COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/lp_base.h @ 540:9db62975c32b

Last change on this file since 540:9db62975c32b was 540:9db62975c32b, checked in by Alpar Juttner <alpar@…>, 11 years ago

Fix newSolver()/cloneSolver() API in LP tools + doc improvements (#230)

  • More logical structure for newSolver()/cloneSolver()
  • Fix compilation problem with gcc-3.3
  • Doc improvements
File size: 60.4 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      ///This means that the problem has been successfully solved: either
56      ///an optimal solution has been found or infeasibility/unboundedness
57      ///has been proved.
58      SOLVED = 0,
59      ///Any other case (including the case when some user specified
60      ///limit has been exceeded)
61      UNSOLVED = 1
62    };
63
64    ///Direction of the optimization
65    enum Sense {
66      /// Minimization
67      MIN,
68      /// Maximization
69      MAX
70    };
71
72    ///The floating point type used by the solver
73    typedef double Value;
74    ///The infinity constant
75    static const Value INF;
76    ///The not a number constant
77    static const Value NaN;
78
79    friend class Col;
80    friend class ColIt;
81    friend class Row;
82    friend class RowIt;
83
84    ///Refer to a column of the LP.
85
86    ///This type is used to refer to a column of the LP.
87    ///
88    ///Its value remains valid and correct even after the addition or erase of
89    ///other columns.
90    ///
91    ///\note This class is similar to other Item types in LEMON, like
92    ///Node and Arc types in digraph.
93    class Col {
94      friend class LpBase;
95    protected:
96      int _id;
97      explicit Col(int id) : _id(id) {}
98    public:
99      typedef Value ExprValue;
100      typedef True LpCol;
101      /// Default constructor
102     
103      /// \warning The default constructor sets the Col to an
104      /// undefined value.
105      Col() {}
106      /// Invalid constructor \& conversion.
107     
108      /// This constructor initializes the Col to be invalid.
109      /// \sa Invalid for more details.     
110      Col(const Invalid&) : _id(-1) {}
111      /// Equality operator
112
113      /// Two \ref Col "Col"s are equal if and only if they point to
114      /// the same LP column or both are invalid.
115      bool operator==(Col c) const  {return _id == c._id;}
116      /// Inequality operator
117
118      /// \sa operator==(Col c)
119      ///
120      bool operator!=(Col c) const  {return _id != c._id;}
121      /// Artificial ordering operator.
122
123      /// To allow the use of this object in std::map or similar
124      /// associative container we require this.
125      ///
126      /// \note This operator only have to define some strict ordering of
127      /// the items; this order has nothing to do with the iteration
128      /// ordering of the items.
129      bool operator<(Col c) const  {return _id < c._id;}
130    };
131
132    ///Iterator for iterate over the columns of an LP problem
133
134    /// Its usage is quite simple, for example you can count the number
135    /// of columns in an LP \c lp:
136    ///\code
137    /// int count=0;
138    /// for (LpBase::ColIt c(lp); c!=INVALID; ++c) ++count;
139    ///\endcode
140    class ColIt : public Col {
141      const LpBase *_solver;
142    public:
143      /// Default constructor
144     
145      /// \warning The default constructor sets the iterator
146      /// to an undefined value.
147      ColIt() {}
148      /// Sets the iterator to the first Col
149     
150      /// Sets the iterator to the first Col.
151      ///
152      ColIt(const LpBase &solver) : _solver(&solver)
153      {
154        _solver->cols.firstItem(_id);
155      }
156      /// Invalid constructor \& conversion
157     
158      /// Initialize the iterator to be invalid.
159      /// \sa Invalid for more details.
160      ColIt(const Invalid&) : Col(INVALID) {}
161      /// Next column
162     
163      /// Assign the iterator to the next column.
164      ///
165      ColIt &operator++()
166      {
167        _solver->cols.nextItem(_id);
168        return *this;
169      }
170    };
171
172    /// \brief Returns the ID of the column.
173    static int id(const Col& col) { return col._id; }
174    /// \brief Returns the column with the given ID.
175    ///
176    /// \pre The argument should be a valid column ID in the LP problem.
177    static Col colFromId(int id) { return Col(id); }
178
179    ///Refer to a row of the LP.
180
181    ///This type is used to refer to a row of the LP.
182    ///
183    ///Its value remains valid and correct even after the addition or erase of
184    ///other rows.
185    ///
186    ///\note This class is similar to other Item types in LEMON, like
187    ///Node and Arc types in digraph.
188    class Row {
189      friend class LpBase;
190    protected:
191      int _id;
192      explicit Row(int id) : _id(id) {}
193    public:
194      typedef Value ExprValue;
195      typedef True LpRow;
196      /// Default constructor
197     
198      /// \warning The default constructor sets the Row to an
199      /// undefined value.
200      Row() {}
201      /// Invalid constructor \& conversion.
202     
203      /// This constructor initializes the Row to be invalid.
204      /// \sa Invalid for more details.     
205      Row(const Invalid&) : _id(-1) {}
206      /// Equality operator
207
208      /// Two \ref Row "Row"s are equal if and only if they point to
209      /// the same LP row or both are invalid.
210      bool operator==(Row r) const  {return _id == r._id;}
211      /// Inequality operator
212     
213      /// \sa operator==(Row r)
214      ///
215      bool operator!=(Row r) const  {return _id != r._id;}
216      /// Artificial ordering operator.
217
218      /// To allow the use of this object in std::map or similar
219      /// associative container we require this.
220      ///
221      /// \note This operator only have to define some strict ordering of
222      /// the items; this order has nothing to do with the iteration
223      /// ordering of the items.
224      bool operator<(Row r) const  {return _id < r._id;}
225    };
226
227    ///Iterator for iterate over the rows of an LP problem
228
229    /// Its usage is quite simple, for example you can count the number
230    /// of rows in an LP \c lp:
231    ///\code
232    /// int count=0;
233    /// for (LpBase::RowIt c(lp); c!=INVALID; ++c) ++count;
234    ///\endcode
235    class RowIt : public Row {
236      const LpBase *_solver;
237    public:
238      /// Default constructor
239     
240      /// \warning The default constructor sets the iterator
241      /// to an undefined value.
242      RowIt() {}
243      /// Sets the iterator to the first Row
244     
245      /// Sets the iterator to the first Row.
246      ///
247      RowIt(const LpBase &solver) : _solver(&solver)
248      {
249        _solver->rows.firstItem(_id);
250      }
251      /// Invalid constructor \& conversion
252     
253      /// Initialize the iterator to be invalid.
254      /// \sa Invalid for more details.
255      RowIt(const Invalid&) : Row(INVALID) {}
256      /// Next row
257     
258      /// Assign the iterator to the next row.
259      ///
260      RowIt &operator++()
261      {
262        _solver->rows.nextItem(_id);
263        return *this;
264      }
265    };
266
267    /// \brief Returns the ID of the row.
268    static int id(const Row& row) { return row._id; }
269    /// \brief Returns the row with the given ID.
270    ///
271    /// \pre The argument should be a valid row ID in the LP problem.
272    static Row rowFromId(int id) { return Row(id); }
273
274  public:
275
276    ///Linear expression of variables and a constant component
277
278    ///This data structure stores a linear expression of the variables
279    ///(\ref Col "Col"s) and also has a constant component.
280    ///
281    ///There are several ways to access and modify the contents of this
282    ///container.
283    ///\code
284    ///e[v]=5;
285    ///e[v]+=12;
286    ///e.erase(v);
287    ///\endcode
288    ///or you can also iterate through its elements.
289    ///\code
290    ///double s=0;
291    ///for(LpBase::Expr::ConstCoeffIt i(e);i!=INVALID;++i)
292    ///  s+=*i * primal(i);
293    ///\endcode
294    ///(This code computes the primal value of the expression).
295    ///- Numbers (<tt>double</tt>'s)
296    ///and variables (\ref Col "Col"s) directly convert to an
297    ///\ref Expr and the usual linear operations are defined, so
298    ///\code
299    ///v+w
300    ///2*v-3.12*(v-w/2)+2
301    ///v*2.1+(3*v+(v*12+w+6)*3)/2
302    ///\endcode
303    ///are valid expressions.
304    ///The usual assignment operations are also defined.
