COIN-OR::LEMON - Graph Library

source: lemon/lemon/lp_base.h @ 1270:dceba191c00d

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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) 2003-2013
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_LP_BASE_H
20#define LEMON_LP_BASE_H
21
22#include<iostream>
23#include<vector>
24#include<map>
25#include<limits>
26#include<lemon/math.h>
27
28#include<lemon/error.h>
29#include<lemon/assert.h>
30
31#include<lemon/core.h>
32#include<lemon/bits/solver_bits.h>
33
34///\file
35///\brief The interface of the LP solver interface.
36///\ingroup lp_group
37namespace lemon {
38
39  ///Common base class for LP and MIP solvers
40
41  ///Usually this class is not used directly, please use one of the concrete
42  ///implementations of the solver interface.
43  ///\ingroup lp_group
44  class LpBase {
45
46  protected:
47
48    _solver_bits::VarIndex rows;
49    _solver_bits::VarIndex cols;
50
51  public:
52
53    ///Possible outcomes of an LP solving procedure
54    enum SolveExitStatus {
55      /// = 0. It means that the problem has been successfully solved: either
56      ///an optimal solution has been found or infeasibility/unboundedness
57      ///has been proved.
58      SOLVED = 0,
59      /// = 1. Any other case (including the case when some user specified
60      ///limit has been exceeded).
61      UNSOLVED = 1
62    };
63
64    ///Direction of the optimization
65    enum Sense {
66      /// Minimization
67      MIN,
68      /// Maximization
69      MAX
70    };
71
72    ///Enum for \c messageLevel() parameter
73    enum MessageLevel {
74      /// No output (default value).
75      MESSAGE_NOTHING,
76      /// Error messages only.
77      MESSAGE_ERROR,
78      /// Warnings.
79      MESSAGE_WARNING,
80      /// Normal output.
81      MESSAGE_NORMAL,
82      /// Verbose output.
83      MESSAGE_VERBOSE
84    };
85
86
87    ///The floating point type used by the solver
88    typedef double Value;
89    ///The infinity constant
90    static const Value INF;
91    ///The not a number constant
92    static const Value NaN;
93
94    friend class Col;
95    friend class ColIt;
96    friend class Row;
97    friend class RowIt;
98
99    ///Refer to a column of the LP.
100
101    ///This type is used to refer to a column of the LP.
102    ///
103    ///Its value remains valid and correct even after the addition or erase of
104    ///other columns.
105    ///
106    ///\note This class is similar to other Item types in LEMON, like
107    ///Node and Arc types in digraph.
108    class Col {
109      friend class LpBase;
110    protected:
111      int _id;
112      explicit Col(int id) : _id(id) {}
113    public:
114      typedef Value ExprValue;
115      typedef True LpCol;
116      /// Default constructor
117
118      /// \warning The default constructor sets the Col to an
119      /// undefined value.
120      Col() {}
121      /// Invalid constructor \& conversion.
122
123      /// This constructor initializes the Col to be invalid.
124      /// \sa Invalid for more details.
125      Col(const Invalid&) : _id(-1) {}
126      /// Equality operator
127
128      /// Two \ref Col "Col"s are equal if and only if they point to
129      /// the same LP column or both are invalid.
130      bool operator==(Col c) const  {return _id == c._id;}
131      /// Inequality operator
132
133      /// \sa operator==(Col c)
134      ///
135      bool operator!=(Col c) const  {return _id != c._id;}
136      /// Artificial ordering operator.
137
138      /// To allow the use of this object in std::map or similar
139      /// associative container we require this.
140      ///
141      /// \note This operator only have to define some strict ordering of
142      /// the items; this order has nothing to do with the iteration
143      /// ordering of the items.
144      bool operator<(Col c) const  {return _id < c._id;}
145    };
146
147    ///Iterator for iterate over the columns of an LP problem
148
149    /// Its usage is quite simple, for example, you can count the number
150    /// of columns in an LP \c lp:
151    ///\code
152    /// int count=0;
153    /// for (LpBase::ColIt c(lp); c!=INVALID; ++c) ++count;
154    ///\endcode
155    class ColIt : public Col {
156      const LpBase *_solver;
157    public:
158      /// Default constructor
159
160      /// \warning The default constructor sets the iterator
161      /// to an undefined value.
162      ColIt() {}
163      /// Sets the iterator to the first Col
164
165      /// Sets the iterator to the first Col.
166      ///
167      ColIt(const LpBase &solver) : _solver(&solver)
168      {
169        _solver->cols.firstItem(_id);
170      }
171      /// Invalid constructor \& conversion
172
173      /// Initialize the iterator to be invalid.
174      /// \sa Invalid for more details.
175      ColIt(const Invalid&) : Col(INVALID) {}
176      /// Next column
177
178      /// Assign the iterator to the next column.
179      ///
180      ColIt &operator++()
181      {
182        _solver->cols.nextItem(_id);
183        return *this;
184      }
185    };
186
187    /// \brief Returns the ID of the column.
188    static int id(const Col& col) { return col._id; }
189    /// \brief Returns the column with the given ID.
190    ///
191    /// \pre The argument should be a valid column ID in the LP problem.
192    static Col colFromId(int id) { return Col(id); }
193
194    ///Refer to a row of the LP.
195
196    ///This type is used to refer to a row of the LP.
197    ///
198    ///Its value remains valid and correct even after the addition or erase of
199    ///other rows.
200    ///
201    ///\note This class is similar to other Item types in LEMON, like
202    ///Node and Arc types in digraph.
203    class Row {
204      friend class LpBase;
205    protected:
206      int _id;
207      explicit Row(int id) : _id(id) {}
208    public:
209      typedef Value ExprValue;
210      typedef True LpRow;
211      /// Default constructor
212
213      /// \warning The default constructor sets the Row to an
214      /// undefined value.
215      Row() {}
216      /// Invalid constructor \& conversion.
217
218      /// This constructor initializes the Row to be invalid.
219      /// \sa Invalid for more details.
220      Row(const Invalid&) : _id(-1) {}
221      /// Equality operator
222
223      /// Two \ref Row "Row"s are equal if and only if they point to
224      /// the same LP row or both are invalid.
225      bool operator==(Row r) const  {return _id == r._id;}
226      /// Inequality operator
227
228      /// \sa operator==(Row r)
229      ///
230      bool operator!=(Row r) const  {return _id != r._id;}
231      /// Artificial ordering operator.
232
233      /// To allow the use of this object in std::map or similar
234      /// associative container we require this.
235      ///
236      /// \note This operator only have to define some strict ordering of
237      /// the items; this order has nothing to do with the iteration
238      /// ordering of the items.
239      bool operator<(Row r) const  {return _id < r._id;}
240    };
241
242    ///Iterator for iterate over the rows of an LP problem
243
244    /// Its usage is quite simple, for example, you can count the number
245    /// of rows in an LP \c lp:
246    ///\code
247    /// int count=0;
248    /// for (LpBase::RowIt c(lp); c!=INVALID; ++c) ++count;
249    ///\endcode
250    class RowIt : public Row {
251      const LpBase *_solver;
252    public:
253      /// Default constructor
254
255      /// \warning The default constructor sets the iterator
256      /// to an undefined value.
257      RowIt() {}
258      /// Sets the iterator to the first Row
259
260      /// Sets the iterator to the first Row.
261      ///
262      RowIt(const LpBase &solver) : _solver(&solver)
263      {
264        _solver->rows.firstItem(_id);
265      }
266      /// Invalid constructor \& conversion
267
268      /// Initialize the iterator to be invalid.
269      /// \sa Invalid for more details.
270      RowIt(const Invalid&) : Row(INVALID) {}
271      /// Next row
272
273      /// Assign the iterator to the next row.
274      ///
275      RowIt &operator++()
276      {
277        _solver->rows.nextItem(_id);
278        return *this;
279      }
280    };
281
282    /// \brief Returns the ID of the row.
283    static int id(const Row& row) { return row._id; }
284    /// \brief Returns the row with the given ID.
285    ///
286    /// \pre The argument should be a valid row ID in the LP problem.
287    static Row rowFromId(int id) { return Row(id); }
288
289  public:
290
291    ///Linear expression of variables and a constant component
292
293    ///This data structure stores a linear expression of the variables
294    ///(\ref Col "Col"s) and also has a constant component.
295    ///
296    ///There are several ways to access and modify the contents of this
297    ///container.
298    ///\code
299    ///e[v]=5;
300    ///e[v]+=12;
301    ///e.erase(v);
302    ///\endcode
303    ///or you can also iterate through its elements.
304    ///\code
305    ///double s=0;
306    ///for(LpBase::Expr::ConstCoeffIt i(e);i!=INVALID;++i)
307    ///  s+=*i * primal(i);
308    ///\endcode
309    ///(This code computes the primal value of the expression).
