COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/lp_base.h @ 1435:8e85e6bbefdf

Last change on this file since 1435:8e85e6bbefdf was 1435:8e85e6bbefdf, checked in by Akos Ladanyi, 15 years ago

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1/* -*- C++ -*-
2 * lemon/lp_base.h - Part of LEMON, a generic C++ optimization library
3 *
4 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Research Group on Combinatorial Optimization, EGRES).
6 *
7 * Permission to use, modify and distribute this software is granted
8 * provided that this copyright notice appears in all copies. For
9 * precise terms see the accompanying LICENSE file.
10 *
11 * This software is provided "AS IS" with no warranty of any kind,
12 * express or implied, and with no claim as to its suitability for any
13 * purpose.
14 *
15 */
16
17#ifndef LEMON_LP_BASE_H
18#define LEMON_LP_BASE_H
19
20#include<vector>
21#include<map>
22#include<limits>
23#include<cmath>
24
25#include<lemon/utility.h>
26#include<lemon/error.h>
27#include<lemon/invalid.h>
28
29//#include"lin_expr.h"
30
31///\file
32///\brief The interface of the LP solver interface.
33///\ingroup gen_opt_group
34namespace lemon {
35 
36  ///Internal data structure to convert floating id's to fix one's
37   
38  ///\todo This might be implemented to be also usable in other places.
39  class _FixId
40  {
41    std::vector<int> index;
42    std::vector<int> cross;
43    int first_free;
44  public:
45    _FixId() : first_free(-1) {};
46    ///Convert a floating id to a fix one
47
48    ///\param n is a floating id
49    ///\return the corresponding fix id
50    int fixId(int n) {return cross[n];}
51    ///Convert a fix id to a floating one
52
53    ///\param n is a fix id
54    ///\return the corresponding floating id
55    int floatingId(int n) { return index[n];}
56    ///Add a new floating id.
57
58    ///\param n is a floating id
59    ///\return the fix id of the new value
60    ///\todo Multiple additions should also be handled.
61    int insert(int n)
62    {
63      if(n>=int(cross.size())) {
64        cross.resize(n+1);
65        if(first_free==-1) {
66          cross[n]=index.size();
67          index.push_back(n);
68        }
69        else {
70          cross[n]=first_free;
71          int next=index[first_free];
72          index[first_free]=n;
73          first_free=next;
74        }
75        return cross[n];
76      }
77      ///\todo Create an own exception type.
78      else throw LogicError(); //floatingId-s must form a continuous range;
79    }
80    ///Remove a fix id.
81
82    ///\param n is a fix id
83    ///
84    void erase(int n)
85    {
86      int fl=index[n];
87      index[n]=first_free;
88      first_free=n;
89      for(int i=fl+1;i<int(cross.size());++i) {
90        cross[i-1]=cross[i];
91        index[cross[i]]--;
92      }
93      cross.pop_back();
94    }
95    ///An upper bound on the largest fix id.
96
97    ///\todo Do we need this?
98    ///
99    std::size_t maxFixId() { return cross.size()-1; }
100 
101  };
102   
103  ///Common base class for LP solvers
104 
105  ///\todo Much more docs
106  ///\ingroup gen_opt_group
107  class LpSolverBase {
108
109  public:
110
111    ///\e
112    enum SolveExitStatus {
113      ///\e
114      SOLVED = 0,
115      ///\e
116      UNSOLVED = 1
117    };
118     
119    ///\e
120    enum SolutionStatus {
121      ///Feasible solution has'n been found (but may exist).
122
123      ///\todo NOTFOUND might be a better name.
124      ///
125      UNDEFINED = 0,
126      ///The problem has no feasible solution
127      INFEASIBLE = 1,
128      ///Feasible solution found
129      FEASIBLE = 2,
130      ///Optimal solution exists and found
131      OPTIMAL = 3,
132      ///The cost function is unbounded
133
134      ///\todo Give a feasible solution and an infinite ray (and the
135      ///corresponding bases)
136      INFINITE = 4
137    };
138     
139    ///The floating point type used by the solver
140    typedef double Value;
141    ///The infinity constant
142    static const Value INF;
143    ///The not a number constant
144    static const Value NaN;
145   
146    ///Refer to a column of the LP.