305    ///\code
306    ///e=v+w;
307    ///e+=2*v-3.12*(v-w/2)+2;
308    ///e*=3.4;
309    ///e/=5;
310    ///\endcode
311    ///- The constant member can be set and read by dereference
312    ///  operator (unary *)
313    ///
314    ///\code
315    ///*e=12;
316    ///double c=*e;
317    ///\endcode
318    ///
319    ///\sa Constr
320    class Expr {
321      friend class LpBase;
322    public:
323      /// The key type of the expression
324      typedef LpBase::Col Key;
325      /// The value type of the expression
326      typedef LpBase::Value Value;
327
328    protected:
329      Value const_comp;
330      std::map<int, Value> comps;
331
332    public:
333      typedef True SolverExpr;
334      /// Default constructor
335     
336      /// Construct an empty expression, the coefficients and
337      /// the constant component are initialized to zero.
338      Expr() : const_comp(0) {}
339      /// Construct an expression from a column
340
341      /// Construct an expression, which has a term with \c c variable
342      /// and 1.0 coefficient.
343      Expr(const Col &c) : const_comp(0) {
344        typedef std::map<int, Value>::value_type pair_type;
345        comps.insert(pair_type(id(c), 1));
346      }
347      /// Construct an expression from a constant
348
349      /// Construct an expression, which's constant component is \c v.
350      ///
351      Expr(const Value &v) : const_comp(v) {}
352      /// Returns the coefficient of the column
353      Value operator[](const Col& c) const {
354        std::map<int, Value>::const_iterator it=comps.find(id(c));
355        if (it != comps.end()) {
356          return it->second;
357        } else {
358          return 0;
359        }
360      }
361      /// Returns the coefficient of the column
362      Value& operator[](const Col& c) {
363        return comps[id(c)];
364      }
365      /// Sets the coefficient of the column
366      void set(const Col &c, const Value &v) {
367        if (v != 0.0) {
368          typedef std::map<int, Value>::value_type pair_type;
369          comps.insert(pair_type(id(c), v));
370        } else {
371          comps.erase(id(c));
372        }
373      }
374      /// Returns the constant component of the expression
375      Value& operator*() { return const_comp; }
376      /// Returns the constant component of the expression
377      const Value& operator*() const { return const_comp; }
378      /// \brief Removes the coefficients which's absolute value does
379      /// not exceed \c epsilon. It also sets to zero the constant
380      /// component, if it does not exceed epsilon in absolute value.
381      void simplify(Value epsilon = 0.0) {
382        std::map<int, Value>::iterator it=comps.begin();
383        while (it != comps.end()) {
384          std::map<int, Value>::iterator jt=it;
385          ++jt;
386          if (std::fabs((*it).second) <= epsilon) comps.erase(it);
387          it=jt;
388        }
389        if (std::fabs(const_comp) <= epsilon) const_comp = 0;
390      }
391
392      void simplify(Value epsilon = 0.0) const {
393        const_cast<Expr*>(this)->simplify(epsilon);
394      }
395
396      ///Sets all coefficients and the constant component to 0.
397      void clear() {
398        comps.clear();
399        const_comp=0;
400      }
401
402      ///Compound assignment
403      Expr &operator+=(const Expr &e) {
404        for (std::map<int, Value>::const_iterator it=e.comps.begin();
405             it!=e.comps.end(); ++it)
406          comps[it->first]+=it->second;
407        const_comp+=e.const_comp;
408        return *this;
409      }
410      ///Compound assignment
411      Expr &operator-=(const Expr &e) {
412        for (std::map<int, Value>::const_iterator it=e.comps.begin();
413             it!=e.comps.end(); ++it)
414          comps[it->first]-=it->second;
415        const_comp-=e.const_comp;
416        return *this;
417      }
418      ///Multiply with a constant
419      Expr &operator*=(const Value &v) {
420        for (std::map<int, Value>::iterator it=comps.begin();
421             it!=comps.end(); ++it)
422          it->second*=v;
423        const_comp*=v;
424        return *this;
425      }
426      ///Division with a constant
427      Expr &operator/=(const Value &c) {
428        for (std::map<int, Value>::iterator it=comps.begin();
429             it!=comps.end(); ++it)
430          it->second/=c;
431        const_comp/=c;
432        return *this;
433      }
434
435      ///Iterator over the expression
436     
437      ///The iterator iterates over the terms of the expression.
438      ///
439      ///\code
440      ///double s=0;
441      ///for(LpBase::Expr::CoeffIt i(e);i!=INVALID;++i)
442      ///  s+= *i * primal(i);
443      ///\endcode
444      class CoeffIt {
445      private:
446
447        std::map<int, Value>::iterator _it, _end;
448
449      public:
450
451        /// Sets the iterator to the first term
452       
453        /// Sets the iterator to the first term of the expression.
454        ///
455        CoeffIt(Expr& e)
456          : _it(e.comps.begin()), _end(e.comps.end()){}
457
458        /// Convert the iterator to the column of the term
459        operator Col() const {
460          return colFromId(_it->first);
461        }
462
463        /// Returns the coefficient of the term
464        Value& operator*() { return _it->second; }
465
466        /// Returns the coefficient of the term
467        const Value& operator*() const { return _it->second; }
468        /// Next term
469       
470        /// Assign the iterator to the next term.
471        ///
472        CoeffIt& operator++() { ++_it; return *this; }
473
474        /// Equality operator
475        bool operator==(Invalid) const { return _it == _end; }
476        /// Inequality operator
477        bool operator!=(Invalid) const { return _it != _end; }
478      };
479
480      /// Const iterator over the expression
481     
482      ///The iterator iterates over the terms of the expression.
483      ///
484      ///\code
485      ///double s=0;
486      ///for(LpBase::Expr::ConstCoeffIt i(e);i!=INVALID;++i)
487      ///  s+=*i * primal(i);
488      ///\endcode
489      class ConstCoeffIt {
490      private:
491
492        std::map<int, Value>::const_iterator _it, _end;
493
494      public:
495
496        /// Sets the iterator to the first term
497       
498        /// Sets the iterator to the first term of the expression.
499        ///
500        ConstCoeffIt(const Expr& e)
501          : _it(e.comps.begin()), _end(e.comps.end()){}
502
503        /// Convert the iterator to the column of the term
504        operator Col() const {
505          return colFromId(_it->first);
506        }
507
508        /// Returns the coefficient of the term
509        const Value& operator*() const { return _it->second; }
510
511        /// Next term
512       
513        /// Assign the iterator to the next term.
514        ///
515        ConstCoeffIt& operator++() { ++_it; return *this; }
516
517        /// Equality operator
518        bool operator==(Invalid) const { return _it == _end; }
519        /// Inequality operator
520        bool operator!=(Invalid) const { return _it != _end; }
521      };
522
523    };
524
525    ///Linear constraint
526
527    ///This data stucture represents a linear constraint in the LP.
528    ///Basically it is a linear expression with a lower or an upper bound
529    ///(or both). These parts of the constraint can be obtained by the member
530    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
531    ///respectively.
532    ///There are two ways to construct a constraint.
533    ///- You can set the linear expression and the bounds directly
534    ///  by the functions above.
535    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
536    ///  are defined between expressions, or even between constraints whenever
537    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
538    ///  \c s and \c t are numbers, then the followings are valid expressions
539    ///  and thus they can be used directly e.g. in \ref addRow() whenever
540    ///  it makes sense.
541    ///\code
542    ///  e<=s
543    ///  e<=f
544    ///  e==f
545    ///  s<=e<=t
546    ///  e>=t
547    ///\endcode
548    ///\warning The validity of a constraint is checked only at run
549    ///time, so e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will
550    ///compile, but will fail an assertion.
551    class Constr
552    {
553    public:
554      typedef LpBase::Expr Expr;
555      typedef Expr::Key Key;
556      typedef Expr::Value Value;
557
558    protected:
559      Expr _expr;
560      Value _lb,_ub;
561    public:
562      ///\e
563      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
564      ///\e
565      Constr(Value lb, const Expr &e, Value ub) :
566        _expr(e), _lb(lb), _ub(ub) {}
567      Constr(const Expr &e) :
568        _expr(e), _lb(NaN), _ub(NaN) {}
569      ///\e
570      void clear()
571      {
572        _expr.clear();
573        _lb=_ub=NaN;
574      }
575
576      ///Reference to the linear expression
577      Expr &expr() { return _expr; }
578      ///Cont reference to the linear expression
579      const Expr &expr() const { return _expr; }
580      ///Reference to the lower bound.
581
582      ///\return
583      ///- \ref INF "INF": the constraint is lower unbounded.
584      ///- \ref NaN "NaN": lower bound has not been set.