310    ///- Numbers (<tt>double</tt>'s)
311    ///and variables (\ref Col "Col"s) directly convert to an
312    ///\ref Expr and the usual linear operations are defined, so
313    ///\code
314    ///v+w
315    ///2*v-3.12*(v-w/2)+2
316    ///v*2.1+(3*v+(v*12+w+6)*3)/2
317    ///\endcode
318    ///are valid expressions.
319    ///The usual assignment operations are also defined.
320    ///\code
321    ///e=v+w;
322    ///e+=2*v-3.12*(v-w/2)+2;
323    ///e*=3.4;
324    ///e/=5;
325    ///\endcode
326    ///- The constant member can be set and read by dereference
327    ///  operator (unary *)
328    ///
329    ///\code
330    ///*e=12;
331    ///double c=*e;
332    ///\endcode
333    ///
334    ///\sa Constr
335    class Expr {
336      friend class LpBase;
337    public:
338      /// The key type of the expression
339      typedef LpBase::Col Key;
340      /// The value type of the expression
341      typedef LpBase::Value Value;
342
343    protected:
344      Value const_comp;
345      std::map<int, Value> comps;
346
347    public:
348      typedef True SolverExpr;
349      /// Default constructor
350
351      /// Construct an empty expression, the coefficients and
352      /// the constant component are initialized to zero.
353      Expr() : const_comp(0) {}
354      /// Construct an expression from a column
355
356      /// Construct an expression, which has a term with \c c variable
357      /// and 1.0 coefficient.
358      Expr(const Col &c) : const_comp(0) {
359        typedef std::map<int, Value>::value_type pair_type;
360        comps.insert(pair_type(id(c), 1));
361      }
362      /// Construct an expression from a constant
363
364      /// Construct an expression, which's constant component is \c v.
365      ///
366      Expr(const Value &v) : const_comp(v) {}
367      /// Returns the coefficient of the column
368      Value operator[](const Col& c) const {
369        std::map<int, Value>::const_iterator it=comps.find(id(c));
370        if (it != comps.end()) {
371          return it->second;
372        } else {
373          return 0;
374        }
375      }
376      /// Returns the coefficient of the column
377      Value& operator[](const Col& c) {
378        return comps[id(c)];
379      }
380      /// Sets the coefficient of the column
381      void set(const Col &c, const Value &v) {
382        if (v != 0.0) {
383          typedef std::map<int, Value>::value_type pair_type;
384          comps.insert(pair_type(id(c), v));
385        } else {
386          comps.erase(id(c));
387        }
388      }
389      /// Returns the constant component of the expression
390      Value& operator*() { return const_comp; }
391      /// Returns the constant component of the expression
392      const Value& operator*() const { return const_comp; }
393      /// \brief Removes the coefficients which's absolute value does
394      /// not exceed \c epsilon. It also sets to zero the constant
395      /// component, if it does not exceed epsilon in absolute value.
396      void simplify(Value epsilon = 0.0) {
397        std::map<int, Value>::iterator it=comps.begin();
398        while (it != comps.end()) {
399          std::map<int, Value>::iterator jt=it;
400          ++jt;
401          if (std::fabs((*it).second) <= epsilon) comps.erase(it);
402          it=jt;
403        }
404        if (std::fabs(const_comp) <= epsilon) const_comp = 0;
405      }
406
407      void simplify(Value epsilon = 0.0) const {
408        const_cast<Expr*>(this)->simplify(epsilon);
409      }
410
411      ///Sets all coefficients and the constant component to 0.
412      void clear() {
413        comps.clear();
414        const_comp=0;
415      }
416
417      ///Compound assignment
418      Expr &operator+=(const Expr &e) {
419        for (std::map<int, Value>::const_iterator it=e.comps.begin();
420             it!=e.comps.end(); ++it)
421          comps[it->first]+=it->second;
422        const_comp+=e.const_comp;
423        return *this;
424      }
425      ///Compound assignment
426      Expr &operator-=(const Expr &e) {
427        for (std::map<int, Value>::const_iterator it=e.comps.begin();
428             it!=e.comps.end(); ++it)
429          comps[it->first]-=it->second;
430        const_comp-=e.const_comp;
431        return *this;
432      }
433      ///Multiply with a constant
434      Expr &operator*=(const Value &v) {
435        for (std::map<int, Value>::iterator it=comps.begin();
436             it!=comps.end(); ++it)
437          it->second*=v;
438        const_comp*=v;
439        return *this;
440      }
441      ///Division with a constant
442      Expr &operator/=(const Value &c) {
443        for (std::map<int, Value>::iterator it=comps.begin();
444             it!=comps.end(); ++it)
445          it->second/=c;
446        const_comp/=c;
447        return *this;
448      }
449
450      ///Iterator over the expression
451
452      ///The iterator iterates over the terms of the expression.
453      ///
454      ///\code
455      ///double s=0;
456      ///for(LpBase::Expr::CoeffIt i(e);i!=INVALID;++i)
457      ///  s+= *i * primal(i);
458      ///\endcode
459      class CoeffIt {
460      private:
461
462        std::map<int, Value>::iterator _it, _end;
463
464      public:
465
466        /// Sets the iterator to the first term
467
468        /// Sets the iterator to the first term of the expression.
469        ///
470        CoeffIt(Expr& e)
471          : _it(e.comps.begin()), _end(e.comps.end()){}
472
473        /// Convert the iterator to the column of the term
474        operator Col() const {
475          return colFromId(_it->first);
476        }
477
478        /// Returns the coefficient of the term
479        Value& operator*() { return _it->second; }
480
481        /// Returns the coefficient of the term
482        const Value& operator*() const { return _it->second; }
483        /// Next term
484
485        /// Assign the iterator to the next term.
486        ///
487        CoeffIt& operator++() { ++_it; return *this; }
488
489        /// Equality operator
490        bool operator==(Invalid) const { return _it == _end; }
491        /// Inequality operator
492        bool operator!=(Invalid) const { return _it != _end; }
493      };
494
495      /// Const iterator over the expression
496
497      ///The iterator iterates over the terms of the expression.
498      ///
499      ///\code
500      ///double s=0;
501      ///for(LpBase::Expr::ConstCoeffIt i(e);i!=INVALID;++i)
502      ///  s+=*i * primal(i);
503      ///\endcode
504      class ConstCoeffIt {
505      private:
506
507        std::map<int, Value>::const_iterator _it, _end;
508
509      public:
510
511        /// Sets the iterator to the first term
512
513        /// Sets the iterator to the first term of the expression.
514        ///
515        ConstCoeffIt(const Expr& e)
516          : _it(e.comps.begin()), _end(e.comps.end()){}
517
518        /// Convert the iterator to the column of the term
519        operator Col() const {
520          return colFromId(_it->first);
521        }
522
523        /// Returns the coefficient of the term
524        const Value& operator*() const { return _it->second; }
525
526        /// Next term
527
528        /// Assign the iterator to the next term.
529        ///
530        ConstCoeffIt& operator++() { ++_it; return *this; }
531
532        /// Equality operator
533        bool operator==(Invalid) const { return _it == _end; }
534        /// Inequality operator
535        bool operator!=(Invalid) const { return _it != _end; }
536      };
537
538    };
539
540    ///Linear constraint
541
542    ///This data stucture represents a linear constraint in the LP.
543    ///Basically it is a linear expression with a lower or an upper bound
544    ///(or both). These parts of the constraint can be obtained by the member
545    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
546    ///respectively.
547    ///There are two ways to construct a constraint.
548    ///- You can set the linear expression and the bounds directly
549    ///  by the functions above.
550    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
551    ///  are defined between expressions, or even between constraints whenever
552    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
553    ///  \c s and \c t are numbers, then the followings are valid expressions
554    ///  and thus they can be used directly e.g. in \ref addRow() whenever
555    ///  it makes sense.
556    ///\code
557    ///  e<=s
558    ///  e<=f
559    ///  e==f
560    ///  s<=e<=t
561    ///  e>=t
562    ///\endcode
563    ///\warning The validity of a constraint is checked only at run
564    ///time, so e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will
565    ///compile, but will fail an assertion.
566    class Constr
567    {
568    public:
569      typedef LpBase::Expr Expr;
570      typedef Expr::Key Key;
571      typedef Expr::Value Value;
572
573    protected:
574      Expr _expr;
575      Value _lb,_ub;
576    public:
577      ///\e
578      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
579      ///\e
580      Constr(Value lb, const Expr &e, Value ub) :
581        _expr(e), _lb(lb), _ub(ub) {}
582      Constr(const Expr &e) :
583        _expr(e), _lb(NaN), _ub(NaN) {}
584      ///\e
585      void clear()
586      {
587        _expr.clear();
588        _lb=_ub=NaN;
589      }
590
591      ///Reference to the linear expression
592      Expr &expr() { return _expr; }
593      ///Cont reference to the linear expression
594      const Expr &expr() const { return _expr; }
595      ///Reference to the lower bound.
596
597      ///\return
598      ///- \ref INF "INF": the constraint is lower unbounded.