147
148    ///This type is used to refer to a column of the LP.
149    ///
150    ///Its value remains valid and correct even after the addition or erase of
151    ///other columns.
152    ///
153    ///\todo Document what can one do with a Col (INVALID, comparing,
154    ///it is similar to Node/Edge)
155    class Col {
156    protected:
157      int id;
158      friend class LpSolverBase;
159    public:
160      typedef Value ExprValue;
161      typedef True LpSolverCol;
162      Col() {}
163      Col(const Invalid&) : id(-1) {}
164      bool operator<(Col c) const  {return id<c.id;}
165      bool operator==(Col c) const  {return id==c.id;}
166      bool operator!=(Col c) const  {return id==c.id;}
167    };
168
169    ///Refer to a row of the LP.
170
171    ///This type is used to refer to a row of the LP.
172    ///
173    ///Its value remains valid and correct even after the addition or erase of
174    ///other rows.
175    ///
176    ///\todo Document what can one do with a Row (INVALID, comparing,
177    ///it is similar to Node/Edge)
178    class Row {
179    protected:
180      int id;
181      friend class LpSolverBase;
182    public:
183      typedef Value ExprValue;
184      typedef True LpSolverRow;
185      Row() {}
186      Row(const Invalid&) : id(-1) {}
187      typedef True LpSolverRow;
188      bool operator<(Row c) const  {return id<c.id;}
189      bool operator==(Row c) const  {return id==c.id;}
190      bool operator!=(Row c) const  {return id==c.id;}
191   };
192   
193    ///Linear expression of variables and a constant component
194   
195    ///This data structure strores a linear expression of the variables
196    ///(\ref Col "Col"s) and also has a constant component.
197    ///
198    ///There are several ways to access and modify the contents of this
199    ///container.
200    ///- Its it fully compatible with \c std::map<Col,double>, so for expamle
201    ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can
202    ///read and modify the coefficients like
203    ///these.
204    ///\code
205    ///e[v]=5;
206    ///e[v]+=12;
207    ///e.erase(v);
208    ///\endcode
209    ///or you can also iterate through its elements.
210    ///\code
211    ///double s=0;
212    ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i)
213    ///  s+=i->second;
214    ///\endcode
215    ///(This code computes the sum of all coefficients).
216    ///- Numbers (<tt>double</tt>'s)
217    ///and variables (\ref Col "Col"s) directly convert to an
218    ///\ref Expr and the usual linear operations are defined so 
219    ///\code
220    ///v+w
221    ///2*v-3.12*(v-w/2)+2
222    ///v*2.1+(3*v+(v*12+w+6)*3)/2
223    ///\endcode
224    ///are valid \ref Expr "Expr"essions.
225    ///The usual assignment operations are also defined.
226    ///\code
227    ///e=v+w;
228    ///e+=2*v-3.12*(v-w/2)+2;
229    ///e*=3.4;
230    ///e/=5;
231    ///\endcode
232    ///- The constant member can be set and read by \ref constComp()
233    ///\code
234    ///e.constComp()=12;
235    ///double c=e.constComp();
236    ///\endcode
237    ///
238    ///\note \ref clear() not only sets all coefficients to 0 but also
239    ///clears the constant components.
240    ///
241    ///\sa Constr
242    ///
243    class Expr : public std::map<Col,Value>
244    {
245    public:
246      typedef LpSolverBase::Col Key;
247      typedef LpSolverBase::Value Value;
248     
249    protected:
250      typedef std::map<Col,Value> Base;
251     
252      Value const_comp;
253  public:
254      typedef True IsLinExpression;
255      ///\e
256      Expr() : Base(), const_comp(0) { }
257      ///\e
258      Expr(const Key &v) : const_comp(0) {
259        Base::insert(std::make_pair(v, 1));
260      }
261      ///\e
262      Expr(const Value &v) : const_comp(v) {}
263      ///\e
264      void set(const Key &v,const Value &c) {
265        Base::insert(std::make_pair(v, c));
266      }
267      ///\e
268      Value &constComp() { return const_comp; }
269      ///\e
270      const Value &constComp() const { return const_comp; }
271     
272      ///Removes the components with zero coefficient.