585      ///- finite number: the lower bound
586      Value &lowerBound() { return _lb; }
587      ///The const version of \ref lowerBound()
588      const Value &lowerBound() const { return _lb; }
589      ///Reference to the upper bound.
590
591      ///\return
592      ///- \ref INF "INF": the constraint is upper unbounded.
593      ///- \ref NaN "NaN": upper bound has not been set.
594      ///- finite number: the upper bound
595      Value &upperBound() { return _ub; }
596      ///The const version of \ref upperBound()
597      const Value &upperBound() const { return _ub; }
598      ///Is the constraint lower bounded?
599      bool lowerBounded() const {
600        return _lb != -INF && !isNaN(_lb);
601      }
602      ///Is the constraint upper bounded?
603      bool upperBounded() const {
604        return _ub != INF && !isNaN(_ub);
605      }
606
607    };
608
609    ///Linear expression of rows
610
611    ///This data structure represents a column of the matrix,
612    ///thas is it strores a linear expression of the dual variables
613    ///(\ref Row "Row"s).
614    ///
615    ///There are several ways to access and modify the contents of this
616    ///container.
617    ///\code
618    ///e[v]=5;
619    ///e[v]+=12;
620    ///e.erase(v);
621    ///\endcode
622    ///or you can also iterate through its elements.
623    ///\code
624    ///double s=0;
625    ///for(LpBase::DualExpr::ConstCoeffIt i(e);i!=INVALID;++i)
626    ///  s+=*i;
627    ///\endcode
628    ///(This code computes the sum of all coefficients).
629    ///- Numbers (<tt>double</tt>'s)
630    ///and variables (\ref Row "Row"s) directly convert to an
631    ///\ref DualExpr and the usual linear operations are defined, so
632    ///\code
633    ///v+w
634    ///2*v-3.12*(v-w/2)
635    ///v*2.1+(3*v+(v*12+w)*3)/2
636    ///\endcode
637    ///are valid \ref DualExpr dual expressions.
638    ///The usual assignment operations are also defined.
639    ///\code
640    ///e=v+w;
641    ///e+=2*v-3.12*(v-w/2);
642    ///e*=3.4;
643    ///e/=5;
644    ///\endcode
645    ///
646    ///\sa Expr
647    class DualExpr {
648      friend class LpBase;
649    public:
650      /// The key type of the expression
651      typedef LpBase::Row Key;
652      /// The value type of the expression
653      typedef LpBase::Value Value;
654
655    protected:
656      std::map<int, Value> comps;
657
658    public:
659      typedef True SolverExpr;
660      /// Default constructor
661     
662      /// Construct an empty expression, the coefficients are
663      /// initialized to zero.
664      DualExpr() {}
665      /// Construct an expression from a row
666
667      /// Construct an expression, which has a term with \c r dual
668      /// variable and 1.0 coefficient.
669      DualExpr(const Row &r) {
670        typedef std::map<int, Value>::value_type pair_type;
671        comps.insert(pair_type(id(r), 1));
672      }
673      /// Returns the coefficient of the row
674      Value operator[](const Row& r) const {
675        std::map<int, Value>::const_iterator it = comps.find(id(r));
676        if (it != comps.end()) {
677          return it->second;
678        } else {
679          return 0;
680        }
681      }
682      /// Returns the coefficient of the row
683      Value& operator[](const Row& r) {
684        return comps[id(r)];
685      }
686      /// Sets the coefficient of the row
687      void set(const Row &r, const Value &v) {
688        if (v != 0.0) {
689          typedef std::map<int, Value>::value_type pair_type;
690          comps.insert(pair_type(id(r), v));
691        } else {
692          comps.erase(id(r));
693        }
694      }
695      /// \brief Removes the coefficients which's absolute value does
696      /// not exceed \c epsilon.
697      void simplify(Value epsilon = 0.0) {
698        std::map<int, Value>::iterator it=comps.begin();
699        while (it != comps.end()) {
700          std::map<int, Value>::iterator jt=it;
701          ++jt;
702          if (std::fabs((*it).second) <= epsilon) comps.erase(it);
703          it=jt;
704        }
705      }
706
707      void simplify(Value epsilon = 0.0) const {
708        const_cast<DualExpr*>(this)->simplify(epsilon);
709      }
710
711      ///Sets all coefficients to 0.
712      void clear() {
713        comps.clear();
714      }
715      ///Compound assignment
716      DualExpr &operator+=(const DualExpr &e) {
717        for (std::map<int, Value>::const_iterator it=e.comps.begin();
718             it!=e.comps.end(); ++it)
719          comps[it->first]+=it->second;
720        return *this;
721      }
722      ///Compound assignment
723      DualExpr &operator-=(const DualExpr &e) {
724        for (std::map<int, Value>::const_iterator it=e.comps.begin();
725             it!=e.comps.end(); ++it)
726          comps[it->first]-=it->second;
727        return *this;
728      }
729      ///Multiply with a constant
730      DualExpr &operator*=(const Value &v) {
731        for (std::map<int, Value>::iterator it=comps.begin();
732             it!=comps.end(); ++it)
733          it->second*=v;
734        return *this;
735      }
736      ///Division with a constant
737      DualExpr &operator/=(const Value &v) {
738        for (std::map<int, Value>::iterator it=comps.begin();
739             it!=comps.end(); ++it)
740          it->second/=v;
741        return *this;
742      }
743
744      ///Iterator over the expression
745     
746      ///The iterator iterates over the terms of the expression.
747      ///
748      ///\code
749      ///double s=0;
750      ///for(LpBase::DualExpr::CoeffIt i(e);i!=INVALID;++i)
751      ///  s+= *i * dual(i);
752      ///\endcode
753      class CoeffIt {
754      private:
755
756        std::map<int, Value>::iterator _it, _end;
757
758      public:
759
760        /// Sets the iterator to the first term
761       
762        /// Sets the iterator to the first term of the expression.
763        ///
764        CoeffIt(DualExpr& e)
765          : _it(e.comps.begin()), _end(e.comps.end()){}
766
767        /// Convert the iterator to the row of the term
768        operator Row() const {
769          return rowFromId(_it->first);
770        }
771
772        /// Returns the coefficient of the term
773        Value& operator*() { return _it->second; }
774
775        /// Returns the coefficient of the term
776        const Value& operator*() const { return _it->second; }
777
778        /// Next term
779       
780        /// Assign the iterator to the next term.
781        ///
782        CoeffIt& operator++() { ++_it; return *this; }
783
784        /// Equality operator
785        bool operator==(Invalid) const { return _it == _end; }
786        /// Inequality operator
787        bool operator!=(Invalid) const { return _it != _end; }
788      };
789
790      ///Iterator over the expression
791     
792      ///The iterator iterates over the terms of the expression.
793      ///
794      ///\code
795      ///double s=0;
796      ///for(LpBase::DualExpr::ConstCoeffIt i(e);i!=INVALID;++i)
797      ///  s+= *i * dual(i);
798      ///\endcode
799      class ConstCoeffIt {
800      private:
801
802        std::map<int, Value>::const_iterator _it, _end;
803
804      public:
805
806        /// Sets the iterator to the first term
807       
808        /// Sets the iterator to the first term of the expression.
809        ///
810        ConstCoeffIt(const DualExpr& e)
811          : _it(e.comps.begin()), _end(e.comps.end()){}
812
813        /// Convert the iterator to the row of the term
814        operator Row() const {
815          return rowFromId(_it->first);
816        }
817
818        /// Returns the coefficient of the term
819        const Value& operator*() const { return _it->second; }
820
821        /// Next term
822       
823        /// Assign the iterator to the next term.