599      ///- \ref NaN "NaN": lower bound has not been set.
600      ///- finite number: the lower bound
601      Value &lowerBound() { return _lb; }
602      ///The const version of \ref lowerBound()
603      const Value &lowerBound() const { return _lb; }
604      ///Reference to the upper bound.
605
606      ///\return
607      ///- \ref INF "INF": the constraint is upper unbounded.
608      ///- \ref NaN "NaN": upper bound has not been set.
609      ///- finite number: the upper bound
610      Value &upperBound() { return _ub; }
611      ///The const version of \ref upperBound()
612      const Value &upperBound() const { return _ub; }
613      ///Is the constraint lower bounded?
614      bool lowerBounded() const {
615        return _lb != -INF && !isNaN(_lb);
616      }
617      ///Is the constraint upper bounded?
618      bool upperBounded() const {
619        return _ub != INF && !isNaN(_ub);
620      }
621
622    };
623
624    ///Linear expression of rows
625
626    ///This data structure represents a column of the matrix,
627    ///thas is it strores a linear expression of the dual variables
628    ///(\ref Row "Row"s).
629    ///
630    ///There are several ways to access and modify the contents of this
631    ///container.
632    ///\code
633    ///e[v]=5;
634    ///e[v]+=12;
635    ///e.erase(v);
636    ///\endcode
637    ///or you can also iterate through its elements.
638    ///\code
639    ///double s=0;
640    ///for(LpBase::DualExpr::ConstCoeffIt i(e);i!=INVALID;++i)
641    ///  s+=*i;
642    ///\endcode
643    ///(This code computes the sum of all coefficients).
644    ///- Numbers (<tt>double</tt>'s)
645    ///and variables (\ref Row "Row"s) directly convert to an
646    ///\ref DualExpr and the usual linear operations are defined, so
647    ///\code
648    ///v+w
649    ///2*v-3.12*(v-w/2)
650    ///v*2.1+(3*v+(v*12+w)*3)/2
651    ///\endcode
652    ///are valid \ref DualExpr dual expressions.
653    ///The usual assignment operations are also defined.
654    ///\code
655    ///e=v+w;
656    ///e+=2*v-3.12*(v-w/2);
657    ///e*=3.4;
658    ///e/=5;
659    ///\endcode
660    ///
661    ///\sa Expr
662    class DualExpr {
663      friend class LpBase;
664    public:
665      /// The key type of the expression
666      typedef LpBase::Row Key;
667      /// The value type of the expression
668      typedef LpBase::Value Value;
669
670    protected:
671      std::map<int, Value> comps;
672
673    public:
674      typedef True SolverExpr;
675      /// Default constructor
676
677      /// Construct an empty expression, the coefficients are
678      /// initialized to zero.
679      DualExpr() {}
680      /// Construct an expression from a row
681
682      /// Construct an expression, which has a term with \c r dual
683      /// variable and 1.0 coefficient.
684      DualExpr(const Row &r) {
685        typedef std::map<int, Value>::value_type pair_type;
686        comps.insert(pair_type(id(r), 1));
687      }
688      /// Returns the coefficient of the row
689      Value operator[](const Row& r) const {
690        std::map<int, Value>::const_iterator it = comps.find(id(r));
691        if (it != comps.end()) {
692          return it->second;
693        } else {
694          return 0;
695        }
696      }
697      /// Returns the coefficient of the row
698      Value& operator[](const Row& r) {
699        return comps[id(r)];
700      }
701      /// Sets the coefficient of the row
702      void set(const Row &r, const Value &v) {
703        if (v != 0.0) {
704          typedef std::map<int, Value>::value_type pair_type;
705          comps.insert(pair_type(id(r), v));
706        } else {
707          comps.erase(id(r));
708        }
709      }
710      /// \brief Removes the coefficients which's absolute value does
711      /// not exceed \c epsilon.
712      void simplify(Value epsilon = 0.0) {
713        std::map<int, Value>::iterator it=comps.begin();
714        while (it != comps.end()) {
715          std::map<int, Value>::iterator jt=it;
716          ++jt;
717          if (std::fabs((*it).second) <= epsilon) comps.erase(it);
718          it=jt;
719        }
720      }
721
722      void simplify(Value epsilon = 0.0) const {
723        const_cast<DualExpr*>(this)->simplify(epsilon);
724      }
725
726      ///Sets all coefficients to 0.
727      void clear() {
728        comps.clear();
729      }
730      ///Compound assignment
731      DualExpr &operator+=(const DualExpr &e) {
732        for (std::map<int, Value>::const_iterator it=e.comps.begin();
733             it!=e.comps.end(); ++it)
734          comps[it->first]+=it->second;
735        return *this;
736      }
737      ///Compound assignment
738      DualExpr &operator-=(const DualExpr &e) {
739        for (std::map<int, Value>::const_iterator it=e.comps.begin();
740             it!=e.comps.end(); ++it)
741          comps[it->first]-=it->second;
742        return *this;
743      }
744      ///Multiply with a constant
745      DualExpr &operator*=(const Value &v) {
746        for (std::map<int, Value>::iterator it=comps.begin();
747             it!=comps.end(); ++it)
748          it->second*=v;
749        return *this;
750      }
751      ///Division with a constant
752      DualExpr &operator/=(const Value &v) {
753        for (std::map<int, Value>::iterator it=comps.begin();
754             it!=comps.end(); ++it)
755          it->second/=v;
756        return *this;
757      }
758
759      ///Iterator over the expression
760
761      ///The iterator iterates over the terms of the expression.
762      ///
763      ///\code
764      ///double s=0;
765      ///for(LpBase::DualExpr::CoeffIt i(e);i!=INVALID;++i)
766      ///  s+= *i * dual(i);
767      ///\endcode
768      class CoeffIt {
769      private:
770
771        std::map<int, Value>::iterator _it, _end;
772
773      public:
774
775        /// Sets the iterator to the first term
776
777        /// Sets the iterator to the first term of the expression.
778        ///
779        CoeffIt(DualExpr& e)
780          : _it(e.comps.begin()), _end(e.comps.end()){}
781
782        /// Convert the iterator to the row of the term
783        operator Row() const {
784          return rowFromId(_it->first);
785        }
786
787        /// Returns the coefficient of the term
788        Value& operator*() { return _it->second; }
789
790        /// Returns the coefficient of the term
791        const Value& operator*() const { return _it->second; }
792
793        /// Next term
794
795        /// Assign the iterator to the next term.
796        ///
797        CoeffIt& operator++() { ++_it; return *this; }
798
799        /// Equality operator
800        bool operator==(Invalid) const { return _it == _end; }
801        /// Inequality operator
802        bool operator!=(Invalid) const { return _it != _end; }
803      };
804
805      ///Iterator over the expression
806
807      ///The iterator iterates over the terms of the expression.
808      ///
809      ///\code
810      ///double s=0;
811      ///for(LpBase::DualExpr::ConstCoeffIt i(e);i!=INVALID;++i)
812      ///  s+= *i * dual(i);
813      ///\endcode
814      class ConstCoeffIt {
815      private:
816
817        std::map<int, Value>::const_iterator _it, _end;
818
819      public:
820
821        /// Sets the iterator to the first term
822
823        /// Sets the iterator to the first term of the expression.
824        ///
825        ConstCoeffIt(const DualExpr& e)
826          : _it(e.comps.begin()), _end(e.comps.end()){}
827
828        /// Convert the iterator to the row of the term
829        operator Row() const {
830          return rowFromId(_it->first);
831        }
832
833        /// Returns the coefficient of the term
834        const Value& operator*() const { return _it->second; }
835
836        /// Next term
837
838        /// Assign the iterator to the next term.