273      void simplify() {
274        for (Base::iterator i=Base::begin(); i!=Base::end();) {
275          Base::iterator j=i;
276          ++j;
277          if ((*i).second==0) Base::erase(i);
278          j=i;
279        }
280      }
281
282      ///Sets all coefficients and the constant component to 0.
283      void clear() {
284        Base::clear();
285        const_comp=0;
286      }
287
288      ///\e
289      Expr &operator+=(const Expr &e) {
290        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
291          (*this)[j->first]+=j->second;
292        ///\todo it might be speeded up using "hints"
293        const_comp+=e.const_comp;
294        return *this;
295      }
296      ///\e
297      Expr &operator-=(const Expr &e) {
298        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
299          (*this)[j->first]-=j->second;
300        const_comp-=e.const_comp;
301        return *this;
302      }
303      ///\e
304      Expr &operator*=(const Value &c) {
305        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
306          j->second*=c;
307        const_comp*=c;
308        return *this;
309      }
310      ///\e
311      Expr &operator/=(const Value &c) {
312        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
313          j->second/=c;
314        const_comp/=c;
315        return *this;
316      }
317    };
318   
319    ///Linear constraint
320
321    ///This data stucture represents a linear constraint in the LP.
322    ///Basically it is a linear expression with a lower or an upper bound
323    ///(or both). These parts of the constraint can be obtained by the member
324    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
325    ///respectively.
326    ///There are two ways to construct a constraint.
327    ///- You can set the linear expression and the bounds directly
328    ///  by the functions above.
329    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
330    ///  are defined between expressions, or even between constraints whenever
331    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
332    ///  \c s and \c t are numbers, then the followings are valid expressions
333    ///  and thus they can be used directly e.g. in \ref addRow() whenever
334    ///  it makes sense.
335    ///  \code
336    ///  e<=s
337    ///  e<=f
338    ///  s<=e<=t
339    ///  e>=t
340    ///  \endcode
341    ///\warning The validity of a constraint is checked only at run time, so
342    ///e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will compile, but will throw a
343    ///\ref LogicError exception.
344    class Constr
345    {
346    public:
347      typedef LpSolverBase::Expr Expr;
348      typedef Expr::Key Key;
349      typedef Expr::Value Value;
350     
351//       static const Value INF;
352//       static const Value NaN;
353
354    protected:
355      Expr _expr;
356      Value _lb,_ub;
357    public:
358      ///\e
359      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
360      ///\e
361      Constr(Value lb,const Expr &e,Value ub) :
362        _expr(e), _lb(lb), _ub(ub) {}
363      ///\e
364      Constr(const Expr &e,Value ub) :
365        _expr(e), _lb(NaN), _ub(ub) {}
366      ///\e
367      Constr(Value lb,const Expr &e) :
368        _expr(e), _lb(lb), _ub(NaN) {}
369      ///\e
370      Constr(const Expr &e) :
371        _expr(e), _lb(NaN), _ub(NaN) {}
372      ///\e
373      void clear()
374      {
375        _expr.clear();
376        _lb=_ub=NaN;
377      }
378
379      ///Reference to the linear expression
380      Expr &expr() { return _expr; }
381      ///Cont reference to the linear expression
382      const Expr &expr() const { return _expr; }
383      ///Reference to the lower bound.
384
385      ///\return
386      ///- -\ref INF: the constraint is lower unbounded.
387      ///- -\ref NaN: lower bound has not been set.
388      ///- finite number: the lower bound
389      Value &lowerBound() { return _lb; }
390      ///The const version of \ref lowerBound()
391      const Value &lowerBound() const { return _lb; }
392      ///Reference to the upper bound.
393
394      ///\return
395      ///- -\ref INF: the constraint is upper unbounded.
396      ///- -\ref NaN: upper bound has not been set.