824        ///
825        ConstCoeffIt& operator++() { ++_it; return *this; }
826
827        /// Equality operator
828        bool operator==(Invalid) const { return _it == _end; }
829        /// Inequality operator
830        bool operator!=(Invalid) const { return _it != _end; }
831      };
832    };
833
834
835  protected:
836
837    class InsertIterator {
838    private:
839
840      std::map<int, Value>& _host;
841      const _solver_bits::VarIndex& _index;
842
843    public:
844
845      typedef std::output_iterator_tag iterator_category;
846      typedef void difference_type;
847      typedef void value_type;
848      typedef void reference;
849      typedef void pointer;
850
851      InsertIterator(std::map<int, Value>& host,
852                   const _solver_bits::VarIndex& index)
853        : _host(host), _index(index) {}
854
855      InsertIterator& operator=(const std::pair<int, Value>& value) {
856        typedef std::map<int, Value>::value_type pair_type;
857        _host.insert(pair_type(_index[value.first], value.second));
858        return *this;
859      }
860
861      InsertIterator& operator*() { return *this; }
862      InsertIterator& operator++() { return *this; }
863      InsertIterator operator++(int) { return *this; }
864
865    };
866
867    class ExprIterator {
868    private:
869      std::map<int, Value>::const_iterator _host_it;
870      const _solver_bits::VarIndex& _index;
871    public:
872
873      typedef std::bidirectional_iterator_tag iterator_category;
874      typedef std::ptrdiff_t difference_type;
875      typedef const std::pair<int, Value> value_type;
876      typedef value_type reference;
877
878      class pointer {
879      public:
880        pointer(value_type& _value) : value(_value) {}
881        value_type* operator->() { return &value; }
882      private:
883        value_type value;
884      };
885
886      ExprIterator(const std::map<int, Value>::const_iterator& host_it,
887                   const _solver_bits::VarIndex& index)
888        : _host_it(host_it), _index(index) {}
889
890      reference operator*() {
891        return std::make_pair(_index(_host_it->first), _host_it->second);
892      }
893
894      pointer operator->() {
895        return pointer(operator*());
896      }
897
898      ExprIterator& operator++() { ++_host_it; return *this; }
899      ExprIterator operator++(int) {
900        ExprIterator tmp(*this); ++_host_it; return tmp;
901      }
902
903      ExprIterator& operator--() { --_host_it; return *this; }
904      ExprIterator operator--(int) {
905        ExprIterator tmp(*this); --_host_it; return tmp;
906      }
907
908      bool operator==(const ExprIterator& it) const {
909        return _host_it == it._host_it;
910      }
911
912      bool operator!=(const ExprIterator& it) const {
913        return _host_it != it._host_it;
914      }
915
916    };
917
918  protected:
919
920    //Abstract virtual functions
921
922    virtual int _addColId(int col) { return cols.addIndex(col); }
923    virtual int _addRowId(int row) { return rows.addIndex(row); }
924
925    virtual void _eraseColId(int col) { cols.eraseIndex(col); }
926    virtual void _eraseRowId(int row) { rows.eraseIndex(row); }
927
928    virtual int _addCol() = 0;
929    virtual int _addRow() = 0;
930
931    virtual void _eraseCol(int col) = 0;
932    virtual void _eraseRow(int row) = 0;
933
934    virtual void _getColName(int col, std::string& name) const = 0;
935    virtual void _setColName(int col, const std::string& name) = 0;
936    virtual int _colByName(const std::string& name) const = 0;
937
938    virtual void _getRowName(int row, std::string& name) const = 0;
939    virtual void _setRowName(int row, const std::string& name) = 0;
940    virtual int _rowByName(const std::string& name) const = 0;
941
942    virtual void _setRowCoeffs(int i, ExprIterator b, ExprIterator e) = 0;
943    virtual void _getRowCoeffs(int i, InsertIterator b) const = 0;
944
945    virtual void _setColCoeffs(int i, ExprIterator b, ExprIterator e) = 0;
946    virtual void _getColCoeffs(int i, InsertIterator b) const = 0;
947
948    virtual void _setCoeff(int row, int col, Value value) = 0;
949    virtual Value _getCoeff(int row, int col) const = 0;
950
951    virtual void _setColLowerBound(int i, Value value) = 0;
952    virtual Value _getColLowerBound(int i) const = 0;
953
954    virtual void _setColUpperBound(int i, Value value) = 0;
955    virtual Value _getColUpperBound(int i) const = 0;
956
957    virtual void _setRowLowerBound(int i, Value value) = 0;
958    virtual Value _getRowLowerBound(int i) const = 0;
959
960    virtual void _setRowUpperBound(int i, Value value) = 0;
961    virtual Value _getRowUpperBound(int i) const = 0;
962
963    virtual void _setObjCoeffs(ExprIterator b, ExprIterator e) = 0;
964    virtual void _getObjCoeffs(InsertIterator b) const = 0;
965
966    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
967    virtual Value _getObjCoeff(int i) const = 0;
968
969    virtual void _setSense(Sense) = 0;
970    virtual Sense _getSense() const = 0;
971
972    virtual void _clear() = 0;
973
974    virtual const char* _solverName() const = 0;
975
976    //Own protected stuff
977
978    //Constant component of the objective function
979    Value obj_const_comp;
980
981    LpBase() : rows(), cols(), obj_const_comp(0) {}
982
983  public:
984
985    /// Virtual destructor
986    virtual ~LpBase() {}
987
988    ///Gives back the name of the solver.
989    const char* solverName() const {return _solverName();}
990
991    ///\name Build up and modify the LP
992
993    ///@{
994
995    ///Add a new empty column (i.e a new variable) to the LP
996    Col addCol() { Col c; c._id = _addColId(_addCol()); return c;}
997
998    ///\brief Adds several new columns (i.e variables) at once
999    ///
1000    ///This magic function takes a container as its argument and fills
1001    ///its elements with new columns (i.e. variables)
1002    ///\param t can be
1003    ///- a standard STL compatible iterable container with
1004    ///\ref Col as its \c values_type like
1005    ///\code
1006    ///std::vector<LpBase::Col>
1007    ///std::list<LpBase::Col>
1008    ///\endcode
1009    ///- a standard STL compatible iterable container with
1010    ///\ref Col as its \c mapped_type like
1011    ///\code
1012    ///std::map<AnyType,LpBase::Col>
1013    ///\endcode
1014    ///- an iterable lemon \ref concepts::WriteMap "write map" like
1015    ///\code
1016    ///ListGraph::NodeMap<LpBase::Col>
1017    ///ListGraph::ArcMap<LpBase::Col>
1018    ///\endcode
1019    ///\return The number of the created column.
1020#ifdef DOXYGEN
1021    template<class T>
1022    int addColSet(T &t) { return 0;}
1023#else
1024    template<class T>
1025    typename enable_if<typename T::value_type::LpCol,int>::type
1026    addColSet(T &t,dummy<0> = 0) {
1027      int s=0;
1028      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
1029      return s;
1030    }
1031    template<class T>
1032    typename enable_if<typename T::value_type::second_type::LpCol,
1033                       int>::type
1034    addColSet(T &t,dummy<1> = 1) {
1035      int s=0;
1036      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1037        i->second=addCol();
1038        s++;
1039      }
1040      return s;
1041    }
1042    template<class T>
1043    typename enable_if<typename T::MapIt::Value::LpCol,
1044                       int>::type
1045    addColSet(T &t,dummy<2> = 2) {
1046      int s=0;
1047      for(typename T::MapIt i(t); i!=INVALID; ++i)
1048        {
1049          i.set(addCol());
1050          s++;
1051        }
1052      return s;
1053    }
1054#endif
1055
1056    ///Set a column (i.e a dual constraint) of the LP
1057
1058    ///\param c is the column to be modified
1059    ///\param e is a dual linear expression (see \ref DualExpr)
1060    ///a better one.
1061    void col(Col c, const DualExpr &e) {
1062      e.simplify();
1063      _setColCoeffs(cols(id(c)), ExprIterator(e.comps.begin(), rows),
1064                    ExprIterator(e.comps.end(), rows));
1065    }
1066
1067    ///Get a column (i.e a dual constraint) of the LP
1068
1069    ///\param c is the column to get
1070    ///\return the dual expression associated to the column
1071    DualExpr col(Col c) const {
1072      DualExpr e;
1073      _getColCoeffs(cols(id(c)), InsertIterator(e.comps, rows));
1074      return e;
1075    }
1076
1077    ///Add a new column to the LP
1078
1079    ///\param e is a dual linear expression (see \ref DualExpr)
1080    ///\param o is the corresponding component of the objective
1081    ///function. It is 0 by default.
1082    ///\return The created column.
1083    Col addCol(const DualExpr &e, Value o = 0) {
1084      Col c=addCol();
1085      col(c,e);
1086      objCoeff(c,o);
1087      return c;
1088    }
1089
1090    ///Add a new empty row (i.e a new constraint) to the LP
1091
1092    ///This function adds a new empty row (i.e a new constraint) to the LP.