839        ///
840        ConstCoeffIt& operator++() { ++_it; return *this; }
841
842        /// Equality operator
843        bool operator==(Invalid) const { return _it == _end; }
844        /// Inequality operator
845        bool operator!=(Invalid) const { return _it != _end; }
846      };
847    };
848
849
850  protected:
851
852    class InsertIterator {
853    private:
854
855      std::map<int, Value>& _host;
856      const _solver_bits::VarIndex& _index;
857
858    public:
859
860      typedef std::output_iterator_tag iterator_category;
861      typedef void difference_type;
862      typedef void value_type;
863      typedef void reference;
864      typedef void pointer;
865
866      InsertIterator(std::map<int, Value>& host,
867                   const _solver_bits::VarIndex& index)
868        : _host(host), _index(index) {}
869
870      InsertIterator& operator=(const std::pair<int, Value>& value) {
871        typedef std::map<int, Value>::value_type pair_type;
872        _host.insert(pair_type(_index[value.first], value.second));
873        return *this;
874      }
875
876      InsertIterator& operator*() { return *this; }
877      InsertIterator& operator++() { return *this; }
878      InsertIterator operator++(int) { return *this; }
879
880    };
881
882    class ExprIterator {
883    private:
884      std::map<int, Value>::const_iterator _host_it;
885      const _solver_bits::VarIndex& _index;
886    public:
887
888      typedef std::bidirectional_iterator_tag iterator_category;
889      typedef std::ptrdiff_t difference_type;
890      typedef const std::pair<int, Value> value_type;
891      typedef value_type reference;
892
893      class pointer {
894      public:
895        pointer(value_type& _value) : value(_value) {}
896        value_type* operator->() { return &value; }
897      private:
898        value_type value;
899      };
900
901      ExprIterator(const std::map<int, Value>::const_iterator& host_it,
902                   const _solver_bits::VarIndex& index)
903        : _host_it(host_it), _index(index) {}
904
905      reference operator*() {
906        return std::make_pair(_index(_host_it->first), _host_it->second);
907      }
908
909      pointer operator->() {
910        return pointer(operator*());
911      }
912
913      ExprIterator& operator++() { ++_host_it; return *this; }
914      ExprIterator operator++(int) {
915        ExprIterator tmp(*this); ++_host_it; return tmp;
916      }
917
918      ExprIterator& operator--() { --_host_it; return *this; }
919      ExprIterator operator--(int) {
920        ExprIterator tmp(*this); --_host_it; return tmp;
921      }
922
923      bool operator==(const ExprIterator& it) const {
924        return _host_it == it._host_it;
925      }
926
927      bool operator!=(const ExprIterator& it) const {
928        return _host_it != it._host_it;
929      }
930
931    };
932
933  protected:
934
935    //Abstract virtual functions
936
937    virtual int _addColId(int col) { return cols.addIndex(col); }
938    virtual int _addRowId(int row) { return rows.addIndex(row); }
939
940    virtual void _eraseColId(int col) { cols.eraseIndex(col); }
941    virtual void _eraseRowId(int row) { rows.eraseIndex(row); }
942
943    virtual int _addCol() = 0;
944    virtual int _addRow() = 0;
945
946    virtual int _addRow(Value l, ExprIterator b, ExprIterator e, Value u) {
947      int row = _addRow();
948      _setRowCoeffs(row, b, e);
949      _setRowLowerBound(row, l);
950      _setRowUpperBound(row, u);
951      return row;
952    }
953
954    virtual void _eraseCol(int col) = 0;
955    virtual void _eraseRow(int row) = 0;
956
957    virtual void _getColName(int col, std::string& name) const = 0;
958    virtual void _setColName(int col, const std::string& name) = 0;
959    virtual int _colByName(const std::string& name) const = 0;
960
961    virtual void _getRowName(int row, std::string& name) const = 0;
962    virtual void _setRowName(int row, const std::string& name) = 0;
963    virtual int _rowByName(const std::string& name) const = 0;
964
965    virtual void _setRowCoeffs(int i, ExprIterator b, ExprIterator e) = 0;
966    virtual void _getRowCoeffs(int i, InsertIterator b) const = 0;
967
968    virtual void _setColCoeffs(int i, ExprIterator b, ExprIterator e) = 0;
969    virtual void _getColCoeffs(int i, InsertIterator b) const = 0;
970
971    virtual void _setCoeff(int row, int col, Value value) = 0;
972    virtual Value _getCoeff(int row, int col) const = 0;
973
974    virtual void _setColLowerBound(int i, Value value) = 0;
975    virtual Value _getColLowerBound(int i) const = 0;
976
977    virtual void _setColUpperBound(int i, Value value) = 0;
978    virtual Value _getColUpperBound(int i) const = 0;
979
980    virtual void _setRowLowerBound(int i, Value value) = 0;
981    virtual Value _getRowLowerBound(int i) const = 0;
982
983    virtual void _setRowUpperBound(int i, Value value) = 0;
984    virtual Value _getRowUpperBound(int i) const = 0;
985
986    virtual void _setObjCoeffs(ExprIterator b, ExprIterator e) = 0;
987    virtual void _getObjCoeffs(InsertIterator b) const = 0;
988
989    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
990    virtual Value _getObjCoeff(int i) const = 0;
991
992    virtual void _setSense(Sense) = 0;
993    virtual Sense _getSense() const = 0;
994
995    virtual void _clear() = 0;
996
997    virtual const char* _solverName() const = 0;
998
999    virtual void _messageLevel(MessageLevel level) = 0;
1000
1001    //Own protected stuff
1002
1003    //Constant component of the objective function
1004    Value obj_const_comp;
1005
1006    LpBase() : rows(), cols(), obj_const_comp(0) {}
1007
1008  public:
1009
1010    ///Unsupported file format exception
1011    class UnsupportedFormatError : public Exception
1012    {
1013      std::string _format;
1014      mutable std::string _what;
1015    public:
1016      explicit UnsupportedFormatError(std::string format) throw()
1017        : _format(format) { }
1018      virtual ~UnsupportedFormatError() throw() {}
1019      virtual const char* what() const throw() {
1020        try {
1021          _what.clear();
1022          std::ostringstream oss;
1023          oss << "lemon::UnsupportedFormatError: " << _format;
1024          _what = oss.str();
1025        }
1026        catch (...) {}
1027        if (!_what.empty()) return _what.c_str();
1028        else return "lemon::UnsupportedFormatError";
1029      }
1030    };
1031
1032  protected:
1033    virtual void _write(std::string, std::string format) const
1034    {
1035      throw UnsupportedFormatError(format);
1036    }
1037
1038  public:
1039
1040    /// Virtual destructor
1041    virtual ~LpBase() {}
1042
1043    ///Gives back the name of the solver.
1044    const char* solverName() const {return _solverName();}
1045
1046    ///\name Build Up and Modify the LP
1047
1048    ///@{
1049
1050    ///Add a new empty column (i.e a new variable) to the LP
1051    Col addCol() { Col c; c._id = _addColId(_addCol()); return c;}
1052
1053    ///\brief Adds several new columns (i.e variables) at once
1054    ///
1055    ///This magic function takes a container as its argument and fills
1056    ///its elements with new columns (i.e. variables)
1057    ///\param t can be
1058    ///- a standard STL compatible iterable container with
1059    ///\ref Col as its \c values_type like
1060    ///\code
1061    ///std::vector<LpBase::Col>
1062    ///std::list<LpBase::Col>
1063    ///\endcode
1064    ///- a standard STL compatible iterable container with
1065    ///\ref Col as its \c mapped_type like
1066    ///\code
1067    ///std::map<AnyType,LpBase::Col>
1068    ///\endcode
1069    ///- an iterable lemon \ref concepts::WriteMap "write map" like
1070    ///\code
1071    ///ListGraph::NodeMap<LpBase::Col>
1072    ///ListGraph::ArcMap<LpBase::Col>
1073    ///\endcode
1074    ///\return The number of the created column.
1075#ifdef DOXYGEN
1076    template<class T>
1077    int addColSet(T &t) { return 0;}
1078#else
1079    template<class T>
1080    typename enable_if<typename T::value_type::LpCol,int>::type
1081    addColSet(T &t,dummy<0> = 0) {
1082      int s=0;
1083      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
1084      return s;
1085    }
1086    template<class T>
1087    typename enable_if<typename T::value_type::second_type::LpCol,
1088                       int>::type
1089    addColSet(T &t,dummy<1> = 1) {
1090      int s=0;
1091      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1092        i->second=addCol();
1093        s++;
1094      }
1095      return s;
1096    }
1097    template<class T>
1098    typename enable_if<typename T::MapIt::Value::LpCol,
1099                       int>::type
1100    addColSet(T &t,dummy<2> = 2) {
1101      int s=0;
1102      for(typename T::MapIt i(t); i!=INVALID; ++i)
1103        {
1104          i.set(addCol());
1105          s++;
1106        }
1107      return s;
1108    }
1109#endif
1110
1111    ///Set a column (i.e a dual constraint) of the LP
1112
1113    ///\param c is the column to be modified
1114    ///\param e is a dual linear expression (see \ref DualExpr)
1115    ///a better one.
1116    void col(Col c, const DualExpr &e) {
1117      e.simplify();
1118      _setColCoeffs(cols(id(c)), ExprIterator(e.comps.begin(), rows),
1119                    ExprIterator(e.comps.end(), rows));
1120    }
1121
1122    ///Get a column (i.e a dual constraint) of the LP
1123
1124    ///\param c is the column to get
1125    ///\return the dual expression associated to the column
1126    DualExpr col(Col c) const {
1127      DualExpr e;
1128      _getColCoeffs(cols(id(c)), InsertIterator(e.comps, rows));
1129      return e;
1130    }
1131
1132    ///Add a new column to the LP
1133
1134    ///\param e is a dual linear expression (see \ref DualExpr)
1135    ///\param o is the corresponding component of the objective
1136    ///function. It is 0 by default.
1137    ///\return The created column.
1138    Col addCol(const DualExpr &e, Value o = 0) {
1139      Col c=addCol();
1140      col(c,e);
1141      objCoeff(c,o);
1142      return c;
1143    }
1144
1145    ///Add a new empty row (i.e a new constraint) to the LP
1146
1147    ///This function adds a new empty row (i.e a new constraint) to the LP.