397      ///- finite number: the upper bound
398      Value &upperBound() { return _ub; }
399      ///The const version of \ref upperBound()
400      const Value &upperBound() const { return _ub; }
401      ///Is the constraint lower bounded?
402      bool lowerBounded() const {
403        using namespace std;
404        return finite(_lb);
405      }
406      ///Is the constraint upper bounded?
407      bool upperBounded() const {
408        using namespace std;
409        return finite(_ub);
410      }
411    };
412   
413
414  protected:
415    _FixId rows;
416    _FixId cols;
417
418    //Abstract virtual functions
419    virtual LpSolverBase &_newLp() = 0;
420    virtual LpSolverBase &_copyLp() = 0;
421
422    virtual int _addCol() = 0;
423    virtual int _addRow() = 0;
424    virtual void _setRowCoeffs(int i,
425                               int length,
426                               int  const * indices,
427                               Value  const * values ) = 0;
428    virtual void _setColCoeffs(int i,
429                               int length,
430                               int  const * indices,
431                               Value  const * values ) = 0;
432    virtual void _setCoeff(int row, int col, Value value) = 0;
433    virtual void _setColLowerBound(int i, Value value) = 0;
434    virtual void _setColUpperBound(int i, Value value) = 0;
435//     virtual void _setRowLowerBound(int i, Value value) = 0;
436//     virtual void _setRowUpperBound(int i, Value value) = 0;
437    virtual void _setRowBounds(int i, Value lower, Value upper) = 0;
438    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
439    virtual void _clearObj()=0;
440//     virtual void _setObj(int length,
441//                          int  const * indices,
442//                          Value  const * values ) = 0;
443    virtual SolveExitStatus _solve() = 0;
444    virtual Value _getPrimal(int i) = 0;
445    virtual Value _getPrimalValue() = 0;
446    virtual SolutionStatus _getPrimalStatus() = 0;
447    virtual void _setMax() = 0;
448    virtual void _setMin() = 0;
449   
450    //Own protected stuff
451   
452    //Constant component of the objective function
453    Value obj_const_comp;
454   
455
456
457   
458  public:
459
460    ///\e
461    LpSolverBase() : obj_const_comp(0) {}
462
463    ///\e
464    virtual ~LpSolverBase() {}
465
466    ///Creates a new LP problem
467    LpSolverBase &newLp() {return _newLp();}
468    ///Makes a copy of the LP problem
469    LpSolverBase &copyLp() {return _copyLp();}
470   
471    ///\name Build up and modify of the LP
472
473    ///@{
474
475    ///Add a new empty column (i.e a new variable) to the LP
476    Col addCol() { Col c; c.id=cols.insert(_addCol()); return c;}
477
478    ///\brief Adds several new columns
479    ///(i.e a variables) at once
480    ///
481    ///This magic function takes a container as its argument
482    ///and fills its elements
483    ///with new columns (i.e. variables)
484    ///\param t can be
485    ///- a standard STL compatible iterable container with
486    ///\ref Col as its \c values_type
487    ///like
488    ///\code
489    ///std::vector<LpSolverBase::Col>
490    ///std::list<LpSolverBase::Col>
491    ///\endcode
492    ///- a standard STL compatible iterable container with
493    ///\ref Col as its \c mapped_type
494    ///like
495    ///\code
496    ///std::map<AnyType,LpSolverBase::Col>
497    ///\endcode
498    ///- an iterable lemon \ref concept::WriteMap "write map" like
499    ///\code
500    ///ListGraph::NodeMap<LpSolverBase::Col>
501    ///ListGraph::EdgeMap<LpSolverBase::Col>
502    ///\endcode
503    ///\return The number of the created column.
504#ifdef DOXYGEN
505    template<class T>
506    int addColSet(T &t) { return 0;}
507#else
508    template<class T>
509    typename enable_if<typename T::value_type::LpSolverCol,int>::type
510    addColSet(T &t,dummy<0> = 0) {
511      int s=0;
512      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
513      return s;
514    }
515    template<class T>
516    typename enable_if<typename T::value_type::second_type::LpSolverCol,
517                       int>::type
518    addColSet(T &t,dummy<1> = 1) {
519      int s=0;
520      for(typename T::iterator i=t.begin();i!=t.end();++i) {
521        i->second=addCol();
522        s++;
523      }
524      return s;
525    }
526    template<class T>
527    typename enable_if<typename T::ValueSet::value_type::LpSolverCol,
528                       int>::type
529    addColSet(T &t,dummy<2> = 2) {
530      ///\bug <tt>return addColSet(t.valueSet());</tt> should also work.