1093    ///\return The created row
1094    Row addRow() { Row r; r._id = _addRowId(_addRow()); return r;}
1095
1096    ///\brief Add several new rows (i.e constraints) at once
1097    ///
1098    ///This magic function takes a container as its argument and fills
1099    ///its elements with new row (i.e. variables)
1100    ///\param t can be
1101    ///- a standard STL compatible iterable container with
1102    ///\ref Row as its \c values_type like
1103    ///\code
1104    ///std::vector<LpBase::Row>
1105    ///std::list<LpBase::Row>
1106    ///\endcode
1107    ///- a standard STL compatible iterable container with
1108    ///\ref Row as its \c mapped_type like
1109    ///\code
1110    ///std::map<AnyType,LpBase::Row>
1111    ///\endcode
1112    ///- an iterable lemon \ref concepts::WriteMap "write map" like
1113    ///\code
1114    ///ListGraph::NodeMap<LpBase::Row>
1115    ///ListGraph::ArcMap<LpBase::Row>
1116    ///\endcode
1117    ///\return The number of rows created.
1118#ifdef DOXYGEN
1119    template<class T>
1120    int addRowSet(T &t) { return 0;}
1121#else
1122    template<class T>
1123    typename enable_if<typename T::value_type::LpRow,int>::type
1124    addRowSet(T &t, dummy<0> = 0) {
1125      int s=0;
1126      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
1127      return s;
1128    }
1129    template<class T>
1130    typename enable_if<typename T::value_type::second_type::LpRow, int>::type
1131    addRowSet(T &t, dummy<1> = 1) {
1132      int s=0;
1133      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1134        i->second=addRow();
1135        s++;
1136      }
1137      return s;
1138    }
1139    template<class T>
1140    typename enable_if<typename T::MapIt::Value::LpRow, int>::type
1141    addRowSet(T &t, dummy<2> = 2) {
1142      int s=0;
1143      for(typename T::MapIt i(t); i!=INVALID; ++i)
1144        {
1145          i.set(addRow());
1146          s++;
1147        }
1148      return s;
1149    }
1150#endif
1151
1152    ///Set a row (i.e a constraint) of the LP
1153
1154    ///\param r is the row to be modified
1155    ///\param l is lower bound (-\ref INF means no bound)
1156    ///\param e is a linear expression (see \ref Expr)
1157    ///\param u is the upper bound (\ref INF means no bound)
1158    void row(Row r, Value l, const Expr &e, Value u) {
1159      e.simplify();
1160      _setRowCoeffs(rows(id(r)), ExprIterator(e.comps.begin(), cols),
1161                    ExprIterator(e.comps.end(), cols));
1162      _setRowLowerBound(rows(id(r)),l - *e);
1163      _setRowUpperBound(rows(id(r)),u - *e);
1164    }
1165
1166    ///Set a row (i.e a constraint) of the LP
1167
1168    ///\param r is the row to be modified
1169    ///\param c is a linear expression (see \ref Constr)
1170    void row(Row r, const Constr &c) {
1171      row(r, c.lowerBounded()?c.lowerBound():-INF,
1172          c.expr(), c.upperBounded()?c.upperBound():INF);
1173    }
1174
1175
1176    ///Get a row (i.e a constraint) of the LP
1177
1178    ///\param r is the row to get
1179    ///\return the expression associated to the row
1180    Expr row(Row r) const {
1181      Expr e;
1182      _getRowCoeffs(rows(id(r)), InsertIterator(e.comps, cols));
1183      return e;
1184    }
1185
1186    ///Add a new row (i.e a new constraint) to the LP
1187
1188    ///\param l is the lower bound (-\ref INF means no bound)
1189    ///\param e is a linear expression (see \ref Expr)
1190    ///\param u is the upper bound (\ref INF means no bound)
1191    ///\return The created row.
1192    Row addRow(Value l,const Expr &e, Value u) {
1193      Row r=addRow();
1194      row(r,l,e,u);
1195      return r;
1196    }
1197
1198    ///Add a new row (i.e a new constraint) to the LP
1199
1200    ///\param c is a linear expression (see \ref Constr)
1201    ///\return The created row.
1202    Row addRow(const Constr &c) {
1203      Row r=addRow();
1204      row(r,c);
1205      return r;
1206    }
1207    ///Erase a column (i.e a variable) from the LP
1208
1209    ///\param c is the column to be deleted
1210    void erase(Col c) {
1211      _eraseCol(cols(id(c)));
1212      _eraseColId(cols(id(c)));
1213    }
1214    ///Erase a row (i.e a constraint) from the LP
1215
1216    ///\param r is the row to be deleted
1217    void erase(Row r) {
1218      _eraseRow(rows(id(r)));
1219      _eraseRowId(rows(id(r)));
1220    }
1221
1222    /// Get the name of a column
1223
1224    ///\param c is the coresponding column
1225    ///\return The name of the colunm
1226    std::string colName(Col c) const {
1227      std::string name;
1228      _getColName(cols(id(c)), name);
1229      return name;
1230    }
1231
1232    /// Set the name of a column
1233
1234    ///\param c is the coresponding column
1235    ///\param name The name to be given
1236    void colName(Col c, const std::string& name) {
1237      _setColName(cols(id(c)), name);
1238    }
1239
1240    /// Get the column by its name
1241
1242    ///\param name The name of the column
1243    ///\return the proper column or \c INVALID
1244    Col colByName(const std::string& name) const {
1245      int k = _colByName(name);
1246      return k != -1 ? Col(cols[k]) : Col(INVALID);
1247    }
1248
1249    /// Get the name of a row
1250
1251    ///\param r is the coresponding row
1252    ///\return The name of the row
1253    std::string rowName(Row r) const {
1254      std::string name;
1255      _getRowName(rows(id(r)), name);
1256      return name;
1257    }
1258
1259    /// Set the name of a row
1260
1261    ///\param r is the coresponding row
1262    ///\param name The name to be given
1263    void rowName(Row r, const std::string& name) {
1264      _setRowName(rows(id(r)), name);
1265    }
1266
1267    /// Get the row by its name
1268
1269    ///\param name The name of the row
1270    ///\return the proper row or \c INVALID
1271    Row rowByName(const std::string& name) const {
1272      int k = _rowByName(name);
1273      return k != -1 ? Row(rows[k]) : Row(INVALID);
1274    }
1275
1276    /// Set an element of the coefficient matrix of the LP
1277
1278    ///\param r is the row of the element to be modified
1279    ///\param c is the column of the element to be modified
1280    ///\param val is the new value of the coefficient
1281    void coeff(Row r, Col c, Value val) {
1282      _setCoeff(rows(id(r)),cols(id(c)), val);
1283    }
1284
1285    /// Get an element of the coefficient matrix of the LP
1286
1287    ///\param r is the row of the element
1288    ///\param c is the column of the element
1289    ///\return the corresponding coefficient
1290    Value coeff(Row r, Col c) const {
1291      return _getCoeff(rows(id(r)),cols(id(c)));
1292    }
1293
1294    /// Set the lower bound of a column (i.e a variable)
1295
1296    /// The lower bound of a variable (column) has to be given by an
1297    /// extended number of type Value, i.e. a finite number of type
1298    /// Value or -\ref INF.
1299    void colLowerBound(Col c, Value value) {
1300      _setColLowerBound(cols(id(c)),value);
1301    }
1302
1303    /// Get the lower bound of a column (i.e a variable)
1304
1305    /// This function returns the lower bound for column (variable) \c c
1306    /// (this might be -\ref INF as well).
1307    ///\return The lower bound for column \c c
1308    Value colLowerBound(Col c) const {
1309      return _getColLowerBound(cols(id(c)));
1310    }
1311
1312    ///\brief Set the lower bound of  several columns
1313    ///(i.e variables) at once
1314    ///
1315    ///This magic function takes a container as its argument
1316    ///and applies the function on all of its elements.
1317    ///The lower bound of a variable (column) has to be given by an
1318    ///extended number of type Value, i.e. a finite number of type
1319    ///Value or -\ref INF.
1320#ifdef DOXYGEN
1321    template<class T>
1322    void colLowerBound(T &t, Value value) { return 0;}
1323#else
1324    template<class T>
1325    typename enable_if<typename T::value_type::LpCol,void>::type
1326    colLowerBound(T &t, Value value,dummy<0> = 0) {
1327      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1328        colLowerBound(*i, value);
1329      }
1330    }
1331    template<class T>
1332    typename enable_if<typename T::value_type::second_type::LpCol,
1333                       void>::type
1334    colLowerBound(T &t, Value value,dummy<1> = 1) {
1335      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1336        colLowerBound(i->second, value);
1337      }
1338    }
1339    template<class T>
1340    typename enable_if<typename T::MapIt::Value::LpCol,
1341                       void>::type
1342    colLowerBound(T &t, Value value,dummy<2> = 2) {
1343      for(typename T::MapIt i(t); i!=INVALID; ++i){
1344        colLowerBound(*i, value);
1345      }
1346    }
1347#endif
1348
1349    /// Set the upper bound of a column (i.e a variable)
1350
1351    /// The upper bound of a variable (column) has to be given by an
1352    /// extended number of type Value, i.e. a finite number of type
1353    /// Value or \ref INF.