1148    ///\return The created row
1149    Row addRow() { Row r; r._id = _addRowId(_addRow()); return r;}
1150
1151    ///\brief Add several new rows (i.e constraints) at once
1152    ///
1153    ///This magic function takes a container as its argument and fills
1154    ///its elements with new row (i.e. variables)
1155    ///\param t can be
1156    ///- a standard STL compatible iterable container with
1157    ///\ref Row as its \c values_type like
1158    ///\code
1159    ///std::vector<LpBase::Row>
1160    ///std::list<LpBase::Row>
1161    ///\endcode
1162    ///- a standard STL compatible iterable container with
1163    ///\ref Row as its \c mapped_type like
1164    ///\code
1165    ///std::map<AnyType,LpBase::Row>
1166    ///\endcode
1167    ///- an iterable lemon \ref concepts::WriteMap "write map" like
1168    ///\code
1169    ///ListGraph::NodeMap<LpBase::Row>
1170    ///ListGraph::ArcMap<LpBase::Row>
1171    ///\endcode
1172    ///\return The number of rows created.
1173#ifdef DOXYGEN
1174    template<class T>
1175    int addRowSet(T &t) { return 0;}
1176#else
1177    template<class T>
1178    typename enable_if<typename T::value_type::LpRow,int>::type
1179    addRowSet(T &t, dummy<0> = 0) {
1180      int s=0;
1181      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
1182      return s;
1183    }
1184    template<class T>
1185    typename enable_if<typename T::value_type::second_type::LpRow, int>::type
1186    addRowSet(T &t, dummy<1> = 1) {
1187      int s=0;
1188      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1189        i->second=addRow();
1190        s++;
1191      }
1192      return s;
1193    }
1194    template<class T>
1195    typename enable_if<typename T::MapIt::Value::LpRow, int>::type
1196    addRowSet(T &t, dummy<2> = 2) {
1197      int s=0;
1198      for(typename T::MapIt i(t); i!=INVALID; ++i)
1199        {
1200          i.set(addRow());
1201          s++;
1202        }
1203      return s;
1204    }
1205#endif
1206
1207    ///Set a row (i.e a constraint) of the LP
1208
1209    ///\param r is the row to be modified
1210    ///\param l is lower bound (-\ref INF means no bound)
1211    ///\param e is a linear expression (see \ref Expr)
1212    ///\param u is the upper bound (\ref INF means no bound)
1213    void row(Row r, Value l, const Expr &e, Value u) {
1214      e.simplify();
1215      _setRowCoeffs(rows(id(r)), ExprIterator(e.comps.begin(), cols),
1216                    ExprIterator(e.comps.end(), cols));
1217      _setRowLowerBound(rows(id(r)),l - *e);
1218      _setRowUpperBound(rows(id(r)),u - *e);
1219    }
1220
1221    ///Set a row (i.e a constraint) of the LP
1222
1223    ///\param r is the row to be modified
1224    ///\param c is a linear expression (see \ref Constr)
1225    void row(Row r, const Constr &c) {
1226      row(r, c.lowerBounded()?c.lowerBound():-INF,
1227          c.expr(), c.upperBounded()?c.upperBound():INF);
1228    }
1229
1230
1231    ///Get a row (i.e a constraint) of the LP
1232
1233    ///\param r is the row to get
1234    ///\return the expression associated to the row
1235    Expr row(Row r) const {
1236      Expr e;
1237      _getRowCoeffs(rows(id(r)), InsertIterator(e.comps, cols));
1238      return e;
1239    }
1240
1241    ///Add a new row (i.e a new constraint) to the LP
1242
1243    ///\param l is the lower bound (-\ref INF means no bound)
1244    ///\param e is a linear expression (see \ref Expr)
1245    ///\param u is the upper bound (\ref INF means no bound)
1246    ///\return The created row.
1247    Row addRow(Value l,const Expr &e, Value u) {
1248      Row r;
1249      e.simplify();
1250      r._id = _addRowId(_addRow(l - *e, ExprIterator(e.comps.begin(), cols),
1251                                ExprIterator(e.comps.end(), cols), u - *e));
1252      return r;
1253    }
1254
1255    ///Add a new row (i.e a new constraint) to the LP
1256
1257    ///\param c is a linear expression (see \ref Constr)
1258    ///\return The created row.
1259    Row addRow(const Constr &c) {
1260      Row r;
1261      c.expr().simplify();
1262      r._id = _addRowId(_addRow(c.lowerBounded()?c.lowerBound()-*c.expr():-INF,
1263                                ExprIterator(c.expr().comps.begin(), cols),
1264                                ExprIterator(c.expr().comps.end(), cols),
1265                                c.upperBounded()?c.upperBound()-*c.expr():INF));
1266      return r;
1267    }
1268    ///Erase a column (i.e a variable) from the LP
1269
1270    ///\param c is the column to be deleted
1271    void erase(Col c) {
1272      _eraseCol(cols(id(c)));
1273      _eraseColId(cols(id(c)));
1274    }
1275    ///Erase a row (i.e a constraint) from the LP
1276
1277    ///\param r is the row to be deleted
1278    void erase(Row r) {
1279      _eraseRow(rows(id(r)));
1280      _eraseRowId(rows(id(r)));
1281    }
1282
1283    /// Get the name of a column
1284
1285    ///\param c is the coresponding column
1286    ///\return The name of the colunm
1287    std::string colName(Col c) const {
1288      std::string name;
1289      _getColName(cols(id(c)), name);
1290      return name;
1291    }
1292
1293    /// Set the name of a column
1294
1295    ///\param c is the coresponding column
1296    ///\param name The name to be given
1297    void colName(Col c, const std::string& name) {
1298      _setColName(cols(id(c)), name);
1299    }
1300
1301    /// Get the column by its name
1302
1303    ///\param name The name of the column
1304    ///\return the proper column or \c INVALID
1305    Col colByName(const std::string& name) const {
1306      int k = _colByName(name);
1307      return k != -1 ? Col(cols[k]) : Col(INVALID);
1308    }
1309
1310    /// Get the name of a row
1311
1312    ///\param r is the coresponding row
1313    ///\return The name of the row
1314    std::string rowName(Row r) const {
1315      std::string name;
1316      _getRowName(rows(id(r)), name);
1317      return name;
1318    }
1319
1320    /// Set the name of a row
1321
1322    ///\param r is the coresponding row
1323    ///\param name The name to be given
1324    void rowName(Row r, const std::string& name) {
1325      _setRowName(rows(id(r)), name);
1326    }
1327
1328    /// Get the row by its name
1329
1330    ///\param name The name of the row
1331    ///\return the proper row or \c INVALID
1332    Row rowByName(const std::string& name) const {
1333      int k = _rowByName(name);
1334      return k != -1 ? Row(rows[k]) : Row(INVALID);
1335    }
1336
1337    /// Set an element of the coefficient matrix of the LP
1338
1339    ///\param r is the row of the element to be modified
1340    ///\param c is the column of the element to be modified
1341    ///\param val is the new value of the coefficient
1342    void coeff(Row r, Col c, Value val) {
1343      _setCoeff(rows(id(r)),cols(id(c)), val);
1344    }
1345
1346    /// Get an element of the coefficient matrix of the LP
1347
1348    ///\param r is the row of the element
1349    ///\param c is the column of the element
1350    ///\return the corresponding coefficient
1351    Value coeff(Row r, Col c) const {
1352      return _getCoeff(rows(id(r)),cols(id(c)));
1353    }
1354
1355    /// Set the lower bound of a column (i.e a variable)
1356
1357    /// The lower bound of a variable (column) has to be given by an
1358    /// extended number of type Value, i.e. a finite number of type
1359    /// Value or -\ref INF.
1360    void colLowerBound(Col c, Value value) {
1361      _setColLowerBound(cols(id(c)),value);
1362    }
1363
1364    /// Get the lower bound of a column (i.e a variable)
1365
1366    /// This function returns the lower bound for column (variable) \c c
1367    /// (this might be -\ref INF as well).
1368    ///\return The lower bound for column \c c
1369    Value colLowerBound(Col c) const {
1370      return _getColLowerBound(cols(id(c)));
1371    }
1372
1373    ///\brief Set the lower bound of  several columns
1374    ///(i.e variables) at once
1375    ///
1376    ///This magic function takes a container as its argument
1377    ///and applies the function on all of its elements.
1378    ///The lower bound of a variable (column) has to be given by an
1379    ///extended number of type Value, i.e. a finite number of type
1380    ///Value or -\ref INF.