531      int s=0;
532      for(typename T::ValueSet::iterator i=t.valueSet().begin();
533          i!=t.valueSet().end();
534          ++i)
535        {
536          *i=addCol();
537          s++;
538        }
539      return s;
540    }
541#endif
542
543    ///Add a new empty row (i.e a new constaint) to the LP
544
545    ///This function adds a new empty row (i.e a new constaint) to the LP.
546    ///\return The created row
547    Row addRow() { Row r; r.id=rows.insert(_addRow()); return r;}
548
549    ///Set a row (i.e a constaint) of the LP
550
551    ///\param r is the row to be modified
552    ///\param l is lower bound (-\ref INF means no bound)
553    ///\param e is a linear expression (see \ref Expr)
554    ///\param u is the upper bound (\ref INF means no bound)
555    ///\bug This is a temportary function. The interface will change to
556    ///a better one.
557    ///\todo Option to control whether a constraint with a single variable is
558    ///added or not.
559    void setRow(Row r, Value l,const Expr &e, Value u) {
560      std::vector<int> indices;
561      std::vector<Value> values;
562      indices.push_back(0);
563      values.push_back(0);
564      for(Expr::const_iterator i=e.begin(); i!=e.end(); ++i)
565        if((*i).second!=0) { ///\bug EPSILON would be necessary here!!!
566          indices.push_back(cols.floatingId((*i).first.id));
567          values.push_back((*i).second);
568        }
569      _setRowCoeffs(rows.floatingId(r.id),indices.size()-1,
570                    &indices[0],&values[0]);
571//       _setRowLowerBound(rows.floatingId(r.id),l-e.constComp());
572//       _setRowUpperBound(rows.floatingId(r.id),u-e.constComp());
573       _setRowBounds(rows.floatingId(r.id),l-e.constComp(),u-e.constComp());
574    }
575
576    ///Set a row (i.e a constaint) of the LP
577
578    ///\param r is the row to be modified
579    ///\param c is a linear expression (see \ref Constr)
580    void setRow(Row r, const Constr &c) {
581      setRow(r,
582             c.lowerBounded()?c.lowerBound():-INF,
583             c.expr(),
584             c.upperBounded()?c.upperBound():INF);
585    }
586
587    ///Add a new row (i.e a new constaint) to the LP
588
589    ///\param l is the lower bound (-\ref INF means no bound)
590    ///\param e is a linear expression (see \ref Expr)
591    ///\param u is the upper bound (\ref INF means no bound)
592    ///\return The created row.
593    ///\bug This is a temportary function. The interface will change to
594    ///a better one.
595    Row addRow(Value l,const Expr &e, Value u) {
596      Row r=addRow();
597      setRow(r,l,e,u);
598      return r;
599    }
600
601    ///Add a new row (i.e a new constaint) to the LP
602
603    ///\param c is a linear expression (see \ref Constr)
604    ///\return The created row.
605    Row addRow(const Constr &c) {
606      Row r=addRow();
607      setRow(r,c);
608      return r;
609    }
610
611    /// Set the lower bound of a column (i.e a variable)
612
613    /// The upper bound of a variable (column) has to be given by an
614    /// extended number of type Value, i.e. a finite number of type
615    /// Value or -\ref INF.
616    void colLowerBound(Col c, Value value) {
617      _setColLowerBound(cols.floatingId(c.id),value);
618    }
619    /// Set the upper bound of a column (i.e a variable)
620
621    /// The upper bound of a variable (column) has to be given by an
622    /// extended number of type Value, i.e. a finite number of type
623    /// Value or \ref INF.