1354    void colUpperBound(Col c, Value value) {
1355      _setColUpperBound(cols(id(c)),value);
1356    };
1357
1358    /// Get the upper bound of a column (i.e a variable)
1359
1360    /// This function returns the upper bound for column (variable) \c c
1361    /// (this might be \ref INF as well).
1362    /// \return The upper bound for column \c c
1363    Value colUpperBound(Col c) const {
1364      return _getColUpperBound(cols(id(c)));
1365    }
1366
1367    ///\brief Set the upper bound of  several columns
1368    ///(i.e variables) at once
1369    ///
1370    ///This magic function takes a container as its argument
1371    ///and applies the function on all of its elements.
1372    ///The upper bound of a variable (column) has to be given by an
1373    ///extended number of type Value, i.e. a finite number of type
1374    ///Value or \ref INF.
1375#ifdef DOXYGEN
1376    template<class T>
1377    void colUpperBound(T &t, Value value) { return 0;}
1378#else
1379    template<class T1>
1380    typename enable_if<typename T1::value_type::LpCol,void>::type
1381    colUpperBound(T1 &t, Value value,dummy<0> = 0) {
1382      for(typename T1::iterator i=t.begin();i!=t.end();++i) {
1383        colUpperBound(*i, value);
1384      }
1385    }
1386    template<class T1>
1387    typename enable_if<typename T1::value_type::second_type::LpCol,
1388                       void>::type
1389    colUpperBound(T1 &t, Value value,dummy<1> = 1) {
1390      for(typename T1::iterator i=t.begin();i!=t.end();++i) {
1391        colUpperBound(i->second, value);
1392      }
1393    }
1394    template<class T1>
1395    typename enable_if<typename T1::MapIt::Value::LpCol,
1396                       void>::type
1397    colUpperBound(T1 &t, Value value,dummy<2> = 2) {
1398      for(typename T1::MapIt i(t); i!=INVALID; ++i){
1399        colUpperBound(*i, value);
1400      }
1401    }
1402#endif
1403
1404    /// Set the lower and the upper bounds of a column (i.e a variable)
1405
1406    /// The lower and the upper bounds of
1407    /// a variable (column) have to be given by an
1408    /// extended number of type Value, i.e. a finite number of type
1409    /// Value, -\ref INF or \ref INF.
1410    void colBounds(Col c, Value lower, Value upper) {
1411      _setColLowerBound(cols(id(c)),lower);
1412      _setColUpperBound(cols(id(c)),upper);
1413    }
1414
1415    ///\brief Set the lower and the upper bound of several columns
1416    ///(i.e variables) at once
1417    ///
1418    ///This magic function takes a container as its argument
1419    ///and applies the function on all of its elements.
1420    /// The lower and the upper bounds of
1421    /// a variable (column) have to be given by an
1422    /// extended number of type Value, i.e. a finite number of type
1423    /// Value, -\ref INF or \ref INF.
1424#ifdef DOXYGEN
1425    template<class T>
1426    void colBounds(T &t, Value lower, Value upper) { return 0;}
1427#else
1428    template<class T2>
1429    typename enable_if<typename T2::value_type::LpCol,void>::type
1430    colBounds(T2 &t, Value lower, Value upper,dummy<0> = 0) {
1431      for(typename T2::iterator i=t.begin();i!=t.end();++i) {
1432        colBounds(*i, lower, upper);
1433      }
1434    }
1435    template<class T2>
1436    typename enable_if<typename T2::value_type::second_type::LpCol, void>::type
1437    colBounds(T2 &t, Value lower, Value upper,dummy<1> = 1) {
1438      for(typename T2::iterator i=t.begin();i!=t.end();++i) {
1439        colBounds(i->second, lower, upper);
1440      }
1441    }
1442    template<class T2>
1443    typename enable_if<typename T2::MapIt::Value::LpCol, void>::type
1444    colBounds(T2 &t, Value lower, Value upper,dummy<2> = 2) {
1445      for(typename T2::MapIt i(t); i!=INVALID; ++i){
1446        colBounds(*i, lower, upper);
1447      }
1448    }
1449#endif
1450
1451    /// Set the lower bound of a row (i.e a constraint)
1452
1453    /// The lower bound of a constraint (row) has to be given by an
1454    /// extended number of type Value, i.e. a finite number of type
1455    /// Value or -\ref INF.
1456    void rowLowerBound(Row r, Value value) {
1457      _setRowLowerBound(rows(id(r)),value);
1458    }
1459
1460    /// Get the lower bound of a row (i.e a constraint)
1461
1462    /// This function returns the lower bound for row (constraint) \c c
1463    /// (this might be -\ref INF as well).
1464    ///\return The lower bound for row \c r
1465    Value rowLowerBound(Row r) const {
1466      return _getRowLowerBound(rows(id(r)));
1467    }
1468
1469    /// Set the upper bound of a row (i.e a constraint)
1470
1471    /// The upper bound of a constraint (row) has to be given by an
1472    /// extended number of type Value, i.e. a finite number of type
1473    /// Value or -\ref INF.
1474    void rowUpperBound(Row r, Value value) {
1475      _setRowUpperBound(rows(id(r)),value);
1476    }
1477
1478    /// Get the upper bound of a row (i.e a constraint)
1479
1480    /// This function returns the upper bound for row (constraint) \c c
1481    /// (this might be -\ref INF as well).
1482    ///\return The upper bound for row \c r
1483    Value rowUpperBound(Row r) const {
1484      return _getRowUpperBound(rows(id(r)));
1485    }
1486
1487    ///Set an element of the objective function
1488    void objCoeff(Col c, Value v) {_setObjCoeff(cols(id(c)),v); };
1489
1490    ///Get an element of the objective function
1491    Value objCoeff(Col c) const { return _getObjCoeff(cols(id(c))); };
1492
1493    ///Set the objective function
1494
1495    ///\param e is a linear expression of type \ref Expr.
1496    ///
1497    void obj(const Expr& e) {
1498      _setObjCoeffs(ExprIterator(e.comps.begin(), cols),
1499                    ExprIterator(e.comps.end(), cols));
1500      obj_const_comp = *e;
1501    }
1502
1503    ///Get the objective function
1504
1505    ///\return the objective function as a linear expression of type
1506    ///Expr.
