906    Value dual(Row r) const { return _getDual(rows(id(r))); }
1907
1908    /// Return the dual value of the dual expression
1909
1910    /// Return the dual value of the dual expression, i.e. the dot
1911    /// product of the dual solution and the dual expression.
1912    /// \pre The problem is solved.
1913    Value dual(const DualExpr& e) const {
1914      double res = 0.0;
1915      for (DualExpr::ConstCoeffIt r(e); r != INVALID; ++r) {
1916        res += *r * dual(r);
1917      }
1918      return res;
1919    }
1920
1921    /// Returns a component of the dual ray
1922   
1923    /// The dual ray is solution of the modified primal problem, where
1924    /// we change each finite bound to 0 (i.e. the objective function
1925    /// coefficients in the primal problem), and we looking for a
1926    /// ositive objective value. If there is such solution, that
1927    /// proofs the unsolvability of the primal problem, and if a
1928    /// feasible dual solution exists, then the unboundness of
1929    /// dual problem.
1930    ///
1931    /// \pre The problem is solved and the primal problem is infeasible.
1932    /// \note Some solvers does not provide dual ray calculation
1933    /// functions.
1934    Value dualRay(Row r) const { return _getDualRay(rows(id(r))); }
1935
1936    /// Return the basis status of the column
1937
1938    /// \see VarStatus
1939    VarStatus colStatus(Col c) const { return _getColStatus(cols(id(c))); }
1940
1941    /// Return the basis status of the row
1942
1943    /// \see VarStatus
1944    VarStatus rowStatus(Row r) const { return _getRowStatus(rows(id(r))); }
1945
1946    ///The value of the objective function
1947
1948    ///\return
1949    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
1950    /// of the primal problem, depending on whether we minimize or maximize.
1951    ///- \ref NaN if no primal solution is found.
1952    ///- The (finite) objective value if an optimal solution is found.
1953    Value primal() const { return _getPrimalValue()+obj_const_comp;}
1954    ///@}
1955
1956  protected:
1957
1958  };
1959
1960
1961  /// \ingroup lp_group
1962  ///
1963  /// \brief Common base class for MIP solvers
1964  ///
1965  /// This class is an abstract base class for MIP solvers. This class
1966  /// provides a full interface for set and modify an MIP problem,
1967  /// solve it and retrieve the solution. You can use one of the
1968  /// descendants as a concrete implementation, or the \c Lp
1969  /// default MIP solver. However, if you would like to handle MIP
1970  /// solvers as reference or pointer in a generic way, you can use
1971  /// this class directly.
1972  class MipSolver : virtual public LpBase {
1973  public:
1974
1975    /// The problem types for MIP problems
1976    enum ProblemType {
1977      /// = 0. Feasible solution hasn't been found (but may exist).
1978      UNDEFINED = 0,
1979      /// = 1. The problem has no feasible solution.
1980      INFEASIBLE = 1,
1981      /// = 2. Feasible solution found.
1982      FEASIBLE = 2,
1983      /// = 3. Optimal solution exists and found.
1984      OPTIMAL = 3,
1985      /// = 4. The cost function is unbounded.
1986      ///The Mip or at least the relaxed problem is unbounded.
1987      UNBOUNDED = 4
1988    };
1989
1990    ///Allocate a new MIP problem instance
1991    virtual MipSolver* newSolver() const = 0;
1992    ///Make a copy of the MIP problem
1993    virtual MipSolver* cloneSolver() const = 0;
1994
1995    ///\name Solve the MIP
1996
1997    ///@{
1998
1999    /// Solve the MIP problem at hand
2000    ///
2001    ///\return The result of the optimization procedure. Possible
2002    ///values and their meanings can be found in the documentation of
2003    ///\ref SolveExitStatus.
2004    SolveExitStatus solve() { return _solve(); }
2005
2006    ///@}
2007
2008    ///\name Set Column Type
2009    ///@{
2010
2011    ///Possible variable (column) types (e.g. real, integer, binary etc.)
2012    enum ColTypes {
2013      /// = 0. Continuous variable (default).
2014      REAL = 0,
2015      /// = 1. Integer variable.
2016      INTEGER = 1
2017    };
2018
2019    ///Sets the type of the given column to the given type
2020
2021    ///Sets the type of the given column to the given type.
2022    ///
2023    void colType(Col c, ColTypes col_type) {
2024      _setColType(cols(id(c)),col_type);
2025    }
2026
2027    ///Gives back the type of the column.
2028
2029    ///Gives back the type of the column.
2030    ///
2031    ColTypes colType(Col c) const {
2032      return _getColType(cols(id(c)));
2033    }
2034    ///@}
2035
2036    ///\name Obtain the Solution
2037
2038    ///@{
2039
2040    /// The type of the MIP problem
2041    ProblemType type() const {
2042      return _getType();
2043    }
2044
2045    /// Return the value of the row in the solution
2046
2047    ///  Return the value of the row in the solution.
2048    /// \pre The problem is solved.
2049    Value sol(Col c) const { return _getSol(cols(id(c))); }
2050
2051    /// Return the value of the expression in the solution
2052
2053    /// Return the value of the expression in the solution, i.e. the
2054    /// dot product of the solution and the expression.
2055    /// \pre The problem is solved.
2056    Value sol(const Expr& e) const {
2057      double res = *e;
2058      for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {
2059        res += *c * sol(c);
2060      }
2061      return res;
2062    }
2063    ///The value of the objective function
2064   
2065    ///\return
2066    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
2067    /// of the problem, depending on whether we minimize or maximize.
2068    ///- \ref NaN if no primal solution is found.
2069    ///- The (finite) objective value if an optimal solution is found.
2070    Value solValue() const { return _getSolValue()+obj_const_comp;}
2071    ///@}
2072
2073  protected:
2074
2075    virtual SolveExitStatus _solve() = 0;
2076    virtual ColTypes _getColType(int col) const = 0;
2077    virtual void _setColType(int col, ColTypes col_type) = 0;
2078    virtual ProblemType _getType() const = 0;
2079    virtual Value _getSol(int i) const = 0;
2080    virtual Value _getSolValue() const = 0;
2081
2082  };
2083
2084
2085
2086} //namespace lemon
2087
2088#endif //LEMON_LP_BASE_H
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