624    void colUpperBound(Col c, Value value) {
625      _setColUpperBound(cols.floatingId(c.id),value);
626    };
627    /// Set the lower and the upper bounds of a column (i.e a variable)
628
629    /// The lower and the upper bounds of
630    /// a variable (column) have to be given by an
631    /// extended number of type Value, i.e. a finite number of type
632    /// Value, -\ref INF or \ref INF.
633    void colBounds(Col c, Value lower, Value upper) {
634      _setColLowerBound(cols.floatingId(c.id),lower);
635      _setColUpperBound(cols.floatingId(c.id),upper);
636    }
637   
638//     /// Set the lower bound of a row (i.e a constraint)
639
640//     /// The lower bound of a linear expression (row) has to be given by an
641//     /// extended number of type Value, i.e. a finite number of type
642//     /// Value or -\ref INF.
643//     void rowLowerBound(Row r, Value value) {
644//       _setRowLowerBound(rows.floatingId(r.id),value);
645//     };
646//     /// Set the upper bound of a row (i.e a constraint)
647
648//     /// The upper bound of a linear expression (row) has to be given by an
649//     /// extended number of type Value, i.e. a finite number of type
650//     /// Value or \ref INF.
651//     void rowUpperBound(Row r, Value value) {
652//       _setRowUpperBound(rows.floatingId(r.id),value);
653//     };
654
655    /// Set the lower and the upper bounds of a row (i.e a constraint)
656
657    /// The lower and the upper bounds of
658    /// a constraint (row) have to be given by an
659    /// extended number of type Value, i.e. a finite number of type
660    /// Value, -\ref INF or \ref INF.
661    void rowBounds(Row c, Value lower, Value upper) {
662      _setRowBounds(rows.floatingId(c.id),lower, upper);
663      // _setRowUpperBound(rows.floatingId(c.id),upper);
664    }
665   
666    ///Set an element of the objective function
667    void objCoeff(Col c, Value v) {_setObjCoeff(cols.floatingId(c.id),v); };
668    ///Set the objective function
669   
670    ///\param e is a linear expression of type \ref Expr.
671    ///\bug The previous objective function is not cleared!
672    void setObj(Expr e) {
673      _clearObj();
674      for (Expr::iterator i=e.begin(); i!=e.end(); ++i)
675        objCoeff((*i).first,(*i).second);
676      obj_const_comp=e.constComp();
677    }
678
679    ///Maximize
680    void max() { _setMax(); }
681    ///Minimize
682    void min() { _setMin(); }
683
684   
685    ///@}
686
687
688    ///\name Solve the LP
689
690    ///@{
691
692    ///\e
693    SolveExitStatus solve() { return _solve(); }
694   
695    ///@}
696   
697    ///\name Obtain the solution
698
699    ///@{
700
701    ///\e
702    SolutionStatus primalStatus() {
703      return _getPrimalStatus();
704    }
705
706    ///\e
707    Value primal(Col c) { return _getPrimal(cols.floatingId(c.id)); }
708
709    ///\e
710
711    ///\return
712    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
713    /// of the primal problem, depending on whether we minimize or maximize.
714    ///- \ref NaN if no primal solution is found.
715    ///- The (finite) objective value if an optimal solution is found.
716    Value primalValue() { return _getPrimalValue()+obj_const_comp;}
717    ///@}
718   
719  }; 
720
721  ///\e
722 
723  ///\relates LpSolverBase::Expr
724  ///
725  inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a,
726                                      const LpSolverBase::Expr &b)
727  {
728    LpSolverBase::Expr tmp(a);
729    tmp+=b; ///\todo Doesn't STL have some special 'merge' algorithm?
730    return tmp;
731  }
732  ///\e
733 
734  ///\relates LpSolverBase::Expr
735  ///
736  inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a,
737                                      const LpSolverBase::Expr &b)
738  {
739    LpSolverBase::Expr tmp(a);
740    tmp-=b; ///\todo Doesn't STL have some special 'merge' algorithm?
741    return tmp;
742  }
743  ///\e
744 
745  ///\relates LpSolverBase::Expr
746  ///
747  inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a,
748                                      const LpSolverBase::Value &b)
749  {
750    LpSolverBase::Expr tmp(a);
751    tmp*=b; ///\todo Doesn't STL have some special 'merge' algorithm?