1507    Expr obj() const {
1508      Expr e;
1509      _getObjCoeffs(InsertIterator(e.comps, cols));
1510      *e = obj_const_comp;
1511      return e;
1512    }
1513
1514
1515    ///Set the direction of optimization
1516    void sense(Sense sense) { _setSense(sense); }
1517
1518    ///Query the direction of the optimization
1519    Sense sense() const {return _getSense(); }
1520
1521    ///Set the sense to maximization
1522    void max() { _setSense(MAX); }
1523
1524    ///Set the sense to maximization
1525    void min() { _setSense(MIN); }
1526
1527    ///Clears the problem
1528    void clear() { _clear(); }
1529
1530    ///@}
1531
1532  };
1533
1534  /// Addition
1535
1536  ///\relates LpBase::Expr
1537  ///
1538  inline LpBase::Expr operator+(const LpBase::Expr &a, const LpBase::Expr &b) {
1539    LpBase::Expr tmp(a);
1540    tmp+=b;
1541    return tmp;
1542  }
1543  ///Substraction
1544
1545  ///\relates LpBase::Expr
1546  ///
1547  inline LpBase::Expr operator-(const LpBase::Expr &a, const LpBase::Expr &b) {
1548    LpBase::Expr tmp(a);
1549    tmp-=b;
1550    return tmp;
1551  }
1552  ///Multiply with constant
1553
1554  ///\relates LpBase::Expr
1555  ///
1556  inline LpBase::Expr operator*(const LpBase::Expr &a, const LpBase::Value &b) {
1557    LpBase::Expr tmp(a);
1558    tmp*=b;
1559    return tmp;
1560  }
1561
1562  ///Multiply with constant
1563
1564  ///\relates LpBase::Expr
1565  ///
1566  inline LpBase::Expr operator*(const LpBase::Value &a, const LpBase::Expr &b) {
1567    LpBase::Expr tmp(b);
1568    tmp*=a;
1569    return tmp;
1570  }
1571  ///Divide with constant
1572
1573  ///\relates LpBase::Expr
1574  ///
1575  inline LpBase::Expr operator/(const LpBase::Expr &a, const LpBase::Value &b) {
1576    LpBase::Expr tmp(a);
1577    tmp/=b;
1578    return tmp;
1579  }
1580
1581  ///Create constraint
1582
1583  ///\relates LpBase::Constr
1584  ///
1585  inline LpBase::Constr operator<=(const LpBase::Expr &e,
1586                                   const LpBase::Expr &f) {
1587    return LpBase::Constr(0, f - e, LpBase::INF);
1588  }
1589
1590  ///Create constraint
1591
1592  ///\relates LpBase::Constr
1593  ///
1594  inline LpBase::Constr operator<=(const LpBase::Value &e,
1595                                   const LpBase::Expr &f) {
1596    return LpBase::Constr(e, f, LpBase::NaN);
1597  }
1598
1599  ///Create constraint
1600
1601  ///\relates LpBase::Constr
1602  ///
1603  inline LpBase::Constr operator<=(const LpBase::Expr &e,
1604                                   const LpBase::Value &f) {
1605    return LpBase::Constr(- LpBase::INF, e, f);
1606  }
1607
1608  ///Create constraint
1609
1610  ///\relates LpBase::Constr
1611  ///
1612  inline LpBase::Constr operator>=(const LpBase::Expr &e,
1613                                   const LpBase::Expr &f) {
1614    return LpBase::Constr(0, e - f, LpBase::INF);
1615  }
1616
1617
1618  ///Create constraint
1619
1620  ///\relates LpBase::Constr
1621  ///
1622  inline LpBase::Constr operator>=(const LpBase::Value &e,
1623                                   const LpBase::Expr &f) {
1624    return LpBase::Constr(LpBase::NaN, f, e);
1625  }
1626
1627
1628  ///Create constraint
1629
1630  ///\relates LpBase::Constr
1631  ///
1632  inline LpBase::Constr operator>=(const LpBase::Expr &e,
1633                                   const LpBase::Value &f) {
1634    return LpBase::Constr(f, e, LpBase::INF);
1635  }
1636
1637  ///Create constraint
1638
1639  ///\relates LpBase::Constr
1640  ///
1641  inline LpBase::Constr operator==(const LpBase::Expr &e,
1642                                   const LpBase::Value &f) {
1643    return LpBase::Constr(f, e, f);
1644  }
1645
1646  ///Create constraint
1647
1648  ///\relates LpBase::Constr
1649  ///
1650  inline LpBase::Constr operator==(const LpBase::Expr &e,
1651                                   const LpBase::Expr &f) {
1652    return LpBase::Constr(0, f - e, 0);
1653  }
1654
1655  ///Create constraint
1656
1657  ///\relates LpBase::Constr
1658  ///
1659  inline LpBase::Constr operator<=(const LpBase::Value &n,
1660                                   const LpBase::Constr &c) {
1661    LpBase::Constr tmp(c);
1662    LEMON_ASSERT(isNaN(tmp.lowerBound()), "Wrong LP constraint");
1663    tmp.lowerBound()=n;
1664    return tmp;
1665  }
1666  ///Create constraint
1667
1668  ///\relates LpBase::Constr
1669  ///
1670  inline LpBase::Constr operator<=(const LpBase::Constr &c,
1671                                   const LpBase::Value &n)
1672  {
1673    LpBase::Constr tmp(c);
1674    LEMON_ASSERT(isNaN(tmp.upperBound()), "Wrong LP constraint");
1675    tmp.upperBound()=n;
1676    return tmp;
1677  }
1678
1679  ///Create constraint
1680
1681  ///\relates LpBase::Constr
1682  ///
1683  inline LpBase::Constr operator>=(const LpBase::Value &n,
1684                                   const LpBase::Constr &c) {
1685    LpBase::Constr tmp(c);
1686    LEMON_ASSERT(isNaN(tmp.upperBound()), "Wrong LP constraint");
1687    tmp.upperBound()=n;
1688    return tmp;
1689  }
1690  ///Create constraint
1691
1692  ///\relates LpBase::Constr
1693  ///
1694  inline LpBase::Constr operator>=(const LpBase::Constr &c,
1695                                   const LpBase::Value &n)
1696  {
1697    LpBase::Constr tmp(c);
1698    LEMON_ASSERT(isNaN(tmp.lowerBound()), "Wrong LP constraint");
1699    tmp.lowerBound()=n;
1700    return tmp;
1701  }
1702
1703  ///Addition
1704
1705  ///\relates LpBase::DualExpr
1706  ///
1707  inline LpBase::DualExpr operator+(const LpBase::DualExpr &a,
1708                                    const LpBase::DualExpr &b) {
1709    LpBase::DualExpr tmp(a);
1710    tmp+=b;
1711    return tmp;
1712  }
1713  ///Substraction
1714
1715  ///\relates LpBase::DualExpr
1716  ///
1717  inline LpBase::DualExpr operator-(const LpBase::DualExpr &a,
1718                                    const LpBase::DualExpr &b) {
1719    LpBase::DualExpr tmp(a);
1720    tmp-=b;
1721    return tmp;
1722  }
1723  ///Multiply with constant
1724
1725  ///\relates LpBase::DualExpr
1726  ///
1727  inline LpBase::DualExpr operator*(const LpBase::DualExpr &a,
1728                                    const LpBase::Value &b) {
1729    LpBase::DualExpr tmp(a);
1730    tmp*=b;
1731    return tmp;
1732  }
1733
1734  ///Multiply with constant
1735
1736  ///\relates LpBase::DualExpr
1737  ///
1738  inline LpBase::DualExpr operator*(const LpBase::Value &a,
1739                                    const LpBase::DualExpr &b) {
1740    LpBase::DualExpr tmp(b);
1741    tmp*=a;
1742    return tmp;
1743  }
1744  ///Divide with constant
1745
1746  ///\relates LpBase::DualExpr
1747  ///
1748  inline LpBase::DualExpr operator/(const LpBase::DualExpr &a,
1749                                    const LpBase::Value &b) {
1750    LpBase::DualExpr tmp(a);
1751    tmp/=b;
1752    return tmp;
1753  }
1754
1755  /// \ingroup lp_group
1756  ///
1757  /// \brief Common base class for LP solvers
1758  ///
1759  /// This class is an abstract base class for LP solvers. This class
1760  /// provides a full interface for set and modify an LP problem,
1761  /// solve it and retrieve the solution. You can use one of the
1762  /// descendants as a concrete implementation, or the \c Lp
1763  /// default LP solver. However, if you would like to handle LP
1764  /// solvers as reference or pointer in a generic way, you can use
1765  /// this class directly.
1766  class LpSolver : virtual public LpBase {
1767  public:
1768
1769    /// The problem types for primal and dual problems
1770    enum ProblemType {
1771      ///Feasible solution hasn't been found (but may exist).
1772      UNDEFINED = 0,
1773      ///The problem has no feasible solution
1774      INFEASIBLE = 1,
1775      ///Feasible solution found
1776      FEASIBLE = 2,
1777      ///Optimal solution exists and found
1778      OPTIMAL = 3,
1779      ///The cost function is unbounded
1780      UNBOUNDED = 4
1781    };
1782
1783    ///The basis status of variables
1784    enum VarStatus {
1785      /// The variable is in the basis
1786      BASIC,
1787      /// The variable is free, but not basic
1788      FREE,
1789      /// The variable has active lower bound
1790      LOWER,
1791      /// The variable has active upper bound
1792      UPPER,
1793      /// The variable is non-basic and fixed
1794      FIXED
1795    };
1796
1797  protected:
1798
1799    virtual SolveExitStatus _solve() = 0;
1800
1801    virtual Value _getPrimal(int i) const = 0;
1802    virtual Value _getDual(int i) const = 0;
1803
1804    virtual Value _getPrimalRay(int i) const = 0;
1805    virtual Value _getDualRay(int i) const = 0;
1806
1807    virtual Value _getPrimalValue() const = 0;
1808
1809    virtual VarStatus _getColStatus(int i) const = 0;
1810    virtual VarStatus _getRowStatus(int i) const = 0;
1811
1812    virtual ProblemType _getPrimalType() const = 0;
1813    virtual ProblemType _getDualType() const = 0;
1814
1815  public:
1816
1817    ///Allocate a new LP problem instance
1818    virtual LpSolver* newSolver() const = 0;
1819    ///Make a copy of the LP problem
1820    virtual LpSolver* cloneSolver() const = 0;
1821
1822    ///\name Solve the LP
1823
1824    ///@{
1825
1826    ///\e Solve the LP problem at hand
1827    ///
1828    ///\return The result of the optimization procedure. Possible
1829    ///values and their meanings can be found in the documentation of
1830    ///\ref SolveExitStatus.