1381#ifdef DOXYGEN
1382    template<class T>
1383    void colLowerBound(T &t, Value value) { return 0;}
1384#else
1385    template<class T>
1386    typename enable_if<typename T::value_type::LpCol,void>::type
1387    colLowerBound(T &t, Value value,dummy<0> = 0) {
1388      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1389        colLowerBound(*i, value);
1390      }
1391    }
1392    template<class T>
1393    typename enable_if<typename T::value_type::second_type::LpCol,
1394                       void>::type
1395    colLowerBound(T &t, Value value,dummy<1> = 1) {
1396      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1397        colLowerBound(i->second, value);
1398      }
1399    }
1400    template<class T>
1401    typename enable_if<typename T::MapIt::Value::LpCol,
1402                       void>::type
1403    colLowerBound(T &t, Value value,dummy<2> = 2) {
1404      for(typename T::MapIt i(t); i!=INVALID; ++i){
1405        colLowerBound(*i, value);
1406      }
1407    }
1408#endif
1409
1410    /// Set the upper bound of a column (i.e a variable)
1411
1412    /// The upper bound of a variable (column) has to be given by an
1413    /// extended number of type Value, i.e. a finite number of type
1414    /// Value or \ref INF.
1415    void colUpperBound(Col c, Value value) {
1416      _setColUpperBound(cols(id(c)),value);
1417    };
1418
1419    /// Get the upper bound of a column (i.e a variable)
1420
1421    /// This function returns the upper bound for column (variable) \c c
1422    /// (this might be \ref INF as well).
1423    /// \return The upper bound for column \c c
1424    Value colUpperBound(Col c) const {
1425      return _getColUpperBound(cols(id(c)));
1426    }
1427
1428    ///\brief Set the upper bound of  several columns
1429    ///(i.e variables) at once
1430    ///
1431    ///This magic function takes a container as its argument
1432    ///and applies the function on all of its elements.
1433    ///The upper bound of a variable (column) has to be given by an
1434    ///extended number of type Value, i.e. a finite number of type
1435    ///Value or \ref INF.
1436#ifdef DOXYGEN
1437    template<class T>
1438    void colUpperBound(T &t, Value value) { return 0;}
1439#else
1440    template<class T1>
1441    typename enable_if<typename T1::value_type::LpCol,void>::type
1442    colUpperBound(T1 &t, Value value,dummy<0> = 0) {
1443      for(typename T1::iterator i=t.begin();i!=t.end();++i) {
1444        colUpperBound(*i, value);
1445      }
1446    }
1447    template<class T1>
1448    typename enable_if<typename T1::value_type::second_type::LpCol,
1449                       void>::type
1450    colUpperBound(T1 &t, Value value,dummy<1> = 1) {
1451      for(typename T1::iterator i=t.begin();i!=t.end();++i) {
1452        colUpperBound(i->second, value);
1453      }
1454    }
1455    template<class T1>
1456    typename enable_if<typename T1::MapIt::Value::LpCol,
1457                       void>::type
1458    colUpperBound(T1 &t, Value value,dummy<2> = 2) {
1459      for(typename T1::MapIt i(t); i!=INVALID; ++i){
1460        colUpperBound(*i, value);
1461      }
1462    }
1463#endif
1464
1465    /// Set the lower and the upper bounds of a column (i.e a variable)
1466
1467    /// The lower and the upper bounds of
1468    /// a variable (column) have to be given by an
1469    /// extended number of type Value, i.e. a finite number of type
1470    /// Value, -\ref INF or \ref INF.
1471    void colBounds(Col c, Value lower, Value upper) {
1472      _setColLowerBound(cols(id(c)),lower);
1473      _setColUpperBound(cols(id(c)),upper);
1474    }
1475
1476    ///\brief Set the lower and the upper bound of several columns
1477    ///(i.e variables) at once
1478    ///
1479    ///This magic function takes a container as its argument
1480    ///and applies the function on all of its elements.
1481    /// The lower and the upper bounds of
1482    /// a variable (column) have to be given by an
1483    /// extended number of type Value, i.e. a finite number of type
1484    /// Value, -\ref INF or \ref INF.
1485#ifdef DOXYGEN
1486    template<class T>
1487    void colBounds(T &t, Value lower, Value upper) { return 0;}
1488#else
1489    template<class T2>
1490    typename enable_if<typename T2::value_type::LpCol,void>::type
1491    colBounds(T2 &t, Value lower, Value upper,dummy<0> = 0) {
1492      for(typename T2::iterator i=t.begin();i!=t.end();++i) {
1493        colBounds(*i, lower, upper);
1494      }
1495    }
1496    template<class T2>
1497    typename enable_if<typename T2::value_type::second_type::LpCol, void>::type
1498    colBounds(T2 &t, Value lower, Value upper,dummy<1> = 1) {
1499      for(typename T2::iterator i=t.begin();i!=t.end();++i) {
1500        colBounds(i->second, lower, upper);
1501      }
1502    }
1503    template<class T2>
1504    typename enable_if<typename T2::MapIt::Value::LpCol, void>::type
1505    colBounds(T2 &t, Value lower, Value upper,dummy<2> = 2) {
1506      for(typename T2::MapIt i(t); i!=INVALID; ++i){
1507        colBounds(*i, lower, upper);
1508      }
1509    }
1510#endif
1511
1512    /// Set the lower bound of a row (i.e a constraint)
1513
1514    /// The lower bound of a constraint (row) has to be given by an
1515    /// extended number of type Value, i.e. a finite number of type
1516    /// Value or -\ref INF.
1517    void rowLowerBound(Row r, Value value) {
1518      _setRowLowerBound(rows(id(r)),value);
1519    }
1520
1521    /// Get the lower bound of a row (i.e a constraint)
1522
1523    /// This function returns the lower bound for row (constraint) \c c
1524    /// (this might be -\ref INF as well).
1525    ///\return The lower bound for row \c r
1526    Value rowLowerBound(Row r) const {
1527      return _getRowLowerBound(rows(id(r)));
1528    }
1529
1530    /// Set the upper bound of a row (i.e a constraint)
1531
1532    /// The upper bound of a constraint (row) has to be given by an
1533    /// extended number of type Value, i.e. a finite number of type
1534    /// Value or -\ref INF.
1535    void rowUpperBound(Row r, Value value) {
1536      _setRowUpperBound(rows(id(r)),value);
1537    }
1538
1539    /// Get the upper bound of a row (i.e a constraint)
1540
1541    /// This function returns the upper bound for row (constraint) \c c
1542    /// (this might be -\ref INF as well).
1543    ///\return The upper bound for row \c r
1544    Value rowUpperBound(Row r) const {
1545      return _getRowUpperBound(rows(id(r)));
1546    }
1547
1548    ///Set an element of the objective function
1549    void objCoeff(Col c, Value v) {_setObjCoeff(cols(id(c)),v); };
1550
1551    ///Get an element of the objective function
1552    Value objCoeff(Col c) const { return _getObjCoeff(cols(id(c))); };
1553
1554    ///Set the objective function
1555
1556    ///\param e is a linear expression of type \ref Expr.
1557    ///
1558    void obj(const Expr& e) {
1559      _setObjCoeffs(ExprIterator(e.comps.begin(), cols),
1560                    ExprIterator(e.comps.end(), cols));
1561      obj_const_comp = *e;
1562    }
1563
1564    ///Get the objective function
1565
1566    ///\return the objective function as a linear expression of type
1567    ///Expr.
1568    Expr obj() const {
1569      Expr e;
1570      _getObjCoeffs(InsertIterator(e.comps, cols));
1571      *e = obj_const_comp;
1572      return e;
1573    }
1574
1575
1576    ///Set the direction of optimization
1577    void sense(Sense sense) { _setSense(sense); }
1578
1579    ///Query the direction of the optimization
1580    Sense sense() const {return _getSense(); }
1581
1582    ///Set the sense to maximization
1583    void max() { _setSense(MAX); }
1584
1585    ///Set the sense to maximization
1586    void min() { _setSense(MIN); }
1587
1588    ///Clear the problem
1589    void clear() { _clear(); rows.clear(); cols.clear(); }
1590
1591    /// Set the message level of the solver
1592    void messageLevel(MessageLevel level) { _messageLevel(level); }
1593
1594    /// Write the problem to a file in the given format
1595
1596    /// This function writes the problem to a file in the given format.
1597    /// Different solver backends may support different formats.
1598    /// Trying to write in an unsupported format will trigger
1599    /// \ref UnsupportedFormatError. For the supported formats,
1600    /// visit the documentation of the base class of the related backends
1601    /// (\ref CplexBase, \ref GlpkBase etc.)
1602    /// \param file The file path
1603    /// \param format The output file format.