752    return tmp;
753  }
754 
755  ///\e
756 
757  ///\relates LpSolverBase::Expr
758  ///
759  inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a,
760                                      const LpSolverBase::Expr &b)
761  {
762    LpSolverBase::Expr tmp(b);
763    tmp*=a; ///\todo Doesn't STL have some special 'merge' algorithm?
764    return tmp;
765  }
766  ///\e
767 
768  ///\relates LpSolverBase::Expr
769  ///
770  inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a,
771                                      const LpSolverBase::Value &b)
772  {
773    LpSolverBase::Expr tmp(a);
774    tmp/=b; ///\todo Doesn't STL have some special 'merge' algorithm?
775    return tmp;
776  }
777 
778  ///\e
779 
780  ///\relates LpSolverBase::Constr
781  ///
782  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
783                                         const LpSolverBase::Expr &f)
784  {
785    return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0);
786  }
787
788  ///\e
789 
790  ///\relates LpSolverBase::Constr
791  ///
792  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e,
793                                         const LpSolverBase::Expr &f)
794  {
795    return LpSolverBase::Constr(e,f);
796  }
797
798  ///\e
799 
800  ///\relates LpSolverBase::Constr
801  ///
802  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
803                                         const LpSolverBase::Value &f)
804  {
805    return LpSolverBase::Constr(e,f);
806  }
807
808  ///\e
809 
810  ///\relates LpSolverBase::Constr
811  ///
812  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
813                                         const LpSolverBase::Expr &f)
814  {
815    return LpSolverBase::Constr(-LpSolverBase::INF,f-e,0);
816  }
817
818
819  ///\e
820 
821  ///\relates LpSolverBase::Constr
822  ///
823  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e,
824                                         const LpSolverBase::Expr &f)
825  {
826    return LpSolverBase::Constr(f,e);
827  }
828
829
830  ///\e
831 
832  ///\relates LpSolverBase::Constr
833  ///
834  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
835                                         const LpSolverBase::Value &f)
836  {
837    return LpSolverBase::Constr(f,e);
838  }
839
840  ///\e
841 
842  ///\relates LpSolverBase::Constr
843  ///
844  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
845                                         const LpSolverBase::Expr &f)
846  {
847    return LpSolverBase::Constr(0,e-f,0);
848  }
849
850  ///\e
851 
852  ///\relates LpSolverBase::Constr
853  ///
854  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n,
855                                         const LpSolverBase::Constr&c)
856  {
857    LpSolverBase::Constr tmp(c);
858    ///\todo Create an own exception type.
859    if(!isnan(tmp.lowerBound())) throw LogicError();
860    else tmp.lowerBound()=n;
861    return tmp;
862  }
863  ///\e
864 
865  ///\relates LpSolverBase::Constr
866  ///
867  inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c,
868                                         const LpSolverBase::Value &n)
869  {
870    LpSolverBase::Constr tmp(c);
871    ///\todo Create an own exception type.
872    if(!isnan(tmp.upperBound())) throw LogicError();
873    else tmp.upperBound()=n;
874    return tmp;
875  }
876
877  ///\e
878 
879  ///\relates LpSolverBase::Constr
880  ///
881  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n,
882                                         const LpSolverBase::Constr&c)
883  {
884    LpSolverBase::Constr tmp(c);
885    ///\todo Create an own exception type.
886    if(!isnan(tmp.upperBound())) throw LogicError();
887    else tmp.upperBound()=n;
888    return tmp;
889  }
890  ///\e
891 
892  ///\relates LpSolverBase::Constr
893  ///
894  inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c,
895                                         const LpSolverBase::Value &n)
896  {
897    LpSolverBase::Constr tmp(c);
898    ///\todo Create an own exception type.
899    if(!isnan(tmp.lowerBound())) throw LogicError();
900    else tmp.lowerBound()=n;
901    return tmp;
902  }
903
904
905} //namespace lemon
906
907#endif //LEMON_LP_BASE_H
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