1831    SolveExitStatus solve() { return _solve(); }
1832
1833    ///@}
1834
1835    ///\name Obtain the solution
1836
1837    ///@{
1838
1839    /// The type of the primal problem
1840    ProblemType primalType() const {
1841      return _getPrimalType();
1842    }
1843
1844    /// The type of the dual problem
1845    ProblemType dualType() const {
1846      return _getDualType();
1847    }
1848
1849    /// Return the primal value of the column
1850
1851    /// Return the primal value of the column.
1852    /// \pre The problem is solved.
1853    Value primal(Col c) const { return _getPrimal(cols(id(c))); }
1854
1855    /// Return the primal value of the expression
1856
1857    /// Return the primal value of the expression, i.e. the dot
1858    /// product of the primal solution and the expression.
1859    /// \pre The problem is solved.
1860    Value primal(const Expr& e) const {
1861      double res = *e;
1862      for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {
1863        res += *c * primal(c);
1864      }
1865      return res;
1866    }
1867    /// Returns a component of the primal ray
1868   
1869    /// The primal ray is solution of the modified primal problem,
1870    /// where we change each finite bound to 0, and we looking for a
1871    /// negative objective value in case of minimization, and positive
1872    /// objective value for maximization. If there is such solution,
1873    /// that proofs the unsolvability of the dual problem, and if a
1874    /// feasible primal solution exists, then the unboundness of
1875    /// primal problem.
1876    ///
1877    /// \pre The problem is solved and the dual problem is infeasible.
1878    /// \note Some solvers does not provide primal ray calculation
1879    /// functions.
1880    Value primalRay(Col c) const { return _getPrimalRay(cols(id(c))); }
1881
1882    /// Return the dual value of the row
1883
1884    /// Return the dual value of the row.
1885    /// \pre The problem is solved.
1886    Value dual(Row r) const { return _getDual(rows(id(r))); }
1887
1888    /// Return the dual value of the dual expression
1889
1890    /// Return the dual value of the dual expression, i.e. the dot
1891    /// product of the dual solution and the dual expression.
1892    /// \pre The problem is solved.
1893    Value dual(const DualExpr& e) const {
1894      double res = 0.0;
1895      for (DualExpr::ConstCoeffIt r(e); r != INVALID; ++r) {
1896        res += *r * dual(r);
1897      }
1898      return res;
1899    }
1900
1901    /// Returns a component of the dual ray
1902   
1903    /// The dual ray is solution of the modified primal problem, where
1904    /// we change each finite bound to 0 (i.e. the objective function
1905    /// coefficients in the primal problem), and we looking for a
1906    /// ositive objective value. If there is such solution, that
1907    /// proofs the unsolvability of the primal problem, and if a
1908    /// feasible dual solution exists, then the unboundness of
1909    /// dual problem.
1910    ///
1911    /// \pre The problem is solved and the primal problem is infeasible.
1912    /// \note Some solvers does not provide dual ray calculation
1913    /// functions.
1914    Value dualRay(Row r) const { return _getDualRay(rows(id(r))); }
1915
1916    /// Return the basis status of the column
1917
1918    /// \see VarStatus
1919    VarStatus colStatus(Col c) const { return _getColStatus(cols(id(c))); }
1920
1921    /// Return the basis status of the row
1922
1923    /// \see VarStatus
1924    VarStatus rowStatus(Row r) const { return _getRowStatus(rows(id(r))); }
1925
1926    ///The value of the objective function
1927
1928    ///\return
1929    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
1930    /// of the primal problem, depending on whether we minimize or maximize.
1931    ///- \ref NaN if no primal solution is found.
1932    ///- The (finite) objective value if an optimal solution is found.
1933    Value primal() const { return _getPrimalValue()+obj_const_comp;}
1934    ///@}
1935
1936  protected:
1937
1938  };
1939
1940
1941  /// \ingroup lp_group
1942  ///
1943  /// \brief Common base class for MIP solvers
1944  ///
1945  /// This class is an abstract base class for MIP solvers. This class
1946  /// provides a full interface for set and modify an MIP problem,
1947  /// solve it and retrieve the solution. You can use one of the
1948  /// descendants as a concrete implementation, or the \c Lp
1949  /// default MIP solver. However, if you would like to handle MIP
1950  /// solvers as reference or pointer in a generic way, you can use
1951  /// this class directly.
1952  class MipSolver : virtual public LpBase {
1953  public:
1954
1955    /// The problem types for MIP problems
1956    enum ProblemType {
1957      ///Feasible solution hasn't been found (but may exist).
1958      UNDEFINED = 0,
1959      ///The problem has no feasible solution
1960      INFEASIBLE = 1,
1961      ///Feasible solution found
1962      FEASIBLE = 2,
1963      ///Optimal solution exists and found
1964      OPTIMAL = 3,
1965      ///The cost function is unbounded
1966      ///
1967      ///The Mip or at least the relaxed problem is unbounded
1968      UNBOUNDED = 4
1969    };
1970
1971    ///Allocate a new MIP problem instance
1972    virtual MipSolver* newSolver() const = 0;
1973    ///Make a copy of the MIP problem
1974    virtual MipSolver* cloneSolver() const = 0;
1975
1976    ///\name Solve the MIP
1977
1978    ///@{
1979
1980    /// Solve the MIP problem at hand
1981    ///
1982    ///\return The result of the optimization procedure. Possible
1983    ///values and their meanings can be found in the documentation of
1984    ///\ref SolveExitStatus.
1985    SolveExitStatus solve() { return _solve(); }
1986
1987    ///@}
1988
1989    ///\name Setting column type
1990    ///@{
1991
1992    ///Possible variable (column) types (e.g. real, integer, binary etc.)
1993    enum ColTypes {
1994      ///Continuous variable (default)
1995      REAL = 0,
1996      ///Integer variable
1997      INTEGER = 1
1998    };
1999
2000    ///Sets the type of the given column to the given type
2001
2002    ///Sets the type of the given column to the given type.
2003    ///
2004    void colType(Col c, ColTypes col_type) {
2005      _setColType(cols(id(c)),col_type);
2006    }
2007
2008    ///Gives back the type of the column.
2009
2010    ///Gives back the type of the column.
2011    ///
2012    ColTypes colType(Col c) const {
2013      return _getColType(cols(id(c)));
2014    }
2015    ///@}
2016
2017    ///\name Obtain the solution
2018
2019    ///@{
2020
2021    /// The type of the MIP problem
2022    ProblemType type() const {
2023      return _getType();
2024    }
2025
2026    /// Return the value of the row in the solution
2027
2028    ///  Return the value of the row in the solution.
2029    /// \pre The problem is solved.
2030    Value sol(Col c) const { return _getSol(cols(id(c))); }
2031
2032    /// Return the value of the expression in the solution
2033
2034    /// Return the value of the expression in the solution, i.e. the
2035    /// dot product of the solution and the expression.
2036    /// \pre The problem is solved.
2037    Value sol(const Expr& e) const {
2038      double res = *e;
2039      for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {
2040        res += *c * sol(c);
2041      }
2042      return res;
2043    }
2044    ///The value of the objective function
2045   
2046    ///\return
2047    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
2048    /// of the problem, depending on whether we minimize or maximize.
2049    ///- \ref NaN if no primal solution is found.
2050    ///- The (finite) objective value if an optimal solution is found.
2051    Value solValue() const { return _getSolValue()+obj_const_comp;}
2052    ///@}
2053
2054  protected:
2055
2056    virtual SolveExitStatus _solve() = 0;
2057    virtual ColTypes _getColType(int col) const = 0;
2058    virtual void _setColType(int col, ColTypes col_type) = 0;
2059    virtual ProblemType _getType() const = 0;
2060    virtual Value _getSol(int i) const = 0;
2061    virtual Value _getSolValue() const = 0;
2062
2063  };
2064
2065
2066
2067} //namespace lemon
2068
2069#endif //LEMON_LP_BASE_H
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