1604    void write(std::string file, std::string format = "MPS") const
1605    {
1606      _write(file.c_str(),format.c_str());
1607    }
1608
1609    ///@}
1610
1611  };
1612
1613  /// Addition
1614
1615  ///\relates LpBase::Expr
1616  ///
1617  inline LpBase::Expr operator+(const LpBase::Expr &a, const LpBase::Expr &b) {
1618    LpBase::Expr tmp(a);
1619    tmp+=b;
1620    return tmp;
1621  }
1622  ///Substraction
1623
1624  ///\relates LpBase::Expr
1625  ///
1626  inline LpBase::Expr operator-(const LpBase::Expr &a, const LpBase::Expr &b) {
1627    LpBase::Expr tmp(a);
1628    tmp-=b;
1629    return tmp;
1630  }
1631  ///Multiply with constant
1632
1633  ///\relates LpBase::Expr
1634  ///
1635  inline LpBase::Expr operator*(const LpBase::Expr &a, const LpBase::Value &b) {
1636    LpBase::Expr tmp(a);
1637    tmp*=b;
1638    return tmp;
1639  }
1640
1641  ///Multiply with constant
1642
1643  ///\relates LpBase::Expr
1644  ///
1645  inline LpBase::Expr operator*(const LpBase::Value &a, const LpBase::Expr &b) {
1646    LpBase::Expr tmp(b);
1647    tmp*=a;
1648    return tmp;
1649  }
1650  ///Divide with constant
1651
1652  ///\relates LpBase::Expr
1653  ///
1654  inline LpBase::Expr operator/(const LpBase::Expr &a, const LpBase::Value &b) {
1655    LpBase::Expr tmp(a);
1656    tmp/=b;
1657    return tmp;
1658  }
1659
1660  ///Create constraint
1661
1662  ///\relates LpBase::Constr
1663  ///
1664  inline LpBase::Constr operator<=(const LpBase::Expr &e,
1665                                   const LpBase::Expr &f) {
1666    return LpBase::Constr(0, f - e, LpBase::NaN);
1667  }
1668
1669  ///Create constraint
1670
1671  ///\relates LpBase::Constr
1672  ///
1673  inline LpBase::Constr operator<=(const LpBase::Value &e,
1674                                   const LpBase::Expr &f) {
1675    return LpBase::Constr(e, f, LpBase::NaN);
1676  }
1677
1678  ///Create constraint
1679
1680  ///\relates LpBase::Constr
1681  ///
1682  inline LpBase::Constr operator<=(const LpBase::Expr &e,
1683                                   const LpBase::Value &f) {
1684    return LpBase::Constr(LpBase::NaN, e, f);
1685  }
1686
1687  ///Create constraint
1688
1689  ///\relates LpBase::Constr
1690  ///
1691  inline LpBase::Constr operator>=(const LpBase::Expr &e,
1692                                   const LpBase::Expr &f) {
1693    return LpBase::Constr(0, e - f, LpBase::NaN);
1694  }
1695
1696
1697  ///Create constraint
1698
1699  ///\relates LpBase::Constr
1700  ///
1701  inline LpBase::Constr operator>=(const LpBase::Value &e,
1702                                   const LpBase::Expr &f) {
1703    return LpBase::Constr(LpBase::NaN, f, e);
1704  }
1705
1706
1707  ///Create constraint
1708
1709  ///\relates LpBase::Constr
1710  ///
1711  inline LpBase::Constr operator>=(const LpBase::Expr &e,
1712                                   const LpBase::Value &f) {
1713    return LpBase::Constr(f, e, LpBase::NaN);
1714  }
1715
1716  ///Create constraint
1717
1718  ///\relates LpBase::Constr
1719  ///
1720  inline LpBase::Constr operator==(const LpBase::Expr &e,
1721                                   const LpBase::Value &f) {
1722    return LpBase::Constr(f, e, f);
1723  }
1724
1725  ///Create constraint
1726
1727  ///\relates LpBase::Constr
1728  ///
1729  inline LpBase::Constr operator==(const LpBase::Expr &e,
1730                                   const LpBase::Expr &f) {
1731    return LpBase::Constr(0, f - e, 0);
1732  }
1733
1734  ///Create constraint
1735
1736  ///\relates LpBase::Constr
1737  ///
1738  inline LpBase::Constr operator<=(const LpBase::Value &n,
1739                                   const LpBase::Constr &c) {
1740    LpBase::Constr tmp(c);
1741    LEMON_ASSERT(isNaN(tmp.lowerBound()), "Wrong LP constraint");
1742    tmp.lowerBound()=n;
1743    return tmp;
1744  }
1745  ///Create constraint
1746
1747  ///\relates LpBase::Constr
1748  ///
1749  inline LpBase::Constr operator<=(const LpBase::Constr &c,
1750                                   const LpBase::Value &n)
1751  {
1752    LpBase::Constr tmp(c);
1753    LEMON_ASSERT(isNaN(tmp.upperBound()), "Wrong LP constraint");
1754    tmp.upperBound()=n;
1755    return tmp;
1756  }
1757
1758  ///Create constraint
1759
1760  ///\relates LpBase::Constr
1761  ///
1762  inline LpBase::Constr operator>=(const LpBase::Value &n,
1763                                   const LpBase::Constr &c) {
1764    LpBase::Constr tmp(c);
1765    LEMON_ASSERT(isNaN(tmp.upperBound()), "Wrong LP constraint");
1766    tmp.upperBound()=n;
1767    return tmp;
1768  }
1769  ///Create constraint
1770
1771  ///\relates LpBase::Constr
1772  ///
1773  inline LpBase::Constr operator>=(const LpBase::Constr &c,
1774                                   const LpBase::Value &n)
1775  {
1776    LpBase::Constr tmp(c);
1777    LEMON_ASSERT(isNaN(tmp.lowerBound()), "Wrong LP constraint");
1778    tmp.lowerBound()=n;
1779    return tmp;
1780  }
1781
1782  ///Addition
1783
1784  ///\relates LpBase::DualExpr
1785  ///
1786  inline LpBase::DualExpr operator+(const LpBase::DualExpr &a,
1787                                    const LpBase::DualExpr &b) {
1788    LpBase::DualExpr tmp(a);
1789    tmp+=b;
1790    return tmp;
1791  }
1792  ///Substraction
1793
1794  ///\relates LpBase::DualExpr
1795  ///
1796  inline LpBase::DualExpr operator-(const LpBase::DualExpr &a,
1797                                    const LpBase::DualExpr &b) {
1798    LpBase::DualExpr tmp(a);
1799    tmp-=b;
1800    return tmp;
1801  }
1802  ///Multiply with constant
1803
1804  ///\relates LpBase::DualExpr
1805  ///
1806  inline LpBase::DualExpr operator*(const LpBase::DualExpr &a,
1807                                    const LpBase::Value &b) {
1808    LpBase::DualExpr tmp(a);
1809    tmp*=b;
1810    return tmp;
1811  }
1812
1813  ///Multiply with constant
1814
1815  ///\relates LpBase::DualExpr
1816  ///
1817  inline LpBase::DualExpr operator*(const LpBase::Value &a,
1818                                    const LpBase::DualExpr &b) {
1819    LpBase::DualExpr tmp(b);
1820    tmp*=a;
1821    return tmp;
1822  }
1823  ///Divide with constant
1824
1825  ///\relates LpBase::DualExpr
1826  ///
1827  inline LpBase::DualExpr operator/(const LpBase::DualExpr &a,
1828                                    const LpBase::Value &b) {
1829    LpBase::DualExpr tmp(a);
1830    tmp/=b;
1831    return tmp;
1832  }
1833
1834  /// \ingroup lp_group
1835  ///
1836  /// \brief Common base class for LP solvers
1837  ///
1838  /// This class is an abstract base class for LP solvers. This class
1839  /// provides a full interface for set and modify an LP problem,
1840  /// solve it and retrieve the solution. You can use one of the
1841  /// descendants as a concrete implementation, or the \c Lp
1842  /// default LP solver. However, if you would like to handle LP
1843  /// solvers as reference or pointer in a generic way, you can use
1844  /// this class directly.
1845  class LpSolver : virtual public LpBase {
1846  public:
1847
1848    /// The problem types for primal and dual problems
1849    enum ProblemType {
1850      /// = 0. Feasible solution hasn't been found (but may exist).
1851      UNDEFINED = 0,
1852      /// = 1. The problem has no feasible solution.
1853      INFEASIBLE = 1,
1854      /// = 2. Feasible solution found.
1855      FEASIBLE = 2,
1856      /// = 3. Optimal solution exists and found.
1857      OPTIMAL = 3,
1858      /// = 4. The cost function is unbounded.
1859      UNBOUNDED = 4
1860    };
1861
1862    ///The basis status of variables
1863    enum VarStatus {
1864      /// The variable is in the basis
1865      BASIC,
1866      /// The variable is free, but not basic
1867      FREE,
1868      /// The variable has active lower bound
1869      LOWER,
1870      /// The variable has active upper bound
1871      UPPER,
1872      /// The variable is non-basic and fixed
1873      FIXED
1874    };
1875
1876  protected:
1877
1878    virtual SolveExitStatus _solve() = 0;
1879
1880    virtual Value _getPrimal(int i) const = 0;
1881    virtual Value _getDual(int i) const = 0;
1882
1883    virtual Value _getPrimalRay(int i) const = 0;
1884    virtual Value _getDualRay(int i) const = 0;
1885
1886    virtual Value _getPrimalValue() const = 0;
1887
1888    virtual VarStatus _getColStatus(int i) const = 0;
1889    virtual VarStatus _getRowStatus(int i) const = 0;
1890
1891    virtual ProblemType _getPrimalType() const = 0;
1892    virtual ProblemType _getDualType() const = 0;
1893
1894  public:
1895
1896    ///Allocate a new LP problem instance
1897    virtual LpSolver* newSolver() const = 0;
1898    ///Make a copy of the LP problem
1899    virtual LpSolver* cloneSolver() const = 0;
1900
1901    ///\name Solve the LP
1902
1903    ///@{
1904
1905    ///\e Solve the LP problem at hand
1906    ///
1907    ///\return The result of the optimization procedure. Possible
1908    ///values and their meanings can be found in the documentation of
1909    ///\ref SolveExitStatus.
1910    SolveExitStatus solve() { return _solve(); }
1911
1912    ///@}
1913
1914    ///\name Obtain the Solution
1915
1916    ///@{
1917
1918    /// The type of the primal problem
1919    ProblemType primalType() const {
1920      return _getPrimalType();
1921    }
1922
1923    /// The type of the dual problem
1924    ProblemType dualType() const {
1925      return _getDualType();
1926    }
1927
1928    /// Return the primal value of the column
1929
1930    /// Return the primal value of the column.
1931    /// \pre The problem is solved.
1932    Value primal(Col c) const { return _getPrimal(cols(id(c))); }
1933
1934    /// Return the primal value of the expression
1935
1936    /// Return the primal value of the expression, i.e. the dot
1937    /// product of the primal solution and the expression.
1938    /// \pre The problem is solved.
1939    Value primal(const Expr& e) const {
1940      double res = *e;
1941      for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {
1942        res += *c * primal(c);
1943      }
1944      return res;
1945    }
1946    /// Returns a component of the primal ray
1947
1948    /// The primal ray is solution of the modified primal problem,
1949    /// where we change each finite bound to 0, and we looking for a
1950    /// negative objective value in case of minimization, and positive
1951    /// objective value for maximization. If there is such solution,
1952    /// that proofs the unsolvability of the dual problem, and if a
1953    /// feasible primal solution exists, then the unboundness of
1954    /// primal problem.
1955    ///
1956    /// \pre The problem is solved and the dual problem is infeasible.
1957    /// \note Some solvers does not provide primal ray calculation
1958    /// functions.
1959    Value primalRay(Col c) const { return _getPrimalRay(cols(id(c))); }
1960
1961    /// Return the dual value of the row
1962
1963    /// Return the dual value of the row.
1964    /// \pre The problem is solved.
1965    Value dual(Row r) const { return _getDual(rows(id(r))); }
1966
1967    /// Return the dual value of the dual expression
1968
1969    /// Return the dual value of the dual expression, i.e. the dot
1970    /// product of the dual solution and the dual expression.
1971    /// \pre The problem is solved.
1972    Value dual(const DualExpr& e) const {
1973      double res = 0.0;
1974      for (DualExpr::ConstCoeffIt r(e); r != INVALID; ++r) {
1975        res += *r * dual(r);
1976      }
1977      return res;
1978    }
1979
1980    /// Returns a component of the dual ray
1981
1982    /// The dual ray is solution of the modified primal problem, where
1983    /// we change each finite bound to 0 (i.e. the objective function
1984    /// coefficients in the primal problem), and we looking for a
1985    /// ositive objective value. If there is such solution, that
1986    /// proofs the unsolvability of the primal problem, and if a
1987    /// feasible dual solution exists, then the unboundness of
1988    /// dual problem.
1989    ///
1990    /// \pre The problem is solved and the primal problem is infeasible.
1991    /// \note Some solvers does not provide dual ray calculation
1992    /// functions.
1993    Value dualRay(Row r) const { return _getDualRay(rows(id(r))); }
1994
1995    /// Return the basis status of the column
1996
1997    /// \see VarStatus
1998    VarStatus colStatus(Col c) const { return _getColStatus(cols(id(c))); }
1999
2000    /// Return the basis status of the row
2001
2002    /// \see VarStatus
2003    VarStatus rowStatus(Row r) const { return _getRowStatus(rows(id(r))); }
2004
2005    ///The value of the objective function
2006
2007    ///\return
2008    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
2009    /// of the primal problem, depending on whether we minimize or maximize.
2010    ///- \ref NaN if no primal solution is found.
2011    ///- The (finite) objective value if an optimal solution is found.
2012    Value primal() const { return _getPrimalValue()+obj_const_comp;}
2013    ///@}
2014
2015  protected:
2016
2017  };
2018
2019
2020  /// \ingroup lp_group
2021  ///
2022  /// \brief Common base class for MIP solvers
2023  ///
2024  /// This class is an abstract base class for MIP solvers. This class
2025  /// provides a full interface for set and modify an MIP problem,
2026  /// solve it and retrieve the solution. You can use one of the
2027  /// descendants as a concrete implementation, or the \c Lp
2028  /// default MIP solver. However, if you would like to handle MIP
2029  /// solvers as reference or pointer in a generic way, you can use
2030  /// this class directly.
2031  class MipSolver : virtual public LpBase {
2032  public:
2033
2034    /// The problem types for MIP problems
2035    enum ProblemType {
2036      /// = 0. Feasible solution hasn't been found (but may exist).
2037      UNDEFINED = 0,
2038      /// = 1. The problem has no feasible solution.
2039      INFEASIBLE = 1,
2040      /// = 2. Feasible solution found.
2041      FEASIBLE = 2,
2042      /// = 3. Optimal solution exists and found.
2043      OPTIMAL = 3,
2044      /// = 4. The cost function is unbounded.
2045      ///The Mip or at least the relaxed problem is unbounded.
2046      UNBOUNDED = 4
2047    };
2048
2049    ///Allocate a new MIP problem instance
2050    virtual MipSolver* newSolver() const = 0;
2051    ///Make a copy of the MIP problem
2052    virtual MipSolver* cloneSolver() const = 0;
2053
2054    ///\name Solve the MIP
2055
2056    ///@{
2057
2058    /// Solve the MIP problem at hand
2059    ///
2060    ///\return The result of the optimization procedure. Possible
2061    ///values and their meanings can be found in the documentation of
2062    ///\ref SolveExitStatus.
2063    SolveExitStatus solve() { return _solve(); }
2064
2065    ///@}
2066
2067    ///\name Set Column Type
2068    ///@{
2069
2070    ///Possible variable (column) types (e.g. real, integer, binary etc.)
2071    enum ColTypes {
2072      /// = 0. Continuous variable (default).
2073      REAL = 0,
2074      /// = 1. Integer variable.
2075      INTEGER = 1
2076    };
2077
2078    ///Sets the type of the given column to the given type
2079
2080    ///Sets the type of the given column to the given type.
2081    ///
2082    void colType(Col c, ColTypes col_type) {
2083      _setColType(cols(id(c)),col_type);
2084    }
2085
2086    ///Gives back the type of the column.
2087
2088    ///Gives back the type of the column.
2089    ///
2090    ColTypes colType(Col c) const {
2091      return _getColType(cols(id(c)));
2092    }
2093    ///@}
2094
2095    ///\name Obtain the Solution
2096
2097    ///@{
2098
2099    /// The type of the MIP problem
2100    ProblemType type() const {
2101      return _getType();
2102    }
2103
2104    /// Return the value of the row in the solution
2105
2106    ///  Return the value of the row in the solution.
2107    /// \pre The problem is solved.
2108    Value sol(Col c) const { return _getSol(cols(id(c))); }
2109
2110    /// Return the value of the expression in the solution
2111
2112    /// Return the value of the expression in the solution, i.e. the
2113    /// dot product of the solution and the expression.
2114    /// \pre The problem is solved.
2115    Value sol(const Expr& e) const {
2116      double res = *e;
2117      for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {
2118        res += *c * sol(c);
2119      }
2120      return res;
2121    }
2122    ///The value of the objective function
2123
2124    ///\return
2125    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
2126    /// of the problem, depending on whether we minimize or maximize.
2127    ///- \ref NaN if no primal solution is found.
2128    ///- The (finite) objective value if an optimal solution is found.
2129    Value solValue() const { return _getSolValue()+obj_const_comp;}
2130    ///@}
2131
2132  protected:
2133
2134    virtual SolveExitStatus _solve() = 0;
2135    virtual ColTypes _getColType(int col) const = 0;
2136    virtual void _setColType(int col, ColTypes col_type) = 0;
2137    virtual ProblemType _getType() const = 0;
2138    virtual Value _getSol(int i) const = 0;
2139    virtual Value _getSolValue() const = 0;
2140
2141  };
2142
2143
2144
2145} //namespace lemon
2146
2147#endif //LEMON_LP_BASE_H
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